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为什么需要 RNN？",[1101,1102,1103],"p",{},"前馈神经网络（Feedforward NN）将每个输入视为独立样本，无法处理具有时序依赖关系的数据。现实世界中大量数据是序列化的——文本、语音、时间序列——它们的当前状态依赖于历史信息。",[1101,1105,1106],{},[1107,1108,1109],"strong",{},"序列数据的典型场景：",[1111,1112,1113,1120,1126,1132],"ul",{},[1114,1115,1116,1119],"li",{},[1107,1117,1118],{},"自然语言文本","：词的含义取决于上下文，\"苹果\"在不同句子中含义不同",[1114,1121,1122,1125],{},[1107,1123,1124],{},"语音信号","：当前音素的识别依赖前后音素的组合",[1114,1127,1128,1131],{},[1107,1129,1130],{},"时间序列","：股价、气温等数据具有时序相关性",[1114,1133,1134,1137],{},[1107,1135,1136],{},"视频帧序列","：动作识别需要理解帧与帧之间的关系",[1096,1139,1141],{"id":1140},"_12-rnn-与前馈网络的关键区别","1.2 RNN 与前馈网络的关键区别",[1101,1143,1144],{},[1107,1145,1146],{},"循环神经网络（RNN）",[1111,1148,1149,1156,1269,1275],{},[1114,1150,1151,1152,1155],{},"具有",[1107,1153,1154],{},"循环连接","（recurrent connection）",[1114,1157,1158,1159,1162,1268],{},"维护",[1107,1160,1161],{},"隐藏状态",[1163,1164,1167,1196],"span",{"className":1165},[1166],"katex",[1163,1168,1171],{"className":1169},[1170],"katex-mathml",[1172,1173,1175],"math",{"xmlns":1174},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1176,1177,1178,1191],"semantics",{},[1179,1180,1181],"mrow",{},[1182,1183,1184,1188],"msub",{},[1185,1186,1187],"mi",{},"h",[1185,1189,1190],{},"t",[1192,1193,1195],"annotation",{"encoding":1194},"application\u002Fx-tex","h_t",[1163,1197,1201],{"className":1198,"ariaHidden":1200},[1199],"katex-html","true",[1163,1202,1205,1210],{"className":1203},[1204],"base",[1163,1206],{"className":1207,"style":1209},[1208],"strut","height:0.8444em;vertical-align:-0.15em;",[1163,1211,1214,1218],{"className":1212},[1213],"mord",[1163,1215,1187],{"className":1216},[1213,1217],"mathnormal",[1163,1219,1222],{"className":1220},[1221],"msupsub",[1163,1223,1227,1259],{"className":1224},[1225,1226],"vlist-t","vlist-t2",[1163,1228,1231,1254],{"className":1229},[1230],"vlist-r",[1163,1232,1236],{"className":1233,"style":1235},[1234],"vlist","height:0.2806em;",[1163,1237,1239,1244],{"style":1238},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1163,1240],{"className":1241,"style":1243},[1242],"pstrut","height:2.7em;",[1163,1245,1251],{"className":1246},[1247,1248,1249,1250],"sizing","reset-size6","size3","mtight",[1163,1252,1190],{"className":1253},[1213,1217,1250],[1163,1255,1258],{"className":1256},[1257],"vlist-s","​",[1163,1260,1262],{"className":1261},[1230],[1163,1263,1266],{"className":1264,"style":1265},[1234],"height:0.15em;",[1163,1267],{}," 作为\"记忆\"",[1114,1270,1271,1272],{},"参数在时间步之间",[1107,1273,1274],{},"共享",[1114,1276,1277],{},"输入\u002F输出长度可变",[1101,1279,1280],{},[1107,1281,1282],{},"前馈神经网络（FNN）",[1111,1284,1285,1292,1295,1298],{},[1114,1286,1287,1288,1291],{},"信号",[1107,1289,1290],{},"单向","从输入层到输出层",[1114,1293,1294],{},"无内部记忆，每个样本独立处理",[1114,1296,1297],{},"各层参数独立",[1114,1299,1300],{},"输入\u002F输出维度固定",[1096,1302,1304],{"id":1303},"_13-基本-rnn-公式","1.3 基本 RNN 公式",[1101,1306,1307],{},[1107,1308,1309],{},"RNN 递推公式：",[1101,1311,1312,1313],{},"隐藏状态更新：",[1163,1314,1316,1408],{"className":1315},[1166],[1163,1317,1319],{"className":1318},[1170],[1172,1320,1321],{"xmlns":1174},[1176,1322,1323,1405],{},[1179,1324,1325,1331,1335,1338,1342,1353,1356,1371,1374,1385,1387,1393,1395,1402],{},[1182,1326,1327,1329],{},[1185,1328,1187],{},[1185,1330,1190],{},[1332,1333,1334],"mo",{},"=",[1185,1336,1337],{},"σ",[1332,1339,1341],{"stretchy":1340},"false","(",[1182,1343,1344,1347],{},[1185,1345,1346],{},"W",[1179,1348,1349,1351],{},[1185,1350,1187],{},[1185,1352,1187],{},[1332,1354,1355],{},"⋅",[1182,1357,1358,1360],{},[1185,1359,1187],{},[1179,1361,1362,1364,1367],{},[1185,1363,1190],{},[1332,1365,1366],{},"−",[1368,1369,1370],"mn",{},"1",[1332,1372,1373],{},"+",[1182,1375,1376,1378],{},[1185,1377,1346],{},[1179,1379,1380,1383],{},[1185,1381,1382],{},"x",[1185,1384,1187],{},[1332,1386,1355],{},[1182,1388,1389,1391],{},[1185,1390,1382],{},[1185,1392,1190],{},[1332,1394,1373],{},[1182,1396,1397,1400],{},[1185,1398,1399],{},"b",[1185,1401,1187],{},[1332,1403,1404],{"stretchy":1340},")",[1192,1406,1407],{"encoding":1194},"h_t = \\sigma(W_{hh} \\cdot h_{t-1} + W_{xh} \\cdot x_t + b_h)",[1163,1409,1411,1469,1542,1609,1671,1727],{"className":1410,"ariaHidden":1200},[1199],[1163,1412,1414,1417,1457,1462,1466],{"className":1413},[1204],[1163,1415],{"className":1416,"style":1209},[1208],[1163,1418,1420,1423],{"className":1419},[1213],[1163,1421,1187],{"className":1422},[1213,1217],[1163,1424,1426],{"className":1425},[1221],[1163,1427,1429,1449],{"className":1428},[1225,1226],[1163,1430,1432,1446],{"className":1431},[1230],[1163,1433,1435],{"className":1434,"style":1235},[1234],[1163,1436,1437,1440],{"style":1238},[1163,1438],{"className":1439,"style":1243},[1242],[1163,1441,1443],{"className":1442},[1247,1248,1249,1250],[1163,1444,1190],{"className":1445},[1213,1217,1250],[1163,1447,1258],{"className":1448},[1257],[1163,1450,1452],{"className":1451},[1230],[1163,1453,1455],{"className":1454,"style":1265},[1234],[1163,1456],{},[1163,1458],{"className":1459,"style":1461},[1460],"mspace","margin-right:0.2778em;",[1163,1463,1334],{"className":1464},[1465],"mrel",[1163,1467],{"className":1468,"style":1461},[1460],[1163,1470,1472,1476,1480,1484,1531,1535,1539],{"className":1471},[1204],[1163,1473],{"className":1474,"style":1475},[1208],"height:1em;vertical-align:-0.25em;",[1163,1477,1337],{"className":1478,"style":1479},[1213,1217],"margin-right:0.0359em;",[1163,1481,1341],{"className":1482},[1483],"mopen",[1163,1485,1487,1491],{"className":1486},[1213],[1163,1488,1346],{"className":1489,"style":1490},[1213,1217],"margin-right:0.1389em;",[1163,1492,1494],{"className":1493},[1221],[1163,1495,1497,1523],{"className":1496},[1225,1226],[1163,1498,1500,1520],{"className":1499},[1230],[1163,1501,1504],{"className":1502,"style":1503},[1234],"height:0.3361em;",[1163,1505,1507,1510],{"style":1506},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1163,1508],{"className":1509,"style":1243},[1242],[1163,1511,1513],{"className":1512},[1247,1248,1249,1250],[1163,1514,1516],{"className":1515},[1213,1250],[1163,1517,1519],{"className":1518},[1213,1217,1250],"hh",[1163,1521,1258],{"className":1522},[1257],[1163,1524,1526],{"className":1525},[1230],[1163,1527,1529],{"className":1528,"style":1265},[1234],[1163,1530],{},[1163,1532],{"className":1533,"style":1534},[1460],"margin-right:0.2222em;",[1163,1536,1355],{"className":1537},[1538],"mbin",[1163,1540],{"className":1541,"style":1534},[1460],[1163,1543,1545,1549,1600,1603,1606],{"className":1544},[1204],[1163,1546],{"className":1547,"style":1548},[1208],"height:0.9028em;vertical-align:-0.2083em;",[1163,1550,1552,1555],{"className":1551},[1213],[1163,1553,1187],{"className":1554},[1213,1217],[1163,1556,1558],{"className":1557},[1221],[1163,1559,1561,1591],{"className":1560},[1225,1226],[1163,1562,1564,1588],{"className":1563},[1230],[1163,1565,1568],{"className":1566,"style":1567},[1234],"height:0.3011em;",[1163,1569,1570,1573],{"style":1238},[1163,1571],{"className":1572,"style":1243},[1242],[1163,1574,1576],{"className":1575},[1247,1248,1249,1250],[1163,1577,1579,1582,1585],{"className":1578},[1213,1250],[1163,1580,1190],{"className":1581},[1213,1217,1250],[1163,1583,1366],{"className":1584},[1538,1250],[1163,1586,1370],{"className":1587},[1213,1250],[1163,1589,1258],{"className":1590},[1257],[1163,1592,1594],{"className":1593},[1230],[1163,1595,1598],{"className":1596,"style":1597},[1234],"height:0.2083em;",[1163,1599],{},[1163,1601],{"className":1602,"style":1534},[1460],[1163,1604,1373],{"className":1605},[1538],[1163,1607],{"className":1608,"style":1534},[1460],[1163,1610,1612,1616,1662,1665,1668],{"className":1611},[1204],[1163,1613],{"className":1614,"style":1615},[1208],"height:0.8333em;vertical-align:-0.15em;",[1163,1617,1619,1622],{"className":1618},[1213],[1163,1620,1346],{"className":1621,"style":1490},[1213,1217],[1163,1623,1625],{"className":1624},[1221],[1163,1626,1628,1654],{"className":1627},[1225,1226],[1163,1629,1631,1651],{"className":1630},[1230],[1163,1632,1634],{"className":1633,"style":1503},[1234],[1163,1635,1636,1639],{"style":1506},[1163,1637],{"className":1638,"style":1243},[1242],[1163,1640,1642],{"className":1641},[1247,1248,1249,1250],[1163,1643,1645,1648],{"className":1644},[1213,1250],[1163,1646,1382],{"className":1647},[1213,1217,1250],[1163,1649,1187],{"className":1650},[1213,1217,1250],[1163,1652,1258],{"className":1653},[1257],[1163,1655,1657],{"className":1656},[1230],[1163,1658,1660],{"className":1659,"style":1265},[1234],[1163,1661],{},[1163,1663],{"className":1664,"style":1534},[1460],[1163,1666,1355],{"className":1667},[1538],[1163,1669],{"className":1670,"style":1534},[1460],[1163,1672,1674,1678,1718,1721,1724],{"className":1673},[1204],[1163,1675],{"className":1676,"style":1677},[1208],"height:0.7333em;vertical-align:-0.15em;",[1163,1679,1681,1684],{"className":1680},[1213],[1163,1682,1382],{"className":1683},[1213,1217],[1163,1685,1687],{"className":1686},[1221],[1163,1688,1690,1710],{"className":1689},[1225,1226],[1163,1691,1693,1707],{"className":1692},[1230],[1163,1694,1696],{"className":1695,"style":1235},[1234],[1163,1697,1698,1701],{"style":1238},[1163,1699],{"className":1700,"style":1243},[1242],[1163,1702,1704],{"className":1703},[1247,1248,1249,1250],[1163,1705,1190],{"className":1706},[1213,1217,1250],[1163,1708,1258],{"className":1709},[1257],[1163,1711,1713],{"className":1712},[1230],[1163,1714,1716],{"className":1715,"style":1265},[1234],[1163,1717],{},[1163,1719],{"className":1720,"style":1534},[1460],[1163,1722,1373],{"className":1723},[1538],[1163,1725],{"className":1726,"style":1534},[1460],[1163,1728,1730,1733,1773],{"className":1729},[1204],[1163,1731],{"className":1732,"style":1475},[1208],[1163,1734,1736,1739],{"className":1735},[1213],[1163,1737,1399],{"className":1738},[1213,1217],[1163,1740,1742],{"className":1741},[1221],[1163,1743,1745,1765],{"className":1744},[1225,1226],[1163,1746,1748,1762],{"className":1747},[1230],[1163,1749,1751],{"className":1750,"style":1503},[1234],[1163,1752,1753,1756],{"style":1238},[1163,1754],{"className":1755,"style":1243},[1242],[1163,1757,1759],{"className":1758},[1247,1248,1249,1250],[1163,1760,1187],{"className":1761},[1213,1217,1250],[1163,1763,1258],{"className":1764},[1257],[1163,1766,1768],{"className":1767},[1230],[1163,1769,1771],{"className":1770,"style":1265},[1234],[1163,1772],{},[1163,1774,1404],{"className":1775},[1776],"mclose",[1101,1778,1779,1780],{},"输出计算：",[1163,1781,1783,1830],{"className":1782},[1166],[1163,1784,1786],{"className":1785},[1170],[1172,1787,1788],{"xmlns":1174},[1176,1789,1790,1827],{},[1179,1791,1792,1799,1801,1811,1813,1819,1821],{},[1182,1793,1794,1797],{},[1185,1795,1796],{},"y",[1185,1798,1190],{},[1332,1800,1334],{},[1182,1802,1803,1805],{},[1185,1804,1346],{},[1179,1806,1807,1809],{},[1185,1808,1187],{},[1185,1810,1796],{},[1332,1812,1355],{},[1182,1814,1815,1817],{},[1185,1816,1187],{},[1185,1818,1190],{},[1332,1820,1373],{},[1182,1822,1823,1825],{},[1185,1824,1399],{},[1185,1826,1796],{},[1192,1828,1829],{"encoding":1194},"y_t = W_{hy} \\cdot h_t + b_y",[1163,1831,1833,1890,1953,2008],{"className":1832,"ariaHidden":1200},[1199],[1163,1834,1836,1840,1881,1884,1887],{"className":1835},[1204],[1163,1837],{"className":1838,"style":1839},[1208],"height:0.625em;vertical-align:-0.1944em;",[1163,1841,1843,1846],{"className":1842},[1213],[1163,1844,1796],{"className":1845,"style":1479},[1213,1217],[1163,1847,1849],{"className":1848},[1221],[1163,1850,1852,1873],{"className":1851},[1225,1226],[1163,1853,1855,1870],{"className":1854},[1230],[1163,1856,1858],{"className":1857,"style":1235},[1234],[1163,1859,1861,1864],{"style":1860},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1163,1862],{"className":1863,"style":1243},[1242],[1163,1865,1867],{"className":1866},[1247,1248,1249,1250],[1163,1868,1190],{"className":1869},[1213,1217,1250],[1163,1871,1258],{"className":1872},[1257],[1163,1874,1876],{"className":1875},[1230],[1163,1877,1879],{"className":1878,"style":1265},[1234],[1163,1880],{},[1163,1882],{"className":1883,"style":1461},[1460],[1163,1885,1334],{"className":1886},[1465],[1163,1888],{"className":1889,"style":1461},[1460],[1163,1891,1893,1897,1944,1947,1950],{"className":1892},[1204],[1163,1894],{"className":1895,"style":1896},[1208],"height:0.9694em;vertical-align:-0.2861em;",[1163,1898,1900,1903],{"className":1899},[1213],[1163,1901,1346],{"className":1902,"style":1490},[1213,1217],[1163,1904,1906],{"className":1905},[1221],[1163,1907,1909,1935],{"className":1908},[1225,1226],[1163,1910,1912,1932],{"className":1911},[1230],[1163,1913,1915],{"className":1914,"style":1503},[1234],[1163,1916,1917,1920],{"style":1506},[1163,1918],{"className":1919,"style":1243},[1242],[1163,1921,1923],{"className":1922},[1247,1248,1249,1250],[1163,1924,1926,1929],{"className":1925},[1213,1250],[1163,1927,1187],{"className":1928},[1213,1217,1250],[1163,1930,1796],{"className":1931,"style":1479},[1213,1217,1250],[1163,1933,1258],{"className":1934},[1257],[1163,1936,1938],{"className":1937},[1230],[1163,1939,1942],{"className":1940,"style":1941},[1234],"height:0.2861em;",[1163,1943],{},[1163,1945],{"className":1946,"style":1534},[1460],[1163,1948,1355],{"className":1949},[1538],[1163,1951],{"className":1952,"style":1534},[1460],[1163,1954,1956,1959,1999,2002,2005],{"className":1955},[1204],[1163,1957],{"className":1958,"style":1209},[1208],[1163,1960,1962,1965],{"className":1961},[1213],[1163,1963,1187],{"className":1964},[1213,1217],[1163,1966,1968],{"className":1967},[1221],[1163,1969,1971,1991],{"className":1970},[1225,1226],[1163,1972,1974,1988],{"className":1973},[1230],[1163,1975,1977],{"className":1976,"style":1235},[1234],[1163,1978,1979,1982],{"style":1238},[1163,1980],{"className":1981,"style":1243},[1242],[1163,1983,1985],{"className":1984},[1247,1248,1249,1250],[1163,1986,1190],{"className":1987},[1213,1217,1250],[1163,1989,1258],{"className":1990},[1257],[1163,1992,1994],{"className":1993},[1230],[1163,1995,1997],{"className":1996,"style":1265},[1234],[1163,1998],{},[1163,2000],{"className":2001,"style":1534},[1460],[1163,2003,1373],{"className":2004},[1538],[1163,2006],{"className":2007,"style":1534},[1460],[1163,2009,2011,2015],{"className":2010},[1204],[1163,2012],{"className":2013,"style":2014},[1208],"height:0.9805em;vertical-align:-0.2861em;",[1163,2016,2018,2021],{"className":2017},[1213],[1163,2019,1399],{"className":2020},[1213,1217],[1163,2022,2024],{"className":2023},[1221],[1163,2025,2027,2048],{"className":2026},[1225,1226],[1163,2028,2030,2045],{"className":2029},[1230],[1163,2031,2034],{"className":2032,"style":2033},[1234],"height:0.1514em;",[1163,2035,2036,2039],{"style":1238},[1163,2037],{"className":2038,"style":1243},[1242],[1163,2040,2042],{"className":2041},[1247,1248,1249,1250],[1163,2043,1796],{"className":2044,"style":1479},[1213,1217,1250],[1163,2046,1258],{"className":2047},[1257],[1163,2049,2051],{"className":2050},[1230],[1163,2052,2054],{"className":2053,"style":1941},[1234],[1163,2055],{},[1101,2057,2058],{},[1107,2059,2060],{},"各符号含义：",[2062,2063,2064,2077],"table",{},[2065,2066,2067],"thead",{},[2068,2069,2070,2074],"tr",{},[2071,2072,2073],"th",{},"符号",[2071,2075,2076],{},"含义",[2078,2079,2080,2159,2235,2327,2414,2498,2585,2719],"tbody",{},[2068,2081,2082,2156],{},[2083,2084,2085],"td",{},[1163,2086,2088,2106],{"className":2087},[1166],[1163,2089,2091],{"className":2090},[1170],[1172,2092,2093],{"xmlns":1174},[1176,2094,2095,2103],{},[1179,2096,2097],{},[1182,2098,2099,2101],{},[1185,2100,1382],{},[1185,2102,1190],{},[1192,2104,2105],{"encoding":1194},"x_t",[1163,2107,2109],{"className":2108,"ariaHidden":1200},[1199],[1163,2110,2112,2116],{"className":2111},[1204],[1163,2113],{"className":2114,"style":2115},[1208],"height:0.5806em;vertical-align:-0.15em;",[1163,2117,2119,2122],{"className":2118},[1213],[1163,2120,1382],{"className":2121},[1213,1217],[1163,2123,2125],{"className":2124},[1221],[1163,2126,2128,2148],{"className":2127},[1225,1226],[1163,2129,2131,2145],{"className":2130},[1230],[1163,2132,2134],{"className":2133,"style":1235},[1234],[1163,2135,2136,2139],{"style":1238},[1163,2137],{"className":2138,"style":1243},[1242],[1163,2140,2142],{"className":2141},[1247,1248,1249,1250],[1163,2143,1190],{"className":2144},[1213,1217,1250],[1163,2146,1258],{"className":2147},[1257],[1163,2149,2151],{"className":2150},[1230],[1163,2152,2154],{"className":2153,"style":1265},[1234],[1163,2155],{},[2083,2157,2158],{},"时刻 t 的输入向量",[2068,2160,2161,2232],{},[2083,2162,2163],{},[1163,2164,2166,2183],{"className":2165},[1166],[1163,2167,2169],{"className":2168},[1170],[1172,2170,2171],{"xmlns":1174},[1176,2172,2173,2181],{},[1179,2174,2175],{},[1182,2176,2177,2179],{},[1185,2178,1187],{},[1185,2180,1190],{},[1192,2182,1195],{"encoding":1194},[1163,2184,2186],{"className":2185,"ariaHidden":1200},[1199],[1163,2187,2189,2192],{"className":2188},[1204],[1163,2190],{"className":2191,"style":1209},[1208],[1163,2193,2195,2198],{"className":2194},[1213],[1163,2196,1187],{"className":2197},[1213,1217],[1163,2199,2201],{"className":2200},[1221],[1163,2202,2204,2224],{"className":2203},[1225,1226],[1163,2205,2207,2221],{"className":2206},[1230],[1163,2208,2210],{"className":2209,"style":1235},[1234],[1163,2211,2212,2215],{"style":1238},[1163,2213],{"className":2214,"style":1243},[1242],[1163,2216,2218],{"className":2217},[1247,1248,1249,1250],[1163,2219,1190],{"className":2220},[1213,1217,1250],[1163,2222,1258],{"className":2223},[1257],[1163,2225,2227],{"className":2226},[1230],[1163,2228,2230],{"className":2229,"style":1265},[1234],[1163,2231],{},[2083,2233,2234],{},"时刻 t 的隐藏状态（hidden state），编码了历史信息",[2068,2236,2237,2324],{},[2083,2238,2239],{},[1163,2240,2242,2266],{"className":2241},[1166],[1163,2243,2245],{"className":2244},[1170],[1172,2246,2247],{"xmlns":1174},[1176,2248,2249,2263],{},[1179,2250,2251],{},[1182,2252,2253,2255],{},[1185,2254,1187],{},[1179,2256,2257,2259,2261],{},[1185,2258,1190],{},[1332,2260,1366],{},[1368,2262,1370],{},[1192,2264,2265],{"encoding":1194},"h_{t-1}",[1163,2267,2269],{"className":2268,"ariaHidden":1200},[1199],[1163,2270,2272,2275],{"className":2271},[1204],[1163,2273],{"className":2274,"style":1548},[1208],[1163,2276,2278,2281],{"className":2277},[1213],[1163,2279,1187],{"className":2280},[1213,1217],[1163,2282,2284],{"className":2283},[1221],[1163,2285,2287,2316],{"className":2286},[1225,1226],[1163,2288,2290,2313],{"className":2289},[1230],[1163,2291,2293],{"className":2292,"style":1567},[1234],[1163,2294,2295,2298],{"style":1238},[1163,2296],{"className":2297,"style":1243},[1242],[1163,2299,2301],{"className":2300},[1247,1248,1249,1250],[1163,2302,2304,2307,2310],{"className":2303},[1213,1250],[1163,2305,1190],{"className":2306},[1213,1217,1250],[1163,2308,1366],{"className":2309},[1538,1250],[1163,2311,1370],{"className":2312},[1213,1250],[1163,2314,1258],{"className":2315},[1257],[1163,2317,2319],{"className":2318},[1230],[1163,2320,2322],{"className":2321,"style":1597},[1234],[1163,2323],{},[2083,2325,2326],{},"上一时刻的隐藏状态",[2068,2328,2329,2411],{},[2083,2330,2331],{},[1163,2332,2334,2356],{"className":2333},[1166],[1163,2335,2337],{"className":2336},[1170],[1172,2338,2339],{"xmlns":1174},[1176,2340,2341,2353],{},[1179,2342,2343],{},[1182,2344,2345,2347],{},[1185,2346,1346],{},[1179,2348,2349,2351],{},[1185,2350,1382],{},[1185,2352,1187],{},[1192,2354,2355],{"encoding":1194},"W_{xh}",[1163,2357,2359],{"className":2358,"ariaHidden":1200},[1199],[1163,2360,2362,2365],{"className":2361},[1204],[1163,2363],{"className":2364,"style":1615},[1208],[1163,2366,2368,2371],{"className":2367},[1213],[1163,2369,1346],{"className":2370,"style":1490},[1213,1217],[1163,2372,2374],{"className":2373},[1221],[1163,2375,2377,2403],{"className":2376},[1225,1226],[1163,2378,2380,2400],{"className":2379},[1230],[1163,2381,2383],{"className":2382,"style":1503},[1234],[1163,2384,2385,2388],{"style":1506},[1163,2386],{"className":2387,"style":1243},[1242],[1163,2389,2391],{"className":2390},[1247,1248,1249,1250],[1163,2392,2394,2397],{"className":2393},[1213,1250],[1163,2395,1382],{"className":2396},[1213,1217,1250],[1163,2398,1187],{"className":2399},[1213,1217,1250],[1163,2401,1258],{"className":2402},[1257],[1163,2404,2406],{"className":2405},[1230],[1163,2407,2409],{"className":2408,"style":1265},[1234],[1163,2410],{},[2083,2412,2413],{},"输入到隐藏层的权重矩阵",[2068,2415,2416,2495],{},[2083,2417,2418],{},[1163,2419,2421,2443],{"className":2420},[1166],[1163,2422,2424],{"className":2423},[1170],[1172,2425,2426],{"xmlns":1174},[1176,2427,2428,2440],{},[1179,2429,2430],{},[1182,2431,2432,2434],{},[1185,2433,1346],{},[1179,2435,2436,2438],{},[1185,2437,1187],{},[1185,2439,1187],{},[1192,2441,2442],{"encoding":1194},"W_{hh}",[1163,2444,2446],{"className":2445,"ariaHidden":1200},[1199],[1163,2447,2449,2452],{"className":2448},[1204],[1163,2450],{"className":2451,"style":1615},[1208],[1163,2453,2455,2458],{"className":2454},[1213],[1163,2456,1346],{"className":2457,"style":1490},[1213,1217],[1163,2459,2461],{"className":2460},[1221],[1163,2462,2464,2487],{"className":2463},[1225,1226],[1163,2465,2467,2484],{"className":2466},[1230],[1163,2468,2470],{"className":2469,"style":1503},[1234],[1163,2471,2472,2475],{"style":1506},[1163,2473],{"className":2474,"style":1243},[1242],[1163,2476,2478],{"className":2477},[1247,1248,1249,1250],[1163,2479,2481],{"className":2480},[1213,1250],[1163,2482,1519],{"className":2483},[1213,1217,1250],[1163,2485,1258],{"className":2486},[1257],[1163,2488,2490],{"className":2489},[1230],[1163,2491,2493],{"className":2492,"style":1265},[1234],[1163,2494],{},[2083,2496,2497],{},"隐藏层到隐藏层的权重矩阵（循环权重）",[2068,2499,2500,2582],{},[2083,2501,2502],{},[1163,2503,2505,2527],{"className":2504},[1166],[1163,2506,2508],{"className":2507},[1170],[1172,2509,2510],{"xmlns":1174},[1176,2511,2512,2524],{},[1179,2513,2514],{},[1182,2515,2516,2518],{},[1185,2517,1346],{},[1179,2519,2520,2522],{},[1185,2521,1187],{},[1185,2523,1796],{},[1192,2525,2526],{"encoding":1194},"W_{hy}",[1163,2528,2530],{"className":2529,"ariaHidden":1200},[1199],[1163,2531,2533,2536],{"className":2532},[1204],[1163,2534],{"className":2535,"style":1896},[1208],[1163,2537,2539,2542],{"className":2538},[1213],[1163,2540,1346],{"className":2541,"style":1490},[1213,1217],[1163,2543,2545],{"className":2544},[1221],[1163,2546,2548,2574],{"className":2547},[1225,1226],[1163,2549,2551,2571],{"className":2550},[1230],[1163,2552,2554],{"className":2553,"style":1503},[1234],[1163,2555,2556,2559],{"style":1506},[1163,2557],{"className":2558,"style":1243},[1242],[1163,2560,2562],{"className":2561},[1247,1248,1249,1250],[1163,2563,2565,2568],{"className":2564},[1213,1250],[1163,2566,1187],{"className":2567},[1213,1217,1250],[1163,2569,1796],{"className":2570,"style":1479},[1213,1217,1250],[1163,2572,1258],{"className":2573},[1257],[1163,2575,2577],{"className":2576},[1230],[1163,2578,2580],{"className":2579,"style":1941},[1234],[1163,2581],{},[2083,2583,2584],{},"隐藏层到输出层的权重矩阵",[2068,2586,2587,2716],{},[2083,2588,2589],{},[1163,2590,2592,2619],{"className":2591},[1166],[1163,2593,2595],{"className":2594},[1170],[1172,2596,2597],{"xmlns":1174},[1176,2598,2599,2616],{},[1179,2600,2601,2607,2610],{},[1182,2602,2603,2605],{},[1185,2604,1399],{},[1185,2606,1187],{},[1332,2608,2609],{"separator":1200},",",[1182,2611,2612,2614],{},[1185,2613,1399],{},[1185,2615,1796],{},[1192,2617,2618],{"encoding":1194},"b_h, b_y",[1163,2620,2622],{"className":2621,"ariaHidden":1200},[1199],[1163,2623,2625,2628,2668,2672,2676],{"className":2624},[1204],[1163,2626],{"className":2627,"style":2014},[1208],[1163,2629,2631,2634],{"className":2630},[1213],[1163,2632,1399],{"className":2633},[1213,1217],[1163,2635,2637],{"className":2636},[1221],[1163,2638,2640,2660],{"className":2639},[1225,1226],[1163,2641,2643,2657],{"className":2642},[1230],[1163,2644,2646],{"className":2645,"style":1503},[1234],[1163,2647,2648,2651],{"style":1238},[1163,2649],{"className":2650,"style":1243},[1242],[1163,2652,2654],{"className":2653},[1247,1248,1249,1250],[1163,2655,1187],{"className":2656},[1213,1217,1250],[1163,2658,1258],{"className":2659},[1257],[1163,2661,2663],{"className":2662},[1230],[1163,2664,2666],{"className":2665,"style":1265},[1234],[1163,2667],{},[1163,2669,2609],{"className":2670},[2671],"mpunct",[1163,2673],{"className":2674,"style":2675},[1460],"margin-right:0.1667em;",[1163,2677,2679,2682],{"className":2678},[1213],[1163,2680,1399],{"className":2681},[1213,1217],[1163,2683,2685],{"className":2684},[1221],[1163,2686,2688,2708],{"className":2687},[1225,1226],[1163,2689,2691,2705],{"className":2690},[1230],[1163,2692,2694],{"className":2693,"style":2033},[1234],[1163,2695,2696,2699],{"style":1238},[1163,2697],{"className":2698,"style":1243},[1242],[1163,2700,2702],{"className":2701},[1247,1248,1249,1250],[1163,2703,1796],{"className":2704,"style":1479},[1213,1217,1250],[1163,2706,1258],{"className":2707},[1257],[1163,2709,2711],{"className":2710},[1230],[1163,2712,2714],{"className":2713,"style":1941},[1234],[1163,2715],{},[2083,2717,2718],{},"偏置项",[2068,2720,2721,2753],{},[2083,2722,2723],{},[1163,2724,2726,2740],{"className":2725},[1166],[1163,2727,2729],{"className":2728},[1170],[1172,2730,2731],{"xmlns":1174},[1176,2732,2733,2737],{},[1179,2734,2735],{},[1185,2736,1337],{},[1192,2738,2739],{"encoding":1194},"\\sigma",[1163,2741,2743],{"className":2742,"ariaHidden":1200},[1199],[1163,2744,2746,2750],{"className":2745},[1204],[1163,2747],{"className":2748,"style":2749},[1208],"height:0.4306em;",[1163,2751,1337],{"className":2752,"style":1479},[1213,1217],[2083,2754,2755],{},"激活函数（通常为 tanh 或 ReLU）",[1096,2757,2759],{"id":2758},"_14-时间展开unfolding-in-time","1.4 时间展开（Unfolding in Time）",[1101,2761,2762,2763,2766,2767,2770,2771,2976],{},"RNN 的循环结构可以沿时间轴",[1107,2764,2765],{},"展开","（unfold），形成一个等价的深度前馈网络。每个时间步对应网络中的一\"层\"，但所有层",[1107,2768,2769],{},"共享相同的参数"," ",[1163,2772,2774,2820],{"className":2773},[1166],[1163,2775,2777],{"className":2776},[1170],[1172,2778,2779],{"xmlns":1174},[1176,2780,2781,2817],{},[1179,2782,2783,2793,2795,2805,2807],{},[1182,2784,2785,2787],{},[1185,2786,1346],{},[1179,2788,2789,2791],{},[1185,2790,1187],{},[1185,2792,1187],{},[1332,2794,2609],{"separator":1200},[1182,2796,2797,2799],{},[1185,2798,1346],{},[1179,2800,2801,2803],{},[1185,2802,1382],{},[1185,2804,1187],{},[1332,2806,2609],{"separator":1200},[1182,2808,2809,2811],{},[1185,2810,1346],{},[1179,2812,2813,2815],{},[1185,2814,1187],{},[1185,2816,1796],{},[1192,2818,2819],{"encoding":1194},"W_{hh}, W_{xh}, W_{hy}",[1163,2821,2823],{"className":2822,"ariaHidden":1200},[1199],[1163,2824,2826,2829,2872,2875,2878,2924,2927,2930],{"className":2825},[1204],[1163,2827],{"className":2828,"style":1896},[1208],[1163,2830,2832,2835],{"className":2831},[1213],[1163,2833,1346],{"className":2834,"style":1490},[1213,1217],[1163,2836,2838],{"className":2837},[1221],[1163,2839,2841,2864],{"className":2840},[1225,1226],[1163,2842,2844,2861],{"className":2843},[1230],[1163,2845,2847],{"className":2846,"style":1503},[1234],[1163,2848,2849,2852],{"style":1506},[1163,2850],{"className":2851,"style":1243},[1242],[1163,2853,2855],{"className":2854},[1247,1248,1249,1250],[1163,2856,2858],{"className":2857},[1213,1250],[1163,2859,1519],{"className":2860},[1213,1217,1250],[1163,2862,1258],{"className":2863},[1257],[1163,2865,2867],{"className":2866},[1230],[1163,2868,2870],{"className":2869,"style":1265},[1234],[1163,2871],{},[1163,2873,2609],{"className":2874},[2671],[1163,2876],{"className":2877,"style":2675},[1460],[1163,2879,2881,2884],{"className":2880},[1213],[1163,2882,1346],{"className":2883,"style":1490},[1213,1217],[1163,2885,2887],{"className":2886},[1221],[1163,2888,2890,2916],{"className":2889},[1225,1226],[1163,2891,2893,2913],{"className":2892},[1230],[1163,2894,2896],{"className":2895,"style":1503},[1234],[1163,2897,2898,2901],{"style":1506},[1163,2899],{"className":2900,"style":1243},[1242],[1163,2902,2904],{"className":2903},[1247,1248,1249,1250],[1163,2905,2907,2910],{"className":2906},[1213,1250],[1163,2908,1382],{"className":2909},[1213,1217,1250],[1163,2911,1187],{"className":2912},[1213,1217,1250],[1163,2914,1258],{"className":2915},[1257],[1163,2917,2919],{"className":2918},[1230],[1163,2920,2922],{"className":2921,"style":1265},[1234],[1163,2923],{},[1163,2925,2609],{"className":2926},[2671],[1163,2928],{"className":2929,"style":2675},[1460],[1163,2931,2933,2936],{"className":2932},[1213],[1163,2934,1346],{"className":2935,"style":1490},[1213,1217],[1163,2937,2939],{"className":2938},[1221],[1163,2940,2942,2968],{"className":2941},[1225,1226],[1163,2943,2945,2965],{"className":2944},[1230],[1163,2946,2948],{"className":2947,"style":1503},[1234],[1163,2949,2950,2953],{"style":1506},[1163,2951],{"className":2952,"style":1243},[1242],[1163,2954,2956],{"className":2955},[1247,1248,1249,1250],[1163,2957,2959,2962],{"className":2958},[1213,1250],[1163,2960,1187],{"className":2961},[1213,1217,1250],[1163,2963,1796],{"className":2964,"style":1479},[1213,1217,1250],[1163,2966,1258],{"className":2967},[1257],[1163,2969,2971],{"className":2970},[1230],[1163,2972,2974],{"className":2973,"style":1941},[1234],[1163,2975],{},"。",[1101,2978,2979],{},[1107,2980,2981],{},"展开后的关键性质：",[1111,2983,2984,2987,2994],{},[1114,2985,2986],{},"网络深度等于序列长度 T，因此长序列 = 极深网络",[1114,2988,2989,2990,2993],{},"参数共享使得模型可以处理",[1107,2991,2992],{},"任意长度","的序列",[1114,2995,2996],{},"展开后可以使用标准的反向传播算法",[1096,2998,3000],{"id":2999},"_15-训练bpttbackpropagation-through-time","1.5 训练：BPTT（Backpropagation Through Time）",[1101,3002,3003],{},"BPTT 是标准反向传播在时间维度上的推广：",[3005,3006,3007,3113,3466,3577],"ol",{},[1114,3008,3009,3012,3013,3112],{},[1107,3010,3011],{},"前向传播","：按时间顺序 ",[1163,3014,3016,3049],{"className":3015},[1166],[1163,3017,3019],{"className":3018},[1170],[1172,3020,3021],{"xmlns":1174},[1176,3022,3023,3046],{},[1179,3024,3025,3027,3029,3031,3033,3036,3038,3041,3043],{},[1185,3026,1190],{},[1332,3028,1334],{},[1368,3030,1370],{},[1332,3032,2609],{"separator":1200},[1368,3034,3035],{},"2",[1332,3037,2609],{"separator":1200},[1332,3039,3040],{},"…",[1332,3042,2609],{"separator":1200},[1185,3044,3045],{},"T",[1192,3047,3048],{"encoding":1194},"t = 1, 2, \\ldots, T",[1163,3050,3052,3071],{"className":3051,"ariaHidden":1200},[1199],[1163,3053,3055,3059,3062,3065,3068],{"className":3054},[1204],[1163,3056],{"className":3057,"style":3058},[1208],"height:0.6151em;",[1163,3060,1190],{"className":3061},[1213,1217],[1163,3063],{"className":3064,"style":1461},[1460],[1163,3066,1334],{"className":3067},[1465],[1163,3069],{"className":3070,"style":1461},[1460],[1163,3072,3074,3078,3081,3084,3087,3090,3093,3096,3100,3103,3106,3109],{"className":3073},[1204],[1163,3075],{"className":3076,"style":3077},[1208],"height:0.8778em;vertical-align:-0.1944em;",[1163,3079,1370],{"className":3080},[1213],[1163,3082,2609],{"className":3083},[2671],[1163,3085],{"className":3086,"style":2675},[1460],[1163,3088,3035],{"className":3089},[1213],[1163,3091,2609],{"className":3092},[2671],[1163,3094],{"className":3095,"style":2675},[1460],[1163,3097,3040],{"className":3098},[3099],"minner",[1163,3101],{"className":3102,"style":2675},[1460],[1163,3104,2609],{"className":3105},[2671],[1163,3107],{"className":3108,"style":2675},[1460],[1163,3110,3045],{"className":3111,"style":1490},[1213,1217]," 计算所有隐藏状态和输出",[1114,3114,3115,3118,3119],{},[1107,3116,3117],{},"计算损失","：",[1163,3120,3122,3185],{"className":3121},[1166],[1163,3123,3125],{"className":3124},[1170],[1172,3126,3127],{"xmlns":1174},[1176,3128,3129,3182],{},[1179,3130,3131,3134,3136,3152,3158,3160,3166,3168,3180],{},[1185,3132,3133],{},"L",[1332,3135,1334],{},[3137,3138,3139,3142,3150],"msubsup",{},[1332,3140,3141],{},"∑",[1179,3143,3144,3146,3148],{},[1185,3145,1190],{},[1332,3147,1334],{},[1368,3149,1370],{},[1185,3151,3045],{},[1182,3153,3154,3156],{},[1185,3155,3133],{},[1185,3157,1190],{},[1332,3159,1341],{"stretchy":1340},[1182,3161,3162,3164],{},[1185,3163,1796],{},[1185,3165,1190],{},[1332,3167,2609],{"separator":1200},[1182,3169,3170,3178],{},[3171,3172,3173,3175],"mover",{"accent":1200},[1185,3174,1796],{},[1332,3176,3177],{},"^",[1185,3179,1190],{},[1332,3181,1404],{"stretchy":1340},[1192,3183,3184],{"encoding":1194},"L = \\sum_{t=1}^{T} L_t(y_t, \\hat{y}_t)",[1163,3186,3188,3207],{"className":3187,"ariaHidden":1200},[1199],[1163,3189,3191,3195,3198,3201,3204],{"className":3190},[1204],[1163,3192],{"className":3193,"style":3194},[1208],"height:0.6833em;",[1163,3196,3133],{"className":3197},[1213,1217],[1163,3199],{"className":3200,"style":1461},[1460],[1163,3202,1334],{"className":3203},[1465],[1163,3205],{"className":3206,"style":1461},[1460],[1163,3208,3210,3214,3285,3288,3328,3331,3371,3374,3377,3463],{"className":3209},[1204],[1163,3211],{"className":3212,"style":3213},[1208],"height:1.2809em;vertical-align:-0.2997em;",[1163,3215,3218,3224],{"className":3216},[3217],"mop",[1163,3219,3141],{"className":3220,"style":3223},[3217,3221,3222],"op-symbol","small-op","position:relative;top:0em;",[1163,3225,3227],{"className":3226},[1221],[1163,3228,3230,3276],{"className":3229},[1225,1226],[1163,3231,3233,3273],{"className":3232},[1230],[1163,3234,3237,3258],{"className":3235,"style":3236},[1234],"height:0.9812em;",[1163,3238,3240,3243],{"style":3239},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1163,3241],{"className":3242,"style":1243},[1242],[1163,3244,3246],{"className":3245},[1247,1248,1249,1250],[1163,3247,3249,3252,3255],{"className":3248},[1213,1250],[1163,3250,1190],{"className":3251},[1213,1217,1250],[1163,3253,1334],{"className":3254},[1465,1250],[1163,3256,1370],{"className":3257},[1213,1250],[1163,3259,3261,3264],{"style":3260},"top:-3.2029em;margin-right:0.05em;",[1163,3262],{"className":3263,"style":1243},[1242],[1163,3265,3267],{"className":3266},[1247,1248,1249,1250],[1163,3268,3270],{"className":3269},[1213,1250],[1163,3271,3045],{"className":3272,"style":1490},[1213,1217,1250],[1163,3274,1258],{"className":3275},[1257],[1163,3277,3279],{"className":3278},[1230],[1163,3280,3283],{"className":3281,"style":3282},[1234],"height:0.2997em;",[1163,3284],{},[1163,3286],{"className":3287,"style":2675},[1460],[1163,3289,3291,3294],{"className":3290},[1213],[1163,3292,3133],{"className":3293},[1213,1217],[1163,3295,3297],{"className":3296},[1221],[1163,3298,3300,3320],{"className":3299},[1225,1226],[1163,3301,3303,3317],{"className":3302},[1230],[1163,3304,3306],{"className":3305,"style":1235},[1234],[1163,3307,3308,3311],{"style":1238},[1163,3309],{"className":3310,"style":1243},[1242],[1163,3312,3314],{"className":3313},[1247,1248,1249,1250],[1163,3315,1190],{"className":3316},[1213,1217,1250],[1163,3318,1258],{"className":3319},[1257],[1163,3321,3323],{"className":3322},[1230],[1163,3324,3326],{"className":3325,"style":1265},[1234],[1163,3327],{},[1163,3329,1341],{"className":3330},[1483],[1163,3332,3334,3337],{"className":3333},[1213],[1163,3335,1796],{"className":3336,"style":1479},[1213,1217],[1163,3338,3340],{"className":3339},[1221],[1163,3341,3343,3363],{"className":3342},[1225,1226],[1163,3344,3346,3360],{"className":3345},[1230],[1163,3347,3349],{"className":3348,"style":1235},[1234],[1163,3350,3351,3354],{"style":1860},[1163,3352],{"className":3353,"style":1243},[1242],[1163,3355,3357],{"className":3356},[1247,1248,1249,1250],[1163,3358,1190],{"className":3359},[1213,1217,1250],[1163,3361,1258],{"className":3362},[1257],[1163,3364,3366],{"className":3365},[1230],[1163,3367,3369],{"className":3368,"style":1265},[1234],[1163,3370],{},[1163,3372,2609],{"className":3373},[2671],[1163,3375],{"className":3376,"style":2675},[1460],[1163,3378,3380,3429],{"className":3379},[1213],[1163,3381,3384],{"className":3382},[1213,3383],"accent",[1163,3385,3387,3420],{"className":3386},[1225,1226],[1163,3388,3390,3417],{"className":3389},[1230],[1163,3391,3394,3404],{"className":3392,"style":3393},[1234],"height:0.6944em;",[1163,3395,3397,3401],{"style":3396},"top:-3em;",[1163,3398],{"className":3399,"style":3400},[1242],"height:3em;",[1163,3402,1796],{"className":3403,"style":1479},[1213,1217],[1163,3405,3406,3409],{"style":3396},[1163,3407],{"className":3408,"style":3400},[1242],[1163,3410,3414],{"className":3411,"style":3413},[3412],"accent-body","left:-0.1944em;",[1163,3415,3177],{"className":3416},[1213],[1163,3418,1258],{"className":3419},[1257],[1163,3421,3423],{"className":3422},[1230],[1163,3424,3427],{"className":3425,"style":3426},[1234],"height:0.1944em;",[1163,3428],{},[1163,3430,3432],{"className":3431},[1221],[1163,3433,3435,3455],{"className":3434},[1225,1226],[1163,3436,3438,3452],{"className":3437},[1230],[1163,3439,3441],{"className":3440,"style":1235},[1234],[1163,3442,3443,3446],{"style":1860},[1163,3444],{"className":3445,"style":1243},[1242],[1163,3447,3449],{"className":3448},[1247,1248,1249,1250],[1163,3450,1190],{"className":3451},[1213,1217,1250],[1163,3453,1258],{"className":3454},[1257],[1163,3456,3458],{"className":3457},[1230],[1163,3459,3461],{"className":3460,"style":1265},[1234],[1163,3462],{},[1163,3464,1404],{"className":3465},[1776],[1114,3467,3468,3471,3472,3523,3524,3576],{},[1107,3469,3470],{},"反向传播","：从 ",[1163,3473,3475,3493],{"className":3474},[1166],[1163,3476,3478],{"className":3477},[1170],[1172,3479,3480],{"xmlns":1174},[1176,3481,3482,3490],{},[1179,3483,3484,3486,3488],{},[1185,3485,1190],{},[1332,3487,1334],{},[1185,3489,3045],{},[1192,3491,3492],{"encoding":1194},"t = T",[1163,3494,3496,3514],{"className":3495,"ariaHidden":1200},[1199],[1163,3497,3499,3502,3505,3508,3511],{"className":3498},[1204],[1163,3500],{"className":3501,"style":3058},[1208],[1163,3503,1190],{"className":3504},[1213,1217],[1163,3506],{"className":3507,"style":1461},[1460],[1163,3509,1334],{"className":3510},[1465],[1163,3512],{"className":3513,"style":1461},[1460],[1163,3515,3517,3520],{"className":3516},[1204],[1163,3518],{"className":3519,"style":3194},[1208],[1163,3521,3045],{"className":3522,"style":1490},[1213,1217]," 逆序回溯到 ",[1163,3525,3527,3545],{"className":3526},[1166],[1163,3528,3530],{"className":3529},[1170],[1172,3531,3532],{"xmlns":1174},[1176,3533,3534,3542],{},[1179,3535,3536,3538,3540],{},[1185,3537,1190],{},[1332,3539,1334],{},[1368,3541,1370],{},[1192,3543,3544],{"encoding":1194},"t = 1",[1163,3546,3548,3566],{"className":3547,"ariaHidden":1200},[1199],[1163,3549,3551,3554,3557,3560,3563],{"className":3550},[1204],[1163,3552],{"className":3553,"style":3058},[1208],[1163,3555,1190],{"className":3556},[1213,1217],[1163,3558],{"className":3559,"style":1461},[1460],[1163,3561,1334],{"className":3562},[1465],[1163,3564],{"className":3565,"style":1461},[1460],[1163,3567,3569,3573],{"className":3568},[1204],[1163,3570],{"className":3571,"style":3572},[1208],"height:0.6444em;",[1163,3574,1370],{"className":3575},[1213],"，累积梯度",[1114,3578,3579,3582],{},[1107,3580,3581],{},"参数更新","：梯度求和后一次性更新共享参数",[1101,3584,3585,3586,3662],{},"对权重 ",[1163,3587,3589,3610],{"className":3588},[1166],[1163,3590,3592],{"className":3591},[1170],[1172,3593,3594],{"xmlns":1174},[1176,3595,3596,3608],{},[1179,3597,3598],{},[1182,3599,3600,3602],{},[1185,3601,1346],{},[1179,3603,3604,3606],{},[1185,3605,1187],{},[1185,3607,1187],{},[1192,3609,2442],{"encoding":1194},[1163,3611,3613],{"className":3612,"ariaHidden":1200},[1199],[1163,3614,3616,3619],{"className":3615},[1204],[1163,3617],{"className":3618,"style":1615},[1208],[1163,3620,3622,3625],{"className":3621},[1213],[1163,3623,1346],{"className":3624,"style":1490},[1213,1217],[1163,3626,3628],{"className":3627},[1221],[1163,3629,3631,3654],{"className":3630},[1225,1226],[1163,3632,3634,3651],{"className":3633},[1230],[1163,3635,3637],{"className":3636,"style":1503},[1234],[1163,3638,3639,3642],{"style":1506},[1163,3640],{"className":3641,"style":1243},[1242],[1163,3643,3645],{"className":3644},[1247,1248,1249,1250],[1163,3646,3648],{"className":3647},[1213,1250],[1163,3649,1519],{"className":3650},[1213,1217,1250],[1163,3652,1258],{"className":3653},[1257],[1163,3655,3657],{"className":3656},[1230],[1163,3658,3660],{"className":3659,"style":1265},[1234],[1163,3661],{}," 的梯度为：",[1101,3664,3665],{},[1163,3666,3668,3810],{"className":3667},[1166],[1163,3669,3671],{"className":3670},[1170],[1172,3672,3673],{"xmlns":1174},[1176,3674,3675,3807],{},[1179,3676,3677,3702,3704,3718,3733,3755,3757,3779,3781],{},[3678,3679,3680,3688],"mfrac",{},[1179,3681,3682,3686],{},[1185,3683,3685],{"mathvariant":3684},"normal","∂",[1185,3687,3133],{},[1179,3689,3690,3692],{},[1185,3691,3685],{"mathvariant":3684},[1182,3693,3694,3696],{},[1185,3695,1346],{},[1179,3697,3698,3700],{},[1185,3699,1187],{},[1185,3701,1187],{},[1332,3703,1334],{},[3137,3705,3706,3708,3716],{},[1332,3707,3141],{},[1179,3709,3710,3712,3714],{},[1185,3711,1190],{},[1332,3713,1334],{},[1368,3715,1370],{},[1185,3717,3045],{},[3137,3719,3720,3722,3731],{},[1332,3721,3141],{},[1179,3723,3724,3727,3729],{},[1185,3725,3726],{},"k",[1332,3728,1334],{},[1368,3730,1370],{},[1185,3732,1190],{},[3678,3734,3735,3745],{},[1179,3736,3737,3739],{},[1185,3738,3685],{"mathvariant":3684},[1182,3740,3741,3743],{},[1185,3742,3133],{},[1185,3744,1190],{},[1179,3746,3747,3749],{},[1185,3748,3685],{"mathvariant":3684},[1182,3750,3751,3753],{},[1185,3752,1187],{},[1185,3754,1190],{},[1332,3756,1355],{},[3678,3758,3759,3769],{},[1179,3760,3761,3763],{},[1185,3762,3685],{"mathvariant":3684},[1182,3764,3765,3767],{},[1185,3766,1187],{},[1185,3768,1190],{},[1179,3770,3771,3773],{},[1185,3772,3685],{"mathvariant":3684},[1182,3774,3775,3777],{},[1185,3776,1187],{},[1185,3778,3726],{},[1332,3780,1355],{},[3678,3782,3783,3793],{},[1179,3784,3785,3787],{},[1185,3786,3685],{"mathvariant":3684},[1182,3788,3789,3791],{},[1185,3790,1187],{},[1185,3792,3726],{},[1179,3794,3795,3797],{},[1185,3796,3685],{"mathvariant":3684},[1182,3798,3799,3801],{},[1185,3800,1346],{},[1179,3802,3803,3805],{},[1185,3804,1187],{},[1185,3806,1187],{},[1192,3808,3809],{"encoding":1194},"\\frac{\\partial L}{\\partial W_{hh}} = \\sum_{t=1}^{T} \\sum_{k=1}^{t} \\frac{\\partial L_t}{\\partial h_t} \\cdot \\frac{\\partial h_t}{\\partial h_k} \\cdot \\frac{\\partial h_k}{\\partial W_{hh}}",[1163,3811,3813,3958,4262,4427],{"className":3812,"ariaHidden":1200},[1199],[1163,3814,3816,3820,3949,3952,3955],{"className":3815},[1204],[1163,3817],{"className":3818,"style":3819},[1208],"height:1.331em;vertical-align:-0.4509em;",[1163,3821,3823,3827,3946],{"className":3822},[1213],[1163,3824],{"className":3825},[1483,3826],"nulldelimiter",[1163,3828,3830],{"className":3829},[3678],[1163,3831,3833,3937],{"className":3832},[1225,1226],[1163,3834,3836,3934],{"className":3835},[1230],[1163,3837,3840,3905,3916],{"className":3838,"style":3839},[1234],"height:0.8801em;",[1163,3841,3843,3846],{"style":3842},"top:-2.655em;",[1163,3844],{"className":3845,"style":3400},[1242],[1163,3847,3849],{"className":3848},[1247,1248,1249,1250],[1163,3850,3852,3856],{"className":3851},[1213,1250],[1163,3853,3685],{"className":3854,"style":3855},[1213,1250],"margin-right:0.0556em;",[1163,3857,3859,3862],{"className":3858},[1213,1250],[1163,3860,1346],{"className":3861,"style":1490},[1213,1217,1250],[1163,3863,3865],{"className":3864},[1221],[1163,3866,3868,3896],{"className":3867},[1225,1226],[1163,3869,3871,3893],{"className":3870},[1230],[1163,3872,3875],{"className":3873,"style":3874},[1234],"height:0.3448em;",[1163,3876,3878,3882],{"style":3877},"top:-2.3488em;margin-left:-0.1389em;margin-right:0.0714em;",[1163,3879],{"className":3880,"style":3881},[1242],"height:2.5em;",[1163,3883,3887],{"className":3884},[1247,3885,3886,1250],"reset-size3","size1",[1163,3888,3890],{"className":3889},[1213,1250],[1163,3891,1519],{"className":3892},[1213,1217,1250],[1163,3894,1258],{"className":3895},[1257],[1163,3897,3899],{"className":3898},[1230],[1163,3900,3903],{"className":3901,"style":3902},[1234],"height:0.1512em;",[1163,3904],{},[1163,3906,3908,3911],{"style":3907},"top:-3.23em;",[1163,3909],{"className":3910,"style":3400},[1242],[1163,3912],{"className":3913,"style":3915},[3914],"frac-line","border-bottom-width:0.04em;",[1163,3917,3919,3922],{"style":3918},"top:-3.394em;",[1163,3920],{"className":3921,"style":3400},[1242],[1163,3923,3925],{"className":3924},[1247,1248,1249,1250],[1163,3926,3928,3931],{"className":3927},[1213,1250],[1163,3929,3685],{"className":3930,"style":3855},[1213,1250],[1163,3932,3133],{"className":3933},[1213,1217,1250],[1163,3935,1258],{"className":3936},[1257],[1163,3938,3940],{"className":3939},[1230],[1163,3941,3944],{"className":3942,"style":3943},[1234],"height:0.4509em;",[1163,3945],{},[1163,3947],{"className":3948},[1776,3826],[1163,3950],{"className":3951,"style":1461},[1460],[1163,3953,1334],{"className":3954},[1465],[1163,3956],{"className":3957,"style":1461},[1460],[1163,3959,3961,3965,4028,4031,4096,4099,4253,4256,4259],{"className":3960},[1204],[1163,3962],{"className":3963,"style":3964},[1208],"height:1.4263em;vertical-align:-0.4451em;",[1163,3966,3968,3971],{"className":3967},[3217],[1163,3969,3141],{"className":3970,"style":3223},[3217,3221,3222],[1163,3972,3974],{"className":3973},[1221],[1163,3975,3977,4020],{"className":3976},[1225,1226],[1163,3978,3980,4017],{"className":3979},[1230],[1163,3981,3983,4003],{"className":3982,"style":3236},[1234],[1163,3984,3985,3988],{"style":3239},[1163,3986],{"className":3987,"style":1243},[1242],[1163,3989,3991],{"className":3990},[1247,1248,1249,1250],[1163,3992,3994,3997,4000],{"className":3993},[1213,1250],[1163,3995,1190],{"className":3996},[1213,1217,1250],[1163,3998,1334],{"className":3999},[1465,1250],[1163,4001,1370],{"className":4002},[1213,1250],[1163,4004,4005,4008],{"style":3260},[1163,4006],{"className":4007,"style":1243},[1242],[1163,4009,4011],{"className":4010},[1247,1248,1249,1250],[1163,4012,4014],{"className":4013},[1213,1250],[1163,4015,3045],{"className":4016,"style":1490},[1213,1217,1250],[1163,4018,1258],{"className":4019},[1257],[1163,4021,4023],{"className":4022},[1230],[1163,4024,4026],{"className":4025,"style":3282},[1234],[1163,4027],{},[1163,4029],{"className":4030,"style":2675},[1460],[1163,4032,4034,4037],{"className":4033},[3217],[1163,4035,3141],{"className":4036,"style":3223},[3217,3221,3222],[1163,4038,4040],{"className":4039},[1221],[1163,4041,4043,4088],{"className":4042},[1225,1226],[1163,4044,4046,4085],{"className":4045},[1230],[1163,4047,4050,4071],{"className":4048,"style":4049},[1234],"height:0.9335em;",[1163,4051,4052,4055],{"style":3239},[1163,4053],{"className":4054,"style":1243},[1242],[1163,4056,4058],{"className":4057},[1247,1248,1249,1250],[1163,4059,4061,4065,4068],{"className":4060},[1213,1250],[1163,4062,3726],{"className":4063,"style":4064},[1213,1217,1250],"margin-right:0.0315em;",[1163,4066,1334],{"className":4067},[1465,1250],[1163,4069,1370],{"className":4070},[1213,1250],[1163,4072,4073,4076],{"style":3260},[1163,4074],{"className":4075,"style":1243},[1242],[1163,4077,4079],{"className":4078},[1247,1248,1249,1250],[1163,4080,4082],{"className":4081},[1213,1250],[1163,4083,1190],{"className":4084},[1213,1217,1250],[1163,4086,1258],{"className":4087},[1257],[1163,4089,4091],{"className":4090},[1230],[1163,4092,4094],{"className":4093,"style":3282},[1234],[1163,4095],{},[1163,4097],{"className":4098,"style":2675},[1460],[1163,4100,4102,4105,4250],{"className":4101},[1213],[1163,4103],{"className":4104},[1483,3826],[1163,4106,4108],{"className":4107},[3678],[1163,4109,4111,4241],{"className":4110},[1225,1226],[1163,4112,4114,4238],{"className":4113},[1230],[1163,4115,4118,4175,4183],{"className":4116,"style":4117},[1234],"height:0.8962em;",[1163,4119,4120,4123],{"style":3842},[1163,4121],{"className":4122,"style":3400},[1242],[1163,4124,4126],{"className":4125},[1247,1248,1249,1250],[1163,4127,4129,4132],{"className":4128},[1213,1250],[1163,4130,3685],{"className":4131,"style":3855},[1213,1250],[1163,4133,4135,4138],{"className":4134},[1213,1250],[1163,4136,1187],{"className":4137},[1213,1217,1250],[1163,4139,4141],{"className":4140},[1221],[1163,4142,4144,4166],{"className":4143},[1225,1226],[1163,4145,4147,4163],{"className":4146},[1230],[1163,4148,4151],{"className":4149,"style":4150},[1234],"height:0.2963em;",[1163,4152,4154,4157],{"style":4153},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1163,4155],{"className":4156,"style":3881},[1242],[1163,4158,4160],{"className":4159},[1247,3885,3886,1250],[1163,4161,1190],{"className":4162},[1213,1217,1250],[1163,4164,1258],{"className":4165},[1257],[1163,4167,4169],{"className":4168},[1230],[1163,4170,4173],{"className":4171,"style":4172},[1234],"height:0.143em;",[1163,4174],{},[1163,4176,4177,4180],{"style":3907},[1163,4178],{"className":4179,"style":3400},[1242],[1163,4181],{"className":4182,"style":3915},[3914],[1163,4184,4186,4189],{"style":4185},"top:-3.4101em;",[1163,4187],{"className":4188,"style":3400},[1242],[1163,4190,4192],{"className":4191},[1247,1248,1249,1250],[1163,4193,4195,4198],{"className":4194},[1213,1250],[1163,4196,3685],{"className":4197,"style":3855},[1213,1250],[1163,4199,4201,4204],{"className":4200},[1213,1250],[1163,4202,3133],{"className":4203},[1213,1217,1250],[1163,4205,4207],{"className":4206},[1221],[1163,4208,4210,4230],{"className":4209},[1225,1226],[1163,4211,4213,4227],{"className":4212},[1230],[1163,4214,4216],{"className":4215,"style":4150},[1234],[1163,4217,4218,4221],{"style":4153},[1163,4219],{"className":4220,"style":3881},[1242],[1163,4222,4224],{"className":4223},[1247,3885,3886,1250],[1163,4225,1190],{"className":4226},[1213,1217,1250],[1163,4228,1258],{"className":4229},[1257],[1163,4231,4233],{"className":4232},[1230],[1163,4234,4236],{"className":4235,"style":4172},[1234],[1163,4237],{},[1163,4239,1258],{"className":4240},[1257],[1163,4242,4244],{"className":4243},[1230],[1163,4245,4248],{"className":4246,"style":4247},[1234],"height:0.4451em;",[1163,4249],{},[1163,4251],{"className":4252},[1776,3826],[1163,4254],{"className":4255,"style":1534},[1460],[1163,4257,1355],{"className":4258},[1538],[1163,4260],{"className":4261,"style":1534},[1460],[1163,4263,4265,4269,4418,4421,4424],{"className":4264},[1204],[1163,4266],{"className":4267,"style":4268},[1208],"height:1.3471em;vertical-align:-0.4509em;",[1163,4270,4272,4275,4415],{"className":4271},[1213],[1163,4273],{"className":4274},[1483,3826],[1163,4276,4278],{"className":4277},[3678],[1163,4279,4281,4407],{"className":4280},[1225,1226],[1163,4282,4284,4404],{"className":4283},[1230],[1163,4285,4287,4342,4350],{"className":4286,"style":4117},[1234],[1163,4288,4289,4292],{"style":3842},[1163,4290],{"className":4291,"style":3400},[1242],[1163,4293,4295],{"className":4294},[1247,1248,1249,1250],[1163,4296,4298,4301],{"className":4297},[1213,1250],[1163,4299,3685],{"className":4300,"style":3855},[1213,1250],[1163,4302,4304,4307],{"className":4303},[1213,1250],[1163,4305,1187],{"className":4306},[1213,1217,1250],[1163,4308,4310],{"className":4309},[1221],[1163,4311,4313,4334],{"className":4312},[1225,1226],[1163,4314,4316,4331],{"className":4315},[1230],[1163,4317,4319],{"className":4318,"style":3874},[1234],[1163,4320,4322,4325],{"style":4321},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[1163,4323],{"className":4324,"style":3881},[1242],[1163,4326,4328],{"className":4327},[1247,3885,3886,1250],[1163,4329,3726],{"className":4330,"style":4064},[1213,1217,1250],[1163,4332,1258],{"className":4333},[1257],[1163,4335,4337],{"className":4336},[1230],[1163,4338,4340],{"className":4339,"style":3902},[1234],[1163,4341],{},[1163,4343,4344,4347],{"style":3907},[1163,4345],{"className":4346,"style":3400},[1242],[1163,4348],{"className":4349,"style":3915},[3914],[1163,4351,4352,4355],{"style":4185},[1163,4353],{"className":4354,"style":3400},[1242],[1163,4356,4358],{"className":4357},[1247,1248,1249,1250],[1163,4359,4361,4364],{"className":4360},[1213,1250],[1163,4362,3685],{"className":4363,"style":3855},[1213,1250],[1163,4365,4367,4370],{"className":4366},[1213,1250],[1163,4368,1187],{"className":4369},[1213,1217,1250],[1163,4371,4373],{"className":4372},[1221],[1163,4374,4376,4396],{"className":4375},[1225,1226],[1163,4377,4379,4393],{"classN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BPTT","：实践中，为减少计算量和缓解梯度问题，通常将序列截断为固定长度的片段进行反向传播，而不是完整回溯到 ",[1163,4594,4596,4614],{"className":4595},[1166],[1163,4597,4599],{"className":4598},[1170],[1172,4600,4601],{"xmlns":1174},[1176,4602,4603,4611],{},[1179,4604,4605,4607,4609],{},[1185,4606,1190],{},[1332,4608,1334],{},[1368,4610,1370],{},[1192,4612,4613],{"encoding":1194},"t=1",[1163,4615,4617,4635],{"className":4616,"ariaHidden":1200},[1199],[1163,4618,4620,4623,4626,4629,4632],{"className":4619},[1204],[1163,4621],{"className":4622,"style":3058},[1208],[1163,4624,1190],{"className":4625},[1213,1217],[1163,4627],{"className":4628,"style":1461},[1460],[1163,4630,1334],{"className":4631},[1465],[1163,4633],{"className":4634,"style":1461},[1460],[1163,4636,4638,4641],{"className":4637},[1204],[1163,4639],{"className":4640,"style":3572},[1208],[1163,4642,1370],{"className":4643},[1213],[4645,4646],"hr",{},[1091,4648,4650],{"id":4649},"二梯度问题","二、梯度问题",[1096,4652,4654],{"id":4653},"_21-问题本质","2.1 问题本质",[1101,4656,4657],{},"在 BPTT 中，梯度从时刻 t 传播到时刻 k 需要经过连乘：",[1101,4659,4660],{},[1107,4661,4662],{},"梯度传播公式：",[1101,4664,4665],{},[1163,4666,4668,4764],{"className":4667},[1166],[1163,4669,4671],{"className":4670},[1170],[1172,4672,4673],{"xmlns":1174},[1176,4674,4675,4761],{},[1179,4676,4677,4699,4701,4721,4731,4733,4737,4739,4748,4750,4757,4759],{},[3678,4678,4679,4689],{},[1179,4680,4681,4683],{},[1185,4682,3685],{"mathvariant":3684},[1182,4684,4685,4687],{},[1185,4686,1187],{},[1185,4688,1190],{},[1179,4690,4691,4693],{},[1185,4692,3685],{"mathvariant":3684},[1182,4694,4695,4697],{},[1185,4696,1187],{},[1185,4698,3726],{},[1332,4700,1334],{},[3137,4702,4703,4706,4719],{},[1332,4704,4705],{},"∏",[1179,4707,4708,4711,4713,4715,4717],{},[1185,4709,4710],{},"i",[1332,4712,1334],{},[1185,4714,3726],{},[1332,4716,1373],{},[1368,4718,1370],{},[1185,4720,1190],{},[1182,4722,4723,4725],{},[1185,4724,1346],{},[1179,4726,4727,4729],{},[1185,4728,1187],{},[1185,4730,1187],{},[1332,4732,1355],{},[4734,4735,4736],"mtext",{},"diag",[1332,4738,1341],{"stretchy":1340},[4740,4741,4742,4744],"msup",{},[1185,4743,1337],{},[1332,4745,4747],{"mathvariant":3684,"lspace":4746,"rspace":4746},"0em","′",[1332,4749,1341],{"stretchy":1340},[1182,4751,4752,4755],{},[1185,4753,4754],{},"z",[1185,4756,4710],{},[1332,4758,1404],{"stretchy":1340},[1332,4760,1404],{"stretchy":1340},[1192,4762,4763],{"encoding":1194},"\\frac{\\partial h_t}{\\partial h_k} = \\prod_{i=k+1}^{t} W_{hh} \\cdot \\text{diag}(\\sigma'(z_i))",[1163,4765,4767,4930,5062],{"className":4766,"ariaHidden":1200},[1199],[1163,4768,4770,4773,4921,4924,4927],{"className":4769},[1204],[1163,4771],{"className":4772,"style":4268},[1208],[1163,4774,4776,4779,4918],{"className":4775},[1213],[1163,4777],{"className":4778},[1483,3826],[1163,4780,4782],{"className":4781},[3678],[1163,4783,4785,4910],{"className":4784},[1225,1226],[1163,4786,4788,4907],{"className":4787},[1230],[1163,4789,4791,4845,4853],{"className":4790,"style":4117},[1234],[1163,4792,4793,4796],{"style":3842},[1163,4794],{"className":4795,"style":3400},[1242],[1163,4797,4799],{"className":4798},[1247,1248,1249,1250],[1163,4800,4802,4805],{"className":4801},[1213,1250],[1163,4803,3685],{"className":4804,"style":3855},[1213,1250],[1163,4806,4808,4811],{"className":4807},[1213,1250],[1163,4809,1187],{"className":4810},[1213,1217,1250],[1163,4812,4814],{"className":4813},[1221],[1163,4815,4817,4837],{"className":4816},[1225,1226],[1163,4818,4820,4834],{"className":4819},[1230],[1163,4821,4823],{"className":4822,"style":3874},[1234],[1163,4824,4825,4828],{"style":4321},[1163,4826],{"className":4827,"style":3881},[1242],[1163,4829,4831],{"className":4830},[1247,3885,3886,1250],[1163,4832,3726],{"className":4833,"style":4064},[1213,1217,1250],[1163,4835,1258],{"className":4836},[1257],[1163,4838,4840],{"className":4839},[1230],[1163,4841,4843],{"className":4842,"style":3902},[1234],[1163,4844],{},[1163,4846,4847,4850],{"style":3907},[1163,4848],{"className":4849,"style":3400},[1242],[1163,4851],{"className":4852,"style":3915},[3914],[1163,4854,4855,4858],{"style":4185},[1163,4856],{"className":4857,"style":3400},[1242],[1163,4859,4861],{"className":4860},[1247,1248,1249,1250],[1163,4862,4864,4867],{"className":4863},[1213,1250],[1163,4865,3685],{"className":4866,"style":3855},[1213,1250],[1163,4868,4870,4873],{"className":4869},[1213,1250],[1163,4871,1187],{"className":4872},[1213,1217,1250],[1163,4874,4876],{"className":4875},[1221],[1163,4877,4879,4899],{"className":4878},[1225,1226],[1163,4880,4882,4896],{"className":4881},[1230],[1163,4883,4885],{"className":4884,"style":4150},[1234],[1163,4886,4887,4890],{"style":4153},[1163,4888],{"className":4889,"style":3881},[1242],[1163,4891,4893],{"className":4892},[1247,3885,3886,1250],[1163,4894,1190],{"className":4895},[1213,1217,1250],[1163,4897,1258],{"className":4898},[1257],[1163,4900,4902],{"className":4901},[1230],[1163,4903,4905],{"className":4904,"style":4172},[1234],[1163,4906],{},[1163,4908,1258],{"className":4909},[1257],[1163,4911,4913],{"className":4912},[1230],[1163,4914,4916],{"className":4915,"style":3943},[1234],[1163,4917],{},[1163,4919],{"className":4920},[1776,3826],[1163,4922],{"className":4923,"style":1461},[1460],[1163,4925,1334],{"className":4926},[1465],[1163,4928],{"className":4929,"style":1461},[1460],[1163,4931,4933,4937,5007,5010,5053,5056,5059],{"className":4932},[1204],[1163,4934],{"className":4935,"style":4936},[1208],"height:1.2915em;vertical-align:-0.358em;",[1163,4938,4940,4943],{"className":4939},[3217],[1163,4941,4705],{"className":4942,"style":3223},[3217,3221,3222],[1163,4944,4946],{"className":4945},[1221],[1163,4947,4949,4998],{"className":4948},[1225,1226],[1163,4950,4952,4995],{"className":4951},[1230],[1163,4953,4955,4981],{"className":4954,"style":4049},[1234],[1163,4956,4957,4960],{"style":3239},[1163,4958],{"className":4959,"style":1243},[1242],[1163,4961,4963],{"className":4962},[1247,1248,1249,1250],[1163,4964,4966,4969,4972,4975,4978],{"className":4965},[1213,1250],[1163,4967,4710],{"className":4968},[1213,1217,1250],[1163,4970,1334],{"className":4971},[1465,1250],[1163,4973,3726],{"className":4974,"style":4064},[1213,1217,1250],[1163,4976,1373],{"className":4977},[1538,1250],[1163,4979,1370],{"className":4980},[1213,1250],[1163,4982,4983,4986],{"style":3260},[1163,4984],{"className":4985,"style":1243},[1242],[1163,4987,4989],{"className":4988},[1247,1248,1249,1250],[1163,4990,4992],{"className":4991},[1213,1250],[1163,4993,1190],{"className":4994},[1213,1217,1250],[1163,4996,1258],{"className":4997},[1257],[1163,4999,5001],{"className":5000},[1230],[1163,5002,5005],{"className":5003,"style":5004},[1234],"height:0.358em;",[1163,5006],{},[1163,5008],{"className":5009,"style":2675},[1460],[1163,5011,5013,5016],{"className":5012},[1213],[1163,5014,1346],{"className":5015,"style":1490},[1213,1217],[1163,5017,5019],{"className":5018},[1221],[1163,5020,5022,5045],{"className":5021},[1225,1226],[1163,5023,5025,5042],{"className":5024},[1230],[1163,5026,5028],{"className":5027,"style":1503},[1234],[1163,5029,5030,5033],{"style":1506},[1163,5031],{"className":5032,"style":1243},[1242],[1163,5034,5036],{"className":5035},[1247,1248,1249,1250],[1163,5037,5039],{"className":5038},[1213,1250],[1163,5040,1519],{"className":5041},[1213,1217,1250],[1163,5043,1258],{"className":5044},[1257],[1163,5046,5048],{"className":5047},[1230],[1163,5049,5051],{"className":5050,"style":1265},[1234],[1163,5052],{},[1163,5054],{"className":5055,"style":1534},[1460],[1163,5057,1355],{"className":5058},[1538],[1163,5060],{"className":5061,"style":1534},[1460],[1163,5063,5065,5069,5076,5079,5113,5116,5159],{"className":5064},[1204],[1163,5066],{"className":5067,"style":5068},[1208],"height:1.0019em;vertical-align:-0.25em;",[1163,5070,5073],{"className":5071},[1213,5072],"text",[1163,5074,4736],{"className":5075},[1213],[1163,5077,1341],{"className":5078},[1483],[1163,5080,5082,5085],{"className":5081},[1213],[1163,5083,1337],{"className":5084,"style":1479},[1213,1217],[1163,5086,5088],{"className":5087},[1221],[1163,5089,5091],{"className":5090},[1225],[1163,5092,5094],{"className":5093},[1230],[1163,5095,5098],{"className":5096,"style":5097},[1234],"height:0.7519em;",[1163,5099,5101,5104],{"style":5100},"top:-3.063em;margin-right:0.05em;",[1163,5102],{"className":5103,"style":1243},[1242],[1163,5105,5107],{"className":5106},[1247,1248,1249,1250],[1163,5108,5110],{"className":5109},[1213,1250],[1163,5111,4747],{"className":5112},[1213,1250],[1163,5114,1341],{"className":5115},[1483],[1163,5117,5119,5123],{"className":5118},[1213],[1163,5120,4754],{"className":5121,"style":5122},[1213,1217],"margin-right:0.044em;",[1163,5124,5126],{"className":5125},[1221],[1163,5127,5129,5151],{"className":5128},[1225,1226],[1163,5130,5132,5148],{"className":5131},[1230],[1163,5133,5136],{"className":5134,"style":5135},[1234],"height:0.3117em;",[1163,5137,5139,5142],{"style":5138},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[1163,5140],{"className":5141,"style":1243},[1242],[1163,5143,5145],{"className":5144},[1247,1248,1249,1250],[1163,5146,4710],{"className":5147},[1213,1217,1250],[1163,5149,1258],{"className":5150},[1257],[1163,5152,5154],{"className":5153},[1230],[1163,5155,5157],{"className":5156,"style":1265},[1234],[1163,5158],{},[1163,5160,5162],{"className":5161},[1776],"))",[1101,5164,5165,5166,5583,5584,5646],{},"其中 ",[1163,5167,5169,5241],{"className":5168},[1166],[1163,5170,5172],{"className":5171},[1170],[1172,5173,5174],{"xmlns":1174},[1176,5175,5176,5238],{},[1179,5177,5178,5184,5186,5196,5198,5210,5212,5222,5224,5230,5232],{},[1182,5179,5180,5182],{},[1185,5181,4754],{},[1185,5183,4710],{},[1332,5185,1334],{},[1182,5187,5188,5190],{},[1185,5189,1346],{},[1179,5191,5192,5194],{},[1185,5193,1187],{},[1185,5195,1187],{},[1332,5197,1355],{},[1182,5199,5200,5202],{},[1185,5201,1187],{},[1179,5203,5204,5206,5208],{},[1185,5205,4710],{},[1332,5207,1366],{},[1368,5209,1370],{},[1332,5211,1373],{},[1182,5213,5214,5216],{},[1185,5215,1346],{},[1179,5217,5218,5220],{},[1185,5219,1382],{},[1185,5221,1187],{},[1332,5223,1355],{},[1182,5225,5226,5228],{},[1185,5227,1382],{},[1185,5229,4710],{},[1332,5231,1373],{},[1182,5233,5234,5236],{},[1185,5235,1399],{},[1185,5237,1187],{},[1192,5239,5240],{"encoding":1194},"z_i = W_{hh} \\cdot h_{i-1} + W_{xh} \\cdot x_i + b_h",[1163,5242,5244,5299,5357,5421,5482,5537],{"className":5243,"ariaHidden":1200},[1199],[1163,5245,5247,5250,5290,5293,5296],{"className":5246},[1204],[1163,5248],{"className":5249,"style":2115},[1208],[1163,5251,5253,5256],{"className":5252},[1213],[1163,5254,4754],{"className":5255,"style":5122},[1213,1217],[1163,5257,5259],{"className":5258},[1221],[1163,5260,5262,5282],{"className":5261},[1225,1226],[1163,5263,5265,5279],{"className":5264},[1230],[1163,5266,5268],{"className":5267,"style":5135},[1234],[1163,5269,5270,5273],{"style":5138},[1163,5271],{"className":5272,"style":1243},[1242],[1163,5274,5276],{"className":5275},[1247,1248,1249,1250],[1163,5277,4710],{"className":5278},[1213,1217,1250],[1163,5280,1258],{"className":5281},[1257],[1163,5283,5285],{"className":5284},[1230],[1163,5286,5288],{"className":5287,"style":1265},[1234],[1163,5289],{},[1163,5291],{"className":5292,"style":1461},[1460],[1163,5294,1334],{"className":5295},[1465],[1163,5297],{"className":5298,"style":1461},[1460],[1163,5300,5302,5305,5348,5351,5354],{"className":5301},[1204],[1163,5303],{"className":5304,"style":1615},[1208],[1163,5306,5308,5311],{"className":5307},[1213],[1163,5309,1346],{"className":5310,"style":1490},[1213,1217],[1163,5312,5314],{"className":5313},[1221],[1163,5315,5317,5340],{"className":5316},[1225,1226],[1163,5318,5320,5337],{"className":5319},[1230],[1163,5321,5323],{"className":5322,"style":1503},[1234],[1163,5324,5325,5328],{"style":1506},[1163,5326],{"className":5327,"style":1243},[1242],[1163,5329,5331],{"className":5330},[1247,1248,1249,1250],[1163,5332,5334],{"className":5333},[1213,1250],[1163,5335,1519],{"className":5336},[1213,1217,1250],[1163,5338,1258],{"className":5339},[1257],[1163,5341,5343],{"className":5342},[1230],[1163,5344,5346],{"className":5345,"style":1265},[1234],[1163,5347],{},[1163,5349],{"className":5350,"style":1534},[1460],[1163,5352,1355],{"className":5353},[1538],[1163,5355],{"className":5356,"style":1534},[1460],[1163,5358,5360,5363,5412,5415,5418],{"className":5359},[1204],[1163,5361],{"className":5362,"style":1548},[1208],[1163,5364,5366,5369],{"className":5365},[1213],[1163,5367,1187],{"className":5368},[1213,1217],[1163,5370,5372],{"className":5371},[1221],[1163,5373,5375,5404],{"className":5374},[1225,1226],[1163,5376,5378,5401],{"className":5377},[1230],[1163,5379,5381],{"className":5380,"style":5135},[1234],[1163,5382,5383,5386],{"style":1238},[1163,5384],{"className":5385,"style":1243},[1242],[1163,5387,5389],{"className":5388},[1247,1248,1249,1250],[1163,5390,5392,5395,5398],{"className":5391},[1213,1250],[1163,5393,4710],{"className":5394},[1213,1217,1250],[1163,5396,1366],{"className":5397},[1538,1250],[1163,5399,1370],{"className":5400},[1213,1250],[1163,5402,1258],{"className":5403},[1257],[1163,5405,5407],{"className":5406},[1230],[1163,5408,5410],{"className":5409,"style":1597},[1234],[1163,5411],{},[1163,5413],{"className":5414,"style":1534},[1460],[1163,5416,1373],{"className":5417},[1538],[1163,5419],{"className":5420,"style":1534},[1460],[1163,5422,5424,5427,5473,5476,5479],{"className":5423},[1204],[1163,5425],{"className":5426,"style":1615},[1208],[1163,5428,5430,5433],{"className":5429},[1213],[1163,5431,1346],{"className":5432,"style":1490},[1213,1217],[1163,5434,5436],{"className":5435},[1221],[1163,5437,5439,5465],{"className":5438},[1225,1226],[1163,5440,5442,5462],{"className":5441},[1230],[1163,5443,5445],{"className":5444,"style":1503},[1234],[1163,5446,5447,5450],{"style":1506},[1163,5448],{"className":5449,"style":1243},[1242],[1163,5451,5453],{"className":5452},[1247,1248,1249,1250],[1163,5454,5456,5459],{"className":5455},[1213,1250],[1163,5457,1382],{"className":5458},[1213,1217,1250],[1163,5460,1187],{"className":5461},[1213,1217,1250],[1163,5463,1258],{"className":5464},[1257],[1163,5466,5468],{"className":5467},[1230],[1163,5469,5471],{"className":5470,"style":1265},[1234],[1163,5472],{},[1163,5474],{"className":5475,"style":1534},[1460],[1163,5477,1355],{"className":5478},[1538],[1163,5480],{"className":5481,"style":1534},[1460],[1163,5483,5485,5488,5528,5531,5534],{"className":5484},[1204],[1163,5486],{"className":5487,"style":1677},[1208],[1163,5489,5491,5494],{"className":5490},[1213],[1163,5492,1382],{"className":5493},[1213,1217],[1163,5495,5497],{"className":5496},[1221],[1163,5498,5500,5520],{"className":5499},[1225,1226],[1163,5501,5503,5517],{"className":5502},[1230],[1163,5504,5506],{"className":5505,"style":5135},[1234],[1163,5507,5508,5511],{"style":1238},[1163,5509],{"className":5510,"style":1243},[1242],[1163,5512,5514],{"className":5513},[1247,1248,1249,1250],[1163,5515,4710],{"className":5516},[1213,1217,1250],[1163,5518,1258],{"className":5519},[1257],[1163,5521,5523],{"className":5522},[1230],[1163,5524,5526],{"className":5525,"style":1265},[1234],[1163,5527],{},[1163,5529],{"className":5530,"style":1534},[1460],[1163,5532,1373],{"className":5533},[1538],[1163,5535],{"className":5536,"style":1534},[1460],[1163,5538,5540,5543],{"className":5539},[1204],[1163,5541],{"className":5542,"style":1209},[1208],[1163,5544,5546,5549],{"className":5545},[1213],[1163,5547,1399],{"className":5548},[1213,1217],[1163,5550,5552],{"className":5551},[1221],[1163,5553,5555,5575],{"className":5554},[1225,1226],[1163,5556,5558,5572],{"className":5557},[1230],[1163,5559,5561],{"className":5560,"style":1503},[1234],[1163,5562,5563,5566],{"style":1238},[1163,5564],{"className":5565,"style":1243},[1242],[1163,5567,5569],{"className":5568},[1247,1248,1249,1250],[1163,5570,1187],{"className":5571},[1213,1217,1250],[1163,5573,1258],{"className":5574},[1257],[1163,5576,5578],{"className":5577},[1230],[1163,5579,5581],{"className":5580,"style":1265},[1234],[1163,5582],{},"，",[1163,5585,5587,5605],{"className":5586},[1166],[1163,5588,5590],{"className":5589},[1170],[1172,5591,5592],{"xmlns":1174},[1176,5593,5594,5602],{},[1179,5595,5596],{},[4740,5597,5598,5600],{},[1185,5599,1337],{},[1332,5601,4747],{"mathvariant":3684,"lspace":4746,"rspace":4746},[1192,5603,5604],{"encoding":1194},"\\sigma'",[1163,5606,5608],{"className":5607,"ariaHidden":1200},[1199],[1163,5609,5611,5614],{"className":5610},[1204],[1163,5612],{"className":5613,"style":5097},[1208],[1163,5615,5617,5620],{"className":5616},[1213],[1163,5618,1337],{"className":5619,"style":1479},[1213,1217],[1163,5621,5623],{"className":5622},[1221],[1163,5624,5626],{"className":5625},[1225],[1163,5627,5629],{"className":5628},[1230],[1163,5630,5632],{"className":5631,"style":5097},[1234],[1163,5633,5634,5637],{"style":5100},[1163,5635],{"className":5636,"style":1243},[1242],[1163,5638,5640],{"className":5639},[1247,1248,1249,1250],[1163,5641,5643],{"className":5642},[1213,1250],[1163,5644,4747],{"className":5645},[1213,1250]," 为激活函数的导数。",[1101,5648,5649,5650,5653,5654,5730],{},"这是一个",[1107,5651,5652],{},"矩阵连乘","，其行为由 ",[1163,5655,5657,5678],{"className":5656},[1166],[1163,5658,5660],{"className":5659},[1170],[1172,5661,5662],{"xmlns":1174},[1176,5663,5664,5676],{},[1179,5665,5666],{},[1182,5667,5668,5670],{},[1185,5669,1346],{},[1179,5671,5672,5674],{},[1185,5673,1187],{},[1185,5675,1187],{},[1192,5677,2442],{"encoding":1194},[1163,5679,5681],{"className":5680,"ariaHidden":1200},[1199],[1163,5682,5684,5687],{"className":5683},[1204],[1163,5685],{"className":5686,"style":1615},[1208],[1163,5688,5690,5693],{"className":5689},[1213],[1163,5691,1346],{"className":5692,"style":1490},[1213,1217],[1163,5694,5696],{"className":5695},[1221],[1163,5697,5699,5722],{"className":5698},[1225,1226],[1163,5700,5702,5719],{"className":5701},[1230],[1163,5703,5705],{"className":5704,"style":1503},[1234],[1163,5706,5707,5710],{"style":1506},[1163,5708],{"className":5709,"style":1243},[1242],[1163,5711,5713],{"className":5712},[1247,1248,1249,1250],[1163,5714,5716],{"className":5715},[1213,1250],[1163,5717,1519],{"className":5718},[1213,1217,1250],[1163,5720,1258],{"className":5721},[1257],[1163,5723,5725],{"className":5724},[1230],[1163,5726,5728],{"className":5727,"style":1265},[1234],[1163,5729],{}," 的特征值决定：",[1096,5732,5734],{"id":5733},"_22-梯度消失-vs-梯度爆炸","2.2 梯度消失 vs 梯度爆炸",[2062,5736,5737,5750],{},[2065,5738,5739],{},[2068,5740,5741,5744,5747],{},[2071,5742,5743],{},"问题",[2071,5745,5746],{},"梯度消失（Vanishing）",[2071,5748,5749],{},"梯度爆炸（Exploding）",[2078,5751,5752,6005,6048,6061,6258],{},[2068,5753,5754,5759,5883],{},[2083,5755,5756],{},[1107,5757,5758],{},"条件",[2083,5760,5761,5837,5838],{},[1163,5762,5764,5785],{"className":5763},[1166],[1163,5765,5767],{"className":5766},[1170],[1172,5768,5769],{"xmlns":1174},[1176,5770,5771,5783],{},[1179,5772,5773],{},[1182,5774,5775,5777],{},[1185,5776,1346],{},[1179,5778,5779,5781],{},[1185,5780,1187],{},[1185,5782,1187],{},[1192,5784,2442],{"encoding":1194},[1163,5786,5788],{"className":5787,"ariaHidden":1200},[1199],[1163,5789,5791,5794],{"className":5790},[1204],[1163,5792],{"className":5793,"style":1615},[1208],[1163,5795,5797,5800],{"className":5796},[1213],[1163,5798,1346],{"className":5799,"style":1490},[1213,1217],[1163,5801,5803],{"className":5802},[1221],[1163,5804,5806,5829],{"className":5805},[1225,1226],[1163,5807,5809,5826],{"className":5808},[1230],[1163,5810,5812],{"className":5811,"style":1503},[1234],[1163,5813,5814,5817],{"style":1506},[1163,5815],{"className":5816,"style":1243},[1242],[1163,5818,5820],{"className":5819},[1247,1248,1249,1250],[1163,5821,5823],{"className":5822},[1213,1250],[1163,5824,1519],{"className":5825},[1213,1217,1250],[1163,5827,1258],{"className":5828},[1257],[1163,5830,5832],{"className":5831},[1230],[1163,5833,5835],{"className":5834,"style":1265},[1234],[1163,5836],{}," 的最大特征值 ",[1163,5839,5841,5858],{"className":5840},[1166],[1163,5842,5844],{"className":5843},[1170],[1172,5845,5846],{"xmlns":1174},[1176,5847,5848,5855],{},[1179,5849,5850,5853],{},[1332,5851,5852],{},"\u003C",[1368,5854,1370],{},[1192,5856,5857],{"encoding":1194},"\u003C 1",[1163,5859,5861,5874],{"className":5860,"ariaHidden":1200},[1199],[1163,5862,5864,5868,5871],{"className":5863},[1204],[1163,5865],{"className":5866,"style":5867},[1208],"height:0.5782em;vertical-align:-0.0391em;",[1163,5869,5852],{"className":5870},[1465],[1163,5872],{"className":5873,"style":1461},[1460],[1163,5875,5877,5880],{"className":5876},[1204],[1163,5878],{"className":5879,"style":3572},[1208],[1163,5881,1370],{"className":5882},[1213],[2083,5884,5885,5837,5961],{},[1163,5886,5888,5909],{"className":5887},[1166],[1163,5889,5891],{"className":5890},[1170],[1172,5892,5893],{"xmlns":1174},[1176,5894,5895,5907],{},[1179,5896,5897],{},[1182,5898,5899,5901],{},[1185,5900,1346],{},[1179,5902,5903,5905],{},[1185,5904,1187],{},[1185,5906,1187],{},[1192,5908,2442],{"encoding":1194},[1163,5910,5912],{"className":5911,"ariaHidden":1200},[1199],[1163,5913,5915,5918],{"className":5914},[1204],[1163,5916],{"className":5917,"style":1615},[1208],[1163,5919,5921,5924],{"className":5920},[1213],[1163,5922,1346],{"className":5923,"style":1490},[1213,1217],[1163,5925,5927],{"className":5926},[1221],[1163,5928,5930,5953],{"className":5929},[1225,1226],[1163,5931,5933,5950],{"className":5932},[1230],[1163,5934,5936],{"className":5935,"style":1503},[1234],[1163,5937,5938,5941],{"style":1506},[1163,5939],{"className":5940,"style":1243},[1242],[1163,5942,5944],{"className":5943},[1247,1248,1249,1250],[1163,5945,5947],{"className":5946},[1213,1250],[1163,5948,1519],{"className":5949},[1213,1217,1250],[1163,5951,1258],{"className":5952},[1257],[1163,5954,5956],{"className":5955},[1230],[1163,5957,5959],{"className":5958,"style":1265},[1234],[1163,5960],{},[1163,5962,5964,5981],{"className":5963},[1166],[1163,5965,5967],{"className":5966},[1170],[1172,5968,5969],{"xmlns":1174},[1176,5970,5971,5978],{},[1179,5972,5973,5976],{},[1332,5974,5975],{},">",[1368,5977,1370],{},[1192,5979,5980],{"encoding":1194},"> 1",[1163,5982,5984,5996],{"className":5983,"ariaHidden":1200},[1199],[1163,5985,5987,5990,5993],{"className":5986},[1204],[1163,5988],{"className":5989,"style":5867},[1208],[1163,5991,5975],{"className":5992},[1465],[1163,5994],{"className":5995,"style":1461},[1460],[1163,5997,5999,6002],{"className":5998},[1204],[1163,6000],{"className":6001,"style":3572},[1208],[1163,6003,1370],{"className":6004},[1213],[2068,6006,6007,6012,6015],{},[2083,6008,6009],{},[1107,6010,6011],{},"现象",[2083,6013,6014],{},"梯度以指数速度趋近于 0",[2083,6016,6017,6018],{},"梯度以指数速度趋近于 ",[1163,6019,6021,6036],{"className":6020},[1166],[1163,6022,6024],{"className":6023},[1170],[1172,6025,6026],{"xmlns":1174},[1176,6027,6028,6033],{},[1179,6029,6030],{},[1185,6031,6032],{"mathvariant":3684},"∞",[1192,6034,6035],{"encoding":1194},"\\infty",[1163,6037,6039],{"className":6038,"ariaHidden":1200},[1199],[1163,6040,6042,6045],{"className":6041},[1204],[1163,6043],{"className":6044,"style":2749},[1208],[1163,6046,6032],{"className":6047},[1213],[2068,6049,6050,6055,6058],{},[2083,6051,6052],{},[1107,6053,6054],{},"后果",[2083,6056,6057],{},"无法学习长程依赖关系",[2083,6059,6060],{},"参数更新过大，训练不稳定（NaN）",[2068,6062,6063,6068,6165],{},[2083,6064,6065],{},[1107,6066,6067],{},"直觉类比",[2083,6069,6070,6071],{},"反复乘以 0.9：",[1163,6072,6074,6100],{"className":6073},[1166],[1163,6075,6077],{"className":6076},[1170],[1172,6078,6079],{"xmlns":1174},[1176,6080,6081,6097],{},[1179,6082,6083,6091,6094],{},[4740,6084,6085,6088],{},[1368,6086,6087],{},"0.9",[1368,6089,6090],{},"100",[1332,6092,6093],{},"≈",[1368,6095,6096],{},"0.000027",[1192,6098,6099],{"encoding":1194},"0.9^{100} \\approx 0.000027",[1163,6101,6103,6156],{"className":6102,"ariaHidden":1200},[1199],[1163,6104,6106,6110,6114,6147,6150,6153],{"className":6105},[1204],[1163,6107],{"className":6108,"style":6109},[1208],"height:0.8141em;",[1163,6111,6113],{"className":6112},[1213],"0.",[1163,6115,6117,6121],{"className":6116},[1213],[1163,6118,6120],{"className":6119},[1213],"9",[1163,6122,6124],{"className":6123},[1221],[1163,6125,6127],{"className":6126},[1225],[1163,6128,6130],{"className":6129},[1230],[1163,6131,6133],{"className":6132,"style":6109},[1234],[1163,6134,6135,6138],{"style":5100},[1163,6136],{"className":6137,"style":1243},[1242],[1163,6139,6141],{"className":6140},[1247,1248,1249,1250],[1163,6142,6144],{"className":6143},[1213,1250],[1163,6145,6090],{"className":6146},[1213,1250],[1163,6148],{"className":6149,"style":1461},[1460],[1163,6151,6093],{"className":6152},[1465],[1163,6154],{"className":6155,"style":1461},[1460],[1163,6157,6159,6162],{"className":6158},[1204],[1163,6160],{"className":6161,"style":3572},[1208],[1163,6163,6096],{"className":6164},[1213],[2083,6166,6167,6168],{},"反复乘以 1.1：",[1163,6169,6171,6195],{"className":6170},[1166],[1163,6172,6174],{"className":6173},[1170],[1172,6175,6176],{"xmlns":1174},[1176,6177,6178,6192],{},[1179,6179,6180,6187,6189],{},[4740,6181,6182,6185],{},[1368,6183,6184],{},"1.1",[1368,6186,6090],{},[1332,6188,6093],{},[1368,6190,6191],{},"13781",[1192,6193,6194],{"encoding":1194},"1.1^{100} \\approx 13781",[1163,6196,6198,6249],{"className":6197,"ariaHidden":1200},[1199],[1163,6199,6201,6204,6208,6240,6243,6246],{"className":6200},[1204],[1163,6202],{"className":6203,"style":6109},[1208],[1163,6205,6207],{"className":6206},[1213],"1.",[1163,6209,6211,6214],{"className":6210},[1213],[1163,6212,1370],{"className":6213},[1213],[1163,6215,6217],{"className":6216},[1221],[1163,6218,6220],{"className":6219},[1225],[1163,6221,6223],{"className":6222},[1230],[1163,6224,6226],{"className":6225,"style":6109},[1234],[1163,6227,6228,6231],{"style":5100},[1163,6229],{"className":6230,"style":1243},[1242],[1163,6232,6234],{"className":6233},[1247,1248,1249,1250],[1163,6235,6237],{"className":6236},[1213,1250],[1163,6238,6090],{"className":6239},[1213,1250],[1163,6241],{"className":6242,"style":1461},[1460],[1163,6244,6093],{"className":6245},[1465],[1163,6247],{"className":6248,"style":1461},[1460],[1163,6250,6252,6255],{"className":6251},[1204],[1163,6253],{"className":6254,"style":3572},[1208],[1163,6256,6191],{"className":6257},[1213],[2068,6259,6260,6265,6268],{},[2083,6261,6262],{},[1107,6263,6264],{},"解决方案",[2083,6266,6267],{},"LSTM\u002FGRU 门控机制、残差连接",[2083,6269,6270],{},"梯度裁剪（Gradient Clipping）",[1096,6272,6274],{"id":6273},"_23-梯度裁剪gradient-clipping","2.3 梯度裁剪（Gradient Clipping）",[1101,6276,6277,6280],{},[1107,6278,6279],{},"梯度裁剪公式","（解决梯度爆炸）：",[1101,6282,6283,6284,6351,6352],{},"若 ",[1163,6285,6287,6312],{"className":6286},[1166],[1163,6288,6290],{"className":6289},[1170],[1172,6291,6292],{"xmlns":1174},[1176,6293,6294,6309],{},[1179,6295,6296,6299,6302,6304,6306],{},[1185,6297,6298],{"mathvariant":3684},"∥",[1185,6300,6301],{},"g",[1185,6303,6298],{"mathvariant":3684},[1332,6305,5975],{},[4734,6307,6308],{},"threshold",[1192,6310,6311],{"encoding":1194},"\\|g\\| > \\text{threshold}",[1163,6313,6315,6339],{"className":6314,"ariaHidden":1200},[1199],[1163,6316,6318,6321,6324,6327,6330,6333,6336],{"className":6317},[1204],[1163,6319],{"className":6320,"style":1475},[1208],[1163,6322,6298],{"className":6323},[1213],[1163,6325,6301],{"className":6326,"style":1479},[1213,1217],[1163,6328,6298],{"className":6329},[1213],[1163,6331],{"className":6332,"style":1461},[1460],[1163,6334,5975],{"className":6335},[1465],[1163,6337],{"className":6338,"style":1461},[1460],[1163,6340,6342,6345],{"className":6341},[1204],[1163,6343],{"className":6344,"style":3393},[1208],[1163,6346,6348],{"className":6347},[1213,5072],[1163,6349,6308],{"className":6350},[1213],"，则：",[1163,6353,6355,6389],{"className":6354},[1166],[1163,6356,6358],{"className":6357},[1170],[1172,6359,6360],{"xmlns":1174},[1176,6361,6362,6386],{},[1179,6363,6364,6366,6369,6371,6374],{},[1185,6365,6301],{},[1332,6367,6368],{},"←",[4734,6370,6308],{},[1332,6372,6373],{},"×",[3678,6375,6376,6378],{},[1185,6377,6301],{},[1179,6379,6380,6382,6384],{},[1185,6381,6298],{"mathvariant":3684},[1185,6383,6301],{},[1185,6385,6298],{"mathvariant":3684},[1192,6387,6388],{"encoding":1194},"g \\leftarrow \\text{threshold} \\times \\frac{g}{\\|g\\|}",[1163,6390,6392,6410,6432],{"className":6391,"ariaHidden":1200},[1199],[1163,6393,6395,6398,6401,6404,6407],{"className":6394},[1204],[1163,6396],{"className":6397,"style":1839},[1208],[1163,6399,6301],{"className":6400,"style":1479},[1213,1217],[1163,6402],{"className":6403,"style":1461},[1460],[1163,6405,6368],{"className":6406},[1465],[1163,6408],{"className":6409,"style":1461},[1460],[1163,6411,6413,6417,6423,6426,6429],{"className":6412},[1204],[1163,6414],{"className":6415,"style":6416},[1208],"height:0.7778em;vertical-align:-0.0833em;",[1163,6418,6420],{"className":6419},[1213,5072],[1163,6421,6308],{"className":6422},[1213],[1163,6424],{"className":6425,"style":1534},[1460],[1163,6427,6373],{"className":6428},[1538],[1163,6430],{"className":6431,"style":1534},[1460],[1163,6433,6435,6439],{"className":6434},[1204],[1163,6436],{"className":6437,"style":6438},[1208],"height:1.2675em;vertical-align:-0.52em;",[1163,6440,6442,6445,6513],{"className":6441},[1213],[1163,6443],{"className":6444},[1483,3826],[1163,6446,6448],{"className":6447},[3678],[1163,6449,6451,6504],{"className":6450},[1225,1226],[1163,6452,6454,6501],{"className":6453},[1230],[1163,6455,6458,6478,6486],{"className":6456,"style":6457},[1234],"height:0.7475em;",[1163,6459,6460,6463],{"style":3842},[1163,6461],{"className":6462,"style":3400},[1242],[1163,6464,6466],{"className":6465},[1247,1248,1249,1250],[1163,6467,6469,6472,6475],{"className":6468},[1213,1250],[1163,6470,6298],{"className":6471},[1213,1250],[1163,6473,6301],{"className":6474,"style":1479},[1213,1217,1250],[1163,6476,6298],{"className":6477},[1213,1250],[1163,6479,6480,6483],{"style":3907},[1163,6481],{"className":6482,"style":3400},[1242],[1163,6484],{"className":6485,"style":3915},[3914],[1163,6487,6489,6492],{"style":6488},"top:-3.4461em;",[1163,6490],{"className":6491,"style":3400},[1242],[1163,6493,6495],{"className":6494},[1247,1248,1249,1250],[1163,6496,6498],{"className":6497},[1213,1250],[1163,6499,6301],{"className":6500,"style":1479},[1213,1217,1250],[1163,6502,1258],{"className":6503},[1257],[1163,6505,6507],{"className":6506},[1230],[1163,6508,6511],{"className":6509,"style":6510},[1234],"height:0.52em;",[1163,6512],{},[1163,6514],{"className":6515},[1776,3826],[1101,6517,6518],{},"即保持梯度方向不变，但将其范数缩放到阈值以内。",[1101,6520,6521,6524],{},[1107,6522,6523],{},"直觉理解","：梯度裁剪相当于在梯度空间中设定一个\"速度上限\"，防止参数更新步幅过大导致训练发散。",[4645,6526],{},[1091,6528,6530],{"id":6529},"三lstmlong-short-term-memory","三、LSTM（Long Short-Term Memory）",[1096,6532,6534],{"id":6533},"_31-设计动机","3.1 设计动机",[1101,6536,6537,6538,6541,6542,6615,6616,6619],{},"引入",[1107,6539,6540],{},"细胞状态","（Cell State）",[1163,6543,6545,6564],{"className":6544},[1166],[1163,6546,6548],{"className":6547},[1170],[1172,6549,6550],{"xmlns":1174},[1176,6551,6552,6561],{},[1179,6553,6554],{},[1182,6555,6556,6559],{},[1185,6557,6558],{},"C",[1185,6560,1190],{},[1192,6562,6563],{"encoding":1194},"C_t",[1163,6565,6567],{"className":6566,"ariaHidden":1200},[1199],[1163,6568,6570,6573],{"className":6569},[1204],[1163,6571],{"className":6572,"style":1615},[1208],[1163,6574,6576,6580],{"className":6575},[1213],[1163,6577,6558],{"className":6578,"style":6579},[1213,1217],"margin-right:0.0715em;",[1163,6581,6583],{"className":6582},[1221],[1163,6584,6586,6607],{"className":6585},[1225,1226],[1163,6587,6589,6604],{"className":6588},[1230],[1163,6590,6592],{"className":6591,"style":1235},[1234],[1163,6593,6595,6598],{"style":6594},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1163,6596],{"className":6597,"style":1243},[1242],[1163,6599,6601],{"className":6600},[1247,1248,1249,1250],[1163,6602,1190],{"className":6603},[1213,1217,1250],[1163,6605,1258],{"className":6606},[1257],[1163,6608,6610],{"className":6609},[1230],[1163,6611,6613],{"className":6612,"style":1265},[1234],[1163,6614],{}," 作为信息传输的\"高速公路\"。细胞状态通过",[1107,6617,6618],{},"加法更新","（而非乘法），使梯度能够无衰减地长距离流动，从根本上解决梯度消失问题。",[1096,6621,6623],{"id":6622},"_32-lstm-结构概览","3.2 LSTM 结构概览",[1096,6625,6627],{"id":6626},"_33-三个门gates详解","3.3 三个门（Gates）详解",[1101,6629,6630,6631,6634,6635,6690],{},"所有门都使用 ",[1107,6632,6633],{},"sigmoid 激活函数","，输出值在 ",[1163,6636,6638,6663],{"className":6637},[1166],[1163,6639,6641],{"className":6640},[1170],[1172,6642,6643],{"xmlns":1174},[1176,6644,6645,6660],{},[1179,6646,6647,6650,6653,6655,6657],{},[1332,6648,6649],{"stretchy":1340},"[",[1368,6651,6652],{},"0",[1332,6654,2609],{"separator":1200},[1368,6656,1370],{},[1332,6658,6659],{"stretchy":1340},"]",[1192,6661,6662],{"encoding":1194},"[0, 1]",[1163,6664,6666],{"className":6665,"ariaHidden":1200},[1199],[1163,6667,6669,6672,6675,6678,6681,6684,6687],{"className":6668},[1204],[1163,6670],{"className":6671,"style":1475},[1208],[1163,6673,6649],{"className":6674},[1483],[1163,6676,6652],{"className":6677},[1213],[1163,6679,2609],{"className":6680},[2671],[1163,6682],{"className":6683,"style":2675},[1460],[1163,6685,1370],{"className":6686},[1213],[1163,6688,6659],{"className":6689},[1776]," 之间，起到\"开关\"的作用：0 表示完全阻断，1 表示完全通过。",[6692,6693,6695],"h3",{"id":6694},"_1遗忘门forget-gate","（1）遗忘门（Forget Gate）",[1101,6697,6698],{},[1107,6699,6700],{},"决定从细胞状态中丢弃什么信息",[1101,6702,6703],{},[1163,6704,6706,6773],{"className":6705},[1166],[1163,6707,6709],{"className":6708},[1170],[1172,6710,6711],{"xmlns":1174},[1176,6712,6713,6770],{},[1179,6714,6715,6722,6724,6726,6728,6734,6736,6738,6750,6752,6758,6760,6762,6768],{},[1182,6716,6717,6720],{},[1185,6718,6719],{},"f",[1185,6721,1190],{},[1332,6723,1334],{},[1185,6725,1337],{},[1332,6727,1341],{"stretchy":1340},[1182,6729,6730,6732],{},[1185,6731,1346],{},[1185,6733,6719],{},[1332,6735,1355],{},[1332,6737,6649],{"stretchy":1340},[1182,6739,6740,6742],{},[1185,6741,1187],{},[1179,6743,6744,6746,6748],{},[1185,6745,1190],{},[1332,6747,1366],{},[1368,6749,1370],{},[1332,6751,2609],{"separator":1200},[1182,6753,6754,6756],{},[1185,6755,1382],{},[1185,6757,1190],{},[1332,6759,6659],{"stretchy":1340},[1332,6761,1373],{},[1182,6763,6764,6766],{},[1185,6765,1399],{},[1185,6767,6719],{},[1332,6769,1404],{"stretchy":1340},[1192,6771,6772],{"encoding":1194},"f_t = \\sigma(W_f \\cdot [h_{t-1}, x_t] + b_f)",[1163,6774,6776,6834,6896,7012],{"className":6775,"ariaHidden":1200},[1199],[1163,6777,6779,6783,6825,6828,6831],{"className":6778},[1204],[1163,6780],{"className":6781,"style":6782},[1208],"height:0.8889em;vertical-align:-0.1944em;",[1163,6784,6786,6790],{"className":6785},[1213],[1163,6787,6719],{"className":6788,"style":6789},[1213,1217],"margin-right:0.1076em;",[1163,6791,6793],{"className":6792},[1221],[1163,6794,6796,6817],{"className":6795},[1225,1226],[1163,6797,6799,6814],{"className":6798},[1230],[1163,6800,6802],{"className":6801,"style":1235},[1234],[1163,6803,6805,6808],{"style":6804},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1163,6806],{"className":6807,"style":1243},[1242],[1163,6809,6811],{"className":6810},[1247,1248,1249,1250],[1163,6812,1190],{"className":6813},[1213,1217,1250],[1163,6815,1258],{"className":6816},[1257],[1163,6818,6820],{"className":6819},[1230],[1163,6821,6823],{"className":6822,"style":1265},[1234],[1163,6824],{},[1163,6826],{"className":6827,"style":1461},[1460],[1163,6829,1334],{"className":6830},[1465],[1163,6832],{"className":6833,"style":1461},[1460],[1163,6835,6837,6841,6844,6847,6887,6890,6893],{"className":6836},[1204],[1163,6838],{"className":6839,"style":6840},[1208],"height:1.0361em;vertical-align:-0.2861em;",[1163,6842,1337],{"className":6843,"style":1479},[1213,1217],[1163,6845,1341],{"className":6846},[1483],[1163,6848,6850,6853],{"className":6849},[1213],[1163,6851,1346],{"className":6852,"style":1490},[1213,1217],[1163,6854,6856],{"className":6855},[1221],[1163,6857,6859,6879],{"className":6858},[1225,1226],[1163,6860,6862,6876],{"className":6861},[1230],[1163,6863,6865],{"className":6864,"style":1503},[1234],[1163,6866,6867,6870],{"style":1506},[1163,6868],{"className":6869,"style":1243},[1242],[1163,6871,6873],{"className":6872},[1247,1248,1249,1250],[1163,6874,6719],{"className":6875,"style":6789},[1213,1217,1250],[1163,6877,1258],{"className":6878},[1257],[1163,6880,6882],{"className":6881},[1230],[1163,6883,6885],{"className":6884,"style":1941},[1234],[1163,6886],{},[1163,6888],{"className":6889,"style":1534},[1460],[1163,6891,1355],{"className":6892},[1538],[1163,6894],{"className":6895,"style":1534},[1460],[1163,6897,6899,6902,6905,6954,6957,6960,7000,7003,7006,7009],{"className":6898},[1204],[1163,6900],{"className":6901,"style":1475},[1208],[1163,6903,6649],{"className":6904},[1483],[1163,6906,6908,6911],{"className":6907},[1213],[1163,6909,1187],{"className":6910},[1213,1217],[1163,6912,6914],{"className":6913},[1221],[1163,6915,6917,6946],{"className":6916},[1225,1226],[1163,6918,6920,6943],{"className":6919},[1230],[1163,6921,6923],{"className":6922,"style":1567},[1234],[1163,6924,6925,6928],{"style":1238},[1163,6926],{"className":6927,"style":1243},[1242],[1163,6929,6931],{"className":6930},[1247,1248,1249,1250],[1163,6932,6934,6937,6940],{"className":6933},[1213,1250],[1163,6935,1190],{"className":6936},[1213,1217,1250],[1163,6938,1366],{"className":6939},[1538,1250],[1163,6941,1370],{"className":6942},[1213,1250],[1163,6944,1258],{"className":6945},[1257],[1163,6947,6949],{"className":6948},[1230],[1163,6950,6952],{"className":6951,"style":1597},[1234],[1163,6953],{},[1163,6955,2609],{"className":6956},[2671],[1163,6958],{"className":6959,"style":2675},[1460],[1163,6961,6963,6966],{"className":6962},[1213],[1163,6964,1382],{"className":6965},[1213,1217],[1163,6967,6969],{"className":6968},[1221],[1163,6970,6972,6992],{"className":6971},[1225,1226],[1163,6973,6975,6989],{"className":6974},[1230],[1163,6976,6978],{"className":6977,"style":1235},[1234],[1163,6979,6980,6983],{"style":1238},[1163,6981],{"className":6982,"style":1243},[1242],[1163,6984,6986],{"className":6985},[1247,1248,1249,1250],[1163,6987,1190],{"className":6988},[1213,1217,1250],[1163,6990,1258],{"className":6991},[1257],[1163,6993,6995],{"className":6994},[1230],[1163,6996,6998],{"className":6997,"style":1265},[1234],[1163,6999],{},[1163,7001,6659],{"className":7002},[1776],[1163,7004],{"className":7005,"style":1534},[1460],[1163,7007,1373],{"className":7008},[1538],[1163,7010],{"className":7011,"style":1534},[1460],[1163,7013,7015,7018,7058],{"className":7014},[1204],[1163,7016],{"className":7017,"style":6840},[1208],[1163,7019,7021,7024],{"className":7020},[1213],[1163,7022,1399],{"className":7023},[1213,1217],[1163,7025,7027],{"className":7026},[1221],[1163,7028,7030,7050],{"className":7029},[1225,1226],[1163,7031,7033,7047],{"className":7032},[1230],[1163,7034,7036],{"className":7035,"style":1503},[1234],[1163,7037,7038,7041],{"style":1238},[1163,7039],{"className":7040,"style":1243},[1242],[1163,7042,7044],{"className":7043},[1247,1248,1249,1250],[1163,7045,6719],{"className":7046,"style":6789},[1213,1217,1250],[1163,7048,1258],{"className":7049},[1257],[1163,7051,7053],{"className":7052},[1230],[1163,7054,7056],{"className":7055,"style":1941},[1234],[1163,7057],{},[1163,7059,1404],{"className":7060},[1776],[1101,7062,7063,7064,7156,7157,7249],{},"当 ",[1163,7065,7067,7089],{"className":7066},[1166],[1163,7068,7070],{"className":7069},[1170],[1172,7071,7072],{"xmlns":1174},[1176,7073,7074,7086],{},[1179,7075,7076,7082,7084],{},[1182,7077,7078,7080],{},[1185,7079,6719],{},[1185,7081,1190],{},[1332,7083,6093],{},[1368,7085,6652],{},[1192,7087,7088],{"encoding":1194},"f_t \\approx 0",[1163,7090,7092,7147],{"className":7091,"ariaHidden":1200},[1199],[1163,7093,7095,7098,7138,7141,7144],{"className":7094},[1204],[1163,7096],{"className":7097,"style":6782},[1208],[1163,7099,7101,7104],{"className":7100},[1213],[1163,7102,6719],{"className":7103,"style":6789},[1213,1217],[1163,7105,7107],{"className":7106},[1221],[1163,7108,7110,7130],{"className":7109},[1225,1226],[1163,7111,7113,7127],{"className":7112},[1230],[1163,7114,7116],{"className":7115,"style":1235},[1234],[1163,7117,7118,7121],{"style":6804},[1163,7119],{"className":7120,"style":1243},[1242],[1163,7122,7124],{"className":7123},[1247,1248,1249,1250],[1163,7125,1190],{"className":7126},[1213,1217,1250],[1163,7128,1258],{"className":7129},[1257],[1163,7131,7133],{"className":7132},[1230],[1163,7134,7136],{"className":7135,"style":1265},[1234],[1163,7137],{},[1163,7139],{"className":7140,"style":1461},[1460],[1163,7142,6093],{"className":7143},[1465],[1163,7145],{"className":7146,"style":1461},[1460],[1163,7148,7150,7153],{"className":7149},[1204],[1163,7151],{"className":7152,"style":3572},[1208],[1163,7154,6652],{"className":7155},[1213]," 时，旧信息被遗忘；当 ",[1163,7158,7160,7182],{"className":7159},[1166],[1163,7161,7163],{"className":7162},[1170],[1172,7164,7165],{"xmlns":1174},[1176,7166,7167,7179],{},[1179,7168,7169,7175,7177],{},[1182,7170,7171,7173],{},[1185,7172,6719],{},[1185,7174,1190],{},[1332,7176,6093],{},[1368,7178,1370],{},[1192,7180,7181],{"encoding":1194},"f_t \\approx 1",[1163,7183,7185,7240],{"className":7184,"ariaHidden":1200},[1199],[1163,7186,7188,7191,7231,7234,7237],{"className":7187},[1204],[1163,7189],{"className":7190,"style":6782},[1208],[1163,7192,7194,7197],{"className":7193},[1213],[1163,7195,6719],{"className":7196,"style":6789},[1213,1217],[1163,7198,7200],{"className":7199},[1221],[1163,7201,7203,7223],{"className":7202},[1225,1226],[1163,7204,7206,7220],{"className":7205},[1230],[1163,7207,7209],{"className":7208,"style":1235},[1234],[1163,7210,7211,7214],{"style":6804},[1163,7212],{"className":7213,"style":1243},[1242],[1163,7215,7217],{"className":7216},[1247,1248,1249,1250],[1163,7218,1190],{"className":7219},[1213,1217,1250],[1163,7221,1258],{"className":7222},[1257],[1163,7224,7226],{"className":7225},[1230],[1163,7227,7229],{"className":7228,"style":1265},[1234],[1163,7230],{},[1163,7232],{"className":7233,"style":1461},[1460],[1163,7235,6093],{"className":7236},[1465],[1163,7238],{"className":7239,"style":1461},[1460],[1163,7241,7243,7246],{"className":7242},[1204],[1163,7244],{"className":7245,"style":3572},[1208],[1163,7247,1370],{"className":7248},[1213]," 时，旧信息被保留。",[6692,7251,7253],{"id":7252},"_2输入门input-gate","（2）输入门（Input Gate）",[1101,7255,7256],{},[1107,7257,7258],{},"决定存储什么新信息到细胞状态",[1101,7260,7261,7262],{},"门控信号：",[1163,7263,7265,7331],{"className":7264},[1166],[1163,7266,7268],{"className":7267},[1170],[1172,7269,7270],{"xmlns":1174},[1176,7271,7272,7328],{},[1179,7273,7274,7280,7282,7284,7286,7292,7294,7296,7308,7310,7316,7318,7320,7326],{},[1182,7275,7276,7278],{},[1185,7277,4710],{},[1185,7279,1190],{},[1332,7281,1334],{},[1185,7283,1337],{},[1332,7285,1341],{"stretchy":1340},[1182,7287,7288,7290],{},[1185,7289,1346],{},[1185,7291,4710],{},[1332,7293,1355],{},[1332,7295,6649],{"stretchy":1340},[1182,7297,7298,7300],{},[1185,7299,1187],{},[1179,7301,7302,7304,7306],{},[1185,7303,1190],{},[1332,7305,1366],{},[1368,7307,1370],{},[1332,7309,2609],{"separator":1200},[1182,7311,7312,7314],{},[1185,7313,1382],{},[1185,7315,1190],{},[1332,7317,6659],{"stretchy":1340},[1332,7319,1373],{},[1182,7321,7322,7324],{},[1185,7323,1399],{},[1185,7325,4710],{},[1332,7327,1404],{"stretchy":1340},[1192,7329,7330],{"encoding":1194},"i_t = \\sigma(W_i \\cdot [h_{t-1}, x_t] + b_i)",[1163,7332,7334,7390,7451,7567],{"className":7333,"ariaHidden":1200},[1199],[1163,7335,7337,7341,7381,7384,7387],{"className":7336},[1204],[1163,7338],{"className":7339,"style":7340},[1208],"height:0.8095em;vertical-align:-0.15em;",[1163,7342,7344,7347],{"className":7343},[1213],[1163,7345,4710],{"className":7346},[1213,1217],[1163,7348,7350],{"className":7349},[1221],[1163,7351,7353,7373],{"className":7352},[1225,1226],[1163,7354,7356,7370],{"className":7355},[1230],[1163,7357,7359],{"className":7358,"style":1235},[1234],[1163,7360,7361,7364],{"style":1238},[1163,7362],{"className":7363,"style":1243},[1242],[1163,7365,7367],{"className":7366},[1247,1248,1249,1250],[1163,7368,1190],{"className":7369},[1213,1217,1250],[1163,7371,1258],{"className":7372},[1257],[1163,7374,7376],{"className":7375},[1230],[1163,7377,7379],{"className":7378,"style":1265},[1234],[1163,7380],{},[1163,7382],{"className":7383,"style":1461},[1460],[1163,7385,1334],{"className":7386},[1465],[1163,7388],{"className":7389,"style":1461},[1460],[1163,7391,7393,7396,7399,7402,7442,7445,7448],{"className":7392},[1204],[1163,7394],{"className":7395,"style":1475},[1208],[1163,7397,1337],{"className":7398,"style":1479},[1213,1217],[1163,7400,1341],{"className":7401},[1483],[1163,7403,7405,7408],{"className":7404},[1213],[1163,7406,1346],{"className":7407,"style":1490},[1213,1217],[1163,7409,7411],{"className":7410},[1221],[1163,7412,7414,7434],{"className":7413},[1225,1226],[1163,7415,7417,7431],{"className":7416},[1230],[1163,7418,7420],{"className":7419,"style":5135},[1234],[1163,7421,7422,7425],{"style":1506},[1163,7423],{"className":7424,"style":1243},[1242],[1163,7426,7428],{"className":7427},[1247,1248,1249,1250],[1163,7429,4710],{"className":7430},[1213,1217,1250],[1163,7432,1258],{"className":7433},[1257],[1163,7435,7437],{"className":7436},[1230],[1163,7438,7440],{"className":7439,"style":1265},[1234],[1163,7441],{},[1163,7443],{"className":7444,"style":1534},[1460],[1163,7446,1355],{"className":7447},[1538],[1163,7449],{"className":7450,"style":1534},[1460],[1163,7452,7454,7457,7460,7509,7512,7515,7555,7558,7561,7564],{"className":7453},[1204],[1163,7455],{"className":7456,"style":1475},[1208],[1163,7458,6649],{"className":7459},[1483],[1163,7461,7463,7466],{"className":7462},[1213],[1163,7464,1187],{"className":7465},[1213,1217],[1163,7467,7469],{"className":7468},[1221],[1163,7470,7472,7501],{"className":7471},[1225,1226],[1163,7473,7475,7498],{"className":7474},[1230],[1163,7476,7478],{"className":7477,"style":1567},[1234],[1163,7479,7480,7483],{"style":1238},[1163,7481],{"className":7482,"style":1243},[1242],[1163,7484,7486],{"className":7485},[1247,1248,1249,1250],[1163,7487,7489,7492,7495],{"className":7488},[1213,1250],[1163,7490,1190],{"className":7491},[1213,1217,1250],[1163,7493,1366],{"className":7494},[1538,1250],[1163,7496,1370],{"className":7497},[1213,1250],[1163,7499,1258],{"className":7500},[1257],[1163,7502,7504],{"className":7503},[1230],[1163,7505,7507],{"className":7506,"style":1597},[1234],[1163,7508],{},[1163,7510,2609],{"className":7511},[2671],[1163,7513],{"className":7514,"style":2675},[1460],[1163,7516,7518,7521],{"className":7517},[1213],[1163,7519,1382],{"className":7520},[1213,1217],[1163,7522,7524],{"className":7523},[1221],[1163,7525,7527,7547],{"className":7526},[1225,1226],[1163,7528,7530,7544],{"className":7529},[1230],[1163,7531,7533],{"className":7532,"style":1235},[1234],[1163,7534,7535,7538],{"style":1238},[1163,7536],{"className":7537,"style":1243},[1242],[1163,7539,7541],{"className":7540},[1247,1248,1249,1250],[1163,7542,1190],{"className":7543},[1213,1217,1250],[1163,7545,1258],{"className":7546},[1257],[1163,7548,7550],{"className":7549},[1230],[1163,7551,7553],{"className":7552,"style":1265},[1234],[1163,7554],{},[1163,7556,6659],{"className":7557},[1776],[1163,7559],{"className":7560,"style":1534},[1460],[1163,7562,1373],{"className":7563},[1538],[1163,7565],{"className":7566,"style":1534},[1460],[1163,7568,7570,7573,7613],{"className":7569},[1204],[1163,7571],{"className":7572,"style":1475},[1208],[1163,7574,7576,7579],{"className":7575},[1213],[1163,7577,1399],{"className":7578},[1213,1217],[1163,7580,7582],{"className":7581},[1221],[1163,7583,7585,7605],{"className":7584},[1225,1226],[1163,7586,7588,7602],{"className":7587},[1230],[1163,7589,7591],{"className":7590,"style":5135},[1234],[1163,7592,7593,7596],{"style":1238},[1163,7594],{"className":7595,"style":1243},[1242],[1163,7597,7599],{"className":7598},[1247,1248,1249,1250],[1163,7600,4710],{"className":7601},[1213,1217,1250],[1163,7603,1258],{"className":7604},[1257],[1163,7606,7608],{"className":7607},[1230],[1163,7609,7611],{"className":7610,"style":1265},[1234],[1163,7612],{},[1163,7614,1404],{"className":7615},[1776],[1101,7617,7618,7619],{},"候选值：",[1163,7620,7622,7697],{"className":7621},[1166],[1163,7623,7625],{"className":7624},[1170],[1172,7626,7627],{"xmlns":1174},[1176,7628,7629,7694],{},[1179,7630,7631,7642,7644,7647,7650,7652,7658,7660,7662,7674,7676,7682,7684,7686,7692],{},[1182,7632,7633,7640],{},[3171,7634,7635,7637],{"accent":1200},[1185,7636,6558],{},[1332,7638,7639],{},"~",[1185,7641,1190],{},[1332,7643,1334],{},[1185,7645,7646],{},"tanh",[1332,7648,7649],{},"⁡",[1332,7651,1341],{"stretchy":1340},[1182,7653,7654,7656],{},[1185,7655,1346],{},[1185,7657,6558],{},[1332,7659,1355],{},[1332,7661,6649],{"stretchy":1340},[1182,7663,7664,7666],{},[1185,7665,1187],{},[1179,7667,7668,7670,7672],{},[1185,7669,1190],{},[1332,7671,1366],{},[1368,7673,1370],{},[1332,7675,2609],{"separator":1200},[1182,7677,7678,7680],{},[1185,7679,1382],{},[1185,7681,1190],{},[1332,7683,6659],{"stretchy":1340},[1332,7685,1373],{},[1182,7687,7688,7690],{},[1185,7689,1399],{},[1185,7691,6558],{},[1332,7693,1404],{"stretchy":1340},[1192,7695,7696],{"encoding":1194},"\\tilde{C}_t = \\tanh(W_C \\cdot [h_{t-1}, x_t] + b_C)",[1163,7698,7700,7787,7849,7965],{"className":7699,"ariaHidden":1200},[1199],[1163,7701,7703,7707,7778,7781,7784],{"className":7702},[1204],[1163,7704],{"className":7705,"style":7706},[1208],"height:1.0702em;vertical-align:-0.15em;",[1163,7708,7710,7744],{"className":7709},[1213],[1163,7711,7713],{"className":7712},[1213,3383],[1163,7714,7716],{"className":7715},[1225],[1163,7717,7719],{"className":7718},[1230],[1163,7720,7723,7731],{"className":7721,"style":7722},[1234],"height:0.9202em;",[1163,7724,7725,7728],{"style":3396},[1163,7726],{"className":7727,"style":3400},[1242],[1163,7729,6558],{"className":7730,"style":6579},[1213,1217],[1163,7732,7734,7737],{"style":7733},"top:-3.6023em;",[1163,7735],{"className":7736,"style":3400},[1242],[1163,7738,7741],{"className":7739,"style":7740},[3412],"left:-0.1667em;",[1163,7742,7639],{"className":7743},[1213],[1163,7745,7747],{"className":7746},[1221],[1163,7748,7750,7770],{"className":7749},[1225,1226],[1163,7751,7753,7767],{"className":7752},[1230],[1163,7754,7756],{"className":7755,"style":1235},[1234],[1163,7757,7758,7761],{"style":6594},[1163,7759],{"className":7760,"style":1243},[1242],[1163,7762,7764],{"className":7763},[1247,1248,1249,1250],[1163,7765,1190],{"className":7766},[1213,1217,1250],[1163,7768,1258],{"className":7769},[1257],[1163,7771,7773],{"className":7772},[1230],[1163,7774,7776],{"className":7775,"style":1265},[1234],[1163,7777],{},[1163,7779],{"className":7780,"style":1461},[1460],[1163,7782,1334],{"className":7783},[1465],[1163,7785],{"className":7786,"style":1461},[1460],[1163,7788,7790,7793,7796,7799,7840,7843,7846],{"className":7789},[1204],[1163,7791],{"className":7792,"style":1475},[1208],[1163,7794,7646],{"className":7795},[3217],[1163,7797,1341],{"className":7798},[1483],[1163,7800,7802,7805],{"className":7801},[1213],[1163,7803,1346],{"className":7804,"style":1490},[1213,1217],[1163,7806,7808],{"className":7807},[1221],[1163,7809,7811,7832],{"className":7810},[1225,1226],[1163,7812,7814,7829],{"className":7813},[1230],[1163,7815,7818],{"className":7816,"style":7817},[1234],"height:0.3283em;",[1163,7819,7820,7823],{"style":1506},[1163,7821],{"className":7822,"style":1243},[1242],[1163,7824,7826],{"className":7825},[1247,1248,1249,1250],[1163,7827,6558],{"className":7828,"style":6579},[1213,1217,1250],[1163,7830,1258],{"className":7831},[1257],[1163,7833,7835],{"className":7834},[1230],[1163,7836,7838],{"className":7837,"style":1265},[1234],[1163,7839],{},[1163,7841],{"className":7842,"style":1534},[1460],[1163,7844,1355],{"className":7845},[1538],[1163,7847],{"className":7848,"style":1534},[1460],[1163,7850,7852,7855,7858,7907,7910,7913,7953,7956,7959,7962],{"className":7851},[1204],[1163,7853],{"className":7854,"style":1475},[1208],[1163,7856,6649],{"className":7857},[1483],[1163,7859,7861,7864],{"className":7860},[1213],[1163,7862,1187],{"className":7863},[1213,1217],[1163,7865,7867],{"className":7866},[1221],[1163,7868,7870,7899],{"className":7869},[1225,1226],[1163,7871,7873,7896],{"className":7872},[1230],[1163,7874,7876],{"className":7875,"style":1567},[1234],[1163,7877,7878,7881],{"style":1238},[1163,7879],{"className":7880,"style":1243},[1242],[1163,7882,7884],{"className":7883},[1247,1248,1249,1250],[1163,7885,7887,7890,7893],{"className":7886},[1213,1250],[1163,7888,1190],{"className":7889},[1213,1217,1250],[1163,7891,1366],{"className":7892},[1538,1250],[1163,7894,1370],{"className":7895},[1213,1250],[1163,7897,1258],{"className":7898},[1257],[1163,7900,7902],{"className":7901},[1230],[1163,7903,7905],{"className":7904,"style":1597},[1234],[1163,7906],{},[1163,7908,2609],{"className":7909},[2671],[1163,7911],{"className":7912,"style":2675},[1460],[1163,7914,7916,7919],{"className":7915},[1213],[1163,7917,1382],{"className":7918},[1213,1217],[1163,7920,7922],{"className":7921},[1221],[1163,7923,7925,7945],{"className":7924},[1225,1226],[1163,7926,7928,7942],{"className":7927},[1230],[1163,7929,7931],{"className":7930,"style":1235},[1234],[1163,7932,7933,7936],{"style":1238},[1163,7934],{"className":7935,"style":1243},[1242],[1163,7937,7939],{"className":7938},[1247,1248,1249,1250],[1163,7940,1190],{"className":7941},[1213,1217,1250],[1163,7943,1258],{"className":7944},[1257],[1163,7946,7948],{"className":7947},[1230],[1163,7949,7951],{"className":7950,"style":1265},[1234],[1163,7952],{},[1163,7954,6659],{"className":7955},[1776],[1163,7957],{"className":7958,"style":1534},[1460],[1163,7960,1373],{"className":7961},[1538],[1163,7963],{"className":7964,"style":1534},[1460],[1163,7966,7968,7971,8011],{"className":7967},[1204],[1163,7969],{"className":7970,"style":1475},[1208],[1163,7972,7974,7977],{"className":7973},[1213],[1163,7975,1399],{"className":7976},[1213,1217],[1163,7978,7980],{"className":7979},[1221],[1163,7981,7983,8003],{"className":7982},[1225,1226],[1163,7984,7986,8000],{"className":7985},[1230],[1163,7987,7989],{"className":7988,"style":7817},[1234],[1163,7990,7991,7994],{"style":1238},[1163,7992],{"className":7993,"style":1243},[1242],[1163,7995,7997],{"className":7996},[1247,1248,1249,1250],[1163,7998,6558],{"className":7999,"style":6579},[1213,1217,1250],[1163,8001,1258],{"className":8002},[1257],[1163,8004,8006],{"className":8005},[1230],[1163,8007,8009],{"className":8008,"style":1265},[1234],[1163,8010],{},[1163,8012,1404],{"className":8013},[1776],[1101,8015,8016,8086],{},[1163,8017,8019,8037],{"className":8018},[1166],[1163,8020,8022],{"className":8021},[1170],[1172,8023,8024],{"xmlns":1174},[1176,8025,8026,8034],{},[1179,8027,8028],{},[1182,8029,8030,8032],{},[1185,8031,4710],{},[1185,8033,1190],{},[1192,8035,8036],{"encoding":1194},"i_t",[1163,8038,8040],{"className":8039,"ariaHidden":1200},[1199],[1163,8041,8043,8046],{"className":8042},[1204],[1163,8044],{"className":8045,"style":7340},[1208],[1163,8047,8049,8052],{"className":8048},[1213],[1163,8050,4710],{"className":8051},[1213,1217],[1163,8053,8055],{"className":8054},[1221],[1163,8056,8058,8078],{"className":8057},[1225,1226],[1163,8059,8061,8075],{"className":8060},[1230],[1163,8062,8064],{"className":8063,"style":1235},[1234],[1163,8065,8066,8069],{"style":1238},[1163,8067],{"className":8068,"style":1243},[1242],[1163,8070,8072],{"className":8071},[1247,1248,1249,1250],[1163,8073,1190],{"className":8074},[1213,1217,1250],[1163,8076,1258],{"className":8077},[1257],[1163,8079,8081],{"className":8080},[1230],[1163,8082,8084],{"className":8083,"style":1265},[1234],[1163,8085],{}," 控制候选值中哪些分量被写入细胞状态。",[6692,8088,8090],{"id":8089},"_3输出门output-gate","（3）输出门（Output Gate）",[1101,8092,8093],{},[1107,8094,8095],{},"决定从细胞状态中输出什么信息作为隐藏状态",[1101,8097,8098],{},[1163,8099,8101,8168],{"className":8100},[1166],[1163,8102,8104],{"className":8103},[1170],[1172,8105,8106],{"xmlns":1174},[1176,8107,8108,8165],{},[1179,8109,8110,8117,8119,8121,8123,8129,8131,8133,8145,8147,8153,8155,8157,8163],{},[1182,8111,8112,8115],{},[1185,8113,8114],{},"o",[1185,8116,1190],{},[1332,8118,1334],{},[1185,8120,1337],{},[1332,8122,1341],{"stretchy":1340},[1182,8124,8125,8127],{},[1185,8126,1346],{},[1185,8128,8114],{},[1332,8130,1355],{},[1332,8132,6649],{"stretchy":1340},[1182,8134,8135,8137],{},[1185,8136,1187],{},[1179,8138,8139,8141,8143],{},[1185,8140,1190],{},[1332,8142,1366],{},[1368,8144,1370],{},[1332,8146,2609],{"separator":1200},[1182,8148,8149,8151],{},[1185,8150,1382],{},[1185,8152,1190],{},[1332,8154,6659],{"stretchy":1340},[1332,8156,1373],{},[1182,8158,8159,8161],{},[1185,8160,1399],{},[1185,8162,8114],{},[1332,8164,1404],{"stretchy":1340},[1192,8166,8167],{"encoding":1194},"o_t = \\sigma(W_o \\cdot [h_{t-1}, x_t] + b_o)",[1163,8169,8171,8226,8287,8403],{"className":8170,"ariaHidden":1200},[1199],[1163,8172,8174,8177,8217,8220,8223],{"className":8173},[1204],[1163,8175],{"className":8176,"style":2115},[1208],[1163,8178,8180,8183],{"className":8179},[1213],[1163,8181,8114],{"className":8182},[1213,1217],[1163,8184,8186],{"className":8185},[1221],[1163,8187,8189,8209],{"className":8188},[1225,1226],[1163,8190,8192,8206],{"className":8191},[1230],[1163,8193,8195],{"className":8194,"style":1235},[1234],[1163,8196,8197,8200],{"style":1238},[1163,8198],{"className":8199,"style":1243},[1242],[1163,8201,8203],{"className":8202},[1247,1248,1249,1250],[1163,8204,1190],{"className":8205},[1213,1217,1250],[1163,8207,1258],{"className":8208},[1257],[1163,8210,8212],{"className":8211},[1230],[1163,8213,8215],{"className":8214,"style":1265},[1234],[1163,8216],{},[1163,8218],{"className":8219,"style":1461},[1460],[1163,8221,1334],{"className":8222},[1465],[1163,8224],{"className":8225,"style":1461},[1460],[1163,8227,8229,8232,8235,8238,8278,8281,8284],{"className":8228},[1204],[1163,8230],{"className":8231,"style":1475},[1208],[1163,8233,1337],{"className":8234,"style":1479},[1213,1217],[1163,8236,1341],{"className":8237},[1483],[1163,8239,8241,8244],{"className":8240},[1213],[1163,8242,1346],{"className":8243,"style":1490},[1213,1217],[1163,8245,8247],{"className":8246},[1221],[1163,8248,8250,8270],{"className":8249},[1225,1226],[1163,8251,8253,8267],{"className":8252},[1230],[1163,8254,8256],{"className":8255,"style":2033},[1234],[1163,8257,8258,8261],{"style":1506},[1163,8259],{"className":8260,"style":1243},[1242],[1163,8262,8264],{"className":8263},[1247,1248,1249,1250],[1163,8265,8114],{"className":8266},[1213,1217,1250],[1163,8268,1258],{"className":8269},[1257],[1163,8271,8273],{"className":8272},[1230],[1163,8274,8276],{"className":8275,"style":1265},[1234],[1163,8277],{},[1163,8279],{"className":8280,"style":1534},[1460],[1163,8282,1355],{"className":8283},[1538],[1163,8285],{"className":8286,"style":1534},[1460],[1163,8288,8290,8293,8296,8345,8348,8351,8391,8394,8397,8400],{"className":8289},[1204],[1163,8291],{"className":8292,"style":1475},[1208],[1163,8294,6649],{"className":8295},[1483],[1163,8297,8299,8302],{"className":8298},[1213],[1163,8300,1187],{"className":8301},[1213,1217],[1163,8303,8305],{"className":8304},[1221],[1163,8306,8308,8337],{"className":8307},[1225,1226],[1163,8309,8311,8334],{"className":8310},[1230],[1163,8312,8314],{"className":8313,"style":1567},[1234],[1163,8315,8316,8319],{"style":1238},[1163,8317],{"className":8318,"style":1243},[1242],[1163,8320,8322],{"className":8321},[1247,1248,1249,1250],[1163,8323,8325,8328,8331],{"className":8324},[1213,1250],[1163,8326,1190],{"className":8327},[1213,1217,1250],[1163,8329,1366],{"className":8330},[1538,1250],[1163,8332,1370],{"className":8333},[1213,1250],[1163,8335,1258],{"className":8336},[1257],[1163,8338,8340],{"className":8339},[1230],[1163,8341,8343],{"className":8342,"style":1597},[1234],[1163,8344],{},[1163,8346,2609],{"className":8347},[2671],[1163,8349],{"className":8350,"style":2675},[1460],[1163,8352,8354,8357],{"className":8353},[1213],[1163,8355,1382],{"className":8356},[1213,1217],[1163,8358,8360],{"className":8359},[1221],[1163,8361,8363,8383],{"className":8362},[1225,1226],[1163,8364,8366,8380],{"className":8365},[1230],[1163,8367,8369],{"className":8368,"style":1235},[1234],[1163,8370,8371,8374],{"style":1238},[1163,8372],{"className":8373,"style":1243},[1242],[1163,8375,8377],{"className":8376},[1247,1248,1249,1250],[1163,8378,1190],{"className":8379},[1213,1217,1250],[1163,8381,1258],{"className":8382},[1257],[1163,8384,8386],{"className":8385},[1230],[1163,8387,8389],{"className":8388,"style":1265},[1234],[1163,8390],{},[1163,8392,6659],{"className":8393},[1776],[1163,8395],{"className":8396,"style":1534},[1460],[1163,8398,1373],{"className":8399},[1538],[1163,8401],{"className":8402,"style":1534},[1460],[1163,8404,8406,8409,8449],{"className":8405},[1204],[1163,8407],{"className":8408,"style":1475},[1208],[1163,8410,8412,8415],{"className":8411},[1213],[1163,8413,1399],{"className":8414},[1213,1217],[1163,8416,8418],{"className":8417},[1221],[1163,8419,8421,8441],{"className":8420},[1225,1226],[1163,8422,8424,8438],{"className":8423},[1230],[1163,8425,8427],{"className":8426,"style":2033},[1234],[1163,8428,8429,8432],{"style":1238},[1163,8430],{"className":8431,"style":1243},[1242],[1163,8433,8435],{"className":8434},[1247,1248,1249,1250],[1163,8436,8114],{"className":8437},[1213,1217,1250],[1163,8439,1258],{"className":8440},[1257],[1163,8442,8444],{"className":8443},[1230],[1163,8445,8447],{"className":8446,"style":1265},[1234],[1163,8448],{},[1163,8450,1404],{"className":8451},[1776],[1101,8453,8454],{},"输出门过滤细胞状态，生成当前时刻的隐藏状态。",[1096,8456,8458],{"id":8457},"_34-状态更新公式","3.4 状态更新公式",[1101,8460,8461],{},[1107,8462,8463],{},"细胞状态更新（加法结构——梯度高速公路）：",[1101,8465,8466],{},[1163,8467,8469,8530],{"className":8468},[1166],[1163,8470,8472],{"className":8471},[1170],[1172,8473,8474],{"xmlns":1174},[1176,8475,8476,8527],{},[1179,8477,8478,8484,8486,8492,8495,8507,8509,8515,8517],{},[1182,8479,8480,8482],{},[1185,8481,6558],{},[1185,8483,1190],{},[1332,8485,1334],{},[1182,8487,8488,8490],{},[1185,8489,6719],{},[1185,8491,1190],{},[1332,8493,8494],{},"⊙",[1182,8496,8497,8499],{},[1185,8498,6558],{},[1179,8500,8501,8503,8505],{},[1185,8502,1190],{},[1332,8504,1366],{},[1368,8506,1370],{},[1332,8508,1373],{},[1182,8510,8511,8513],{},[1185,8512,4710],{},[1185,8514,1190],{},[1332,8516,8494],{},[1182,8518,8519,8525],{},[3171,8520,8521,8523],{"accent":1200},[1185,8522,6558],{},[1332,8524,7639],{},[1185,8526,1190],{},[1192,8528,8529],{"encoding":1194},"C_t = f_t \\odot C_{t-1} + i_t \\odot \\tilde{C}_t",[1163,8531,8533,8588,8643,8708,8763],{"className":8532,"ariaHidden":1200},[1199],[1163,8534,8536,8539,8579,8582,8585],{"className":8535},[1204],[1163,8537],{"className":8538,"style":1615},[1208],[1163,8540,8542,8545],{"className":8541},[1213],[1163,8543,6558],{"className":8544,"style":6579},[1213,1217],[1163,8546,8548],{"className":8547},[1221],[1163,8549,8551,8571],{"className":8550},[1225,1226],[1163,8552,8554,8568],{"className":8553},[1230],[1163,8555,8557],{"className":8556,"style":1235},[1234],[1163,8558,8559,8562],{"style":6594},[1163,8560],{"className":8561,"style":1243},[1242],[1163,8563,8565],{"className":8564},[1247,1248,1249,1250],[1163,8566,1190],{"className":8567},[1213,1217,1250],[1163,8569,1258],{"className":8570},[1257],[1163,8572,8574],{"className":8573},[1230],[1163,8575,8577],{"className":8576,"style":1265},[1234],[1163,8578],{},[1163,8580],{"className":8581,"style":1461},[1460],[1163,8583,1334],{"className":8584},[1465],[1163,8586],{"className":8587,"style":1461},[1460],[1163,8589,8591,8594,8634,8637,8640],{"className":8590},[1204],[1163,8592],{"className":8593,"style":6782},[1208],[1163,8595,8597,8600],{"className":8596},[1213],[1163,8598,6719],{"className":8599,"style":6789},[1213,1217],[1163,8601,8603],{"className":8602},[1221],[1163,8604,8606,8626],{"className":8605},[1225,1226],[1163,8607,8609,8623],{"className":8608},[1230],[1163,8610,8612],{"className":8611,"style":1235},[1234],[1163,8613,8614,8617],{"style":6804},[1163,8615],{"className":8616,"style":1243},[1242],[1163,8618,8620],{"className":8619},[1247,1248,1249,1250],[1163,8621,1190],{"className":8622},[1213,1217,1250],[1163,8624,1258],{"className":8625},[1257],[1163,8627,8629],{"className":8628},[1230],[1163,8630,8632],{"className":8631,"style":1265},[1234],[1163,8633],{},[1163,8635],{"className":8636,"style":1534},[1460],[1163,8638,8494],{"className":8639},[1538],[1163,8641],{"className":8642,"style":1534},[1460],[1163,8644,8646,8650,8699,8702,8705],{"className":8645},[1204],[1163,8647],{"className":8648,"style":8649},[1208],"height:0.8917em;vertical-align:-0.2083em;",[1163,8651,8653,8656],{"className":8652},[1213],[1163,8654,6558],{"className":8655,"style":6579},[1213,1217],[1163,8657,8659],{"className":8658},[1221],[1163,8660,8662,8691],{"className":8661},[1225,1226],[1163,8663,8665,8688],{"className":8664},[1230],[1163,8666,8668],{"className":8667,"style":1567},[1234],[1163,8669,8670,8673],{"style":6594},[1163,8671],{"className":8672,"style":1243},[1242],[1163,8674,8676],{"className":8675},[1247,1248,1249,1250],[1163,8677,8679,8682,8685],{"className":8678},[1213,1250],[1163,8680,1190],{"className":8681},[1213,1217,1250],[1163,8683,1366],{"className":8684},[1538,1250],[1163,8686,1370],{"className":8687},[1213,1250],[1163,8689,1258],{"className":8690},[1257],[1163,8692,8694],{"className":8693},[1230],[1163,8695,8697],{"className":8696,"style":1597},[1234],[1163,8698],{},[1163,8700],{"className":8701,"style":1534},[1460],[1163,8703,1373],{"className":8704},[1538],[1163,8706],{"className":8707,"style":1534},[1460],[1163,8709,8711,8714,8754,8757,8760],{"className":8710},[1204],[1163,8712],{"className":8713,"style":7340},[1208],[1163,8715,8717,8720],{"className":8716},[1213],[1163,8718,4710],{"className":8719},[1213,1217],[1163,8721,8723],{"className":8722},[1221],[1163,8724,8726,8746],{"className":8725},[1225,1226],[1163,8727,8729,8743],{"className":8728},[1230],[1163,8730,8732],{"className":8731,"style":1235},[1234],[1163,8733,8734,8737],{"style":1238},[1163,8735],{"className":8736,"style":1243},[1242],[1163,8738,8740],{"className":8739},[1247,1248,1249,1250],[1163,8741,1190],{"className":8742},[1213,1217,1250],[1163,8744,1258],{"className":8745},[1257],[1163,8747,8749],{"className":8748},[1230],[1163,8750,8752],{"className":8751,"style":1265},[1234],[1163,8753],{},[1163,8755],{"className":8756,"style":1534},[1460],[1163,8758,8494],{"className":8759},[1538],[1163,8761],{"className":8762,"style":1534},[1460],[1163,8764,8766,8769],{"className":8765},[1204],[1163,8767],{"className":8768,"style":7706},[1208],[1163,8770,8772,8803],{"className":8771},[1213],[1163,8773,8775],{"className":8774},[1213,3383],[1163,8776,8778],{"className":8777},[1225],[1163,8779,8781],{"className":8780},[1230],[1163,8782,8784,8792],{"className":8783,"style":7722},[1234],[1163,8785,8786,8789],{"style":3396},[1163,8787],{"className":8788,"style":3400},[1242],[1163,8790,6558],{"className":8791,"style":6579},[1213,1217],[1163,8793,8794,8797],{"style":7733},[1163,8795],{"className":8796,"style":3400},[1242],[1163,8798,8800],{"className":8799,"style":7740},[3412],[1163,8801,7639],{"className":8802},[1213],[1163,8804,8806],{"className":8805},[1221],[1163,8807,8809,8829],{"className":8808},[1225,1226],[1163,8810,8812,8826],{"className":8811},[1230],[1163,8813,8815],{"className":8814,"style":1235},[1234],[1163,8816,8817,8820],{"style":6594},[1163,8818],{"className":8819,"style":1243},[1242],[1163,8821,8823],{"className":8822},[1247,1248,1249,1250],[1163,8824,1190],{"className":8825},[1213,1217,1250],[1163,8827,1258],{"className":8828},[1257],[1163,8830,8832],{"className":8831},[1230],[1163,8833,8835],{"className":8834,"style":1265},[1234],[1163,8836],{},[1101,8838,8839],{},[1107,8840,8841],{},"隐藏状态输出：",[1101,8843,8844],{},[1163,8845,8847,8889],{"className":8846},[1166],[1163,8848,8850],{"className":8849},[1170],[1172,8851,8852],{"xmlns":1174},[1176,8853,8854,8886],{},[1179,8855,8856,8862,8864,8870,8872,8874,8876,8878,8884],{},[1182,8857,8858,8860],{},[1185,8859,1187],{},[1185,8861,1190],{},[1332,8863,1334],{},[1182,8865,8866,8868],{},[1185,8867,8114],{},[1185,8869,1190],{},[1332,8871,8494],{},[1185,8873,7646],{},[1332,8875,7649],{},[1332,8877,1341],{"stretchy":1340},[1182,8879,8880,8882],{},[1185,8881,6558],{},[1185,8883,1190],{},[1332,8885,1404],{"stretchy":1340},[1192,8887,8888],{"encoding":1194},"h_t = o_t \\odot \\tanh(C_t)",[1163,8890,8892,8947,9002],{"className":8891,"ariaHidden":1200},[1199],[1163,8893,8895,8898,8938,8941,8944],{"className":8894},[1204],[1163,8896],{"className":8897,"style":1209},[1208],[1163,8899,8901,8904],{"className":8900},[1213],[1163,8902,1187],{"className":8903},[1213,1217],[1163,8905,8907],{"className":8906},[1221],[1163,8908,8910,8930],{"className":8909},[1225,1226],[1163,8911,8913,8927],{"className":8912},[1230],[1163,8914,8916],{"className":8915,"style":1235},[1234],[1163,8917,8918,8921],{"style":1238},[1163,8919],{"className":8920,"style":1243},[1242],[1163,8922,8924],{"className":8923},[1247,1248,1249,1250],[1163,8925,1190],{"className":8926},[1213,1217,1250],[1163,8928,1258],{"className":8929},[1257],[1163,8931,8933],{"className":8932},[1230],[1163,8934,8936],{"className":8935,"style":1265},[1234],[1163,8937],{},[1163,8939],{"className":8940,"style":1461},[1460],[1163,8942,1334],{"className":8943},[1465],[1163,8945],{"className":8946,"style":1461},[1460],[1163,8948,8950,8953,8993,8996,8999],{"className":8949},[1204],[1163,8951],{"className":8952,"style":1677},[1208],[1163,8954,8956,8959],{"className":8955},[1213],[1163,8957,8114],{"className":8958},[1213,1217],[1163,8960,8962],{"className":8961},[1221],[1163,8963,8965,8985],{"className":8964},[1225,1226],[1163,8966,8968,8982],{"className":8967},[1230],[1163,8969,8971],{"className":8970,"style":1235},[1234],[1163,8972,8973,8976],{"style":1238},[1163,8974],{"className":8975,"style":1243},[1242],[1163,8977,8979],{"className":8978},[1247,1248,1249,1250],[1163,8980,1190],{"className":8981},[1213,1217,1250],[1163,8983,1258],{"className":8984},[1257],[1163,8986,8988],{"className":8987},[1230],[1163,8989,8991],{"className":8990,"style":1265},[1234],[1163,8992],{},[1163,8994],{"className":8995,"style":1534},[1460],[1163,8997,8494],{"className":8998},[1538],[1163,9000],{"className":9001,"style":1534},[1460],[1163,9003,9005,9008,9011,9014,9054],{"className":9004},[1204],[1163,9006],{"className":9007,"style":1475},[1208],[1163,9009,7646],{"className":9010},[3217],[1163,9012,1341],{"className":9013},[1483],[1163,9015,9017,9020],{"className":9016},[1213],[1163,9018,6558],{"className":9019,"style":6579},[1213,1217],[1163,9021,9023],{"className":9022},[1221],[1163,9024,9026,9046],{"className":9025},[1225,1226],[1163,9027,9029,9043],{"className":9028},[1230],[1163,9030,9032],{"className":9031,"style":1235},[1234],[1163,9033,9034,9037],{"style":6594},[1163,9035],{"className":9036,"style":1243},[1242],[1163,9038,9040],{"className":9039},[1247,1248,1249,1250],[1163,9041,1190],{"className":9042},[1213,1217,1250],[1163,9044,1258],{"className":9045},[1257],[1163,9047,9049],{"className":9048},[1230],[1163,9050,9052],{"className":9051,"style":1265},[1234],[1163,9053],{},[1163,9055,1404],{"className":9056},[1776],[1101,9058,9059],{},[1107,9060,9061],{},"梯度消失的解决方案",[1111,9063,9064,9418,9492],{},[1114,9065,9066,9067,9070,9071,9140,9141],{},"细胞状态通过",[1107,9068,9069],{},"加法","更新，梯度沿 ",[1163,9072,9074,9091],{"className":9073},[1166],[1163,9075,9077],{"className":9076},[1170],[1172,9078,9079],{"xmlns":1174},[1176,9080,9081,9089],{},[1179,9082,9083],{},[1182,9084,9085,9087],{},[1185,9086,6558],{},[1185,9088,1190],{},[1192,9090,6563],{"encoding":1194},[1163,9092,9094],{"className":9093,"ariaHidden":1200},[1199],[1163,9095,9097,9100],{"className":9096},[1204],[1163,9098],{"className":9099,"style":1615},[1208],[1163,9101,9103,9106],{"className":9102},[1213],[1163,9104,6558],{"className":9105,"style":6579},[1213,1217],[1163,9107,9109],{"className":9108},[1221],[1163,9110,9112,9132],{"className":9111},[1225,1226],[1163,9113,9115,9129],{"className":9114},[1230],[1163,9116,9118],{"className":9117,"style":1235},[1234],[1163,9119,9120,9123],{"style":6594},[1163,9121],{"className":9122,"style":1243},[1242],[1163,9124,9126],{"className":9125},[1247,1248,1249,1250],[1163,9127,1190],{"className":9128},[1213,1217,1250],[1163,9130,1258],{"className":9131},[1257],[1163,9133,9135],{"className":9134},[1230],[1163,9136,9138],{"className":9137,"style":1265},[1234],[1163,9139],{}," 传播时：",[1163,9142,9144,9192],{"className":9143},[1166],[1163,9145,9147],{"className":9146},[1170],[1172,9148,9149],{"xmlns":1174},[1176,9150,9151,9189],{},[1179,9152,9153,9181,9183],{},[3678,9154,9155,9165],{},[1179,9156,9157,9159],{},[1185,9158,3685],{"mathvariant":3684},[1182,9160,9161,9163],{},[1185,9162,6558],{},[1185,9164,1190],{},[1179,9166,9167,9169],{},[1185,9168,3685],{"mathvariant":3684},[1182,9170,9171,9173],{},[1185,9172,6558],{},[1179,9174,9175,9177,9179],{},[1185,9176,1190],{},[1332,9178,1366],{},[1368,9180,1370],{},[1332,9182,1334],{},[1182,9184,9185,9187],{},[1185,9186,6719],{},[1185,9188,1190],{},[1192,9190,9191],{"encoding":1194},"\\frac{\\partial C_t}{\\partial C_{t-1}} = f_t",[1163,9193,9195,9372],{"className":9194,"ariaHidden":1200},[1199],[1163,9196,9198,9202,9363,9366,9369],{"className":9197},[1204],[1163,9199],{"className":9200,"style":9201},[1208],"height:1.383em;vertical-align:-0.4868em;",[1163,9203,9205,9208,9360],{"className":9204},[1213],[1163,9206],{"className":9207},[1483,3826],[1163,9209,9211],{"className":9210},[3678],[1163,9212,9214,9351],{"className":9213},[1225,1226],[1163,9215,9217,9348],{"className":9216},[1230],[1163,9218,9220,9286,9294],{"className":9219,"style":4117},[1234],[1163,9221,9222,9225],{"style":3842},[1163,9223],{"className":9224,"style":3400},[1242],[1163,9226,9228],{"className":9227},[1247,1248,1249,1250],[1163,9229,9231,9234],{"className":9230},[1213,1250],[1163,9232,3685],{"className":9233,"style":3855},[1213,1250],[1163,9235,9237,9240],{"className":9236},[1213,1250],[1163,9238,6558],{"className":9239,"style":6579},[1213,1217,1250],[1163,9241,9243],{"className":9242},[1221],[1163,9244,9246,9277],{"className":9245},[1225,1226],[1163,9247,9249,9274],{"className":9248},[1230],[1163,9250,9253],{"className":9251,"style":9252},[1234],"height:0.3173em;",[1163,9254,9256,9259],{"style":9255},"top:-2.357em;margin-left:-0.0715em;margin-right:0.0714em;",[1163,9257],{"className":9258,"style":3881},[1242],[1163,9260,9262],{"className":9261},[1247,3885,3886,1250],[1163,9263,9265,9268,9271],{"className":9264},[1213,1250],[1163,9266,1190],{"className":9267},[1213,1217,1250],[1163,9269,1366],{"className":9270},[1538,1250],[1163,9272,1370],{"className":9273},[1213,1250],[1163,9275,1258],{"className":9276},[1257],[1163,9278,9280],{"className":9279},[1230],[1163,9281,9284],{"className":9282,"style":9283},[1234],"height:0.2025em;",[1163,9285],{},[1163,9287,9288,9291],{"style":3907},[1163,9289],{"className":9290,"style":3400},[1242],[1163,9292],{"className":9293,"style":3915},[3914],[1163,9295,9296,9299],{"style":4185},[1163,9297],{"className":9298,"style":3400},[1242],[1163,9300,9302],{"className":9301},[1247,1248,1249,1250],[1163,9303,9305,9308],{"className":9304},[1213,1250],[1163,9306,3685],{"className":9307,"style":3855},[1213,1250],[1163,9309,9311,9314],{"className":9310},[1213,1250],[1163,9312,6558],{"className":9313,"style":6579},[1213,1217,1250],[1163,9315,9317],{"className":9316},[1221],[1163,9318,9320,9340],{"className":9319},[1225,1226],[1163,9321,9323,9337],{"className":9322},[1230],[1163,9324,9326],{"className":9325,"style":4150},[1234],[1163,9327,9328,9331],{"style":9255},[1163,9329],{"className":9330,"style":3881},[1242],[1163,9332,9334],{"className":9333},[1247,3885,3886,1250],[1163,9335,1190],{"className":9336},[1213,1217,1250],[1163,9338,1258],{"className":9339},[1257],[1163,9341,9343],{"className":9342},[1230],[1163,9344,9346],{"className":9345,"style":4172},[1234],[1163,9347],{},[1163,9349,1258],{"className":9350},[1257],[1163,9352,9354],{"className":9353},[1230],[1163,9355,9358],{"className":9356,"style":9357},[1234],"height:0.4868em;",[1163,9359],{},[1163,9361],{"className":9362},[1776,3826],[1163,9364],{"className":9365,"style":1461},[1460],[1163,9367,1334],{"className":9368},[1465],[1163,9370],{"className":9371,"style":1461},[1460],[1163,9373,9375,9378],{"className":9374},[1204],[1163,9376],{"className":9377,"style":6782},[1208],[1163,9379,9381,9384],{"className":9380},[1213],[1163,9382,6719],{"className":9383,"style":6789},[1213,1217],[1163,9385,9387],{"className":9386},[1221],[1163,9388,9390,9410],{"className":9389},[1225,1226],[1163,9391,9393,9407],{"className":9392},[1230],[1163,9394,9396],{"className":9395,"style":1235},[1234],[1163,9397,9398,9401],{"style":6804},[1163,9399],{"className":9400,"style":1243},[1242],[1163,9402,9404],{"className":9403},[1247,1248,1249,1250],[1163,9405,1190],{"className":9406},[1213,1217,1250],[1163,9408,1258],{"className":9409},[1257],[1163,9411,9413],{"className":9412},[1230],[1163,9414,9416],{"className":9415,"style":1265},[1234],[1163,9417],{},[1114,9419,9420,9421,9491],{},"遗忘门 ",[1163,9422,9424,9442],{"className":9423},[1166],[1163,9425,9427],{"className":9426},[1170],[1172,9428,9429],{"xmlns":1174},[1176,9430,9431,9439],{},[1179,9432,9433],{},[1182,9434,9435,9437],{},[1185,9436,6719],{},[1185,9438,1190],{},[1192,9440,9441],{"encoding":1194},"f_t",[1163,9443,9445],{"className":9444,"ariaHidden":1200},[1199],[1163,9446,9448,9451],{"className":9447},[1204],[1163,9449],{"className":9450,"style":6782},[1208],[1163,9452,9454,9457],{"className":9453},[1213],[1163,9455,6719],{"className":9456,"style":6789},[1213,1217],[1163,9458,9460],{"className":9459},[1221],[1163,9461,9463,9483],{"className":9462},[1225,1226],[1163,9464,9466,9480],{"className":9465},[1230],[1163,9467,9469],{"className":9468,"style":1235},[1234],[1163,9470,9471,9474],{"style":6804},[1163,9472],{"className":9473,"style":1243},[1242],[1163,9475,9477],{"className":9476},[1247,1248,1249,1250],[1163,9478,1190],{"className":9479},[1213,1217,1250],[1163,9481,1258],{"className":9482},[1257],[1163,9484,9486],{"className":9485},[1230],[1163,9487,9489],{"className":9488,"style":1265},[1234],[1163,9490],{}," 可以学习到接近 1 的值，使梯度几乎无损传播",[1114,9493,9494],{},"相比标准 RNN 的连续矩阵乘法，LSTM 的加法结构避免了指数衰减",[4645,9496],{},[1091,9498,9500],{"id":9499},"四grugated-recurrent-unit","四、GRU（Gated Recurrent Unit）",[1096,9502,9504],{"id":9503},"_41-关于gru","4.1 关于GRU",[1101,9506,9507,9508,9511,9512,9515],{},"GRU 是 LSTM 的",[1107,9509,9510],{},"简化版本","，将 3 个门简化为 2 个门，同时将细胞状态和隐藏状态",[1107,9513,9514],{},"合并","为一个状态。在许多任务上 GRU 的性能与 LSTM 相当，但参数更少、训练更快。",[1101,9517,9518,9521],{},[1107,9519,9520],{},"更新门","（合并了 LSTM 的遗忘门和输入门）：",[1101,9523,9524],{},[1163,9525,9527,9585],{"className":9526},[1166],[1163,9528,9530],{"className":9529},[1170],[1172,9531,9532],{"xmlns":1174},[1176,9533,9534,9582],{},[1179,9535,9536,9542,9544,9546,9548,9554,9556,9558,9570,9572,9578,9580],{},[1182,9537,9538,9540],{},[1185,9539,4754],{},[1185,9541,1190],{},[1332,9543,1334],{},[1185,9545,1337],{},[1332,9547,1341],{"stretchy":1340},[1182,9549,9550,9552],{},[1185,9551,1346],{},[1185,9553,4754],{},[1332,9555,1355],{},[1332,9557,6649],{"stretchy":1340},[1182,9559,9560,9562],{},[1185,9561,1187],{},[1179,9563,9564,9566,9568],{},[1185,9565,1190],{},[1332,9567,1366],{},[1368,9569,1370],{},[1332,9571,2609],{"separator":1200},[1182,9573,9574,9576],{},[1185,9575,1382],{},[1185,9577,1190],{},[1332,9579,6659],{"stretchy":1340},[1332,9581,1404],{"stretchy":1340},[1192,9583,9584],{"encoding":1194},"z_t = \\sigma(W_z \\cdot [h_{t-1}, x_t])",[1163,9586,9588,9643,9704],{"className":9587,"ariaHidden":1200},[1199],[1163,9589,9591,9594,9634,9637,9640],{"className":9590},[1204],[1163,9592],{"className":9593,"style":2115},[1208],[1163,9595,9597,9600],{"className":9596},[1213],[1163,9598,4754],{"className":9599,"style":5122},[1213,1217],[1163,9601,9603],{"className":9602},[1221],[1163,9604,9606,9626],{"className":9605},[1225,1226],[1163,9607,9609,9623],{"className":9608},[1230],[1163,9610,9612],{"className":9611,"style":1235},[1234],[1163,9613,9614,9617],{"style":5138},[1163,9615],{"className":9616,"style":1243},[1242],[1163,9618,9620],{"className":9619},[1247,1248,1249,1250],[1163,9621,1190],{"className":9622},[1213,1217,1250],[1163,9624,1258],{"className":9625},[1257],[1163,9627,9629],{"className":9628},[1230],[1163,9630,9632],{"className":9631,"style":1265},[1234],[1163,9633],{},[1163,9635],{"className":9636,"style":1461},[1460],[1163,9638,1334],{"className":9639},[1465],[1163,9641],{"className":9642,"style":1461},[1460],[1163,9644,9646,9649,9652,9655,9695,9698,9701],{"className":9645},[1204],[1163,9647],{"className":9648,"style":1475},[1208],[1163,9650,1337],{"className":9651,"style":1479},[1213,1217],[1163,9653,1341],{"className":9654},[1483],[1163,9656,9658,9661],{"className":9657},[1213],[1163,9659,1346],{"className":9660,"style":1490},[1213,1217],[1163,9662,9664],{"className":9663},[1221],[1163,9665,9667,9687],{"className":9666},[1225,1226],[1163,9668,9670,9684],{"className":9669},[1230],[1163,9671,9673],{"className":9672,"style":2033},[1234],[1163,9674,9675,9678],{"style":1506},[1163,9676],{"className":9677,"style":1243},[1242],[1163,9679,9681],{"className":9680},[1247,1248,1249,1250],[1163,9682,4754],{"className":9683,"style":5122},[1213,1217,1250],[1163,9685,1258],{"className":9686},[1257],[1163,9688,9690],{"className":9689},[1230],[1163,9691,9693],{"className":9692,"style":1265},[1234],[1163,9694],{},[1163,9696],{"className":9697,"style":1534},[1460],[1163,9699,1355],{"className":9700},[1538],[1163,9702],{"className":9703,"style":1534},[1460],[1163,9705,9707,9710,9713,9762,9765,9768,9808],{"className":9706},[1204],[1163,9708],{"className":9709,"style":1475},[1208],[1163,9711,6649],{"className":9712},[1483],[1163,9714,9716,9719],{"className":9715},[1213],[1163,9717,1187],{"className":9718},[1213,1217],[1163,9720,9722],{"className":9721},[1221],[1163,9723,9725,9754],{"className":9724},[1225,1226],[1163,9726,9728,9751],{"className":9727},[1230],[1163,9729,9731],{"className":9730,"style":1567},[1234],[1163,9732,9733,9736],{"style":1238},[1163,9734],{"className":9735,"style":1243},[1242],[1163,9737,9739],{"className":9738},[1247,1248,1249,1250],[1163,9740,9742,9745,9748],{"className":9741},[1213,1250],[1163,9743,1190],{"className":9744},[1213,1217,1250],[1163,9746,1366],{"className":9747},[1538,1250],[1163,9749,1370],{"className":9750},[1213,1250],[1163,9752,1258],{"className":9753},[1257],[1163,9755,9757],{"className":9756},[1230],[1163,9758,9760],{"className":9759,"style":1597},[1234],[1163,9761],{},[1163,9763,2609],{"className":9764},[2671],[1163,9766],{"className":9767,"style":2675},[1460],[1163,9769,9771,9774],{"className":9770},[1213],[1163,9772,1382],{"className":9773},[1213,1217],[1163,9775,9777],{"className":9776},[1221],[1163,9778,9780,9800],{"className":9779},[1225,1226],[1163,9781,9783,9797],{"className":9782},[1230],[1163,9784,9786],{"className":9785,"style":1235},[1234],[1163,9787,9788,9791],{"style":1238},[1163,9789],{"className":9790,"style":1243},[1242],[1163,9792,9794],{"className":9793},[1247,1248,1249,1250],[1163,9795,1190],{"className":9796},[1213,1217,1250],[1163,9798,1258],{"className":9799},[1257],[1163,9801,9803],{"className":9802},[1230],[1163,9804,9806],{"className":9805,"style":1265},[1234],[1163,9807],{},[1163,9809,9811],{"className":9810},[1776],"])",[1101,9813,9814,9817],{},[1107,9815,9816],{},"重置门","（控制遗忘多少历史信息）：",[1101,9819,9820],{},[1163,9821,9823,9882],{"className":9822},[1166],[1163,9824,9826],{"className":9825},[1170],[1172,9827,9828],{"xmlns":1174},[1176,9829,9830,9879],{},[1179,9831,9832,9839,9841,9843,9845,9851,9853,9855,9867,9869,9875,9877],{},[1182,9833,9834,9837],{},[1185,9835,9836],{},"r",[1185,9838,1190],{},[1332,9840,1334],{},[1185,9842,1337],{},[1332,9844,1341],{"stretchy":1340},[1182,9846,9847,9849],{},[1185,9848,1346],{},[1185,9850,9836],{},[1332,9852,1355],{},[1332,9854,6649],{"stretchy":1340},[1182,9856,9857,9859],{},[1185,9858,1187],{},[1179,9860,9861,9863,9865],{},[1185,9862,1190],{},[1332,9864,1366],{},[1368,9866,1370],{},[1332,9868,2609],{"separator":1200},[1182,9870,9871,9873],{},[1185,9872,1382],{},[1185,9874,1190],{},[1332,9876,6659],{"stretchy":1340},[1332,9878,1404],{"stretchy":1340},[1192,9880,9881],{"encoding":1194},"r_t = \\sigma(W_r \\cdot [h_{t-1}, x_t])",[1163,9883,9885,9942,10003],{"className":9884,"ariaHidden":1200},[1199],[1163,9886,9888,9891,9933,9936,9939],{"className":9887},[1204],[1163,9889],{"className":9890,"style":2115},[1208],[1163,9892,9894,9898],{"className":9893},[1213],[1163,9895,9836],{"className":9896,"style":9897},[1213,1217],"margin-right:0.0278em;",[1163,9899,9901],{"className":9900},[1221],[1163,9902,9904,9925],{"className":9903},[1225,1226],[1163,9905,9907,9922],{"className":9906},[1230],[1163,9908,9910],{"className":9909,"style":1235},[1234],[1163,9911,9913,9916],{"style":9912},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1163,9914],{"className":9915,"style":1243},[1242],[1163,9917,9919],{"className":9918},[1247,1248,1249,1250],[1163,9920,1190],{"className":9921},[1213,1217,1250],[1163,9923,1258],{"className":9924},[1257],[1163,9926,9928],{"className":9927},[1230],[1163,9929,9931],{"className":9930,"style":1265},[1234],[1163,9932],{},[1163,9934],{"className":9935,"style":1461},[1460],[1163,9937,1334],{"className":9938},[1465],[1163,9940],{"className":9941,"style":1461},[1460],[1163,9943,9945,9948,9951,9954,9994,9997,10000],{"className":9944},[1204],[1163,9946],{"className":9947,"style":1475},[1208],[1163,9949,1337],{"className":9950,"style":1479},[1213,1217],[1163,9952,1341],{"className":9953},[1483],[1163,9955,9957,9960],{"className":9956},[1213],[1163,9958,1346],{"className":9959,"style":1490},[1213,1217],[1163,9961,9963],{"className":9962},[1221],[1163,9964,9966,9986],{"className":9965},[1225,1226],[1163,9967,9969,9983],{"className":9968},[1230],[1163,9970,9972],{"className":9971,"style":2033},[1234],[1163,9973,9974,9977],{"style":1506},[1163,9975],{"className":9976,"style":1243},[1242],[1163,9978,9980],{"className":9979},[1247,1248,1249,1250],[1163,9981,9836],{"className":9982,"style":9897},[1213,1217,1250],[1163,9984,1258],{"className":9985},[1257],[1163,9987,9989],{"className":9988},[1230],[1163,9990,9992],{"className":9991,"style":1265},[1234],[1163,9993],{},[1163,9995],{"className":9996,"style":1534},[1460],[1163,9998,1355],{"className":9999},[1538],[1163,10001],{"className":10002,"style":1534},[1460],[1163,10004,10006,10009,10012,10061,10064,10067,10107],{"className":10005},[1204],[1163,10007],{"className":10008,"style":1475},[1208],[1163,10010,6649],{"className":10011},[1483],[1163,10013,10015,10018],{"className":10014},[1213],[1163,10016,1187],{"className":10017},[1213,1217],[1163,10019,10021],{"className":10020},[1221],[1163,10022,10024,10053],{"className":10023},[1225,1226],[1163,10025,10027,10050],{"className":10026},[1230],[1163,10028,10030],{"className":10029,"style":1567},[1234],[1163,10031,10032,10035],{"style":1238},[1163,10033],{"className":10034,"style":1243},[1242],[1163,10036,10038],{"className":10037},[1247,1248,1249,1250],[1163,10039,10041,10044,10047],{"className":10040},[1213,1250],[1163,10042,1190],{"className":10043},[1213,1217,1250],[1163,10045,1366],{"className":10046},[1538,1250],[1163,10048,1370],{"className":10049},[1213,1250],[1163,10051,1258],{"className":10052},[1257],[1163,10054,10056],{"className":10055},[1230],[1163,10057,10059],{"className":10058,"style":1597},[1234],[1163,10060],{},[1163,10062,2609],{"className":10063},[2671],[1163,10065],{"className":10066,"style":2675},[1460],[1163,10068,10070,10073],{"className":10069},[1213],[1163,10071,1382],{"className":10072},[1213,1217],[1163,10074,10076],{"className":10075},[1221],[1163,10077,10079,10099],{"className":10078},[1225,1226],[1163,10080,10082,10096],{"className":10081},[1230],[1163,10083,10085],{"className":10084,"style":1235},[1234],[1163,10086,10087,10090],{"style":1238},[1163,10088],{"className":10089,"style":1243},[1242],[1163,10091,10093],{"className":10092},[1247,1248,1249,1250],[1163,10094,1190],{"className":10095},[1213,1217,1250],[1163,10097,1258],{"className":10098},[1257],[1163,10100,10102],{"className":10101},[1230],[1163,10103,10105],{"className":10104,"style":1265},[1234],[1163,10106],{},[1163,10108,9811],{"className":10109},[1776],[1101,10111,10112,3118],{},[1107,10113,10114],{},"候选隐藏状态",[1101,10116,10117],{},[1163,10118,10120,10188],{"className":10119},[1166],[1163,10121,10123],{"className":10122},[1170],[1172,10124,10125],{"xmlns":1174},[1176,10126,10127,10185],{},[1179,10128,10129,10139,10141,10143,10145,10147,10149,10151,10153,10159,10161,10173,10175,10181,10183],{},[1182,10130,10131,10137],{},[3171,10132,10133,10135],{"accent":1200},[1185,10134,1187],{},[1332,10136,7639],{},[1185,10138,1190],{},[1332,10140,1334],{},[1185,10142,7646],{},[1332,10144,7649],{},[1332,10146,1341],{"stretchy":1340},[1185,10148,1346],{},[1332,10150,1355],{},[1332,10152,6649],{"stretchy":1340},[1182,10154,10155,10157],{},[1185,10156,9836],{},[1185,10158,1190],{},[1332,10160,8494],{},[1182,10162,10163,10165],{},[1185,10164,1187],{},[1179,10166,10167,10169,10171],{},[1185,10168,1190],{},[1332,10170,1366],{},[1368,10172,1370],{},[1332,10174,2609],{"separator":1200},[1182,10176,10177,10179],{},[1185,10178,1382],{},[1185,10180,119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= \\tanh(W \\cdot [r_t \\odot h_{t-1}, x_t])",[1163,10189,10191,10278,10302,10360],{"className":10190,"ariaHidden":1200},[1199],[1163,10192,10194,10198,10269,10272,10275],{"className":10193},[1204],[1163,10195],{"className":10196,"style":10197},[1208],"height:1.0813em;vertical-align:-0.15em;",[1163,10199,10201,10235],{"className":10200},[1213],[1163,10202,10204],{"className":10203},[1213,3383],[1163,10205,10207],{"className":10206},[1225],[1163,10208,10210],{"className":10209},[1230],[1163,10211,10214,10222],{"className":10212,"style":10213},[1234],"height:0.9313em;",[1163,10215,10216,10219],{"style":3396},[1163,10217],{"className":10218,"style":3400},[1242],[1163,10220,1187],{"className":10221},[1213,1217],[1163,10223,10225,10228],{"style":10224},"top:-3.6134em;",[1163,10226],{"className":10227,"style":3400},[1242],[1163,10229,10232],{"className":10230,"style":10231},[3412],"left:-0.25em;",[1163,10233,7639],{"className":10234},[1213],[1163,10236,10238],{"className":10237},[1221],[1163,10239,10241,10261],{"className":10240},[1225,1226],[1163,10242,10244,10258],{"className":10243},[1230],[1163,10245,10247],{"className":10246,"style":1235},[1234],[1163,10248,10249,10252],{"style":1238},[1163,10250],{"className":10251,"style":1243},[1242],[1163,10253,10255],{"className":10254},[1247,1248,1249,1250],[1163,10256,1190],{"className":10257},[1213,1217,1250],[1163,10259,1258],{"className":10260},[1257],[1163,10262,10264],{"className":10263},[1230],[1163,10265,10267],{"className":10266,"style":1265},[1234],[1163,10268],{},[1163,10270],{"className":10271,"style":1461},[1460],[1163,10273,1334],{"className":10274},[1465],[1163,10276],{"className":10277,"style":1461},[1460],[1163,10279,10281,10284,10287,10290,10293,10296,10299],{"className":10280},[1204],[1163,10282],{"className":10283,"style":1475},[1208],[1163,10285,7646],{"className":10286},[3217],[1163,10288,1341],{"className":10289},[1483],[1163,10291,1346],{"className":10292,"style":1490},[1213,1217],[1163,10294],{"className":10295,"style":1534},[1460],[1163,10297,1355],{"className":10298},[1538],[1163,10300],{"className":10301,"style":1534},[1460],[1163,10303,10305,10308,10311,10351,10354,10357],{"className":10304},[1204],[1163,10306],{"className":10307,"style":1475},[1208],[1163,10309,6649],{"className":10310},[1483],[1163,10312,10314,10317],{"className":10313},[1213],[1163,10315,9836],{"className":10316,"style":9897},[1213,1217],[1163,10318,10320],{"className":10319},[1221],[1163,10321,10323,10343],{"className":10322},[1225,1226],[1163,10324,10326,10340],{"className":10325},[1230],[1163,10327,10329],{"className":10328,"style":1235},[1234],[1163,10330,10331,10334],{"style":9912},[1163,10332],{"className":10333,"style":1243},[1242],[1163,10335,10337],{"className":10336},[1247,1248,1249,1250],[1163,10338,1190],{"className":10339},[1213,1217,1250],[1163,10341,1258],{"className":10342},[1257],[1163,10344,10346],{"className":10345},[1230],[1163,10347,10349],{"className":10348,"style":1265},[1234],[1163,10350],{},[1163,10352],{"className":10353,"style":1534},[1460],[1163,10355,8494],{"className":10356},[1538],[1163,10358],{"className":10359,"style":1534},[1460],[1163,10361,10363,10366,10415,10418,10421,10461],{"className":10362},[1204],[1163,10364],{"className":10365,"style":1475},[1208],[1163,10367,10369,10372],{"className":10368},[1213],[1163,10370,1187],{"className":10371},[1213,1217],[1163,10373,10375],{"className":10374},[1221],[1163,10376,10378,10407],{"className":10377},[1225,1226],[1163,10379,10381,10404],{"className":10380},[1230],[1163,10382,10384],{"className":10383,"style":1567},[1234],[1163,10385,10386,10389],{"style":1238},[1163,10387],{"className":10388,"style":1243},[1242],[1163,10390,10392],{"className":10391},[1247,1248,1249,1250],[1163,10393,10395,10398,10401],{"className":10394},[1213,1250],[1163,10396,1190],{"className":10397},[1213,1217,1250],[1163,10399,1366],{"className":10400},[1538,1250],[1163,10402,1370],{"className":10403},[1213,1250],[1163,10405,1258],{"className":10406},[1257],[1163,10408,10410],{"className":10409},[1230],[1163,10411,10413],{"className":10412,"style":1597},[1234],[1163,10414],{},[1163,10416,2609],{"className":10417},[2671],[1163,10419],{"className":10420,"style":2675},[1460],[1163,10422,10424,10427],{"className":10423},[1213],[1163,10425,1382],{"className":10426},[1213,1217],[1163,10428,10430],{"className":10429},[1221],[1163,10431,10433,10453],{"className":10432},[1225,1226],[1163,10434,10436,10450],{"className":10435},[1230],[1163,10437,10439],{"className":10438,"style":1235},[1234],[1163,10440,10441,10444],{"style":1238},[1163,10442],{"className":10443,"style":1243},[1242],[1163,10445,10447],{"className":10446},[1247,1248,1249,1250],[1163,10448,1190],{"className":10449},[1213,1217,1250],[1163,10451,1258],{"className":10452},[1257],[1163,10454,10456],{"className":10455},[1230],[1163,10457,10459],{"className":10458,"style":1265},[1234],[1163,10460],{},[1163,10462,9811],{"className":10463},[1776],[1101,10465,10466,10469],{},[1107,10467,10468],{},"最终隐藏状态","（插值更新）：",[1101,10471,10472],{},[1163,10473,10475,10543],{"className":10474},[1166],[1163,10476,10478],{"className":10477},[1170],[1172,10479,10480],{"xmlns":1174},[1176,10481,10482,10540],{},[1179,10483,10484,10490,10492,10494,10496,10498,10504,10506,10508,10520,10522,10528,10530],{},[1182,10485,10486,10488],{},[1185,10487,1187],{},[1185,10489,1190],{},[1332,10491,1334],{},[1332,10493,1341],{"stretchy":1340},[1368,10495,1370],{},[1332,10497,1366],{},[1182,10499,10500,10502],{},[1185,10501,4754],{},[1185,10503,1190],{},[1332,10505,1404],{"stretchy":1340},[1332,10507,8494],{},[1182,10509,10510,10512],{},[1185,10511,1187],{},[1179,10513,10514,10516,10518],{},[1185,10515,1190],{},[1332,10517,1366],{},[1368,10519,1370],{},[1332,10521,1373],{},[1182,10523,10524,10526],{},[1185,10525,4754],{},[1185,10527,1190],{},[1332,10529,8494],{},[1182,10531,10532,10538],{},[3171,10533,10534,10536],{"accent":1200},[1185,10535,1187],{},[1332,10537,7639],{},[1185,10539,1190],{},[1192,10541,10542],{"encoding":1194},"h_t = (1 - z_t) \\odot h_{t-1} + z_t \\odot \\tilde{h}_t",[1163,10544,10546,10601,10622,10680,10744,10799],{"className":10545,"ariaHidden":1200},[1199],[1163,10547,10549,10552,10592,10595,10598],{"className":10548},[1204],[1163,10550],{"className":10551,"style":1209},[1208],[1163,10553,10555,10558],{"className":10554},[1213],[1163,10556,1187],{"className":10557},[1213,1217],[1163,10559,10561],{"className":10560},[1221],[1163,10562,10564,10584],{"className":10563},[1225,1226],[1163,10565,10567,10581],{"className":10566},[1230],[1163,10568,10570],{"className":10569,"style":1235},[1234],[1163,10571,10572,10575],{"style":1238},[1163,10573],{"className":10574,"style":1243},[1242],[1163,10576,10578],{"className":10577},[1247,1248,1249,1250],[1163,10579,1190],{"className":10580},[1213,1217,1250],[1163,10582,1258],{"className":10583},[1257],[1163,10585,10587],{"className":10586},[1230],[1163,10588,10590],{"className":10589,"style":1265},[1234],[1163,10591],{},[1163,10593],{"className":10594,"style":1461},[1460],[1163,10596,1334],{"className":10597},[1465],[1163,10599],{"className":10600,"style":1461},[1460],[1163,10602,10604,10607,10610,10613,10616,10619],{"className":10603},[1204],[1163,10605],{"className":10606,"style":1475},[1208],[1163,10608,1341],{"className":10609},[1483],[1163,10611,1370],{"className":10612},[1213],[1163,10614],{"className":10615,"style":1534},[1460],[1163,10617,1366],{"className":10618},[1538],[1163,10620],{"className":10621,"style":1534},[1460],[1163,10623,10625,10628,10668,10671,10674,10677],{"className":10624},[1204],[1163,10626],{"className":10627,"style":1475},[1208],[1163,10629,10631,10634],{"className":10630},[1213],[1163,10632,4754],{"className":10633,"style":5122},[1213,1217],[1163,10635,10637],{"className":10636},[1221],[1163,10638,10640,10660],{"className":10639},[1225,1226],[1163,10641,10643,10657],{"className":10642},[1230],[1163,10644,10646],{"className":10645,"style":1235},[1234],[1163,10647,10648,10651],{"style":5138},[1163,10649],{"className":10650,"style":1243},[1242],[1163,10652,10654],{"className":10653},[1247,1248,1249,1250],[1163,10655,1190],{"className":10656},[1213,1217,1250],[1163,10658,1258],{"className":10659},[1257],[1163,10661,10663],{"className":10662},[1230],[1163,10664,10666],{"className":10665,"style":1265},[1234],[1163,10667],{},[1163,10669,1404],{"className":10670},[1776],[1163,10672],{"className":10673,"style":1534},[1460],[1163,10675,8494],{"className":10676},[1538],[1163,10678],{"className":10679,"style":1534},[1460],[1163,10681,10683,10686,10735,10738,10741],{"className":10682},[1204],[1163,10684],{"className":10685,"style":1548},[1208],[1163,10687,10689,10692],{"className":10688},[1213],[1163,10690,1187],{"className":10691},[1213,1217],[1163,10693,10695],{"className":10694},[1221],[1163,10696,10698,10727],{"className":10697},[1225,1226],[1163,10699,10701,10724],{"className":10700},[1230],[1163,10702,10704],{"className":10703,"style":1567},[1234],[1163,10705,10706,10709],{"style":1238},[1163,10707],{"className":10708,"style":1243},[1242],[1163,10710,10712],{"className":10711},[1247,1248,1249,1250],[1163,10713,10715,10718,10721],{"className":10714},[1213,1250],[1163,10716,1190],{"className":10717},[1213,1217,1250],[1163,10719,1366],{"className":10720},[1538,1250],[1163,10722,1370],{"className":10723},[1213,1250],[1163,10725,1258],{"className":10726},[1257],[1163,10728,10730],{"className":10729},[1230],[1163,10731,10733],{"className":10732,"style":1597},[1234],[1163,10734],{},[1163,10736],{"className":10737,"style":1534},[1460],[1163,10739,1373],{"className":10740},[1538],[1163,10742],{"className":10743,"style":1534},[1460],[1163,10745,10747,10750,10790,10793,10796],{"className":10746},[1204],[1163,10748],{"className":10749,"style":1677},[1208],[1163,10751,10753,10756],{"className":10752},[1213],[1163,10754,4754],{"className":10755,"style":5122},[1213,1217],[1163,10757,10759],{"className":10758},[1221],[1163,10760,10762,10782],{"className":10761},[1225,1226],[1163,10763,10765,10779],{"className":10764},[1230],[1163,10766,10768],{"className":10767,"style":1235},[1234],[1163,10769,10770,10773],{"style":5138},[1163,10771],{"className":10772,"style":1243},[1242],[1163,10774,10776],{"className":10775},[1247,1248,1249,1250],[1163,10777,1190],{"className":10778},[1213,1217,1250],[1163,10780,1258],{"className":10781},[1257],[1163,10783,10785],{"className":10784},[1230],[1163,10786,10788],{"className":10787,"style":1265},[1234],[1163,10789],{},[1163,10791],{"className":10792,"style":1534},[1460],[1163,10794,8494],{"className":10795},[1538],[1163,10797],{"className":10798,"style":1534},[1460],[1163,10800,10802,10805],{"className":10801},[1204],[1163,10803],{"className":10804,"style":10197},[1208],[1163,10806,10808,10839],{"className":10807},[1213],[1163,10809,10811],{"className":10810},[1213,3383],[1163,10812,10814],{"className":10813},[1225],[1163,10815,10817],{"className":10816},[1230],[1163,10818,10820,10828],{"className":10819,"style":10213},[1234],[1163,10821,10822,10825],{"style":3396},[1163,10823],{"className":10824,"style":3400},[1242],[1163,10826,1187],{"className":10827},[1213,1217],[1163,10829,10830,10833],{"style":10224},[1163,10831],{"className":10832,"style":3400},[1242],[1163,10834,10836],{"className":10835,"style":10231},[3412],[1163,10837,7639],{"className":10838},[1213],[1163,10840,10842],{"className":10841},[1221],[1163,10843,10845,10865],{"className":10844},[1225,1226],[1163,10846,10848,10862],{"className":10847},[1230],[1163,10849,10851],{"className":10850,"style":1235},[1234],[1163,10852,10853,10856],{"style":1238},[1163,10854],{"className":10855,"style":1243},[1242],[1163,10857,10859],{"className":10858},[1247,1248,1249,1250],[1163,10860,1190],{"className":10861},[1213,1217,1250],[1163,10863,1258],{"className":10864},[1257],[1163,10866,10868],{"className":10867},[1230],[1163,10869,10871],{"className":10870,"style":1265},[1234],[1163,10872],{},[1101,10874,10875],{},[1107,10876,10877],{},"直觉理解：",[1111,10879,10880,11141],{},[1114,10881,10882,2770,10884,10954,10955,11047,11048,11140],{},[1107,10883,9520],{},[1163,10885,10887,10905],{"className":10886},[1166],[1163,10888,10890],{"className":10889},[1170],[1172,10891,10892],{"xmlns":1174},[1176,10893,10894,10902],{},[1179,10895,10896],{},[1182,10897,10898,10900],{},[1185,10899,4754],{},[1185,10901,1190],{},[1192,10903,10904],{"encoding":1194},"z_t",[1163,10906,10908],{"className":10907,"ariaHidden":1200},[1199],[1163,10909,10911,10914],{"className":10910},[1204],[1163,10912],{"className":10913,"style":2115},[1208],[1163,10915,10917,10920],{"className":10916},[1213],[1163,10918,4754],{"className":10919,"style":5122},[1213,1217],[1163,10921,10923],{"className":10922},[1221],[1163,10924,10926,10946],{"className":10925},[1225,1226],[1163,10927,10929,10943],{"className":10928},[1230],[1163,10930,10932],{"className":10931,"style":1235},[1234],[1163,10933,10934,10937],{"style":5138},[1163,10935],{"className":10936,"style":1243},[1242],[1163,10938,10940],{"className":10939},[1247,1248,1249,1250],[1163,10941,1190],{"className":10942},[1213,1217,1250],[1163,10944,1258],{"className":10945},[1257],[1163,10947,10949],{"className":10948},[1230],[1163,10950,10952],{"className":10951,"style":1265},[1234],[1163,10953],{},"：决定\"保留多少旧状态 vs 接受多少新信息\"——当 ",[1163,10956,10958,10980],{"className":10957},[1166],[1163,10959,10961],{"className":10960},[1170],[1172,10962,10963],{"xmlns":1174},[1176,10964,10965,10977],{},[1179,10966,10967,10973,10975],{},[1182,10968,10969,10971],{},[1185,10970,4754],{},[1185,10972,1190],{},[1332,10974,1334],{},[1368,10976,6652],{},[1192,10978,10979],{"encoding":1194},"z_t = 0",[1163,10981,10983,11038],{"className":10982,"ariaHidden":1200},[1199],[1163,10984,10986,10989,11029,11032,11035],{"className":10985},[1204],[1163,10987],{"className":10988,"style":2115},[1208],[1163,10990,10992,10995],{"className":10991},[1213],[1163,10993,4754],{"className":10994,"style":5122},[1213,1217],[1163,10996,10998],{"className":10997},[1221],[1163,10999,11001,11021],{"className":11000},[1225,1226],[1163,11002,11004,11018],{"className":11003},[1230],[1163,11005,11007],{"className":11006,"style":1235},[1234],[1163,11008,11009,11012],{"style":5138},[1163,11010],{"className":11011,"style":1243},[1242],[1163,11013,11015],{"className":11014},[1247,1248,1249,1250],[1163,11016,1190],{"className":11017},[1213,1217,1250],[1163,11019,1258],{"className":11020},[1257],[1163,11022,11024],{"className":11023},[1230],[1163,11025,11027],{"className":11026,"style":1265},[1234],[1163,11028],{},[1163,11030],{"className":11031,"style":1461},[1460],[1163,11033,1334],{"className":11034},[1465],[1163,11036],{"className":11037,"style":1461},[1460],[1163,11039,11041,11044],{"className":11040},[1204],[1163,11042],{"className":11043,"style":3572},[1208],[1163,11045,6652],{"className":11046},[1213]," 时完全保留旧状态，",[1163,11049,11051,11073],{"className":11050},[1166],[1163,11052,11054],{"className":11053},[1170],[1172,11055,11056],{"xmlns":1174},[1176,11057,11058,11070],{},[1179,11059,11060,11066,11068],{},[1182,11061,11062,11064],{},[1185,11063,4754],{},[1185,11065,1190],{},[1332,11067,1334],{},[1368,11069,1370],{},[1192,11071,11072],{"encoding":1194},"z_t = 1",[1163,11074,11076,11131],{"className":11075,"ariaHidden":1200},[1199],[1163,11077,11079,11082,11122,11125,11128],{"className":11078},[1204],[1163,11080],{"className":11081,"style":2115},[1208],[1163,11083,11085,11088],{"className":11084},[1213],[1163,11086,4754],{"className":11087,"style":5122},[1213,1217],[1163,11089,11091],{"className":11090},[1221],[1163,11092,11094,11114],{"className":11093},[1225,1226],[1163,11095,11097,11111],{"className":11096},[1230],[1163,11098,11100],{"className":11099,"style":1235},[1234],[1163,11101,11102,11105],{"style":5138},[1163,11103],{"className":11104,"style":1243},[1242],[1163,11106,11108],{"className":11107},[1247,1248,1249,1250],[1163,11109,1190],{"className":11110},[1213,1217,1250],[1163,11112,1258],{"className":11113},[1257],[1163,11115,11117],{"className":11116},[1230],[1163,11118,11120],{"className":11119,"style":1265},[1234],[1163,11121],{},[1163,11123],{"className":11124,"style":1461},[1460],[1163,11126,1334],{"className":11127},[1465],[1163,11129],{"className":11130,"style":1461},[1460],[1163,11132,11134,11137],{"className":11133},[1204],[1163,11135],{"className":11136,"style":3572},[1208],[1163,11138,1370],{"className":11139},[1213]," 时完全使用新候选值",[1114,11142,11143,2770,11145,11215,11216,11308],{},[1107,11144,9816],{},[1163,11146,11148,11166],{"className":11147},[1166],[1163,11149,11151],{"className":11150},[1170],[1172,11152,11153],{"xmlns":1174},[1176,11154,11155,11163],{},[1179,11156,11157],{},[1182,11158,11159,11161],{},[1185,11160,9836],{},[1185,11162,1190],{},[1192,11164,11165],{"encoding":1194},"r_t",[1163,11167,11169],{"className":11168,"ariaHidden":1200},[1199],[1163,11170,11172,11175],{"className":11171},[1204],[1163,11173],{"className":11174,"style":2115},[1208],[1163,11176,11178,11181],{"className":11177},[1213],[1163,11179,9836],{"className":11180,"style":9897},[1213,1217],[1163,11182,11184],{"className":11183},[1221],[1163,11185,11187,11207],{"className":11186},[1225,1226],[1163,11188,11190,11204],{"className":11189},[1230],[1163,11191,11193],{"className":11192,"style":1235},[1234],[1163,11194,11195,11198],{"style":9912},[1163,11196],{"className":11197,"style":1243},[1242],[1163,11199,11201],{"className":11200},[1247,1248,1249,1250],[1163,11202,1190],{"className":11203},[1213,1217,1250],[1163,11205,1258],{"className":11206},[1257],[1163,11208,11210],{"className":11209},[1230],[1163,11211,11213],{"className":11212,"style":1265},[1234],[1163,11214],{},"：决定计算候选值时\"参考多少历史\"——当 ",[1163,11217,11219,11241],{"className":11218},[1166],[1163,11220,11222],{"className":11221},[1170],[1172,11223,11224],{"xmlns":1174},[1176,11225,11226,11238],{},[1179,11227,11228,11234,11236],{},[1182,11229,11230,11232],{},[1185,11231,9836],{},[1185,11233,1190],{},[1332,11235,1334],{},[1368,11237,6652],{},[1192,11239,11240],{"encoding":1194},"r_t = 0",[1163,11242,11244,11299],{"className":11243,"ariaHidden":1200},[1199],[1163,11245,11247,11250,11290,11293,11296],{"className":11246},[1204],[1163,11248],{"className":11249,"style":2115},[1208],[1163,11251,11253,11256],{"className":11252},[1213],[1163,11254,9836],{"className":11255,"style":9897},[1213,1217],[1163,11257,11259],{"className":11258},[1221],[1163,11260,11262,11282],{"className":11261},[1225,1226],[1163,11263,11265,11279],{"className":11264},[1230],[1163,11266,11268],{"className":11267,"style":1235},[1234],[1163,11269,11270,11273],{"style":9912},[1163,11271],{"className":11272,"style":1243},[1242],[1163,11274,11276],{"className":11275},[1247,1248,1249,1250],[1163,11277,1190],{"className":11278},[1213,1217,1250],[1163,11280,1258],{"className":11281},[1257],[1163,11283,11285],{"className":11284},[1230],[1163,11286,11288],{"className":11287,"style":1265},[1234],[1163,11289],{},[1163,11291],{"className":11292,"style":1461},[1460],[1163,11294,1334],{"className":11295},[1465],[1163,11297],{"className":11298,"style":1461},[1460],[1163,11300,11302,11305],{"className":11301},[1204],[1163,11303],{"className":11304,"style":3572},[1208],[1163,11306,6652],{"className":11307},[1213]," 时忽略历史，相当于从头开始",[1096,11310,11312],{"id":11311},"_42-lstm-与-gru-的对比","4.2 LSTM 与 GRU 的对比",[2062,11314,11315,11328],{},[2065,11316,11317],{},[2068,11318,11319,11322,11325],{},[2071,11320,11321],{},"特性",[2071,11323,11324],{},"LSTM",[2071,11326,11327],{},"GRU",[2078,11329,11330,11343,11564,11857,11870,11883,11896,11909],{},[2068,11331,11332,11337,11340],{},[2083,11333,11334],{},[1107,11335,11336],{},"门的数量",[2083,11338,11339],{},"3 个（遗忘、输入、输出）",[2083,11341,11342],{},"2 个（更新、重置）",[2068,11344,11345,11350,11492],{},[2083,11346,11347],{},[1107,11348,11349],{},"状态",[2083,11351,11352,11353,11422,11423],{},"细胞状态 ",[1163,11354,11356,11373],{"className":11355},[1166],[1163,11357,11359],{"className":11358},[1170],[1172,11360,11361],{"xmlns":1174},[1176,11362,11363,11371],{},[1179,11364,11365],{},[1182,11366,11367,11369],{},[1185,11368,6558],{},[1185,11370,1190],{},[1192,11372,6563],{"encoding":1194},[1163,11374,11376],{"className":11375,"ariaHidden":1200},[1199],[1163,11377,11379,11382],{"className":11378},[1204],[1163,11380],{"className":11381,"style":1615},[1208],[1163,11383,11385,11388],{"className":11384},[1213],[1163,11386,6558],{"className":11387,"style":6579},[1213,1217],[1163,11389,11391],{"className":11390},[1221],[1163,11392,11394,11414],{"className":11393},[1225,1226],[1163,11395,11397,11411],{"className":11396},[1230],[1163,11398,11400],{"className":11399,"style":1235},[1234],[1163,11401,11402,11405],{"style":6594},[1163,11403],{"className":11404,"style":1243},[1242],[1163,11406,11408],{"className":11407},[1247,1248,1249,1250],[1163,11409,1190],{"className":11410},[1213,1217,1250],[1163,11412,1258],{"className":11413},[1257],[1163,11415,11417],{"className":11416},[1230],[1163,11418,11420],{"className":11419,"style":1265},[1234],[1163,11421],{}," + 隐藏状态 ",[1163,11424,11426,11443],{"className":11425},[1166],[1163,11427,11429],{"className":11428},[1170],[1172,11430,11431],{"xmlns":1174},[1176,11432,11433,11441],{},[1179,11434,11435],{},[1182,11436,11437,11439],{},[1185,11438,1187],{},[1185,11440,1190],{},[1192,11442,1195],{"encoding":1194},[1163,11444,11446],{"className":11445,"ariaHidden":1200},[1199],[1163,11447,11449,11452],{"className":11448},[1204],[1163,11450],{"className":11451,"style":1209},[1208],[1163,11453,11455,11458],{"className":11454},[1213],[1163,11456,1187],{"className":11457},[1213,1217],[1163,11459,11461],{"className":11460},[1221],[1163,11462,11464,11484],{"className":11463},[1225,1226],[1163,11465,11467,11481],{"className":11466},[1230],[1163,11468,11470],{"className":11469,"style":1235},[1234],[1163,11471,11472,11475],{"style":1238},[1163,11473],{"className":11474,"style":1243},[1242],[1163,11476,11478],{"className":11477},[1247,1248,1249,1250],[1163,11479,1190],{"className":11480},[1213,1217,1250],[1163,11482,1258],{"className":11483},[1257],[1163,11485,11487],{"className":11486},[1230],[1163,11488,11490],{"className":11489,"style":1265},[1234],[1163,11491],{},[2083,11493,11494,11495],{},"仅隐藏状态 ",[1163,11496,11498,11515],{"className":11497},[1166],[1163,11499,11501],{"className":11500},[1170],[1172,11502,11503],{"xmlns":1174},[1176,11504,11505,11513],{},[1179,11506,11507],{},[1182,11508,11509,11511],{},[1185,11510,1187],{},[1185,11512,1190],{},[1192,11514,1195],{"encoding":1194},[1163,11516,11518],{"className":11517,"ariaHidden":1200},[1199],[1163,11519,11521,11524],{"className":11520},[1204],[1163,11522],{"className":11523,"style":1209},[1208],[1163,11525,11527,11530],{"className":11526},[1213],[1163,11528,1187],{"className":11529},[1213,1217],[1163,11531,11533],{"className":11532},[1221],[1163,11534,11536,11556],{"className":11535},[1225,1226],[1163,11537,11539,11553],{"className":11538},[1230],[1163,11540,11542],{"className":11541,"style":1235},[1234],[1163,11543,11544,11547],{"style":1238},[1163,11545],{"className":11546,"style":1243},[1242],[1163,11548,11550],{"className":11549},[1247,1248,1249,1250],[1163,11551,1190],{"className":11552},[1213,1217,1250],[1163,11554,1258],{"className":11555},[1257],[1163,11557,11559],{"className":11558},[1230],[1163,11560,11562],{"className":11561,"style":1265},[1234],[1163,11563],{},[2068,11565,11566,11571,11717],{},[2083,11567,11568],{},[1107,11569,11570],{},"参数量",[2083,11572,11573],{},[1163,11574,11576,11615],{"className":11575},[1166],[1163,11577,11579],{"className":11578},[1170],[1172,11580,11581],{"xmlns":1174},[1176,11582,11583,11612],{},[1179,11584,11585,11588,11590,11592,11599,11601,11603,11606,11608,11610],{},[1368,11586,11587],{},"4",[1332,11589,6373],{},[1332,11591,1341],{"stretchy":1340},[4740,11593,11594,11597],{},[1185,11595,11596],{},"n",[1368,11598,3035],{},[1332,11600,1373],{},[1185,11602,11596],{},[1185,11604,11605],{},"m",[1332,11607,1373],{},[1185,11609,11596],{},[1332,11611,1404],{"stretchy":1340},[1192,11613,11614],{"encoding":1194},"4 \\times (n^2 + nm + n)",[1163,11616,11618,11637,11685,11705],{"className":11617,"ariaHidden":1200},[1199],[1163,11619,11621,11625,11628,11631,11634],{"className":11620},[1204],[1163,11622],{"className":11623,"style":11624},[1208],"height:0.7278em;vertical-align:-0.0833em;",[1163,11626,11587],{"className":11627},[1213],[1163,11629],{"className":11630,"style":1534},[1460],[1163,11632,6373],{"className":11633},[1538],[1163,11635],{"className":11636,"style":1534},[1460],[1163,11638,11640,11644,11647,11676,11679,11682],{"className":11639},[1204],[1163,11641],{"className":11642,"style":11643},[1208],"height:1.0641em;vertical-align:-0.25em;",[1163,11645,1341],{"className":11646},[1483],[1163,11648,11650,11653],{"className":11649},[1213],[1163,11651,11596],{"className":11652},[1213,1217],[1163,11654,11656],{"className":11655},[1221],[1163,11657,11659],{"className":11658},[1225],[1163,11660,11662],{"className":11661},[1230],[1163,11663,11665],{"className":11664,"style":6109},[1234],[1163,11666,11667,11670],{"style":5100},[1163,11668],{"className":11669,"style":1243},[1242],[1163,11671,11673],{"className":11672},[1247,1248,1249,1250],[1163,11674,3035],{"className":11675},[1213,1250],[1163,11677],{"className":11678,"style":1534},[1460],[1163,11680,1373],{"className":11681},[1538],[1163,11683],{"className":11684,"style":1534},[1460],[1163,11686,11688,11692,11696,11699,11702],{"className":11687},[1204],[1163,11689],{"className":11690,"style":11691},[1208],"height:0.6667em;vertical-align:-0.0833em;",[1163,11693,11695],{"className":11694},[1213,1217],"nm",[1163,11697],{"className":11698,"style":1534},[1460],[1163,11700,1373],{"className":11701},[1538],[1163,11703],{"className":11704,"style":1534},[1460],[1163,11706,11708,11711,11714],{"className":11707},[1204],[1163,11709],{"className":11710,"style":1475},[1208],[1163,11712,11596],{"className":11713},[1213,1217],[1163,11715,1404],{"className":11716},[1776],[2083,11718,11719],{},[1163,11720,11722,11759],{"className":11721},[1166],[1163,11723,11725],{"className":11724},[1170],[1172,11726,11727],{"xmlns":1174},[1176,11728,11729,11756],{},[1179,11730,11731,11734,11736,11738,11744,11746,11748,11750,11752,11754],{},[1368,11732,11733],{},"3",[1332,11735,6373],{},[1332,11737,1341],{"stretchy":1340},[4740,11739,11740,11742],{},[1185,11741,11596],{},[1368,11743,3035],{},[1332,11745,1373],{},[1185,11747,11596],{},[1185,11749,11605],{},[1332,11751,1373],{},[1185,11753,11596],{},[1332,11755,1404],{"stretchy":1340},[1192,11757,11758],{"encoding":1194},"3 \\times (n^2 + nm + n)",[1163,11760,11762,11780,11827,11845],{"className":11761,"ariaHidden":1200},[1199],[1163,11763,11765,11768,11771,11774,11777],{"className":11764},[1204],[1163,11766],{"className":11767,"style":11624},[1208],[1163,11769,11733],{"className":11770},[1213],[1163,11772],{"className":11773,"style":1534},[1460],[1163,11775,6373],{"className":11776},[1538],[1163,11778],{"className":11779,"style":1534},[1460],[1163,11781,11783,11786,11789,11818,11821,11824],{"className":11782},[1204],[1163,11784],{"className":11785,"style":11643},[1208],[1163,11787,1341],{"className":11788},[1483],[1163,11790,11792,11795],{"className":11791},[1213],[1163,11793,11596],{"className":11794},[1213,1217],[1163,11796,11798],{"className":11797},[1221],[1163,11799,11801],{"className":11800},[1225],[1163,11802,11804],{"className":11803},[1230],[1163,11805,11807],{"className":11806,"style":6109},[1234],[1163,11808,11809,11812],{"style":5100},[1163,11810],{"className":11811,"style":1243},[1242],[1163,11813,11815],{"className":11814},[1247,1248,1249,1250],[1163,11816,3035],{"className":11817},[1213,1250],[1163,11819],{"className":11820,"style":1534},[1460],[1163,11822,1373],{"className":11823},[1538],[1163,11825],{"className":11826,"style":1534},[1460],[1163,11828,11830,11833,11836,11839,11842],{"className":11829},[1204],[1163,11831],{"className":11832,"style":11691},[1208],[1163,11834,11695],{"className":11835},[1213,1217],[1163,11837],{"className":11838,"style":1534},[1460],[1163,11840,1373],{"className":11841},[1538],[1163,11843],{"className":11844,"style":1534},[1460],[1163,11846,11848,11851,11854],{"className":11847},[1204],[1163,11849],{"className":11850,"style":1475},[1208],[1163,11852,11596],{"className":11853},[1213,1217],[1163,11855,1404],{"className":11856},[1776],[2068,11858,11859,11864,11867],{},[2083,11860,11861],{},[1107,11862,11863],{},"计算复杂度",[2083,11865,11866],{},"较高（更多矩阵运算）",[2083,11868,11869],{},"较低（约 LSTM 的 75%）",[2068,11871,11872,11877,11880],{},[2083,11873,11874],{},[1107,11875,11876],{},"长序列建模",[2083,11878,11879],{},"略优（独立的细胞状态通道）",[2083,11881,11882],{},"稍逊",[2068,11884,11885,11890,11893],{},[2083,11886,11887],{},[1107,11888,11889],{},"训练速度",[2083,11891,11892],{},"较慢",[2083,11894,11895],{},"较快",[2068,11897,11898,11903,11906],{},[2083,11899,11900],{},[1107,11901,11902],{},"适用场景",[2083,11904,11905],{},"长序列、需要精细记忆控制",[2083,11907,11908],{},"中等序列、计算资源有限",[2068,11910,11911,11916,11919],{},[2083,11912,11913],{},[1107,11914,11915],{},"输出暴露",[2083,11917,11918],{},"通过输出门过滤",[2083,11920,11921],{},"直接暴露全部状态",[4645,11923],{},[1091,11925,11927],{"id":11926},"五rnn-应用模式","五、RNN 应用模式",[1096,11929,11931],{"id":11930},"_51-四种基本模式","5.1 四种基本模式",[1101,11933,11934],{},[1107,11935,11936],{},"Many-to-One（序列分类）",[1101,11938,11939,11940],{},"输入：整个序列 ",[1163,11941,11943,11981],{"className":11942},[1166],[1163,11944,11946],{"className":11945},[1170],[1172,11947,11948],{"xmlns":1174},[1176,11949,11950,11978],{},[1179,11951,11952,11958,11960,11966,11968,11970,11972],{},[1182,11953,11954,11956],{},[1185,11955,1382],{},[1368,11957,1370],{},[1332,11959,2609],{"separator":1200},[1182,11961,11962,11964],{},[1185,11963,1382],{},[1368,11965,3035],{},[1332,11967,2609],{"separator":1200},[1332,11969,3040],{},[1332,11971,2609],{"separator":1200},[1182,11973,11974,11976],{},[1185,11975,1382],{},[1185,11977,3045],{},[1192,11979,11980],{"encoding":1194},"x_1, x_2, \\ldots, x_T",[1163,11982,11984],{"className":11983,"ariaHidden":1200},[1199],[1163,11985,11987,11990,12030,12033,12036,12076,12079,12082,12085,12088,12091,12094],{"className":11986},[1204],[1163,11988],{"className":11989,"style":1839},[1208],[1163,11991,11993,11996],{"className":11992},[1213],[1163,11994,1382],{"className":11995},[1213,1217],[1163,11997,11999],{"className":11998},[1221],[1163,12000,12002,12022],{"className":12001},[1225,1226],[1163,12003,12005,12019],{"className":12004},[1230],[1163,12006,12008],{"className":12007,"style":1567},[1234],[1163,12009,12010,12013],{"style":1238},[1163,12011],{"className":12012,"style":1243},[1242],[1163,12014,12016],{"className":12015},[1247,1248,1249,1250],[1163,12017,1370],{"className":12018},[1213,1250],[1163,12020,1258],{"className":12021},[1257],[1163,12023,12025],{"className":12024},[1230],[1163,12026,12028],{"className":12027,"style":1265},[1234],[1163,12029],{},[1163,12031,2609],{"className":12032},[2671],[1163,12034],{"className":12035,"style":2675},[1460],[1163,12037,12039,12042],{"className":12038},[1213],[1163,12040,1382],{"className":12041},[1213,1217],[1163,12043,12045],{"className":12044},[1221],[1163,12046,12048,12068],{"className":12047},[1225,1226],[1163,12049,12051,12065],{"className":12050},[1230],[1163,12052,12054],{"className":12053,"style":1567},[1234],[1163,12055,12056,12059],{"style":1238},[1163,12057],{"className":12058,"style":1243},[1242],[1163,12060,12062],{"className":12061},[1247,1248,1249,1250],[1163,12063,3035],{"className":12064},[1213,1250],[1163,12066,1258],{"className":12067},[1257],[1163,12069,12071],{"className":12070},[1230],[1163,12072,12074],{"className":12073,"style":1265},[1234],[1163,12075],{},[1163,12077,2609],{"className":12078},[2671],[1163,12080],{"className":12081,"style":2675},[1460],[1163,12083,3040],{"className":12084},[3099],[1163,12086],{"className":12087,"style":2675},[1460],[1163,12089,2609],{"className":12090},[2671],[1163,12092],{"className":12093,"style":2675},[1460],[1163,12095,12097,12100],{"className":12096},[1213],[1163,12098,1382],{"className":12099},[1213,1217],[1163,12101,12103],{"className":12102},[1221],[1163,12104,12106,12126],{"className":12105},[1225,1226],[1163,12107,12109,12123],{"className":12108},[1230],[1163,12110,12112],{"className":12111,"style":7817},[1234],[1163,12113,12114,12117],{"style":1238},[1163,12115],{"className":12116,"style":1243},[1242],[1163,12118,12120],{"className":12119},[1247,1248,1249,1250],[1163,12121,3045],{"className":12122,"style":1490},[1213,1217,1250],[1163,12124,1258],{"className":12125},[1257],[1163,12127,12129],{"className":12128},[1230],[1163,12130,12132],{"className":12131,"style":1265},[1234],[1163,12133],{},[1101,12135,12136,12137],{},"输出：单个标签 ",[1163,12138,12140,12153],{"className":12139},[1166],[1163,12141,12143],{"className":12142},[1170],[1172,12144,12145],{"xmlns":1174},[1176,12146,12147,12151],{},[1179,12148,12149],{},[1185,12150,1796],{},[1192,12152,1796],{"encoding":1194},[1163,12154,12156],{"className":12155,"ariaHidden":1200},[1199],[1163,12157,12159,12162],{"className":12158},[1204],[1163,12160],{"className":12161,"style":1839},[1208],[1163,12163,1796],{"className":12164,"style":1479},[1213,1217],[1101,12166,12167],{},"典型应用：情感分析、文档分类",[1101,12169,12170,12171,12241],{},"方法：取最后时刻隐藏状态 ",[1163,12172,12174,12192],{"className":12173},[1166],[1163,12175,12177],{"className":12176},[1170],[1172,12178,12179],{"xmlns":1174},[1176,12180,12181,12189],{},[1179,12182,12183],{},[1182,12184,12185,12187],{},[1185,12186,1187],{},[1185,12188,3045],{},[1192,12190,12191],{"encoding":1194},"h_T",[1163,12193,12195],{"className":12194,"ariaHidden":1200},[1199],[1163,12196,12198,12201],{"className":12197},[1204],[1163,12199],{"className":12200,"style":1209},[1208],[1163,12202,12204,12207],{"className":12203},[1213],[1163,12205,1187],{"className":12206},[1213,1217],[1163,12208,12210],{"className":12209},[1221],[1163,12211,12213,12233],{"className":12212},[1225,1226],[1163,12214,12216,12230],{"className":12215},[1230],[1163,12217,12219],{"className":12218,"style":7817},[1234],[1163,12220,12221,12224],{"style":1238},[1163,12222],{"className":12223,"style":1243},[1242],[1163,12225,12227],{"className":12226},[1247,1248,1249,1250],[1163,12228,3045],{"className":12229,"style":1490},[1213,1217,1250],[1163,12231,1258],{"className":12232},[1257],[1163,12234,12236],{"className":12235},[1230],[1163,12237,12239],{"className":12238,"style":1265},[1234],[1163,12240],{}," 进行分类",[1101,12243,12244],{},[1107,12245,12246],{},"One-to-Many（序列生成）",[1101,12248,12249,12250,12278],{},"输入：单个向量 ",[1163,12251,12253,12266],{"className":12252},[1166],[1163,12254,12256],{"className":12255},[1170],[1172,12257,12258],{"xmlns":1174},[1176,12259,12260,12264],{},[1179,12261,12262],{},[1185,12263,1382],{},[1192,12265,1382],{"encoding":1194},[1163,12267,12269],{"className":12268,"ariaHidden":1200},[1199],[1163,12270,12272,12275],{"className":12271},[1204],[1163,12273],{"className":12274,"style":2749},[1208],[1163,12276,1382],{"className":12277},[1213,1217],"（如图像特征）",[1101,12280,12281,12282],{},"输出：序列 ",[1163,12283,12285,12323],{"className":12284},[1166],[1163,12286,12288],{"className":12287},[1170],[1172,12289,12290],{"xmlns":1174},[1176,12291,12292,12320],{},[1179,12293,12294,12300,12302,12308,12310,12312,12314],{},[1182,12295,12296,12298],{},[1185,12297,1796],{},[1368,12299,1370],{},[1332,12301,2609],{"separator":1200},[1182,12303,12304,12306],{},[1185,12305,1796],{},[1368,12307,3035],{},[1332,12309,2609],{"separator":1200},[1332,12311,3040],{},[1332,12313,2609],{"separator":1200},[1182,12315,12316,12318],{},[1185,12317,1796],{},[1185,12319,3045],{},[1192,12321,12322],{"encoding":1194},"y_1, y_2, \\ldots, y_T",[1163,12324,12326],{"className":12325,"ariaHidden":1200},[1199],[1163,12327,12329,12332,12372,12375,12378,12418,12421,12424,12427,12430,12433,12436],{"className":12328},[1204],[1163,12330],{"className":12331,"style":1839},[1208],[1163,12333,12335,12338],{"className":12334},[1213],[1163,12336,1796],{"className":12337,"style":1479},[1213,1217],[1163,12339,12341],{"className":12340},[1221],[1163,12342,12344,12364],{"className":12343},[1225,1226],[1163,12345,12347,12361],{"className":12346},[1230],[1163,12348,12350],{"className":12349,"style":1567},[1234],[1163,12351,12352,12355],{"style":1860},[1163,12353],{"className":12354,"style":1243},[1242],[1163,12356,12358],{"className":12357},[1247,1248,1249,1250],[1163,12359,1370],{"className":12360},[1213,1250],[1163,12362,1258],{"className":12363},[1257],[1163,12365,12367],{"className":12366},[1230],[1163,12368,12370],{"className":12369,"style":1265},[1234],[1163,12371],{},[1163,12373,2609],{"className":12374},[2671],[1163,12376],{"className":12377,"style":2675},[1460],[1163,12379,12381,12384],{"className":12380},[1213],[1163,12382,1796],{"className":12383,"style":1479},[1213,1217],[1163,12385,12387],{"className":12386},[1221],[1163,12388,12390,12410],{"className":12389},[1225,1226],[1163,12391,12393,12407],{"className":12392},[1230],[1163,12394,12396],{"className":12395,"style":1567},[1234],[1163,12397,12398,12401],{"style":1860},[1163,12399],{"className":12400,"style":1243},[1242],[1163,12402,12404],{"className":12403},[1247,1248,1249,1250],[1163,12405,3035],{"className":12406},[1213,1250],[1163,12408,1258],{"className":12409},[1257],[1163,12411,12413],{"className":12412},[1230],[1163,12414,12416],{"className":12415,"style":1265},[1234],[1163,12417],{},[1163,12419,2609],{"className":12420},[2671],[1163,12422],{"className":12423,"style":2675},[1460],[1163,12425,3040],{"className":12426},[3099],[1163,12428],{"className":12429,"style":2675},[1460],[1163,12431,2609],{"className":12432},[2671],[1163,12434],{"className":12435,"style":2675},[1460],[1163,12437,12439,12442],{"className":12438},[1213],[1163,12440,1796],{"className":12441,"style":1479},[1213,1217],[1163,12443,12445],{"className":12444},[1221],[1163,12446,12448,12468],{"className":12447},[1225,1226],[1163,12449,12451,12465],{"className":12450},[1230],[1163,12452,12454],{"className":12453,"style":7817},[1234],[1163,12455,12456,12459],{"style":1860},[1163,12457],{"className":12458,"style":1243},[1242],[1163,12460,12462],{"className":12461},[1247,1248,1249,1250],[1163,12463,3045],{"className":12464,"style":1490},[1213,1217,1250],[1163,12466,1258],{"className":12467},[1257],[1163,12469,12471],{"className":12470},[1230],[1163,12472,12474],{"className":12473,"style":1265},[1234],[1163,12475],{},[1101,12477,12478],{},"典型应用：图像描述生成、音乐生成",[1101,12480,12481],{},"方法：初始输入驱动，逐步生成",[1101,12483,12484],{},[1107,12485,12486],{},"Many-to-Many（Seq2Seq）",[1101,12488,12489,12490],{},"输入：序列 ",[1163,12491,12493,12523],{"className":12492},[1166],[1163,12494,12496],{"className":12495},[1170],[1172,12497,12498],{"xmlns":1174},[1176,12499,12500,12520],{},[1179,12501,12502,12508,12510,12512,12514],{},[1182,12503,12504,12506],{},[1185,12505,1382],{},[1368,12507,1370],{},[1332,12509,2609],{"separator":1200},[1332,12511,3040],{},[1332,12513,2609],{"separator":1200},[1182,12515,12516,12518],{},[1185,12517,1382],{},[1185,12519,3045],{},[1192,12521,12522],{"encoding":1194},"x_1, \\ldots, x_T",[1163,12524,12526],{"className":12525,"ariaHidden":1200},[1199],[1163,12527,12529,12532,12572,12575,12578,12581,12584,12587,12590],{"className":12528},[1204],[1163,12530],{"className":12531,"style":1839},[1208],[1163,12533,12535,12538],{"className":12534},[1213],[1163,12536,1382],{"className":12537},[1213,1217],[1163,12539,12541],{"className":12540},[1221],[1163,12542,12544,12564],{"className":12543},[1225,1226],[1163,12545,12547,12561],{"className":12546},[1230],[1163,12548,12550],{"className":12549,"style":1567},[1234],[1163,12551,12552,12555],{"style":1238},[1163,12553],{"className":12554,"style":1243},[1242],[1163,12556,12558],{"className":12557},[1247,1248,1249,1250],[1163,12559,1370],{"className":12560},[1213,1250],[1163,12562,1258],{"className":12563},[1257],[1163,12565,12567],{"className":12566},[1230],[1163,12568,12570],{"className":12569,"style":1265},[1234],[1163,12571],{},[1163,12573,2609],{"className":12574},[2671],[1163,12576],{"className":12577,"style":2675},[1460],[1163,12579,3040],{"className":12580},[3099],[1163,12582],{"className":12583,"style":2675},[1460],[1163,12585,2609],{"className":12586},[2671],[1163,12588],{"className":12589,"style":2675},[1460],[1163,12591,12593,12596],{"className":12592},[1213],[1163,12594,1382],{"className":12595},[1213,1217],[1163,12597,12599],{"className":12598},[1221],[1163,12600,12602,12622],{"className":12601},[1225,1226],[1163,12603,12605,12619],{"className":12604},[1230],[1163,12606,12608],{"className":12607,"style":7817},[1234],[1163,12609,12610,12613],{"style":1238},[1163,12611],{"className":12612,"style":1243},[1242],[1163,12614,12616],{"className":12615},[1247,1248,1249,1250],[1163,12617,3045],{"className":12618,"style":1490},[1213,1217,1250],[1163,12620,1258],{"className":12621},[1257],[1163,12623,12625],{"className":12624},[1230],[1163,12626,12628],{"className":12627,"style":1265},[1234],[1163,12629],{},[1101,12631,12632,12633],{},"输出：不同长度序列 ",[1163,12634,12636,12670],{"className":12635},[1166],[1163,12637,12639],{"className":12638},[1170],[1172,12640,12641],{"xmlns":1174},[1176,12642,12643,12667],{},[1179,12644,12645,12651,12653,12655,12657],{},[1182,12646,12647,12649],{},[1185,12648,1796],{},[1368,12650,1370],{},[1332,12652,2609],{"separator":1200},[1332,12654,3040],{},[1332,12656,2609],{"separator":1200},[1182,12658,12659,12661],{},[1185,12660,1796],{},[4740,12662,12663,12665],{},[1185,12664,3045],{},[1332,12666,4747],{"mathvariant":3684,"lspace":4746,"rspace":4746},[1192,12668,12669],{"encoding":1194},"y_1, \\ldots, y_{T'}",[1163,12671,12673],{"className":12672,"ariaHidden":1200},[1199],[1163,12674,12676,12679,12719,12722,12725,12728,12731,12734,12737],{"className":12675},[1204],[1163,12677],{"className":12678,"style":1839},[1208],[1163,12680,12682,12685],{"className":12681},[1213],[1163,12683,1796],{"className":12684,"style":1479},[1213,1217],[1163,12686,12688],{"className":12687},[1221],[1163,12689,12691,12711],{"className":12690},[1225,1226],[1163,12692,12694,12708],{"className":12693},[1230],[1163,12695,12697],{"className":12696,"style":1567},[1234],[1163,12698,12699,12702],{"style":1860},[1163,12700],{"className":12701,"style":1243},[1242],[1163,12703,12705],{"className":12704},[1247,1248,1249,1250],[1163,12706,1370],{"className":12707},[1213,1250],[1163,12709,1258],{"className":12710},[1257],[1163,12712,12714],{"className":12713},[1230],[1163,12715,12717],{"className":12716,"style":1265},[1234],[1163,12718],{},[1163,12720,2609],{"className":12721},[2671],[1163,12723],{"className":12724,"style":2675},[1460],[1163,12726,3040],{"className":12727},[3099],[1163,12729],{"className":12730,"style":2675},[1460],[1163,12732,2609],{"className":12733},[2671],[1163,12735],{"className":12736,"style":2675},[1460],[1163,12738,12740,12743],{"className":12739},[1213],[1163,12741,1796],{"className":12742,"style":1479},[1213,1217],[1163,12744,12746],{"className":12745},[1221],[1163,12747,12749,12803],{"className":12748},[1225,1226],[1163,12750,12752,12800],{"className":12751},[1230],[1163,12753,12755],{"className":12754,"style":7817},[1234],[1163,12756,12757,12760],{"style":1860},[1163,12758],{"className":12759,"style":1243},[1242],[1163,12761,12763],{"className":12762},[1247,1248,1249,1250],[1163,12764,12766],{"className":12765},[1213,1250],[1163,12767,12769,12772],{"className":12768},[1213,1250],[1163,12770,3045],{"className":12771,"style":1490},[1213,1217,1250],[1163,12773,12775],{"className":12774},[1221],[1163,12776,12778],{"className":12777},[1225],[1163,12779,12781],{"className":12780},[1230],[1163,12782,12785],{"className":12783,"style":12784},[1234],"height:0.6828em;",[1163,12786,12788,12791],{"style":12787},"top:-2.786em;margin-right:0.0714em;",[1163,12789],{"className":12790,"style":3881},[1242],[1163,12792,12794],{"className":12793},[1247,3885,3886,1250],[1163,12795,12797],{"className":12796},[1213,1250],[1163,12798,4747],{"className":12799},[1213,1250],[1163,12801,1258],{"className":12802},[1257],[1163,12804,12806],{"className":12805},[1230],[1163,12807,12809],{"className":12808,"style":1265},[1234],[1163,12810],{},[1101,12812,12813],{},"典型应用：机器翻译、文本摘要",[1101,12815,12816],{},"方法：Encoder-Decoder 架构",[1101,12818,12819],{},[1107,12820,12821],{},"Many-to-Many Synced（序列标注）",[1101,12823,12489,12824],{},[1163,12825,12827,12864],{"className":12826},[1166],[1163,12828,12830],{"className":12829},[1170],[1172,12831,12832],{"xmlns":1174},[1176,12833,12834,12862],{},[1179,12835,12836,12842,12844,12850,12852,12854,12856],{},[1182,12837,12838,12840],{},[1185,12839,1382],{},[1368,12841,1370],{},[1332,12843,2609],{"separator":1200},[1182,12845,12846,12848],{},[1185,12847,1382],{},[1368,12849,3035],{},[1332,12851,2609],{"separator":1200},[1332,12853,3040],{},[1332,12855,2609],{"separator":1200},[1182,12857,12858,12860],{},[1185,12859,1382],{},[1185,12861,3045],{},[1192,12863,11980],{"encoding":1194},[1163,12865,12867],{"className":12866,"ariaHidden":1200},[1199],[1163,12868,12870,12873,12913,12916,12919,12959,12962,12965,12968,12971,12974,12977],{"className":12869},[1204],[1163,12871],{"className":12872,"style":1839},[1208],[1163,12874,12876,12879],{"className":12875},[1213],[1163,12877,1382],{"className":12878},[1213,1217],[1163,12880,12882],{"className":12881},[1221],[1163,12883,12885,12905],{"className":12884},[1225,1226],[1163,12886,12888,12902],{"className":12887},[1230],[1163,12889,12891],{"className":12890,"style":1567},[1234],[1163,12892,12893,12896],{"style":1238},[1163,12894],{"className":12895,"style":1243},[1242],[1163,12897,12899],{"className":12898},[1247,1248,1249,1250],[1163,12900,1370],{"className":12901},[1213,1250],[1163,12903,1258],{"className":12904},[1257],[1163,12906,12908],{"className":12907},[1230],[1163,12909,12911],{"className":12910,"style":1265},[1234],[1163,12912],{},[1163,12914,2609],{"className":12915},[2671],[1163,12917],{"className":12918,"style":2675},[1460],[1163,12920,12922,12925],{"className":12921},[1213],[1163,12923,1382],{"className":12924},[1213,1217],[1163,12926,12928],{"className":12927},[1221],[1163,12929,12931,12951],{"className":12930},[1225,1226],[1163,12932,12934,12948],{"className":12933},[1230],[1163,12935,12937],{"className":12936,"style":1567},[1234],[1163,12938,12939,12942],{"style":1238},[1163,12940],{"className":12941,"style":1243},[1242],[1163,12943,12945],{"className":12944},[1247,1248,1249,1250],[1163,12946,3035],{"className":12947},[1213,1250],[1163,12949,1258],{"className":12950},[1257],[1163,12952,12954],{"className":12953},[1230],[1163,12955,12957],{"className":12956,"style":1265},[1234],[1163,12958],{},[1163,12960,2609],{"className":12961},[2671],[1163,12963],{"className":12964,"style":2675},[1460],[1163,12966,3040],{"className":12967},[3099],[1163,12969],{"className":12970,"style":2675},[1460],[1163,12972,2609],{"className":12973},[2671],[1163,12975],{"className":12976,"style":2675},[1460],[1163,12978,12980,12983],{"className":12979},[1213],[1163,12981,1382],{"className":12982},[1213,1217],[1163,12984,12986],{"className":12985},[1221],[1163,12987,12989,13009],{"className":12988},[1225,1226],[1163,12990,12992,13006],{"className":12991},[1230],[1163,12993,12995],{"className":12994,"style":7817},[1234],[1163,12996,12997,13000],{"style":1238},[1163,12998],{"className":12999,"style":1243},[1242],[1163,13001,13003],{"className":13002},[1247,1248,1249,1250],[1163,13004,3045],{"className":13005,"style":1490},[1213,1217,1250],[1163,13007,1258],{"className":13008},[1257],[1163,13010,13012],{"className":13011},[1230],[1163,13013,13015],{"className":13014,"style":1265},[1234],[1163,13016],{},[1101,13018,13019,13020],{},"输出：等长序列 ",[1163,13021,13023,13060],{"className":13022},[1166],[1163,13024,13026],{"className":13025},[1170],[1172,13027,13028],{"xmlns":1174},[1176,13029,13030,13058],{},[1179,13031,13032,13038,13040,13046,13048,13050,13052],{},[1182,13033,13034,13036],{},[1185,13035,1796],{},[1368,13037,1370],{},[1332,13039,2609],{"separator":1200},[1182,13041,13042,13044],{},[1185,13043,1796],{},[1368,13045,3035],{},[1332,13047,2609],{"separator":1200},[1332,13049,3040],{},[1332,13051,2609],{"separator":1200},[1182,13053,13054,13056],{},[1185,13055,1796],{},[1185,13057,3045],{},[1192,13059,12322],{"encoding":1194},[1163,13061,13063],{"className":13062,"ariaHidden":1200},[1199],[1163,13064,13066,13069,13109,13112,13115,13155,13158,13161,13164,13167,13170,13173],{"className":13065},[1204],[1163,13067],{"className":13068,"style":1839},[1208],[1163,13070,13072,13075],{"className":13071},[1213],[1163,13073,1796],{"className":13074,"style":1479},[1213,1217],[1163,13076,13078],{"className":13077},[1221],[1163,13079,13081,13101],{"className":13080},[1225,1226],[1163,13082,13084,13098],{"className":13083},[1230],[1163,13085,13087],{"className":13086,"style":1567},[1234],[1163,13088,13089,13092],{"style":1860},[1163,13090],{"className":13091,"style":1243},[1242],[1163,13093,13095],{"className":13094},[1247,1248,1249,1250],[1163,13096,1370],{"className":13097},[1213,1250],[1163,13099,1258],{"className":13100},[1257],[1163,13102,13104],{"className":13103},[1230],[1163,13105,13107],{"className":13106,"style":1265},[1234],[1163,13108],{},[1163,13110,2609],{"className":13111},[2671],[1163,13113],{"className":13114,"style":2675},[1460],[1163,13116,13118,13121],{"className":13117},[1213],[1163,13119,1796],{"className":13120,"style":1479},[1213,1217],[1163,13122,13124],{"className":13123},[1221],[1163,13125,13127,13147],{"className":13126},[1225,1226],[1163,13128,13130,13144],{"className":13129},[1230],[1163,13131,13133],{"className":13132,"style":1567},[1234],[1163,13134,13135,13138],{"style":1860},[1163,13136],{"className":13137,"style":1243},[1242],[1163,13139,13141],{"className":13140},[1247,1248,1249,1250],[1163,13142,3035],{"className":13143},[1213,1250],[1163,13145,1258],{"className":13146},[1257],[1163,13148,13150],{"className":13149},[1230],[1163,13151,13153],{"className":13152,"style":1265},[1234],[1163,13154],{},[1163,13156,2609],{"className":13157},[2671],[1163,13159],{"className":13160,"style":2675},[1460],[1163,13162,3040],{"className":13163},[3099],[1163,13165],{"className":13166,"style":2675},[1460],[1163,13168,2609],{"className":13169},[2671],[1163,13171],{"className":13172,"style":2675},[1460],[1163,13174,13176,13179],{"className":13175},[1213],[1163,13177,1796],{"className":13178,"style":1479},[1213,1217],[1163,13180,13182],{"className":13181},[1221],[1163,13183,13185,13205],{"className":13184},[1225,1226],[1163,13186,13188,13202],{"className":13187},[1230],[1163,13189,13191],{"className":13190,"style":7817},[1234],[1163,13192,13193,13196],{"style":1860},[1163,13194],{"className":13195,"style":1243},[1242],[1163,13197,13199],{"className":13198},[1247,1248,1249,1250],[1163,13200,3045],{"className":13201,"style":1490},[1213,1217,1250],[1163,13203,1258],{"className":13204},[1257],[1163,13206,13208],{"className":13207},[1230],[1163,13209,13211],{"className":13210,"style":1265},[1234],[1163,13212],{},[1101,13214,13215],{},"典型应用：词性标注（POS）、NER",[1101,13217,13218],{},"方法：每个时间步都有对应输出",[1096,13220,13222],{"id":13221},"_52-encoder-decoder-架构seq2seq","5.2 Encoder-Decoder 架构（Seq2Seq）",[1101,13224,13225],{},[1107,13226,13227],{},"工作流程：",[3005,13229,13230,13362,13368],{},[1114,13231,13232,13235,13236],{},[1107,13233,13234],{},"Encoder","：将输入序列编码为固定长度的上下文向量 ",[1163,13237,13239,13271],{"className":13238},[1166],[1163,13240,13242],{"className":13241},[1170],[1172,13243,13244],{"xmlns":1174},[1176,13245,13246,13268],{},[1179,13247,13248,13251,13253],{},[1185,13249,13250],{},"c",[1332,13252,1334],{},[3137,13254,13255,13257,13259],{},[1185,13256,1187],{},[1185,13258,3045],{},[1179,13260,13261,13264,13266],{},[1185,13262,13263],{},"e",[1185,13265,11596],{},[1185,13267,13250],{},[1192,13269,13270],{"encoding":1194},"c = h_T^{enc}",[1163,13272,13274,13292],{"className":13273,"ariaHidden":1200},[1199],[1163,13275,13277,13280,13283,13286,13289],{"className":13276},[1204],[1163,13278],{"className":13279,"style":2749},[1208],[1163,13281,13250],{"className":13282},[1213,1217],[1163,13284],{"className":13285,"style":1461},[1460],[1163,13287,1334],{"className":13288},[1465],[1163,13290],{"className":13291,"style":1461},[1460],[1163,13293,13295,13299],{"className":13294},[1204],[1163,13296],{"className":13297,"style":13298},[1208],"height:0.9698em;vertical-align:-0.2753em;",[1163,13300,13302,13305],{"className":13301},[1213],[1163,13303,1187],{"className":13304},[1213,1217],[1163,13306,13308],{"className":13307},[1221],[1163,13309,13311,13353],{"className":13310},[1225,1226],[1163,13312,13314,13350],{"className":13313},[1230],[1163,13315,13318,13330],{"className":13316,"style":13317},[1234],"height:0.6644em;",[1163,13319,13321,13324],{"style":13320},"top:-2.4247em;margin-left:0em;margin-right:0.05em;",[1163,13322],{"className":13323,"style":1243},[1242],[1163,13325,13327],{"className":13326},[1247,1248,1249,1250],[1163,13328,3045],{"className":13329,"style":1490},[1213,1217,1250],[1163,13331,13332,13335],{"style":5100},[1163,13333],{"className":13334,"style":1243},[1242],[1163,13336,13338],{"className":13337},[1247,1248,1249,1250],[1163,13339,13341,13344,13347],{"className":13340},[1213,1250],[1163,13342,13263],{"className":13343},[1213,1217,1250],[1163,13345,11596],{"className":13346},[1213,1217,1250],[1163,13348,13250],{"className":13349},[1213,1217,1250],[1163,13351,1258],{"className":13352},[1257],[1163,13354,13356],{"className":13355},[1230],[1163,13357,13360],{"className":13358,"style":13359},[1234],"height:0.2753em;",[1163,13361],{},[1114,13363,13364,13367],{},[1107,13365,13366],{},"Decoder","：以上下文向量为初始状态，逐步生成输出序列",[1114,13369,13370],{},"Decoder 每一步的输入为上一步的输出（Teacher Forcing 训练时用真实标签）",[1101,13372,13373,13376,13377,13405,13406,13409],{},[1107,13374,13375],{},"瓶颈问题","：所有输入信息被压缩为单个向量 ",[1163,13378,13380,13393],{"className":13379},[1166],[1163,13381,13383],{"className":13382},[1170],[1172,13384,13385],{"xmlns":1174},[1176,13386,13387,13391],{},[1179,13388,13389],{},[1185,13390,13250],{},[1192,13392,13250],{"encoding":1194},[1163,13394,13396],{"className":13395,"ariaHidden":1200},[1199],[1163,13397,13399,13402],{"className":13398},[1204],[1163,13400],{"className":13401,"style":2749},[1208],[1163,13403,13250],{"className":13404},[1213,1217],"，对长序列信息损失严重。这一问题催生了",[1107,13407,13408],{},"注意力机制","（Attention），将在后续课程中详细讨论。",[4645,13411],{},[1091,13413,13415],{"id":13414},"六双向-rnnbidirectional-rnn","六、双向 RNN（Bidirectional RNN）",[1101,13417,13418,13419,13422],{},"标准 RNN 只能利用过去的信息（从左到右），但很多任务中",[1107,13420,13421],{},"未来的上下文","同样重要。例如在命名实体识别中，判断一个词是否为人名需要同时看其前后的词。",[1101,13424,13425],{},[1107,13426,13427],{},"双向 RNN 结构：",[1101,13429,13430,13431],{},"前向隐藏状态：",[1163,13432,13434,13529],{"className":13433},[1166],[1163,13435,13437],{"className":13436},[1170],[1172,13438,13439],{"xmlns":1174},[1176,13440,13441,13526],{},[1179,13442,13443,13454,13456,13458,13460,13470,13472,13488,13490,13504,13506,13512,13514,13524],{},[3171,13444,13445,13451],{"accent":1200},[1182,13446,13447,13449],{},[1185,13448,1187],{},[1185,13450,1190],{},[1332,13452,13453],{"stretchy":1200},"→",[1332,13455,1334],{},[1185,13457,1337],{},[1332,13459,1341],{"stretchy":1340},[1182,13461,13462,13464],{},[1185,13463,1346],{},[3171,13465,13466,13468],{"accent":1200},[1185,13467,1187],{},[1332,13469,13453],{"stretchy":1200},[1332,13471,1355],{},[3171,13473,13474,13486],{"accent":1200},[1182,13475,13476,13478],{},[1185,13477,1187],{},[1179,13479,13480,13482,13484],{},[1185,13481,1190],{},[1332,13483,1366],{},[1368,13485,1370],{},[1332,13487,13453],{"stretchy":1200},[1332,13489,1373],{},[1182,13491,13492,13494],{},[1185,13493,1346],{},[1179,13495,13496,13498],{},[1185,13497,1382],{},[3171,13499,13500,13502],{"accent":1200},[1185,13501,1187],{},[1332,13503,13453],{"stretchy":1200},[1332,13505,1355],{},[1182,13507,13508,13510],{},[1185,13509,1382],{},[1185,13511,1190],{},[1332,13513,1373],{},[1182,13515,13516,13518],{},[1185,13517,1399],{},[3171,13519,13520,13522],{"accent":1200},[1185,13521,1187],{},[1332,13523,13453],{"stretchy":1200},[1332,13525,1404],{"stretchy":1340},[1192,13527,13528],{"encoding":1194},"\\overrightarrow{h_t} = \\sigma(W_{\\overrightarrow{h}} \\cdot \\overrightarrow{h_{t-1}} + W_{x\\overrightarrow{h}} \\cdot x_t + b_{\\overrightarrow{h}})",[1163,13530,13532,13642,13742,13848,13940,13995],{"className":13531,"ariaHidden":1200},[1199],[1163,13533,13535,13539,13633,13636,13639],{"className":13534},[1204],[1163,13536],{"className":13537,"style":13538},[1208],"height:1.3664em;vertical-align:-0.15em;",[1163,13540,13542],{"className":13541},[1213,3383],[1163,13543,13545,13625],{"className":13544},[1225,1226],[1163,13546,13548,13622],{"className":13547},[1230],[1163,13549,13552,13597],{"className":13550,"style":13551},[1234],"height:1.2164em;",[1163,13553,13554,13557],{"style":3396},[1163,13555],{"className":13556,"style":3400},[1242],[1163,13558,13560,13563],{"className":13559},[1213],[1163,13561,1187],{"className":13562},[1213,1217],[1163,13564,13566],{"className":13565},[1221],[1163,13567,13569,13589],{"className":13568},[1225,1226],[1163,13570,13572,13586],{"className":13571},[1230],[1163,13573,13575],{"className":13574,"style":1235},[1234],[1163,13576,13577,13580],{"style":1238},[1163,13578],{"className":13579,"style":1243},[1242],[1163,13581,13583],{"className":13582},[1247,1248,1249,1250],[1163,13584,1190],{"className":13585},[1213,1217,1250],[1163,13587,1258],{"className":13588},[1257],[1163,13590,13592],{"className":13591},[1230],[1163,13593,13595],{"className":13594,"style":1265},[1234],[1163,13596],{},[1163,13598,13602,13605],{"className":13599,"style":13601},[13600],"svg-align","top:-3.6944em;",[1163,13603],{"className":13604,"style":3400},[1242],[1163,13606,13610],{"className":13607,"style":13609},[13608],"hide-tail","height:0.522em;min-width:0.888em;",[13611,13612,13618],"svg",{"xmlns":13613,"width":13614,"height":13615,"viewBox":13616,"preserveAspectRatio":13617},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","0.522em","0 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0,14533],{"style":13700},[1163,14531],{"className":14532,"style":1243},[1242],[1163,14534,1187],{"className":14535},[1213,1217,1250],[1163,14537,14539,14542],{"className":14538,"style":13710},[13600],[1163,14540],{"className":14541,"style":1243},[1242],[1163,14543,14545],{"className":14544,"style":13609},[13608,1250],[13611,14546,14547],{"xmlns":13613,"width":13614,"height":13615,"viewBox":13616,"preserveAspectRatio":14255},[13619,14548],{"d":14258},[1163,14550,1258],{"className":14551},[1257],[1163,14553,14555],{"className":14554},[1230],[1163,14556,14558],{"className":14557,"style":13730},[1234],[1163,14559],{},[1163,14561],{"className":14562,"style":1534},[1460],[1163,14564,1355],{"className":14565},[1538],[1163,14567],{"className":14568,"style":1534},[1460],[1163,14570,14572,14575,14615,14618,14621],{"className":14571},[1204],[1163,14573],{"className":14574,"style":1677},[1208],[1163,14576,14578,14581],{"className":14577},[1213],[1163,14579,1382],{"className":14580},[1213,1217],[1163,14582,14584],{"className":14583},[1221],[1163,14585,14587,14607],{"className":14586},[1225,1226],[1163,14588,14590,14604],{"className":14589},[1230],[1163,14591,14593],{"className":14592,"style":1235},[1234],[1163,14594,14595,14598],{"style":1238},[1163,14596],{"className":14597,"style":1243},[1242],[1163,14599,14601],{"className":14600},[1247,1248,1249,1250],[1163,14602,1190],{"className":14603},[1213,1217,1250],[1163,14605,1258],{"className":14606},[1257],[1163,14608,14610],{"className":14609},[1230],[1163,14611,14613],{"className":14612,"style":1265},[1234],[1163,14614],{},[1163,14616],{"className":14617,"style":1534},[1460],[1163,14619,1373],{"className":14620},[1538],[1163,14622],{"className":14623,"style":1534},[1460],[1163,14625,14627,14630,14703],{"className":14626},[1204],[1163,14628],{"className":14629,"style":13648},[1208],[1163,14631,14633,14636],{"className":14632},[1213],[1163,14634,1399],{"className":14635},[1213,1217],[1163,14637,14639],{"className":14638},[1221],[1163,14640,14642,14695],{"className":14641},[1225,1226],[1163,14643,14645,14692],{"className":14644},[1230],[1163,14646,14648],{"className":14647,"style":3874},[1234],[1163,14649,14650,14653],{"style":14021},[1163,14651],{"className":14652,"style":13679},[1242],[1163,14654,14656],{"className":14655},[1247,1248,1249,1250],[1163,14657,14659],{"className":14658},[1213,1250],[1163,14660,14662],{"className":14661},[1213,3383,1250],[1163,14663,14665],{"className":14664},[1225],[1163,14666,14668],{"className":14667},[1230],[1163,14669,14671,14679],{"className":14670,"style":13551},[1234],[1163,14672,14673,14676],{"style":13700},[1163,14674],{"className":14675,"style":1243},[1242],[1163,14677,1187],{"className":14678},[1213,1217,1250],[1163,14680,14682,14685],{"className":14681,"style":13710},[13600],[1163,14683],{"className":14684,"style":1243},[1242],[1163,14686,14688],{"className":14687,"style":13609},[13608,1250],[13611,14689,14690],{"xmlns":13613,"width":13614,"height":13615,"viewBox":13616,"preserveAspectRatio":14255},[13619,14691],{"d":14258},[1163,14693,1258],{"className":14694},[1257],[1163,14696,14698],{"className":14697},[1230],[1163,14699,14701],{"className":14700,"style":13730},[1234],[1163,14702],{},[1163,14704,1404],{"className":14705},[1776],[1101,14707,14708,14709,14998],{},"最终表示：",[1163,14710,14712,14759],{"className":14711},[1166],[1163,14713,14715],{"className":14714},[1170],[1172,14716,14717],{"xmlns":1174},[1176,14718,14719,14756],{},[1179,14720,14721,14727,14729,14731,14741,14744,14754],{},[1182,14722,14723,14725],{},[1185,14724,1187],{},[1185,14726,1190],{},[1332,14728,1334],{},[1332,14730,6649],{"stretchy":1340},[3171,14732,14733,14739],{"accent":1200},[1182,14734,14735,14737],{},[1185,14736,1187],{},[1185,14738,1190],{},[1332,14740,13453],{"stretchy":1200},[1332,14742,14743],{"separator":1200},";",[3171,14745,14746,14752],{"accent":1200},[1182,14747,14748,14750],{},[1185,14749,1187],{},[1185,14751,1190],{},[1332,14753,6368],{"stretchy":1200},[1332,14755,6659],{"stretchy":1340},[1192,14757,14758],{"encoding":1194},"h_t = [\\overrightarrow{h_t}; \\overleftarrow{h_t}]",[1163,14760,14762,14817],{"className":14761,"ariaHidden":1200},[1199],[1163,14763,14765,14768,14808,14811,14814],{"className":14764},[1204],[1163,14766],{"className":14767,"style":1209},[1208],[1163,14769,14771,14774],{"className":14770},[1213],[1163,14772,1187],{"className":14773},[1213,1217],[1163,14775,14777],{"className":14776},[1221],[1163,14778,14780,14800],{"className":14779},[1225,1226],[1163,14781,14783,14797],{"className":14782},[1230],[1163,14784,14786],{"className":14785,"style":1235},[1234],[1163,14787,14788,14791],{"style":1238},[1163,14789],{"className":14790,"style":1243},[1242],[1163,14792,14794],{"className":14793},[1247,1248,1249,1250],[1163,14795,1190],{"className":14796},[1213,1217,1250],[1163,14798,1258],{"className":14799},[1257],[1163,14801,14803],{"className":14802},[1230],[1163,14804,14806],{"className":14805,"style":1265},[1234],[1163,14807],{},[1163,14809],{"className":14810,"style":1461},[1460],[1163,14812,1334],{"className":14813},[1465],[1163,14815],{"className":14816,"style":1461},[1460],[1163,14818,14820,14824,14827,14908,14911,14914,14995],{"className":14819},[1204],[1163,14821],{"className":14822,"style":14823},[1208],"height:1.4664em;vertical-align:-0.25em;",[1163,14825,6649],{"className":14826},[1483],[1163,14828,14830],{"className":14829},[1213,3383],[1163,14831,14833,14900],{"className":14832},[1225,1226],[1163,14834,14836,14897],{"className":14835},[1230],[1163,14837,14839,14884],{"className":14838,"style":13551},[1234],[1163,14840,14841,14844],{"style":3396},[1163,14842],{"className":14843,"style":3400},[1242],[1163,14845,14847,14850],{"className":14846},[1213],[1163,14848,1187],{"className":14849},[1213,1217],[1163,14851,14853],{"className":14852},[1221],[1163,14854,14856,14876],{"className":14855},[1225,1226],[1163,14857,14859,14873],{"className":14858},[1230],[1163,14860,14862],{"className":14861,"style":1235},[1234],[1163,14863,14864,14867],{"style":1238},[1163,14865],{"className":14866,"style":1243},[1242],[1163,14868,14870],{"className":14869},[1247,1248,1249,1250],[1163,14871,1190],{"className":14872},[1213,1217,1250],[1163,14874,1258],{"className":14875},[1257],[1163,14877,14879],{"className":14878},[1230],[1163,14880,14882],{"className":14881,"style":1265},[1234],[1163,14883],{},[1163,14885,14887,14890],{"className":14886,"style":13601},[13600],[1163,14888],{"className":14889,"style":3400},[1242],[1163,14891,14893],{"className":14892,"style":13609},[13608],[13611,14894,14895],{"xmlns":13613,"width":13614,"height":13615,"viewBox":13616,"preserveAspectRatio":13617},[13619,14896],{"d":13621},[1163,14898,1258],{"className":14899},[1257],[1163,14901,14903],{"className":14902},[1230],[1163,14904,14906],{"className":14905,"style":1265},[1234],[1163,14907],{},[1163,14909,14743],{"className":14910},[2671],[1163,14912],{"className":14913,"style":2675},[1460],[1163,14915,14917],{"className":14916},[1213,3383],[1163,14918,14920,14987],{"className":14919},[1225,1226],[1163,14921,14923,14984],{"className":14922},[1230],[1163,14924,14926,14971],{"className":14925,"style":13551},[1234],[1163,14927,14928,14931],{"style":3396},[1163,14929],{"className":14930,"style":3400},[1242],[1163,14932,14934,14937],{"className":14933},[1213],[1163,14935,1187],{"className":14936},[1213,1217],[1163,14938,14940],{"className":14939},[1221],[1163,14941,14943,14963],{"className":14942},[1225,1226],[1163,14944,14946,14960],{"className":14945},[1230],[1163,14947,14949],{"className":14948,"style":1235},[1234],[1163,14950,14951,14954],{"style":1238},[1163,14952],{"className":14953,"style":1243},[1242],[1163,14955,14957],{"className":14956},[1247,1248,1249,1250],[1163,14958,1190],{"className":14959},[1213,1217,1250],[1163,14961,1258],{"className":14962},[1257],[1163,14964,14966],{"className":14965},[1230],[1163,14967,14969],{"className":14968,"style":1265},[1234],[1163,14970],{},[1163,14972,14974,14977],{"className":14973,"style":13601},[13600],[1163,14975],{"className":14976,"style":3400},[1242],[1163,14978,14980],{"className":14979,"style":13609},[13608],[13611,14981,14982],{"xmlns":13613,"width":13614,"height":13615,"viewBox":13616,"preserveAspectRatio":14255},[13619,14983],{"d":14258},[1163,14985,1258],{"className":14986},[1257],[1163,14988,14990],{"className":14989},[1230],[1163,14991,14993],{"className":14992,"style":1265},[1234],[1163,14994],{},[1163,14996,6659],{"className":14997},[1776],"（拼接）",[1101,15000,15001],{},[1107,15002,15003],{},"特点：",[1111,15005,15006,15013,15016,15019],{},[1114,15007,15008,15009,15012],{},"每个时刻的表示融合了",[1107,15010,15011],{},"过去和未来","的完整上下文信息",[1114,15014,15015],{},"参数量翻倍（前向和反向各有独立参数）",[1114,15017,15018],{},"不适用于实时\u002F在线任务（需要完整序列才能计算反向状态）",[1114,15020,15021],{},"非常适合分类和标注任务（如 BERT 的本质就是双向编码）",[4645,15023],{},[1091,15025,15027],{"id":15026},"七深层-rnndeepstacked-rnn","七、深层 RNN（Deep\u002FStacked RNN）",[1096,15029,15031],{"id":15030},"_71-结构","7.1 结构",[1101,15033,15034,15035,15038],{},"将多个 RNN 层",[1107,15036,15037],{},"垂直堆叠","，下层的隐藏状态序列作为上层的输入序列：",[1101,15040,15041],{},[1163,15042,15044,15175],{"className":15043},[1166],[1163,15045,15047],{"className":15046},[1170],[1172,15048,15049],{"xmlns":1174},[1176,15050,15051,15172],{},[1179,15052,15053,15068,15070,15072,15074,15092,15094,15114,15116,15134,15136,15154,15156,15170],{},[3137,15054,15055,15057,15059],{},[1185,15056,1187],{},[1185,15058,1190],{},[1179,15060,15061,15063,15066],{},[1332,15062,1341],{"stretchy":1340},[1185,15064,15065],{},"l",[1332,15067,1404],{"stretchy":1340},[1332,15069,1334],{},[1185,15071,1337],{},[1332,15073,1341],{"stretchy":1340},[3137,15075,15076,15078,15084],{},[1185,15077,1346],{},[1179,15079,15080,15082],{},[1185,15081,1187],{},[1185,15083,1187],{},[1179,15085,15086,15088,15090],{},[1332,15087,1341],{"stretchy":1340},[1185,15089,15065],{},[1332,15091,1404],{"stretchy":1340},[1332,15093,1355],{},[3137,15095,15096,15098,15106],{},[1185,15097,1187],{},[1179,15099,15100,15102,15104],{},[1185,15101,1190],{},[1332,15103,1366],{},[1368,15105,1370],{},[1179,15107,15108,15110,15112],{},[1332,15109,1341],{"stretchy":1340},[1185,15111,15065],{},[1332,15113,1404],{"stretchy":1340},[1332,15115,1373],{},[3137,15117,15118,15120,15126],{},[1185,15119,1346],{},[1179,15121,15122,15124],{},[1185,15123,1382],{},[1185,15125,1187],{},[1179,15127,15128,15130,15132],{},[1332,15129,1341],{"stretchy":1340},[1185,15131,15065],{},[1332,15133,1404],{"stretchy":1340},[1332,15135,1355],{},[3137,15137,15138,15140,15142],{},[1185,15139,1187],{},[1185,15141,1190],{},[1179,15143,15144,15146,15148,15150,15152],{},[1332,15145,1341],{"stretchy":1340},[1185,15147,15065],{},[1332,15149,1366],{},[1368,15151,1370],{},[1332,15153,1404],{"stretchy":1340},[1332,15155,1373],{},[3137,15157,15158,15160,15162],{},[1185,15159,1399],{},[1185,15161,1187],{},[1179,15163,15164,15166,15168],{},[1332,15165,1341],{"stretchy":1340},[1185,15167,15065],{},[1332,15169,1404],{"stretchy":1340},[1332,15171,1404],{"stretchy":1340},[1192,15173,15174],{"encoding":1194},"h_t^{(l)} = \\sigma(W_{hh}^{(l)} \\cdot h_{t-1}^{(l)} + W_{xh}^{(l)} \\cdot h_t^{(l-1)} + b_h^{(l)})",[1163,15176,15178,15259,15346,15433,15514,15595],{"className":15177,"ariaHidden":1200},[1199],[1163,15179,15181,15185,15250,15253,15256],{"className":15180},[1204],[1163,15182],{"className":15183,"style":15184},[1208],"height:1.2906em;vertical-align:-0.2458em;",[1163,15186,15188,15191],{"className":15187},[1213],[1163,15189,1187],{"className":15190},[1213,1217],[1163,15192,15194],{"className":15193},[1221],[1163,15195,15197,15241],{"className":15196},[1225,1226],[1163,15198,15200,15238],{"className":15199},[1230],[1163,15201,15204,15216],{"className":15202,"style":15203},[1234],"height:1.0448em;",[1163,15205,15207,15210],{"style":15206},"top:-2.4542em;margin-left:0em;margin-right:0.05em;",[1163,15208],{"className":15209,"style":1243},[1242],[1163,15211,15213],{"className":15212},[1247,1248,1249,1250],[1163,15214,1190],{"className":15215},[1213,1217,1250],[1163,15217,15219,15222],{"style":15218},"top:-3.2198em;margin-right:0.05em;",[1163,15220],{"className":15221,"style":1243},[1242],[1163,15223,15225],{"className":15224},[1247,1248,1249,1250],[1163,15226,15228,15231,15235],{"className":15227},[1213,1250],[1163,15229,1341],{"className":15230},[1483,1250],[1163,15232,15065],{"className":15233,"style":15234},[1213,1217,1250],"margin-right:0.0197em;",[1163,15236,1404],{"className":15237},[1776,1250],[1163,15239,1258],{"className":15240},[1257],[1163,15242,15244],{"className":15243},[1230],[1163,15245,15248],{"className":15246,"style":15247},[1234],"height:0.2458em;",[1163,15249],{},[1163,15251],{"className":15252,"style":1461},[1460],[1163,15254,1334],{"className":15255},[1465],[1163,15257],{"className":15258,"style":1461},[1460],[1163,15260,15262,15266,15269,15272,15337,15340,15343],{"className":15261},[1204],[1163,15263],{"className":15264,"style":15265},[1208],"height:1.3461em;vertical-align:-0.3013em;",[1163,15267,1337],{"className":15268,"style":1479},[1213,1217],[1163,15270,1341],{"className":15271},[1483],[1163,15273,15275,15278],{"className":15274},[1213],[1163,15276,1346],{"className":15277,"style":1490},[1213,1217],[1163,15279,15281],{"className":15280},[1221],[1163,15282,15284,15328],{"className":15283},[1225,1226],[1163,15285,15287,15325],{"className":15286},[1230],[1163,15288,15290,15305],{"className":15289,"style":15203},[1234],[1163,15291,15293,15296],{"style":15292},"top:-2.3987em;margin-left:-0.1389em;margin-right:0.05em;",[1163,15294],{"className":15295,"style":1243},[1242],[1163,15297,15299],{"className":15298},[1247,1248,1249,1250],[1163,15300,15302],{"className":15301},[1213,1250],[1163,15303,1519],{"className":15304},[1213,1217,1250],[1163,15306,15307,15310],{"style":15218},[1163,15308],{"className":15309,"style":1243},[1242],[1163,15311,15313],{"className":15312},[1247,1248,1249,1250],[1163,15314,15316,15319,15322],{"className":15315},[1213,1250],[1163,15317,1341],{"className":15318},[1483,1250],[1163,15320,15065],{"className":15321,"style":15234},[1213,1217,1250],[1163,15323,1404],{"className":15324},[1776,1250],[1163,15326,1258],{"className":15327},[1257],[1163,15329,15331],{"className":15330},[1230],[1163,15332,15335],{"className":15333,"style":15334},[1234],"height:0.3013em;",[1163,15336],{},[1163,15338],{"className":15339,"style":1534},[1460],[1163,15341,1355],{"className":15342},[1538],[1163,15344],{"className":15345,"style":1534},[1460],[1163,15347,15349,15353,15424,15427,15430],{"className":15348},[1204],[1163,15350],{"className":15351,"style":15352},[1208],"height:1.3694em;vertical-align:-0.3246em;",[1163,15354,15356,15359],{"className":15355},[1213],[1163,15357,1187],{"className":15358},[1213,1217],[1163,15360,15362],{"className":15361},[1221],[1163,15363,15365,15415],{"className":15364},[1225,1226],[1163,15366,15368,15412],{"className":15367},[1230],[1163,15369,15371,15392],{"className":15370,"style":15203},[1234],[1163,15372,15374,15377],{"style":15373},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[1163,15375],{"className":15376,"style":1243},[1242],[1163,15378,15380],{"className":15379},[1247,1248,1249,1250],[1163,15381,15383,15386,15389],{"className":15382},[1213,1250],[1163,15384,1190],{"className":15385},[1213,1217,1250],[1163,15387,1366],{"className":15388},[1538,1250],[1163,15390,1370],{"className":15391},[1213,1250],[1163,15393,15394,15397],{"style":15218},[1163,15395],{"className":15396,"style":1243},[1242],[1163,15398,15400],{"className":15399},[1247,1248,1249,1250],[1163,15401,15403,15406,15409],{"className":15402},[1213,1250],[1163,15404,1341],{"className":15405},[1483,1250],[1163,15407,15065],{"className":15408,"style":15234},[1213,1217,1250],[1163,15410,1404],{"className":15411},[1776,1250],[1163,15413,1258],{"className":15414},[1257],[1163,15416,15418],{"className":15417},[1230],[1163,15419,15422],{"className":15420,"style":15421},[1234],"height:0.3246em;",[1163,15423],{},[1163,15425],{"className":15426,"style":1534},[1460],[1163,15428,1373],{"className":15429},[1538],[1163,15431],{"className":15432,"style":1534},[1460],[1163,15434,15436,15439,15505,15508,15511],{"className":15435},[1204],[1163,15437],{"className":15438,"style":15265},[1208],[1163,15440,15442,15445],{"className":15441},[1213],[1163,15443,1346],{"className":15444,"style":1490},[1213,1217],[1163,15446,15448],{"className":15447},[1221],[1163,15449,15451,15497],{"className":15450},[1225,1226],[1163,15452,15454,15494],{"className":15453},[1230],[1163,15455,15457,15474],{"className":15456,"style":15203},[1234],[1163,15458,15459,15462],{"style":15292},[1163,15460],{"className":15461,"style":1243},[1242],[1163,15463,15465],{"className":15464},[1247,1248,1249,1250],[1163,15466,15468,15471],{"className":15467},[1213,1250],[1163,15469,1382],{"className":15470},[1213,1217,1250],[1163,15472,1187],{"className":15473},[1213,1217,1250],[1163,15475,15476,15479],{"style":15218},[1163,15477],{"className":15478,"style":1243},[1242],[1163,15480,15482],{"className":15481},[1247,1248,1249,1250],[1163,15483,15485,15488,15491],{"className":15484},[1213,1250],[1163,15486,1341],{"className":15487},[1483,1250],[1163,15489,15065],{"className":15490,"style":15234},[1213,1217,1250],[1163,15492,1404],{"className":15493},[1776,1250],[1163,15495,1258],{"className":15496},[1257],[1163,15498,15500],{"className":15499},[1230],[1163,15501,15503],{"className":15502,"style":15334},[1234],[1163,15504],{},[1163,15506],{"className":15507,"style":1534},[1460],[1163,15509,1355],{"className":15510},[1538],[1163,15512],{"className":15513,"style":1534},[1460],[1163,15515,15517,15520,15586,15589,15592],{"className":15516},[1204],[1163,15518],{"className":15519,"style":15184},[1208],[1163,15521,15523,15526],{"className":15522},[1213],[1163,15524,1187],{"className":15525},[1213,1217],[1163,15527,15529],{"className":15528},[1221],[1163,15530,15532,15578],{"className":15531},[1225,1226],[1163,15533,15535,15575],{"className":15534},[1230],[1163,15536,15538,15549],{"className":15537,"style":15203},[1234],[1163,15539,15540,15543],{"style":15206},[1163,15541],{"className":15542,"style":1243},[1242],[1163,15544,15546],{"className":15545},[1247,1248,1249,1250],[1163,15547,1190],{"className":15548},[1213,1217,1250],[1163,15550,15551,15554],{"style":15218},[1163,15552],{"className":15553,"style":1243},[1242],[1163,15555,15557],{"className":15556},[1247,1248,1249,1250],[1163,15558,15560,15563,15566,15569,15572],{"className":15559},[1213,1250],[1163,15561,1341],{"className":15562},[1483,1250],[1163,15564,15065],{"className":15565,"style":15234},[1213,1217,1250],[1163,15567,1366],{"className":15568},[1538,1250],[1163,15570,1370],{"className":15571},[1213,1250],[1163,15573,1404],{"className":15574},[1776,1250],[1163,15576,1258],{"className":15577},[1257],[1163,15579,15581],{"className":15580},[1230],[1163,15582,15584],{"className":15583,"style":15247},[1234],[1163,15585],{},[1163,15587],{"className":15588,"style":1534},[1460],[1163,15590,1373],{"className":15591},[1538],[1163,15593],{"className":15594,"style":1534},[1460],[1163,15596,15598,15601,15662],{"className":15597},[1204],[1163,15599],{"className":15600,"style":15265},[1208],[1163,15602,15604,15607],{"className":15603},[1213],[1163,15605,1399],{"className":15606},[1213,1217],[1163,15608,15610],{"className":15609},[1221],[1163,15611,15613,15654],{"className":15612},[1225,1226],[1163,15614,15616,15651],{"className":15615},[1230],[1163,15617,15619,15631],{"className":15618,"style":15203},[1234],[1163,15620,15622,15625],{"style":15621},"top:-2.3987em;margin-left:0em;margin-right:0.05em;",[1163,15623],{"className":15624,"style":1243},[1242],[1163,15626,15628],{"className":15627},[1247,1248,1249,1250],[1163,15629,1187],{"className":15630},[1213,1217,1250],[1163,15632,15633,15636],{"style":15218},[1163,15634],{"className":15635,"style":1243},[1242],[1163,15637,15639],{"className":15638},[1247,1248,1249,1250],[1163,15640,15642,15645,15648],{"className":15641},[1213,1250],[1163,15643,1341],{"className":15644},[1483,1250],[1163,15646,15065],{"className":15647,"style":15234},[1213,1217,1250],[1163,15649,1404],{"className":15650},[1776,1250],[1163,15652,1258],{"className":15653},[1257],[1163,15655,15657],{"className":15656},[1230],[1163,15658,15660],{"className":15659,"style":15334},[1234],[1163,15661],{},[1163,15663,1404],{"className":15664},[1776],[1101,15666,5165,15667,15695,15696,2976],{},[1163,15668,15670,15683],{"className":15669},[1166],[1163,15671,15673],{"className":15672},[1170],[1172,15674,15675],{"xmlns":1174},[1176,15676,15677,15681],{},[1179,15678,15679],{},[1185,15680,15065],{},[1192,15682,15065],{"encoding":1194},[1163,15684,15686],{"className":15685,"ariaHidden":1200},[1199],[1163,15687,15689,15692],{"className":15688},[1204],[1163,15690],{"className":15691,"style":3393},[1208],[1163,15693,15065],{"className":15694,"style":15234},[1213,1217]," 表示层索引，",[1163,15697,15699,15733],{"className":15698},[1166],[1163,15700,15702],{"className":15701},[1170],[1172,15703,15704],{"xmlns":1174},[1176,15705,15706,15730],{},[1179,15707,15708,15722,15724],{},[3137,15709,15710,15712,15714],{},[1185,15711,1187],{},[1185,15713,1190],{},[1179,15715,15716,15718,15720],{},[1332,15717,1341],{"stretchy":1340},[1368,15719,6652],{},[1332,15721,1404],{"stretchy":1340},[1332,15723,1334],{},[1182,15725,15726,15728],{},[1185,15727,1382],{},[1185,15729,1190],{},[1192,15731,15732],{"encoding":1194},"h_t^{(0)} = x_t",[1163,15734,15736,15811],{"className":15735,"ariaHidden":1200},[1199],[1163,15737,15739,15742,15802,15805,15808],{"className":15738},[1204],[1163,15740],{"className":15741,"style":15184},[1208],[1163,15743,15745,15748],{"className":15744},[1213],[1163,15746,1187],{"className":15747},[1213,1217],[1163,15749,15751],{"className":15750},[1221],[1163,15752,15754,15794],{"className":15753},[1225,1226],[1163,15755,15757,15791],{"className":15756},[1230],[1163,15758,15760,15771],{"className":15759,"style":15203},[1234],[1163,15761,15762,15765],{"style":15206},[1163,15763],{"className":15764,"style":1243},[1242],[1163,15766,15768],{"className":15767},[1247,1248,1249,1250],[1163,15769,1190],{"className":15770},[1213,1217,1250],[1163,15772,15773,15776],{"style":15218},[1163,15774],{"className":15775,"style":1243},[1242],[1163,15777,15779],{"className":15778},[1247,1248,1249,1250],[1163,15780,15782,15785,15788],{"className":15781},[1213,1250],[1163,15783,1341],{"className":15784},[1483,1250],[1163,15786,6652],{"className":15787},[1213,1250],[1163,15789,1404],{"className":15790},[1776,1250],[1163,15792,1258],{"className":15793},[1257],[1163,15795,15797],{"className":15796},[1230],[1163,15798,15800],{"className":15799,"style":15247},[1234],[1163,15801],{},[1163,15803],{"className":15804,"style":1461},[1460],[1163,15806,1334],{"className":15807},[1465],[1163,15809],{"className":15810,"style":1461},[1460],[1163,15812,15814,15817],{"className":15813},[1204],[1163,15815],{"className":15816,"style":2115},[1208],[1163,15818,15820,15823],{"className":15819},[1213],[1163,15821,1382],{"className":15822},[1213,1217],[1163,15824,15826],{"className":15825},[1221],[1163,15827,15829,15849],{"className":15828},[1225,1226],[1163,15830,15832,15846],{"className":15831},[1230],[1163,15833,15835],{"className":15834,"style":1235},[1234],[1163,15836,15837,15840],{"style":1238},[1163,15838],{"className":15839,"style":1243},[1242],[1163,15841,15843],{"className":15842},[1247,1248,1249,1250],[1163,15844,1190],{"className":15845},[1213,1217,1250],[1163,15847,1258],{"className":15848},[1257],[1163,15850,15852],{"className":15851},[1230],[1163,15853,15855],{"className":15854,"style":1265},[1234],[1163,15856],{},[1096,15858,15859],{"id":15859},"相关公式",[2062,15861,15862,15872],{},[2065,15863,15864],{},[2068,15865,15866,15869],{},[2071,15867,15868],{},"模型\u002F概念",[2071,15870,15871],{},"核心公式",[2078,15873,15874,16281,16769,16992,17353,17714,18109,18470,18847,19068,19363,19658],{},[2068,15875,15876,15881],{},[2083,15877,15878],{},[1107,15879,15880],{},"基本 RNN",[2083,15882,15883],{},[1163,15884,15886,15960],{"className":15885},[1166],[1163,15887,15889],{"className":15888},[1170],[1172,15890,15891],{"xmlns":1174},[1176,15892,15893,15957],{},[1179,15894,15895,15901,15903,15905,15907,15917,15929,15931,15941,15947,15949,15955],{},[1182,15896,15897,15899],{},[1185,15898,1187],{},[1185,15900,1190],{},[1332,15902,1334],{},[1185,15904,1337],{},[1332,15906,1341],{"stretchy":1340},[1182,15908,15909,15911],{},[1185,15910,1346],{},[1179,15912,15913,15915],{},[1185,15914,1187],{},[1185,15916,1187],{},[1182,15918,15919,15921],{},[1185,15920,1187],{},[1179,15922,15923,15925,15927],{},[1185,15924,1190],{},[1332,15926,1366],{},[1368,15928,1370],{},[1332,15930,1373],{},[1182,15932,15933,15935],{},[1185,15934,1346],{},[1179,15936,15937,15939],{},[1185,15938,1382],{},[1185,15940,1187],{},[1182,15942,15943,15945],{},[1185,15944,1382],{},[1185,15946,1190],{},[1332,15948,1373],{},[1182,15950,15951,15953],{},[1185,15952,1399],{},[1185,15954,1187],{},[1332,15956,1404],{"stretchy":1340},[1192,15958,15959],{"encoding":1194},"h_t = \\sigma(W_{hh} h_{t-1} + W_{xh} x_t + b_h)",[1163,15961,15963,16018,16131,16232],{"className":15962,"ariaHidden":1200},[1199],[1163,15964,15966,15969,16009,16012,16015],{"className":15965},[1204],[1163,15967],{"className":15968,"style":1209},[1208],[1163,15970,15972,15975],{"className":15971},[1213],[1163,15973,1187],{"className":15974},[1213,1217],[1163,15976,15978],{"className":15977},[1221],[1163,15979,15981,16001],{"className":15980},[1225,1226],[1163,15982,15984,15998],{"className":15983},[1230],[1163,15985,15987],{"className":15986,"style":1235},[1234],[1163,15988,15989,15992],{"style":1238},[1163,15990],{"className":15991,"style":1243},[1242],[1163,15993,15995],{"className":15994},[1247,1248,1249,1250],[1163,15996,1190],{"className":15997},[1213,1217,1250],[1163,15999,1258],{"className":16000},[1257],[1163,16002,16004],{"className":16003},[1230],[1163,16005,16007],{"className":16006,"style":1265},[1234],[1163,16008],{},[1163,16010],{"className":16011,"style":1461},[1460],[1163,16013,1334],{"className":16014},[1465],[1163,16016],{"className":16017,"style":1461},[1460],[1163,16019,16021,16024,16027,16030,16073,16122,16125,16128],{"className":16020},[1204],[1163,16022],{"className":16023,"style":1475},[1208],[1163,16025,1337],{"className":16026,"style":1479},[1213,1217],[1163,16028,1341],{"className":16029},[1483],[1163,16031,16033,16036],{"className":16032},[1213],[1163,16034,1346],{"className":16035,"style":1490},[1213,1217],[1163,16037,16039],{"className":16038},[1221],[1163,16040,16042,16065],{"className":16041},[1225,1226],[1163,16043,16045,16062],{"className":16044},[1230],[1163,16046,16048],{"className":16047,"style":1503},[1234],[1163,16049,16050,16053],{"style":1506},[1163,16051],{"className":16052,"style":1243},[1242],[1163,16054,16056],{"className":16055},[1247,1248,1249,1250],[1163,16057,16059],{"className":16058},[1213,1250],[1163,16060,1519],{"className":16061},[1213,1217,1250],[1163,16063,1258],{"className":16064},[1257],[1163,16066,16068],{"className":16067},[1230],[1163,16069,16071],{"className":16070,"style":1265},[1234],[1163,16072],{},[1163,16074,16076,16079],{"className":16075},[1213],[1163,16077,1187],{"className":16078},[1213,1217],[1163,16080,16082],{"className":16081},[1221],[1163,16083,16085,16114],{"className":16084},[1225,1226],[1163,16086,16088,16111],{"className":16087},[1230],[1163,16089,16091],{"className":16090,"style":1567},[1234],[1163,16092,16093,16096],{"style":1238},[1163,16094],{"className":16095,"style":1243},[1242],[1163,16097,16099],{"className":16098},[1247,1248,1249,1250],[1163,16100,16102,16105,16108],{"className":16101},[1213,1250],[1163,16103,1190],{"className":16104},[1213,1217,1250],[1163,16106,1366],{"className":16107},[1538,1250],[1163,16109,1370],{"className":16110},[1213,1250],[1163,16112,1258],{"className":16113},[1257],[1163,16115,16117],{"className":16116},[1230],[1163,16118,16120],{"className":16119,"style":1597},[1234],[1163,16121],{},[1163,16123],{"className":16124,"style":1534},[1460],[1163,16126,1373],{"className":16127},[1538],[1163,16129],{"className":16130,"style":1534},[1460],[1163,16132,16134,16137,16183,16223,16226,16229],{"className":16133},[1204],[1163,16135],{"className":16136,"style":1615},[1208],[1163,16138,16140,16143],{"className":16139},[1213],[1163,16141,1346],{"className":16142,"style":1490},[1213,1217],[1163,16144,16146],{"className":16145},[1221],[1163,16147,16149,16175],{"className":16148},[1225,1226],[1163,16150,16152,16172],{"className":16151},[1230],[1163,16153,16155],{"className":16154,"style":1503},[1234],[1163,16156,16157,16160],{"style":1506},[1163,16158],{"className":16159,"style":1243},[1242],[1163,16161,16163],{"className":16162},[1247,1248,1249,1250],[1163,16164,16166,16169],{"className":16165},[1213,1250],[1163,16167,1382],{"className":16168},[1213,1217,1250],[1163,16170,1187],{"className":16171},[1213,1217,1250],[1163,16173,1258],{"className":16174},[1257],[1163,16176,16178],{"className":16177},[1230],[1163,16179,16181],{"className":16180,"style":1265},[1234],[1163,16182],{},[1163,16184,16186,16189],{"className":16185},[1213],[1163,16187,1382],{"className":16188},[1213,1217],[1163,16190,16192],{"className":16191},[1221],[1163,16193,16195,16215],{"className":16194},[1225,1226],[1163,16196,16198,16212],{"className":16197},[1230],[1163,16199,16201],{"className":16200,"style":1235},[1234],[1163,16202,16203,16206],{"style":1238},[1163,16204],{"className":16205,"style":1243},[1242],[1163,16207,16209],{"className":16208},[1247,1248,1249,1250],[1163,16210,1190],{"className":16211},[1213,1217,1250],[1163,16213,1258],{"className":16214},[1257],[1163,16216,16218],{"className":16217},[1230],[1163,16219,16221],{"className":16220,"style":1265},[1234],[1163,16222],{},[1163,16224],{"className":16225,"style":1534},[1460],[1163,16227,1373],{"className":16228},[1538],[1163,16230],{"className":16231,"style":1534},[1460],[1163,16233,16235,16238,16278],{"className":16234},[1204],[1163,16236],{"className":16237,"style":1475},[1208],[1163,16239,16241,16244],{"className":16240},[1213],[1163,16242,1399],{"className":16243},[1213,1217],[1163,16245,16247],{"className":16246},[1221],[1163,16248,16250,16270],{"className":16249},[1225,1226],[1163,16251,16253,16267],{"className":16252},[1230],[1163,16254,16256],{"className":16255,"style":1503},[1234],[1163,16257,16258,16261],{"style":1238},[1163,16259],{"className":16260,"style":1243},[1242],[1163,16262,16264],{"className":16263},[1247,1248,1249,1250],[1163,16265,1187],{"className":16266},[1213,1217,1250],[1163,16268,1258],{"className":16269},[1257],[1163,16271,16273],{"className":16272},[1230],[1163,16274,16276],{"className":16275,"style":1265},[1234],[1163,16277],{},[1163,16279,1404],{"className":16280},[1776],[2068,16282,16283,16288],{},[2083,16284,16285],{},[1107,16286,16287],{},"梯度传播",[2083,16289,16290],{},[1163,16291,16293,16380],{"className":16292},[1166],[1163,16294,16296],{"className":16295},[1170],[1172,16297,16298],{"xmlns":1174},[1176,16299,16300,16378],{},[1179,16301,16302,16324,16326,16344,16354,16356,16358,16360,16366,16368,16374,16376],{},[3678,16303,16304,16314],{},[1179,16305,16306,16308],{},[1185,16307,3685],{"mathvariant":3684},[1182,16309,16310,16312],{},[1185,16311,1187],{},[1185,16313,1190],{},[1179,16315,16316,16318],{},[1185,16317,3685],{"mathvariant":3684},[1182,16319,16320,16322],{},[1185,16321,1187],{},[1185,16323,3726],{},[1332,16325,1334],{},[3137,16327,16328,16330,16342],{},[1332,16329,4705],{},[1179,16331,16332,16334,16336,16338,16340],{},[1185,16333,4710],{},[1332,16335,1334],{},[1185,16337,3726],{},[1332,16339,1373],{},[1368,16341,1370],{},[1185,16343,1190],{},[1182,16345,16346,16348],{},[1185,16347,1346],{},[1179,16349,16350,16352],{},[1185,16351,1187],{},[1185,16353,1187],{},[1332,16355,1355],{},[4734,16357,4736],{},[1332,16359,1341],{"stretchy":1340},[4740,16361,16362,16364],{},[1185,16363,1337],{},[1332,16365,4747],{"mathvariant":3684,"lspace":4746,"rspace":4746},[1332,16367,1341],{"stretchy":1340},[1182,16369,16370,16372],{},[1185,16371,4754],{},[1185,16373,4710],{},[1332,16375,1404],{"stretchy":1340},[1332,16377,1404],{"stretchy":1340},[1192,16379,4763],{"encoding":1194},[1163,16381,16383,16546,16676],{"className":16382,"ariaHidden":1200},[1199],[1163,16384,16386,16389,16537,16540,16543],{"className":16385},[1204],[1163,16387],{"className":16388,"style":4268},[1208],[1163,16390,16392,16395,16534],{"className":16391},[1213],[1163,16393],{"className":16394},[1483,3826],[1163,16396,16398],{"className":16397},[3678],[1163,16399,16401,16526],{"className":16400},[1225,1226],[1163,16402,16404,16523],{"className":16403},[1230],[1163,16405,16407,16461,16469],{"className":16406,"style":4117},[1234],[1163,16408,16409,16412],{"style":3842},[1163,16410],{"className":16411,"style":3400},[1242],[1163,16413,16415],{"className":16414},[1247,1248,1249,1250],[1163,16416,16418,16421],{"className":16417},[1213,1250],[1163,16419,3685],{"className":16420,"style":3855},[1213,1250],[1163,16422,16424,16427],{"className":16423},[1213,1250],[1163,16425,1187],{"className":16426},[1213,1217,1250],[1163,16428,16430],{"className":16429},[1221],[1163,16431,16433,16453],{"className":16432},[1225,1226],[1163,16434,16436,16450],{"className":16435},[1230],[1163,16437,16439],{"className":16438,"style":3874},[1234],[1163,16440,16441,16444],{"style":4321},[1163,16442],{"className":16443,"style":3881},[1242],[1163,16445,16447],{"className":16446},[1247,3885,3886,1250],[1163,16448,3726],{"className":16449,"style":4064},[1213,1217,1250],[1163,16451,1258],{"className":16452},[1257],[1163,16454,16456],{"className":16455},[1230],[1163,16457,16459],{"className":16458,"style":3902},[1234],[1163,16460],{},[1163,16462,16463,16466],{"style":3907},[1163,16464],{"className":16465,"style":3400},[1242],[1163,16467],{"className":16468,"style":3915},[3914],[1163,16470,16471,16474],{"style":4185},[1163,16472],{"className":16473,"style":3400},[1242],[1163,16475,16477],{"className":16476},[1247,1248,1249,1250],[1163,16478,16480,16483],{"className":16479},[1213,1250],[1163,16481,3685],{"className":16482,"style":3855},[1213,1250],[1163,16484,16486,16489],{"className":16485},[1213,1250],[1163,16487,1187],{"className":16488},[1213,1217,1250],[1163,16490,16492],{"className":16491},[1221],[1163,16493,16495,16515],{"className":16494},[1225,1226],[1163,16496,16498,16512],{"className":16497},[1230],[1163,16499,16501],{"className":16500,"style":4150},[1234],[1163,16502,16503,16506],{"style":4153},[1163,16504],{"className":16505,"style":3881},[1242],[1163,16507,16509],{"className":16508},[1247,3885,3886,1250],[1163,16510,1190],{"className":16511},[1213,1217,1250],[1163,16513,1258],{"className":16514},[1257],[1163,16516,16518],{"className":16517},[1230],[1163,16519,16521],{"className":16520,"style":4172},[1234],[1163,16522],{},[1163,16524,1258],{"className":16525},[1257],[1163,16527,16529],{"className":16528},[1230],[1163,16530,16532],{"className":16531,"style":3943},[1234],[1163,16533],{},[1163,16535],{"className":16536},[1776,3826],[1163,16538],{"className":1653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\\leftarrow \\text{threshold} \\times \\frac{g}{\\lVert g \\rVert} \\quad \\text{if } \\lVert g \\rVert > \\text{threshold}",[1163,16830,16832,16850,16871,16980],{"className":16831,"ariaHidden":1200},[1199],[1163,16833,16835,16838,16841,16844,16847],{"className":16834},[1204],[1163,16836],{"className":16837,"style":1839},[1208],[1163,16839,6301],{"className":16840,"style":1479},[1213,1217],[1163,16842],{"className":16843,"style":1461},[1460],[1163,16845,6368],{"className":16846},[1465],[1163,16848],{"className":16849,"style":1461},[1460],[1163,16851,16853,16856,16862,16865,16868],{"className":16852},[1204],[1163,16854],{"className":16855,"style":6416},[1208],[1163,16857,16859],{"className":16858},[1213,5072],[1163,16860,6308],{"className":16861},[1213],[1163,16863],{"className":16864,"style":1534},[1460],[1163,16866,6373],{"className":16867},[1538],[1163,16869],{"className":16870,"style":1534},[1460],[1163,16872,16874,16878,16952,16956,16962,16965,16968,16971,16974,16977],{"className":16873},[1204],[1163,16875],{"className":16876,"style":16877},[1208],"height:1.27em;vertical-align:-0.52em;",[1163,16879,16881,16884,16949],{"className":16880},[1213],[1163,16882],{"className":16883},[1483,3826],[1163,16885,16887],{"className":16886},[3678],[1163,16888,16890,16941],{"className":16889},[1225,1226],[1163,16891,16893,16938],{"className":16892},[1230],[1163,16894,16896,16916,16924],{"className":16895,"style":6457},[1234],[1163,16897,16898,16901],{"style":3842},[1163,16899],{"className":16900,"style":3400},[1242],[1163,16902,16904],{"className":16903},[1247,1248,1249,1250],[1163,16905,16907,16910,16913],{"className":16906},[1213,1250],[1163,16908,6298],{"className":16909},[1483,1250],[1163,16911,6301],{"className":16912,"style":1479},[1213,1217,1250],[1163,16914,6298],{"className":16915},[1776,1250],[1163,16917,16918,16921],{"style":3907},[1163,16919],{"className":16920,"style":3400},[1242],[1163,16922],{"className":16923,"style":3915},[3914],[1163,16925,16926,16929],{"style":6488},[1163,16927],{"className":16928,"style":3400},[1242],[1163,16930,16932],{"className":16931},[1247,1248,1249,1250],[1163,16933,16935],{"className":16934},[1213,1250],[1163,16936,6301],{"className":16937,"style":1479},[1213,1217,1250],[1163,16939,1258],{"className":16940},[1257],[1163,16942,16944],{"className":16943},[1230],[1163,16945,16947],{"className":16946,"style":6510},[1234],[1163,16948],{},[1163,16950],{"className":16951},[1776,3826],[1163,16953],{"className":16954,"style":16955},[1460],"margin-right:1em;",[1163,16957,16959],{"className":16958},[1213,5072],[1163,16960,16815],{"className":16961},[1213],[1163,16963,6298],{"className":16964},[1483],[1163,16966,6301],{"className":16967,"style":1479},[1213,1217],[1163,16969,6298],{"className":16970},[1776],[1163,16972],{"className":16973,"style":1461},[1460],[1163,16975,5975],{"className":16976},[1465],[1163,16978],{"className":16979,"style":1461},[1460],[1163,16981,16983,16986],{"className":16982},[1204],[1163,16984],{"className":16985,"style":3393},[1208],[1163,16987,16989],{"className":16988},[1213,5072],[1163,16990,6308],{"className":16991},[1213],[2068,16993,16994,16999],{},[2083,16995,16996],{},[1107,16997,16998],{},"LSTM 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