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w_2, \\ldots, w_n",[1124,1466,1468],{"className":1467,"ariaHidden":1156},[1196],[1124,1469,1471,1474,1516,1519,1522,1562,1565,1568,1571,1574,1577,1580],{"className":1470},[1200],[1124,1472],{"className":1473,"style":1205},[1204],[1124,1475,1477,1481],{"className":1476},[1209],[1124,1478,1439],{"className":1479,"style":1480},[1209,1213],"margin-right:0.0269em;",[1124,1482,1484],{"className":1483},[1217],[1124,1485,1487,1508],{"className":1486},[1221,1222],[1124,1488,1490,1505],{"className":1489},[1226],[1124,1491,1493],{"className":1492,"style":1231},[1230],[1124,1494,1496,1499],{"style":1495},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1124,1497],{"className":1498,"style":1239},[1238],[1124,1500,1502],{"className":1501},[1243,1244,1245,1246],[1124,1503,1152],{"className":1504},[1209,1246],[1124,1506,1254],{"className":1507},[1253],[1124,1509,1511],{"className":1510},[1226],[1124,1512,1514],{"className":1513,"style":1261},[1230],[1124,1515],{},[1124,1517,1157],{"className":1518},[1267],[1124,1520],{"className":1521,"style":1272},[1271],[1124,1523,1525,1528],{"className":1524},[1209],[1124,1526,1439],{"className":1527,"style":1480},[1209,1213],[1124,1529,1531],{"className":1530},[1217],[1124,1532,1534,1554],{"className":1533},[1221,1222],[1124,1535,1537,1551],{"className":1536},[1226],[1124,1538,1540],{"className":1539,"style":1231},[1230],[1124,1541,1542,1545],{"style":1495},[1124,1543],{"className":1544,"style":1239},[1238],[1124,1546,1548],{"className":1547},[1243,1244,1245,1246],[1124,1549,1164],{"className":1550},[1209,1246],[1124,1552,1254],{"className":1553},[1253],[1124,1555,1557],{"className":1556},[1226],[1124,1558,1560],{"className":1559,"style":1261},[1230],[1124,1561],{},[1124,1563,1157],{"className":1564},[1267],[1124,1566],{"className":1567,"style":1272},[1271],[1124,1569,1178],{"className":1570},[1368],[1124,1572],{"className":1573,"style":1272},[1271],[1124,1575,1157],{"className":1576},[1267],[1124,1578],{"className":1579,"style":1272},[1271],[1124,1581,1583,1586],{"className":1582},[1209],[1124,1584,1439],{"className":1585,"style":1480},[1209,1213],[1124,1587,1589],{"className":1588},[1217],[1124,1590,1592,1612],{"className":1591},[1221,1222],[1124,1593,1595,1609],{"className":1594},[1226],[1124,1596,1598],{"className":1597,"style":1396},[1230],[1124,1599,1600,1603],{"style":1495},[1124,1601],{"className":1602,"style":1239},[1238],[1124,1604,1606],{"className":1605},[1243,1244,1245,1246],[1124,1607,1187],{"className":1608},[1209,1213,1246],[1124,1610,1254],{"className":1611},[1253],[1124,1613,1615],{"className":1614},[1226],[1124,1616,1618],{"className":1617,"style":1261},[1230],[1124,1619],{},"（表示各输入的重要性）",[1120,1622,1623],{},"输出：单一的二进制输出（0 或 1）",[1101,1625,1626],{},[1107,1627,1628],{},"输出规则",[1101,1630,1631],{},"原始形式（使用阈值 threshold）：",[1101,1633,1634],{},[1124,1635,1637,1754],{"className":1636},[1127],[1124,1638,1640],{"className":1639},[1131],[1133,1641,1642],{"xmlns":1135},[1137,1643,1644,1751],{},[1140,1645,1646,1650,1653],{},[1647,1648,1649],"mtext",{},"output",[1154,1651,1652],{},"=",[1140,1654,1655,1658],{},[1154,1656,1657],{"fence":1156},"{",[1659,1660,1664,1712],"mtable",{"rowspacing":1661,"columnalign":1662,"columnspacing":1663},"0.36em","left 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= \\begin{cases} 0 & \\text{if } \\sum_j w_j x_j \\leq \\text{threshold} \\\\ 1 & \\text{if } \\sum_j w_j x_j > \\text{threshold} \\end{cases}",[1124,1755,1757,1782],{"className":1756,"ariaHidden":1156},[1196],[1124,1758,1760,1764,1771,1775,1779],{"className":1759},[1200],[1124,1761],{"className":1762,"style":1763},[1204],"height:0.8095em;vertical-align:-0.1944em;",[1124,1765,1768],{"className":1766},[1209,1767],"text",[1124,1769,1649],{"className":1770},[1209],[1124,1772],{"className":1773,"style":1774},[1271],"margin-right:0.2778em;",[1124,1776,1652],{"className":1777},[1778],"mrel",[1124,1780],{"className":1781,"style":1774},[1271],[1124,1783,1785,1789],{"className":1784},[1200],[1124,1786],{"className":1787,"style":1788},[1204],"height:3em;vertical-align:-1.25em;",[1124,1790,1792,1803,2208],{"className":1791},[1368],[1124,1793,1798],{"className":1794,"style":1797},[1795,1796],"mopen","delimcenter","top:0em;",[1124,1799,1657],{"className":1800},[1801,1802],"delimsizing","size4",[1124,1804,1806],{"className":1805},[1209],[1124,1807,1809,1860,1865],{"className":1808},[1659],[1124,1810,1813],{"className":1811},[1812],"col-align-l",[1124,1814,1816,1851],{"className":1815},[1221,1222],[1124,1817,1819,1848],{"className":1818},[1226],[1124,1820,1823,1836],{"className":1821,"style":1822},[1230],"height:1.6938em;",[1124,1824,1826,1830],{"style":1825},"top:-3.6938em;",[1124,1827],{"className":1828,"style":1829},[1238],"height:3.008em;",[1124,1831,1833],{"className":1832},[1209],[1124,1834,1673],{"className":1835},[1209],[1124,1837,1839,1842],{"style":1838},"top:-2.25em;",[1124,1840],{"className":1841,"style":1829},[1238],[1124,1843,1845],{"className":1844},[1209],[1124,1846,1152],{"className":1847},[1209],[1124,1849,1254],{"className":1850},[1253],[1124,1852,1854],{"className":1853},[1226],[1124,1855,1858],{"className":1856,"style":1857},[1230],"height:1.1938em;",[1124,1859],{},[1124,1861],{"className":1862,"style":1864},[1863],"arraycolsep","width:1em;",[1124,1866,1868],{"className":1867},[1812],[1124,1869,1871,2200],{"className":1870},[1221,1222],[1124,1872,1874,2197],{"className":1873},[1226],[1124,1875,1877,2042],{"className":1876,"style":1822},[1230],[1124,1878,1879,1882],{"style":1825},[1124,1880],{"className":1881,"style":1829},[1238],[1124,1883,1885,1891,1894,1942,1945,1987,2027,2030,2033,2036],{"className":1884},[1209],[1124,1886,1888],{"className":1887},[1209,1767],[1124,1889,1685],{"className":1890},[1209],[1124,1892],{"className":1893,"style":1272},[1271],[1124,1895,1898,1904],{"className":1896},[1897],"mop",[1124,1899,1690],{"className":1900,"style":1903},[1897,1901,1902],"op-symbol","small-op","position:relative;top:0em;",[1124,1905,1907],{"className":1906},[1217],[1124,1908,1910,1933],{"className":1909},[1221,1222],[1124,1911,1913,1930],{"className":1912},[1226],[1124,1914,1917],{"className":1915,"style":1916},[1230],"height:0.162em;",[1124,1918,1920,1923],{"style":1919},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1124,1921],{"className":1922,"style":1239},[1238],[1124,1924,1926],{"className":1925},[1243,1244,1245,1246],[1124,1927,1693],{"className":1928,"style":1929},[1209,1213,1246],"margin-right:0.0572em;",[1124,1931,1254],{"className":1932},[1253],[1124,1934,1936],{"className":1935},[1226],[1124,1937,1940],{"className":1938,"style":1939},[1230],"height:0.4358em;",[1124,1941],{},[1124,1943],{"className":1944,"style":1272},[1271],[1124,1946,1948,1951],{"className":1947},[1209],[1124,1949,1439],{"className":1950,"style":1480},[1209,1213],[1124,1952,1954],{"className":1953},[1217],[1124,1955,1957,1978],{"className":1956},[1221,1222],[1124,1958,1960,1975],{"className":1959},[1226],[1124,1961,1964],{"className":1962,"style":1963},[1230],"height:0.3117em;",[1124,1965,1966,1969],{"style":1495},[1124,1967],{"className":1968,"style":1239},[1238],[1124,1970,1972],{"className":1971},[1243,1244,1245,1246],[1124,1973,1693],{"className":1974,"style":1929},[1209,1213,1246],[1124,1976,1254],{"className":1977},[1253],[1124,1979,1981],{"className":1980},[1226],[1124,1982,1985],{"className":1983,"style":1984},[1230],"height:0.2861em;",[1124,1986],{},[1124,1988,1990,1993],{"className":1989},[1209],[1124,1991,1148],{"className":1992},[1209,1213],[1124,1994,1996],{"className":1995},[1217],[1124,1997,1999,2019],{"className":1998},[1221,1222],[1124,2000,2002,2016],{"className":2001},[1226],[1124,2003,2005],{"className":2004,"style":1963},[1230],[1124,2006,2007,2010],{"style":1234},[1124,2008],{"className":2009,"style":1239},[1238],[1124,2011,2013],{"className":2012},[1243,1244,1245,1246],[1124,2014,1693],{"className":2015,"style":1929},[1209,1213,1246],[1124,2017,1254],{"className":2018},[1253],[1124,2020,2022],{"className":2021},[1226],[1124,2023,2025],{"className":2024,"style":1984},[1230],[1124,2026],{},[1124,2028],{"className":2029,"style":1774},[1271],[1124,2031,1708],{"className":2032},[1778],[1124,2034],{"className":2035,"style":1774},[1271],[1124,2037,2039],{"className":2038},[1209,1767],[1124,2040,1711],{"className":2041},[1209],[1124,2043,2044,2047],{"style":1838},[1124,2045],{"className":2046,"style":1829},[1238],[1124,2048,2050,2056,2059,2099,2102,2142,2182,2185,2188,2191],{"className":2049},[1209],[1124,2051,2053],{"className":2052},[1209,1767],[1124,2054,1685],{"className":2055},[1209],[1124,2057],{"className":2058,"style":1272},[1271],[1124,2060,2062,2065],{"className":2061},[1897],[1124,2063,1690],{"className":2064,"style":1903},[1897,1901,1902],[1124,2066,2068],{"className":2067},[1217],[1124,2069,2071,2091],{"className":2070},[1221,1222],[1124,2072,2074,2088],{"className":2073},[1226],[1124,2075,2077],{"className":2076,"style":1916},[1230],[1124,2078,2079,2082],{"style":1919},[1124,2080],{"className":2081,"style":1239},[1238],[1124,2083,2085],{"className":2084},[1243,1244,1245,1246],[1124,2086,1693],{"className":2087,"style":1929},[1209,1213,1246],[1124,2089,1254],{"className":2090},[1253],[1124,2092,2094],{"className":2093},[1226],[1124,2095,2097],{"className":2096,"style":1939},[1230],[1124,2098],{},[1124,2100],{"className":2101,"style":1272},[1271],[1124,2103,2105,2108],{"className":2104},[1209],[1124,2106,1439],{"className":2107,"style":1480},[1209,1213],[1124,2109,2111],{"className":2110},[1217],[1124,2112,2114,2134],{"className":2113},[1221,1222],[1124,2115,2117,2131],{"className":2116},[1226],[1124,2118,2120],{"className":2119,"style":1963},[1230],[1124,2121,2122,2125],{"style":1495},[1124,2123],{"className":2124,"style":1239},[1238],[1124,2126,2128],{"className":2127},[1243,1244,1245,1246],[1124,2129,1693],{"className":2130,"style":1929},[1209,1213,1246],[1124,2132,1254],{"className":2133},[1253],[1124,2135,2137],{"className":2136},[1226],[1124,2138,2140],{"className":2139,"style":1984},[1230],[1124,2141],{},[1124,2143,2145,2148],{"className":2144},[1209],[1124,2146,1148],{"className":2147},[1209,1213],[1124,2149,2151],{"className":2150},[1217],[1124,2152,2154,2174],{"className":2153},[1221,1222],[1124,2155,2157,2171],{"className":2156},[1226],[1124,2158,2160],{"className":2159,"style":1963},[1230],[1124,2161,2162,2165],{"style":1234},[1124,2163],{"className":2164,"style":1239},[1238],[1124,2166,2168],{"className":2167},[1243,1244,1245,1246],[1124,2169,1693],{"className":2170,"style":1929},[1209,1213,1246],[1124,2172,1254],{"className":2173},[1253],[1124,2175,2177],{"className":2176},[1226],[1124,2178,2180],{"className":2179,"style":1984},[1230],[1124,2181],{},[1124,2183],{"className":2184,"style":1774},[1271],[1124,2186,1748],{"className":2187},[1778],[1124,2189],{"className":2190,"style":1774},[1271],[1124,2192,2194],{"className":2193},[1209,1767],[1124,2195,1711],{"className":2196},[1209],[1124,2198,1254],{"className":2199},[1253],[1124,2201,2203],{"className":2202},[1226],[1124,2204,2206],{"className":2205,"style":1857},[1230],[1124,2207],{},[1124,2209],{"className":2210},[2211,2212],"mclose","nulldelimiter",[1101,2214,2215,2216,2279],{},"引入偏置 ",[1124,2217,2219,2241],{"className":2218},[1127],[1124,2220,2222],{"className":2221},[1131],[1133,2223,2224],{"xmlns":1135},[1137,2225,2226,2238],{},[1140,2227,2228,2231,2233,2236],{},[1146,2229,2230],{},"b",[1154,2232,1652],{},[1154,2234,2235],{},"−",[1647,2237,1711],{},[1189,2239,2240],{"encoding":1191},"b = -\\text{threshold}",[1124,2242,2244,2263],{"className":2243,"ariaHidden":1156},[1196],[1124,2245,2247,2251,2254,2257,2260],{"className":2246},[1200],[1124,2248],{"className":2249,"style":2250},[1204],"height:0.6944em;",[1124,2252,2230],{"className":2253},[1209,1213],[1124,2255],{"className":2256,"style":1774},[1271],[1124,2258,1652],{"className":2259},[1778],[1124,2261],{"className":2262,"style":1774},[1271],[1124,2264,2266,2270,2273],{"className":2265},[1200],[1124,2267],{"className":2268,"style":2269},[1204],"height:0.7778em;vertical-align:-0.0833em;",[1124,2271,2235],{"className":2272},[1209],[1124,2274,2276],{"className":2275},[1209,1767],[1124,2277,1711],{"className":2278},[1209]," 简化表示：",[1101,2281,2282],{},[1124,2283,2285,2370],{"className":2284},[1127],[1124,2286,2288],{"className":2287},[1131],[1133,2289,2290],{"xmlns":1135},[1137,2291,2292,2367],{},[1140,2293,2294,2296,2298],{},[1647,2295,1649],{},[1154,2297,1652],{},[1140,2299,2300,2302],{},[1154,2301,1657],{"fence":1156},[1659,2303,2304,2337],{"rowspacing":1661,"columnalign":1662,"columnspacing":1663},[1665,2305,2306,2312],{},[1668,2307,2308],{},[1671,2309,2310],{"scriptlevel":1673,"displaystyle":1674},[1150,2311,1673],{},[1668,2313,2314],{},[1671,2315,2316],{"scriptlevel":1673,"displaystyle":1674},[1140,2317,2318,2320,2323,2326,2328,2331,2333,2335],{},[1647,2319,1685],{},[1146,2321,1439],{"mathvariant":2322},"bold",[1154,2324,2325],{},"⋅",[1146,2327,1148],{"mathvariant":2322},[1154,2329,2330],{},"+",[1146,2332,2230],{},[1154,2334,1708],{},[1150,2336,1673],{},[1665,2338,2339,2345],{},[1668,2340,2341],{},[1671,2342,2343],{"scriptlevel":1673,"displaystyle":1674},[1150,2344,1152],{},[1668,2346,2347],{},[1671,2348,2349],{"scriptlevel":1673,"displaystyle":1674},[1140,2350,2351,2353,2355,2357,2359,2361,2363,2365],{},[1647,2352,1685],{},[1146,2354,1439],{"mathvariant":2322},[1154,2356,2325],{},[1146,2358,1148],{"mathvariant":2322},[1154,2360,2330],{},[1146,2362,2230],{},[1154,2364,1748],{},[1150,2366,1673],{},[1189,2368,2369],{"encoding":1191},"\\text{output} = \\begin{cases} 0 & \\text{if } \\mathbf{w} \\cdot \\mathbf{x} + b \\leq 0 \\\\ 1 & \\text{if } \\mathbf{w} \\cdot \\mathbf{x} + b > 0 \\end{cases}",[1124,2371,2373,2394],{"className":2372,"ariaHidden":1156},[1196],[1124,2374,2376,2379,2385,2388,2391],{"className":2375},[1200],[1124,2377],{"className":2378,"style":1763},[1204],[1124,2380,2382],{"className":2381},[1209,1767],[1124,2383,1649],{"className":2384},[1209],[1124,2386],{"className":2387,"style":1774},[1271],[1124,2389,1652],{"className":2390},[1778],[1124,2392],{"className":2393,"style":1774},[1271],[1124,2395,2397,2400],{"className":2396},[1200],[1124,2398],{"className":2399,"style":1788},[1204],[1124,2401,2403,2409,2599],{"className":2402},[1368],[1124,2404,2406],{"className":2405,"style":1797},[1795,1796],[1124,2407,1657],{"className":2408},[1801,1802],[1124,2410,2412],{"className":2411},[1209],[1124,2413,2415,2463,2466],{"className":2414},[1659],[1124,2416,2418],{"className":2417},[1812],[1124,2419,2421,2454],{"className":2420},[1221,1222],[1124,2422,2424,2451],{"className":2423},[1226],[1124,2425,2428,2440],{"className":2426,"style":2427},[1230],"height:1.69em;",[1124,2429,2431,2434],{"style":2430},"top:-3.69em;",[1124,2432],{"className":2433,"style":1829},[1238],[1124,2435,2437],{"className":2436},[1209],[1124,2438,1673],{"className":2439},[1209],[1124,2441,2442,2445],{"style":1838},[1124,2443],{"className":2444,"style":1829},[1238],[1124,2446,2448],{"className":2447},[1209],[1124,2449,1152],{"className":2450},[1209],[1124,2452,1254],{"className":2453},[1253],[1124,2455,2457],{"className":2456},[1226],[1124,2458,2461],{"className":2459,"style":2460},[1230],"height:1.19em;",[1124,2462],{},[1124,2464],{"className":2465,"style":1864},[1863],[1124,2467,2469],{"className":2468},[1812],[1124,2470,2472,2591],{"className":2471},[1221,1222],[1124,2473,2475,2588],{"className":2474},[1226],[1124,2476,2478,2535],{"className":2477,"style":2427},[1230],[1124,2479,2480,2483],{"style":2430},[1124,2481],{"className":2482,"style":1829},[1238],[1124,2484,2486,2492,2497,2501,2505,2508,2511,2514,2517,2520,2523,2526,2529,2532],{"className":2485},[1209],[1124,2487,2489],{"className":2488},[1209,1767],[1124,2490,1685],{"className":2491},[1209],[1124,2493,1439],{"className":2494,"style":2496},[1209,2495],"mathbf","margin-right:0.016em;",[1124,2498],{"className":2499,"style":2500},[1271],"margin-right:0.2222em;",[1124,2502,2325],{"className":2503},[2504],"mbin",[1124,2506],{"className":2507,"style":2500},[1271],[1124,2509,1148],{"className":2510},[1209,2495],[1124,2512],{"className":2513,"style":2500},[1271],[1124,2515,2330],{"className":2516},[2504],[1124,2518],{"className":2519,"style":2500},[1271],[1124,2521,2230],{"className":2522},[1209,1213],[1124,2524],{"className":2525,"style":1774},[1271],[1124,2527,1708],{"className":2528},[1778],[1124,2530],{"className":2531,"style":1774},[1271],[1124,2533,1673],{"className":2534},[1209],[1124,2536,2537,2540],{"style":1838},[1124,2538],{"className":2539,"style":1829},[1238],[1124,2541,2543,2549,2552,2555,2558,2561,2564,2567,2570,2573,2576,2579,2582,2585],{"className":2542},[1209],[1124,2544,2546],{"className":2545},[1209,1767],[1124,2547,1685],{"className":2548},[1209],[1124,2550,1439],{"className":2551,"style":2496},[1209,2495],[1124,2553],{"className":2554,"style":2500},[1271],[1124,2556,2325],{"className":2557},[2504],[1124,2559],{"className":2560,"style":2500},[1271],[1124,2562,1148],{"className":2563},[1209,2495],[1124,2565],{"className":2566,"style":2500},[1271],[1124,2568,2330],{"className":2569},[2504],[1124,2571],{"className":2572,"style":2500},[1271],[1124,2574,2230],{"className":2575},[1209,1213],[1124,2577],{"className":2578,"style":1774},[1271],[1124,2580,1748],{"className":2581},[1778],[1124,2583],{"className":2584,"style":1774},[1271],[1124,2586,1673],{"className":2587},[1209],[1124,2589,1254],{"className":2590},[1253],[1124,2592,2594],{"className":2593},[1226],[1124,2595,2597],{"className":2596,"style":2460},[1230],[1124,2598],{},[1124,2600],{"className":2601},[2211,2212],[1101,2603,2604],{},[1107,2605,2606],{},"逻辑门实现",[1101,2608,2609],{},"感知机可以实现基本逻辑门：NAND 门、AND 门、OR 门。由于 NAND 门是通用门（可以组合构建任何逻辑运算），感知机具有通用计算能力。",[1101,2611,2612],{},[1107,2613,2614],{},"感知机 vs Sigmoid 神经元 对比",[2616,2617,2618,2634],"table",{},[2619,2620,2621],"thead",{},[2622,2623,2624,2628,2631],"tr",{},[2625,2626,2627],"th",{},"特性",[2625,2629,2630],{},"感知机",[2625,2632,2633],{},"Sigmoid 神经元",[2635,2636,2637,2649,2711,2722,2733],"tbody",{},[2622,2638,2639,2643,2646],{},[2640,2641,2642],"td",{},"输出值",[2640,2644,2645],{},"二进制：0 或 1",[2640,2647,2648],{},"连续值：0 到 1 之间",[2622,2650,2651,2654,2657],{},[2640,2652,2653],{},"激活函数",[2640,2655,2656],{},"阶跃函数（step function）",[2640,2658,2659,2660],{},"Sigmoid 函数 ",[1124,2661,2663,2687],{"className":2662},[1127],[1124,2664,2666],{"className":2665},[1131],[1133,2667,2668],{"xmlns":1135},[1137,2669,2670,2684],{},[1140,2671,2672,2675,2678,2681],{},[1146,2673,2674],{},"σ",[1154,2676,2677],{"stretchy":1674},"(",[1146,2679,2680],{},"z",[1154,2682,2683],{"stretchy":1674},")",[1189,2685,2686],{"encoding":1191},"\\sigma(z)",[1124,2688,2690],{"className":2689,"ariaHidden":1156},[1196],[1124,2691,2693,2697,2701,2704,2708],{"className":2692},[1200],[1124,2694],{"className":2695,"style":2696},[1204],"height:1em;vertical-align:-0.25em;",[1124,2698,2674],{"className":2699,"style":2700},[1209,1213],"margin-right:0.0359em;",[1124,2702,2677],{"className":2703},[1795],[1124,2705,2680],{"className":2706,"style":2707},[1209,1213],"margin-right:0.044em;",[1124,2709,2683],{"className":2710},[2211],[2622,2712,2713,2716,2719],{},[2640,2714,2715],{},"可微性",[2640,2717,2718],{},"不可微（不连续）",[2640,2720,2721],{},"处处可微（光滑曲线）",[2622,2723,2724,2727,2730],{},[2640,2725,2726],{},"权重微调响应",[2640,2728,2729],{},"小变化可能导致输出完全翻转",[2640,2731,2732],{},"小变化仅导致输出的小变化",[2622,2734,2735,2738,2741],{},[2640,2736,2737],{},"学习适用性",[2640,2739,2740],{},"难以用梯度方法学习",[2640,2742,2743],{},"适合梯度下降优化",[2745,2746],"hr",{},[1096,2748,2750],{"id":2749},"_12-sigmoid-神经元","1.2 Sigmoid 神经元",[1101,2752,2753],{},[1107,2754,2755],{},"感知机的问题",[1101,2757,2758],{},"感知机的输出是阶跃函数，权重或偏置的微小变化可能导致输出从 0 突变到 1（或反之）。这使得我们无法通过逐步微调权重来\"学习\"——因为微小调整的效果不可预测。",[1101,2760,2761],{},[1107,2762,2763],{},"Sigmoid 神经元的解决方案",[1101,2765,2766],{},"Sigmoid 神经元的输出为：",[1101,2768,2769],{},[1124,2770,2772,2804],{"className":2771},[1127],[1124,2773,2775],{"className":2774},[1131],[1133,2776,2777],{"xmlns":1135},[1137,2778,2779,2801],{},[1140,2780,2781,2783,2785,2787,2789,2791,2793,2795,2797,2799],{},[1647,2782,1649],{},[1154,2784,1652],{},[1146,2786,2674],{},[1154,2788,2677],{"stretchy":1674},[1146,2790,1439],{"mathvariant":2322},[1154,2792,2325],{},[1146,2794,1148],{"mathvariant":2322},[1154,2796,2330],{},[1146,2798,2230],{},[1154,2800,2683],{"stretchy":1674},[1189,2802,2803],{"encoding":1191},"\\text{output} = \\sigma(\\mathbf{w} \\cdot \\mathbf{x} + b)",[1124,2805,2807,2828,2852,2871],{"className":2806,"ariaHidden":1156},[1196],[1124,2808,2810,2813,2819,2822,2825],{"className":2809},[1200],[1124,2811],{"className":2812,"style":1763},[1204],[1124,2814,2816],{"className":2815},[1209,1767],[1124,2817,1649],{"className":2818},[1209],[1124,2820],{"className":2821,"style":1774},[1271],[1124,2823,1652],{"className":2824},[1778],[1124,2826],{"className":2827,"style":1774},[1271],[1124,2829,2831,2834,2837,2840,2843,2846,2849],{"className":2830},[1200],[1124,2832],{"className":2833,"style":2696},[1204],[1124,2835,2674],{"className":2836,"style":2700},[1209,1213],[1124,2838,2677],{"className":2839},[1795],[1124,2841,1439],{"className":2842,"style":2496},[1209,2495],[1124,2844],{"className":2845,"style":2500},[1271],[1124,2847,2325],{"className":2848},[2504],[1124,2850],{"className":2851,"style":2500},[1271],[1124,2853,2855,2859,2862,2865,2868],{"className":2854},[1200],[1124,2856],{"className":2857,"style":2858},[1204],"height:0.6667em;vertical-align:-0.0833em;",[1124,2860,1148],{"className":2861},[1209,2495],[1124,2863],{"className":2864,"style":2500},[1271],[1124,2866,2330],{"className":2867},[2504],[1124,2869],{"className":2870,"style":2500},[1271],[1124,2872,2874,2877,2880],{"className":2873},[1200],[1124,2875],{"className":2876,"style":2696},[1204],[1124,2878,2230],{"className":2879},[1209,1213],[1124,2881,2683],{"className":2882},[2211],[1101,2884,2885],{},"其中 Sigmoid 函数定义为：",[1101,2887,2888],{},[1124,2889,2891,2936],{"className":2890},[1127],[1124,2892,2894],{"className":2893},[1131],[1133,2895,2896],{"xmlns":1135},[1137,2897,2898,2933],{},[1140,2899,2900,2902,2904,2906,2908,2910],{},[1146,2901,2674],{},[1154,2903,2677],{"stretchy":1674},[1146,2905,2680],{},[1154,2907,2683],{"stretchy":1674},[1154,2909,1652],{},[2911,2912,2913,2915],"mfrac",{},[1150,2914,1152],{},[1140,2916,2917,2919,2921],{},[1150,2918,1152],{},[1154,2920,2330],{},[2922,2923,2924,2927],"msup",{},[1146,2925,2926],{},"e",[1140,2928,2929,2931],{},[1154,2930,2235],{},[1146,2932,2680],{},[1189,2934,2935],{"encoding":1191},"\\sigma(z) = \\frac{1}{1 + e^{-z}}",[1124,2937,2939,2966],{"className":2938,"ariaHidden":1156},[1196],[1124,2940,2942,2945,2948,2951,2954,2957,2960,2963],{"className":2941},[1200],[1124,2943],{"className":2944,"style":2696},[1204],[1124,2946,2674],{"className":2947,"style":2700},[1209,1213],[1124,2949,2677],{"className":2950},[1795],[1124,2952,2680],{"className":2953,"style":2707},[1209,1213],[1124,2955,2683],{"className":2956},[2211],[1124,2958],{"className":2959,"style":1774},[1271],[1124,2961,1652],{"className":2962},[1778],[1124,2964],{"className":2965,"style":1774},[1271],[1124,2967,2969,2973],{"className":2968},[1200],[1124,2970],{"className":2971,"style":2972},[1204],"height:1.2484em;vertical-align:-0.4033em;",[1124,2974,2976,2979,3089],{"className":2975},[1209],[1124,2977],{"className":2978},[1795,2212],[1124,2980,2982],{"className":2981},[2911],[1124,2983,2985,3080],{"className":2984},[1221,1222],[1124,2986,2988,3077],{"className":2987},[1226],[1124,2989,2992,3051,3062],{"className":2990,"style":2991},[1230],"height:0.8451em;",[1124,2993,2995,2999],{"style":2994},"top:-2.655em;",[1124,2996],{"className":2997,"style":2998},[1238],"height:3em;",[1124,3000,3002],{"className":3001},[1243,1244,1245,1246],[1124,3003,3005,3008,3011],{"className":3004},[1209,1246],[1124,3006,1152],{"className":3007},[1209,1246],[1124,3009,2330],{"className":3010},[2504,1246],[1124,3012,3014,3017],{"className":3013},[1209,1246],[1124,3015,2926],{"className":3016},[1209,1213,1246],[1124,3018,3020],{"className":3019},[1217],[1124,3021,3023],{"className":3022},[1221],[1124,3024,3026],{"className":3025},[1226],[1124,3027,3030],{"className":3028,"style":3029},[1230],"height:0.7027em;",[1124,3031,3033,3037],{"style":3032},"top:-2.786em;margin-right:0.0714em;",[1124,3034],{"className":3035,"style":3036},[1238],"height:2.5em;",[1124,3038,3042],{"className":3039},[1243,3040,3041,1246],"reset-size3","size1",[1124,3043,3045,3048],{"className":3044},[1209,1246],[1124,3046,2235],{"className":3047},[1209,1246],[1124,3049,2680],{"className":3050,"style":2707},[1209,1213,1246],[1124,3052,3054,3057],{"style":3053},"top:-3.23em;",[1124,3055],{"className":3056,"style":2998},[1238],[1124,3058],{"className":3059,"style":3061},[3060],"frac-line","border-bottom-width:0.04em;",[1124,3063,3065,3068],{"style":3064},"top:-3.394em;",[1124,3066],{"className":3067,"style":2998},[1238],[1124,3069,3071],{"className":3070},[1243,1244,1245,1246],[1124,3072,3074],{"className":3073},[1209,1246],[1124,3075,1152],{"className":3076},[1209,1246],[1124,3078,1254],{"className":3079},[1253],[1124,3081,3083],{"className":3082},[1226],[1124,3084,3087],{"className":3085,"style":3086},[1230],"height:0.4033em;",[1124,3088],{},[1124,3090],{"className":3091},[2211,2212],[1101,3093,3094,3097,3098,3128],{},[1107,3095,3096],{},"关键性质","：由于 ",[1124,3099,3101,3115],{"className":3100},[1127],[1124,3102,3104],{"className":3103},[1131],[1133,3105,3106],{"xmlns":1135},[1137,3107,3108,3112],{},[1140,3109,3110],{},[1146,3111,2674],{},[1189,3113,3114],{"encoding":1191},"\\sigma",[1124,3116,3118],{"className":3117,"ariaHidden":1156},[1196],[1124,3119,3121,3125],{"className":3120},[1200],[1124,3122],{"className":3123,"style":3124},[1204],"height:0.4306em;",[1124,3126,2674],{"className":3127,"style":2700},[1209,1213]," 是光滑函数，权重和偏置的微小变化只会导致输出的微小变化：",[1101,3130,3131],{},[1124,3132,3134,3208],{"className":3133},[1127],[1124,3135,3137],{"className":3136},[1131],[1133,3138,3139],{"xmlns":1135},[1137,3140,3141,3205],{},[1140,3142,3143,3147,3149,3152,3158,3177,3179,3185,3187,3201,3203],{},[1146,3144,3146],{"mathvariant":3145},"normal","Δ",[1647,3148,1649],{},[1154,3150,3151],{},"≈",[1143,3153,3154,3156],{},[1154,3155,1690],{},[1146,3157,1693],{},[2911,3159,3160,3167],{},[1140,3161,3162,3165],{},[1146,3163,3164],{"mathvariant":3145},"∂",[1647,3166,1649],{},[1140,3168,3169,3171],{},[1146,3170,3164],{"mathvariant":3145},[1143,3172,3173,3175],{},[1146,3174,1439],{},[1146,3176,1693],{},[1146,3178,3146],{"mathvariant":3145},[1143,3180,3181,3183],{},[1146,3182,1439],{},[1146,3184,1693],{},[1154,3186,2330],{},[2911,3188,3189,3195],{},[1140,3190,3191,3193],{},[1146,3192,3164],{"mathvariant":3145},[1647,3194,1649],{},[1140,3196,3197,3199],{},[1146,3198,3164],{"mathvariant":3145},[1146,3200,2230],{},[1146,3202,3146],{"mathvariant":3145},[1146,3204,2230],{},[1189,3206,3207],{"encoding":1191},"\\Delta \\text{output} \\approx \\sum_j \\frac{\\partial \\text{output}}{\\partial w_j} \\Delta w_j + \\frac{\\partial \\text{output}}{\\partial b} \\Delta b",[1124,3209,3211,3236,3459],{"className":3210,"ariaHidden":1156},[1196],[1124,3212,3214,3218,3221,3227,3230,3233],{"className":3213},[1200],[1124,3215],{"className":3216,"style":3217},[1204],"height:0.8778em;vertical-align:-0.1944em;",[1124,3219,3146],{"className":3220},[1209],[1124,3222,3224],{"className":3223},[1209,1767],[1124,3225,1649],{"className":3226},[1209],[1124,3228],{"className":3229,"style":1774},[1271],[1124,3231,3151],{"className":3232},[1778],[1124,3234],{"className":3235,"style":1774},[1271],[1124,3237,3239,3243,3283,3286,3407,3410,3450,3453,3456],{"className":3238},[1200],[1124,3240],{"className":3241,"style":3242},[1204],"height:1.4745em;vertical-align:-0.5423em;",[1124,3244,3246,3249],{"className":3245},[1897],[1124,3247,1690],{"className":3248,"style":1903},[1897,1901,1902],[1124,3250,3252],{"className":3251},[1217],[1124,3253,3255,3275],{"className":3254},[1221,1222],[1124,3256,3258,3272],{"className":3257},[1226],[1124,3259,3261],{"className":3260,"style":1916},[1230],[1124,3262,3263,3266],{"style":1919},[1124,3264],{"className":3265,"style":1239},[1238],[1124,3267,3269],{"className":3268},[1243,1244,1245,1246],[1124,3270,1693],{"className":3271,"style":1929},[1209,1213,1246],[1124,3273,1254],{"className":3274},[1253],[1124,3276,3278],{"className":3277},[1226],[1124,3279,3281],{"className":3280,"style":1939},[1230],[1124,3282],{},[1124,3284],{"className":3285,"style":1272},[1271],[1124,3287,3289,3292,3404],{"className":3288},[1209],[1124,3290],{"className":3291},[1795,2212],[1124,3293,3295],{"className":3294},[2911],[1124,3296,3298,3395],{"className":3297},[1221,1222],[1124,3299,3301,3392],{"className":3300},[1226],[1124,3302,3305,3363,3371],{"className":3303,"style":3304},[1230],"height:0.9322em;",[1124,3306,3307,3310],{"style":2994},[1124,3308],{"className":3309,"style":2998},[1238],[1124,3311,3313],{"className":3312},[1243,1244,1245,1246],[1124,3314,3316,3320],{"className":3315},[1209,1246],[1124,3317,3164],{"className":3318,"style":3319},[1209,1246],"margin-right:0.0556em;",[1124,3321,3323,3326],{"className":3322},[1209,1246],[1124,3324,1439],{"className":3325,"style":1480},[1209,1213,1246],[1124,3327,3329],{"className":3328},[1217],[1124,3330,3332,3354],{"className":3331},[1221,1222],[1124,3333,3335,3351],{"className":3334},[1226],[1124,3336,3339],{"className":3337,"style":3338},[1230],"height:0.3281em;",[1124,3340,3342,3345],{"style":3341},"top:-2.357em;margin-left:-0.0269em;margin-right:0.0714em;",[1124,3343],{"className":3344,"style":3036},[1238],[1124,3346,3348],{"className":3347},[1243,3040,3041,1246],[1124,3349,1693],{"className":3350,"style":1929},[1209,1213,1246],[1124,3352,1254],{"className":3353},[1253],[1124,3355,3357],{"className":3356},[1226],[1124,3358,3361],{"className":3359,"style":3360},[1230],"height:0.2819em;",[1124,3362],{},[1124,3364,3365,3368],{"style":3053},[1124,3366],{"className":3367,"style":2998},[1238],[1124,3369],{"className":3370,"style":3061},[3060],[1124,3372,3374,3377],{"style":3373},"top:-3.4461em;",[1124,3375],{"className":3376,"style":2998},[1238],[1124,3378,3380],{"className":3379},[1243,1244,1245,1246],[1124,3381,3383,3386],{"className":3382},[1209,1246],[1124,3384,3164],{"className":3385,"style":3319},[1209,1246],[1124,3387,3389],{"className":3388},[1209,1767,1246],[1124,3390,1649],{"className":3391},[1209,1246],[1124,3393,1254],{"className":3394},[1253],[1124,3396,3398],{"className":3397},[1226],[1124,3399,3402],{"className":3400,"style":3401},[1230],"height:0.5423em;",[1124,3403],{},[1124,3405],{"className":3406},[2211,2212],[1124,3408,3146],{"className":3409},[1209],[1124,3411,3413,3416],{"className":3412},[1209],[1124,3414,1439],{"className":3415,"style":1480},[1209,1213],[1124,3417,3419],{"className":3418},[1217],[1124,3420,3422,3442],{"className":3421},[1221,1222],[1124,3423,3425,3439],{"className":3424},[1226],[1124,3426,3428],{"className":3427,"style":1963},[1230],[1124,3429,3430,3433],{"style":1495},[1124,3431],{"className":3432,"style":1239},[1238],[1124,3434,3436],{"className":3435},[1243,1244,1245,1246],[1124,3437,1693],{"className":3438,"style":1929},[1209,1213,1246],[1124,3440,1254],{"className":3441},[1253],[1124,3443,3445],{"className":3444},[1226],[1124,3446,3448],{"className":3447,"style":1984},[1230],[1124,3449],{},[1124,3451],{"className":3452,"style":2500},[1271],[1124,3454,2330],{"className":3455},[2504],[1124,3457],{"className":3458,"style":2500},[1271],[1124,3460,3462,3466,3544,3547],{"className":3461},[1200],[1124,3463],{"className":3464,"style":3465},[1204],"height:1.2772em;vertical-align:-0.345em;",[1124,3467,3469,3472,3541],{"className":3468},[1209],[1124,3470],{"className":3471},[1795,2212],[1124,3473,3475],{"className":3474},[2911],[1124,3476,3478,3532],{"className":3477},[1221,1222],[1124,3479,3481,3529],{"className":3480},[1226],[1124,3482,3484,3501,3509],{"className":3483,"style":3304},[1230],[1124,3485,3486,3489],{"style":2994},[1124,3487],{"className":3488,"style":2998},[1238],[1124,3490,3492],{"className":3491},[1243,1244,1245,1246],[1124,3493,3495,3498],{"className":3494},[1209,1246],[1124,3496,3164],{"className":3497,"style":3319},[1209,1246],[1124,3499,2230],{"className":3500},[1209,1213,1246],[1124,3502,3503,3506],{"style":3053},[1124,3504],{"className":3505,"style":2998},[1238],[1124,3507],{"className":3508,"style":3061},[3060],[1124,3510,3511,3514],{"style":3373},[1124,3512],{"className":3513,"style":2998},[1238],[1124,3515,3517],{"className":3516},[1243,1244,1245,1246],[1124,3518,3520,3523],{"className":3519},[1209,1246],[1124,3521,3164],{"className":3522,"style":3319},[1209,1246],[1124,3524,3526],{"className":3525},[1209,1767,1246],[1124,3527,1649],{"className":3528},[1209,1246],[1124,3530,1254],{"className":3531},[1253],[1124,3533,3535],{"className":3534},[1226],[1124,3536,3539],{"className":3537,"style":3538},[1230],"height:0.345em;",[1124,3540],{},[1124,3542],{"className":3543},[2211,2212],[1124,3545,3146],{"className":3546},[1209],[1124,3548,2230],{"className":3549},[1209,1213],[1101,3551,3552],{},[1107,3553,3554],{},"Sigmoid 函数特性",[1117,3556,3557,3560,3689,3813,3816],{},[1120,3558,3559],{},"输出范围：(0, 1)",[1120,3561,3562,3563,3621,3622],{},"当 ",[1124,3564,3566,3588],{"className":3565},[1127],[1124,3567,3569],{"className":3568},[1131],[1133,3570,3571],{"xmlns":1135},[1137,3572,3573,3585],{},[1140,3574,3575,3577,3580,3582],{},[1146,3576,2680],{},[1154,3578,3579],{},"→",[1154,3581,2330],{},[1146,3583,3584],{"mathvariant":3145},"∞",[1189,3586,3587],{"encoding":1191},"z \\to +\\infty",[1124,3589,3591,3609],{"className":3590,"ariaHidden":1156},[1196],[1124,3592,3594,3597,3600,3603,3606],{"className":3593},[1200],[1124,3595],{"className":3596,"style":3124},[1204],[1124,3598,2680],{"className":3599,"style":2707},[1209,1213],[1124,3601],{"className":3602,"style":1774},[1271],[1124,3604,3579],{"className":3605},[1778],[1124,3607],{"className":3608,"style":1774},[1271],[1124,3610,3612,3615,3618],{"className":3611},[1200],[1124,3613],{"className":3614,"style":2858},[1204],[1124,3616,2330],{"className":3617},[1209],[1124,3619,3584],{"className":3620},[1209]," 时，",[1124,3623,3625,3649],{"className":3624},[1127],[1124,3626,3628],{"className":3627},[1131],[1133,3629,3630],{"xmlns":1135},[1137,3631,3632,3646],{},[1140,3633,3634,3636,3638,3640,3642,3644],{},[1146,3635,2674],{},[1154,3637,2677],{"stretchy":1674},[1146,3639,2680],{},[1154,3641,2683],{"stretchy":1674},[1154,3643,3579],{},[1150,3645,1152],{},[1189,3647,3648],{"encoding":1191},"\\sigma(z) \\to 1",[1124,3650,3652,3679],{"className":3651,"ariaHidden":1156},[1196],[1124,3653,3655,3658,3661,3664,3667,3670,3673,3676],{"className":3654},[1200],[1124,3656],{"className":3657,"style":2696},[1204],[1124,3659,2674],{"className":3660,"style":2700},[1209,1213],[1124,3662,2677],{"className":3663},[1795],[1124,3665,2680],{"className":3666,"style":2707},[1209,1213],[1124,3668,2683],{"className":3669},[2211],[1124,3671],{"className":3672,"style":1774},[1271],[1124,3674,3579],{"className":3675},[1778],[1124,3677],{"className":3678,"style":1774},[1271],[1124,3680,3682,3686],{"className":3681},[1200],[1124,3683],{"className":3684,"style":3685},[1204],"height:0.6444em;",[1124,3687,1152],{"className":3688},[1209],[1120,3690,3562,3691,3621,3747],{},[1124,3692,3694,3714],{"className":3693},[1127],[1124,3695,3697],{"className":3696},[1131],[1133,3698,3699],{"xmlns":1135},[1137,3700,3701,3711],{},[1140,3702,3703,3705,3707,3709],{},[1146,3704,2680],{},[1154,3706,3579],{},[1154,3708,2235],{},[1146,3710,3584],{"mathvariant":3145},[1189,3712,3713],{"encoding":1191},"z \\to -\\infty",[1124,3715,3717,3735],{"className":3716,"ariaHidden":1156},[1196],[1124,3718,3720,3723,3726,3729,3732],{"className":3719},[1200],[1124,3721],{"className":3722,"style":3124},[1204],[1124,3724,2680],{"className":3725,"style":2707},[1209,1213],[1124,3727],{"className":3728,"style":1774},[1271],[1124,3730,3579],{"className":3731},[1778],[1124,3733],{"className":3734,"style":1774},[1271],[1124,3736,3738,3741,3744],{"className":3737},[1200],[1124,3739],{"className":3740,"style":2858},[1204],[1124,3742,2235],{"className":3743},[1209],[1124,3745,3584],{"className":3746},[1209],[1124,3748,3750,3774],{"className":3749},[1127],[1124,3751,3753],{"className":3752},[1131],[1133,3754,3755],{"xmlns":1135},[1137,3756,3757,3771],{},[1140,3758,3759,3761,3763,3765,3767,3769],{},[1146,3760,2674],{},[1154,3762,2677],{"stretchy":1674},[1146,3764,2680],{},[1154,3766,2683],{"stretchy":1674},[1154,3768,3579],{},[1150,3770,1673],{},[1189,3772,3773],{"encoding":1191},"\\sigma(z) \\to 0",[1124,3775,3777,3804],{"className":3776,"ariaHidden":1156},[1196],[1124,3778,3780,3783,3786,3789,3792,3795,3798,3801],{"className":3779},[1200],[1124,3781],{"className":3782,"style":2696},[1204],[1124,3784,2674],{"className":3785,"style":2700},[1209,1213],[1124,3787,2677],{"className":3788},[1795],[1124,3790,2680],{"className":3791,"style":2707},[1209,1213],[1124,3793,2683],{"className":3794},[2211],[1124,3796],{"className":3797,"style":1774},[1271],[1124,3799,3579],{"className":3800},[1778],[1124,3802],{"className":3803,"style":1774},[1271],[1124,3805,3807,3810],{"className":3806},[1200],[1124,3808],{"className":3809,"style":3685},[1204],[1124,3811,1673],{"className":3812},[1209],[1120,3814,3815],{},"处处光滑可微",[1120,3817,3818,3819],{},"导数：",[1124,3820,3822,3874],{"className":3821},[1127],[1124,3823,3825],{"className":3824},[1131],[1133,3826,3827],{"xmlns":1135},[1137,3828,3829,3871],{},[1140,3830,3831,3839,3841,3843,3845,3847,3849,3851,3853,3855,3857,3859,3861,3863,3865,3867,3869],{},[2922,3832,3833,3835],{},[1146,3834,2674],{},[1154,3836,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},"0em","′",[1154,3840,2677],{"stretchy":1674},[1146,3842,2680],{},[1154,3844,2683],{"stretchy":1674},[1154,3846,1652],{},[1146,3848,2674],{},[1154,3850,2677],{"stretchy":1674},[1146,3852,2680],{},[1154,3854,2683],{"stretchy":1674},[1154,3856,2677],{"stretchy":1674},[1150,3858,1152],{},[1154,3860,2235],{},[1146,3862,2674],{},[1154,3864,2677],{"stretchy":1674},[1146,3866,2680],{},[1154,3868,2683],{"stretchy":1674},[1154,3870,2683],{"stretchy":1674},[1189,3872,3873],{"encoding":1191},"\\sigma'(z) = \\sigma(z)(1-\\sigma(z))",[1124,3875,3877,3936,3969],{"className":3876,"ariaHidden":1156},[1196],[1124,3878,3880,3884,3918,3921,3924,3927,3930,3933],{"className":3879},[1200],[1124,3881],{"className":3882,"style":3883},[1204],"height:1.0019em;vertical-align:-0.25em;",[1124,3885,3887,3890],{"className":3886},[1209],[1124,3888,2674],{"className":3889,"style":2700},[1209,1213],[1124,3891,3893],{"className":3892},[1217],[1124,3894,3896],{"className":3895},[1221],[1124,3897,3899],{"className":3898},[1226],[1124,3900,3903],{"className":3901,"style":3902},[1230],"height:0.7519em;",[1124,3904,3906,3909],{"style":3905},"top:-3.063em;margin-right:0.05em;",[1124,3907],{"className":3908,"style":1239},[1238],[1124,3910,3912],{"className":3911},[1243,1244,1245,1246],[1124,3913,3915],{"className":3914},[1209,1246],[1124,3916,3838],{"className":3917},[1209,1246],[1124,3919,2677],{"className":3920},[1795],[1124,3922,2680],{"className":3923,"style":2707},[1209,1213],[1124,3925,2683],{"className":3926},[2211],[1124,3928],{"className":3929,"style":1774},[1271],[1124,3931,1652],{"className":3932},[1778],[1124,3934],{"className":3935,"style":1774},[1271],[1124,3937,3939,3942,3945,3948,3951,3954,3957,3960,3963,3966],{"className":3938},[1200],[1124,3940],{"className":3941,"style":2696},[1204],[1124,3943,2674],{"className":3944,"style":2700},[1209,1213],[1124,3946,2677],{"className":3947},[1795],[1124,3949,2680],{"className":3950,"style":2707},[1209,1213],[1124,3952,2683],{"className":3953},[2211],[1124,3955,2677],{"className":3956},[1795],[1124,3958,1152],{"className":3959},[1209],[1124,3961],{"className":3962,"style":2500},[1271],[1124,3964,2235],{"className":3965},[2504],[1124,3967],{"className":3968,"style":2500},[1271],[1124,3970,3972,3975,3978,3981,3984],{"className":3971},[1200],[1124,3973],{"className":3974,"style":2696},[1204],[1124,3976,2674],{"className":3977,"style":2700},[1209,1213],[1124,3979,2677],{"className":3980},[1795],[1124,3982,2680],{"className":3983,"style":2707},[1209,1213],[1124,3985,3987],{"className":3986},[2211],"))",[1101,3989,3990],{},[1107,3991,3992],{},"阶跃函数特性",[1117,3994,3995,3998,4053,4108,4163],{},[1120,3996,3997],{},"输出值：仅 0 或 1",[1120,3999,3562,4000,4052],{},[1124,4001,4003,4021],{"className":4002},[1127],[1124,4004,4006],{"className":4005},[1131],[1133,4007,4008],{"xmlns":1135},[1137,4009,4010,4018],{},[1140,4011,4012,4014,4016],{},[1146,4013,2680],{},[1154,4015,1748],{},[1150,4017,1673],{},[1189,4019,4020],{"encoding":1191},"z > 0",[1124,4022,4024,4043],{"className":4023,"ariaHidden":1156},[1196],[1124,4025,4027,4031,4034,4037,4040],{"className":4026},[1200],[1124,4028],{"className":4029,"style":4030},[1204],"height:0.5782em;vertical-align:-0.0391em;",[1124,4032,2680],{"className":4033,"style":2707},[1209,1213],[1124,4035],{"className":4036,"style":1774},[1271],[1124,4038,1748],{"className":4039},[1778],[1124,4041],{"className":4042,"style":1774},[1271],[1124,4044,4046,4049],{"className":4045},[1200],[1124,4047],{"className":4048,"style":3685},[1204],[1124,4050,1673],{"className":4051},[1209]," 时，输出 = 1",[1120,4054,3562,4055,4107],{},[1124,4056,4058,4076],{"className":4057},[1127],[1124,4059,4061],{"className":4060},[1131],[1133,4062,4063],{"xmlns":1135},[1137,4064,4065,4073],{},[1140,4066,4067,4069,4071],{},[1146,4068,2680],{},[1154,4070,1708],{},[1150,4072,1673],{},[1189,4074,4075],{"encoding":1191},"z \\leq 0",[1124,4077,4079,4098],{"className":4078,"ariaHidden":1156},[1196],[1124,4080,4082,4086,4089,4092,4095],{"className":4081},[1200],[1124,4083],{"className":4084,"style":4085},[1204],"height:0.7719em;vertical-align:-0.136em;",[1124,4087,2680],{"className":4088,"style":2707},[1209,1213],[1124,4090],{"className":4091,"style":1774},[1271],[1124,4093,1708],{"className":4094},[1778],[1124,4096],{"className":4097,"style":1774},[1271],[1124,4099,4101,4104],{"className":4100},[1200],[1124,4102],{"className":4103,"style":3685},[1204],[1124,4105,1673],{"className":4106},[1209]," 时，输出 = 0",[1120,4109,4110,4111,4162],{},"在 ",[1124,4112,4114,4132],{"className":4113},[1127],[1124,4115,4117],{"className":4116},[1131],[1133,4118,4119],{"xmlns":1135},[1137,4120,4121,4129],{},[1140,4122,4123,4125,4127],{},[1146,4124,2680],{},[1154,4126,1652],{},[1150,4128,1673],{},[1189,4130,4131],{"encoding":1191},"z=0",[1124,4133,4135,4153],{"className":4134,"ariaHidden":1156},[1196],[1124,4136,4138,4141,4144,4147,4150],{"className":4137},[1200],[1124,4139],{"className":4140,"style":3124},[1204],[1124,4142,2680],{"className":4143,"style":2707},[1209,1213],[1124,4145],{"className":4146,"style":1774},[1271],[1124,4148,1652],{"className":4149},[1778],[1124,4151],{"className":4152,"style":1774},[1271],[1124,4154,4156,4159],{"className":4155},[1200],[1124,4157],{"className":4158,"style":3685},[1204],[1124,4160,1673],{"className":4161},[1209]," 处不连续",[1120,4164,4165,4166,4216],{},"导数：除 ",[1124,4167,4169,4186],{"className":4168},[1127],[1124,4170,4172],{"className":4171},[1131],[1133,4173,4174],{"xmlns":1135},[1137,4175,4176,4184],{},[1140,4177,4178,4180,4182],{},[1146,4179,2680],{},[1154,4181,1652],{},[1150,4183,1673],{},[1189,4185,4131],{"encoding":1191},[1124,4187,4189,4207],{"className":4188,"ariaHidden":1156},[1196],[1124,4190,4192,4195,4198,4201,4204],{"className":4191},[1200],[1124,4193],{"className":4194,"style":3124},[1204],[1124,4196,2680],{"className":4197,"style":2707},[1209,1213],[1124,4199],{"className":4200,"style":1774},[1271],[1124,4202,1652],{"className":4203},[1778],[1124,4205],{"className":4206,"style":1774},[1271],[1124,4208,4210,4213],{"className":4209},[1200],[1124,4211],{"className":4212,"style":3685},[1204],[1124,4214,1673],{"className":4215},[1209]," 外处处为 0",[2745,4218],{},[1096,4220,4222],{"id":4221},"_13-神经网络架构","1.3 神经网络架构",[1101,4224,4225],{},"神经网络由多层神经元组成，信息从输入层经过隐藏层最终到达输出层。",[1117,4227,4228,4234,4240],{},[1120,4229,4230,4233],{},[1107,4231,4232],{},"输入层（Input Layer）","：接收外部数据，神经元数量由输入特征维度决定",[1120,4235,4236,4239],{},[1107,4237,4238],{},"隐藏层（Hidden Layers）","：执行中间计算，可以有一层或多层",[1120,4241,4242,4245],{},[1107,4243,4244],{},"输出层（Output Layer）","：产生最终结果",[1101,4247,4248,4251],{},[1107,4249,4250],{},"前馈网络（Feedforward Networks）","：信息仅从前往后流动，没有循环连接。前一层的输出作为下一层的输入。",[2745,4253],{},[1096,4255,4257],{"id":4256},"_14-使用神经网络识别手写数字","1.4 使用神经网络识别手写数字",[1101,4259,4260],{},"以 MNIST 手写数字识别为例，展示神经网络的实际应用。",[1101,4262,4263],{},[1107,4264,4265],{},"网络结构",[1117,4267,4268,4274,4280],{},[1120,4269,4270,4273],{},[1107,4271,4272],{},"输入层","：784 个神经元（28x28 像素图像，每个像素作为一个输入，灰度值 0.0-1.0）",[1120,4275,4276,4279],{},[1107,4277,4278],{},"隐藏层","：例如 15 或 30 个神经元（可调节）",[1120,4281,4282,4285],{},[1107,4283,4284],{},"输出层","：10 个神经元（对应数字 0-9，哪个神经元激活值最高即为预测结果）",[1101,4287,4288],{},"网络结构简记：784 → 隐藏层(15\u002F30) → 10",[1101,4290,4291],{},"MNIST 数据集包含 60,000 张训练图像和 10,000 张测试图像。每张图像是 28x28 的灰度图，已经过居中和归一化处理。",[2745,4293],{},[1096,4295,4297],{"id":4296},"_15-梯度下降算法","1.5 梯度下降算法",[1101,4299,4300],{},"梯度下降是训练神经网络的核心优化方法。",[1101,4302,4303],{},[1107,4304,4305],{},"代价函数（Cost Function）",[1101,4307,4308],{},"均方误差（MSE）代价函数：",[1101,4310,4311],{},[1124,4312,4314,4380],{"className":4313},[1127],[1124,4315,4317],{"className":4316},[1131],[1133,4318,4319],{"xmlns":1135},[1137,4320,4321,4377],{},[1140,4322,4323,4326,4328,4330,4332,4334,4336,4338,4348,4354,4357,4360,4362,4364,4366,4368,4371],{},[1146,4324,4325],{},"C",[1154,4327,2677],{"stretchy":1674},[1146,4329,1439],{"mathvariant":2322},[1154,4331,1157],{"separator":1156},[1146,4333,2230],{},[1154,4335,2683],{"stretchy":1674},[1154,4337,1652],{},[2911,4339,4340,4342],{},[1150,4341,1152],{},[1140,4343,4344,4346],{},[1150,4345,1164],{},[1146,4347,1187],{},[1143,4349,4350,4352],{},[1154,4351,1690],{},[1146,4353,1148],{},[1146,4355,4356],{"mathvariant":3145},"∥",[1146,4358,4359],{},"y",[1154,4361,2677],{"stretchy":1674},[1146,4363,1148],{},[1154,4365,2683],{"stretchy":1674},[1154,4367,2235],{},[1146,4369,4370],{},"a",[2922,4372,4373,4375],{},[1146,4374,4356],{"mathvariant":3145},[1150,4376,1164],{},[1189,4378,4379],{"encoding":1191},"C(\\mathbf{w}, b) = \\frac{1}{2n} \\sum_x \\| y(x) - a \\|^2",[1124,4381,4383,4420,4570],{"className":4382,"ariaHidden":1156},[1196],[1124,4384,4386,4389,4393,4396,4399,4402,4405,4408,4411,4414,4417],{"className":4385},[1200],[1124,4387],{"className":4388,"style":2696},[1204],[1124,4390,4325],{"className":4391,"style":4392},[1209,1213],"margin-right:0.0715em;",[1124,4394,2677],{"className":4395},[1795],[1124,4397,1439],{"className":4398,"style":2496},[1209,2495],[1124,4400,1157],{"className":4401},[1267],[1124,4403],{"className":4404,"style":1272},[1271],[1124,4406,2230],{"className":4407},[1209,1213],[1124,4409,2683],{"className":4410},[2211],[1124,4412],{"className":4413,"style":1774},[1271],[1124,4415,1652],{"className":4416},[1778],[1124,4418],{"className":4419,"style":1774},[1271],[1124,4421,4423,4427,4498,4501,4543,4546,4549,4552,4555,4558,4561,4564,4567],{"className":4422},[1200],[1124,4424],{"className":4425,"style":4426},[1204],"height:1.1901em;vertical-align:-0.345em;",[1124,4428,4430,4433,4495],{"className":4429},[1209],[1124,4431],{"className":4432},[1795,2212],[1124,4434,4436],{"className":4435},[2911],[1124,4437,4439,4487],{"className":4438},[1221,1222],[1124,4440,4442,4484],{"className":4441},[1226],[1124,4443,4445,4462,4470],{"className":4444,"style":2991},[1230],[1124,4446,4447,4450],{"style":2994},[1124,4448],{"className":4449,"style":2998},[1238],[1124,4451,4453],{"className":4452},[1243,1244,1245,1246],[1124,4454,4456,4459],{"className":4455},[1209,1246],[1124,4457,1164],{"className":4458},[1209,1246],[1124,4460,1187],{"className":4461},[1209,1213,1246],[1124,4463,4464,4467],{"style":3053},[1124,4465],{"className":4466,"style":2998},[1238],[1124,4468],{"className":4469,"style":3061},[3060],[1124,4471,4472,4475],{"style":3064},[1124,4473],{"className":4474,"style":2998},[1238],[1124,4476,4478],{"className":4477},[1243,1244,1245,1246],[1124,4479,4481],{"className":4480},[1209,1246],[1124,4482,1152],{"className":4483},[1209,1246],[1124,4485,1254],{"className":4486},[1253],[1124,4488,4490],{"className":4489},[1226],[1124,4491,4493],{"className":4492,"style":3538},[1230],[1124,4494],{},[1124,4496],{"className":4497},[2211,2212],[1124,4499],{"className":4500,"style":1272},[1271],[1124,4502,4504,4507],{"className":4503},[1897],[1124,4505,1690],{"className":4506,"style":1903},[1897,1901,1902],[1124,4508,4510],{"className":4509},[1217],[1124,4511,4513,4534],{"className":4512},[1221,1222],[1124,4514,4516,4531],{"className":4515},[1226],[1124,4517,4520],{"className":4518,"style":4519},[1230],"height:0.0017em;",[1124,4521,4522,4525],{"style":1919},[1124,4523],{"className":4524,"style":1239},[1238],[1124,4526,4528],{"className":4527},[1243,1244,1245,1246],[1124,4529,1148],{"className":4530},[1209,1213,1246],[1124,4532,1254],{"className":4533},[1253],[1124,4535,4537],{"className":4536},[1226],[1124,4538,4541],{"className":4539,"style":4540},[1230],"height:0.2997em;",[1124,4542],{},[1124,4544],{"className":4545,"style":1272},[1271],[1124,4547,4356],{"className":4548},[1209],[1124,4550,4359],{"className":4551,"style":2700},[1209,1213],[1124,4553,2677],{"className":4554},[1795],[1124,4556,1148],{"className":4557},[1209,1213],[1124,4559,2683],{"className":4560},[2211],[1124,4562],{"className":4563,"style":2500},[1271],[1124,4565,2235],{"className":4566},[2504],[1124,4568],{"className":4569,"style":2500},[1271],[1124,4571,4573,4577,4580],{"className":4572},[1200],[1124,4574],{"className":4575,"style":4576},[1204],"height:1.0641em;vertical-align:-0.25em;",[1124,4578,4370],{"className":4579},[1209,1213],[1124,4581,4583,4586],{"className":4582},[1209],[1124,4584,4356],{"className":4585},[1209],[1124,4587,4589],{"className":4588},[1217],[1124,4590,4592],{"className":4591},[1221],[1124,4593,4595],{"className":4594},[1226],[1124,4596,4599],{"className":4597,"style":4598},[1230],"height:0.8141em;",[1124,4600,4601,4604],{"style":3905},[1124,4602],{"className":4603,"style":1239},[1238],[1124,4605,4607],{"className":4606},[1243,1244,1245,1246],[1124,4608,1164],{"className":4609},[1209,1246],[1101,4611,4612,4613,4641,4642,4686,4687,4715],{},"其中 ",[1124,4614,4616,4629],{"className":4615},[1127],[1124,4617,4619],{"className":4618},[1131],[1133,4620,4621],{"xmlns":1135},[1137,4622,4623,4627],{},[1140,4624,4625],{},[1146,4626,1187],{},[1189,4628,1187],{"encoding":1191},[1124,4630,4632],{"className":4631,"ariaHidden":1156},[1196],[1124,4633,4635,4638],{"className":4634},[1200],[1124,4636],{"className":4637,"style":3124},[1204],[1124,4639,1187],{"className":4640},[1209,1213]," 是训练样本数，",[1124,4643,4645,4665],{"className":4644},[1127],[1124,4646,4648],{"className":4647},[1131],[1133,4649,4650],{"xmlns":1135},[1137,4651,4652,4662],{},[1140,4653,4654,4656,4658,4660],{},[1146,4655,4359],{},[1154,4657,2677],{"stretchy":1674},[1146,4659,1148],{},[1154,4661,2683],{"stretchy":1674},[1189,4663,4664],{"encoding":1191},"y(x)",[1124,4666,4668],{"className":4667,"ariaHidden":1156},[1196],[1124,4669,4671,4674,4677,4680,4683],{"className":4670},[1200],[1124,4672],{"className":4673,"style":2696},[1204],[1124,4675,4359],{"className":4676,"style":2700},[1209,1213],[1124,4678,2677],{"className":4679},[1795],[1124,4681,1148],{"className":4682},[1209,1213],[1124,4684,2683],{"className":4685},[2211]," 是期望输出，",[1124,4688,4690,4703],{"className":4689},[1127],[1124,4691,4693],{"className":4692},[1131],[1133,4694,4695],{"xmlns":1135},[1137,4696,4697,4701],{},[1140,4698,4699],{},[1146,4700,4370],{},[1189,4702,4370],{"encoding":1191},[1124,4704,4706],{"className":4705,"ariaHidden":1156},[1196],[1124,4707,4709,4712],{"className":4708},[1200],[1124,4710],{"className":4711,"style":3124},[1204],[1124,4713,4370],{"className":4714},[1209,1213]," 是网络实际输出。",[1101,4717,4718],{},[1107,4719,4720],{},"梯度",[1101,4722,4723],{},[1124,4724,4726,4795],{"className":4725},[1127],[1124,4727,4729],{"className":4728},[1131],[1133,4730,4731],{"xmlns":1135},[1137,4732,4733,4792],{},[1140,4734,4735,4738,4740,4742],{},[1146,4736,4737],{"mathvariant":3145},"∇",[1146,4739,4325],{},[1154,4741,1652],{},[2922,4743,4744,4789],{},[1140,4745,4746,4748,4767,4769,4787],{},[1154,4747,2677],{"fence":1156},[2911,4749,4750,4756],{},[1140,4751,4752,4754],{},[1146,4753,3164],{"mathvariant":3145},[1146,4755,4325],{},[1140,4757,4758,4760],{},[1146,4759,3164],{"mathvariant":3145},[1143,4761,4762,4765],{},[1146,4763,4764],{},"v",[1150,4766,1152],{},[1154,4768,1157],{"separator":1156},[2911,4770,4771,4777],{},[1140,4772,4773,4775],{},[1146,4774,3164],{"mathvariant":3145},[1146,4776,4325],{},[1140,4778,4779,4781],{},[1146,4780,3164],{"mathvariant":3145},[1143,4782,4783,4785],{},[1146,4784,4764],{},[1150,4786,1164],{},[1154,4788,2683],{"fence":1156},[1146,4790,4791],{},"T",[1189,4793,4794],{"encoding":1191},"\\nabla C = \\left( \\frac{\\partial C}{\\partial v_1}, \\frac{\\partial C}{\\partial v_2} \\right)^T",[1124,4796,4798,4820],{"className":4797,"ariaHidden":1156},[1196],[1124,4799,4801,4805,4808,4811,4814,4817],{"className":4800},[1200],[1124,4802],{"className":4803,"style":4804},[1204],"height:0.6833em;",[1124,4806,4737],{"className":4807},[1209],[1124,4809,4325],{"className":4810,"style":4392},[1209,1213],[1124,4812],{"className":4813,"style":1774},[1271],[1124,4815,1652],{"className":4816},[1778],[1124,4818],{"className":4819,"style":1774},[1271],[1124,4821,4823,4827],{"className":4822},[1200],[1124,4824],{"className":4825,"style":4826},[1204],"height:2.0313em;vertical-align:-0.65em;",[1124,4828,4830,5079],{"className":4829},[1368],[1124,4831,4833,4840,4956,4959,4962,5073],{"className":4832},[1368],[1124,4834,4836],{"className":4835,"style":1797},[1795,1796],[1124,4837,2677],{"className":4838},[1801,4839],"size2",[1124,4841,4843,4846,4953],{"className":4842},[1209],[1124,4844],{"className":4845},[1795,2212],[1124,4847,4849],{"className":4848},[2911],[1124,4850,4852,4944],{"className":4851},[1221,1222],[1124,4853,4855,4941],{"className":4854},[1226],[1124,4856,4859,4916,4924],{"className":4857,"style":4858},[1230],"height:0.8801em;",[1124,4860,4861,4864],{"style":2994},[1124,4862],{"className":4863,"style":2998},[1238],[1124,4865,4867],{"className":4866},[1243,1244,1245,1246],[1124,4868,4870,4873],{"className":4869},[1209,1246],[1124,4871,3164],{"className":4872,"style":3319},[1209,1246],[1124,4874,4876,4879],{"className":4875},[1209,1246],[1124,4877,4764],{"className":4878,"style":2700},[1209,1213,1246],[1124,4880,4882],{"className":4881},[1217],[1124,4883,4885,4907],{"className":4884},[1221,1222],[1124,4886,4888,4904],{"className":4887},[1226],[1124,4889,4892],{"className":4890,"style":4891},[1230],"height:0.3173em;",[1124,4893,4895,4898],{"style":4894},"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;",[1124,4896],{"className":4897,"style":3036},[1238],[1124,4899,4901],{"className":4900},[1243,3040,3041,1246],[1124,4902,1152],{"className":4903},[1209,1246],[1124,4905,1254],{"className":4906},[1253],[1124,4908,4910],{"className":4909},[1226],[1124,4911,4914],{"className":4912,"style":4913},[1230],"height:0.143em;",[1124,4915],{},[1124,4917,4918,4921],{"style":3053},[1124,4919],{"className":4920,"style":2998},[1238],[1124,4922],{"className":4923,"style":3061},[3060],[1124,4925,4926,4929],{"style":3064},[1124,4927],{"className":4928,"style":2998},[1238],[1124,4930,4932],{"className":4931},[1243,1244,1245,1246],[1124,4933,4935,4938],{"className":4934},[1209,1246],[1124,4936,3164],{"className":4937,"style":3319},[1209,1246],[1124,4939,4325],{"className":4940,"style":4392},[1209,1213,1246],[1124,4942,1254],{"className":4943},[1253],[1124,4945,4947],{"className":4946},[1226],[1124,4948,4951],{"className":4949,"style":4950},[1230],"height:0.4451em;",[1124,4952],{},[1124,4954],{"className":4955},[2211,2212],[1124,4957,1157],{"className":4958},[1267],[1124,4960],{"className":4961,"style":1272},[1271],[1124,4963,4965,4968,5070],{"className":4964},[1209],[1124,4966],{"className":4967},[1795,2212],[1124,4969,4971],{"className":4970},[2911],[1124,4972,4974,5062],{"className":4973},[1221,1222],[1124,4975,4977,5059],{"className":4976},[1226],[1124,4978,4980,5034,5042],{"className":4979,"style":4858},[1230],[1124,4981,4982,4985],{"style":2994},[1124,4983],{"className":4984,"style":2998},[1238],[1124,4986,4988],{"className":4987},[1243,1244,1245,1246],[1124,4989,4991,4994],{"className":4990},[1209,1246],[1124,4992,3164],{"className":4993,"style":3319},[1209,1246],[1124,4995,4997,5000],{"className":4996},[1209,1246],[1124,4998,4764],{"className":4999,"style":2700},[1209,1213,1246],[1124,5001,5003],{"className":5002},[1217],[1124,5004,5006,5026],{"className":5005},[1221,1222],[1124,5007,5009,5023],{"className":5008},[1226],[1124,5010,5012],{"className":5011,"style":4891},[1230],[1124,5013,5014,5017],{"style":4894},[1124,5015],{"className":5016,"style":3036},[1238],[1124,5018,5020],{"className":5019},[1243,3040,3041,1246],[1124,5021,1164],{"className":5022},[1209,1246],[1124,5024,1254],{"className":5025},[1253],[1124,5027,5029],{"className":5028},[1226],[1124,5030,5032],{"className":5031,"style":4913},[1230],[1124,5033],{},[1124,5035,5036,5039],{"style":3053},[1124,5037],{"className":5038,"style":2998},[1238],[1124,5040],{"className":5041,"style":3061},[3060],[1124,5043,5044,5047],{"style":3064},[1124,5045],{"className":5046,"style":2998},[1238],[1124,5048,5050],{"className":5049},[1243,1244,1245,1246],[1124,5051,5053,5056],{"className":5052},[1209,1246],[1124,5054,3164],{"className":5055,"style":3319},[1209,1246],[1124,5057,4325],{"className":5058,"style":4392},[1209,1213,1246],[1124,5060,1254],{"className":5061},[1253],[1124,5063,5065],{"className":5064},[1226],[1124,5066,5068],{"className":5067,"style":4950},[1230],[1124,5069],{},[1124,5071],{"className":5072},[2211,2212],[1124,5074,5076],{"className":5075,"style":1797},[2211,1796],[1124,5077,2683],{"className":5078},[1801,4839],[1124,5080,5082],{"className":5081},[1217],[1124,5083,5085],{"className":5084},[1221],[1124,5086,5088],{"className":5087},[1226],[1124,5089,5092],{"className":5090,"style":5091},[1230],"height:1.3812em;",[1124,5093,5095,5098],{"style":5094},"top:-3.6029em;margin-right:0.05em;",[1124,5096],{"className":5097,"style":1239},[1238],[1124,5099,5101],{"className":5100},[1243,1244,1245,1246],[1124,5102,4791],{"className":5103,"style":5104},[1209,1213,1246],"margin-right:0.1389em;",[1101,5106,5107],{},"梯度向量指向函数增长最快的方向，负梯度方向即为下降最快方向。",[1101,5109,5110],{},[1107,5111,5112],{},"参数更新规则",[1101,5114,5115],{},[1124,5116,5118,5153],{"className":5117},[1127],[1124,5119,5121],{"className":5120},[1131],[1133,5122,5123],{"xmlns":1135},[1137,5124,5125,5150],{},[1140,5126,5127,5129,5131,5137,5139,5141,5143,5146,5148],{},[1146,5128,4764],{"mathvariant":2322},[1154,5130,3579],{},[2922,5132,5133,5135],{},[1146,5134,4764],{"mathvariant":2322},[1154,5136,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,5138,1652],{},[1146,5140,4764],{"mathvariant":2322},[1154,5142,2235],{},[1146,5144,5145],{},"η",[1146,5147,4737],{"mathvariant":3145},[1146,5149,4325],{},[1189,5151,5152],{"encoding":1191},"\\mathbf{v} \\to \\mathbf{v}' = \\mathbf{v} - \\eta \\nabla C",[1124,5154,5156,5175,5222,5240],{"className":5155,"ariaHidden":1156},[1196],[1124,5157,5159,5163,5166,5169,5172],{"className":5158},[1200],[1124,5160],{"className":5161,"style":5162},[1204],"height:0.4444em;",[1124,5164,4764],{"className":5165,"style":2496},[1209,2495],[1124,5167],{"className":5168,"style":1774},[1271],[1124,5170,3579],{"className":5171},[1778],[1124,5173],{"className":5174,"style":1774},[1271],[1124,5176,5178,5181,5213,5216,5219],{"className":5177},[1200],[1124,5179],{"className":5180,"style":3902},[1204],[1124,5182,5184,5187],{"className":5183},[1209],[1124,5185,4764],{"className":5186,"style":2496},[1209,2495],[1124,5188,5190],{"className":5189},[1217],[1124,5191,5193],{"className":5192},[1221],[1124,5194,5196],{"className":5195},[1226],[1124,5197,5199],{"className":5198,"style":3902},[1230],[1124,5200,5201,5204],{"style":3905},[1124,5202],{"className":5203,"style":1239},[1238],[1124,5205,5207],{"className":5206},[1243,1244,1245,1246],[1124,5208,5210],{"className":5209},[1209,1246],[1124,5211,3838],{"className":5212},[1209,1246],[1124,5214],{"className":5215,"style":1774},[1271],[1124,5217,1652],{"className":5218},[1778],[1124,5220],{"className":5221,"style":1774},[1271],[1124,5223,5225,5228,5231,5234,5237],{"className":5224},[1200],[1124,5226],{"className":5227,"style":2858},[1204],[1124,5229,4764],{"className":5230,"style":2496},[1209,2495],[1124,5232],{"className":5233,"style":2500},[1271],[1124,5235,2235],{"className":5236},[2504],[1124,5238],{"className":5239,"style":2500},[1271],[1124,5241,5243,5246,5249,5252],{"className":5242},[1200],[1124,5244],{"className":5245,"style":3217},[1204],[1124,5247,5145],{"className":5248,"style":2700},[1209,1213],[1124,5250,4737],{"className":5251},[1209],[1124,5253,4325],{"className":5254,"style":4392},[1209,1213],[1101,5256,5257],{},"对于神经网络的权重和偏置：",[1101,5259,5260],{},[1124,5261,5263,5323],{"className":5262},[1127],[1124,5264,5266],{"className":5265},[1131],[1133,5267,5268],{"xmlns":1135},[1137,5269,5270,5320],{},[1140,5271,5272,5279,5281,5290,5292,5298,5300,5302],{},[1143,5273,5274,5276],{},[1146,5275,1439],{},[1146,5277,5278],{},"k",[1154,5280,3579],{},[5282,5283,5284,5286,5288],"msubsup",{},[1146,5285,1439],{},[1146,5287,5278],{},[1154,5289,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,5291,1652],{},[1143,5293,5294,5296],{},[1146,5295,1439],{},[1146,5297,5278],{},[1154,5299,2235],{},[1146,5301,5145],{},[2911,5303,5304,5310],{},[1140,5305,5306,5308],{},[1146,5307,3164],{"mathvariant":3145},[1146,5309,4325],{},[1140,5311,5312,5314],{},[1146,5313,3164],{"mathvariant":3145},[1143,5315,5316,5318],{},[1146,5317,1439],{},[1146,5319,5278],{},[1189,5321,5322],{"encoding":1191},"w_k \\to w_k' = w_k - \\eta \\frac{\\partial C}{\\partial w_k}",[1124,5324,5326,5384,5456,5512],{"className":5325,"ariaHidden":1156},[1196],[1124,5327,5329,5333,5375,5378,5381],{"className":5328},[1200],[1124,5330],{"className":5331,"style":5332},[1204],"height:0.5806em;vertical-align:-0.15em;",[1124,5334,5336,5339],{"className":5335},[1209],[1124,5337,1439],{"className":5338,"style":1480},[1209,1213],[1124,5340,5342],{"className":5341},[1217],[1124,5343,5345,5367],{"className":5344},[1221,1222],[1124,5346,5348,5364],{"className":5347},[1226],[1124,5349,5352],{"className":5350,"style":5351},[1230],"height:0.3361em;",[1124,5353,5354,5357],{"style":1495},[1124,5355],{"className":5356,"style":1239},[1238],[1124,5358,5360],{"className":5359},[1243,1244,1245,1246],[1124,5361,5278],{"className":5362,"style":5363},[1209,1213,1246],"margin-right:0.0315em;",[1124,5365,1254],{"className":5366},[1253],[1124,5368,5370],{"className":5369},[1226],[1124,5371,5373],{"className":5372,"style":1261},[1230],[1124,5374],{},[1124,5376],{"className":5377,"style":1774},[1271],[1124,5379,3579],{"className":5380},[1778],[1124,5382],{"className":5383,"style":1774},[1271],[1124,5385,5387,5391,5447,5450,5453],{"className":5386},[1200],[1124,5388],{"className":5389,"style":5390},[1204],"height:1.035em;vertical-align:-0.2831em;",[1124,5392,5394,5397],{"className":5393},[1209],[1124,5395,1439],{"className":5396,"style":1480},[1209,1213],[1124,5398,5400],{"className":5399},[1217],[1124,5401,5403,5438],{"className":5402},[1221,1222],[1124,5404,5406,5435],{"className":5405},[1226],[1124,5407,5409,5421],{"className":5408,"style":3902},[1230],[1124,5410,5412,5415],{"style":5411},"top:-2.4169em;margin-left:-0.0269em;margin-right:0.05em;",[1124,5413],{"className":5414,"style":1239},[1238],[1124,5416,5418],{"className":5417},[1243,1244,1245,1246],[1124,5419,5278],{"className":5420,"style":5363},[1209,1213,1246],[1124,5422,5423,5426],{"style":3905},[1124,5424],{"className":5425,"style":1239},[1238],[1124,5427,5429],{"className":5428},[1243,1244,1245,1246],[1124,5430,5432],{"className":5431},[1209,1246],[1124,5433,3838],{"className":5434},[1209,1246],[1124,5436,1254],{"className":5437},[1253],[1124,5439,5441],{"className":5440},[1226],[1124,5442,5445],{"className":5443,"style":5444},[1230],"height:0.2831em;",[1124,5446],{},[1124,5448],{"className":5449,"style":1774},[1271],[1124,5451,1652],{"className":5452},[1778],[1124,5454],{"className":5455,"style":1774},[1271],[1124,5457,5459,5463,5503,5506,5509],{"className":5458},[1200],[1124,5460],{"className":5461,"style":5462},[1204],"height:0.7333em;vertical-align:-0.15em;",[1124,5464,5466,5469],{"className":5465},[1209],[1124,5467,1439],{"className":5468,"style":1480},[1209,1213],[1124,5470,5472],{"className":5471},[1217],[1124,5473,5475,5495],{"className":5474},[1221,1222],[1124,5476,5478,5492],{"className":5477},[1226],[1124,5479,5481],{"className":5480,"style":5351},[1230],[1124,5482,5483,5486],{"style":1495},[1124,5484],{"className":5485,"style":1239},[1238],[1124,5487,5489],{"className":5488},[1243,1244,1245,1246],[1124,5490,5278],{"className":5491,"style":5363},[1209,1213,1246],[1124,5493,1254],{"className":5494},[1253],[1124,5496,5498],{"className":5497},[1226],[1124,5499,5501],{"className":5500,"style":1261},[1230],[1124,5502],{},[1124,5504],{"className":5505,"style":2500},[1271],[1124,5507,2235],{"className":5508},[2504],[1124,5510],{"className":5511,"style":2500},[1271],[1124,5513,5515,5519,5522],{"className":5514},[1200],[1124,5516],{"className":5517,"style":5518},[1204],"height:1.331em;vertical-align:-0.4509em;",[1124,5520,5145],{"className":5521,"style":2700},[1209,1213],[1124,5523,5525,5528,5634],{"className":5524},[1209],[1124,5526],{"className":5527},[1795,2212],[1124,5529,5531],{"className":5530},[2911],[1124,5532,5534,5625],{"className":5533},[1221,1222],[1124,5535,5537,5622],{"className":5536},[1226],[1124,5538,5540,5597,5605],{"className":5539,"style":4858},[1230],[1124,5541,5542,5545],{"style":2994},[1124,5543],{"className":5544,"style":2998},[1238],[1124,5546,5548],{"className":5547},[1243,1244,1245,1246],[1124,5549,5551,5554],{"className":5550},[1209,1246],[1124,5552,3164],{"className":5553,"style":3319},[1209,1246],[1124,5555,5557,5560],{"className":5556},[1209,1246],[1124,5558,1439],{"className":5559,"style":1480},[1209,1213,1246],[1124,5561,5563],{"className":5562},[1217],[1124,5564,5566,5588],{"className":5565},[1221,1222],[1124,5567,5569,5585],{"className":5568},[1226],[1124,5570,5573],{"className":5571,"style":5572},[1230],"height:0.3448em;",[1124,5574,5576,5579],{"style":5575},"top:-2.3488em;margin-left:-0.0269em;margin-right:0.0714em;",[1124,5577],{"className":5578,"style":3036},[1238],[1124,5580,5582],{"className":5581},[1243,3040,3041,1246],[1124,5583,5278],{"className":5584,"style":5363},[1209,1213,1246],[1124,5586,1254],{"className":5587},[1253],[1124,5589,5591],{"className":5590},[1226],[1124,5592,5595],{"className":5593,"style":5594},[1230],"height:0.1512em;",[1124,5596],{},[1124,5598,5599,5602],{"style":3053},[1124,5600],{"className":5601,"style":2998},[1238],[1124,5603],{"className":5604,"style":3061},[3060],[1124,5606,5607,5610],{"style":3064},[1124,5608],{"className":5609,"style":2998},[1238],[1124,5611,5613],{"className":5612},[1243,1244,1245,1246],[1124,5614,5616,5619],{"className":5615},[1209,1246],[1124,5617,3164],{"className":5618,"style":3319},[1209,1246],[1124,5620,4325],{"className":5621,"style":4392},[1209,1213,1246],[1124,5623,1254],{"className":5624},[1253],[1124,5626,5628],{"className":5627},[1226],[1124,5629,5632],{"className":5630,"style":5631},[1230],"height:0.4509em;",[1124,5633],{},[1124,5635],{"className":5636},[2211,2212],[1101,5638,5639],{},[1124,5640,5642,5701],{"className":5641},[1127],[1124,5643,5645],{"className":5644},[1131],[1133,5646,5647],{"xmlns":1135},[1137,5648,5649,5698],{},[1140,5650,5651,5658,5660,5668,5670,5676,5678,5680],{},[1143,5652,5653,5655],{},[1146,5654,2230],{},[1146,5656,5657],{},"l",[1154,5659,3579],{},[5282,5661,5662,5664,5666],{},[1146,5663,2230],{},[1146,5665,5657],{},[1154,5667,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,5669,1652],{},[1143,5671,5672,5674],{},[1146,5673,2230],{},[1146,5675,5657],{},[1154,5677,2235],{},[1146,5679,5145],{},[2911,5681,5682,5688],{},[1140,5683,5684,5686],{},[1146,5685,3164],{"mathvariant":3145},[1146,5687,4325],{},[1140,5689,5690,5692],{},[1146,5691,3164],{"mathvariant":3145},[1143,5693,5694,5696],{},[1146,5695,2230],{},[1146,5697,5657],{},[1189,5699,5700],{"encoding":1191},"b_l \\to b_l' = b_l - \\eta \\frac{\\partial C}{\\partial b_l}",[1124,5702,5704,5761,5831,5886],{"className":5703,"ariaHidden":1156},[1196],[1124,5705,5707,5711,5752,5755,5758],{"className":5706},[1200],[1124,5708],{"className":5709,"style":5710},[1204],"height:0.8444em;vertical-align:-0.15em;",[1124,5712,5714,5717],{"className":5713},[1209],[1124,5715,2230],{"className":5716},[1209,1213],[1124,5718,5720],{"className":5719},[1217],[1124,5721,5723,5744],{"className":5722},[1221,1222],[1124,5724,5726,5741],{"className":5725},[1226],[1124,5727,5729],{"className":5728,"style":5351},[1230],[1124,5730,5731,5734],{"style":1234},[1124,5732],{"className":5733,"style":1239},[1238],[1124,5735,5737],{"className":5736},[1243,1244,1245,1246],[1124,5738,5657],{"className":5739,"style":5740},[1209,1213,1246],"margin-right:0.0197em;",[1124,5742,1254],{"className":5743},[1253],[1124,5745,5747],{"className":5746},[1226],[1124,5748,5750],{"className":5749,"style":1261},[1230],[1124,5751],{},[1124,5753],{"className":5754,"style":1774},[1271],[1124,5756,3579],{"className":5757},[1778],[1124,5759],{"className":5760,"style":1774},[1271],[1124,5762,5764,5767,5822,5825,5828],{"className":5763},[1200],[1124,5765],{"className":5766,"style":5390},[1204],[1124,5768,5770,5773],{"className":5769},[1209],[1124,5771,2230],{"className":5772},[1209,1213],[1124,5774,5776],{"className":5775},[1217],[1124,5777,5779,5814],{"className":5778},[1221,1222],[1124,5780,5782,5811],{"className":5781},[1226],[1124,5783,5785,5797],{"className":5784,"style":3902},[1230],[1124,5786,5788,5791],{"style":5787},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[1124,5789],{"className":5790,"style":1239},[1238],[1124,5792,5794],{"className":5793},[1243,1244,1245,1246],[1124,5795,5657],{"className":5796,"style":5740},[1209,1213,1246],[1124,5798,5799,5802],{"style":3905},[1124,5800],{"className":5801,"style":1239},[1238],[1124,5803,5805],{"className":5804},[1243,1244,1245,1246],[1124,5806,5808],{"className":5807},[1209,1246],[1124,5809,3838],{"className":5810},[1209,1246],[1124,5812,1254],{"className":5813},[1253],[1124,5815,5817],{"className":5816},[1226],[1124,5818,5820],{"className":5819,"style":5444},[1230],[1124,5821],{},[1124,5823],{"className":5824,"style":1774},[1271],[1124,5826,1652],{"className":5827},[1778],[1124,5829],{"className":5830,"style":1774},[1271],[1124,5832,5834,5837,5877,5880,5883],{"className":5833},[1200],[1124,5835],{"className":5836,"style":5710},[1204],[1124,5838,5840,5843],{"className":5839},[1209],[1124,5841,2230],{"className":5842},[1209,1213],[1124,5844,5846],{"className":5845},[1217],[1124,5847,5849,5869],{"className":5848},[1221,1222],[1124,5850,5852,5866],{"className":5851},[1226],[1124,5853,5855],{"className":5854,"style":5351},[1230],[1124,5856,5857,5860],{"style":1234},[1124,5858],{"className":5859,"style":1239},[1238],[1124,5861,5863],{"className":5862},[1243,1244,1245,1246],[1124,5864,5657],{"className":5865,"style":5740},[1209,1213,1246],[1124,5867,1254],{"className":5868},[1253],[1124,5870,5872],{"className":5871},[1226],[1124,5873,5875],{"className":5874,"style":1261},[1230],[1124,5876],{},[1124,5878],{"className":5879,"style":2500},[1271],[1124,5881,2235],{"className":5882},[2504],[1124,5884],{"className":5885,"style":2500},[1271],[1124,5887,5889,5892,5895],{"className":5888},[1200],[1124,5890],{"className":5891,"style":5518},[1204],[1124,5893,5145],{"className":5894,"style":2700},[1209,1213],[1124,5896,5898,5901,6004],{"className":5897},[1209],[1124,5899],{"className":5900},[1795,2212],[1124,5902,5904],{"className":5903},[2911],[1124,5905,5907,5996],{"className":5906},[1221,1222],[1124,5908,5910,5993],{"className":5909},[1226],[1124,5911,5913,5968,5976],{"className":5912,"style":4858},[1230],[1124,5914,5915,5918],{"style":2994},[1124,5916],{"className":5917,"style":2998},[1238],[1124,5919,5921],{"className":5920},[1243,1244,1245,1246],[1124,5922,5924,5927],{"className":5923},[1209,1246],[1124,5925,3164],{"className":5926,"style":3319},[1209,1246],[1124,5928,5930,5933],{"className":5929},[1209,1246],[1124,5931,2230],{"className":5932},[1209,1213,1246],[1124,5934,5936],{"className":5935},[1217],[1124,5937,5939,5960],{"className":5938},[1221,1222],[1124,5940,5942,5957],{"className":5941},[1226],[1124,5943,5945],{"className":5944,"style":5572},[1230],[1124,5946,5948,5951],{"style":5947},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[1124,5949],{"className":5950,"style":3036},[1238],[1124,5952,5954],{"className":5953},[1243,3040,3041,1246],[1124,5955,5657],{"className":5956,"style":5740},[1209,1213,1246],[1124,5958,1254],{"className":5959},[1253],[1124,5961,5963],{"className":5962},[1226],[1124,5964,5966],{"className":5965,"style":5594},[1230],[1124,5967],{},[1124,5969,5970,5973],{"style":3053},[1124,5971],{"className":5972,"style":2998},[1238],[1124,5974],{"className":5975,"style":3061},[3060],[1124,5977,5978,5981],{"style":3064},[1124,5979],{"className":5980,"style":2998},[1238],[1124,5982,5984],{"className":5983},[1243,1244,1245,1246],[1124,5985,5987,5990],{"className":5986},[1209,1246],[1124,5988,3164],{"className":5989,"style":3319},[1209,1246],[1124,5991,4325],{"className":5992,"style":4392},[1209,1213,1246],[1124,5994,1254],{"className":5995},[1253],[1124,5997,5999],{"className":5998},[1226],[1124,6000,6002],{"className":6001,"style":5631},[1230],[1124,6003],{},[1124,6005],{"className":6006},[2211,2212],[1101,6008,4612,6009,6038],{},[1124,6010,6012,6026],{"className":6011},[1127],[1124,6013,6015],{"className":6014},[1131],[1133,6016,6017],{"xmlns":1135},[1137,6018,6019,6023],{},[1140,6020,6021],{},[1146,6022,5145],{},[1189,6024,6025],{"encoding":1191},"\\eta",[1124,6027,6029],{"className":6028,"ariaHidden":1156},[1196],[1124,6030,6032,6035],{"className":6031},[1200],[1124,6033],{"className":6034,"style":1205},[1204],[1124,6036,5145],{"className":6037,"style":2700},[1209,1213]," 为学习率（learning rate），控制每步更新的幅度。",[2745,6040],{},[1096,6042,6044],{"id":6043},"_16-随机梯度下降sgd","1.6 随机梯度下降（SGD）",[1101,6046,6047,6050],{},[1107,6048,6049],{},"问题","：当训练集很大时，计算所有样本的梯度非常耗时。",[1101,6052,6053,6056],{},[1107,6054,6055],{},"解决方案","：使用 Mini-batch 随机梯度下降。",[1117,6058,6059,6092],{},[1120,6060,6061,6062,6091],{},"随机选取 ",[1124,6063,6065,6079],{"className":6064},[1127],[1124,6066,6068],{"className":6067},[1131],[1133,6069,6070],{"xmlns":1135},[1137,6071,6072,6077],{},[1140,6073,6074],{},[1146,6075,6076],{},"m",[1189,6078,6076],{"encoding":1191},[1124,6080,6082],{"className":6081,"ariaHidden":1156},[1196],[1124,6083,6085,6088],{"className":6084},[1200],[1124,6086],{"className":6087,"style":3124},[1204],[1124,6089,6076],{"className":6090},[1209,1213]," 个训练样本作为一个 mini-batch",[1120,6093,6094],{},"用 mini-batch 的平均梯度估计全局梯度：",[1101,6096,6097],{},[1124,6098,6100,6151],{"className":6099},[1127],[1124,6101,6103],{"className":6102},[1131],[1133,6104,6105],{"xmlns":1135},[1137,6106,6107,6148],{},[1140,6108,6109,6111,6113,6115,6121,6135,6137],{},[1146,6110,4737],{"mathvariant":3145},[1146,6112,4325],{},[1154,6114,3151],{},[2911,6116,6117,6119],{},[1150,6118,1152],{},[1146,6120,6076],{},[5282,6122,6123,6125,6133],{},[1154,6124,1690],{},[1140,6126,6127,6129,6131],{},[1146,6128,1693],{},[1154,6130,1652],{},[1150,6132,1152],{},[1146,6134,6076],{},[1146,6136,4737],{"mathvariant":3145},[1143,6138,6139,6141],{},[1146,6140,4325],{},[1143,6142,6143,6146],{},[1146,6144,6145],{},"X",[1146,6147,1693],{},[1189,6149,6150],{"encoding":1191},"\\nabla C \\approx \\frac{1}{m} \\sum_{j=1}^{m} \\nabla C_{X_j}",[1124,6152,6154,6175],{"className":6153,"ariaHidden":1156},[1196],[1124,6155,6157,6160,6163,6166,6169,6172],{"className":6156},[1200],[1124,6158],{"className":6159,"style":4804},[1204],[1124,6161,4737],{"className":6162},[1209],[1124,6164,4325],{"className":6165,"style":4392},[1209,1213],[1124,6167],{"className":6168,"style":1774},[1271],[1124,6170,3151],{"className":6171},[1778],[1124,6173],{"className":6174,"style":1774},[1271],[1124,6176,6178,6182,6250,6253,6318,6321,6324],{"className":6177},[1200],[1124,6179],{"className":6180,"style":6181},[1204],"height:1.2809em;vertical-align:-0.4358em;",[1124,6183,6185,6188,6247],{"className":6184},[1209],[1124,6186],{"className":6187},[1795,2212],[1124,6189,6191],{"className":6190},[2911],[1124,6192,6194,6239],{"className":6193},[1221,1222],[1124,6195,6197,6236],{"className":6196},[1226],[1124,6198,6200,6214,6222],{"className":6199,"style":2991},[1230],[1124,6201,6202,6205],{"style":2994},[1124,6203],{"className":6204,"style":2998},[1238],[1124,6206,6208],{"className":6207},[1243,1244,1245,1246],[1124,6209,6211],{"className":6210},[1209,1246],[1124,6212,6076],{"className":6213},[1209,1213,1246],[1124,6215,6216,6219],{"style":3053},[1124,6217],{"className":6218,"style":2998},[1238],[1124,6220],{"className":6221,"style":3061},[3060],[1124,6223,6224,6227],{"style":3064},[1124,6225],{"className":6226,"style":2998},[1238],[1124,6228,6230],{"className":6229},[1243,1244,1245,1246],[1124,6231,6233],{"className":6232},[1209,1246],[1124,6234,1152],{"className":6235},[1209,1246],[1124,6237,1254],{"className":6238},[1253],[1124,6240,6242],{"className":6241},[1226],[1124,6243,6245],{"className":6244,"style":3538},[1230],[1124,6246],{},[1124,6248],{"className":6249},[2211,2212],[1124,6251],{"className":6252,"style":1272},[1271],[1124,6254,6256,6259],{"className":6255},[1897],[1124,6257,1690],{"className":6258,"style":1903},[1897,1901,1902],[1124,6260,6262],{"className":6261},[1217],[1124,6263,6265,6310],{"className":6264},[1221,1222],[1124,6266,6268,6307],{"className":6267},[1226],[1124,6269,6272,6292],{"className":6270,"style":6271},[1230],"height:0.8043em;",[1124,6273,6274,6277],{"style":1919},[1124,6275],{"className":6276,"style":1239},[1238],[1124,6278,6280],{"className":6279},[1243,1244,1245,1246],[1124,6281,6283,6286,6289],{"className":6282},[1209,1246],[1124,6284,1693],{"className":6285,"style":1929},[1209,1213,1246],[1124,6287,1652],{"className":6288},[1778,1246],[1124,6290,1152],{"className":6291},[1209,1246],[1124,6293,6295,6298],{"style":6294},"top:-3.2029em;margin-right:0.05em;",[1124,6296],{"className":6297,"style":1239},[1238],[1124,6299,6301],{"className":6300},[1243,1244,1245,1246],[1124,6302,6304],{"className":6303},[1209,1246],[1124,6305,6076],{"className":6306},[1209,1213,1246],[1124,6308,1254],{"className":6309},[1253],[1124,6311,6313],{"className":6312},[1226],[1124,6314,6316],{"className":6315,"style":1939},[1230],[1124,6317],{},[1124,6319],{"className":6320,"style":1272},[1271],[1124,6322,4737],{"className":6323},[1209],[1124,6325,6327,6330],{"className":6326},[1209],[1124,6328,4325],{"className":6329,"style":4392},[1209,1213],[1124,6331,6333],{"className":6332},[1217],[1124,6334,6336,6400],{"className":6335},[1221,1222],[1124,6337,6339,6397],{"className":6338},[1226],[1124,6340,6343],{"className":6341,"style":6342},[1230],"height:0.3283em;",[1124,6344,6346,6349],{"style":6345},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1124,6347],{"className":6348,"style":1239},[1238],[1124,6350,6352],{"className":6351},[1243,1244,1245,1246],[1124,6353,6355],{"className":6354},[1209,1246],[1124,6356,6358,6362],{"className":6357},[1209,1246],[1124,6359,6145],{"className":6360,"style":6361},[1209,1213,1246],"margin-right:0.0785em;",[1124,6363,6365],{"className":6364},[1217],[1124,6366,6368,6389],{"className":6367},[1221,1222],[1124,6369,6371,6386],{"className":6370},[1226],[1124,6372,6374],{"className":6373,"style":3338},[1230],[1124,6375,6377,6380],{"style":6376},"top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;",[1124,6378],{"className":6379,"style":3036},[1238],[1124,6381,6383],{"className":6382},[1243,3040,3041,1246],[1124,6384,1693],{"className":6385,"style":1929},[1209,1213,1246],[1124,6387,1254],{"className":6388},[1253],[1124,6390,6392],{"className":6391},[1226],[1124,6393,6395],{"className":6394,"style":3360},[1230],[1124,6396],{},[1124,6398,1254],{"className":6399},[1253],[1124,6401,6403],{"className":6402},[1226],[1124,6404,6407],{"className":6405,"style":6406},[1230],"height:0.3473em;",[1124,6408],{},[1101,6410,6411,6414],{},[1107,6412,6413],{},"更新规则","：",[1101,6416,6417],{},[1124,6418,6420,6496],{"className":6419},[1127],[1124,6421,6423],{"className":6422},[1131],[1133,6424,6425],{"xmlns":1135},[1137,6426,6427,6493],{},[1140,6428,6429,6435,6437,6445,6447,6453,6455,6461,6467],{},[1143,6430,6431,6433],{},[1146,6432,1439],{},[1146,6434,5278],{},[1154,6436,3579],{},[5282,6438,6439,6441,6443],{},[1146,6440,1439],{},[1146,6442,5278],{},[1154,6444,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,6446,1652],{},[1143,6448,6449,6451],{},[1146,6450,1439],{},[1146,6452,5278],{},[1154,6454,2235],{},[2911,6456,6457,6459],{},[1146,6458,5145],{},[1146,6460,6076],{},[1143,6462,6463,6465],{},[1154,6464,1690],{},[1146,6466,1693],{},[2911,6468,6469,6483],{},[1140,6470,6471,6473],{},[1146,6472,3164],{"mathvariant":3145},[1143,6474,6475,6477],{},[1146,6476,4325],{},[1143,6478,6479,6481],{},[1146,6480,6145],{},[1146,6482,1693],{},[1140,6484,6485,6487],{},[1146,6486,3164],{"mathvariant":3145},[1143,6488,6489,6491],{},[1146,6490,1439],{},[1146,6492,5278],{},[1189,6494,6495],{"encoding":1191},"w_k \\to w_k' = w_k - \\frac{\\eta}{m} \\sum_j \\frac{\\partial C_{X_j}}{\\partial w_k}",[1124,6497,6499,6554,6623,6678],{"className":6498,"ariaHidden":1156},[1196],[1124,6500,6502,6505,6545,6548,6551],{"className":6501},[1200],[1124,6503],{"className":6504,"style":5332},[1204],[1124,6506,6508,6511],{"className":6507},[1209],[1124,6509,1439],{"className":6510,"style":1480},[1209,1213],[1124,6512,6514],{"className":6513},[1217],[1124,6515,6517,6537],{"className":6516},[1221,1222],[1124,6518,6520,6534],{"className":6519},[1226],[1124,6521,6523],{"className":6522,"style":5351},[1230],[1124,6524,6525,6528],{"style":1495},[1124,6526],{"className":6527,"style":1239},[1238],[1124,6529,6531],{"className":6530},[1243,1244,1245,1246],[1124,6532,5278],{"className":6533,"style":5363},[1209,1213,1246],[1124,6535,1254],{"className":6536},[1253],[1124,6538,6540],{"className":6539},[1226],[1124,6541,6543],{"className":6542,"style":1261},[1230],[1124,6544],{},[1124,6546],{"className":6547,"style":1774},[1271],[1124,6549,3579],{"className":6550},[1778],[1124,6552],{"className":6553,"style":1774},[1271],[1124,6555,6557,6560,6614,6617,6620],{"className":6556},[1200],[1124,6558],{"className":6559,"style":5390},[1204],[1124,6561,6563,6566],{"className":6562},[1209],[1124,6564,1439],{"className":6565,"style":1480},[1209,1213],[1124,6567,6569],{"className":6568},[1217],[1124,6570,6572,6606],{"className":6571},[1221,1222],[1124,6573,6575,6603],{"className":6574},[1226],[1124,6576,6578,6589],{"className":6577,"style":3902},[1230],[1124,6579,6580,6583],{"style":5411},[1124,6581],{"className":6582,"style":1239},[1238],[1124,6584,6586],{"className":6585},[1243,1244,1245,1246],[1124,6587,5278],{"className":6588,"style":5363},[1209,1213,1246],[1124,6590,6591,6594],{"style":3905},[1124,6592],{"className":6593,"style":1239},[1238],[1124,6595,6597],{"className":6596},[1243,1244,1245,1246],[1124,6598,6600],{"className":6599},[1209,1246],[1124,6601,3838],{"className":6602},[1209,1246],[1124,6604,1254],{"className":6605},[1253],[1124,6607,6609],{"className":6608},[1226],[1124,6610,6612],{"className":6611,"style":5444},[1230],[1124,6613],{},[1124,6615],{"className":6616,"style":1774},[1271],[1124,6618,1652],{"className":6619},[1778],[1124,6621],{"className":6622,"style":1774},[1271],[1124,6624,6626,6629,6669,6672,6675],{"className":6625},[1200],[1124,6627],{"className":6628,"style":5462},[1204],[1124,6630,6632,6635],{"className":6631},[1209],[1124,6633,1439],{"className":6634,"style":1480},[1209,1213],[1124,6636,6638],{"className":6637},[1217],[1124,6639,6641,6661],{"className":6640},[1221,1222],[1124,6642,6644,6658],{"className":6643},[1226],[1124,6645,6647],{"className":6646,"style":5351},[1230],[1124,6648,6649,6652],{"style":1495},[1124,6650],{"className":6651,"style":1239},[1238],[1124,6653,6655],{"className":6654},[1243,1244,1245,1246],[1124,6656,5278],{"className":6657,"style":5363},[1209,1213,1246],[1124,6659,1254],{"className":6660},[1253],[1124,6662,6664],{"className":6663},[1226],[1124,6665,6667],{"className":6666,"style":1261},[1230],[1124,6668],{},[1124,6670],{"className":6671,"style":2500},[1271],[1124,6673,2235],{"className":6674},[2504],[1124,6676],{"className":6677,"style":2500},[1271],[1124,6679,6681,6685,6754,6757,6797,6800],{"className":6680},[1200],[1124,6682],{"className":6683,"style":6684},[1204],"height:1.6019em;vertical-align:-0.4509em;",[1124,6686,6688,6691,6751],{"className":6687},[1209],[1124,6689],{"className":6690},[1795,2212],[1124,6692,6694],{"className":6693},[2911],[1124,6695,6697,6743],{"className":6696},[1221,1222],[1124,6698,6700,6740],{"className":6699},[1226],[1124,6701,6704,6718,6726],{"className":6702,"style":6703},[1230],"height:0.7475em;",[1124,6705,6706,6709],{"style":2994},[1124,6707],{"className":6708,"style":2998},[1238],[1124,6710,6712],{"className":6711},[1243,1244,1245,1246],[1124,6713,6715],{"className":6714},[1209,1246],[1124,6716,6076],{"className":6717},[1209,1213,1246],[1124,6719,6720,6723],{"style":3053},[1124,6721],{"className":6722,"style":2998},[1238],[1124,6724],{"className":6725,"style":3061},[3060],[1124,6727,6728,6731],{"style":3373},[1124,6729],{"className":6730,"style":2998},[1238],[1124,6732,6734],{"className":6733},[1243,1244,1245,1246],[1124,6735,6737],{"className":6736},[1209,1246],[1124,6738,5145],{"className":6739,"style":2700},[1209,1213,1246],[1124,6741,1254],{"className":6742},[1253],[1124,6744,6746],{"className":6745},[1226],[1124,6747,6749],{"className":6748,"style":3538},[1230],[1124,6750],{},[1124,6752],{"className":6753},[2211,2212],[1124,6755],{"className":6756,"style":1272},[1271],[1124,6758,6760,6763],{"className":6759},[1897],[1124,6761,1690],{"className":6762,"style":1903},[1897,1901,1902],[1124,6764,6766],{"className":6765},[1217],[1124,6767,6769,6789],{"className":6768},[1221,1222],[1124,6770,6772,6786],{"className":6771},[1226],[1124,6773,6775],{"className":6774,"style":1916},[1230],[1124,6776,6777,6780],{"style":1919},[1124,6778],{"className":6779,"style":1239},[1238],[1124,6781,6783],{"className":6782},[1243,1244,1245,1246],[1124,6784,1693],{"className":6785,"style":1929},[1209,1213,1246],[1124,6787,1254],{"className":6788},[1253],[1124,6790,6792],{"className":6791},[1226],[1124,6793,6795],{"className":6794,"style":1939},[1230],[1124,6796],{},[1124,6798],{"className":6799,"style":1272},[1271],[1124,6801,6803,6806,6989],{"className":6802},[1209],[1124,6804],{"className":6805},[1795,2212],[1124,6807,6809],{"className":6808},[2911],[1124,6810,6812,6981],{"className":6811},[1221,1222],[1124,6813,6815,6978],{"className":6814},[1226],[1124,6816,6819,6873,6881],{"className":6817,"style":6818},[1230],"height:1.151em;",[1124,6820,6821,6824],{"style":2994},[1124,6822],{"className":6823,"style":2998},[1238],[1124,6825,6827],{"className":6826},[1243,1244,1245,1246],[1124,6828,6830,6833],{"className":6829},[1209,1246],[1124,6831,3164],{"className":6832,"style":3319},[1209,1246],[1124,6834,6836,6839],{"className":6835},[1209,1246],[1124,6837,1439],{"className":6838,"style":1480},[1209,1213,1246],[1124,6840,6842],{"className":6841},[1217],[1124,6843,6845,6865],{"className":6844},[1221,1222],[1124,6846,6848,6862],{"className":6847},[1226],[1124,6849,6851],{"className":6850,"style":5572},[1230],[1124,6852,6853,6856],{"style":5575},[1124,6854],{"className":6855,"style":3036},[1238],[1124,6857,6859],{"className":6858},[1243,3040,3041,1246],[1124,6860,5278],{"className":6861,"style":5363},[1209,1213,1246],[1124,6863,1254],{"className":6864},[1253],[1124,6866,6868],{"className":6867},[1226],[1124,6869,6871],{"className":6870,"style":5594},[1230],[1124,6872],{},[1124,6874,6875,6878],{"style":3053},[1124,6876],{"className":6877,"style":2998},[1238],[1124,6879],{"className":6880,"style":3061},[3060],[1124,6882,6884,6887],{"style":6883},"top:-3.6649em;",[1124,6885],{"className":6886,"style":2998},[1238],[1124,6888,6890],{"className":6889},[1243,1244,1245,1246],[1124,6891,6893,6896],{"className":6892},[1209,1246],[1124,6894,3164],{"className":6895,"style":3319},[1209,1246],[1124,6897,6899,6902],{"className":6898},[1209,1246],[1124,6900,4325],{"className":6901,"style":4392},[1209,1213,1246],[1124,6903,6905],{"className":6904},[1217],[1124,6906,6908,6969],{"className":6907},[1221,1222],[1124,6909,6911,6966],{"className":6910},[1226],[1124,6912,6914],{"className":6913,"style":5572},[1230],[1124,6915,6917,6920],{"style":6916},"top:-2.3567em;margin-left:-0.0715em;margin-right:0.0714em;",[1124,6918],{"className":6919,"style":3036},[1238],[1124,6921,6923],{"className":6922},[1243,3040,3041,1246],[1124,6924,6926],{"className":6925},[1209,1246],[1124,6927,6929,6932],{"className":6928},[1209,1246],[1124,6930,6145],{"className":6931,"style":6361},[1209,1213,1246],[1124,6933,6935],{"className":6934},[1217],[1124,6936,6938,6957],{"className":6937},[1221,1222],[1124,6939,6941,6954],{"className":6940},[1226],[1124,6942,6944],{"className":6943,"style":5572},[1230],[1124,6945,6947,6951],{"style":6946},"top:-2.3448em;margin-left:-0.0785em;margin-right:0.1em;",[1124,6948],{"className":6949,"style":6950},[1238],"height:2.6595em;",[1124,6952,1693],{"className":6953,"style":1929},[1209,1213,1246],[1124,6955,1254],{"className":6956},[1253],[1124,6958,6960],{"className":6959},[1226],[1124,6961,6964],{"className":6962,"style":6963},[1230],"height:0.5092em;",[1124,6965],{},[1124,6967,1254],{"className":6968},[1253],[1124,6970,6972],{"className":6971},[1226],[1124,6973,6976],{"className":6974,"style":6975},[1230],"height:0.507em;",[1124,6977],{},[1124,6979,1254],{"className":6980},[1253],[1124,6982,6984],{"className":6983},[1226],[1124,6985,6987],{"className":6986,"style":5631},[1230],[1124,6988],{},[1124,6990],{"className":6991},[2211,2212],[1101,6993,6994],{},[1124,6995,6997,7073],{"className":6996},[1127],[1124,6998,7000],{"className":6999},[1131],[1133,7001,7002],{"xmlns":1135},[1137,7003,7004,7070],{},[1140,7005,7006,7012,7014,7022,7024,7030,7032,7038,7044],{},[1143,7007,7008,7010],{},[1146,7009,2230],{},[1146,7011,5657],{},[1154,7013,3579],{},[5282,7015,7016,7018,7020],{},[1146,7017,2230],{},[1146,7019,5657],{},[1154,7021,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,7023,1652],{},[1143,7025,7026,7028],{},[1146,7027,2230],{},[1146,7029,5657],{},[1154,7031,2235],{},[2911,7033,7034,7036],{},[1146,7035,5145],{},[1146,7037,6076],{},[1143,7039,7040,7042],{},[1154,7041,1690],{},[1146,7043,1693],{},[2911,7045,7046,7060],{},[1140,7047,7048,7050],{},[1146,7049,3164],{"mathvariant":3145},[1143,7051,7052,7054],{},[1146,7053,4325],{},[1143,7055,7056,7058],{},[1146,7057,6145],{},[1146,7059,1693],{},[1140,7061,7062,7064],{},[1146,7063,3164],{"mathvariant":3145},[1143,7065,7066,7068],{},[1146,7067,2230],{},[1146,7069,5657],{},[1189,7071,7072],{"encoding":1191},"b_l \\to b_l' = b_l - \\frac{\\eta}{m} \\sum_j \\frac{\\partial C_{X_j}}{\\partial b_l}",[1124,7074,7076,7131,7200,7255],{"className":7075,"ariaHidden":1156},[1196],[1124,7077,7079,7082,7122,7125,7128],{"className":7078},[1200],[1124,7080],{"className":7081,"style":5710},[1204],[1124,7083,7085,7088],{"className":7084},[1209],[1124,7086,2230],{"className":7087},[1209,1213],[1124,7089,7091],{"className":7090},[1217],[1124,7092,7094,7114],{"className":7093},[1221,1222],[1124,7095,7097,7111],{"className":7096},[1226],[1124,7098,7100],{"className":7099,"style":5351},[1230],[1124,7101,7102,7105],{"style":1234},[1124,7103],{"className":7104,"style":1239},[1238],[1124,7106,7108],{"className":7107},[1243,1244,1245,1246],[1124,7109,5657],{"className":7110,"style":5740},[1209,1213,1246],[1124,7112,1254],{"className":7113},[1253],[1124,7115,7117],{"className":7116},[1226],[1124,7118,7120],{"className":7119,"style":1261},[1230],[1124,7121],{},[1124,7123],{"className":7124,"style":1774},[1271],[1124,7126,3579],{"className":7127},[1778],[1124,7129],{"className":7130,"style":1774},[1271],[1124,7132,7134,7137,7191,7194,7197],{"className":7133},[1200],[1124,7135],{"className":7136,"style":5390},[1204],[1124,7138,7140,7143],{"className":7139},[1209],[1124,7141,2230],{"className":7142},[1209,1213],[1124,7144,7146],{"className":7145},[1217],[1124,7147,7149,7183],{"className":7148},[1221,1222],[1124,7150,7152,7180],{"className":7151},[1226],[1124,7153,7155,7166],{"className":7154,"style":3902},[1230],[1124,7156,7157,7160],{"style":5787},[1124,7158],{"className":7159,"style":1239},[1238],[1124,7161,7163],{"className":7162},[1243,1244,1245,1246],[1124,7164,5657],{"className":7165,"style":5740},[1209,1213,1246],[1124,7167,7168,7171],{"style":3905},[1124,7169],{"className":7170,"style":1239},[1238],[1124,7172,7174],{"className":7173},[1243,1244,1245,1246],[1124,7175,7177],{"className":7176},[1209,1246],[1124,7178,3838],{"className":7179},[1209,1246],[1124,7181,1254],{"className":7182},[1253],[1124,7184,7186],{"className":7185},[1226],[1124,7187,7189],{"className":7188,"style":5444},[1230],[1124,7190],{},[1124,7192],{"className":7193,"style":1774},[1271],[1124,7195,1652],{"className":7196},[1778],[1124,7198],{"className":7199,"style":1774},[1271],[1124,7201,7203,7206,7246,7249,7252],{"className":7202},[1200],[1124,7204],{"className":7205,"style":5710},[1204],[1124,7207,7209,7212],{"className":7208},[1209],[1124,7210,2230],{"className":7211},[1209,1213],[1124,7213,7215],{"className":7214},[1217],[1124,7216,7218,7238],{"className":7217},[1221,1222],[1124,7219,7221,7235],{"className":7220},[1226],[1124,7222,7224],{"className":7223,"style":5351},[1230],[1124,7225,7226,7229],{"style":1234},[1124,7227],{"className":7228,"style":1239},[1238],[1124,7230,7232],{"className":7231},[1243,1244,1245,1246],[1124,7233,5657],{"className":7234,"style":5740},[1209,1213,1246],[1124,7236,1254],{"className":7237},[1253],[1124,7239,7241],{"className":7240},[1226],[1124,7242,7244],{"className":7243,"style":1261},[1230],[1124,7245],{},[1124,7247],{"className":7248,"style":2500},[1271],[1124,7250,2235],{"className":7251},[2504],[1124,7253],{"className":7254,"style":2500},[1271],[1124,7256,7258,7261,7329,7332,7372,7375],{"className":7257},[1200],[1124,7259],{"className":7260,"style":6684},[1204],[1124,7262,7264,7267,7326],{"className":7263},[1209],[1124,7265],{"className":7266},[1795,2212],[1124,7268,7270],{"className":7269},[2911],[1124,7271,7273,7318],{"className":7272},[1221,1222],[1124,7274,7276,7315],{"className":7275},[1226],[1124,7277,7279,7293,7301],{"className":7278,"style":6703},[1230],[1124,7280,7281,7284],{"style":2994},[1124,7282],{"className":7283,"style":2998},[1238],[1124,7285,7287],{"className":7286},[1243,1244,1245,1246],[1124,7288,7290],{"className":7289},[1209,1246],[1124,7291,6076],{"className":7292},[1209,1213,1246],[1124,7294,7295,7298],{"style":3053},[1124,7296],{"className":7297,"style":2998},[1238],[1124,7299],{"className":7300,"style":3061},[3060],[1124,7302,7303,7306],{"style":3373},[1124,7304],{"className":7305,"style":2998},[1238],[1124,7307,7309],{"className":7308},[1243,1244,1245,1246],[1124,7310,7312],{"className":7311},[1209,1246],[1124,7313,5145],{"className":7314,"style":2700},[1209,1213,1246],[1124,7316,1254],{"className":7317},[1253],[1124,7319,7321],{"className":7320},[1226],[1124,7322,7324],{"className":7323,"style":3538},[1230],[1124,7325],{},[1124,7327],{"className":7328},[2211,2212],[1124,7330],{"className":7331,"style":1272},[1271],[1124,7333,7335,7338],{"className":7334},[1897],[1124,7336,1690],{"className":7337,"style":1903},[1897,1901,1902],[1124,7339,7341],{"className":7340},[1217],[1124,7342,7344,7364],{"className":7343},[1221,1222],[1124,7345,7347,7361],{"className":7346},[1226],[1124,7348,7350],{"className":7349,"style":1916},[1230],[1124,7351,7352,7355],{"style":1919},[1124,7353],{"className":7354,"style":1239},[1238],[1124,7356,7358],{"className":7357},[1243,1244,1245,1246],[1124,7359,1693],{"className":7360,"style":1929},[1209,1213,1246],[1124,7362,1254],{"className":7363},[1253],[1124,73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mini-batch），称为完成了一个 epoch。之后打乱数据重新划分 mini-batch，开始下一个 epoch 的训练。",[2745,7567],{},[1091,7569,7571],{"id":7570},"第二部分前向传播和反向传播算法","第二部分：前向传播和反向传播算法",[1096,7573,7575],{"id":7574},"_21-前向传播forward-propagation","2.1 前向传播（Forward Propagation）",[1101,7577,7578,7579,7582],{},"前向传播就是",[1107,7580,7581],{},"把输入数据从第一层开始，逐层计算，一直算到输出层得到最终结果","的过程。信息只往一个方向流动：输入 → 隐藏层 → 输出。",[2616,7584,7585,7597],{},[2619,7586,7587],{},[2622,7588,7589,7594],{},[2625,7590,7591],{},[1107,7592,7593],{},"预测时",[2625,7595,7596],{},"前向传播就是使用网络的全部过程——给输入，算输出",[2635,7598,7599,7609],{},[2622,7600,7601,7606],{},[2640,7602,7603],{},[1107,7604,7605],{},"训练时",[2640,7607,7608],{},"前向传播是第一步，算出预测值后才能计算损失，然后才能反向传播求梯度",[2622,7610,7611,7616],{},[2640,7612,7613],{},[1107,7614,7615],{},"计算中间值",[2640,7617,7618,7619,7679,7680,7739],{},"前向传播过程中保存的每一层的 ",[1124,7620,7622,7640],{"className":7621},[1127],[1124,7623,7625],{"className":7624},[1131],[1133,7626,7627],{"xmlns":1135},[1137,7628,7629,7637],{},[1140,7630,7631],{},[2922,7632,7633,7635],{},[1146,7634,2680],{},[1146,7636,5657],{},[1189,7638,7639],{"encoding":1191},"z^l",[1124,7641,7643],{"className":7642,"ariaHidden":1156},[1196],[1124,7644,7646,7650],{"className":7645},[1200],[1124,7647],{"className":7648,"style":7649},[1204],"height:0.8491em;",[1124,7651,7653,7656],{"className":7652},[1209],[1124,7654,2680],{"className":7655,"style":2707},[1209,1213],[1124,7657,7659],{"className":7658},[1217],[1124,7660,7662],{"className":7661},[1221],[1124,7663,7665],{"className":7664},[1226],[1124,7666,7668],{"className":7667,"style":7649},[1230],[1124,7669,7670,7673],{"style":3905},[1124,7671],{"className":7672,"style":1239},[1238],[1124,7674,7676],{"className":7675},[1243,1244,1245,1246],[1124,7677,5657],{"className":7678,"style":5740},[1209,1213,1246]," 和 ",[1124,7681,7683,7701],{"className":7682},[1127],[1124,7684,7686],{"className":7685},[1131],[1133,7687,7688],{"xmlns":1135},[1137,7689,7690,7698],{},[1140,7691,7692],{},[2922,7693,7694,7696],{},[1146,7695,4370],{},[1146,7697,5657],{},[1189,7699,7700],{"encoding":1191},"a^l",[1124,7702,7704],{"className":7703,"ariaHidden":1156},[1196],[1124,7705,7707,7710],{"className":7706},[1200],[1124,7708],{"className":7709,"style":7649},[1204],[1124,7711,7713,7716],{"className":7712},[1209],[1124,7714,4370],{"className":7715},[1209,1213],[1124,7717,7719],{"className":7718},[1217],[1124,7720,7722],{"className":7721},[1221],[1124,7723,7725],{"className":7724},[1226],[1124,7726,7728],{"className":7727,"style":7649},[1230],[1124,7729,7730,7733],{"style":3905},[1124,7731],{"className":7732,"style":1239},[1238],[1124,7734,7736],{"className":7735},[1243,1244,1245,1246],[1124,7737,5657],{"className":7738,"style":5740},[1209,1213,1246],"，在反向传播时要用到",[2745,7741],{},[7743,7744,7745],"h3",{"id":7745},"基本步骤",[1101,7747,7748,7749,7777],{},"对于第 ",[1124,7750,7752,7765],{"className":7751},[1127],[1124,7753,7755],{"className":7754},[1131],[1133,7756,7757],{"xmlns":1135},[1137,7758,7759,7763],{},[1140,7760,7761],{},[1146,7762,5657],{},[1189,7764,5657],{"encoding":1191},[1124,7766,7768],{"className":7767,"ariaHidden":1156},[1196],[1124,7769,7771,7774],{"className":7770},[1200],[1124,7772],{"className":7773,"style":2250},[1204],[1124,7775,5657],{"className":7776,"style":5740},[1209,1213]," 层的每个神经元，计算分两步：",[1101,7779,7780],{},[1107,7781,7782],{},"第一步：计算加权输入 z",[1101,7784,7785],{},[1124,7786,7788,7836],{"className":7787},[1127],[1124,7789,7791],{"className":7790},[1131],[1133,7792,7793],{"xmlns":1135},[1137,7794,7795,7833],{},[1140,7796,7797,7803,7805,7811,7813,7825,7827],{},[2922,7798,7799,7801],{},[1146,7800,2680],{},[1146,7802,5657],{},[1154,7804,1652],{},[2922,7806,7807,7809],{},[1146,7808,1439],{},[1146,7810,5657],{},[1154,7812,2325],{},[2922,7814,7815,7817],{},[1146,7816,4370],{},[1140,7818,7819,7821,7823],{},[1146,7820,5657],{},[1154,7822,2235],{},[1150,7824,1152],{},[1154,7826,2330],{},[2922,7828,7829,7831],{},[1146,7830,2230],{},[1146,7832,5657],{},[1189,7834,7835],{"encoding":1191},"z^l = w^l \\cdot a^{l-1} + b^l",[1124,7837,7839,7883,7927,7981],{"className":7838,"ariaHidden":1156},[1196],[1124,7840,7842,7845,7874,7877,7880],{"className":7841},[1200],[1124,7843],{"className":7844,"style":7649},[1204],[1124,7846,7848,7851],{"className":7847},[1209],[1124,7849,2680],{"className":7850,"style":2707},[1209,1213],[1124,7852,7854],{"className":7853},[1217],[1124,7855,7857],{"className":7856},[1221],[1124,7858,7860],{"className":7859},[1226],[1124,7861,7863],{"className":7862,"style":7649},[1230],[1124,7864,7865,7868],{"style":3905},[1124,7866],{"className":7867,"style":1239},[1238],[1124,7869,7871],{"className":7870},[1243,1244,1245,1246],[1124,7872,5657],{"className":7873,"style":5740},[1209,1213,1246],[1124,7875],{"className":7876,"style":1774},[1271],[1124,7878,1652],{"className":7879},[1778],[1124,7881],{"className":7882,"style":1774},[1271],[1124,7884,7886,7889,7918,7921,7924],{"className":7885},[1200],[1124,7887],{"className":7888,"style":7649},[1204],[1124,7890,7892,7895],{"className":7891},[1209],[1124,7893,1439],{"className":7894,"style":1480},[1209,1213],[1124,7896,7898],{"className":7897},[1217],[1124,7899,7901],{"className":7900},[1221],[1124,7902,7904],{"className":7903},[1226],[1124,7905,7907],{"className":7906,"style":7649},[1230],[1124,7908,7909,7912],{"style":3905},[1124,7910],{"className":7911,"style":1239},[1238],[1124,7913,7915],{"className":7914},[1243,1244,1245,1246],[1124,7916,5657],{"className":7917,"style":5740},[1209,1213,1246],[1124,7919],{"className":7920,"style":2500},[1271],[1124,7922,2325],{"className":7923},[2504],[1124,7925],{"className":7926,"style":2500},[1271],[1124,7928,7930,7934,7972,7975,7978],{"className":7929},[1200],[1124,7931],{"className":7932,"style":7933},[1204],"height:0.9324em;vertical-align:-0.0833em;",[1124,7935,7937,7940],{"className":7936},[1209],[1124,7938,4370],{"className":7939},[1209,1213],[1124,7941,7943],{"className":7942},[1217],[1124,7944,7946],{"className":7945},[1221],[1124,7947,7949],{"className":7948},[1226],[1124,7950,7952],{"className":7951,"style":7649},[1230],[1124,7953,7954,7957],{"style":3905},[1124,7955],{"className":7956,"style":1239},[1238],[1124,7958,7960],{"className":7959},[1243,1244,1245,1246],[1124,7961,7963,7966,7969],{"className":7962},[1209,1246],[1124,7964,5657],{"className":7965,"style":5740},[1209,1213,1246],[1124,7967,2235],{"className":7968},[2504,1246],[1124,7970,1152],{"className":7971},[1209,1246],[1124,7973],{"className":7974,"style":2500},[1271],[1124,7976,2330],{"className":7977},[2504],[1124,7979],{"className":7980,"style":2500},[1271],[1124,7982,7984,7987],{"className":7983},[1200],[1124,7985],{"className":7986,"style":7649},[1204],[1124,7988,7990,7993],{"className":7989},[1209],[1124,7991,2230],{"className":7992},[1209,1213],[1124,7994,7996],{"className":7995},[1217],[1124,7997,7999],{"className":7998},[1221],[1124,8000,8002],{"className":8001},[1226],[1124,8003,8005],{"className":8004,"style":7649},[1230],[1124,8006,8007,8010],{"style":3905},[1124,8008],{"className":8009,"style":1239},[1238],[1124,8011,8013],{"className":8012},[1243,1244,1245,1246],[1124,8014,5657],{"className":8015,"style":5740},[1209,1213,1246],[1101,8017,8018],{},[1107,8019,8020],{},"第二步：通过激活函数得到输出 a",[1101,8022,8023],{},[1124,8024,8026,8058],{"className":8025},[1127],[1124,8027,8029],{"className":8028},[1131],[1133,8030,8031],{"xmlns":1135},[1137,8032,8033,8055],{},[1140,8034,8035,8041,8043,8045,8047,8053],{},[2922,8036,8037,8039],{},[1146,8038,4370],{},[1146,8040,5657],{},[1154,8042,1652],{},[1146,8044,2674],{},[1154,8046,2677],{"stretchy":1674},[2922,8048,8049,8051],{},[1146,8050,2680],{},[1146,8052,5657],{},[1154,8054,2683],{"stretchy":1674},[1189,8056,8057],{"encoding":1191},"a^l = \\sigma(z^l)",[1124,8059,8061,8105],{"className":8060,"ariaHidden":1156},[1196],[1124,8062,8064,8067,8096,8099,8102],{"className":8063},[1200],[1124,8065],{"className":8066,"style":7649},[1204],[1124,8068,8070,8073],{"className":8069},[1209],[1124,8071,4370],{"className":8072},[1209,1213],[1124,8074,8076],{"className":8075},[1217],[1124,8077,8079],{"className":8078},[1221],[1124,8080,8082],{"className":8081},[1226],[1124,8083,8085],{"className":8084,"style":7649},[1230],[1124,8086,8087,8090],{"style":3905},[1124,8088],{"className":8089,"style":1239},[1238],[1124,8091,8093],{"className":8092},[1243,1244,1245,1246],[1124,8094,5657],{"className":8095,"style":5740},[1209,1213,1246],[1124,8097],{"className":8098,"style":1774},[1271],[1124,8100,1652],{"className":8101},[1778],[1124,8103],{"className":8104,"style":1774},[1271],[1124,8106,8108,8112,8115,8118,8147],{"className":8107},[1200],[1124,8109],{"className":8110,"style":8111},[1204],"height:1.0991em;vertical-align:-0.25em;",[1124,8113,2674],{"className":8114,"style":2700},[1209,1213],[1124,8116,2677],{"className":8117},[1795],[1124,8119,8121,8124],{"className":8120},[1209],[1124,8122,2680],{"className":8123,"style":2707},[1209,1213],[1124,8125,8127],{"className":8126},[1217],[1124,8128,8130],{"className":8129},[1221],[1124,8131,8133],{"className":8132},[1226],[1124,8134,8136],{"className":8135,"style":7649},[1230],[1124,8137,8138,8141],{"style":3905},[1124,8139],{"className":8140,"style":1239},[1238],[1124,8142,8144],{"className":8143},[1243,1244,1245,1246],[1124,8145,5657],{"className":8146,"style":5740},[1209,1213,1246],[1124,8148,2683],{"className":8149},[2211],[1101,8151,8152],{},"合并写成一个简洁形式：",[1101,8154,8155],{},[1124,8156,8158,8224],{"className":8157},[1127],[1124,8159,8161],{"className":8160},[1131],[1133,8162,8163],{"xmlns":1135},[1137,8164,8165,8221],{},[1140,8166,8167],{},[8168,8169,8171],"menclose",{"notation":8170},"box",[1671,8172,8173],{"scriptlevel":1673,"displaystyle":1674},[1671,8174,8175],{"scriptlevel":1673,"displaystyle":1674},[1671,8176,8177],{"scriptlevel":1673,"displaystyle":1156},[1140,8178,8179,8185,8187,8189,8191,8197,8199,8211,8213,8219],{},[2922,8180,8181,8183],{},[1146,8182,4370],{},[1146,8184,5657],{},[1154,8186,1652],{},[1146,8188,2674],{},[1154,8190,2677],{"stretchy":1674},[2922,8192,8193,8195],{},[1146,8194,1439],{},[1146,8196,5657],{},[1154,8198,2325],{},[2922,8200,8201,8203],{},[1146,8202,4370],{},[1140,8204,8205,8207,8209],{},[1146,8206,5657],{},[1154,8208,2235],{},[1150,8210,1152],{},[1154,8212,2330],{},[2922,8214,8215,8217],{},[1146,8216,2230],{},[1146,8218,5657],{},[1154,8220,2683],{"stretchy":1674},[1189,8222,8223],{"encoding":1191},"\\boxed{a^l = \\sigma(w^l \\cdot a^{l-1} + b^l)}",[1124,8225,8227],{"className":8226,"ariaHidden":1156},[1196],[1124,8228,8230,8234],{"className":8229},[1200],[1124,8231],{"className":8232,"style":8233},[1204],"height:1.8291em;vertical-align:-0.59em;",[1124,8235,8237],{"className":8236},[1209],[1124,8238,8240,8442],{"className":8239},[1221,1222],[1124,8241,8243,8439],{"className":8242},[1226],[1124,8244,8247,8427],{"className":8245,"style":8246},[1230],"height:1.2391em;",[1124,8248,8250,8254],{"style":8249},"top:-3.8291em;",[1124,8251],{"className":8252,"style":8253},[1238],"height:3.8291em;",[1124,8255,8258],{"className":8256},[8257],"boxpad",[1124,8259,8261],{"className":8260},[1209],[1124,8262,8264,8295,8298,8301,8304,8307,8310,8339,8342,8345,8348,8386,8389,8392,8395,8424],{"className":8263},[1209],[1124,8265,8267,8270],{"className":8266},[1209],[1124,8268,4370],{"className":8269},[1209,1213],[1124,8271,8273],{"className":8272},[1217],[1124,8274,8276],{"className":8275},[1221],[1124,8277,8279],{"className":8278},[1226],[1124,8280,8283],{"className":8281,"style":8282},[1230],"height:0.8991em;",[1124,8284,8286,8289],{"style":8285},"top:-3.113em;margin-right:0.05em;",[1124,8287],{"className":8288,"style":1239},[1238],[1124,8290,8292],{"className":8291},[1243,1244,1245,1246],[1124,8293,5657],{"className":8294,"style":5740},[1209,1213,1246],[1124,8296],{"className":8297,"style":1774},[1271],[1124,8299,1652],{"className":8300},[1778],[1124,8302],{"className":8303,"style":1774},[1271],[1124,8305,2674],{"className":8306,"style":2700},[1209,1213],[1124,8308,2677],{"className":8309},[1795],[1124,8311,8313,8316],{"className":8312},[1209],[1124,8314,1439],{"className":8315,"style":1480},[1209,1213],[1124,8317,8319],{"className":8318},[1217],[1124,8320,8322],{"className":8321},[1221],[1124,8323,8325],{"className":8324},[1226],[1124,8326,8328],{"className":8327,"style":8282},[1230],[1124,8329,8330,8333],{"style":8285},[1124,8331],{"className":8332,"style":1239},[1238],[1124,8334,8336],{"className":8335},[1243,1244,1245,1246],[1124,8337,5657],{"className":8338,"style":5740},[1209,1213,1246],[1124,8340],{"className":8341,"style":2500},[1271],[1124,8343,2325],{"className":8344},[2504],[1124,8346],{"className":8347,"style":2500},[1271],[1124,8349,8351,8354],{"className":8350},[1209],[1124,8352,4370],{"className":8353},[1209,1213],[1124,8355,8357],{"className":8356},[1217],[1124,8358,8360],{"className":8359},[1221],[1124,8361,8363],{"className":8362},[1226],[1124,8364,8366],{"className":8365,"style":8282},[1230],[1124,8367,8368,8371],{"style":8285},[1124,8369],{"className":8370,"style":1239},[1238],[1124,8372,8374],{"className":8373},[1243,1244,1245,1246],[1124,8375,8377,8380,8383],{"className":8376},[1209,1246],[1124,8378,5657],{"className":8379,"style":5740},[1209,1213,1246],[1124,8381,2235],{"className":8382},[2504,1246],[1124,8384,1152],{"className":8385},[1209,1246],[1124,8387],{"className":8388,"style":2500},[1271],[1124,8390,2330],{"className":8391},[2504],[1124,8393],{"className":8394,"style":2500},[1271],[1124,8396,8398,8401],{"className":8397},[1209],[1124,8399,2230],{"className":8400},[1209,1213],[1124,8402,8404],{"className":8403},[1217],[1124,8405,8407],{"className":8406},[1221],[1124,8408,8410],{"className":8409},[1226],[1124,8411,8413],{"className":8412,"style":8282},[1230],[1124,8414,8415,8418],{"style":8285},[1124,8416],{"className":8417,"style":1239},[1238],[1124,8419,8421],{"className":8420},[1243,1244,1245,1246],[1124,8422,5657],{"className":8423,"style":5740},[1209,1213,1246],[1124,8425,2683],{"className":8426},[2211],[1124,8428,8430,8433],{"style":8429},"top:-3.2391em;",[1124,8431],{"className":8432,"style":8253},[1238],[1124,8434],{"className":8435,"style":8438},[8436,8437],"stretchy","fbox","height:1.8291em;border-style:solid;border-width:0.04em;",[1124,8440,1254],{"className":8441},[1253],[1124,8443,8445],{"className":8444},[1226],[1124,8446,8449],{"className":8447,"style":8448},[1230],"height:0.59em;",[1124,8450],{},[1101,8452,8453],{},"其中：",[1117,8455,8456,8533,8595,8657],{},[1120,8457,8458,8532],{},[1124,8459,8461,8485],{"className":8460},[1127],[1124,8462,8464],{"className":8463},[1131],[1133,8465,8466],{"xmlns":1135},[1137,8467,8468,8482],{},[1140,8469,8470],{},[2922,8471,8472,8474],{},[1146,8473,4370],{},[1140,8475,8476,8478,8480],{},[1146,8477,5657],{},[1154,8479,2235],{},[1150,8481,1152],{},[1189,8483,8484],{"encoding":1191},"a^{l-1}",[1124,8486,8488],{"className":8487,"ariaHidden":1156},[1196],[1124,8489,8491,8494],{"className":8490},[1200],[1124,8492],{"className":8493,"style":7649},[1204],[1124,8495,8497,8500],{"className":8496},[1209],[1124,8498,4370],{"className":8499},[1209,1213],[1124,8501,8503],{"className":8502},[1217],[1124,8504,8506],{"className":8505},[1221],[1124,8507,8509],{"className":8508},[1226],[1124,8510,8512],{"className":8511,"style":7649},[1230],[1124,8513,8514,8517],{"style":3905},[1124,8515],{"className":8516,"style":1239},[1238],[1124,8518,8520],{"className":8519},[1243,1244,1245,1246],[1124,8521,8523,8526,8529],{"className":8522},[1209,1246],[1124,8524,5657],{"className":8525,"style":5740},[1209,1213,1246],[1124,8527,2235],{"className":8528},[2504,1246],[1124,8530,1152],{"className":8531},[1209,1246],"：上一层的输出（第一层时就是输入 x）",[1120,8534,8535,8594],{},[1124,8536,8538,8556],{"className":8537},[1127],[1124,8539,8541],{"className":8540},[1131],[1133,8542,8543],{"xmlns":1135},[1137,8544,8545,8553],{},[1140,8546,8547],{},[2922,8548,8549,8551],{},[1146,8550,1439],{},[1146,8552,5657],{},[1189,8554,8555],{"encoding":1191},"w^l",[1124,8557,8559],{"className":8558,"ariaHidden":1156},[1196],[1124,8560,8562,8565],{"className":8561},[1200],[1124,8563],{"className":8564,"style":7649},[1204],[1124,8566,8568,8571],{"className":8567},[1209],[1124,8569,1439],{"className":8570,"style":1480},[1209,1213],[1124,8572,8574],{"className":8573},[1217],[1124,8575,8577],{"className":8576},[1221],[1124,8578,8580],{"className":8579},[1226],[1124,8581,8583],{"className":8582,"style":7649},[1230],[1124,8584,8585,8588],{"style":3905},[1124,8586],{"className":8587,"style":1239},[1238],[1124,8589,8591],{"className":8590},[1243,1244,1245,1246],[1124,8592,5657],{"className":8593,"style":5740},[1209,1213,1246],"：第 l 层的权重矩阵",[1120,8596,8597,8656],{},[1124,8598,8600,8618],{"className":8599},[1127],[1124,8601,8603],{"className":8602},[1131],[1133,8604,8605],{"xmlns":1135},[1137,8606,8607,8615],{},[1140,8608,8609],{},[2922,8610,8611,8613],{},[1146,8612,2230],{},[1146,8614,5657],{},[1189,8616,8617],{"encoding":1191},"b^l",[1124,8619,8621],{"className":8620,"ariaHidden":1156},[1196],[1124,8622,8624,8627],{"className":8623},[1200],[1124,8625],{"className":8626,"style":7649},[1204],[1124,8628,8630,8633],{"className":8629},[1209],[1124,8631,2230],{"className":8632},[1209,1213],[1124,8634,8636],{"className":8635},[1217],[1124,8637,8639],{"className":8638},[1221],[1124,8640,8642],{"className":8641},[1226],[1124,8643,8645],{"className":8644,"style":7649},[1230],[1124,8646,8647,8650],{"style":3905},[1124,8648],{"className":8649,"style":1239},[1238],[1124,8651,8653],{"className":8652},[1243,1244,1245,1246],[1124,8654,5657],{"className":8655,"style":5740},[1209,1213,1246],"：第 l 层的偏置向量",[1120,8658,8659,8687],{},[1124,8660,8662,8675],{"className":8661},[1127],[1124,8663,8665],{"className":8664},[1131],[1133,8666,8667],{"xmlns":1135},[1137,8668,8669,8673],{},[1140,8670,8671],{},[1146,8672,2674],{},[1189,8674,3114],{"encoding":1191},[1124,8676,8678],{"className":8677,"ariaHidden":1156},[1196],[1124,8679,8681,8684],{"className":8680},[1200],[1124,8682],{"className":8683,"style":3124},[1204],[1124,8685,2674],{"className":8686,"style":2700},[1209,1213],"：激活函数（如 sigmoid）",[2745,8689],{},[7743,8691,8692],{"id":8692},"逐层传递过程",[1101,8694,8695],{},"以一个 3 层网络为例（输入层 → 隐藏层 → 输出层）：",[8697,8698,8704],"pre",{"className":8699,"code":8701,"language":8702,"meta":8703},[8700],"language-Plain","输入 x → [第1层计算] → a¹ → [第2层计算] → a² → [第3层计算] → a³ (最终输出)\n","Plain","Text",[8705,8706,8701],"code",{"__ignoreMap":8707},"",[2616,8709,8710,8726],{},[2619,8711,8712],{},[2622,8713,8714,8717,8720,8723],{},[2625,8715,8716],{},"层",[2625,8718,8719],{},"输入",[2625,8721,8722],{},"计算",[2625,8724,8725],{},"输出",[2635,8727,8728,8821,9275],{},[2622,8729,8730,8732,8735,8738],{},[2640,8731,4272],{},[2640,8733,8734],{},"原始数据 x",[2640,8736,8737],{},"无计算",[2640,8739,8740],{},[1124,8741,8743,8765],{"className":8742},[1127],[1124,8744,8746],{"className":8745},[1131],[1133,8747,8748],{"xmlns":1135},[1137,8749,8750,8762],{},[1140,8751,8752,8758,8760],{},[2922,8753,8754,8756],{},[1146,8755,4370],{},[1150,8757,1673],{},[1154,8759,1652],{},[1146,8761,1148],{},[1189,8763,8764],{"encoding":1191},"a^0 = x",[1124,8766,8768,8812],{"className":8767,"ariaHidden":1156},[1196],[1124,8769,8771,8774,8803,8806,8809],{"className":8770},[1200],[1124,8772],{"className":8773,"style":4598},[1204],[1124,8775,8777,8780],{"className":8776},[1209],[1124,8778,4370],{"className":8779},[1209,1213],[1124,8781,8783],{"className":8782},[1217],[1124,8784,8786],{"className":8785},[1221],[1124,8787,8789],{"className":8788},[1226],[1124,8790,8792],{"className":8791,"style":4598},[1230],[1124,8793,8794,8797],{"style":3905},[1124,8795],{"className":8796,"style":1239},[1238],[1124,8798,8800],{"className":8799},[1243,1244,1245,1246],[1124,8801,1673],{"className":8802},[1209,1246],[1124,8804],{"className":8805,"style":1774},[1271],[1124,8807,1652],{"className":8808},[1778],[1124,8810],{"className":8811,"style":1774},[1271],[1124,8813,8815,8818],{"className":8814},[1200],[1124,8816],{"className":8817,"style":3124},[1204],[1124,8819,1148],{"className":8820},[1209,1213],[2622,8822,8823,8825,8886,9214],{},[2640,8824,4278],{},[2640,8826,8827],{},[1124,8828,8830,8848],{"className":8829},[1127],[1124,8831,8833],{"className":8832},[1131],[1133,8834,8835],{"xmlns":1135},[1137,8836,8837,8845],{},[1140,8838,8839],{},[2922,8840,8841,8843],{},[1146,8842,4370],{},[1150,8844,1673],{},[1189,8846,8847],{"encoding":1191},"a^0",[1124,8849,8851],{"className":8850,"ariaHidden":1156},[1196],[1124,8852,8854,8857],{"className":8853},[1200],[1124,8855],{"className":8856,"style":4598},[1204],[1124,8858,8860,8863],{"className":8859},[1209],[1124,8861,4370],{"className":8862},[1209,1213],[1124,8864,8866],{"className":8865},[1217],[1124,8867,8869],{"className":8868},[1221],[1124,8870,8872],{"className":8871},[1226],[1124,8873,8875],{"className":8874,"style":4598},[1230],[1124,8876,8877,8880],{"style":3905},[1124,8878],{"className":8879,"style":1239},[1238],[1124,8881,8883],{"className":8882},[1243,1244,1245,1246],[1124,8884,1673],{"className":8885},[1209,1246],[2640,8887,8888,9087,9088],{},[1124,8889,8891,8931],{"className":8890},[1127],[1124,8892,8894],{"className":8893},[1131],[1133,8895,8896],{"xmlns":1135},[1137,8897,8898,8928],{},[1140,8899,8900,8906,8908,8914,8920,8922],{},[2922,8901,8902,8904],{},[1146,8903,2680],{},[1150,8905,1152],{},[1154,8907,1652],{},[2922,8909,8910,8912],{},[1146,8911,1439],{},[1150,8913,1152],{},[2922,8915,8916,8918],{},[1146,8917,4370],{},[1150,8919,1673],{},[1154,8921,2330],{},[2922,8923,8924,8926],{},[1146,8925,2230],{},[1150,8927,1152],{},[1189,8929,8930],{"encoding":1191},"z^1 = w^1 a^0 + b^1",[1124,8932,8934,8978,9052],{"className":8933,"ariaHidden":1156},[1196],[1124,8935,8937,8940,8969,8972,8975],{"className":8936},[1200],[1124,8938],{"className":8939,"style":4598},[1204],[1124,8941,8943,8946],{"className":8942},[1209],[1124,8944,2680],{"className":8945,"style":2707},[1209,1213],[1124,8947,8949],{"className":8948},[1217],[1124,8950,8952],{"className":8951},[1221],[1124,8953,8955],{"className":8954},[1226],[1124,8956,8958],{"className":8957,"style":4598},[1230],[1124,8959,8960,8963],{"style":3905},[1124,8961],{"className":8962,"style":1239},[1238],[1124,8964,8966],{"className":8965},[1243,1244,1245,1246],[1124,8967,1152],{"className":8968},[1209,1246],[1124,8970],{"className":8971,"style":1774},[1271],[1124,8973,1652],{"className":8974},[1778],[1124,8976],{"className":8977,"style":1774},[1271],[1124,8979,8981,8985,9014,9043,9046,9049],{"className":8980},[1200],[1124,8982],{"className":8983,"style":8984},[1204],"height:0.8974em;vertical-align:-0.0833em;",[1124,8986,8988,8991],{"className":8987},[1209],[1124,8989,1439],{"className":8990,"style":1480},[1209,1213],[1124,8992,8994],{"className":8993},[1217],[1124,8995,8997],{"className":8996},[1221],[1124,8998,9000],{"className":8999},[1226],[1124,9001,9003],{"className":9002,"style":4598},[1230],[1124,9004,9005,9008],{"style":3905},[1124,9006],{"className":9007,"style":1239},[1238],[1124,9009,9011],{"className":9010},[1243,1244,1245,1246],[1124,9012,1152],{"className":9013},[1209,1246],[1124,9015,9017,9020],{"className":9016},[1209],[1124,9018,4370],{"className":9019},[1209,1213],[1124,9021,9023],{"className":9022},[1217],[1124,9024,9026],{"className":9025},[1221],[1124,9027,9029],{"className":9028},[1226],[1124,9030,9032],{"className":9031,"style":4598},[1230],[1124,9033,9034,9037],{"style":3905},[1124,9035],{"className":9036,"style":1239},[1238],[1124,9038,9040],{"className":9039},[1243,1244,1245,1246],[1124,9041,1673],{"className":9042},[1209,1246],[1124,9044],{"className":9045,"style":2500},[1271],[1124,9047,2330],{"className":9048},[2504],[1124,9050],{"className":9051,"style":2500},[1271],[1124,9053,9055,9058],{"className":9054},[1200],[1124,9056],{"className":9057,"style":4598},[1204],[1124,9059,9061,9064],{"className":9060},[1209],[1124,9062,2230],{"className":9063},[1209,1213],[1124,9065,9067],{"className":9066},[1217],[1124,9068,9070],{"className":9069},[1221],[1124,9071,9073],{"className":9072},[1226],[1124,9074,9076],{"className":9075,"style":4598},[1230],[1124,9077,9078,9081],{"style":3905},[1124,9079],{"className":9080,"style":1239},[1238],[1124,9082,9084],{"className":9083},[1243,1244,1245,1246],[1124,9085,1152],{"className":9086},[1209,1246],"，",[1124,9089,9091,9123],{"className":9090},[1127],[1124,9092,9094],{"className":9093},[1131],[1133,9095,9096],{"xmlns":1135},[1137,9097,9098,9120],{},[1140,9099,9100,9106,9108,9110,9112,9118],{},[2922,9101,9102,9104],{},[1146,9103,4370],{},[1150,9105,1152],{},[1154,9107,1652],{},[1146,9109,2674],{},[1154,9111,2677],{"stretchy":1674},[2922,9113,9114,9116],{},[1146,9115,2680],{},[1150,9117,1152],{},[1154,9119,2683],{"stretchy":1674},[1189,9121,9122],{"encoding":1191},"a^1 = \\sigma(z^1)",[1124,9124,9126,9170],{"className":9125,"ariaHidden":1156},[1196],[1124,9127,9129,9132,9161,9164,9167],{"className":9128},[1200],[1124,9130],{"className":9131,"style":4598},[1204],[1124,9133,9135,9138],{"className":9134},[1209],[1124,9136,4370],{"className":9137},[1209,1213],[1124,9139,9141],{"className":9140},[1217],[1124,9142,9144],{"className":9143},[1221],[1124,9145,9147],{"className":9146},[1226],[1124,9148,9150],{"className":9149,"style":4598},[1230],[1124,9151,9152,9155],{"style":3905},[1124,9153],{"className":9154,"style":1239},[1238],[1124,9156,9158],{"className":9157},[1243,1244,1245,1246],[1124,9159,1152],{"className":9160},[1209,1246],[1124,9162],{"className":9163,"style":1774},[1271],[1124,9165,1652],{"className":9166},[1778],[1124,9168],{"className":9169,"style":1774},[1271],[1124,9171,9173,9176,9179,9182,9211],{"className":9172},[1200],[1124,9174],{"className":9175,"style":4576},[1204],[1124,9177,2674],{"className":9178,"style":2700},[1209,1213],[1124,9180,2677],{"className":9181},[1795],[1124,9183,9185,9188],{"className":9184},[1209],[1124,9186,2680],{"className":9187,"style":2707},[1209,1213],[1124,9189,9191],{"className":9190},[1217],[1124,9192,9194],{"className":9193},[1221],[1124,9195,9197],{"className":9196},[1226],[1124,9198,9200],{"className":9199,"style":4598},[1230],[1124,9201,9202,9205],{"style":3905},[1124,9203],{"className":9204,"style":1239},[1238],[1124,9206,9208],{"className":9207},[1243,1244,1245,1246],[1124,9209,1152],{"className":9210},[1209,1246],[1124,9212,2683],{"className":9213},[2211],[2640,9215,9216],{},[1124,9217,9219,9237],{"className":9218},[1127],[1124,9220,9222],{"className":9221},[1131],[1133,9223,9224],{"xmlns":1135},[1137,9225,9226,9234],{},[1140,9227,9228],{},[2922,9229,9230,9232],{},[1146,9231,4370],{},[1150,9233,1152],{},[1189,9235,9236],{"encoding":1191},"a^1",[1124,9238,9240],{"className":9239,"ariaHidden":1156},[1196],[1124,9241,9243,9246],{"className":9242},[1200],[1124,9244],{"className":9245,"style":4598},[1204],[1124,9247,9249,9252],{"className":9248},[1209],[1124,9250,4370],{"className":9251},[1209,1213],[1124,9253,9255],{"className":9254},[1217],[1124,9256,9258],{"className":9257},[1221],[1124,9259,9261],{"className":9260},[1226],[1124,9262,9264],{"className":9263,"style":4598},[1230],[1124,9265,9266,9269],{"style":3905},[1124,9267],{"className":9268,"style":1239},[1238],[1124,9270,9272],{"className":9271},[1243,1244,1245,1246],[1124,9273,1152],{"className":9274},[1209,1246],[2622,9276,9277,9279,9339,9665],{},[2640,9278,4284],{},[2640,9280,9281],{},[1124,9282,9284,9301],{"className":9283},[1127],[1124,9285,9287],{"className":9286},[1131],[1133,9288,9289],{"xmlns":1135},[1137,9290,9291,9299],{},[1140,9292,9293],{},[2922,9294,9295,9297],{},[1146,9296,4370],{},[1150,9298,1152],{},[1189,9300,9236],{"encoding":1191},[1124,9302,9304],{"className":9303,"ariaHidden":1156},[1196],[1124,9305,9307,9310],{"className":9306},[1200],[1124,9308],{"className":9309,"style":4598},[1204],[1124,9311,9313,9316],{"className":9312},[1209],[1124,9314,4370],{"className":9315},[1209,1213],[1124,9317,9319],{"className":9318},[1217],[1124,9320,9322],{"className":9321},[1221],[1124,9323,9325],{"className":9324},[1226],[1124,9326,9328],{"className":9327,"style":4598},[1230],[1124,9329,9330,9333],{"style":3905},[1124,9331],{"className":9332,"style":1239},[1238],[1124,9334,9336],{"className":9335},[1243,1244,1245,1246],[1124,9337,1152],{"className":9338},[1209,1246],[2640,9340,9341,9087,9539],{},[1124,9342,9344,9384],{"className":9343},[1127],[1124,9345,9347],{"className":9346},[1131],[1133,9348,9349],{"xmlns":1135},[1137,9350,9351,9381],{},[1140,9352,9353,9359,9361,9367,9373,9375],{},[2922,9354,9355,9357],{},[1146,9356,2680],{},[1150,9358,1164],{},[1154,9360,1652],{},[2922,9362,9363,9365],{},[1146,9364,1439],{},[1150,9366,1164],{},[2922,9368,9369,9371],{},[1146,9370,4370],{},[1150,9372,1152],{},[1154,9374,2330],{},[2922,9376,9377,9379],{},[1146,9378,2230],{},[1150,9380,1164],{},[1189,9382,9383],{"encoding":1191},"z^2 = w^2 a^1 + b^2",[1124,9385,9387,9431,9504],{"className":9386,"ariaHidden":1156},[1196],[1124,9388,9390,9393,9422,9425,9428],{"className":9389},[1200],[1124,9391],{"className":9392,"style":4598},[1204],[1124,9394,9396,9399],{"className":9395},[1209],[1124,9397,2680],{"className":9398,"style":2707},[1209,1213],[1124,9400,9402],{"className":9401},[1217],[1124,9403,9405],{"className":9404},[1221],[1124,9406,9408],{"className":9407},[1226],[1124,9409,9411],{"className":9410,"style":4598},[1230],[1124,9412,9413,9416],{"style":3905},[1124,9414],{"className":9415,"style":1239},[1238],[1124,9417,9419],{"className":9418},[1243,1244,1245,1246],[1124,9420,1164],{"className":9421},[1209,1246],[1124,9423],{"className":9424,"style":1774},[1271],[1124,9426,1652],{"className":9427},[1778],[1124,9429],{"className":9430,"style":1774},[1271],[1124,9432,9434,9437,9466,9495,9498,9501],{"className":9433},[1200],[1124,9435],{"className":9436,"style":8984},[1204],[1124,9438,9440,9443],{"className":9439},[1209],[1124,9441,1439],{"className":9442,"style":1480},[1209,1213],[1124,9444,9446],{"className":9445},[1217],[1124,9447,9449],{"className":9448},[1221],[1124,9450,9452],{"className":9451},[1226],[1124,9453,9455],{"className":9454,"style":4598},[1230],[1124,9456,9457,9460],{"style":3905},[1124,9458],{"className":9459,"style":1239},[1238],[1124,9461,9463],{"className":9462},[1243,1244,1245,1246],[1124,9464,1164],{"className":9465},[1209,1246],[1124,9467,9469,9472],{"className":9468},[1209],[1124,9470,4370],{"className":9471},[1209,1213],[1124,9473,9475],{"className":9474},[1217],[1124,9476,9478],{"className":9477},[1221],[1124,9479,9481],{"className":9480},[1226],[1124,9482,9484],{"className":9483,"style":4598},[1230],[1124,9485,9486,9489],{"style":3905},[1124,9487],{"className":9488,"style":1239},[1238],[1124,9490,9492],{"className":9491},[1243,1244,1245,1246],[1124,9493,1152],{"className":9494},[1209,1246],[1124,9496],{"className":9497,"style":2500},[1271],[1124,9499,2330],{"className":9500},[2504],[1124,9502],{"className":9503,"style":2500},[1271],[1124,9505,9507,9510],{"className":9506},[1200],[1124,9508],{"className":9509,"style":4598},[1204],[1124,9511,9513,9516],{"className":9512},[1209],[1124,9514,2230],{"className":9515},[1209,1213],[1124,9517,9519],{"className":9518},[1217],[1124,9520,9522],{"className":9521},[1221],[1124,9523,9525],{"className":9524},[1226],[1124,9526,9528],{"className":9527,"style":4598},[1230],[1124,9529,9530,9533],{"style":3905},[1124,9531],{"className":9532,"style":1239},[1238],[1124,9534,9536],{"className":9535},[1243,1244,1245,1246],[1124,9537,1164],{"className":9538},[1209,1246],[1124,9540,9542,9574],{"className":9541},[1127],[1124,9543,9545],{"className":9544},[1131],[1133,9546,9547],{"xmlns":1135},[1137,9548,9549,9571],{},[1140,9550,9551,9557,9559,9561,9563,9569],{},[2922,9552,9553,9555],{},[1146,9554,4370],{},[1150,9556,1164],{},[1154,9558,1652],{},[1146,9560,2674],{},[1154,9562,2677],{"stretchy":1674},[2922,9564,9565,9567],{},[1146,9566,2680],{},[1150,9568,1164],{},[1154,9570,2683],{"stretchy":1674},[1189,9572,9573],{"encoding":1191},"a^2 = \\sigma(z^2)",[1124,9575,9577,9621],{"className":9576,"ariaHidden":1156},[1196],[1124,9578,9580,9583,9612,9615,9618],{"className":9579},[1200],[1124,9581],{"className":9582,"style":4598},[1204],[1124,9584,9586,9589],{"className":9585},[1209],[1124,9587,4370],{"className":9588},[1209,1213],[1124,9590,9592],{"className":9591},[1217],[1124,9593,9595],{"className":9594},[1221],[1124,9596,9598],{"className":9597},[1226],[1124,9599,9601],{"className":9600,"style":4598},[1230],[1124,9602,9603,9606],{"style":3905},[1124,9604],{"className":9605,"style":1239},[1238],[1124,9607,9609],{"className":9608},[1243,1244,1245,1246],[1124,9610,1164],{"className":9611},[1209,1246],[1124,9613],{"className":9614,"style":1774},[1271],[1124,9616,1652],{"className":9617},[1778],[1124,9619],{"className":9620,"style":1774},[1271],[1124,9622,9624,9627,9630,9633,9662],{"className":9623},[1200],[1124,9625],{"className":9626,"style":4576},[1204],[1124,9628,2674],{"className":9629,"style":2700},[1209,1213],[1124,9631,2677],{"className":9632},[1795],[1124,9634,9636,9639],{"className":9635},[1209],[1124,9637,2680],{"className":9638,"style":2707},[1209,1213],[1124,9640,9642],{"className":9641},[1217],[1124,9643,9645],{"className":9644},[1221],[1124,9646,9648],{"className":9647},[1226],[1124,9649,9651],{"className":9650,"style":4598},[1230],[1124,9652,9653,9656],{"style":3905},[1124,9654],{"className":9655,"style":1239},[1238],[1124,9657,9659],{"className":9658},[1243,1244,1245,1246],[1124,9660,1164],{"className":9661},[1209,1246],[1124,9663,2683],{"className":9664},[2211],[2640,9666,9667,9726],{},[1124,9668,9670,9688],{"className":9669},[1127],[1124,9671,9673],{"className":9672},[1131],[1133,9674,9675],{"xmlns":1135},[1137,9676,9677,9685],{},[1140,9678,9679],{},[2922,9680,9681,9683],{},[1146,9682,4370],{},[1150,9684,1164],{},[1189,9686,9687],{"encoding":1191},"a^2",[1124,9689,9691],{"className":9690,"ariaHidden":1156},[1196],[1124,9692,9694,9697],{"className":9693},[1200],[1124,9695],{"className":9696,"style":4598},[1204],[1124,9698,9700,9703],{"className":9699},[1209],[1124,9701,4370],{"className":9702},[1209,1213],[1124,9704,9706],{"className":9705},[1217],[1124,9707,9709],{"className":9708},[1221],[1124,9710,9712],{"className":9711},[1226],[1124,9713,9715],{"className":9714,"style":4598},[1230],[1124,9716,9717,9720],{"style":3905},[1124,9718],{"className":9719,"style":1239},[1238],[1124,9721,9723],{"className":9722},[1243,1244,1245,1246],[1124,9724,1164],{"className":9725},[1209,1246],"（最终预测）",[1101,9728,9729],{},"示例",[1101,9731,9732],{},"一个最简单的网络：2 个输入 → 2 个隐藏神经元 → 1 个输出",[1101,9734,9735],{},[1107,9736,9737],{},"参数：",[1101,9739,9740],{},[1124,9741,9743,9847],{"className":9742},[1127],[1124,9744,9746],{"className":9745},[1131],[1133,9747,9748],{"xmlns":1135},[1137,9749,9750,9844],{},[1140,9751,9752,9758,9760,9802,9804,9806,9812,9814],{},[2922,9753,9754,9756],{},[1146,9755,1439],{},[1150,9757,1152],{},[1154,9759,1652],{},[1140,9761,9762,9764,9800],{},[1154,9763,2677],{"fence":1156},[1659,9765,9768,9784],{"rowspacing":9766,"columnalign":9767,"columnspacing":1663},"0.16em","center center",[1665,9769,9770,9777],{},[1668,9771,9772],{},[1671,9773,9774],{"scriptlevel":1673,"displaystyle":1674},[1150,9775,9776],{},"0.3",[1668,9778,9779],{},[1671,9780,9781],{"scriptlevel":1673,"displaystyle":1674},[1150,9782,9783],{},"0.5",[1665,9785,9786,9793],{},[1668,9787,9788],{},[1671,9789,9790],{"scriptlevel":1673,"displaystyle":1674},[1150,9791,9792],{},"0.4",[1668,9794,9795],{},[1671,9796,9797],{"scriptlevel":1673,"displaystyle":1674},[1150,9798,9799],{},"0.2",[1154,9801,2683],{"fence":1156},[1154,9803,1157],{"separator":1156},[1271,9805],{"width":1663},[2922,9807,9808,9810],{},[1146,9809,2230],{},[1150,9811,1152],{},[1154,9813,1652],{},[1140,9815,9816,9818,9842],{},[1154,9817,2677],{"fence":1156},[1659,9819,9821,9830],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},"center",[1665,9822,9823],{},[1668,9824,9825],{},[1671,9826,9827],{"scriptlevel":1673,"displaystyle":1674},[1150,9828,9829],{},"0.1",[1665,9831,9832],{},[1668,9833,9834],{},[1671,9835,9836],{"scriptlevel":1673,"displaystyle":1674},[1140,9837,9838,9840],{},[1154,9839,2235],{},[1150,9841,9829],{},[1154,9843,2683],{"fence":1156},[1189,9845,9846],{"encoding":1191},"w^1 = \\begin{pmatrix} 0.3 & 0.5 \\\\ 0.4 & 0.2 \\end{pmatrix}, \\quad b^1 = \\begin{pmatrix} 0.1 \\\\ -0.1 \\end{pmatrix}",[1124,9848,9850,9894,10075],{"className":9849,"ariaHidden":1156},[1196],[1124,9851,9853,9856,9885,9888,9891],{"className":9852},[1200],[1124,9854],{"className":9855,"style":4598},[1204],[1124,9857,9859,9862],{"className":9858},[1209],[1124,9860,1439],{"className":9861,"style":1480},[1209,1213],[1124,9863,9865],{"className":9864},[1217],[1124,9866,9868],{"className":9867},[1221],[1124,9869,9871],{"className":9870},[1226],[1124,9872,9874],{"className":9873,"style":4598},[1230],[1124,9875,9876,9879],{"style":3905},[1124,9877],{"className":9878,"style":1239},[1238],[1124,9880,9882],{"className":9881},[1243,1244,1245,1246],[1124,9883,1152],{"className":9884},[1209,1246],[1124,9886],{"className":9887,"style":1774},[1271],[1124,9889,1652],{"className":9890},[1778],[1124,9892],{"className":9893,"style":1774},[1271],[1124,9895,9897,9901,10024,10027,10030,10034,10037,10066,10069,10072],{"className":9896},[1200],[1124,9898],{"className":9899,"style":9900},[1204],"height:2.4em;vertical-align:-0.95em;",[1124,9902,9904,9910,10018],{"className":9903},[1368],[1124,9905,9907],{"className":9906,"style":1797},[1795,1796],[1124,9908,2677],{"className":9909},[1801,1245],[1124,9911,9913],{"className":9912},[1209],[1124,9914,9916,9966,9970,9973],{"className":9915},[1659],[1124,9917,9920],{"className":9918},[9919],"col-align-c",[1124,9921,9923,9957],{"className":9922},[1221,1222],[1124,9924,9926,9954],{"className":9925},[1226],[1124,9927,9930,9942],{"className":9928,"style":9929},[1230],"height:1.45em;",[1124,9931,9933,9936],{"style":9932},"top:-3.61em;",[1124,9934],{"className":9935,"style":2998},[1238],[1124,9937,9939],{"className":9938},[1209],[1124,9940,9776],{"className":9941},[1209],[1124,9943,9945,9948],{"style":9944},"top:-2.41em;",[1124,9946],{"className":9947,"style":2998},[1238],[1124,9949,9951],{"className":9950},[1209],[1124,9952,9792],{"className":9953},[1209],[1124,9955,1254],{"className":9956},[1253],[1124,9958,9960],{"className":9959},[1226],[1124,9961,9964],{"className":9962,"style":9963},[1230],"height:0.95em;",[1124,9965],{},[1124,9967],{"className":9968,"style":9969},[1863],"width:0.5em;",[1124,9971],{"className":9972,"style":9969},[1863],[1124,9974,9976],{"className":9975},[9919],[1124,9977,9979,10010],{"className":9978},[1221,1222],[1124,9980,9982,10007],{"className":9981},[1226],[1124,9983,9985,9996],{"className":9984,"style":9929},[1230],[1124,9986,9987,9990],{"style":9932},[1124,9988],{"className":9989,"style":2998},[1238],[1124,9991,9993],{"className":9992},[1209],[1124,9994,9783],{"className":9995},[1209],[1124,9997,9998,10001],{"style":9944},[1124,9999],{"className":10000,"style":2998},[1238],[1124,10002,10004],{"className":10003},[1209],[1124,10005,9799],{"className":10006},[1209],[1124,10008,1254],{"className":10009},[1253],[1124,10011,10013],{"className":10012},[1226],[1124,10014,10016],{"className":10015,"style":9963},[1230],[1124,10017],{},[1124,10019,10021],{"className":10020,"style":1797},[2211,1796],[1124,10022,2683],{"className":10023},[1801,1245],[1124,10025],{"className":10026,"style":1272},[1271],[1124,10028,1157],{"className":10029},[1267],[1124,10031],{"className":10032,"style":10033},[1271],"margin-right:1em;",[1124,10035],{"className":10036,"style":1272},[1271],[1124,10038,10040,10043],{"className":10039},[1209],[1124,10041,2230],{"className":10042},[1209,1213],[1124,10044,10046],{"className":10045},[1217],[1124,10047,10049],{"className":10048},[1221],[1124,10050,10052],{"className":10051},[1226],[1124,10053,10055],{"className":10054,"style":4598},[1230],[1124,10056,10057,10060],{"style":3905},[1124,10058],{"className":10059,"style":1239},[1238],[1124,10061,10063],{"className":10062},[1243,1244,1245,1246],[1124,10064,1152],{"className":10065},[1209,1246],[1124,10067],{"className":10068,"style":1774},[1271],[1124,10070,1652],{"className":10071},[1778],[1124,10073],{"className":10074,"style":1774},[1271],[1124,10076,10078,10081],{"className":10077},[1200],[1124,10079],{"className":10080,"style":9900},[1204],[1124,10082,10084,10090,10144],{"className":10083},[1368],[1124,10085,10087],{"className":10086,"style":1797},[1795,1796],[1124,10088,2677],{"className":10089},[1801,1245],[1124,10091,10093],{"className":10092},[1209],[1124,10094,10096],{"className":10095},[1659],[1124,10097,10099],{"className":10098},[9919],[1124,10100,10102,10136],{"className":10101},[1221,1222],[1124,10103,10105,10133],{"className":10104},[1226],[1124,10106,10108,10119],{"className":10107,"style":9929},[1230],[1124,10109,10110,10113],{"style":9932},[1124,10111],{"className":10112,"style":2998},[1238],[1124,10114,10116],{"className":10115},[1209],[1124,10117,9829],{"className":10118},[1209],[1124,10120,10121,10124],{"style":9944},[1124,10122],{"className":10123,"style":2998},[1238],[1124,10125,10127,10130],{"className":10126},[1209],[1124,10128,2235],{"className":10129},[1209],[1124,10131,9829],{"className":10132},[1209],[1124,10134,1254],{"className":10135},[1253],[1124,10137,10139],{"className":10138},[1226],[1124,10140,10142],{"className":10141,"style":9963},[1230],[1124,10143],{},[1124,10145,10147],{"className":10146,"style":1797},[2211,1796],[1124,10148,2683],{"className":10149},[1801,1245],[1101,10151,10152],{},[1124,10153,10155,10215],{"className":10154},[1127],[1124,10156,10158],{"className":10157},[1131],[1133,10159,10160],{"xmlns":1135},[1137,10161,10162,10212],{},[1140,10163,10164,10170,10172,10196,10198,10200,10206,10208,10210],{},[2922,10165,10166,10168],{},[1146,10167,1439],{},[1150,10169,1164],{},[1154,10171,1652],{},[1140,10173,10174,10176,10194],{},[1154,10175,2677],{"fence":1156},[1659,10177,10178],{"rowspacing":9766,"columnalign":9767,"columnspacing":1663},[1665,10179,10180,10187],{},[1668,10181,10182],{},[1671,10183,10184],{"scriptlevel":1673,"displaystyle":1674},[1150,10185,10186],{},"0.6",[1668,10188,10189],{},[1671,10190,10191],{"scriptlevel":1673,"displaystyle":1674},[1150,10192,10193],{},"0.7",[1154,10195,2683],{"fence":1156},[1154,10197,1157],{"separator":1156},[1271,10199],{"width":1663},[2922,10201,10202,10204],{},[1146,10203,2230],{},[1150,10205,1164],{},[1154,10207,1652],{},[1154,10209,2235],{},[1150,10211,9799],{},[1189,10213,10214],{"encoding":1191},"w^2 = \\begin{pmatrix} 0.6 & 0.7 \\end{pmatrix}, \\quad b^2 = -0.2",[1124,10216,10218,10262,10417],{"className":10217,"ariaHidden":1156},[1196],[1124,10219,10221,10224,10253,10256,10259],{"className":10220},[1200],[1124,10222],{"className":10223,"style":4598},[1204],[1124,10225,10227,10230],{"className":10226},[1209],[1124,10228,1439],{"className":10229,"style":1480},[1209,1213],[1124,10231,10233],{"className":10232},[1217],[1124,10234,10236],{"className":10235},[1221],[1124,10237,10239],{"className":10238},[1226],[1124,10240,10242],{"className":10241,"style":4598},[1230],[1124,10243,10244,10247],{"style":3905},[1124,10245],{"className":10246,"style":1239},[1238],[1124,10248,10250],{"className":10249},[1243,1244,1245,1246],[1124,10251,1164],{"className":10252},[1209,1246],[1124,10254],{"className":10255,"style":1774},[1271],[1124,10257,1652],{"className":10258},[1778],[1124,10260],{"className":10261,"style":1774},[1271],[1124,10263,10265,10269,10367,10370,10373,10376,10379,10408,10411,10414],{"className":10264},[1200],[1124,10266],{"className":10267,"style":10268},[1204],"height:1.2em;vertical-align:-0.35em;",[1124,10270,10272,10278,10361],{"className":10271},[1368],[1124,10273,10275],{"className":10274,"style":1797},[1795,1796],[1124,10276,2677],{"className":10277},[1801,3041],[1124,10279,10281],{"className":10280},[1209],[1124,10282,10284,10321,10324,10327],{"className":10283},[1659],[1124,10285,10287],{"className":10286},[9919],[1124,10288,10290,10312],{"className":10289},[1221,1222],[1124,10291,10293,10309],{"className":10292},[1226],[1124,10294,10297],{"className":10295,"style":10296},[1230],"height:0.85em;",[1124,10298,10300,10303],{"style":10299},"top:-3.01em;",[1124,10301],{"className":10302,"style":2998},[1238],[1124,10304,10306],{"className":10305},[1209],[1124,10307,10186],{"className":10308},[1209],[1124,10310,1254],{"className":10311},[1253],[1124,10313,10315],{"className":10314},[1226],[1124,10316,10319],{"className":10317,"style":10318},[1230],"height:0.35em;",[1124,10320],{},[1124,10322],{"className":10323,"style":9969},[1863],[1124,10325],{"className":10326,"style":9969},[1863],[1124,10328,10330],{"className":10329},[9919],[1124,10331,10333,10353],{"className":10332},[1221,1222],[1124,10334,10336,10350],{"className":10335},[1226],[1124,10337,10339],{"className":10338,"style":10296},[1230],[1124,10340,10341,10344],{"style":10299},[1124,10342],{"className":10343,"style":2998},[1238],[1124,10345,10347],{"className":10346},[1209],[1124,10348,10193],{"className":10349},[1209],[1124,10351,1254],{"className":10352},[1253],[1124,10354,10356],{"className":10355},[1226],[1124,10357,10359],{"className":10358,"style":10318},[1230],[1124,10360],{},[1124,10362,10364],{"className":10363,"style":1797},[2211,1796],[1124,10365,2683],{"className":10366},[1801,3041],[1124,10368],{"className":10369,"style":1272},[1271],[1124,10371,1157],{"className":10372},[1267],[1124,10374],{"className":10375,"style":10033},[1271],[1124,10377],{"className":10378,"style":1272},[1271],[1124,10380,10382,10385],{"className":10381},[1209],[1124,10383,2230],{"className":10384},[1209,1213],[1124,10386,10388],{"className":10387},[1217],[1124,10389,10391],{"className":10390},[1221],[1124,10392,10394],{"className":10393},[1226],[1124,10395,10397],{"className":10396,"style":4598},[1230],[1124,10398,10399,10402],{"style":3905},[1124,10400],{"className":10401,"style":1239},[1238],[1124,10403,10405],{"className":10404},[1243,1244,1245,1246],[1124,10406,1164],{"className":10407},[1209,1246],[1124,10409],{"className":10410,"style":1774},[1271],[1124,10412,1652],{"className":10413},[1778],[1124,10415],{"className":10416,"style":1774},[1271],[1124,10418,10420,10424,10427],{"className":10419},[1200],[1124,10421],{"className":10422,"style":10423},[1204],"height:0.7278em;vertical-align:-0.0833em;",[1124,10425,2235],{"className":10426},[1209],[1124,10428,9799],{"className":10429},[1209],[1101,10431,10432,10434,10435],{},[1107,10433,1122],{}," ",[1124,10436,10438,10468],{"className":10437},[1127],[1124,10439,10441],{"className":10440},[1131],[1133,10442,10443],{"xmlns":1135},[1137,10444,10445,10465],{},[1140,10446,10447,10449,10451,10453,10455,10457,10459],{},[1146,10448,1148],{},[1154,10450,1652],{},[1154,10452,2677],{"stretchy":1674},[1150,10454,1152],{},[1154,10456,1157],{"separator":1156},[1150,10458,9783],{},[2922,10460,10461,10463],{},[1154,10462,2683],{"stretchy":1674},[1146,10464,4791],{},[1189,10466,10467],{"encoding":1191},"x = (1, 0.5)^T",[1124,10469,10471,10489],{"className":10470,"ariaHidden":1156},[1196],[1124,10472,10474,10477,10480,10483,10486],{"className":10473},[1200],[1124,10475],{"className":10476,"style":3124},[1204],[1124,10478,1148],{"className":10479},[1209,1213],[1124,10481],{"className":10482,"style":1774},[1271],[1124,10484,1652],{"className":10485},[1778],[1124,10487],{"className":10488,"style":1774},[1271],[1124,10490,10492,10496,10499,10502,10505,10508,10511],{"className":10491},[1200],[1124,10493],{"className":10494,"style":10495},[1204],"height:1.0913em;vertical-align:-0.25em;",[1124,10497,2677],{"className":10498},[1795],[1124,10500,1152],{"className":10501},[1209],[1124,10503,1157],{"className":10504},[1267],[1124,10506],{"className":10507,"style":1272},[1271],[1124,10509,9783],{"className":10510},[1209],[1124,10512,10514,10517],{"className":10513},[2211],[1124,10515,2683],{"className":10516},[2211],[1124,10518,10520],{"className":10519},[1217],[1124,10521,10523],{"className":10522},[1221],[1124,10524,10526],{"className":10525},[1226],[1124,10527,10530],{"className":10528,"style":10529},[1230],"height:0.8413em;",[1124,10531,10532,10535],{"style":3905},[1124,10533],{"className":10534,"style":1239},[1238],[1124,10536,10538],{"className":10537},[1243,1244,1245,1246],[1124,10539,4791],{"className":10540,"style":5104},[1209,1213,1246],[2745,10542],{},[1101,10544,10545],{},[1107,10546,10547],{},"第一步：计算隐藏层",[1101,10549,10550],{},[1124,10551,10553,10744],{"className":10552},[1127],[1124,10554,10556],{"className":10555},[1131],[1133,10557,10558],{"xmlns":1135},[1137,10559,10560,10741],{},[1140,10561,10562,10568,10570,10576,10578,10580,10582,10588,10590,10643,10645,10673,10675,10713,10715],{},[2922,10563,10564,10566],{},[1146,10565,2680],{},[1150,10567,1152],{},[1154,10569,1652],{},[2922,10571,10572,10574],{},[1146,10573,1439],{},[1150,10575,1152],{},[1154,10577,2325],{},[1146,10579,1148],{},[1154,10581,2330],{},[2922,10583,10584,10586],{},[1146,10585,2230],{},[1150,10587,1152],{},[1154,10589,1652],{},[1140,10591,10592,10594,10641],{},[1154,10593,2677],{"fence":1156},[1659,10595,10596,10619],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},[1665,10597,10598],{},[1668,10599,10600],{},[1671,10601,10602],{"scriptlevel":1673,"displaystyle":1674},[1140,10603,10604,10606,10609,10611,10613,10615,10617],{},[1150,10605,9776],{},[1154,10607,10608],{},"×",[1150,10610,1152],{},[1154,10612,2330],{},[1150,10614,9783],{},[1154,10616,10608],{},[1150,10618,9783],{},[1665,10620,10621],{},[1668,10622,10623],{},[1671,10624,10625],{"scriptlevel":1673,"displaystyle":1674},[1140,10626,10627,10629,10631,10633,10635,10637,10639],{},[1150,10628,9792],{},[1154,10630,10608],{},[1150,10632,1152],{},[1154,10634,2330],{},[1150,10636,9799],{},[1154,10638,10608],{},[1150,10640,9783],{},[1154,10642,2683],{"fence":1156},[1154,10644,2330],{},[1140,10646,10647,10649,10671],{},[1154,10648,2677],{"fence":1156},[1659,10650,10651,10659],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},[1665,10652,10653],{},[1668,10654,10655],{},[1671,10656,10657],{"scriptlevel":1673,"displaystyle":1674},[1150,10658,9829],{},[1665,10660,10661],{},[1668,10662,10663],{},[1671,10664,10665],{"scriptlevel":1673,"displaystyle":1674},[1140,10666,10667,10669],{},[1154,10668,2235],{},[1150,10670,9829],{},[1154,10672,2683],{"fence":1156},[1154,10674,1652],{},[1140,10676,10677,10679,10711],{},[1154,10678,2677],{"fence":1156},[1659,10680,10681,10696],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},[1665,10682,10683],{},[1668,10684,10685],{},[1671,10686,10687],{"scriptlevel":1673,"displaystyle":1674},[1140,10688,10689,10692,10694],{},[1150,10690,10691],{},"0.55",[1154,10693,2330],{},[1150,10695,9829],{},[1665,10697,10698],{},[1668,10699,10700],{},[1671,10701,10702],{"scriptlevel":1673,"displaystyle":1674},[1140,10703,10704,10707,10709],{},[1150,10705,10706],{},"0.50",[1154,10708,2235],{},[1150,10710,9829],{},[1154,10712,2683],{"fence":1156},[1154,10714,1652],{},[1140,10716,10717,10719,10739],{},[1154,10718,2677],{"fence":1156},[1659,10720,10721,10730],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},[1665,10722,10723],{},[1668,10724,10725],{},[1671,10726,10727],{"scriptlevel":1673,"displaystyle":1674},[1150,10728,10729],{},"0.65",[1665,10731,10732],{},[1668,10733,10734],{},[1671,10735,10736],{"scriptlevel":1673,"displaystyle":1674},[1150,10737,10738],{},"0.40",[1154,10740,2683],{"fence":1156},[1189,10742,10743],{"encoding":1191},"z^1 = w^1 \\cdot x + b^1 = \\begin{pmatrix} 0.3\\times1 + 0.5\\times0.5 \\\\ 0.4\\times1 + 0.2\\times0.5 \\end{pmatrix} + \\begin{pmatrix} 0.1 \\\\ -0.1 \\end{pmatrix} = \\begin{pmatrix} 0.55 + 0.1 \\\\ 0.50 - 0.1 \\end{pmatrix} = \\begin{pmatrix} 0.65 \\\\ 0.40 \\end{pmatrix}",[1124,10745,10747,10791,10835,10853,10897,11050,11134,11239],{"className":10746,"ariaHidden":1156},[1196],[1124,10748,10750,10753,10782,10785,10788],{"className":10749},[1200],[1124,10751],{"className":10752,"style":4598},[1204],[1124,10754,10756,10759],{"className":10755},[1209],[1124,10757,2680],{"className":10758,"style":2707},[1209,1213],[1124,10760,10762],{"className":10761},[1217],[1124,10763,10765],{"className":10764},[1221],[1124,10766,10768],{"className":10767},[1226],[1124,10769,10771],{"className":10770,"style":4598},[1230],[1124,10772,10773,10776],{"style":3905},[1124,10774],{"className":10775,"style":1239},[1238],[1124,10777,10779],{"className":10778},[1243,1244,1245,1246],[1124,10780,1152],{"className":10781},[1209,1246],[1124,10783],{"className":10784,"style":1774},[1271],[1124,10786,1652],{"className":10787},[1778],[1124,10789],{"className":10790,"style":1774},[1271],[1124,10792,10794,10797,10826,10829,10832],{"className":10793},[1200],[1124,10795],{"className":10796,"style":4598},[1204],[1124,10798,10800,10803],{"className":10799},[1209],[1124,10801,1439],{"className":10802,"style":1480},[1209,1213],[1124,10804,10806],{"className":10805},[1217],[1124,10807,10809],{"className":10808},[1221],[1124,10810,10812],{"className":10811},[1226],[1124,10813,10815],{"className":10814,"style":4598},[1230],[1124,10816,10817,10820],{"style":3905},[1124,10818],{"className":10819,"style":1239},[1238],[1124,10821,10823],{"className":10822},[1243,1244,1245,1246],[1124,10824,1152],{"className":10825},[1209,1246],[1124,10827],{"className":10828,"style":2500},[1271],[1124,10830,2325],{"className":10831},[2504],[1124,10833],{"className":10834,"style":2500},[1271],[1124,10836,10838,10841,10844,10847,10850],{"className":10837},[1200],[1124,10839],{"className":10840,"style":2858},[1204],[1124,10842,1148],{"className":10843},[1209,1213],[1124,10845],{"className":10846,"style":2500},[1271],[1124,10848,2330],{"className":10849},[2504],[1124,10851],{"className":10852,"style":2500},[1271],[1124,10854,10856,10859,10888,10891,10894],{"className":10855},[1200],[1124,10857],{"className":10858,"style":4598},[1204],[1124,10860,10862,10865],{"className":10861},[1209],[1124,10863,2230],{"className":10864},[1209,1213],[1124,10866,10868],{"className":10867},[1217],[1124,10869,10871],{"className":10870},[1221],[1124,10872,10874],{"className":10873},[1226],[1124,10875,10877],{"className":10876,"style":4598},[1230],[1124,10878,10879,10882],{"style":3905},[1124,10880],{"className":10881,"style":1239},[1238],[1124,10883,10885],{"className":10884},[1243,1244,1245,1246],[1124,10886,1152],{"className":10887},[1209,1246],[1124,10889],{"className":10890,"style":1774},[1271],[1124,10892,1652],{"className":10893},[1778],[1124,10895],{"className":10896,"style":1774},[1271],[1124,10898,10900,10903,11041,11044,11047],{"className":10899},[1200],[1124,10901],{"className":10902,"style":9900},[1204],[1124,10904,10906,10912,11035],{"className":10905},[1368],[1124,10907,10909],{"className":10908,"style":1797},[1795,1796],[1124,10910,2677],{"className":10911},[1801,1245],[1124,10913,10915],{"className":10914},[1209],[1124,10916,10918],{"className":10917},[1659],[1124,10919,10921],{"className":10920},[9919],[1124,10922,10924,11027],{"className":10923},[1221,1222],[1124,10925,10927,11024],{"className":10926},[1226],[1124,10928,10930,10977],{"className":10929,"style":9929},[1230],[1124,10931,10932,10935],{"style":9932},[1124,10933],{"className":10934,"style":2998},[1238],[1124,10936,10938,10941,10944,10947,10950,10953,10956,10959,10962,10965,10968,10971,10974],{"className":10937},[1209],[1124,10939,9776],{"className":10940},[1209],[1124,10942],{"className":10943,"style":2500},[1271],[1124,10945,10608],{"className":10946},[2504],[1124,10948],{"className":10949,"style":2500},[1271],[1124,10951,1152],{"className":10952},[1209],[1124,10954],{"className":10955,"style":2500},[1271],[1124,10957,2330],{"className":10958},[2504],[1124,10960],{"className":10961,"style":2500},[1271],[1124,10963,9783],{"className":10964},[1209],[1124,10966],{"className":10967,"style":2500},[1271],[1124,10969,10608],{"className":10970},[2504],[1124,10972],{"className":10973,"style":2500},[1271],[1124,10975,9783],{"className":10976},[1209],[1124,10978,10979,10982],{"style":9944},[1124,10980],{"className":10981,"style":2998},[1238],[1124,10983,10985,10988,10991,10994,10997,11000,11003,11006,11009,11012,11015,11018,11021],{"className":10984},[1209],[1124,10986,9792],{"className":10987},[1209],[1124,10989],{"className":10990,"style":2500},[1271],[1124,10992,10608],{"className":10993},[2504],[1124,10995],{"className":10996,"style":2500},[1271],[1124,10998,1152],{"className":10999},[1209],[1124,11001],{"className":11002,"style":2500},[1271],[1124,11004,2330],{"className":11005},[2504],[1124,11007],{"className":11008,"style":2500},[1271],[1124,11010,9799],{"className":11011},[1209],[1124,11013],{"className":11014,"style":2500},[1271],[1124,11016,10608],{"className":11017},[2504],[1124,11019],{"className":11020,"style":2500},[1271],[1124,11022,9783],{"className":11023},[1209],[1124,11025,1254],{"className":11026},[1253],[1124,11028,11030],{"className":11029},[1226],[1124,11031,11033],{"className":11032,"style":9963},[1230],[1124,11034],{},[1124,11036,11038],{"className":11037,"style":1797},[2211,1796],[1124,11039,2683],{"className":11040},[1801,1245],[1124,11042],{"className":11043,"style":2500},[1271],[1124,11045,2330],{"className":11046},[2504],[1124,11048],{"className":11049,"style":2500},[1271],[1124,11051,11053,11056,11125,11128,11131],{"className":11052},[1200],[1124,11054],{"className":11055,"style":9900},[1204],[1124,11057,11059,11065,11119],{"className":11058},[1368],[1124,11060,11062],{"className":11061,"style":1797},[1795,1796],[1124,11063,2677],{"className":11064},[1801,1245],[1124,11066,11068],{"className":11067},[1209],[1124,11069,11071],{"className":11070},[1659],[1124,11072,11074],{"className":11073},[9919],[1124,11075,11077,11111],{"className":11076},[1221,1222],[1124,11078,11080,11108],{"className":11079},[1226],[1124,11081,11083,11094],{"className":11082,"style":9929},[1230],[1124,11084,11085,11088],{"style":9932},[1124,11086],{"className":11087,"style":2998},[1238],[1124,11089,11091],{"className":11090},[1209],[1124,11092,9829],{"className":11093},[1209],[1124,11095,11096,11099],{"style":9944},[1124,11097],{"className":11098,"style":2998},[1238],[1124,11100,11102,11105],{"className":11101},[1209],[1124,11103,2235],{"className":11104},[1209],[1124,11106,9829],{"className":11107},[1209],[1124,11109,1254],{"className":11110},[1253],[1124,11112,11114],{"className":11113},[1226],[1124,11115,11117],{"className":11116,"style":9963},[1230],[1124,11118],{},[1124,11120,11122],{"className":11121,"style":1797},[2211,1796],[1124,11123,2683],{"className":11124},[1801,1245],[1124,11126],{"className":11127,"style":1774},[1271],[1124,11129,1652],{"className":11130},[1778],[1124,11132],{"className":11133,"style":1774},[1271],[1124,11135,11137,11140,11230,11233,11236],{"className":11136},[1200],[1124,11138],{"className":11139,"style":9900},[1204],[1124,11141,11143,11149,11224],{"className":11142},[1368],[1124,11144,11146],{"className":11145,"style":1797},[1795,1796],[1124,11147,2677],{"className":11148},[1801,1245],[1124,11150,11152],{"className":11151},[1209],[1124,11153,11155],{"className":11154},[1659],[1124,11156,11158],{"className":11157},[9919],[1124,11159,11161,11216],{"className":11160},[1221,1222],[1124,11162,11164,11213],{"className":11163},[1226],[1124,11165,11167,11190],{"className":11166,"style":9929},[1230],[1124,11168,11169,11172],{"style":9932},[1124,11170],{"className":11171,"style":2998},[1238],[1124,11173,11175,11178,11181,11184,11187],{"className":11174},[1209],[1124,11176,10691],{"className":11177},[1209],[1124,11179],{"className":11180,"style":2500},[1271],[1124,11182,2330],{"className":11183},[2504],[1124,11185],{"className":11186,"style":2500},[1271],[1124,11188,9829],{"className":11189},[1209],[1124,11191,11192,11195],{"style":9944},[1124,11193],{"className":11194,"style":2998},[1238],[1124,11196,11198,11201,11204,11207,11210],{"className":11197},[1209],[1124,11199,10706],{"className":11200},[1209],[1124,11202],{"className":11203,"style":2500},[1271],[1124,11205,2235],{"className":11206},[2504],[1124,11208],{"className":11209,"style":2500},[1271],[1124,11211,9829],{"className":11212},[1209],[1124,11214,1254],{"className":11215},[1253],[1124,11217,11219],{"className":11218},[1226],[1124,11220,11222],{"className":11221,"style":9963},[1230],[1124,11223],{},[1124,11225,11227],{"className":11226,"style":1797},[2211,1796],[1124,11228,2683],{"className":11229},[1801,1245],[1124,11231],{"className":11232,"style":1774},[1271],[1124,11234,1652],{"className":11235},[1778],[1124,11237],{"className":11238,"style":1774},[1271],[1124,11240,11242,11245],{"className":11241},[1200],[1124,11243],{"className":11244,"style":9900},[1204],[1124,11246,11248,11254,11305],{"className":11247},[1368],[1124,11249,11251],{"className":11250,"style":1797},[1795,1796],[1124,11252,2677],{"className":11253},[1801,1245],[1124,11255,11257],{"className":11256},[1209],[1124,11258,11260],{"className":11259},[1659],[1124,11261,11263],{"className":11262},[9919],[1124,11264,11266,11297],{"className":11265},[1221,1222],[1124,11267,11269,11294],{"className":11268},[1226],[1124,11270,11272,11283],{"className":11271,"style":9929},[1230],[1124,11273,11274,11277],{"style":9932},[1124,11275],{"className":11276,"style":2998},[1238],[1124,11278,11280],{"className":11279},[1209],[1124,11281,10729],{"className":11282},[1209],[1124,11284,11285,11288],{"style":9944},[1124,11286],{"className":11287,"style":2998},[1238],[1124,11289,11291],{"className":11290},[1209],[1124,11292,10738],{"className":11293},[1209],[1124,11295,1254],{"className":11296},[1253],[1124,11298,11300],{"className":11299},[1226],[1124,11301,11303],{"className":11302,"style":9963},[1230],[1124,11304],{},[1124,11306,11308],{"className":11307,"style":1797},[2211,1796],[1124,11309,2683],{"className":11310},[1801,1245],[1101,11312,11313],{},[1124,11314,11316,11418],{"className":11315},[1127],[1124,11317,11319],{"className":11318},[1131],[1133,11320,11321],{"xmlns":1135},[1137,11322,11323,11415],{},[1140,11324,11325,11331,11333,11335,11337,11343,11345,11347,11387,11389],{},[2922,11326,11327,11329],{},[1146,11328,4370],{},[1150,11330,1152],{},[1154,11332,1652],{},[1146,11334,2674],{},[1154,11336,2677],{"stretchy":1674},[2922,11338,11339,11341],{},[1146,11340,2680],{},[1150,11342,1152],{},[1154,11344,2683],{"stretchy":1674},[1154,11346,1652],{},[1140,11348,11349,11351,11385],{},[1154,11350,2677],{"fence":1156},[1659,11352,11353,11369],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},[1665,11354,11355],{},[1668,11356,11357],{},[1671,11358,11359],{"scriptlevel":1673,"displaystyle":1674},[1140,11360,11361,11363,11365,11367],{},[1146,11362,2674],{},[1154,11364,2677],{"stretchy":1674},[1150,11366,10729],{},[1154,11368,2683],{"stretchy":1674},[1665,11370,11371],{},[1668,11372,11373],{},[1671,11374,11375],{"scriptlevel":1673,"displaystyle":1674},[1140,11376,11377,11379,11381,11383],{},[1146,11378,2674],{},[1154,11380,2677],{"stretchy":1674},[1150,11382,10738],{},[1154,11384,2683],{"stretchy":1674},[1154,11386,2683],{"fence":1156},[1154,11388,1652],{},[1140,11390,11391,11393,11413],{},[1154,11392,2677],{"fence":1156},[1659,11394,11395,11404],{"rowspacing":9766,"columnalign":9820,"columnspacing":1663},[1665,11396,11397],{},[1668,11398,11399],{},[1671,11400,11401],{"scriptlevel":1673,"displaystyle":1674},[1150,11402,11403],{},"0.657",[1665,11405,11406],{},[1668,11407,11408],{},[1671,11409,11410],{"scriptlevel":1673,"displaystyle":1674},[1150,11411,11412],{},"0.599",[1154,11414,2683],{"fence":1156},[1189,11416,11417],{"encoding":1191},"a^1 = \\sigma(z^1) = \\begin{pmatrix} \\sigma(0.65) \\\\ \\sigma(0.40) \\end{pmatrix} = \\begin{pmatrix} 0.657 \\\\ 0.599 \\end{pmatrix}",[1124,11419,11421,11465,11518,11617],{"className":11420,"ariaHidden":1156},[1196],[1124,11422,11424,11427,11456,11459,11462],{"className":11423},[1200],[1124,11425],{"className":11426,"style":4598},[1204],[1124,11428,11430,11433],{"className":11429},[1209],[1124,11431,4370],{"className":11432},[1209,1213],[1124,11434,11436],{"className":11435},[1217],[1124,11437,11439],{"className":11438},[1221],[1124,11440,11442],{"className":11441},[1226],[1124,11443,11445],{"className":11444,"style":4598},[1230],[1124,11446,11447,11450],{"style":3905},[1124,11448],{"className":11449,"style":1239},[1238],[1124,11451,11453],{"className":11452},[1243,1244,1245,1246],[1124,11454,1152],{"className":11455},[1209,1246],[1124,11457],{"className":11458,"style":1774},[1271],[1124,11460,1652],{"className":11461},[1778],[1124,11463],{"className":11464,"style":1774},[1271],[1124,11466,11468,11471,11474,11477,11506,11509,11512,11515],{"className":11467},[1200],[1124,11469],{"className":11470,"style":4576},[1204],[1124,11472,2674],{"className":11473,"style":2700},[1209,1213],[1124,11475,2677],{"className":11476},[1795],[1124,11478,11480,11483],{"className":11479},[1209],[1124,11481,2680],{"className":11482,"style":2707},[1209,1213],[1124,11484,11486],{"className":11485},[1217],[1124,11487,11489],{"className":11488},[1221],[1124,11490,11492],{"className":11491},[1226],[1124,11493,11495],{"className":11494,"style":4598},[1230],[1124,11496,11497,11500],{"style":3905},[1124,11498],{"className":11499,"style":1239},[1238],[1124,11501,11503],{"className":11502},[1243,1244,1245,1246],[1124,11504,1152],{"className":11505},[1209,1246],[1124,11507,2683],{"className":11508},[2211],[1124,11510],{"className":11511,"style":1774},[1271],[1124,11513,1652],{"className":11514},[1778],[1124,11516],{"className":11517,"style":1774},[1271],[1124,11519,11521,11524,11608,11611,11614],{"className":11520},[1200],[1124,11522],{"className":11523,"style":9900},[1204],[1124,11525,11527,11533,11602],{"className":11526},[1368],[1124,11528,11530],{"className":11529,"style":1797},[1795,1796],[1124,11531,2677],{"className":11532},[1801,1245],[1124,11534,11536],{"className":11535},[1209],[1124,11537,11539],{"className":11538},[1659],[1124,11540,11542],{"className":11541},[9919],[1124,11543,11545,11594],{"className":11544},[1221,1222],[1124,11546,11548,11591],{"className":11547},[1226],[1124,11549,11551,11571],{"className":11550,"style":9929},[1230],[1124,11552,11553,11556],{"style":9932},[1124,11554],{"className":11555,"style":2998},[1238],[1124,11557,11559,11562,11565,11568],{"className":11558},[1209],[1124,11560,2674],{"className":11561,"style":2700},[1209,1213],[1124,11563,2677],{"className":11564},[1795],[1124,11566,10729],{"className":11567},[1209],[1124,11569,2683],{"className":11570},[2211],[1124,11572,11573,11576],{"style":9944},[1124,11574],{"className":11575,"style":2998},[1238],[1124,11577,11579,11582,11585,11588],{"className":11578},[1209],[1124,11580,2674],{"className":11581,"style":2700},[1209,1213],[1124,11583,2677],{"className":11584},[1795],[1124,11586,10738],{"className":11587},[1209],[1124,11589,2683],{"className":11590},[2211],[1124,11592,1254],{"className":11593},[1253],[1124,11595,11597],{"className":11596},[1226],[1124,11598,11600],{"className":11599,"style":9963},[1230],[1124,11601],{},[1124,11603,11605],{"className":11604,"style":1797},[2211,1796],[1124,11606,2683],{"className":11607},[1801,1245],[1124,11609],{"className":11610,"style":1774},[1271],[1124,11612,1652],{"className":11613},[1778],[1124,11615],{"className":11616,"style":1774},[1271],[1124,11618,11620,11623],{"className":11619},[1200],[1124,11621],{"className":11622,"style":9900},[1204],[1124,11624,11626,11632,11683],{"className":11625},[1368],[1124,11627,11629],{"className":11628,"style":1797},[1795,1796],[1124,11630,2677],{"className":11631},[1801,1245],[1124,11633,11635],{"className":11634},[1209],[1124,11636,11638],{"className":11637},[1659],[1124,11639,11641],{"className":11640},[9919],[1124,11642,11644,11675],{"className":11643},[1221,1222],[1124,11645,11647,11672],{"className":11646},[1226],[1124,11648,11650,11661],{"className":11649,"style":9929},[1230],[1124,11651,11652,11655],{"style":9932},[1124,11653],{"className":11654,"style":2998},[1238],[1124,11656,11658],{"className":11657},[1209],[1124,11659,11403],{"className":11660},[1209],[1124,11662,11663,11666],{"style":9944},[1124,11664],{"className":11665,"style":2998},[1238],[1124,11667,11669],{"className":11668},[1209],[1124,11670,11412],{"className":11671},[1209],[1124,11673,1254],{"className":11674},[1253],[1124,11676,11678],{"className":11677},[1226],[1124,11679,11681],{"className":11680,"style":9963},[1230],[1124,11682],{},[1124,11684,11686],{"className":11685,"style":1797},[2211,1796],[1124,11687,2683],{"className":11688},[1801,1245],[2745,11690],{},[1101,11692,11693],{},[1107,11694,11695],{},"第二步：计算输出层",[1101,11697,11698],{},[1124,11699,11701,11788],{"className":11700},[1127],[1124,11702,11704],{"className":11703},[1131],[1133,11705,11706],{"xmlns":1135},[1137,11707,11708,11785],{},[1140,11709,11710,11716,11718,11724,11726,11732,11734,11740,11742,11744,11746,11748,11750,11752,11754,11756,11758,11760,11762,11764,11766,11768,11771,11773,11776,11778,11780,11782],{},[2922,11711,11712,11714],{},[1146,11713,2680],{},[1150,11715,1164],{},[1154,11717,1652],{},[2922,11719,11720,11722],{},[1146,11721,1439],{},[1150,11723,1164],{},[1154,11725,2325],{},[2922,11727,11728,11730],{},[1146,11729,4370],{},[1150,11731,1152],{},[1154,11733,2330],{},[2922,11735,11736,11738],{},[1146,11737,2230],{},[1150,11739,1164],{},[1154,11741,1652],{},[1150,11743,10186],{},[1154,11745,10608],{},[1150,11747,11403],{},[1154,11749,2330],{},[1150,11751,10193],{},[1154,11753,10608],{},[1150,11755,11412],{},[1154,11757,2330],{},[1154,11759,2677],{"stretchy":1674},[1154,11761,2235],{},[1150,11763,9799],{},[1154,11765,2683],{"stretchy":1674},[1154,11767,1652],{},[1150,11769,11770],{},"0.394",[1154,11772,2330],{},[1150,11774,11775],{},"0.419",[1154,11777,2235],{},[1150,11779,9799],{},[1154,11781,1652],{},[1150,11783,11784],{},"0.613",[1189,11786,11787],{"encoding":1191},"z^2 = w^2 \\cdot a^1 + b^2 = 0.6\\times0.657 + 0.7\\times0.599 + (-0.2) = 0.394 + 0.419 - 0.2 = 0.613",[1124,11789,11791,11835,11879,11923,11967,11985,12003,12021,12039,12066,12084,12102,12120],{"className":11790,"ariaHidden":1156},[1196],[1124,11792,11794,11797,11826,11829,11832],{"className":11793},[1200],[1124,11795],{"className":11796,"style":4598},[1204],[1124,11798,11800,11803],{"className":11799},[1209],[1124,11801,2680],{"className":11802,"style":2707},[1209,1213],[1124,11804,11806],{"className":11805},[1217],[1124,11807,11809],{"className":11808},[1221],[1124,11810,11812],{"className":11811},[1226],[1124,11813,11815],{"className":11814,"style":4598},[1230],[1124,11816,11817,11820],{"style":3905},[1124,11818],{"className":11819,"style":1239},[1238],[1124,11821,11823],{"className":11822},[1243,1244,1245,1246],[1124,11824,1164],{"className":11825},[1209,1246],[1124,11827],{"className":11828,"style":1774},[1271],[1124,11830,1652],{"className":11831},[1778],[1124,11833],{"className":11834,"style":1774},[1271],[1124,11836,11838,11841,11870,11873,11876],{"className":11837},[1200],[1124,11839],{"className":11840,"style":4598},[1204],[1124,11842,11844,11847],{"className":11843},[1209],[1124,11845,1439],{"className":11846,"style":1480},[1209,1213],[1124,11848,11850],{"className":11849},[1217],[1124,11851,11853],{"className":11852},[1221],[1124,11854,11856],{"className":11855},[1226],[1124,11857,11859],{"className":11858,"style":4598},[1230],[1124,11860,11861,11864],{"style":3905},[1124,11862],{"className":11863,"style":1239},[1238],[1124,11865,11867],{"className":11866},[1243,1244,1245,1246],[1124,11868,1164],{"className":11869},[1209,1246],[1124,11871],{"className":11872,"style":2500},[1271],[1124,11874,2325],{"className":11875},[2504],[1124,11877],{"className":11878,"style":2500},[1271],[1124,11880,11882,11885,11914,11917,11920],{"className":11881},[1200],[1124,11883],{"className":11884,"style":8984},[1204],[1124,11886,11888,11891],{"className":11887},[1209],[1124,11889,4370],{"className":11890},[1209,1213],[1124,11892,11894],{"className":11893},[1217],[1124,11895,11897],{"className":11896},[1221],[1124,11898,11900],{"className":11899},[1226],[1124,11901,11903],{"className":11902,"style":4598},[1230],[1124,11904,11905,11908],{"style":3905},[1124,11906],{"className":11907,"style":1239},[1238],[1124,11909,11911],{"className":11910},[1243,1244,1245,1246],[1124,11912,1152],{"className":11913},[1209,1246],[1124,11915],{"className":11916,"style":2500},[1271],[1124,11918,2330],{"className":11919},[2504],[1124,11921],{"className":11922,"style":2500},[1271],[1124,11924,11926,11929,11958,11961,11964],{"className":11925},[1200],[1124,11927],{"className":11928,"style":4598},[1204],[1124,11930,11932,11935],{"className":11931},[1209],[1124,11933,2230],{"className":11934},[1209,1213],[1124,11936,11938],{"className":11937},[1217],[1124,11939,11941],{"className":11940},[1221],[1124,11942,11944],{"className":11943},[1226],[1124,11945,11947],{"className":11946,"style":4598},[1230],[1124,11948,11949,11952],{"style":3905},[1124,11950],{"className":11951,"style":1239},[1238],[1124,11953,11955],{"className":11954},[1243,1244,1245,1246],[1124,11956,1164],{"className":11957},[1209,1246],[1124,11959],{"className":11960,"style":1774},[1271],[1124,11962,1652],{"className":11963},[1778],[1124,11965],{"className":11966,"style":1774},[1271],[1124,11968,11970,11973,11976,11979,11982],{"className":11969},[1200],[1124,11971],{"className":11972,"style":10423},[1204],[1124,11974,10186],{"className":11975},[1209],[1124,11977],{"className":11978,"style":2500},[1271],[1124,11980,10608],{"className":11981},[2504],[1124,11983],{"className":11984,"style":2500},[1271],[1124,11986,11988,11991,11994,11997,12000],{"className":11987},[1200],[1124,11989],{"className":11990,"style":10423},[1204],[1124,11992,11403],{"className":11993},[1209],[1124,11995],{"className":11996,"style":2500},[1271],[1124,11998,2330],{"className":11999},[2504],[1124,12001],{"className":12002,"style":2500},[1271],[1124,12004,12006,12009,12012,12015,12018],{"className":12005},[1200],[1124,12007],{"className":12008,"style":10423},[1204],[1124,12010,10193],{"className":12011},[1209],[1124,12013],{"className":12014,"style":2500},[1271],[1124,12016,10608],{"className":12017},[2504],[1124,12019],{"className":12020,"style":2500},[1271],[1124,12022,12024,12027,12030,12033,12036],{"className":12023},[1200],[1124,12025],{"className":12026,"style":10423},[1204],[1124,12028,11412],{"className":12029},[1209],[1124,12031],{"className":12032,"style":2500},[1271],[1124,12034,2330],{"className":12035},[2504],[1124,12037],{"className":12038,"style":2500},[1271],[1124,12040,12042,12045,12048,12051,12054,12057,12060,12063],{"className":12041},[1200],[1124,12043],{"className":12044,"style":2696},[1204],[1124,12046,2677],{"className":12047},[1795],[1124,12049,2235],{"className":12050},[1209],[1124,12052,9799],{"className":12053},[1209],[1124,12055,2683],{"className":12056},[2211],[1124,12058],{"className":12059,"style":1774},[1271],[1124,12061,1652],{"className":12062},[1778],[1124,12064],{"className":12065,"style":1774},[1271],[1124,12067,12069,12072,12075,12078,12081],{"className":12068},[1200],[1124,12070],{"className":12071,"style":10423},[1204],[1124,12073,11770],{"className":12074},[1209],[1124,12076],{"className":12077,"style":2500},[1271],[1124,12079,2330],{"className":12080},[2504],[1124,12082],{"className":12083,"style":2500},[1271],[1124,12085,12087,12090,12093,12096,12099],{"className":12086},[1200],[1124,12088],{"className":12089,"style":10423},[1204],[1124,12091,11775],{"className":12092},[1209],[1124,12094],{"className":12095,"style":2500},[1271],[1124,12097,2235],{"className":12098},[2504],[1124,12100],{"className":12101,"style":2500},[1271],[1124,12103,12105,12108,12111,12114,12117],{"className":12104},[1200],[1124,12106],{"className":12107,"style":3685},[1204],[1124,12109,9799],{"className":12110},[1209],[1124,12112],{"className":12113,"style":1774},[1271],[1124,12115,1652],{"className":12116},[1778],[1124,12118],{"className":12119,"style":1774},[1271],[1124,12121,12123,12126],{"className":12122},[1200],[1124,12124],{"className":12125,"style":3685},[1204],[1124,12127,11784],{"className":12128},[1209],[1101,12130,12131],{},[1124,12132,12134,12167],{"className":12133},[1127],[1124,12135,12137],{"className":12136},[1131],[1133,12138,12139],{"xmlns":1135},[1137,12140,12141,12164],{},[1140,12142,12143,12149,12151,12153,12155,12157,12159,12161],{},[2922,12144,12145,12147],{},[1146,12146,4370],{},[1150,12148,1164],{},[1154,12150,1652],{},[1146,12152,2674],{},[1154,12154,2677],{"stretchy":1674},[1150,12156,11784],{},[1154,12158,2683],{"stretchy":1674},[1154,12160,1652],{},[1150,12162,12163],{},"0.649",[1189,12165,12166],{"encoding":1191},"a^2 = \\sigma(0.613) = 0.649",[1124,12168,12170,12214,12241],{"className":12169,"ariaHidden":1156},[1196],[1124,12171,12173,12176,12205,12208,12211],{"className":12172},[1200],[1124,12174],{"className":12175,"style":4598},[1204],[1124,12177,12179,12182],{"className":12178},[1209],[1124,12180,4370],{"className":12181},[1209,1213],[1124,12183,12185],{"className":12184},[1217],[1124,12186,12188],{"className":12187},[1221],[1124,12189,12191],{"className":12190},[1226],[1124,12192,12194],{"className":12193,"style":4598},[1230],[1124,12195,12196,12199],{"style":3905},[1124,12197],{"className":12198,"style":1239},[1238],[1124,12200,12202],{"className":12201},[1243,1244,1245,1246],[1124,12203,1164],{"className":12204},[1209,1246],[1124,12206],{"className":12207,"style":1774},[1271],[1124,12209,1652],{"className":12210},[1778],[1124,12212],{"className":12213,"style":1774},[1271],[1124,12215,12217,12220,12223,12226,12229,12232,12235,12238],{"className":12216},[1200],[1124,12218],{"className":12219,"style":2696},[1204],[1124,12221,2674],{"className":12222,"style":2700},[1209,1213],[1124,12224,2677],{"className":12225},[1795],[1124,12227,11784],{"className":12228},[1209],[1124,12230,2683],{"className":12231},[2211],[1124,12233],{"className":12234,"style":1774},[1271],[1124,12236,1652],{"className":12237},[1778],[1124,12239],{"className":12240,"style":1774},[1271],[1124,12242,12244,12247],{"className":12243},[1200],[1124,12245],{"className":12246,"style":3685},[1204],[1124,12248,12163],{"className":12249},[1209],[2745,12251],{},[1101,12253,12254,12257,12258,12310,12311],{},[1107,12255,12256],{},"结果："," 输入 ",[1124,12259,12261,12283],{"className":12260},[1127],[1124,12262,12264],{"className":12263},[1131],[1133,12265,12266],{"xmlns":1135},[1137,12267,12268,12280],{},[1140,12269,12270,12272,12274,12276,12278],{},[1154,12271,2677],{"stretchy":1674},[1150,12273,1152],{},[1154,12275,1157],{"separator":1156},[1150,12277,9783],{},[1154,12279,2683],{"stretchy":1674},[1189,12281,12282],{"encoding":1191},"(1, 0.5)",[1124,12284,12286],{"className":12285,"ariaHidden":1156},[1196],[1124,12287,12289,12292,12295,12298,12301,12304,12307],{"className":12288},[1200],[1124,12290],{"className":12291,"style":2696},[1204],[1124,12293,2677],{"className":12294},[1795],[1124,12296,1152],{"className":12297},[1209],[1124,12299,1157],{"className":12300},[1267],[1124,12302],{"className":12303,"style":1272},[1271],[1124,12305,9783],{"className":12306},[1209],[1124,12308,2683],{"className":12309},[2211],"，网络输出 ",[1124,12312,12314,12336],{"className":12313},[1127],[1124,12315,12317],{"className":12316},[1131],[1133,12318,12319],{"xmlns":1135},[1137,12320,12321,12333],{},[1140,12322,12323],{},[8168,12324,12325],{"notation":8170},[1671,12326,12327],{"scriptlevel":1673,"displaystyle":1674},[1671,12328,12329],{"scriptlevel":1673,"displaystyle":1674},[1671,12330,12331],{"scriptlevel":1673,"displaystyle":1156},[1150,12332,12163],{},[1189,12334,12335],{"encoding":1191},"\\boxed{0.649}",[1124,12337,12339],{"className":12338,"ariaHidden":1156},[1196],[1124,12340,12342,12346],{"className":12341},[1200],[1124,12343],{"className":12344,"style":12345},[1204],"height:1.3244em;vertical-align:-0.34em;",[1124,12347,12349],{"className":12348},[1209],[1124,12350,12352,12391],{"className":12351},[1221,1222],[1124,12353,12355,12388],{"className":12354},[1226],[1124,12356,12359,12378],{"className":12357,"style":12358},[1230],"height:0.9844em;",[1124,12360,12362,12366],{"style":12361},"top:-3.3244em;",[1124,12363],{"className":12364,"style":12365},[1238],"height:3.3244em;",[1124,12367,12369],{"className":12368},[8257],[1124,12370,12372],{"className":12371},[1209],[1124,12373,12375],{"className":12374},[1209],[1124,12376,12163],{"className":12377},[1209],[1124,12379,12381,12384],{"style":12380},"top:-2.9844em;",[1124,12382],{"className":12383,"style":12365},[1238],[1124,12385],{"className":12386,"style":12387},[8436,8437],"height:1.3244em;border-style:solid;border-width:0.04em;",[1124,12389,1254],{"className":12390},[1253],[1124,12392,12394],{"className":12393},[1226],[1124,12395,12398],{"className":12396,"style":12397},[1230],"height:0.34em;",[1124,12399],{},[1096,12401,12403],{"id":12402},"_22-反向传播-backward-propagation","2.2 反向传播 （Backward Propagation）",[7743,12405,12406],{"id":12406},"符号定义与矩阵表示",[1101,12408,12409],{},"为了精确描述反向传播，首先建立统一的符号体系。",[2616,12411,12412,12422],{},[2619,12413,12414],{},[2622,12415,12416,12419],{},[2625,12417,12418],{},"符号",[2625,12420,12421],{},"含义",[2635,12423,12424,12675,12825,12971,13118],{},[2622,12425,12426,12523],{},[2640,12427,12428],{},[1124,12429,12431,12455],{"className":12430},[1127],[1124,12432,12434],{"className":12433},[1131],[1133,12435,12436],{"xmlns":1135},[1137,12437,12438,12452],{},[1140,12439,12440],{},[5282,12441,12442,12444,12450],{},[1146,12443,1439],{},[1140,12445,12446,12448],{},[1146,12447,1693],{},[1146,12449,5278],{},[1146,12451,5657],{},[1189,12453,12454],{"encoding":1191},"w^l_{jk}",[1124,12456,12458],{"className":12457,"ariaHidden":1156},[1196],[1124,12459,12461,12465],{"className":12460},[1200],[1124,12462],{"className":12463,"style":12464},[1204],"height:1.2683em;vertical-align:-0.4192em;",[1124,12466,12468,12471],{"className":12467},[1209],[1124,12469,1439],{"className":12470,"style":1480},[1209,1213],[1124,12472,12474],{"className":12473},[1217],[1124,12475,12477,12514],{"className":12476},[1221,1222],[1124,12478,12480,12511],{"className":12479},[1226],[1124,12481,12483,12500],{"className":12482,"style":7649},[1230],[1124,12484,12485,12488],{"style":5411},[1124,12486],{"className":12487,"style":1239},[1238],[1124,12489,12491],{"className":12490},[1243,1244,1245,1246],[1124,12492,12494,12497],{"className":12493},[1209,1246],[1124,12495,1693],{"className":12496,"style":1929},[1209,1213,1246],[1124,12498,5278],{"className":12499,"style":5363},[1209,1213,1246],[1124,12501,12502,12505],{"style":3905},[1124,12503],{"className":12504,"style":1239},[1238],[1124,12506,12508],{"className":12507},[1243,1244,1245,1246],[1124,12509,5657],{"className":12510,"style":5740},[1209,1213,1246],[1124,12512,1254],{"className":12513},[1253],[1124,12515,12517],{"className":12516},[1226],[1124,12518,12521],{"className":12519,"style":12520},[1230],"height:0.4192em;",[1124,12522],{},[2640,12524,12525,12526,12587,12588,12616,12617,12587,12645,12674],{},"从第 ",[1124,12527,12529,12551],{"className":12528},[1127],[1124,12530,12532],{"className":12531},[1131],[1133,12533,12534],{"xmlns":1135},[1137,12535,12536,12548],{},[1140,12537,12538,12540,12542,12544,12546],{},[1154,12539,2677],{"stretchy":1674},[1146,12541,5657],{},[1154,12543,2235],{},[1150,12545,1152],{},[1154,12547,2683],{"stretchy":1674},[1189,12549,12550],{"encoding":1191},"(l-1)",[1124,12552,12554,12575],{"className":12553,"ariaHidden":1156},[1196],[1124,12555,12557,12560,12563,12566,12569,12572],{"className":12556},[1200],[1124,12558],{"className":12559,"style":2696},[1204],[1124,12561,2677],{"className":12562},[1795],[1124,12564,5657],{"className":12565,"style":5740},[1209,1213],[1124,12567],{"className":12568,"style":2500},[1271],[1124,12570,2235],{"className":12571},[2504],[1124,12573],{"className":12574,"style":2500},[1271],[1124,12576,12578,12581,12584],{"className":12577},[1200],[1124,12579],{"className":12580,"style":2696},[1204],[1124,12582,1152],{"className":12583},[1209],[1124,12585,2683],{"className":12586},[2211]," 层第 ",[1124,12589,12591,12604],{"className":12590},[1127],[1124,12592,12594],{"className":12593},[1131],[1133,12595,12596],{"xmlns":1135},[1137,12597,12598,12602],{},[1140,12599,12600],{},[1146,12601,5278],{},[1189,12603,5278],{"encoding":1191},[1124,12605,12607],{"className":12606,"ariaHidden":1156},[1196],[1124,12608,12610,12613],{"className":12609},[1200],[1124,12611],{"className":12612,"style":2250},[1204],[1124,12614,5278],{"className":12615,"style":5363},[1209,1213]," 个神经元到第 ",[1124,12618,12620,12633],{"className":12619},[1127],[1124,12621,12623],{"className":12622},[1131],[1133,12624,12625],{"xmlns":1135},[1137,12626,12627,12631],{},[1140,12628,12629],{},[1146,12630,5657],{},[1189,12632,5657],{"encoding":1191},[1124,12634,12636],{"className":12635,"ariaHidden":1156},[1196],[1124,12637,12639,12642],{"className":12638},[1200],[1124,12640],{"className":12641,"style":2250},[1204],[1124,12643,5657],{"className":12644,"style":5740},[1209,1213],[1124,12646,12648,12661],{"className":12647},[1127],[1124,12649,12651],{"className":12650},[1131],[1133,12652,12653],{"xmlns":1135},[1137,12654,12655,12659],{},[1140,12656,12657],{},[1146,12658,1693],{},[1189,12660,1693],{"encoding":1191},[1124,12662,12664],{"className":12663,"ariaHidden":1156},[1196],[1124,12665,12667,12671],{"className":12666},[1200],[1124,12668],{"className":12669,"style":12670},[1204],"height:0.854em;vertical-align:-0.1944em;",[1124,12672,1693],{"className":12673,"style":1929},[1209,1213]," 个神经元的权重",[2622,12676,12677,12765],{},[2640,12678,12679],{},[1124,12680,12682,12702],{"className":12681},[1127],[1124,12683,12685],{"className":12684},[1131],[1133,12686,12687],{"xmlns":1135},[1137,12688,12689,12699],{},[1140,12690,12691],{},[5282,12692,12693,12695,12697],{},[1146,12694,2230],{},[1146,12696,1693],{},[1146,12698,5657],{},[1189,12700,12701],{"encoding":1191},"b^l_j",[1124,12703,12705],{"className":12704,"ariaHidden":1156},[1196],[1124,12706,12708,12712],{"className":12707},[1200],[1124,12709],{"className":12710,"style":12711},[1204],"height:1.2439em;vertical-align:-0.3948em;",[1124,12713,12715,12718],{"className":12714},[1209],[1124,12716,2230],{"className":12717},[1209,1213],[1124,12719,12721],{"className":12720},[1217],[1124,12722,12724,12756],{"className":12723},[1221,1222],[1124,12725,12727,12753],{"className":12726},[1226],[1124,12728,12730,12742],{"className":12729,"style":7649},[1230],[1124,12731,12733,12736],{"style":12732},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[1124,12734],{"className":12735,"style":1239},[1238],[1124,12737,12739],{"className":12738},[1243,1244,1245,1246],[1124,12740,1693],{"className":12741,"style":1929},[1209,1213,1246],[1124,12743,12744,12747],{"style":3905},[1124,12745],{"className":12746,"style":1239},[1238],[1124,12748,12750],{"className":12749},[1243,1244,1245,1246],[1124,12751,5657],{"className":12752,"style":5740},[1209,1213,1246],[1124,12754,1254],{"className":12755},[1253],[1124,12757,12759],{"className":12758},[1226],[1124,12760,12763],{"className":12761,"style":12762},[1230],"height:0.3948em;",[1124,12764],{},[2640,12766,12767,12768,12587,12796,12824],{},"第 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个神经元的偏置",[2622,12826,12827,12912],{},[2640,12828,12829],{},[1124,12830,12832,12852],{"className":12831},[1127],[1124,12833,12835],{"className":12834},[1131],[1133,12836,12837],{"xmlns":1135},[1137,12838,12839,12849],{},[1140,12840,12841],{},[5282,12842,12843,12845,12847],{},[1146,12844,4370],{},[1146,12846,1693],{},[1146,12848,5657],{},[1189,12850,12851],{"encoding":1191},"a^l_j",[1124,12853,12855],{"className":12854,"ariaHidden":1156},[1196],[1124,12856,12858,12861],{"className":12857},[1200],[1124,12859],{"className":12860,"style":12711},[1204],[1124,12862,12864,12867],{"className":12863},[1209],[1124,12865,4370],{"className":12866},[1209,1213],[1124,12868,12870],{"className":12869},[1217],[1124,12871,12873,12904],{"className":12872},[1221,1222],[1124,12874,12876,12901],{"className":12875},[1226],[1124,12877,12879,12890],{"className":12878,"style":7649},[1230],[1124,12880,12881,12884],{"style":12732},[1124,12882],{"className":12883,"style":1239},[1238],[1124,12885,12887],{"className":12886},[1243,1244,1245,1246],[1124,12888,1693],{"className":12889,"style":1929},[1209,1213,1246],[1124,12891,12892,12895],{"style":3905},[1124,12893],{"className":12894,"style":1239},[1238],[1124,12896,12898],{"className":12897},[1243,1244,1245,1246],[1124,12899,5657],{"className":12900,"style":5740},[1209,1213,1246],[1124,12902,1254],{"className":12903},[1253],[1124,12905,12907],{"className":12906},[1226],[1124,12908,12910],{"className":12909,"style":12762},[1230],[1124,12911],{},[2640,12913,12767,12914,12587,12942,12970],{},[1124,12915,12917,12930],{"className":12916},[1127],[1124,12918,12920],{"className":12919},[1131],[1133,12921,12922],{"xmlns":1135},[1137,12923,12924,12928],{},[1140,12925,12926],{},[1146,12927,5657],{},[1189,12929,5657],{"encoding":1191},[1124,12931,12933],{"className":12932,"ariaHidden":1156},[1196],[1124,12934,12936,12939],{"className":12935},[1200],[1124,12937],{"className":12938,"style":2250},[1204],[1124,12940,5657],{"className":12941,"style":5740},[1209,1213],[1124,12943,12945,12958],{"className":12944},[1127],[1124,12946,12948],{"className":12947},[1131],[1133,12949,12950],{"xmlns":1135},[1137,12951,12952,12956],{},[1140,12953,12954],{},[1146,12955,1693],{},[1189,12957,1693],{"encoding":1191},[1124,12959,12961],{"className":12960,"ariaHidden":1156},[1196],[1124,12962,12964,12967],{"className":12963},[1200],[1124,12965],{"className":12966,"style":12670},[1204],[1124,12968,1693],{"className":12969,"style":1929},[1209,1213]," 个神经元的激活值",[2622,12972,12973,13059],{},[2640,12974,12975],{},[1124,12976,12978,12998],{"className":12977},[1127],[1124,12979,12981],{"className":12980},[1131],[1133,12982,12983],{"xmlns":1135},[1137,12984,12985,12995],{},[1140,12986,12987],{},[5282,12988,12989,12991,12993],{},[1146,12990,2680],{},[1146,12992,1693],{},[1146,12994,5657],{},[1189,12996,12997],{"encoding":1191},"z^l_j",[1124,12999,13001],{"className":13000,"ariaHidden":1156},[1196],[1124,13002,13004,13007],{"className":13003},[1200],[1124,13005],{"className":13006,"style":12711},[1204],[1124,13008,13010,13013],{"className":13009},[1209],[1124,13011,2680],{"className":13012,"style":2707},[1209,1213],[1124,13014,13016],{"className":13015},[1217],[1124,13017,13019,13051],{"className":13018},[1221,1222],[1124,13020,13022,13048],{"className":13021},[1226],[1124,13023,13025,13037],{"className":13024,"style":7649},[1230],[1124,13026,13028,13031],{"style":13027},"top:-2.4413em;margin-left:-0.044em;margin-right:0.05em;",[1124,13029],{"className":13030,"style":1239},[1238],[1124,13032,13034],{"className":13033},[1243,1244,1245,1246],[1124,13035,1693],{"className":13036,"style":1929},[1209,1213,1246],[1124,13038,13039,13042],{"style":3905},[1124,13040],{"className":13041,"style":1239},[1238],[1124,13043,13045],{"className":13044},[1243,1244,1245,1246],[1124,13046,5657],{"className":13047,"style":5740},[1209,1213,1246],[1124,13049,1254],{"className":13050},[1253],[1124,13052,13054],{"className":13053},[1226],[1124,13055,13057],{"className":13056,"style":12762},[1230],[1124,13058],{},[2640,13060,12767,13061,12587,13089,13117],{},[1124,13062,13064,13077],{"className":13063},[1127],[1124,13065,13067],{"className":13066},[1131],[1133,13068,13069],{"xmlns":1135},[1137,13070,13071,13075],{},[1140,13072,13073],{},[1146,13074,5657],{},[1189,13076,5657],{"encoding":1191},[1124,13078,13080],{"className":13079,"ariaHidden":1156},[1196],[1124,13081,13083,13086],{"className":13082},[1200],[1124,13084],{"className":13085,"style":2250},[1204],[1124,13087,5657],{"className":13088,"style":5740},[1209,1213],[1124,13090,13092,13105],{"className":13091},[1127],[1124,13093,13095],{"className":13094},[1131],[1133,13096,13097],{"xmlns":1135},[1137,13098,13099,13103],{},[1140,13100,13101],{},[1146,13102,1693],{},[1189,13104,1693],{"encoding":1191},[1124,13106,13108],{"className":13107,"ariaHidden":1156},[1196],[1124,13109,13111,13114],{"className":13110},[1200],[1124,13112],{"className":13113,"style":12670},[1204],[1124,13115,1693],{"className":13116,"style":1929},[1209,1213]," 个神经元的加权输入",[2622,13119,13120,13208],{},[2640,13121,13122],{},[1124,13123,13125,13146],{"className":13124},[1127],[1124,13126,13128],{"className":13127},[1131],[1133,13129,13130],{"xmlns":1135},[1137,13131,13132,13143],{},[1140,13133,13134],{},[5282,13135,13136,13139,13141],{},[1146,13137,13138],{},"δ",[1146,13140,1693],{},[1146,13142,5657],{},[1189,13144,13145],{"encoding":1191},"\\delta^l_j",[1124,13147,13149],{"className":13148,"ariaHidden":1156},[1196],[1124,13150,13152,13155],{"className":13151},[1200],[1124,13153],{"className":13154,"style":12711},[1204],[1124,13156,13158,13162],{"className":13157},[1209],[1124,13159,13138],{"className":13160,"style":13161},[1209,1213],"margin-right:0.0379em;",[1124,13163,13165],{"className":13164},[1217],[1124,13166,13168,13200],{"className":13167},[1221,1222],[1124,13169,13171,13197],{"className":13170},[1226],[1124,13172,13174,13186],{"className":13173,"style":7649},[1230],[1124,13175,13177,13180],{"style":13176},"top:-2.4413em;margin-left:-0.0379em;margin-right:0.05em;",[1124,13178],{"className":13179,"style":1239},[1238],[1124,13181,13183],{"className":13182},[1243,1244,1245,1246],[1124,13184,1693],{"className":13185,"style":1929},[1209,1213,1246],[1124,13187,13188,13191],{"style":3905},[1124,13189],{"className":13190,"style":1239},[1238],[1124,13192,13194],{"className":13193},[1243,1244,1245,1246],[1124,13195,5657],{"className":13196,"style":5740},[1209,1213,1246],[1124,13198,1254],{"className":13199},[1253],[1124,13201,13203],{"className":13202},[1226],[1124,13204,13206],{"className":13205,"style":12762},[1230],[1124,13207],{},[2640,13209,12767,13210,12587,13238,13266],{},[1124,13211,13213,13226],{"className":13212},[1127],[1124,13214,13216],{"className":13215},[1131],[1133,13217,13218],{"xmlns":1135},[1137,13219,13220,13224],{},[1140,13221,13222],{},[1146,13223,5657],{},[1189,13225,5657],{"encoding":1191},[1124,13227,13229],{"className":13228,"ariaHidden":1156},[1196],[1124,13230,13232,13235],{"className":13231},[1200],[1124,13233],{"className":13234,"style":2250},[1204],[1124,13236,5657],{"className":13237,"style":5740},[1209,1213],[1124,13239,13241,13254],{"className":13240},[1127],[1124,13242,13244],{"className":13243},[1131],[1133,13245,13246],{"xmlns":1135},[1137,13247,13248,13252],{},[1140,13249,13250],{},[1146,13251,1693],{},[1189,13253,1693],{"encoding":1191},[1124,13255,13257],{"className":13256,"ariaHidden":1156},[1196],[1124,13258,13260,13263],{"className":13259},[1200],[1124,13261],{"className":13262,"style":12670},[1204],[1124,13264,1693],{"className":13265,"style":1929},[1209,1213]," 个神经元的误差",[1101,13268,13269],{},[1107,13270,13271],{},"矩阵形式",[1101,13273,13274],{},"激活值的递推关系：",[1101,13276,13277],{},[1124,13278,13280,13334],{"className":13279},[1127],[1124,13281,13283],{"className":13282},[1131],[1133,13284,13285],{"xmlns":1135},[1137,13286,13287,13331],{},[1140,13288,13289,13295,13297,13299,13301,13307,13309,13321,13323,13329],{},[2922,13290,13291,13293],{},[1146,13292,4370],{},[1146,13294,5657],{},[1154,13296,1652],{},[1146,13298,2674],{},[1154,13300,2677],{"stretchy":1674},[2922,13302,13303,13305],{},[1146,13304,1439],{},[1146,13306,5657],{},[1154,13308,2325],{},[2922,13310,13311,13313],{},[1146,13312,4370],{},[1140,13314,13315,13317,13319],{},[1146,13316,5657],{},[1154,13318,2235],{},[1150,13320,1152],{},[1154,13322,2330],{},[2922,13324,13325,13327],{},[1146,13326,2230],{},[1146,13328,5657],{},[1154,13330,2683],{"stretchy":1674},[1189,13332,13333],{"encoding":1191},"a^l = \\sigma(w^l \\cdot a^{l-1} + b^l)",[1124,13335,13337,13381,13431,13484],{"className":13336,"ariaHidden":1156},[1196],[1124,13338,13340,13343,13372,13375,13378],{"className":13339},[1200],[1124,13341],{"className":13342,"style":7649},[1204],[1124,13344,13346,13349],{"className":13345},[1209],[1124,13347,4370],{"className":13348},[1209,1213],[1124,13350,13352],{"className":13351},[1217],[1124,13353,13355],{"className":13354},[1221],[1124,13356,13358],{"className":13357},[1226],[1124,13359,13361],{"className":13360,"style":7649},[1230],[1124,13362,13363,13366],{"style":3905},[1124,13364],{"className":13365,"style":1239},[1238],[1124,13367,13369],{"className":13368},[1243,1244,1245,1246],[1124,13370,5657],{"className":13371,"style":5740},[1209,1213,1246],[1124,13373],{"className":13374,"style":1774},[1271],[1124,13376,1652],{"className":13377},[1778],[1124,13379],{"className":13380,"style":1774},[1271],[1124,13382,13384,13387,13390,13393,13422,13425,13428],{"className":13383},[1200],[1124,13385],{"className":13386,"style":8111},[1204],[1124,13388,2674],{"className":13389,"style":2700},[1209,1213],[1124,13391,2677],{"className":13392},[1795],[1124,13394,13396,13399],{"className":13395},[1209],[1124,13397,1439],{"className":13398,"style":1480},[1209,1213],[1124,13400,13402],{"className":13401},[1217],[1124,13403,13405],{"className":13404},[1221],[1124,13406,13408],{"className":13407},[1226],[1124,13409,13411],{"className":13410,"style":7649},[1230],[1124,13412,13413,13416],{"style":3905},[1124,13414],{"className":13415,"style":1239},[1238],[1124,13417,13419],{"className":13418},[1243,1244,1245,1246],[1124,13420,5657],{"className":13421,"style":5740},[1209,1213,1246],[1124,13423],{"className":13424,"style":2500},[1271],[1124,13426,2325],{"className":13427},[2504],[1124,13429],{"className":13430,"style":2500},[1271],[1124,13432,13434,13437,13475,13478,13481],{"className":13433},[1200],[1124,13435],{"className":13436,"style":7933},[1204],[1124,13438,13440,13443],{"className":13439},[1209],[1124,13441,4370],{"className":13442},[1209,1213],[1124,13444,13446],{"className":13445},[1217],[1124,13447,13449],{"className":13448},[1221],[1124,13450,13452],{"className":13451},[1226],[1124,13453,13455],{"className":13454,"style":7649},[1230],[1124,13456,13457,13460],{"style":3905},[1124,13458],{"className":13459,"style":1239},[1238],[1124,13461,13463],{"className":13462},[1243,1244,1245,1246],[1124,13464,13466,13469,13472],{"className":13465},[1209,1246],[1124,13467,5657],{"className":13468,"style":5740},[1209,1213,1246],[1124,13470,2235],{"className":13471},[2504,1246],[1124,13473,1152],{"className":13474},[1209,1246],[1124,13476],{"className":13477,"style":2500},[1271],[1124,13479,2330],{"className":13480},[2504],[1124,13482],{"className":13483,"style":2500},[1271],[1124,13485,13487,13490,13519],{"className":13486},[1200],[1124,13488],{"className":13489,"style":8111},[1204],[1124,13491,13493,13496],{"className":13492},[1209],[1124,13494,2230],{"className":13495},[1209,1213],[1124,13497,13499],{"className":13498},[1217],[1124,13500,13502],{"className":13501},[1221],[1124,13503,13505],{"className":13504},[1226],[1124,13506,13508],{"className":13507,"style":7649},[1230],[1124,13509,13510,13513],{"style":3905},[1124,13511],{"className":13512,"style":1239},[1238],[1124,13514,13516],{"className":13515},[1243,1244,1245,1246],[1124,13517,5657],{"className":13518,"style":5740},[1209,1213,1246],[1124,13520,2683],{"className":13521},[2211],[1101,13523,13524],{},"定义加权输入（weighted input）：",[1101,13526,13527],{},[1124,13528,13530,13577],{"className":13529},[1127],[1124,13531,13533],{"className":13532},[1131],[1133,13534,13535],{"xmlns":1135},[1137,13536,13537,13575],{},[1140,13538,13539,13545,13547,13553,13555,13567,13569],{},[2922,13540,13541,13543],{},[1146,13542,2680],{},[1146,13544,5657],{},[1154,13546,1652],{},[2922,13548,13549,13551],{},[1146,13550,1439],{},[1146,13552,5657],{},[1154,13554,2325],{},[2922,13556,13557,13559],{},[1146,13558,4370],{},[1140,13560,13561,13563,13565],{},[1146,13562,5657],{},[1154,13564,2235],{},[1150,13566,1152],{},[1154,13568,2330],{},[2922,13570,13571,13573],{},[1146,13572,2230],{},[1146,13574,5657],{},[1189,13576,7835],{"encoding":1191},[1124,13578,13580,13624,13668,13721],{"className":13579,"ariaHidden":1156},[1196],[1124,13581,13583,13586,13615,13618,13621],{"className":13582},[1200],[1124,13584],{"className":13585,"style":7649},[1204],[1124,13587,13589,13592],{"className":13588},[1209],[1124,13590,2680],{"className":13591,"style":2707},[1209,1213],[1124,13593,13595],{"className":13594},[1217],[1124,13596,13598],{"className":13597},[1221],[1124,13599,13601],{"className":13600},[1226],[1124,13602,13604],{"className":13603,"style":7649},[1230],[1124,13605,13606,13609],{"style":3905},[1124,13607],{"className":13608,"style":1239},[1238],[1124,13610,13612],{"className":13611},[1243,1244,1245,1246],[1124,13613,5657],{"className":13614,"style":5740},[1209,1213,1246],[1124,13616],{"className":13617,"style":1774},[1271],[1124,13619,1652],{"className":13620},[1778],[1124,13622],{"className":13623,"style":1774},[1271],[1124,13625,13627,13630,13659,13662,13665],{"className":13626},[1200],[1124,13628],{"className":13629,"style":7649},[1204],[1124,13631,13633,13636],{"className":13632},[1209],[1124,13634,1439],{"className":13635,"style":1480},[1209,1213],[1124,13637,13639],{"className":13638},[1217],[1124,13640,13642],{"className":13641},[1221],[1124,13643,13645],{"className":13644},[1226],[1124,13646,13648],{"className":13647,"style":7649},[1230],[1124,13649,13650,13653],{"style":3905},[1124,13651],{"className":13652,"style":1239},[1238],[1124,13654,13656],{"className":13655},[1243,1244,1245,1246],[1124,13657,5657],{"className":13658,"style":5740},[1209,1213,1246],[1124,13660],{"className":13661,"style":2500},[1271],[1124,13663,2325],{"className":13664},[2504],[1124,13666],{"className":13667,"style":2500},[1271],[1124,13669,13671,13674,13712,13715,13718],{"className":13670},[1200],[1124,13672],{"className":13673,"style":7933},[1204],[1124,13675,13677,13680],{"className":13676},[1209],[1124,13678,4370],{"className":13679},[1209,1213],[1124,13681,13683],{"className":13682},[1217],[1124,13684,13686],{"className":13685},[1221],[1124,13687,13689],{"className":13688},[1226],[1124,13690,13692],{"className":13691,"style":7649},[1230],[1124,13693,13694,13697],{"style":3905},[1124,13695],{"className":13696,"style":1239},[1238],[1124,13698,13700],{"className":13699},[1243,1244,1245,1246],[1124,13701,13703,13706,13709],{"className":13702},[1209,1246],[1124,13704,5657],{"className":13705,"style":5740},[1209,1213,1246],[1124,13707,2235],{"className":13708},[2504,1246],[1124,13710,1152],{"className":13711},[1209,1246],[1124,13713],{"className":13714,"style":2500},[1271],[1124,13716,2330],{"className":13717},[2504],[1124,13719],{"className":13720,"style":2500},[1271],[1124,13722,13724,13727],{"className":13723},[1200],[1124,13725],{"className":13726,"style":7649},[1204],[1124,13728,13730,13733],{"className":13729},[1209],[1124,13731,2230],{"className":13732},[1209,1213],[1124,13734,13736],{"className":13735},[1217],[1124,13737,13739],{"className":13738},[1221],[1124,13740,13742],{"className":13741},[1226],[1124,13743,13745],{"className":13744,"style":7649},[1230],[1124,13746,13747,13750],{"style":3905},[1124,13748],{"className":13749,"style":1239},[1238],[1124,13751,13753],{"className":13752},[1243,1244,1245,1246],[1124,13754,5657],{"className":13755,"style":5740},[1209,1213,1246],[1101,13757,13758,13759,13884],{},"因此 ",[1124,13760,13762,13793],{"className":13761},[1127],[1124,13763,13765],{"className":13764},[1131],[1133,13766,13767],{"xmlns":1135},[1137,13768,13769,13791],{},[1140,13770,13771,13777,13779,13781,13783,13789],{},[2922,13772,13773,13775],{},[1146,13774,4370],{},[1146,13776,5657],{},[1154,13778,1652],{},[1146,13780,2674],{},[1154,13782,2677],{"stretchy":1674},[2922,13784,13785,13787],{},[1146,13786,2680],{},[1146,13788,5657],{},[1154,13790,2683],{"stretchy":1674},[1189,13792,8057],{"encoding":1191},[1124,13794,13796,13840],{"className":13795,"ariaHidden":1156},[1196],[1124,13797,13799,13802,13831,13834,13837],{"className":13798},[1200],[1124,13800],{"className":13801,"style":7649},[1204],[1124,13803,13805,13808],{"className":13804},[1209],[1124,13806,4370],{"className":13807},[1209,1213],[1124,13809,13811],{"className":13810},[1217],[1124,13812,13814],{"className":13813},[1221],[1124,13815,13817],{"className":13816},[1226],[1124,13818,13820],{"className":13819,"style":7649},[1230],[1124,13821,13822,13825],{"style":3905},[1124,13823],{"className":13824,"style":1239},[1238],[1124,13826,13828],{"className":13827},[1243,1244,1245,1246],[1124,13829,5657],{"className":13830,"style":5740},[1209,1213,1246],[1124,13832],{"className":13833,"style":1774},[1271],[1124,13835,1652],{"className":13836},[1778],[1124,13838],{"className":13839,"style":1774},[1271],[1124,13841,13843,13846,13849,13852,13881],{"className":13842},[1200],[1124,13844],{"className":13845,"style":8111},[1204],[1124,13847,2674],{"className":13848,"style":2700},[1209,1213],[1124,13850,2677],{"className":13851},[1795],[1124,13853,13855,13858],{"className":13854},[1209],[1124,13856,2680],{"className":13857,"style":2707},[1209,1213],[1124,13859,13861],{"className":13860},[1217],[1124,13862,13864],{"className":13863},[1221],[1124,13865,13867],{"className":13866},[1226],[1124,13868,13870],{"className":13869,"style":7649},[1230],[1124,13871,13872,13875],{"style":3905},[1124,13873],{"className":13874,"style":1239},[1238],[1124,13876,13878],{"className":13877},[1243,1244,1245,1246],[1124,13879,5657],{"className":13880,"style":5740},[1209,1213,1246],[1124,13882,2683],{"className":13883},[2211],"，即每层的激活值是对加权输入施加激活函数的结果。",[2745,13886],{},[7743,13888,13890],{"id":13889},"反向传播的-4-个基本方程","反向传播的 4 个基本方程",[1101,13892,13893],{},"以下四个方程是反向传播算法的数学基础，它们给出了计算代价函数关于网络中任意权重和偏置的梯度的完整方法。",[1101,13895,13896,13897,14146,14147,12587,14175,14203],{},"定义误差：",[1124,13898,13900,13942],{"className":13899},[1127],[1124,13901,13903],{"className":13902},[1131],[1133,13904,13905],{"xmlns":1135},[1137,13906,13907,13939],{},[1140,13908,13909,13917,13919],{},[5282,13910,13911,13913,13915],{},[1146,13912,13138],{},[1146,13914,1693],{},[1146,13916,5657],{},[1154,13918,1652],{},[2911,13920,13921,13927],{},[1140,13922,13923,13925],{},[1146,13924,3164],{"mathvariant":3145},[1146,13926,4325],{},[1140,13928,13929,13931],{},[1146,13930,3164],{"mathvariant":3145},[5282,13932,13933,13935,13937],{},[1146,13934,2680],{},[1146,13936,1693],{},[1146,13938,5657],{},[1189,13940,13941],{"encoding":1191},"\\delta^l_j = \\frac{\\partial C}{\\partial z^l_j}",[1124,13943,13945,14011],{"className":13944,"ariaHidden":1156},[1196],[1124,13946,13948,13951,14002,14005,14008],{"className":13947},[1200],[1124,13949],{"className":13950,"style":12711},[1204],[1124,13952,13954,13957],{"className":13953},[1209],[1124,13955,13138],{"className":13956,"style":13161},[1209,1213],[1124,13958,13960],{"className":13959},[1217],[1124,13961,13963,13994],{"className":13962},[1221,1222],[1124,13964,13966,13991],{"className":13965},[1226],[1124,13967,13969,13980],{"className":13968,"style":7649},[1230],[1124,13970,13971,13974],{"style":13176},[1124,13972],{"className":13973,"style":1239},[1238],[1124,13975,13977],{"className":13976},[1243,1244,1245,1246],[1124,13978,1693],{"className":13979,"style":1929},[1209,1213,1246],[1124,13981,13982,13985],{"style":3905},[1124,13983],{"className":13984,"style":1239},[1238],[1124,13986,13988],{"className":13987},[1243,1244,1245,1246],[1124,13989,5657],{"className":13990,"style":5740},[1209,1213,1246],[1124,13992,1254],{"className":13993},[1253],[1124,13995,13997],{"className":13996},[1226],[1124,13998,14000],{"className":13999,"style":12762},[1230],[1124,14001],{},[1124,14003],{"className":14004,"style":1774},[1271],[1124,14006,1652],{"className":14007},[1778],[1124,14009],{"className":14010,"style":1774},[1271],[1124,14012,14014,14018],{"className":14013},[1200],[1124,14015],{"className":14016,"style":14017},[1204],"height:1.6015em;vertical-align:-0.7214em;",[1124,14019,14021,14024,14143],{"className":14020},[1209],[1124,14022],{"className":14023},[1795,2212],[1124,14025,14027],{"className":14026},[2911],[1124,14028,14030,14134],{"className":14029},[1221,1222],[1124,14031,14033,14131],{"className":14032},[1226],[1124,14034,14036,14106,14114],{"className":14035,"style":4858},[1230],[1124,14037,14039,14042],{"style":14038},"top:-2.6014em;",[1124,14040],{"className":14041,"style":2998},[1238],[1124,14043,14045],{"className":14044},[1243,1244,1245,1246],[1124,14046,14048,14051],{"className":14047},[1209,1246],[1124,14049,3164],{"className":14050,"style":3319},[1209,1246],[1124,14052,14054,14057],{"className":14053},[1209,1246],[1124,14055,2680],{"className":14056,"style":2707},[1209,1213,1246],[1124,14058,14060],{"className":14059},[1217],[1124,14061,14063,14097],{"className":14062},[1221,1222],[1124,14064,14066,14094],{"className":14065},[1226],[1124,14067,14070,14082],{"className":14068,"style":14069},[1230],"height:0.8408em;",[1124,14071,14073,14076],{"style":14072},"top:-2.1777em;margin-left:-0.044em;margin-right:0.0714em;",[1124,14074],{"className":14075,"style":3036},[1238],[1124,14077,14079],{"className":14078},[1243,3040,3041,1246],[1124,14080,1693],{"className":14081,"style":1929},[1209,1213,1246],[1124,14083,14085,14088],{"style":14084},"top:-2.8448em;margin-right:0.0714em;",[1124,14086],{"className":14087,"style":3036},[1238],[1124,14089,14091],{"className":14090},[1243,3040,3041,1246],[1124,14092,5657],{"className":14093,"style":5740},[1209,1213,1246],[1124,14095,1254],{"className":14096},[1253],[1124,14098,14100],{"className":14099},[1226],[1124,14101,14104],{"className":14102,"style":14103},[1230],"height:0.4612em;",[1124,14105],{},[1124,14107,14108,14111],{"style":3053},[1124,14109],{"className":14110,"style":2998},[1238],[1124,14112],{"className":14113,"style":3061},[3060],[1124,14115,14116,14119],{"style":3064},[1124,14117],{"className":14118,"style":2998},[1238],[1124,14120,14122],{"className":14121},[1243,1244,1245,1246],[1124,14123,14125,14128],{"className":14124},[1209,1246],[1124,14126,3164],{"className":14127,"style":3319},[1209,1246],[1124,14129,4325],{"className":14130,"style":4392},[1209,1213,1246],[1124,14132,1254],{"className":14133},[1253],[1124,14135,14137],{"className":14136},[1226],[1124,14138,14141],{"className":14139,"style":14140},[1230],"height:0.7214em;",[1124,14142],{},[1124,14144],{"className":14145},[2211,2212],"（代价函数对第 ",[1124,14148,14150,14163],{"className":14149},[1127],[1124,14151,14153],{"className":14152},[1131],[1133,14154,14155],{"xmlns":1135},[1137,14156,14157,14161],{},[1140,14158,14159],{},[1146,14160,5657],{},[1189,14162,5657],{"encoding":1191},[1124,14164,14166],{"className":14165,"ariaHidden":1156},[1196],[1124,14167,14169,14172],{"className":14168},[1200],[1124,14170],{"className":14171,"style":2250},[1204],[1124,14173,5657],{"className":14174,"style":5740},[1209,1213],[1124,14176,14178,14191],{"className":14177},[1127],[1124,14179,14181],{"className":14180},[1131],[1133,14182,14183],{"xmlns":1135},[1137,14184,14185,14189],{},[1140,14186,14187],{},[1146,14188,1693],{},[1189,14190,1693],{"encoding":1191},[1124,14192,14194],{"className":14193,"ariaHidden":1156},[1196],[1124,14195,14197,14200],{"className":14196},[1200],[1124,14198],{"className":14199,"style":12670},[1204],[1124,14201,1693],{"className":14202,"style":1929},[1209,1213]," 个神经元加权输入的偏导数）",[2616,14205,14206,14218],{},[2619,14207,14208],{},[2622,14209,14210,14213,14216],{},[2625,14211,14212],{},"方程",[2625,14214,14215],{},"公式",[2625,14217,12421],{},[2635,14219,14220,14605,14942,15196],{},[2622,14221,14222,14227,14602],{},[2640,14223,14224],{},[1107,14225,14226],{},"BP1",[2640,14228,14229],{},[1124,14230,14232,14295],{"className":14231},[1127],[1124,14233,14235],{"className":14234},[1131],[1133,14236,14237],{"xmlns":1135},[1137,14238,14239,14292],{},[1140,14240,14241,14250,14252,14272,14274,14280,14282,14290],{},[5282,14242,14243,14245,14247],{},[1146,14244,13138],{},[1146,14246,1693],{},[1146,14248,14249],{},"L",[1154,14251,1652],{},[2911,14253,14254,14260],{},[1140,14255,14256,14258],{},[1146,14257,3164],{"mathvariant":3145},[1146,14259,4325],{},[1140,14261,14262,14264],{},[1146,14263,3164],{"mathvariant":3145},[5282,14265,14266,14268,14270],{},[1146,14267,4370],{},[1146,14269,1693],{},[1146,14271,14249],{},[1154,14273,2325],{},[2922,14275,14276,14278],{},[1146,14277,2674],{},[1154,14279,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,14281,2677],{"stretchy":1674},[5282,14283,14284,14286,14288],{},[1146,14285,2680],{},[1146,14287,1693],{},[1146,14289,14249],{},[1154,14291,2683],{"stretchy":1674},[1189,14293,14294],{"encoding":1191},"\\delta^L_j = \\frac{\\partial C}{\\partial a^L_j} \\cdot \\sigma'(z^L_j)",[1124,14296,14298,14365,14507],{"className":14297,"ariaHidden":1156},[1196],[1124,14299,14301,14305,14356,14359,14362],{"className":14300},[1200],[1124,14302],{"className":14303,"style":14304},[1204],"height:1.2361em;vertical-align:-0.3948em;",[1124,14306,14308,14311],{"className":14307},[1209],[1124,14309,13138],{"className":14310,"style":13161},[1209,1213],[1124,14312,14314],{"className":14313},[1217],[1124,14315,14317,14348],{"className":14316},[1221,1222],[1124,14318,14320,14345],{"className":14319},[1226],[1124,14321,14323,14334],{"className":14322,"style":10529},[1230],[1124,14324,14325,14328],{"style":13176},[1124,14326],{"className":14327,"style":1239},[1238],[1124,14329,14331],{"className":14330},[1243,1244,1245,1246],[1124,14332,1693],{"className":14333,"style":1929},[1209,1213,1246],[1124,14335,14336,14339],{"style":3905},[1124,14337],{"className":14338,"style":1239},[1238],[1124,14340,14342],{"className":14341},[1243,1244,1245,1246],[1124,14343,14249],{"className":14344},[1209,1213,1246],[1124,14346,1254],{"className":14347},[1253],[1124,14349,14351],{"className":14350},[1226],[1124,14352,14354],{"className":14353,"style":12762},[1230],[1124,14355],{},[1124,14357],{"className":14358,"style":1774},[1271],[1124,14360,1652],{"className":14361},[1778],[1124,14363],{"className":14364,"style":1774},[1271],[1124,14366,14368,14372,14498,14501,14504],{"className":14367},[1200],[1124,14369],{"className":14370,"style":14371},[1204],"height:1.596em;vertical-align:-0.7158em;",[1124,14373,14375,14378,14495],{"className":14374},[1209],[1124,14376],{"className":14377},[1795,2212],[1124,14379,14381],{"className":14380},[2911],[1124,14382,14384,14486],{"className":14383},[1221,1222],[1124,14385,14387,14483],{"className":14386},[1226],[1124,14388,14390,14458,14466],{"className":14389,"style":4858},[1230],[1124,14391,14393,14396],{"style":14392},"top:-2.607em;",[1124,14394],{"className":14395,"style":2998},[1238],[1124,14397,14399],{"className":14398},[1243,1244,1245,1246],[1124,14400,14402,14405],{"className":14401},[1209,1246],[1124,14403,3164],{"className":14404,"style":3319},[1209,1246],[1124,14406,14408,14411],{"className":14407},[1209,1246],[1124,14409,4370],{"className":14410},[1209,1213,1246],[1124,14412,14414],{"className":14413},[1217],[1124,14415,14417,14450],{"className":14416},[1221,1222],[1124,14418,14420,14447],{"className":14419},[1226],[1124,14421,14424,14436],{"className":14422,"style":14423},[1230],"height:0.8329em;",[1124,14425,14427,14430],{"style":14426},"top:-2.1777em;margin-left:0em;margin-right:0.0714em;",[1124,14428],{"className":14429,"style":3036},[1238],[1124,14431,14433],{"className":14432},[1243,3040,3041,1246],[1124,14434,1693],{"className":14435,"style":1929},[1209,1213,1246],[1124,14437,14438,14441],{"style":14084},[1124,14439],{"className":14440,"style":3036},[1238],[1124,14442,14444],{"className":14443},[1243,3040,3041,1246],[1124,14445,14249],{"className":14446},[1209,1213,1246],[1124,14448,1254],{"className":14449},[1253],[1124,14451,14453],{"className":14452},[1226],[1124,14454,14456],{"className":14455,"style":14103},[1230],[1124,14457],{},[1124,14459,14460,14463],{"style":3053},[1124,14461],{"className":14462,"style":2998},[1238],[1124,14464],{"className":14465,"style":3061},[3060],[1124,14467,14468,14471],{"style":3064},[1124,14469],{"className":14470,"style":2998},[1238],[1124,14472,14474],{"className":14473},[1243,1244,1245,1246],[1124,14475,14477,14480],{"className":14476},[1209,1246],[1124,14478,3164],{"className":14479,"style":3319},[1209,1246],[1124,14481,4325],{"className":14482,"style":4392},[1209,1213,1246],[1124,14484,1254],{"className":14485},[1253],[1124,14487,14489],{"className":14488},[1226],[1124,14490,14493],{"className":14491,"style":14492},[1230],"height:0.7158em;",[1124,14494],{},[1124,14496],{"className":14497},[2211,2212],[1124,14499],{"className":14500,"style":2500},[1271],[1124,14502,2325],{"className":14503},[2504],[1124,14505],{"className":14506,"style":2500},[1271],[1124,14508,14510,14513,14545,14548,14599],{"className":14509},[1200],[1124,14511],{"className":14512,"style":14304},[1204],[1124,14514,14516,14519],{"className":14515},[1209],[1124,14517,2674],{"className":14518,"style":2700},[1209,1213],[1124,14520,14522],{"className":14521},[1217],[1124,14523,14525],{"className":14524},[1221],[1124,14526,14528],{"className":14527},[1226],[1124,14529,14531],{"className":14530,"style":3902},[1230],[1124,14532,14533,14536],{"style":3905},[1124,14534],{"className":14535,"style":1239},[1238],[1124,14537,14539],{"className":14538},[1243,1244,1245,1246],[1124,14540,14542],{"className":14541},[1209,1246],[1124,14543,3838],{"className":14544},[1209,1246],[1124,14546,2677],{"className":14547},[1795],[1124,14549,14551,14554],{"className":14550},[1209],[1124,14552,2680],{"className":14553,"style":2707},[1209,1213],[1124,14555,14557],{"className":14556},[1217],[1124,14558,14560,14591],{"className":14559},[1221,1222],[1124,14561,14563,14588],{"className":14562},[1226],[1124,14564,14566,14577],{"className":14565,"style":10529},[1230],[1124,14567,14568,14571],{"style":13027},[1124,14569],{"className":14570,"style":1239},[1238],[1124,14572,14574],{"className":14573},[1243,1244,1245,1246],[1124,14575,1693],{"className":14576,"style":1929},[1209,1213,1246],[1124,14578,14579,14582],{"style":3905},[1124,14580],{"className":14581,"style":1239},[1238],[1124,14583,14585],{"className":14584},[1243,1244,1245,1246],[1124,14586,14249],{"className":14587},[1209,1213,1246],[1124,14589,1254],{"className":14590},[1253],[1124,14592,14594],{"className":14593},[1226],[1124,14595,14597],{"className":14596,"style":12762},[1230],[1124,14598],{},[1124,14600,2683],{"className":14601},[2211],[2640,14603,14604],{},"输出层误差：代价函数对输出激活的变化率乘以激活函数的导数",[2622,14606,14607,14612,14939],{},[2640,14608,14609],{},[1107,14610,14611],{},"BP2",[2640,14613,14614],{},[1124,14615,14617,14692],{"className":14616},[1127],[1124,14618,14620],{"className":14619},[1131],[1133,14621,14622],{"xmlns":1135},[1137,14623,14624,14689],{},[1140,14625,14626,14632,14634,14636,14638,14650,14656,14668,14670,14673,14679,14681,14687],{},[2922,14627,14628,14630],{},[1146,14629,13138],{},[1146,14631,5657],{},[1154,14633,1652],{},[1154,14635,2677],{"stretchy":1674},[1154,14637,2677],{"stretchy":1674},[2922,14639,14640,14642],{},[1146,14641,1439],{},[1140,14643,14644,14646,14648],{},[1146,14645,5657],{},[1154,14647,2330],{},[1150,14649,1152],{},[2922,14651,14652,14654],{},[1154,14653,2683],{"stretchy":1674},[1146,14655,4791],{},[2922,14657,14658,14660],{},[1146,14659,13138],{},[1140,14661,14662,14664,14666],{},[1146,14663,5657],{},[1154,14665,2330],{},[1150,14667,1152],{},[1154,14669,2683],{"stretchy":1674},[1154,14671,14672],{},"⊙",[2922,14674,14675,14677],{},[1146,14676,2674],{},[1154,14678,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,14680,2677],{"stretchy":1674},[2922,14682,14683,14685],{},[1146,14684,2680],{},[1146,14686,5657],{},[1154,14688,2683],{"stretchy":1674},[1189,14690,14691],{"encoding":1191},"\\delta^l = ((w^{l+1})^T \\delta^{l+1}) \\odot \\sigma'(z^l)",[1124,14693,14695,14739,14866],{"className":14694,"ariaHidden":1156},[1196],[1124,14696,14698,14701,14730,14733,14736],{"className":14697},[1200],[1124,14699],{"className":14700,"style":7649},[1204],[1124,14702,14704,14707],{"className":14703},[1209],[1124,14705,13138],{"className":14706,"style":13161},[1209,1213],[1124,14708,14710],{"className":14709},[1217],[1124,14711,14713],{"className":14712},[1221],[1124,14714,14716],{"className":14715},[1226],[1124,14717,14719],{"className":14718,"style":7649},[1230],[1124,14720,14721,14724],{"style":3905},[1124,14722],{"className":14723,"style":1239},[1238],[1124,14725,14727],{"className":14726},[1243,1244,1245,1246],[1124,14728,5657],{"className":14729,"style":5740},[1209,1213,1246],[1124,14731],{"className":14732,"style":1774},[1271],[1124,14734,1652],{"className":14735},[1778],[1124,14737],{"className":14738,"style":1774},[1271],[1124,14740,14742,14745,14749,14787,14816,14854,14857,14860,14863],{"className":14741},[1200],[1124,14743],{"className":14744,"style":8111},[1204],[1124,14746,14748],{"className":14747},[1795],"((",[1124,14750,14752,14755],{"className":14751},[1209],[1124,14753,1439],{"className":14754,"style":1480},[1209,1213],[1124,14756,14758],{"className":14757},[1217],[1124,14759,14761],{"className":14760},[1221],[1124,14762,14764],{"className":14763},[1226],[1124,14765,14767],{"className":14766,"style":7649},[1230],[1124,14768,14769,14772],{"style":3905},[1124,14770],{"className":14771,"style":1239},[1238],[1124,14773,14775],{"className":14774},[1243,1244,1245,1246],[1124,14776,14778,14781,14784],{"className":14777},[1209,1246],[1124,14779,5657],{"className":14780,"style":5740},[1209,1213,1246],[1124,14782,2330],{"className":14783},[2504,1246],[1124,14785,1152],{"className":14786},[1209,1246],[1124,14788,14790,14793],{"className":14789},[2211],[1124,14791,2683],{"className":14792},[2211],[1124,14794,14796],{"className":14795},[1217],[1124,14797,14799],{"className":14798},[1221],[1124,14800,14802],{"className":14801},[1226],[1124,14803,14805],{"className":14804,"style":10529},[1230],[1124,14806,14807,14810],{"style":3905},[1124,14808],{"className":14809,"style":1239},[1238],[1124,14811,14813],{"className":14812},[1243,1244,1245,1246],[1124,14814,4791],{"className":14815,"style":5104},[1209,1213,1246],[1124,14817,14819,14822],{"className":14818},[1209],[1124,14820,13138],{"className":14821,"style":13161},[1209,1213],[1124,14823,14825],{"className":14824},[1217],[1124,14826,14828],{"className":14827},[1221],[1124,14829,14831],{"className":14830},[1226],[1124,14832,14834],{"className":14833,"style":7649},[1230],[1124,14835,14836,14839],{"style":3905},[1124,14837],{"className":14838,"style":1239},[1238],[1124,14840,14842],{"className":14841},[1243,1244,1245,1246],[1124,14843,14845,14848,14851],{"className":14844},[1209,1246],[1124,14846,5657],{"className":14847,"style":5740},[1209,1213,1246],[1124,14849,2330],{"className":14850},[2504,1246],[1124,14852,1152],{"className":14853},[1209,1246],[1124,14855,2683],{"className":14856},[2211],[1124,14858],{"className":14859,"style":2500},[1271],[1124,14861,14672],{"className":14862},[2504],[1124,14864],{"className":14865,"style":2500},[1271],[1124,14867,14869,14872,14904,14907,14936],{"className":14868},[1200],[1124,14870],{"className":14871,"style":8111},[1204],[1124,14873,14875,14878],{"className":14874},[1209],[1124,14876,2674],{"className":14877,"style":2700},[1209,1213],[1124,14879,14881],{"className":14880},[1217],[1124,14882,14884],{"className":14883},[1221],[1124,14885,14887],{"className":14886},[1226],[1124,14888,14890],{"className":14889,"style":3902},[1230],[1124,14891,14892,14895],{"style":3905},[1124,14893],{"className":14894,"style":1239},[1238],[1124,14896,14898],{"className":14897},[1243,1244,1245,1246],[1124,14899,14901],{"className":14900},[1209,1246],[1124,14902,3838],{"className":14903},[1209,1246],[1124,14905,2677],{"className":14906},[1795],[1124,14908,14910,14913],{"className":14909},[1209],[1124,14911,2680],{"className":14912,"style":2707},[1209,1213],[1124,14914,14916],{"className":14915},[1217],[1124,14917,14919],{"className":14918},[1221],[1124,14920,14922],{"className":14921},[1226],[1124,14923,14925],{"className":14924,"style":7649},[1230],[1124,14926,14927,14930],{"style":3905},[1124,14928],{"className":14929,"style":1239},[1238],[1124,14931,14933],{"className":14932},[1243,1244,1245,1246],[1124,14934,5657],{"className":14935,"style":5740},[1209,1213,1246],[1124,14937,2683],{"className":14938},[2211],[2640,14940,14941],{},"误差反向传播：用下一层的误差和权重矩阵计算当前层误差",[2622,14943,14944,14949,15193],{},[2640,14945,14946],{},[1107,14947,14948],{},"BP3",[2640,14950,14951],{},[1124,14952,14954,14996],{"className":14953},[1127],[1124,14955,14957],{"className":14956},[1131],[1133,14958,14959],{"xmlns":1135},[1137,14960,14961,14993],{},[1140,14962,14963,14983,14985],{},[2911,14964,14965,14971],{},[1140,14966,14967,14969],{},[1146,14968,3164],{"mathvariant":3145},[1146,14970,4325],{},[1140,14972,14973,14975],{},[1146,14974,3164],{"mathvariant":3145},[5282,14976,14977,14979,14981],{},[1146,14978,2230],{},[1146,14980,1693],{},[1146,14982,5657],{},[1154,14984,1652],{},[5282,14986,14987,14989,14991],{},[1146,14988,13138],{},[1146,14990,1693],{},[1146,14992,5657],{},[1189,14994,14995],{"encoding":1191},"\\frac{\\partial C}{\\partial b^l_j} = \\delta^l_j",[1124,14997,14999,15136],{"className":14998,"ariaHidden":1156},[1196],[1124,15000,15002,15005,15127,15130,15133],{"className":15001},[1200],[1124,15003],{"className":15004,"style":14017},[1204],[1124,15006,15008,15011,15124],{"className":15007},[1209],[1124,15009],{"className":15010},[1795,2212],[1124,15012,15014],{"className":15013},[2911],[1124,15015,15017,15116],{"className":15016},[1221,1222],[1124,15018,15020,15113],{"className":15019},[1226],[1124,15021,15023,15088,15096],{"className":15022,"style":4858},[1230],[1124,15024,15025,15028],{"style":14038},[1124,15026],{"className":15027,"style":2998},[1238],[1124,15029,15031],{"className":15030},[1243,1244,1245,1246],[1124,15032,15034,15037],{"className":15033},[1209,1246],[1124,15035,3164],{"className":15036,"style":3319},[1209,1246],[1124,15038,15040,15043],{"className":15039},[1209,1246],[1124,15041,2230],{"className":15042},[1209,1213,1246],[1124,15044,15046],{"className":15045},[1217],[1124,15047,15049,15080],{"className":15048},[1221,1222],[1124,15050,15052,15077],{"className":15051},[1226],[1124,15053,15055,15066],{"className":15054,"style":14069},[1230],[1124,15056,15057,15060],{"style":14426},[1124,15058],{"className":15059,"style":3036},[1238],[1124,15061,15063],{"className":15062},[1243,3040,3041,1246],[1124,15064,1693],{"className":15065,"style":1929},[1209,1213,1246],[1124,15067,15068,15071],{"style":14084},[1124,15069],{"className":15070,"style":3036},[1238],[1124,15072,15074],{"className":15073},[1243,3040,3041,1246],[1124,15075,5657],{"className":15076,"style":5740},[1209,1213,1246],[1124,15078,1254],{"className":15079},[1253],[1124,15081,15083],{"className":15082},[1226],[1124,15084,15086],{"className":15085,"style":14103},[1230],[1124,15087],{},[1124,15089,15090,15093],{"style":3053},[1124,15091],{"className":15092,"style":2998},[1238],[1124,15094],{"className":15095,"style":3061},[3060],[1124,15097,15098,15101],{"style":3064},[1124,15099],{"className":15100,"style":2998},[1238],[1124,15102,15104],{"className":15103},[1243,1244,1245,1246],[1124,15105,15107,15110],{"className":15106},[1209,1246],[1124,15108,3164],{"className":15109,"style":3319},[1209,1246],[1124,15111,4325],{"className":15112,"style":4392},[1209,1213,1246],[1124,15114,1254],{"className":15115},[1253],[1124,15117,15119],{"className":15118},[1226],[1124,15120,15122],{"className":15121,"style":14140},[1230],[1124,15123],{},[1124,15125],{"className":15126},[2211,2212],[1124,15128],{"className":15129,"style":1774},[1271],[1124,15131,1652],{"className":15132},[1778],[1124,15134],{"className":15135,"style":1774},[1271],[1124,15137,15139,15142],{"className":15138},[1200],[1124,15140],{"className":15141,"style":12711},[1204],[1124,15143,15145,15148],{"className":15144},[1209],[1124,15146,13138],{"className":15147,"style":13161},[1209,1213],[1124,15149,15151],{"className":15150},[1217],[1124,15152,15154,15185],{"className":15153},[1221,1222],[1124,15155,15157,15182],{"className":15156},[1226],[1124,15158,15160,15171],{"className":15159,"style":7649},[1230],[1124,15161,15162,15165],{"style":13176},[1124,15163],{"className":15164,"style":1239},[1238],[1124,15166,15168],{"className":15167},[1243,1244,1245,1246],[1124,15169,1693],{"className":15170,"style":1929},[1209,1213,1246],[1124,15172,15173,15176],{"style":3905},[1124,15174],{"className":15175,"style":1239},[1238],[1124,15177,15179],{"className":15178},[1243,1244,1245,1246],[1124,15180,5657],{"className":15181,"style":5740},[1209,1213,1246],[1124,15183,1254],{"className":15184},[1253],[1124,15186,15188],{"className":15187},[1226],[1124,15189,15191],{"className":15190,"style":12762},[1230],[1124,15192],{},[2640,15194,15195],{},"偏置梯度：等于该神经元的误差",[2622,15197,15198,15203,15557],{},[2640,15199,15200],{},[1107,15201,15202],{},"BP4",[2640,15204,15205],{},[1124,15206,15208,15270],{"className":15207},[1127],[1124,15209,15211],{"className":15210},[1131],[1133,15212,15213],{"xmlns":1135},[1137,15214,15215,15267],{},[1140,15216,15217,15241,15243,15257,15259],{},[2911,15218,15219,15225],{},[1140,15220,15221,15223],{},[1146,15222,3164],{"mathvariant":3145},[1146,15224,4325],{},[1140,15226,15227,15229],{},[1146,15228,3164],{"mathvariant":3145},[5282,15230,15231,15233,15239],{},[1146,15232,1439],{},[1140,15234,15235,15237],{},[1146,15236,1693],{},[1146,15238,5278],{},[1146,15240,5657],{},[1154,15242,1652],{},[5282,15244,15245,15247,15249],{},[1146,15246,4370],{},[1146,15248,5278],{},[1140,15250,15251,15253,15255],{},[1146,15252,5657],{},[1154,15254,2235],{},[1150,15256,1152],{},[1154,15258,2325],{},[5282,15260,15261,15263,15265],{},[1146,15262,13138],{},[1146,15264,1693],{},[1146,15266,5657],{},[1189,15268,15269],{"encoding":1191},"\\frac{\\partial C}{\\partial w^l_{jk}} = a^{l-1}_k \\cdot \\delta^l_j",[1124,15271,15273,15420,15500],{"className":15272,"ariaHidden":1156},[1196],[1124,15274,15276,15280,15411,15414,15417],{"className":15275},[1200],[1124,15277],{"className":15278,"style":15279},[1204],"height:1.619em;vertical-align:-0.7389em;",[1124,15281,15283,15286,15408],{"className":15282},[1209],[1124,15284],{"className":15285},[1795,2212],[1124,15287,15289],{"className":15288},[2911],[1124,15290,15292,15399],{"className":15291},[1221,1222],[1124,15293,15295,15396],{"className":15294},[1226],[1124,15296,15298,15371,15379],{"className":15297,"style":4858},[1230],[1124,15299,15300,15303],{"style":14038},[1124,15301],{"className":15302,"style":2998},[1238],[1124,15304,15306],{"className":15305},[1243,1244,1245,1246],[1124,15307,15309,15312],{"className":15308},[1209,1246],[1124,15310,3164],{"className":15311,"style":3319},[1209,1246],[1124,15313,15315,15318],{"className":15314},[1209,1246],[1124,15316,1439],{"className":15317,"style":1480},[1209,1213,1246],[1124,15319,15321],{"className":15320},[1217],[1124,15322,15324,15362],{"className":15323},[1221,1222],[1124,15325,15327,15359],{"className":15326},[1226],[1124,15328,15330,15348],{"className":15329,"style":14069},[1230],[1124,15331,15333,15336],{"style":15332},"top:-2.1528em;margin-left:-0.0269em;margin-right:0.0714em;",[1124,15334],{"className":15335,"style":3036},[1238],[1124,15337,15339],{"className":15338},[1243,3040,3041,1246],[1124,15340,15342,15345],{"className":15341},[1209,1246],[1124,15343,1693],{"className":15344,"style":1929},[1209,1213,1246],[1124,15346,5278],{"className":15347,"style":5363},[1209,1213,1246],[1124,15349,15350,15353],{"style":14084},[1124,15351],{"className":15352,"style":3036},[1238],[1124,15354,15356],{"className":15355},[1243,3040,3041,1246],[1124,15357,5657],{"className":15358,"style":5740},[1209,1213,1246],[1124,15360,1254],{"className":15361},[1253],[1124,15363,15365],{"className":15364},[1226],[1124,15366,15369],{"className":15367,"style":15368},[1230],"height:0.4861em;",[1124,15370],{},[1124,15372,15373,15376],{"style":3053},[1124,15374],{"className":15375,"style":2998},[1238],[1124,15377],{"className":15378,"style":3061},[3060],[1124,15380,15381,15384],{"style":3064},[1124,15382],{"className":15383,"style":2998},[1238],[1124,15385,15387],{"className":15386},[1243,1244,1245,1246],[1124,15388,15390,15393],{"className":15389},[1209,1246],[1124,15391,3164],{"className":15392,"style":3319},[1209,1246],[1124,15394,4325],{"className":15395,"style":4392},[1209,1213,1246],[1124,15397,1254],{"className":15398},[1253],[1124,15400,15402],{"className":15401},[1226],[1124,15403,15406],{"className":15404,"style":15405},[1230],"height:0.7389em;",[1124,15407],{},[1124,15409],{"className":15410},[2211,2212],[1124,15412],{"className":15413,"style":1774},[1271],[1124,15415,1652],{"className":15416},[1778],[1124,15418],{"className":15419,"style":1774},[1271],[1124,15421,15423,15427,15491,15494,15497],{"className":15422},[1200],[1124,15424],{"className":15425,"style":15426},[1204],"height:1.1905em;vertical-align:-0.3013em;",[1124,15428,15430,15433],{"className":15429},[1209],[1124,15431,4370],{"className":15432},[1209,1213],[1124,15434,15436],{"className":15435},[1217],[1124,15437,15439,15482],{"className":15438},[1221,1222],[1124,15440,15442,15479],{"className":15441},[1226],[1124,15443,15446,15458],{"className":15444,"style":15445},[1230],"height:0.8892em;",[1124,15447,15449,15452],{"style":15448},"top:-2.3987em;margin-left:0em;margin-right:0.05em;",[1124,15450],{"className":15451,"style":1239},[1238],[1124,15453,15455],{"className":15454},[1243,1244,1245,1246],[1124,15456,5278],{"className":15457,"style":5363},[1209,1213,1246],[1124,15459,15461,15464],{"style":15460},"top:-3.1031em;margin-right:0.05em;",[1124,15462],{"className":15463,"style":1239},[1238],[1124,15465,15467],{"className":15466},[1243,1244,1245,1246],[1124,15468,15470,15473,15476],{"className":15469},[1209,1246],[1124,15471,5657],{"className":15472,"style":5740},[1209,1213,1246],[1124,15474,2235],{"className":15475},[2504,1246],[1124,15477,1152],{"className":15478},[1209,1246],[1124,15480,1254],{"className":15481},[1253],[1124,15483,15485],{"className":15484},[1226],[1124,15486,15489],{"className":15487,"style":15488},[1230],"height:0.3013em;",[1124,15490],{},[1124,15492],{"className":15493,"style":2500},[1271],[1124,15495,2325],{"className":15496},[2504],[1124,15498],{"className":15499,"style":2500},[1271],[1124,15501,15503,15506],{"className":15502},[1200],[1124,15504],{"className":15505,"style":12711},[1204],[1124,15507,15509,15512],{"className":15508},[1209],[1124,15510,13138],{"className":15511,"style":13161},[1209,1213],[1124,15513,15515],{"className":15514},[1217],[1124,15516,15518,15549],{"className":15517},[1221,1222],[1124,15519,15521,15546],{"className":15520},[1226],[1124,15522,15524,15535],{"className":15523,"style":7649},[1230],[1124,15525,15526,15529],{"style":13176},[1124,15527],{"className":15528,"style":1239},[1238],[1124,15530,15532],{"className":15531},[1243,1244,1245,1246],[1124,15533,1693],{"className":15534,"style":1929},[1209,1213,1246],[1124,15536,15537,15540],{"style":3905},[1124,15538],{"className":15539,"style":1239},[1238],[1124,15541,15543],{"className":15542},[1243,1244,1245,1246],[1124,15544,5657],{"className":15545,"style":5740},[1209,1213,1246],[1124,15547,1254],{"className":15548},[1253],[1124,15550,15552],{"className":15551},[1226],[1124,15553,15555],{"className":15554,"style":12762},[1230],[1124,15556],{},[2640,15558,15559],{},"权重梯度：等于前一层激活值乘以当前层误差",[1101,15561,15562],{},[1107,15563,15564],{},"理解要点",[1117,15566,15567,15572,15577,15583],{},[1120,15568,15569,15571],{},[1107,15570,14226],{}," 是起点：从输出层开始计算误差",[1120,15573,15574,15576],{},[1107,15575,14611],{}," 是递推：将误差从后向前传播（这就是\"反向传播\"名称的由来）",[1120,15578,15579,15582],{},[1107,15580,15581],{},"BP3 + BP4"," 是目标：将误差转化为我们需要的梯度信息",[1120,15584,15585,15614],{},[1124,15586,15588,15602],{"className":15587},[1127],[1124,15589,15591],{"className":15590},[1131],[1133,15592,15593],{"xmlns":1135},[1137,15594,15595,15599],{},[1140,15596,15597],{},[1154,15598,14672],{},[1189,15600,15601],{"encoding":1191},"\\odot",[1124,15603,15605],{"className":15604,"ariaHidden":1156},[1196],[1124,15606,15608,15611],{"className":15607},[1200],[1124,15609],{"className":15610,"style":2858},[1204],[1124,15612,14672],{"className":15613},[1209]," 表示 Hadamard 积（逐元素相乘）",[2745,15616],{},[7743,15618,15619],{"id":15619},"算法步骤",[1101,15621,15622],{},"反向传播算法结合随机梯度下降的完整步骤：",[15624,15625,15626,15631,16004,16237,16705,17278],"ol",{},[1120,15627,15628,15630],{},[1107,15629,8719],{},"：取一个 mini-batch（m 个训练样本）",[1120,15632,15633,15636,15637,15665,15666,7679,15879],{},[1107,15634,15635],{},"前向传播","：对每个样本 ",[1124,15638,15640,15653],{"className":15639},[1127],[1124,15641,15643],{"className":15642},[1131],[1133,15644,15645],{"xmlns":1135},[1137,15646,15647,15651],{},[1140,15648,15649],{},[1146,15650,1148],{},[1189,15652,1148],{"encoding":1191},[1124,15654,15656],{"className":15655,"ariaHidden":1156},[1196],[1124,15657,15659,15662],{"className":15658},[1200],[1124,15660],{"className":15661,"style":3124},[1204],[1124,15663,1148],{"className":15664},[1209,1213],"，逐层计算 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b^l",[1124,15716,15718,15762,15844],{"className":15717,"ariaHidden":1156},[1196],[1124,15719,15721,15724,15753,15756,15759],{"className":15720},[1200],[1124,15722],{"className":15723,"style":7649},[1204],[1124,15725,15727,15730],{"className":15726},[1209],[1124,15728,2680],{"className":15729,"style":2707},[1209,1213],[1124,15731,15733],{"className":15732},[1217],[1124,15734,15736],{"className":15735},[1221],[1124,15737,15739],{"className":15738},[1226],[1124,15740,15742],{"className":15741,"style":7649},[1230],[1124,15743,15744,15747],{"style":3905},[1124,15745],{"className":15746,"style":1239},[1238],[1124,15748,15750],{"className":15749},[1243,1244,1245,1246],[1124,15751,5657],{"className":15752,"style":5740},[1209,1213,1246],[1124,15754],{"className":15755,"style":1774},[1271],[1124,15757,1652],{"className":15758},[1778],[1124,15760],{"className":15761,"style":1774},[1271],[1124,15763,15765,15768,15797,15835,15838,15841],{"className":15764},[1200],[1124,15766],{"className":15767,"style":7933},[1204],[1124,15769,15771,15774],{"className":15770},[1209],[1124,15772,1439],{"className":15773,"style":1480},[1209,1213],[1124,15775,15777],{"className":15776},[1217],[1124,15778,15780],{"className":15779},[1221],[1124,15781,15783],{"className":15782},[1226],[1124,15784,15786],{"className":15785,"style":7649},[1230],[1124,15787,15788,15791],{"style":3905},[1124,15789],{"className":15790,"style":1239},[1238],[1124,15792,15794],{"className":15793},[1243,1244,1245,1246],[1124,15795,5657],{"className":15796,"style":5740},[1209,1213,1246],[1124,15798,15800,15803],{"className":15799},[1209],[1124,15801,4370],{"className":15802},[1209,1213],[1124,15804,15806],{"className":15805},[1217],[1124,15807,15809],{"className":15808},[1221],[1124,15810,15812],{"className":15811},[1226],[1124,15813,15815],{"className":15814,"style":7649},[1230],[1124,15816,15817,15820],{"style":3905},[1124,15818],{"className":15819,"style":1239},[1238],[1124,15821,15823],{"className":15822},[1243,1244,1245,1246],[1124,15824,15826,15829,15832],{"className":15825},[1209,1246],[1124,15827,5657],{"className":15828,"style":5740},[1209,1213,1246],[1124,15830,2235],{"className":15831},[2504,1246],[1124,15833,1152],{"className":15834},[1209,1246],[1124,15836],{"className":15837,"style":2500},[1271],[1124,15839,2330],{"className":15840},[2504],[1124,15842],{"className":15843,"style":2500},[1271],[1124,15845,15847,15850],{"className":15846},[1200],[1124,15848],{"className":15849,"style":7649},[1204],[1124,15851,15853,15856],{"className":15852},[1209],[1124,15854,2230],{"className":15855},[1209,1213],[1124,15857,15859],{"className":15858},[1217],[1124,15860,15862],{"className":15861},[1221],[1124,15863,15865],{"className":15864},[1226],[1124,15866,15868],{"className":15867,"style":7649},[1230],[1124,15869,15870,15873],{"style":3905},[1124,15871],{"className":15872,"style":1239},[1238],[1124,15874,15876],{"className":15875},[1243,1244,1245,1246],[1124,15877,5657],{"className":15878,"style":5740},[1209,1213,1246],[1124,15880,15882,15913],{"className":15881},[1127],[1124,15883,15885],{"className":15884},[1131],[1133,15886,15887],{"xmlns":1135},[1137,15888,15889,15911],{},[1140,15890,15891,15897,15899,15901,15903,15909],{},[2922,15892,15893,15895],{},[1146,15894,4370],{},[1146,15896,5657],{},[1154,15898,1652],{},[1146,15900,2674],{},[1154,15902,2677],{"stretchy":1674},[2922,15904,15905,15907],{},[1146,15906,2680],{},[1146,15908,5657],{},[1154,15910,2683],{"stretchy":1674},[1189,15912,8057],{"encoding":1191},[1124,15914,15916,15960],{"className":15915,"ariaHidden":1156},[1196],[1124,15917,15919,15922,15951,15954,15957],{"className":15918},[1200],[1124,15920],{"className":15921,"style":7649},[1204],[1124,15923,15925,15928],{"className":15924},[1209],[1124,15926,4370],{"className":15927},[1209,1213],[1124,15929,15931],{"className":15930},[1217],[1124,15932,15934],{"className":15933},[1221],[1124,15935,15937],{"className":15936},[1226],[1124,15938,15940],{"className":15939,"style":7649},[1230],[1124,15941,15942,15945],{"style":3905},[1124,15943],{"className":15944,"style":1239},[1238],[1124,15946,15948],{"className":15947},[1243,1244,1245,1246],[1124,15949,5657],{"className":15950,"style":5740},[1209,1213,1246],[1124,15952],{"className":15953,"style":1774},[1271],[1124,15955,1652],{"className":15956},[1778],[1124,15958],{"className":15959,"style":1774},[1271],[1124,15961,15963,15966,15969,15972,16001],{"className":15962},[1200],[1124,15964],{"className":15965,"style":8111},[1204],[1124,15967,2674],{"className":15968,"style":2700},[1209,1213],[1124,15970,2677],{"className":15971},[1795],[1124,15973,15975,15978],{"className":15974},[1209],[1124,15976,2680],{"className":15977,"style":2707},[1209,1213],[1124,15979,15981],{"className":15980},[1217],[1124,15982,15984],{"className":15983},[1221],[1124,15985,15987],{"className":15986},[1226],[1124,15988,15990],{"className":15989,"style":7649},[1230],[1124,15991,15992,15995],{"style":3905},[1124,15993],{"className":15994,"styl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逐层计算 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className":16669},[1209,1246],[1124,16671,2677],{"className":16672},[1795],[1124,16674,16676,16679],{"className":16675},[1209],[1124,16677,2680],{"className":16678,"style":2707},[1209,1213],[1124,16680,16682],{"className":16681},[1217],[1124,16683,16685],{"className":16684},[1221],[1124,16686,16688],{"className":16687},[1226],[1124,16689,16691],{"className":16690,"style":7649},[1230],[1124,16692,16693,16696],{"style":3905},[1124,16694],{"className":16695,"style":1239},[1238],[1124,16697,16699],{"className":16698},[1243,1244,1245,1246],[1124,16700,5657],{"className":16701,"style":5740},[1209,1213,1246],[1124,16703,2683],{"className":16704},[2211],[1120,16706,16707,6414,16710,7679,17037],{},[1107,16708,16709],{},"计算梯度",[1124,16711,16713,16773],{"className":16712},[1127],[1124,16714,16716],{"className":16715},[1131],[1133,16717,16718],{"xmlns":1135},[1137,16719,16720,16770],{},[1140,16721,16722,16746,16748,16762],{},[2911,16723,16724,16730],{},[1140,16725,16726,16728],{},[1146,16727,3164],{"mathvariant":3145},[1146,16729,4325],{},[1140,16731,16732,16734],{},[1146,16733,3164],{"mathvariant":3145},[5282,16735,16736,16738,16744],{},[1146,16737,1439],{},[1140,16739,16740,16742],{},[1146,16741,1693],{},[1146,16743,5278],{},[1146,16745,5657],{},[1154,16747,1652],{},[5282,16749,16750,16752,16754],{},[1146,16751,4370],{},[1146,16753,5278],{},[1140,16755,16756,16758,16760],{},[1146,16757,5657],{},[1154,16759,2235],{},[1150,16761,1152],{},[5282,16763,16764,16766,16768],{},[1146,16765,13138],{},[1146,16767,1693],{},[1146,16769,5657],{},[1189,16771,16772],{"encoding":1191},"\\frac{\\partial C}{\\partial w^l_{jk}} = a^{l-1}_k \\delta^l_j",[1124,16774,16776,16919],{"className":16775,"ariaHidden":1156},[1196],[1124,16777,16779,16782,16910,16913,16916],{"className":16778},[1200],[1124,16780],{"className":16781,"style":15279},[1204],[1124,16783,16785,16788,16907],{"className":16784},[1209],[1124,16786],{"className":16787},[1795,2212],[1124,16789,16791],{"className":16790},[2911],[1124,16792,16794,16899],{"className":16793},[1221,1222],[1124,16795,16797,16896],{"className":16796},[1226],[1124,16798,16800,16871,16879],{"className":16799,"style":4858},[1230],[1124,16801,16802,16805],{"style":14038},[1124,16803],{"className":16804,"style":2998},[1238],[1124,16806,16808],{"className":16807},[1243,1244,1245,1246],[1124,16809,16811,16814],{"className":16810},[1209,1246],[1124,16812,3164],{"className":16813,"style":3319},[1209,1246],[1124,16815,16817,16820],{"className":16816},[1209,1246],[1124,16818,1439],{"className":16819,"style":1480},[1209,1213,1246],[1124,16821,16823],{"className":16822},[1217],[1124,16824,16826,16863],{"className":16825},[1221,1222],[1124,16827,16829,16860],{"className":16828},[1226],[1124,16830,16832,16849],{"className":16831,"style":14069},[1230],[1124,16833,16834,16837],{"style":15332},[1124,16835],{"className":16836,"style":3036},[1238],[1124,16838,16840],{"className":16839},[1243,3040,3041,1246],[1124,16841,16843,16846],{"className":16842},[1209,1246],[1124,16844,1693],{"className":16845,"style":1929},[1209,1213,1246],[1124,16847,5278],{"className":16848,"style":5363},[1209,1213,1246],[1124,16850,16851,16854],{"style":14084},[1124,16852],{"className":16853,"style":3036},[1238],[1124,16855,16857],{"className":16856},[1243,3040,3041,1246],[1124,16858,5657],{"className":16859,"style":5740},[1209,1213,1246],[1124,16861,1254],{"className":16862},[1253],[1124,16864,16866],{"className":16865},[1226],[1124,16867,16869],{"className":16868,"style":15368},[1230],[1124,16870],{},[1124,16872,16873,16876],{"style":3053},[1124,16874],{"className":16875,"style":2998},[1238],[1124,16877],{"className":16878,"style":3061},[3060],[1124,16880,16881,16884],{"style":3064},[1124,16882],{"className":16883,"style":2998},[1238],[1124,16885,16887],{"className":16886},[1243,1244,1245,1246],[1124,16888,16890,16893],{"className":16889},[1209,1246],[1124,16891,3164],{"className":16892,"style":3319},[1209,1246],[1124,16894,4325],{"className":16895,"style":4392},[1209,1213,1246],[1124,16897,1254],{"className":16898},[1253],[1124,16900,16902],{"className":16901},[1226],[1124,16903,16905],{"className":16904,"style":15405},[1230],[1124,16906],{},[1124,16908],{"className":16909},[2211,2212],[1124,16911],{"className":16912,"style":1774},[1271],[1124,16914,1652],{"className":16915},[1778],[1124,16917],{"className":16918,"style":1774},[1271],[1124,16920,16922,16926,16986],{"className":16921},[1200],[1124,16923],{"className":16924,"style":16925},[1204],"height:1.284em;vertical-align:-0.3948em;",[1124,16927,16929,16932],{"className":16928},[1209],[1124,16930,4370],{"className":16931},[1209,1213],[1124,16933,16935],{"className":16934},[1217],[1124,16936,16938,16978],{"className":16937},[1221,1222],[1124,16939,16941,16975],{"className":16940},[1226],[1124,16942,16944,16955],{"className":16943,"style":15445},[1230],[1124,16945,16946,16949],{"style":15448},[1124,16947],{"className":16948,"style":1239},[1238],[1124,16950,16952],{"className":16951},[1243,1244,1245,1246],[1124,16953,5278],{"className":16954,"style":5363},[1209,1213,1246],[1124,16956,16957,16960],{"style":15460},[1124,16958],{"className":16959,"style":1239},[1238],[1124,16961,16963],{"className":16962},[1243,1244,1245,1246],[1124,16964,16966,16969,16972],{"className":16965},[1209,1246],[1124,16967,5657],{"className":16968,"style":5740},[1209,1213,1246],[1124,16970,2235],{"className":16971},[2504,1246],[1124,16973,1152],{"className":16974},[1209,1246],[1124,16976,1254],{"className":16977},[1253],[1124,16979,16981],{"className":16980},[1226],[1124,16982,16984],{"className":16983,"style":15488},[1230],[1124,16985],{},[1124,16987,16989,16992],{"className":16988},[1209],[1124,16990,13138],{"className":16991,"style":13161},[1209,1213],[1124,16993,16995],{"className":16994},[1217],[1124,16996,16998,17029],{"className":16997},[1221,1222],[1124,16999,17001,17026],{"className":17000},[1226],[1124,17002,17004,17015],{"className":17003,"style":7649},[1230],[1124,17005,17006,17009],{"style":13176},[1124,17007],{"className":17008,"style":1239},[1238],[1124,17010,17012],{"className":17011},[1243,1244,1245,1246],[1124,17013,1693],{"className":17014,"style":1929},[1209,1213,1246],[1124,17016,17017,17020],{"style":3905},[1124,17018],{"className":17019,"style":1239},[1238],[1124,17021,17023],{"className":17022},[1243,1244,1245,1246],[1124,17024,5657],{"className":17025,"style":5740},[1209,1213,1246],[1124,17027,1254],{"className":17028},[1253],[1124,17030,17032],{"className":17031},[1226],[1124,17033,17035],{"className":17034,"style":12762},[1230],[1124,17036],{},[1124,17038,17040,17081],{"className":17039},[1127],[1124,17041,17043],{"className":17042},[1131],[1133,17044,17045],{"xmlns":1135},[1137,17046,17047,17079],{},[1140,17048,17049,17069,17071],{},[2911,17050,17051,17057],{},[1140,17052,17053,17055],{},[1146,17054,3164],{"mathvariant":3145},[1146,17056,4325],{},[1140,17058,17059,17061],{},[1146,17060,3164],{"mathvariant":3145},[5282,17062,17063,17065,17067],{},[1146,17064,2230],{},[1146,17066,1693],{},[1146,17068,5657],{},[1154,17070,1652],{},[5282,17072,17073,17075,17077],{},[1146,17074,13138],{},[1146,17076,1693],{},[1146,17078,5657],{},[1189,17080,14995],{"encoding":1191},[1124,17082,17084,17221],{"className":17083,"ariaHidden":1156},[1196],[1124,17085,17087,17090,17212,17215,17218],{"className":17086},[1200],[1124,17088],{"className":17089,"style":14017},[1204],[1124,17091,17093,17096,17209],{"className":17092},[1209],[1124,17094],{"className":17095},[1795,2212],[1124,17097,17099],{"className":17098},[2911],[1124,17100,17102,17201],{"className":17101},[1221,1222],[1124,17103,17105,17198],{"className":17104},[1226],[1124,17106,17108,17173,17181],{"className":17107,"style":4858},[1230],[1124,17109,17110,17113],{"style":14038},[1124,17111],{"className":17112,"style":2998},[1238],[1124,17114,17116],{"className":17115},[1243,1244,1245,1246],[1124,17117,17119,17122],{"className":17118},[1209,1246],[1124,17120,3164],{"className":17121,"style":3319},[1209,1246],[1124,17123,17125,17128],{"className":17124},[1209,1246],[1124,17126,2230],{"className":17127},[1209,1213,1246],[1124,17129,17131],{"className":17130},[1217],[1124,17132,17134,17165],{"className":17133},[1221,1222],[1124,17135,17137,17162],{"className":17136},[1226],[1124,17138,17140,17151],{"className":17139,"style":14069},[1230],[1124,17141,17142,17145],{"style":14426},[1124,17143],{"className":17144,"style":3036},[1238],[1124,17146,17148],{"className":17147},[1243,3040,3041,1246],[1124,17149,1693],{"className":17150,"style":1929},[1209,1213,1246],[1124,17152,17153,17156],{"style":14084},[1124,17154],{"className":17155,"style":3036},[1238],[1124,17157,17159],{"className":17158},[1243,3040,3041,1246],[1124,17160,5657],{"className":17161,"style":5740},[1209,1213,1246],[1124,17163,1254],{"className":17164},[1253],[1124,17166,17168],{"className":17167},[1226],[1124,17169,17171],{"className":17170,"style":14103},[1230],[1124,17172],{},[1124,17174,17175,17178],{"style":3053},[1124,17176],{"className":17177,"style":2998},[1238],[1124,17179],{"className":17180,"style":3061},[3060],[1124,17182,17183,17186],{"style":3064},[1124,17184],{"className":17185,"style":2998},[1238],[1124,17187,17189],{"className":17188},[1243,1244,1245,1246],[1124,17190,17192,17195],{"className":17191},[1209,1246],[1124,17193,3164],{"className":17194,"style":3319},[1209,1246],[1124,17196,4325],{"className":17197,"style":4392},[1209,1213,1246],[1124,17199,1254],{"className":17200},[1253],[1124,17202,17204],{"className":17203},[1226],[1124,17205,17207],{"className":17206,"style":14140},[1230],[1124,17208],{},[1124,17210],{"className":17211},[2211,2212],[1124,17213],{"className":17214,"style":1774},[1271],[1124,17216,1652],{"className":17217},[1778],[1124,17219],{"className":17220,"style":1774},[1271],[1124,17222,17224,17227],{"className":17223},[1200],[1124,17225],{"className":17226,"style":12711},[1204],[1124,17228,17230,17233],{"className":17229},[1209],[1124,17231,13138],{"className":17232,"style":13161},[1209,1213],[1124,17234,17236],{"className":17235},[1217],[1124,17237,17239,17270],{"className":17238},[1221,1222],[1124,17240,17242,17267],{"className":17241},[1226],[1124,17243,17245,17256],{"className":17244,"style":7649},[1230],[1124,17246,17247,17250],{"style":13176},[1124,17248],{"className":17249,"style":1239},[1238],[1124,17251,17253],{"className":17252},[1243,1244,1245,1246],[1124,17254,1693],{"className":17255,"style":1929},[1209,1213,1246],[1124,17257,17258,17261],{"style":3905},[1124,17259],{"className":17260,"style":1239},[1238],[1124,17262,17264],{"className":17263},[1243,1244,1245,1246],[1124,17265,5657],{"className":17266,"style":5740},[1209,1213,1246],[1124,17268,1254],{"className":17269},[1253],[1124,17271,17273],{"className":17272},[1226],[1124,17274,17276],{"className":17275,"style":12762},[1230],[1124,17277],{},[1120,17279,17280,6414,17283,7679,17688],{},[1107,17281,17282],{},"更新参数",[1124,17284,17286,17362],{"className":17285},[1127],[1124,17287,17289],{"className":17288},[1131],[1133,17290,17291],{"xmlns":1135},[1137,17292,17293,17359],{},[1140,17294,17295,17301,17303,17309,17311,17317,17323,17335,17337,17353],{},[2922,17296,17297,17299],{},[1146,17298,1439],{},[1146,17300,5657],{},[1154,17302,3579],{},[2922,17304,17305,17307],{},[1146,17306,1439],{},[1146,17308,5657],{},[1154,17310,2235],{},[2911,17312,17313,17315],{},[1146,17314,5145],{},[1146,17316,6076],{},[1143,17318,17319,17321],{},[1154,17320,1690],{},[1146,17322,1148],{},[2922,17324,17325,17327],{},[1146,17326,13138],{},[1140,17328,17329,17331,17333],{},[1146,17330,1148],{},[1154,17332,1157],{"separator":1156},[1146,17334,5657],{},[1154,17336,2677],{"stretchy":1674},[2922,17338,17339,17341],{},[1146,17340,4370],{},[1140,17342,17343,17345,17347,17349,17351],{},[1146,17344,1148],{},[1154,17346,1157],{"separator":1156},[1146,17348,5657],{},[1154,17350,2235],{},[1150,17352,1152],{},[2922,17354,17355,17357],{},[1154,17356,2683],{"stretchy":1674},[1146,17358,4791],{},[1189,17360,17361],{"encoding":1191},"w^l \\to w^l - \\frac{\\eta}{m} \\sum_x \\delta^{x,l} (a^{x,l-1})^T",[1124,17363,17365,17409,17453],{"className":17364,"ariaHidden":1156},[1196],[1124,17366,17368,17371,17400,17403,17406],{"className":17367},[1200],[1124,17369],{"className":17370,"style":7649},[1204],[1124,17372,17374,17377],{"className":17373},[1209],[1124,17375,1439],{"className":17376,"style":1480},[1209,1213],[1124,17378,17380],{"className":17379},[1217],[1124,17381,17383],{"className":17382},[1221],[1124,17384,17386],{"className":17385},[1226],[1124,17387,17389],{"className":17388,"style":7649},[1230],[1124,17390,17391,17394],{"style":3905},[1124,17392],{"className":17393,"style":1239},[1238],[1124,17395,17397],{"className":17396},[1243,1244,1245,1246],[1124,17398,5657],{"className":17399,"style":5740},[1209,1213,1246],[1124,17401],{"className":17402,"style":1774},[1271],[1124,17404,3579],{"className":17405},[1778],[1124,17407],{"className":17408,"style":1774},[1271],[1124,17410,17412,17415,17444,17447,17450],{"className":17411},[1200],[1124,17413],{"className":17414,"style":7933},[1204],[1124,17416,17418,17421],{"className":17417},[1209],[1124,17419,1439],{"className":17420,"style":1480},[1209,1213],[1124,17422,17424],{"className":17423},[1217],[1124,17425,17427],{"className":17426},[1221],[1124,17428,17430],{"className":17429},[1226],[1124,17431,17433],{"className":17432,"style":7649},[1230],[1124,17434,17435,17438],{"style":3905},[1124,17436],{"className":17437,"style":1239},[1238],[1124,17439,17441],{"className":17440},[1243,1244,1245,1246],[1124,17442,5657],{"className":17443,"style":5740},[1209,1213,1246],[1124,17445],{"className":17446,"style":2500},[1271],[1124,17448,2235],{"className":17449},[2504],[1124,17451],{"className":17452,"style":2500},[1271],[1124,17454,17456,17460,17528,17531,17571,17574,17612,17615,17659],{"className":17455},[1200],[1124,17457],{"className":17458,"style":17459},[1204],"height:1.1941em;vertical-align:-0.345em;",[1124,17461,17463,17466,17525],{"className":17462},[1209],[1124,17464],{"className":17465},[1795,2212],[1124,17467,17469],{"className":17468},[2911],[1124,17470,17472,17517],{"className":17471},[1221,1222],[1124,17473,17475,17514],{"className":17474},[1226],[1124,17476,17478,17492,17500],{"className":17477,"style":6703},[1230],[1124,17479,17480,17483],{"style":2994},[1124,17481],{"className":17482,"style":2998},[1238],[1124,17484,17486],{"className":17485},[1243,1244,1245,1246],[1124,17487,17489],{"className":17488},[1209,1246],[1124,17490,6076],{"className":17491},[1209,1213,1246],[1124,17493,17494,17497],{"style":3053},[1124,17495],{"className":17496,"style":2998},[1238],[1124,17498],{"className":17499,"style":3061},[3060],[1124,17501,17502,17505],{"style":3373},[1124,17503],{"className":17504,"style":2998},[1238],[1124,17506,17508],{"className":17507},[1243,1244,1245,1246],[1124,17509,17511],{"className":17510},[1209,1246],[1124,17512,5145],{"className":17513,"style":2700},[1209,1213,1246],[1124,17515,1254],{"className":17516},[1253],[1124,17518,17520],{"className":17519},[1226],[1124,17521,17523],{"className":17522,"style":3538},[1230],[1124,17524],{},[1124,17526],{"className":17527},[2211,2212],[1124,17529],{"className":17530,"style":1272},[1271],[1124,17532,17534,17537],{"className":17533},[1897],[1124,17535,1690],{"className":17536,"style":1903},[1897,1901,1902],[1124,17538,17540],{"className":17539},[1217],[1124,17541,17543,17563],{"className":17542},[1221,1222],[1124,17544,17546,17560],{"className":17545},[1226],[1124,17547,17549],{"className":17548,"style":4519},[1230],[1124,17550,17551,17554],{"style":1919},[1124,17552],{"className":17553,"style":1239},[1238],[1124,17555,17557],{"className":17556},[1243,1244,1245,1246],[1124,17558,1148],{"className":17559},[1209,1213,1246],[1124,17561,1254],{"className":17562},[1253],[1124,17564,17566],{"className":17565},[1226],[1124,17567,17569],{"className":17568,"style":4540},[1230],[1124,17570],{},[1124,17572],{"className":17573,"style":1272},[1271],[1124,17575,17577,17580],{"className":17576},[1209],[1124,17578,13138],{"className":17579,"style":13161},[1209,1213],[1124,17581,17583],{"className":17582},[1217],[1124,17584,17586],{"className":17585},[1221],[1124,17587,17589],{"className":17588},[1226],[1124,17590,17592],{"className":17591,"style":7649},[1230],[1124,17593,17594,17597],{"style":3905},[1124,17595],{"className":17596,"style":1239},[1238],[1124,17598,17600],{"className":17599},[1243,1244,1245,1246],[1124,17601,17603,17606,17609],{"className":17602},[1209,1246],[1124,17604,1148],{"className":17605},[1209,1213,1246],[1124,17607,1157],{"className":17608},[1267,1246],[1124,17610,5657],{"className":17611,"style":5740},[1209,1213,1246],[1124,17613,2677],{"className":17614},[1795],[1124,17616,17618,17621],{"className":17617},[1209],[1124,17619,4370],{"className":17620},[1209,1213],[1124,17622,17624],{"className":17623},[1217],[1124,17625,17627],{"className":17626},[1221],[1124,17628,17630],{"className":17629},[1226],[1124,17631,17633],{"className":17632,"style":7649},[1230],[1124,17634,17635,17638],{"style":3905},[1124,17636],{"className":17637,"style":1239},[1238],[1124,17639,17641],{"className":17640},[1243,1244,1245,1246],[1124,17642,17644,17647,17650,17653,17656],{"className":17643},[1209,1246],[1124,17645,1148],{"className":17646},[1209,1213,1246],[1124,17648,1157],{"className":17649},[1267,1246],[1124,17651,5657],{"className":17652,"style":5740},[1209,1213,1246],[1124,17654,2235],{"className":17655},[2504,1246],[1124,17657,1152],{"className":17658},[1209,1246],[1124,17660,17662,17665],{"className":17661},[2211],[1124,17663,2683],{"className":17664},[2211],[1124,17666,17668],{"className":17667},[1217],[1124,17669,17671],{"className":17670},[1221],[1124,17672,17674],{"className":17673},[1226],[1124,17675,17677],{"className":17676,"style":10529},[1230],[1124,17678,17679,17682],{"style":3905},[1124,17680],{"className":17681,"style":1239},[1238],[1124,17683,17685],{"className":17684},[1243,1244,1245,1246],[1124,17686,4791],{"className":17687,"style":5104},[1209,1213,1246],[1124,17689,17691,17743],{"className":17690},[1127],[1124,17692,17694],{"className":17693},[1131],[1133,17695,17696],{"xmlns":1135},[1137,17697,17698,17740],{},[1140,17699,17700,17706,17708,17714,17716,17722,17728],{},[2922,17701,17702,17704],{},[1146,17703,2230],{},[1146,17705,5657],{},[1154,17707,3579],{},[2922,17709,17710,17712],{},[1146,17711,2230],{},[1146,17713,5657],{},[1154,17715,2235],{},[2911,17717,17718,17720],{},[1146,17719,5145],{},[1146,17721,6076],{},[1143,17723,17724,17726],{},[1154,17725,1690],{},[1146,17727,1148],{},[2922,17729,17730,17732],{},[1146,17731,13138],{},[1140,17733,17734,17736,17738],{},[1146,17735,1148],{},[1154,17737,1157],{"separator":1156},[1146,17739,5657],{},[1189,17741,17742],{"encoding":1191},"b^l \\to b^l - \\frac{\\eta}{m} \\sum_x \\delta^{x,l}",[1124,17744,17746,17790,17834],{"className":17745,"ariaHidden":1156},[1196],[1124,17747,17749,17752,17781,17784,17787],{"className":17748},[1200],[1124,17750],{"className":17751,"style":7649},[1204],[1124,17753,17755,17758],{"className":17754},[1209],[1124,17756,2230],{"className":17757},[1209,1213],[1124,17759,17761],{"className":17760},[1217],[1124,17762,17764],{"className":17763},[1221],[1124,17765,17767],{"className":17766},[1226],[1124,17768,17770],{"className":17769,"style":7649},[1230],[1124,17771,17772,17775],{"style":3905},[1124,17773],{"className":17774,"style":1239},[1238],[1124,17776,17778],{"className":17777},[1243,1244,1245,1246],[1124,17779,5657],{"className":17780,"style":5740},[1209,1213,1246],[1124,17782],{"className":17783,"style":1774},[1271],[1124,17785,3579],{"className":17786},[1778],[1124,17788],{"className":17789,"style":1774},[1271],[1124,17791,17793,17796,17825,17828,17831],{"className":17792},[1200],[1124,17794],{"className":17795,"style":7933},[1204],[1124,17797,17799,17802],{"className":17798},[1209],[1124,17800,2230],{"className":17801},[1209,1213],[1124,17803,17805],{"className":17804},[1217],[1124,17806,17808],{"className":17807},[1221],[1124,17809,17811],{"className":17810},[1226],[1124,17812,17814],{"className":17813,"style":7649},[1230],[1124,17815,17816,17819],{"style":3905},[1124,17817],{"className":17818,"style":1239},[1238],[1124,17820,17822],{"className":17821},[1243,1244,1245,1246],[1124,17823,5657],{"className":17824,"style":5740},[1209,1213,1246],[1124,17826],{"className":17827,"style":2500},[1271],[1124,17829,2235],{"className":17830},[2504],[1124,17832],{"className":17833,"style":2500},[1271],[1124,17835,17837,17840,17908,17911,17951,17954],{"className":17836},[1200],[1124,17838],{"className":17839,"style":17459},[1204],[1124,17841,17843,17846,17905],{"className":17842},[1209],[1124,17844],{"className":17845},[1795,2212],[1124,17847,17849],{"className":17848},[2911],[1124,17850,17852,17897],{"className":17851},[1221,1222],[1124,17853,17855,17894],{"className":17854},[1226],[1124,17856,17858,17872,17880],{"className":17857,"style":6703},[1230],[1124,17859,17860,17863],{"style":2994},[1124,17861],{"className":17862,"style":2998},[1238],[1124,17864,17866],{"className":17865},[1243,1244,1245,1246],[1124,17867,17869],{"className":17868},[1209,1246],[1124,17870,6076],{"className":17871},[1209,1213,1246],[1124,17873,17874,17877],{"style":3053},[1124,17875],{"className":17876,"style":2998},[1238],[1124,17878],{"className":17879,"style":3061},[3060],[1124,17881,17882,17885],{"style":3373},[1124,17883],{"className":17884,"style":2998},[1238],[1124,17886,17888],{"className":17887},[1243,1244,1245,1246],[1124,17889,17891],{"className":17890},[1209,1246],[1124,17892,5145],{"className":17893,"style":2700},[1209,1213,1246],[1124,17895,1254],{"className":17896},[1253],[1124,17898,17900],{"className":17899},[1226],[1124,17901,17903],{"className":17902,"style":3538},[1230],[1124,17904],{},[1124,17906],{"className":17907},[2211,2212],[1124,17909],{"className":17910,"style":1272},[1271],[1124,17912,17914,17917],{"className":17913},[1897],[1124,17915,1690],{"className":17916,"style":1903},[1897,1901,1902],[1124,17918,17920],{"className":17919},[1217],[1124,17921,17923,17943],{"className":17922},[1221,1222],[1124,17924,17926,17940],{"className":17925},[1226],[1124,17927,17929],{"className":17928,"style":4519},[1230],[1124,17930,17931,17934],{"style":1919},[1124,17932],{"className":17933,"style":1239},[1238],[1124,17935,17937],{"className":17936},[1243,1244,1245,1246],[1124,17938,1148],{"className":17939},[1209,1213,1246],[1124,17941,1254],{"className":17942},[1253],[1124,17944,17946],{"className":17945},[1226],[1124,17947,17949],{"className":17948,"style":4540},[1230],[1124,17950],{},[1124,17952],{"className":17953,"style":1272},[1271],[1124,17955,17957,17960],{"className":17956},[1209],[1124,17958,13138],{"className":17959,"style":13161},[1209,1213],[1124,17961,17963],{"className":17962},[1217],[1124,17964,17966],{"className":17965},[1221],[1124,17967,17969],{"className":17968},[1226],[1124,17970,17972],{"className":17971,"style":7649},[1230],[1124,17973,17974,17977],{"style":3905},[1124,17975],{"className":17976,"style":1239},[1238],[1124,17978,17980],{"className":17979},[1243,1244,1245,1246],[1124,17981,17983,17986,17989],{"className":17982},[1209,1246],[1124,17984,1148],{"className":17985},[1209,1213,1246],[1124,17987,1157],{"className":17988},[1267,1246],[1124,17990,5657],{"className":17991,"style":5740},[1209,1213,1246],[2745,17993],{},[7743,17995,17996],{"id":17996},"反向传播的全局观",[1101,17998,17999],{},"从直觉上理解反向传播，可以想象对某个权重做一个微小的扰动，然后追踪这个扰动如何\"涟漪般\"传播到最终的代价函数。",[1101,18001,18002],{},[1107,18003,18004],{},"直觉理解",[1101,18006,18007,18008,18100,18101,6414],{},"假设对权重 ",[1124,18009,18011,18034],{"className":18010},[1127],[1124,18012,18014],{"className":18013},[1131],[1133,18015,18016],{"xmlns":1135},[1137,18017,18018,18032],{},[1140,18019,18020],{},[5282,18021,18022,18024,18030],{},[1146,18023,1439],{},[1140,18025,18026,18028],{},[1146,18027,1693],{},[1146,18029,5278],{},[1146,18031,5657],{},[1189,18033,12454],{"encoding":1191},[1124,18035,18037],{"className":18036,"ariaHidden":1156},[1196],[1124,18038,18040,18043],{"className":18039},[1200],[1124,18041],{"className":18042,"style":12464},[1204],[1124,18044,18046,18049],{"className":18045},[1209],[1124,18047,1439],{"className":18048,"style":1480},[1209,1213],[1124,18050,18052],{"className":18051},[1217],[1124,18053,18055,18092],{"className":18054},[1221,1222],[1124,18056,18058,18089],{"className":18057},[1226],[1124,18059,18061,18078],{"className":18060,"style":7649},[1230],[1124,18062,18063,18066],{"style":5411},[1124,18064],{"className":18065,"style":1239},[1238],[1124,18067,18069],{"className":18068},[1243,1244,1245,1246],[1124,18070,18072,18075],{"className":18071},[1209,1246],[1124,18073,1693],{"className":18074,"style":1929},[1209,1213,1246],[1124,18076,5278],{"className":18077,"style":5363},[1209,1213,1246],[1124,18079,18080,18083],{"style":3905},[1124,18081],{"className":18082,"style":1239},[1238],[1124,18084,18086],{"className":18085},[1243,1244,1245,1246],[1124,18087,5657],{"className":18088,"style":5740},[1209,1213,1246],[1124,18090,1254],{"className":18091},[1253],[1124,18093,18095],{"className":18094},[1226],[1124,18096,18098],{"className":18097,"style":12520},[1230],[1124,18099],{}," 做微小变化 ",[1124,18102,18104,18130],{"className":18103},[1127],[1124,18105,18107],{"className":18106},[1131],[1133,18108,18109],{"xmlns":1135},[1137,18110,18111,18127],{},[1140,18112,18113,18115],{},[1146,18114,3146],{"mathvariant":3145},[5282,18116,18117,18119,18125],{},[1146,18118,1439],{},[1140,18120,18121,18123],{},[1146,18122,1693],{},[1146,18124,5278],{},[1146,18126,5657],{},[1189,18128,18129],{"encoding":1191},"\\Delta w^l_{jk}",[1124,18131,18133],{"className":18132,"ariaHidden":1156},[1196],[1124,18134,18136,18139,18142],{"className":18135},[1200],[1124,18137],{"className":18138,"style":12464},[1204],[1124,18140,3146],{"className":18141},[1209],[1124,18143,18145,18148],{"className":18144},[1209],[1124,18146,1439],{"className":18147,"style":1480},[1209,1213],[1124,18149,18151],{"className":18150},[1217],[1124,18152,18154,18191],{"className":18153},[1221,1222],[1124,18155,18157,18188],{"className":18156},[1226],[1124,18158,18160,18177],{"className":18159,"style":7649},[1230],[1124,18161,18162,18165],{"style":5411},[1124,18163],{"className":18164,"style":1239},[1238],[1124,18166,18168],{"className":18167},[1243,1244,1245,1246],[1124,18169,18171,18174],{"className":18170},[1209,1246],[1124,18172,1693],{"className":18173,"style":1929},[1209,1213,1246],[1124,18175,5278],{"className":18176,"style":5363},[1209,1213,1246],[1124,18178,18179,18182],{"style":3905},[1124,18180],{"className":18181,"style":1239},[1238],[1124,18183,18185],{"className":18184},[1243,1244,1245,1246],[1124,18186,5657],{"className":18187,"style":5740},[1209,1213,1246],[1124,18189,1254],{"className":18190},[1253],[1124,18192,18194],{"className":18193},[1226],[1124,18195,18197],{"className":18196,"style":12520},[1230],[1124,18198],{},[15624,18200,18201,18349,18414,18537],{},[1120,18202,18203,18204,12587,18232,18260,18261],{},"首先引起第 ",[1124,18205,18207,18220],{"className":18206},[1127],[1124,18208,18210],{"className":18209},[1131],[1133,18211,18212],{"xmlns":1135},[1137,18213,18214,18218],{},[1140,18215,18216],{},[1146,18217,5657],{},[1189,18219,5657],{"encoding":1191},[1124,18221,18223],{"className":18222,"ariaHidden":1156},[1196],[1124,18224,18226,18229],{"className":18225},[1200],[1124,18227],{"className":18228,"style":2250},[1204],[1124,18230,5657],{"className":18231,"style":5740},[1209,1213],[1124,18233,18235,18248],{"className":18234},[1127],[1124,18236,18238],{"className":18237},[1131],[1133,18239,18240],{"xmlns":1135},[1137,18241,18242,18246],{},[1140,18243,18244],{},[1146,18245,1693],{},[1189,18247,1693],{"encoding":1191},[1124,18249,18251],{"className":18250,"ariaHidden":1156},[1196],[1124,18252,18254,18257],{"className":18253},[1200],[1124,18255],{"className":18256,"style":12670},[1204],[1124,18258,1693],{"className":18259,"style":1929},[1209,1213]," 个神经元激活值的变化：",[1124,18262,18264,18286],{"className":18263},[1127],[1124,18265,18267],{"className":18266},[1131],[1133,18268,18269],{"xmlns":1135},[1137,18270,18271,18283],{},[1140,18272,18273,18275],{},[1146,18274,3146],{"mathvariant":3145},[5282,18276,18277,18279,18281],{},[1146,18278,4370],{},[1146,18280,1693],{},[1146,18282,5657],{},[1189,18284,18285],{"encoding":1191},"\\Delta a^l_j",[1124,18287,18289],{"className":18288,"ariaHidden":1156},[1196],[1124,18290,18292,18295,18298],{"className":18291},[1200],[1124,18293],{"className":18294,"style":12711},[1204],[1124,18296,3146],{"className":18297},[1209],[1124,18299,18301,18304],{"className":18300},[1209],[1124,18302,4370],{"className":18303},[1209,1213],[1124,18305,18307],{"className":18306},[1217],[1124,18308,18310,18341],{"className":18309},[1221,1222],[1124,18311,18313,18338],{"className":18312},[1226],[1124,18314,18316,18327],{"className":18315,"style":7649},[1230],[1124,18317,18318,18321],{"style":12732},[1124,18319],{"className":18320,"style":1239},[1238],[1124,18322,18324],{"className":18323},[1243,1244,1245,1246],[1124,18325,1693],{"className":18326,"style":1929},[1209,1213,1246],[1124,18328,18329,18332],{"style":3905},[1124,18330],{"className":18331,"style":1239},[1238],[1124,18333,18335],{"className":18334},[1243,1244,1245,1246],[1124,18336,5657],{"className":18337,"style":5740},[1209,1213,1246],[1124,18339,1254],{"className":18340},[1253],[1124,18342,18344],{"className":18343},[1226],[1124,18345,18347],{"className":18346,"style":12762},[1230],[1124,18348],{},[1120,18350,18351,18352,18413],{},"该变化传播到第 ",[1124,18353,18355,18377],{"className":18354},[1127],[1124,18356,18358],{"className":18357},[1131],[1133,18359,18360],{"xmlns":1135},[1137,18361,18362,18374],{},[1140,18363,18364,18366,18368,18370,18372],{},[1154,18365,2677],{"stretchy":1674},[1146,18367,5657],{},[1154,18369,2330],{},[1150,18371,1152],{},[1154,18373,2683],{"stretchy":1674},[1189,18375,18376],{"encoding":1191},"(l+1)",[1124,18378,18380,18401],{"className":18379,"ariaHidden":1156},[1196],[1124,18381,18383,18386,18389,18392,18395,18398],{"className":18382},[1200],[1124,18384],{"className":18385,"style":2696},[1204],[1124,18387,2677],{"className":18388},[1795],[1124,18390,5657],{"className":18391,"style":5740},[1209,1213],[1124,18393],{"className":18394,"style":2500},[1271],[1124,18396,2330],{"className":18397},[2504],[1124,18399],{"className":18400,"style":2500},[1271],[1124,18402,18404,18407,18410],{"className":18403},[1200],[1124,18405],{"className":18406,"style":2696},[1204],[1124,18408,1152],{"className":18409},[1209],[1124,18411,2683],{"className":18412},[2211]," 层所有与之连接的神经元",[1120,18415,18416,18417,18536],{},"继续逐层传播，经过第 ",[1124,18418,18420,18458],{"className":18419},[1127],[1124,18421,18423],{"className":18422},[1131],[1133,18424,18425],{"xmlns":1135},[1137,18426,18427,18455],{},[1140,18428,18429,18431,18433,18435,18437,18439,18441,18443,18445,18447,18449,18451,18453],{},[1154,18430,2677],{"stretchy":1674},[1146,18432,5657],{},[1154,18434,2330],{},[1150,18436,1164],{},[1154,18438,2683],{"stretchy":1674},[1154,18440,1157],{"separator":1156},[1154,18442,2677],{"stretchy":1674},[1146,18444,5657],{},[1154,18446,2330],{},[1150,18448,1173],{},[1154,18450,2683],{"stretchy":1674},[1154,18452,1157],{"separator":1156},[1154,18454,1178],{},[1189,18456,18457],{"encoding":1191},"(l+2), (l+3), \\ldots",[1124,18459,18461,18482,18515],{"className":18460,"ariaHidden":1156},[1196],[1124,18462,18464,18467,18470,18473,18476,18479],{"className":18463},[1200],[1124,18465],{"className":18466,"style":2696},[1204],[1124,18468,2677],{"className":18469},[1795],[1124,18471,5657],{"className":18472,"style":5740},[1209,1213],[1124,18474],{"className":18475,"style":2500},[1271],[1124,18477,2330],{"className":18478},[2504],[1124,18480],{"className":18481,"style":2500},[1271],[1124,18483,18485,18488,18491,18494,18497,18500,18503,18506,18509,18512],{"className":18484},[1200],[1124,18486],{"className":18487,"style":2696},[1204],[1124,18489,1164],{"className":18490},[1209],[1124,18492,2683],{"className":18493},[2211],[1124,18495,1157],{"className":18496},[1267],[1124,18498],{"className":18499,"style":1272},[1271],[1124,18501,2677],{"className":18502},[1795],[1124,18504,5657],{"className":18505,"style":5740},[1209,1213],[1124,18507],{"className":18508,"style":2500},[1271],[1124,18510,2330],{"className":18511},[2504],[1124,18513],{"className":18514,"style":2500},[1271],[1124,18516,18518,18521,18524,18527,18530,18533],{"className":18517},[1200],[1124,18519],{"className":18520,"style":2696},[1204],[1124,18522,1173],{"className":18523},[1209],[1124,18525,2683],{"className":18526},[2211],[1124,18528,1157],{"className":18529},[1267],[1124,18531],{"className":18532,"style":1272},[1271],[1124,18534,1178],{"className":18535},[1368]," 层",[1120,18538,18539,18540],{},"最终到达输出层，引起代价函数的变化 ",[1124,18541,18543,18559],{"className":18542},[1127],[1124,18544,18546],{"className":18545},[1131],[1133,18547,18548],{"xmlns":1135},[1137,18549,18550,18556],{},[1140,18551,18552,18554],{},[1146,18553,3146],{"mathvariant":3145},[1146,18555,4325],{},[1189,18557,18558],{"encoding":1191},"\\Delta C",[1124,18560,18562],{"className":18561,"ariaHidden":1156},[1196],[1124,18563,18565,18568,18571],{"className":18564},[1200],[1124,18566],{"className":18567,"style":4804},[1204],[1124,18569,3146],{"className":18570},[1209],[1124,18572,4325],{"className":18573,"style":4392},[1209,1213],[1101,18575,18576],{},[1107,18577,18578],{},"路径求和公式",[1101,18580,18581],{},"代价函数关于权重的偏导数可以表达为所有从该权重到输出的路径上偏导数乘积的求和：",[1101,18583,18584],{},[1124,18585,18587,18643],{"className":18586},[1127],[1124,18588,18590],{"className":18589},[1131],[1133,18591,18592],{"xmlns":1135},[1137,18593,18594,18640],{},[1140,18595,18596,18620,18622,18629,18637],{},[2911,18597,18598,18604],{},[1140,18599,18600,18602],{},[1146,18601,3164],{"mathvariant":3145},[1146,18603,4325],{},[1140,18605,18606,18608],{},[1146,18607,3164],{"mathvariant":3145},[5282,18609,18610,18612,18618],{},[1146,18611,1439],{},[1140,18613,18614,18616],{},[1146,18615,1693],{},[1146,18617,5278],{},[1146,18619,5657],{},[1154,18621,1652],{},[1143,18623,18624,18626],{},[1154,18625,1690],{},[1647,18627,18628],{},"paths",[1143,18630,18631,18634],{},[1154,18632,18633],{},"∏",[1647,18635,18636],{},"edges along path",[1647,18638,18639],{},"(partial derivatives)",[1189,18641,18642],{"encoding":1191},"\\frac{\\partial C}{\\partial w^l_{jk}} = \\sum_{\\text{paths}} \\prod_{\\text{edges along path}} \\text{(partial derivatives)}",[1124,18644,18646,18789],{"className":18645,"ariaHidden":1156},[1196],[1124,18647,18649,18652,18780,18783,18786],{"className":18648},[1200],[1124,18650],{"className":18651,"style":15279},[1204],[1124,18653,18655,18658,18777],{"className":18654},[1209],[1124,18656],{"className":18657},[1795,2212],[1124,18659,18661],{"className":18660},[2911],[1124,18662,18664,18769],{"className":18663},[1221,1222],[1124,18665,18667,18766],{"className":18666},[1226],[1124,18668,18670,18741,18749],{"className":18669,"style":4858},[1230],[1124,18671,18672,18675],{"style":14038},[1124,18673],{"className":18674,"style":2998},[1238],[1124,18676,18678],{"className":18677},[1243,1244,1245,1246],[1124,18679,18681,18684],{"className":18680},[1209,1246],[1124,18682,3164],{"className":18683,"style":3319},[1209,1246],[1124,18685,18687,18690],{"className":18686},[1209,1246],[1124,18688,1439],{"className":18689,"style":1480},[1209,1213,1246],[1124,18691,18693],{"className":18692},[1217],[1124,18694,18696,18733],{"className":18695},[1221,1222],[1124,18697,18699,18730],{"className":18698},[1226],[1124,18700,18702,18719],{"className":18701,"style":14069},[1230],[1124,18703,18704,18707],{"style":15332},[1124,18705],{"className":18706,"style":3036},[1238],[1124,18708,18710],{"className":18709},[1243,3040,3041,1246],[1124,18711,18713,18716],{"className":18712},[1209,1246],[1124,18714,1693],{"className":18715,"style":1929},[1209,1213,1246],[1124,18717,5278],{"className":18718,"style":5363},[1209,1213,1246],[1124,18720,18721,18724],{"style":14084},[1124,18722],{"className":18723,"style":3036},[1238],[1124,18725,18727],{"className":18726},[1243,3040,3041,1246],[1124,18728,5657],{"className":18729,"style":5740},[1209,1213,1246],[1124,18731,1254],{"className":18732},[1253],[1124,18734,18736],{"className":18735},[1226],[1124,18737,18739],{"className":18738,"style":15368},[1230],[1124,18740],{},[1124,18742,18743,18746],{"style":3053},[1124,18744],{"className":18745,"style":2998},[1238],[1124,18747],{"className":18748,"style":3061},[3060],[1124,18750,18751,18754],{"style":3064},[1124,18752],{"className":18753,"style":2998},[1238],[1124,18755,18757],{"className":18756},[1243,1244,1245,1246],[1124,18758,18760,18763],{"className":18759},[1209,1246],[1124,18761,3164],{"className":18762,"style":3319},[1209,1246],[1124,18764,4325],{"className":18765,"style":4392},[1209,1213,1246],[1124,18767,1254],{"className":18768},[1253],[1124,18770,18772],{"className":18771},[1226],[1124,18773,18775],{"className":18774,"style":15405},[1230],[1124,18776],{},[1124,18778],{"className":18779},[2211,2212],[1124,18781],{"className":18782,"style":1774},[1271],[1124,18784,1652],{"className":18785},[1778],[1124,18787],{"className":18788,"style":1774},[1271],[1124,18790,18792,18796,18843,18846,18892,18895],{"className":18791},[1200],[1124,18793],{"className":18794,"style":18795},[1204],"height:1.1858em;vertical-align:-0.4358em;",[1124,18797,18799,18802],{"className":18798},[1897],[1124,18800,1690],{"className":18801,"style":1903},[1897,1901,1902],[1124,18803,18805],{"className":18804},[1217],[1124,18806,18808,18835],{"className":18807},[1221,1222],[1124,18809,18811,18832],{"className":18810},[1226],[1124,18812,18815],{"className":18813,"style":18814},[1230],"height:0.1864em;",[1124,18816,18817,18820],{"style":1919},[1124,18818],{"className":18819,"style":1239},[1238],[1124,18821,18823],{"className":18822},[1243,1244,1245,1246],[1124,18824,18826],{"className":18825},[1209,1246],[1124,18827,18829],{"className":18828},[1209,1767,1246],[1124,18830,18628],{"className":18831},[1209,1246],[1124,18833,1254],{"className":18834},[1253],[1124,18836,18838],{"className":18837},[1226],[1124,18839,18841],{"className":18840,"style":1939},[1230],[1124,18842],{},[1124,18844],{"className":18845,"style":1272},[1271],[1124,18847,18849,18852],{"className":18848},[1897],[1124,18850,18633],{"className":18851,"style":1903},[1897,1901,1902],[1124,18853,18855],{"className":18854},[1217],[1124,18856,18858,18884],{"className":18857},[1221,1222],[1124,18859,18861,18881],{"className":18860},[1226],[1124,18862,18864],{"className":18863,"style":18814},[1230],[1124,18865,18866,18869],{"style":1919},[1124,18867],{"className":18868,"style":1239},[1238],[1124,18870,18872],{"className":18871},[1243,1244,1245,1246],[1124,18873,18875],{"className":18874},[1209,1246],[1124,18876,18878],{"className":18877},[1209,1767,1246],[1124,18879,18636],{"className":18880},[1209,1246],[1124,18882,1254],{"className":18883},[1253],[1124,18885,18887],{"className":18886},[1226],[1124,18888,18890],{"className":18889,"style":1939},[1230],[1124,18891],{},[1124,18893],{"className":18894,"style":1272},[1271],[1124,18896,18898],{"className":18897},[1209,1767],[1124,18899,18639],{"className":18900},[1209],[1101,18902,18903],{},"具体展开：",[1101,18905,18906],{},[1124,18907,18909,19168],{"className":18908},[1127],[1124,18910,18912],{"className":18911},[1131],[1133,18913,18914],{"xmlns":1135},[1137,18915,18916,19165],{},[1140,18917,18918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C}{\\partial w^l_{jk}} = \\sum_{p_l, p_{l+1}, \\ldots, p_L} \\frac{\\partial C}{\\partial a^L_{p_L}} \\cdot \\sigma'(z^L_{p_L}) \\cdot w^L_{p_L, p_{L-1}} \\cdots \\sigma'(z^{l+1}_{p_{l+1}}) \\cdot w^{l+1}_{p_{l+1}, j} \\cdot \\sigma'(z^l_j) \\cdot 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[1243,1244,1245,1246],[1124,20252,20254,20257,20260],{"className":20253},[1209,1246],[1124,20255,5657],{"className":20256,"style":5740},[1209,1213,1246],[1124,20258,2330],{"className":20259},[2504,1246],[1124,20261,1152],{"className":20262},[1209,1246],[1124,20264,1254],{"className":20265},[1253],[1124,20267,20269],{"className":20268},[1226],[1124,20270,20273],{"className":20271,"style":20272},[1230],"height:0.4244em;",[1124,20274],{},[1124,20276],{"className":20277,"style":2500},[1271],[1124,20279,2325],{"className":20280},[2504],[1124,20282],{"className":20283,"style":2500},[1271],[1124,20285,20287,20290,20322,20325,20376,20379,20382,20385],{"className":20286},[1200],[1124,20288],{"className":20289,"style":12711},[1204],[1124,20291,20293,20296],{"className":20292},[1209],[1124,20294,2674],{"className":20295,"style":2700},[1209,1213],[1124,20297,20299],{"className":20298},[1217],[1124,20300,20302],{"className":20301},[1221],[1124,20303,20305],{"className":20304},[1226],[1124,20306,20308],{"className":20307,"style":3902},[1230],[1124,20309,20310,20313],{"style":3905},[1124,20311],{"className":20312,"style":1239},[1238],[1124,20314,20316],{"className":20315},[1243,1244,1245,1246],[1124,20317,20319],{"className":20318},[1209,1246],[1124,20320,3838],{"className":20321},[1209,1246],[1124,20323,2677],{"className":20324},[1795],[1124,20326,20328,20331],{"className":20327},[1209],[1124,20329,2680],{"className":20330,"style":2707},[1209,1213],[1124,20332,20334],{"className":20333},[1217],[1124,20335,20337,20368],{"className":20336},[1221,1222],[1124,20338,20340,20365],{"className":20339},[1226],[1124,20341,20343,20354],{"className":20342,"style":7649},[1230],[1124,20344,20345,20348],{"style":13027},[1124,20346],{"className":20347,"style":1239},[1238],[1124,20349,20351],{"className":20350},[1243,1244,1245,1246],[1124,20352,1693],{"className":20353,"style":1929},[1209,1213,1246],[1124,20355,20356,20359],{"style":3905},[1124,20357],{"className":20358,"style":1239},[1238],[1124,20360,20362],{"className":20361},[1243,1244,1245,1246],[1124,20363,5657],{"className":20364,"style":5740},[1209,1213,1246],[1124,20366,1254],{"className":20367},[1253],[1124,20369,20371],{"className":20370},[1226],[1124,20372,20374],{"className":20373,"style":12762},[1230],[1124,20375],{},[1124,20377,2683],{"className":20378},[2211],[1124,20380],{"className":20381,"style":2500},[1271],[1124,20383,2325],{"className":20384},[2504],[1124,20386],{"className":20387,"style":2500},[1271],[1124,20389,20391,20394],{"className":20390},[1200],[1124,20392],{"className":20393,"style":15426},[1204],[1124,20395,20397,20400],{"className":20396},[1209],[1124,20398,4370],{"className":20399},[1209,1213],[1124,20401,20403],{"className":20402},[1217],[1124,20404,20406,20446],{"className":20405},[1221,1222],[1124,20407,20409,20443],{"className":20408},[1226],[1124,20410,20412,20423],{"className":20411,"style":15445},[1230],[1124,20413,20414,20417],{"style":15448},[1124,20415],{"className":20416,"style":1239},[1238],[1124,20418,20420],{"className":20419},[1243,1244,1245,1246],[1124,20421,5278],{"className":20422,"style":5363},[1209,1213,1246],[1124,20424,20425,20428],{"style":15460},[1124,20426],{"className":20427,"style":1239},[1238],[1124,20429,20431],{"className":20430},[1243,1244,1245,1246],[1124,20432,20434,20437,20440],{"className":20433},[1209,1246],[1124,20435,5657],{"className":20436,"style":5740},[1209,1213,1246],[1124,20438,2235],{"className":20439},[2504,1246],[1124,20441,1152],{"className":20442},[1209,1246],[1124,20444,1254],{"className":20445},[1253],[1124,20447,20449],{"className":20448},[1226],[1124,20450,20452],{"className":20451,"style":15488},[1230],[1124,20453],{},[1101,20455,20456,20459],{},[1107,20457,20458],{},"总结","：反向传播不是什么\"魔法\"——它本质上就是链式法则的系统应用。通过从输出层开始逐层向后计算误差，我们能高效地获得所有参数的梯度，而不需要对每个参数单独做扰动实验。这使得训练拥有数百万参数的深度网络成为可能。",[1101,20461,20462],{},"案例：",[1091,20464,20466],{"id":20465},"示例2-层网络的完整前向传播与反向传播","示例：2 层网络的完整前向传播与反向传播",[8697,20468,20471],{"className":20469,"code":20470,"language":8702,"meta":8703},[8700],"输入层(1个)  →  隐藏层(1个神经元)  →  输出层(1个神经元)\n    x       →       a¹              →       a²（预测值）\n",[8705,20472,20470],{"__ignoreMap":8707},[1101,20474,20475],{},[1107,20476,9737],{},[1117,20478,20479,20601,20722],{},[1120,20480,20481,20482,20541,20542],{},"隐藏层：权重 ",[1124,20483,20485,20503],{"className":20484},[1127],[1124,20486,20488],{"className":20487},[1131],[1133,20489,20490],{"xmlns":1135},[1137,20491,20492,20500],{},[1140,20493,20494],{},[2922,20495,20496,20498],{},[1146,20497,1439],{},[1150,20499,1152],{},[1189,20501,20502],{"encoding":1191},"w^1",[1124,20504,20506],{"className":20505,"ariaHidden":1156},[1196],[1124,20507,20509,20512],{"className":20508},[1200],[1124,20510],{"className":20511,"style":4598},[1204],[1124,20513,20515,20518],{"className":20514},[1209],[1124,20516,1439],{"className":20517,"style":1480},[1209,1213],[1124,20519,20521],{"className":20520},[1217],[1124,20522,20524],{"className":20523},[1221],[1124,20525,20527],{"className":20526},[1226],[1124,20528,20530],{"className":20529,"style":4598},[1230],[1124,20531,20532,20535],{"style":3905},[1124,20533],{"className":20534,"style":1239},[1238],[1124,20536,20538],{"className":20537},[1243,1244,1245,1246],[1124,20539,1152],{"className":20540},[1209,1246],"，偏置 ",[1124,20543,20545,20563],{"className":20544},[1127],[1124,20546,20548],{"className":20547},[1131],[1133,20549,20550],{"xmlns":1135},[1137,20551,20552,20560],{},[1140,20553,20554],{},[2922,20555,20556,20558],{},[1146,20557,2230],{},[1150,20559,1152],{},[1189,20561,20562],{"encoding":1191},"b^1",[1124,20564,20566],{"className":20565,"ariaHidden":1156},[1196],[1124,20567,20569,20572],{"className":20568},[1200],[1124,20570],{"className":20571,"style":4598},[1204],[1124,20573,20575,20578],{"className":20574},[1209],[1124,20576,2230],{"className":20577},[1209,1213],[1124,20579,20581],{"className":20580},[1217],[1124,20582,20584],{"className":20583},[1221],[1124,20585,20587],{"className":20586},[1226],[1124,20588,20590],{"className":20589,"style":4598},[1230],[1124,20591,20592,20595],{"style":3905},[1124,20593],{"className":20594,"style":1239},[1238],[1124,20596,20598],{"className":20597},[1243,1244,1245,1246],[1124,20599,1152],{"className":20600},[1209,1246],[1120,20602,20603,20604,20541,20663],{},"输出层：权重 ",[1124,20605,20607,20625],{"className":20606},[1127],[1124,20608,20610],{"className":20609},[1131],[1133,20611,20612],{"xmlns":1135},[1137,20613,20614,20622],{},[1140,20615,20616],{},[2922,20617,20618,20620],{},[1146,20619,1439],{},[1150,20621,1164],{},[1189,20623,20624],{"encoding":1191},"w^2",[1124,20626,20628],{"className":20627,"ariaHidden":1156},[1196],[1124,20629,20631,20634],{"className":20630},[1200],[1124,20632],{"className":20633,"style":4598},[1204],[1124,20635,20637,20640],{"className":20636},[1209],[1124,20638,1439],{"className":20639,"style":1480},[1209,1213],[1124,20641,20643],{"className":20642},[1217],[1124,20644,20646],{"className":20645},[1221],[1124,20647,20649],{"className":20648},[1226],[1124,20650,20652],{"className":20651,"style":4598},[1230],[1124,20653,20654,20657],{"style":3905},[1124,20655],{"className":20656,"style":1239},[1238],[1124,20658,20660],{"className":20659},[1243,1244,1245,1246],[1124,20661,1164],{"className":20662},[1209,1246],[1124,20664,20666,20684],{"className":20665},[1127],[1124,20667,20669],{"className":20668},[1131],[1133,20670,20671],{"xmlns":1135},[1137,20672,20673,20681],{},[1140,20674,20675],{},[2922,20676,20677,20679],{},[1146,20678,2230],{},[1150,20680,1164],{},[1189,20682,20683],{"encoding":1191},"b^2",[1124,20685,20687],{"className":20686,"ariaHidden":1156},[1196],[1124,20688,20690,20693],{"className":20689},[1200],[1124,20691],{"className":20692,"style":4598},[1204],[1124,20694,20696,20699],{"className":20695},[1209],[1124,20697,2230],{"className":20698},[1209,1213],[1124,20700,20702],{"className":20701},[1217],[1124,20703,20705],{"className":20704},[1221],[1124,20706,20708],{"className":20707},[1226],[1124,20709,20711],{"className":20710,"style":4598},[1230],[1124,20712,20713,20716],{"style":3905},[1124,20714],{"className":20715,"style":1239},[1238],[1124,20717,20719],{"className":20718},[1243,1244,1245,1246],[1124,20720,1164],{"className":20721},[1209,1246],[1120,20723,20724,20725],{},"激活函数：sigmoid ",[1124,20726,20728,20770],{"className":20727},[1127],[1124,20729,20731],{"className":20730},[1131],[1133,20732,20733],{"xmlns":1135},[1137,20734,20735,20767],{},[1140,20736,20737,20739,20741,20743,20745,20747],{},[1146,20738,2674],{},[1154,20740,2677],{"stretchy":1674},[1146,20742,2680],{},[1154,20744,2683],{"stretchy":1674},[1154,20746,1652],{},[2911,20748,20749,20751],{},[1150,20750,1152],{},[1140,20752,20753,20755,20757],{},[1150,20754,1152],{},[1154,20756,2330],{},[2922,20758,20759,20761],{},[1146,20760,2926],{},[1140,20762,20763,20765],{},[1154,20764,2235],{},[1146,20766,2680],{},[1189,20768,20769],{"encoding":1191},"\\sigma(z) = \\frac{1}{1+e^{-z}}",[1124,20771,20773,20800],{"className":20772,"ariaHidden":1156},[1196],[1124,20774,20776,20779,20782,20785,20788,20791,20794,20797],{"className":20775},[1200],[1124,20777],{"className":20778,"style":2696},[1204],[1124,20780,2674],{"className":20781,"style":2700},[1209,1213],[1124,20783,2677],{"className":20784},[1795],[1124,20786,2680],{"className":20787,"style":2707},[1209,1213],[1124,20789,2683],{"className":20790},[2211],[1124,20792],{"className":20793,"style":1774},[1271],[1124,20795,1652],{"className":20796},[1778],[1124,20798],{"className":20799,"style":1774},[1271],[1124,20801,20803,20806],{"className":20802},[1200],[1124,20804],{"className":20805,"style":2972},[1204],[1124,20807,20809,20812,20909],{"className":20808},[1209],[1124,20810],{"className":20811},[1795,2212],[1124,20813,20815],{"className":20814},[2911],[1124,20816,20818,20901],{"className":20817},[1221,1222],[1124,20819,20821,20898],{"className":20820},[1226],[1124,20822,20824,20876,20884],{"className":20823,"style":2991},[1230],[1124,20825,20826,20829],{"style":2994},[1124,20827],{"className":20828,"style":2998},[1238],[1124,20830,20832],{"className":20831},[1243,1244,1245,1246],[1124,20833,20835,20838,20841],{"className":20834},[1209,1246],[1124,20836,1152],{"className":20837},[1209,1246],[1124,20839,2330],{"className":20840},[2504,1246],[1124,20842,20844,20847],{"className":20843},[1209,1246],[1124,20845,2926],{"className":20846},[1209,1213,1246],[1124,20848,20850],{"className":20849},[1217],[1124,20851,20853],{"className":20852},[1221],[1124,20854,20856],{"className":20855},[1226],[1124,20857,20859],{"className":20858,"style":3029},[1230],[1124,20860,20861,20864],{"style":3032},[1124,20862],{"className":20863,"style":3036},[1238],[1124,20865,20867],{"className":20866},[1243,3040,3041,1246],[1124,20868,20870,20873],{"className":20869},[1209,1246],[1124,20871,2235],{"className":20872},[1209,1246],[1124,20874,2680],{"className":20875,"style":2707},[1209,1213,1246],[1124,20877,20878,20881],{"style":3053},[1124,20879],{"className":20880,"style":2998},[1238],[1124,20882],{"className":20883,"style":3061},[3060],[1124,20885,20886,20889],{"style":3064},[1124,20887],{"className":20888,"style":2998},[1238],[1124,20890,20892],{"className":20891},[1243,1244,1245,1246],[1124,20893,20895],{"className":20894},[1209,1246],[1124,20896,1152],{"className":20897},[1209,1246],[1124,20899,1254],{"className":20900},[1253],[1124,20902,20904],{"className":20903},[1226],[1124,20905,20907],{"className":20906,"style":3086},[1230],[1124,20908],{},[1124,20910],{"className":20911},[2211,2212],[2616,20913,20914,20924],{},[2619,20915,20916],{},[2622,20917,20918,20921],{},[2625,20919,20920],{},"参数",[2625,20922,20923],{},"值",[2635,20925,20926,20990,21054,21118,21182,21218,21254],{},[2622,20927,20928,20988],{},[2640,20929,20930],{},[1124,20931,20933,20950],{"className":20932},[1127],[1124,20934,20936],{"className":20935},[1131],[1133,20937,20938],{"xmlns":1135},[1137,20939,20940,20948],{},[1140,20941,20942],{},[2922,20943,20944,20946],{},[1146,20945,1439],{},[1150,20947,1152],{},[1189,20949,20502],{"encoding":1191},[1124,20951,20953],{"className":20952,"ariaHidden":1156},[1196],[1124,20954,20956,20959],{"className":20955},[1200],[1124,20957],{"className":20958,"style":4598},[1204],[1124,20960,20962,20965],{"className":20961},[1209],[1124,20963,1439],{"className":20964,"style":1480},[1209,1213],[1124,20966,20968],{"className":20967},[1217],[1124,20969,20971],{"className":20970},[1221],[1124,20972,20974],{"className":20973},[1226],[1124,20975,20977],{"className":20976,"style":4598},[1230],[1124,20978,20979,20982],{"style":3905},[1124,20980],{"className":20981,"style":1239},[1238],[1124,20983,20985],{"className":20984},[1243,1244,1245,1246],[1124,20986,1152],{"className":20987},[1209,1246],[2640,20989,9792],{},[2622,20991,20992,21052],{},[2640,20993,20994],{},[1124,20995,20997,21014],{"className":20996},[1127],[1124,20998,21000],{"className":20999},[1131],[1133,21001,21002],{"xmlns":1135},[1137,21003,21004,21012],{},[1140,21005,21006],{},[2922,21007,21008,21010],{},[1146,21009,2230],{},[1150,21011,1152],{},[1189,21013,20562],{"encoding":1191},[1124,21015,21017],{"className":21016,"ariaHidden":1156},[1196],[1124,21018,21020,21023],{"className":21019},[1200],[1124,21021],{"className":21022,"style":4598},[1204],[1124,21024,21026,21029],{"className":21025},[1209],[1124,21027,2230],{"className":21028},[1209,1213],[1124,21030,21032],{"className":21031},[1217],[1124,21033,21035],{"className":21034},[1221],[1124,21036,21038],{"className":21037},[1226],[1124,21039,21041],{"className":21040,"style":4598},[1230],[1124,21042,21043,21046],{"style":3905},[1124,21044],{"className":21045,"style":1239},[1238],[1124,21047,21049],{"className":21048},[1243,1244,1245,1246],[1124,21050,1152],{"className":21051},[1209,1246],[2640,21053,9829],{},[2622,21055,21056,21116],{},[2640,21057,21058],{},[1124,21059,21061,21078],{"className":21060},[1127],[1124,21062,21064],{"className":21063},[1131],[1133,21065,21066],{"xmlns":1135},[1137,21067,21068,21076],{},[1140,21069,21070],{},[2922,21071,21072,21074],{},[1146,21073,1439],{},[1150,21075,1164],{},[1189,21077,20624],{"encoding":1191},[1124,21079,21081],{"className":21080,"ariaHidden":1156},[1196],[1124,21082,21084,21087],{"className":21083},[1200],[1124,21085],{"className":21086,"style":4598},[1204],[1124,21088,21090,21093],{"className":21089},[1209],[1124,21091,1439],{"className":21092,"style":1480},[1209,1213],[1124,21094,21096],{"className":21095},[1217],[1124,21097,21099],{"className":21098},[1221],[1124,21100,21102],{"className":21101},[1226],[1124,21103,21105],{"className":21104,"style":4598},[1230],[1124,21106,21107,21110],{"style":3905},[1124,21108],{"className":21109,"style":1239},[1238],[1124,21111,21113],{"className":21112},[1243,1244,1245,1246],[1124,21114,1164],{"className":21115},[1209,1246],[2640,21117,10186],{},[2622,21119,21120,21180],{},[2640,21121,21122],{},[1124,21123,21125,21142],{"className":21124},[1127],[1124,21126,21128],{"className":21127},[1131],[1133,21129,21130],{"xmlns":1135},[1137,21131,21132,21140],{},[1140,21133,21134],{},[2922,21135,21136,21138],{},[1146,21137,2230],{},[1150,21139,1164],{},[1189,21141,20683],{"encoding":1191},[1124,21143,21145],{"className":21144,"ariaHidden":1156},[1196],[1124,21146,21148,21151],{"className":21147},[1200],[1124,21149],{"className":21150,"style":4598},[1204],[1124,21152,21154,21157],{"className":21153},[1209],[1124,21155,2230],{"className":21156},[1209,1213],[1124,21158,21160],{"className":21159},[1217],[1124,21161,21163],{"className":21162},[1221],[1124,21164,21166],{"className":21165},[1226],[1124,21167,21169],{"className":21168,"style":4598},[1230],[1124,21170,21171,21174],{"style":3905},[1124,21172],{"className":21173,"style":1239},[1238],[1124,21175,21177],{"className":21176},[1243,1244,1245,1246],[1124,21178,1164],{"className":21179},[1209,1246],[2640,21181,9799],{},[2622,21183,21184,21215],{},[2640,21185,21186,21187],{},"输入 ",[1124,21188,21190,21203],{"className":21189},[1127],[1124,21191,21193],{"className":21192},[1131],[1133,21194,21195],{"xmlns":1135},[1137,21196,21197,21201],{},[1140,21198,21199],{},[1146,21200,1148],{},[1189,21202,1148],{"encoding":1191},[1124,21204,21206],{"className":21205,"ariaHidden":1156},[1196],[1124,21207,21209,21212],{"className":21208},[1200],[1124,21210],{"className":21211,"style":3124},[1204],[1124,21213,1148],{"className":21214},[1209,1213],[2640,21216,21217],{},"2.0",[2622,21219,21220,21251],{},[2640,21221,21222,21223],{},"期望输出 ",[1124,21224,21226,21239],{"className":21225},[1127],[1124,21227,21229],{"className":21228},[1131],[1133,21230,21231],{"xmlns":1135},[1137,21232,21233,21237],{},[1140,21234,21235],{},[1146,21236,4359],{},[1189,21238,4359],{"encoding":1191},[1124,21240,21242],{"className":21241,"ariaHidden":1156},[1196],[1124,21243,21245,21248],{"className":21244},[1200],[1124,21246],{"className":21247,"style":1205},[1204],[1124,21249,4359],{"className":21250,"style":2700},[1209,1213],[2640,21252,21253],{},"1.0",[2622,21255,21256,21287],{},[2640,21257,21258,21259],{},"学习率 ",[1124,21260,21262,21275],{"className":21261},[1127],[1124,21263,21265],{"className":21264},[1131],[1133,21266,21267],{"xmlns":1135},[1137,21268,21269,21273],{},[1140,21270,21271],{},[1146,21272,5145],{},[1189,21274,6025],{"encoding":1191},[1124,21276,21278],{"className":21277,"ariaHidden":1156},[1196],[1124,21279,21281,21284],{"className":21280},[1200],[1124,21282],{"className":21283,"style":1205},[1204],[1124,21285,5145],{"className":21286,"style":2700},[1209,1213],[2640,21288,9783],{},[1101,21290,21291,21292],{},"代价函数：",[1124,21293,21295,21335],{"className":21294},[1127],[1124,21296,21298],{"className":21297},[1131],[1133,21299,21300],{"xmlns":1135},[1137,21301,21302,21332],{},[1140,21303,21304,21306,21308,21314,21316,21322,21324,21326],{},[1146,21305,4325],{},[1154,21307,1652],{},[2911,21309,21310,21312],{},[1150,21311,1152],{},[1150,21313,1164],{},[1154,21315,2677],{"stretchy":1674},[2922,21317,21318,21320],{},[1146,21319,4370],{},[1150,21321,1164],{},[1154,21323,2235],{},[1146,21325,4359],{},[2922,21327,21328,21330],{},[1154,21329,2683],{"stretchy":1674},[1150,21331,1164],{},[1189,21333,21334],{"encoding":1191},"C = \\frac{1}{2}(a^2 - y)^2",[1124,21336,21338,21356,21471],{"className":21337,"ariaHidden":1156},[1196],[1124,21339,21341,21344,21347,21350,21353],{"className":21340},[1200],[1124,21342],{"className":21343,"style":4804},[1204],[1124,21345,4325],{"className":21346,"style":4392},[1209,1213],[1124,21348],{"className":21349,"style":1774},[1271],[1124,21351,1652],{"className":21352},[1778],[1124,21354],{"className":21355,"style":1774},[1271],[1124,21357,21359,21362,21430,21433,21462,21465,21468],{"className":21358},[1200],[1124,21360],{"className":21361,"style":4426},[1204],[1124,21363,21365,21368,21427],{"className":21364},[1209],[1124,21366],{"className":21367},[1795,2212],[1124,21369,21371],{"className":21370},[2911],[1124,21372,21374,21419],{"className":21373},[1221,1222],[1124,21375,21377,21416],{"className":21376},[1226],[1124,21378,21380,21394,21402],{"className":21379,"style":2991},[1230],[1124,21381,21382,21385],{"style":2994},[1124,21383],{"className":21384,"style":2998},[1238],[1124,21386,21388],{"className":21387},[1243,1244,1245,1246],[1124,21389,21391],{"className":21390},[1209,1246],[1124,21392,1164],{"className":21393},[1209,1246],[1124,21395,21396,21399],{"style":3053},[1124,21397],{"className":21398,"style":2998},[1238],[1124,21400],{"className":21401,"style":3061},[3060],[1124,21403,21404,21407],{"style":3064},[1124,21405],{"className":21406,"style":2998},[1238],[1124,21408,21410],{"className":21409},[1243,1244,1245,1246],[1124,21411,21413],{"className":21412},[1209,1246],[1124,21414,1152],{"className":21415},[1209,1246],[1124,21417,1254],{"className":21418},[1253],[1124,21420,21422],{"className":21421},[1226],[1124,21423,21425],{"className":21424,"style":3538},[1230],[1124,21426],{},[1124,21428],{"className":21429},[2211,2212],[1124,21431,2677],{"className":21432},[1795],[1124,21434,21436,21439],{"className":21435},[1209],[1124,21437,4370],{"className":21438},[1209,1213],[1124,21440,21442],{"className":21441},[1217],[1124,21443,21445],{"className":21444},[1221],[1124,21446,21448],{"className":21447},[1226],[1124,21449,21451],{"className":21450,"style":4598},[1230],[1124,21452,21453,21456],{"style":3905},[1124,21454],{"className":21455,"style":1239},[1238],[1124,21457,21459],{"className":21458},[1243,1244,1245,1246],[1124,21460,1164],{"className":21461},[1209,1246],[1124,21463],{"className":21464,"style":2500},[1271],[1124,21466,2235],{"className":21467},[2504],[1124,21469],{"className":21470,"style":2500},[1271],[1124,21472,21474,21477,21480],{"className":21473},[1200],[1124,21475],{"className":21476,"style":4576},[1204],[1124,21478,4359],{"className":21479,"style":2700},[1209,1213],[1124,21481,21483,21486],{"className":21482},[2211],[1124,21484,2683],{"className":21485},[2211],[1124,21487,21489],{"className":21488},[1217],[1124,21490,21492],{"className":21491},[1221],[1124,21493,21495],{"className":21494},[1226],[1124,21496,21498],{"className":21497,"style":4598},[1230],[1124,21499,21500,21503],{"style":3905},[1124,21501],{"className":21502,"style":1239},[1238],[1124,21504,21506],{"className":21505},[1243,1244,1245,1246],[1124,21507,1164],{"className":21508},[1209,1246],[2745,21510],{},[1096,21512,15635],{"id":15635},[1101,21514,21515],{},"第 1 层（隐藏层）",[1101,21517,21518],{},[1124,21519,21521,21576],{"className":21520},[1127],[1124,21522,21524],{"className":21523},[1131],[1133,21525,21526],{"xmlns":1135},[1137,21527,21528,21573],{},[1140,21529,21530,21536,21538,21544,21546,21548,21550,21556,21558,21560,21562,21564,21566,21568,21570],{},[2922,21531,21532,21534],{},[1146,21533,2680],{},[1150,21535,1152],{},[1154,21537,1652],{},[2922,21539,21540,21542],{},[1146,21541,1439],{},[1150,21543,1152],{},[1154,21545,2325],{},[1146,21547,1148],{},[1154,21549,2330],{},[2922,21551,21552,21554],{},[1146,21553,2230],{},[1150,21555,1152],{},[1154,21557,1652],{},[1150,21559,9792],{},[1154,21561,10608],{},[1150,21563,21217],{},[1154,21565,2330],{},[1150,21567,9829],{},[1154,21569,1652],{},[1150,21571,21572],{},"0.9",[1189,21574,21575],{"encoding":1191},"z^1 = w^1 \\cdot x + b^1 = 0.4 \\times 2.0 + 0.1 = 0.9",[1124,21577,21579,21623,21667,21685,21729,21747,21765,21783],{"className":21578,"ariaHidden":1156},[1196],[1124,21580,21582,21585,21614,21617,21620],{"className":21581},[1200],[1124,21583],{"className":21584,"style":4598},[1204],[1124,21586,21588,21591],{"className":21587},[1209],[1124,21589,2680],{"className":21590,"style":2707},[1209,1213],[1124,21592,21594],{"className":21593},[1217],[1124,21595,21597],{"className":21596},[1221],[1124,21598,21600],{"className":21599},[1226],[1124,21601,21603],{"className":21602,"style":4598},[1230],[1124,21604,21605,21608],{"style":3905},[1124,21606],{"className":21607,"style":1239},[1238],[1124,21609,21611],{"className":21610},[1243,1244,1245,1246],[1124,21612,1152],{"className":21613},[1209,1246],[1124,21615],{"className":21616,"style":1774},[1271],[1124,21618,1652],{"className":21619},[1778],[1124,21621],{"className":21622,"style":1774},[1271],[1124,21624,21626,21629,21658,21661,21664],{"className":21625},[1200],[1124,21627],{"className":21628,"style":4598},[1204],[1124,21630,21632,21635],{"className":21631},[1209],[1124,21633,1439],{"className":21634,"style":1480},[1209,1213],[1124,21636,21638],{"className":21637},[1217],[1124,21639,21641],{"className":21640},[1221],[1124,21642,21644],{"className":21643},[1226],[1124,21645,21647],{"className":21646,"style":4598},[1230],[1124,21648,21649,21652],{"style":3905},[1124,21650],{"className":21651,"style":1239},[1238],[1124,21653,21655],{"className":21654},[1243,1244,1245,1246],[1124,21656,1152],{"className":21657},[1209,1246],[1124,21659],{"className":21660,"style":2500},[1271],[1124,21662,2325],{"className":21663},[2504],[1124,21665],{"className":21666,"style":2500},[1271],[1124,21668,21670,21673,21676,21679,21682],{"className":21669},[1200],[1124,21671],{"className":21672,"style":2858},[1204],[1124,21674,1148],{"className":21675},[1209,1213],[1124,21677],{"className":21678,"style":2500},[1271],[1124,21680,2330],{"className":21681},[2504],[1124,21683],{"className":21684,"style":2500},[1271],[1124,21686,21688,21691,21720,21723,21726],{"className":21687},[1200],[1124,21689],{"className":21690,"style":4598},[1204],[1124,21692,21694,21697],{"className":21693},[1209],[1124,21695,2230],{"className":21696},[1209,1213],[1124,21698,21700],{"className":21699},[1217],[1124,21701,21703],{"className":21702},[1221],[1124,21704,21706],{"className":21705},[1226],[1124,21707,21709],{"className":21708,"style":4598},[1230],[1124,21710,21711,21714],{"style":3905},[1124,21712],{"className":21713,"style":1239},[1238],[1124,21715,21717],{"className":21716},[1243,1244,1245,1246],[1124,21718,1152],{"className":21719},[1209,1246],[1124,21721],{"className":21722,"style":1774},[1271],[1124,21724,1652],{"className":21725},[1778],[1124,21727],{"className":21728,"style":1774},[1271],[1124,21730,21732,21735,21738,21741,21744],{"className":21731},[1200],[1124,21733],{"className":21734,"style":10423},[1204],[1124,21736,9792],{"className":21737},[1209],[1124,21739],{"className":21740,"style":2500},[1271],[1124,21742,10608],{"className":21743},[2504],[1124,21745],{"className":21746,"style":2500},[1271],[1124,21748,21750,21753,21756,21759,21762],{"className":21749},[1200],[1124,21751],{"className":21752,"style":10423},[1204],[1124,21754,21217],{"className":21755},[1209],[1124,21757],{"className":21758,"style":2500},[1271],[1124,21760,2330],{"className":21761},[2504],[1124,21763],{"className":21764,"style":2500},[1271],[1124,21766,21768,21771,21774,21777,21780],{"className":21767},[1200],[1124,21769],{"className":21770,"style":3685},[1204],[1124,21772,9829],{"className":21773},[1209],[1124,21775],{"className":21776,"style":1774},[1271],[1124,21778,1652],{"className":21779},[1778],[1124,21781],{"className":21782,"style":1774},[1271],[1124,21784,21786,21789],{"className":21785},[1200],[1124,21787],{"className":21788,"style":3685},[1204],[1124,21790,21572],{"className":21791},[1209],[1101,21793,21794],{},[1124,21795,21797,21881],{"className":21796},[1127],[1124,21798,21800],{"className":21799},[1131],[1133,21801,21802],{"xmlns":1135},[1137,21803,21804,21878],{},[1140,21805,21806,21812,21814,21816,21818,21824,21826,21828,21830,21832,21834,21836,21838,21858,21860,21873,21875],{},[2922,21807,21808,21810],{},[1146,21809,4370],{},[1150,21811,1152],{},[1154,21813,1652],{},[1146,21815,2674],{},[1154,21817,2677],{"stretchy":1674},[2922,21819,21820,21822],{},[1146,21821,2680],{},[1150,21823,1152],{},[1154,21825,2683],{"stretchy":1674},[1154,21827,1652],{},[1146,21829,2674],{},[1154,21831,2677],{"stretchy":1674},[1150,21833,21572],{},[1154,21835,2683],{"stretchy":1674},[1154,21837,1652],{},[2911,21839,21840,21842],{},[1150,21841,1152],{},[1140,21843,21844,21846,21848],{},[1150,21845,1152],{},[1154,21847,2330],{},[2922,21849,21850,21852],{},[1146,21851,2926],{},[1140,21853,21854,21856],{},[1154,21855,2235],{},[1150,21857,21572],{},[1154,21859,1652],{},[2911,21861,21862,21864],{},[1150,21863,1152],{},[1140,21865,21866,21868,21870],{},[1150,21867,1152],{},[1154,21869,233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= \\sigma(z^1) = \\sigma(0.9) = \\frac{1}{1+e^{-0.9}} = \\frac{1}{1+0.407} = 0.711",[1124,21882,21884,21928,21981,22008,22130,22219],{"className":21883,"ariaHidden":1156},[1196],[1124,21885,21887,21890,21919,21922,21925],{"className":21886},[1200],[1124,21888],{"className":21889,"style":4598},[1204],[1124,21891,21893,21896],{"className":21892},[1209],[1124,21894,4370],{"className":21895},[1209,1213],[1124,21897,21899],{"className":21898},[1217],[1124,21900,21902],{"className":21901},[1221],[1124,21903,21905],{"className":21904},[1226],[1124,21906,21908],{"className":21907,"style":4598},[1230],[1124,21909,21910,21913],{"style":3905},[1124,21911],{"className":21912,"style":1239},[1238],[1124,21914,21916],{"className":21915},[1243,1244,1245,1246],[1124,21917,1152],{"className":21918},[1209,1246],[1124,21920],{"className":21921,"style":1774},[1271],[1124,21923,1652],{"className":21924},[1778],[1124,21926],{"className":21927,"style":1774},[1271],[1124,21929,21931,21934,21937,21940,21969,21972,21975,21978],{"className":21930},[1200],[1124,21932],{"className":21933,"style":4576},[1204],[1124,21935,2674],{"className":21936,"style":2700},[1209,1213],[1124,21938,2677],{"className":21939},[1795],[1124,21941,21943,21946],{"className":21942},[1209],[1124,21944,2680],{"className":21945,"style":2707},[1209,1213],[1124,21947,21949],{"className":21948},[1217],[1124,21950,21952],{"className":21951},[1221],[1124,21953,21955],{"className":21954},[1226],[1124,21956,21958],{"className":21957,"style":4598},[1230],[1124,21959,21960,21963],{"style":3905},[1124,21961],{"className":21962,"style":1239},[1238],[1124,21964,21966],{"className":21965},[1243,1244,1245,1246],[1124,21967,1152],{"className":21968},[1209,1246],[1124,21970,2683],{"className":21971},[2211],[1124,21973],{"className":21974,"style":1774},[1271],[1124,21976,1652],{"className":21977},[1778],[1124,21979],{"className":21980,"style":1774},[1271],[1124,21982,21984,21987,21990,21993,21996,21999,22002,22005],{"className":21983},[1200],[1124,21985],{"className":21986,"style":2696},[1204],[1124,21988,2674],{"className":21989,"style":2700},[1209,1213],[1124,21991,2677],{"className":21992},[1795],[1124,21994,21572],{"className":21995},[1209],[1124,21997,2683],{"className":21998},[2211],[1124,22000],{"className":22001,"style":1774},[1271],[1124,22003,1652],{"className":22004},[1778],[1124,22006],{"className":22007,"style":1774},[1271],[1124,22009,22011,22014,22121,22124,22127],{"className":22010},[1200],[1124,22012],{"className":22013,"style":2972},[1204],[1124,22015,22017,22020,22118],{"className":22016},[1209],[1124,22018],{"className":22019},[1795,2212],[1124,22021,22023],{"className":22022},[2911],[1124,22024,22026,22110],{"className":22025},[1221,1222],[1124,22027,22029,22107],{"className":22028},[1226],[1124,22030,22032,22085,22093],{"className":22031,"style":2991},[1230],[1124,22033,22034,22037],{"style":2994},[1124,22035],{"className":22036,"style":2998},[1238],[1124,22038,22040],{"className":22039},[1243,1244,1245,1246],[1124,22041,22043,22046,22049],{"className":22042},[1209,1246],[1124,22044,1152],{"className":22045},[1209,1246],[1124,22047,2330],{"className":22048},[2504,1246],[1124,22050,22052,22055],{"className":22051},[1209,1246],[1124,22053,2926],{"className":22054},[1209,1213,1246],[1124,22056,22058],{"className":22057},[1217],[1124,22059,22061],{"className":22060},[1221],[1124,22062,22064],{"className":22063},[1226],[1124,22065,22068],{"className":22066,"style":22067},[1230],"height:0.7463em;",[1124,22069,22070,22073],{"style":3032},[1124,22071],{"className":22072,"style":3036},[1238],[1124,22074,22076],{"className":22075},[1243,3040,3041,1246],[1124,22077,22079,22082],{"className":22078},[1209,1246],[1124,22080,2235],{"className":22081},[1209,1246],[1124,22083,21572],{"className":22084},[1209,1246],[1124,22086,22087,22090],{"style":3053},[1124,22088],{"className":22089,"style":2998},[1238],[1124,22091],{"className":22092,"style":3061},[3060],[1124,22094,22095,22098],{"style":3064},[1124,22096],{"className":22097,"style":2998},[1238],[1124,22099,22101],{"className":22100},[1243,1244,1245,1246],[1124,22102,22104],{"className":22103},[1209,1246],[1124,22105,1152],{"className":22106},[1209,1246],[1124,22108,1254],{"className":22109},[1253],[1124,22111,22113],{"className":22112},[1226],[1124,22114,22116],{"className":22115,"style":3086},[1230],[1124,22117],{},[1124,22119],{"className":22120},[2211,2212],[1124,22122],{"className":22123,"style":1774},[1271],[1124,22125,1652],{"className":22126},[1778],[1124,22128],{"className":22129,"style":1774},[1271],[1124,22131,22133,22136,22210,22213,22216],{"className":22132},[1200],[1124,22134],{"className":22135,"style":2972},[1204],[1124,22137,22139,22142,22207],{"className":22138},[1209],[1124,22140],{"className":22141},[1795,2212],[1124,22143,22145],{"className":22144},[2911],[1124,22146,22148,22199],{"className":22147},[1221,1222],[1124,22149,22151,22196],{"className":22150},[1226],[1124,22152,22154,22174,22182],{"className":22153,"style":2991},[1230],[1124,22155,22156,22159],{"style":2994},[1124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2 层（输出层）",[1101,22232,22233],{},[1124,22234,22236,22304],{"className":22235},[1127],[1124,22237,22239],{"className":22238},[1131],[1133,22240,22241],{"xmlns":1135},[1137,22242,22243,22301],{},[1140,22244,22245,22251,22253,22259,22261,22267,22269,22275,22277,22279,22281,22283,22285,22287,22289,22292,22294,22296,22298],{},[2922,22246,22247,22249],{},[1146,22248,2680],{},[1150,22250,1164],{},[1154,22252,1652],{},[2922,22254,22255,22257],{},[1146,22256,1439],{},[1150,22258,1164],{},[1154,22260,2325],{},[2922,22262,22263,22265],{},[1146,22264,4370],{},[1150,22266,1152],{},[1154,22268,2330],{},[2922,22270,22271,22273],{},[1146,22272,2230],{},[1150,22274,1164],{},[1154,22276,1652],{},[1150,22278,10186],{},[1154,22280,10608],{},[1150,22282,21877],{},[1154,22284,2330],{},[1150,22286,9799],{},[1154,22288,1652],{},[1150,22290,22291],{},"0.427",[1154,22293,2330],{},[1150,22295,9799],{},[1154,22297,1652],{},[1150,22299,22300],{},"0.627",[1189,22302,22303],{"encoding":1191},"z^2 = w^2 \\cdot a^1 + b^2 = 0.6 \\times 0.711 + 0.2 = 0.427 + 0.2 = 0.627",[1124,22305,22307,22351,22395,22439,22483,22501,22519,22537,22555,22573],{"className":22306,"ariaHidden":1156},[1196],[1124,22308,22310,22313,22342,22345,22348],{"className":22309},[1200],[1124,22311],{"className":22312,"style":4598},[1204],[1124,22314,22316,22319],{"className":22315},[1209],[1124,22317,2680],{"className":22318,"style":2707},[1209,1213],[1124,22320,22322],{"className":22321},[1217],[1124,22323,22325],{"className":22324},[1221],[1124,22326,22328],{"className":22327},[1226],[1124,22329,22331],{"className":22330,"style":4598},[1230],[1124,22332,22333,22336],{"style":3905},[1124,22334],{"className":22335,"style":1239},[1238],[1124,22337,22339],{"className":22338},[1243,1244,1245,1246],[1124,22340,1164],{"className":22341},[1209,1246],[1124,22343],{"className":22344,"style":1774},[1271],[1124,22346,1652],{"className":22347},[1778],[1124,22349],{"className":22350,"style":1774},[1271],[1124,22352,22354,22357,22386,22389,22392],{"className":22353},[1200],[1124,22355],{"className":22356,"style":4598},[1204],[1124,22358,22360,22363],{"className":22359},[1209],[1124,22361,1439],{"className":22362,"style":1480},[1209,1213],[1124,22364,22366],{"className":22365},[1217],[1124,22367,22369],{"className":22368},[1221],[1124,22370,22372],{"className":22371},[1226],[1124,22373,22375],{"className":22374,"style":4598},[1230],[1124,22376,22377,22380],{"style":3905},[1124,22378],{"className":22379,"style":1239},[1238],[1124,22381,22383],{"className":22382},[1243,1244,1245,1246],[1124,22384,1164],{"className":22385},[1209,1246],[1124,22387],{"className":22388,"style":2500},[1271],[1124,22390,2325],{"className":22391},[2504],[1124,22393],{"className":22394,"style":2500},[1271],[1124,22396,22398,22401,22430,22433,22436],{"className":22397},[1200],[1124,22399],{"className":22400,"style":8984},[1204],[1124,22402,22404,22407],{"className":22403},[1209],[1124,22405,4370],{"className":22406},[1209,1213],[1124,22408,22410],{"className":22409},[1217],[1124,22411,22413],{"className":22412},[1221],[1124,22414,22416],{"className":22415},[1226],[1124,22417,22419],{"className":22418,"style":4598},[1230],[1124,22420,22421,22424],{"style":3905},[1124,22422],{"className":22423,"style":1239},[1238],[1124,22425,22427],{"className":22426},[1243,1244,1245,1246],[1124,22428,1152],{"className":22429},[1209,1246],[1124,22431],{"className":22432,"style":2500},[1271],[1124,22434,2330],{"className":22435},[2504],[1124,22437],{"className":22438,"style":2500},[1271],[1124,22440,22442,22445,22474,22477,22480],{"className":22441},[1200],[1124,22443],{"className":22444,"style":4598},[1204],[1124,22446,22448,22451],{"className":22447},[1209],[1124,22449,2230],{"className":22450},[1209,1213],[1124,22452,22454],{"className":22453},[1217],[1124,22455,22457],{"className":22456},[1221],[1124,22458,22460],{"className":22459},[1226],[1124,22461,22463],{"className":22462,"style":4598},[1230],[1124,22464,22465,22468],{"style":3905},[1124,22466],{"className":22467,"style":1239},[1238],[1124,22469,22471],{"className":22470},[1243,1244,1245,1246],[1124,22472,1164],{"className":22473},[1209,1246],[1124,22475],{"className":22476,"style":1774},[1271],[1124,22478,1652],{"className":22479},[1778],[1124,22481],{"className":22482,"style":1774},[1271],[1124,22484,22486,22489,22492,22495,22498],{"className":22485},[1200],[1124,22487],{"className":22488,"style":10423},[1204],[1124,22490,10186],{"className":22491},[1209],[1124,22493],{"className":22494,"style":2500},[1271],[1124,22496,10608],{"className":22497},[2504],[1124,22499],{"className":22500,"style":2500},[1271],[1124,22502,22504,22507,22510,22513,22516],{"className":22503},[1200],[1124,22505],{"className":22506,"style":10423},[1204],[1124,22508,21877],{"className":22509},[1209],[1124,22511],{"className":22512,"style":2500},[1271],[1124,22514,2330],{"className":22515},[2504],[1124,22517],{"className":22518,"style":2500},[1271],[1124,22520,22522,22525,22528,22531,22534],{"className":22521},[1200],[1124,22523],{"className":22524,"style":3685},[1204],[1124,22526,9799],{"className":22527},[1209],[1124,22529],{"className":22530,"style":1774},[1271],[1124,22532,1652],{"className":22533},[1778],[1124,22535],{"className":22536,"style":1774},[1271],[1124,22538,22540,22543,22546,22549,22552],{"className":22539},[1200],[1124,22541],{"className":22542,"style":10423},[1204],[1124,22544,22291],{"className":22545},[1209],[1124,22547],{"className":22548,"style":2500},[1271],[1124,22550,2330],{"className":22551},[2504],[1124,22553],{"className":22554,"style":2500},[1271],[1124,22556,22558,22561,22564,22567,22570],{"className":22557},[1200],[1124,22559],{"className":22560,"style":3685},[1204],[1124,22562,9799],{"className":22563},[1209],[1124,22565],{"className":22566,"style":1774},[1271],[1124,22568,1652],{"className":22569},[1778],[1124,22571],{"className":22572,"style":1774},[1271],[1124,22574,22576,22579],{"className":22575},[1200],[1124,22577],{"className":22578,"style":3685},[1204],[1124,22580,22300],{"className":22581},[1209],[1101,22583,22584],{},[1124,22585,22587,22671],{"className":22586},[1127],[1124,22588,22590],{"className":22589},[1131],[1133,22591,22592],{"xmlns":1135},[1137,22593,22594,22668],{},[1140,22595,22596,22602,22604,22606,22608,22614,22616,22618,22620,22622,22624,22626,22628,22648,22650,22663,22665],{},[2922,22597,22598,22600],{},[1146,22599,4370],{},[1150,22601,1164],{},[1154,22603,1652],{},[1146,22605,2674],{},[1154,22607,2677],{"stretchy":1674},[2922,22609,22610,22612],{},[1146,22611,2680],{},[1150,22613,1164],{},[1154,22615,2683],{"stretchy":1674},[1154,22617,1652],{},[1146,22619,2674],{},[1154,22621,2677],{"stretchy":1674},[1150,22623,22300],{},[1154,22625,2683],{"stretchy":1674},[1154,22627,1652],{},[2911,22629,22630,22632],{},[1150,22631,1152],{},[1140,22633,22634,22636,22638],{},[1150,22635,1152],{},[1154,22637,2330],{},[2922,22639,22640,22642],{},[1146,22641,2926],{},[1140,22643,22644,22646],{},[1154,22645,2235],{},[1150,22647,22300],{},[1154,22649,1652],{},[2911,22651,22652,22654],{},[1150,22653,1152],{},[1140,22655,22656,22658,22660],{},[1150,22657,1152],{},[1154,22659,2330],{},[1150,22661,22662],{},"0.534",[1154,22664,1652],{},[1150,22666,22667],{},"0.652",[1189,22669,22670],{"encoding":1191},"a^2 = \\sigma(z^2) = \\sigma(0.627) = \\frac{1}{1+e^{-0.627}} = \\frac{1}{1+0.534} = 0.652",[1124,22672,22674,22718,22771,22798,22919,23008],{"className":22673,"ariaHidden":1156},[1196],[1124,22675,22677,22680,22709,22712,22715],{"className":22676},[1200],[1124,22678],{"className":22679,"style":4598},[1204],[1124,22681,22683,22686],{"className":22682},[1209],[1124,22684,4370],{"className":22685},[1209,1213],[1124,22687,22689],{"className":22688},[1217],[1124,22690,22692],{"className":22691},[1221],[1124,22693,22695],{"className":22694},[1226],[1124,22696,22698],{"className":22697,"style":4598},[1230],[1124,22699,22700,22703],{"style":3905},[1124,22701],{"className":22702,"style":1239},[1238],[1124,22704,22706],{"className":22705},[1243,1244,1245,1246],[1124,22707,1164],{"className":22708},[1209,1246],[1124,22710],{"className":22711,"style":1774},[1271],[1124,22713,1652],{"className":22714},[1778],[1124,22716],{"className":22717,"style":1774},[1271],[1124,22719,22721,22724,22727,22730,22759,22762,22765,22768],{"className":22720},[1200],[1124,22722],{"className":22723,"style":4576},[1204],[1124,22725,2674],{"className":22726,"style":2700},[1209,1213],[1124,22728,2677],{"className":22729},[1795],[1124,22731,22733,22736],{"className":22732},[1209],[1124,22734,2680],{"className":22735,"style":2707},[1209,1213],[1124,22737,22739],{"className":22738},[1217],[1124,22740,22742],{"className":22741},[1221],[1124,22743,22745],{"className":22744},[1226],[1124,22746,22748],{"className":22747,"style":4598},[1230],[1124,22749,22750,22753],{"style":3905},[1124,22751],{"className":22752,"style":1239},[1238],[1124,22754,22756],{"className":22755},[1243,1244,1245,1246],[1124,22757,1164],{"className":22758},[1209,1246],[1124,22760,2683],{"className":22761},[2211],[1124,22763],{"className":22764,"style":1774},[1271],[1124,22766,1652],{"className":22767},[1778],[1124,22769],{"className":22770,"style":1774},[1271],[1124,22772,22774,22777,22780,22783,22786,22789,22792,22795],{"className":22773},[1200],[1124,22775],{"className":22776,"style":2696},[1204],[1124,22778,2674],{"className":22779,"style":2700},[1209,1213],[1124,22781,2677],{"className":22782},[1795],[1124,22784,22300],{"className":22785},[1209],[1124,22787,2683],{"className":22788},[2211],[1124,22790],{"className":22791,"style":1774},[1271],[1124,22793,1652],{"className":22794},[1778],[1124,22796],{"className":22797,"style":1774},[1271],[1124,22799,22801,22804,22910,22913,22916],{"className":22800},[1200],[1124,22802],{"className":22803,"style":2972},[1204],[1124,22805,22807,22810,22907],{"className":22806},[1209],[1124,22808],{"className":22809},[1795,2212],[1124,22811,22813],{"className":22812},[2911],[1124,22814,22816,22899],{"className":22815},[1221,1222],[1124,22817,22819,22896],{"className":22818},[1226],[1124,22820,22822,22874,22882],{"className":22821,"style":2991},[1230],[1124,22823,22824,22827],{"style":2994},[1124,22825],{"className":22826,"style":2998},[1238],[1124,22828,22830],{"className":22829},[1243,1244,1245,1246],[1124,22831,22833,22836,22839],{"className":22832},[1209,1246],[1124,22834,1152],{"className":22835},[1209,1246],[1124,22837,2330],{"className":22838},[2504,1246],[1124,22840,22842,22845],{"className":22841},[1209,1246],[1124,22843,2926],{"className":22844},[1209,1213,1246],[1124,22846,22848],{"className":22847},[1217],[1124,22849,22851],{"className":22850},[1221],[1124,22852,22854],{"className":22853},[1226],[1124,22855,22857],{"className":22856,"style":22067},[1230],[1124,22858,22859,22862],{"style":3032},[1124,22860],{"className":22861,"style":3036},[1238],[1124,22863,22865],{"className":22864},[1243,3040,3041,1246],[1124,22866,22868,22871],{"className":22867},[1209,1246],[1124,22869,2235],{"className":22870},[1209,1246],[1124,22872,22300],{"className":22873},[1209,1246],[1124,22875,22876,22879],{"style":3053},[1124,22877],{"className":22878,"style":2998},[1238],[1124,22880],{"className":22881,"style":3061},[3060],[1124,22883,22884,22887],{"style":3064},[1124,22885],{"className":22886,"style":2998},[1238],[1124,22888,22890],{"className":22889},[1243,1244,1245,1246],[1124,22891,22893],{"className":22892},[1209,1246],[1124,22894,1152],{"className":22895},[1209,1246],[1124,22897,1254],{"className":22898},[1253],[1124,22900,22902],{"className":22901},[1226],[1124,22903,22905],{"className":22904,"style":3086},[1230],[1124,22906],{},[1124,22908],{"className":22909},[2211,2212],[1124,22911],{"className":22912,"style":1774},[1271],[1124,22914,1652],{"className":22915},[1778],[1124,22917],{"className":22918,"style":1774},[1271],[1124,22920,22922,22925,22999,23002,23005],{"className":22921},[1200],[1124,22923],{"className":22924,"style":2972},[1204],[1124,22926,22928,22931,22996],{"className":22927},[1209],[1124,22929],{"className":22930},[1795,2212],[1124,22932,22934],{"className":22933},[2911],[1124,22935,22937,22988],{"className":22936},[1221,1222],[1124,22938,22940,22985],{"className":22939},[1226],[1124,22941,22943,22963,22971],{"className":22942,"style":2991},[1230],[1124,22944,22945,22948],{"style":2994},[1124,22946],{"className":22947,"style":2998},[1238],[1124,22949,22951],{"className":22950},[1243,1244,1245,1246],[1124,22952,22954,22957,22960],{"className":22953},[1209,1246],[1124,22955,1152],{"className":22956},[1209,1246],[1124,22958,2330],{"className":22959},[2504,1246],[1124,22961,22662],{"className":22962},[1209,1246],[1124,22964,22965,22968],{"style":3053},[1124,22966],{"className":22967,"style":2998},[1238],[1124,22969],{"className":22970,"style":3061},[3060],[1124,22972,22973,22976],{"style":3064},[1124,22974],{"className":22975,"style":2998},[1238],[1124,22977,22979],{"className":22978},[1243,1244,1245,1246],[1124,22980,22982],{"className":22981},[1209,1246],[1124,22983,1152],{"className":22984},[1209,1246],[1124,22986,1254],{"className":22987},[1253],[1124,22989,22991],{"className":22990},[1226],[1124,22992,22994],{"className":22993,"style":3086},[1230],[1124,22995],{},[1124,22997],{"className":22998},[2211,2212],[1124,23000],{"className":23001,"style":1774},[1271],[1124,23003,1652],{"className":23004},[1778],[1124,23006],{"className":23007,"style":1774},[1271],[1124,23009,23011,23014],{"className":23010},[1200],[1124,23012],{"className":23013,"style":3685},[1204],[1124,23015,22667],{"className":23016},[1209],[1101,23018,23019],{},"计算代价",[1101,23021,23022],{},[1124,23023,23025,23111],{"className":23024},[1127],[1124,23026,23028],{"className":23027},[1131],[1133,23029,23030],{"xmlns":1135},[1137,23031,23032,23108],{},[1140,23033,23034,23036,23038,23044,23046,23052,23054,23056,23062,23064,23070,23072,23074,23076,23078,23084,23086,23092,23094,23097,23103,23105],{},[1146,23035,4325],{},[1154,23037,1652],{},[2911,23039,23040,23042],{},[1150,23041,1152],{},[1150,23043,1164],{},[1154,23045,2677],{"stretchy":1674},[2922,23047,23048,23050],{},[1146,23049,4370],{},[1150,23051,1164],{},[1154,23053,2235],{},[1146,23055,4359],{},[2922,23057,23058,23060],{},[1154,23059,2683],{"stretchy":1674},[1150,23061,1164],{},[1154,23063,1652],{},[2911,23065,23066,23068],{},[1150,23067,1152],{},[1150,23069,1164],{},[1154,23071,2677],{"stretchy":1674},[1150,23073,22667],{},[1154,23075,2235],{},[1150,23077,1152],{},[2922,23079,23080,23082],{},[1154,23081,2683],{"stretchy":1674},[1150,23083,1164],{},[1154,23085,1652],{},[2911,23087,23088,23090],{},[1150,23089,1152],{},[1150,23091,1164],{},[1154,23093,2677],{"stretchy":1674},[1150,23095,23096],{},"0.348",[2922,23098,23099,23101],{},[1154,23100,2683],{"stretchy":1674},[1150,23102,1164],{},[1154,23104,1652],{},[1150,23106,23107],{},"0.0606",[1189,23109,23110],{"encoding":1191},"C = \\frac{1}{2}(a^2 - y)^2 = \\frac{1}{2}(0.652 - 1)^2 = \\frac{1}{2}(0.348)^2 = 0.0606",[1124,23112,23114,23132,23247,23294,23383,23430,23548],{"className":23113,"ariaHidden":1156},[1196],[1124,23115,23117,23120,23123,23126,23129],{"className":23116},[1200],[1124,23118],{"className":23119,"style":4804},[1204],[1124,23121,4325],{"className":23122,"style":4392},[1209,1213],[1124,23124],{"className":23125,"style":1774},[1271],[1124,23127,1652],{"className":23128},[1778],[1124,23130],{"className":23131,"style":1774},[1271],[1124,23133,23135,23138,23206,23209,23238,23241,23244],{"className":23134},[1200],[1124,23136],{"className":23137,"style":4426},[1204],[1124,23139,23141,23144,23203],{"className":23140},[1209],[1124,23142],{"className":23143},[1795,2212],[1124,23145,23147],{"className":23146},[2911],[1124,23148,23150,23195],{"className":23149},[1221,1222],[1124,23151,23153,23192],{"className":23152},[1226],[1124,23154,23156,23170,23178],{"className":23155,"style":2991},[1230],[1124,23157,23158,23161],{"style":2994},[1124,23159],{"className":23160,"style":2998},[1238],[1124,23162,23164],{"className":23163},[1243,1244,1245,1246],[1124,23165,23167],{"className":23166},[1209,1246],[1124,23168,1164],{"className":23169},[1209,1246],[1124,23171,23172,23175],{"style":3053},[1124,23173],{"className":23174,"style":2998},[1238],[1124,23176],{"className":23177,"style":3061},[3060],[1124,23179,23180,23183],{"style":3064},[1124,23181],{"className":23182,"style":2998},[1238],[1124,23184,23186],{"className":23185},[1243,1244,1245,1246],[1124,23187,23189],{"className":23188},[1209,1246],[1124,23190,1152],{"className":23191},[1209,1246],[1124,23193,1254],{"className":23194},[1253],[1124,23196,23198],{"className":23197},[1226],[1124,23199,23201],{"className":23200,"style":3538},[1230],[1124,23202],{},[1124,23204],{"className":23205},[2211,2212],[1124,23207,2677],{"className":23208},[1795],[1124,23210,23212,23215],{"className":23211},[1209],[1124,23213,4370],{"className":23214},[1209,1213],[1124,23216,23218],{"className":23217},[1217],[1124,23219,23221],{"className":23220},[1221],[1124,23222,23224],{"className":23223},[1226],[1124,23225,23227],{"className":23226,"style":4598},[1230],[1124,23228,23229,23232],{"style":3905},[1124,23230],{"className":23231,"style":1239},[1238],[1124,23233,23235],{"className":23234},[1243,1244,1245,1246],[1124,23236,1164],{"className":23237},[1209,1246],[1124,23239],{"className":23240,"style":2500},[1271],[1124,23242,2235],{"className":23243},[2504],[1124,23245],{"className":23246,"style":2500},[1271],[1124,23248,23250,23253,23256,23285,23288,23291],{"className":23249},[1200],[1124,23251],{"className":23252,"style":4576},[1204],[1124,23254,4359],{"className":23255,"style":2700},[1209,1213],[1124,23257,23259,23262],{"className":23258},[2211],[1124,23260,2683],{"className":23261},[2211],[1124,23263,23265],{"className":23264},[1217],[1124,23266,23268],{"className":23267},[1221],[1124,23269,23271],{"className":23270},[1226],[1124,23272,23274],{"className":23273,"style":4598},[1230],[1124,23275,23276,23279],{"style":3905},[1124,23277],{"className":23278,"style":1239},[1238],[1124,23280,23282],{"className":23281},[1243,1244,1245,1246],[1124,23283,1164],{"className":23284},[1209,1246],[1124,23286],{"className":23287,"style":1774},[1271],[1124,23289,1652],{"className":23290},[1778],[1124,23292],{"className":23293,"style":1774},[1271],[1124,23295,23297,23300,23368,23371,23374,23377,23380],{"className":23296},[1200],[1124,23298],{"className":23299,"style":4426},[1204],[1124,23301,23303,23306,23365],{"className":23302},[1209],[1124,23304],{"className":23305},[1795,2212],[1124,23307,23309],{"className":23308},[2911],[1124,23310,23312,23357],{"className":23311},[1221,1222],[1124,23313,23315,23354],{"className":23314},[1226],[1124,23316,23318,23332,23340],{"className":23317,"style":2991},[1230],[1124,23319,23320,23323],{"style":2994},[1124,23321],{"className":23322,"style":2998},[1238],[1124,23324,23326],{"className":23325},[1243,1244,1245,1246],[1124,23327,23329],{"className":23328},[1209,1246],[1124,23330,1164],{"className":23331},[1209,1246],[1124,23333,23334,23337],{"style":3053},[1124,23335],{"className":23336,"style":2998},[1238],[1124,23338],{"className":23339,"style":3061},[3060],[1124,23341,23342,23345],{"style":3064},[1124,23343],{"className":23344,"style":2998},[1238],[1124,23346,23348],{"className":23347},[1243,1244,1245,1246],[1124,23349,23351],{"className":23350},[1209,1246],[1124,23352,1152],{"className":23353},[1209,1246],[1124,23355,1254],{"className":23356},[1253],[1124,23358,23360],{"className":23359},[1226],[1124,23361,23363],{"className":23362,"style":3538},[1230],[1124,23364],{},[1124,23366],{"className":23367},[2211,2212],[1124,23369,2677],{"className":23370},[1795],[1124,23372,22667],{"className":23373},[1209],[1124,23375],{"className":23376,"style":2500},[1271],[1124,23378,2235],{"className":23379},[2504],[1124,23381],{"className":23382,"style":2500},[1271],[1124,23384,23386,23389,23392,23421,23424,23427],{"className":23385},[1200],[1124,23387],{"className":23388,"style":4576},[1204],[1124,23390,1152],{"className":23391},[1209],[1124,23393,23395,23398],{"className":23394},[2211],[1124,23396,2683],{"className":23397},[2211],[1124,23399,23401],{"className":23400},[1217],[1124,23402,23404],{"className":23403},[1221],[1124,23405,23407],{"className":23406},[1226],[1124,23408,23410],{"className":23409,"style":4598},[1230],[1124,23411,23412,23415],{"style":3905},[1124,23413],{"className":23414,"style":1239},[1238],[1124,23416,23418],{"className":23417},[1243,1244,1245,1246],[1124,23419,1164],{"className":23420},[1209,1246],[1124,23422],{"className":23423,"style":1774},[1271],[1124,23425,1652],{"className":23426},[1778],[1124,23428],{"className":23429,"style":1774},[1271],[1124,23431,23433,23436,23504,23507,23510,23539,23542,23545],{"className":23432},[1200],[1124,23434],{"className":23435,"style":4426},[1204],[1124,23437,23439,23442,23501],{"className":23438},[1209],[1124,23440],{"className":23441},[1795,2212],[1124,23443,23445],{"className":23444},[2911],[1124,23446,23448,23493],{"className":23447},[1221,1222],[1124,23449,23451,23490],{"className":23450},[1226],[1124,23452,23454,23468,23476],{"className":23453,"style":2991},[1230],[1124,23455,23456,23459],{"style":2994},[1124,23457],{"className":23458,"style":2998},[1238],[1124,23460,23462],{"className":23461},[1243,1244,1245,1246],[1124,23463,23465],{"className":23464},[1209,1246],[1124,23466,1164],{"className":23467},[1209,1246],[1124,23469,23470,23473],{"style":3053},[1124,23471],{"className":23472,"style":2998},[1238],[1124,23474],{"className":23475,"style":3061},[3060],[1124,23477,23478,23481],{"style":3064},[1124,23479],{"className":23480,"style":2998},[1238],[1124,23482,23484],{"className":23483},[1243,1244,1245,1246],[1124,23485,23487],{"className":23486},[1209,1246],[1124,23488,1152],{"className":23489},[1209,1246],[1124,23491,1254],{"className":23492},[1253],[1124,23494,23496],{"className":23495},[1226],[1124,23497,23499],{"className":23498,"style":3538},[1230],[1124,23500],{},[1124,23502],{"className":23503},[2211,2212],[1124,23505,2677],{"className":23506},[1795],[1124,23508,23096],{"className":23509},[1209],[1124,23511,23513,23516],{"className":23512},[2211],[1124,23514,2683],{"className":23515},[2211],[1124,23517,23519],{"className":23518},[1217],[1124,23520,23522],{"className":23521},[1221],[1124,23523,23525],{"className":23524},[1226],[1124,23526,23528],{"className":23527,"style":4598},[1230],[1124,23529,23530,23533],{"style":3905},[1124,23531],{"className":23532,"style":1239},[1238],[1124,23534,23536],{"className":23535},[1243,1244,1245,1246],[1124,23537,1164],{"className":23538},[1209,1246],[1124,23540],{"className":23541,"style":1774},[1271],[1124,23543,1652],{"className":23544},[1778],[1124,23546],{"className":23547,"style":1774},[1271],[1124,23549,23551,23554],{"className":23550},[1200],[1124,23552],{"className":23553,"style":3685},[1204],[1124,23555,23107],{"className":23556},[1209],[2745,23558],{},[1101,23560,23561],{},[1107,23562,23563],{},"前向传播汇总：",[2616,23565,23566,23575],{},[2619,23567,23568],{},[2622,23569,23570,23573],{},[2625,23571,23572],{},"变量",[2625,23574,20923],{},[2635,23576,23577,23642,23706,23771,23835],{},[2622,23578,23579,23640],{},[2640,23580,23581],{},[1124,23582,23584,23602],{"className":23583},[1127],[1124,23585,23587],{"className":23586},[1131],[1133,23588,23589],{"xmlns":1135},[1137,23590,23591,23599],{},[1140,23592,23593],{},[2922,23594,23595,23597],{},[1146,23596,2680],{},[1150,23598,1152],{},[1189,23600,23601],{"encoding":1191},"z^1",[1124,23603,23605],{"className":23604,"ariaHidden":1156},[1196],[1124,23606,23608,23611],{"className":23607},[1200],[1124,23609],{"className":23610,"style":4598},[1204],[1124,23612,23614,23617],{"className":23613},[1209],[1124,23615,2680],{"className":23616,"style":2707},[1209,1213],[1124,23618,23620],{"className":23619},[1217],[1124,23621,23623],{"className":23622},[1221],[1124,23624,23626],{"className":23625},[1226],[1124,23627,23629],{"className":23628,"style":4598},[1230],[1124,23630,23631,23634],{"style":3905},[1124,23632],{"className":23633,"style":1239},[1238],[1124,23635,23637],{"className":23636},[1243,1244,1245,1246],[1124,23638,1152],{"className":23639},[1209,1246],[2640,23641,21572],{},[2622,23643,23644,23704],{},[2640,23645,23646],{},[1124,23647,23649,23666],{"className":23648},[1127],[1124,23650,23652],{"className":23651},[1131],[1133,23653,23654],{"xmlns":1135},[1137,23655,23656,23664],{},[1140,23657,23658],{},[2922,23659,23660,23662],{},[1146,23661,4370],{},[1150,23663,1152],{},[1189,23665,9236],{"encoding":1191},[1124,23667,23669],{"className":23668,"ariaHidden":1156},[1196],[1124,23670,23672,23675],{"className":23671},[1200],[1124,23673],{"className":23674,"style":4598},[1204],[1124,23676,23678,23681],{"className":23677},[1209],[1124,23679,4370],{"className":23680},[1209,1213],[1124,23682,23684],{"className":23683},[1217],[1124,23685,23687],{"className":23686},[1221],[1124,23688,23690],{"className":23689},[1226],[1124,23691,23693],{"className":23692,"style":4598},[1230],[1124,23694,23695,23698],{"style":3905},[1124,23696],{"className":23697,"style":1239},[1238],[1124,23699,23701],{"className":23700},[1243,1244,1245,1246],[1124,23702,1152],{"className":23703},[1209,1246],[2640,23705,21877],{},[2622,23707,23708,23769],{},[2640,23709,23710],{},[1124,23711,23713,23731],{"className":23712},[1127],[1124,23714,23716],{"className":23715},[1131],[1133,23717,23718],{"xmlns":1135},[1137,23719,23720,23728],{},[1140,23721,23722],{},[2922,23723,23724,23726],{},[1146,23725,2680],{},[1150,23727,1164],{},[1189,23729,23730],{"encoding":1191},"z^2",[1124,23732,23734],{"className":23733,"ariaHidden":1156},[1196],[1124,23735,23737,23740],{"className":23736},[1200],[1124,23738],{"className":23739,"style":4598},[1204],[1124,23741,23743,23746],{"className":23742},[1209],[1124,23744,2680],{"className":23745,"style":2707},[1209,1213],[1124,23747,23749],{"className":23748},[1217],[1124,23750,23752],{"className":23751},[1221],[1124,23753,23755],{"className":23754},[1226],[1124,23756,23758],{"className":23757,"style":4598},[1230],[1124,23759,23760,23763],{"style":3905},[1124,23761],{"className":23762,"style":1239},[1238],[1124,23764,23766],{"className":23765},[1243,1244,1245,1246],[1124,23767,1164],{"className":23768},[1209,1246],[2640,23770,22300],{},[2622,23772,23773,23833],{},[2640,23774,23775],{},[1124,23776,23778,23795],{"className":23777},[1127],[1124,23779,23781],{"className":23780},[1131],[1133,23782,23783],{"xmlns":1135},[1137,23784,23785,23793],{},[1140,23786,23787],{},[2922,23788,23789,23791],{},[1146,23790,4370],{},[1150,23792,1164],{},[1189,23794,9687],{"encoding":1191},[1124,23796,23798],{"className":23797,"ariaHidden":1156},[1196],[1124,23799,23801,23804],{"className":23800},[1200],[1124,23802],{"className":23803,"style":4598},[1204],[1124,23805,23807,23810],{"className":23806},[1209],[1124,23808,4370],{"className":23809},[1209,1213],[1124,23811,23813],{"className":23812},[1217],[1124,23814,23816],{"className":23815},[1221],[1124,23817,23819],{"className":23818},[1226],[1124,23820,23822],{"className":23821,"style":4598},[1230],[1124,23823,23824,23827],{"style":3905},[1124,23825],{"className":23826,"style":1239},[1238],[1124,23828,23830],{"className":23829},[1243,1244,1245,1246],[1124,23831,1164],{"className":23832},[1209,1246],[2640,23834,22667],{},[2622,23836,23837,23867],{},[2640,23838,23839],{},[1124,23840,23842,23855],{"className":23841},[1127],[1124,23843,23845],{"className":23844},[1131],[1133,23846,23847],{"xmlns":1135},[1137,23848,23849,23853],{},[1140,23850,23851],{},[1146,23852,4325],{},[1189,23854,4325],{"encoding":1191},[1124,23856,23858],{"className":23857,"ariaHidden":1156},[1196],[1124,23859,23861,23864],{"className":23860},[1200],[1124,23862],{"className":23863,"style":4804},[1204],[1124,23865,4325],{"className":23866,"style":4392},[1209,1213],[2640,23868,23107],{},[2745,23870],{},[1096,23872,23874],{"id":23873},"反向传播用链式法则推导每个梯度","反向传播——用链式法则推导每个梯度",[1101,23876,23877,23878,24021,24022,24021,24164,24021,24306],{},"现在的目标是求：",[1124,23879,23881,23911],{"className":23880},[1127],[1124,23882,23884],{"className":23883},[1131],[1133,23885,23886],{"xmlns":1135},[1137,23887,23888,23908],{},[1140,23889,23890],{},[2911,23891,23892,23898],{},[1140,23893,23894,23896],{},[1146,23895,3164],{"mathvariant":3145},[1146,23897,4325],{},[1140,23899,23900,23902],{},[1146,23901,3164],{"mathvariant":3145},[2922,23903,23904,23906],{},[1146,23905,1439],{},[1150,23907,1164],{},[1189,23909,23910],{"encoding":1191},"\\frac{\\partial C}{\\partial w^2}",[1124,23912,23914],{"className":23913,"ariaHidden":1156},[1196],[1124,23915,23917,23921],{"className":23916},[1200],[1124,23918],{"className":23919,"style":23920},[1204],"height:1.2251em;vertical-align:-0.345em;",[1124,23922,23924,23927,24018],{"className":23923},[1209],[1124,23925],{"className":23926},[1795,2212],[1124,23928,23930],{"className":23929},[2911],[1124,23931,23933,24010],{"className":23932},[1221,1222],[1124,23934,23936,24007],{"className":23935},[1226],[1124,23937,23939,23982,23990],{"className":23938,"style":4858},[1230],[1124,23940,23941,23944],{"style":2994},[1124,23942],{"className":23943,"style":2998},[1238],[1124,23945,23947],{"className":23946},[1243,1244,1245,1246],[1124,23948,23950,23953],{"className":23949},[1209,1246],[1124,23951,3164],{"className":23952,"style":3319},[1209,1246],[1124,23954,23956,23959],{"className":23955},[1209,1246],[1124,23957,1439],{"className":23958,"style":1480},[1209,1213,1246],[1124,23960,23962],{"className":23961},[1217],[1124,23963,23965],{"className":23964},[1221],[1124,23966,23968],{"className":23967},[1226],[1124,23969,23971],{"className":23970,"style":22067},[1230],[1124,23972,23973,23976],{"style":3032},[1124,23974],{"className":23975,"style":3036},[1238],[1124,23977,23979],{"className":23978},[1243,3040,3041,1246],[1124,23980,1164],{"className":23981},[1209,1246],[1124,23983,23984,23987],{"style":3053},[1124,23985],{"className":23986,"style":2998},[1238],[1124,23988],{"className":23989,"style":3061},[3060],[1124,23991,23992,23995],{"style":3064},[1124,23993],{"className":23994,"style":2998},[1238],[1124,23996,23998],{"className":23997},[1243,1244,1245,1246],[1124,23999,24001,24004],{"className":24000},[1209,1246],[1124,24002,3164],{"className":24003,"style":3319},[1209,1246],[1124,24005,4325],{"className":24006,"style":4392},[1209,1213,1246],[1124,24008,1254],{"className":24009},[1253],[1124,24011,24013],{"className":24012},[1226],[1124,24014,24016],{"className":24015,"style":3538},[1230],[1124,24017],{},[1124,24019],{"className":24020},[2211,2212],"、",[1124,24023,24025,24055],{"className":24024},[1127],[1124,24026,24028],{"className":24027},[1131],[1133,24029,24030],{"xmlns":1135},[1137,24031,24032,24052],{},[1140,24033,24034],{},[2911,24035,24036,24042],{},[1140,24037,24038,24040],{},[1146,24039,3164],{"mathvariant":3145},[1146,24041,4325],{},[1140,24043,24044,24046],{},[1146,24045,3164],{"mathvariant":3145},[2922,24047,24048,24050],{},[1146,24049,2230],{},[1150,24051,1164],{},[1189,24053,24054],{"encoding":1191},"\\frac{\\partial C}{\\partial b^2}",[1124,24056,24058],{"className":24057,"ariaHidden":1156},[1196],[1124,24059,24061,24064],{"className":24060},[1200],[1124,24062],{"className":24063,"style":23920},[1204],[1124,24065,24067,24070,24161],{"className":24066},[1209],[1124,24068],{"className":24069},[1795,2212],[1124,24071,24073],{"className":24072},[2911],[1124,24074,24076,24153],{"className":24075},[1221,1222],[1124,24077,24079,24150],{"className":24078},[1226],[1124,24080,24082,24125,24133],{"className":24081,"style":4858},[1230],[1124,24083,24084,24087],{"style":2994},[1124,24085],{"className":24086,"style":2998},[1238],[1124,24088,24090],{"className":24089},[1243,1244,1245,1246],[1124,24091,24093,24096],{"className":24092},[1209,1246],[1124,24094,3164],{"className":24095,"style":3319},[1209,1246],[1124,24097,24099,24102],{"className":24098},[1209,1246],[1124,24100,2230],{"className":24101},[1209,1213,1246],[1124,24103,24105],{"className":24104},[1217],[1124,24106,24108],{"className":24107},[1221],[1124,24109,24111],{"className":24110},[1226],[1124,24112,24114],{"className":24113,"style":22067},[1230],[1124,24115,24116,24119],{"style":3032},[1124,24117],{"className":24118,"style":3036},[1238],[1124,24120,24122],{"className":24121},[1243,3040,3041,1246],[1124,24123,1164],{"className":24124},[1209,1246],[1124,24126,24127,24130],{"style":3053},[1124,24128],{"className":24129,"style":2998},[1238],[1124,24131],{"className":24132,"style":3061},[3060],[1124,24134,24135,24138],{"style":3064},[1124,24136],{"className":24137,"style":2998},[1238],[1124,24139,24141],{"className":24140},[1243,1244,1245,1246],[1124,24142,24144,24147],{"className":24143},[1209,1246],[1124,24145,3164],{"className":24146,"style":3319},[1209,1246],[1124,24148,4325],{"className":24149,"style":4392},[1209,1213,1246],[1124,24151,1254],{"className":24152},[1253],[1124,24154,24156],{"className":24155},[1226],[1124,24157,24159],{"className":24158,"style":3538},[1230],[1124,24160],{},[1124,24162],{"className":24163},[2211,2212],[1124,24165,24167,24197],{"className":24166},[1127],[1124,24168,24170],{"className":24169},[1131],[1133,24171,24172],{"xmlns":1135},[1137,24173,24174,24194],{},[1140,24175,24176],{},[2911,24177,24178,24184],{},[1140,24179,24180,24182],{},[1146,24181,3164],{"mathvariant":3145},[1146,24183,4325],{},[1140,24185,24186,24188],{},[1146,24187,3164],{"mathvariant":3145},[2922,24189,24190,24192],{},[1146,24191,1439],{},[1150,24193,1152],{},[1189,24195,24196],{"encoding":1191},"\\frac{\\partial C}{\\partial w^1}",[1124,24198,24200],{"className":24199,"ariaHidden":1156},[1196],[1124,24201,24203,24206],{"className":24202},[1200],[1124,24204],{"className":24205,"style":23920},[1204],[1124,24207,24209,24212,24303],{"className":24208},[1209],[1124,24210],{"className":24211},[1795,2212],[1124,24213,24215],{"className":24214},[2911],[1124,24216,24218,24295],{"className":24217},[1221,1222],[1124,24219,24221,24292],{"className":24220},[1226],[1124,24222,24224,24267,24275],{"className":24223,"style":4858},[1230],[1124,24225,24226,24229],{"style":2994},[1124,24227],{"className":24228,"style":2998},[1238],[1124,24230,24232],{"className":24231},[1243,1244,1245,1246],[1124,24233,24235,24238],{"className":24234},[1209,1246],[1124,24236,3164],{"className":24237,"style":3319},[1209,1246],[1124,24239,24241,24244],{"className":24240},[1209,1246],[1124,24242,1439],{"className":24243,"style":1480},[1209,1213,1246],[1124,24245,24247],{"className":24246},[1217],[1124,24248,24250],{"className":24249},[1221],[1124,24251,24253],{"className":24252},[1226],[1124,24254,24256],{"className":24255,"style":22067},[1230],[1124,24257,24258,24261],{"style":3032},[1124,24259],{"className":24260,"style":3036},[1238],[1124,24262,24264],{"className":24263},[1243,3040,3041,1246],[1124,24265,1152],{"className":24266},[1209,1246],[1124,24268,24269,24272],{"style":3053},[1124,24270],{"className":24271,"style":2998},[1238],[1124,24273],{"className":24274,"style":3061},[3060],[1124,24276,24277,24280],{"style":3064},[1124,24278],{"className":24279,"style":2998},[1238],[1124,24281,24283],{"className":24282},[1243,1244,1245,1246],[1124,24284,24286,24289],{"className":24285},[1209,1246],[1124,24287,3164],{"className":24288,"style":3319},[1209,1246],[1124,24290,4325],{"className":24291,"style":4392},[1209,1213,1246],[1124,24293,1254],{"className":24294},[1253],[1124,24296,24298],{"className":24297},[1226],[1124,24299,24301],{"className":24300,"style":3538},[1230],[1124,24302],{},[1124,24304],{"className":24305},[2211,2212],[1124,24307,24309,24339],{"className":24308},[1127],[1124,24310,24312],{"className":24311},[1131],[1133,24313,24314],{"xmlns":1135},[1137,24315,24316,24336],{},[1140,24317,24318],{},[2911,24319,24320,24326],{},[1140,24321,24322,24324],{},[1146,24323,3164],{"mathvariant":3145},[1146,24325,4325],{},[1140,24327,24328,24330],{},[1146,24329,3164],{"mathvariant":3145},[2922,24331,24332,24334],{},[1146,24333,2230],{},[1150,24335,1152],{},[1189,24337,24338],{"encoding":1191},"\\frac{\\partial C}{\\partial b^1}",[1124,24340,24342],{"className":24341,"ariaHidden":1156},[1196],[1124,24343,24345,24348],{"className":24344},[1200],[1124,24346],{"className":24347,"style":23920},[1204],[1124,24349,24351,24354,24445],{"className":24350},[1209],[1124,24352],{"className":24353},[1795,2212],[1124,24355,24357],{"className":24356},[2911],[1124,24358,24360,24437],{"className":24359},[1221,1222],[1124,24361,24363,24434],{"className":24362},[1226],[1124,24364,24366,24409,24417],{"className":24365,"style":4858},[1230],[1124,24367,24368,24371],{"style":2994},[1124,24369],{"className":24370,"style":2998},[1238],[1124,24372,24374],{"className":24373},[1243,1244,1245,1246],[1124,24375,24377,24380],{"className":24376},[1209,1246],[1124,24378,3164],{"className":24379,"style":3319},[1209,1246],[1124,24381,24383,24386],{"className":24382},[1209,1246],[1124,24384,2230],{"className":24385},[1209,1213,1246],[1124,24387,24389],{"className":24388},[1217],[1124,24390,24392],{"className":24391},[1221],[1124,24393,24395],{"className":24394},[1226],[1124,24396,24398],{"className":24397,"style":22067},[1230],[1124,24399,24400,24403],{"style":3032},[1124,24401],{"className":24402,"style":3036},[1238],[1124,24404,24406],{"className":24405},[1243,3040,3041,1246],[1124,24407,1152],{"className":24408},[1209,1246],[1124,24410,24411,24414],{"style":3053},[1124,24412],{"className":24413,"style":2998},[1238],[1124,24415],{"className":24416,"style":3061},[3060],[1124,24418,24419,24422],{"style":3064},[1124,24420],{"className":24421,"style":2998},[1238],[1124,24423,24425],{"className":24424},[1243,1244,1245,1246],[1124,24426,24428,24431],{"className":24427},[1209,1246],[1124,24429,3164],{"className":24430,"style":3319},[1209,1246],[1124,24432,4325],{"className":24433,"style":4392},[1209,1213,1246],[1124,24435,1254],{"className":24436},[1253],[1124,24438,24440],{"className":24439},[1226],[1124,24441,24443],{"className":24442,"style":3538},[1230],[1124,24444],{},[1124,24446],{"className":24447},[2211,2212],[2745,24449],{},[7743,24451,24453],{"id":24452},"_21-输出层权重","2.1 输出层权重",[1101,24455,24456,24457,24598],{},"求 ",[1124,24458,24460,24489],{"className":24459},[1127],[1124,24461,24463],{"className":24462},[1131],[1133,24464,24465],{"xmlns":1135},[1137,24466,24467,24487],{},[1140,24468,24469],{},[2911,24470,24471,24477],{},[1140,24472,24473,24475],{},[1146,24474,3164],{"mathvariant":3145},[1146,24476,4325],{},[1140,24478,24479,24481],{},[1146,24480,3164],{"mathvariant":3145},[2922,24482,24483,24485],{},[1146,24484,1439],{},[1150,24486,1164],{},[1189,24488,23910],{"encoding":1191},[1124,24490,24492],{"className":24491,"ariaHidden":1156},[1196],[1124,24493,24495,24498],{"className":24494},[1200],[1124,24496],{"className":24497,"style":23920},[1204],[1124,24499,24501,24504,24595],{"className":24500},[1209],[1124,24502],{"className":24503},[1795,2212],[1124,24505,24507],{"className":24506},[2911],[1124,24508,24510,24587],{"className":24509},[1221,1222],[1124,24511,24513,24584],{"className":24512},[1226],[1124,24514,24516,24559,24567],{"className":24515,"style":4858},[1230],[1124,24517,24518,24521],{"style":2994},[1124,24519],{"className":24520,"style":2998},[1238],[1124,24522,24524],{"className":24523},[1243,1244,1245,1246],[1124,24525,24527,24530],{"className":24526},[1209,1246],[1124,24528,3164],{"className":24529,"style":3319},[1209,1246],[1124,24531,24533,24536],{"className":24532},[1209,1246],[1124,24534,1439],{"className":24535,"style":1480},[1209,1213,1246],[1124,24537,24539],{"className":24538},[1217],[1124,24540,24542],{"className":24541},[1221],[1124,24543,24545],{"className":24544},[1226],[1124,24546,24548],{"className":24547,"style":22067},[1230],[1124,24549,24550,24553],{"style":3032},[1124,24551],{"className":24552,"style":3036},[1238],[1124,24554,24556],{"className":24555},[1243,3040,3041,1246],[1124,24557,1164],{"className":24558},[1209,1246],[1124,24560,24561,24564],{"style":3053},[1124,24562],{"className":24563,"style":2998},[1238],[1124,24565],{"className":24566,"style":3061},[3060],[1124,24568,24569,24572],{"style":3064},[1124,24570],{"className":24571,"style":2998},[1238],[1124,24573,24575],{"className":24574},[1243,1244,1245,1246],[1124,24576,24578,24581],{"className":24577},[1209,1246],[1124,24579,3164],{"className":24580,"style":3319},[1209,1246],[1124,24582,4325],{"className":24583,"style":4392},[1209,1213,1246],[1124,24585,1254],{"className":24586},[1253],[1124,24588,24590],{"className":24589},[1226],[1124,24591,24593],{"className":24592,"style":3538},[1230],[1124,24594],{},[1124,24596],{"className":24597},[2211,2212],"（输出层权重）",[1101,24600,24601,10434,24604],{},[1107,24602,24603],{},"依赖链路：",[1124,24605,24607,24645],{"className":24606},[1127],[1124,24608,24610],{"className":24609},[1131],[1133,24611,24612],{"xmlns":1135},[1137,24613,24614,24642],{},[1140,24615,24616,24622,24624,24630,24632,24638,24640],{},[2922,24617,24618,24620],{},[1146,24619,1439],{},[1150,24621,1164],{},[1154,24623,3579],{},[2922,24625,24626,24628],{},[1146,24627,2680],{},[1150,24629,1164],{},[1154,24631,3579],{},[2922,24633,24634,24636],{},[1146,24635,4370],{},[1150,24637,1164],{},[1154,24639,3579],{},[1146,24641,4325],{},[1189,24643,24644],{"encoding":1191},"w^2 \\rightarrow z^2 \\rightarrow a^2 \\rightarrow C",[1124,24646,24648,24692,24736,24780],{"className":24647,"ariaHidden":1156},[1196],[1124,24649,24651,24654,24683,24686,24689],{"className":24650},[1200],[1124,24652],{"className":24653,"style":4598},[1204],[1124,24655,24657,24660],{"className":24656},[1209],[1124,24658,1439],{"className":24659,"style":1480},[1209,1213],[1124,24661,24663],{"className":24662},[1217],[1124,24664,24666],{"className":24665},[1221],[1124,24667,24669],{"className":24668},[1226],[1124,24670,24672],{"className":24671,"style":4598},[1230],[1124,24673,24674,24677],{"style":3905},[1124,24675],{"className":24676,"style":1239},[1238],[1124,24678,24680],{"className":24679},[1243,1244,1245,1246],[1124,24681,1164],{"className":24682},[1209,1246],[1124,24684],{"className":24685,"style":1774},[1271],[1124,24687,3579],{"className":24688},[1778],[1124,24690],{"className":24691,"style":1774},[1271],[1124,24693,24695,24698,24727,24730,24733],{"className":24694},[1200],[1124,24696],{"className":24697,"style":4598},[1204],[1124,24699,24701,24704],{"className":24700},[1209],[1124,24702,2680],{"className":24703,"style":2707},[1209,1213],[1124,24705,24707],{"className":24706},[1217],[1124,24708,24710],{"className":24709},[1221],[1124,24711,24713],{"className":24712},[1226],[1124,24714,24716],{"className":24715,"style":4598},[1230],[1124,24717,24718,24721],{"style":3905},[1124,24719],{"className":24720,"style":1239},[1238],[1124,24722,24724],{"className":24723},[1243,1244,1245,1246],[1124,24725,1164],{"className":24726},[1209,1246],[1124,24728],{"className":24729,"style":1774},[1271],[1124,24731,3579],{"className":24732},[1778],[1124,24734],{"className":24735,"style":1774},[1271],[1124,24737,24739,24742,24771,24774,24777],{"className":24738},[1200],[1124,24740],{"className":24741,"style":4598},[1204],[1124,24743,24745,24748],{"className":24744},[1209],[1124,24746,4370],{"className":24747},[1209,1213],[1124,24749,24751],{"className":24750},[1217],[1124,24752,24754],{"className":24753},[1221],[1124,24755,24757],{"className":24756},[1226],[1124,24758,24760],{"className":24759,"style":4598},[1230],[1124,24761,24762,24765],{"style":3905},[1124,24763],{"className":24764,"style":1239},[1238],[1124,24766,24768],{"className":24767},[1243,1244,1245,1246],[1124,24769,1164],{"className":24770},[1209,1246],[1124,24772],{"className":24773,"style":1774},[1271],[1124,24775,3579],{"className":24776},[1778],[1124,24778],{"className":24779,"style":1774},[1271],[1124,24781,24783,24786],{"className":24782},[1200],[1124,24784],{"className":24785,"style":4804},[1204],[1124,24787,4325],{"className":24788,"style":4392},[1209,1213],[1101,24790,24791],{},"用链式法则展开：",[1101,24793,24794],{},[1124,24795,24797,24895],{"className":24796},[1127],[1124,24798,24800],{"className":24799},[1131],[1133,24801,24802],{"xmlns":1135},[1137,24803,24804,24892],{},[1140,24805,24806,24824,24826,24844,24846,24868,24870],{},[2911,24807,24808,24814],{},[1140,24809,24810,24812],{},[1146,24811,3164],{"mathvariant":3145},[1146,24813,4325],{},[1140,24815,24816,24818],{},[1146,24817,3164],{"mathvariant":3145},[2922,24819,24820,24822],{},[1146,24821,1439],{},[1150,24823,1164],{},[1154,24825,1652],{},[2911,24827,24828,24834],{},[1140,24829,24830,24832],{},[1146,24831,3164],{"mathvariant":3145},[1146,24833,4325],{},[1140,24835,24836,24838],{},[1146,24837,3164],{"mathvariant":3145},[2922,24839,24840,24842],{},[1146,24841,4370],{},[1150,24843,1164],{},[1154,24845,2325],{},[2911,24847,24848,24858],{},[1140,24849,24850,24852],{},[1146,24851,3164],{"mathvariant":3145},[2922,24853,24854,24856],{},[1146,24855,4370],{},[1150,24857,1164],{},[1140,24859,24860,24862],{},[1146,24861,3164],{"mathvariant":3145},[2922,24863,24864,24866],{},[1146,24865,2680],{},[1150,24867,1164],{},[1154,24869,2325],{},[2911,24871,24872,24882],{},[1140,24873,24874,24876],{},[1146,24875,3164],{"mathvariant":3145},[2922,24877,24878,24880],{},[1146,24879,2680],{},[1150,24881,1164],{},[1140,24883,24884,24886],{},[1146,24885,3164],{"mathvariant":3145},[2922,24887,24888,24890],{},[1146,24889,1439],{},[1150,24891,1164],{},[1189,24893,24894],{"encoding":1191},"\\frac{\\partial C}{\\partial w^2} = \\frac{\\partial C}{\\partial a^2} \\cdot \\frac{\\partial a^2}{\\partial z^2} \\cdot \\frac{\\partial z^2}{\\partial w^2}",[1124,24896,24898,25013,25128,25273],{"className":24897,"ariaHidden":1156},[1196],[1124,24899,24901,24904,25004,25007,25010],{"className":24900},[1200],[1124,24902],{"className":24903,"style":23920},[1204],[1124,24905,24907,24910,25001],{"className":24906},[1209],[1124,24908],{"className":24909},[1795,2212],[1124,24911,24913],{"className":24912},[2911],[1124,24914,24916,24993],{"className":24915},[1221,1222],[1124,24917,24919,24990],{"className":24918},[1226],[1124,24920,24922,24965,24973],{"className":24921,"style":4858},[1230],[1124,24923,24924,24927],{"style":2994},[1124,24925],{"className":24926,"style":2998},[1238],[1124,24928,24930],{"className":24929},[1243,1244,1245,1246],[1124,24931,24933,24936],{"className":24932},[1209,1246],[1124,24934,3164],{"className":24935,"style":3319},[1209,1246],[1124,24937,24939,24942],{"className":24938},[1209,1246],[1124,24940,1439],{"className":24941,"style":1480},[1209,1213,1246],[1124,24943,24945],{"className":24944},[1217],[1124,24946,24948],{"className":24947},[1221],[1124,24949,24951],{"className":24950},[1226],[1124,24952,24954],{"className":24953,"style":22067},[1230],[1124,24955,24956,24959],{"style":3032},[1124,24957],{"className":24958,"style":3036},[1238],[1124,24960,24962],{"className":24961},[1243,3040,3041,1246],[1124,24963,1164],{"className":24964},[1209,1246],[1124,24966,24967,24970],{"style":3053},[1124,24968],{"className":24969,"style":2998},[1238],[1124,24971],{"className":24972,"style":3061},[3060],[1124,24974,24975,24978],{"style":3064},[1124,24976],{"className":24977,"style":2998},[1238],[1124,24979,24981],{"className":24980},[1243,1244,1245,1246],[1124,24982,24984,24987],{"className":24983},[1209,1246],[1124,24985,3164],{"className":24986,"style":3319},[1209,1246],[1124,24988,4325],{"className":24989,"style":4392},[1209,1213,1246],[1124,24991,1254],{"className":24992},[1253],[1124,24994,24996],{"className":24995},[1226],[1124,24997,24999],{"className":24998,"style":3538},[1230],[1124,25000],{},[1124,25002],{"className":25003},[2211,2212],[1124,25005],{"className":25006,"style":1774},[1271],[1124,25008,1652],{"className":25009},[1778],[1124,25011],{"className":25012,"style":1774},[1271],[1124,25014,25016,25019,25119,25122,25125],{"className":25015},[1200],[1124,25017],{"className":25018,"style":23920},[1204],[1124,25020,25022,25025,25116],{"className":25021},[1209],[1124,25023],{"className":25024},[1795,2212],[1124,25026,25028],{"className":25027},[2911],[1124,25029,25031,25108],{"className":25030},[1221,1222],[1124,25032,25034,25105],{"className":25033},[1226],[1124,25035,25037,25080,25088],{"className":25036,"style":4858},[1230],[1124,25038,25039,25042],{"style":2994},[1124,25040],{"className":25041,"style":2998},[1238],[1124,25043,25045],{"className":25044},[1243,1244,1245,1246],[1124,25046,25048,25051],{"className":25047},[1209,1246],[1124,25049,3164],{"className":25050,"style":3319},[1209,1246],[1124,25052,25054,25057],{"className":25053},[1209,1246],[1124,25055,4370],{"className":25056},[1209,1213,1246],[1124,25058,25060],{"className":25059},[1217],[1124,25061,25063],{"className":25062},[1221],[1124,25064,25066],{"className":25065},[1226],[1124,25067,25069],{"className":25068,"style":22067},[1230],[1124,25070,25071,25074],{"style":3032},[1124,25072],{"className":25073,"style":3036},[1238],[1124,25075,25077],{"className":25076},[1243,3040,3041,1246],[1124,25078,1164],{"className":25079},[1209,1246],[1124,25081,25082,25085],{"style":3053},[1124,25083],{"className":25084,"style":2998},[1238],[1124,25086],{"className":25087,"style":3061},[3060],[1124,25089,25090,25093],{"style":3064},[1124,25091],{"className":25092,"style":2998},[1238],[1124,25094,25096],{"className":25095},[1243,1244,1245,1246],[1124,25097,25099,25102],{"className":25098},[1209,1246],[1124,25100,3164],{"className":25101,"style":3319},[1209,1246],[1124,25103,4325],{"className":25104,"style":4392},[1209,1213,1246],[1124,25106,1254],{"className":25107},[1253],[1124,25109,25111],{"className":25110},[1226],[1124,25112,25114],{"className":25113,"style":3538},[1230],[1124,25115],{},[1124,25117],{"className":25118},[2211,2212],[1124,25120],{"className":25121,"style":2500},[1271],[1124,25123,2325],{"className":25124},[2504],[1124,25126],{"className":25127,"style":2500},[1271],[1124,25129,25131,25135,25264,25267,25270],{"className":25130},[1200],[1124,25132],{"className":25133,"style":25134},[1204],"height:1.3629em;vertical-align:-0.345em;",[1124,25136,25138,25141,25261],{"className":25137},[1209],[1124,25139],{"className":25140},[1795,2212],[1124,25142,25144],{"className":25143},[2911],[1124,25145,25147,25253],{"className":25146},[1221,1222],[1124,25148,25150,25250],{"className":25149},[1226],[1124,25151,25154,25197,25205],{"className":25152,"style":25153},[1230],"height:1.0179em;",[1124,25155,25156,25159],{"style":2994},[1124,25157],{"className":25158,"style":2998},[1238],[1124,25160,25162],{"className":25161},[1243,1244,1245,1246],[1124,25163,25165,25168],{"className":25164},[1209,1246],[1124,25166,3164],{"className":25167,"style":3319},[1209,1246],[1124,25169,25171,25174],{"className":25170},[1209,1246],[1124,25172,2680],{"className":25173,"style":2707},[1209,1213,1246],[1124,25175,25177],{"className":25176},[1217],[1124,25178,25180],{"className":25179},[1221],[1124,25181,25183],{"className":25182},[1226],[1124,25184,25186],{"className":25185,"style":22067},[1230],[1124,25187,25188,25191],{"style":3032},[1124,25189],{"className":25190,"style":3036},[1238],[1124,25192,25194],{"className":25193},[1243,3040,3041,1246],[1124,25195,1164],{"className":25196},[1209,1246],[1124,25198,25199,25202],{"style":3053},[1124,25200],{"className":25201,"style":2998},[1238],[1124,25203],{"className":25204,"style":3061},[3060],[1124,25206,25207,25210],{"style":3064},[1124,25208],{"className":25209,"style":2998},[1238],[1124,25211,25213],{"className":25212},[1243,1244,1245,1246],[1124,25214,25216,25219],{"className":25215},[1209,1246],[1124,25217,3164],{"className":25218,"style":3319},[1209,1246],[1124,25220,25222,25225],{"className":25221},[1209,1246],[1124,25223,4370],{"className":25224},[1209,1213,1246],[1124,25226,25228],{"className":25227},[1217],[1124,25229,25231],{"className":25230},[1221],[1124,25232,25234],{"className":25233},[1226],[1124,25235,25238],{"className":25236,"style":25237},[1230],"height:0.8913em;",[1124,25239,25241,25244],{"style":25240},"top:-2.931em;margin-right:0.0714em;",[1124,25242],{"className":25243,"style":3036},[1238],[1124,25245,25247],{"className":25246},[1243,3040,3041,1246],[1124,25248,1164],{"className":25249},[1209,1246],[1124,25251,1254],{"className":25252},[1253],[1124,25254,25256],{"className":25255},[1226],[1124,25257,25259],{"className":25258,"style":3538},[1230],[1124,25260],{},[1124,25262],{"className":25263},[2211,2212],[1124,25265],{"className":25266,"style":2500},[1271],[1124,25268,2325],{"className":25269},[2504],[1124,25271],{"className":25272,"style":2500},[1271],[1124,25274,25276,25279],{"className":25275},[1200],[1124,25277],{"className":25278,"style":25134},[1204],[1124,25280,25282,25285,25402],{"className":25281},[1209],[1124,25283],{"className":25284},[1795,2212],[1124,25286,25288],{"className":25287},[2911],[1124,25289,25291,25394],{"className":25290},[1221,1222],[1124,25292,25294,25391],{"className":25293},[1226],[1124,25295,25297,25340,25348],{"className":25296,"style":25153},[1230],[1124,25298,25299,25302],{"style":2994},[1124,25300],{"className":25301,"style":2998},[1238],[1124,25303,25305],{"className":25304},[1243,1244,1245,1246],[1124,25306,25308,25311],{"className":25307},[1209,1246],[1124,25309,3164],{"className":25310,"style":3319},[1209,1246],[1124,25312,25314,25317],{"className":25313},[1209,1246],[1124,25315,1439],{"className":25316,"style":1480},[1209,1213,1246],[1124,25318,25320],{"className":25319},[1217],[1124,25321,25323],{"className":25322},[1221],[1124,25324,25326],{"className":25325},[1226],[1124,25327,25329],{"className":25328,"style":22067},[1230],[1124,25330,25331,25334],{"style":3032},[1124,25332],{"className":25333,"style":3036},[1238],[1124,25335,25337],{"className":25336},[1243,3040,3041,1246],[1124,25338,1164],{"className":25339},[1209,1246],[1124,25341,25342,25345],{"style":3053},[1124,25343],{"className":25344,"style":2998},[1238],[1124,25346],{"className":25347,"style":3061},[3060],[1124,25349,25350,25353],{"style":3064},[1124,25351],{"className":25352,"style":2998},[1238],[1124,25354,25356],{"className":25355},[1243,1244,1245,1246],[1124,25357,25359,25362],{"className":25358},[1209,1246],[1124,25360,3164],{"className":25361,"style":3319},[1209,1246],[1124,25363,25365,25368],{"className":25364},[1209,1246],[1124,25366,2680],{"className":25367,"style":2707},[1209,1213,1246],[1124,25369,25371],{"className":25370},[1217],[1124,25372,25374],{"className":25373},[1221],[1124,25375,25377],{"className":25376},[1226],[1124,25378,25380],{"className":25379,"style":25237},[1230],[1124,25381,25382,25385],{"style":25240},[1124,25383],{"className":25384,"style":3036},[1238],[1124,25386,25388],{"className":25387},[1243,3040,3041,1246],[1124,25389,1164],{"className":25390},[1209,1246],[1124,25392,1254],{"className":25393},[1253],[1124,25395,25397],{"className":25396},[1226],[1124,25398,25400],{"className":25399,"style":3538},[1230],[1124,25401],{},[1124,25403],{"className":25404},[2211,2212],[1101,25406,25407],{},"逐项计算：",[1101,25409,25410],{},[1124,25411,25413,25469],{"className":25412},[1127],[1124,25414,25416],{"className":25415},[1131],[1133,25417,25418],{"xmlns":1135},[1137,25419,25420,25466],{},[1140,25421,25422,25440,25442,25448,25450,25452,25454,25456,25458,25460,25462,25464],{},[2911,25423,25424,25430],{},[1140,25425,25426,25428],{},[1146,25427,3164],{"mathvariant":3145},[1146,25429,4325],{},[1140,25431,25432,25434],{},[1146,25433,3164],{"mathvariant":3145},[2922,25435,25436,25438],{},[1146,25437,4370],{},[1150,25439,1164],{},[1154,25441,1652],{},[2922,25443,25444,25446],{},[1146,25445,4370],{},[1150,25447,1164],{},[1154,25449,2235],{},[1146,25451,4359],{},[1154,25453,1652],{},[1150,25455,22667],{},[1154,25457,2235],{},[1150,25459,1152],{},[1154,25461,1652],{},[1154,25463,2235],{},[1150,25465,23096],{},[1189,25467,25468],{"encoding":1191},"\\frac{\\partial C}{\\partial a^2} = a^2 - y = 0.652 - 1 = 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64],{},[1154,25750,2683],{"stretchy":1674},[1154,25752,1652],{},[2922,25754,25755,25757],{},[1146,25756,4370],{},[1150,25758,1164],{},[1154,25760,2677],{"stretchy":1674},[1150,25762,1152],{},[1154,25764,2235],{},[2922,25766,25767,25769],{},[1146,25768,4370],{},[1150,25770,1164],{},[1154,25772,2683],{"stretchy":1674},[1154,25774,1652],{},[1150,25776,22667],{},[1154,25778,10608],{},[1150,25780,23096],{},[1154,25782,1652],{},[1150,25784,25785],{},"0.227",[1189,25787,25788],{"encoding":1191},"\\frac{\\partial a^2}{\\partial z^2} = \\sigma'(z^2) = a^2(1-a^2) = 0.652 \\times 0.348 = 0.227",[1124,25790,25792,25933,26015,26065,26112,26130,26148],{"className":25791,"ariaHidden":1156},[1196],[1124,25793,25795,25798,25924,25927,25930],{"className":25794},[1200],[1124,25796],{"className":25797,"style":25134},[1204],[1124,25799,25801,25804,25921],{"className":25800},[1209],[1124,25802],{"className":25803},[1795,2212],[1124,25805,25807],{"className":25806},[2911],[1124,25808,25810,25913],{"className":25809},[1221,1222],[1124,25811,25813,25910],{"className":25812},[1226],[1124,25814,25816,25859,25867],{"className":25815,"style":25153},[1230],[1124,25817,25818,25821],{"style":2994},[1124,25819],{"className":25820,"style":2998},[1238],[1124,25822,25824],{"className":25823},[1243,1244,1245,1246],[1124,25825,25827,25830],{"className":25826},[1209,1246],[1124,25828,3164],{"className":25829,"style":3319},[1209,1246],[1124,25831,25833,25836],{"className":25832},[1209,1246],[1124,25834,2680],{"className":25835,"style":2707},[1209,1213,1246],[1124,25837,25839],{"className":25838},[1217],[1124,25840,25842],{"className":25841},[1221],[1124,25843,25845],{"className":25844},[1226],[1124,25846,25848],{"className":25847,"style":22067},[1230],[1124,25849,25850,25853],{"style":3032},[1124,25851],{"className":25852,"style":3036},[1238],[1124,25854,25856],{"className":25855},[1243,3040,3041,1246],[1124,25857,1164],{"className":25858},[1209,1246],[1124,25860,25861,25864],{"style":3053},[1124,25862],{"className":25863,"style":2998},[1238],[1124,25865],{"className":25866,"style":3061},[3060],[1124,25868,25869,25872],{"style":3064},[1124,25870],{"className":25871,"style":2998},[1238],[1124,25873,25875],{"className":25874},[1243,1244,1245,1246],[1124,25876,25878,25881],{"className":25877},[1209,1246],[1124,25879,3164],{"className":25880,"style":3319},[1209,1246],[1124,25882,25884,25887],{"className":25883},[1209,1246],[1124,25885,4370],{"className":25886},[1209,1213,1246],[1124,25888,25890],{"className":25889},[1217],[1124,25891,25893],{"className":25892},[1221],[1124,25894,25896],{"className":25895},[1226],[1124,25897,25899],{"className":25898,"style":25237},[1230],[1124,25900,25901,25904],{"style":25240},[1124,25902],{"className":25903,"style":3036},[1238],[1124,25905,25907],{"className":25906},[1243,3040,3041,1246],[1124,25908,1164],{"className":25909},[1209,1246],[1124,25911,1254],{"className":25912},[1253],[1124,25914,25916],{"className":25915},[1226],[1124,25917,25919],{"className":25918,"style":3538},[1230],[1124,25920],{},[1124,25922],{"className":25923},[2211,2212],[1124,25925],{"className":25926,"style":1774},[1271],[1124,25928,1652],{"className":25929},[1778],[1124,25931],{"className":25932,"style":1774},[1271],[1124,25934,25936,25939,25971,25974,26003,26006,26009,26012],{"className":25935},[1200],[1124,25937],{"className":25938,"style":4576},[1204],[1124,25940,25942,25945],{"className":25941},[1209],[1124,25943,2674],{"className":25944,"style":2700},[1209,1213],[1124,25946,25948],{"className":25947},[1217],[1124,25949,25951],{"className":25950},[1221],[1124,25952,25954],{"className":25953},[1226],[1124,25955,25957],{"className":25956,"style":3902},[1230],[1124,25958,25959,25962],{"style":3905},[1124,25960],{"className":25961,"style":1239},[1238],[1124,25963,25965],{"className":25964},[1243,1244,1245,1246],[1124,25966,25968],{"className":25967},[1209,1246],[1124,25969,3838],{"className":25970},[1209,1246],[1124,25972,2677],{"className":25973},[1795],[1124,25975,25977,25980],{"className":25976},[1209],[1124,25978,2680],{"className":25979,"style":2707},[1209,1213],[1124,25981,25983],{"className":25982},[1217],[1124,25984,25986],{"className":25985},[1221],[1124,25987,25989],{"className":25988},[1226],[1124,25990,25992],{"className":25991,"style":4598},[1230],[1124,25993,25994,25997],{"style":3905},[1124,25995],{"className":25996,"style":1239},[1238],[1124,25998,26000],{"className":25999},[1243,1244,1245,1246],[1124,26001,1164],{"className":26002},[1209,1246],[1124,26004,2683],{"className":26005},[2211],[1124,26007],{"className":26008,"style":1774},[1271],[1124,26010,1652],{"className":26011},[1778],[1124,26013],{"className":26014,"style":1774},[1271],[1124,26016,26018,26021,26050,26053,26056,26059,26062],{"className":26017},[1200],[1124,26019],{"className":26020,"style":4576},[1204],[1124,26022,26024,26027],{"className":26023},[1209],[1124,26025,4370],{"className":26026},[1209,1213],[1124,26028,26030],{"className":26029},[1217],[1124,26031,26033],{"className":26032},[1221],[1124,26034,26036],{"className":26035},[1226],[1124,26037,26039],{"className":26038,"style":4598},[1230],[1124,26040,26041,26044],{"style":3905},[1124,26042],{"className":26043,"style":1239},[1238],[1124,26045,26047],{"className":26046},[1243,1244,1245,1246],[1124,26048,1164],{"className":26049},[1209,1246],[1124,26051,2677],{"className":26052},[1795],[1124,26054,1152],{"className":26055},[1209],[1124,26057],{"className":26058,"style":2500},[1271],[1124,26060,2235],{"className":26061},[2504],[1124,26063],{"className":26064,"style":2500},[1271],[1124,26066,26068,26071,26100,26103,26106,26109],{"className":26067},[1200],[1124,26069],{"className":26070,"style":4576},[1204],[1124,26072,26074,26077],{"className":26073},[1209],[1124,26075,4370],{"className":26076},[1209,1213],[1124,26078,26080],{"className":26079},[1217],[1124,26081,26083],{"className":26082},[1221],[1124,26084,26086],{"className":26085},[1226],[1124,26087,26089],{"className":26088,"style":4598},[1230],[1124,26090,26091,26094],{"style":3905},[1124,26092],{"className":26093,"style":1239},[1238],[1124,26095,26097],{"className":26096},[1243,1244,1245,1246],[1124,26098,1164],{"className":26099},[1209,1246],[1124,26101,2683],{"className":26102},[2211],[1124,26104],{"className":26105,"style":1774},[1271],[1124,26107,1652],{"className":26108},[1778],[1124,26110],{"className":26111,"style":1774},[1271],[1124,26113,26115,26118,26121,26124,26127],{"className":26114},[1200],[1124,26116],{"className":26117,"style":10423},[1204],[1124,26119,22667],{"className":26120},[1209],[1124,26122],{"className":26123,"style":2500},[1271],[1124,26125,10608],{"className":26126},[2504],[1124,26128],{"className":26129,"style":2500},[1271],[1124,26131,26133,26136,26139,26142,26145],{"className":26132},[1200],[1124,26134],{"className":26135,"style":3685},[1204],[1124,26137,23096],{"className":26138},[1209],[1124,26140],{"className":26141,"style":1774},[1271],[1124,26143,1652],{"className":26144},[1778],[1124,26146],{"className":26147,"style":1774},[1271],[1124,26149,26151,26154],{"className":26150},[1200],[1124,26152],{"className":26153,"style":3685},[1204],[1124,26155,25785],{"className":26156},[1209],[1101,26158,26159],{},[1124,26160,26162,26208],{"className":26161},[1127],[1124,26163,26165],{"className":26164},[1131],[1133,26166,26167],{"xmlns":1135},[1137,26168,26169,26205],{},[1140,26170,26171,26193,26195,26201,26203],{},[2911,26172,26173,26183],{},[1140,26174,26175,26177],{},[1146,26176,3164],{"mathvariant":3145},[2922,26178,26179,26181],{},[1146,26180,2680],{},[1150,26182,1164],{},[1140,26184,26185,26187],{},[1146,26186,3164],{"mathvariant":3145},[2922,26188,26189,26191],{},[1146,26190,1439],{},[1150,26192,1164],{},[1154,26194,1652],{},[2922,26196,26197,26199],{},[1146,26198,4370],{},[1150,26200,1152],{},[1154,26202,1652],{},[1150,26204,21877],{},[1189,26206,26207],{"encoding":1191},"\\frac{\\partial z^2}{\\partial w^2} = a^1 = 0.711",[1124,26209,26211,26352,26396],{"className":26210,"ariaHidden":1156},[1196],[1124,26212,26214,26217,26343,26346,26349],{"className":26213},[1200],[1124,26215],{"className":26216,"style":25134},[1204],[1124,26218,26220,26223,26340],{"className":26219},[1209],[1124,26221],{"className":26222},[1795,2212],[1124,26224,26226],{"className":26225},[2911],[1124,26227,26229,26332],{"className":26228},[1221,1222],[1124,26230,26232,26329],{"className":26231},[1226],[1124,26233,26235,26278,26286],{"className":26234,"style":25153},[1230],[1124,26236,26237,26240],{"style":2994},[1124,26238],{"className":26239,"style":2998},[1238],[1124,26241,26243],{"className":26242},[1243,1244,1245,1246],[1124,26244,26246,26249],{"className":26245},[1209,1246],[1124,26247,3164],{"className":26248,"style":3319},[1209,1246],[1124,26250,26252,26255],{"className":26251},[1209,1246],[1124,26253,1439],{"className":26254,"style":1480},[1209,1213,1246],[1124,26256,26258],{"className":26257},[1217],[1124,26259,26261],{"className":26260},[1221],[1124,26262,26264],{"className":26263},[1226],[1124,26265,26267],{"className":26266,"style":22067},[1230],[1124,26268,26269,26272],{"style":3032},[1124,26270],{"className":26271,"style":3036},[1238],[1124,26273,26275],{"className":26274},[1243,3040,3041,1246],[1124,26276,1164],{"className":26277},[1209,1246],[1124,26279,26280,26283],{"style":3053},[1124,26281],{"className":26282,"style":2998},[1238],[1124,26284],{"className":26285,"style":3061},[3060],[1124,26287,26288,26291],{"style":3064},[1124,26289],{"className":26290,"style":2998},[1238],[1124,26292,26294],{"className":26293},[1243,1244,1245,1246],[1124,26295,26297,26300],{"className":26296},[1209,1246],[1124,26298,3164],{"className":26299,"style":3319},[1209,1246],[1124,26301,26303,26306],{"className":26302},[1209,1246],[1124,26304,2680],{"className":26305,"style":2707},[1209,1213,1246],[1124,26307,26309],{"className":26308},[1217],[1124,26310,26312],{"className":26311},[1221],[1124,26313,26315],{"className":26314},[1226],[1124,26316,26318],{"className":26317,"style":25237},[1230],[1124,26319,26320,26323],{"style":25240},[1124,26321],{"className":26322,"style":3036},[1238],[1124,26324,26326],{"className":26325},[1243,3040,3041,1246],[1124,26327,1164],{"className":26328},[1209,1246],[1124,26330,1254],{"className":26331},[1253],[1124,26333,26335],{"className":26334},[1226],[1124,26336,26338],{"className":26337,"style":3538},[1230],[1124,26339],{},[1124,26341],{"className":26342},[2211,2212],[1124,26344],{"className":26345,"style":1774},[1271],[1124,26347,1652],{"className":26348},[1778],[1124,26350],{"className":26351,"style":1774},[1271],[1124,26353,26355,26358,26387,26390,26393],{"className":26354},[1200],[1124,26356],{"className":26357,"style":4598},[1204],[1124,26359,26361,26364],{"className":26360},[1209],[1124,26362,4370],{"className":26363},[1209,1213],[1124,26365,26367],{"className":26366},[1217],[1124,26368,26370],{"className":26369},[1221],[1124,26371,26373],{"className":26372},[1226],[1124,26374,26376],{"className":26375,"style":4598},[1230],[1124,26377,26378,26381],{"style":3905},[1124,26379],{"className":26380,"style":1239},[1238],[1124,26382,26384],{"className":26383},[1243,1244,1245,1246],[1124,26385,1152],{"className":26386},[1209,1246],[1124,26388],{"className":26389,"style":1774},[1271],[1124,26391,1652],{"className":26392},[1778],[1124,26394],{"className":26395,"style":1774},[1271],[1124,26397,26399,26402],{"className":26398},[1200],[1124,26400],{"className":26401,"style":3685},[1204],[1124,26403,21877],{"className":26404},[1209],[1101,26406,26407],{},[1107,26408,26409],{},"相乘：",[1101,26411,26412],{},[1124,26413,26415,26480],{"className":26414},[1127],[1124,26416,26418],{"className":26417},[1131],[1133,26419,26420],{"xmlns":1135},[1137,26421,26422,26477],{},[1140,26423,26424,26442,26444,26446,26448,26450,26452,26454,26456,26458,26460,26462],{},[2911,26425,26426,26432],{},[1140,26427,26428,26430],{},[1146,26429,3164],{"mathvariant":3145},[1146,26431,4325],{},[1140,26433,26434,26436],{},[1146,26435,3164],{"mathvariant":3145},[2922,26437,26438,26440],{},[1146,26439,1439],{},[1150,26441,1164],{},[1154,26443,1652],{},[1154,26445,2677],{"stretchy":1674},[1154,26447,2235],{},[1150,26449,23096],{},[1154,26451,2683],{"stretchy":1674},[1154,26453,10608],{},[1150,26455,25785],{},[1154,26457,10608],{},[1150,26459,21877],{},[1154,26461,1652],{},[8168,26463,26464],{"notation":8170},[1671,26465,26466],{"scriptlevel":1673,"displaystyle":1674},[1671,26467,26468],{"scriptlevel":1673,"displaystyle":1674},[1671,26469,26470],{"scriptlevel":1673,"displaystyle":1156},[1140,26471,26472,26474],{},[1154,26473,2235],{},[1150,26475,26476],{},"0.0562",[1189,26478,26479],{"encoding":1191},"\\frac{\\partial C}{\\partial w^2} = (-0.348) \\times 0.227 \\times 0.711 = \\boxed{-0.0562}",[1124,26481,26483,26598,26625,26643,26661],{"className":26482,"ariaHidden":1156},[1196],[1124,26484,26486,26489,26589,26592,26595],{"className":26485},[1200],[1124,26487],{"className":26488,"style":23920},[1204],[1124,26490,26492,26495,26586],{"className":26491},[1209],[1124,26493],{"className":26494},[1795,2212],[1124,26496,26498],{"className":26497},[2911],[1124,26499,26501,26578],{"className":26500},[1221,1222],[1124,26502,26504,26575],{"className":26503},[1226],[1124,26505,26507,26550,26558],{"className":26506,"style":4858},[1230],[1124,26508,26509,26512],{"style":2994},[1124,26510],{"className":26511,"style":2998},[1238],[1124,26513,26515],{"className":26514},[1243,1244,1245,1246],[1124,26516,26518,26521],{"className":26517},[1209,1246],[1124,26519,3164],{"className":26520,"style":3319},[1209,1246],[1124,26522,26524,26527],{"className":26523},[1209,1246],[1124,26525,1439],{"className":26526,"style":1480},[1209,1213,1246],[1124,26528,26530],{"className":26529},[1217],[1124,26531,26533],{"className":26532},[1221],[1124,26534,26536],{"className":26535},[1226],[1124,26537,26539],{"className":26538,"style":22067},[1230],[1124,26540,26541,26544],{"style":3032},[1124,26542],{"className":26543,"style":3036},[1238],[1124,26545,26547],{"className":26546},[1243,3040,3041,1246],[1124,26548,1164],{"className":26549},[1209,1246],[1124,26551,26552,26555],{"style":3053},[1124,26553],{"className":26554,"style":2998},[1238],[1124,26556],{"className":26557,"style":3061},[3060],[1124,26559,26560,26563],{"style":3064},[1124,26561],{"className":26562,"style":2998},[1238],[1124,26564,26566],{"className":26565},[1243,1244,1245,1246],[1124,26567,26569,26572],{"className":26568},[1209,1246],[1124,26570,3164],{"className":26571,"style":3319},[1209,1246],[1124,26573,4325],{"className":26574,"style":4392},[1209,1213,1246],[1124,26576,1254],{"className":26577},[1253],[1124,26579,26581],{"className":26580},[1226],[1124,26582,26584],{"className":26583,"style":3538},[1230],[1124,26585],{},[1124,26587],{"className":26588},[2211,2212],[1124,26590],{"className":26591,"style":1774},[1271],[1124,26593,1652],{"className":26594},[1778],[1124,26596],{"className":26597,"style":1774},[1271],[1124,26599,26601,26604,26607,26610,26613,26616,26619,26622],{"className":26600},[1200],[1124,26602],{"className":26603,"style":2696},[1204],[1124,26605,2677],{"className":26606},[1795],[1124,26608,2235],{"className":26609},[1209],[1124,26611,23096],{"className":26612},[1209],[1124,26614,2683],{"className":26615},[2211],[1124,26617],{"className":26618,"style":2500},[1271],[1124,26620,10608],{"className":26621},[2504],[1124,26623],{"className":26624,"style":2500},[1271],[1124,26626,26628,26631,26634,26637,26640],{"className":26627},[1200],[1124,26629],{"className":26630,"style":10423},[1204],[1124,26632,25785],{"className":26633},[1209],[1124,26635],{"className":26636,"style":2500},[1271],[1124,26638,10608],{"className":26639},[2504],[1124,26641],{"className":26642,"style":2500},[1271],[1124,26644,26646,26649,26652,26655,26658],{"className":26645},[1200],[1124,26647],{"className":26648,"style":3685},[1204],[1124,26650,21877],{"className":26651},[1209],[1124,26653],{"className":26654,"style":1774},[1271],[1124,26656,1652],{"className":26657},[1778],[1124,26659],{"className":26660,"style":1774},[1271],[1124,26662,26664,26668],{"className":26663},[1200],[1124,26665],{"className":26666,"style":26667},[1204],"height:1.4078em;vertical-align:-0.4233em;",[1124,26669,26671],{"className":26670},[1209],[1124,26672,26674,26714],{"className":26673},[1221,1222],[1124,26675,26677,26711],{"className":26676},[1226],[1124,26678,26680,26702],{"className":26679,"style":12358},[1230],[1124,26681,26683,26687],{"style":26682},"top:-3.4078em;",[1124,26684],{"className":26685,"style":26686},[1238],"height:3.4078em;",[1124,26688,26690],{"className":26689},[8257],[1124,26691,26693],{"className":26692},[1209],[1124,26694,26696,26699],{"className":26695},[1209],[1124,26697,2235],{"className":26698},[1209],[1124,26700,26476],{"className":26701},[1209],[1124,26703,26704,26707],{"style":12380},[1124,26705],{"className":26706,"style":26686},[1238],[1124,26708],{"className":26709,"style":26710},[8436,8437],"height:1.4078em;border-style:solid;border-width:0.04em;",[1124,26712,1254],{"className":26713},[1253],[1124,26715,26717],{"className":26716},[1226],[1124,26718,26721],{"className":26719,"style":26720},[1230],"height:0.4233em;",[1124,26722],{},[2745,26724],{},[7743,26726,26728],{"id":26727},"_22-输出层偏置","2.2 输出层偏置",[1101,26730,24456,26731,26872],{},[1124,26732,26734,26763],{"className":26733},[1127],[1124,26735,26737],{"className":26736},[1131],[1133,26738,26739],{"xmlns":1135},[1137,26740,26741,26761],{},[1140,26742,26743],{},[2911,26744,26745,26751],{},[1140,26746,26747,26749],{},[1146,26748,3164],{"mathvariant":3145},[1146,26750,4325],{},[1140,26752,26753,26755],{},[1146,26754,3164],{"mathvariant":3145},[2922,26756,26757,26759],{},[1146,26758,2230],{},[1150,26760,1164],{},[1189,26762,24054],{"encoding":1191},[1124,26764,26766],{"className":26765,"ariaHidden":1156},[1196],[1124,26767,26769,26772],{"className":26768},[1200],[1124,26770],{"className":26771,"style":23920},[1204],[1124,26773,26775,26778,26869],{"className":26774},[1209],[1124,26776],{"className":26777},[1795,2212],[1124,26779,26781],{"className":26780},[2911],[1124,26782,26784,26861],{"className":26783},[1221,1222],[1124,26785,26787,26858],{"className":26786},[1226],[1124,26788,26790,26833,26841],{"className":26789,"style":4858},[1230],[1124,26791,26792,26795],{"style":2994},[1124,26793],{"className":26794,"style":2998},[1238],[1124,26796,26798],{"className":26797},[1243,1244,1245,1246],[1124,26799,26801,26804],{"className":26800},[1209,1246],[1124,26802,3164],{"className":26803,"style":3319},[1209,1246],[1124,26805,26807,26810],{"className":26806},[1209,1246],[1124,26808,2230],{"className":26809},[1209,1213,1246],[1124,26811,26813],{"className":26812},[1217],[1124,26814,26816],{"className":26815},[1221],[1124,26817,26819],{"className":26818},[1226],[1124,26820,26822],{"className":26821,"style":22067},[1230],[1124,26823,26824,26827],{"style":3032},[1124,26825],{"className":26826,"style":3036},[1238],[1124,26828,26830],{"className":26829},[1243,3040,3041,1246],[1124,26831,1164],{"className":26832},[1209,1246],[1124,26834,26835,26838],{"style":3053},[1124,26836],{"className":26837,"style":2998},[1238],[1124,26839],{"className":26840,"style":3061},[3060],[1124,26842,26843,26846],{"style":3064},[1124,26844],{"className":26845,"style":2998},[1238],[1124,26847,26849],{"className":26848},[1243,1244,1245,1246],[1124,26850,26852,26855],{"className":26851},[1209,1246],[1124,26853,3164],{"className":26854,"style":3319},[1209,1246],[1124,26856,4325],{"className":26857,"style":4392},[1209,1213,1246],[1124,26859,1254],{"className":26860},[1253],[1124,26862,26864],{"className":26863},[1226],[1124,26865,26867],{"className":26866,"style":3538},[1230],[1124,26868],{},[1124,26870],{"className":26871},[2211,2212],"（输出层偏置）",[1101,26874,26875,10434,26877],{},[1107,26876,24603],{},[1124,26878,26880,26918],{"className":26879},[1127],[1124,26881,26883],{"className":26882},[1131],[1133,26884,26885],{"xmlns":1135},[1137,26886,26887,26915],{},[1140,26888,26889,26895,26897,26903,26905,26911,26913],{},[2922,26890,26891,26893],{},[1146,26892,2230],{},[1150,26894,1164],{},[1154,26896,3579],{},[2922,26898,26899,26901],{},[1146,26900,2680],{},[1150,26902,1164],{},[1154,26904,3579],{},[2922,26906,26907,26909],{},[1146,26908,4370],{},[1150,26910,1164],{},[1154,26912,3579],{},[1146,26914,4325],{},[1189,26916,26917],{"encoding":1191},"b^2 \\rightarrow z^2 \\rightarrow a^2 \\rightarrow C",[1124,26919,26921,26965,27009,27053],{"className":26920,"ariaHidden":1156},[1196],[1124,26922,26924,26927,26956,26959,26962],{"className":26923},[1200],[1124,26925],{"className":26926,"style":4598},[1204],[1124,26928,26930,26933],{"className":26929},[1209],[1124,26931,2230],{"className":26932},[1209,1213],[1124,26934,26936],{"className":26935},[1217],[1124,26937,26939],{"className":26938},[1221],[1124,26940,26942],{"className":26941},[1226],[1124,26943,26945],{"className":26944,"style":4598},[1230],[1124,26946,26947,26950],{"style":3905},[1124,26948],{"className":26949,"style":1239},[1238],[1124,26951,26953],{"className":26952},[1243,1244,1245,1246],[1124,26954,1164],{"className":26955},[1209,1246],[1124,26957],{"className":26958,"style":1774},[1271],[1124,26960,3579],{"className":26961},[1778],[1124,26963],{"className":26964,"style":1774},[1271],[1124,26966,26968,26971,27000,27003,27006],{"className":26967},[1200],[1124,26969],{"className":26970,"style":4598},[1204],[1124,26972,26974,26977],{"className":26973},[1209],[1124,26975,2680],{"className":26976,"style":2707},[1209,1213],[1124,26978,26980],{"className":26979},[1217],[1124,26981,26983],{"className":26982},[1221],[1124,26984,26986],{"className":26985},[1226],[1124,26987,26989],{"className":26988,"style":4598},[1230],[1124,26990,26991,26994],{"style":3905},[1124,26992],{"className":26993,"style":1239},[1238],[1124,26995,26997],{"className":26996},[1243,1244,1245,1246],[1124,26998,1164],{"className":26999},[1209,1246],[1124,27001],{"className":27002,"style":1774},[1271],[1124,27004,3579],{"className":27005},[1778],[1124,27007],{"className":27008,"style":1774},[1271],[1124,27010,27012,27015,27044,27047,27050],{"className":27011},[1200],[1124,27013],{"className":27014,"style":4598},[1204],[1124,27016,27018,27021],{"className":27017},[1209],[1124,27019,4370],{"className":27020},[1209,1213],[1124,27022,27024],{"className":27023},[1217],[1124,27025,27027],{"className":27026},[1221],[1124,27028,27030],{"className":27029},[1226],[1124,27031,27033],{"className":27032,"style":4598},[1230],[1124,27034,27035,27038],{"style":3905},[1124,27036],{"className":27037,"style":1239},[1238],[1124,27039,27041],{"className":27040},[1243,1244,1245,1246],[1124,27042,1164],{"className":27043},[1209,1246],[1124,27045],{"className":27046,"style":1774},[1271],[1124,27048,3579],{"className":27049},[1778],[1124,27051],{"className":27052,"style":1774},[1271],[1124,27054,27056,27059],{"className":27055},[1200],[1124,27057],{"className":27058,"style":4804},[1204],[1124,27060,4325],{"className":27061,"style":4392},[1209,1213],[1101,27063,27064],{},[1124,27065,27067,27165],{"className":27066},[1127],[1124,27068,27070],{"className":27069},[1131],[1133,27071,27072],{"xmlns":1135},[1137,27073,27074,27162],{},[1140,27075,27076,27094,27096,27114,27116,27138,27140],{},[2911,27077,27078,27084],{},[1140,27079,27080,27082],{},[1146,27081,3164],{"mathvariant":3145},[1146,27083,4325],{},[1140,27085,27086,27088],{},[1146,27087,3164],{"mathvariant":3145},[2922,27089,27090,27092],{},[1146,27091,2230],{},[1150,27093,1164],{},[1154,27095,1652],{},[2911,27097,27098,27104],{},[1140,27099,27100,27102],{},[1146,27101,3164],{"mathvariant":3145},[1146,27103,4325],{},[1140,27105,27106,27108],{},[1146,27107,3164],{"mathvariant":3145},[2922,27109,27110,27112],{},[1146,27111,4370],{},[1150,27113,1164],{},[1154,27115,2325],{},[2911,27117,27118,27128],{},[1140,27119,27120,27122],{},[1146,27121,3164],{"mathvariant":3145},[2922,27123,27124,27126],{},[1146,27125,4370],{},[1150,27127,1164],{},[1140,27129,27130,27132],{},[1146,27131,3164],{"mathvariant":3145},[2922,27133,27134,27136],{},[1146,27135,2680],{},[1150,27137,1164],{},[1154,27139,2325],{},[2911,27141,27142,27152],{},[1140,27143,27144,27146],{},[1146,27145,3164],{"mathvariant":3145},[2922,27147,27148,27150],{},[1146,27149,2680],{},[1150,27151,1164],{},[1140,27153,27154,27156],{},[1146,27155,3164],{"mathvariant":3145},[2922,27157,27158,27160],{},[1146,27159,2230],{},[1150,27161,1164],{},[1189,27163,27164],{"encoding":1191},"\\frac{\\partial C}{\\partial b^2} = \\frac{\\partial C}{\\partial a^2} \\cdot \\frac{\\partial a^2}{\\partial z^2} \\cdot \\frac{\\partial z^2}{\\partial b^2}",[1124,27166,27168,27283,27398,27539],{"className":27167,"ariaHidden":1156},[1196],[1124,27169,27171,27174,27274,27277,27280],{"className":27170},[1200],[1124,27172],{"className":27173,"style":23920},[1204],[1124,27175,27177,27180,27271],{"className":27176},[1209],[1124,27178],{"className":27179},[1795,2212],[1124,27181,27183],{"className":27182},[2911],[1124,27184,27186,27263],{"className":27185},[1221,1222],[1124,27187,27189,27260],{"className":27188},[1226],[1124,27190,27192,27235,27243],{"className":27191,"style":4858},[1230],[1124,27193,27194,27197],{"style":2994},[1124,27195],{"className":27196,"style":2998},[1238],[1124,27198,27200],{"className":27199},[1243,1244,1245,1246],[1124,27201,27203,27206],{"className":27202},[1209,1246],[1124,27204,3164],{"className":27205,"style":3319},[1209,1246],[1124,27207,27209,27212],{"className":27208},[1209,1246],[1124,27210,2230],{"className":27211},[1209,1213,1246],[1124,27213,27215],{"className":27214},[1217],[1124,27216,27218],{"className":27217},[1221],[1124,27219,27221],{"className":27220},[1226],[1124,27222,27224],{"className":27223,"style":22067},[1230],[1124,27225,27226,27229],{"style":3032},[1124,27227],{"className":27228,"style":3036},[1238],[1124,27230,27232],{"className":27231},[1243,3040,3041,1246],[1124,27233,1164],{"className":27234},[1209,1246],[1124,27236,27237,27240],{"style":3053},[1124,27238],{"className":27239,"style":2998},[1238],[1124,27241],{"className":27242,"style":3061},[3060],[1124,27244,27245,27248],{"style":3064},[1124,27246],{"className":27247,"style":2998},[1238],[1124,27249,27251],{"className":27250},[1243,1244,1245,1246],[1124,27252,27254,27257],{"className":27253},[1209,1246],[1124,27255,3164],{"className":27256,"style":3319},[1209,1246],[1124,27258,4325],{"className":27259,"style":4392},[1209,1213,1246],[1124,27261,1254],{"className":27262},[1253],[1124,27264,27266],{"className":27265},[1226],[1124,27267,27269],{"className":27268,"style":3538},[1230],[1124,27270],{},[1124,27272],{"className":27273},[2211,2212],[1124,27275],{"className":27276,"style":1774},[1271],[1124,27278,1652],{"className":27279},[1778],[1124,27281],{"className":27282,"style":1774},[1271],[1124,27284,27286,27289,27389,27392,27395],{"className":27285},[1200],[1124,27287],{"className":27288,"style":23920},[1204],[1124,27290,27292,27295,27386],{"className":27291},[1209],[1124,27293],{"className":27294},[1795,2212],[1124,27296,27298],{"className":27297},[2911],[1124,27299,27301,27378],{"className":27300},[1221,1222],[1124,27302,27304,27375],{"className":27303},[1226],[1124,27305,27307,27350,27358],{"className":27306,"style":4858},[1230],[1124,27308,27309,27312],{"style":2994},[1124,27310],{"className":27311,"style":2998},[1238],[1124,27313,27315],{"className":27314},[1243,1244,1245,1246],[1124,27316,27318,27321],{"className":27317},[1209,1246],[1124,27319,3164],{"className":27320,"style":3319},[1209,1246],[1124,27322,27324,27327],{"className":27323},[1209,1246],[1124,27325,4370],{"className":27326},[1209,1213,1246],[1124,27328,27330],{"className":27329},[1217],[1124,27331,27333],{"className":27332},[1221],[1124,27334,27336],{"className":27335},[1226],[1124,27337,27339],{"className":27338,"style":22067},[1230],[1124,27340,27341,27344],{"style":3032},[1124,27342],{"className":27343,"style":3036},[1238],[1124,27345,27347],{"className":27346},[1243,3040,3041,1246],[1124,27348,1164],{"className":27349},[1209,1246],[1124,27351,27352,27355],{"style":3053},[1124,27353],{"className":27354,"style":2998},[1238],[1124,27356],{"className":27357,"style":3061},[3060],[1124,27359,27360,27363],{"style":3064},[1124,27361],{"className":27362,"style":2998},[1238],[1124,27364,27366],{"className":27365},[1243,1244,1245,1246],[1124,27367,27369,27372],{"className":27368},[1209,1246],[1124,27370,3164],{"className":27371,"style":3319},[1209,1246],[1124,27373,4325],{"className":27374,"style":4392},[1209,1213,1246],[1124,27376,1254],{"className":27377},[1253],[1124,27379,27381],{"className":27380},[1226],[1124,27382,27384],{"className":27383,"style":3538},[1230],[1124,27385],{},[1124,27387],{"className":27388},[2211,2212],[1124,27390],{"className":27391,"style":2500},[1271],[1124,27393,2325],{"className":27394},[2504],[1124,27396],{"className":27397,"style":2500},[1271],[1124,27399,27401,27404,27530,27533,27536],{"className":27400},[1200],[1124,27402],{"className":27403,"style":25134},[1204],[1124,27405,27407,27410,27527],{"className":27406},[1209],[1124,27408],{"className":27409},[1795,2212],[1124,27411,27413],{"className":27412},[2911],[1124,27414,27416,27519],{"className":27415},[1221,1222],[1124,27417,27419,27516],{"className":27418},[1226],[1124,27420,27422,27465,27473],{"className":27421,"style":25153},[1230],[1124,27423,27424,27427],{"style":2994},[1124,27425],{"className":27426,"style":2998},[1238],[1124,27428,27430],{"className":27429},[1243,1244,1245,1246],[1124,27431,27433,27436],{"className":27432},[1209,1246],[1124,27434,3164],{"className":27435,"style":3319},[1209,1246],[1124,27437,27439,27442],{"className":27438},[1209,1246],[1124,27440,2680],{"className":27441,"style":2707},[1209,1213,1246],[1124,27443,27445],{"className":27444},[1217],[1124,27446,27448],{"className":27447},[1221],[1124,27449,27451],{"className":27450},[1226],[1124,27452,27454],{"className":27453,"style":22067},[1230],[1124,27455,27456,27459],{"style":3032},[1124,27457],{"className":27458,"style":3036},[1238],[1124,27460,27462],{"className":27461},[1243,3040,3041,1246],[1124,27463,1164],{"className":27464},[1209,1246],[1124,27466,27467,27470],{"style":3053},[1124,27468],{"className":27469,"style":2998},[1238],[1124,27471],{"className":27472,"style":3061},[3060],[1124,27474,27475,27478],{"style":3064},[1124,27476],{"className":27477,"style":2998},[1238],[1124,27479,27481],{"className":27480},[1243,1244,1245,1246],[1124,27482,27484,27487],{"className":27483},[1209,1246],[1124,27485,3164],{"className":27486,"style":3319},[1209,1246],[1124,27488,27490,27493],{"className":27489},[1209,1246],[1124,27491,4370],{"className":27492},[1209,1213,1246],[1124,27494,27496],{"className":27495},[1217],[1124,27497,27499],{"className":27498},[1221],[1124,27500,27502],{"className":27501},[1226],[1124,27503,27505],{"className":27504,"style":25237},[1230],[1124,27506,27507,27510],{"style":25240},[1124,27508],{"className":27509,"style":3036},[1238],[1124,27511,27513],{"className":27512},[1243,3040,3041,1246],[1124,27514,1164],{"className":27515},[1209,1246],[1124,27517,1254],{"className":27518},[1253],[1124,27520,27522],{"className":27521},[1226],[1124,27523,27525],{"className":27524,"style":3538},[1230],[1124,27526],{},[1124,27528],{"className":27529},[2211,2212],[1124,27531],{"className":27532,"style":2500},[1271],[1124,27534,2325],{"className":27535},[2504],[1124,27537],{"className":27538,"style":2500},[1271],[1124,27540,27542,27545],{"className":27541},[1200],[1124,27543],{"className":27544,"style":25134},[1204],[1124,27546,27548,27551,27668],{"className":27547},[1209],[1124,27549],{"className":27550},[1795,2212],[1124,27552,27554],{"className":27553},[2911],[1124,27555,27557,27660],{"className":27556},[1221,1222],[1124,27558,27560,27657],{"className":27559},[1226],[1124,27561,27563,27606,27614],{"className":27562,"style":25153},[1230],[1124,27564,27565,27568],{"style":2994},[1124,27566],{"className":27567,"style":2998},[1238],[1124,27569,27571],{"className":27570},[1243,1244,1245,1246],[1124,27572,27574,27577],{"className":27573},[1209,1246],[1124,27575,3164],{"className":27576,"style":3319},[1209,1246],[1124,27578,27580,27583],{"className":27579},[1209,1246],[1124,27581,2230],{"className":27582},[1209,1213,1246],[1124,27584,27586],{"className":27585},[1217],[1124,27587,27589],{"className":27588},[1221],[1124,27590,27592],{"className":27591},[1226],[1124,27593,27595],{"className":27594,"style":22067},[1230],[1124,27596,27597,27600],{"style":3032},[1124,27598],{"className":27599,"style":3036},[1238],[1124,27601,27603],{"className":27602},[1243,3040,3041,1246],[1124,27604,1164],{"className":27605},[1209,1246],[1124,27607,27608,27611],{"style":3053},[1124,27609],{"className":27610,"style":2998},[1238],[1124,27612],{"className":27613,"style":3061},[3060],[1124,27615,27616,27619],{"style":3064},[1124,27617],{"className":27618,"style":2998},[1238],[1124,27620,27622],{"className":27621},[1243,1244,1245,1246],[1124,27623,27625,27628],{"className":27624},[1209,1246],[1124,27626,3164],{"className":27627,"style":3319},[1209,1246],[1124,27629,27631,27634],{"className":27630},[1209,1246],[1124,27632,2680],{"className":27633,"style":2707},[1209,1213,1246],[1124,27635,27637],{"className":27636},[1217],[1124,27638,27640],{"className":27639},[1221],[1124,27641,27643],{"className":27642},[1226],[1124,27644,27646],{"className":27645,"style":25237},[1230],[1124,27647,27648,27651],{"style":25240},[1124,27649],{"className":27650,"style":3036},[1238],[1124,27652,27654],{"className":27653},[1243,3040,3041,1246],[1124,27655,1164],{"className":27656},[1209,1246],[1124,27658,1254],{"className":27659},[1253],[1124,27661,27663],{"className":27662},[1226],[1124,27664,27666],{"className":27665,"style":3538},[1230],[1124,27667],{},[1124,27669],{"className":27670},[2211,2212],[1101,27672,27673],{},"前两项和上面一样，第三项：",[1101,27675,27676],{},[1124,27677,27679,27717],{"className":27678},[1127],[1124,27680,27682],{"className":27681},[1131],[1133,27683,27684],{"xmlns":1135},[1137,27685,27686,27714],{},[1140,27687,27688,27710,27712],{},[2911,27689,27690,27700],{},[1140,27691,27692,27694],{},[1146,27693,3164],{"mathvariant":3145},[2922,27695,27696,27698],{},[1146,27697,2680],{},[1150,27699,1164],{},[1140,27701,27702,27704],{},[1146,27703,3164],{"mathvariant":3145},[2922,27705,27706,27708],{},[1146,27707,2230],{},[1150,27709,1164],{},[1154,27711,1652],{},[1150,27713,1152],{},[1189,27715,27716],{"encoding":1191},"\\frac{\\partial z^2}{\\partial b^2} = 1",[1124,27718,27720,27861],{"className":27719,"ariaHidden":1156},[1196],[1124,27721,27723,27726,27852,27855,27858],{"className":27722},[1200],[1124,27724],{"className":27725,"style":25134},[1204],[1124,27727,27729,27732,27849],{"className":27728},[1209],[1124,27730],{"className":27731},[1795,2212],[1124,27733,27735],{"className":27734},[2911],[1124,27736,27738,27841],{"className":27737},[1221,1222],[1124,27739,27741,27838],{"className":27740},[1226],[1124,27742,27744,27787,27795],{"className":27743,"style":25153},[1230],[1124,27745,27746,27749],{"style":2994},[1124,27747],{"className":27748,"style":2998},[1238],[1124,27750,27752],{"className":27751},[1243,1244,1245,1246],[1124,27753,27755,27758],{"className":27754},[1209,1246],[1124,27756,3164],{"className":27757,"style":3319},[1209,1246],[1124,27759,27761,27764],{"className":27760},[1209,1246],[1124,27762,2230],{"className":27763},[1209,1213,1246],[1124,27765,27767],{"className":27766},[1217],[1124,27768,27770],{"className":27769},[1221],[1124,27771,27773],{"className":27772},[1226],[1124,27774,27776],{"className":27775,"style":22067},[1230],[1124,27777,27778,27781],{"style":3032},[1124,27779],{"className":27780,"style":3036},[1238],[1124,27782,27784],{"className":27783},[1243,3040,3041,1246],[1124,27785,1164],{"className":27786},[1209,1246],[1124,27788,27789,27792],{"style":3053},[1124,27790],{"className":27791,"style":2998},[1238],[1124,27793],{"className":27794,"style":3061},[3060],[1124,27796,27797,27800],{"style":3064},[1124,27798],{"className":27799,"style":2998},[1238],[1124,27801,27803],{"className":27802},[1243,1244,1245,1246],[1124,27804,27806,27809],{"className":27805},[1209,1246],[1124,27807,3164],{"className":27808,"style":3319},[1209,1246],[1124,27810,27812,27815],{"className":27811},[1209,1246],[1124,27813,2680],{"className":27814,"style":2707},[1209,1213,1246],[1124,27816,27818],{"className":27817},[1217],[1124,27819,27821],{"className":27820},[1221],[1124,27822,27824],{"className":27823},[1226],[1124,27825,27827],{"className":27826,"style":25237},[1230],[1124,27828,27829,27832],{"style":25240},[1124,27830],{"className":27831,"style":3036},[1238],[1124,27833,27835],{"className":27834},[1243,3040,3041,1246],[1124,27836,1164],{"className":27837},[1209,1246],[1124,27839,1254],{"className":27840},[1253],[1124,27842,27844],{"className":27843},[1226],[1124,27845,27847],{"className":27846,"style":3538},[1230],[1124,27848],{},[1124,27850],{"className":27851},[2211,2212],[1124,27853],{"className":27854,"style":1774},[1271],[1124,27856,1652],{"className":27857},[1778],[1124,27859],{"className":27860,"style":1774},[1271],[1124,27862,27864,27867],{"className":27863},[1200],[1124,27865],{"className":27866,"style":3685},[1204],[1124,27868,1152],{"className":27869},[1209],[1101,27871,27872],{},[1107,27873,26409],{},[1101,27875,27876],{},[1124,27877,27879,27944],{"className":27878},[1127],[1124,27880,27882],{"className":27881},[1131],[1133,27883,27884],{"xmlns":1135},[1137,27885,27886,27941],{},[1140,27887,27888,27906,27908,27910,27912,27914,27916,27918,27920,27922,27924,27926],{},[2911,27889,27890,27896],{},[1140,27891,27892,27894],{},[1146,27893,3164],{"mathvariant":3145},[1146,27895,4325],{},[1140,27897,27898,27900],{},[1146,27899,3164],{"mathvariant":3145},[2922,27901,27902,27904],{},[1146,27903,2230],{},[1150,27905,1164],{},[1154,27907,1652],{},[1154,27909,2677],{"stretchy":1674},[1154,27911,2235],{},[1150,27913,23096],{},[1154,27915,2683],{"stretchy":1674},[1154,27917,10608],{},[1150,27919,25785],{},[1154,27921,10608],{},[1150,27923,1152],{},[1154,27925,1652],{},[8168,27927,27928],{"notation":8170},[1671,27929,27930],{"scriptlevel":1673,"displaystyle":1674},[1671,27931,27932],{"scriptlevel":1673,"displaystyle":1674},[1671,27933,27934],{"scriptlevel":1673,"displaystyle":1156},[1140,27935,27936,27938],{},[1154,27937,2235],{},[1150,27939,27940],{},"0.0790",[1189,27942,27943],{"encoding":1191},"\\frac{\\partial C}{\\partial b^2} = (-0.348) \\times 0.227 \\times 1 = \\boxed{-0.0790}",[1124,27945,27947,28062,28089,28107,28125],{"className":27946,"ariaHidden":1156},[1196],[1124,27948,27950,27953,28053,28056,28059],{"className":27949},[1200],[1124,27951],{"className":27952,"style":23920},[1204],[1124,27954,27956,27959,28050],{"className":27955},[1209],[1124,27957],{"className":27958},[1795,2212],[1124,27960,27962],{"className":27961},[2911],[1124,27963,27965,28042],{"className":27964},[1221,1222],[1124,27966,27968,28039],{"className":27967},[1226],[1124,27969,27971,28014,28022],{"className":27970,"style":4858},[1230],[1124,27972,27973,27976],{"style":2994},[1124,27974],{"className":27975,"style":2998},[1238],[1124,27977,27979],{"className":27978},[1243,1244,1245,1246],[1124,27980,27982,27985],{"className":27981},[1209,1246],[1124,27983,3164],{"className":27984,"style":3319},[1209,1246],[1124,27986,27988,27991],{"className":27987},[1209,1246],[1124,27989,2230],{"className":27990},[1209,1213,1246],[1124,27992,27994],{"className":27993},[1217],[1124,27995,27997],{"className":27996},[1221],[1124,27998,28000],{"className":27999},[1226],[1124,28001,28003],{"className":28002,"style":22067},[1230],[1124,28004,28005,28008],{"style":3032},[1124,28006],{"className":28007,"style":3036},[1238],[1124,28009,28011],{"className":28010},[1243,3040,3041,1246],[1124,28012,1164],{"className":28013},[1209,1246],[1124,28015,28016,28019],{"style":3053},[1124,28017],{"className":28018,"style":2998},[1238],[1124,28020],{"className":28021,"style":3061},[3060],[1124,28023,28024,28027],{"style":3064},[1124,28025],{"className":28026,"style":2998},[1238],[1124,28028,28030],{"className":28029},[1243,1244,1245,1246],[1124,28031,28033,28036],{"className":28032},[1209,1246],[1124,28034,3164],{"className":28035,"style":3319},[1209,1246],[1124,28037,4325],{"className":28038,"style":4392},[1209,1213,1246],[1124,28040,1254],{"className":28041},[1253],[1124,28043,28045],{"className":28044},[1226],[1124,28046,28048],{"className":28047,"style":3538},[1230],[1124,28049],{},[1124,28051],{"className":28052},[2211,2212],[1124,28054],{"className":28055,"style":1774},[1271],[1124,28057,1652],{"className":28058},[1778],[1124,28060],{"className":28061,"style":1774},[1271],[1124,28063,28065,28068,28071,28074,28077,28080,28083,28086],{"className":28064},[1200],[1124,28066],{"className":28067,"style":2696},[1204],[1124,28069,2677],{"className":28070},[1795],[1124,28072,2235],{"className":28073},[1209],[1124,28075,23096],{"className":28076},[1209],[1124,28078,2683],{"className":28079},[2211],[1124,28081],{"className":28082,"style":2500},[1271],[1124,28084,10608],{"className":28085},[2504],[1124,28087],{"className":28088,"style":2500},[1271],[1124,28090,28092,28095,28098,28101,28104],{"className":28091},[1200],[1124,28093],{"className":28094,"style":10423},[1204],[1124,28096,25785],{"className":28097},[1209],[1124,28099],{"className":28100,"style":2500},[1271],[1124,28102,10608],{"className":28103},[2504],[1124,28105],{"className":28106,"style":2500},[1271],[1124,28108,28110,28113,28116,28119,28122],{"className":28109},[1200],[1124,28111],{"className":28112,"style":3685},[1204],[1124,28114,1152],{"className":28115},[1209],[1124,28117],{"className":28118,"style":1774},[1271],[1124,28120,1652],{"className":28121},[1778],[1124,28123],{"className":28124,"style":1774},[1271],[1124,28126,28128,28131],{"className":28127},[1200],[1124,28129],{"className":28130,"style":26667},[1204],[1124,28132,28134],{"className":28133},[1209],[1124,28135,28137,28174],{"className":28136},[1221,1222],[1124,28138,28140,28171],{"className":28139},[1226],[1124,28141,28143,28163],{"className":28142,"style":12358},[1230],[1124,28144,28145,28148],{"style":26682},[1124,28146],{"className":28147,"style":26686},[1238],[1124,28149,28151],{"className":28150},[8257],[1124,28152,28154],{"className":28153},[1209],[1124,28155,28157,28160],{"className":28156},[1209],[1124,28158,2235],{"className":28159},[1209],[1124,28161,27940],{"className":28162},[1209],[1124,28164,28165,28168],{"style":12380},[1124,28166],{"className":28167,"style":26686},[1238],[1124,28169],{"className":28170,"style":26710},[8436,8437],[1124,28172,1254],{"className":28173},[1253],[1124,28175,28177],{"className":28176},[1226],[1124,28178,28180],{"className":28179,"style":26720},[1230],[1124,28181],{},[2745,28183],{},[28185,28186,28187,28572,28635],"blockquote",{},[1101,28188,28189,10434,28192],{},[1107,28190,28191],{},"定义输出层误差：",[1124,28193,28195,28271],{"className":28194},[1127],[1124,28196,28198],{"className":28197},[1131],[1133,28199,28200],{"xmlns":1135},[1137,28201,28202,28268],{},[1140,28203,28204,28210,28212,28230,28232,28238,28240,28246,28248,28250,28252,28254,28256,28258,28260,28262,28264,28266],{},[2922,28205,28206,28208],{},[1146,28207,13138],{},[1150,28209,1164],{},[1154,28211,1652],{},[2911,28213,28214,28220],{},[1140,28215,28216,28218],{},[1146,28217,3164],{"mathvariant":3145},[1146,28219,4325],{},[1140,28221,28222,28224],{},[1146,28223,3164],{"mathvariant":3145},[2922,28225,28226,28228],{},[1146,28227,4370],{},[1150,28229,1164],{},[1154,28231,2325],{},[2922,28233,28234,28236],{},[1146,28235,2674],{},[1154,28237,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,28239,2677],{"stretchy":1674},[2922,28241,28242,28244],{},[1146,28243,2680],{},[1150,28245,1164],{},[1154,28247,2683],{"stretchy":1674},[1154,28249,1652],{},[1154,28251,2677],{"stretchy":1674},[1154,28253,2235],{},[1150,28255,23096],{},[1154,28257,2683],{"stretchy":1674},[1154,28259,10608],{},[1150,28261,25785],{},[1154,28263,1652],{},[1154,28265,2235],{},[1150,28267,27940],{},[1189,28269,28270],{"encoding":1191},"\\delta^2 = \\frac{\\partial C}{\\partial a^2} \\cdot \\sigma'(z^2) = (-0.348) \\times 0.227 = -0.0790",[1124,28272,28274,28318,28433,28515,28542,28560],{"className":28273,"ariaHidden":1156},[1196],[1124,28275,28277,28280,28309,28312,28315],{"className":28276},[1200],[1124,28278],{"className":28279,"style":4598},[1204],[1124,28281,28283,28286],{"className":28282},[1209],[1124,28284,13138],{"className":28285,"style":13161},[1209,1213],[1124,28287,28289],{"className":28288},[1217],[1124,28290,28292],{"className":28291},[1221],[1124,28293,28295],{"className":28294},[1226],[1124,28296,28298],{"className":28297,"style":4598},[1230],[1124,28299,28300,28303],{"style":3905},[1124,28301],{"className":28302,"style":1239},[1238],[1124,28304,28306],{"className":28305},[1243,1244,1245,1246],[1124,28307,1164],{"className":28308},[1209,1246],[1124,28310],{"className":28311,"style":1774},[1271],[1124,28313,1652],{"className":28314},[1778],[1124,28316],{"className":28317,"style":1774},[1271],[1124,28319,28321,28324,28424,28427,28430],{"className":28320},[1200],[1124,28322],{"className":28323,"style":23920},[1204],[1124,28325,28327,28330,28421],{"className":28326},[1209],[1124,28328],{"className":28329},[1795,2212],[1124,28331,28333],{"className":28332},[2911],[1124,28334,28336,28413],{"className":28335},[1221,1222],[1124,28337,28339,28410],{"className":28338},[1226],[1124,28340,28342,28385,28393],{"className":28341,"style":4858},[1230],[1124,28343,28344,28347],{"style":2994},[1124,28345],{"className":28346,"style":2998},[1238],[1124,28348,28350],{"className":28349},[1243,1244,1245,1246],[1124,28351,28353,28356],{"className":28352},[1209,1246],[1124,28354,3164],{"className":28355,"style":3319},[1209,1246],[1124,28357,28359,28362],{"className":28358},[1209,1246],[1124,28360,4370],{"className":28361},[1209,1213,1246],[1124,28363,28365],{"className":28364},[1217],[1124,28366,28368],{"className":28367},[1221],[1124,28369,28371],{"className":28370},[1226],[1124,28372,28374],{"className":28373,"style":22067},[1230],[1124,28375,28376,28379],{"style":3032},[1124,28377],{"className":28378,"style":3036},[1238],[1124,28380,28382],{"className":28381},[1243,3040,3041,1246],[1124,28383,1164],{"className":28384},[1209,1246],[1124,28386,28387,28390],{"style":3053},[1124,28388],{"className":28389,"style":2998},[1238],[1124,28391],{"className":28392,"style":3061},[3060],[1124,28394,28395,28398],{"style":3064},[1124,28396],{"className":28397,"style":2998},[1238],[1124,28399,28401],{"className":28400},[1243,1244,1245,1246],[1124,28402,28404,28407],{"className":28403},[1209,1246],[1124,28405,3164],{"className":28406,"style":3319},[1209,1246],[1124,28408,4325],{"className":28409,"style":4392},[1209,1213,1246],[1124,28411,1254],{"className":28412},[1253],[1124,28414,28416],{"className":28415},[1226],[1124,28417,28419],{"className":28418,"style":3538},[1230],[1124,28420],{},[1124,28422],{"className":28423},[2211,2212],[1124,28425],{"className":28426,"style":2500},[1271],[1124,28428,2325],{"className":28429},[2504],[1124,28431],{"className":28432,"style":2500},[1271],[1124,28434,28436,28439,28471,28474,28503,28506,28509,28512],{"className":28435},[1200],[1124,28437],{"className":28438,"style":4576},[1204],[1124,28440,28442,28445],{"className":28441},[1209],[1124,28443,2674],{"className":28444,"style":2700},[1209,1213],[1124,28446,28448],{"className":28447},[1217],[1124,28449,28451],{"className":28450},[1221],[1124,28452,28454],{"className":28453},[1226],[1124,28455,28457],{"className":28456,"style":3902},[1230],[1124,28458,28459,28462],{"style":3905},[1124,28460],{"className":28461,"style":1239},[1238],[1124,28463,28465],{"className":28464},[1243,1244,1245,1246],[1124,28466,28468],{"className":28467},[1209,1246],[1124,28469,3838],{"className":28470},[1209,1246],[1124,28472,2677],{"className":28473},[1795],[1124,28475,28477,28480],{"className":28476},[1209],[1124,28478,2680],{"className":28479,"style":2707},[1209,1213],[1124,28481,28483],{"className":28482},[1217],[1124,28484,28486],{"className":28485},[1221],[1124,28487,28489],{"className":28488},[1226],[1124,28490,28492],{"className":28491,"style":4598},[1230],[1124,28493,28494,28497],{"style":3905},[1124,28495],{"className":28496,"style":1239},[1238],[1124,28498,28500],{"className":28499},[1243,1244,1245,1246],[1124,28501,1164],{"className":28502},[1209,1246],[1124,28504,2683],{"className":28505},[2211],[1124,28507],{"className":28508,"style":1774},[1271],[1124,28510,1652],{"className":28511},[1778],[1124,28513],{"className":28514,"style":1774},[1271],[1124,28516,28518,28521,28524,28527,28530,28533,28536,28539],{"className":28517},[1200],[1124,28519],{"className":28520,"style":2696},[1204],[1124,28522,2677],{"className":28523},[1795],[1124,28525,2235],{"className":28526},[1209],[1124,28528,23096],{"className":28529},[1209],[1124,28531,2683],{"className":28532},[2211],[1124,28534],{"className":28535,"style":2500},[1271],[1124,28537,10608],{"className":28538},[2504],[1124,28540],{"className":28541,"style":2500},[1271],[1124,28543,28545,28548,28551,28554,28557],{"className":28544},[1200],[1124,28546],{"className":28547,"style":3685},[1204],[1124,28549,25785],{"className":28550},[1209],[1124,28552],{"className":28553,"style":1774},[1271],[1124,28555,1652],{"className":28556},[1778],[1124,28558],{"className":28559,"style":1774},[1271],[1124,28561,28563,28566,28569],{"className":28562},[1200],[1124,28564],{"className":28565,"style":10423},[1204],[1124,28567,2235],{"className":28568},[1209],[1124,28570,27940],{"className":28571},[1209],[1101,28573,28574,28575,28634],{},"有了 ",[1124,28576,28578,28596],{"className":28577},[1127],[1124,28579,28581],{"className":28580},[1131],[1133,28582,28583],{"xmlns":1135},[1137,28584,28585,28593],{},[1140,28586,28587],{},[2922,28588,28589,28591],{},[1146,28590,13138],{},[1150,28592,1164],{},[1189,28594,28595],{"encoding":1191},"\\delta^2",[1124,28597,28599],{"className":28598,"ariaHidden":1156},[1196],[1124,28600,28602,28605],{"className":28601},[1200],[1124,28603],{"className":28604,"style":4598},[1204],[1124,28606,28608,28611],{"className":28607},[1209],[1124,28609,13138],{"className":28610,"style":13161},[1209,1213],[1124,28612,28614],{"className":28613},[1217],[1124,28615,28617],{"className":28616},[1221],[1124,28618,28620],{"className":28619},[1226],[1124,28621,28623],{"className":28622,"style":4598},[1230],[1124,28624,28625,28628],{"style":3905},[1124,28626],{"className":28627,"style":1239},[1238],[1124,28629,28631],{"className":28630},[1243,1244,1245,1246],[1124,28632,1164],{"className":28633},[1209,1246],"，后面的计算更简洁：",[1117,28636,28637,28962],{},[1120,28638,28639,28961],{},[1124,28640,28642,28704],{"className":28641},[1127],[1124,28643,28645],{"className":28644},[1131],[1133,28646,28647],{"xmlns":1135},[1137,28648,28649,28701],{},[1140,28650,28651,28669,28671,28677,28679,28685,28687,28689,28691,28693,28695,28697,28699],{},[2911,28652,28653,28659],{},[1140,28654,28655,28657],{},[1146,28656,3164],{"mathvariant":3145},[1146,28658,4325],{},[1140,28660,28661,28663],{},[1146,28662,3164],{"mathvariant":3145},[2922,28664,28665,28667],{},[1146,28666,1439],{},[1150,28668,1164],{},[1154,28670,1652],{},[2922,28672,28673,28675],{},[1146,28674,13138],{},[1150,28676,1164],{},[1154,28678,2325],{},[2922,28680,28681,28683],{},[1146,28682,4370],{},[1150,28684,1152],{},[1154,28686,1652],{},[1154,28688,2235],{},[1150,28690,27940],{},[1154,28692,10608],{},[1150,28694,21877],{},[1154,28696,1652],{},[1154,28698,2235],{},[1150,28700,26476],{},[1189,28702,28703],{"encoding":1191},"\\frac{\\partial C}{\\partial w^2} = \\delta^2 \\cdot a^1 = -0.0790 \\times 0.711 = -0.0562",[1124,28705,28707,28822,28866,28910,28931,28949],{"className":28706,"ariaHidden":1156},[1196],[1124,28708,28710,28713,28813,28816,28819],{"className":28709},[1200],[1124,28711],{"className":28712,"style":23920},[1204],[1124,28714,28716,28719,28810],{"className":28715},[1209],[1124,28717],{"className":28718},[1795,2212],[1124,28720,28722],{"className":28721},[2911],[1124,28723,28725,28802],{"className":28724},[1221,1222],[1124,28726,28728,28799],{"className":28727},[1226],[1124,28729,28731,28774,28782],{"className":28730,"style":4858},[1230],[1124,28732,28733,28736],{"style":2994},[1124,28734],{"className":28735,"style":2998},[1238],[1124,28737,28739],{"className":28738},[1243,1244,1245,1246],[1124,28740,28742,28745],{"className":28741},[1209,1246],[1124,28743,3164],{"className":28744,"style":3319},[1209,1246],[1124,28746,28748,28751],{"className":28747},[1209,1246],[1124,28749,1439],{"className":28750,"style":1480},[1209,1213,1246],[1124,28752,28754],{"className":28753},[1217],[1124,28755,28757],{"className":28756},[1221],[1124,28758,28760],{"className":28759},[1226],[1124,28761,28763],{"className":28762,"style":22067},[1230],[1124,28764,28765,28768],{"style":3032},[1124,28766],{"className":28767,"style":3036},[1238],[1124,28769,28771],{"className":28770},[1243,3040,3041,1246],[1124,28772,1164],{"className":28773},[1209,1246],[1124,28775,28776,28779],{"style":3053},[1124,28777],{"className":28778,"style":2998},[1238],[1124,28780],{"className":28781,"style":3061},[3060],[1124,28783,28784,28787],{"style":3064},[1124,28785],{"className":28786,"style":2998},[1238],[1124,28788,28790],{"className":28789},[1243,1244,1245,1246],[1124,28791,28793,28796],{"className":28792},[1209,1246],[1124,28794,3164],{"className":28795,"style":3319},[1209,1246],[1124,28797,4325],{"className":28798,"style":4392},[1209,1213,1246],[1124,28800,1254],{"className":28801},[1253],[1124,28803,28805],{"className":28804},[1226],[1124,28806,28808],{"className":28807,"style":3538},[1230],[1124,28809],{},[1124,28811],{"className":28812},[2211,2212],[1124,28814],{"className":28815,"style":1774},[1271],[1124,28817,1652],{"className":28818},[1778],[1124,28820],{"className":28821,"style":1774},[1271],[1124,28823,28825,28828,28857,28860,28863],{"className":28824},[1200],[1124,28826],{"className":28827,"style":4598},[1204],[1124,28829,28831,28834],{"className":28830},[1209],[1124,28832,13138],{"className":28833,"style":13161},[1209,1213],[1124,28835,28837],{"className":28836},[1217],[1124,28838,28840],{"className":28839},[1221],[1124,28841,28843],{"className":28842},[1226],[1124,28844,28846],{"className":28845,"style":4598},[1230],[1124,28847,28848,28851],{"style":3905},[1124,28849],{"className":28850,"style":1239},[1238],[1124,28852,28854],{"className":28853},[1243,1244,1245,1246],[1124,28855,1164],{"className":28856},[1209,1246],[1124,28858],{"className":28859,"style":2500},[1271],[1124,28861,2325],{"className":28862},[2504],[1124,28864],{"className":28865,"style":2500},[1271],[1124,28867,28869,28872,28901,28904,28907],{"className":28868},[1200],[1124,28870],{"className":28871,"style":4598},[1204],[1124,28873,28875,28878],{"className":28874},[1209],[1124,28876,4370],{"className":28877},[1209,1213],[1124,28879,28881],{"className":28880},[1217],[1124,28882,28884],{"className":28883},[1221],[1124,28885,28887],{"className":28886},[1226],[1124,28888,28890],{"className":28889,"style":4598},[1230],[1124,28891,28892,28895],{"style":3905},[1124,28893],{"className":28894,"style":1239},[1238],[1124,28896,28898],{"className":28897},[1243,1244,1245,1246],[1124,28899,1152],{"className":28900},[1209,1246],[1124,28902],{"className":28903,"style":1774},[1271],[1124,28905,1652],{"className":28906},[1778],[1124,28908],{"className":28909,"style":1774},[1271],[1124,28911,28913,28916,28919,28922,28925,28928],{"className":28912},[1200],[1124,28914],{"className":28915,"style":10423},[1204],[1124,28917,2235],{"className":28918},[1209],[1124,28920,27940],{"className":28921},[1209],[1124,28923],{"className":28924,"style":2500},[1271],[1124,28926,10608],{"className":28927},[2504],[1124,28929],{"className":28930,"style":2500},[1271],[1124,28932,28934,28937,28940,28943,28946],{"className":28933},[1200],[1124,28935],{"className":28936,"style":3685},[1204],[1124,28938,21877],{"className":28939},[1209],[1124,28941],{"className":28942,"style":1774},[1271],[1124,28944,1652],{"className":28945},[1778],[1124,28947],{"className":28948,"style":1774},[1271],[1124,28950,28952,28955,28958],{"className":28951},[1200],[1124,28953],{"className":28954,"style":10423},[1204],[1124,28956,2235],{"className":28957},[1209],[1124,28959,26476],{"className":28960},[1209]," ✓",[1120,28963,28964,28961],{},[1124,28965,28967,29011],{"className":28966},[1127],[1124,28968,28970],{"className":28969},[1131],[1133,28971,28972],{"xmlns":1135},[1137,28973,28974,29008],{},[1140,28975,28976,28994,28996,29002,29004,29006],{},[2911,28977,28978,28984],{},[1140,28979,28980,28982],{},[1146,28981,3164],{"mathvariant":3145},[1146,28983,4325],{},[1140,28985,28986,28988],{},[1146,28987,3164],{"mathvariant":3145},[2922,28989,28990,28992],{},[1146,28991,2230],{},[1150,28993,1164],{},[1154,28995,1652],{},[2922,28997,28998,29000],{},[1146,28999,13138],{},[1150,29001,1164],{},[1154,29003,1652],{},[1154,29005,2235],{},[1150,29007,27940],{},[1189,29009,29010],{"encoding":1191},"\\frac{\\partial C}{\\partial b^2} = \\delta^2 = -0.0790",[1124,29012,29014,29129,29173],{"className":29013,"ariaHidden":1156},[1196],[1124,29015,29017,29020,29120,29123,29126],{"className":29016},[1200],[1124,29018],{"className":29019,"style":23920},[1204],[1124,29021,29023,29026,29117],{"className":29022},[1209],[1124,29024],{"className":29025},[1795,2212],[1124,29027,29029],{"className":29028},[2911],[1124,29030,29032,29109],{"className":29031},[1221,1222],[1124,29033,29035,29106],{"className":29034},[1226],[1124,29036,29038,29081,29089],{"className":29037,"style":4858},[1230],[1124,29039,29040,29043],{"style":2994},[1124,29041],{"className":29042,"style":2998},[1238],[1124,29044,29046],{"className":29045},[1243,1244,1245,1246],[1124,29047,29049,29052],{"className":29048},[1209,1246],[1124,29050,3164],{"className":29051,"style":3319},[1209,1246],[1124,29053,29055,29058],{"className":29054},[1209,1246],[1124,29056,2230],{"className":29057},[1209,1213,1246],[1124,29059,29061],{"className":29060},[1217],[1124,29062,29064],{"className":29063},[1221],[1124,29065,29067],{"className":29066},[1226],[1124,29068,29070],{"className":29069,"style":22067},[1230],[1124,29071,29072,29075],{"style":3032},[1124,29073],{"className":29074,"style":3036},[1238],[1124,29076,29078],{"className":29077},[1243,3040,3041,1246],[1124,29079,1164],{"className":29080},[1209,1246],[1124,29082,29083,29086],{"style":3053},[1124,29084],{"className":29085,"style":2998},[1238],[1124,29087],{"className":29088,"style":3061},[3060],[1124,29090,29091,29094],{"style":3064},[1124,29092],{"className":29093,"style":2998},[1238],[1124,29095,29097],{"className":29096},[1243,1244,1245,1246],[1124,29098,29100,29103],{"className":29099},[1209,1246],[1124,29101,3164],{"className":29102,"style":3319},[1209,1246],[1124,29104,4325],{"className":29105,"style":4392},[1209,1213,1246],[1124,29107,1254],{"className":29108},[1253],[1124,29110,29112],{"className":29111},[1226],[1124,29113,29115],{"className":29114,"style":3538},[1230],[1124,29116],{},[1124,29118],{"className":29119},[2211,2212],[1124,29121],{"className":29122,"style":1774},[1271],[1124,29124,1652],{"className":29125},[1778],[1124,29127],{"className":29128,"style":1774},[1271],[1124,29130,29132,29135,29164,29167,29170],{"className":29131},[1200],[1124,29133],{"className":29134,"style":4598},[1204],[1124,29136,29138,29141],{"className":29137},[1209],[1124,29139,13138],{"className":29140,"style":13161},[1209,1213],[1124,29142,29144],{"className":29143},[1217],[1124,29145,29147],{"className":29146},[1221],[1124,29148,29150],{"className":29149},[1226],[1124,29151,29153],{"className":29152,"style":4598},[1230],[1124,29154,29155,29158],{"style":3905},[1124,29156],{"className":29157,"style":1239},[1238],[1124,29159,29161],{"className":29160},[1243,1244,1245,1246],[1124,29162,1164],{"className":29163},[1209,1246],[1124,29165],{"className":29166,"style":1774},[1271],[1124,29168,1652],{"className":29169},[1778],[1124,29171],{"className":29172,"style":1774},[1271],[1124,29174,29176,29179,29182],{"className":29175},[1200],[1124,29177],{"className":29178,"style":10423},[1204],[1124,29180,2235],{"className":29181},[1209],[1124,29183,27940],{"className":29184},[1209],[2745,29186],{},[7743,29188,29190],{"id":29189},"_23-隐藏层权重","2.3 隐藏层权重",[1101,29192,24456,29193,29334],{},[1124,29194,29196,29225],{"className":29195},[1127],[1124,29197,29199],{"className":29198},[1131],[1133,29200,29201],{"xmlns":1135},[1137,29202,29203,29223],{},[1140,29204,29205],{},[2911,29206,29207,29213],{},[1140,29208,29209,29211],{},[1146,29210,3164],{"mathvariant":3145},[1146,29212,4325],{},[1140,29214,29215,29217],{},[1146,29216,3164],{"mathvariant":3145},[2922,29218,29219,29221],{},[1146,29220,1439],{},[1150,29222,1152],{},[1189,29224,24196],{"encoding":1191},[1124,29226,29228],{"className":29227,"ariaHidden":1156},[1196],[1124,29229,29231,29234],{"className":29230},[1200],[1124,29232],{"className":29233,"style":23920},[1204],[1124,29235,29237,29240,29331],{"className":29236},[1209],[1124,29238],{"className":29239},[1795,2212],[1124,29241,29243],{"className":29242},[2911],[1124,29244,29246,29323],{"className":29245},[1221,1222],[1124,29247,29249,29320],{"className":29248},[1226],[1124,29250,29252,29295,29303],{"className":29251,"style":4858},[1230],[1124,29253,29254,29257],{"style":2994},[1124,29255],{"className":29256,"style":2998},[1238],[1124,29258,29260],{"className":29259},[1243,1244,1245,1246],[1124,29261,29263,29266],{"className":29262},[1209,1246],[1124,29264,3164],{"className":29265,"style":3319},[1209,1246],[1124,29267,29269,29272],{"className":29268},[1209,1246],[1124,29270,1439],{"className":29271,"style":1480},[1209,1213,1246],[1124,29273,29275],{"className":29274},[1217],[1124,29276,29278],{"className":29277},[1221],[1124,29279,29281],{"className":29280},[1226],[1124,29282,29284],{"className":29283,"style":22067},[1230],[1124,29285,29286,29289],{"style":3032},[1124,29287],{"className":29288,"style":3036},[1238],[1124,29290,29292],{"className":29291},[1243,3040,3041,1246],[1124,29293,1152],{"className":29294},[1209,1246],[1124,29296,29297,29300],{"style":3053},[1124,29298],{"className":29299,"style":2998},[1238],[1124,29301],{"className":29302,"style":3061},[3060],[1124,29304,29305,29308],{"style":3064},[1124,29306],{"className":29307,"style":2998},[1238],[1124,29309,29311],{"className":29310},[1243,1244,1245,1246],[1124,29312,29314,29317],{"className":29313},[1209,1246],[1124,29315,3164],{"className":29316,"style":3319},[1209,1246],[1124,29318,4325],{"className":29319,"style":4392},[1209,1213,1246],[1124,29321,1254],{"className":29322},[1253],[1124,29324,29326],{"className":29325},[1226],[1124,29327,29329],{"className":29328,"style":3538},[1230],[1124,29330],{},[1124,29332],{"className":29333},[2211,2212],"（隐藏层权重）——链式法则的关键",[1101,29336,29337,10434,29340],{},[1107,29338,29339],{},"依赖链路更长了：",[1124,29341,29343,29397],{"className":29342},[1127],[1124,29344,29346],{"className":29345},[1131],[1133,29347,29348],{"xmlns":1135},[1137,29349,29350,29394],{},[1140,29351,29352,29358,29360,29366,29368,29374,29376,29382,29384,29390,29392],{},[2922,29353,29354,29356],{},[1146,29355,1439],{},[1150,29357,1152],{},[1154,29359,3579],{},[2922,29361,29362,29364],{},[1146,29363,2680],{},[1150,29365,1152],{},[1154,29367,3579],{},[2922,29369,29370,29372],{},[1146,29371,4370],{},[1150,29373,1152],{},[1154,29375,3579],{},[2922,29377,29378,29380],{},[1146,29379,2680],{},[1150,29381,1164],{},[1154,29383,3579],{},[2922,29385,29386,29388],{},[1146,29387,4370],{},[1150,29389,1164],{},[1154,29391,3579],{},[1146,29393,4325],{},[1189,29395,29396],{"encoding":1191},"w^1 \\rightarrow z^1 \\rightarrow a^1 \\rightarrow z^2 \\rightarrow a^2 \\rightarrow C",[1124,29398,29400,29444,29488,29532,29576,29620],{"className":29399,"ariaHidden":1156},[1196],[1124,29401,29403,29406,29435,29438,29441],{"className":29402},[1200],[1124,29404],{"className":29405,"style":4598},[1204],[1124,29407,29409,29412],{"className":29408},[1209],[1124,29410,1439],{"className":29411,"style":1480},[1209,1213],[1124,29413,29415],{"className":29414},[1217],[1124,29416,29418],{"className":29417},[1221],[1124,29419,29421],{"className":29420},[1226],[1124,29422,29424],{"className":29423,"style":4598},[1230],[1124,29425,29426,29429],{"style":3905},[1124,29427],{"className":29428,"style":1239},[1238],[1124,29430,29432],{"className":29431},[1243,1244,1245,1246],[1124,29433,1152],{"className":29434},[1209,1246],[1124,29436],{"className":29437,"style":1774},[1271],[1124,29439,3579],{"className":29440},[1778],[1124,29442],{"className":29443,"style":1774},[1271],[1124,29445,29447,29450,29479,29482,29485],{"className":29446},[1200],[1124,29448],{"className":29449,"style":4598},[1204],[1124,29451,29453,29456],{"className":29452},[1209],[1124,29454,2680],{"className":29455,"style":2707},[1209,1213],[1124,29457,29459],{"className":29458},[1217],[1124,29460,29462],{"className":29461},[1221],[1124,29463,29465],{"className":29464},[1226],[1124,29466,29468],{"className":29467,"style":4598},[1230],[1124,29469,29470,29473],{"style":3905},[1124,29471],{"className":29472,"style":1239},[1238],[1124,29474,29476],{"className":29475},[1243,1244,1245,1246],[1124,29477,1152],{"className":29478},[1209,1246],[1124,29480],{"className":29481,"style":1774},[1271],[1124,29483,3579],{"className":29484},[1778],[1124,29486],{"className":29487,"style":1774},[1271],[1124,29489,29491,29494,29523,29526,29529],{"className":29490},[1200],[1124,29492],{"className":29493,"style":4598},[1204],[1124,29495,29497,29500],{"className":29496},[1209],[1124,29498,4370],{"className":29499},[1209,1213],[1124,29501,29503],{"className":29502},[1217],[1124,29504,29506],{"className":29505},[1221],[1124,29507,29509],{"className":29508},[1226],[1124,29510,29512],{"className":29511,"style":4598},[1230],[1124,29513,29514,29517],{"style":3905},[1124,29515],{"className":29516,"style":1239},[1238],[1124,29518,29520],{"className":29519},[1243,1244,1245,1246],[1124,29521,1152],{"className":29522},[1209,1246],[1124,29524],{"className":29525,"style":1774},[1271],[1124,29527,3579],{"className":29528},[1778],[1124,29530],{"className":29531,"style":1774},[1271],[1124,29533,29535,29538,29567,29570,29573],{"className":29534},[1200],[1124,29536],{"className":29537,"style":4598},[1204],[1124,29539,29541,29544],{"className":29540},[1209],[1124,29542,2680],{"className":29543,"style":2707},[1209,1213],[1124,29545,29547],{"className":29546},[1217],[1124,29548,29550],{"className":29549},[1221],[1124,29551,29553],{"className":29552},[1226],[1124,29554,29556],{"className":29555,"style":4598},[1230],[1124,29557,29558,29561],{"style":3905},[1124,29559],{"className":29560,"style":1239},[1238],[1124,29562,29564],{"className":29563},[1243,1244,1245,1246],[1124,29565,1164],{"className":29566},[1209,1246],[1124,29568],{"className":29569,"style":1774},[1271],[1124,29571,3579],{"className":29572},[1778],[1124,29574],{"className":29575,"style":1774},[1271],[1124,29577,29579,29582,29611,29614,29617],{"className":29578},[1200],[1124,29580],{"className":29581,"style":4598},[1204],[1124,29583,29585,29588],{"className":29584},[1209],[1124,29586,4370],{"className":29587},[1209,1213],[1124,29589,29591],{"className":29590},[1217],[1124,29592,29594],{"className":29593},[1221],[1124,29595,29597],{"className":29596},[1226],[1124,29598,29600],{"className":29599,"style":4598},[1230],[1124,29601,29602,29605],{"style":3905},[1124,29603],{"className":29604,"style":1239},[1238],[1124,29606,29608],{"className":29607},[1243,1244,1245,1246],[1124,29609,1164],{"className":29610},[1209,1246],[1124,29612],{"className":29613,"style":1774},[1271],[1124,29615,3579],{"className":29616},[1778],[1124,29618],{"className":29619,"style":1774},[1271],[1124,29621,29623,29626],{"className":29622},[1200],[1124,29624],{"className":29625,"style":4804},[1204],[1124,29627,4325],{"className":29628,"style":4392},[1209,1213],[1101,29630,29631],{},[1124,29632,29634,29780],{"className":29633},[1127],[1124,29635,29637],{"className":29636},[1131],[1133,29638,29639],{"xmlns":1135},[1137,29640,29641,29777],{},[1140,29642,29643,29661,29663,29681,29683,29705,29707,29729,29731,29753,29755],{},[2911,29644,29645,29651],{},[1140,29646,29647,29649],{},[1146,29648,3164],{"mathvariant":3145},[1146,29650,4325],{},[1140,29652,29653,29655],{},[1146,29654,3164],{"mathvariant":3145},[2922,29656,29657,29659],{},[1146,29658,1439],{},[1150,29660,1152],{},[1154,29662,1652],{},[2911,29664,29665,29671],{},[1140,29666,29667,29669],{},[1146,29668,3164],{"mathvariant":3145},[1146,29670,4325],{},[1140,29672,29673,29675],{},[1146,29674,3164],{"mathvariant":3145},[2922,29676,29677,29679],{},[1146,29678,4370],{},[1150,29680,1164],{},[1154,29682,2325],{},[2911,29684,29685,29695],{},[1140,29686,29687,29689],{},[1146,29688,3164],{"mathvariant":3145},[2922,29690,29691,29693],{},[1146,29692,4370],{},[1150,29694,1164],{},[1140,29696,29697,29699],{},[1146,29698,3164],{"mathvariant":3145},[2922,29700,29701,29703],{},[1146,29702,2680],{},[1150,29704,1164],{},[1154,29706,2325],{},[2911,29708,29709,29719],{},[1140,29710,29711,29713],{},[1146,29712,3164],{"mathvariant":3145},[2922,29714,29715,29717],{},[1146,29716,2680],{},[1150,29718,1164],{},[1140,29720,29721,29723],{},[1146,29722,3164],{"mathvariant":3145},[2922,29724,29725,29727],{},[1146,29726,4370],{},[1150,29728,1152],{},[1154,29730,2325],{},[2911,29732,29733,29743],{},[1140,29734,29735,29737],{},[1146,29736,3164],{"mathvariant":3145},[2922,29738,29739,29741],{},[1146,29740,4370],{},[1150,29742,1152],{},[1140,29744,29745,29747],{},[1146,29746,3164],{"mathvariant":3145},[2922,29748,29749,29751],{},[1146,29750,2680],{},[1150,29752,1152],{},[1154,29754,2325],{},[2911,29756,29757,29767],{},[1140,29758,29759,29761],{},[1146,29760,3164],{"mathvariant":3145},[2922,29762,29763,29765],{},[1146,29764,2680],{},[1150,29766,1152],{},[1140,29768,29769,29771],{},[1146,29770,3164],{"mathvariant":3145},[2922,29772,29773,29775],{},[1146,29774,1439],{},[1150,29776,1152],{},[1189,29778,29779],{"encoding":1191},"\\frac{\\partial C}{\\partial w^1} = \\frac{\\partial C}{\\partial a^2} \\cdot \\frac{\\partial a^2}{\\partial z^2} \\cdot \\frac{\\partial z^2}{\\partial a^1} \\cdot \\frac{\\partial a^1}{\\partial z^1} \\cdot \\frac{\\partial z^1}{\\partial w^1}",[1124,29781,29783,29898,30013,30154,30295,30436],{"className":29782,"ariaHidden":1156},[1196],[1124,29784,29786,29789,29889,29892,29895],{"className":29785},[1200],[1124,29787],{"className":29788,"style":23920},[1204],[1124,29790,29792,29795,29886],{"className":29791},[1209],[1124,29793],{"className":29794},[1795,2212],[1124,29796,29798],{"className":29797},[2911],[1124,29799,29801,29878],{"className":29800},[1221,1222],[1124,29802,29804,29875],{"className":29803},[1226],[1124,29805,29807,29850,29858],{"className":29806,"style":4858},[1230],[1124,29808,29809,29812],{"style":2994},[1124,29810],{"className":29811,"style":2998},[1238],[1124,29813,29815],{"className":29814},[1243,1244,1245,1246],[1124,29816,29818,29821],{"className":29817},[1209,1246],[1124,29819,3164],{"className":29820,"style":3319},[1209,1246],[1124,29822,29824,29827],{"className":29823},[1209,1246],[1124,29825,1439],{"className":29826,"style":1480},[1209,1213,1246],[1124,29828,29830],{"className":29829},[1217],[1124,29831,29833],{"className":29832},[1221],[1124,29834,29836],{"className":29835},[1226],[1124,29837,29839],{"className":29838,"style":22067},[1230],[1124,29840,29841,29844],{"style":3032},[1124,29842],{"className":29843,"style":3036},[1238],[1124,29845,29847],{"className":29846},[1243,3040,3041,1246],[1124,29848,1152],{"className":29849},[1209,1246],[1124,29851,29852,29855],{"style":3053},[1124,29853],{"className":29854,"style":2998},[1238],[1124,29856],{"className":29857,"style":3061},[3060],[1124,29859,29860,29863],{"style":3064},[1124,29861],{"className":29862,"style":2998},[1238],[1124,29864,29866],{"className":29865},[1243,1244,1245,1246],[1124,29867,29869,29872],{"className":29868},[1209,1246],[1124,29870,3164],{"className":29871,"style":3319},[1209,1246],[1124,29873,4325],{"className":29874,"style":4392},[1209,1213,1246],[1124,29876,1254],{"className":29877},[1253],[1124,29879,29881],{"className":29880},[1226],[1124,29882,29884],{"className":29883,"style":3538},[1230],[1124,29885],{},[1124,29887],{"className":29888},[2211,2212],[1124,29890],{"className":29891,"style":1774},[1271],[1124,29893,1652],{"className":29894},[1778],[1124,29896],{"className":29897,"style":1774},[1271],[1124,29899,29901,29904,30004,30007,30010],{"className":29900},[1200],[1124,29902],{"className":29903,"style":23920},[1204],[1124,29905,29907,29910,30001],{"className":29906},[1209],[1124,29908],{"className":29909},[1795,2212],[1124,29911,29913],{"className":29912},[2911],[1124,29914,29916,29993],{"className":29915},[1221,1222],[1124,29917,29919,29990],{"className":29918},[1226],[1124,29920,29922,29965,29973],{"className":29921,"style":4858},[1230],[1124,29923,29924,29927],{"style":2994},[1124,29925],{"className":29926,"style":2998},[1238],[1124,29928,29930],{"className":29929},[1243,1244,1245,1246],[1124,29931,29933,29936],{"className":29932},[1209,1246],[1124,29934,3164],{"className":29935,"style":3319},[1209,1246],[1124,29937,29939,29942],{"className":29938},[1209,1246],[1124,29940,4370],{"className":29941},[1209,1213,1246],[1124,29943,29945],{"className":29944},[1217],[1124,29946,29948],{"className":29947},[1221],[1124,29949,29951],{"className":29950},[1226],[1124,29952,29954],{"className":29953,"style":22067},[1230],[1124,29955,29956,29959],{"style":3032},[1124,29957],{"className":29958,"style":3036},[1238],[1124,29960,29962],{"className":29961},[1243,3040,3041,1246],[1124,29963,1164],{"className":29964},[1209,1246],[1124,29966,29967,29970],{"style":3053},[1124,29968],{"className":29969,"style":2998},[1238],[1124,29971],{"className":29972,"style":3061},[3060],[1124,29974,29975,29978],{"style":3064},[1124,29976],{"className":29977,"style":2998},[1238],[1124,29979,29981],{"className":29980},[1243,1244,1245,1246],[1124,29982,29984,29987],{"className":29983},[1209,1246],[1124,29985,3164],{"className":29986,"style":3319},[1209,1246],[1124,29988,4325],{"className":29989,"style":4392},[1209,1213,1246],[1124,29991,1254],{"className":29992},[1253],[1124,29994,29996],{"className":29995},[1226],[1124,29997,29999],{"className":29998,"style":3538},[1230],[1124,30000],{},[1124,30002],{"className":30003},[2211,2212],[1124,30005],{"className":30006,"style":2500},[1271],[1124,30008,2325],{"className":30009},[2504],[1124,30011],{"className":30012,"style":2500},[1271],[1124,30014,30016,30019,30145,30148,30151],{"className":30015},[1200],[1124,30017],{"className":30018,"style":25134},[1204],[1124,30020,30022,30025,30142],{"className":30021},[1209],[1124,30023],{"className":30024},[1795,2212],[1124,30026,30028],{"className":30027},[2911],[1124,30029,30031,30134],{"className":30030},[1221,1222],[1124,30032,30034,30131],{"className":30033},[1226],[1124,30035,30037,30080,30088],{"className":30036,"style":25153},[1230],[1124,30038,30039,30042],{"style":2994},[1124,30040],{"className":30041,"style":2998},[1238],[1124,30043,30045],{"className":30044},[1243,1244,1245,1246],[1124,30046,30048,30051],{"className":30047},[1209,1246],[1124,30049,3164],{"className":30050,"st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ncoding":1191},"\\frac{\\partial C}{\\partial a^2} = -0.348 \\quad \\text{（已算过）}",[1124,30617,30619,30734],{"className":30618,"ariaHidden":1156},[1196],[1124,30620,30622,30625,30725,30728,30731],{"className":30621},[1200],[1124,30623],{"className":30624,"style":23920},[1204],[1124,30626,30628,30631,30722],{"className":30627},[1209],[1124,30629],{"className":30630},[1795,2212],[1124,30632,30634],{"className":30633},[2911],[1124,30635,30637,30714],{"className":30636},[1221,1222],[1124,30638,30640,30711],{"className":30639},[1226],[1124,30641,30643,30686,30694],{"className":30642,"style":4858},[1230],[1124,30644,30645,30648],{"style":2994},[1124,30646],{"className":30647,"style":2998},[1238],[1124,30649,30651],{"className":30650},[1243,1244,1245,1246],[1124,30652,30654,30657],{"className":30653},[1209,1246],[1124,30655,3164],{"className":30656,"style":3319},[1209,1246],[1124,30658,30660,30663],{"className":30659},[1209,1246],[1124,30661,4370],{"className":30662},[1209,1213,1246],[1124,30664,30666],{"className":30665},[1217],[1124,30667,30669],{"className":30668},[1221],[1124,30670,30672],{"className":30671},[1226],[1124,30673,30675],{"className":30674,"style":22067},[1230],[1124,30676,30677,30680],{"style":3032},[1124,30678],{"className":30679,"style":3036},[1238],[1124,30681,30683],{"className":30682},[1243,3040,3041,1246],[1124,30684,1164],{"className":30685},[1209,1246],[1124,30687,30688,30691],{"style":3053},[1124,30689],{"className":30690,"style":2998},[1238],[1124,30692],{"className":30693,"style":3061},[3060],[1124,30695,30696,30699],{"style":3064},[1124,30697],{"className":30698,"style":2998},[1238],[1124,30700,30702],{"className":30701},[1243,1244,1245,1246],[1124,30703,30705,30708],{"className":30704},[1209,1246],[1124,30706,3164],{"className":30707,"style":3319},[1209,1246],[1124,30709,4325],{"className":30710,"style":4392},[1209,1213,1246],[1124,30712,1254],{"className":30713},[1253],[1124,30715,30717],{"className":30716},[1226],[1124,30718,30720],{"className":30719,"style":3538},[1230],[1124,30721],{},[1124,30723],{"className":30724},[2211,2212],[1124,30726],{"className":30727,"style":1774},[1271],[1124,30729,1652],{"className":30730},[1778],[1124,30732],{"className":30733,"style":1774},[1271],[1124,30735,30737,30740,30743,30746,30749],{"className":30736},[1200],[1124,30738],{"className":30739,"style":16311},[1204],[1124,30741,2235],{"className":30742},[1209],[1124,30744,23096],{"className":30745},[1209],[1124,30747],{"className":30748,"style":10033},[1271],[1124,30750,30752],{"className":30751},[1209,1767],[1124,30753,30612],{"className":30754},[1209,30755],"cjk_fallback",[1101,30757,30758],{},[1124,30759,30761,30803],{"className":30760},[1127],[1124,30762,30764],{"className":30763},[1131],[1133,30765,30766],{"xmlns":1135},[1137,30767,30768,30800],{},[1140,30769,30770,30792,30794,30796,30798],{},[2911,30771,30772,30782],{},[1140,30773,30774,30776],{},[1146,30775,3164],{"mathvariant":3145},[2922,30777,30778,30780],{},[1146,30779,4370],{},[1150,30781,1164],{},[1140,30783,30784,30786],{},[1146,30785,3164],{"mathvariant":3145},[2922,30787,30788,30790],{},[1146,30789,2680],{},[1150,30791,1164],{},[1154,30793,1652],{},[1150,30795,25785],{},[1271,30797],{"width":1663},[1647,30799,30612],{},[1189,30801,30802],{"encoding":1191},"\\frac{\\partial a^2}{\\partial z^2} = 0.227 \\quad \\text{（已算过）}",[1124,30804,30806,30947],{"className":30805,"ariaHidden":1156},[1196],[1124,30807,30809,30812,30938,30941,30944],{"className":30808},[1200],[1124,30810],{"className":30811,"style":25134},[1204],[1124,30813,30815,30818,30935],{"className":30814},[1209],[1124,30816],{"className":30817},[1795,2212],[1124,30819,30821],{"className":30820},[2911],[1124,30822,30824,30927],{"className":30823},[1221,1222],[1124,30825,30827,30924],{"className":30826},[1226],[1124,30828,30830,30873,30881],{"className":30829,"style":25153},[1230],[1124,30831,30832,30835],{"style":2994},[1124,30833],{"className":30834,"style":2998},[1238],[1124,30836,30838],{"className":30837},[1243,1244,1245,1246],[1124,30839,30841,30844],{"className":30840},[1209,1246],[1124,30842,3164],{"className":30843,"style":3319},[1209,1246],[1124,30845,30847,30850],{"className":30846},[1209,1246],[1124,30848,2680],{"className":30849,"style":2707},[1209,1213,1246],[1124,30851,30853],{"className":30852},[1217],[1124,30854,30856],{"className":30855},[1221],[1124,30857,30859],{"className":30858},[1226],[1124,30860,30862],{"className":30861,"style":22067},[1230],[1124,30863,30864,30867],{"style":3032},[1124,30865],{"className":30866,"style":3036},[1238],[1124,30868,30870],{"className":30869},[1243,3040,3041,1246],[1124,30871,1164],{"className":30872},[1209,1246],[1124,30874,30875,30878],{"style":3053},[1124,30876],{"className":30877,"style":2998},[1238],[1124,30879],{"className":30880,"style":3061},[3060],[1124,30882,30883,30886],{"style":3064},[1124,30884],{"className":30885,"style":2998},[1238],[1124,30887,30889],{"className":30888},[1243,1244,1245,1246],[1124,30890,30892,30895],{"className":30891},[1209,1246],[1124,30893,3164],{"className":30894,"style":3319},[1209,1246],[1124,30896,30898,30901],{"className":30897},[1209,1246],[1124,30899,4370],{"className":30900},[1209,1213,1246],[1124,30902,30904],{"className":30903},[1217],[1124,30905,30907],{"className":30906},[1221],[1124,30908,30910],{"className":30909},[1226],[1124,30911,30913],{"className":30912,"style":25237},[1230],[1124,30914,30915,30918],{"style":25240},[1124,30916],{"className":30917,"style":3036},[1238],[1124,30919,30921],{"className":30920},[1243,3040,3041,1246],[1124,30922,1164],{"className":30923},[1209,1246],[1124,30925,1254],{"className":30926},[1253],[1124,30928,30930],{"className":30929},[1226],[1124,30931,30933],{"className":30932,"style":3538},[1230],[1124,30934],{},[1124,30936],{"className":30937},[2211,2212],[1124,30939],{"className":30940,"style":1774},[1271],[1124,30942,1652],{"className":30943},[1778],[1124,30945],{"className":30946,"style":1774},[1271],[1124,30948,30950,30953,30956,30959],{"className":30949},[1200],[1124,30951],{"className":30952,"style":4804},[1204],[1124,30954,25785],{"className":30955},[1209],[1124,30957],{"className":30958,"style":10033},[1271],[1124,30960,30962],{"className":30961},[1209,1767],[1124,30963,30612],{"className":30964},[1209,30755],[1101,30966,30967],{},[1124,30968,30970,31016],{"className":30969},[1127],[1124,30971,30973],{"className":30972},[1131],[1133,30974,30975],{"xmlns":1135},[1137,30976,30977,31013],{},[1140,30978,30979,31001,31003,31009,31011],{},[2911,30980,30981,30991],{},[1140,30982,30983,30985],{},[1146,30984,3164],{"mathvariant":3145},[2922,30986,30987,30989],{},[1146,30988,2680],{},[1150,30990,1164],{},[1140,30992,30993,30995],{},[1146,30994,3164],{"mathvariant":3145},[2922,30996,30997,30999],{},[1146,30998,4370],{},[1150,31000,1152],{},[1154,31002,1652],{},[2922,31004,31005,31007],{},[1146,31006,1439],{},[1150,31008,1164],{},[1154,31010,1652],{},[1150,31012,10186],{},[1189,31014,31015],{"encoding":1191},"\\frac{\\partial z^2}{\\partial a^1} = w^2 = 0.6",[1124,31017,31019,31160,31204],{"className":31018,"ariaHidden":1156},[1196],[1124,31020,31022,31025,31151,31154,31157],{"className":31021},[1200],[1124,31023],{"className":31024,"style":25134},[1204],[1124,31026,31028,31031,31148],{"className":31027},[1209],[1124,31029],{"className":31030},[1795,2212],[1124,31032,31034],{"className":31033},[2911],[1124,31035,31037,31140],{"className":31036},[1221,1222],[1124,31038,31040,31137],{"className":31039},[1226],[1124,31041,31043,31086,31094],{"className":31042,"style":25153},[1230],[1124,31044,31045,31048],{"style":2994},[1124,31046],{"className":31047,"style":2998},[1238],[1124,31049,31051],{"className":31050},[1243,1244,1245,1246],[1124,31052,31054,31057],{"className":31053},[1209,1246],[1124,31055,3164],{"className":31056,"style":3319},[1209,1246],[1124,31058,31060,31063],{"className":31059},[1209,1246],[1124,31061,4370],{"className":31062},[1209,1213,1246],[1124,31064,31066],{"className":31065},[1217],[1124,31067,31069],{"className":31068},[1221],[1124,31070,31072],{"className":31071},[1226],[1124,31073,31075],{"className":31074,"style":22067},[1230],[1124,31076,31077,31080],{"style":3032},[1124,31078],{"className":31079,"style":3036},[1238],[1124,31081,31083],{"className":31082},[1243,3040,3041,1246],[1124,31084,1152],{"className":31085},[1209,1246],[1124,31087,31088,31091],{"style":3053},[1124,31089],{"className":31090,"style":2998},[1238],[1124,31092],{"className":31093,"style":3061},[3060],[1124,31095,31096,31099],{"style":3064},[1124,31097],{"className":31098,"style":2998},[1238],[1124,31100,31102],{"className":31101},[1243,1244,1245,1246],[1124,31103,31105,31108],{"className":31104},[1209,1246],[1124,31106,3164],{"className":31107,"style":3319},[1209,1246],[1124,31109,31111,31114],{"className":31110},[1209,1246],[1124,31112,2680],{"className":31113,"style":2707},[1209,1213,1246],[1124,31115,31117],{"className":31116},[1217],[1124,31118,31120],{"className":31119},[1221],[1124,31121,31123],{"className":31122},[1226],[1124,31124,31126],{"className":31125,"style":25237},[1230],[1124,31127,31128,31131],{"style":25240},[1124,31129],{"className":31130,"style":3036},[1238],[1124,31132,31134],{"className":31133},[1243,3040,3041,1246],[1124,31135,1164],{"className":31136},[1209,1246],[1124,31138,1254],{"className":31139},[1253],[1124,31141,31143],{"className":31142},[1226],[1124,31144,31146],{"className":31145,"style":3538},[1230],[1124,31147],{},[1124,31149],{"className":31150},[2211,2212],[1124,31152],{"className":31153,"style":1774},[1271],[1124,31155,1652],{"className":31156},[1778],[1124,31158],{"className":31159,"style":1774},[1271],[1124,31161,31163,31166,31195,31198,31201],{"className":31162},[1200],[1124,31164],{"className":31165,"style":4598},[1204],[1124,31167,31169,31172],{"className":31168},[1209],[1124,31170,1439],{"className":31171,"style":1480},[1209,1213],[1124,31173,31175],{"className":31174},[1217],[1124,31176,31178],{"className":31177},[1221],[1124,31179,31181],{"className":31180},[1226],[1124,31182,31184],{"className":31183,"style":4598},[1230],[1124,31185,31186,31189],{"style":3905},[1124,31187],{"className":31188,"style":1239},[1238],[1124,31190,31192],{"className":31191},[1243,1244,1245,1246],[1124,31193,1164],{"className":31194},[1209,1246],[1124,31196],{"className":31197,"style":1774},[1271],[1124,31199,1652],{"className":31200},[1778],[1124,31202],{"className":31203,"style":1774},[1271],[1124,31205,31207,31210],{"className":31206},[1200],[1124,31208],{"className":31209,"style":3685},[1204],[1124,31211,10186],{"className":31212},[1209],[1101,31214,31215],{},[1124,31216,31218,31306],{"className":31217},[1127],[1124,31219,31221],{"className":31220},[1131],[1133,31222,31223],{"xmlns":1135},[1137,31224,31225,31303],{},[1140,31226,31227,31249,31251,31257,31259,31265,31267,31269,31275,31277,31279,31281,31287,31289,31291,31293,31295,31298,31300],{},[2911,31228,31229,31239],{},[1140,31230,31231,31233],{},[1146,31232,3164],{"mathvariant":3145},[2922,31234,31235,31237],{},[1146,31236,4370],{},[1150,31238,1152],{},[1140,31240,31241,31243],{},[1146,31242,3164],{"mathvariant":3145},[2922,31244,31245,31247],{},[1146,31246,2680],{},[1150,31248,1152],{},[1154,31250,1652],{},[2922,31252,31253,31255],{},[1146,31254,2674],{},[1154,31256,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,31258,2677],{"stretchy":1674},[2922,31260,31261,31263],{},[1146,31262,2680],{},[1150,31264,1152],{},[1154,31266,2683],{"stretchy":1674},[1154,31268,1652],{},[2922,31270,31271,31273],{},[1146,31272,4370],{},[1150,31274,1152],{},[1154,31276,2677],{"stretchy":1674},[1150,31278,1152],{},[1154,31280,2235],{},[2922,31282,31283,31285],{},[1146,31284,4370],{},[1150,31286,1152],{},[1154,31288,2683],{"stretchy":1674},[1154,31290,1652],{},[1150,31292,21877],{},[1154,31294,10608],{},[1150,31296,31297],{},"0.289",[1154,31299,1652],{},[1150,31301,31302],{},"0.205",[1189,31304,31305],{"encoding":1191},"\\frac{\\partial a^1}{\\partial z^1} = \\sigma'(z^1) = a^1(1-a^1) = 0.711 \\times 0.289 = 0.205",[1124,31307,31309,31450,31532,31582,31629,31647,31665],{"className":31308,"ariaHidden":1156},[1196],[1124,31310,31312,31315,31441,31444,31447],{"className":31311},[1200],[1124,31313],{"className":31314,"style":25134},[1204],[1124,31316,31318,31321,31438],{"className":31317},[1209],[1124,31319],{"className":31320},[1795,2212],[1124,31322,31324],{"className":31323},[2911],[1124,31325,31327,31430],{"className":31326},[1221,1222],[1124,31328,31330,31427],{"className":31329},[1226],[1124,31331,31333,31376,31384],{"className":31332,"style":25153},[1230],[1124,31334,31335,31338],{"style":2994},[1124,31336],{"className":31337,"style":2998},[1238],[1124,31339,31341],{"className":31340},[1243,1244,1245,1246],[1124,31342,31344,31347],{"className":31343},[1209,1246],[1124,31345,3164],{"className":31346,"style":3319},[1209,1246],[1124,31348,31350,31353],{"className":31349},[1209,1246],[1124,31351,2680],{"className":31352,"style":2707},[1209,1213,1246],[1124,31354,31356],{"className":31355},[1217],[1124,31357,31359],{"className":31358},[1221],[1124,31360,31362],{"className":31361},[1226],[1124,31363,31365],{"className":31364,"style":22067},[1230],[1124,31366,31367,31370],{"style":3032},[1124,31368],{"className":31369,"style":3036},[1238],[1124,31371,31373],{"className":31372},[1243,3040,3041,1246],[1124,31374,1152],{"className":31375},[1209,1246],[1124,31377,31378,31381],{"style":3053},[1124,31379],{"className":31380,"style":2998},[1238],[1124,31382],{"className":31383,"style":3061},[3060],[1124,31385,31386,31389],{"style":3064},[1124,31387],{"className":31388,"style":2998},[1238],[1124,31390,31392],{"className":31391},[1243,1244,1245,1246],[1124,31393,31395,31398],{"className":31394},[1209,1246],[1124,31396,3164],{"className":31397,"style":3319},[1209,1246],[1124,31399,31401,31404],{"className":31400},[1209,1246],[1124,31402,4370],{"className":31403},[1209,1213,1246],[1124,31405,31407],{"className":31406},[1217],[1124,31408,31410],{"className":31409},[1221],[1124,31411,31413],{"className":31412},[1226],[1124,31414,31416],{"className":31415,"style":25237},[1230],[1124,31417,31418,31421],{"style":25240},[1124,31419],{"className":31420,"style":3036},[1238],[1124,31422,31424],{"className":31423},[1243,3040,3041,1246],[1124,31425,1152],{"className":31426},[1209,1246],[1124,31428,1254],{"className":31429},[1253],[1124,31431,31433],{"className":31432},[1226],[1124,31434,31436],{"className":31435,"style":3538},[1230],[1124,31437],{},[1124,31439],{"className":31440},[2211,2212],[1124,31442],{"className":31443,"style":1774},[1271],[1124,31445,1652],{"className":31446},[1778],[1124,31448],{"className":31449,"style":1774},[1271],[1124,31451,31453,31456,31488,31491,31520,31523,31526,31529],{"className":31452},[1200],[1124,31454],{"className":31455,"style":4576},[1204],[1124,31457,31459,31462],{"className":31458},[1209],[1124,31460,2674],{"className":31461,"style":2700},[1209,1213],[1124,31463,31465],{"className":31464},[1217],[1124,31466,31468],{"className":31467},[1221],[1124,31469,31471],{"className":31470},[1226],[1124,31472,31474],{"className":31473,"style":3902},[1230],[1124,31475,31476,31479],{"style":3905},[1124,31477],{"className":31478,"style":1239},[1238],[1124,31480,31482],{"className":31481},[1243,1244,1245,1246],[1124,31483,31485],{"className":31484},[1209,1246],[1124,31486,3838],{"className":31487},[1209,1246],[1124,31489,2677],{"className":31490},[1795],[1124,31492,31494,31497],{"className":31493},[1209],[1124,31495,2680],{"className":31496,"style":2707},[1209,1213],[1124,31498,31500],{"className":31499},[1217],[1124,31501,31503],{"className":31502},[1221],[1124,31504,31506],{"className":31505},[1226],[1124,31507,31509],{"className":31508,"style":4598},[1230],[1124,31510,31511,31514],{"style":3905},[1124,31512],{"className":31513,"style":1239},[1238],[1124,31515,31517],{"className":31516},[1243,1244,1245,1246],[1124,31518,1152],{"className":31519},[1209,1246],[1124,31521,2683],{"className":31522},[2211],[1124,31524],{"className":31525,"style":1774},[1271],[1124,31527,1652],{"className":31528},[1778],[1124,31530],{"className":31531,"style":1774},[1271],[1124,31533,31535,31538,31567,31570,31573,31576,31579],{"className":31534},[1200],[1124,31536],{"className":31537,"style":4576},[1204],[1124,31539,31541,31544],{"className":31540},[1209],[1124,31542,4370],{"className":31543},[1209,1213],[1124,31545,31547],{"className":31546},[1217],[1124,31548,31550],{"className":31549},[1221],[1124,31551,31553],{"className":31552},[1226],[1124,31554,31556],{"className":31555,"style":4598},[1230],[1124,31557,31558,31561],{"style":3905},[1124,31559],{"className":31560,"style":1239},[1238],[1124,31562,31564],{"className":31563},[1243,1244,1245,1246],[1124,31565,1152],{"className":31566},[1209,1246],[1124,31568,2677],{"className":31569},[1795],[1124,31571,1152],{"className":31572},[1209],[1124,31574],{"className":31575,"style":2500},[1271],[1124,31577,2235],{"className":31578},[2504],[1124,31580],{"className":31581,"style":2500},[1271],[1124,31583,31585,31588,31617,31620,31623,31626],{"className":31584},[1200],[1124,31586],{"className":31587,"style":4576},[1204],[1124,31589,31591,31594],{"className":31590},[1209],[1124,31592,4370],{"className":31593},[1209,1213],[1124,31595,31597],{"className":31596},[1217],[1124,31598,31600],{"className":31599},[1221],[1124,31601,31603],{"className":31602},[1226],[1124,31604,31606],{"className":31605,"style":4598},[1230],[1124,31607,31608,31611],{"style":3905},[1124,31609],{"className":31610,"style":1239},[1238],[1124,31612,31614],{"className":31613},[1243,1244,1245,1246],[1124,31615,1152],{"className":31616},[1209,1246],[1124,31618,2683],{"className":31619},[2211],[1124,31621],{"className":31622,"style":1774},[1271],[1124,31624,1652],{"className":31625},[1778],[1124,31627],{"className":31628,"style":1774},[1271],[1124,31630,31632,31635,31638,31641,31644],{"className":31631},[1200],[1124,31633],{"className":31634,"style":10423},[1204],[1124,31636,21877],{"className":31637},[1209],[1124,31639],{"className":31640,"style":2500},[1271],[1124,31642,10608],{"className":31643},[2504],[1124,31645],{"className":31646,"style":2500},[1271],[1124,31648,31650,31653,31656,31659,31662],{"className":31649},[1200],[1124,31651],{"className":31652,"style":3685},[1204],[1124,31654,31297],{"className":31655},[1209],[1124,31657],{"className":31658,"style":1774},[1271],[1124,31660,1652],{"className":31661},[1778],[1124,31663],{"className":31664,"style":1774},[1271],[1124,31666,31668,31671],{"className":31667},[1200],[1124,31669],{"className":31670,"style":3685},[1204],[1124,31672,31302],{"className":31673},[1209],[1101,31675,31676],{},[1124,31677,31679,31721],{"className":31678},[1127],[1124,31680,31682],{"className":31681},[1131],[1133,31683,31684],{"xmlns":1135},[1137,31685,31686,31718],{},[1140,31687,31688,31710,31712,31714,31716],{},[2911,31689,31690,31700],{},[1140,31691,31692,31694],{},[1146,31693,3164],{"mathvariant":3145},[2922,31695,31696,31698],{},[1146,31697,2680],{},[1150,31699,1152],{},[1140,31701,31702,31704],{},[1146,31703,3164],{"mathvariant":3145},[2922,31705,31706,31708],{},[1146,31707,1439],{},[1150,31709,1152],{},[1154,31711,1652],{},[1146,31713,1148],{},[1154,31715,1652],{},[1150,31717,21217],{},[1189,31719,31720],{"encoding":1191},"\\frac{\\partial z^1}{\\partial w^1} = x = 2.0",[1124,31722,31724,31865,31883],{"className":31723,"ariaHidden":1156},[1196],[1124,31725,31727,31730,31856,31859,31862],{"className":31726},[1200],[1124,31728],{"className":31729,"style":25134},[1204],[1124,31731,31733,31736,31853],{"className":31732},[1209],[1124,31734],{"className":31735},[1795,2212],[1124,31737,31739],{"className":31738},[2911],[1124,31740,31742,31845],{"className":31741},[1221,1222],[1124,31743,31745,31842],{"className":31744},[1226],[1124,31746,31748,31791,31799],{"className":31747,"style":25153},[1230],[1124,31749,31750,31753],{"style":2994},[1124,31751],{"className":31752,"style":2998},[1238],[1124,31754,31756],{"className":31755},[1243,1244,1245,1246],[1124,31757,31759,31762],{"className":31758},[1209,1246],[1124,31760,3164],{"className":31761,"style":3319},[1209,1246],[1124,31763,31765,31768],{"className":31764},[1209,1246],[1124,31766,1439],{"className":31767,"style":1480},[1209,1213,1246],[1124,31769,31771],{"className":31770},[1217],[1124,31772,31774],{"className":31773},[1221],[1124,31775,31777],{"className":31776},[1226],[1124,31778,31780],{"className":31779,"style":22067},[1230],[1124,31781,31782,31785],{"style":3032},[1124,31783],{"className":31784,"style":3036},[1238],[1124,31786,31788],{"className":31787},[1243,3040,3041,1246],[1124,31789,1152],{"className":31790},[1209,1246],[1124,31792,31793,31796],{"style":3053},[1124,31794],{"className":31795,"style":2998},[1238],[1124,31797],{"className":31798,"style":3061},[3060],[1124,31800,31801,31804],{"style":3064},[1124,31802],{"className":31803,"style":2998},[1238],[1124,31805,31807],{"className":31806},[1243,1244,1245,1246],[1124,31808,31810,31813],{"className":31809},[1209,1246],[1124,31811,3164],{"className":31812,"style":3319},[1209,1246],[1124,31814,31816,31819],{"className":31815},[1209,1246],[1124,31817,2680],{"className":31818,"style":2707},[1209,1213,1246],[1124,31820,31822],{"className":31821},[1217],[1124,31823,31825],{"className":31824},[1221],[1124,31826,31828],{"className":31827},[1226],[1124,31829,31831],{"className":31830,"style":25237},[1230],[1124,31832,31833,31836],{"style":25240},[1124,31834],{"className":31835,"style":3036},[1238],[1124,31837,31839],{"className":31838},[1243,3040,3041,1246],[1124,31840,1152],{"className":31841},[1209,1246],[1124,31843,1254],{"className":31844},[1253],[1124,31846,31848],{"className":31847},[1226],[1124,31849,31851],{"className":31850,"style":3538},[1230],[1124,31852],{},[1124,31854],{"className":31855},[2211,2212],[1124,31857],{"className":31858,"style":1774},[1271],[1124,31860,1652],{"className":31861},[1778],[1124,31863],{"className":31864,"style":1774},[1271],[1124,31866,31868,31871,31874,31877,31880],{"className":31867},[1200],[1124,31869],{"className":31870,"style":3124},[1204],[1124,31872,1148],{"className":31873},[1209,1213],[1124,31875],{"className":31876,"style":1774},[1271],[1124,31878,1652],{"className":31879},[1778],[1124,31881],{"className":31882,"style":1774},[1271],[1124,31884,31886,31889],{"className":31885},[1200],[1124,31887],{"className":31888,"style":3685},[1204],[1124,31890,21217],{"className":31891},[1209],[1101,31893,31894],{},[1107,31895,31896],{},"全部相乘：",[1101,31898,31899],{},[1124,31900,31902,31958],{"className":31901},[1127],[1124,31903,31905],{"className":31904},[1131],[1133,31906,31907],{"xmlns":1135},[1137,31908,31909,31955],{},[1140,31910,31911,31929,31931,31933,31935,31937,31939,31941,31943,31945,31947,31949,31951,31953],{},[2911,31912,31913,31919],{},[1140,31914,31915,31917],{},[1146,31916,3164],{"mathvariant":3145},[1146,31918,4325],{},[1140,31920,31921,31923],{},[1146,31922,3164],{"mathvariant":3145},[2922,31924,31925,31927],{},[1146,31926,1439],{},[1150,31928,1152],{},[1154,31930,1652],{},[1154,31932,2677],{"stretchy":1674},[1154,31934,2235],{},[1150,31936,23096],{},[1154,31938,2683],{"stretchy":1674},[1154,31940,10608],{},[1150,31942,25785],{},[1154,31944,10608],{},[1150,31946,10186],{},[1154,31948,10608],{},[1150,31950,31302],{},[1154,31952,10608],{},[1150,31954,21217],{},[1189,31956,31957],{"encoding":1191},"\\frac{\\partial C}{\\partial w^1} = (-0.348) \\times 0.227 \\times 0.6 \\times 0.205 \\times 2.0",[1124,31959,31961,32076,32103,32121,32139,32157],{"className":31960,"ariaHidden":1156},[1196],[1124,31962,31964,31967,32067,32070,32073],{"className":31963},[1200],[1124,31965],{"className":31966,"style":23920},[1204],[1124,31968,31970,31973,32064],{"className":31969},[1209],[1124,31971],{"className":31972},[1795,2212],[1124,31974,31976],{"className":31975},[2911],[1124,31977,31979,32056],{"className":31978},[1221,1222],[1124,31980,31982,32053],{"className":31981},[1226],[1124,31983,31985,32028,32036],{"className":31984,"style":4858},[1230],[1124,31986,31987,31990],{"style":2994},[1124,31988],{"className":31989,"style":2998},[1238],[1124,31991,31993],{"className":31992},[1243,1244,1245,1246],[1124,31994,31996,31999],{"className":31995},[1209,1246],[1124,31997,3164],{"className":31998,"style":3319},[1209,1246],[1124,32000,32002,32005],{"className":32001},[1209,1246],[1124,32003,1439],{"className":32004,"style":1480},[1209,1213,1246],[1124,32006,32008],{"className":32007},[1217],[1124,32009,32011],{"className":32010},[1221],[1124,32012,32014],{"className":32013},[1226],[1124,32015,32017],{"className":32016,"style":22067},[1230],[1124,32018,32019,32022],{"style":3032},[1124,32020],{"className":32021,"style":3036},[1238],[1124,32023,32025],{"className":32024},[1243,3040,3041,1246],[1124,32026,1152],{"className":32027},[1209,1246],[1124,32029,32030,32033],{"style":3053},[1124,32031],{"className":32032,"style":2998},[1238],[1124,32034],{"className":32035,"style":3061},[3060],[1124,32037,32038,32041],{"style":3064},[1124,32039],{"className":32040,"style":2998},[1238],[1124,32042,32044],{"className":32043},[1243,1244,1245,1246],[1124,32045,32047,32050],{"className":32046},[1209,1246],[1124,32048,3164],{"className":32049,"style":3319},[1209,1246],[1124,32051,4325],{"className":32052,"style":4392},[1209,1213,1246],[1124,32054,1254],{"className":32055},[1253],[1124,32057,32059],{"className":32058},[1226],[1124,32060,32062],{"className":32061,"style":3538},[1230],[1124,32063],{},[1124,32065],{"className":32066},[2211,2212],[1124,32068],{"className":32069,"style":1774},[1271],[1124,32071,1652],{"className":32072},[1778],[1124,32074],{"className":32075,"style":1774},[1271],[1124,32077,32079,32082,32085,32088,32091,32094,32097,32100],{"className":32078},[1200],[1124,32080],{"className":32081,"style":2696},[1204],[1124,32083,2677],{"className":32084},[1795],[1124,32086,2235],{"className":32087},[1209],[1124,32089,23096],{"className":32090},[1209],[1124,32092,2683],{"className":32093},[2211],[1124,32095],{"className":32096,"style":2500},[1271],[1124,32098,10608],{"className":32099},[2504],[1124,32101],{"className":32102,"style":2500},[1271],[1124,32104,32106,32109,32112,32115,32118],{"className":32105},[1200],[1124,32107],{"className":32108,"style":10423},[1204],[1124,32110,25785],{"className":32111},[1209],[1124,32113],{"className":32114,"style":2500},[1271],[1124,32116,10608],{"className":32117},[2504],[1124,32119],{"className":32120,"style":2500},[1271],[1124,32122,32124,32127,32130,32133,32136],{"className":32123},[1200],[1124,32125],{"className":32126,"style":10423},[1204],[1124,32128,10186],{"className":32129},[1209],[1124,32131],{"className":32132,"style":2500},[1271],[1124,32134,10608],{"className":32135},[2504],[1124,32137],{"className":32138,"style":2500},[1271],[1124,32140,32142,32145,32148,32151,32154],{"className":32141},[1200],[1124,32143],{"className":32144,"style":10423},[1204],[1124,32146,31302],{"className":32147},[1209],[1124,32149],{"className":32150,"style":2500},[1271],[1124,32152,10608],{"className":32153},[2504],[1124,32155],{"className":32156,"style":2500},[1271],[1124,32158,32160,32163],{"className":32159},[1200],[1124,32161],{"className":32162,"style":3685},[1204],[1124,32164,21217],{"className":32165},[1209],[1101,32167,32168],{},[1124,32169,32171,32201],{"className":32170},[1127],[1124,32172,32174],{"className":32173},[1131],[1133,32175,32176],{"xmlns":1135},[1137,32177,32178,32198],{},[1140,32179,32180,32182,32184,32186,32188,32190,32192,32194,32196],{},[1154,32181,1652],{},[1154,32183,2235],{},[1150,32185,27940],{},[1154,32187,10608],{},[1150,32189,10186],{},[1154,32191,10608],{},[1150,32193,31302],{},[1154,32195,10608],{},[1150,32197,21217],{},[1189,32199,32200],{"encoding":1191},"= -0.0790 \\times 0.6 \\times 0.205 \\times 2.0",[1124,32202,32204,32217,32238,32256,32274],{"className":32203,"ariaHidden":1156},[1196],[1124,32205,32207,32211,32214],{"className":32206},[1200],[1124,32208],{"className":32209,"style":32210},[1204],"height:0.3669em;",[1124,32212,1652],{"className":32213},[1778],[1124,32215],{"className":32216,"style":1774},[1271],[1124,32218,32220,32223,32226,32229,32232,32235],{"className":32219},[1200],[1124,32221],{"className":32222,"style":10423},[1204],[1124,32224,2235],{"className":32225},[1209],[1124,32227,27940],{"className":32228},[1209],[1124,32230],{"className":32231,"style":2500},[1271],[1124,32233,10608],{"className":32234},[2504],[1124,32236],{"className":32237,"style":2500},[1271],[1124,32239,32241,32244,32247,32250,32253],{"className":32240},[1200],[1124,32242],{"className":32243,"style":10423},[1204],[1124,32245,10186],{"className":32246},[1209],[1124,32248],{"className":32249,"style":2500},[1271],[1124,32251,10608],{"className":32252},[2504],[1124,32254],{"className":32255,"style":2500},[1271],[1124,32257,32259,32262,32265,32268,32271],{"className":32258},[1200],[1124,32260],{"className":32261,"style":10423},[1204],[1124,32263,31302],{"className":32264},[1209],[1124,32266],{"className":32267,"style":2500},[1271],[1124,32269,10608],{"className":32270},[2504],[1124,32272],{"className":32273,"style":2500},[1271],[1124,32275,32277,32280],{"className":32276},[1200],[1124,32278],{"className":32279,"style":3685},[1204],[1124,32281,21217],{"className":32282},[1209],[1101,32284,32285],{},[1124,32286,32288,32315],{"className":32287},[1127],[1124,32289,32291],{"className":32290},[1131],[1133,32292,32293],{"xmlns":1135},[1137,32294,32295,32312],{},[1140,32296,32297,32299,32301,32304,32306,32308,32310],{},[1154,32298,1652],{},[1154,32300,2235],{},[1150,32302,32303],{},"0.0474",[1154,32305,10608],{},[1150,32307,31302],{},[1154,32309,10608],{},[1150,32311,21217],{},[1189,32313,32314],{"encoding":1191},"= -0.0474 \\times 0.205 \\times 2.0",[1124,32316,32318,32330,32351,32369],{"className":32317,"ariaHidden":1156},[1196],[1124,32319,32321,32324,32327],{"className":32320},[1200],[1124,32322],{"className":32323,"style":32210},[1204],[1124,32325,1652],{"className":32326},[1778],[1124,32328],{"className":32329,"style":1774},[1271],[1124,32331,32333,32336,32339,32342,32345,32348],{"className":32332},[1200],[1124,32334],{"className":32335,"style":10423},[1204],[1124,32337,2235],{"className":32338},[1209],[1124,32340,32303],{"className":32341},[1209],[1124,32343],{"className":32344,"style":2500},[1271],[1124,32346,10608],{"className":32347},[2504],[1124,32349],{"className":32350,"style":2500},[1271],[1124,32352,32354,32357,32360,32363,32366],{"className":32353},[1200],[1124,32355],{"className":32356,"style":10423},[1204],[1124,32358,31302],{"className":32359},[1209],[1124,32361],{"className":32362,"style":2500},[1271],[1124,32364,10608],{"className":32365},[2504],[1124,32367],{"className":32368,"style":2500},[1271],[1124,32370,32372,32375],{"className":32371},[1200],[1124,32373],{"className":32374,"style":3685},[1204],[1124,32376,21217],{"className":32377},[1209],[1101,32379,32380],{},[1124,32381,32383,32423],{"className":32382},[1127],[1124,32384,32386],{"className":32385},[1131],[1133,32387,32388],{"xmlns":1135},[1137,32389,32390,32420],{},[1140,32391,32392,32394,32396,32399,32401,32403,32405],{},[1154,32393,1652],{},[1154,32395,2235],{},[1150,32397,32398],{},"0.00972",[1154,32400,10608],{},[1150,32402,21217],{},[1154,32404,1652],{},[8168,32406,32407],{"notation":8170},[1671,32408,32409],{"scriptlevel":1673,"displaystyle":1674},[1671,32410,32411],{"scriptlevel":1673,"displaystyle":1674},[1671,32412,32413],{"scriptlevel":1673,"displaystyle":1156},[1140,32414,32415,32417],{},[1154,32416,2235],{},[1150,32418,32419],{},"0.0194",[1189,32421,32422],{"encoding":1191},"= -0.00972 \\times 2.0 = \\boxed{-0.0194}",[1124,32424,32426,32438,32459,32477],{"className":32425,"ariaHidden":1156},[1196],[1124,32427,32429,32432,32435],{"className":32428},[1200],[1124,32430],{"className":32431,"style":32210},[1204],[1124,32433,1652],{"className":32434},[1778],[1124,32436],{"className":32437,"style":1774},[1271],[1124,32439,32441,32444,32447,32450,32453,32456],{"className":32440},[1200],[1124,32442],{"className":32443,"style":10423},[1204],[1124,32445,2235],{"className":32446},[1209],[1124,32448,32398],{"className":32449},[1209],[1124,32451],{"className":32452,"style":2500},[1271],[1124,32454,10608],{"className":32455},[2504],[1124,32457],{"className":32458,"style":2500},[1271],[1124,32460,32462,32465,32468,32471,32474],{"className":32461},[1200],[1124,32463],{"className":32464,"style":3685},[1204],[1124,32466,21217],{"className":32467},[1209],[1124,32469],{"className":32470,"style":1774},[1271],[1124,32472,1652],{"className":32473},[1778],[1124,32475],{"className":32476,"style":1774},[1271],[1124,32478,32480,32483],{"className":32479},[1200],[1124,32481],{"className":32482,"style":26667},[1204],[1124,32484,32486],{"className":32485},[1209],[1124,32487,32489,32526],{"className":32488},[1221,1222],[1124,32490,32492,32523],{"className":32491},[1226],[1124,32493,32495,32515],{"className":32494,"style":12358},[1230],[1124,32496,32497,32500],{"style":26682},[1124,32498],{"className":32499,"style":26686},[1238],[1124,32501,32503],{"className":32502},[8257],[1124,32504,32506],{"className":32505},[1209],[1124,32507,32509,32512],{"className":32508},[1209],[1124,32510,2235],{"className":32511},[1209],[1124,32513,32419],{"className":32514},[1209],[1124,32516,32517,32520],{"style":12380},[1124,32518],{"className":32519,"style":26686},[1238],[1124,32521],{"className":32522,"style":26710},[8436,8437],[1124,32524,1254],{"className":32525},[1253],[1124,32527,32529],{"className":32528},[1226],[1124,32530,32532],{"className":32531,"style":26720},[1230],[1124,32533],{},[2745,32535],{},[7743,32537,32539],{"id":32538},"_24-隐藏层偏置","2.4 隐藏层偏置",[1101,32541,24456,32542,32683],{},[1124,32543,32545,32574],{"className":32544},[1127],[1124,32546,32548],{"className":32547},[1131],[1133,32549,32550],{"xmlns":1135},[1137,32551,32552,32572],{},[1140,32553,32554],{},[2911,32555,32556,32562],{},[1140,32557,32558,32560],{},[1146,32559,3164],{"mathvariant":3145},[1146,32561,4325],{},[1140,32563,32564,32566],{},[1146,32565,3164],{"mathvariant":3145},[2922,32567,32568,32570],{},[1146,32569,2230],{},[1150,32571,1152],{},[1189,32573,24338],{"encoding":1191},[1124,32575,32577],{"className":32576,"ariaHidden":1156},[1196],[1124,32578,32580,32583],{"className":32579},[1200],[1124,32581],{"className":32582,"style":23920},[1204],[1124,32584,32586,32589,32680],{"className":32585},[1209],[1124,32587],{"className":32588},[1795,2212],[1124,32590,32592],{"className":32591},[2911],[1124,32593,32595,32672],{"className":32594},[1221,1222],[1124,32596,32598,32669],{"className":32597},[1226],[1124,32599,32601,32644,32652],{"className":32600,"style":4858},[1230],[1124,32602,32603,32606],{"style":2994},[1124,32604],{"className":32605,"style":2998},[1238],[1124,32607,32609],{"className":32608},[1243,1244,1245,1246],[1124,32610,32612,32615],{"className":32611},[1209,1246],[1124,32613,3164],{"className":32614,"style":3319},[1209,1246],[1124,32616,32618,32621],{"className":32617},[1209,1246],[1124,32619,2230],{"className":32620},[1209,1213,1246],[1124,32622,32624],{"className":32623},[1217],[1124,32625,32627],{"className":32626},[1221],[1124,32628,32630],{"className":32629},[1226],[1124,32631,32633],{"className":32632,"style":22067},[1230],[1124,32634,32635,32638],{"style":3032},[1124,32636],{"className":32637,"style":3036},[1238],[1124,32639,32641],{"className":32640},[1243,3040,3041,1246],[1124,32642,1152],{"className":32643},[1209,1246],[1124,32645,32646,32649],{"style":3053},[1124,32647],{"className":32648,"style":2998},[1238],[1124,32650],{"className":32651,"style":3061},[3060],[1124,32653,32654,32657],{"style":3064},[1124,32655],{"className":32656,"style":2998},[1238],[1124,32658,32660],{"className":32659},[1243,1244,1245,1246],[1124,32661,32663,32666],{"className":32662},[1209,1246],[1124,32664,3164],{"className":32665,"style":3319},[1209,1246],[1124,32667,4325],{"className":32668,"style":4392},[1209,1213,1246],[1124,32670,1254],{"className":32671},[1253],[1124,32673,32675],{"className":32674},[1226],[1124,32676,32678],{"className":32677,"style":3538},[1230],[1124,32679],{},[1124,32681],{"className":32682},[2211,2212],"（隐藏层偏置）",[1101,32685,32686,10434,32689],{},[1107,32687,32688],{},"链路：",[1124,32690,32692,32746],{"className":32691},[1127],[1124,32693,32695],{"className":32694},[1131],[1133,32696,32697],{"xmlns":1135},[1137,32698,32699,32743],{},[1140,32700,32701,32707,32709,32715,32717,32723,32725,32731,32733,32739,32741],{},[2922,32702,32703,32705],{},[1146,32704,2230],{},[1150,32706,1152],{},[1154,32708,3579],{},[2922,32710,32711,32713],{},[1146,32712,2680],{},[1150,32714,1152],{},[1154,32716,3579],{},[2922,32718,32719,32721],{},[1146,32720,4370],{},[1150,32722,1152],{},[1154,32724,3579],{},[2922,32726,32727,32729],{},[1146,32728,2680],{},[1150,32730,1164],{},[1154,32732,3579],{},[2922,32734,32735,32737],{},[1146,32736,4370],{},[1150,32738,1164],{},[1154,32740,3579],{},[1146,32742,4325],{},[1189,32744,32745],{"encoding":1191},"b^1 \\rightarrow z^1 \\rightarrow a^1 \\rightarrow z^2 \\rightarrow a^2 \\rightarrow C",[1124,32747,32749,32793,32837,32881,32925,32969],{"className":32748,"ariaHidden":1156},[1196],[1124,32750,32752,32755,32784,32787,32790],{"className":32751},[1200],[1124,32753],{"className":32754,"style":4598},[1204],[1124,32756,32758,32761],{"className":32757},[1209],[1124,32759,2230],{"className":32760},[1209,1213],[1124,32762,32764],{"className":32763},[1217],[1124,32765,32767],{"className":32766},[1221],[1124,32768,32770],{"className":32769},[1226],[1124,32771,32773],{"className":32772,"style":4598},[1230],[1124,32774,32775,32778],{"style":3905},[1124,32776],{"className":32777,"style":1239},[1238],[1124,32779,32781],{"className":32780},[1243,1244,1245,1246],[1124,32782,1152],{"className":32783},[1209,1246],[1124,32785],{"className":32786,"style":1774},[1271],[1124,32788,3579],{"className":32789},[1778],[1124,32791],{"className":32792,"style":1774},[1271],[1124,32794,32796,32799,32828,32831,32834],{"className":32795},[1200],[1124,32797],{"className":32798,"style":4598},[1204],[1124,32800,32802,32805],{"className":32801},[1209],[1124,32803,2680],{"className":32804,"style":2707},[1209,1213],[1124,32806,32808],{"className":32807},[1217],[1124,32809,32811],{"className":32810},[1221],[1124,32812,32814],{"className":32813},[1226],[1124,32815,32817],{"className":32816,"style":4598},[1230],[1124,32818,32819,32822],{"style":3905},[1124,32820],{"className":32821,"style":1239},[1238],[1124,32823,32825],{"className":32824},[1243,1244,1245,1246],[1124,32826,1152],{"className":32827},[1209,1246],[1124,32829],{"className":32830,"style":1774},[1271],[1124,32832,3579],{"className":32833},[1778],[1124,32835],{"className":32836,"style":1774},[1271],[1124,32838,32840,32843,32872,32875,32878],{"className":32839},[1200],[1124,32841],{"className":32842,"style":4598},[1204],[1124,32844,32846,32849],{"className":32845},[1209],[1124,32847,4370],{"className":32848},[1209,1213],[1124,32850,32852],{"className":32851},[1217],[1124,32853,32855],{"className":32854},[1221],[1124,32856,32858],{"className":32857},[1226],[1124,32859,32861],{"className":32860,"style":4598},[1230],[1124,32862,32863,32866],{"style":3905},[1124,32864],{"className":32865,"style":1239},[1238],[1124,32867,32869],{"className":32868},[1243,1244,1245,1246],[1124,32870,1152],{"className":32871},[1209,1246],[1124,32873],{"className":32874,"style":1774},[1271],[1124,32876,3579],{"className":32877},[1778],[1124,32879],{"className":32880,"style":1774},[1271],[1124,32882,32884,32887,32916,32919,32922],{"className":32883},[1200],[1124,32885],{"className":32886,"style":4598},[1204],[1124,32888,32890,32893],{"className":32889},[1209],[1124,32891,2680],{"className":32892,"style":2707},[1209,1213],[1124,32894,32896],{"className":32895},[1217],[1124,32897,32899],{"className":32898},[1221],[1124,32900,32902],{"className":32901},[1226],[1124,32903,32905],{"className":32904,"style":4598},[1230],[1124,32906,32907,32910],{"style":3905},[1124,32908],{"className":32909,"style":1239},[1238],[1124,32911,32913],{"className":32912},[1243,1244,1245,1246],[1124,32914,1164],{"className":32915},[1209,1246],[1124,32917],{"className":32918,"style":1774},[1271],[1124,32920,3579],{"className":32921},[1778],[1124,32923],{"className":32924,"style":1774},[1271],[1124,32926,32928,32931,32960,32963,32966],{"className":32927},[1200],[1124,32929],{"className":32930,"style":4598},[1204],[1124,32932,32934,32937],{"className":32933},[1209],[1124,32935,4370],{"className":32936},[1209,1213],[1124,32938,32940],{"className":32939},[1217],[1124,32941,32943],{"className":32942},[1221],[1124,32944,32946],{"className":32945},[1226],[1124,32947,32949],{"className":32948,"style":4598},[1230],[1124,32950,32951,32954],{"style":3905},[1124,32952],{"className":32953,"style":1239},[1238],[1124,32955,32957],{"className":32956},[1243,1244,1245,1246],[1124,32958,1164],{"className":32959},[1209,1246],[1124,32961],{"className":32962,"style":1774},[1271],[1124,32964,3579],{"className":32965},[1778],[1124,32967],{"className":32968,"style":1774},[1271],[1124,32970,32972,32975],{"className":32971},[1200],[1124,32973],{"className":32974,"style":4804},[1204],[1124,32976,4325],{"className":32977,"style":4392},[1209,1213],[1101,32979,32980,32981,33039,33040,33234,33235,33286],{},"与 ",[1124,32982,32984,33001],{"className":32983},[1127],[1124,32985,32987],{"className":32986},[1131],[1133,32988,32989],{"xmlns":1135},[1137,32990,32991,32999],{},[1140,32992,32993],{},[2922,32994,32995,32997],{},[1146,32996,1439],{},[1150,32998,1152],{},[1189,33000,20502],{"encoding":1191},[1124,33002,33004],{"className":33003,"ariaHidden":1156},[1196],[1124,33005,33007,33010],{"className":33006},[1200],[1124,33008],{"className":33009,"style":4598},[1204],[1124,33011,33013,33016],{"className":33012},[1209],[1124,33014,1439],{"className":33015,"style":1480},[1209,1213],[1124,33017,33019],{"className":33018},[1217],[1124,33020,33022],{"className":33021},[1221],[1124,33023,33025],{"className":33024},[1226],[1124,33026,33028],{"className":33027,"style":4598},[1230],[1124,33029,33030,33033],{"style":3905},[1124,33031],{"className":33032,"style":1239},[1238],[1124,33034,33036],{"className":33035},[1243,1244,1245,1246],[1124,33037,1152],{"className":33038},[1209,1246]," 的链路只有最后一项不同：",[1124,33041,33043,33081],{"className":33042},[1127],[1124,33044,33046],{"className":33045},[1131],[1133,33047,33048],{"xmlns":1135},[1137,33049,33050,33078],{},[1140,33051,33052,33074,33076],{},[2911,33053,33054,33064],{},[1140,33055,33056,33058],{},[1146,33057,3164],{"mathvariant":3145},[2922,33059,33060,33062],{},[1146,33061,2680],{},[1150,33063,1152],{},[1140,33065,33066,33068],{},[1146,33067,3164],{"mathvariant":3145},[2922,33069,33070,33072],{},[1146,33071,2230],{},[1150,33073,1152],{},[1154,33075,1652],{},[1150,33077,1152],{},[1189,33079,33080],{"encoding":1191},"\\frac{\\partial z^1}{\\partial b^1} = 1",[1124,33082,33084,33225],{"className":33083,"ariaHidden":1156},[1196],[1124,33085,33087,33090,33216,33219,33222],{"className":33086},[1200],[1124,33088],{"className":33089,"style":25134},[1204],[1124,33091,33093,33096,33213],{"className":33092},[1209],[1124,33094],{"className":33095},[1795,2212],[1124,33097,33099],{"className":33098},[2911],[1124,33100,33102,33205],{"className":33101},[1221,1222],[1124,33103,33105,33202],{"className":33104},[1226],[1124,33106,33108,33151,33159],{"className":33107,"style":25153},[1230],[1124,33109,33110,33113],{"style":2994},[1124,33111],{"className":33112,"style":2998},[1238],[1124,33114,33116],{"className":33115},[1243,1244,1245,1246],[1124,33117,33119,33122],{"className":33118},[1209,1246],[1124,33120,3164],{"className":33121,"style":3319},[1209,1246],[1124,33123,33125,33128],{"className":33124},[1209,1246],[1124,33126,2230],{"className":33127},[1209,1213,1246],[1124,33129,33131],{"className":33130},[1217],[1124,33132,33134],{"className":33133},[1221],[1124,33135,33137],{"className":33136},[1226],[1124,33138,33140],{"className":33139,"style":22067},[1230],[1124,33141,33142,33145],{"style":3032},[1124,33143],{"className":33144,"style":3036},[1238],[1124,33146,33148],{"className":33147},[1243,3040,3041,1246],[1124,33149,1152],{"className":33150},[1209,1246],[1124,33152,33153,33156],{"style":3053},[1124,33154],{"className":33155,"style":2998},[1238],[1124,33157],{"className":33158,"style":3061},[3060],[1124,33160,33161,33164],{"style":3064},[1124,33162],{"className":33163,"style":2998},[1238],[1124,33165,33167],{"className":33166},[1243,1244,1245,1246],[1124,33168,33170,33173],{"className":33169},[1209,1246],[1124,33171,3164],{"className":33172,"style":3319},[1209,1246],[1124,33174,33176,33179],{"className":33175},[1209,1246],[1124,33177,2680],{"className":33178,"style":2707},[1209,1213,1246],[1124,33180,33182],{"className":33181},[1217],[1124,33183,33185],{"className":33184},[1221],[1124,33186,33188],{"className":33187},[1226],[1124,33189,33191],{"className":33190,"style":25237},[1230],[1124,33192,33193,33196],{"style":25240},[1124,33194],{"className":33195,"style":3036},[1238],[1124,33197,33199],{"className":33198},[1243,3040,3041,1246],[1124,33200,1152],{"className":33201},[1209,1246],[1124,33203,1254],{"className":33204},[1253],[1124,33206,33208],{"className":33207},[1226],[1124,33209,33211],{"className":33210,"style":3538},[1230],[1124,33212],{},[1124,33214],{"className":33215},[2211,2212],[1124,33217],{"className":33218,"style":1774},[1271],[1124,33220,1652],{"className":33221},[1778],[1124,33223],{"className":33224,"style":1774},[1271],[1124,33226,33228,33231],{"className":33227},[1200],[1124,33229],{"className":33230,"style":3685},[1204],[1124,33232,1152],{"className":33233},[1209],"（而不是 ",[1124,33236,33238,33256],{"className":33237},[1127],[1124,33239,33241],{"className":33240},[1131],[1133,33242,33243],{"xmlns":1135},[1137,33244,33245,33253],{},[1140,33246,33247,33249,33251],{},[1146,33248,1148],{},[1154,33250,1652],{},[1150,33252,1164],{},[1189,33254,33255],{"encoding":1191},"x = 2",[1124,33257,33259,33277],{"className":33258,"ariaHidden":1156},[1196],[1124,33260,33262,33265,33268,33271,33274],{"className":33261},[1200],[1124,33263],{"className":33264,"style":3124},[1204],[1124,33266,1148],{"className":33267},[1209,1213],[1124,33269],{"className":33270,"style":1774},[1271],[1124,33272,1652],{"className":33273},[1778],[1124,33275],{"className":33276,"style":1774},[1271],[1124,33278,33280,33283],{"className":33279},[1200],[1124,33281],{"className":33282,"style":3685},[1204],[1124,33284,1164],{"className":33285},[1209],"）",[1101,33288,33289],{},[1124,33290,33292,33364],{"className":33291},[1127],[1124,33293,33295],{"className":33294},[1131],[1133,33296,33297],{"xmlns":1135},[1137,33298,33299,33361],{},[1140,33300,33301,33319,33321,33323,33325,33327,33329,33331,33333,33335,33337,33339,33341,33343,33345,33347],{},[2911,33302,33303,33309],{},[1140,33304,33305,33307],{},[1146,33306,3164],{"mathvariant":3145},[1146,33308,4325],{},[1140,33310,33311,33313],{},[1146,33312,3164],{"mathvariant":3145},[2922,33314,33315,33317],{},[1146,33316,2230],{},[1150,33318,1152],{},[1154,33320,1652],{},[1154,33322,2677],{"stretchy":1674},[1154,33324,2235],{},[1150,33326,23096],{},[1154,33328,2683],{"stretchy":1674},[1154,33330,10608],{},[1150,33332,25785],{},[1154,33334,10608],{},[1150,33336,10186],{},[1154,33338,10608],{},[1150,33340,31302],{},[1154,33342,10608],{},[1150,33344,1152],{},[1154,33346,1652],{},[8168,33348,33349],{"notation":8170},[1671,33350,33351],{"scriptlevel":1673,"displaystyle":1674},[1671,33352,33353],{"scriptlevel":1673,"displaystyle":1674},[1671,33354,33355],{"scriptlevel":1673,"displaystyle":1156},[1140,33356,33357,33359],{},[1154,33358,2235],{},[1150,33360,32398],{},[1189,33362,33363],{"encoding":1191},"\\frac{\\partial C}{\\partial b^1} = (-0.348) \\times 0.227 \\times 0.6 \\times 0.205 \\times 1 = \\boxed{-0.00972}",[1124,33365,33367,33482,33509,33527,33545,33563,33581],{"className":33366,"ariaHidden":1156},[1196],[1124,33368,33370,33373,33473,33476,33479],{"className":33369},[1200],[1124,33371],{"className":33372,"style":23920},[1204],[1124,33374,33376,33379,33470],{"className":33375},[1209],[1124,33377],{"className":33378},[1795,2212],[1124,33380,33382],{"className":33381},[2911],[1124,33383,33385,33462],{"className":33384},[1221,1222],[1124,33386,33388,33459],{"className":33387},[1226],[1124,33389,33391,33434,33442],{"className":33390,"style":4858},[1230],[1124,33392,33393,33396],{"style":2994},[1124,33394],{"className":33395,"style":2998},[1238],[1124,33397,33399],{"className":33398},[1243,1244,1245,1246],[1124,33400,33402,33405],{"className":33401},[1209,1246],[1124,33403,3164],{"className":33404,"style":3319},[1209,1246],[1124,33406,33408,33411],{"className":33407},[1209,1246],[1124,33409,2230],{"className":33410},[1209,1213,1246],[1124,33412,33414],{"className":33413},[1217],[1124,33415,33417],{"className":33416},[1221],[1124,33418,33420],{"className":33419},[1226],[1124,33421,33423],{"className":33422,"style":22067},[1230],[1124,33424,33425,33428],{"style":3032},[1124,33426],{"className":33427,"style":3036},[1238],[1124,33429,33431],{"className":33430},[1243,3040,3041,1246],[1124,33432,1152],{"className":33433},[1209,1246],[1124,33435,33436,33439],{"style":3053},[1124,33437],{"className":33438,"style":2998},[1238],[1124,33440],{"className":33441,"style":3061},[3060],[1124,33443,33444,33447],{"style":3064},[1124,33445],{"className":33446,"style":2998},[1238],[1124,33448,33450],{"className":33449},[1243,1244,1245,1246],[1124,33451,33453,33456],{"className":33452},[1209,1246],[1124,33454,3164],{"className":33455,"style":3319},[1209,1246],[1124,33457,4325],{"className":33458,"style":4392},[1209,1213,1246],[1124,33460,1254],{"className":33461},[1253],[1124,33463,33465],{"className":33464},[1226],[1124,33466,33468],{"className":33467,"style":3538},[1230],[1124,33469],{},[1124,33471],{"className":33472},[2211,2212],[1124,33474],{"className":33475,"style":1774},[1271],[1124,33477,1652],{"className":33478},[1778],[1124,33480],{"className":33481,"style":1774},[1271],[1124,33483,33485,33488,33491,33494,33497,33500,33503,33506],{"className":33484},[1200],[1124,33486],{"className":33487,"style":2696},[1204],[1124,33489,2677],{"className":33490},[1795],[1124,33492,2235],{"className":33493},[1209],[1124,33495,23096],{"className":33496},[1209],[1124,33498,2683],{"className":33499},[2211],[1124,33501],{"className":33502,"style":2500},[1271],[1124,33504,10608],{"className":33505},[2504],[1124,33507],{"className":33508,"style":2500},[1271],[1124,33510,33512,33515,33518,33521,33524],{"className":33511},[1200],[1124,33513],{"className":33514,"style":10423},[1204],[1124,33516,25785],{"className":33517},[1209],[1124,33519],{"className":33520,"style":2500},[1271],[1124,33522,10608],{"className":33523},[2504],[1124,33525],{"className":33526,"style":2500},[1271],[1124,33528,33530,33533,33536,33539,33542],{"className":33529},[1200],[1124,33531],{"className":33532,"style":10423},[1204],[1124,33534,10186],{"className":33535},[1209],[1124,33537],{"className":33538,"style":2500},[1271],[1124,33540,10608],{"className":33541},[2504],[1124,33543],{"className":33544,"style":2500},[1271],[1124,33546,33548,33551,33554,33557,33560],{"className":33547},[1200],[1124,33549],{"className":33550,"style":10423},[1204],[1124,33552,31302],{"className":33553},[1209],[1124,33555],{"className":33556,"style":2500},[1271],[1124,33558,10608],{"className":33559},[2504],[1124,33561],{"className":33562,"style":2500},[1271],[1124,33564,33566,33569,33572,33575,33578],{"className":33565},[1200],[1124,33567],{"className":33568,"style":3685},[1204],[1124,33570,1152],{"className":33571},[1209],[1124,33573],{"className":33574,"style":1774},[1271],[1124,33576,1652],{"className":33577},[1778],[1124,33579],{"className":33580,"style":1774},[1271],[1124,33582,33584,33587],{"className":33583},[1200],[1124,33585],{"className":33586,"style":26667},[1204],[1124,33588,33590],{"className":33589},[1209],[1124,33591,33593,33630],{"className":33592},[1221,1222],[1124,33594,33596,33627],{"className":33595},[1226],[1124,33597,33599,33619],{"className":33598,"style":12358},[1230],[1124,33600,33601,33604],{"style":26682},[1124,33602],{"className":33603,"style":26686},[1238],[1124,33605,33607],{"className":33606},[8257],[1124,33608,33610],{"className":33609},[1209],[1124,33611,33613,33616],{"className":33612},[1209],[1124,33614,2235],{"className":33615},[1209],[1124,33617,32398],{"className":33618},[1209],[1124,33620,33621,33624],{"style":12380},[1124,33622],{"className":33623,"style":26686},[1238],[1124,33625],{"className":33626,"style":26710},[8436,8437],[1124,33628,1254],{"className":33629},[1253],[1124,33631,33633],{"className":33632},[1226],[1124,33634,33636],{"className":33635,"style":26720},[1230],[1124,33637],{},[28185,33639,33640,34014,34017],{},[1101,33641,33642,33643],{},"隐藏层误差：",[1124,33644,33646,33722],{"className":33645},[1127],[1124,33647,33649],{"className":33648},[1131],[1133,33650,33651],{"xmlns":1135},[1137,33652,33653,33719],{},[1140,33654,33655,33661,33663,33669,33671,33677,33679,33685,33687,33693,33695,33697,33699,33701,33703,33705,33707,33709,33711,33713,33715,33717],{},[2922,33656,33657,33659],{},[1146,33658,13138],{},[1150,33660,1152],{},[1154,33662,1652],{},[2922,33664,33665,33667],{},[1146,33666,1439],{},[1150,33668,1164],{},[1154,33670,2325],{},[2922,33672,33673,33675],{},[1146,33674,13138],{},[1150,33676,1164],{},[1154,33678,2325],{},[2922,33680,33681,33683],{},[1146,33682,2674],{},[1154,33684,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,33686,2677],{"stretchy":1674},[2922,33688,33689,33691],{},[1146,33690,2680],{},[1150,33692,1152],{},[1154,33694,2683],{"stretchy":1674},[1154,33696,1652],{},[1150,33698,10186],{},[1154,33700,10608],{},[1154,33702,2677],{"stretchy":1674},[1154,33704,2235],{},[1150,33706,27940],{},[1154,33708,2683],{"stretchy":1674},[1154,33710,10608],{},[1150,33712,31302],{},[1154,33714,1652],{},[1154,33716,2235],{},[1150,33718,32398],{},[1189,33720,33721],{"encoding":1191},"\\delta^1 = w^2 \\cdot \\delta^2 \\cdot \\sigma'(z^1) = 0.6 \\times (-0.0790) \\times 0.205 = -0.00972",[1124,33723,33725,33769,33813,33857,33939,33957,33984,34002],{"className":33724,"ariaHidden":1156},[1196],[1124,33726,33728,33731,33760,33763,33766],{"className":33727},[1200],[1124,33729],{"className":33730,"style":4598},[1204],[1124,33732,33734,33737],{"className":33733},[1209],[1124,33735,13138],{"className":33736,"style":13161},[1209,1213],[1124,33738,33740],{"className":33739},[1217],[1124,33741,33743],{"className":33742},[1221],[1124,33744,33746],{"className":33745},[1226],[1124,33747,33749],{"className":33748,"style":4598},[1230],[1124,33750,33751,33754],{"style":3905},[1124,33752],{"className":33753,"style":1239},[1238],[1124,33755,33757],{"className":33756},[1243,1244,1245,1246],[1124,33758,1152],{"className":33759},[1209,1246],[1124,33761],{"className":33762,"style":1774},[1271],[1124,33764,1652],{"className":33765},[1778],[1124,33767],{"className":33768,"style":1774},[1271],[1124,33770,33772,33775,33804,33807,33810],{"className":33771},[1200],[1124,33773],{"className":33774,"style":4598},[1204],[1124,33776,33778,33781],{"className":33777},[1209],[1124,33779,1439],{"className":33780,"style":1480},[1209,1213],[1124,33782,33784],{"className":33783},[1217],[1124,33785,33787],{"className":33786},[1221],[1124,33788,33790],{"className":33789},[1226],[1124,33791,33793],{"className":33792,"style":4598},[1230],[1124,33794,33795,33798],{"style":3905},[1124,33796],{"className":33797,"style":1239},[1238],[1124,33799,33801],{"className":33800},[1243,1244,1245,1246],[1124,33802,1164],{"className":33803},[1209,1246],[1124,33805],{"className":33806,"style":2500},[1271],[1124,33808,2325],{"className":33809},[2504],[1124,33811],{"className":33812,"style":2500},[1271],[1124,33814,33816,33819,33848,33851,33854],{"className":33815},[1200],[1124,33817],{"className":33818,"style":4598},[1204],[1124,33820,33822,33825],{"className":33821},[1209],[1124,33823,13138],{"className":33824,"style":13161},[1209,1213],[1124,33826,33828],{"className":33827},[1217],[1124,33829,33831],{"className":33830},[1221],[1124,33832,33834],{"className":33833},[1226],[1124,33835,33837],{"className":33836,"style":4598},[1230],[1124,33838,33839,33842],{"style":3905},[1124,33840],{"className":33841,"style":1239},[1238],[1124,33843,33845],{"className":33844},[1243,1244,1245,1246],[1124,33846,1164],{"className":33847},[1209,1246],[1124,33849],{"className":33850,"style":2500},[1271],[1124,33852,2325],{"className":33853},[2504],[1124,33855],{"className":33856,"style":2500},[1271],[1124,33858,33860,33863,33895,33898,33927,33930,33933,33936],{"className":33859},[1200],[1124,33861],{"className":33862,"style":4576},[1204],[1124,33864,33866,33869],{"className":33865},[1209],[1124,33867,2674],{"className":33868,"style":2700},[1209,1213],[1124,33870,33872],{"className":33871},[1217],[1124,33873,33875],{"className":33874},[1221],[1124,33876,33878],{"className":33877},[1226],[1124,33879,33881],{"className":33880,"style":3902},[1230],[1124,33882,33883,33886],{"style":3905},[1124,33884],{"className":33885,"style":1239},[1238],[1124,33887,33889],{"className":33888},[1243,1244,1245,1246],[1124,33890,33892],{"className":33891},[1209,1246],[1124,33893,3838],{"className":33894},[1209,1246],[1124,33896,2677],{"className":33897},[1795],[1124,33899,33901,33904],{"className":33900},[1209],[1124,33902,2680],{"className":33903,"style":2707},[1209,1213],[1124,33905,33907],{"className":33906},[1217],[1124,33908,33910],{"className":33909},[1221],[1124,33911,33913],{"className":33912},[1226],[1124,33914,33916],{"className":33915,"style":4598},[1230],[1124,33917,33918,33921],{"style":3905},[1124,33919],{"className":33920,"style":1239},[1238],[1124,33922,33924],{"className":33923},[1243,1244,1245,1246],[1124,33925,1152],{"className":33926},[1209,1246],[1124,33928,2683],{"className":33929},[2211],[1124,33931],{"className":33932,"style":1774},[1271],[1124,33934,1652],{"className":33935},[1778],[1124,33937],{"className":33938,"style":1774},[1271],[1124,33940,33942,33945,33948,33951,33954],{"className":33941},[1200],[1124,33943],{"className":33944,"style":10423},[1204],[1124,33946,10186],{"className":33947},[1209],[1124,33949],{"className":33950,"style":2500},[1271],[1124,33952,10608],{"className":33953},[2504],[1124,33955],{"className":33956,"style":2500},[1271],[1124,33958,33960,33963,33966,33969,33972,33975,33978,33981],{"className":33959},[1200],[1124,33961],{"className":33962,"style":2696},[1204],[1124,33964,2677],{"className":33965},[1795],[1124,33967,2235],{"className":33968},[1209],[1124,33970,27940],{"className":33971},[1209],[1124,33973,2683],{"className":33974},[2211],[1124,33976],{"className":33977,"style":2500},[1271],[1124,33979,10608],{"className":33980},[2504],[1124,33982],{"className":33983,"style":2500},[1271],[1124,33985,33987,33990,33993,33996,33999],{"className":33986},[1200],[1124,33988],{"className":33989,"style":3685},[1204],[1124,33991,31302],{"className":33992},[1209],[1124,33994],{"className":33995,"style":1774},[1271],[1124,33997,1652],{"className":33998},[1778],[1124,34000],{"className":34001,"style":1774},[1271],[1124,34003,34005,34008,34011],{"className":34004},[1200],[1124,34006],{"className":34007,"style":10423},[1204],[1124,34009,2235],{"className":34010},[1209],[1124,34012,32398],{"className":34013},[1209],[1101,34015,34016],{},"验证：",[1117,34018,34019,34313],{},[1120,34020,34021,28961],{},[1124,34022,34024,34082],{"className":34023},[1127],[1124,34025,34027],{"className":34026},[1131],[1133,34028,34029],{"xmlns":1135},[1137,34030,34031,34079],{},[1140,34032,34033,34051,34053,34059,34061,34063,34065,34067,34069,34071,34073,34075,34077],{},[2911,34034,34035,34041],{},[1140,34036,34037,34039],{},[1146,34038,3164],{"mathvariant":3145},[1146,34040,4325],{},[1140,34042,34043,34045],{},[1146,34044,3164],{"mathvariant":3145},[2922,34046,34047,34049],{},[1146,34048,1439],{},[1150,34050,1152],{},[1154,34052,1652],{},[2922,34054,34055,34057],{},[1146,34056,13138],{},[1150,34058,1152],{},[1154,34060,2325],{},[1146,34062,1148],{},[1154,34064,1652],{},[1154,34066,2235],{},[1150,34068,32398],{},[1154,34070,10608],{},[1150,34072,21217],{},[1154,34074,1652],{},[1154,34076,2235],{},[1150,34078,32419],{},[1189,34080,34081],{"encoding":1191},"\\frac{\\partial C}{\\partial w^1} = \\delta^1 \\cdot x = -0.00972 \\times 2.0 = -0.0194",[1124,34083,34085,34200,34244,34262,34283,34301],{"className":34084,"ariaHidden":1156},[1196],[1124,34086,34088,34091,34191,34194,34197],{"className":34087},[1200],[1124,34089],{"className":34090,"style":23920},[1204],[1124,34092,34094,34097,34188],{"className":34093},[1209],[1124,34095],{"className":34096},[1795,2212],[1124,34098,34100],{"className":34099},[2911],[1124,34101,34103,34180],{"className":34102},[1221,1222],[1124,34104,34106,34177],{"className":34105},[1226],[1124,34107,34109,34152,34160],{"className":34108,"style":4858},[1230],[1124,34110,34111,34114],{"style":2994},[1124,34112],{"className":34113,"style":2998},[1238],[1124,34115,34117],{"className":34116},[1243,1244,1245,1246],[1124,34118,34120,34123],{"className":34119},[1209,1246],[1124,34121,3164],{"className":34122,"style":3319},[1209,1246],[1124,34124,34126,34129],{"className":34125},[1209,1246],[1124,34127,1439],{"className":34128,"style":1480},[1209,1213,1246],[1124,34130,34132],{"className":34131},[1217],[1124,34133,34135],{"className":34134},[1221],[1124,34136,34138],{"className":34137},[1226],[1124,34139,34141],{"className":34140,"style":22067},[1230],[1124,34142,34143,34146],{"style":3032},[1124,34144],{"className":34145,"style":3036},[1238],[1124,34147,34149],{"className":34148},[1243,3040,3041,1246],[1124,34150,1152],{"className":34151},[1209,1246],[1124,34153,34154,34157],{"style":3053},[1124,34155],{"className":34156,"style":2998},[1238],[1124,34158],{"className":34159,"style":3061},[3060],[1124,34161,34162,34165],{"style":3064},[1124,34163],{"className":34164,"style":2998},[1238],[1124,34166,34168],{"className":34167},[1243,1244,1245,1246],[1124,34169,34171,34174],{"className":34170},[1209,1246],[1124,34172,3164],{"className":34173,"style":3319},[1209,1246],[1124,34175,4325],{"className":34176,"style":4392},[1209,1213,1246],[1124,34178,1254],{"className":34179},[1253],[1124,34181,34183],{"className":34182},[1226],[1124,34184,34186],{"className":34185,"style":3538},[1230],[1124,34187],{},[1124,34189],{"className":34190},[2211,2212],[1124,34192],{"className":34193,"style":1774},[1271],[1124,34195,1652],{"className":34196},[1778],[1124,34198],{"className":34199,"style":1774},[1271],[1124,34201,34203,34206,34235,34238,34241],{"className":34202},[1200],[1124,34204],{"className":34205,"style":4598},[1204],[1124,34207,34209,34212],{"className":34208},[1209],[1124,34210,13138],{"className":34211,"style":13161},[1209,1213],[1124,34213,34215],{"className":34214},[1217],[1124,34216,34218],{"className":34217},[1221],[1124,34219,34221],{"className":34220},[1226],[1124,34222,34224],{"className":34223,"style":4598},[1230],[1124,34225,34226,34229],{"style":3905},[1124,34227],{"className":34228,"style":1239},[1238],[1124,34230,34232],{"className":34231},[1243,1244,1245,1246],[1124,34233,1152],{"className":34234},[1209,1246],[1124,34236],{"className":34237,"style":2500},[1271],[1124,34239,2325],{"className":34240},[2504],[1124,34242],{"className":34243,"style":2500},[1271],[1124,34245,34247,34250,34253,34256,34259],{"className":34246},[1200],[1124,34248],{"className":34249,"style":3124},[1204],[1124,34251,1148],{"className":34252},[1209,1213],[1124,34254],{"className":34255,"style":1774},[1271],[1124,34257,1652],{"className":34258},[1778],[1124,34260],{"className":34261,"style":1774},[1271],[1124,34263,34265,34268,34271,34274,34277,34280],{"className":34264},[1200],[1124,34266],{"className":34267,"style":10423},[1204],[1124,34269,2235],{"className":34270},[1209],[1124,34272,32398],{"className":34273},[1209],[1124,34275],{"className":34276,"style":2500},[1271],[1124,34278,10608],{"className":34279},[2504],[1124,34281],{"className":34282,"style":2500},[1271],[1124,34284,34286,34289,34292,34295,34298],{"className":34285},[1200],[1124,34287],{"className":34288,"style":3685},[1204],[1124,34290,21217],{"className":34291},[1209],[1124,34293],{"className":34294,"style":1774},[1271],[1124,34296,1652],{"className":34297},[1778],[1124,34299],{"className":34300,"style":1774},[1271],[1124,34302,34304,34307,34310],{"className":34303},[1200],[1124,34305],{"className":34306,"style":10423},[1204],[1124,34308,2235],{"className":34309},[1209],[1124,34311,32419],{"className":34312},[1209],[1120,34314,34315,28961],{},[1124,34316,34318,34362],{"className":34317},[1127],[1124,34319,34321],{"className":34320},[1131],[1133,34322,34323],{"xmlns":1135},[1137,34324,34325,34359],{},[1140,34326,34327,34345,34347,34353,34355,34357],{},[2911,34328,34329,34335],{},[1140,34330,34331,34333],{},[1146,34332,3164],{"mathvariant":3145},[1146,34334,4325],{},[1140,34336,34337,34339],{},[1146,34338,3164],{"mathvariant":3145},[2922,34340,34341,34343],{},[1146,34342,2230],{},[1150,34344,1152],{},[1154,34346,1652],{},[2922,34348,34349,34351],{},[1146,34350,13138],{},[1150,34352,1152],{},[1154,34354,1652],{},[1154,34356,2235],{},[1150,34358,32398],{},[1189,34360,34361],{"encoding":1191},"\\frac{\\partial C}{\\partial b^1} = \\delta^1 = -0.00972",[1124,34363,34365,34480,34524],{"className":34364,"ariaHidden":1156},[1196],[1124,34366,34368,34371,34471,34474,34477],{"className":34367},[1200],[1124,34369],{"className":34370,"style":23920},[1204],[1124,34372,34374,34377,34468],{"className":34373},[1209],[1124,34375],{"className":34376},[1795,2212],[1124,34378,34380],{"className":34379},[2911],[1124,34381,34383,34460],{"className":34382},[1221,1222],[1124,34384,34386,34457],{"className":34385},[1226],[1124,34387,34389,34432,34440],{"className":34388,"style":4858},[1230],[1124,34390,34391,34394],{"style":2994},[1124,34392],{"className":34393,"style":2998},[1238],[1124,34395,34397],{"className":34396},[1243,1244,1245,1246],[1124,34398,34400,34403],{"className":34399},[1209,1246],[1124,34401,3164],{"className":34402,"style":3319},[1209,1246],[1124,34404,34406,34409],{"className":34405},[1209,1246],[1124,34407,2230],{"className":34408},[1209,1213,1246],[1124,34410,34412],{"className":34411},[1217],[1124,34413,34415],{"className":34414},[1221],[1124,34416,34418],{"className":34417},[1226],[1124,34419,34421],{"className":34420,"style":22067},[1230],[1124,34422,34423,34426],{"style":3032},[1124,34424],{"className":34425,"style":3036},[1238],[1124,34427,34429],{"className":34428},[1243,3040,3041,1246],[1124,34430,1152],{"className":34431},[1209,1246],[1124,34433,34434,34437],{"style":3053},[1124,34435],{"className":34436,"style":2998},[1238],[1124,34438],{"className":34439,"style":3061},[3060],[1124,34441,34442,34445],{"style":3064},[1124,34443],{"className":34444,"style":2998},[1238],[1124,34446,34448],{"className":34447},[1243,1244,1245,1246],[1124,34449,34451,34454],{"className":34450},[1209,1246],[1124,34452,3164],{"className":34453,"style":3319},[1209,1246],[1124,34455,4325],{"className":34456,"style":4392},[1209,1213,1246],[1124,34458,1254],{"className":34459},[1253],[1124,34461,34463],{"className":34462},[1226],[1124,34464,34466],{"className":34465,"style":3538},[1230],[1124,34467],{},[1124,34469],{"className":34470},[2211,2212],[1124,34472],{"className":34473,"style":1774},[1271],[1124,34475,1652],{"className":34476},[1778],[1124,34478],{"className":34479,"style":1774},[1271],[1124,34481,34483,34486,34515,34518,34521],{"className":34482},[1200],[1124,34484],{"className":34485,"style":4598},[1204],[1124,34487,34489,34492],{"className":34488},[1209],[1124,34490,13138],{"className":34491,"style":13161},[1209,1213],[1124,34493,34495],{"className":34494},[1217],[1124,34496,34498],{"className":34497},[1221],[1124,34499,34501],{"className":34500},[1226],[1124,34502,34504],{"className":34503,"style":4598},[1230],[1124,34505,34506,34509],{"style":3905},[1124,34507],{"className":34508,"style":1239},[1238],[1124,34510,34512],{"className":34511},[1243,1244,1245,1246],[1124,34513,1152],{"className":34514},[1209,1246],[1124,34516],{"className":34517,"style":1774},[1271],[1124,34519,1652],{"className":34520},[1778],[1124,34522],{"className":34523,"style":1774},[1271],[1124,34525,34527,34530,34533],{"className":34526},[1200],[1124,34528],{"className":34529,"style":10423},[1204],[1124,34531,2235],{"className":34532},[1209],[1124,34534,32398],{"className":34535},[1209],[1101,34537,34538],{},[1107,34539,34540],{},"链式法则 = 路径上所有偏导数连乘：从 C 到任何参数，就是沿着依赖路径把每一步的局部导数相乘",[28185,34542,34543],{},[1101,34544,34545,34546,34623],{},"反向传播就是从输出层开始，沿着\"C → a² → z² → a¹ → z¹ → 参数\"的路径，用链式法则把每一步的局部导数连乘起来，得到代价函数对每个参数的梯度。误差像水流一样从后往前\"流淌\"，每经过一层就被 ",[1124,34547,34549,34573],{"className":34548},[1127],[1124,34550,34552],{"className":34551},[1131],[1133,34553,34554],{"xmlns":1135},[1137,34555,34556,34570],{},[1140,34557,34558,34564,34566,34568],{},[2922,34559,34560,34562],{},[1146,34561,2674],{},[1154,34563,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,34565,2677],{"stretchy":1674},[1146,34567,2680],{},[1154,34569,2683],{"stretchy":1674},[1189,34571,34572],{"encoding":1191},"\\sigma'(z)",[1124,34574,34576],{"className":34575,"ariaHidden":1156},[1196],[1124,34577,34579,34582,34614,34617,34620],{"className":34578},[1200],[1124,34580],{"className":34581,"style":3883},[1204],[1124,34583,34585,34588],{"className":34584},[1209],[1124,34586,2674],{"className":34587,"style":2700},[1209,1213],[1124,34589,34591],{"className":34590},[1217],[1124,34592,34594],{"className":34593},[1221],[1124,34595,34597],{"className":34596},[1226],[1124,34598,34600],{"className":34599,"style":3902},[1230],[1124,34601,34602,34605],{"style":3905},[1124,34603],{"className":34604,"style":1239},[1238],[1124,34606,34608],{"className":34607},[1243,1244,1245,1246],[1124,34609,34611],{"className":34610},[1209,1246],[1124,34612,3838],{"className":34613},[1209,1246],[1124,34615,2677],{"className":34616},[1795],[1124,34618,2680],{"className":34619,"style":2707},[1209,1213],[1124,34621,2683],{"className":34622},[2211]," 和权重\"衰减\"一些——这既是反向传播的精妙之处，也是深层网络梯度消失的根源。",[2745,34625],{},[1096,34627,34629],{"id":34628},"梯度汇总-参数更新","梯度汇总 & 参数更新",[2616,34631,34632,34759],{},[2619,34633,34634],{},[2622,34635,34636,34638,34640,34756],{},[2625,34637,20920],{},[2625,34639,4720],{},[2625,34641,34642,34643,4720],{},"更新：",[1124,34644,34646,34675],{"className":34645},[1127],[1124,34647,34649],{"className":34648},[1131],[1133,34650,34651],{"xmlns":1135},[1137,34652,34653,34672],{},[1140,34654,34655,34662,34664,34666,34668,34670],{},[2922,34656,34657,34660],{},[1146,34658,34659],{},"θ",[1154,34661,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,34663,1652],{},[1146,34665,34659],{},[1154,34667,2235],{},[1150,34669,9783],{},[1154,34671,10608],{},[1189,34673,34674],{"encoding":1191},"\\theta' = \\theta - 0.5 \\times",[1124,34676,34678,34726,34744],{"className":34677,"ariaHidden":1156},[1196],[1124,34679,34681,34684,34717,34720,34723],{"className":34680},[1200],[1124,34682],{"className":34683,"style":3902},[1204],[1124,34685,34687,34691],{"className":34686},[1209],[1124,34688,34659],{"className":34689,"style":34690},[1209,1213],"margin-right:0.0278em;",[1124,34692,34694],{"className":34693},[1217],[1124,34695,34697],{"className":34696},[1221],[1124,34698,34700],{"className":34699},[1226],[1124,34701,34703],{"className":34702,"style":3902},[1230],[1124,34704,34705,34708],{"style":3905},[1124,34706],{"className":34707,"style":1239},[1238],[1124,34709,34711],{"className":34710},[1243,1244,1245,1246],[1124,34712,34714],{"className":34713},[1209,1246],[1124,34715,3838],{"className":34716},[1209,1246],[1124,34718],{"className":34719,"style":1774},[1271],[1124,34721,1652],{"className":34722},[1778],[1124,34724],{"className":34725,"style":1774},[1271],[1124,34727,34729,34732,34735,34738,34741],{"className":34728},[1200],[1124,34730],{"className":34731,"style":2269},[1204],[1124,34733,34659],{"className":34734,"style":34690},[1209,1213],[1124,34736],{"className":34737,"style":2500},[1271],[1124,34739,2235],{"className":34740},[2504],[1124,34742],{"className":34743,"style":2500},[1271],[1124,34745,34747,34750,34753],{"className":34746},[1200],[1124,34748],{"className":34749,"style":10423},[1204],[1124,34751,9783],{"className":34752},[1209],[1124,34754,10608],{"className":34755},[1209],[2625,34757,34758],{},"新值",[2635,34760,34761,34921,35081,35241],{},[2622,34762,34763,34823,34826,34916],{},[2640,34764,34765],{},[1124,34766,34768,34785],{"className":34767},[1127],[1124,34769,34771],{"className":34770},[1131],[1133,34772,34773],{"xmlns":1135},[1137,34774,34775,34783],{},[1140,34776,34777],{},[2922,34778,34779,34781],{},[1146,34780,1439],{},[1150,34782,1164],{},[1189,34784,20624],{"encoding":1191},[1124,34786,34788],{"className":34787,"ariaHidden":1156},[1196],[1124,34789,34791,34794],{"className":34790},[1200],[1124,34792],{"className":34793,"style":4598},[1204],[1124,34795,34797,34800],{"className":34796},[1209],[1124,34798,1439],{"className":34799,"style":1480},[1209,1213],[1124,34801,34803],{"className":34802},[1217],[1124,34804,34806],{"className":34805},[1221],[1124,34807,34809],{"className":34808},[1226],[1124,34810,34812],{"className":34811,"style":4598},[1230],[1124,34813,34814,34817],{"style":3905},[1124,34815],{"className":34816,"style":1239},[1238],[1124,34818,34820],{"className":34819},[1243,1244,1245,1246],[1124,34821,1164],{"className":34822},[1209,1246],[2640,34824,34825],{},"-0.0562",[2640,34827,34828],{},[1124,34829,34831,34859],{"className":34830},[1127],[1124,34832,34834],{"className":34833},[1131],[1133,34835,34836],{"xmlns":1135},[1137,34837,34838,34856],{},[1140,34839,34840,34842,34844,34846,34848,34850,34852,34854],{},[1150,34841,10186],{},[1154,34843,2235],{},[1150,34845,9783],{},[1154,34847,10608],{},[1154,34849,2677],{"stretchy":1674},[1154,34851,2235],{},[1150,34853,26476],{},[1154,34855,2683],{"stretchy":1674},[1189,34857,34858],{"encoding":1191},"0.6 - 0.5\\times(-0.0562)",[1124,34860,34862,34880,34898],{"className":34861,"ariaHidden":1156},[1196],[1124,34863,34865,34868,34871,34874,34877],{"className":34864},[1200],[1124,34866],{"className":34867,"style":10423},[1204],[1124,34869,10186],{"className":34870},[1209],[1124,34872],{"className":34873,"style":2500},[1271],[1124,34875,2235],{"className":34876},[2504],[1124,34878],{"className":34879,"style":2500},[1271],[1124,34881,34883,34886,34889,34892,34895],{"className":34882},[1200],[1124,34884],{"className":34885,"style":10423},[1204],[1124,34887,9783],{"className":34888},[1209],[1124,34890],{"className":34891,"style":2500},[1271],[1124,34893,10608],{"className":34894},[2504],[1124,34896],{"className":34897,"style":2500},[1271],[1124,34899,34901,34904,34907,34910,34913],{"className":34900},[1200],[1124,34902],{"className":34903,"style":2696},[1204],[1124,34905,2677],{"className":34906},[1795],[1124,34908,2235],{"className":34909},[1209],[1124,34911,26476],{"className":34912},[1209],[1124,34914,2683],{"className":34915},[2211],[2640,34917,34918],{},[1107,34919,34920],{},"0.628",[2622,34922,34923,34983,34986,35076],{},[2640,34924,34925],{},[1124,34926,34928,34945],{"className":34927},[1127],[1124,34929,34931],{"className":34930},[1131],[1133,34932,34933],{"xmlns":1135},[1137,34934,34935,34943],{},[1140,34936,34937],{},[2922,34938,34939,34941],{},[1146,34940,2230],{},[1150,34942,1164],{},[1189,34944,20683],{"encoding":1191},[1124,34946,34948],{"className":34947,"ariaHidden":1156},[1196],[1124,34949,34951,34954],{"className":34950},[1200],[1124,34952],{"className":34953,"style":4598},[1204],[1124,34955,34957,34960],{"className":34956},[1209],[1124,34958,2230],{"className":34959},[1209,1213],[1124,34961,34963],{"className":34962},[1217],[1124,34964,34966],{"className":34965},[1221],[1124,34967,34969],{"className":34968},[1226],[1124,34970,34972],{"className":34971,"style":4598},[1230],[1124,34973,34974,34977],{"style":3905},[1124,34975],{"className":34976,"style":1239},[1238],[1124,34978,34980],{"className":34979},[1243,1244,1245,1246],[1124,34981,1164],{"className":34982},[1209,1246],[2640,34984,34985],{},"-0.0790",[2640,34987,34988],{},[1124,34989,34991,35019],{"className":34990},[1127],[1124,34992,34994],{"className":34993},[1131],[1133,34995,34996],{"xmlns":1135},[1137,34997,34998,35016],{},[1140,34999,35000,35002,35004,35006,35008,35010,35012,35014],{},[1150,35001,9799],{},[1154,35003,2235],{},[1150,35005,9783],{},[1154,35007,10608],{},[1154,35009,2677],{"stretchy":1674},[1154,35011,2235],{},[1150,35013,27940],{},[1154,35015,2683],{"stretchy":1674},[1189,35017,35018],{"encoding":1191},"0.2 - 0.5\\times(-0.0790)",[1124,35020,35022,35040,35058],{"className":35021,"ariaHidden":1156},[1196],[1124,35023,35025,35028,35031,35034,35037],{"className":35024},[1200],[1124,35026],{"className":35027,"style":10423},[1204],[1124,35029,9799],{"className":35030},[1209],[1124,35032],{"className":35033,"style":2500},[1271],[1124,35035,2235],{"className":35036},[2504],[1124,35038],{"className":35039,"style":2500},[1271],[1124,35041,35043,35046,35049,35052,35055],{"className":35042},[1200],[1124,35044],{"className":35045,"style":10423},[1204],[1124,35047,9783],{"className":35048},[1209],[1124,35050],{"className":35051,"style":2500},[1271],[1124,35053,10608],{"className":35054},[2504],[1124,35056],{"className":35057,"style":2500},[1271],[1124,35059,35061,35064,35067,35070,35073],{"className":35060},[1200],[1124,35062],{"className":35063,"style":2696},[1204],[1124,35065,2677],{"className":35066},[1795],[1124,35068,2235],{"className":35069},[1209],[1124,35071,27940],{"className":35072},[1209],[1124,35074,2683],{"className":35075},[2211],[2640,35077,35078],{},[1107,35079,35080],{},"0.240",[2622,35082,35083,35143,35146,35236],{},[2640,35084,35085],{},[1124,35086,35088,35105],{"className":35087},[1127],[1124,35089,35091],{"className":35090},[1131],[1133,35092,35093],{"xmlns":1135},[1137,35094,35095,35103],{},[1140,35096,35097],{},[2922,35098,35099,35101],{},[1146,35100,1439],{},[1150,35102,1152],{},[1189,35104,20502],{"encoding":1191},[1124,35106,35108],{"className":35107,"ariaHidden":1156},[1196],[1124,35109,35111,35114],{"className":35110},[1200],[1124,35112],{"className":35113,"style":4598},[1204],[1124,35115,35117,35120],{"className":35116},[1209],[1124,35118,1439],{"className":35119,"style":1480},[1209,1213],[1124,35121,35123],{"className":35122},[1217],[1124,35124,35126],{"className":35125},[1221],[1124,35127,35129],{"className":35128},[1226],[1124,35130,35132],{"className":35131,"style":4598},[1230],[1124,35133,35134,35137],{"style":3905},[1124,35135],{"className":35136,"style":1239},[1238],[1124,35138,35140],{"className":35139},[1243,1244,1245,1246],[1124,35141,1152],{"className":35142},[1209,1246],[2640,35144,35145],{},"-0.0194",[2640,35147,35148],{},[1124,35149,35151,35179],{"className":35150},[1127],[1124,35152,35154],{"className":35153},[1131],[1133,35155,35156],{"xmlns":1135},[1137,35157,35158,35176],{},[1140,35159,35160,35162,35164,35166,35168,35170,35172,35174],{},[1150,35161,9792],{},[1154,35163,2235],{},[1150,35165,9783],{},[1154,35167,10608],{},[1154,35169,2677],{"stretchy":1674},[1154,35171,2235],{},[1150,35173,32419],{},[1154,35175,2683],{"stretchy":1674},[1189,35177,35178],{"encoding":1191},"0.4 - 0.5\\times(-0.0194)",[1124,35180,35182,35200,35218],{"className":35181,"ariaHidden":1156},[1196],[1124,35183,35185,35188,35191,35194,35197],{"className":35184},[1200],[1124,35186],{"className":35187,"style":10423},[1204],[1124,35189,9792],{"className":35190},[1209],[1124,35192],{"className":35193,"style":2500},[1271],[1124,35195,2235],{"className":35196},[2504],[1124,35198],{"className":35199,"style":2500},[1271],[1124,35201,35203,35206,35209,35212,35215],{"className":35202},[1200],[1124,35204],{"className":35205,"style":10423},[1204],[1124,35207,9783],{"className":35208},[1209],[1124,35210],{"className":35211,"style":2500},[1271],[1124,35213,10608],{"className":35214},[2504],[1124,35216],{"className":35217,"style":2500},[1271],[1124,35219,35221,35224,35227,35230,35233],{"className":35220},[1200],[1124,35222],{"className":35223,"style":2696},[1204],[1124,35225,2677],{"className":35226},[1795],[1124,35228,2235],{"className":35229},[1209],[1124,35231,32419],{"className":35232},[1209],[1124,35234,2683],{"className":35235},[2211],[2640,35237,35238],{},[1107,35239,35240],{},"0.410",[2622,35242,35243,35303,35306,35396],{},[2640,35244,35245],{},[1124,35246,35248,35265],{"className":35247},[1127],[1124,35249,35251],{"className":35250},[1131],[1133,35252,35253],{"xmlns":1135},[1137,35254,35255,35263],{},[1140,35256,35257],{},[2922,35258,35259,35261],{},[1146,35260,2230],{},[1150,35262,1152],{},[1189,35264,20562],{"encoding":1191},[1124,35266,35268],{"className":35267,"ariaHidden":1156},[1196],[1124,35269,35271,35274],{"className":35270},[1200],[1124,35272],{"className":35273,"style":4598},[1204],[1124,35275,35277,35280],{"className":35276},[1209],[1124,35278,2230],{"className":35279},[1209,1213],[1124,35281,35283],{"className":35282},[1217],[1124,35284,35286],{"className":35285},[1221],[1124,35287,35289],{"className":35288},[1226],[1124,35290,35292],{"className":35291,"style":4598},[1230],[1124,35293,35294,35297],{"style":3905},[1124,35295],{"className":35296,"style":1239},[1238],[1124,35298,35300],{"className":35299},[1243,1244,1245,1246],[1124,35301,1152],{"className":35302},[1209,1246],[2640,35304,35305],{},"-0.00972",[2640,35307,35308],{},[1124,35309,35311,35339],{"className":35310},[1127],[1124,35312,35314],{"className":35313},[1131],[1133,35315,35316],{"xmlns":1135},[1137,35317,35318,35336],{},[1140,35319,35320,35322,35324,35326,35328,35330,35332,35334],{},[1150,35321,9829],{},[1154,35323,2235],{},[1150,35325,9783],{},[1154,35327,10608],{},[1154,35329,2677],{"stretchy":1674},[1154,35331,2235],{},[1150,35333,32398],{},[1154,35335,2683],{"stretchy":1674},[1189,35337,35338],{"encoding":1191},"0.1 - 0.5\\times(-0.00972)",[1124,35340,35342,35360,35378],{"className":35341,"ariaHidden":1156},[1196],[1124,35343,35345,35348,35351,35354,35357],{"className":35344},[1200],[1124,35346],{"className":35347,"style":10423},[1204],[1124,35349,9829],{"className":35350},[1209],[1124,35352],{"className":35353,"style":2500},[1271],[1124,35355,2235],{"className":35356},[2504],[1124,35358],{"className":35359,"style":2500},[1271],[1124,35361,35363,35366,35369,35372,35375],{"className":35362},[1200],[1124,35364],{"className":35365,"style":10423},[1204],[1124,35367,9783],{"className":35368},[1209],[1124,35370],{"className":35371,"style":2500},[1271],[1124,35373,10608],{"className":35374},[2504],[1124,35376],{"className":35377,"style":2500},[1271],[1124,35379,35381,35384,35387,35390,35393],{"className":35380},[1200],[1124,35382],{"className":35383,"style":2696},[1204],[1124,35385,2677],{"className":35386},[1795],[1124,35388,2235],{"className":35389},[1209],[1124,35391,32398],{"className":35392},[1209],[1124,35394,2683],{"className":35395},[2211],[2640,35397,35398],{},[1107,35399,35400],{},"0.105",[28185,35402,35403],{},[1101,35404,35405,35406,35464,35465,35516],{},"所有梯度为负，所以所有参数都增大，这意味着网络输出 ",[1124,35407,35409,35426],{"className":35408},[1127],[1124,35410,35412],{"className":35411},[1131],[1133,35413,35414],{"xmlns":1135},[1137,35415,35416,35424],{},[1140,35417,35418],{},[2922,35419,35420,35422],{},[1146,35421,4370],{},[1150,35423,1164],{},[1189,35425,9687],{"encoding":1191},[1124,35427,35429],{"className":35428,"ariaHidden":1156},[1196],[1124,35430,35432,35435],{"className":35431},[1200],[1124,35433],{"className":35434,"style":4598},[1204],[1124,35436,35438,35441],{"className":35437},[1209],[1124,35439,4370],{"className":35440},[1209,1213],[1124,35442,35444],{"className":35443},[1217],[1124,35445,35447],{"className":35446},[1221],[1124,35448,35450],{"className":35449},[1226],[1124,35451,35453],{"className":35452,"style":4598},[1230],[1124,35454,35455,35458],{"style":3905},[1124,35456],{"className":35457,"style":1239},[1238],[1124,35459,35461],{"className":35460},[1243,1244,1245,1246],[1124,35462,1164],{"className":35463},[1209,1246]," 会增大（更接近目标值 ",[1124,35466,35468,35486],{"className":35467},[1127],[1124,35469,35471],{"className":35470},[1131],[1133,35472,35473],{"xmlns":1135},[1137,35474,35475,35483],{},[1140,35476,35477,35479,35481],{},[1146,35478,4359],{},[1154,35480,1652],{},[1150,35482,1152],{},[1189,35484,35485],{"encoding":1191},"y=1",[1124,35487,35489,35507],{"className":35488,"ariaHidden":1156},[1196],[1124,35490,35492,35495,35498,35501,35504],{"className":35491},[1200],[1124,35493],{"className":35494,"style":1205},[1204],[1124,35496,4359],{"className":35497,"style":2700},[1209,1213],[1124,35499],{"className":35500,"style":1774},[1271],[1124,35502,1652],{"className":35503},[1778],[1124,35505],{"className":35506,"style":1774},[1271],[1124,35508,35510,35513],{"className":35509},[1200],[1124,35511],{"className":35512,"style":3685},[1204],[1124,35514,1152],{"className":35515},[1209],"），代价 C 会减小。",[1101,35518,35519],{},"梯度的用途：更新参数，让 C 变小。",[1101,35521,35522],{},[1124,35523,35525,35564],{"className":35524},[1127],[1124,35526,35528],{"className":35527},[1131],[1133,35529,35530],{"xmlns":1135},[1137,35531,35532,35561],{},[1140,35533,35534,35536,35539,35541,35543,35545,35547],{},[1146,35535,1439],{},[1154,35537,35538],{},"←",[1146,35540,1439],{},[1154,35542,2235],{},[1146,35544,5145],{},[1154,35546,2325],{},[2911,35548,35549,35555],{},[1140,35550,35551,35553],{},[1146,35552,3164],{"mathvariant":3145},[1146,35554,4325],{},[1140,35556,35557,35559],{},[1146,35558,3164],{"mathvariant":3145},[1146,35560,1439],{},[1189,35562,35563],{"encoding":1191},"w \\leftarrow w - \\eta \\cdot \\frac{\\partial C}{\\partial w}",[1124,35565,35567,35585,35603,35622],{"className":35566,"ariaHidden":1156},[1196],[1124,35568,35570,35573,35576,35579,35582],{"className":35569},[1200],[1124,35571],{"className":35572,"style":3124},[1204],[1124,35574,1439],{"className":35575,"style":1480},[1209,1213],[1124,35577],{"className":35578,"style":1774},[1271],[1124,35580,35538],{"className":35581},[1778],[1124,35583],{"className":35584,"style":1774},[1271],[1124,35586,35588,35591,35594,35597,35600],{"className":35587},[1200],[1124,35589],{"className":35590,"style":2858},[1204],[1124,35592,1439],{"className":35593,"style":1480},[1209,1213],[1124,35595],{"className":35596,"style":2500},[1271],[1124,35598,2235],{"className":35599},[2504],[1124,35601],{"className":35602,"style":2500},[1271],[1124,35604,35606,35610,35613,35616,35619],{"className":35605},[1200],[1124,35607],{"className":35608,"style":35609},[1204],"height:0.6389em;vertical-align:-0.1944em;",[1124,35611,5145],{"className":35612,"style":2700},[1209,1213],[1124,35614],{"className":35615,"style":2500},[1271],[1124,35617,2325],{"className":35618},[2504],[1124,35620],{"className":35621,"style":2500},[1271],[1124,35623,35625,35628],{"className":35624},[1200],[1124,35626],{"className":35627,"style":23920},[1204],[1124,35629,35631,35634,35699],{"className":35630},[1209],[1124,35632],{"className":35633},[1795,2212],[1124,35635,35637],{"className":35636},[2911],[1124,35638,35640,35691],{"className":35639},[1221,1222],[1124,35641,35643,35688],{"className":35642},[1226],[1124,35644,35646,35663,35671],{"className":35645,"style":4858},[1230],[1124,35647,35648,35651],{"style":2994},[1124,35649],{"className":35650,"style":2998},[1238],[1124,35652,35654],{"className":35653},[1243,1244,1245,1246],[1124,35655,35657,35660],{"className":35656},[1209,1246],[1124,35658,3164],{"className":35659,"style":3319},[1209,1246],[1124,35661,1439],{"className":35662,"style":1480},[1209,1213,1246],[1124,35664,35665,35668],{"style":3053},[1124,35666],{"className":35667,"style":2998},[1238],[1124,35669],{"className":35670,"style":3061},[3060],[1124,35672,35673,35676],{"style":3064},[1124,35674],{"className":35675,"style":2998},[1238],[1124,35677,35679],{"className":35678},[1243,1244,1245,1246],[1124,35680,35682,35685],{"className":35681},[1209,1246],[1124,35683,3164],{"className":35684,"style":3319},[1209,1246],[1124,35686,4325],{"className":35687,"style":4392},[1209,1213,1246],[1124,35689,1254],{"className":35690},[1253],[1124,35692,35694],{"className":35693},[1226],[1124,35695,35697],{"className":35696,"style":3538},[1230],[1124,35698],{},[1124,35700],{"className":35701},[2211,2212],[1101,35703,35704],{},"整个训练过程就是不断重复这个循环：",[8697,35706,35709],{"className":35707,"code":35708,"language":8702,"meta":8703},[8700],"前向传播：用当前参数算出预测值\n     ↓\n计算 C：看预测值和真实值差多少\n     ↓\n反向传播：算出每个参数的梯度（C对该参数有多敏感）\n     ↓\n更新参数：沿着梯度反方向调整参数，让C减小\n     ↓\n回到第一步，重复……直到 C 足够小\n",[8705,35710,35708],{"__ignoreMap":8707},[1101,35712,35713,35714,35717,35718,35720],{},"C 足够小，说明对于所有训练样本，网络的预测值 ",[35715,35716,4370],"em",{}," 非常接近真实标签 ",[35715,35719,4359],{},"。",[1101,35722,35723,35724,7679,35726,35728],{},"也就是得到了一组好的参数 ",[35715,35725,1439],{},[35715,35727,2230],{},"，使网络 \"学会\" 了输入到输出的映射规律，预测 ≈ 真实标签",[1096,35730,35732],{"id":35731},"梯度消失vanishing-gradient","梯度消失（Vanishing Gradient）",[1101,35734,35735],{},"反向传播时，梯度从输出层往输入层逐层传递。如果每经过一层梯度都变小，传到前面几层时梯度就接近于 0，导致前面的层几乎无法更新权重 —— 这就是梯度消失。",[1101,35737,35738],{},[1107,35739,35740],{},"越靠近输入，梯度越小",[1101,35742,35743,9087,35918,36092],{},[1124,35744,35746,35785],{"className":35745},[1127],[1124,35747,35749],{"className":35748},[1131],[1133,35750,35751],{"xmlns":1135},[1137,35752,35753,35782],{},[1140,35754,35755,35758,35776,35778,35780],{},[1146,35756,35757],{"mathvariant":3145},"∣",[2911,35759,35760,35766],{},[1140,35761,35762,35764],{},[1146,35763,3164],{"mathvariant":3145},[1146,35765,4325],{},[1140,35767,35768,35770],{},[1146,35769,3164],{"mathvariant":3145},[2922,35771,35772,35774],{},[1146,35773,1439],{},[1150,35775,1164],{},[1146,35777,35757],{"mathvariant":3145},[1154,35779,1652],{},[1150,35781,26476],{},[1189,35783,35784],{"encoding":1191},"|\\frac{\\partial C}{\\partial w^2}| = 0.0562",[1124,35786,35788,35909],{"className":35787,"ariaHidden":1156},[1196],[1124,35789,35791,35794,35797,35897,35900,35903,35906],{"className":35790},[1200],[1124,35792],{"className":35793,"style":23920},[1204],[1124,35795,35757],{"className":35796},[1209],[1124,35798,35800,35803,35894],{"className":35799},[1209],[1124,35801],{"className":35802},[1795,2212],[1124,35804,35806],{"className":35805},[2911],[1124,35807,35809,35886],{"className":35808},[1221,1222],[1124,35810,35812,35883],{"className":35811},[1226],[1124,35813,35815,35858,35866],{"className":35814,"style":4858},[1230],[1124,35816,35817,35820],{"style":2994},[1124,35818],{"className":35819,"style":2998},[1238],[1124,35821,35823],{"className":35822},[1243,1244,1245,1246],[1124,35824,35826,35829],{"className":35825},[1209,1246],[1124,35827,3164],{"className":35828,"style":3319},[1209,1246],[1124,35830,35832,35835],{"className":35831},[1209,1246],[1124,35833,1439],{"className":35834,"style":1480},[1209,1213,1246],[1124,35836,35838],{"className":35837},[1217],[1124,35839,35841],{"className":35840},[1221],[1124,35842,35844],{"className":35843},[1226],[1124,35845,35847],{"className":35846,"style":22067},[1230],[1124,35848,35849,35852],{"style":3032},[1124,35850],{"className":35851,"style":3036},[1238],[1124,35853,35855],{"className":35854},[1243,3040,3041,1246],[1124,35856,1164],{"className":35857},[1209,1246],[1124,35859,35860,35863],{"style":3053},[1124,35861],{"className":35862,"style":2998},[1238],[1124,35864],{"className":35865,"style":3061},[3060],[1124,35867,35868,35871],{"style":3064},[1124,35869],{"className":35870,"style":2998},[1238],[1124,35872,35874],{"className":35873},[1243,1244,1245,1246],[1124,35875,35877,35880],{"className":35876},[1209,1246],[1124,35878,3164],{"className":35879,"style":3319},[1209,1246],[1124,35881,4325],{"className":35882,"style":4392},[1209,1213,1246],[1124,35884,1254],{"className":35885},[1253],[1124,35887,35889],{"className":35888},[1226],[1124,35890,35892],{"className":35891,"style":3538},[1230],[1124,35893],{},[1124,35895],{"className":35896},[2211,2212],[1124,35898,35757],{"className":35899},[1209],[1124,35901],{"className":35902,"style":1774},[1271],[1124,35904,1652],{"className":35905},[1778],[1124,35907],{"className":35908,"style":1774},[1271],[1124,35910,35912,35915],{"className":35911},[1200],[1124,35913],{"className":35914,"style":3685},[1204],[1124,35916,26476],{"className":35917},[1209],[1124,35919,35921,35959],{"className":35920},[1127],[1124,35922,35924],{"className":35923},[1131],[1133,35925,35926],{"xmlns":1135},[1137,35927,35928,35956],{},[1140,35929,35930,35932,35950,35952,35954],{},[1146,35931,35757],{"mathvariant":3145},[2911,35933,35934,35940],{},[1140,35935,35936,35938],{},[1146,35937,3164],{"mathvariant":3145},[1146,35939,4325],{},[1140,35941,35942,35944],{},[1146,35943,3164],{"mathvariant":3145},[2922,35945,35946,35948],{},[1146,35947,1439],{},[1150,35949,1152],{},[1146,35951,35757],{"mathvariant":3145},[1154,35953,1652],{},[1150,35955,32419],{},[1189,35957,35958],{"encoding":1191},"|\\frac{\\partial C}{\\partial w^1}| = 0.0194",[1124,35960,35962,36083],{"className":35961,"ariaHidden":1156},[1196],[1124,35963,35965,35968,35971,36071,36074,36077,36080],{"className":35964},[1200],[1124,35966],{"className":35967,"style":23920},[1204],[1124,35969,35757],{"className":35970},[1209],[1124,35972,35974,35977,36068],{"className":35973},[1209],[1124,35975],{"className":35976},[1795,2212],[1124,35978,35980],{"className":35979},[2911],[1124,35981,35983,36060],{"className":35982},[1221,1222],[1124,35984,35986,36057],{"className":35985},[1226],[1124,35987,35989,36032,36040],{"className":35988,"style":4858},[1230],[1124,35990,35991,35994],{"style":2994},[1124,35992],{"className":35993,"style":2998},[1238],[1124,35995,35997],{"className":35996},[1243,1244,1245,1246],[1124,35998,36000,36003],{"className":35999},[1209,1246],[1124,36001,3164],{"className":36002,"style":3319},[1209,1246],[1124,36004,36006,36009],{"className":36005},[1209,1246],[1124,36007,1439],{"className":36008,"style":1480},[1209,1213,1246],[1124,36010,36012],{"className":36011},[1217],[1124,36013,36015],{"className":36014},[1221],[1124,36016,36018],{"className":36017},[1226],[1124,36019,36021],{"className":36020,"style":22067},[1230],[1124,36022,36023,36026],{"style":3032},[1124,36024],{"className":36025,"style":3036},[1238],[1124,36027,36029],{"className":36028},[1243,3040,3041,1246],[1124,36030,1152],{"className":36031},[1209,1246],[1124,36033,36034,36037],{"style":3053},[1124,36035],{"className":36036,"style":2998},[1238],[1124,36038],{"className":36039,"style":3061},[3060],[1124,36041,36042,36045],{"style":3064},[1124,36043],{"className":36044,"style":2998},[1238],[1124,36046,36048],{"className":36047},[1243,1244,1245,1246],[1124,36049,36051,36054],{"className":36050},[1209,1246],[1124,36052,3164],{"className":36053,"style":3319},[1209,1246],[1124,36055,4325],{"className":36056,"style":4392},[1209,1213,1246],[1124,36058,1254],{"className":36059},[1253],[1124,36061,36063],{"className":36062},[1226],[1124,36064,36066],{"className":36065,"style":3538},[1230],[1124,36067],{},[1124,36069],{"className":36070},[2211,2212],[1124,36072,35757],{"className":36073},[1209],[1124,36075],{"className":36076,"style":1774},[1271],[1124,36078,1652],{"className":36079},[1778],[1124,36081],{"className":36082,"style":1774},[1271],[1124,36084,36086,36089],{"className":36085},[1200],[1124,36087],{"className":36088,"style":3685},[1204],[1124,36090,32419],{"className":36091},[1209],"。隐藏层梯度只有输出层的 1\u002F3",[2745,36094],{},[1101,36096,36097],{},"回顾反向传播的误差递推公式（BP2）",[1101,36099,36100,36101,36177],{},"误差每经过一层就要乘以 ",[1124,36102,36104,36127],{"className":36103},[1127],[1124,36105,36107],{"className":36106},[1131],[1133,36108,36109],{"xmlns":1135},[1137,36110,36111,36125],{},[1140,36112,36113,36119,36121,36123],{},[2922,36114,36115,36117],{},[1146,36116,2674],{},[1154,36118,3838],{"mathvariant":3145,"lspace":3837,"rspace":3837},[1154,36120,2677],{"stretchy":1674},[1146,36122,2680],{},[1154,36124,2683],{"stretchy":1674},[1189,36126,34572],{"encoding":1191},[1124,36128,36130],{"className":36129,"ariaHidden":1156},[1196],[1124,36131,36133,36136,36168,36171,36174],{"className":36132},[1200],[1124,36134],{"className":36135,"style":3883},[1204],[1124,36137,36139,36142],{"className":36138},[1209],[1124,36140,2674],{"className":36141,"style":2700},[1209,1213],[1124,36143,36145],{"className":36144},[1217],[1124,36146,36148],{"className":36147},[1221],[1124,36149,36151],{"className":36150},[1226],[1124,36152,36154],{"className":36153,"style":3902},[1230],[1124,36155,36156,36159],{"style":3905},[1124,36157],{"className":36158,"style":1239},[1238],[1124,36160,36162],{"className":36161},[1243,1244,1245,1246],[1124,36163,36165],{"className":36164},[1209,1246],[1124,36166,3838],{"className":36167},[1209,1246],[1124,36169,2677],{"className":36170},[1795],[1124,36172,2680],{"className":36173,"style":2707},[1209,1213],[1124,36175,2683],{"className":36176},[2211],"（最大值 0.25）和权重，不断缩小，层数越多，前面层的梯度越小，学习越慢，多层连乘后梯度趋近于 0，前面的层几乎学不到东西。这是深层网络训练困难的核心原因，也是 ReLU、残差连接、LSTM 等技术诞生的动机。",{"title":8707,"searchDepth":36179,"depth":36179,"links":36180},4,[36181,36183,36184,36185,36186,36187,36188,36193,36199,36200,36206,36207],{"id":1098,"depth":36182,"text":1099},2,{"id":2749,"depth":36182,"text":2750},{"id":4221,"depth":36182,"text":4222},{"id":4256,"depth":36182,"text":4257},{"id":4296,"depth":36182,"text":4297},{"id":6043,"depth":36182,"text":6044},{"id":7574,"depth":36182,"text":7575,"children":36189},[36190,36192],{"id":7745,"depth":36191,"text":7745},3,{"id":8692,"depth":36191,"text":8692},{"id":12402,"depth":36182,"text":12403,"children":36194},[36195,36196,36197,36198],{"id":12406,"depth":36191,"text":12406},{"id":13889,"depth":36191,"text":13890},{"id":15619,"depth":36191,"text":15619},{"id":17996,"depth":36191,"text":17996},{"id":15635,"depth":36182,"text":15635},{"id":23873,"depth":36182,"text":23874,"children":36201},[36202,36203,36204,36205],{"id":24452,"depth":36191,"text":24453},{"id":26727,"depth":36191,"text":26728},{"id":29189,"depth":36191,"text":29190},{"id":32538,"depth":36191,"text":32539},{"id":34628,"depth":36182,"text":34629},{"id":35731,"depth":36182,"text":35732},"https:\u002F\u002Fpicx.zhimg.com\u002F80\u002Fv2-51a7689293e592646e7e1d26c33d198f_720w.webp?source=d16d100b","本文介绍神经网络入门知识，包括感知机、Sigmoid神经元、网络架构、手写数字识别以及梯度下降算法；第二部分深入讲解反向传播算法，包括符号定义、四个基本方程、算法步骤及其全局直觉理解","md",true,{"uuid":36213,"slots":36214},"093d8792-1054-11f0-9848-0b32a1ee406d",{},11,{"title":1085,"description":36209},"posts\u002F神经网络\u002F神经网络与深度学习：神经网络基础",[40],"OhtRZpIkpcgt9XORvFOiExEdLtzqRSafnU88pENxGPQ",1790443284611]