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3",[1107,1146,1150,1175,1193],{"className":1147,"ariaHidden":1149},[1148],"katex-html","true",[1107,1151,1154,1159,1163,1168,1172],{"className":1152},[1153],"base",[1107,1155],{"className":1156,"style":1158},[1157],"strut","height:0.7278em;vertical-align:-0.0833em;",[1107,1160,1128],{"className":1161},[1162],"mord",[1107,1164],{"className":1165,"style":1167},[1166],"mspace","margin-right:0.2222em;",[1107,1169,1132],{"className":1170},[1171],"mbin",[1107,1173],{"className":1174,"style":1167},[1166],[1107,1176,1178,1181,1184,1187,1190],{"className":1177},[1153],[1107,1179],{"className":1180,"style":1158},[1157],[1107,1182,1128],{"className":1183},[1162],[1107,1185],{"className":1186,"style":1167},[1166],[1107,1188,1132],{"className":1189},[1171],[1107,1191],{"className":1192,"style":1167},[1166],[1107,1194,1196,1200],{"className":1195},[1153],[1107,1197],{"className":1198,"style":1199},[1157],"height:0.6444em;",[1107,1201,1139],{"className":1202},[1162]," 的彩色图像，输入层有 ",[1107,1205,1207,1235],{"className":1206},[1110],[1107,1208,1210],{"className":1209},[1114],[1116,1211,1212],{"xmlns":1118},[1120,1213,1214,1232],{},[1123,1215,1216,1218,1220,1222,1224,1226,1229],{},[1126,1217,1128],{},[1130,1219,1132],{},[1126,1221,1128],{},[1130,1223,1132],{},[1126,1225,1139],{},[1130,1227,1228],{},"=",[1126,1230,1231],{},"150,528",[1141,1233,1234],{"encoding":1143},"224 \\times 224 \\times 3 = 150{,}528",[1107,1236,1238,1256,1274,1294],{"className":1237,"ariaHidden":1149},[1148],[1107,1239,1241,1244,1247,1250,1253],{"className":1240},[1153],[1107,1242],{"className":1243,"style":1158},[1157],[1107,1245,1128],{"className":1246},[1162],[1107,1248],{"className":1249,"style":1167},[1166],[1107,1251,1132],{"className":1252},[1171],[1107,1254],{"className":1255,"style":1167},[1166],[1107,1257,1259,1262,1265,1268,1271],{"className":1258},[1153],[1107,1260],{"className":1261,"style":1158},[1157],[1107,1263,1128],{"className":1264},[1162],[1107,1266],{"className":1267,"style":1167},[1166],[1107,1269,1132],{"className":1270},[1171],[1107,1272],{"className":1273,"style":1167},[1166],[1107,1275,1277,1280,1283,1287,1291],{"className":1276},[1153],[1107,1278],{"className":1279,"style":1199},[1157],[1107,1281,1139],{"className":1282},[1162],[1107,1284],{"className":1285,"style":1286},[1166],"margin-right:0.2778em;",[1107,1288,1228],{"className":1289},[1290],"mrel",[1107,1292],{"className":1293,"style":1286},[1166],[1107,1295,1297,1301,1305,1313],{"className":1296},[1153],[1107,1298],{"className":1299,"style":1300},[1157],"height:0.8389em;vertical-align:-0.1944em;",[1107,1302,1304],{"className":1303},[1162],"150",[1107,1306,1308],{"className":1307},[1162],[1107,1309,1312],{"className":1310},[1311],"mpunct",",",[1107,1314,1316],{"className":1315},[1162],"528"," 个神经元。若第一隐藏层有 1000 个神经元，则仅第一层就有 ",[1107,1319,1321,1357],{"className":1320},[1110],[1107,1322,1324],{"className":1323},[1114],[1116,1325,1326],{"xmlns":1118},[1120,1327,1328,1354],{},[1123,1329,1330,1332,1334,1337,1340,1343,1345],{},[1126,1331,1231],{},[1130,1333,1132],{},[1126,1335,1336],{},"1000",[1130,1338,1339],{},"≈",[1126,1341,1342],{},"1.5",[1130,1344,1132],{},[1346,1347,1348,1351],"msup",{},[1126,1349,1350],{},"10",[1126,1352,1353],{},"8",[1141,1355,1356],{"encoding":1143},"150{,}528 \\times 1000 \\approx 1.5 \\times 10^8",[1107,1358,1360,1387,1405,1423],{"className":1359,"ariaHidden":1149},[1148],[1107,1361,1363,1366,1369,1375,1378,1381,1384],{"className":1362},[1153],[1107,1364],{"className":1365,"style":1300},[1157],[1107,1367,1304],{"className":1368},[1162],[1107,1370,1372],{"className":1371},[1162],[1107,1373,1312],{"className":1374},[1311],[1107,1376,1316],{"className":1377},[1162],[1107,1379],{"className":1380,"style":1167},[1166],[1107,1382,1132],{"className":1383},[1171],[1107,1385],{"className":1386,"style":1167},[1166],[1107,1388,1390,1393,1396,1399,1402],{"className":1389},[1153],[1107,1391],{"className":1392,"style":1199},[1157],[1107,1394,1336],{"className":1395},[1162],[1107,1397],{"className":1398,"style":1286},[1166],[1107,1400,1339],{"className":1401},[1290],[1107,1403],{"className":1404,"style":1286},[1166],[1107,1406,1408,1411,1414,1417,1420],{"className":1407},[1153],[1107,1409],{"className":1410,"style":1158},[1157],[1107,1412,1342],{"className":1413},[1162],[1107,1415],{"className":1416,"style":1167},[1166],[1107,1418,1132],{"className":1419},[1171],[1107,1421],{"className":1422,"style":1167},[1166],[1107,1424,1426,1430,1434],{"className":1425},[1153],[1107,1427],{"className":1428,"style":1429},[1157],"height:0.8141em;",[1107,1431,1433],{"className":1432},[1162],"1",[1107,1435,1437,1441],{"className":1436},[1162],[1107,1438,1440],{"className":1439},[1162],"0",[1107,1442,1445],{"className":1443},[1444],"msupsub",[1107,1446,1449],{"className":1447},[1448],"vlist-t",[1107,1450,1453],{"className":1451},[1452],"vlist-r",[1107,1454,1457],{"className":1455,"style":1429},[1456],"vlist",[1107,1458,1460,1465],{"style":1459},"top:-3.063em;margin-right:0.05em;",[1107,1461],{"className":1462,"style":1464},[1463],"pstrut","height:2.7em;",[1107,1466,1472],{"className":1467},[1468,1469,1470,1471],"sizing","reset-size6","size3","mtight",[1107,1473,1353],{"className":1474},[1162,1471]," 个参数，极易过拟合且计算代价极高",[1100,1477,1478,1479],{},"CNN 通过两个关键思想解决此问题：",[1480,1481,1482,1483,1486],"strong",{},"局部连接（Local Connectivity）",[1480,1484,1485],{},"和","权值共享（Weight Sharing）",[1096,1488,1482],{"id":1489},"局部连接local-connectivity",[1100,1491,1492,1493,1496],{},"（",[1480,1494,1495],{},"感受野","，Receptive Field）指的是卷积神经网络每一层输出的特征图（feature map）上每个像素点映射回输入图像上的区域大小。神经元感受野的范围越大表示其能接触到的原始图像范围就越大，也意味着它能学习更为全局，语义层次更高的特征信息；相反，范围越小则表示其所包含的特征越趋向局部和细节。",[1100,1498,1499],{},"因此感受野的范围可以用来大致判断每一层的抽象层次。并且我们可以很明显地知道网络越深，神经元的感受野越大。由此可知，深度卷积神经网络中靠前的层感受野较小，提取到的是图像的纹理、边缘等局部的、通用的特征；靠后的层由于感受野较大，提取到的是图像更深层次、更具象的特征。",[1100,1501,1502],{},"在视觉感知中，每个神经元只需关注图像的一个局部区域（感受野），而非整幅图像。CNN 中每个神经元仅与输入的一个局部区域相连接，大幅减少连接数。",[1100,1504,1505],{},[1480,1506,1507],{},"全连接网络",[1100,1509,1510],{},"每个神经元连接所有输入像素",[1100,1512,1513,1514],{},"参数量：",[1107,1515,1517,1584],{"className":1516},[1110],[1107,1518,1520],{"className":1519},[1114],[1116,1521,1522],{"xmlns":1118},[1120,1523,1524,1581],{},[1123,1525,1526,1530,1534,1555,1557,1578],{},[1527,1528,1529],"mi",{},"O",[1130,1531,1533],{"stretchy":1532},"false","(",[1535,1536,1537,1540],"msub",{},[1527,1538,1539],{},"n",[1123,1541,1542,1545,1547,1549,1552],{},[1527,1543,1544],{},"i",[1527,1546,1539],{},[1527,1548,1100],{},[1527,1550,1551],{},"u",[1527,1553,1554],{},"t",[1130,1556,1132],{},[1535,1558,1559,1561],{},[1527,1560,1539],{},[1123,1562,1563,1566,1568,1571,1573,1576],{},[1527,1564,1565],{},"h",[1527,1567,1544],{},[1527,1569,1570],{},"d",[1527,1572,1570],{},[1527,1574,1575],{},"e",[1527,1577,1539],{},[1130,1579,1580],{"stretchy":1532},")",[1141,1582,1583],{"encoding":1143},"O(n_{input} \\times n_{hidden})",[1107,1585,1587,1671],{"className":1586,"ariaHidden":1149},[1148],[1107,1588,1590,1594,1599,1603,1662,1665,1668],{"className":1589},[1153],[1107,1591],{"className":1592,"style":1593},[1157],"height:1.0361em;vertical-align:-0.2861em;",[1107,1595,1529],{"className":1596,"style":1598},[1162,1597],"mathnormal","margin-right:0.0278em;",[1107,1600,1533],{"className":1601},[1602],"mopen",[1107,1604,1606,1609],{"className":1605},[1162],[1107,1607,1539],{"className":1608},[1162,1597],[1107,1610,1612],{"className":1611},[1444],[1107,1613,1616,1653],{"className":1614},[1448,1615],"vlist-t2",[1107,1617,1619,1648],{"className":1618},[1452],[1107,1620,1623],{"className":1621,"style":1622},[1456],"height:0.3117em;",[1107,1624,1626,1629],{"style":1625},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1107,1627],{"className":1628,"style":1464},[1463],[1107,1630,1632],{"className":1631},[1468,1469,1470,1471],[1107,1633,1635,1639,1642,1645],{"className":1634},[1162,1471],[1107,1636,1638],{"className":1637},[1162,1597,1471],"in",[1107,1640,1100],{"className":1641},[1162,1597,1471],[1107,1643,1551],{"className":1644},[1162,1597,1471],[1107,1646,1554],{"className":1647},[1162,1597,1471],[1107,1649,1652],{"className":1650},[1651],"vlist-s","​",[1107,1654,1656],{"className":1655},[1452],[1107,1657,1660],{"className":1658,"style":1659},[1456],"height:0.2861em;",[1107,1661],{},[1107,1663],{"className":1664,"style":1167},[1166],[1107,1666,1132],{"className":1667},[1171],[1107,1669],{"className":1670,"style":1167},[1166],[1107,1672,1674,1678,1734],{"className":1673},[1153],[1107,1675],{"className":1676,"style":1677},[1157],"height:1em;vertical-align:-0.25em;",[1107,1679,1681,1684],{"className":1680},[1162],[1107,1682,1539],{"className":1683},[1162,1597],[1107,1685,1687],{"className":1686},[1444],[1107,1688,1690,1725],{"className":1689},[1448,1615],[1107,1691,1693,1722],{"className":1692},[1452],[1107,1694,1697],{"className":1695,"style":1696},[1456],"height:0.3361em;",[1107,1698,1699,1702],{"style":1625},[1107,1700],{"className":1701,"style":1464},[1463],[1107,1703,1705],{"className":1704},[1468,1469,1470,1471],[1107,1706,1708,1712,1716,1719],{"className":1707},[1162,1471],[1107,1709,1711],{"className":1710},[1162,1597,1471],"hi",[1107,1713,1715],{"className":1714},[1162,1597,1471],"dd",[1107,1717,1575],{"className":1718},[1162,1597,1471],[1107,1720,1539],{"className":1721},[1162,1597,1471],[1107,1723,1652],{"className":1724},[1651],[1107,1726,1728],{"className":1727},[1452],[1107,1729,1732],{"className":1730,"style":1731},[1456],"height:0.15em;",[1107,1733],{},[1107,1735,1580],{"className":1736},[1737],"mclose",[1100,1739,1740],{},[1480,1741,1742],{},"局部连接网络",[1100,1744,1745],{},"每个神经元仅连接局部区域",[1100,1747,1513,1748],{},[1107,1749,1751,1797],{"className":1750},[1110],[1107,1752,1754],{"className":1753},[1114],[1116,1755,1756],{"xmlns":1118},[1120,1757,1758,1794],{},[1123,1759,1760,1762,1764,1772,1774,1792],{},[1527,1761,1529],{},[1130,1763,1533],{"stretchy":1532},[1346,1765,1766,1769],{},[1527,1767,1768],{},"F",[1126,1770,1771],{},"2",[1130,1773,1132],{},[1535,1775,1776,1778],{},[1527,1777,1539],{},[1123,1779,1780,1782,1784,1786,1788,1790],{},[1527,1781,1565],{},[1527,1783,1544],{},[1527,1785,1570],{},[1527,1787,1570],{},[1527,1789,1575],{},[1527,1791,1539],{},[1130,1793,1580],{"stretchy":1532},[1141,1795,1796],{"encoding":1143},"O(F^2 \\times n_{hidden})",[1107,1798,1800,1852],{"className":1799,"ariaHidden":1149},[1148],[1107,1801,1803,1807,1810,1813,1843,1846,1849],{"className":1802},[1153],[1107,1804],{"className":1805,"style":1806},[1157],"height:1.0641em;vertical-align:-0.25em;",[1107,1808,1529],{"className":1809,"style":1598},[1162,1597],[1107,1811,1533],{"className":1812},[1602],[1107,1814,1816,1820],{"className":1815},[1162],[1107,1817,1768],{"className":1818,"style":1819},[1162,1597],"margin-right:0.1389em;",[1107,1821,1823],{"className":1822},[1444],[1107,1824,1826],{"className":1825},[1448],[1107,1827,1829],{"className":1828},[1452],[1107,1830,1832],{"className":1831,"style":1429},[1456],[1107,1833,1834,1837],{"style":1459},[1107,1835],{"className":1836,"style":1464},[1463],[1107,1838,1840],{"className":1839},[1468,1469,1470,1471],[1107,1841,1771],{"className":1842},[1162,1471],[1107,1844],{"className":1845,"style":1167},[1166],[1107,1847,1132],{"className":1848},[1171],[1107,1850],{"className":1851,"style":1167},[1166],[1107,1853,1855,1858,1910],{"className":1854},[1153],[1107,1856],{"className":1857,"style":1677},[1157],[1107,1859,1861,1864],{"className":1860},[1162],[1107,1862,1539],{"className":1863},[1162,1597],[1107,1865,1867],{"className":1866},[1444],[1107,1868,1870,1902],{"className":1869},[1448,1615],[1107,1871,1873,1899],{"className":1872},[1452],[1107,1874,1876],{"className":1875,"style":1696},[1456],[1107,1877,1878,1881],{"style":1625},[1107,1879],{"className":1880,"style":1464},[1463],[1107,1882,1884],{"className":1883},[1468,1469,1470,1471],[1107,1885,1887,1890,1893,1896],{"className":1886},[1162,1471],[1107,1888,1711],{"className":1889},[1162,1597,1471],[1107,1891,1715],{"className":1892},[1162,1597,1471],[1107,1894,1575],{"className":1895},[1162,1597,1471],[1107,1897,1539],{"className":1898},[1162,1597,1471],[1107,1900,1652],{"className":1901},[1651],[1107,1903,1905],{"className":1904},[1452],[1107,1906,1908],{"className":1907,"style":1731},[1456],[1107,1909],{},[1107,1911,1580],{"className":1912},[1737],[1096,1914,1486],{"id":1915},"权值共享weight-sharing",[1100,1917,1918,1919,2086,2087,2161],{},"同一个特征（如边缘、角点）可能出现在图像的任何位置。CNN 让同一个卷积核（filter）在整个图像上滑动，所有位置共享相同的权重参数。这进一步将参数量从 ",[1107,1920,1922,1967],{"className":1921},[1110],[1107,1923,1925],{"className":1924},[1114],[1116,1926,1927],{"xmlns":1118},[1120,1928,1929,1964],{},[1123,1930,1931,1933,1935,1941,1943,1962],{},[1527,1932,1529],{},[1130,1934,1533],{"stretchy":1532},[1346,1936,1937,1939],{},[1527,1938,1768],{},[1126,1940,1771],{},[1130,1942,1132],{},[1535,1944,1945,1947],{},[1527,1946,1539],{},[1123,1948,1949,1952,1954,1956,1958,1960],{},[1527,1950,1951],{},"o",[1527,1953,1551],{},[1527,1955,1554],{},[1527,1957,1100],{},[1527,1959,1551],{},[1527,1961,1554],{},[1130,1963,1580],{"stretchy":1532},[1141,1965,1966],{"encoding":1143},"O(F^2 \\times n_{output})",[1107,1968,1970,2020],{"className":1969,"ariaHidden":1149},[1148],[1107,1971,1973,1976,1979,1982,2011,2014,2017],{"className":1972},[1153],[1107,1974],{"className":1975,"style":1806},[1157],[1107,1977,1529],{"className":1978,"style":1598},[1162,1597],[1107,1980,1533],{"className":1981},[1602],[1107,1983,1985,1988],{"className":1984},[1162],[1107,1986,1768],{"className":1987,"style":1819},[1162,1597],[1107,1989,1991],{"className":1990},[1444],[1107,1992,1994],{"className":1993},[1448],[1107,1995,1997],{"className":1996},[1452],[1107,1998,2000],{"className":1999,"style":1429},[1456],[1107,2001,2002,2005],{"style":1459},[1107,2003],{"className":2004,"style":1464},[1463],[1107,2006,2008],{"className":2007},[1468,1469,1470,1471],[1107,2009,1771],{"className":2010},[1162,1471],[1107,2012],{"className":2013,"style":1167},[1166],[1107,2015,1132],{"className":2016},[1171],[1107,2018],{"className":2019,"style":1167},[1166],[1107,2021,2023,2026,2083],{"className":2022},[1153],[1107,2024],{"className":2025,"style":1593},[1157],[1107,2027,2029,2032],{"className":2028},[1162],[1107,2030,1539],{"className":2031},[1162,1597],[1107,2033,2035],{"className":2034},[1444],[1107,2036,2038,2075],{"className":2037},[1448,1615],[1107,2039,2041,2072],{"className":2040},[1452],[1107,2042,2045],{"className":2043,"style":2044},[1456],"height:0.2806em;",[1107,2046,2047,2050],{"style":1625},[1107,2048],{"className":2049,"style":1464},[1463],[1107,2051,2053],{"className":2052},[1468,1469,1470,1471],[1107,2054,2056,2059,2062,2066,2069],{"className":2055},[1162,1471],[1107,2057,1951],{"className":2058},[1162,1597,1471],[1107,2060,1551],{"className":2061},[1162,1597,1471],[1107,2063,2065],{"className":2064},[1162,1597,1471],"tp",[1107,2067,1551],{"className":2068},[1162,1597,1471],[1107,2070,1554],{"className":2071},[1162,1597,1471],[1107,2073,1652],{"className":2074},[1651],[1107,2076,2078],{"className":2077},[1452],[1107,2079,2081],{"className":2080,"style":1659},[1456],[1107,2082],{},[1107,2084,1580],{"className":2085},[1737]," 降低到 ",[1107,2088,2090,2114],{"className":2089},[1110],[1107,2091,2093],{"className":2092},[1114],[1116,2094,2095],{"xmlns":1118},[1120,2096,2097,2111],{},[1123,2098,2099,2101,2103,2109],{},[1527,2100,1529],{},[1130,2102,1533],{"stretchy":1532},[1346,2104,2105,2107],{},[1527,2106,1768],{},[1126,2108,1771],{},[1130,2110,1580],{"stretchy":1532},[1141,2112,2113],{"encoding":1143},"O(F^2)",[1107,2115,2117],{"className":2116,"ariaHidden":1149},[1148],[1107,2118,2120,2123,2126,2129,2158],{"className":2119},[1153],[1107,2121],{"className":2122,"style":1806},[1157],[1107,2124,1529],{"className":2125,"style":1598},[1162,1597],[1107,2127,1533],{"className":2128},[1602],[1107,2130,2132,2135],{"className":2131},[1162],[1107,2133,1768],{"className":2134,"style":1819},[1162,1597],[1107,2136,2138],{"className":2137},[1444],[1107,2139,2141],{"className":2140},[1448],[1107,2142,2144],{"className":2143},[1452],[1107,2145,2147],{"className":2146,"style":1429},[1456],[1107,2148,2149,2152],{"style":1459},[1107,2150],{"className":2151,"style":1464},[1463],[1107,2153,2155],{"className":2154},[1468,1469,1470,1471],[1107,2156,1771],{"className":2157},[1162,1471],[1107,2159,1580],{"className":2160},[1737],"（单个卷积核）。",[2163,2164],"hr",{},[1091,2166,2168],{"id":2167},"二cnn","二、CNN",[1096,2170,2171],{"id":2171},"整体架构",[1100,2173,2174],{},[2175,2176,2177],"em",{},"CNN 架构 = 多次 \"卷积 →ReLU→ 池化\" 逐层提取从简单到复杂的特征，特征图越来越小但通道越来越多，最后展平接全连接层做分类。这种设计同时实现了参数少、利用空间结构、自动学习特征三个目标",[1100,2179,2180,2181,2184],{},"一个典型的 CNN 由多个",[1480,2182,2183],{},"卷积-池化","单元堆叠而成，最终接全连接层进行分类",[2186,2187],"mermaid",{"code":2188},"flowchart LR\n    INPUT[输入图像] --> C1[卷积层 → ReLU → 池化]\n    C1 --> C2[卷积层 → ReLU → 池化]\n    C2 --> C3[卷积层 → ReLU → 池化]\n    C3 --> FC1[全连接层]\n    FC1 --> FC2[全连接层]\n    FC2 --> SM[Softmax]\n    SM --> OUTPUT[输出类别]\n\n    subgraph FE[特征提取部分]\n        C1\n        C2\n        C3\n    end\n\n    subgraph CLS[分类部分]\n        FC1\n        FC2\n        SM\n    end",[2163,2190],{},[1100,2192,2193],{},"前半部分：特征提取器（Feature Extractor）",[1100,2195,2196],{},"Conv → ReLU → Pool（循环多次）",[1100,2198,2199],{},"这部分的工作是从原始像素中逐层提取越来越抽象的特征，随着网络深度增加，特征图的空间尺寸逐渐减小（通过池化或大步长卷积），而深度（通道数）逐渐增加（通过增加卷积核数量）",[2201,2202,2203,2207,2210],"ul",{},[2204,2205,2206],"li",{},"浅层：边缘、颜色、纹理",[2204,2208,2209],{},"中层：局部形状、部件（眼睛、轮子）",[2204,2211,2212],{},"深层：整体语义（人脸、汽车）",[1100,2214,2215],{},"输出是一组压缩后的特征图（比如 7×7×512），浓缩了图像的关键信息。",[2163,2217],{},[1100,2219,2220],{},"后半部分：分类器（Classifier）",[1100,2222,2223],{},"Flatten → FC → Softmax",[1100,2225,2226],{},"这部分的工作是拿提取好的特征做决策：",[2201,2228,2229,2232,2235],{},[2204,2230,2231],{},"Flatten：把三维特征图铺平成一维向量（纯形状转换，无计算）",[2204,2233,2234],{},"FC：对所有特征做加权组合，学习 \"哪些特征组合代表哪个类别\"",[2204,2236,2237],{},"Softmax：把原始分数转为概率，输出最终预测",[2163,2239],{},[1100,2241,2242],{},"卷积提特征 → ReLU 加非线性 → 池化降尺寸 → 展平变向量 → 全连接做决策 → Softmax 出概率",[1100,2244,2245],{},"前面的层负责\"看\"，后面的层负责\"判断\"",[2247,2248,2250],"h3",{"id":2249},"_1-卷积层conv","1. 卷积层（Conv）",[1100,2252,2253],{},"卷积层是 CNN 的核心。卷积操作的核心是用一个小的**卷积核（Filter \u002F Kernel）**在输入特征图上滑动，每个位置做元素乘积求和，输出一个值。每个卷积核提取一种特征（边缘、纹理、形状等），多个卷积核产生多通道特征图。",[1100,2255,2256],{},[1480,2257,2258],{},"卷积计算公式：",[1100,2260,2261],{},[1107,2262,2264,2423],{"className":2263},[1110],[1107,2265,2267],{"className":2266},[1114],[1116,2268,2269],{"xmlns":1118},[1120,2270,2271,2420],{},[1123,2272,2273,2276,2278,2280,2282,2285,2287,2289,2313,2333,2354,2357,2359,2361,2364,2367,2370,2372,2374,2378,2380,2382,2384,2386,2388,2390,2392,2394,2396,2398,2401,2403,2405,2407,2409,2411,2413,2415,2417],{},[1527,2274,2275],{},"y",[1130,2277,1533],{"stretchy":1532},[1527,2279,1544],{},[1130,2281,1312],{"separator":1149},[1527,2283,2284],{},"j",[1130,2286,1580],{"stretchy":1532},[1130,2288,1228],{},[2290,2291,2292,2295,2304],"msubsup",{},[1130,2293,2294],{},"∑",[1123,2296,2297,2300,2302],{},[1527,2298,2299],{},"m",[1130,2301,1228],{},[1126,2303,1440],{},[1123,2305,2306,2308,2311],{},[1527,2307,1768],{},[1130,2309,2310],{},"−",[1126,2312,1433],{},[2290,2314,2315,2317,2325],{},[1130,2316,2294],{},[1123,2318,2319,2321,2323],{},[1527,2320,1539],{},[1130,2322,1228],{},[1126,2324,1440],{},[1123,2326,2327,2329,2331],{},[1527,2328,1768],{},[1130,2330,2310],{},[1126,2332,1433],{},[2290,2334,2335,2337,2345],{},[1130,2336,2294],{},[1123,2338,2339,2341,2343],{},[1527,2340,1570],{},[1130,2342,1228],{},[1126,2344,1440],{},[1123,2346,2347,2350,2352],{},[1527,2348,2349],{},"D",[1130,2351,2310],{},[1126,2353,1433],{},[1527,2355,2356],{},"x",[1130,2358,1533],{"stretchy":1532},[1527,2360,1544],{},[1130,2362,2363],{},"⋅",[1527,2365,2366],{},"S",[1130,2368,2369],{},"+",[1527,2371,2299],{},[1130,2373,1312],{"separator":1149},[2375,2376,2377],"mtext",{},"  ",[1527,2379,2284],{},[1130,2381,2363],{},[1527,2383,2366],{},[1130,2385,2369],{},[1527,2387,1539],{},[1130,2389,1312],{"separator":1149},[2375,2391,2377],{},[1527,2393,1570],{},[1130,2395,1580],{"stretchy":1532},[1130,2397,2363],{},[1527,2399,2400],{},"w",[1130,2402,1533],{"stretchy":1532},[1527,2404,2299],{},[1130,2406,1312],{"separator":1149},[1527,2408,1539],{},[1130,2410,1312],{"separator":1149},[1527,2412,1570],{},[1130,2414,1580],{"stretchy":1532},[1130,2416,2369],{},[1527,2418,2419],{},"b",[1141,2421,2422],{"encoding":1143},"y(i, j) = \\sum_{m=0}^{F-1} \\sum_{n=0}^{F-1} \\sum_{d=0}^{D-1} x(i \\cdot S + m,\\; j \\cdot S + n,\\; d) \\cdot w(m, n, d) + b",[1107,2424,2426,2465,2714,2734,2765,2783,2816,2862],{"className":2425,"ariaHidden":1149},[1148],[1107,2427,2429,2432,2436,2439,2442,2445,2449,2453,2456,2459,2462],{"className":2428},[1153],[1107,2430],{"className":2431,"style":1677},[1157],[1107,2433,2275],{"className":2434,"style":2435},[1162,1597],"margin-right:0.0359em;",[1107,2437,1533],{"className":2438},[1602],[1107,2440,1544],{"className":2441},[1162,1597],[1107,2443,1312],{"className":2444},[1311],[1107,2446],{"className":2447,"style":2448},[1166],"margin-right:0.1667em;",[1107,2450,2284],{"className":2451,"style":2452},[1162,1597],"margin-right:0.0572em;",[1107,2454,1580],{"className":2455},[1737],[1107,2457],{"className":2458,"style":1286},[1166],[1107,2460,1228],{"className":2461},[1290],[1107,2463],{"className":2464,"style":1286},[1166],[1107,2466,2468,2472,2549,2552,2621,2624,2693,2696,2699,2702,2705,2708,2711],{"className":2467},[1153],[1107,2469],{"className":2470,"style":2471},[1157],"height:1.2809em;vertical-align:-0.2997em;",[1107,2473,2476,2482],{"className":2474},[2475],"mop",[1107,2477,2294],{"className":2478,"style":2481},[2475,2479,2480],"op-symbol","small-op","position:relative;top:0em;",[1107,2483,2485],{"className":2484},[1444],[1107,2486,2488,2540],{"className":2487},[1448,1615],[1107,2489,2491,2537],{"className":2490},[1452],[1107,2492,2495,2516],{"className":2493,"style":2494},[1456],"height:0.9812em;",[1107,2496,2498,2501],{"style":2497},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1107,2499],{"className":2500,"style":1464},[1463],[1107,2502,2504],{"className":2503},[1468,1469,1470,1471],[1107,2505,2507,2510,2513],{"className":2506},[1162,1471],[1107,2508,2299],{"className":2509},[1162,1597,1471],[1107,2511,1228],{"className":2512},[1290,1471],[1107,2514,1440],{"className":2515},[1162,1471],[1107,2517,2519,2522],{"style":2518},"top:-3.2029em;margin-right:0.05em;",[1107,2520],{"className":2521,"style":1464},[1463],[1107,2523,2525],{"className":2524},[1468,1469,1470,1471],[1107,2526,2528,2531,2534],{"className":2527},[1162,1471],[1107,2529,1768],{"className":2530,"style":1819},[1162,1597,1471],[1107,2532,2310],{"className":2533},[1171,1471],[1107,2535,1433],{"className":2536},[1162,1471],[1107,2538,1652],{"className":2539},[1651],[1107,2541,2543],{"className":2542},[1452],[1107,2544,2547],{"className":2545,"style":2546},[1456],"height:0.2997em;",[1107,2548],{},[1107,2550],{"className":2551,"style":2448},[1166],[1107,2553,2555,2558],{"className":2554},[2475],[1107,2556,2294],{"className":2557,"style":2481},[2475,2479,2480],[1107,2559,2561],{"className":2560},[1444],[1107,2562,2564,2613],{"className":2563},[1448,1615],[1107,2565,2567,2610],{"className":2566},[1452],[1107,2568,2570,2590],{"className":2569,"style":2494},[1456],[1107,2571,2572,2575],{"style":2497},[1107,2573],{"className":2574,"style":1464},[1463],[1107,2576,2578],{"className":2577},[1468,1469,1470,1471],[1107,2579,2581,2584,2587],{"className":2580},[1162,1471],[1107,2582,1539],{"className":2583},[1162,1597,1471],[1107,2585,1228],{"className":2586},[1290,1471],[1107,2588,1440],{"className":2589},[1162,1471],[1107,2591,2592,2595],{"style":2518},[1107,2593],{"className":2594,"style":1464},[1463],[1107,2596,2598],{"className":2597},[1468,1469,1470,1471],[1107,2599,2601,2604,2607],{"className":2600},[1162,1471],[1107,2602,1768],{"className":2603,"style":1819},[1162,1597,1471],[1107,2605,2310],{"className":2606},[1171,1471],[1107,2608,1433],{"className":2609},[1162,1471],[1107,2611,1652],{"className":2612},[1651],[1107,2614,2616],{"className":2615},[1452],[1107,2617,2619],{"className":2618,"style":2546},[1456],[1107,2620],{},[1107,2622],{"className":2623,"style":2448},[1166],[1107,2625,2627,2630],{"className":2626},[2475],[1107,2628,2294],{"className":2629,"style":2481},[2475,2479,2480],[1107,2631,2633],{"className":2632},[1444],[1107,2634,2636,2685],{"className":2635},[1448,1615],[1107,2637,2639,2682],{"className":2638},[1452],[1107,2640,2642,2662],{"className":2641,"style":2494},[1456],[1107,2643,2644,2647],{"style":2497},[1107,2645],{"className":2646,"style":1464},[1463],[1107,2648,2650],{"className":2649},[1468,1469,1470,1471],[1107,2651,2653,2656,2659],{"className":2652},[1162,1471],[1107,2654,1570],{"className":2655},[1162,1597,1471],[1107,2657,1228],{"className":2658},[1290,1471],[1107,2660,1440],{"className":2661},[1162,1471],[1107,2663,2664,2667],{"style":2518},[1107,2665],{"className":2666,"style":1464},[1463],[1107,2668,2670],{"className":2669},[1468,1469,1470,1471],[1107,2671,2673,2676,2679],{"className":2672},[1162,1471],[1107,2674,2349],{"className":2675,"style":1598},[1162,1597,1471],[1107,2677,2310],{"className":2678},[1171,1471],[1107,2680,1433],{"className":2681},[1162,1471],[1107,2683,1652],{"className":2684},[1651],[1107,2686,2688],{"className":2687},[1452],[1107,2689,2691],{"className":2690,"style":2546},[1456],[1107,2692],{},[1107,2694],{"className":2695,"style":2448},[1166],[1107,2697,2356],{"className":2698},[1162,1597],[1107,2700,1533],{"className":2701},[1602],[1107,2703,1544],{"className":2704},[1162,1597],[1107,2706],{"className":2707,"style":1167},[1166],[1107,2709,2363],{"className":2710},[1171],[1107,2712],{"className":2713,"style":1167},[1166],[1107,2715,2717,2721,2725,2728,2731],{"className":2716},[1153],[1107,2718],{"className":2719,"style":2720},[1157],"height:0.7667em;vertical-align:-0.0833em;",[1107,2722,2366],{"className":2723,"style":2724},[1162,1597],"margin-right:0.0576em;",[1107,2726],{"className":2727,"style":1167},[1166],[1107,2729,2369],{"className":2730},[1171],[1107,2732],{"className":2733,"style":1167},[1166],[1107,2735,2737,2741,2744,2747,2750,2753,2756,2759,2762],{"className":2736},[1153],[1107,2738],{"className":2739,"style":2740},[1157],"height:0.854em;vertical-align:-0.1944em;",[1107,2742,2299],{"className":2743},[1162,1597],[1107,2745,1312],{"className":2746},[1311],[1107,2748],{"className":2749,"style":1286},[1166],[1107,2751],{"className":2752,"style":2448},[1166],[1107,2754,2284],{"className":2755,"style":2452},[1162,1597],[1107,2757],{"className":2758,"style":1167},[1166],[1107,2760,2363],{"className":2761},[1171],[1107,2763],{"className":2764,"style":1167},[1166],[1107,2766,2768,2771,2774,2777,2780],{"className":2767},[1153],[1107,2769],{"className":2770,"style":2720},[1157],[1107,2772,2366],{"className":2773,"style":2724},[1162,1597],[1107,2775],{"className":2776,"style":1167},[1166],[1107,2778,2369],{"className":2779},[1171],[1107,2781],{"className":2782,"style":1167},[1166],[1107,2784,2786,2789,2792,2795,2798,2801,2804,2807,2810,2813],{"className":2785},[1153],[1107,2787],{"className":2788,"style":1677},[1157],[1107,2790,1539],{"className":2791},[1162,1597],[1107,2793,1312],{"className":2794},[1311],[1107,2796],{"className":2797,"style":1286},[1166],[1107,2799],{"className":2800,"style":2448},[1166],[1107,2802,1570],{"className":2803},[1162,1597],[1107,2805,1580],{"className":2806},[1737],[1107,2808],{"className":2809,"style":1167},[1166],[1107,2811,2363],{"className":2812},[1171],[1107,2814],{"className":2815,"style":1167},[1166],[1107,2817,2819,2822,2826,2829,2832,2835,2838,2841,2844,2847,2850,2853,2856,2859],{"className":2818},[1153],[1107,2820],{"className":2821,"style":1677},[1157],[1107,2823,2400],{"className":2824,"style":2825},[1162,1597],"margin-right:0.0269em;",[1107,2827,1533],{"className":2828},[1602],[1107,2830,2299],{"className":2831},[1162,1597],[1107,2833,1312],{"className":2834},[1311],[1107,2836],{"className":2837,"style":2448},[1166],[1107,2839,1539],{"className":2840},[1162,1597],[1107,2842,1312],{"className":2843},[1311],[1107,2845],{"className":2846,"style":2448},[1166],[1107,2848,1570],{"className":2849},[1162,1597],[1107,2851,1580],{"className":2852},[1737],[1107,2854],{"className":2855,"style":1167},[1166],[1107,2857,2369],{"className":2858},[1171],[1107,2860],{"className":2861,"style":1167},[1166],[1107,2863,2865,2869],{"className":2864},[1153],[1107,2866],{"className":2867,"style":2868},[1157],"height:0.6944em;",[1107,2870,2419],{"className":2871},[1162,1597],[1100,2873,2874,2875,2904,2905,2933,2934,2962,2963,2991],{},"其中 ",[1107,2876,2878,2891],{"className":2877},[1110],[1107,2879,2881],{"className":2880},[1114],[1116,2882,2883],{"xmlns":1118},[1120,2884,2885,2889],{},[1123,2886,2887],{},[1527,2888,1768],{},[1141,2890,1768],{"encoding":1143},[1107,2892,2894],{"className":2893,"ariaHidden":1149},[1148],[1107,2895,2897,2901],{"className":2896},[1153],[1107,2898],{"className":2899,"style":2900},[1157],"height:0.6833em;",[1107,2902,1768],{"className":2903,"style":1819},[1162,1597]," 为卷积核大小，",[1107,2906,2908,2921],{"className":2907},[1110],[1107,2909,2911],{"className":2910},[1114],[1116,2912,2913],{"xmlns":1118},[1120,2914,2915,2919],{},[1123,2916,2917],{},[1527,2918,2349],{},[1141,2920,2349],{"encoding":1143},[1107,2922,2924],{"className":2923,"ariaHidden":1149},[1148],[1107,2925,2927,2930],{"className":2926},[1153],[1107,2928],{"className":2929,"style":2900},[1157],[1107,2931,2349],{"className":2932,"style":1598},[1162,1597]," 为输入深度，",[1107,2935,2937,2950],{"className":2936},[1110],[1107,2938,2940],{"className":2939},[1114],[1116,2941,2942],{"xmlns":1118},[1120,2943,2944,2948],{},[1123,2945,2946],{},[1527,2947,2366],{},[1141,2949,2366],{"encoding":1143},[1107,2951,2953],{"className":2952,"ariaHidden":1149},[1148],[1107,2954,2956,2959],{"className":2955},[1153],[1107,2957],{"className":2958,"style":2900},[1157],[1107,2960,2366],{"className":2961,"style":2724},[1162,1597]," 为步长，",[1107,2964,2966,2979],{"className":2965},[1110],[1107,2967,2969],{"className":2968},[1114],[1116,2970,2971],{"xmlns":1118},[1120,2972,2973,2977],{},[1123,2974,2975],{},[1527,2976,2419],{},[1141,2978,2419],{"encoding":1143},[1107,2980,2982],{"className":2981,"ariaHidden":1149},[1148],[1107,2983,2985,2988],{"className":2984},[1153],[1107,2986],{"className":2987,"style":2868},[1157],[1107,2989,2419],{"className":2990},[1162,1597]," 为偏置。",[1100,2993,2994],{},"卷积参数与输出尺寸",[2996,2997,2998,3011],"table",{},[2999,3000,3001],"thead",{},[3002,3003,3004,3008],"tr",{},[3005,3006,3007],"th",{},"参数",[3005,3009,3010],{},"说明",[3012,3013,3014,3099,3180,3216,3253],"tbody",{},[3002,3015,3016,3020],{},[3017,3018,3019],"td",{},"输入尺寸",[3017,3021,3022,3098],{},[1107,3023,3025,3049],{"className":3024},[1110],[1107,3026,3028],{"className":3027},[1114],[1116,3029,3030],{"xmlns":1118},[1120,3031,3032,3046],{},[1123,3033,3034,3037,3039,3042,3044],{},[1527,3035,3036],{},"W",[1130,3038,1132],{},[1527,3040,3041],{},"H",[1130,3043,1132],{},[1527,3045,2349],{},[1141,3047,3048],{"encoding":1143},"W \\times H \\times D",[1107,3050,3052,3070,3089],{"className":3051,"ariaHidden":1149},[1148],[1107,3053,3055,3058,3061,3064,3067],{"className":3054},[1153],[1107,3056],{"className":3057,"style":2720},[1157],[1107,3059,3036],{"className":3060,"style":1819},[1162,1597],[1107,3062],{"className":3063,"style":1167},[1166],[1107,3065,1132],{"className":3066},[1171],[1107,3068],{"className":3069,"style":1167},[1166],[1107,3071,3073,3076,3080,3083,3086],{"className":3072},[1153],[1107,3074],{"className":3075,"style":2720},[1157],[1107,3077,3041],{"className":3078,"style":3079},[1162,1597],"margin-right:0.0813em;",[1107,3081],{"className":3082,"style":1167},[1166],[1107,3084,1132],{"className":3085},[1171],[1107,3087],{"className":3088,"style":1167},[1166],[1107,3090,3092,3095],{"className":3091},[1153],[1107,3093],{"className":3094,"style":2900},[1157],[1107,3096,2349],{"className":3097,"style":1598},[1162,1597],"（宽 × 高 × 深度\u002F通道数）",[3002,3100,3101,3104],{},[3017,3102,3103],{},"卷积核尺寸",[3017,3105,3106,3179],{},[1107,3107,3109,3131],{"className":3108},[1110],[1107,3110,3112],{"className":3111},[1114],[1116,3113,3114],{"xmlns":1118},[1120,3115,3116,3128],{},[1123,3117,3118,3120,3122,3124,3126],{},[1527,3119,1768],{},[1130,3121,1132],{},[1527,3123,1768],{},[1130,3125,1132],{},[1527,3127,2349],{},[1141,3129,3130],{"encoding":1143},"F \\times F \\times D",[1107,3132,3134,3152,3170],{"className":3133,"ariaHidden":1149},[1148],[1107,3135,3137,3140,3143,3146,3149],{"className":3136},[1153],[1107,3138],{"className":3139,"style":2720},[1157],[1107,3141,1768],{"className":3142,"style":1819},[1162,1597],[1107,3144],{"className":3145,"style":1167},[1166],[1107,3147,1132],{"className":3148},[1171],[1107,3150],{"className":3151,"style":1167},[1166],[1107,3153,3155,3158,3161,3164,3167],{"className":3154},[1153],[1107,3156],{"className":3157,"style":2720},[1157],[1107,3159,1768],{"className":3160,"style":1819},[1162,1597],[1107,3162],{"className":3163,"style":1167},[1166],[1107,3165,1132],{"className":3166},[1171],[1107,3168],{"className":3169,"style":1167},[1166],[1107,3171,3173,3176],{"className":3172},[1153],[1107,3174],{"className":3175,"style":2900},[1157],[1107,3177,2349],{"className":3178,"style":1598},[1162,1597],"（卷积核的深度必须与输入深度一致）",[3002,3181,3182,3185],{},[3017,3183,3184],{},"步长（Stride）",[3017,3186,3187,3215],{},[1107,3188,3190,3203],{"className":3189},[1110],[1107,3191,3193],{"className":3192},[1114],[1116,3194,3195],{"xmlns":1118},[1120,3196,3197,3201],{},[1123,3198,3199],{},[1527,3200,2366],{},[1141,3202,2366],{"encoding":1143},[1107,3204,3206],{"className":3205,"ariaHidden":1149},[1148],[1107,3207,3209,3212],{"className":3208},[1153],[1107,3210],{"className":3211,"style":2900},[1157],[1107,3213,2366],{"className":3214,"style":2724},[1162,1597],"：卷积核每次移动的像素数",[3002,3217,3218,3221],{},[3017,3219,3220],{},"填充（Padding）",[3017,3222,3223,3252],{},[1107,3224,3226,3240],{"className":3225},[1110],[1107,3227,3229],{"className":3228},[1114],[1116,3230,3231],{"xmlns":1118},[1120,3232,3233,3238],{},[1123,3234,3235],{},[1527,3236,3237],{},"P",[1141,3239,3237],{"encoding":1143},[1107,3241,3243],{"className":3242,"ariaHidden":1149},[1148],[1107,3244,3246,3249],{"className":3245},[1153],[1107,3247],{"className":3248,"style":2900},[1157],[1107,3250,3237],{"className":3251,"style":1819},[1162,1597],"：在输入边界补零的圈数",[3002,3254,3255,3258],{},[3017,3256,3257],{},"卷积核数量",[3017,3259,3260,3290],{},[1107,3261,3263,3277],{"className":3262},[1110],[1107,3264,3266],{"className":3265},[1114],[1116,3267,3268],{"xmlns":1118},[1120,3269,3270,3275],{},[1123,3271,3272],{},[1527,3273,3274],{},"K",[1141,3276,3274],{"encoding":1143},[1107,3278,3280],{"className":3279,"ariaHidden":1149},[1148],[1107,3281,3283,3286],{"className":3282},[1153],[1107,3284],{"className":3285,"style":2900},[1157],[1107,3287,3274],{"className":3288,"style":3289},[1162,1597],"margin-right:0.0715em;","：使用多少个不同的卷积核",[1100,3292,3293],{},[1480,3294,3295],{},"输出尺寸公式：",[1100,3297,3298],{},[1107,3299,3301,3350],{"className":3300},[1110],[1107,3302,3304],{"className":3303},[1114],[1116,3305,3306],{"xmlns":1118},[1120,3307,3308,3347],{},[1123,3309,3310,3322,3324,3343,3345],{},[1535,3311,3312,3314],{},[1527,3313,3036],{},[1123,3315,3316,3318,3320],{},[1527,3317,1951],{},[1527,3319,1551],{},[1527,3321,1554],{},[1130,3323,1228],{},[3325,3326,3327,3341],"mfrac",{},[1123,3328,3329,3331,3333,3335,3337,3339],{},[1527,3330,3036],{},[1130,3332,2310],{},[1527,3334,1768],{},[1130,3336,2369],{},[1126,3338,1771],{},[1527,3340,3237],{},[1527,3342,2366],{},[1130,3344,2369],{},[1126,3346,1433],{},[1141,3348,3349],{"encoding":1143},"W_{out} = \\frac{W - F + 2P}{S} + 1",[1107,3351,3353,3419,3527],{"className":3352,"ariaHidden":1149},[1148],[1107,3354,3356,3360,3410,3413,3416],{"className":3355},[1153],[1107,3357],{"className":3358,"style":3359},[1157],"height:0.8333em;vertical-align:-0.15em;",[1107,3361,3363,3366],{"className":3362},[1162],[1107,3364,3036],{"className":3365,"style":1819},[1162,1597],[1107,3367,3369],{"className":3368},[1444],[1107,3370,3372,3402],{"className":3371},[1448,1615],[1107,3373,3375,3399],{"className":3374},[1452],[1107,3376,3378],{"className":3377,"style":2044},[1456],[1107,3379,3381,3384],{"style":3380},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1107,3382],{"className":3383,"style":1464},[1463],[1107,3385,3387],{"className":3386},[1468,1469,1470,1471],[1107,3388,3390,3393,3396],{"className":3389},[1162,1471],[1107,3391,1951],{"className":3392},[1162,1597,1471],[1107,3394,1551],{"className":3395},[1162,1597,1471],[1107,3397,1554],{"className":3398},[1162,1597,1471],[1107,3400,1652],{"className":3401},[1651],[1107,3403,3405],{"className":3404},[1452],[1107,3406,3408],{"className":3407,"style":1731},[1456],[1107,3409],{},[1107,3411],{"className":3412,"style":1286},[1166],[1107,3414,1228],{"className":3415},[1290],[1107,3417],{"className":3418,"style":1286},[1166],[1107,3420,3422,3426,3518,3521,3524],{"className":3421},[1153],[1107,3423],{"className":3424,"style":3425},[1157],"height:1.2173em;vertical-align:-0.345em;",[1107,3427,3429,3433,3515],{"className":3428},[1162],[1107,3430],{"className":3431},[1602,3432],"nulldelimiter",[1107,3434,3436],{"className":3435},[3325],[1107,3437,3439,3506],{"className":3438},[1448,1615],[1107,3440,3442,3503],{"className":3441},[1452],[1107,3443,3446,3462,3473],{"className":3444,"style":3445},[1456],"height:0.8723em;",[1107,3447,3449,3453],{"style":3448},"top:-2.655em;",[1107,3450],{"className":3451,"style":3452},[1463],"height:3em;",[1107,3454,3456],{"className":3455},[1468,1469,1470,1471],[1107,3457,3459],{"className":3458},[1162,1471],[1107,3460,2366],{"className":3461,"style":2724},[1162,1597,1471],[1107,3463,3465,3468],{"style":3464},"top:-3.23em;",[1107,3466],{"className":3467,"style":3452},[1463],[1107,3469],{"className":3470,"style":3472},[3471],"frac-line","border-bottom-width:0.04em;",[1107,3474,3476,3479],{"style":3475},"top:-3.394em;",[1107,3477],{"className":3478,"style":3452},[1463],[1107,3480,3482],{"className":3481},[1468,1469,1470,1471],[1107,3483,3485,3488,3491,3494,3497,3500],{"className":3484},[1162,1471],[1107,3486,3036],{"className":3487,"style":1819},[1162,1597,1471],[1107,3489,2310],{"className":3490},[1171,1471],[1107,3492,1768],{"className":3493,"style":1819},[1162,1597,1471],[1107,3495,2369],{"className":3496},[1171,1471],[1107,3498,1771],{"className":3499},[1162,1471],[1107,3501,3237],{"className":3502,"style":1819},[1162,1597,1471],[1107,3504,1652],{"className":3505},[1651],[1107,3507,3509],{"className":3508},[1452],[1107,3510,3513],{"className":3511,"style":3512},[1456],"height:0.345em;",[1107,3514],{},[1107,3516],{"className":3517},[1737,3432],[1107,3519],{"className":3520,"style":1167},[1166],[1107,3522,2369],{"className":3523},[1171],[1107,3525],{"className":3526,"style":1167},[1166],[1107,3528,3530,3533],{"className":3529},[1153],[1107,3531],{"className":3532,"style":1199},[1157],[1107,3534,1433],{"className":3535},[1162],[1100,3537,3538],{},[1107,3539,3541,3589],{"className":3540},[1110],[1107,3542,3544],{"className":3543},[1114],[1116,3545,3546],{"xmlns":1118},[1120,3547,3548,3586],{},[1123,3549,3550,3562,3564,3582,3584],{},[1535,3551,3552,3554],{},[1527,3553,3041],{},[1123,3555,3556,3558,3560],{},[1527,3557,1951],{},[1527,3559,1551],{},[1527,3561,1554],{},[1130,3563,1228],{},[3325,3565,3566,3580],{},[1123,3567,3568,3570,3572,3574,3576,3578],{},[1527,3569,3041],{},[1130,3571,2310],{},[1527,3573,1768],{},[1130,3575,2369],{},[1126,3577,1771],{},[1527,3579,3237],{},[1527,3581,2366],{},[1130,3583,2369],{},[1126,3585,1433],{},[1141,3587,3588],{"encoding":1143},"H_{out} = \\frac{H - F + 2P}{S} + 1",[1107,3590,3592,3657,3755],{"className":3591,"ariaHidden":1149},[1148],[1107,3593,3595,3598,3648,3651,3654],{"className":3594},[1153],[1107,3596],{"className":3597,"style":3359},[1157],[1107,3599,3601,3604],{"className":3600},[1162],[1107,3602,3041],{"className":3603,"style":3079},[1162,1597],[1107,3605,3607],{"className":3606},[1444],[1107,3608,3610,3640],{"className":3609},[1448,1615],[1107,3611,3613,3637],{"className":3612},[1452],[1107,3614,3616],{"className":3615,"style":2044},[1456],[1107,3617,3619,3622],{"style":3618},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[1107,3620],{"className":3621,"style":1464},[1463],[1107,3623,3625],{"className":3624},[1468,1469,1470,1471],[1107,3626,3628,3631,3634],{"className":3627},[1162,1471],[1107,3629,1951],{"className":3630},[1162,1597,1471],[1107,3632,1551],{"className":3633},[1162,1597,1471],[1107,3635,1554],{"className":3636},[1162,1597,1471],[1107,3638,1652],{"className":3639},[1651],[1107,3641,3643],{"className":3642},[1452],[1107,3644,3646],{"className":3645,"style":1731},[1456],[1107,3647],{},[1107,3649],{"className":3650,"style":1286},[1166],[1107,3652,1228],{"className":3653},[1290],[1107,3655],{"className":3656,"style":1286},[1166],[1107,3658,3660,3663,3746,3749,3752],{"className":3659},[1153],[1107,3661],{"className":3662,"style":3425},[1157],[1107,3664,3666,3669,3743],{"className":3665},[1162],[1107,3667],{"className":3668},[1602,3432],[1107,3670,3672],{"className":3671},[3325],[1107,3673,3675,3735],{"className":3674},[1448,1615],[1107,3676,3678,3732],{"className":3677},[1452],[1107,3679,3681,3695,3703],{"className":3680,"style":3445},[1456],[1107,3682,3683,3686],{"style":3448},[1107,3684],{"className":3685,"style":3452},[1463],[1107,3687,3689],{"className":3688},[1468,1469,1470,1471],[1107,3690,3692],{"className":3691},[1162,1471],[1107,3693,2366],{"className":3694,"style":2724},[1162,1597,1471],[1107,3696,3697,3700],{"style":3464},[1107,3698],{"className":3699,"style":3452},[1463],[1107,3701],{"className":3702,"style":3472},[3471],[1107,3704,3705,3708],{"style":3475},[1107,3706],{"className":3707,"style":3452},[1463],[1107,3709,3711],{"className":3710},[1468,1469,1470,1471],[1107,3712,3714,3717,3720,3723,3726,3729],{"className":3713},[1162,1471],[1107,3715,3041],{"className":3716,"style":3079},[1162,1597,1471],[1107,3718,2310],{"className":3719},[1171,1471],[1107,3721,1768],{"className":3722,"style":1819},[1162,1597,1471],[1107,3724,2369],{"className":3725},[1171,1471],[1107,3727,1771],{"className":3728},[1162,1471],[1107,3730,3237],{"className":3731,"style":1819},[1162,1597,1471],[1107,3733,1652],{"className":3734},[1651],[1107,3736,3738],{"className":3737},[1452],[1107,3739,3741],{"className":3740,"style":3512},[1456],[1107,3742],{},[1107,3744],{"className":3745},[1737,3432],[1107,3747],{"className":3748,"style":1167},[1166],[1107,3750,2369],{"className":3751},[1171],[1107,3753],{"className":3754,"style":1167},[1166],[1107,3756,3758,3761],{"className":3757},[1153],[1107,3759],{"className":3760,"style":1199},[1157],[1107,3762,1433],{"className":3763},[1162],[1100,3765,3766,3874],{},[1107,3767,3769,3797],{"className":3768},[1110],[1107,3770,3772],{"className":3771},[1114],[1116,3773,3774],{"xmlns":1118},[1120,3775,3776,3794],{},[1123,3777,3778,3790,3792],{},[1535,3779,3780,3782],{},[1527,3781,2349],{},[1123,3783,3784,3786,3788],{},[1527,3785,1951],{},[1527,3787,1551],{},[1527,3789,1554],{},[1130,3791,1228],{},[1527,3793,3274],{},[1141,3795,3796],{"encoding":1143},"D_{out} = K",[1107,3798,3800,3865],{"className":3799,"ariaHidden":1149},[1148],[1107,3801,3803,3806,3856,3859,3862],{"className":3802},[1153],[1107,3804],{"className":3805,"style":3359},[1157],[1107,3807,3809,3812],{"className":3808},[1162],[1107,3810,2349],{"className":3811,"style":1598},[1162,1597],[1107,3813,3815],{"className":3814},[1444],[1107,3816,3818,3848],{"className":3817},[1448,1615],[1107,3819,3821,3845],{"className":3820},[1452],[1107,3822,3824],{"className":3823,"style":2044},[1456],[1107,3825,3827,3830],{"style":3826},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1107,3828],{"className":3829,"style":1464},[1463],[1107,3831,3833],{"className":3832},[1468,1469,1470,1471],[1107,3834,3836,3839,3842],{"className":3835},[1162,1471],[1107,3837,1951],{"className":3838},[1162,1597,1471],[1107,3840,1551],{"className":3841},[1162,1597,1471],[1107,3843,1554],{"className":3844},[1162,1597,1471],[1107,3846,1652],{"className":3847},[1651],[1107,3849,3851],{"className":3850},[1452],[1107,3852,3854],{"className":3853,"style":1731},[1456],[1107,3855],{},[1107,3857],{"className":3858,"style":1286},[1166],[1107,3860,1228],{"className":3861},[1290],[1107,3863],{"className":3864,"style":1286},[1166],[1107,3866,3868,3871],{"className":3867},[1153],[1107,3869],{"className":3870,"style":2900},[1157],[1107,3872,3274],{"className":3873,"style":3289},[1162,1597],"（输出深度 = 卷积核数量）",[1100,3876,3877,3878,3952,3953,4005],{},"输入 ",[1107,3879,3881,3904],{"className":3880},[1110],[1107,3882,3884],{"className":3883},[1114],[1116,3885,3886],{"xmlns":1118},[1120,3887,3888,3901],{},[1123,3889,3890,3893,3895,3897,3899],{},[1126,3891,3892],{},"32",[1130,3894,1132],{},[1126,3896,3892],{},[1130,3898,1132],{},[1126,3900,1139],{},[1141,3902,3903],{"encoding":1143},"32 \\times 32 \\times 3",[1107,3905,3907,3925,3943],{"className":3906,"ariaHidden":1149},[1148],[1107,3908,3910,3913,3916,3919,3922],{"className":3909},[1153],[1107,3911],{"className":3912,"style":1158},[1157],[1107,3914,3892],{"className":3915},[1162],[1107,3917],{"className":3918,"style":1167},[1166],[1107,3920,1132],{"className":3921},[1171],[1107,3923],{"className":3924,"style":1167},[1166],[1107,3926,3928,3931,3934,3937,3940],{"className":3927},[1153],[1107,3929],{"className":3930,"style":1158},[1157],[1107,3932,3892],{"className":3933},[1162],[1107,3935],{"className":3936,"style":1167},[1166],[1107,3938,1132],{"className":3939},[1171],[1107,3941],{"className":3942,"style":1167},[1166],[1107,3944,3946,3949],{"className":3945},[1153],[1107,3947],{"className":3948,"style":1199},[1157],[1107,3950,1139],{"className":3951},[1162],"，使用 10 个 ",[1107,3954,3956,3975],{"className":3955},[1110],[1107,3957,3959],{"className":3958},[1114],[1116,3960,3961],{"xmlns":1118},[1120,3962,3963,3972],{},[1123,3964,3965,3968,3970],{},[1126,3966,3967],{},"5",[1130,3969,1132],{},[1126,3971,3967],{},[1141,3973,3974],{"encoding":1143},"5 \\times 5",[1107,3976,3978,3996],{"className":3977,"ariaHidden":1149},[1148],[1107,3979,3981,3984,3987,3990,3993],{"className":3980},[1153],[1107,3982],{"className":3983,"style":1158},[1157],[1107,3985,3967],{"className":3986},[1162],[1107,3988],{"className":3989,"style":1167},[1166],[1107,3991,1132],{"className":3992},[1171],[1107,3994],{"className":3995,"style":1167},[1166],[1107,3997,3999,4002],{"className":3998},[1153],[1107,4000],{"className":4001,"style":1199},[1157],[1107,4003,3967],{"className":4004},[1162]," 卷积核，stride=1，padding=0：",[2201,4007,4008,4178,4344,4375,4451],{},[2204,4009,4010,4011],{},"输出宽度：",[1107,4012,4014,4051],{"className":4013},[1110],[1107,4015,4017],{"className":4016},[1114],[1116,4018,4019],{"xmlns":1118},[1120,4020,4021,4048],{},[1123,4022,4023,4039,4041,4043,4045],{},[3325,4024,4025,4037],{},[1123,4026,4027,4029,4031,4033,4035],{},[1126,4028,3892],{},[1130,4030,2310],{},[1126,4032,3967],{},[1130,4034,2369],{},[1126,4036,1440],{},[1126,4038,1433],{},[1130,4040,2369],{},[1126,4042,1433],{},[1130,4044,1228],{},[1126,4046,4047],{},"28",[1141,4049,4050],{"encoding":1143},"\\frac{32 - 5 + 0}{1} + 1 = 28",[1107,4052,4054,4151,4169],{"className":4053,"ariaHidden":1149},[1148],[1107,4055,4057,4061,4142,4145,4148],{"className":4056},[1153],[1107,4058],{"className":4059,"style":4060},[1157],"height:1.1901em;vertical-align:-0.345em;",[1107,4062,4064,4067,4139],{"className":4063},[1162],[1107,4065],{"className":4066},[1602,3432],[1107,4068,4070],{"className":4069},[3325],[1107,4071,4073,4131],{"className":4072},[1448,1615],[1107,4074,4076,4128],{"className":4075},[1452],[1107,4077,4080,4094,4102],{"className":4078,"style":4079},[1456],"height:0.8451em;",[1107,4081,4082,4085],{"style":3448},[1107,4083],{"className":4084,"style":3452},[1463],[1107,4086,4088],{"className":4087},[1468,1469,1470,1471],[1107,4089,4091],{"className":4090},[1162,1471],[1107,4092,1433],{"className":4093},[1162,1471],[1107,4095,4096,4099],{"style":3464},[1107,4097],{"className":4098,"style":3452},[1463],[1107,4100],{"className":4101,"style":3472},[3471],[1107,4103,4104,4107],{"style":3475},[1107,4105],{"className":4106,"style":3452},[1463],[1107,4108,4110],{"className":4109},[1468,1469,1470,1471],[1107,4111,4113,4116,4119,4122,4125],{"className":4112},[1162,1471],[1107,4114,3892],{"className":4115},[1162,1471],[1107,4117,2310],{"className":4118},[1171,1471],[1107,4120,3967],{"className":4121},[1162,1471],[1107,4123,2369],{"className":4124},[1171,1471],[1107,4126,1440],{"className":4127},[1162,1471],[1107,4129,1652],{"className":4130},[1651],[1107,4132,4134],{"className":4133},[1452],[1107,4135,4137],{"className":4136,"style":3512},[1456],[1107,4138],{},[1107,4140],{"className":4141},[1737,3432],[1107,4143],{"className":4144,"style":1167},[1166],[1107,4146,2369],{"className":4147},[1171],[1107,4149],{"className":4150,"style":1167},[1166],[1107,4152,4154,4157,4160,4163,4166],{"className":4153},[1153],[1107,4155],{"className":4156,"style":1199},[1157],[1107,4158,1433],{"className":4159},[1162],[1107,4161],{"className":4162,"style":1286},[1166],[1107,4164,1228],{"className":4165},[1290],[1107,4167],{"className":4168,"style":1286},[1166],[1107,4170,4172,4175],{"className":4171},[1153],[1107,4173],{"className":4174,"style":1199},[1157],[1107,4176,4047],{"className":4177},[1162],[2204,4179,4180,4181],{},"输出高度：",[1107,4182,4184,4219],{"className":4183},[1110],[1107,4185,4187],{"className":4186},[1114],[1116,4188,4189],{"xmlns":1118},[1120,4190,4191,4217],{},[1123,4192,4193,4209,4211,4213,4215],{},[3325,4194,4195,4207],{},[1123,4196,4197,4199,4201,4203,4205],{},[1126,4198,3892],{},[1130,4200,2310],{},[1126,4202,3967],{},[1130,4204,2369],{},[1126,4206,1440],{},[1126,4208,1433],{},[1130,4210,2369],{},[1126,4212,1433],{},[1130,4214,1228],{},[1126,4216,4047],{},[1141,4218,4050],{"encoding":1143},[1107,4220,4222,4317,4335],{"className":4221,"ariaHidden":1149},[1148],[1107,4223,4225,4228,4308,4311,4314],{"className":4224},[1153],[1107,4226],{"className":4227,"style":4060},[1157],[1107,4229,4231,4234,4305],{"className":4230},[1162],[1107,4232],{"className":4233},[1602,3432],[1107,4235,4237],{"className":4236},[3325],[1107,4238,4240,4297],{"className":4239},[1448,1615],[1107,4241,4243,4294],{"className":4242},[1452],[1107,4244,4246,4260,4268],{"className":4245,"style":4079},[1456],[1107,4247,4248,4251],{"style":3448},[1107,4249],{"className":4250,"style":3452},[1463],[1107,4252,4254],{"className":4253},[1468,1469,1470,1471],[1107,4255,4257],{"className":4256},[1162,1471],[1107,4258,1433],{"className":4259},[1162,1471],[1107,4261,4262,4265],{"style":3464},[1107,4263],{"className":4264,"style":3452},[1463],[1107,4266],{"className":4267,"style":3472},[3471],[1107,4269,4270,4273],{"style":3475},[1107,4271],{"className":4272,"style":3452},[1463],[1107,4274,4276],{"className":4275},[1468,1469,1470,1471],[1107,4277,4279,4282,4285,4288,4291],{"className":4278},[1162,1471],[1107,4280,3892],{"className":4281},[1162,1471],[1107,4283,2310],{"className":4284},[1171,1471],[1107,4286,3967],{"className":4287},[1162,1471],[1107,4289,2369],{"className":4290},[1171,1471],[1107,4292,1440],{"className":4293},[1162,1471],[1107,4295,1652],{"className":4296},[1651],[1107,4298,4300],{"className":4299},[1452],[1107,4301,4303],{"className":4302,"style":3512},[1456],[1107,4304],{},[1107,4306],{"className":4307},[1737,3432],[1107,4309],{"className":4310,"style":1167},[1166],[1107,4312,2369],{"className":4313},[1171],[1107,4315],{"className":4316,"style":1167},[1166],[1107,4318,4320,4323,4326,4329,4332],{"className":4319},[1153],[1107,4321],{"className":4322,"style":1199},[1157],[1107,4324,1433],{"className":4325},[1162],[1107,4327],{"className":4328,"style":1286},[1166],[1107,4330,1228],{"className":4331},[1290],[1107,4333],{"className":4334,"style":1286},[1166],[1107,4336,4338,4341],{"className":4337},[1153],[1107,4339],{"className":4340,"style":1199},[1157],[1107,4342,4047],{"className":4343},[1162],[2204,4345,4346,4347],{},"输出深度：",[1107,4348,4350,4363],{"className":4349},[1110],[1107,4351,4353],{"className":4352},[1114],[1116,4354,4355],{"xmlns":1118},[1120,4356,4357,4361],{},[1123,4358,4359],{},[1126,4360,1350],{},[1141,4362,1350],{"encoding":1143},[1107,4364,4366],{"className":4365,"ariaHidden":1149},[1148],[1107,4367,4369,4372],{"className":4368},[1153],[1107,4370],{"className":4371,"style":1199},[1157],[1107,4373,1350],{"className":4374},[1162],[2204,4376,4377,4378],{},"输出尺寸：",[1107,4379,4381,4403],{"className":4380},[1110],[1107,4382,4384],{"className":4383},[1114],[1116,4385,4386],{"xmlns":1118},[1120,4387,4388,4400],{},[1123,4389,4390,4392,4394,4396,4398],{},[1126,4391,4047],{},[1130,4393,1132],{},[1126,4395,4047],{},[1130,4397,1132],{},[1126,4399,1350],{},[1141,4401,4402],{"encoding":1143},"28 \\times 28 \\times 10",[1107,4404,4406,4424,4442],{"className":4405,"ariaHidden":1149},[1148],[1107,4407,4409,4412,4415,4418,4421],{"className":4408},[1153],[1107,4410],{"className":4411,"style":1158},[1157],[1107,4413,4047],{"className":4414},[1162],[1107,4416],{"className":4417,"style":1167},[1166],[1107,4419,1132],{"className":4420},[1171],[1107,4422],{"className":4423,"style":1167},[1166],[1107,4425,4427,4430,4433,4436,4439],{"className":4426},[1153],[1107,4428],{"className":4429,"style":1158},[1157],[1107,4431,4047],{"className":4432},[1162],[1107,4434],{"className":4435,"style":1167},[1166],[1107,4437,1132],{"className":4438},[1171],[1107,4440],{"className":4441,"style":1167},[1166],[1107,4443,4445,4448],{"className":4444},[1153],[1107,4446],{"className":4447,"style":1199},[1157],[1107,4449,1350],{"className":4450},[1162],[2204,4452,4453,4454],{},"该层参数量：",[1107,4455,4457,4496],{"className":4456},[1110],[1107,4458,4460],{"className":4459},[1114],[1116,4461,4462],{"xmlns":1118},[1120,4463,4464,4493],{},[1123,4465,4466,4468,4470,4472,4474,4476,4478,4480,4482,4484,4486,4488,4490],{},[1126,4467,1350],{},[1130,4469,1132],{},[1130,4471,1533],{"stretchy":1532},[1126,4473,3967],{},[1130,4475,1132],{},[1126,4477,3967],{},[1130,4479,1132],{},[1126,4481,1139],{},[1130,4483,2369],{},[1126,4485,1433],{},[1130,4487,1580],{"stretchy":1532},[1130,4489,1228],{},[1126,4491,4492],{},"760",[1141,4494,4495],{"encoding":1143},"10 \\times (5 \\times 5 \\times 3 + 1) = 760",[1107,4497,4499,4517,4538,4556,4574,4595],{"className":4498,"ariaHidden":1149},[1148],[1107,4500,4502,4505,4508,4511,4514],{"className":4501},[1153],[1107,4503],{"className":4504,"style":1158},[1157],[1107,4506,1350],{"className":4507},[1162],[1107,4509],{"className":4510,"style":1167},[1166],[1107,4512,1132],{"className":4513},[1171],[1107,4515],{"className":4516,"style":1167},[1166],[1107,4518,4520,4523,4526,4529,4532,4535],{"className":4519},[1153],[1107,4521],{"className":4522,"style":1677},[1157],[1107,4524,1533],{"className":4525},[1602],[1107,4527,3967],{"className":4528},[1162],[1107,4530],{"className":4531,"style":1167},[1166],[1107,4533,1132],{"className":4534},[1171],[1107,4536],{"className":4537,"style":1167},[1166],[1107,4539,4541,4544,4547,4550,4553],{"className":4540},[1153],[1107,4542],{"className":4543,"style":1158},[1157],[1107,4545,3967],{"className":4546},[1162],[1107,4548],{"className":4549,"style":1167},[1166],[1107,4551,1132],{"className":4552},[1171],[1107,4554],{"className":4555,"style":1167},[1166],[1107,4557,4559,4562,4565,4568,4571],{"className":4558},[1153],[1107,4560],{"className":4561,"style":1158},[1157],[1107,4563,1139],{"className":4564},[1162],[1107,4566],{"className":4567,"style":1167},[1166],[1107,4569,2369],{"className":4570},[1171],[1107,4572],{"className":4573,"style":1167},[1166],[1107,4575,4577,4580,4583,4586,4589,4592],{"className":4576},[1153],[1107,4578],{"className":4579,"style":1677},[1157],[1107,4581,1433],{"className":4582},[1162],[1107,4584,1580],{"className":4585},[1737],[1107,4587],{"className":4588,"style":1286},[1166],[1107,4590,1228],{"className":4591},[1290],[1107,4593],{"className":4594,"style":1286},[1166],[1107,4596,4598,4601],{"className":4597},[1153],[1107,4599],{"className":4600,"style":1199},[1157],[1107,4602,4492],{"className":4603},[1162],[1100,4605,4606],{},"常用 Padding 策略",[2996,4608,4609,4622],{},[2999,4610,4611],{},[3002,4612,4613,4616,4619],{},[3005,4614,4615],{},"策略",[3005,4617,4618],{},"Padding 值",[3005,4620,4621],{},"效果",[3012,4623,4624,4685],{},[3002,4625,4626,4629,4682],{},[3017,4627,4628],{},"Valid（无填充）",[3017,4630,4631],{},[1107,4632,4634,4652],{"className":4633},[1110],[1107,4635,4637],{"className":4636},[1114],[1116,4638,4639],{"xmlns":1118},[1120,4640,4641,4649],{},[1123,4642,4643,4645,4647],{},[1527,4644,3237],{},[1130,4646,1228],{},[1126,4648,1440],{},[1141,4650,4651],{"encoding":1143},"P = 0",[1107,4653,4655,4673],{"className":4654,"ariaHidden":1149},[1148],[1107,4656,4658,4661,4664,4667,4670],{"className":4657},[1153],[1107,4659],{"className":4660,"style":2900},[1157],[1107,4662,3237],{"className":4663,"style":1819},[1162,1597],[1107,4665],{"className":4666,"style":1286},[1166],[1107,4668,1228],{"className":4669},[1290],[1107,4671],{"className":4672,"style":1286},[1166],[1107,4674,4676,4679],{"className":4675},[1153],[1107,4677],{"className":4678,"style":1199},[1157],[1107,4680,1440],{"className":4681},[1162],[3017,4683,4684],{},"输出尺寸缩小",[3002,4686,4687,4690,4824],{},[3017,4688,4689],{},"Same（等尺寸）",[3017,4691,4692],{},[1107,4693,4695,4723],{"className":4694},[1110],[1107,4696,4698],{"className":4697},[1114],[1116,4699,4700],{"xmlns":1118},[1120,4701,4702,4720],{},[1123,4703,4704,4706,4708],{},[1527,4705,3237],{},[1130,4707,1228],{},[3325,4709,4710,4718],{},[1123,4711,4712,4714,4716],{},[1527,4713,1768],{},[1130,4715,2310],{},[1126,4717,1433],{},[1126,4719,1771],{},[1141,4721,4722],{"encoding":1143},"P = \\frac{F-1}{2}",[1107,4724,4726,4744],{"className":4725,"ariaHidden":1149},[1148],[1107,4727,4729,4732,4735,4738,4741],{"className":4728},[1153],[1107,4730],{"className":4731,"style":2900},[1157],[1107,4733,3237],{"className":4734,"style":1819},[1162,1597],[1107,4736],{"className":4737,"style":1286},[1166],[1107,4739,1228],{"className":4740},[1290],[1107,4742],{"className":4743,"style":1286},[1166],[1107,4745,4747,4750],{"className":4746},[1153],[1107,4748],{"className":4749,"style":3425},[1157],[1107,4751,4753,4756,4821],{"className":4752},[1162],[1107,4754],{"className":4755},[1602,3432],[1107,4757,4759],{"className":4758},[3325],[1107,4760,4762,4813],{"className":4761},[1448,1615],[1107,4763,4765,4810],{"className":4764},[1452],[1107,4766,4768,4782,4790],{"className":4767,"style":3445},[1456],[1107,4769,4770,4773],{"style":3448},[1107,4771],{"className":4772,"style":3452},[1463],[1107,4774,4776],{"className":4775},[1468,1469,1470,1471],[1107,4777,4779],{"className":4778},[1162,1471],[1107,4780,1771],{"className":4781},[1162,1471],[1107,4783,4784,4787],{"style":3464},[1107,4785],{"className":4786,"style":3452},[1463],[1107,4788],{"className":4789,"style":3472},[3471],[1107,4791,4792,4795],{"style":3475},[1107,4793],{"className":4794,"style":3452},[1463],[1107,4796,4798],{"className":4797},[1468,1469,1470,1471],[1107,4799,4801,4804,4807],{"className":4800},[1162,1471],[1107,4802,1768],{"className":4803,"style":1819},[1162,1597,1471],[1107,4805,2310],{"className":4806},[1171,1471],[1107,4808,1433],{"className":4809},[1162,1471],[1107,4811,1652],{"className":4812},[1651],[1107,4814,4816],{"className":4815},[1452],[1107,4817,4819],{"className":4818,"style":3512},[1456],[1107,4820],{},[1107,4822],{"className":4823},[1737,3432],[3017,4825,4826,4827,4878],{},"当 ",[1107,4828,4830,4848],{"className":4829},[1110],[1107,4831,4833],{"className":4832},[1114],[1116,4834,4835],{"xmlns":1118},[1120,4836,4837,4845],{},[1123,4838,4839,4841,4843],{},[1527,4840,2366],{},[1130,4842,1228],{},[1126,4844,1433],{},[1141,4846,4847],{"encoding":1143},"S=1",[1107,4849,4851,4869],{"className":4850,"ariaHidden":1149},[1148],[1107,4852,4854,4857,4860,4863,4866],{"className":4853},[1153],[1107,4855],{"className":4856,"style":2900},[1157],[1107,4858,2366],{"className":4859,"style":2724},[1162,1597],[1107,4861],{"className":4862,"style":1286},[1166],[1107,4864,1228],{"className":4865},[1290],[1107,4867],{"className":4868,"style":1286},[1166],[1107,4870,4872,4875],{"className":4871},[1153],[1107,4873],{"className":4874,"style":1199},[1157],[1107,4876,1433],{"className":4877},[1162]," 时，输出尺寸 = 输入尺寸",[2163,4880],{},[2247,4882,4884],{"id":4883},"_2-激活层relu","2. 激活层（ReLU）",[1100,4886,4887],{},"卷积的输出是线性运算结果，必须加非线性激活才能让网络学到复杂模式。ReLU 定义为：",[1100,4889,4890],{},[1107,4891,4893,4932],{"className":4892},[1110],[1107,4894,4896],{"className":4895},[1114],[1116,4897,4898],{"xmlns":1118},[1120,4899,4900,4929],{},[1123,4901,4902,4905,4907,4909,4911,4913,4916,4919,4921,4923,4925,4927],{},[1527,4903,4904],{},"f",[1130,4906,1533],{"stretchy":1532},[1527,4908,2356],{},[1130,4910,1580],{"stretchy":1532},[1130,4912,1228],{},[1527,4914,4915],{},"max",[1130,4917,4918],{},"⁡",[1130,4920,1533],{"stretchy":1532},[1126,4922,1440],{},[1130,4924,1312],{"separator":1149},[1527,4926,2356],{},[1130,4928,1580],{"stretchy":1532},[1141,4930,4931],{"encoding":1143},"f(x) = \\max(0, x)",[1107,4933,4935,4963],{"className":4934,"ariaHidden":1149},[1148],[1107,4936,4938,4941,4945,4948,4951,4954,4957,4960],{"className":4937},[1153],[1107,4939],{"className":4940,"style":1677},[1157],[1107,4942,4904],{"className":4943,"style":4944},[1162,1597],"margin-right:0.1076em;",[1107,4946,1533],{"className":4947},[1602],[1107,4949,2356],{"className":4950},[1162,1597],[1107,4952,1580],{"className":4953},[1737],[1107,4955],{"className":4956,"style":1286},[1166],[1107,4958,1228],{"className":4959},[1290],[1107,4961],{"className":4962,"style":1286},[1166],[1107,4964,4966,4969,4972,4975,4978,4981,4984,4987],{"className":4965},[1153],[1107,4967],{"className":4968,"style":1677},[1157],[1107,4970,4915],{"className":4971},[2475],[1107,4973,1533],{"className":4974},[1602],[1107,4976,1440],{"className":4977},[1162],[1107,4979,1312],{"className":4980},[1311],[1107,4982],{"className":4983,"style":2448},[1166],[1107,4985,2356],{"className":4986},[1162,1597],[1107,4988,1580],{"className":4989},[1737],[1100,4991,4992],{},"正值原样通过，负值直接置零。优点是计算快、缓解梯度消失。ReLU 紧跟在每个卷积层之后，不增加参数。",[2163,4994],{},[2247,4996,4998],{"id":4997},"_3-池化层pool","3. 池化层（Pool）",[1100,5000,5001,5002,5005],{},"池化对每个特征图的局部区域做降采样，减小空间尺寸。最常用的是 ",[1480,5003,5004],{},"2×2 最大池化，步长 2","，每个 2×2 区域取最大值，特征图长宽各缩小一半。",[1100,5007,5008],{},"池化的作用",[2201,5010,5011,5014,5017],{},[2204,5012,5013],{},"**降低空间维度：**减少后续层的计算量和参数量",[2204,5015,5016],{},"**提供平移不变性：**对特征位置的微小变化具有鲁棒性",[2204,5018,5019],{},"**控制过拟合：**减少特征图的冗余信息",[1100,5021,5022],{},[1480,5023,5024],{},"最大池化（Max Pooling）",[1100,5026,5027],{},"取窗口内的最大值",[1100,5029,5030],{},"保留最显著的特征激活",[1100,5032,5033],{},"实践中更常用",[1100,5035,5036],{},"示例（2×2 窗口）：",[1100,5038,5039],{},[1107,5040,5042,5104],{"className":5041},[1110],[1107,5043,5045],{"className":5044},[1114],[1116,5046,5047],{"xmlns":1118},[1120,5048,5049,5101],{},[1123,5050,5051,5096,5099],{},[1123,5052,5053,5056,5093],{},[1130,5054,5055],{"fence":1149},"[",[5057,5058,5062,5079],"mtable",{"rowspacing":5059,"columnalign":5060,"columnspacing":5061},"0.16em","center center","1em",[5063,5064,5065,5073],"mtr",{},[5066,5067,5068],"mtd",{},[5069,5070,5071],"mstyle",{"scriptlevel":1440,"displaystyle":1532},[1126,5072,1433],{},[5066,5074,5075],{},[5069,5076,5077],{"scriptlevel":1440,"displaystyle":1532},[1126,5078,1139],{},[5063,5080,5081,5087],{},[5066,5082,5083],{},[5069,5084,5085],{"scriptlevel":1440,"displaystyle":1532},[1126,5086,3967],{},[5066,5088,5089],{},[5069,5090,5091],{"scriptlevel":1440,"displaystyle":1532},[1126,5092,1771],{},[1130,5094,5095],{"fence":1149},"]",[1130,5097,5098],{},"→",[1126,5100,3967],{},[1141,5102,5103],{"encoding":1143},"\\begin{bmatrix} 1 & 3 \\\\ 5 & 2 \\end{bmatrix} \\rightarrow 5",[1107,5105,5107,5251],{"className":5106,"ariaHidden":1149},[1148],[1107,5108,5110,5114,5242,5245,5248],{"className":5109},[1153],[1107,5111],{"className":5112,"style":5113},[1157],"height:2.4em;vertical-align:-0.95em;",[1107,5115,5118,5127,5236],{"className":5116},[5117],"minner",[1107,5119,5123],{"className":5120,"style":5122},[1602,5121],"delimcenter","top:0em;",[1107,5124,5055],{"className":5125},[5126,1470],"delimsizing",[1107,5128,5130],{"className":5129},[1162],[1107,5131,5133,5183,5188,5191],{"className":5132},[5057],[1107,5134,5137],{"className":5135},[5136],"col-align-c",[1107,5138,5140,5174],{"className":5139},[1448,1615],[1107,5141,5143,5171],{"className":5142},[1452],[1107,5144,5147,5159],{"className":5145,"style":5146},[1456],"height:1.45em;",[1107,5148,5150,5153],{"style":5149},"top:-3.61em;",[1107,5151],{"className":5152,"style":3452},[1463],[1107,5154,5156],{"className":5155},[1162],[1107,5157,1433],{"className":5158},[1162],[1107,5160,5162,5165],{"style":5161},"top:-2.41em;",[1107,5163],{"className":5164,"style":3452},[1463],[1107,5166,5168],{"className":5167},[1162],[1107,5169,3967],{"className":5170},[1162],[1107,5172,1652],{"className":5173},[1651],[1107,5175,5177],{"className":5176},[1452],[1107,5178,5181],{"className":5179,"style":5180},[1456],"height:0.95em;",[1107,5182],{},[1107,5184],{"className":5185,"style":5187},[5186],"arraycolsep","width:0.5em;",[1107,5189],{"className":5190,"style":5187},[5186],[1107,5192,5194],{"className":5193},[5136],[1107,5195,5197,5228],{"className":5196},[1448,1615],[1107,5198,5200,5225],{"className":5199},[1452],[1107,5201,5203,5214],{"className":5202,"style":5146},[1456],[1107,5204,5205,5208],{"style":5149},[1107,5206],{"className":5207,"style":3452},[1463],[1107,5209,5211],{"className":5210},[1162],[1107,5212,1139],{"className":5213},[1162],[1107,5215,5216,5219],{"style":5161},[1107,5217],{"className":5218,"style":3452},[1463],[1107,5220,5222],{"className":5221},[1162],[1107,5223,1771],{"className":5224},[1162],[1107,5226,1652],{"className":5227},[1651],[1107,5229,5231],{"className":5230},[1452],[1107,5232,5234],{"className":5233,"style":5180},[1456],[1107,5235],{},[1107,5237,5239],{"className":5238,"style":5122},[1737,5121],[1107,5240,5095],{"className":5241},[5126,1470],[1107,5243],{"className":5244,"style":1286},[1166],[1107,5246,5098],{"className":5247},[1290],[1107,5249],{"className":5250,"style":1286},[1166],[1107,5252,5254,5257],{"className":5253},[1153],[1107,5255],{"className":5256,"style":1199},[1157],[1107,5258,3967],{"className":5259},[1162],[1100,5261,5262],{},[1480,5263,5264],{},"平均池化（Average Pooling）",[1100,5266,5267],{},"取窗口内的平均值",[1100,5269,5270],{},"保留区域的整体信息",[1100,5272,5273],{},"常用于网络最后一层（GAP）",[1100,5275,5036],{},[1100,5277,5278],{},[1107,5279,5281,5334],{"className":5280},[1110],[1107,5282,5284],{"className":5283},[1114],[1116,5285,5286],{"xmlns":1118},[1120,5287,5288,5331],{},[1123,5289,5290,5326,5328],{},[1123,5291,5292,5294,5324],{},[1130,5293,5055],{"fence":1149},[5057,5295,5296,5310],{"rowspacing":5059,"columnalign":5060,"columnspacing":5061},[5063,5297,5298,5304],{},[5066,5299,5300],{},[5069,5301,5302],{"scriptlevel":1440,"displaystyle":1532},[1126,5303,1433],{},[5066,5305,5306],{},[5069,5307,5308],{"scriptlevel":1440,"displaystyle":1532},[1126,5309,1139],{},[5063,5311,5312,5318],{},[5066,5313,5314],{},[5069,5315,5316],{"scriptlevel":1440,"displaystyle":1532},[1126,5317,3967],{},[5066,5319,5320],{},[5069,5321,5322],{"scriptlevel":1440,"displaystyle":1532},[1126,5323,1771],{},[1130,5325,5095],{"fence":1149},[1130,5327,5098],{},[1126,5329,5330],{},"2.75",[1141,5332,5333],{"encoding":1143},"\\begin{bmatrix} 1 & 3 \\\\ 5 & 2 \\end{bmatrix} \\rightarrow 2.75",[1107,5335,5337,5469],{"className":5336,"ariaHidden":1149},[1148],[1107,5338,5340,5343,5460,5463,5466],{"className":5339},[1153],[1107,5341],{"className":5342,"style":5113},[1157],[1107,5344,5346,5352,5454],{"className":5345},[5117],[1107,5347,5349],{"className":5348,"style":5122},[1602,5121],[1107,5350,5055],{"className":5351},[5126,1470],[1107,5353,5355],{"className":5354},[1162],[1107,5356,5358,5403,5406,5409],{"className":5357},[5057],[1107,5359,5361],{"className":5360},[5136],[1107,5362,5364,5395],{"className":5363},[1448,1615],[1107,5365,5367,5392],{"className":5366},[1452],[1107,5368,5370,5381],{"className":5369,"style":5146},[1456],[1107,5371,5372,5375],{"style":5149},[1107,5373],{"className":5374,"style":3452},[1463],[1107,5376,5378],{"className":5377},[1162],[1107,5379,1433],{"className":5380},[1162],[1107,5382,5383,5386],{"style":5161},[1107,5384],{"className":5385,"style":3452},[1463],[1107,5387,5389],{"className":5388},[1162],[1107,5390,3967],{"className":5391},[1162],[1107,5393,1652],{"className":5394},[1651],[1107,5396,5398],{"className":5397},[1452],[1107,5399,5401],{"className":5400,"style":5180},[1456],[1107,5402],{},[1107,5404],{"className":5405,"style":5187},[5186],[1107,5407],{"className":5408,"style":5187},[5186],[1107,5410,5412],{"className":5411},[5136],[1107,5413,5415,5446],{"className":5414},[1448,1615],[1107,5416,5418,5443],{"className":5417},[1452],[1107,5419,5421,5432],{"className":5420,"style":5146},[1456],[1107,5422,5423,5426],{"style":5149},[1107,5424],{"className":5425,"style":3452},[1463],[1107,5427,5429],{"className":5428},[1162],[1107,5430,1139],{"className":5431},[1162],[1107,5433,5434,5437],{"style":5161},[1107,5435],{"className":5436,"style":3452},[1463],[1107,5438,5440],{"className":5439},[1162],[1107,5441,1771],{"className":5442},[1162],[1107,5444,1652],{"className":5445},[1651],[1107,5447,5449],{"className":5448},[1452],[1107,5450,5452],{"className":5451,"style":5180},[1456],[1107,5453],{},[1107,5455,5457],{"className":5456,"style":5122},[1737,5121],[1107,5458,5095],{"className":5459},[5126,1470],[1107,5461],{"className":5462,"style":1286},[1166],[1107,5464,5098],{"className":5465},[1290],[1107,5467],{"className":5468,"style":1286},[1166],[1107,5470,5472,5475],{"className":5471},[1153],[1107,5473],{"className":5474,"style":1199},[1157],[1107,5476,5330],{"className":5477},[1162],[1100,5479,5480,5481,5532,5533,5584,5585,5683],{},"典型配置：窗口大小 ",[1107,5482,5484,5502],{"className":5483},[1110],[1107,5485,5487],{"className":5486},[1114],[1116,5488,5489],{"xmlns":1118},[1120,5490,5491,5499],{},[1123,5492,5493,5495,5497],{},[1126,5494,1771],{},[1130,5496,1132],{},[1126,5498,1771],{},[1141,5500,5501],{"encoding":1143},"2 \\times 2",[1107,5503,5505,5523],{"className":5504,"ariaHidden":1149},[1148],[1107,5506,5508,5511,5514,5517,5520],{"className":5507},[1153],[1107,5509],{"className":5510,"style":1158},[1157],[1107,5512,1771],{"className":5513},[1162],[1107,5515],{"className":5516,"style":1167},[1166],[1107,5518,1132],{"className":5519},[1171],[1107,5521],{"className":5522,"style":1167},[1166],[1107,5524,5526,5529],{"className":5525},[1153],[1107,5527],{"className":5528,"style":1199},[1157],[1107,5530,1771],{"className":5531},[1162],"，步长 ",[1107,5534,5536,5554],{"className":5535},[1110],[1107,5537,5539],{"className":5538},[1114],[1116,5540,5541],{"xmlns":1118},[1120,5542,5543,5551],{},[1123,5544,5545,5547,5549],{},[1527,5546,2366],{},[1130,5548,1228],{},[1126,5550,1771],{},[1141,5552,5553],{"encoding":1143},"S = 2",[1107,5555,5557,5575],{"className":5556,"ariaHidden":1149},[1148],[1107,5558,5560,5563,5566,5569,5572],{"className":5559},[1153],[1107,5561],{"className":5562,"style":2900},[1157],[1107,5564,2366],{"className":5565,"style":2724},[1162,1597],[1107,5567],{"className":5568,"style":1286},[1166],[1107,5570,1228],{"className":5571},[1290],[1107,5573],{"className":5574,"style":1286},[1166],[1107,5576,5578,5581],{"className":5577},[1153],[1107,5579],{"className":5580,"style":1199},[1157],[1107,5582,1771],{"className":5583},[1162],"，将特征图的空间维度缩小为原来的 ",[1107,5586,5588,5606],{"className":5587},[1110],[1107,5589,5591],{"className":5590},[1114],[1116,5592,5593],{"xmlns":1118},[1120,5594,5595,5603],{},[1123,5596,5597],{},[3325,5598,5599,5601],{},[1126,5600,1433],{},[1126,5602,1771],{},[1141,5604,5605],{"encoding":1143},"\\frac{1}{2}",[1107,5607,5609],{"className":5608,"ariaHidden":1149},[1148],[1107,5610,5612,5615],{"className":5611},[1153],[1107,5613],{"className":5614,"style":4060},[1157],[1107,5616,5618,5621,5680],{"className":5617},[1162],[1107,5619],{"className":5620},[1602,3432],[1107,5622,5624],{"className":5623},[3325],[1107,5625,5627,5672],{"className":5626},[1448,1615],[1107,5628,5630,5669],{"className":5629},[1452],[1107,5631,5633,5647,5655],{"className":5632,"style":4079},[1456],[1107,5634,5635,5638],{"style":3448},[1107,5636],{"className":5637,"style":3452},[1463],[1107,5639,5641],{"className":5640},[1468,1469,1470,1471],[1107,5642,5644],{"className":5643},[1162,1471],[1107,5645,1771],{"className":5646},[1162,1471],[1107,5648,5649,5652],{"style":3464},[1107,5650],{"className":5651,"style":3452},[1463],[1107,5653],{"className":5654,"style":3472},[3471],[1107,5656,5657,5660],{"style":3475},[1107,5658],{"className":5659,"style":3452},[1463],[1107,5661,5663],{"className":5662},[1468,1469,1470,1471],[1107,5664,5666],{"className":5665},[1162,1471],[1107,5667,1433],{"className":5668},[1162,1471],[1107,5670,1652],{"className":5671},[1651],[1107,5673,5675],{"className":5674},[1452],[1107,5676,5678],{"className":5677,"style":3512},[1456],[1107,5679],{},[1107,5681],{"className":5682},[1737,3432],"。",[1100,5685,5686,5687,5690],{},"池化层",[1480,5688,5689],{},"没有可学习参数","，它仅对每个特征图独立操作，不改变深度（通道数）",[2163,5692],{},[2247,5694,5696],{"id":5695},"_4-展平flatten","4. 展平（Flatten）",[1100,5698,5699],{},"经过多层卷积+池化后，特征图是三维张量（高 × 宽 × 通道）。展平就是把它拉成一维向量，例如 7×7×512 → 25088 维向量。这一步没有计算，纯粹是形状变换，目的是衔接后面的全连接层。",[2163,5701],{},[2247,5703,5705],{"id":5704},"_5-全连接层fc","5. 全连接层（FC）",[1100,5707,5708],{},"与普通神经网络相同——每个神经元和前一层所有神经元相连。全连接层负责把卷积提取到的空间特征\"汇总\"为高层语义表示，最终映射到类别数量的维度。",[1100,5710,5711,5714],{},[1480,5712,5713],{},"注意："," 全连接层是参数最多的部分（AlexNet 中 FC 占总参数的 90% 以上），现代网络趋向用全局平均池化替代。",[2163,5716],{},[2247,5718,5720],{"id":5719},"_6-softmax","6. Softmax",[1100,5722,5723,5724,5752],{},"网络最后一层输出 ",[1107,5725,5727,5740],{"className":5726},[1110],[1107,5728,5730],{"className":5729},[1114],[1116,5731,5732],{"xmlns":1118},[1120,5733,5734,5738],{},[1123,5735,5736],{},[1527,5737,3274],{},[1141,5739,3274],{"encoding":1143},[1107,5741,5743],{"className":5742,"ariaHidden":1149},[1148],[1107,5744,5746,5749],{"className":5745},[1153],[1107,5747],{"className":5748,"style":2900},[1157],[1107,5750,3274],{"className":5751,"style":3289},[1162,1597]," 个原始分数（logits），Softmax 将其转换为概率分布：",[1100,5754,5755],{},[1107,5756,5758,5824],{"className":5757},[1110],[1107,5759,5761],{"className":5760},[1114],[1116,5762,5763],{"xmlns":1118},[1120,5764,5765,5821],{},[1123,5766,5767,5769,5771,5773,5775,5778,5780,5782],{},[1527,5768,3237],{},[1130,5770,1533],{"stretchy":1532},[1527,5772,2275],{},[1130,5774,1228],{},[1527,5776,5777],{},"k",[1130,5779,1580],{"stretchy":1532},[1130,5781,1228],{},[3325,5783,5784,5795],{},[1346,5785,5786,5788],{},[1527,5787,1575],{},[1535,5789,5790,5793],{},[1527,5791,5792],{},"z",[1527,5794,5777],{},[1123,5796,5797,5811],{},[2290,5798,5799,5801,5809],{},[1130,5800,2294],{},[1123,5802,5803,5805,5807],{},[1527,5804,2284],{},[1130,5806,1228],{},[1126,5808,1433],{},[1527,5810,3274],{},[1346,5812,5813,5815],{},[1527,5814,1575],{},[1535,5816,5817,5819],{},[1527,5818,5792],{},[1527,5820,2284],{},[1141,5822,5823],{"encoding":1143},"P(y=k) = \\frac{e^{z_k}}{\\sum_{j=1}^{K} e^{z_j}}",[1107,5825,5827,5851,5873],{"className":5826,"ariaHidden":1149},[1148],[1107,5828,5830,5833,5836,5839,5842,5845,5848],{"className":5829},[1153],[1107,5831],{"className":5832,"style":1677},[1157],[1107,5834,3237],{"className":5835,"style":1819},[1162,1597],[1107,5837,1533],{"className":5838},[1602],[1107,5840,2275],{"className":5841,"style":2435},[1162,1597],[1107,5843],{"className":5844,"style":1286},[1166],[1107,5846,1228],{"className":5847},[1290],[1107,5849],{"className":5850,"style":1286},[1166],[1107,5852,5854,5857,5861,5864,5867,5870],{"className":5853},[1153],[1107,5855],{"className":5856,"style":1677},[1157],[1107,5858,5777],{"className":5859,"style":5860},[1162,1597],"margin-right:0.0315em;",[1107,5862,1580],{"className":5863},[1737],[1107,5865],{"className":5866,"style":1286},[1166],[1107,5868,1228],{"className":5869},[1290],[1107,5871],{"className":5872,"style":1286},[1166],[1107,5874,5876,5880],{"className":5875},[1153],[1107,5877],{"className":5878,"style":5879},[1157],"height:1.6629em;vertical-align:-0.7519em;",[1107,5881,5883,5886,6159],{"className":5882},[1162],[1107,5884],{"className":5885},[1602,3432],[1107,5887,5889],{"className":5888},[3325],[1107,5890,5892,6150],{"className":5891},[1448,1615],[1107,5893,5895,6147],{"className":5894},[1452],[1107,5896,5899,6058,6066],{"className":5897,"style":5898},[1456],"height:0.911em;",[1107,5900,5902,5905],{"style":5901},"top:-2.5703em;",[1107,5903],{"className":5904,"style":3452},[1463],[1107,5906,5908],{"className":5907},[1468,1469,1470,1471],[1107,5909,5911,5981,5985],{"className":5910},[1162,1471],[1107,5912,5914,5917],{"className":5913},[2475,1471],[1107,5915,2294],{"className":5916,"style":2481},[2475,2479,2480,1471],[1107,5918,5920],{"className":5919},[1444],[1107,5921,5923,5972],{"className":5922},[1448,1615],[1107,5924,5926,5969],{"className":5925},[1452],[1107,5927,5930,5954],{"className":5928,"style":5929},[1456],"height:0.8852em;",[1107,5931,5933,5937],{"style":5932},"top:-2.1786em;margin-left:0em;margin-right:0.0714em;",[1107,5934],{"className":5935,"style":5936},[1463],"height:2.5em;",[1107,5938,5942],{"className":5939},[1468,5940,5941,1471],"reset-size3","size1",[1107,5943,5945,5948,5951],{"className":5944},[1162,1471],[1107,5946,2284],{"className":5947,"style":2452},[1162,1597,1471],[1107,5949,1228],{"className":5950},[1290,1471],[1107,5952,1433],{"className":5953},[1162,1471],[1107,5955,5957,5960],{"style":5956},"top:-2.8971em;margin-right:0.0714em;",[1107,5958],{"className":5959,"style":5936},[1463],[1107,5961,5963],{"className":5962},[1468,5940,5941,1471],[1107,5964,5966],{"className":5965},[1162,1471],[1107,5967,3274],{"className":5968,"style":3289},[1162,1597,1471],[1107,5970,1652],{"className":5971},[1651],[1107,5973,5975],{"className":5974},[1452],[1107,5976,5979],{"className":5977,"style":5978},[1456],"height:0.4603em;",[1107,5980],{},[1107,5982],{"className":5983,"style":5984},[1166,1471],"margin-right:0.1952em;",[1107,5986,5988,5991],{"className":5987},[1162,1471],[1107,5989,1575],{"className":5990},[1162,1597,1471],[1107,5992,5994],{"className":5993},[1444],[1107,5995,5997],{"className":5996},[1448],[1107,5998,6000],{"className":5999},[1452],[1107,6001,6004],{"className":6002,"style":6003},[1456],"height:0.779em;",[1107,6005,6007,6010],{"style":6006},"top:-2.9714em;margin-right:0.0714em;",[1107,6008],{"className":6009,"style":5936},[1463],[1107,6011,6013],{"className":6012},[1468,5940,5941,1471],[1107,6014,6016],{"className":6015},[1162,1471],[1107,6017,6019,6023],{"className":6018},[1162,1471],[1107,6020,5792],{"className":6021,"style":6022},[1162,1597,1471],"margin-right:0.044em;",[1107,6024,6026],{"className":6025},[1444],[1107,6027,6029,6049],{"className":6028},[1448,1615],[1107,6030,6032,6046],{"className":6031},[1452],[1107,6033,6036],{"className":6034,"style":6035},[1456],"height:0.3448em;",[1107,6037,6039,6043],{"style":6038},"top:-2.3448em;margin-left:-0.044em;margin-right:0.1em;",[1107,6040],{"className":6041,"style":6042},[1463],"height:2.6595em;",[1107,6044,2284],{"className":6045,"style":2452},[1162,1597,1471],[1107,6047,1652],{"className":6048},[1651],[1107,6050,6052],{"className":6051},[1452],[1107,6053,6056],{"className":6054,"style":6055},[1456],"height:0.5092em;",[1107,6057],{},[1107,6059,6060,6063],{"style":3464},[1107,6061],{"className":6062,"style":3452},[1463],[1107,6064],{"className":6065,"style":3472},[3471],[1107,6067,6068,6071],{"style":3475},[1107,6069],{"className":6070,"style":3452},[1463],[1107,6072,6074],{"className":6073},[1468,1469,1470,1471],[1107,6075,6077],{"className":6076},[1162,1471],[1107,6078,6080,6083],{"className":6079},[1162,1471],[1107,6081,1575],{"className":6082},[1162,1597,1471],[1107,6084,6086],{"className":6085},[1444],[1107,6087,6089],{"className":6088},[1448],[1107,6090,6092],{"className":6091},[1452],[1107,6093,6096],{"className":6094,"style":6095},[1456],"height:0.7385em;",[1107,6097,6099,6102],{"style":6098},"top:-2.931em;margin-right:0.0714em;",[1107,6100],{"className":6101,"style":5936},[1463],[1107,6103,6105],{"className":6104},[1468,5940,5941,1471],[1107,6106,6108],{"className":6107},[1162,1471],[1107,6109,6111,6114],{"className":6110},[1162,1471],[1107,6112,5792],{"className":6113,"style":6022},[1162,1597,1471],[1107,6115,6117],{"className":6116},[1444],[1107,6118,6120,6138],{"className":6119},[1448,1615],[1107,6121,6123,6135],{"className":6122},[1452],[1107,6124,6126],{"className":6125,"style":6035},[1456],[1107,6127,6128,6132],{"style":6038},[1107,6129],{"className":6130,"style":6131},[1463],"height:2.6944em;",[1107,6133,5777],{"className":6134,"style":5860},[1162,1597,1471],[1107,6136,1652],{"className":6137},[1651],[1107,6139,6141],{"className":6140},[1452],[1107,6142,6145],{"className":6143,"style":6144},[1456],"height:0.3496em;",[1107,6146],{},[1107,6148,1652],{"className":6149},[1651],[1107,6151,6153],{"className":6152},[1452],[1107,6154,6157],{"className":6155,"style":6156},[1456],"height:0.7519em;",[1107,6158],{},[1107,6160],{"className":6161},[1737,3432],[1100,6163,6164,6165,6193],{},"输出的 ",[1107,6166,6168,6181],{"className":6167},[1110],[1107,6169,6171],{"className":6170},[1114],[1116,6172,6173],{"xmlns":1118},[1120,6174,6175,6179],{},[1123,6176,6177],{},[1527,6178,3274],{},[1141,6180,3274],{"encoding":1143},[1107,6182,6184],{"className":6183,"ariaHidden":1149},[1148],[1107,6185,6187,6190],{"className":6186},[1153],[1107,6188],{"className":6189,"style":2900},[1157],[1107,6191,3274],{"className":6192,"style":3289},[1162,1597]," 个值都在 (0,1) 之间且和为 1，最大概率对应的类别就是预测结果。训练时配合交叉熵损失函数使用。",[1091,6195,6197],{"id":6196},"三一些经典-cnn-架构","三、一些经典 CNN 架构",[2247,6199,6201],{"id":6200},"lenet-51990s","LeNet-5（1990s）",[1100,6203,6204],{},"手写数字识别的开山之作，90 年代被美国银行用于支票识别。",[2201,6206,6207,6210],{},[2204,6208,6209],{},"结构：7 层（卷积 + 池化 + 全连接交替）",[2204,6211,6212],{},"意义：奠定了 \"卷积 + 池化 + 全连接\" 的 CNN 基本范式",[2247,6214,6216],{"id":6215},"alexnet2012","AlexNet（2012）",[1100,6218,6219],{},"ImageNet 2012 冠军，top-5 错误率 15.3%（第二名 26.2%），开启深度学习时代。",[2201,6221,6222,6225,6245],{},[2204,6223,6224],{},"结构： 5 个卷积层 + 3 个全连接层，约 60M 参数",[2204,6226,6227,6228],{},"创新：",[2201,6229,6230,6233,6236,6239,6242],{},[2204,6231,6232],{},"ReLU 替代 Sigmoid → 训练快 6 倍，缓解梯度消失",[2204,6234,6235],{},"Dropout（FC 层 0.5）→ 减少过拟合",[2204,6237,6238],{},"数据增强 → 裁剪、翻转、颜色扰动扩充数据",[2204,6240,6241],{},"GPU 并行训练 → 首次用两块 GPU 训练大网络",[2204,6243,6244],{},"LRN（局部响应归一化） → 后来被 Batch Norm 取代",[2204,6246,6247],{},"意义： 证明了更大的数据 + 更深的网络 + GPU 算力可以碾压传统方法",[2163,6249],{},[2247,6251,6253],{"id":6252},"vggnet2014","VGGNet（2014）",[1100,6255,6256],{},"核心思想 ——深度且简洁，一律用 3×3 小核，靠堆深度来提升性能。",[2201,6258,6259,6262,6276,6286,6289],{},[2204,6260,6261],{},"结构： VGG-16（13 卷积 + 3 FC）或 VGG-19，约 138M 参数",[2204,6263,6264,6265],{},"特点：",[2201,6266,6267,6270,6273],{},[2204,6268,6269],{},"所有卷积核统一 3×3，步长 1，等宽填充",[2204,6271,6272],{},"所有池化统一 2×2，步长 2",[2204,6274,6275],{},"每次池化后通道数翻倍：64 → 128 → 256 → 512 → 512",[2204,6277,6278,6279,6282,6283,6285],{},"两个 3×3 卷积的感受野 = 一个 5×5，但参数从 25",[2175,6280,6281],{},"C","2 降为 18",[2175,6284,6281],{},"2（减少 28%），且多一次 ReLU 非线性，表达能力更强",[2204,6287,6288],{},"训练技巧： 先训练浅版本（VGG-11），用其权重初始化更深的版本",[2204,6290,6291],{},"缺点： 参数量巨大（138M），全连接层占了大部分",[2163,6293],{},[2247,6295,6297],{"id":6296},"googlenet-inception2014","GoogLeNet \u002F Inception（2014）",[1100,6299,6300],{},"2014 ILSVRC 冠军，22 层但只有 5M 参数（AlexNet 的 1\u002F15），错误率 6.7%。",[2201,6302,6303,6320,6323,6326,6329],{},[2204,6304,6305,6306],{},"核心创新 ——Inception 模块： 在同一层并行使用多种卷积核，再拼接：",[2201,6307,6308,6311,6314,6317],{},[2204,6309,6310],{},"1×1 卷积：降维 + 捕获通道关系",[2204,6312,6313],{},"3×3 卷积：中等尺度特征",[2204,6315,6316],{},"5×5 卷积：大尺度特征",[2204,6318,6319],{},"3×3 最大池化：保留显著特征",[2204,6321,6322],{},"1×1 卷积降维： 在 3×3 和 5×5 之前先用 1×1 减少通道数，大幅减少计算量（这是参数少的关键原因）",[2204,6324,6325],{},"全局平均池化： 用 GAP 替代全连接层，把 7×7×1024 的特征图直接平均为 1×1×1024，极大减少参数",[2204,6327,6328],{},"辅助分类器： 在中间层加额外分类头，缓解深层网络的梯度消失",[2204,6330,6331],{},"设计哲学： 不是单纯加深，而是加宽（多尺度并行），用巧妙结构换效率",[2163,6333],{},[2247,6335,6337],{"id":6336},"resnet2015","ResNet（2015）",[1100,6339,6340],{},"152 层，top-5 错误率 3.6%，首次超越人类水平（5.1%）。",[2201,6342,6343,6346,6360,6388,6391,6394,6397],{},[2204,6344,6345],{},"核心创新 —— 残差连接（Skip Connection）：",[2204,6347,6348,1533,6350,6352,6353,1533,6355,6357,6358],{},[2175,6349,3041],{},[2175,6351,2356],{},")=",[2175,6354,1768],{},[2175,6356,2356],{},")+",[2175,6359,2356],{},[2204,6361,6362,6363,1533,6365,6367,6368,1533,6370,6352,6372,1533,6374,6376,6377,6379,6380,1533,6382,6384,6385,6387],{},"不再让网络直接学目标映射 ",[2175,6364,3041],{},[2175,6366,2356],{},")，而是学残差 ",[2175,6369,1768],{},[2175,6371,2356],{},[2175,6373,3041],{},[2175,6375,2356],{},")−",[2175,6378,2356],{},"。如果某层不需要做任何变换，",[2175,6381,1768],{},[2175,6383,2356],{},")=0 即可，梯度可以通过 +",[2175,6386,2356],{}," 直接跳过该层回传。",[2204,6389,6390],{},"解决的问题： 网络加深到一定程度后性能反而下降（退化问题），不是过拟合而是优化困难。残差连接让梯度畅通无阻，使训练上百层成为可能。",[2204,6392,6393],{},"结构： 大量使用 3×3 卷积 + BN + ReLU，无全连接层（GAP 直接接分类）",[2204,6395,6396],{},"参数量： 25M（比 VGG 的 138M 少得多，但性能远超）",[2204,6398,6399],{},"Bottleneck 设计： 深版本用 1×1→3×3→1×1 结构进一步减少计算量",[2163,6401],{},[1096,6403,6404],{"id":6404},"相关公式",[2201,6406,6407,6701,6879,7300,7457],{},[2204,6408,6409,6410],{},"卷积输出尺寸：",[1107,6411,6413,6475],{"className":6412},[1110],[1107,6414,6416],{"className":6415},[1114],[1116,6417,6418],{"xmlns":1118},[1120,6419,6420,6472],{},[1123,6421,6422,6434,6436,6439,6465,6468,6470],{},[1535,6423,6424,6426],{},[1527,6425,3036],{},[1123,6427,6428,6430,6432],{},[1527,6429,1951],{},[1527,6431,1551],{},[1527,6433,1554],{},[1130,6435,1228],{},[1130,6437,6438],{"stretchy":1532},"⌊",[3325,6440,6441,6463],{},[1123,6442,6443,6453,6455,6457,6459,6461],{},[1535,6444,6445,6447],{},[1527,6446,3036],{},[1123,6448,6449,6451],{},[1527,6450,1544],{},[1527,6452,1539],{},[1130,6454,2310],{},[1527,6456,1768],{},[1130,6458,2369],{},[1126,6460,1771],{},[1527,6462,3237],{},[1527,6464,2366],{},[1130,6466,6467],{"stretchy":1532},"⌋",[1130,6469,2369],{},[1126,6471,1433],{},[1141,6473,6474],{"encoding":1143},"W_{out} = \\lfloor \\frac{W_{in} - F + 2P}{S} \\rfloor + 1",[1107,6476,6478,6542,6692],{"className":6477,"ariaHidden":1149},[1148],[1107,6479,6481,6484,6533,6536,6539],{"className":6480},[1153],[1107,6482],{"className":6483,"style":3359},[1157],[1107,6485,6487,6490],{"className":6486},[1162],[1107,6488,3036],{"className":6489,"style":1819},[1162,1597],[1107,6491,6493],{"className":6492},[1444],[1107,6494,6496,6525],{"className":6495},[1448,1615],[1107,6497,6499,6522],{"className":6498},[1452],[1107,6500,6502],{"className":6501,"style":2044},[1456],[1107,6503,6504,6507],{"style":3380},[1107,6505],{"className":6506,"style":1464},[1463],[1107,6508,6510],{"className":6509},[1468,1469,1470,1471],[1107,6511,6513,6516,6519],{"className":6512},[1162,1471],[1107,6514,1951],{"className":6515},[1162,1597,1471],[1107,6517,1551],{"className":6518},[1162,1597,1471],[1107,6520,1554],{"className":6521},[1162,1597,1471],[1107,6523,1652],{"className":6524},[1651],[1107,6526,6528],{"className":6527},[1452],[1107,6529,6531],{"className":6530,"style":1731},[1456],[1107,6532],{},[1107,6534],{"className":6535,"style":1286},[1166],[1107,6537,1228],{"className":6538},[1290],[1107,6540],{"className":6541,"style":1286},[1166],[1107,6543,6545,6549,6552,6680,6683,6686,6689],{"className":6544},[1153],[1107,6546],{"className":6547,"style":6548},[1157],"height:1.2334em;vertical-align:-0.345em;",[1107,6550,6438],{"className":6551},[1602],[1107,6553,6555,6558,6677],{"className":6554},[1162],[1107,6556],{"className":6557},[1602,3432],[1107,6559,6561],{"className":6560},[3325],[1107,6562,6564,6669],{"className":6563},[1448,1615],[1107,6565,6567,6666],{"className":6566},[1452],[1107,6568,6571,6585,6593],{"className":6569,"style":6570},[1456],"height:0.8884em;",[1107,6572,6573,6576],{"style":3448},[1107,6574],{"className":6575,"style":3452},[1463],[1107,6577,6579],{"className":6578},[1468,1469,1470,1471],[1107,6580,6582],{"className":6581},[1162,1471],[1107,6583,2366],{"className":6584,"style":2724},[1162,1597,1471],[1107,6586,6587,6590],{"style":3464},[1107,6588],{"className":6589,"style":3452},[1463],[1107,6591],{"className":6592,"style":3472},[3471],[1107,6594,6596,6599],{"style":6595},"top:-3.4101em;",[1107,6597],{"className":6598,"style":3452},[1463],[1107,6600,6602],{"className":6601},[1468,1469,1470,1471],[1107,6603,6605,6651,6654,6657,6660,6663],{"className":6604},[1162,1471],[1107,6606,6608,6611],{"className":6607},[1162,1471],[1107,6609,3036],{"className":6610,"style":1819},[1162,1597,1471],[1107,6612,6614],{"className":6613},[1444],[1107,6615,6617,6642],{"className":6616},[1448,1615],[1107,6618,6620,6639],{"className":6619},[1452],[1107,6621,6624],{"className":6622,"style":6623},[1456],"height:0.3281em;",[1107,6625,6627,6630],{"style":6626},"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;",[1107,6628],{"className":6629,"style":5936},[1463],[1107,6631,6633],{"className":6632},[1468,5940,5941,1471],[1107,6634,6636],{"className":6635},[1162,1471],[1107,6637,1638],{"className":6638},[1162,1597,1471],[1107,6640,1652],{"className":6641},[1651],[1107,6643,6645],{"className":6644},[1452],[1107,6646,6649],{"className":6647,"style":6648},[1456],"height:0.143em;",[1107,6650],{},[1107,6652,2310],{"className":6653},[1171,1471],[1107,6655,1768],{"className":6656,"style":1819},[1162,1597,1471],[1107,6658,2369],{"className":6659},[1171,1471],[1107,6661,1771],{"className":6662},[1162,1471],[1107,6664,3237],{"className":6665,"style":1819},[1162,1597,1471],[1107,6667,1652],{"className":6668},[1651],[1107,6670,6672],{"className":6671},[1452],[1107,6673,6675],{"className":6674,"style":3512},[1456],[1107,6676],{},[1107,6678],{"className":6679},[1737,3432],[1107,6681,6467],{"className":6682},[1737],[1107,6684],{"className":6685,"style":1167},[1166],[1107,6687,2369],{"className":6688},[1171],[1107,6690],{"className":6691,"style":1167},[1166],[1107,6693,6695,6698],{"className":6694},[1153],[1107,6696],{"className":6697,"style":1199},[1157],[1107,6699,1433],{"className":6700},[1162],[2204,6702,6703,6704],{},"卷积层参数量：",[1107,6705,6707,6749],{"className":6706},[1110],[1107,6708,6710],{"className":6709},[1114],[1116,6711,6712],{"xmlns":1118},[1120,6713,6714,6746],{},[1123,6715,6716,6718,6720,6722,6724,6726,6728,6730,6740,6742,6744],{},[1527,6717,3274],{},[1130,6719,1132],{},[1130,6721,1533],{"stretchy":1532},[1527,6723,1768],{},[1130,6725,1132],{},[1527,6727,1768],{},[1130,6729,1132],{},[1535,6731,6732,6734],{},[1527,6733,2349],{},[1123,6735,6736,6738],{},[1527,6737,1544],{},[1527,6739,1539],{},[1130,6741,2369],{},[1126,6743,1433],{},[1130,6745,1580],{"stretchy":1532},[1141,6747,6748],{"encoding":1143},"K \\times (F \\times F \\times D_{in} + 1)",[1107,6750,6752,6770,6791,6809,6867],{"className":6751,"ariaHidden":1149},[1148],[1107,6753,6755,6758,6761,6764,6767],{"className":6754},[1153],[1107,6756],{"className":6757,"style":2720},[1157],[1107,6759,3274],{"className":6760,"style":3289},[1162,1597],[1107,6762],{"className":6763,"style":1167},[1166],[1107,6765,1132],{"className":6766},[1171],[1107,6768],{"className":6769,"style":1167},[1166],[1107,6771,6773,6776,6779,6782,6785,6788],{"className":6772},[1153],[1107,6774],{"className":6775,"style":1677},[1157],[1107,6777,1533],{"className":6778},[1602],[1107,6780,1768],{"className":6781,"style":1819},[1162,1597],[1107,6783],{"className":6784,"style":1167},[1166],[1107,6786,1132],{"className":6787},[1171],[1107,6789],{"className":6790,"style":1167},[1166],[1107,6792,6794,6797,6800,6803,6806],{"className":6793},[1153],[1107,6795],{"className":6796,"style":2720},[1157],[1107,6798,1768],{"className":6799,"style":1819},[1162,1597],[1107,6801],{"className":6802,"style":1167},[1166],[1107,6804,1132],{"className":6805},[1171],[1107,6807],{"className":6808,"style":1167},[1166],[1107,6810,6812,6815,6858,6861,6864],{"className":6811},[1153],[1107,6813],{"className":6814,"style":3359},[1157],[1107,6816,6818,6821],{"className":6817},[1162],[1107,6819,2349],{"className":6820,"style":1598},[1162,1597],[1107,6822,6824],{"className":6823},[1444],[1107,6825,6827,6850],{"className":6826},[1448,1615],[1107,6828,6830,6847],{"className":6829},[1452],[1107,6831,6833],{"className":6832,"style":1622},[1456],[1107,6834,6835,6838],{"style":3826},[1107,6836],{"className":6837,"style":1464},[1463],[1107,6839,6841],{"className":6840},[1468,1469,1470,1471],[1107,6842,6844],{"className":6843},[1162,1471],[1107,6845,1638],{"className":6846},[1162,1597,1471],[1107,6848,1652],{"className":6849},[1651],[1107,6851,6853],{"className":6852},[1452],[1107,6854,6856],{"className":6855,"style":1731},[1456],[1107,6857],{},[1107,6859],{"className":6860,"style":1167},[1166],[1107,6862,2369],{"className":6863},[1171],[1107,6865],{"className":6866,"style":1167},[1166],[1107,6868,6870,6873,6876],{"className":6869},[1153],[1107,6871],{"className":6872,"style":1677},[1157],[1107,6874,1433],{"className":6875},[1162],[1107,6877,1580],{"className":6878},[1737],[2204,6880,6881,6882],{},"感受野递推：",[1107,6883,6885,6968],{"className":6884},[1110],[1107,6886,6888],{"className":6887},[1114],[1116,6889,6890],{"xmlns":1118},[1120,6891,6892,6965],{},[1123,6893,6894,6897,6904,6906,6908,6920,6922,6924,6930,6932,6934,6936,6938,6959],{},[1527,6895,6896],{},"R",[1535,6898,6899,6901],{},[1527,6900,1768],{},[1527,6902,6903],{},"l",[1130,6905,1228],{},[1527,6907,6896],{},[1535,6909,6910,6912],{},[1527,6911,1768],{},[1123,6913,6914,6916,6918],{},[1527,6915,6903],{},[1130,6917,2310],{},[1126,6919,1433],{},[1130,6921,2369],{},[1130,6923,1533],{"stretchy":1532},[1535,6925,6926,6928],{},[1527,6927,1768],{},[1527,6929,6903],{},[1130,6931,2310],{},[1126,6933,1433],{},[1130,6935,1580],{"stretchy":1532},[1130,6937,1132],{},[2290,6939,6940,6943,6951],{},[1130,6941,6942],{},"∏",[1123,6944,6945,6947,6949],{},[1527,6946,1544],{},[1130,6948,1228],{},[1126,6950,1433],{},[1123,6952,6953,6955,6957],{},[1527,6954,6903],{},[1130,6956,2310],{},[1126,6958,1433],{},[1535,6960,6961,6963],{},[1527,6962,2366],{},[1527,6964,1544],{},[1141,6966,6967],{"encoding":1143},"RF_l = RF_{l-1} + (F_l - 1) \\times \\prod_{i=1}^{l-1} S_i",[1107,6969,6971,7031,7100,7158,7179],{"className":6970,"ariaHidden":1149},[1148],[1107,6972,6974,6977,6981,7022,7025,7028],{"className":6973},[1153],[1107,6975],{"className":6976,"style":3359},[1157],[1107,6978,6896],{"className":6979,"style":6980},[1162,1597],"margin-right:0.0077em;",[1107,6982,6984,6987],{"className":6983},[1162],[1107,6985,1768],{"className":6986,"style":1819},[1162,1597],[1107,6988,6990],{"className":6989},[1444],[1107,6991,6993,7014],{"className":6992},[1448,1615],[1107,6994,6996,7011],{"className":6995},[1452],[1107,6997,6999],{"className":6998,"style":1696},[1456],[1107,7000,7001,7004],{"style":3380},[1107,7002],{"className":7003,"style":1464},[1463],[1107,7005,7007],{"className":7006},[1468,1469,1470,1471],[1107,7008,6903],{"className":7009,"style":7010},[1162,1597,1471],"margin-right:0.0197em;",[1107,7012,1652],{"className":7013},[1651],[1107,7015,7017],{"className":7016},[1452],[1107,7018,7020],{"className":7019,"style":1731},[1456],[1107,7021],{},[1107,7023],{"className":7024,"style":1286},[1166],[1107,7026,1228],{"className":7027},[1290],[1107,7029],{"className":7030,"style":1286},[1166],[1107,7032,7034,7038,7041,7091,7094,7097],{"className":7033},[1153],[1107,7035],{"className":7036,"style":7037},[1157],"height:0.8917em;vertical-align:-0.2083em;",[1107,7039,6896],{"className":7040,"style":6980},[1162,1597],[1107,7042,7044,7047],{"className":7043},[1162],[1107,7045,1768],{"className":7046,"style":1819},[1162,1597],[1107,7048,7050],{"className":7049},[1444],[1107,7051,7053,7082],{"className":7052},[1448,1615],[1107,7054,7056,7079],{"className":7055},[1452],[1107,7057,7059],{"className":7058,"style":1696},[1456],[1107,7060,7061,7064],{"style":3380},[1107,7062],{"className":7063,"style":1464},[1463],[1107,7065,7067],{"className":7066},[1468,1469,1470,1471],[1107,7068,7070,7073,7076],{"className":7069},[1162,1471],[1107,7071,6903],{"className":7072,"style":7010},[1162,1597,1471],[1107,7074,2310],{"className":7075},[1171,1471],[1107,7077,1433],{"className":7078},[1162,1471],[1107,7080,1652],{"className":7081},[1651],[1107,7083,7085],{"className":7084},[1452],[1107,7086,7089],{"className":7087,"style":7088},[1456],"height:0.2083em;",[1107,7090],{},[1107,7092],{"className":7093,"style":1167},[1166],[1107,7095,2369],{"className":7096},[1171],[1107,7098],{"className":7099,"style":1167},[1166],[1107,7101,7103,7106,7109,7149,7152,7155],{"className":7102},[1153],[1107,7104],{"className":7105,"style":1677},[1157],[1107,7107,1533],{"className":7108},[1602],[1107,7110,7112,7115],{"className":7111},[1162],[1107,7113,1768],{"className":7114,"style":1819},[1162,1597],[1107,7116,7118],{"className":7117},[1444],[1107,7119,7121,7141],{"className":7120},[1448,1615],[1107,7122,7124,7138],{"className":7123},[1452],[1107,7125,7127],{"className":7126,"style":1696},[1456],[1107,7128,7129,7132],{"style":3380},[1107,7130],{"className":7131,"style":1464},[1463],[1107,7133,7135],{"className":7134},[1468,1469,1470,1471],[1107,7136,6903],{"className":7137,"style":7010},[1162,1597,1471],[1107,7139,1652],{"className":7140},[1651],[1107,7142,7144],{"className":7143},[1452],[1107,7145,7147],{"className":7146,"style":1731},[1456],[1107,7148],{},[1107,7150],{"className":7151,"style":1167},[1166],[1107,7153,2310],{"className":7154},[1171],[1107,7156],{"className":7157,"style":1167},[1166],[1107,7159,7161,7164,7167,7170,7173,7176],{"className":7160},[1153],[1107,7162],{"className":7163,"style":1677},[1157],[1107,7165,1433],{"className":7166},[1162],[1107,7168,1580],{"className":7169},[1737],[1107,7171],{"className":7172,"style":1167},[1166],[1107,7174,1132],{"className":7175},[1171],[1107,7177],{"className":7178,"style":1167},[1166],[1107,7180,7182,7186,7256,7259],{"className":7181},[1153],[1107,7183],{"className":7184,"style":7185},[1157],"height:1.2887em;vertical-align:-0.2997em;",[1107,7187,7189,7192],{"className":7188},[2475],[1107,7190,6942],{"className":7191,"style":2481},[2475,2479,2480],[1107,7193,7195],{"className":7194},[1444],[1107,7196,7198,7248],{"className":7197},[1448,1615],[1107,7199,7201,7245],{"className":7200},[1452],[1107,7202,7205,7225],{"className":7203,"style":7204},[1456],"height:0.989em;",[1107,7206,7207,7210],{"style":2497},[1107,7208],{"className":7209,"style":1464},[1463],[1107,7211,7213],{"className":7212},[1468,1469,1470,1471],[1107,7214,7216,7219,7222],{"className":7215},[1162,1471],[1107,7217,1544],{"className":7218},[1162,1597,1471],[1107,7220,1228],{"className":7221},[1290,1471],[1107,7223,1433],{"className":7224},[1162,1471],[1107,7226,7227,7230],{"style":2518},[1107,7228],{"className":7229,"style":1464},[1463],[1107,7231,7233],{"className":7232},[1468,1469,1470,1471],[1107,7234,7236,7239,7242],{"className":7235},[1162,1471],[1107,7237,6903],{"className":7238,"style":7010},[1162,1597,1471],[1107,7240,2310],{"className":7241},[1171,1471],[1107,7243,1433],{"className":7244},[1162,1471],[1107,7246,1652],{"className":7247},[1651],[1107,7249,7251],{"className":7250},[1452],[1107,7252,7254],{"className":7253,"style":2546},[1456],[1107,7255],{},[1107,7257],{"className":7258,"style":2448},[1166],[1107,7260,7262,7265],{"className":7261},[1162],[1107,7263,2366],{"className":7264,"style":2724},[1162,1597],[1107,7266,7268],{"className":7267},[1444],[1107,7269,7271,7292],{"className":7270},[1448,1615],[1107,7272,7274,7289],{"className":7273},[1452],[1107,7275,7277],{"className":7276,"style":1622},[1456],[1107,7278,7280,7283],{"style":7279},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[1107,7281],{"className":7282,"style":1464},[1463],[1107,7284,7286],{"className":7285},[1468,1469,1470,1471],[1107,7287,1544],{"className":7288},[1162,1597,1471],[1107,7290,1652],{"className":7291},[1651],[1107,7293,7295],{"className":7294},[1452],[1107,7296,7298],{"className":7297,"style":1731},[1456],[1107,7299],{},[2204,7301,7302,7303],{},"残差连接：",[1107,7304,7306,7348],{"className":7305},[1110],[1107,7307,7309],{"className":7308},[1114],[1116,7310,7311],{"xmlns":1118},[1120,7312,7313,7345],{},[1123,7314,7315,7317,7319,7321,7323,7325,7327,7330,7336,7339,7341,7343],{},[1527,7316,2275],{},[1130,7318,1228],{},[1527,7320,1768],{},[1130,7322,1533],{"stretchy":1532},[1527,7324,2356],{},[1130,7326,1312],{"separator":1149},[1130,7328,7329],{"stretchy":1532},"{",[1535,7331,7332,7334],{},[1527,7333,3036],{},[1527,7335,1544],{},[1130,7337,7338],{"stretchy":1532},"}",[1130,7340,1580],{"stretchy":1532},[1130,7342,2369],{},[1527,7344,2356],{},[1141,7346,7347],{"encoding":1143},"y = F(x, \\{W_i\\}) + x",[1107,7349,7351,7370,7447],{"className":7350,"ariaHidden":1149},[1148],[1107,7352,7354,7358,7361,7364,7367],{"className":7353},[1153],[1107,7355],{"className":7356,"style":7357},[1157],"height:0.625em;vertical-align:-0.1944em;",[1107,7359,2275],{"className":7360,"style":2435},[1162,1597],[1107,7362],{"className":7363,"style":1286},[1166],[1107,7365,1228],{"className":7366},[1290],[1107,7368],{"className":7369,"style":1286},[1166],[1107,7371,7373,7376,7379,7382,7385,7388,7391,7394,7434,7438,7441,7444],{"className":7372},[1153],[1107,7374],{"className":7375,"style":1677},[1157],[1107,7377,1768],{"className":7378,"style":1819},[1162,1597],[1107,7380,1533],{"className":7381},[1602],[1107,7383,2356],{"className":7384},[1162,1597],[1107,7386,1312],{"className":7387},[1311],[1107,7389],{"className":7390,"style":2448},[1166],[1107,7392,7329],{"className":7393},[1602],[1107,7395,7397,7400],{"className":7396},[1162],[1107,7398,3036],{"className":7399,"style":1819},[1162,1597],[1107,7401,7403],{"className":7402},[1444],[1107,7404,7406,7426],{"className":7405},[1448,1615],[1107,7407,7409,7423],{"className":7408},[1452],[1107,7410,7412],{"className":7411,"style":1622},[1456],[1107,7413,7414,7417],{"style":3380},[1107,7415],{"className":7416,"style":1464},[1463],[1107,7418,7420],{"className":7419},[1468,1469,1470,1471],[1107,7421,1544],{"className":7422},[1162,1597,1471],[1107,7424,1652],{"className":7425},[1651],[1107,7427,7429],{"className":7428},[1452],[1107,7430,7432],{"className":7431,"style":1731},[1456],[1107,7433],{},[1107,7435,7437],{"className":7436},[1737],"})",[1107,7439],{"className":7440,"style":1167},[1166],[1107,7442,2369],{"className":7443},[1171],[1107,7445],{"className":7446,"style":1167},[1166],[1107,7448,7450,7454],{"className":7449},[1153],[1107,7451],{"className":7452,"style":7453},[1157],"height:0.4306em;",[1107,7455,2356],{"className":7456},[1162,1597],[2204,7458,7459,7460,7488,7489,7529,7530],{},"瓶颈降维：1×1 Conv 将 ",[1107,7461,7463,7476],{"className":7462},[1110],[1107,7464,7466],{"className":7465},[1114],[1116,7467,7468],{"xmlns":1118},[1120,7469,7470,7474],{},[1123,7471,7472],{},[1527,7473,6281],{},[1141,7475,6281],{"encoding":1143},[1107,7477,7479],{"className":7478,"ariaHidden":1149},[1148],[1107,7480,7482,7485],{"className":7481},[1153],[1107,7483],{"className":7484,"style":2900},[1157],[1107,7486,6281],{"className":7487,"style":3289},[1162,1597]," 通道降至 ",[1107,7490,7492,7513],{"className":7491},[1110],[1107,7493,7495],{"className":7494},[1114],[1116,7496,7497],{"xmlns":1118},[1120,7498,7499,7510],{},[1123,7500,7501,7503,7507],{},[1527,7502,6281],{},[1527,7504,7506],{"mathvariant":7505},"normal","\u002F",[1126,7508,7509],{},"4",[1141,7511,7512],{"encoding":1143},"C\u002F4",[1107,7514,7516],{"className":7515,"ariaHidden":1149},[1148],[1107,7517,7519,7522,7525],{"className":7518},[1153],[1107,7520],{"className":7521,"style":1677},[1157],[1107,7523,6281],{"className":7524,"style":3289},[1162,1597],[1107,7526,7528],{"className":7527},[1162],"\u002F4","，3×3 Conv 处理后再 1×1 升回 ",[1107,7531,7533,7546],{"className":7532},[1110],[1107,7534,7536],{"className":7535},[1114],[1116,7537,7538],{"xmlns":1118},[1120,7539,7540,7544],{},[1123,7541,7542],{},[1527,7543,6281],{},[1141,7545,6281],{"encoding":1143},[1107,7547,7549],{"className":7548,"ariaHidden":1149},[1148],[1107,7550,7552,7555],{"className":7551},[1153],[1107,7553],{"className":7554,"style":2900},[1157],[1107,7556,6281],{"className":7557,"style":3289},[1162,1597],[2163,7559],{},[1096,7561,7562],{"id":7562},"相关概念",[2996,7564,7565,7575],{},[2999,7566,7567],{},[3002,7568,7569,7572],{},[3005,7570,7571],{},"概念",[3005,7573,7574],{},"要点",[3012,7576,7577,7585,7593,7600,7608,7616,7624,7632],{},[3002,7578,7579,7582],{},[3017,7580,7581],{},"感受野（Receptive Field）",[3017,7583,7584],{},"每个神经元在原始输入上\"看到\"的区域大小，随网络深度增大",[3002,7586,7587,7590],{},[3017,7588,7589],{},"特征图（Feature Map）",[3017,7591,7592],{},"一个卷积核在整张图上滑动后得到的输出，反映该卷积核检测到的特征分布",[3002,7594,7595,7597],{},[3017,7596,3184],{},[3017,7598,7599],{},"卷积核移动的步幅，stride > 1 可替代池化实现下采样",[3002,7601,7602,7605],{},[3017,7603,7604],{},"零填充（Zero Padding）",[3017,7606,7607],{},"在输入边缘补零，保持空间尺寸或避免边缘信息丢失",[3002,7609,7610,7613],{},[3017,7611,7612],{},"全局平均池化（GAP）",[3017,7614,7615],{},"对每个特征图取全局均值，输出一个数，替代全连接层减少参数",[3002,7617,7618,7621],{},[3017,7619,7620],{},"Batch Normalization",[3017,7622,7623],{},"对每个 mini-batch 的特征进行归一化，加速训练、允许更大学习率",[3002,7625,7626,7629],{},[3017,7627,7628],{},"Skip Connection",[3017,7630,7631],{},"将输入跳跃式传递到后面的层，缓解梯度消失，使超深网络可训练",[3002,7633,7634,7637],{},[3017,7635,7636],{},"数据增强",[3017,7638,7639],{},"通过随机变换（翻转、裁剪、旋转、颜色抖动）扩充训练集，减少过拟合",{"title":7641,"searchDepth":7642,"depth":7642,"links":7643},"",4,[7644,7646,7647,7648,7662,7663],{"id":1098,"depth":7645,"text":1098},2,{"id":1489,"depth":7645,"text":1482},{"id":1915,"depth":7645,"text":1486},{"id":2171,"depth":7645,"text":2171,"children":7649},[7650,7652,7653,7654,7655,7656,7657,7658,7659,7660,7661],{"id":2249,"depth":7651,"text":2250},3,{"id":4883,"depth":7651,"text":4884},{"id":4997,"depth":7651,"text":4998},{"id":5695,"depth":7651,"text":5696},{"id":5704,"depth":7651,"text":5705},{"id":5719,"depth":7651,"text":5720},{"id":6200,"depth":7651,"text":6201},{"id":6215,"depth":7651,"text":6216},{"id":6252,"depth":7651,"text":6253},{"id":6296,"depth":7651,"text":6297},{"id":6336,"depth":7651,"text":6337},{"id":6404,"depth":7645,"text":6404},{"id":7562,"depth":7645,"text":7562},"https:\u002F\u002Fpic1.zhimg.com\u002F80\u002Fv2-983df4f09f8d6cbfd081306730fa7061_720w.webp?source=d16d100b","本文从全连接网络的局限性出发，介绍卷积操作、池化层等基础组件，并系统梳理 LeNet-5、AlexNet、VGGNet、GoogLeNet\u002FInception、ResNet 五大经典架构的设计思想与演进脉络。","md",true,{"uuid":7669,"slots":7670},"093d8792-1234-11f0-9848-0b39a1ee406d",{},11,{"title":1085,"description":7665},"posts\u002F神经网络\u002F神经网络与深度学习：卷积神经网络",[40],"-fJ419Xw01kBQhKS8Uyt2vqqC8bg5CeuJOsP8AsAZyc",1790443284563]