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和值 ",[58,658,660,689],{"className":659},[61],[58,661,663],{"className":662},[65],[67,664,665],{"xmlns":69},[71,666,667,686],{},[74,668,669,672,674],{},[90,670,671],{},"V",[460,673,462],{},[464,675,676,678],{},[90,677,469],{"mathvariant":468},[74,679,680,682,684],{},[90,681,365],{},[460,683,476],{},[90,685,425],{},[97,687,688],{"encoding":99},"V \\in \\mathbb{R}^{m \\times 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的缩放点积注意力是：",[14,758,759],{},[58,760,762,867],{"className":761},[61],[58,763,765],{"className":764},[65],[67,766,767],{"xmlns":69},[71,768,769,864],{},[74,770,771,774,777,779,782,784,786,789,792,794,798,800,803,805,807,809,812,815,819,822,845,847,849,861],{},[90,772,773],{},"A",[90,775,776],{},"t",[90,778,776],{},[90,780,781],{},"e",[90,783,334],{},[90,785,776],{},[90,787,788],{},"i",[90,790,791],{},"o",[90,793,334],{},[460,795,797],{"stretchy":796},"false","(",[90,799,458],{},[460,801,802],{"separator":105},",",[90,804,571],{},[460,806,802],{"separator":105},[90,808,671],{},[460,810,811],{"stretchy":796},")",[460,813,814],{},"=",[90,816,818],{"mathvariant":817},"normal","softmax",[460,820,821],{},"⁡",[74,823,824,826,843],{},[460,825,797],{"fence":105},[77,827,828,839],{},[74,829,830,832],{},[90,831,458],{},[464,833,834,836],{},[90,835,571],{},[90,837,838],{"mathvariant":817},"⊤",[84,840,841],{},[90,842,92],{},[460,844,811],{"fence":105},[90,846,671],{},[460,848,462],{},[464,850,851,853],{},[90,852,469],{"mathvariant":468},[74,854,855,857,859],{},[90,856,334],{},[460,858,476],{},[90,860,425],{},[90,862,863],{"mathvariant":817},".",[97,865,866],{"encoding":99}," Attention(Q,K,V) = \\operatorname{softmax}\\left(\\frac{QK^\\top}{\\sqrt{d}}\\right)V \\in \\mathbb{R}^{n \\times v}.",[58,868,870,940,1142],{"className":869,"ariaHidden":105},[104],[58,871,873,877,880,884,887,890,893,896,899,902,905,908,912,916,919,922,925,928,931,934,937],{"className":872},[109],[58,874],{"className":875,"style":876},[113],"height:1em;vertical-align:-0.25em;",[58,878,773],{"className":879},[118,191],[58,881,883],{"className":882},[118,191],"tt",[58,885,781],{"className":886},[118,191],[58,888,334],{"className":889},[118,191],[58,891,776],{"className":892},[118,191],[58,894,788],{"className":895},[118,191],[58,897,791],{"className":898},[118,191],[58,900,334],{"className":901},[118,191],[58,903,797],{"className":904},[122],[58,906,458],{"className":907},[118,191],[58,909,802],{"className":910},[911],"mpunct",[58,913],{"className":914,"style":915},[498],"margin-right:0.1667em;",[58,917,571],{"className":918,"style":602},[118,191],[58,920,802],{"className":921},[911],[58,923],{"className":924,"style":915},[498],[58,926,671],{"className":927,"style":701},[118,191],[58,929,811],{"className":930},[312],[58,932],{"className":933,"style":499},[498],[58,935,814],{"className":936},[503],[58,938],{"className":939,"style":499},[498],[58,941,943,947,955,958,1127,1130,1133,1136,1139],{"className":942},[109],[58,944],{"className":945,"style":946},[113],"height:1.8em;vertical-align:-0.65em;",[58,948,951],{"className":949},[950],"mop",[58,952,818],{"className":953},[118,954],"mathrm",[58,956],{"className":957,"style":915},[498],[58,959,962,972,1121],{"className":960},[961],"minner",[58,963,967],{"className":964,"style":966},[122,965],"delimcenter","top:0em;",[58,968,797],{"className":969},[970,971],"delimsizing","size2",[58,973,975,978,1118],{"className":974},[118],[58,976],{"className":977},[122,123],[58,979,981],{"className":980},[77],[58,982,984,1110],{"className":983},[130,131],[58,985,987,1107],{"className":986},[135],[58,988,991,1053,1061],{"className":989,"style":990},[139],"height:1.095em;",[58,992,994,997],{"style":993},"top:-2.5335em;",[58,995],{"className":996,"style":148},[147],[58,998,1000],{"className":999},[152,153,154,155],[58,1001,1003],{"className":1002},[118,155],[58,1004,1006],{"className":1005},[118,162,155],[58,1007,1009,1044],{"className":1008},[130,131],[58,1010,1012,1041],{"className":1011},[135],[58,1013,1016,1028],{"className":1014,"style":1015},[139],"height:0.9378em;",[58,1017,1019,1022],{"className":1018,"style":177},[176],[58,1020],{"className":1021,"style":148},[147],[58,1023,1025],{"className":1024,"style":184},[118,155],[58,1026,92],{"className":1027},[118,191,155],[58,1029,1031,1034],{"style":1030},"top:-2.8978em;",[58,1032],{"className":1033,"style":148},[147],[58,1035,1037],{"className":1036,"style":246},[245,155],[248,1038,1039],{"xmlns":250,"width":251,"height":252,"viewBox":253,"preserveAspectRatio":254},[256,1040],{"d":258},[58,1042,226],{"className":1043},[225],[58,1045,1047],{"className":1046},[135],[58,1048,1051],{"className":1049,"style":1050},[139],"height:0.1022em;",[58,1052],{},[58,1054,1055,1058],{"style":273},[58,1056],{"className":1057,"style":148},[147],[58,1059],{"className":1060,"style":281},[280],[58,1062,1064,1067],{"style":1063},"top:-3.4461em;",[58,1065],{"className":1066,"style":148},[147],[58,1068,1070],{"className":1069},[152,153,154,155],[58,1071,1073,1076],{"className":1072},[118,155],[58,1074,458],{"className":1075},[118,191,155],[58,1077,1079,1082],{"className":1078},[118,155],[58,1080,571],{"className":1081,"style":602},[118,191,155],[58,1083,1085],{"className":1084},[195],[58,1086,1088],{"className":1087},[130],[58,1089,1091],{"className":1090},[135],[58,1092,1095],{"className":1093,"style":1094},[139],"height:0.927em;",[58,1096,1098,1101],{"style":1097},"top:-2.931em;margin-right:0.0714em;",[58,1099],{"className":1100,"style":212},[147],[58,1102,1104],{"className":1103},[152,216,217,155],[58,1105,838],{"className":1106},[118,155],[58,1108,226],{"className":1109},[225],[58,1111,1113],{"className":1112},[135],[58,1114,1116],{"className":1115,"style":306},[139],[58,1117],{},[58,1119],{"className":1120},[312,123],[58,1122,1124],{"className":1123,"style":966},[312,965],[58,1125,811],{"className":1126},[970,971],[58,1128],{"className":1129,"style":915},[498],[58,1131,671],{"className":1132,"style":701},[118,191],[58,1134],{"className":1135,"style":499},[498],[58,1137,462],{"className":1138},[503],[58,1140],{"className":1141,"style":499},[498],[58,1143,1145,1148,1186],{"className":1144},[109],[58,1146],{"className":1147,"style":717},[113],[58,1149,1151,1154],{"className":1150},[118],[58,1152,469],{"className":1153},[118,520],[58,1155,1157],{"className":1156},[195],[58,1158,1160],{"className":1159},[130],[58,1161,1163],{"className":1162},[135],[58,1164,1166],{"className":1165,"style":717},[139],[58,1167,1168,1171],{"style":535},[58,1169],{"className":1170,"style":539},[147],[58,1172,1174],{"className":1173},[152,153,154,155],[58,1175,1177,1180,1183],{"className":1176},[118,155],[58,1178,334],{"className":1179},[118,191,155],[58,1181,476],{"className":1182},[552,155],[58,1184,425],{"className":1185,"style":440},[118,191,155],[58,1187,863],{"className":1188},[118],[14,1190,1191],{},[40,1192],{"alt":1193,"src":1194},"注意力","transformer/attention.png",[14,1196,1197,1198,1272,1273,1344,1345,1465],{},"缩放点积注意力的输入由维度为 ",[58,1199,1201,1219],{"className":1200},[61],[58,1202,1204],{"className":1203},[65],[67,1205,1206],{"xmlns":69},[71,1207,1208,1216],{},[74,1209,1210],{},[87,1211,1212,1214],{},[90,1213,92],{},[90,1215,95],{},[97,1217,1218],{"encoding":99},"d_k",[58,1220,1222],{"className":1221,"ariaHidden":105},[104],[58,1223,1225,1229],{"className":1224},[109],[58,1226],{"className":1227,"style":1228},[113],"height:0.8444em;vertical-align:-0.15em;",[58,1230,1232,1235],{"className":1231},[118],[58,1233,92],{"className":1234},[118,191],[58,1236,1238],{"className":1237},[195],[58,1239,1241,1263],{"className":1240},[130,131],[58,1242,1244,1260],{"className":1243},[135],[58,1245,1248],{"className":1246,"style":1247},[139],"height:0.3361em;",[58,1249,1251,1254],{"style":1250},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[58,1252],{"className":1253,"style":539},[147],[58,1255,1257],{"className":1256},[152,153,154,155],[58,1258,95],{"className":1259,"style":221},[118,191,155],[58,1261,226],{"className":1262},[225],[58,1264,1266],{"className":1265},[135],[58,1267,1270],{"className":1268,"style":1269},[139],"height:0.15em;",[58,1271],{}," ​的查询和键以及维度为 ",[58,1274,1276,1294],{"className":1275},[61],[58,1277,1279],{"className":1278},[65],[67,1280,1281],{"xmlns":69},[71,1282,1283,1291],{},[74,1284,1285],{},[87,1286,1287,1289],{},[90,1288,92],{},[90,1290,425],{},[97,1292,1293],{"encoding":99},"d_v",[58,1295,1297],{"className":1296,"ariaHidden":105},[104],[58,1298,1300,1303],{"className":1299},[109],[58,1301],{"className":1302,"style":1228},[113],[58,1304,1306,1309],{"className":1305},[118],[58,1307,92],{"className":1308},[118,191],[58,1310,1312],{"className":1311},[195],[58,1313,1315,1336],{"className":1314},[130,131],[58,1316,1318,1333],{"className":1317},[135],[58,1319,1322],{"className":1320,"style":1321},[139],"height:0.1514em;",[58,1323,1324,1327],{"style":1250},[58,1325],{"className":1326,"style":539},[147],[58,1328,1330],{"className":1329},[152,153,154,155],[58,1331,425],{"className":1332,"style":440},[118,191,155],[58,1334,226],{"className":1335},[225],[58,1337,1339],{"className":1338},[135],[58,1340,1342],{"className":1341,"style":1269},[139],[58,1343],{}," ​的值组成。我们计算查询与所有键的点积，将每个点积除以 ",[58,1346,1348,1368],{"className":1347},[61],[58,1349,1351],{"className":1350},[65],[67,1352,1353],{"xmlns":69},[71,1354,1355,1365],{},[74,1356,1357],{},[84,1358,1359],{},[87,1360,1361,1363],{},[90,1362,92],{},[90,1364,95],{},[97,1366,1367],{"encoding":99},"\\sqrt{d_k}",[58,1369,1371],{"className":1370,"ariaHidden":105},[104],[58,1372,1374,1378],{"className":1373},[109],[58,1375],{"className":1376,"style":1377},[113],"height:1.04em;vertical-align:-0.1828em;",[58,1379,1381],{"className":1380},[118,162],[58,1382,1384,1456],{"className":1383},[130,131],[58,1385,1387,1453],{"className":1386},[135],[58,1388,1391,1440],{"className":1389,"style":1390},[139],"height:0.8572em;",[58,1392,1394,1397],{"className":1393,"style":177},[176],[58,1395],{"className":1396,"style":148},[147],[58,1398,1400],{"className":1399,"style":184},[118],[58,1401,1403,1406],{"className":1402},[118],[58,1404,92],{"className":1405},[118,191],[58,1407,1409],{"className":1408},[195],[58,1410,1412,1432],{"className":1411},[130,131],[58,1413,1415,1429],{"className":1414},[135],[58,1416,1418],{"className":1417,"style":1247},[139],[58,1419,1420,1423],{"style":1250},[58,1421],{"className":1422,"style":539},[147],[58,1424,1426],{"className":1425},[152,153,154,155],[58,1427,95],{"className":1428,"style":221},[118,191,155],[58,1430,226],{"className":1431},[225],[58,1433,1435],{"className":1434},[135],[58,1436,1438],{"className":1437,"style":1269},[139],[58,1439],{},[58,1441,1443,1446],{"style":1442},"top:-2.8172em;",[58,1444],{"className":1445,"style":148},[147],[58,1447,1449],{"className":1448,"style":246},[245],[248,1450,1451],{"xmlns":250,"width":251,"height":252,"viewBox":253,"preserveAspectRatio":254},[256,1452],{"d":258},[58,1454,226],{"className":1455},[225],[58,1457,1459],{"className":1458},[135],[58,1460,1463],{"className":1461,"style":1462},[139],"height:0.1828em;",[58,1464],{},"​​，并应用softmax函数以获得值上的权重。",[14,1467,1468,1469,1538,1539,1608,1609,1678,1679,1709,1710,1738,1739,1769,1770,1798,1799,2102,2103,1769,2131,2200,2201,313],{},"对于较小的 ",[58,1470,1472,1489],{"className":1471},[61],[58,1473,1475],{"className":1474},[65],[67,1476,1477],{"xmlns":69},[71,1478,1479,1487],{},[74,1480,1481],{},[87,1482,1483,1485],{},[90,1484,92],{},[90,1486,95],{},[97,1488,1218],{"encoding":99},[58,1490,1492],{"className":1491,"ariaHidden":105},[104],[58,1493,1495,1498],{"className":1494},[109],[58,1496],{"className":1497,"style":1228},[113],[58,1499,1501,1504],{"className":1500},[118],[58,1502,92],{"className":1503},[118,191],[58,1505,1507],{"className":1506},[195],[58,1508,1510,1530],{"className":1509},[130,131],[58,1511,1513,1527],{"className":1512},[135],[58,1514,1516],{"className":1515,"style":1247},[139],[58,1517,1518,1521],{"style":1250},[58,1519],{"className":1520,"style":539},[147],[58,1522,1524],{"className":1523},[152,153,154,155],[58,1525,95],{"className":1526,"style":221},[118,191,155],[58,1528,226],{"className":1529},[225],[58,1531,1533],{"className":1532},[135],[58,1534,1536],{"className":1535,"style":1269},[139],[58,1537],{}," 值来说，加性注意力和点积注意力的表现相似，但加性注意力在 ",[58,1540,1542,1559],{"className":1541},[61],[58,1543,1545],{"className":1544},[65],[67,1546,1547],{"xmlns":69},[71,1548,1549,1557],{},[74,1550,1551],{},[87,1552,1553,1555],{},[90,1554,92],{},[90,1556,95],{},[97,1558,1218],{"encoding":99},[58,1560,1562],{"className":1561,"ariaHidden":105},[104],[58,1563,1565,1568],{"className":1564},[109],[58,1566],{"className":1567,"style":1228},[113],[58,1569,1571,1574],{"className":1570},[118],[58,1572,92],{"className":1573},[118,191],[58,1575,1577],{"className":1576},[195],[58,1578,1580,1600],{"className":1579},[130,131],[58,1581,1583,1597],{"className":1582},[135],[58,1584,1586],{"className":1585,"style":1247},[139],[58,1587,1588,1591],{"style":1250},[58,1589],{"className":1590,"style":539},[147],[58,1592,1594],{"className":1593},[152,153,154,155],[58,1595,95],{"className":1596,"style":221},[118,191,155],[58,1598,226],{"className":1599},[225],[58,1601,1603],{"className":1602},[135],[58,1604,1606],{"className":1605,"style":1269},[139],[58,1607],{}," 值较大时会优于点积注意力。我们怀疑在 ",[58,1610,1612,1629],{"className":1611},[61],[58,1613,1615],{"className":1614},[65],[67,1616,1617],{"xmlns":69},[71,1618,1619,1627],{},[74,1620,1621],{},[87,1622,1623,1625],{},[90,1624,92],{},[90,1626,95],{},[97,1628,1218],{"encoding":99},[58,1630,1632],{"className":1631,"ariaHidden":105},[104],[58,1633,1635,1638],{"className":1634},[109],[58,1636],{"className":1637,"style":1228},[113],[58,1639,1641,1644],{"className":1640},[118],[58,1642,92],{"className":1643},[118,191],[58,1645,1647],{"className":1646},[195],[58,1648,1650,1670],{"className":1649},[130,131],[58,1651,1653,1667],{"className":1652},[135],[58,1654,1656],{"className":1655,"style":1247},[139],[58,1657,1658,1661],{"style":1250},[58,1659],{"className":1660,"style":539},[147],[58,1662,1664],{"className":1663},[152,153,154,155],[58,1665,95],{"className":1666,"style":221},[118,191,155],[58,1668,226],{"className":1669},[225],[58,1671,1673],{"className":1672},[135],[58,1674,1676],{"className":1675,"style":1269},[139],[58,1677],{}," 值较大时，点积的值会很大，导致 softmax 集中在很小的一个区域内。为了更好地说明这一点，我们假设查询 ",[58,1680,1682,1696],{"className":1681},[61],[58,1683,1685],{"className":1684},[65],[67,1686,1687],{"xmlns":69},[71,1688,1689,1694],{},[74,1690,1691],{},[90,1692,1693],{},"q",[97,1695,1693],{"encoding":99},[58,1697,1699],{"className":1698,"ariaHidden":105},[104],[58,1700,1702,1706],{"className":1701},[109],[58,1703],{"className":1704,"style":1705},[113],"height:0.625em;vertical-align:-0.1944em;",[58,1707,1693],{"className":1708,"style":440},[118,191]," 和键 ",[58,1711,1713,1726],{"className":1712},[61],[58,1714,1716],{"className":1715},[65],[67,1717,1718],{"xmlns":69},[71,1719,1720,1724],{},[74,1721,1722],{},[90,1723,95],{},[97,1725,95],{"encoding":99},[58,1727,1729],{"className":1728,"ariaHidden":105},[104],[58,1730,1732,1735],{"className":1731},[109],[58,1733],{"className":1734,"style":406},[113],[58,1736,95],{"className":1737,"style":221},[118,191]," 都符合一个均值为 ",[58,1740,1742,1756],{"className":1741},[61],[58,1743,1745],{"className":1744},[65],[67,1746,1747],{"xmlns":69},[71,1748,1749,1754],{},[74,1750,1751],{},[80,1752,1753],{},"0",[97,1755,1753],{"encoding":99},[58,1757,1759],{"className":1758,"ariaHidden":105},[104],[58,1760,1762,1766],{"className":1761},[109],[58,1763],{"className":1764,"style":1765},[113],"height:0.6444em;",[58,1767,1753],{"className":1768},[118],"，方差为 ",[58,1771,1773,1786],{"className":1772},[61],[58,1774,1776],{"className":1775},[65],[67,1777,1778],{"xmlns":69},[71,1779,1780,1784],{},[74,1781,1782],{},[80,1783,82],{},[97,1785,82],{"encoding":99},[58,1787,1789],{"className":1788,"ariaHidden":105},[104],[58,1790,1792,1795],{"className":1791},[109],[58,1793],{"className":1794,"style":1765},[113],[58,1796,82],{"className":1797},[118]," 的随机变量。他们点积的结果 ",[58,1800,1802,1855],{"className":1801},[61],[58,1803,1805],{"className":1804},[65],[67,1806,1807],{"xmlns":69},[71,1808,1809,1852],{},[74,1810,1811,1813,1816,1818,1820,1840,1846],{},[90,1812,1693],{},[460,1814,1815],{},"⋅",[90,1817,95],{},[460,1819,814],{},[1821,1822,1823,1826,1834],"msubsup",{},[460,1824,1825],{},"∑",[74,1827,1828,1830,1832],{},[90,1829,788],{},[460,1831,814],{},[80,1833,82],{},[87,1835,1836,1838],{},[90,1837,92],{},[90,1839,95],{},[87,1841,1842,1844],{},[90,1843,1693],{},[90,1845,788],{},[87,1847,1848,1850],{},[90,1849,95],{},[90,1851,788],{},[97,1853,1854],{"encoding":99},"q \\cdot k = \\sum_{i=1}^{d_k}q_{i}k_{i}",[58,1856,1858,1878,1896],{"className":1857,"ariaHidden":105},[104],[58,1859,1861,1865,1868,1872,1875],{"className":1860},[109],[58,1862],{"className":1863,"style":1864},[113],"height:0.6389em;vertical-align:-0.1944em;",[58,1866,1693],{"className":1867,"style":440},[118,191],[58,1869],{"className":1870,"style":1871},[498],"margin-right:0.2222em;",[58,1873,1815],{"className":1874},[552],[58,1876],{"className":1877,"style":1871},[498],[58,1879,1881,1884,1887,1890,1893],{"className":1880},[109],[58,1882],{"className":1883,"style":406},[113],[58,1885,95],{"className":1886,"style":221},[118,191],[58,1888],{"className":1889,"style":499},[498],[58,1891,814],{"className":1892},[503],[58,1894],{"className":1895,"style":499},[498],[58,1897,1899,1903,2010,2013,2058],{"className":1898},[109],[58,1900],{"className":1901,"style":1902},[113],"height:1.2887em;vertical-align:-0.2997em;",[58,1904,1906,1912],{"className":1905},[950],[58,1907,1825],{"className":1908,"style":1911},[950,1909,1910],"op-symbol","small-op","position:relative;top:0em;",[58,1913,1915],{"className":1914},[195],[58,1916,1918,2001],{"className":1917},[130,131],[58,1919,1921,1998],{"className":1920},[135],[58,1922,1925,1946],{"className":1923,"style":1924},[139],"height:0.989em;",[58,1926,1928,1931],{"style":1927},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[58,1929],{"className":1930,"style":539},[147],[58,1932,1934],{"className":1933},[152,153,154,155],[58,1935,1937,1940,1943],{"className":1936},[118,155],[58,1938,788],{"className":1939},[118,191,155],[58,1941,814],{"className":1942},[503,155],[58,1944,82],{"className":1945},[118,155],[58,1947,1949,1952],{"style":1948},"top:-3.2029em;margin-right:0.05em;",[58,1950],{"className":1951,"style":539},[147],[58,1953,1955],{"className":1954},[152,153,154,155],[58,1956,1958],{"className":1957},[118,155],[58,1959,1961,1964],{"className":1960},[118,155],[58,1962,92],{"className":1963},[118,191,155],[58,1965,1967],{"className":1966},[195],[58,1968,1970,1990],{"className":1969},[130,131],[58,1971,1973,1987],{"className":1972},[135],[58,1974,1976],{"className":1975,"style":205},[139],[58,1977,1978,1981],{"style":208},[58,1979],{"className":1980,"style":212},[147],[58,1982,1984],{"className":1983},[152,216,217,155],[58,1985,95],{"className":1986,"style":221},[118,191,155],[58,1988,226],{"className":1989},[225],[58,1991,1993],{"className":1992},[135],[58,1994,1996],{"className":1995,"style":233},[139],[58,1997],{},[58,1999,226],{"className":2000},[225],[58,2002,2004],{"className":2003},[135],[58,2005,2008],{"className":2006,"style":2007},[139],"height:0.2997em;",[58,2009],{},[58,2011],{"className":2012,"style":915},[498],[58,2014,2016,2019],{"className":2015},[118],[58,2017,1693],{"className":2018,"style":440},[118,191],[58,2020,2022],{"className":2021},[195],[58,2023,2025,2050],{"className":2024},[130,131],[58,2026,2028,2047],{"className":2027},[135],[58,2029,2032],{"className":2030,"style":2031},[139],"height:0.3117em;",[58,2033,2035,2038],{"style":2034},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[58,2036],{"className":2037,"style":539},[147],[58,2039,2041],{"className":2040},[152,153,154,155],[58,2042,2044],{"className":2043},[118,155],[58,2045,788],{"className":2046},[118,191,155],[58,2048,226],{"className":2049},[225],[58,2051,2053],{"className":2052},[135],[58,2054,2056],{"className":2055,"style":1269},[139],[58,2057],{},[58,2059,2061,2064],{"className":2060},[118],[58,2062,95],{"className":2063,"style":221},[118,191],[58,2065,2067],{"className":2066},[195],[58,2068,2070,2094],{"className":2069},[130,131],[58,2071,2073,2091],{"className":2072},[135],[58,2074,2076],{"className":2075,"style":2031},[139],[58,2077,2079,2082],{"style":2078},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[58,2080],{"className":2081,"style":539},[147],[58,2083,2085],{"className":2084},[152,153,154,155],[58,2086,2088],{"className":2087},[118,155],[58,2089,788],{"className":2090},[118,191,155],[58,2092,226],{"className":2093},[225],[58,2095,2097],{"className":2096},[135],[58,2098,2100],{"className":2099,"style":1269},[139],[58,2101],{}," 的均值为 ",[58,2104,2106,2119],{"className":2105},[61],[58,2107,2109],{"className":2108},[65],[67,2110,2111],{"xmlns":69},[71,2112,2113,2117],{},[74,2114,2115],{},[80,2116,1753],{},[97,2118,1753],{"encoding":99},[58,2120,2122],{"className":2121,"ariaHidden":105},[104],[58,2123,2125,2128],{"className":2124},[109],[58,2126],{"className":2127,"style":1765},[113],[58,2129,1753],{"className":2130},[118],[58,2132,2134,2151],{"className":2133},[61],[58,2135,2137],{"className":2136},[65],[67,2138,2139],{"xmlns":69},[71,2140,2141,2149],{},[74,2142,2143],{},[87,2144,2145,2147],{},[90,2146,92],{},[90,2148,95],{},[97,2150,1218],{"encoding":99},[58,2152,2154],{"className":2153,"ariaHidden":105},[104],[58,2155,2157,2160],{"className":2156},[109],[58,2158],{"className":2159,"style":1228},[113],[58,2161,2163,2166],{"className":2162},[118],[58,2164,92],{"className":2165},[118,191],[58,2167,2169],{"className":2168},[195],[58,2170,2172,2192],{"className":2171},[130,131],[58,2173,2175,2189],{"className":2174},[135],[58,2176,2178],{"className":2177,"style":1247},[139],[58,2179,2180,2183],{"style":1250},[58,2181],{"className":2182,"style":539},[147],[58,2184,2186],{"className":2185},[152,153,154,155],[58,2187,95],{"className":2188,"style":221},[118,191,155],[58,2190,226],{"className":2191},[225],[58,2193,2195],{"className":2194},[135],[58,2196,2198],{"className":2197,"style":1269},[139],[58,2199],{},"，为了抵消这种影响，我们要乘以一个缩放因子 ",[58,2202,2204,2227],{"className":2203},[61],[58,2205,2207],{"className":2206},[65],[67,2208,2209],{"xmlns":69},[71,2210,2211,2225],{},[74,2212,2213],{},[77,2214,2215,2217],{},[80,2216,82],{},[84,2218,2219],{},[87,2220,2221,2223],{},[90,2222,92],{},[90,2224,95],{},[97,2226,100],{"encoding":99},[58,2228,2230],{"className":2229,"ariaHidden":105},[104],[58,2231,2233,2236],{"className":2232},[109],[58,2234],{"className":2235,"style":114},[113],[58,2237,2239,2242,2382],{"className":2238},[118],[58,2240],{"className":2241},[122,123],[58,2243,2245],{"className":2244},[77],[58,2246,2248,2374],{"className":2247},[130,131],[58,2249,2251,2371],{"className":2250},[135],[58,2252,2254,2349,2357],{"className":2253,"style":140},[139],[58,2255,2256,2259],{"style":143},[58,2257],{"className":2258,"style":148},[147],[58,2260,2262],{"className":2261},[152,153,154,155],[58,2263,2265],{"className":2264},[118,155],[58,2266,2268],{"className":2267},[118,162,155],[58,2269,2271,2341],{"className":2270},[130,131],[58,2272,2274,2338],{"className":2273},[135],[58,2275,2277,2326],{"className":2276,"style":172},[139],[58,2278,2280,2283],{"className":2279,"style":177},[176],[58,2281],{"className":2282,"style":148},[147],[58,2284,2286],{"className":2285,"style":184},[118,155],[58,2287,2289,2292],{"className":2288},[118,155],[58,2290,92],{"className":2291},[118,191,155],[58,2293,2295],{"className":2294},[195],[58,2296,2298,2318],{"className":2297},[130,131],[58,2299,2301,2315],{"className":2300},[135],[58,2302,2304],{"className":2303,"style":205},[139],[58,2305,2306,2309],{"style":208},[58,2307],{"className":2308,"style":212},[147],[58,2310,2312],{"className":2311},[152,216,217,155],[58,2313,95],{"className":2314,"style":221},[118,191,155],[58,2316,226],{"className":2317},[225],[58,2319,2321],{"className":2320},[135],[58,2322,2324],{"className":2323,"style":233},[139],[58,2325],{},[58,2327,2328,2331],{"style":238},[58,2329],{"className":2330,"style":148},[147],[58,2332,2334],{"className":2333,"style":246},[245,155],[248,2335,2336],{"xmlns":250,"width":251,"height":252,"viewBox":253,"preserveAspectRatio":254},[256,2337],{"d":258},[58,2339,226],{"className":2340},[225],[58,2342,2344],{"className":2343},[135],[58,2345,2347],{"className":2346,"style":268},[139],[58,2348],{},[58,2350,2351,2354],{"style":273},[58,2352],{"className":2353,"style":148},[147],[58,2355],{"className":2356,"style":281},[280],[58,2358,2359,2362],{"style":284},[58,2360],{"className":2361,"style":148},[147],[58,2363,2365],{"className":2364},[152,153,154,155],[58,2366,2368],{"className":2367},[118,155],[58,2369,82],{"className":2370},[118,155],[58,2372,226],{"className":2373},[225],[58,2375,2377],{"className":2376},[135],[58,2378,2380],{"className":2379,"style":306},[139],[58,2381],{},[58,2383],{"className":2384},[312,123],[14,2386,2387],{},"因为在训练和推理时，并非所有的值都应该加入注意力汇聚操作中，所以我们首先实现 masked_softmax 函数来保证在注意力汇聚时仅加入有意义的值。",[2389,2390,2395],"pre",{"className":2391,"code":2392,"language":2393,"meta":2394,"style":2394},"language-python shiki shiki-themes github-light dracula","def masked_softmax(X, valid_lens):\n    \"\"\"通过在最后一个轴上掩蔽元素来执行softmax操作\"\"\"\n    # X:3D张量，valid_lens:1D或2D张量\n    if valid_lens is None:\n        return nn.functional.softmax(X, dim=-1)\n    else:\n        shape = X.shape\n        if valid_lens.dim() == 1:\n            valid_lens = torch.repeat_interleave(valid_lens, shape[1])\n        else:\n            valid_lens = valid_lens.reshape(-1)\n        # 最后一轴上被掩蔽的元素使用一个非常大的负值替换，从而其softmax输出为0\n        X = d2l.sequence_mask(X.reshape(-1, shape[-1]), valid_lens,\n                              value=-1e6)\n        return nn.functional.softmax(X.reshape(shape), dim=-1)\n","python","",[2396,2397,2398,2426,2433,2440,2459,2480,2488,2499,2516,2532,2540,2557,2563,2588,2601],"code",{"__ignoreMap":2394},[58,2399,2402,2406,2410,2413,2417,2420,2423],{"class":2400,"line":2401},"line",1,[58,2403,2405],{"class":2404},"szJfE","def",[58,2407,2409],{"class":2408},"sCLZk"," masked_softmax",[58,2411,797],{"class":2412},"scbbO",[58,2414,2416],{"class":2415},"syNf4","X",[58,2418,2419],{"class":2412},", ",[58,2421,2422],{"class":2415},"valid_lens",[58,2424,2425],{"class":2412},"):\n",[58,2427,2429],{"class":2400,"line":2428},2,[58,2430,2432],{"class":2431},"seLWX","    \"\"\"通过在最后一个轴上掩蔽元素来执行softmax操作\"\"\"\n",[58,2434,2436],{"class":2400,"line":2435},3,[58,2437,2439],{"class":2438},"sfgPZ","    # X:3D张量，valid_lens:1D或2D张量\n",[58,2441,2443,2446,2449,2452,2456],{"class":2400,"line":2442},4,[58,2444,2445],{"class":2404},"    if",[58,2447,2448],{"class":2412}," valid_lens ",[58,2450,2451],{"class":2404},"is",[58,2453,2455],{"class":2454},"soDru"," None",[58,2457,2458],{"class":2412},":\n",[58,2460,2462,2465,2468,2472,2475,2477],{"class":2400,"line":2461},5,[58,2463,2464],{"class":2404},"        return",[58,2466,2467],{"class":2412}," nn.functional.softmax(X, ",[58,2469,2471],{"class":2470},"sQkXh","dim",[58,2473,2474],{"class":2404},"=-",[58,2476,82],{"class":2454},[58,2478,2479],{"class":2412},")\n",[58,2481,2483,2486],{"class":2400,"line":2482},6,[58,2484,2485],{"class":2404},"    else",[58,2487,2458],{"class":2412},[58,2489,2491,2494,2496],{"class":2400,"line":2490},7,[58,2492,2493],{"class":2412},"        shape ",[58,2495,814],{"class":2404},[58,2497,2498],{"class":2412}," X.shape\n",[58,2500,2502,2505,2508,2511,2514],{"class":2400,"line":2501},8,[58,2503,2504],{"class":2404},"        if",[58,2506,2507],{"class":2412}," valid_lens.dim() ",[58,2509,2510],{"class":2404},"==",[58,2512,2513],{"class":2454}," 1",[58,2515,2458],{"class":2412},[58,2517,2519,2522,2524,2527,2529],{"class":2400,"line":2518},9,[58,2520,2521],{"class":2412},"            valid_lens ",[58,2523,814],{"class":2404},[58,2525,2526],{"class":2412}," torch.repeat_interleave(valid_lens, shape[",[58,2528,82],{"class":2454},[58,2530,2531],{"class":2412},"])\n",[58,2533,2535,2538],{"class":2400,"line":2534},10,[58,2536,2537],{"class":2404},"        else",[58,2539,2458],{"class":2412},[58,2541,2543,2545,2547,2550,2553,2555],{"class":2400,"line":2542},11,[58,2544,2521],{"class":2412},[58,2546,814],{"class":2404},[58,2548,2549],{"class":2412}," valid_lens.reshape(",[58,2551,2552],{"class":2404},"-",[58,2554,82],{"class":2454},[58,2556,2479],{"class":2412},[58,2558,2560],{"class":2400,"line":2559},12,[58,2561,2562],{"class":2438},"        # 最后一轴上被掩蔽的元素使用一个非常大的负值替换，从而其softmax输出为0\n",[58,2564,2566,2569,2571,2574,2576,2578,2581,2583,2585],{"class":2400,"line":2565},13,[58,2567,2568],{"class":2412},"        X ",[58,2570,814],{"class":2404},[58,2572,2573],{"class":2412}," d2l.sequence_mask(X.reshape(",[58,2575,2552],{"class":2404},[58,2577,82],{"class":2454},[58,2579,2580],{"class":2412},", shape[",[58,2582,2552],{"class":2404},[58,2584,82],{"class":2454},[58,2586,2587],{"class":2412},"]), valid_lens,\n",[58,2589,2591,2594,2596,2599],{"class":2400,"line":2590},14,[58,2592,2593],{"class":2470},"                              value",[58,2595,2474],{"class":2404},[58,2597,2598],{"class":2454},"1e6",[58,2600,2479],{"class":2412},[58,2602,2604,2606,2609,2611,2613,2615],{"class":2400,"line":2603},15,[58,2605,2464],{"class":2404},[58,2607,2608],{"class":2412}," nn.functional.softmax(X.reshape(shape), ",[58,2610,2471],{"class":2470},[58,2612,2474],{"class":2404},[58,2614,82],{"class":2454},[58,2616,2479],{"class":2412},[14,2618,2619],{},"下面实现缩放点积注意力。",[2389,2621,2623],{"className":2391,"code":2622,"language":2393,"meta":2394,"style":2394},"class DotProductAttention(nn.Module):\n    \"\"\"缩放点积注意力\"\"\"\n    def __init__(self, dropout, **kwargs):\n        super(DotProductAttention, self).__init__(**kwargs)\n        self.dropout = nn.Dropout(dropout)\n\n    # queries的形状：(batch_size，查询的个数，d)\n    # keys的形状：(batch_size，“键－值”对的个数，d)\n    # values的形状：(batch_size，“键－值”对的个数，值的维度)\n    # valid_lens的形状:(batch_size，)或者(batch_size，查询的个数)\n    def forward(self, queries, keys, values, valid_lens=None):\n        d = queries.shape[-1]\n        # 设置transpose_b=True为了交换keys的最后两个维度\n        scores = torch.bmm(queries, keys.transpose(1,2)) / math.sqrt(d)\n        self.attention_weights = masked_softmax(scores, valid_lens)\n        return torch.bmm(self.dropout(self.attention_weights), values)\n",[2396,2624,2625,2647,2652,2681,2706,2719,2725,2730,2735,2740,2745,2782,2799,2804,2830,2842],{"__ignoreMap":2394},[58,2626,2627,2630,2634,2636,2640,2642,2645],{"class":2400,"line":2401},[58,2628,2629],{"class":2404},"class",[58,2631,2633],{"class":2632},"skCyd"," DotProductAttention",[58,2635,797],{"class":2412},[58,2637,2639],{"class":2638},"sDP9b","nn",[58,2641,863],{"class":2412},[58,2643,2644],{"class":2638},"Module",[58,2646,2425],{"class":2412},[58,2648,2649],{"class":2400,"line":2428},[58,2650,2651],{"class":2431},"    \"\"\"缩放点积注意力\"\"\"\n",[58,2653,2654,2657,2660,2662,2666,2668,2671,2673,2676,2679],{"class":2400,"line":2435},[58,2655,2656],{"class":2404},"    def",[58,2658,2659],{"class":2454}," __init__",[58,2661,797],{"class":2412},[58,2663,2665],{"class":2664},"sD3jg","self",[58,2667,2419],{"class":2412},[58,2669,2670],{"class":2415},"dropout",[58,2672,2419],{"class":2412},[58,2674,2675],{"class":2404},"**",[58,2677,2678],{"class":2415},"kwargs",[58,2680,2425],{"class":2412},[58,2682,2683,2687,2690,2693,2696,2699,2701,2703],{"class":2400,"line":2442},[58,2684,2686],{"class":2685},"sPGBF","        super",[58,2688,2689],{"class":2412},"(DotProductAttention, ",[58,2691,2665],{"class":2692},"sJti5",[58,2694,2695],{"class":2412},").",[58,2697,2698],{"class":2454},"__init__",[58,2700,797],{"class":2412},[58,2702,2675],{"class":2404},[58,2704,2705],{"class":2412},"kwargs)\n",[58,2707,2708,2711,2714,2716],{"class":2400,"line":2461},[58,2709,2710],{"class":2692},"        self",[58,2712,2713],{"class":2412},".dropout ",[58,2715,814],{"class":2404},[58,2717,2718],{"class":2412}," nn.Dropout(dropout)\n",[58,2720,2721],{"class":2400,"line":2482},[58,2722,2724],{"emptyLinePlaceholder":2723},true,"\n",[58,2726,2727],{"class":2400,"line":2490},[58,2728,2729],{"class":2438},"    # queries的形状：(batch_size，查询的个数，d)\n",[58,2731,2732],{"class":2400,"line":2501},[58,2733,2734],{"class":2438},"    # keys的形状：(batch_size，“键－值”对的个数，d)\n",[58,2736,2737],{"class":2400,"line":2518},[58,2738,2739],{"class":2438},"    # values的形状：(batch_size，“键－值”对的个数，值的维度)\n",[58,2741,2742],{"class":2400,"line":2534},[58,2743,2744],{"class":2438},"    # valid_lens的形状:(batch_size，)或者(batch_size，查询的个数)\n",[58,2746,2747,2749,2752,2754,2756,2758,2761,2763,2766,2768,2771,2773,2775,2777,2780],{"class":2400,"line":2542},[58,2748,2656],{"class":2404},[58,2750,2751],{"class":2408}," forward",[58,2753,797],{"class":2412},[58,2755,2665],{"class":2664},[58,2757,2419],{"class":2412},[58,2759,2760],{"class":2415},"queries",[58,2762,2419],{"class":2412},[58,2764,2765],{"class":2415},"keys",[58,2767,2419],{"class":2412},[58,2769,2770],{"class":2415},"values",[58,2772,2419],{"class":2412},[58,2774,2422],{"class":2415},[58,2776,814],{"class":2404},[58,2778,2779],{"class":2454},"None",[58,2781,2425],{"class":2412},[58,2783,2784,2787,2789,2792,2794,2796],{"class":2400,"line":2559},[58,2785,2786],{"class":2412},"        d ",[58,2788,814],{"class":2404},[58,2790,2791],{"class":2412}," queries.shape[",[58,2793,2552],{"class":2404},[58,2795,82],{"class":2454},[58,2797,2798],{"class":2412},"]\n",[58,2800,2801],{"class":2400,"line":2565},[58,2802,2803],{"class":2438},"        # 设置transpose_b=True为了交换keys的最后两个维度\n",[58,2805,2806,2809,2811,2814,2816,2818,2821,2824,2827],{"class":2400,"line":2590},[58,2807,2808],{"class":2412},"        scores ",[58,2810,814],{"class":2404},[58,2812,2813],{"class":2412}," torch.bmm(queries, keys.transpose(",[58,2815,82],{"class":2454},[58,2817,802],{"class":2412},[58,2819,2820],{"class":2454},"2",[58,2822,2823],{"class":2412},")) ",[58,2825,2826],{"class":2404},"/",[58,2828,2829],{"class":2412}," math.sqrt(d)\n",[58,2831,2832,2834,2837,2839],{"class":2400,"line":2603},[58,2833,2710],{"class":2692},[58,2835,2836],{"class":2412},".attention_weights ",[58,2838,814],{"class":2404},[58,2840,2841],{"class":2412}," masked_softmax(scores, valid_lens)\n",[58,2843,2845,2847,2850,2852,2855,2857],{"class":2400,"line":2844},16,[58,2846,2464],{"class":2404},[58,2848,2849],{"class":2412}," torch.bmm(",[58,2851,2665],{"class":2692},[58,2853,2854],{"class":2412},".dropout(",[58,2856,2665],{"class":2692},[58,2858,2859],{"class":2412},".attention_weights), values)\n",[14,2861,2862,2863,2866],{},"代码中函数的 ",[2396,2864,2865],{},"**kwargs","表示任意关键字参数，为了符合 Pytorch 的继承约定。",[48,2868,2869],{"id":2869},"多头注意力",[14,2871,2872],{},"多头注意力机制允许模型在不同位置上同时关注来自不同表示子空间的信息。使用单一注意力头时，平均操作会抑制这种能力。",[14,2874,2875],{},[40,2876],{"alt":2394,"src":2877},"transformer/MHA.png",[14,2879,2880],{},[58,2881,2883,2999],{"className":2882},[61],[58,2884,2886],{"className":2885},[65],[67,2887,2888],{"xmlns":69},[71,2889,2890,2996],{},[74,2891,2892,2916,2918,2920,2922,2924,2926,2928,2930,2932,2948,2950,2965,2967,2970,2972,2986,2988],{},[74,2893,2894,2897,2900,2903,2905,2907,2910,2912,2914],{},[90,2895,2896],{"mathvariant":817},"M",[90,2898,2899],{"mathvariant":817},"u",[90,2901,2902],{"mathvariant":817},"l",[90,2904,776],{"mathvariant":817},[90,2906,788],{"mathvariant":817},[90,2908,2909],{"mathvariant":817},"H",[90,2911,781],{"mathvariant":817},[90,2913,21],{"mathvariant":817},[90,2915,92],{"mathvariant":817},[460,2917,797],{"stretchy":796},[90,2919,458],{},[460,2921,802],{"separator":105},[90,2923,571],{},[460,2925,802],{"separator":105},[90,2927,671],{},[460,2929,811],{"stretchy":796},[460,2931,814],{},[74,2933,2934,2937,2939,2941,2944,2946],{},[90,2935,2936],{"mathvariant":817},"C",[90,2938,791],{"mathvariant":817},[90,2940,334],{"mathvariant":817},[90,2942,2943],{"mathvariant":817},"c",[90,2945,21],{"mathvariant":817},[90,2947,776],{"mathvariant":817},[460,2949,797],{"stretchy":796},[87,2951,2952,2963],{},[74,2953,2954,2957,2959,2961],{},[90,2955,2956],{"mathvariant":817},"h",[90,2958,781],{"mathvariant":817},[90,2960,21],{"mathvariant":817},[90,2962,92],{"mathvariant":817},[80,2964,82],{},[460,2966,802],{"separator":105},[460,2968,2969],{},"…",[460,2971,802],{"separator":105},[87,2973,2974,2984],{},[74,2975,2976,2978,2980,2982],{},[90,2977,2956],{"mathvariant":817},[90,2979,781],{"mathvariant":817},[90,2981,21],{"mathvariant":817},[90,2983,92],{"mathvariant":817},[90,2985,2956],{},[460,2987,811],{"stretchy":796},[464,2989,2990,2993],{},[90,2991,2992],{},"W",[90,2994,2995],{},"O",[97,2997,2998],{"encoding":99},"\\mathrm{MultiHead}(Q, K, V) = \\mathrm{Concat}(\\mathrm{head}_1, \\ldots, \\mathrm{head}_h) W^O",[58,3000,3002,3051],{"className":3001,"ariaHidden":105},[104],[58,3003,3005,3008,3015,3018,3021,3024,3027,3030,3033,3036,3039,3042,3045,3048],{"className":3004},[109],[58,3006],{"className":3007,"style":876},[113],[58,3009,3011],{"className":3010},[118],[58,3012,3014],{"className":3013},[118,954],"MultiHead",[58,3016,797],{"className":3017},[122],[58,3019,458],{"className":3020},[118,191],[58,3022,802],{"className":3023},[911],[58,3025],{"className":3026,"style":915},[498],[58,3028,571],{"className":3029,"style":602},[118,191],[58,3031,802],{"className":3032},[911],[58,3034],{"className":3035,"style":915},[498],[58,3037,671],{"className":3038,"style":701},[118,191],[58,3040,811],{"className":3041},[312],[58,3043],{"className":3044,"style":499},[498],[58,3046,814],{"className":3047},[503],[58,3049],{"className":3050,"style":499},[498],[58,3052,3054,3058,3065,3068,3114,3117,3120,3123,3126,3129,3132,3175,3178],{"className":3053},[109],[58,3055],{"className":3056,"style":3057},[113],"height:1.0913em;vertical-align:-0.25em;",[58,3059,3061],{"className":3060},[118],[58,3062,3064],{"className":3063},[118,954],"Concat",[58,3066,797],{"className":3067},[122],[58,3069,3071,3078],{"className":3070},[118],[58,3072,3074],{"className":3073},[118],[58,3075,3077],{"className":3076},[118,954],"head",[58,3079,3081],{"className":3080},[195],[58,3082,3084,3106],{"className":3083},[130,131],[58,3085,3087,3103],{"className":3086},[135],[58,3088,3091],{"className":3089,"style":3090},[139],"height:0.3011em;",[58,3092,3094,3097],{"style":3093},"top:-2.55em;margin-right:0.05em;",[58,3095],{"className":3096,"style":539},[147],[58,3098,3100],{"className":3099},[152,153,154,155],[58,3101,82],{"className":3102},[118,155],[58,3104,226],{"className":3105},[225],[58,3107,3109],{"className":3108},[135],[58,3110,3112],{"className":3111,"style":1269},[139],[58,3113],{},[58,3115,802],{"className":3116},[911],[58,3118],{"className":3119,"style":915},[498],[58,3121,2969],{"className":3122},[961],[58,3124],{"className":3125,"style":915},[498],[58,3127,802],{"className":3128},[911],[58,3130],{"className":3131,"style":915},[498],[58,3133,3135,3141],{"className":3134},[118],[58,3136,3138],{"className":3137},[118],[58,3139,3077],{"className":3140},[118,954],[58,3142,3144],{"className":3143},[195],[58,3145,3147,3167],{"className":3146},[130,131],[58,3148,3150,3164],{"className":3149},[135],[58,3151,3153],{"className":3152,"style":1247},[139],[58,3154,3155,3158],{"style":3093},[58,3156],{"className":3157,"style":539},[147],[58,3159,3161],{"className":3160},[152,153,154,155],[58,3162,2956],{"className":3163},[118,191,155],[58,3165,226],{"className":3166},[225],[58,3168,3170],{"className":3169},[135],[58,3171,3173],{"className":3172,"style":1269},[139],[58,3174],{},[58,3176,811],{"className":3177},[312],[58,3179,3181,3185],{"className":3180},[118],[58,3182,2992],{"className":3183,"style":3184},[118,191],"margin-right:0.13889em;",[58,3186,3188],{"className":3187},[195],[58,3189,3191],{"className":3190},[130],[58,3192,3194],{"className":3193},[135],[58,3195,3198],{"className":3196,"style":3197},[139],"height:0.8413em;",[58,3199,3200,3203],{"style":535},[58,3201],{"className":3202,"style":539},[147],[58,3204,3206],{"className":3205},[152,153,154,155],[58,3207,2995],{"className":3208,"style":3209},[118,191,155],"margin-right:0.02778em;",[14,3211,3212,3213,3575,3576,3825,3826,3825,4075,4326,4327,863],{},"其中 ",[58,3214,3216,3308],{"className":3215},[61],[58,3217,3219],{"className":3218},[65],[67,3220,3221],{"xmlns":69},[71,3222,3223,3305],{},[74,3224,3225,3239,3241,3261,3263,3265,3273,3275,3279,3281,3289,3291,3293,3295,3303],{},[87,3226,3227,3237],{},[74,3228,3229,3231,3233,3235],{},[90,3230,2956],{"mathvariant":817},[90,3232,781],{"mathvariant":817},[90,3234,21],{"mathvariant":817},[90,3236,92],{"mathvariant":817},[90,3238,788],{},[460,3240,814],{},[74,3242,3243,3245,3247,3249,3251,3253,3255,3257,3259],{},[90,3244,773],{"mathvariant":817},[90,3246,776],{"mathvariant":817},[90,3248,776],{"mathvariant":817},[90,3250,781],{"mathvariant":817},[90,3252,334],{"mathvariant":817},[90,3254,776],{"mathvariant":817},[90,3256,788],{"mathvariant":817},[90,3258,791],{"mathvariant":817},[90,3260,334],{"mathvariant":817},[460,3262,797],{"stretchy":796},[90,3264,458],{},[1821,3266,3267,3269,3271],{},[90,3268,2992],{},[90,3270,788],{},[90,3272,458],{},[460,3274,802],{"separator":105},[3276,3277,3278],"mtext",{},"  ",[90,3280,571],{},[1821,3282,3283,3285,3287],{},[90,3284,2992],{},[90,3286,788],{},[90,3288,571],{},[460,3290,802],{"separator":105},[3276,3292,3278],{},[90,3294,671],{},[1821,3296,3297,3299,3301],{},[90,3298,2992],{},[90,3300,788],{},[90,3302,671],{},[460,3304,811],{"stretchy":796},[97,3306,3307],{"encoding":99},"\\mathrm{head}_i=\\mathrm{Attention}(QW_i^Q,\\; KW_i^K,\\; VW_i^V)",[58,3309,3311,3369],{"className":3310,"ariaHidden":105},[104],[58,3312,3314,3317,3360,3363,3366],{"className":3313},[109],[58,3315],{"className":3316,"style":1228},[113],[58,3318,3320,3326],{"className":3319},[118],[58,3321,3323],{"className":3322},[118],[58,3324,3077],{"className":3325},[118,954],[58,3327,3329],{"className":3328},[195],[58,3330,3332,3352],{"className":3331},[130,131],[58,3333,3335,3349],{"className":3334},[135],[58,3336,3338],{"className":3337,"style":2031},[139],[58,3339,3340,3343],{"style":3093},[58,3341],{"className":3342,"style":539},[147],[58,3344,3346],{"className":3345},[152,153,154,155],[58,3347,788],{"className":3348},[118,191,155],[58,3350,226],{"className":3351},[225],[58,3353,3355],{"className":3354},[135],[58,3356,3358],{"className":3357,"style":1269},[139],[58,3359],{},[58,3361],{"className":3362,"style":499},[498],[58,3364,814],{"className":3365},[503],[58,3367],{"className":3368,"style":499},[498],[58,3370,3372,3376,3383,3386,3389,3444,3447,3450,3453,3456,3509,3512,3515,3518,3521,3572],{"className":3371},[109],[58,3373],{"className":3374,"style":3375},[113],"height:1.2361em;vertical-align:-0.2769em;",[58,3377,3379],{"className":3378},[118],[58,3380,3382],{"className":3381},[118,954],"Attention",[58,3384,797],{"className":3385},[122],[58,3387,458],{"className":3388},[118,191],[58,3390,3392,3395],{"className":3391},[118],[58,3393,2992],{"className":3394,"style":3184},[118,191],[58,3396,3398],{"className":3397},[195],[58,3399,3401,3435],{"className":3400},[130,131],[58,3402,3404,3432],{"className":3403},[135],[58,3405,3408,3420],{"className":3406,"style":3407},[139],"height:0.9592em;",[58,3409,3411,3414],{"style":3410},"top:-2.4231em;margin-left:-0.1389em;margin-right:0.05em;",[58,3412],{"className":3413,"style":539},[147],[58,3415,3417],{"className":3416},[152,153,154,155],[58,3418,788],{"className":3419},[118,191,155],[58,3421,3423,3426],{"style":3422},"top:-3.1809em;margin-right:0.05em;",[58,3424],{"className":3425,"style":539},[147],[58,3427,3429],{"className":3428},[152,153,154,155],[58,3430,458],{"className":3431},[118,191,155],[58,3433,226],{"className":3434},[225],[58,3436,3438],{"className":3437},[135],[58,3439,3442],{"className":3440,"style":3441},[139],"height:0.2769em;",[58,3443],{},[58,3445,802],{"className":3446},[911],[58,3448],{"className":3449,"style":499},[498],[58,3451],{"className":3452,"style":915},[498],[58,3454,571],{"className":3455,"style":602},[118,191],[58,3457,3459,3462],{"className":3458},[118],[58,3460,2992],{"className":3461,"style":3184},[118,191],[58,3463,3465],{"className":3464},[195],[58,3466,3468,3500],{"className":3467},[130,131],[58,3469,3471,3497],{"className":3470},[135],[58,3472,3474,3486],{"className":3473,"style":3197},[139],[58,3475,3477,3480],{"style":3476},"top:-2.4413em;margin-left:-0.1389em;margin-right:0.05em;",[58,3478],{"className":3479,"style":539},[147],[58,3481,3483],{"className":3482},[152,153,154,155],[58,3484,788],{"className":3485},[118,191,155],[58,3487,3488,3491],{"style":535},[58,3489],{"className":3490,"style":539},[147],[58,3492,3494],{"className":3493},[152,153,154,155],[58,3495,571],{"className":3496,"style":602},[118,191,155],[58,3498,226],{"className":3499},[225],[58,3501,3503],{"className":3502},[135],[58,3504,3507],{"className":3505,"style":3506},[139],"height:0.2587em;",[58,3508],{},[58,3510,802],{"className":3511},[911],[58,3513],{"className":3514,"style":499},[498],[58,3516],{"className":3517,"style":915},[498],[58,3519,671],{"className":3520,"style":701},[118,191],[58,3522,3524,3527],{"className":3523},[118],[58,3525,2992],{"className":3526,"style":3184},[118,191],[58,3528,3530],{"className":3529},[195],[58,3531,3533,3564],{"className":3532},[130,131],[58,3534,3536,3561],{"className":3535},[135],[58,3537,3539,3550],{"className":3538,"style":3197},[139],[58,3540,3541,3544],{"style":3476},[58,3542],{"className":3543,"style":539},[147],[58,3545,3547],{"className":3546},[152,153,154,155],[58,3548,788],{"className":3549},[118,191,155],[58,3551,3552,3555],{"style":535},[58,3553],{"className":3554,"style":539},[147],[58,3556,3558],{"className":3557},[152,153,154,155],[58,3559,671],{"className":3560,"style":701},[118,191,155],[58,3562,226],{"className":3563},[225],[58,3565,3567],{"className":3566},[135],[58,3568,3570],{"className":3569,"style":3506},[139],[58,3571],{},[58,3573,811],{"className":3574},[312],"，投影参数是矩阵\n",[58,3577,3579,3631],{"className":3578},[61],[58,3580,3582],{"className":3581},[65],[67,3583,3584],{"xmlns":69},[71,3585,3586,3628],{},[74,3587,3588,3596,3598],{},[1821,3589,3590,3592,3594],{},[90,3591,2992],{},[90,3593,788],{},[90,3595,458],{},[460,3597,462],{},[464,3599,3600,3602],{},[90,3601,469],{"mathvariant":468},[74,3603,3604,3620,3622],{},[87,3605,3606,3608],{},[90,3607,92],{},[74,3609,3610,3612,3614,3616,3618],{},[90,3611,365],{"mathvariant":817},[90,3613,791],{"mathvariant":817},[90,3615,92],{"mathvariant":817},[90,3617,781],{"mathvariant":817},[90,3619,2902],{"mathvariant":817},[460,3621,476],{},[87,3623,3624,3626],{},[90,3625,92],{},[90,3627,95],{},[97,3629,3630],{"encoding":99},"W_i^Q \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[58,3632,3634,3700],{"className":3633,"ariaHidden":105},[104],[58,3635,3637,3640,3691,3694,3697],{"className":3636},[109],[58,3638],{"className":3639,"style":3375},[113],[58,3641,3643,3646],{"className":3642},[118],[58,3644,2992],{"className":3645,"style":3184},[118,191],[58,3647,3649],{"className":3648},[195],[58,3650,3652,3683],{"className":3651},[130,131],[58,3653,3655,3680],{"className":3654},[135],[58,3656,3658,3669],{"className":3657,"style":3407},[139],[58,3659,3660,3663],{"style":3410},[58,3661],{"className":3662,"style":539},[147],[58,3664,3666],{"className":3665},[152,153,154,155],[58,3667,788],{"className":3668},[118,191,155],[58,3670,3671,3674],{"style":3422},[58,3672],{"className":3673,"style":539},[147],[58,3675,3677],{"className":3676},[152,153,154,155],[58,3678,458],{"className":3679},[118,191,155],[58,3681,226],{"className":3682},[225],[58,3684,3686],{"className":3685},[135],[58,3687,3689],{"className":3688,"style":3441},[139],[58,3690],{},[58,3692],{"className":3693,"style":499},[498],[58,3695,462],{"className":3696},[503],[58,3698],{"className":3699,"style":499},[498],[58,3701,3703,3706],{"className":3702},[109],[58,3704],{"className":3705,"style":513},[113],[58,3707,3709,3712],{"className":3708},[118],[58,3710,469],{"className":3711},[118,520],[58,3713,3715],{"className":3714},[195],[58,3716,3718],{"className":3717},[130],[58,3719,3721],{"className":3720},[135],[58,3722,3724],{"className":3723,"style":513},[139],[58,3725,3726,3729],{"style":535},[58,3727],{"className":3728,"style":539},[147],[58,3730,3732],{"className":3731},[152,153,154,155],[58,3733,3735,3782,3785],{"className":3734},[118,155],[58,3736,3738,3741],{"className":3737},[118,155],[58,3739,92],{"className":3740},[118,191,155],[58,3742,3744],{"className":3743},[195],[58,3745,3747,3774],{"className":3746},[130,131],[58,3748,3750,3771],{"className":3749},[135],[58,3751,3753],{"className":3752,"style":205},[139],[58,3754,3755,3758],{"style":208},[58,3756],{"className":3757,"style":212},[147],[58,3759,3761],{"className":3760},[152,216,217,155],[58,3762,3764],{"className":3763},[118,155],[58,3765,3767],{"className":3766},[118,155],[58,3768,3770],{"className":3769},[118,954,155],"model",[58,3772,226],{"className":3773},[225],[58,3775,3777],{"className":3776},[135],[58,3778,3780],{"className":3779,"style":233},[139],[58,3781],{},[58,3783,476],{"className":3784},[552,155],[58,3786,3788,3791],{"className":3787},[118,155],[58,3789,92],{"className":3790},[118,191,155],[58,3792,3794],{"className":3793},[195],[58,3795,3797,3817],{"className":3796},[130,131],[58,3798,3800,3814],{"className":3799},[135],[58,3801,3803],{"className":3802,"style":205},[139],[58,3804,3805,3808],{"style":208},[58,3806],{"className":3807,"style":212},[147],[58,3809,3811],{"className":3810},[152,216,217,155],[58,3812,95],{"className":3813,"style":221},[118,191,155],[58,3815,226],{"className":3816},[225],[58,3818,3820],{"className":3819},[135],[58,3821,3823],{"className":3822,"style":233},[139],[58,3824],{},",\n",[58,3827,3829,3881],{"className":3828},[61],[58,3830,3832],{"className":3831},[65],[67,3833,3834],{"xmlns":69},[71,3835,3836,3878],{},[74,3837,3838,3846,3848],{},[1821,3839,3840,3842,3844],{},[90,3841,2992],{},[90,3843,788],{},[90,3845,571],{},[460,3847,462],{},[464,3849,3850,3852],{},[90,3851,469],{"mathvariant":468},[74,3853,3854,3870,3872],{},[87,3855,3856,3858],{},[90,3857,92],{},[74,3859,3860,3862,3864,3866,3868],{},[90,3861,365],{"mathvariant":817},[90,3863,791],{"mathvariant":817},[90,3865,92],{"mathvariant":817},[90,3867,781],{"mathvariant":817},[90,3869,2902],{"mathvariant":817},[460,3871,476],{},[87,3873,3874,3876],{},[90,3875,92],{},[90,3877,95],{},[97,3879,3880],{"encoding":99},"W_i^K \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[58,3882,3884,3951],{"className":3883,"ariaHidden":105},[104],[58,3885,3887,3891,3942,3945,3948],{"className":3886},[109],[58,3888],{"className":3889,"style":3890},[113],"height:1.1em;vertical-align:-0.2587em;",[58,3892,3894,3897],{"className":3893},[118],[58,3895,2992],{"className":3896,"style":3184},[118,191],[58,3898,3900],{"className":3899},[195],[58,3901,3903,3934],{"className":3902},[130,131],[58,3904,3906,3931],{"className":3905},[135],[58,3907,3909,3920],{"className":3908,"style":3197},[139],[58,3910,3911,3914],{"style":3476},[58,3912],{"className":3913,"style":539},[147],[58,3915,3917],{"className":3916},[152,153,154,155],[58,3918,788],{"className":3919},[118,191,155],[58,3921,3922,3925],{"style":535},[58,3923],{"className":3924,"style":539},[147],[58,3926,3928],{"className":3927},[152,153,154,155],[58,3929,571],{"className":3930,"style":602},[118,191,155],[58,3932,226],{"className":3933},[225],[58,3935,3937],{"className":3936},[135],[58,3938,3940],{"className":3939,"style":3506},[139],[58,3941],{},[58,3943],{"className":3944,"style":499},[498],[58,3946,462],{"className":3947},[503],[58,3949],{"className":3950,"style":499},[498],[58,3952,3954,3957],{"className":3953},[109],[58,3955],{"className":3956,"style":513},[113],[58,3958,3960,3963],{"className":3959},[118],[58,3961,469],{"className":3962},[118,520],[58,3964,3966],{"className":3965},[195],[58,3967,3969],{"className":3968},[130],[58,3970,3972],{"className":3971},[135],[58,3973,3975],{"className":3974,"style":513},[139],[58,3976,3977,3980],{"style":535},[58,3978],{"className":3979,"style":539},[147],[58,3981,3983],{"className":3982},[152,153,154,155],[58,3984,3986,4032,4035],{"className":3985},[118,155],[58,3987,3989,3992],{"className":3988},[118,155],[58,3990,92],{"className":3991},[118,191,155],[58,3993,3995],{"className":3994},[195],[58,3996,3998,4024],{"className":3997},[130,131],[58,3999,4001,4021],{"className":4000},[135],[58,4002,4004],{"className":4003,"style":205},[139],[58,4005,4006,4009],{"style":208},[58,4007],{"className":4008,"style":212},[147],[58,4010,4012],{"className":4011},[152,216,217,155],[58,4013,4015],{"className":4014},[118,155],[58,4016,4018],{"className":4017},[118,155],[58,4019,3770],{"className":4020},[118,954,155],[58,4022,226],{"className":4023},[225],[58,4025,4027],{"className":4026},[135],[58,4028,4030],{"className":4029,"style":233},[139],[58,4031],{},[58,4033,476],{"className":4034},[552,155],[58,4036,4038,4041],{"className":4037},[118,155],[58,4039,92],{"className":4040},[118,191,155],[58,4042,4044],{"className":4043},[195],[58,4045,4047,4067],{"className":4046},[130,131],[58,4048,4050,4064],{"className":4049},[135],[58,4051,4053],{"className":4052,"style":205},[139],[58,4054,4055,4058],{"style":208},[58,4056],{"className":4057,"style":212},[147],[58,4059,4061],{"className":4060},[152,216,217,155],[58,4062,95],{"className":4063,"style":221},[118,191,155],[58,4065,226],{"className":4066},[225],[58,4068,4070],{"className":4069},[135],[58,4071,4073],{"className":4072,"style":233},[139],[58,4074],{},[58,4076,4078,4130],{"className":4077},[61],[58,4079,4081],{"className":4080},[65],[67,4082,4083],{"xmlns":69},[71,4084,4085,4127],{},[74,4086,4087,4095,4097],{},[1821,4088,4089,4091,4093],{},[90,4090,2992],{},[90,4092,788],{},[90,4094,671],{},[460,4096,462],{},[464,4098,4099,4101],{},[90,4100,469],{"mathvariant":468},[74,4102,4103,4119,4121],{},[87,4104,4105,4107],{},[90,4106,92],{},[74,4108,4109,4111,4113,4115,4117],{},[90,4110,365],{"mathvariant":817},[90,4112,791],{"mathvariant":817},[90,4114,92],{"mathvariant":817},[90,4116,781],{"mathvariant":817},[90,4118,2902],{"mathvariant":817},[460,4120,476],{},[87,4122,4123,4125],{},[90,4124,92],{},[90,4126,425],{},[97,4128,4129],{"encoding":99},"W_i^V \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_v}",[58,4131,4133,4199],{"className":4132,"ariaHidden":105},[104],[58,4134,4136,4139,4190,4193,4196],{"className":4135},[109],[58,4137],{"className":4138,"style":3890},[113],[58,4140,4142,4145],{"className":4141},[118],[58,4143,2992],{"className":4144,"style":3184},[118,191],[58,4146,4148],{"className":4147},[195],[58,4149,4151,4182],{"className":4150},[130,131],[58,4152,4154,4179],{"className":4153},[135],[58,4155,4157,4168],{"className":4156,"style":3197},[139],[58,4158,4159,4162],{"style":3476},[58,4160],{"className":4161,"style":539},[147],[58,4163,4165],{"className":4164},[152,153,154,155],[58,4166,788],{"className":4167},[118,191,155],[58,4169,4170,4173],{"style":535},[58,4171],{"className":4172,"style":539},[147],[58,4174,4176],{"className":4175},[152,153,154,155],[58,4177,671],{"className":4178,"style":701},[118,191,155],[58,4180,226],{"className":4181},[225],[58,4183,4185],{"className":4184},[135],[58,4186,4188],{"className":4187,"style":3506},[139],[58,4189],{},[58,4191],{"className":4192,"style":499},[498],[58,4194,462],{"className":4195},[503],[58,4197],{"className":4198,"style":499},[498],[58,4200,4202,4205],{"className":4201},[109],[58,4203],{"className":4204,"style":513},[113],[58,4206,4208,4211],{"className":4207},[118],[58,4209,469],{"className":4210},[118,520],[58,4212,4214],{"className":4213},[195],[58,4215,4217],{"className":4216},[130],[58,4218,4220],{"className":4219},[135],[58,4221,4223],{"className":4222,"style":513},[139],[58,4224,4225,4228],{"style":535},[58,4226],{"className":4227,"style":539},[147],[58,4229,4231],{"className":4230},[152,153,154,155],[58,4232,4234,4280,4283],{"className":4233},[118,155],[58,4235,4237,4240],{"className":4236},[118,155],[58,4238,92],{"className":4239},[118,191,155],[58,4241,4243],{"className":4242},[195],[58,4244,4246,4272],{"className":4245},[130,131],[58,4247,4249,4269],{"className":4248},[135],[58,4250,4252],{"className":4251,"style":205},[139],[58,4253,4254,4257],{"style":208},[58,4255],{"className":4256,"style":212},[147],[58,4258,4260],{"className":4259},[152,216,217,155],[58,4261,4263],{"className":4262},[118,155],[58,4264,4266],{"className":4265},[118,155],[58,4267,3770],{"className":4268},[118,954,155],[58,4270,226],{"className":4271},[225],[58,4273,4275],{"className":4274},[135],[58,4276,4278],{"className":4277,"style":233},[139],[58,4279],{},[58,4281,476],{"className":4282},[552,155],[58,4284,4286,4289],{"className":4285},[118,155],[58,4287,92],{"className":4288},[118,191,155],[58,4290,4292],{"className":4291},[195],[58,4293,4295,4317],{"className":4294},[130,131],[58,4296,4298,4314],{"className":4297},[135],[58,4299,4302],{"className":4300,"style":4301},[139],"height:0.1645em;",[58,4303,4305,4308],{"style":4304},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[58,4306],{"className":4307,"style":212},[147],[58,4309,4311],{"className":4310},[152,216,217,155],[58,4312,425],{"className":4313,"style":440},[118,191,155],[58,4315,226],{"className":4316},[225],[58,4318,4320],{"className":4319},[135],[58,4321,4324],{"className":4322,"style":4323},[139],"height:0.143em;",[58,4325],{},"\n和\n",[58,4328,4330,4382],{"className":4329},[61],[58,4331,4333],{"className":4332},[65],[67,4334,4335],{"xmlns":69},[71,4336,4337,4379],{},[74,4338,4339,4345,4347],{},[464,4340,4341,4343],{},[90,4342,2992],{},[90,4344,2995],{},[460,4346,462],{},[464,4348,4349,4351],{},[90,4350,469],{"mathvariant":468},[74,4352,4353,4355,4361,4363],{},[90,4354,2956],{},[87,4356,4357,4359],{},[90,4358,92],{},[90,4360,425],{},[460,4362,476],{},[87,4364,4365,4367],{},[90,4366,92],{},[74,4368,4369,4371,4373,4375,4377],{},[90,4370,365],{"mathvariant":817},[90,4372,791],{"mathvariant":817},[90,4374,92],{"mathvariant":817},[90,4376,781],{"mathvariant":817},[90,4378,2902],{"mathvariant":817},[97,4380,4381],{"encoding":99},"W^O \\in \\mathbb{R}^{h d_v \\times d_{\\mathrm{model}}}",[58,4383,4385,4430],{"className":4384,"ariaHidden":105},[104],[58,4386,4388,4392,4421,4424,4427],{"className":4387},[109],[58,4389],{"className":4390,"style":4391},[113],"height:0.8804em;vertical-align:-0.0391em;",[58,4393,4395,4398],{"className":4394},[118],[58,4396,2992],{"className":4397,"style":3184},[118,191],[58,4399,4401],{"className":4400},[195],[58,4402,4404],{"className":4403},[130],[58,4405,4407],{"className":4406},[135],[58,4408,4410],{"className":4409,"style":3197},[139],[58,4411,4412,4415],{"style":535},[58,4413],{"className":4414,"style":539},[147],[58,4416,4418],{"className":4417},[152,153,154,155],[58,4419,2995],{"className":4420,"style":3209},[118,191,155],[58,4422],{"className":4423,"style":499},[498],[58,4425,462],{"className":4426},[503],[58,4428],{"className":4429,"style":499},[498],[58,4431,4433,4436],{"className":4432},[109],[58,4434],{"className":4435,"style":513},[113],[58,4437,4439,4442],{"className":4438},[118],[58,4440,469],{"className":4441},[118,520],[58,4443,4445],{"className":4444},[195],[58,4446,4448],{"className":4447},[130],[58,4449,4451],{"className":4450},[135],[58,4452,4454],{"className":4453,"style":513},[139],[58,4455,4456,4459],{"style":535},[58,4457],{"className":4458,"style":539},[147],[58,4460,4462],{"className":4461},[152,153,154,155],[58,4463,4465,4468,4508,4511],{"className":4464},[118,155],[58,4466,2956],{"className":4467},[118,191,155],[58,4469,4471,4474],{"className":4470},[118,155],[58,4472,92],{"className":4473},[118,191,155],[58,4475,4477],{"className":4476},[195],[58,4478,4480,4500],{"className":4479},[130,131],[58,4481,4483,4497],{"className":4482},[135],[58,4484,4486],{"className":4485,"style":4301},[139],[58,4487,4488,4491],{"style":4304},[58,4489],{"className":4490,"style":212},[147],[58,4492,4494],{"className":4493},[152,216,217,155],[58,4495,425],{"className":4496,"style":440},[118,191,155],[58,4498,226],{"className":4499},[225],[58,4501,4503],{"className":4502},[135],[58,4504,4506],{"className":4505,"style":4323},[139],[58,4507],{},[58,4509,476],{"className":4510},[552,155],[58,4512,4514,4517],{"className":4513},[118,155],[58,4515,92],{"className":4516},[118,191,155],[58,4518,4520],{"className":4519},[195],[58,4521,4523,4549],{"className":4522},[130,131],[58,4524,4526,4546],{"className":4525},[135],[58,4527,4529],{"className":4528,"style":205},[139],[58,4530,4531,4534],{"style":208},[58,4532],{"className":4533,"style":212},[147],[58,4535,4537],{"className":4536},[152,216,217,155],[58,4538,4540],{"className":4539},[118,155],[58,4541,4543],{"className":4542},[118,155],[58,4544,3770],{"className":4545},[118,954,155],[58,4547,226],{"className":4548},[225],[58,4550,4552],{"className":4551},[135],[58,4553,4555],{"className":4554,"style":233},[139],[58,4556],{},[14,4558,4559,4560,4563,4564,4567,4568,4570,4571,4573],{},"为了能使多个头并行计算，我们定义两个转置函数 ",[2396,4561,4562],{},"transpose_output"," 和 ",[2396,4565,4566],{},"transpose_qkv","，其中 ",[2396,4569,4562],{}," 还原了 ",[2396,4572,4566],{}," 的结果。",[2389,4575,4577],{"className":2391,"code":4576,"language":2393,"meta":2394,"style":2394},"def transpose_qkv(X, num_heads):\n    \"\"\"为了多注意力头的并行计算而变换形状\"\"\"\n    # 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)\n    # 输出X的形状:(batch_size，查询或者“键－值”对的个数，num_heads，num_hiddens/num_heads)\n    X = X.reshape(X.shape[0], X.shape[1], num_heads, -1)\n\n    # 输出X的形状:(batch_size，num_heads，查询或者“键－值”对的个数, num_hiddens/num_heads)\n    X = X.permute(0, 2, 1, 3)\n\n    # 最终输出的形状:(batch_size*num_heads,查询或者“键－值”对的个数, num_hiddens/num_heads)\n    return X.reshape(-1, X.shape[2], X.shape[3])\n\ndef transpose_output(X, num_heads):\n    \"\"\"逆转transpose_qkv函数的操作\"\"\"\n    X = X.reshape(-1, num_heads, X.shape[1], X.shape[2])\n    X = X.permute(0, 2, 1, 3)\n    return X.reshape(X.shape[0], X.shape[1], -1)\n",[2396,4578,4579,4597,4602,4607,4612,4638,4642,4647,4673,4677,4682,4705,4709,4726,4731,4754,4778],{"__ignoreMap":2394},[58,4580,4581,4583,4586,4588,4590,4592,4595],{"class":2400,"line":2401},[58,4582,2405],{"class":2404},[58,4584,4585],{"class":2408}," transpose_qkv",[58,4587,797],{"class":2412},[58,4589,2416],{"class":2415},[58,4591,2419],{"class":2412},[58,4593,4594],{"class":2415},"num_heads",[58,4596,2425],{"class":2412},[58,4598,4599],{"class":2400,"line":2428},[58,4600,4601],{"class":2431},"    \"\"\"为了多注意力头的并行计算而变换形状\"\"\"\n",[58,4603,4604],{"class":2400,"line":2435},[58,4605,4606],{"class":2438},"    # 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[58,4608,4609],{"class":2400,"line":2442},[58,4610,4611],{"class":2438},"    # 输出X的形状:(batch_size，查询或者“键－值”对的个数，num_heads，num_hiddens/num_heads)\n",[58,4613,4614,4617,4619,4622,4624,4627,4629,4632,4634,4636],{"class":2400,"line":2461},[58,4615,4616],{"class":2412},"    X ",[58,4618,814],{"class":2404},[58,4620,4621],{"class":2412}," X.reshape(X.shape[",[58,4623,1753],{"class":2454},[58,4625,4626],{"class":2412},"], X.shape[",[58,4628,82],{"class":2454},[58,4630,4631],{"class":2412},"], num_heads, ",[58,4633,2552],{"class":2404},[58,4635,82],{"class":2454},[58,4637,2479],{"class":2412},[58,4639,4640],{"class":2400,"line":2482},[58,4641,2724],{"emptyLinePlaceholder":2723},[58,4643,4644],{"class":2400,"line":2490},[58,4645,4646],{"class":2438},"    # 输出X的形状:(batch_size，num_heads，查询或者“键－值”对的个数, num_hiddens/num_heads)\n",[58,4648,4649,4651,4653,4656,4658,4660,4662,4664,4666,4668,4671],{"class":2400,"line":2501},[58,4650,4616],{"class":2412},[58,4652,814],{"class":2404},[58,4654,4655],{"class":2412}," X.permute(",[58,4657,1753],{"class":2454},[58,4659,2419],{"class":2412},[58,4661,2820],{"class":2454},[58,4663,2419],{"class":2412},[58,4665,82],{"class":2454},[58,4667,2419],{"class":2412},[58,4669,4670],{"class":2454},"3",[58,4672,2479],{"class":2412},[58,4674,4675],{"class":2400,"line":2518},[58,4676,2724],{"emptyLinePlaceholder":2723},[58,4678,4679],{"class":2400,"line":2534},[58,4680,4681],{"class":2438},"    # 最终输出的形状:(batch_size*num_heads,查询或者“键－值”对的个数, num_hiddens/num_heads)\n",[58,4683,4684,4687,4690,4692,4694,4697,4699,4701,4703],{"class":2400,"line":2542},[58,4685,4686],{"class":2404},"    return",[58,4688,4689],{"class":2412}," X.reshape(",[58,4691,2552],{"class":2404},[58,4693,82],{"class":2454},[58,4695,4696],{"class":2412},", X.shape[",[58,4698,2820],{"class":2454},[58,4700,4626],{"class":2412},[58,4702,4670],{"class":2454},[58,4704,2531],{"class":2412},[58,4706,4707],{"class":2400,"line":2559},[58,4708,2724],{"emptyLinePlaceholder":2723},[58,4710,4711,4713,4716,4718,4720,4722,4724],{"class":2400,"line":2565},[58,4712,2405],{"class":2404},[58,4714,4715],{"class":2408}," transpose_output",[58,4717,797],{"class":2412},[58,4719,2416],{"class":2415},[58,4721,2419],{"class":2412},[58,4723,4594],{"class":2415},[58,4725,2425],{"class":2412},[58,4727,4728],{"class":2400,"line":2590},[58,4729,4730],{"class":2431},"    \"\"\"逆转transpose_qkv函数的操作\"\"\"\n",[58,4732,4733,4735,4737,4739,4741,4743,4746,4748,4750,4752],{"class":2400,"line":2603},[58,4734,4616],{"class":2412},[58,4736,814],{"class":2404},[58,4738,4689],{"class":2412},[58,4740,2552],{"class":2404},[58,4742,82],{"class":2454},[58,4744,4745],{"class":2412},", num_heads, X.shape[",[58,4747,82],{"class":2454},[58,4749,4626],{"class":2412},[58,4751,2820],{"class":2454},[58,4753,2531],{"class":2412},[58,4755,4756,4758,4760,4762,4764,4766,4768,4770,4772,4774,4776],{"class":2400,"line":2844},[58,4757,4616],{"class":2412},[58,4759,814],{"class":2404},[58,4761,4655],{"class":2412},[58,4763,1753],{"class":2454},[58,4765,2419],{"class":2412},[58,4767,2820],{"class":2454},[58,4769,2419],{"class":2412},[58,4771,82],{"class":2454},[58,4773,2419],{"class":2412},[58,4775,4670],{"class":2454},[58,4777,2479],{"class":2412},[58,4779,4781,4783,4785,4787,4789,4791,4794,4796,4798],{"class":2400,"line":4780},17,[58,4782,4686],{"class":2404},[58,4784,4621],{"class":2412},[58,4786,1753],{"class":2454},[58,4788,4626],{"class":2412},[58,4790,82],{"class":2454},[58,4792,4793],{"class":2412},"], ",[58,4795,2552],{"class":2404},[58,4797,82],{"class":2454},[58,4799,2479],{"class":2412},[2389,4801,4803],{"className":2391,"code":4802,"language":2393,"meta":2394,"style":2394},"#@save\nclass MultiHeadAttention(nn.Module):\n    \"\"\"多头注意力\"\"\"\n    def __init__(self, key_size, query_size, value_size, num_hiddens,\n                 num_heads, dropout, bias=False, **kwargs):\n        super(MultiHeadAttention, self).__init__(**kwargs)\n        self.num_heads = num_heads\n        self.attention = d2l.DotProductAttention(dropout)\n        self.W_q = nn.Linear(query_size, num_hiddens, bias=bias)\n        self.W_k = nn.Linear(key_size, num_hiddens, bias=bias)\n        self.W_v = nn.Linear(value_size, num_hiddens, bias=bias)\n        self.W_o = nn.Linear(num_hiddens, num_hiddens, bias=bias)\n\n    def forward(self, queries, keys, values, valid_lens):\n        # queries，keys，values的形状:\n        # (batch_size，查询或者“键－值”对的个数，num_hiddens)\n        # valid_lens　的形状:\n        # (batch_size，)或(batch_size，查询的个数)\n        # 经过变换后，输出的queries，keys，values 的形状:\n        # (batch_size*num_heads，查询或者“键－值”对的个数，num_hiddens/num_heads)\n        queries = transpose_qkv(self.W_q(queries), self.num_heads)\n        keys = transpose_qkv(self.W_k(keys), self.num_heads)\n        values = transpose_qkv(self.W_v(values), self.num_heads)\n\n        if valid_lens is not None:\n            # 在轴0，将第一项（标量或者矢量）复制num_heads次，\n            # 然后如此复制第二项，然后诸如此类。\n            valid_lens = torch.repeat_interleave(\n                valid_lens, repeats=self.num_heads, dim=0)\n\n        # output的形状:(batch_size*num_heads，查询的个数， num_hiddens/num_heads)\n        output = self.attention(queries, keys, values, valid_lens)\n\n        # output_concat的形状:(batch_size，查询的个数，num_hiddens)\n        output_concat = transpose_output(output, self.num_heads)\n        return self.W_o(output_concat)\n",[2396,4804,4805,4810,4827,4832,4864,4891,4910,4922,4934,4953,4971,4989,5007,5011,5039,5044,5049,5054,5060,5066,5072,5093,5112,5131,5136,5152,5158,5164,5174,5198,5203,5209,5223,5228,5234,5249],{"__ignoreMap":2394},[58,4806,4807],{"class":2400,"line":2401},[58,4808,4809],{"class":2438},"#@save\n",[58,4811,4812,4814,4817,4819,4821,4823,4825],{"class":2400,"line":2428},[58,4813,2629],{"class":2404},[58,4815,4816],{"class":2632}," MultiHeadAttention",[58,4818,797],{"class":2412},[58,4820,2639],{"class":2638},[58,4822,863],{"class":2412},[58,4824,2644],{"class":2638},[58,4826,2425],{"class":2412},[58,4828,4829],{"class":2400,"line":2435},[58,4830,4831],{"class":2431},"    \"\"\"多头注意力\"\"\"\n",[58,4833,4834,4836,4838,4840,4842,4844,4847,4849,4852,4854,4857,4859,4862],{"class":2400,"line":2442},[58,4835,2656],{"class":2404},[58,4837,2659],{"class":2454},[58,4839,797],{"class":2412},[58,4841,2665],{"class":2664},[58,4843,2419],{"class":2412},[58,4845,4846],{"class":2415},"key_size",[58,4848,2419],{"class":2412},[58,4850,4851],{"class":2415},"query_size",[58,4853,2419],{"class":2412},[58,4855,4856],{"class":2415},"value_size",[58,4858,2419],{"class":2412},[58,4860,4861],{"class":2415},"num_hiddens",[58,4863,3825],{"class":2412},[58,4865,4866,4869,4871,4873,4875,4878,4880,4883,4885,4887,4889],{"class":2400,"line":2461},[58,4867,4868],{"class":2415},"                 num_heads",[58,4870,2419],{"class":2412},[58,4872,2670],{"class":2415},[58,4874,2419],{"class":2412},[58,4876,4877],{"class":2415},"bias",[58,4879,814],{"class":2404},[58,4881,4882],{"class":2454},"False",[58,4884,2419],{"class":2412},[58,4886,2675],{"class":2404},[58,4888,2678],{"class":2415},[58,4890,2425],{"class":2412},[58,4892,4893,4895,4898,4900,4902,4904,4906,4908],{"class":2400,"line":2482},[58,4894,2686],{"class":2685},[58,4896,4897],{"class":2412},"(MultiHeadAttention, ",[58,4899,2665],{"class":2692},[58,4901,2695],{"class":2412},[58,4903,2698],{"class":2454},[58,4905,797],{"class":2412},[58,4907,2675],{"class":2404},[58,4909,2705],{"class":2412},[58,4911,4912,4914,4917,4919],{"class":2400,"line":2490},[58,4913,2710],{"class":2692},[58,4915,4916],{"class":2412},".num_heads ",[58,4918,814],{"class":2404},[58,4920,4921],{"class":2412}," num_heads\n",[58,4923,4924,4926,4929,4931],{"class":2400,"line":2501},[58,4925,2710],{"class":2692},[58,4927,4928],{"class":2412},".attention ",[58,4930,814],{"class":2404},[58,4932,4933],{"class":2412}," d2l.DotProductAttention(dropout)\n",[58,4935,4936,4938,4941,4943,4946,4948,4950],{"class":2400,"line":2518},[58,4937,2710],{"class":2692},[58,4939,4940],{"class":2412},".W_q ",[58,4942,814],{"class":2404},[58,4944,4945],{"class":2412}," nn.Linear(query_size, num_hiddens, ",[58,4947,4877],{"class":2470},[58,4949,814],{"class":2404},[58,4951,4952],{"class":2412},"bias)\n",[58,4954,4955,4957,4960,4962,4965,4967,4969],{"class":2400,"line":2534},[58,4956,2710],{"class":2692},[58,4958,4959],{"class":2412},".W_k ",[58,4961,814],{"class":2404},[58,4963,4964],{"class":2412}," nn.Linear(key_size, num_hiddens, ",[58,4966,4877],{"class":2470},[58,4968,814],{"class":2404},[58,4970,4952],{"class":2412},[58,4972,4973,4975,4978,4980,4983,4985,4987],{"class":2400,"line":2542},[58,4974,2710],{"class":2692},[58,4976,4977],{"class":2412},".W_v ",[58,4979,814],{"class":2404},[58,4981,4982],{"class":2412}," nn.Linear(value_size, num_hiddens, ",[58,4984,4877],{"class":2470},[58,4986,814],{"class":2404},[58,4988,4952],{"class":2412},[58,4990,4991,4993,4996,4998,5001,5003,5005],{"class":2400,"line":2559},[58,4992,2710],{"class":2692},[58,4994,4995],{"class":2412},".W_o ",[58,4997,814],{"class":2404},[58,4999,5000],{"class":2412}," nn.Linear(num_hiddens, num_hiddens, ",[58,5002,4877],{"class":2470},[58,5004,814],{"class":2404},[58,5006,4952],{"class":2412},[58,5008,5009],{"class":2400,"line":2565},[58,5010,2724],{"emptyLinePlaceholder":2723},[58,5012,5013,5015,5017,5019,5021,5023,5025,5027,5029,5031,5033,5035,5037],{"class":2400,"line":2590},[58,5014,2656],{"class":2404},[58,5016,2751],{"class":2408},[58,5018,797],{"class":2412},[58,5020,2665],{"class":2664},[58,5022,2419],{"class":2412},[58,5024,2760],{"class":2415},[58,5026,2419],{"class":2412},[58,5028,2765],{"class":2415},[58,5030,2419],{"class":2412},[58,5032,2770],{"class":2415},[58,5034,2419],{"class":2412},[58,5036,2422],{"class":2415},[58,5038,2425],{"class":2412},[58,5040,5041],{"class":2400,"line":2603},[58,5042,5043],{"class":2438},"        # queries，keys，values的形状:\n",[58,5045,5046],{"class":2400,"line":2844},[58,5047,5048],{"class":2438},"        # (batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[58,5050,5051],{"class":2400,"line":4780},[58,5052,5053],{"class":2438},"        # valid_lens　的形状:\n",[58,5055,5057],{"class":2400,"line":5056},18,[58,5058,5059],{"class":2438},"        # (batch_size，)或(batch_size，查询的个数)\n",[58,5061,5063],{"class":2400,"line":5062},19,[58,5064,5065],{"class":2438},"        # 经过变换后，输出的queries，keys，values 的形状:\n",[58,5067,5069],{"class":2400,"line":5068},20,[58,5070,5071],{"class":2438},"        # (batch_size*num_heads，查询或者“键－值”对的个数，num_hiddens/num_heads)\n",[58,5073,5075,5078,5080,5083,5085,5088,5090],{"class":2400,"line":5074},21,[58,5076,5077],{"class":2412},"        queries ",[58,5079,814],{"class":2404},[58,5081,5082],{"class":2412}," transpose_qkv(",[58,5084,2665],{"class":2692},[58,5086,5087],{"class":2412},".W_q(queries), ",[58,5089,2665],{"class":2692},[58,5091,5092],{"class":2412},".num_heads)\n",[58,5094,5096,5099,5101,5103,5105,5108,5110],{"class":2400,"line":5095},22,[58,5097,5098],{"class":2412},"        keys ",[58,5100,814],{"class":2404},[58,5102,5082],{"class":2412},[58,5104,2665],{"class":2692},[58,5106,5107],{"class":2412},".W_k(keys), ",[58,5109,2665],{"class":2692},[58,5111,5092],{"class":2412},[58,5113,5115,5118,5120,5122,5124,5127,5129],{"class":2400,"line":5114},23,[58,5116,5117],{"class":2412},"        values ",[58,5119,814],{"class":2404},[58,5121,5082],{"class":2412},[58,5123,2665],{"class":2692},[58,5125,5126],{"class":2412},".W_v(values), ",[58,5128,2665],{"class":2692},[58,5130,5092],{"class":2412},[58,5132,5134],{"class":2400,"line":5133},24,[58,5135,2724],{"emptyLinePlaceholder":2723},[58,5137,5139,5141,5143,5145,5148,5150],{"class":2400,"line":5138},25,[58,5140,2504],{"class":2404},[58,5142,2448],{"class":2412},[58,5144,2451],{"class":2404},[58,5146,5147],{"class":2404}," not",[58,5149,2455],{"class":2454},[58,5151,2458],{"class":2412},[58,5153,5155],{"class":2400,"line":5154},26,[58,5156,5157],{"class":2438},"            # 在轴0，将第一项（标量或者矢量）复制num_heads次，\n",[58,5159,5161],{"class":2400,"line":5160},27,[58,5162,5163],{"class":2438},"            # 然后如此复制第二项，然后诸如此类。\n",[58,5165,5167,5169,5171],{"class":2400,"line":5166},28,[58,5168,2521],{"class":2412},[58,5170,814],{"class":2404},[58,5172,5173],{"class":2412}," torch.repeat_interleave(\n",[58,5175,5177,5180,5183,5185,5187,5190,5192,5194,5196],{"class":2400,"line":5176},29,[58,5178,5179],{"class":2412},"                valid_lens, ",[58,5181,5182],{"class":2470},"repeats",[58,5184,814],{"class":2404},[58,5186,2665],{"class":2692},[58,5188,5189],{"class":2412},".num_heads, ",[58,5191,2471],{"class":2470},[58,5193,814],{"class":2404},[58,5195,1753],{"class":2454},[58,5197,2479],{"class":2412},[58,5199,5201],{"class":2400,"line":5200},30,[58,5202,2724],{"emptyLinePlaceholder":2723},[58,5204,5206],{"class":2400,"line":5205},31,[58,5207,5208],{"class":2438},"        # output的形状:(batch_size*num_heads，查询的个数， num_hiddens/num_heads)\n",[58,5210,5212,5215,5217,5220],{"class":2400,"line":5211},32,[58,5213,5214],{"class":2412},"        output ",[58,5216,814],{"class":2404},[58,5218,5219],{"class":2692}," self",[58,5221,5222],{"class":2412},".attention(queries, keys, values, valid_lens)\n",[58,5224,5226],{"class":2400,"line":5225},33,[58,5227,2724],{"emptyLinePlaceholder":2723},[58,5229,5231],{"class":2400,"line":5230},34,[58,5232,5233],{"class":2438},"        # output_concat的形状:(batch_size，查询的个数，num_hiddens)\n",[58,5235,5237,5240,5242,5245,5247],{"class":2400,"line":5236},35,[58,5238,5239],{"class":2412},"        output_concat ",[58,5241,814],{"class":2404},[58,5243,5244],{"class":2412}," transpose_output(output, ",[58,5246,2665],{"class":2692},[58,5248,5092],{"class":2412},[58,5250,5252,5254,5256],{"class":2400,"line":5251},36,[58,5253,2464],{"class":2404},[58,5255,5219],{"class":2692},[58,5257,5258],{"class":2412},".W_o(output_concat)\n",[10,5260,5261],{"id":5261},"位置编码",[14,5263,5264,5265,5356],{},"在处理 token 序列时 RNN 采用了按顺序逐个处理 token 的，但注意力机制为了并行计算放弃了顺序处理，这会导致其失去位置信息。为了使模型能够使用到位置信息，我们需要在 token 中注入一些和位置相关的信息，我们使用位置编码来注入绝对的或相对的位置信息。位置编码与嵌入的维度相同，均为 ",[58,5266,5268,5294],{"className":5267},[61],[58,5269,5271],{"className":5270},[65],[67,5272,5273],{"xmlns":69},[71,5274,5275,5291],{},[74,5276,5277,5283,5285,5287,5289],{},[87,5278,5279,5281],{},[90,5280,92],{},[90,5282,365],{},[90,5284,791],{},[90,5286,92],{},[90,5288,781],{},[90,5290,2902],{},[97,5292,5293],{"encoding":99},"d_model",[58,5295,5297],{"className":5296,"ariaHidden":105},[104],[58,5298,5300,5303,5343,5346,5349,5352],{"className":5299},[109],[58,5301],{"className":5302,"style":1228},[113],[58,5304,5306,5309],{"className":5305},[118],[58,5307,92],{"className":5308},[118,191],[58,5310,5312],{"className":5311},[195],[58,5313,5315,5335],{"className":5314},[130,131],[58,5316,5318,5332],{"className":5317},[135],[58,5319,5321],{"className":5320,"style":1321},[139],[58,5322,5323,5326],{"style":1250},[58,5324],{"className":5325,"style":539},[147],[58,5327,5329],{"className":5328},[152,153,154,155],[58,5330,365],{"className":5331},[118,191,155],[58,5333,226],{"className":5334},[225],[58,5336,5338],{"className":5337},[135],[58,5339,5341],{"className":5340,"style":1269},[139],[58,5342],{},[58,5344,791],{"className":5345},[118,191],[58,5347,92],{"className":5348},[118,191],[58,5350,781],{"className":5351},[118,191],[58,5353,2902],{"className":5354,"style":5355},[118,191],"margin-right:0.01968em;","，因此两者可以相加。位置编码可以通过学习得到也可以直接固定得到。",[14,5358,5359],{},"在这里，我们使用的是基于正弦函数和余弦函数的位置编码。",[14,5361,5362,5363,5528,5529,5557,5558,5586,5587,5759,5760,5821,5822,5851,5852,5889,5890,5946],{},"假设输入表示 ",[58,5364,5366,5409],{"className":5365},[61],[58,5367,5369],{"className":5368},[65],[67,5370,5371],{"xmlns":69},[71,5372,5373,5406],{},[74,5374,5375,5378,5380],{},[90,5376,2416],{"mathvariant":5377},"bold",[460,5379,462],{},[464,5381,5382,5384],{},[90,5383,469],{"mathvariant":468},[74,5385,5386,5388,5390],{},[90,5387,334],{},[460,5389,476],{},[87,5391,5392,5394],{},[90,5393,92],{},[74,5395,5396,5398,5400,5402,5404],{},[90,5397,365],{},[90,5399,791],{},[90,5401,92],{},[90,5403,781],{},[90,5405,2902],{},[97,5407,5408],{"encoding":99},"\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{model}}",[58,5410,5412,5432],{"className":5411,"ariaHidden":105},[104],[58,5413,5415,5419,5423,5426,5429],{"className":5414},[109],[58,5416],{"className":5417,"style":5418},[113],"height:0.7252em;vertical-align:-0.0391em;",[58,5420,2416],{"className":5421},[118,5422],"mathbf",[58,5424],{"className":5425,"style":499},[498],[58,5427,462],{"className":5428},[503],[58,5430],{"className":5431,"style":499},[498],[58,5433,5435,5438],{"className":5434},[109],[58,5436],{"className":5437,"style":513},[113],[58,5439,5441,5444],{"className":5440},[118],[58,5442,469],{"className":5443},[118,520],[58,5445,5447],{"className":5446},[195],[58,5448,5450],{"className":5449},[130],[58,5451,5453],{"className":5452},[135],[58,5454,5456],{"className":5455,"style":513},[139],[58,5457,5458,5461],{"style":535},[58,5459],{"className":5460,"style":539},[147],[58,5462,5464],{"className":5463},[152,153,154,155],[58,5465,5467,5470,5473],{"className":5466},[118,155],[58,5468,334],{"className":5469},[118,191,155],[58,5471,476],{"className":5472},[552,155],[58,5474,5476,5479],{"className":5475},[118,155],[58,5477,92],{"className":5478},[118,191,155],[58,5480,5482],{"className":5481},[195],[58,5483,5485,5520],{"className":5484},[130,131],[58,5486,5488,5517],{"className":5487},[135],[58,5489,5491],{"className":5490,"style":205},[139],[58,5492,5493,5496],{"style":208},[58,5494],{"className":5495,"style":212},[147],[58,5497,5499],{"className":5498},[152,216,217,155],[58,5500,5502,5505,5508,5511,5514],{"className":5501},[118,155],[58,5503,365],{"className":5504},[118,191,155],[58,5506,791],{"className":5507},[118,191,155],[58,5509,92],{"className":5510},[118,191,155],[58,5512,781],{"className":5513},[118,191,155],[58,5515,2902],{"className":5516,"style":5355},[118,191,155],[58,5518,226],{"className":5519},[225],[58,5521,5523],{"className":5522},[135],[58,5524,5526],{"className":5525,"style":233},[139],[58,5527],{}," 包含一个序列中 ",[58,5530,5532,5545],{"className":5531},[61],[58,5533,5535],{"className":5534},[65],[67,5536,5537],{"xmlns":69},[71,5538,5539,5543],{},[74,5540,5541],{},[90,5542,334],{},[97,5544,334],{"encoding":99},[58,5546,5548],{"className":5547,"ariaHidden":105},[104],[58,5549,5551,5554],{"className":5550},[109],[58,5552],{"className":5553,"style":346},[113],[58,5555,334],{"className":5556},[118,191]," 个词元的 ",[58,5559,5561,5574],{"className":5560},[61],[58,5562,5564],{"className":5563},[65],[67,5565,5566],{"xmlns":69},[71,5567,5568,5572],{},[74,5569,5570],{},[90,5571,92],{},[97,5573,92],{"encoding":99},[58,5575,5577],{"className":5576,"ariaHidden":105},[104],[58,5578,5580,5583],{"className":5579},[109],[58,5581],{"className":5582,"style":406},[113],[58,5584,92],{"className":5585},[118,191]," 维嵌入表示。位置编码使用相同形状的位置嵌入矩阵 ",[58,5588,5590,5638],{"className":5589},[61],[58,5591,5593],{"className":5592},[65],[67,5594,5595],{"xmlns":69},[71,5596,5597,5635],{},[74,5598,5599,5607,5609],{},[74,5600,5601,5604],{},[90,5602,5603],{"mathvariant":5377},"P",[90,5605,5606],{"mathvariant":5377},"E",[460,5608,462],{},[464,5610,5611,5613],{},[90,5612,469],{"mathvariant":468},[74,5614,5615,5617,5619],{},[90,5616,334],{},[460,5618,476],{},[87,5620,5621,5623],{},[90,5622,92],{},[74,5624,5625,5627,5629,5631,5633],{},[90,5626,365],{},[90,5628,791],{},[90,5630,92],{},[90,5632,781],{},[90,5634,2902],{},[97,5636,5637],{"encoding":99},"\\mathbf{PE} \\in \\mathbb{R}^{n \\times d_{model}}",[58,5639,5641,5663],{"className":5640,"ariaHidden":105},[104],[58,5642,5644,5647,5654,5657,5660],{"className":5643},[109],[58,5645],{"className":5646,"style":5418},[113],[58,5648,5650],{"className":5649},[118],[58,5651,5653],{"className":5652},[118,5422],"PE",[58,5655],{"className":5656,"style":499},[498],[58,5658,462],{"className":5659},[503],[58,5661],{"className":5662,"style":499},[498],[58,5664,5666,5669],{"className":5665},[109],[58,5667],{"className":5668,"style":513},[113],[58,5670,5672,5675],{"className":5671},[118],[58,5673,469],{"className":5674},[118,520],[58,5676,5678],{"className":5677},[195],[58,5679,5681],{"className":5680},[130],[58,5682,5684],{"className":5683},[135],[58,5685,5687],{"className":5686,"style":513},[139],[58,5688,5689,5692],{"style":535},[58,5690],{"className":5691,"style":539},[147],[58,5693,5695],{"className":5694},[152,153,154,155],[58,5696,5698,5701,5704],{"className":5697},[118,155],[58,5699,334],{"className":5700},[118,191,155],[58,5702,476],{"className":5703},[552,155],[58,5705,5707,5710],{"className":5706},[118,155],[58,5708,92],{"className":5709},[118,191,155],[58,5711,5713],{"className":5712},[195],[58,5714,5716,5751],{"className":5715},[130,131],[58,5717,5719,5748],{"className":5718},[135],[58,5720,5722],{"className":5721,"style":205},[139],[58,5723,5724,5727],{"style":208},[58,5725],{"className":5726,"style":212},[147],[58,5728,5730],{"className":5729},[152,216,217,155],[58,5731,5733,5736,5739,5742,5745],{"className":5732},[118,155],[58,5734,365],{"className":5735},[118,191,155],[58,5737,791],{"className":5738},[118,191,155],[58,5740,92],{"className":5741},[118,191,155],[58,5743,781],{"className":5744},[118,191,155],[58,5746,2902],{"className":5747,"style":5355},[118,191,155],[58,5749,226],{"className":5750},[225],[58,5752,5754],{"className":5753},[135],[58,5755,5757],{"className":5756,"style":233},[139],[58,5758],{}," 输出 ",[58,5761,5763,5786],{"className":5762},[61],[58,5764,5766],{"className":5765},[65],[67,5767,5768],{"xmlns":69},[71,5769,5770,5783],{},[74,5771,5772,5774,5777],{},[90,5773,2416],{"mathvariant":5377},[460,5775,5776],{},"+",[74,5778,5779,5781],{},[90,5780,5603],{"mathvariant":5377},[90,5782,5606],{"mathvariant":5377},[97,5784,5785],{"encoding":99},"\\mathbf{X} + \\mathbf{PE}",[58,5787,5789,5808],{"className":5788,"ariaHidden":105},[104],[58,5790,5792,5796,5799,5802,5805],{"className":5791},[109],[58,5793],{"className":5794,"style":5795},[113],"height:0.7694em;vertical-align:-0.0833em;",[58,5797,2416],{"className":5798},[118,5422],[58,5800],{"className":5801,"style":1871},[498],[58,5803,5776],{"className":5804},[552],[58,5806],{"className":5807,"style":1871},[498],[58,5809,5811,5815],{"className":5810},[109],[58,5812],{"className":5813,"style":5814},[113],"height:0.6861em;",[58,5816,5818],{"className":5817},[118],[58,5819,5653],{"className":5820},[118,5422],"，矩阵第 ",[58,5823,5825,5838],{"className":5824},[61],[58,5826,5828],{"className":5827},[65],[67,5829,5830],{"xmlns":69},[71,5831,5832,5836],{},[74,5833,5834],{},[90,5835,788],{},[97,5837,788],{"encoding":99},[58,5839,5841],{"className":5840,"ariaHidden":105},[104],[58,5842,5844,5848],{"className":5843},[109],[58,5845],{"className":5846,"style":5847},[113],"height:0.6595em;",[58,5849,788],{"className":5850},[118,191]," 行、第 ",[58,5853,5855,5872],{"className":5854},[61],[58,5856,5858],{"className":5857},[65],[67,5859,5860],{"xmlns":69},[71,5861,5862,5869],{},[74,5863,5864,5866],{},[80,5865,2820],{},[90,5867,5868],{},"j",[97,5870,5871],{"encoding":99},"2j",[58,5873,5875],{"className":5874,"ariaHidden":105},[104],[58,5876,5878,5882,5885],{"className":5877},[109],[58,5879],{"className":5880,"style":5881},[113],"height:0.854em;vertical-align:-0.1944em;",[58,5883,2820],{"className":5884},[118],[58,5886,5868],{"className":5887,"style":5888},[118,191],"margin-right:0.05724em;"," 列和 ",[58,5891,5893,5913],{"className":5892},[61],[58,5894,5896],{"className":5895},[65],[67,5897,5898],{"xmlns":69},[71,5899,5900,5910],{},[74,5901,5902,5904,5906,5908],{},[80,5903,2820],{},[90,5905,5868],{},[460,5907,5776],{},[80,5909,82],{},[97,5911,5912],{"encoding":99},"2j+1",[58,5914,5916,5937],{"className":5915,"ariaHidden":105},[104],[58,5917,5919,5922,5925,5928,5931,5934],{"className":5918},[109],[58,5920],{"className":5921,"style":5881},[113],[58,5923,2820],{"className":5924},[118],[58,5926,5868],{"className":5927,"style":5888},[118,191],[58,5929],{"className":5930,"style":1871},[498],[58,5932,5776],{"className":5933},[552],[58,5935],{"className":5936,"style":1871},[498],[58,5938,5940,5943],{"className":5939},[109],[58,5941],{"className":5942,"style":1765},[113],[58,5944,82],{"className":5945},[118]," 列上的元素为：",[14,5948,5949],{},[58,5950,5952,6030],{"className":5951},[61],[58,5953,5955],{"className":5954},[65],[67,5956,5957],{"xmlns":69},[71,5958,5959,6027],{},[74,5960,5961,5963,5981,5983,5986,5988],{},[90,5962,5603],{},[87,5964,5965,5967],{},[90,5966,5606],{},[74,5968,5969,5971,5973,5975,5977,5979],{},[460,5970,797],{"stretchy":796},[90,5972,788],{},[460,5974,802],{"separator":105},[80,5976,2820],{},[90,5978,5868],{},[460,5980,811],{"stretchy":796},[460,5982,814],{},[90,5984,5985],{},"sin",[460,5987,821],{},[74,5989,5990,5992,6025],{},[460,5991,797],{"fence":105},[77,5993,5994,5996],{},[90,5995,788],{},[464,5997,5998,6001],{},[80,5999,6000],{},"10000",[74,6002,6003,6005,6007,6009],{},[80,6004,2820],{},[90,6006,5868],{},[90,6008,2826],{"mathvariant":817},[87,6010,6011,6013],{},[90,6012,92],{},[74,6014,6015,6017,6019,6021,6023],{},[90,6016,365],{},[90,6018,791],{},[90,6020,92],{},[90,6022,781],{},[90,6024,2902],{},[460,6026,811],{"fence":105},[97,6028,6029],{"encoding":99}," PE_{(i,2j)} = \\sin\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[58,6031,6033,6113],{"className":6032,"ariaHidden":105},[104],[58,6034,6036,6040,6043,6104,6107,6110],{"className":6035},[109],[58,6037],{"className":6038,"style":6039},[113],"height:1.0385em;vertical-align:-0.3552em;",[58,6041,5603],{"className":6042,"style":3184},[118,191],[58,6044,6046,6050],{"className":6045},[118],[58,6047,5606],{"className":6048,"style":6049},[118,191],"margin-right:0.05764em;",[58,6051,6053],{"className":6052},[195],[58,6054,6056,6095],{"className":6055},[130,131],[58,6057,6059,6092],{"className":6058},[135],[58,6060,6062],{"className":6061,"style":205},[139],[58,6063,6065,6068],{"style":6064},"top:-2.5198em;margin-left:-0.0576em;margin-right:0.05em;",[58,6066],{"className":6067,"style":539},[147],[58,6069,6071],{"className":6070},[152,153,154,155],[58,6072,6074,6077,6080,6083,6086,6089],{"className":6073},[118,155],[58,6075,797],{"className":6076},[122,155],[58,6078,788],{"className":6079},[118,191,155],[58,6081,802],{"className":6082},[911,155],[58,6084,2820],{"className":6085},[118,155],[58,6087,5868],{"className":6088,"style":5888},[118,191,155],[58,6090,811],{"className":6091},[312,155],[58,6093,226],{"className":6094},[225],[58,6096,6098],{"className":6097},[135],[58,6099,6102],{"className":6100,"style":6101},[139],"height:0.3552em;",[58,6103],{},[58,6105],{"className":6106,"style":499},[498],[58,6108,814],{"className":6109},[503],[58,6111],{"className":6112,"style":499},[498],[58,6114,6116,6119,6122,6125],{"className":6115},[109],[58,6117],{"className":6118,"style":946},[113],[58,6120,5985],{"className":6121},[950],[58,6123],{"className":6124,"style":915},[498],[58,6126,6128,6134,6302],{"className":6127},[961],[58,6129,6131],{"className":6130,"style":966},[122,965],[58,6132,797],{"className":6133},[970,971],[58,6135,6137,6140,6299],{"className":6136},[118],[58,6138],{"className":6139},[122,123],[58,6141,6143],{"className":6142},[77],[58,6144,6146,6290],{"className":6145},[130,131],[58,6147,6149,6287],{"className":6148},[135],[58,6150,6153,6265,6273],{"className":6151,"style":6152},[139],"height:0.8557em;",[58,6154,6156,6159],{"style":6155},"top:-2.5648em;",[58,6157],{"className":6158,"style":148},[147],[58,6160,6162],{"className":6161},[152,153,154,155],[58,6163,6165,6169],{"className":6164},[118,155],[58,6166,6168],{"className":6167},[118,155],"1000",[58,6170,6172,6175],{"className":6171},[118,155],[58,6173,1753],{"className":6174},[118,155],[58,6176,6178],{"className":6177},[195],[58,6179,6181],{"className":6180},[130],[58,6182,6184],{"className":6183},[135],[58,6185,6188],{"className":6186,"style":6187},[139],"height:0.8932em;",[58,6189,6191,6195],{"style":6190},"top:-2.8932em;margin-right:0.0714em;",[58,6192],{"className":6193,"style":6194},[147],"height:2.5357em;",[58,6196,6198],{"className":6197},[152,216,217,155],[58,6199,6201,6204,6207,6210],{"className":6200},[118,155],[58,6202,2820],{"className":6203},[118,155],[58,6205,5868],{"className":6206,"style":5888},[118,191,155],[58,6208,2826],{"className":6209},[118,155],[58,6211,6213,6216],{"className":6212},[118,155],[58,6214,92],{"className":6215},[118,191,155],[58,6217,6219],{"className":6218},[195],[58,6220,6222,6256],{"className":6221},[130,131],[58,6223,6225,6253],{"className":6224},[135],[58,6226,6228],{"className":6227,"style":205},[139],[58,6229,6231,6235],{"style":6230},"top:-2.3448em;margin-left:0em;margin-right:0.1em;",[58,6232],{"className":6233,"style":6234},[147],"height:2.6944em;",[58,6236,6238,6241,6244,6247,6250],{"className":6237},[118,155],[58,6239,365],{"className":6240},[118,191,155],[58,6242,791],{"className":6243},[118,191,155],[58,6245,92],{"className":6246},[118,191,155],[58,6248,781],{"className":6249},[118,191,155],[58,6251,2902],{"className":6252,"style":5355},[118,191,155],[58,6254,226],{"className":6255},[225],[58,6257,6259],{"className":6258},[135],[58,6260,6263],{"className":6261,"style":6262},[139],"height:0.3496em;",[58,6264],{},[58,6266,6267,6270],{"style":273},[58,6268],{"className":6269,"style":148},[147],[58,6271],{"className":6272,"style":281},[280],[58,6274,6275,6278],{"style":284},[58,6276],{"className":6277,"style":148},[147],[58,6279,6281],{"className":6280},[152,153,154,155],[58,6282,6284],{"className":6283},[118,155],[58,6285,788],{"className":6286},[118,191,155],[58,6288,226],{"className":6289},[225],[58,6291,6293],{"className":6292},[135],[58,6294,6297],{"className":6295,"style":6296},[139],"height:0.4352em;",[58,6298],{},[58,6300],{"className":6301},[312,123],[58,6303,6305],{"className":6304,"style":966},[312,965],[58,6306,811],{"className":6307},[970,971],[14,6309,6310],{},[58,6311,6313,6394],{"className":6312},[61],[58,6314,6316],{"className":6315},[65],[67,6317,6318],{"xmlns":69},[71,6319,6320,6391],{},[74,6321,6322,6324,6346,6348,6351,6353],{},[90,6323,5603],{},[87,6325,6326,6328],{},[90,6327,5606],{},[74,6329,6330,6332,6334,6336,6338,6340,6342,6344],{},[460,6331,797],{"stretchy":796},[90,6333,788],{},[460,6335,802],{"separator":105},[80,6337,2820],{},[90,6339,5868],{},[460,6341,5776],{},[80,6343,82],{},[460,6345,811],{"stretchy":796},[460,6347,814],{},[90,6349,6350],{},"cos",[460,6352,821],{},[74,6354,6355,6357,6389],{},[460,6356,797],{"fence":105},[77,6358,6359,6361],{},[90,6360,788],{},[464,6362,6363,6365],{},[80,6364,6000],{},[74,6366,6367,6369,6371,6373],{},[80,6368,2820],{},[90,6370,5868],{},[90,6372,2826],{"mathvariant":817},[87,6374,6375,6377],{},[90,6376,92],{},[74,6378,6379,6381,6383,6385,6387],{},[90,6380,365],{},[90,6382,791],{},[90,6384,92],{},[90,6386,781],{},[90,6388,2902],{},[460,6390,811],{"fence":105},[97,6392,6393],{"encoding":99}," PE_{(i,2j+1)} = \\cos\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[58,6395,6397,6479],{"className":6396,"ariaHidden":105},[104],[58,6398,6400,6403,6406,6470,6473,6476],{"className":6399},[109],[58,6401],{"className":6402,"style":6039},[113],[58,6404,5603],{"className":6405,"style":3184},[118,191],[58,6407,6409,6412],{"className":6408},[118],[58,6410,5606],{"className":6411,"style":6049},[118,191],[58,6413,6415],{"className":6414},[195],[58,6416,6418,6462],{"className":6417},[130,131],[58,6419,6421,6459],{"className":6420},[135],[58,6422,6424],{"className":6423,"style":205},[139],[58,6425,6426,6429],{"style":6064},[58,6427],{"className":6428,"style":539},[147],[58,6430,6432],{"className":6431},[152,153,154,155],[58,6433,6435,6438,6441,6444,6447,6450,6453,6456],{"className":6434},[118,155],[58,6436,797],{"className":6437},[122,155],[58,6439,788],{"className":6440},[118,191,155],[58,6442,802],{"className":6443},[911,155],[58,6445,2820],{"className":6446},[118,155],[58,6448,5868],{"className":6449,"style":5888},[118,191,155],[58,6451,5776],{"className":6452},[552,155],[58,6454,82],{"className":6455},[118,155],[58,6457,811],{"className":6458},[312,155],[58,6460,226],{"className":6461},[225],[58,6463,6465],{"className":6464},[135],[58,6466,6468],{"className":6467,"style":6101},[139],[58,6469],{},[58,6471],{"className":6472,"style":499},[498],[58,6474,814],{"className":6475},[503],[58,6477],{"className":6478,"style":499},[498],[58,6480,6482,6485,6488,6491],{"className":6481},[109],[58,6483],{"className":6484,"style":946},[113],[58,6486,6350],{"className":6487},[950],[58,6489],{"className":6490,"style":915},[498],[58,6492,6494,6500,6658],{"className":6493},[961],[58,6495,6497],{"className":6496,"style":966},[122,965],[58,6498,797],{"className":6499},[970,971],[58,6501,6503,6506,6655],{"className":6502},[118],[58,6504],{"className":6505},[122,123],[58,6507,6509],{"className":6508},[77],[58,6510,6512,6647],{"className":6511},[130,131],[58,6513,6515,6644],{"className":6514},[135],[58,6516,6518,6622,6630],{"className":6517,"style":6152},[139],[58,6519,6520,6523],{"style":6155},[58,6521],{"className":6522,"style":148},[147],[58,6524,6526],{"className":6525},[152,153,154,155],[58,6527,6529,6532],{"className":6528},[118,155],[58,6530,6168],{"className":6531},[118,155],[58,6533,6535,6538],{"className":6534},[118,155],[58,6536,1753],{"className":6537},[118,155],[58,6539,6541],{"className":6540},[195],[58,6542,6544],{"className":6543},[130],[58,6545,6547],{"className":6546},[135],[58,6548,6550],{"className":6549,"style":6187},[139],[58,6551,6552,6555],{"style":6190},[58,6553],{"className":6554,"style":6194},[147],[58,6556,6558],{"className":6557},[152,216,217,155],[58,6559,6561,6564,6567,6570],{"className":6560},[118,155],[58,6562,2820],{"className":6563},[118,155],[58,6565,5868],{"className":6566,"style":5888},[118,191,155],[58,6568,2826],{"className":6569},[118,155],[58,6571,6573,6576],{"className":6572},[118,155],[58,6574,92],{"className":6575},[118,191,155],[58,6577,6579],{"className":6578},[195],[58,6580,6582,6614],{"className":6581},[130,131],[58,6583,6585,6611],{"className":6584},[135],[58,6586,6588],{"className":6587,"style":205},[139],[58,6589,6590,6593],{"style":6230},[58,6591],{"className":6592,"style":6234},[147],[58,6594,6596,6599,6602,6605,6608],{"className":6595},[118,155],[58,6597,365],{"className":6598},[118,191,155],[58,6600,791],{"className":6601},[118,191,155],[58,6603,92],{"className":6604},[118,191,155],[58,6606,781],{"className":6607},[118,191,155],[58,6609,2902],{"className":6610,"style":5355},[118,191,155],[58,6612,226],{"className":6613},[225],[58,6615,6617],{"className":6616},[135],[58,6618,6620],{"className":6619,"style":6262},[139],[58,6621],{},[58,6623,6624,6627],{"style":273},[58,6625],{"className":6626,"style":148},[147],[58,6628],{"className":6629,"style":281},[280],[58,6631,6632,6635],{"style":284},[58,6633],{"className":6634,"style":148},[147],[58,6636,6638],{"className":6637},[152,153,154,155],[58,6639,6641],{"className":6640},[118,155],[58,6642,788],{"className":6643},[118,191,155],[58,6645,226],{"className":6646},[225],[58,6648,6650],{"className":6649},[135],[58,6651,6653],{"className":6652,"style":6296},[139],[58,6654],{},[58,6656],{"className":6657},[312,123],[58,6659,6661],{"className":6660,"style":966},[312,965],[58,6662,811],{"className":6663},[970,971],[14,6665,6666,6667,6695,6696,6724,6725,6760,6761,6817,6818,6846,6847,6940,6941,7020],{},"其中，",[58,6668,6670,6683],{"className":6669},[61],[58,6671,6673],{"className":6672},[65],[67,6674,6675],{"xmlns":69},[71,6676,6677,6681],{},[74,6678,6679],{},[90,6680,788],{},[97,6682,788],{"encoding":99},[58,6684,6686],{"className":6685,"ariaHidden":105},[104],[58,6687,6689,6692],{"className":6688},[109],[58,6690],{"className":6691,"style":5847},[113],[58,6693,788],{"className":6694},[118,191]," 表示位置，",[58,6697,6699,6712],{"className":6698},[61],[58,6700,6702],{"className":6701},[65],[67,6703,6704],{"xmlns":69},[71,6705,6706,6710],{},[74,6707,6708],{},[90,6709,5868],{},[97,6711,5868],{"encoding":99},[58,6713,6715],{"className":6714,"ariaHidden":105},[104],[58,6716,6718,6721],{"className":6717},[109],[58,6719],{"className":6720,"style":5881},[113],[58,6722,5868],{"className":6723,"style":5888},[118,191]," 表示维度。也就是说，位置编码的每一个维度都对应一个正弦曲线。其波长从 ",[58,6726,6728,6745],{"className":6727},[61],[58,6729,6731],{"className":6730},[65],[67,6732,6733],{"xmlns":69},[71,6734,6735,6742],{},[74,6736,6737,6739],{},[80,6738,2820],{},[90,6740,6741],{},"π",[97,6743,6744],{"encoding":99},"2\\pi",[58,6746,6748],{"className":6747,"ariaHidden":105},[104],[58,6749,6751,6754,6757],{"className":6750},[109],[58,6752],{"className":6753,"style":1765},[113],[58,6755,2820],{"className":6756},[118],[58,6758,6741],{"className":6759,"style":440},[118,191]," 到 ",[58,6762,6764,6784],{"className":6763},[61],[58,6765,6767],{"className":6766},[65],[67,6768,6769],{"xmlns":69},[71,6770,6771,6781],{},[74,6772,6773,6775,6777,6779],{},[80,6774,6000],{},[460,6776,1815],{},[80,6778,2820],{},[90,6780,6741],{},[97,6782,6783],{"encoding":99},"10000 \\cdot 2\\pi",[58,6785,6787,6805],{"className":6786,"ariaHidden":105},[104],[58,6788,6790,6793,6796,6799,6802],{"className":6789},[109],[58,6791],{"className":6792,"style":1765},[113],[58,6794,6000],{"className":6795},[118],[58,6797],{"className":6798,"style":1871},[498],[58,6800,1815],{"className":6801},[552],[58,6803],{"className":6804,"style":1871},[498],[58,6806,6808,6811,6814],{"className":6807},[109],[58,6809],{"className":6810,"style":1765},[113],[58,6812,2820],{"className":6813},[118],[58,6815,6741],{"className":6816,"style":440},[118,191]," 按几何级数增长。我们选择这个函数，是因为我们假设它能够使模型更容易学习关注相对位置，因为对于任意固定的偏移量 ",[58,6819,6821,6834],{"className":6820},[61],[58,6822,6824],{"className":6823},[65],[67,6825,6826],{"xmlns":69},[71,6827,6828,6832],{},[74,6829,6830],{},[90,6831,95],{},[97,6833,95],{"encoding":99},[58,6835,6837],{"className":6836,"ariaHidden":105},[104],[58,6838,6840,6843],{"className":6839},[109],[58,6841],{"className":6842,"style":406},[113],[58,6844,95],{"className":6845,"style":221},[118,191],"，",[58,6848,6850,6876],{"className":6849},[61],[58,6851,6853],{"className":6852},[65],[67,6854,6855],{"xmlns":69},[71,6856,6857,6873],{},[74,6858,6859,6861],{},[90,6860,5603],{},[87,6862,6863,6865],{},[90,6864,5606],{},[74,6866,6867,6869,6871],{},[90,6868,788],{},[460,6870,5776],{},[90,6872,95],{},[97,6874,6875],{"encoding":99},"PE_{i+k}",[58,6877,6879],{"className":6878,"ariaHidden":105},[104],[58,6880,6882,6886,6889],{"className":6881},[109],[58,6883],{"className":6884,"style":6885},[113],"height:0.8917em;vertical-align:-0.2083em;",[58,6887,5603],{"className":6888,"style":3184},[118,191],[58,6890,6892,6895],{"className":6891},[118],[58,6893,5606],{"className":6894,"style":6049},[118,191],[58,6896,6898],{"className":6897},[195],[58,6899,6901,6931],{"className":6900},[130,131],[58,6902,6904,6928],{"className":6903},[135],[58,6905,6907],{"className":6906,"style":1247},[139],[58,6908,6910,6913],{"style":6909},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[58,6911],{"className":6912,"style":539},[147],[58,6914,6916],{"className":6915},[152,153,154,155],[58,6917,6919,6922,6925],{"className":6918},[118,155],[58,6920,788],{"className":6921},[118,191,155],[58,6923,5776],{"className":6924},[552,155],[58,6926,95],{"className":6927,"style":221},[118,191,155],[58,6929,226],{"className":6930},[225],[58,6932,6934],{"className":6933},[135],[58,6935,6938],{"className":6936,"style":6937},[139],"height:0.2083em;",[58,6939],{}," 都可以表示为 ",[58,6942,6944,6964],{"className":6943},[61],[58,6945,6947],{"className":6946},[65],[67,6948,6949],{"xmlns":69},[71,6950,6951,6961],{},[74,6952,6953,6955],{},[90,6954,5603],{},[87,6956,6957,6959],{},[90,6958,5606],{},[90,6960,788],{},[97,6962,6963],{"encoding":99},"PE_{i}",[58,6965,6967],{"className":6966,"ariaHidden":105},[104],[58,6968,6970,6974,6977],{"className":6969},[109],[58,6971],{"className":6972,"style":6973},[113],"height:0.8333em;vertical-align:-0.15em;",[58,6975,5603],{"className":6976,"style":3184},[118,191],[58,6978,6980,6983],{"className":6979},[118],[58,6981,5606],{"className":6982,"style":6049},[118,191],[58,6984,6986],{"className":6985},[195],[58,6987,6989,7012],{"className":6988},[130,131],[58,6990,6992,7009],{"className":6991},[135],[58,6993,6995],{"className":6994,"style":2031},[139],[58,6996,6997,7000],{"style":6909},[58,6998],{"className":6999,"style":539},[147],[58,7001,7003],{"className":7002},[152,153,154,155],[58,7004,7006],{"className":7005},[118,155],[58,7007,788],{"className":7008},[118,191,155],[58,7010,226],{"className":7011},[225],[58,7013,7015],{"className":7014},[135],[58,7016,7018],{"className":7017,"style":1269},[139],[58,7019],{}," 的线性函数。",[2389,7022,7024],{"className":2391,"code":7023,"language":2393,"meta":2394,"style":2394},"class PositionalEncoding(nn.Block):\n    \"\"\"位置编码\"\"\"\n    def __init__(self, num_hiddens, dropout, max_len=1000):\n        super(PositionalEncoding, self).__init__()\n        self.dropout = nn.Dropout(dropout)\n        # 创建一个足够长的P\n        self.P = np.zeros((1, max_len, num_hiddens))\n        X = np.arange(max_len).reshape(-1, 1) / np.power(\n            10000, np.arange(0, num_hiddens, 2) / num_hiddens)\n        self.P[:, :, 0::2] = np.sin(X)\n        self.P[:, :, 1::2] = np.cos(X)\n\n    def forward(self, X):\n        X = X + self.P[:, :X.shape[1], :].as_in_ctx(X.ctx)\n        return self.dropout(X)\n",[2396,7025,7026,7044,7049,7078,7094,7104,7109,7126,7151,7173,7205,7232,7236,7252,7285],{"__ignoreMap":2394},[58,7027,7028,7030,7033,7035,7037,7039,7042],{"class":2400,"line":2401},[58,7029,2629],{"class":2404},[58,7031,7032],{"class":2632}," PositionalEncoding",[58,7034,797],{"class":2412},[58,7036,2639],{"class":2638},[58,7038,863],{"class":2412},[58,7040,7041],{"class":2638},"Block",[58,7043,2425],{"class":2412},[58,7045,7046],{"class":2400,"line":2428},[58,7047,7048],{"class":2431},"    \"\"\"位置编码\"\"\"\n",[58,7050,7051,7053,7055,7057,7059,7061,7063,7065,7067,7069,7072,7074,7076],{"class":2400,"line":2435},[58,7052,2656],{"class":2404},[58,7054,2659],{"class":2454},[58,7056,797],{"class":2412},[58,7058,2665],{"class":2664},[58,7060,2419],{"class":2412},[58,7062,4861],{"class":2415},[58,7064,2419],{"class":2412},[58,7066,2670],{"class":2415},[58,7068,2419],{"class":2412},[58,7070,7071],{"class":2415},"max_len",[58,7073,814],{"class":2404},[58,7075,6168],{"class":2454},[58,7077,2425],{"class":2412},[58,7079,7080,7082,7085,7087,7089,7091],{"class":2400,"line":2442},[58,7081,2686],{"class":2685},[58,7083,7084],{"class":2412},"(PositionalEncoding, ",[58,7086,2665],{"class":2692},[58,7088,2695],{"class":2412},[58,7090,2698],{"class":2454},[58,7092,7093],{"class":2412},"()\n",[58,7095,7096,7098,7100,7102],{"class":2400,"line":2461},[58,7097,2710],{"class":2692},[58,7099,2713],{"class":2412},[58,7101,814],{"class":2404},[58,7103,2718],{"class":2412},[58,7105,7106],{"class":2400,"line":2482},[58,7107,7108],{"class":2438},"        # 创建一个足够长的P\n",[58,7110,7111,7113,7116,7118,7121,7123],{"class":2400,"line":2490},[58,7112,2710],{"class":2692},[58,7114,7115],{"class":2412},".P ",[58,7117,814],{"class":2404},[58,7119,7120],{"class":2412}," np.zeros((",[58,7122,82],{"class":2454},[58,7124,7125],{"class":2412},", max_len, num_hiddens))\n",[58,7127,7128,7130,7132,7135,7137,7139,7141,7143,7146,7148],{"class":2400,"line":2501},[58,7129,2568],{"class":2412},[58,7131,814],{"class":2404},[58,7133,7134],{"class":2412}," np.arange(max_len).reshape(",[58,7136,2552],{"class":2404},[58,7138,82],{"class":2454},[58,7140,2419],{"class":2412},[58,7142,82],{"class":2454},[58,7144,7145],{"class":2412},") ",[58,7147,2826],{"class":2404},[58,7149,7150],{"class":2412}," np.power(\n",[58,7152,7153,7156,7159,7161,7164,7166,7168,7170],{"class":2400,"line":2518},[58,7154,7155],{"class":2454},"            10000",[58,7157,7158],{"class":2412},", np.arange(",[58,7160,1753],{"class":2454},[58,7162,7163],{"class":2412},", num_hiddens, ",[58,7165,2820],{"class":2454},[58,7167,7145],{"class":2412},[58,7169,2826],{"class":2404},[58,7171,7172],{"class":2412}," num_hiddens)\n",[58,7174,7175,7177,7180,7184,7186,7188,7190,7192,7195,7197,7200,7202],{"class":2400,"line":2534},[58,7176,2710],{"class":2692},[58,7178,7179],{"class":2412},".P[",[58,7181,7183],{"class":7182},"sDoOe",":",[58,7185,2419],{"class":2412},[58,7187,7183],{"class":7182},[58,7189,2419],{"class":2412},[58,7191,1753],{"class":2454},[58,7193,7194],{"class":7182},"::",[58,7196,2820],{"class":2454},[58,7198,7199],{"class":2412},"] ",[58,7201,814],{"class":2404},[58,7203,7204],{"class":2412}," np.sin(X)\n",[58,7206,7207,7209,7211,7213,7215,7217,7219,7221,7223,7225,7227,7229],{"class":2400,"line":2542},[58,7208,2710],{"class":2692},[58,7210,7179],{"class":2412},[58,7212,7183],{"class":7182},[58,7214,2419],{"class":2412},[58,7216,7183],{"class":7182},[58,7218,2419],{"class":2412},[58,7220,82],{"class":2454},[58,7222,7194],{"class":7182},[58,7224,2820],{"class":2454},[58,7226,7199],{"class":2412},[58,7228,814],{"class":2404},[58,7230,7231],{"class":2412}," np.cos(X)\n",[58,7233,7234],{"class":2400,"line":2559},[58,7235,2724],{"emptyLinePlaceholder":2723},[58,7237,7238,7240,7242,7244,7246,7248,7250],{"class":2400,"line":2565},[58,7239,2656],{"class":2404},[58,7241,2751],{"class":2408},[58,7243,797],{"class":2412},[58,7245,2665],{"class":2664},[58,7247,2419],{"class":2412},[58,7249,2416],{"class":2415},[58,7251,2425],{"class":2412},[58,7253,7254,7256,7258,7261,7263,7265,7267,7269,7271,7273,7276,7278,7280,7282],{"class":2400,"line":2590},[58,7255,2568],{"class":2412},[58,7257,814],{"class":2404},[58,7259,7260],{"class":2412}," X ",[58,7262,5776],{"class":2404},[58,7264,5219],{"class":2692},[58,7266,7179],{"class":2412},[58,7268,7183],{"class":7182},[58,7270,2419],{"class":2412},[58,7272,7183],{"class":7182},[58,7274,7275],{"class":2412},"X.shape[",[58,7277,82],{"class":2454},[58,7279,4793],{"class":2412},[58,7281,7183],{"class":7182},[58,7283,7284],{"class":2412},"].as_in_ctx(X.ctx)\n",[58,7286,7287,7289,7291],{"class":2400,"line":2603},[58,7288,2464],{"class":2404},[58,7290,5219],{"class":2692},[58,7292,7293],{"class":2412},".dropout(X)\n",[10,7295,7296],{"id":7296},"前馈神经网络",[14,7298,7299],{},"除了注意力子层外，我们的编码器和解码器的每一层中都包含一个全连接的前馈神经网络，该网络分别且相同地应用于每个位置。这包括两个线性变换，中间使用ReLU激活函数。",[14,7301,7302],{},[58,7303,7305,7378],{"className":7304},[61],[58,7306,7308],{"className":7307},[65],[67,7309,7310],{"xmlns":69},[71,7311,7312,7375],{},[74,7313,7314,7317,7319,7322,7324,7327,7329,7331,7334,7336,7338,7340,7342,7344,7350,7352,7359,7361,7367,7369],{},[90,7315,7316],{},"F",[90,7318,7316],{},[90,7320,7321],{},"N",[460,7323,797],{"stretchy":796},[90,7325,7326],{},"x",[460,7328,811],{"stretchy":796},[460,7330,814],{},[90,7332,7333],{},"max",[460,7335,821],{},[460,7337,797],{"stretchy":796},[80,7339,1753],{},[460,7341,802],{"separator":105},[90,7343,7326],{},[87,7345,7346,7348],{},[90,7347,2992],{},[80,7349,82],{},[460,7351,5776],{},[87,7353,7354,7357],{},[90,7355,7356],{},"b",[80,7358,82],{},[460,7360,811],{"stretchy":796},[87,7362,7363,7365],{},[90,7364,2992],{},[80,7366,2820],{},[460,7368,5776],{},[87,7370,7371,7373],{},[90,7372,7356],{},[80,7374,2820],{},[97,7376,7377],{"encoding":99}," FFN(x) = \\max(0,xW_1+b_1)W_2+b_2",[58,7379,7381,7415,7489,7587],{"className":7380,"ariaHidden":105},[104],[58,7382,7384,7387,7390,7393,7397,7400,7403,7406,7409,7412],{"className":7383},[109],[58,7385],{"className":7386,"style":876},[113],[58,7388,7316],{"className":7389,"style":3184},[118,191],[58,7391,7316],{"className":7392,"style":3184},[118,191],[58,7394,7321],{"className":7395,"style":7396},[118,191],"margin-right:0.10903em;",[58,7398,797],{"className":7399},[122],[58,7401,7326],{"className":7402},[118,191],[58,7404,811],{"className":7405},[312],[58,7407],{"className":7408,"style":499},[498],[58,7410,814],{"className":7411},[503],[58,7413],{"className":7414,"style":499},[498],[58,7416,7418,7421,7424,7427,7430,7433,7436,7439,7480,7483,7486],{"className":7417},[109],[58,7419],{"className":7420,"style":876},[113],[58,7422,7333],{"className":7423},[950],[58,7425,797],{"className":7426},[122],[58,7428,1753],{"className":7429},[118],[58,7431,802],{"className":7432},[911],[58,7434],{"className":7435,"style":915},[498],[58,7437,7326],{"className":7438},[118,191],[58,7440,7442,7445],{"className":7441},[118],[58,7443,2992],{"className":7444,"style":3184},[118,191],[58,7446,7448],{"className":7447},[195],[58,7449,7451,7472],{"className":7450},[130,131],[58,7452,7454,7469],{"className":7453},[135],[58,7455,7457],{"className":7456,"style":3090},[139],[58,7458,7460,7463],{"style":7459},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[58,7461],{"className":7462,"style":539},[147],[58,7464,7466],{"className":7465},[152,153,154,155],[58,7467,82],{"className":7468},[118,155],[58,7470,226],{"className":7471},[225],[58,7473,7475],{"className":7474},[135],[58,7476,7478],{"className":7477,"style":1269},[139],[58,7479],{},[58,7481],{"className":7482,"style":1871},[498],[58,7484,5776],{"className":7485},[552],[58,7487],{"className":7488,"style":1871},[498],[58,7490,7492,7495,7535,7538,7578,7581,7584],{"className":7491},[109],[58,7493],{"className":7494,"style":876},[113],[58,7496,7498,7501],{"className":7497},[118],[58,7499,7356],{"className":7500},[118,191],[58,7502,7504],{"className":7503},[195],[58,7505,7507,7527],{"className":7506},[130,131],[58,7508,7510,7524],{"className":7509},[135],[58,7511,7513],{"className":7512,"style":3090},[139],[58,7514,7515,7518],{"style":1250},[58,7516],{"className":7517,"style":539},[147],[58,7519,7521],{"className":7520},[152,153,154,155],[58,7522,82],{"className":7523},[118,155],[58,7525,226],{"className":7526},[225],[58,7528,7530],{"className":7529},[135],[58,7531,7533],{"className":7532,"style":1269},[139],[58,7534],{},[58,7536,811],{"className":7537},[312],[58,7539,7541,7544],{"className":7540},[118],[58,7542,2992],{"className":7543,"style":3184},[118,191],[58,7545,7547],{"className":7546},[195],[58,7548,7550,7570],{"className":7549},[130,131],[58,7551,7553,7567],{"className":7552},[135],[58,7554,7556],{"className":7555,"style":3090},[139],[58,7557,7558,7561],{"style":7459},[58,7559],{"className":7560,"style":539},[147],[58,7562,7564],{"className":7563},[152,153,154,155],[58,7565,2820],{"className":7566},[118,155],[58,7568,226],{"className":7569},[225],[58,7571,7573],{"className":7572},[135],[58,7574,7576],{"className":7575,"style":1269},[139],[58,7577],{},[58,7579],{"className":7580,"style":1871},[498],[58,7582,5776],{"className":7583},[552],[58,7585],{"className":7586,"style":1871},[498],[58,7588,7590,7593],{"className":7589},[109],[58,7591],{"className":7592,"style":1228},[113],[58,7594,7596,7599],{"className":7595},[118],[58,7597,7356],{"className":7598},[118,191],[58,7600,7602],{"className":7601},[195],[58,7603,7605,7625],{"className":7604},[130,131],[58,7606,7608,7622],{"className":7607},[135],[58,7609,7611],{"className":7610,"style":3090},[139],[58,7612,7613,7616],{"style":1250},[58,7614],{"className":7615,"style":539},[147],[58,7617,7619],{"className":7618},[152,153,154,155],[58,7620,2820],{"className":7621},[118,155],[58,7623,226],{"className":7624},[225],[58,7626,7628],{"className":7627},[135],[58,7629,7631],{"className":7630,"style":1269},[139],[58,7632],{},[2389,7634,7636],{"className":2391,"code":7635,"language":2393,"meta":2394,"style":2394},"class PositionWiseFFN(nn.Module):\n    \"\"\"基于位置的前馈网络\"\"\"\n    def __init__(self, ffn_num_input, ffn_num_hiddens, ffn_num_outputs,\n                 **kwargs):\n        super(PositionWiseFFN, self).__init__(**kwargs)\n        self.dense1 = nn.Linear(ffn_num_input, ffn_num_hiddens)\n        self.relu = nn.ReLU()\n        self.dense2 = nn.Linear(ffn_num_hiddens, ffn_num_outputs)\n\n    def forward(self, X):\n        return self.dense2(self.relu(self.dense1(X)))\n",[2396,7637,7638,7655,7660,7687,7696,7715,7727,7739,7751,7755,7771],{"__ignoreMap":2394},[58,7639,7640,7642,7645,7647,7649,7651,7653],{"class":2400,"line":2401},[58,7641,2629],{"class":2404},[58,7643,7644],{"class":2632}," PositionWiseFFN",[58,7646,797],{"class":2412},[58,7648,2639],{"class":2638},[58,7650,863],{"class":2412},[58,7652,2644],{"class":2638},[58,7654,2425],{"class":2412},[58,7656,7657],{"class":2400,"line":2428},[58,7658,7659],{"class":2431},"    \"\"\"基于位置的前馈网络\"\"\"\n",[58,7661,7662,7664,7666,7668,7670,7672,7675,7677,7680,7682,7685],{"class":2400,"line":2435},[58,7663,2656],{"class":2404},[58,7665,2659],{"class":2454},[58,7667,797],{"class":2412},[58,7669,2665],{"class":2664},[58,7671,2419],{"class":2412},[58,7673,7674],{"class":2415},"ffn_num_input",[58,7676,2419],{"class":2412},[58,7678,7679],{"class":2415},"ffn_num_hiddens",[58,7681,2419],{"class":2412},[58,7683,7684],{"class":2415},"ffn_num_outputs",[58,7686,3825],{"class":2412},[58,7688,7689,7692,7694],{"class":2400,"line":2442},[58,7690,7691],{"class":2404},"                 **",[58,7693,2678],{"class":2415},[58,7695,2425],{"class":2412},[58,7697,7698,7700,7703,7705,7707,7709,7711,7713],{"class":2400,"line":2461},[58,7699,2686],{"class":2685},[58,7701,7702],{"class":2412},"(PositionWiseFFN, ",[58,7704,2665],{"class":2692},[58,7706,2695],{"class":2412},[58,7708,2698],{"class":2454},[58,7710,797],{"class":2412},[58,7712,2675],{"class":2404},[58,7714,2705],{"class":2412},[58,7716,7717,7719,7722,7724],{"class":2400,"line":2482},[58,7718,2710],{"class":2692},[58,7720,7721],{"class":2412},".dense1 ",[58,7723,814],{"class":2404},[58,7725,7726],{"class":2412}," nn.Linear(ffn_num_input, ffn_num_hiddens)\n",[58,7728,7729,7731,7734,7736],{"class":2400,"line":2490},[58,7730,2710],{"class":2692},[58,7732,7733],{"class":2412},".relu ",[58,7735,814],{"class":2404},[58,7737,7738],{"class":2412}," nn.ReLU()\n",[58,7740,7741,7743,7746,7748],{"class":2400,"line":2501},[58,7742,2710],{"class":2692},[58,7744,7745],{"class":2412},".dense2 ",[58,7747,814],{"class":2404},[58,7749,7750],{"class":2412}," nn.Linear(ffn_num_hiddens, ffn_num_outputs)\n",[58,7752,7753],{"class":2400,"line":2518},[58,7754,2724],{"emptyLinePlaceholder":2723},[58,7756,7757,7759,7761,7763,7765,7767,7769],{"class":2400,"line":2534},[58,7758,2656],{"class":2404},[58,7760,2751],{"class":2408},[58,7762,797],{"class":2412},[58,7764,2665],{"class":2664},[58,7766,2419],{"class":2412},[58,7768,2416],{"class":2415},[58,7770,2425],{"class":2412},[58,7772,7773,7775,7777,7780,7782,7785,7787],{"class":2400,"line":2542},[58,7774,2464],{"class":2404},[58,7776,5219],{"class":2692},[58,7778,7779],{"class":2412},".dense2(",[58,7781,2665],{"class":2692},[58,7783,7784],{"class":2412},".relu(",[58,7786,2665],{"class":2692},[58,7788,7789],{"class":2412},".dense1(X)))\n",[10,7791,7792],{"id":7792},"残差连接和层规范化",[14,7794,7795],{},"我们在每个子层之间加入了一个残差连接和层归一化。",[14,7797,7798,7799,4567,7924,7987],{},"因此，每个子层的输出都是 ",[58,7800,7802,7870],{"className":7801},[61],[58,7803,7805],{"className":7804},[65],[67,7806,7807],{"xmlns":69},[71,7808,7809,7867],{},[74,7810,7811,7834,7836,7838,7840,7859,7861,7863,7865],{},[74,7812,7813,7816,7818,7821,7823,7826,7828,7830,7832],{},[90,7814,7815],{"mathvariant":817},"L",[90,7817,21],{"mathvariant":817},[90,7819,7820],{"mathvariant":817},"y",[90,7822,781],{"mathvariant":817},[90,7824,7825],{"mathvariant":817},"r",[90,7827,7321],{"mathvariant":817},[90,7829,791],{"mathvariant":817},[90,7831,7825],{"mathvariant":817},[90,7833,365],{"mathvariant":817},[460,7835,797],{"stretchy":796},[90,7837,7326],{},[460,7839,5776],{},[74,7841,7842,7845,7847,7849,7851,7853,7855,7857],{},[90,7843,7844],{"mathvariant":817},"S",[90,7846,2899],{"mathvariant":817},[90,7848,7356],{"mathvariant":817},[90,7850,2902],{"mathvariant":817},[90,7852,21],{"mathvariant":817},[90,7854,7820],{"mathvariant":817},[90,7856,781],{"mathvariant":817},[90,7858,7825],{"mathvariant":817},[460,7860,797],{"stretchy":796},[90,7862,7326],{},[460,7864,811],{"stretchy":796},[460,7866,811],{"stretchy":796},[97,7868,7869],{"encoding":99},"\\mathrm{LayerNorm}(x + \\mathrm{Sublayer}(x))",[58,7871,7873,7901],{"className":7872,"ariaHidden":105},[104],[58,7874,7876,7879,7886,7889,7892,7895,7898],{"className":7875},[109],[58,7877],{"className":7878,"style":876},[113],[58,7880,7882],{"className":7881},[118],[58,7883,7885],{"className":7884},[118,954],"LayerNorm",[58,7887,797],{"className":7888},[122],[58,7890,7326],{"className":7891},[118,191],[58,7893],{"className":7894,"style":1871},[498],[58,7896,5776],{"className":7897},[552],[58,7899],{"className":7900,"style":1871},[498],[58,7902,7904,7907,7914,7917,7920],{"className":7903},[109],[58,7905],{"className":7906,"style":876},[113],[58,7908,7910],{"className":7909},[118],[58,7911,7913],{"className":7912},[118,954],"Sublayer",[58,7915,797],{"className":7916},[122],[58,7918,7326],{"className":7919},[118,191],[58,7921,7923],{"className":7922},[312],"))",[58,7925,7927,7963],{"className":7926},[61],[58,7928,7930],{"className":7929},[65],[67,7931,7932],{"xmlns":69},[71,7933,7934,7960],{},[74,7935,7936,7954,7956,7958],{},[74,7937,7938,7940,7942,7944,7946,7948,7950,7952],{},[90,7939,7844],{"mathvariant":817},[90,7941,2899],{"mathvariant":817},[90,7943,7356],{"mathvariant":817},[90,7945,2902],{"mathvariant":817},[90,7947,21],{"mathvariant":817},[90,7949,7820],{"mathvariant":817},[90,7951,781],{"mathvariant":817},[90,7953,7825],{"mathvariant":817},[460,7955,797],{"stretchy":796},[90,7957,7326],{},[460,7959,811],{"stretchy":796},[97,7961,7962],{"encoding":99},"\\mathrm{Sublayer}(x)",[58,7964,7966],{"className":7965,"ariaHidden":105},[104],[58,7967,7969,7972,7978,7981,7984],{"className":7968},[109],[58,7970],{"className":7971,"style":876},[113],[58,7973,7975],{"className":7974},[118],[58,7976,7913],{"className":7977},[118,954],[58,7979,797],{"className":7980},[122],[58,7982,7326],{"className":7983},[118,191],[58,7985,811],{"className":7986},[312]," 是由该子层本身实现的函数。我们在每个子层的输出上应用 dropout，然后再将其加到子层输入并进行归一化。",[2389,7989,7991],{"className":2391,"code":7990,"language":2393,"meta":2394,"style":2394},"class AddNorm(nn.Module):\n    \"\"\"残差连接后进行层规范化\"\"\"\n    def __init__(self, normalized_shape, dropout, **kwargs):\n        super(AddNorm, self).__init__(**kwargs)\n        self.dropout = nn.Dropout(dropout)\n        self.ln = nn.LayerNorm(normalized_shape)\n\n    def forward(self, X, Y):\n        return self.ln(self.dropout(Y) + X)\n",[2396,7992,7993,8010,8015,8042,8061,8071,8083,8087,8108],{"__ignoreMap":2394},[58,7994,7995,7997,8000,8002,8004,8006,8008],{"class":2400,"line":2401},[58,7996,2629],{"class":2404},[58,7998,7999],{"class":2632}," AddNorm",[58,8001,797],{"class":2412},[58,8003,2639],{"class":2638},[58,8005,863],{"class":2412},[58,8007,2644],{"class":2638},[58,8009,2425],{"class":2412},[58,8011,8012],{"class":2400,"line":2428},[58,8013,8014],{"class":2431},"    \"\"\"残差连接后进行层规范化\"\"\"\n",[58,8016,8017,8019,8021,8023,8025,8027,8030,8032,8034,8036,8038,8040],{"class":2400,"line":2435},[58,8018,2656],{"class":2404},[58,8020,2659],{"class":2454},[58,8022,797],{"class":2412},[58,8024,2665],{"class":2664},[58,8026,2419],{"class":2412},[58,8028,8029],{"class":2415},"normalized_shape",[58,8031,2419],{"class":2412},[58,8033,2670],{"class":2415},[58,8035,2419],{"class":2412},[58,8037,2675],{"class":2404},[58,8039,2678],{"class":2415},[58,8041,2425],{"class":2412},[58,8043,8044,8046,8049,8051,8053,8055,8057,8059],{"class":2400,"line":2442},[58,8045,2686],{"class":2685},[58,8047,8048],{"class":2412},"(AddNorm, ",[58,8050,2665],{"class":2692},[58,8052,2695],{"class":2412},[58,8054,2698],{"class":2454},[58,8056,797],{"class":2412},[58,8058,2675],{"class":2404},[58,8060,2705],{"class":2412},[58,8062,8063,8065,8067,8069],{"class":2400,"line":2461},[58,8064,2710],{"class":2692},[58,8066,2713],{"class":2412},[58,8068,814],{"class":2404},[58,8070,2718],{"class":2412},[58,8072,8073,8075,8078,8080],{"class":2400,"line":2482},[58,8074,2710],{"class":2692},[58,8076,8077],{"class":2412},".ln ",[58,8079,814],{"class":2404},[58,8081,8082],{"class":2412}," nn.LayerNorm(normalized_shape)\n",[58,8084,8085],{"class":2400,"line":2490},[58,8086,2724],{"emptyLinePlaceholder":2723},[58,8088,8089,8091,8093,8095,8097,8099,8101,8103,8106],{"class":2400,"line":2501},[58,8090,2656],{"class":2404},[58,8092,2751],{"class":2408},[58,8094,797],{"class":2412},[58,8096,2665],{"class":2664},[58,8098,2419],{"class":2412},[58,8100,2416],{"class":2415},[58,8102,2419],{"class":2412},[58,8104,8105],{"class":2415},"Y",[58,8107,2425],{"class":2412},[58,8109,8110,8112,8114,8117,8119,8122,8124],{"class":2400,"line":2518},[58,8111,2464],{"class":2404},[58,8113,5219],{"class":2692},[58,8115,8116],{"class":2412},".ln(",[58,8118,2665],{"class":2692},[58,8120,8121],{"class":2412},".dropout(Y) ",[58,8123,5776],{"class":2404},[58,8125,8126],{"class":2412}," X)\n",[10,8128,8129],{"id":8129},"编码器-解码器架构",[14,8131,8132,8133,8283,8284,8460,8461,8490,8491,8641],{},"大多数主流的神经序列转换模型都采用编码器—解码器结构。其中，编码器将符号表示组成的输入序列 ",[58,8134,8136,8170],{"className":8135},[61],[58,8137,8139],{"className":8138},[65],[67,8140,8141],{"xmlns":69},[71,8142,8143,8167],{},[74,8144,8145,8147,8153,8155,8157,8159,8165],{},[460,8146,797],{"stretchy":796},[87,8148,8149,8151],{},[90,8150,7326],{},[80,8152,82],{},[460,8154,802],{"separator":105},[460,8156,2969],{},[460,8158,802],{"separator":105},[87,8160,8161,8163],{},[90,8162,7326],{},[90,8164,334],{},[460,8166,811],{"stretchy":796},[97,8168,8169],{"encoding":99},"(x_1, \\ldots, x_n)",[58,8171,8173],{"className":8172,"ariaHidden":105},[104],[58,8174,8176,8179,8182,8222,8225,8228,8231,8234,8237,8240,8280],{"className":8175},[109],[58,8177],{"className":8178,"style":876},[113],[58,8180,797],{"className":8181},[122],[58,8183,8185,8188],{"className":8184},[118],[58,8186,7326],{"className":8187},[118,191],[58,8189,8191],{"className":8190},[195],[58,8192,8194,8214],{"className":8193},[130,131],[58,8195,8197,8211],{"className":8196},[135],[58,8198,8200],{"className":8199,"style":3090},[139],[58,8201,8202,8205],{"style":1250},[58,8203],{"className":8204,"style":539},[147],[58,8206,8208],{"className":8207},[152,153,154,155],[58,8209,82],{"className":8210},[118,155],[58,8212,226],{"className":8213},[225],[58,8215,8217],{"className":8216},[135],[58,8218,8220],{"className":8219,"style":1269},[139],[58,8221],{},[58,8223,802],{"className":8224},[911],[58,8226],{"className":8227,"style":915},[498],[58,8229,2969],{"className":8230},[961],[58,8232],{"className":8233,"style":915},[498],[58,8235,802],{"className":8236},[911],[58,8238],{"className":8239,"style":915},[498],[58,8241,8243,8246],{"className":8242},[118],[58,8244,7326],{"className":8245},[118,191],[58,8247,8249],{"className":8248},[195],[58,8250,8252,8272],{"className":8251},[130,131],[58,8253,8255,8269],{"className":8254},[135],[58,8256,8258],{"className":8257,"style":1321},[139],[58,8259,8260,8263],{"style":1250},[58,8261],{"className":8262,"style":539},[147],[58,8264,8266],{"className":8265},[152,153,154,155],[58,8267,334],{"className":8268},[118,191,155],[58,8270,226],{"className":8271},[225],[58,8273,8275],{"className":8274},[135],[58,8276,8278],{"className":8277,"style":1269},[139],[58,8279],{},[58,8281,811],{"className":8282},[312]," 映射为连续表示序列 ",[58,8285,8287,8326],{"className":8286},[61],[58,8288,8290],{"className":8289},[65],[67,8291,8292],{"xmlns":69},[71,8293,8294,8323],{},[74,8295,8296,8299,8301,8303,8309,8311,8313,8315,8321],{},[90,8297,8298],{"mathvariant":5377},"z",[460,8300,814],{},[460,8302,797],{"stretchy":796},[87,8304,8305,8307],{},[90,8306,8298],{},[80,8308,82],{},[460,8310,802],{"separator":105},[460,8312,2969],{},[460,8314,802],{"separator":105},[87,8316,8317,8319],{},[90,8318,8298],{},[90,8320,334],{},[460,8322,811],{"stretchy":796},[97,8324,8325],{"encoding":99},"\\mathbf{z} = (z_1, \\ldots, z_n)",[58,8327,8329,8348],{"className":8328,"ariaHidden":105},[104],[58,8330,8332,8336,8339,8342,8345],{"className":8331},[109],[58,8333],{"className":8334,"style":8335},[113],"height:0.4444em;",[58,8337,8298],{"className":8338},[118,5422],[58,8340],{"className":8341,"style":499},[498],[58,8343,814],{"className":8344},[503],[58,8346],{"className":8347,"style":499},[498],[58,8349,8351,8354,8357,8399,8402,8405,8408,8411,8414,8417,8457],{"className":8350},[109],[58,8352],{"className":8353,"style":876},[113],[58,8355,797],{"className":8356},[122],[58,8358,8360,8364],{"className":8359},[118],[58,8361,8298],{"className":8362,"style":8363},[118,191],"margin-right:0.04398em;",[58,8365,8367],{"className":8366},[195],[58,8368,8370,8391],{"className":8369},[130,131],[58,8371,8373,8388],{"className":8372},[135],[58,8374,8376],{"className":8375,"style":3090},[139],[58,8377,8379,8382],{"style":8378},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[58,8380],{"className":8381,"style":539},[147],[58,8383,8385],{"className":8384},[152,153,154,155],[58,8386,82],{"className":8387},[118,155],[58,8389,226],{"className":8390},[225],[58,8392,8394],{"className":8393},[135],[58,8395,8397],{"className":8396,"style":1269},[139],[58,8398],{},[58,8400,802],{"className":8401},[911],[58,8403],{"className":8404,"style":915},[498],[58,8406,2969],{"className":8407},[961],[58,8409],{"className":8410,"style":915},[498],[58,8412,802],{"className":8413},[911],[58,8415],{"className":8416,"style":915},[498],[58,8418,8420,8423],{"className":8419},[118],[58,8421,8298],{"className":8422,"style":8363},[118,191],[58,8424,8426],{"className":8425},[195],[58,8427,8429,8449],{"className":8428},[130,131],[58,8430,8432,8446],{"className":8431},[135],[58,8433,8435],{"className":8434,"style":1321},[139],[58,8436,8437,8440],{"style":8378},[58,8438],{"className":8439,"style":539},[147],[58,8441,8443],{"className":8442},[152,153,154,155],[58,8444,334],{"className":8445},[118,191,155],[58,8447,226],{"className":8448},[225],[58,8450,8452],{"className":8451},[135],[58,8453,8455],{"className":8454,"style":1269},[139],[58,8456],{},[58,8458,811],{"className":8459},[312],"。给定 ",[58,8462,8464,8478],{"className":8463},[61],[58,8465,8467],{"className":8466},[65],[67,8468,8469],{"xmlns":69},[71,8470,8471,8475],{},[74,8472,8473],{},[90,8474,8298],{"mathvariant":5377},[97,8476,8477],{"encoding":99},"\\mathbf{z}",[58,8479,8481],{"className":8480,"ariaHidden":105},[104],[58,8482,8484,8487],{"className":8483},[109],[58,8485],{"className":8486,"style":8335},[113],[58,8488,8298],{"className":8489},[118,5422],"，解码器随后一次生成一个元素的输出符号序列 ",[58,8492,8494,8528],{"className":8493},[61],[58,8495,8497],{"className":8496},[65],[67,8498,8499],{"xmlns":69},[71,8500,8501,8525],{},[74,8502,8503,8505,8511,8513,8515,8517,8523],{},[460,8504,797],{"stretchy":796},[87,8506,8507,8509],{},[90,8508,7820],{},[80,8510,82],{},[460,8512,802],{"separator":105},[460,8514,2969],{},[460,8516,802],{"separator":105},[87,8518,8519,8521],{},[90,8520,7820],{},[90,8522,365],{},[460,8524,811],{"stretchy":796},[97,8526,8527],{"encoding":99},"(y_1, \\ldots, y_m)",[58,8529,8531],{"className":8530,"ariaHidden":105},[104],[58,8532,8534,8537,8540,8580,8583,8586,8589,8592,8595,8598,8638],{"className":8533},[109],[58,8535],{"className":8536,"style":876},[113],[58,8538,797],{"className":8539},[122],[58,8541,8543,8546],{"className":8542},[118],[58,8544,7820],{"className":8545,"style":440},[118,191],[58,8547,8549],{"className":8548},[195],[58,8550,8552,8572],{"className":8551},[130,131],[58,8553,8555,8569],{"className":8554},[135],[58,8556,8558],{"className":8557,"style":3090},[139],[58,8559,8560,8563],{"style":2034},[58,8561],{"className":8562,"style":539},[147],[58,8564,8566],{"className":8565},[152,153,154,155],[58,8567,82],{"className":8568},[118,155],[58,8570,226],{"className":8571},[225],[58,8573,8575],{"className":8574},[135],[58,8576,8578],{"className":8577,"style":1269},[139],[58,8579],{},[58,8581,802],{"className":8582},[911],[58,8584],{"className":8585,"style":915},[498],[58,8587,2969],{"className":8588},[961],[58,8590],{"className":8591,"style":915},[498],[58,8593,802],{"className":8594},[911],[58,8596],{"className":8597,"style":915},[498],[58,8599,8601,8604],{"className":8600},[118],[58,8602,7820],{"className":8603,"style":440},[118,191],[58,8605,8607],{"className":8606},[195],[58,8608,8610,8630],{"className":8609},[130,131],[58,8611,8613,8627],{"className":8612},[135],[58,8614,8616],{"className":8615,"style":1321},[139],[58,8617,8618,8621],{"style":2034},[58,8619],{"className":8620,"style":539},[147],[58,8622,8624],{"className":8623},[152,153,154,155],[58,8625,365],{"className":8626},[118,191,155],[58,8628,226],{"className":8629},[225],[58,8631,8633],{"className":8632},[135],[58,8634,8636],{"className":8635,"style":1269},[139],[58,8637],{},[58,8639,811],{"className":8640},[312],"。在每一个时间步，模型都是自回归的，即在生成下一个符号时，会将之前已经生成的符号作为额外输入。",[2389,8643,8645],{"className":2391,"code":8644,"language":2393,"meta":2394,"style":2394},"class Encoder(nn.Module):\n    \"\"\"编码器-解码器架构的基本编码器接口\"\"\"\n    def __init__(self, **kwargs):\n        super(Encoder, self).__init__(**kwargs)\n\n    def forward(self, X, *args):\n        raise NotImplementedError\n\nclass Decoder(nn.Module):\n    \"\"\"编码器-解码器架构的基本解码器接口\"\"\"\n    def __init__(self, **kwargs):\n        super(Decoder, self).__init__(**kwargs)\n\n    def init_state(self, enc_outputs, *args):\n        raise NotImplementedError\n\n    def forward(self, X, state):\n        raise NotImplementedError\n\nclass EncoderDecoder(nn.Module):\n    \"\"\"编码器-解码器架构的基类\"\"\"\n    def __init__(self, encoder, decoder, **kwargs):\n        super(EncoderDecoder, self).__init__(**kwargs)\n        self.encoder = encoder\n        self.decoder = decoder\n\n    def forward(self, enc_X, dec_X, *args):\n        enc_outputs = self.encoder(enc_X, *args)\n        dec_state = self.decoder.init_state(enc_outputs, *args)\n        return self.decoder(dec_X, dec_state)\n",[2396,8646,8647,8664,8669,8687,8706,8710,8734,8742,8746,8763,8768,8786,8805,8809,8833,8839,8843,8864,8870,8874,8891,8896,8924,8943,8955,8967,8971,8999,9016,9032],{"__ignoreMap":2394},[58,8648,8649,8651,8654,8656,8658,8660,8662],{"class":2400,"line":2401},[58,8650,2629],{"class":2404},[58,8652,8653],{"class":2632}," Encoder",[58,8655,797],{"class":2412},[58,8657,2639],{"class":2638},[58,8659,863],{"class":2412},[58,8661,2644],{"class":2638},[58,8663,2425],{"class":2412},[58,8665,8666],{"class":2400,"line":2428},[58,8667,8668],{"class":2431},"    \"\"\"编码器-解码器架构的基本编码器接口\"\"\"\n",[58,8670,8671,8673,8675,8677,8679,8681,8683,8685],{"class":2400,"line":2435},[58,8672,2656],{"class":2404},[58,8674,2659],{"class":2454},[58,8676,797],{"class":2412},[58,8678,2665],{"class":2664},[58,8680,2419],{"class":2412},[58,8682,2675],{"class":2404},[58,8684,2678],{"class":2415},[58,8686,2425],{"class":2412},[58,8688,8689,8691,8694,8696,8698,8700,8702,8704],{"class":2400,"line":2442},[58,8690,2686],{"class":2685},[58,8692,8693],{"class":2412},"(Encoder, ",[58,8695,2665],{"class":2692},[58,8697,2695],{"class":2412},[58,8699,2698],{"class":2454},[58,8701,797],{"class":2412},[58,8703,2675],{"class":2404},[58,8705,2705],{"class":2412},[58,8707,8708],{"class":2400,"line":2461},[58,8709,2724],{"emptyLinePlaceholder":2723},[58,8711,8712,8714,8716,8718,8720,8722,8724,8726,8729,8732],{"class":2400,"line":2482},[58,8713,2656],{"class":2404},[58,8715,2751],{"class":2408},[58,8717,797],{"class":2412},[58,8719,2665],{"class":2664},[58,8721,2419],{"class":2412},[58,8723,2416],{"class":2415},[58,8725,2419],{"class":2412},[58,8727,8728],{"class":2404},"*",[58,8730,8731],{"class":2415},"args",[58,8733,2425],{"class":2412},[58,8735,8736,8739],{"class":2400,"line":2490},[58,8737,8738],{"class":2404},"        raise",[58,8740,8741],{"class":2685}," NotImplementedError\n",[58,8743,8744],{"class":2400,"line":2501},[58,8745,2724],{"emptyLinePlaceholder":2723},[58,8747,8748,8750,8753,8755,8757,8759,8761],{"class":2400,"line":2518},[58,8749,2629],{"class":2404},[58,8751,8752],{"class":2632}," Decoder",[58,8754,797],{"class":2412},[58,8756,2639],{"class":2638},[58,8758,863],{"class":2412},[58,8760,2644],{"class":2638},[58,8762,2425],{"class":2412},[58,8764,8765],{"class":2400,"line":2534},[58,8766,8767],{"class":2431},"    \"\"\"编码器-解码器架构的基本解码器接口\"\"\"\n",[58,8769,8770,8772,8774,8776,8778,8780,8782,8784],{"class":2400,"line":2542},[58,8771,2656],{"class":2404},[58,8773,2659],{"class":2454},[58,8775,797],{"class":2412},[58,8777,2665],{"class":2664},[58,8779,2419],{"class":2412},[58,8781,2675],{"class":2404},[58,8783,2678],{"class":2415},[58,8785,2425],{"class":2412},[58,8787,8788,8790,8793,8795,8797,8799,8801,8803],{"class":2400,"line":2559},[58,8789,2686],{"class":2685},[58,8791,8792],{"class":2412},"(Decoder, ",[58,8794,2665],{"class":2692},[58,8796,2695],{"class":2412},[58,8798,2698],{"class":2454},[58,8800,797],{"class":2412},[58,8802,2675],{"class":2404},[58,8804,2705],{"class":2412},[58,8806,8807],{"class":2400,"line":2565},[58,8808,2724],{"emptyLinePlaceholder":2723},[58,8810,8811,8813,8816,8818,8820,8822,8825,8827,8829,8831],{"class":2400,"line":2590},[58,8812,2656],{"class":2404},[58,8814,8815],{"class":2408}," init_state",[58,8817,797],{"class":2412},[58,8819,2665],{"class":2664},[58,8821,2419],{"class":2412},[58,8823,8824],{"class":2415},"enc_outputs",[58,8826,2419],{"class":2412},[58,8828,8728],{"class":2404},[58,8830,8731],{"class":2415},[58,8832,2425],{"class":2412},[58,8834,8835,8837],{"class":2400,"line":2603},[58,8836,8738],{"class":2404},[58,8838,8741],{"class":2685},[58,8840,8841],{"class":2400,"line":2844},[58,8842,2724],{"emptyLinePlaceholder":2723},[58,8844,8845,8847,8849,8851,8853,8855,8857,8859,8862],{"class":2400,"line":4780},[58,8846,2656],{"class":2404},[58,8848,2751],{"class":2408},[58,8850,797],{"class":2412},[58,8852,2665],{"class":2664},[58,8854,2419],{"class":2412},[58,8856,2416],{"class":2415},[58,8858,2419],{"class":2412},[58,8860,8861],{"class":2415},"state",[58,8863,2425],{"class":2412},[58,8865,8866,8868],{"class":2400,"line":5056},[58,8867,8738],{"class":2404},[58,8869,8741],{"class":2685},[58,8871,8872],{"class":2400,"line":5062},[58,8873,2724],{"emptyLinePlaceholder":2723},[58,8875,8876,8878,8881,8883,8885,8887,8889],{"class":2400,"line":5068},[58,8877,2629],{"class":2404},[58,8879,8880],{"class":2632}," EncoderDecoder",[58,8882,797],{"class":2412},[58,8884,2639],{"class":2638},[58,8886,863],{"class":2412},[58,8888,2644],{"class":2638},[58,8890,2425],{"class":2412},[58,8892,8893],{"class":2400,"line":5074},[58,8894,8895],{"class":2431},"    \"\"\"编码器-解码器架构的基类\"\"\"\n",[58,8897,8898,8900,8902,8904,8906,8908,8911,8913,8916,8918,8920,8922],{"class":2400,"line":5095},[58,8899,2656],{"class":2404},[58,8901,2659],{"class":2454},[58,8903,797],{"class":2412},[58,8905,2665],{"class":2664},[58,8907,2419],{"class":2412},[58,8909,8910],{"class":2415},"encoder",[58,8912,2419],{"class":2412},[58,8914,8915],{"class":2415},"decoder",[58,8917,2419],{"class":2412},[58,8919,2675],{"class":2404},[58,8921,2678],{"class":2415},[58,8923,2425],{"class":2412},[58,8925,8926,8928,8931,8933,8935,8937,8939,8941],{"class":2400,"line":5114},[58,8927,2686],{"class":2685},[58,8929,8930],{"class":2412},"(EncoderDecoder, ",[58,8932,2665],{"class":2692},[58,8934,2695],{"class":2412},[58,8936,2698],{"class":2454},[58,8938,797],{"class":2412},[58,8940,2675],{"class":2404},[58,8942,2705],{"class":2412},[58,8944,8945,8947,8950,8952],{"class":2400,"line":5133},[58,8946,2710],{"class":2692},[58,8948,8949],{"class":2412},".encoder ",[58,8951,814],{"class":2404},[58,8953,8954],{"class":2412}," encoder\n",[58,8956,8957,8959,8962,8964],{"class":2400,"line":5138},[58,8958,2710],{"class":2692},[58,8960,8961],{"class":2412},".decoder ",[58,8963,814],{"class":2404},[58,8965,8966],{"class":2412}," decoder\n",[58,8968,8969],{"class":2400,"line":5154},[58,8970,2724],{"emptyLinePlaceholder":2723},[58,8972,8973,8975,8977,8979,8981,8983,8986,8988,8991,8993,8995,8997],{"class":2400,"line":5160},[58,8974,2656],{"class":2404},[58,8976,2751],{"class":2408},[58,8978,797],{"class":2412},[58,8980,2665],{"class":2664},[58,8982,2419],{"class":2412},[58,8984,8985],{"class":2415},"enc_X",[58,8987,2419],{"class":2412},[58,8989,8990],{"class":2415},"dec_X",[58,8992,2419],{"class":2412},[58,8994,8728],{"class":2404},[58,8996,8731],{"class":2415},[58,8998,2425],{"class":2412},[58,9000,9001,9004,9006,9008,9011,9013],{"class":2400,"line":5166},[58,9002,9003],{"class":2412},"        enc_outputs ",[58,9005,814],{"class":2404},[58,9007,5219],{"class":2692},[58,9009,9010],{"class":2412},".encoder(enc_X, ",[58,9012,8728],{"class":2404},[58,9014,9015],{"class":2412},"args)\n",[58,9017,9018,9021,9023,9025,9028,9030],{"class":2400,"line":5176},[58,9019,9020],{"class":2412},"        dec_state ",[58,9022,814],{"class":2404},[58,9024,5219],{"class":2692},[58,9026,9027],{"class":2412},".decoder.init_state(enc_outputs, ",[58,9029,8728],{"class":2404},[58,9031,9015],{"class":2412},[58,9033,9034,9036,9038],{"class":2400,"line":5200},[58,9035,2464],{"class":2404},[58,9037,5219],{"class":2692},[58,9039,9040],{"class":2412},".decoder(dec_X, dec_state)\n",[10,9042,9044],{"id":9043},"transformer-编码器","transformer 编码器",[14,9046,9047],{},"代码实现如下：",[2389,9049,9051],{"className":2391,"code":9050,"language":2393,"meta":2394,"style":2394},"class EncoderBlock(nn.Module):\n    \"\"\"Transformer编码器块\"\"\"\n    def __init__(self, key_size, query_size, value_size, num_hiddens,\n                 norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,\n                 dropout, use_bias=False, **kwargs):\n        super(EncoderBlock, self).__init__(**kwargs)\n        self.attention = d2l.MultiHeadAttention(\n            key_size, query_size, value_size, num_hiddens, num_heads, dropout,\n            use_bias)\n        self.addnorm1 = AddNorm(norm_shape, dropout)\n        self.ffn = PositionWiseFFN(\n            ffn_num_input, ffn_num_hiddens, num_hiddens)\n        self.addnorm2 = AddNorm(norm_shape, dropout)\n\n    def forward(self, X, valid_lens):\n        Y = self.addnorm1(X, self.attention(X, X, X, valid_lens))\n        return self.addnorm2(Y, self.ffn(Y))\n\nclass TransformerEncoder(Encoder):\n    \"\"\"Transformer编码器\"\"\"\n    def __init__(self, vocab_size, key_size, query_size, value_size,\n                 num_hiddens, norm_shape, ffn_num_input, ffn_num_hiddens,\n                 num_heads, num_layers, dropout, use_bias=False, **kwargs):\n        super(TransformerEncoder, self).__init__(**kwargs)\n        self.num_hiddens = num_hiddens\n        self.embedding = nn.Embedding(vocab_size, num_hiddens)\n        self.pos_encoding = PositionalEncoding(num_hiddens, dropout)\n        self.blks = nn.Sequential()\n        for i in range(num_layers):\n            self.blks.add_module(\"block\"+str(i),\n                EncoderBlock(key_size, query_size, value_size, num_hiddens,\n                             norm_shape, ffn_num_input, ffn_num_hiddens,\n                             num_heads, dropout, use_bias))\n\n    def forward(self, X, valid_lens, *args):\n        # 因为位置编码值在-1和1之间，\n        # 因此嵌入值乘以嵌入维度的平方根进行缩放，\n        # 然后再与位置编码相加。\n        X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))\n        self.attention_weights = [None] * len(self.blks)\n        for i, blk in enumerate(self.blks):\n            X = blk(X, valid_lens)\n            self.attention_weights[i] = blk.attention.attention.attention_weights\n        return X\n",[2396,9052,9053,9070,9075,9103,9122,9144,9163,9174,9179,9184,9196,9208,9213,9224,9228,9248,9265,9279,9283,9297,9302,9331,9351,9380,9399,9411,9423,9435,9447,9465,9491,9496,9501,9506,9510,9536,9541,9547,9553,9580,9608,9628,9639,9652],{"__ignoreMap":2394},[58,9054,9055,9057,9060,9062,9064,9066,9068],{"class":2400,"line":2401},[58,9056,2629],{"class":2404},[58,9058,9059],{"class":2632}," EncoderBlock",[58,9061,797],{"class":2412},[58,9063,2639],{"class":2638},[58,9065,863],{"class":2412},[58,9067,2644],{"class":2638},[58,9069,2425],{"class":2412},[58,9071,9072],{"class":2400,"line":2428},[58,9073,9074],{"class":2431},"    \"\"\"Transformer编码器块\"\"\"\n",[58,9076,9077,9079,9081,9083,9085,9087,9089,9091,9093,9095,9097,9099,9101],{"class":2400,"line":2435},[58,9078,2656],{"class":2404},[58,9080,2659],{"class":2454},[58,9082,797],{"class":2412},[58,9084,2665],{"class":2664},[58,9086,2419],{"class":2412},[58,9088,4846],{"class":2415},[58,9090,2419],{"class":2412},[58,9092,4851],{"class":2415},[58,9094,2419],{"class":2412},[58,9096,4856],{"class":2415},[58,9098,2419],{"class":2412},[58,9100,4861],{"class":2415},[58,9102,3825],{"class":2412},[58,9104,9105,9108,9110,9112,9114,9116,9118,9120],{"class":2400,"line":2442},[58,9106,9107],{"class":2415},"                 norm_shape",[58,9109,2419],{"class":2412},[58,9111,7674],{"class":2415},[58,9113,2419],{"class":2412},[58,9115,7679],{"class":2415},[58,9117,2419],{"class":2412},[58,9119,4594],{"class":2415},[58,9121,3825],{"class":2412},[58,9123,9124,9127,9129,9132,9134,9136,9138,9140,9142],{"class":2400,"line":2461},[58,9125,9126],{"class":2415},"                 dropout",[58,9128,2419],{"class":2412},[58,9130,9131],{"class":2415},"use_bias",[58,9133,814],{"class":2404},[58,9135,4882],{"class":2454},[58,9137,2419],{"class":2412},[58,9139,2675],{"class":2404},[58,9141,2678],{"class":2415},[58,9143,2425],{"class":2412},[58,9145,9146,9148,9151,9153,9155,9157,9159,9161],{"class":2400,"line":2482},[58,9147,2686],{"class":2685},[58,9149,9150],{"class":2412},"(EncoderBlock, ",[58,9152,2665],{"class":2692},[58,9154,2695],{"class":2412},[58,9156,2698],{"class":2454},[58,9158,797],{"class":2412},[58,9160,2675],{"class":2404},[58,9162,2705],{"class":2412},[58,9164,9165,9167,9169,9171],{"class":2400,"line":2490},[58,9166,2710],{"class":2692},[58,9168,4928],{"class":2412},[58,9170,814],{"class":2404},[58,9172,9173],{"class":2412}," d2l.MultiHeadAttention(\n",[58,9175,9176],{"class":2400,"line":2501},[58,9177,9178],{"class":2412},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout,\n",[58,9180,9181],{"class":2400,"line":2518},[58,9182,9183],{"class":2412},"            use_bias)\n",[58,9185,9186,9188,9191,9193],{"class":2400,"line":2534},[58,9187,2710],{"class":2692},[58,9189,9190],{"class":2412},".addnorm1 ",[58,9192,814],{"class":2404},[58,9194,9195],{"class":2412}," AddNorm(norm_shape, dropout)\n",[58,9197,9198,9200,9203,9205],{"class":2400,"line":2542},[58,9199,2710],{"class":2692},[58,9201,9202],{"class":2412},".ffn ",[58,9204,814],{"class":2404},[58,9206,9207],{"class":2412}," PositionWiseFFN(\n",[58,9209,9210],{"class":2400,"line":2559},[58,9211,9212],{"class":2412},"            ffn_num_input, ffn_num_hiddens, num_hiddens)\n",[58,9214,9215,9217,9220,9222],{"class":2400,"line":2565},[58,9216,2710],{"class":2692},[58,9218,9219],{"class":2412},".addnorm2 ",[58,9221,814],{"class":2404},[58,9223,9195],{"class":2412},[58,9225,9226],{"class":2400,"line":2590},[58,9227,2724],{"emptyLinePlaceholder":2723},[58,9229,9230,9232,9234,9236,9238,9240,9242,9244,9246],{"class":2400,"line":2603},[58,9231,2656],{"class":2404},[58,9233,2751],{"class":2408},[58,9235,797],{"class":2412},[58,9237,2665],{"class":2664},[58,9239,2419],{"class":2412},[58,9241,2416],{"class":2415},[58,9243,2419],{"class":2412},[58,9245,2422],{"class":2415},[58,9247,2425],{"class":2412},[58,9249,9250,9253,9255,9257,9260,9262],{"class":2400,"line":2844},[58,9251,9252],{"class":2412},"        Y ",[58,9254,814],{"class":2404},[58,9256,5219],{"class":2692},[58,9258,9259],{"class":2412},".addnorm1(X, ",[58,9261,2665],{"class":2692},[58,9263,9264],{"class":2412},".attention(X, X, X, valid_lens))\n",[58,9266,9267,9269,9271,9274,9276],{"class":2400,"line":4780},[58,9268,2464],{"class":2404},[58,9270,5219],{"class":2692},[58,9272,9273],{"class":2412},".addnorm2(Y, ",[58,9275,2665],{"class":2692},[58,9277,9278],{"class":2412},".ffn(Y))\n",[58,9280,9281],{"class":2400,"line":5056},[58,9282,2724],{"emptyLinePlaceholder":2723},[58,9284,9285,9287,9290,9292,9295],{"class":2400,"line":5062},[58,9286,2629],{"class":2404},[58,9288,9289],{"class":2632}," TransformerEncoder",[58,9291,797],{"class":2412},[58,9293,9294],{"class":2638},"Encoder",[58,9296,2425],{"class":2412},[58,9298,9299],{"class":2400,"line":5068},[58,9300,9301],{"class":2431},"    \"\"\"Transformer编码器\"\"\"\n",[58,9303,9304,9306,9308,9310,9312,9314,9317,9319,9321,9323,9325,9327,9329],{"class":2400,"line":5074},[58,9305,2656],{"class":2404},[58,9307,2659],{"class":2454},[58,9309,797],{"class":2412},[58,9311,2665],{"class":2664},[58,9313,2419],{"class":2412},[58,9315,9316],{"class":2415},"vocab_size",[58,9318,2419],{"class":2412},[58,9320,4846],{"class":2415},[58,9322,2419],{"class":2412},[58,9324,4851],{"class":2415},[58,9326,2419],{"class":2412},[58,9328,4856],{"class":2415},[58,9330,3825],{"class":2412},[58,9332,9333,9336,9338,9341,9343,9345,9347,9349],{"class":2400,"line":5095},[58,9334,9335],{"class":2415},"                 num_hiddens",[58,9337,2419],{"class":2412},[58,9339,9340],{"class":2415},"norm_shape",[58,9342,2419],{"class":2412},[58,9344,7674],{"class":2415},[58,9346,2419],{"class":2412},[58,9348,7679],{"class":2415},[58,9350,3825],{"class":2412},[58,9352,9353,9355,9357,9360,9362,9364,9366,9368,9370,9372,9374,9376,9378],{"class":2400,"line":5114},[58,9354,4868],{"class":2415},[58,9356,2419],{"class":2412},[58,9358,9359],{"class":2415},"num_layers",[58,9361,2419],{"class":2412},[58,9363,2670],{"class":2415},[58,9365,2419],{"class":2412},[58,9367,9131],{"class":2415},[58,9369,814],{"class":2404},[58,9371,4882],{"class":2454},[58,9373,2419],{"class":2412},[58,9375,2675],{"class":2404},[58,9377,2678],{"class":2415},[58,9379,2425],{"class":2412},[58,9381,9382,9384,9387,9389,9391,9393,9395,9397],{"class":2400,"line":5133},[58,9383,2686],{"class":2685},[58,9385,9386],{"class":2412},"(TransformerEncoder, ",[58,9388,2665],{"class":2692},[58,9390,2695],{"class":2412},[58,9392,2698],{"class":2454},[58,9394,797],{"class":2412},[58,9396,2675],{"class":2404},[58,9398,2705],{"class":2412},[58,9400,9401,9403,9406,9408],{"class":2400,"line":5138},[58,9402,2710],{"class":2692},[58,9404,9405],{"class":2412},".num_hiddens ",[58,9407,814],{"class":2404},[58,9409,9410],{"class":2412}," num_hiddens\n",[58,9412,9413,9415,9418,9420],{"class":2400,"line":5154},[58,9414,2710],{"class":2692},[58,9416,9417],{"class":2412},".embedding ",[58,9419,814],{"class":2404},[58,9421,9422],{"class":2412}," nn.Embedding(vocab_size, num_hiddens)\n",[58,9424,9425,9427,9430,9432],{"class":2400,"line":5160},[58,9426,2710],{"class":2692},[58,9428,9429],{"class":2412},".pos_encoding ",[58,9431,814],{"class":2404},[58,9433,9434],{"class":2412}," PositionalEncoding(num_hiddens, dropout)\n",[58,9436,9437,9439,9442,9444],{"class":2400,"line":5166},[58,9438,2710],{"class":2692},[58,9440,9441],{"class":2412},".blks ",[58,9443,814],{"class":2404},[58,9445,9446],{"class":2412}," nn.Sequential()\n",[58,9448,9449,9452,9455,9458,9462],{"class":2400,"line":5176},[58,9450,9451],{"class":2404},"        for",[58,9453,9454],{"class":2412}," i ",[58,9456,9457],{"class":2404},"in",[58,9459,9461],{"class":9460},"sDgm9"," range",[58,9463,9464],{"class":2412},"(num_layers):\n",[58,9466,9467,9470,9473,9477,9481,9483,9485,9488],{"class":2400,"line":5200},[58,9468,9469],{"class":2692},"            self",[58,9471,9472],{"class":2412},".blks.add_module(",[58,9474,9476],{"class":9475},"sMWOi","\"",[58,9478,9480],{"class":9479},"sEzAm","block",[58,9482,9476],{"class":9475},[58,9484,5776],{"class":2404},[58,9486,9487],{"class":2685},"str",[58,9489,9490],{"class":2412},"(i),\n",[58,9492,9493],{"class":2400,"line":5205},[58,9494,9495],{"class":2412},"                EncoderBlock(key_size, query_size, value_size, num_hiddens,\n",[58,9497,9498],{"class":2400,"line":5211},[58,9499,9500],{"class":2412},"                             norm_shape, ffn_num_input, ffn_num_hiddens,\n",[58,9502,9503],{"class":2400,"line":5225},[58,9504,9505],{"class":2412},"                             num_heads, dropout, use_bias))\n",[58,9507,9508],{"class":2400,"line":5230},[58,9509,2724],{"emptyLinePlaceholder":2723},[58,9511,9512,9514,9516,9518,9520,9522,9524,9526,9528,9530,9532,9534],{"class":2400,"line":5236},[58,9513,2656],{"class":2404},[58,9515,2751],{"class":2408},[58,9517,797],{"class":2412},[58,9519,2665],{"class":2664},[58,9521,2419],{"class":2412},[58,9523,2416],{"class":2415},[58,9525,2419],{"class":2412},[58,9527,2422],{"class":2415},[58,9529,2419],{"class":2412},[58,9531,8728],{"class":2404},[58,9533,8731],{"class":2415},[58,9535,2425],{"class":2412},[58,9537,9538],{"class":2400,"line":5251},[58,9539,9540],{"class":2438},"        # 因为位置编码值在-1和1之间，\n",[58,9542,9544],{"class":2400,"line":9543},37,[58,9545,9546],{"class":2438},"        # 因此嵌入值乘以嵌入维度的平方根进行缩放，\n",[58,9548,9550],{"class":2400,"line":9549},38,[58,9551,9552],{"class":2438},"        # 然后再与位置编码相加。\n",[58,9554,9556,9558,9560,9562,9565,9567,9570,9572,9575,9577],{"class":2400,"line":9555},39,[58,9557,2568],{"class":2412},[58,9559,814],{"class":2404},[58,9561,5219],{"class":2692},[58,9563,9564],{"class":2412},".pos_encoding(",[58,9566,2665],{"class":2692},[58,9568,9569],{"class":2412},".embedding(X) ",[58,9571,8728],{"class":2404},[58,9573,9574],{"class":2412}," math.sqrt(",[58,9576,2665],{"class":2692},[58,9578,9579],{"class":2412},".num_hiddens))\n",[58,9581,9583,9585,9587,9589,9592,9594,9596,9598,9601,9603,9605],{"class":2400,"line":9582},40,[58,9584,2710],{"class":2692},[58,9586,2836],{"class":2412},[58,9588,814],{"class":2404},[58,9590,9591],{"class":2412}," [",[58,9593,2779],{"class":2454},[58,9595,7199],{"class":2412},[58,9597,8728],{"class":2404},[58,9599,9600],{"class":9460}," len",[58,9602,797],{"class":2412},[58,9604,2665],{"class":2692},[58,9606,9607],{"class":2412},".blks)\n",[58,9609,9611,9613,9616,9618,9621,9623,9625],{"class":2400,"line":9610},41,[58,9612,9451],{"class":2404},[58,9614,9615],{"class":2412}," i, blk ",[58,9617,9457],{"class":2404},[58,9619,9620],{"class":9460}," enumerate",[58,9622,797],{"class":2412},[58,9624,2665],{"class":2692},[58,9626,9627],{"class":2412},".blks):\n",[58,9629,9631,9634,9636],{"class":2400,"line":9630},42,[58,9632,9633],{"class":2412},"            X ",[58,9635,814],{"class":2404},[58,9637,9638],{"class":2412}," blk(X, valid_lens)\n",[58,9640,9642,9644,9647,9649],{"class":2400,"line":9641},43,[58,9643,9469],{"class":2692},[58,9645,9646],{"class":2412},".attention_weights[i] ",[58,9648,814],{"class":2404},[58,9650,9651],{"class":2412}," blk.attention.attention.attention_weights\n",[58,9653,9655,9657],{"class":2400,"line":9654},44,[58,9656,2464],{"class":2404},[58,9658,9659],{"class":2412}," X\n",[10,9661,9663],{"id":9662},"transformer-解码器","transformer 解码器",[14,9665,9666],{},"代码如下：",[2389,9668,9670],{"className":2391,"code":9669,"language":2393,"meta":2394,"style":2394},"class DecoderBlock(nn.Module):\n    \"\"\"解码器中第i个块\"\"\"\n    def __init__(self, key_size, query_size, value_size, num_hiddens,\n                 norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,\n                 dropout, i, **kwargs):\n        super(DecoderBlock, self).__init__(**kwargs)\n        self.i = i\n        self.attention1 = d2l.MultiHeadAttention(\n            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n        self.addnorm1 = AddNorm(norm_shape, dropout)\n        self.attention2 = d2l.MultiHeadAttention(\n            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n        self.addnorm2 = AddNorm(norm_shape, dropout)\n        self.ffn = PositionWiseFFN(ffn_num_input, ffn_num_hiddens,\n                                   num_hiddens)\n        self.addnorm3 = AddNorm(norm_shape, dropout)\n\n    def forward(self, X, state):\n        enc_outputs, enc_valid_lens = state[0], state[1]\n        # 训练阶段，输出序列的所有词元都在同一时间处理，\n        # 因此state[2][self.i]初始化为None。\n        # 预测阶段，输出序列是通过词元一个接着一个解码的，\n        # 因此state[2][self.i]包含着直到当前时间步第i个块解码的输出表示\n        if state[2][self.i] is None:\n            key_values = X\n        else:\n            key_values = torch.cat((state[2][self.i], X), axis=1)\n        state[2][self.i] = key_values\n        if self.training:\n            batch_size, num_steps, _ = X.shape\n            # dec_valid_lens的开头:(batch_size,num_steps),\n            # 其中每一行是[1,2,...,num_steps]\n            dec_valid_lens = torch.arange(\n                1, num_steps + 1, device=X.device).repeat(batch_size, 1)\n        else:\n            dec_valid_lens = None\n\n        # 自注意力\n        X2 = self.attention1(X, key_values, key_values, dec_valid_lens)\n        Y = self.addnorm1(X, X2)\n        # 编码器－解码器注意力。\n        # enc_outputs的开头:(batch_size,num_steps,num_hiddens)\n        Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n        Z = self.addnorm2(Y, Y2)\n        return self.addnorm3(Z, self.ffn(Z)), state\n\nclass TransformerDecoder(AttentionDecoder):\n    def __init__(self, vocab_size, key_size, query_size, value_size,\n                 num_hiddens, norm_shape, ffn_num_input, ffn_num_hiddens,\n                 num_heads, num_layers, dropout, **kwargs):\n        super(TransformerDecoder, self).__init__(**kwargs)\n        self.num_hiddens = num_hiddens\n        self.num_layers = num_layers\n        self.embedding = nn.Embedding(vocab_size, num_hiddens)\n        self.pos_encoding = PositionalEncoding(num_hiddens, dropout)\n        self.blks = nn.Sequential()\n        for i in range(num_layers):\n            self.blks.add_module(\"block\"+str(i),\n                DecoderBlock(key_size, query_size, value_size, num_hiddens,\n                             norm_shape, ffn_num_input, ffn_num_hiddens,\n                             num_heads, dropout, i))\n        self.dense = nn.Linear(num_hiddens, vocab_size)\n\n    def init_state(self, enc_outputs, enc_valid_lens, *args):\n        return [enc_outputs, enc_valid_lens, [None] * self.num_layers]\n\n    def forward(self, X, state):\n        X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))\n        self._attention_weights = [[None] * len(self.blks) for _ in range (2)]\n        for i, blk in enumerate(self.blks):\n            X, state = blk(X, state)\n            # 解码器自注意力权重\n            self._attention_weights[0][i] = blk.attention1.attention.attention_weights\n            # “编码器－解码器”自注意力权重\n            self._attention_weights[1][i] = blk.attention2.attention.attention_weights\n        return self.dense(X), state\n\n    @property\n    def attention_weights(self):\n        return self._attention_weights\n",[2396,9671,9672,9689,9694,9722,9740,9756,9775,9787,9798,9803,9813,9824,9828,9838,9849,9854,9865,9869,9889,9908,9913,9918,9923,9928,9950,9959,9965,9992,10010,10019,10028,10033,10038,10048,10074,10080,10089,10093,10098,10110,10121,10126,10131,10143,10155,10170,10175,10190,10219,10238,10259,10279,10290,10303,10314,10325,10336,10349,10368,10374,10379,10385,10398,10403,10431,10450,10455,10476,10499,10545,10562,10573,10579,10597,10603,10619,10629,10634,10643,10657],{"__ignoreMap":2394},[58,9673,9674,9676,9679,9681,9683,9685,9687],{"class":2400,"line":2401},[58,9675,2629],{"class":2404},[58,9677,9678],{"class":2632}," DecoderBlock",[58,9680,797],{"class":2412},[58,9682,2639],{"class":2638},[58,9684,863],{"class":2412},[58,9686,2644],{"class":2638},[58,9688,2425],{"class":2412},[58,9690,9691],{"class":2400,"line":2428},[58,9692,9693],{"class":2431},"    \"\"\"解码器中第i个块\"\"\"\n",[58,9695,9696,9698,9700,9702,9704,9706,9708,9710,9712,9714,9716,9718,9720],{"class":2400,"line":2435},[58,9697,2656],{"class":2404},[58,9699,2659],{"class":2454},[58,9701,797],{"class":2412},[58,9703,2665],{"class":2664},[58,9705,2419],{"class":2412},[58,9707,4846],{"class":2415},[58,9709,2419],{"class":2412},[58,9711,4851],{"class":2415},[58,9713,2419],{"class":2412},[58,9715,4856],{"class":2415},[58,9717,2419],{"class":2412},[58,9719,4861],{"class":2415},[58,9721,3825],{"class":2412},[58,9723,9724,9726,9728,9730,9732,9734,9736,9738],{"class":2400,"line":2442},[58,9725,9107],{"class":2415},[58,9727,2419],{"class":2412},[58,9729,7674],{"class":2415},[58,9731,2419],{"class":2412},[58,9733,7679],{"class":2415},[58,9735,2419],{"class":2412},[58,9737,4594],{"class":2415},[58,9739,3825],{"class":2412},[58,9741,9742,9744,9746,9748,9750,9752,9754],{"class":2400,"line":2461},[58,9743,9126],{"class":2415},[58,9745,2419],{"class":2412},[58,9747,788],{"class":2415},[58,9749,2419],{"class":2412},[58,9751,2675],{"class":2404},[58,9753,2678],{"class":2415},[58,9755,2425],{"class":2412},[58,9757,9758,9760,9763,9765,9767,9769,9771,9773],{"class":2400,"line":2482},[58,9759,2686],{"class":2685},[58,9761,9762],{"class":2412},"(DecoderBlock, ",[58,9764,2665],{"class":2692},[58,9766,2695],{"class":2412},[58,9768,2698],{"class":2454},[58,9770,797],{"class":2412},[58,9772,2675],{"class":2404},[58,9774,2705],{"class":2412},[58,9776,9777,9779,9782,9784],{"class":2400,"line":2490},[58,9778,2710],{"class":2692},[58,9780,9781],{"class":2412},".i ",[58,9783,814],{"class":2404},[58,9785,9786],{"class":2412}," i\n",[58,9788,9789,9791,9794,9796],{"class":2400,"line":2501},[58,9790,2710],{"class":2692},[58,9792,9793],{"class":2412},".attention1 ",[58,9795,814],{"class":2404},[58,9797,9173],{"class":2412},[58,9799,9800],{"class":2400,"line":2518},[58,9801,9802],{"class":2412},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n",[58,9804,9805,9807,9809,9811],{"class":2400,"line":2534},[58,9806,2710],{"class":2692},[58,9808,9190],{"class":2412},[58,9810,814],{"class":2404},[58,9812,9195],{"class":2412},[58,9814,9815,9817,9820,9822],{"class":2400,"line":2542},[58,9816,2710],{"class":2692},[58,9818,9819],{"class":2412},".attention2 ",[58,9821,814],{"class":2404},[58,9823,9173],{"class":2412},[58,9825,9826],{"class":2400,"line":2559},[58,9827,9802],{"class":2412},[58,9829,9830,9832,9834,9836],{"class":2400,"line":2565},[58,9831,2710],{"class":2692},[58,9833,9219],{"class":2412},[58,9835,814],{"class":2404},[58,9837,9195],{"class":2412},[58,9839,9840,9842,9844,9846],{"class":2400,"line":2590},[58,9841,2710],{"class":2692},[58,9843,9202],{"class":2412},[58,9845,814],{"class":2404},[58,9847,9848],{"class":2412}," PositionWiseFFN(ffn_num_input, ffn_num_hiddens,\n",[58,9850,9851],{"class":2400,"line":2603},[58,9852,9853],{"class":2412},"                                   num_hiddens)\n",[58,9855,9856,9858,9861,9863],{"class":2400,"line":2844},[58,9857,2710],{"class":2692},[58,9859,9860],{"class":2412},".addnorm3 ",[58,9862,814],{"class":2404},[58,9864,9195],{"class":2412},[58,9866,9867],{"class":2400,"line":4780},[58,9868,2724],{"emptyLinePlaceholder":2723},[58,9870,9871,9873,9875,9877,9879,9881,9883,9885,9887],{"class":2400,"line":5056},[58,9872,2656],{"class":2404},[58,9874,2751],{"class":2408},[58,9876,797],{"class":2412},[58,9878,2665],{"class":2664},[58,9880,2419],{"class":2412},[58,9882,2416],{"class":2415},[58,9884,2419],{"class":2412},[58,9886,8861],{"class":2415},[58,9888,2425],{"class":2412},[58,9890,9891,9894,9896,9899,9901,9904,9906],{"class":2400,"line":5062},[58,9892,9893],{"class":2412},"        enc_outputs, enc_valid_lens ",[58,9895,814],{"class":2404},[58,9897,9898],{"class":2412}," state[",[58,9900,1753],{"class":2454},[58,9902,9903],{"class":2412},"], state[",[58,9905,82],{"class":2454},[58,9907,2798],{"class":2412},[58,9909,9910],{"class":2400,"line":5068},[58,9911,9912],{"class":2438},"        # 训练阶段，输出序列的所有词元都在同一时间处理，\n",[58,9914,9915],{"class":2400,"line":5074},[58,9916,9917],{"class":2438},"        # 因此state[2][self.i]初始化为None。\n",[58,9919,9920],{"class":2400,"line":5095},[58,9921,9922],{"class":2438},"        # 预测阶段，输出序列是通过词元一个接着一个解码的，\n",[58,9924,9925],{"class":2400,"line":5114},[58,9926,9927],{"class":2438},"        # 因此state[2][self.i]包含着直到当前时间步第i个块解码的输出表示\n",[58,9929,9930,9932,9934,9936,9939,9941,9944,9946,9948],{"class":2400,"line":5133},[58,9931,2504],{"class":2404},[58,9933,9898],{"class":2412},[58,9935,2820],{"class":2454},[58,9937,9938],{"class":2412},"][",[58,9940,2665],{"class":2692},[58,9942,9943],{"class":2412},".i] ",[58,9945,2451],{"class":2404},[58,9947,2455],{"class":2454},[58,9949,2458],{"class":2412},[58,9951,9952,9955,9957],{"class":2400,"line":5138},[58,9953,9954],{"class":2412},"            key_values ",[58,9956,814],{"class":2404},[58,9958,9659],{"class":2412},[58,9960,9961,9963],{"class":2400,"line":5154},[58,9962,2537],{"class":2404},[58,9964,2458],{"class":2412},[58,9966,9967,9969,9971,9974,9976,9978,9980,9983,9986,9988,9990],{"class":2400,"line":5160},[58,9968,9954],{"class":2412},[58,9970,814],{"class":2404},[58,9972,9973],{"class":2412}," torch.cat((state[",[58,9975,2820],{"class":2454},[58,9977,9938],{"class":2412},[58,9979,2665],{"class":2692},[58,9981,9982],{"class":2412},".i], X), ",[58,9984,9985],{"class":2470},"axis",[58,9987,814],{"class":2404},[58,9989,82],{"class":2454},[58,9991,2479],{"class":2412},[58,9993,9994,9997,9999,10001,10003,10005,10007],{"class":2400,"line":5166},[58,9995,9996],{"class":2412},"        state[",[58,9998,2820],{"class":2454},[58,10000,9938],{"class":2412},[58,10002,2665],{"class":2692},[58,10004,9943],{"class":2412},[58,10006,814],{"class":2404},[58,10008,10009],{"class":2412}," key_values\n",[58,10011,10012,10014,10016],{"class":2400,"line":5176},[58,10013,2504],{"class":2404},[58,10015,5219],{"class":2692},[58,10017,10018],{"class":2412},".training:\n",[58,10020,10021,10024,10026],{"class":2400,"line":5200},[58,10022,10023],{"class":2412},"            batch_size, num_steps, _ ",[58,10025,814],{"class":2404},[58,10027,2498],{"class":2412},[58,10029,10030],{"class":2400,"line":5205},[58,10031,10032],{"class":2438},"            # dec_valid_lens的开头:(batch_size,num_steps),\n",[58,10034,10035],{"class":2400,"line":5211},[58,10036,10037],{"class":2438},"            # 其中每一行是[1,2,...,num_steps]\n",[58,10039,10040,10043,10045],{"class":2400,"line":5225},[58,10041,10042],{"class":2412},"            dec_valid_lens ",[58,10044,814],{"class":2404},[58,10046,10047],{"class":2412}," torch.arange(\n",[58,10049,10050,10053,10056,10058,10060,10062,10065,10067,10070,10072],{"class":2400,"line":5230},[58,10051,10052],{"class":2454},"                1",[58,10054,10055],{"class":2412},", num_steps ",[58,10057,5776],{"class":2404},[58,10059,2513],{"class":2454},[58,10061,2419],{"class":2412},[58,10063,10064],{"class":2470},"device",[58,10066,814],{"class":2404},[58,10068,10069],{"class":2412},"X.device).repeat(batch_size, ",[58,10071,82],{"class":2454},[58,10073,2479],{"class":2412},[58,10075,10076,10078],{"class":2400,"line":5236},[58,10077,2537],{"class":2404},[58,10079,2458],{"class":2412},[58,10081,10082,10084,10086],{"class":2400,"line":5251},[58,10083,10042],{"class":2412},[58,10085,814],{"class":2404},[58,10087,10088],{"class":2454}," None\n",[58,10090,10091],{"class":2400,"line":9543},[58,10092,2724],{"emptyLinePlaceholder":2723},[58,10094,10095],{"class":2400,"line":9549},[58,10096,10097],{"class":2438},"        # 自注意力\n",[58,10099,10100,10103,10105,10107],{"class":2400,"line":9555},[58,10101,10102],{"class":2412},"        X2 ",[58,10104,814],{"class":2404},[58,10106,5219],{"class":2692},[58,10108,10109],{"class":2412},".attention1(X, key_values, key_values, dec_valid_lens)\n",[58,10111,10112,10114,10116,10118],{"class":2400,"line":9582},[58,10113,9252],{"class":2412},[58,10115,814],{"class":2404},[58,10117,5219],{"class":2692},[58,10119,10120],{"class":2412},".addnorm1(X, X2)\n",[58,10122,10123],{"class":2400,"line":9610},[58,10124,10125],{"class":2438},"        # 编码器－解码器注意力。\n",[58,10127,10128],{"class":2400,"line":9630},[58,10129,10130],{"class":2438},"        # enc_outputs的开头:(batch_size,num_steps,num_hiddens)\n",[58,10132,10133,10136,10138,10140],{"class":2400,"line":9641},[58,10134,10135],{"class":2412},"        Y2 ",[58,10137,814],{"class":2404},[58,10139,5219],{"class":2692},[58,10141,10142],{"class":2412},".attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n",[58,10144,10145,10148,10150,10152],{"class":2400,"line":9654},[58,10146,10147],{"class":2412},"        Z ",[58,10149,814],{"class":2404},[58,10151,5219],{"class":2692},[58,10153,10154],{"class":2412},".addnorm2(Y, Y2)\n",[58,10156,10158,10160,10162,10165,10167],{"class":2400,"line":10157},45,[58,10159,2464],{"class":2404},[58,10161,5219],{"class":2692},[58,10163,10164],{"class":2412},".addnorm3(Z, ",[58,10166,2665],{"class":2692},[58,10168,10169],{"class":2412},".ffn(Z)), state\n",[58,10171,10173],{"class":2400,"line":10172},46,[58,10174,2724],{"emptyLinePlaceholder":2723},[58,10176,10178,10180,10183,10185,10188],{"class":2400,"line":10177},47,[58,10179,2629],{"class":2404},[58,10181,10182],{"class":2632}," TransformerDecoder",[58,10184,797],{"class":2412},[58,10186,10187],{"class":2638},"AttentionDecoder",[58,10189,2425],{"class":2412},[58,10191,10193,10195,10197,10199,10201,10203,10205,10207,10209,10211,10213,10215,10217],{"class":2400,"line":10192},48,[58,10194,2656],{"class":2404},[58,10196,2659],{"class":2454},[58,10198,797],{"class":2412},[58,10200,2665],{"class":2664},[58,10202,2419],{"class":2412},[58,10204,9316],{"class":2415},[58,10206,2419],{"class":2412},[58,10208,4846],{"class":2415},[58,10210,2419],{"class":2412},[58,10212,4851],{"class":2415},[58,10214,2419],{"class":2412},[58,10216,4856],{"class":2415},[58,10218,3825],{"class":2412},[58,10220,10222,10224,10226,10228,10230,10232,10234,10236],{"class":2400,"line":10221},49,[58,10223,9335],{"class":2415},[58,10225,2419],{"class":2412},[58,10227,9340],{"class":2415},[58,10229,2419],{"class":2412},[58,10231,7674],{"class":2415},[58,10233,2419],{"class":2412},[58,10235,7679],{"class":2415},[58,10237,3825],{"class":2412},[58,10239,10241,10243,10245,10247,10249,10251,10253,10255,10257],{"class":2400,"line":10240},50,[58,10242,4868],{"class":2415},[58,10244,2419],{"class":2412},[58,10246,9359],{"class":2415},[58,10248,2419],{"class":2412},[58,10250,2670],{"class":2415},[58,10252,2419],{"class":2412},[58,10254,2675],{"class":2404},[58,10256,2678],{"class":2415},[58,10258,2425],{"class":2412},[58,10260,10262,10264,10267,10269,10271,10273,10275,10277],{"class":2400,"line":10261},51,[58,10263,2686],{"class":2685},[58,10265,10266],{"class":2412},"(TransformerDecoder, ",[58,10268,2665],{"class":2692},[58,10270,2695],{"class":2412},[58,10272,2698],{"class":2454},[58,10274,797],{"class":2412},[58,10276,2675],{"class":2404},[58,10278,2705],{"class":2412},[58,10280,10282,10284,10286,10288],{"class":2400,"line":10281},52,[58,10283,2710],{"class":2692},[58,10285,9405],{"class":2412},[58,10287,814],{"class":2404},[58,10289,9410],{"class":2412},[58,10291,10293,10295,10298,10300],{"class":2400,"line":10292},53,[58,10294,2710],{"class":2692},[58,10296,10297],{"class":2412},".num_layers ",[58,10299,814],{"class":2404},[58,10301,10302],{"class":2412}," num_layers\n",[58,10304,10306,10308,10310,10312],{"class":2400,"line":10305},54,[58,10307,2710],{"class":2692},[58,10309,9417],{"class":2412},[58,10311,814],{"class":2404},[58,10313,9422],{"class":2412},[58,10315,10317,10319,10321,10323],{"class":2400,"line":10316},55,[58,10318,2710],{"class":2692},[58,10320,9429],{"class":2412},[58,10322,814],{"class":2404},[58,10324,9434],{"class":2412},[58,10326,10328,10330,10332,10334],{"class":2400,"line":10327},56,[58,10329,2710],{"class":2692},[58,10331,9441],{"class":2412},[58,10333,814],{"class":2404},[58,10335,9446],{"class":2412},[58,10337,10339,10341,10343,10345,10347],{"class":2400,"line":10338},57,[58,10340,9451],{"class":2404},[58,10342,9454],{"class":2412},[58,10344,9457],{"class":2404},[58,10346,9461],{"class":9460},[58,10348,9464],{"class":2412},[58,10350,10352,10354,10356,10358,10360,10362,10364,10366],{"class":2400,"line":10351},58,[58,10353,9469],{"class":2692},[58,10355,9472],{"class":2412},[58,10357,9476],{"class":9475},[58,10359,9480],{"class":9479},[58,10361,9476],{"class":9475},[58,10363,5776],{"class":2404},[58,10365,9487],{"class":2685},[58,10367,9490],{"class":2412},[58,10369,10371],{"class":2400,"line":10370},59,[58,10372,10373],{"class":2412},"                DecoderBlock(key_size, query_size, value_size, num_hiddens,\n",[58,10375,10377],{"class":2400,"line":10376},60,[58,10378,9500],{"class":2412},[58,10380,10382],{"class":2400,"line":10381},61,[58,10383,10384],{"class":2412},"                             num_heads, dropout, i))\n",[58,10386,10388,10390,10393,10395],{"class":2400,"line":10387},62,[58,10389,2710],{"class":2692},[58,10391,10392],{"class":2412},".dense ",[58,10394,814],{"class":2404},[58,10396,10397],{"class":2412}," nn.Linear(num_hiddens, vocab_size)\n",[58,10399,10401],{"class":2400,"line":10400},63,[58,10402,2724],{"emptyLinePlaceholder":2723},[58,10404,10406,10408,10410,10412,10414,10416,10418,10420,10423,10425,10427,10429],{"class":2400,"line":10405},64,[58,10407,2656],{"class":2404},[58,10409,8815],{"class":2408},[58,10411,797],{"class":2412},[58,10413,2665],{"class":2664},[58,10415,2419],{"class":2412},[58,10417,8824],{"class":2415},[58,10419,2419],{"class":2412},[58,10421,10422],{"class":2415},"enc_valid_lens",[58,10424,2419],{"class":2412},[58,10426,8728],{"class":2404},[58,10428,8731],{"class":2415},[58,10430,2425],{"class":2412},[58,10432,10434,10436,10439,10441,10443,10445,10447],{"class":2400,"line":10433},65,[58,10435,2464],{"class":2404},[58,10437,10438],{"class":2412}," [enc_outputs, enc_valid_lens, [",[58,10440,2779],{"class":2454},[58,10442,7199],{"class":2412},[58,10444,8728],{"class":2404},[58,10446,5219],{"class":2692},[58,10448,10449],{"class":2412},".num_layers]\n",[58,10451,10453],{"class":2400,"line":10452},66,[58,10454,2724],{"emptyLinePlaceholder":2723},[58,10456,10458,10460,10462,10464,10466,10468,10470,10472,10474],{"class":2400,"line":10457},67,[58,10459,2656],{"class":2404},[58,10461,2751],{"class":2408},[58,10463,797],{"class":2412},[58,10465,2665],{"class":2664},[58,10467,2419],{"class":2412},[58,10469,2416],{"class":2415},[58,10471,2419],{"class":2412},[58,10473,8861],{"class":2415},[58,10475,2425],{"class":2412},[58,10477,10479,10481,10483,10485,10487,10489,10491,10493,10495,10497],{"class":2400,"line":10478},68,[58,10480,2568],{"class":2412},[58,10482,814],{"class":2404},[58,10484,5219],{"class":2692},[58,10486,9564],{"class":2412},[58,10488,2665],{"class":2692},[58,10490,9569],{"class":2412},[58,10492,8728],{"class":2404},[58,10494,9574],{"class":2412},[58,10496,2665],{"class":2692},[58,10498,9579],{"class":2412},[58,10500,10502,10504,10507,10509,10512,10514,10516,10518,10520,10522,10524,10527,10530,10533,10535,10537,10540,10542],{"class":2400,"line":10501},69,[58,10503,2710],{"class":2692},[58,10505,10506],{"class":2412},"._attention_weights ",[58,10508,814],{"class":2404},[58,10510,10511],{"class":2412}," [[",[58,10513,2779],{"class":2454},[58,10515,7199],{"class":2412},[58,10517,8728],{"class":2404},[58,10519,9600],{"class":9460},[58,10521,797],{"class":2412},[58,10523,2665],{"class":2692},[58,10525,10526],{"class":2412},".blks) ",[58,10528,10529],{"class":2404},"for",[58,10531,10532],{"class":2412}," _ ",[58,10534,9457],{"class":2404},[58,10536,9461],{"class":9460},[58,10538,10539],{"class":2412}," (",[58,10541,2820],{"class":2454},[58,10543,10544],{"class":2412},")]\n",[58,10546,10548,10550,10552,10554,10556,10558,10560],{"class":2400,"line":10547},70,[58,10549,9451],{"class":2404},[58,10551,9615],{"class":2412},[58,10553,9457],{"class":2404},[58,10555,9620],{"class":9460},[58,10557,797],{"class":2412},[58,10559,2665],{"class":2692},[58,10561,9627],{"class":2412},[58,10563,10565,10568,10570],{"class":2400,"line":10564},71,[58,10566,10567],{"class":2412},"            X, state ",[58,10569,814],{"class":2404},[58,10571,10572],{"class":2412}," blk(X, state)\n",[58,10574,10576],{"class":2400,"line":10575},72,[58,10577,10578],{"class":2438},"            # 解码器自注意力权重\n",[58,10580,10582,10584,10587,10589,10592,10594],{"class":2400,"line":10581},73,[58,10583,9469],{"class":2692},[58,10585,10586],{"class":2412},"._attention_weights[",[58,10588,1753],{"class":2454},[58,10590,10591],{"class":2412},"][i] ",[58,10593,814],{"class":2404},[58,10595,10596],{"class":2412}," blk.attention1.attention.attention_weights\n",[58,10598,10600],{"class":2400,"line":10599},74,[58,10601,10602],{"class":2438},"            # “编码器－解码器”自注意力权重\n",[58,10604,10606,10608,10610,10612,10614,10616],{"class":2400,"line":10605},75,[58,10607,9469],{"class":2692},[58,10609,10586],{"class":2412},[58,10611,82],{"class":2454},[58,10613,10591],{"class":2412},[58,10615,814],{"class":2404},[58,10617,10618],{"class":2412}," blk.attention2.attention.attention_weights\n",[58,10620,10622,10624,10626],{"class":2400,"line":10621},76,[58,10623,2464],{"class":2404},[58,10625,5219],{"class":2692},[58,10627,10628],{"class":2412},".dense(X), state\n",[58,10630,10632],{"class":2400,"line":10631},77,[58,10633,2724],{"emptyLinePlaceholder":2723},[58,10635,10637,10640],{"class":2400,"line":10636},78,[58,10638,10639],{"class":2408},"    @",[58,10641,10642],{"class":2685},"property\n",[58,10644,10646,10648,10651,10653,10655],{"class":2400,"line":10645},79,[58,10647,2656],{"class":2404},[58,10649,10650],{"class":2408}," attention_weights",[58,10652,797],{"class":2412},[58,10654,2665],{"class":2664},[58,10656,2425],{"class":2412},[58,10658,10660,10662,10664],{"class":2400,"line":10659},80,[58,10661,2464],{"class":2404},[58,10663,5219],{"class":2692},[58,10665,10666],{"class":2412},"._attention_weights\n",[10,10668,10669],{"id":10669},"训练",[14,10671,10672],{},"同样，训练时需要屏蔽部分不需要的内容：",[2389,10674,10676],{"className":2391,"code":10675,"language":2393,"meta":2394,"style":2394},"def sequence_mask(X, valid_len, value=0):\n    \"\"\"在序列中屏蔽不相关的项\"\"\"\n    maxlen = X.size(1)\n    mask = torch.arange((maxlen), dtype=torch.float32,\n                        device=X.device)[None, :] \u003C valid_len[:, None]\n    X[~mask] = value\n    return X\n\nclass MaskedSoftmaxCELoss(nn.CrossEntropyLoss):\n    \"\"\"带遮蔽的softmax交叉熵损失函数\"\"\"\n    # pred的形状：(batch_size,num_steps,vocab_size)\n    # label的形状：(batch_size,num_steps)\n    # valid_len的形状：(batch_size,)\n    def forward(self, pred, label, valid_len):\n        weights = torch.ones_like(label)\n        weights = sequence_mask(weights, valid_len)\n        self.reduction='none'\n        unweighted_loss = super(MaskedSoftmaxCELoss, self).forward(\n            pred.permute(0, 2, 1), label)\n        weighted_loss = (unweighted_loss * weights).mean(dim=1)\n        return weighted_loss\n",[2396,10677,10678,10705,10710,10724,10742,10771,10787,10793,10797,10815,10820,10825,10830,10835,10861,10871,10880,10898,10916,10934,10957],{"__ignoreMap":2394},[58,10679,10680,10682,10685,10687,10689,10691,10694,10696,10699,10701,10703],{"class":2400,"line":2401},[58,10681,2405],{"class":2404},[58,10683,10684],{"class":2408}," sequence_mask",[58,10686,797],{"class":2412},[58,10688,2416],{"class":2415},[58,10690,2419],{"class":2412},[58,10692,10693],{"class":2415},"valid_len",[58,10695,2419],{"class":2412},[58,10697,10698],{"class":2415},"value",[58,10700,814],{"class":2404},[58,10702,1753],{"class":2454},[58,10704,2425],{"class":2412},[58,10706,10707],{"class":2400,"line":2428},[58,10708,10709],{"class":2431},"    \"\"\"在序列中屏蔽不相关的项\"\"\"\n",[58,10711,10712,10715,10717,10720,10722],{"class":2400,"line":2435},[58,10713,10714],{"class":2412},"    maxlen ",[58,10716,814],{"class":2404},[58,10718,10719],{"class":2412}," X.size(",[58,10721,82],{"class":2454},[58,10723,2479],{"class":2412},[58,10725,10726,10729,10731,10734,10737,10739],{"class":2400,"line":2442},[58,10727,10728],{"class":2412},"    mask ",[58,10730,814],{"class":2404},[58,10732,10733],{"class":2412}," torch.arange((maxlen), ",[58,10735,10736],{"class":2470},"dtype",[58,10738,814],{"class":2404},[58,10740,10741],{"class":2412},"torch.float32,\n",[58,10743,10744,10747,10749,10752,10754,10757,10760,10763,10765,10767,10769],{"class":2400,"line":2461},[58,10745,10746],{"class":2470},"                        device",[58,10748,814],{"class":2404},[58,10750,10751],{"class":2412},"X.device)[",[58,10753,2779],{"class":2454},[58,10755,10756],{"class":2412},", :] ",[58,10758,10759],{"class":2404},"\u003C",[58,10761,10762],{"class":2412}," valid_len[",[58,10764,7183],{"class":7182},[58,10766,2419],{"class":2412},[58,10768,2779],{"class":2454},[58,10770,2798],{"class":2412},[58,10772,10773,10776,10779,10782,10784],{"class":2400,"line":2482},[58,10774,10775],{"class":2412},"    X[",[58,10777,10778],{"class":2404},"~",[58,10780,10781],{"class":2412},"mask] ",[58,10783,814],{"class":2404},[58,10785,10786],{"class":2412}," value\n",[58,10788,10789,10791],{"class":2400,"line":2490},[58,10790,4686],{"class":2404},[58,10792,9659],{"class":2412},[58,10794,10795],{"class":2400,"line":2501},[58,10796,2724],{"emptyLinePlaceholder":2723},[58,10798,10799,10801,10804,10806,10808,10810,10813],{"class":2400,"line":2518},[58,10800,2629],{"class":2404},[58,10802,10803],{"class":2632}," MaskedSoftmaxCELoss",[58,10805,797],{"class":2412},[58,10807,2639],{"class":2638},[58,10809,863],{"class":2412},[58,10811,10812],{"class":2638},"CrossEntropyLoss",[58,10814,2425],{"class":2412},[58,10816,10817],{"class":2400,"line":2534},[58,10818,10819],{"class":2431},"    \"\"\"带遮蔽的softmax交叉熵损失函数\"\"\"\n",[58,10821,10822],{"class":2400,"line":2542},[58,10823,10824],{"class":2438},"    # pred的形状：(batch_size,num_steps,vocab_size)\n",[58,10826,10827],{"class":2400,"line":2559},[58,10828,10829],{"class":2438},"    # label的形状：(batch_size,num_steps)\n",[58,10831,10832],{"class":2400,"line":2565},[58,10833,10834],{"class":2438},"    # valid_len的形状：(batch_size,)\n",[58,10836,10837,10839,10841,10843,10845,10847,10850,10852,10855,10857,10859],{"class":2400,"line":2590},[58,10838,2656],{"class":2404},[58,10840,2751],{"class":2408},[58,10842,797],{"class":2412},[58,10844,2665],{"class":2664},[58,10846,2419],{"class":2412},[58,10848,10849],{"class":2415},"pred",[58,10851,2419],{"class":2412},[58,10853,10854],{"class":2415},"label",[58,10856,2419],{"class":2412},[58,10858,10693],{"class":2415},[58,10860,2425],{"class":2412},[58,10862,10863,10866,10868],{"class":2400,"line":2603},[58,10864,10865],{"class":2412},"        weights ",[58,10867,814],{"class":2404},[58,10869,10870],{"class":2412}," torch.ones_like(label)\n",[58,10872,10873,10875,10877],{"class":2400,"line":2844},[58,10874,10865],{"class":2412},[58,10876,814],{"class":2404},[58,10878,10879],{"class":2412}," sequence_mask(weights, valid_len)\n",[58,10881,10882,10884,10887,10889,10892,10895],{"class":2400,"line":4780},[58,10883,2710],{"class":2692},[58,10885,10886],{"class":2412},".reduction",[58,10888,814],{"class":2404},[58,10890,10891],{"class":9475},"'",[58,10893,10894],{"class":9479},"none",[58,10896,10897],{"class":9475},"'\n",[58,10899,10900,10903,10905,10908,10911,10913],{"class":2400,"line":5056},[58,10901,10902],{"class":2412},"        unweighted_loss ",[58,10904,814],{"class":2404},[58,10906,10907],{"class":2685}," super",[58,10909,10910],{"class":2412},"(MaskedSoftmaxCELoss, ",[58,10912,2665],{"class":2692},[58,10914,10915],{"class":2412},").forward(\n",[58,10917,10918,10921,10923,10925,10927,10929,10931],{"class":2400,"line":5062},[58,10919,10920],{"class":2412},"            pred.permute(",[58,10922,1753],{"class":2454},[58,10924,2419],{"class":2412},[58,10926,2820],{"class":2454},[58,10928,2419],{"class":2412},[58,10930,82],{"class":2454},[58,10932,10933],{"class":2412},"), label)\n",[58,10935,10936,10939,10941,10944,10946,10949,10951,10953,10955],{"class":2400,"line":5068},[58,10937,10938],{"class":2412},"        weighted_loss ",[58,10940,814],{"class":2404},[58,10942,10943],{"class":2412}," (unweighted_loss ",[58,10945,8728],{"class":2404},[58,10947,10948],{"class":2412}," weights).mean(",[58,10950,2471],{"class":2470},[58,10952,814],{"class":2404},[58,10954,82],{"class":2454},[58,10956,2479],{"class":2412},[58,10958,10959,10961],{"class":2400,"line":5074},[58,10960,2464],{"class":2404},[58,10962,10963],{"class":2412}," weighted_loss\n",[14,10965,10966],{},"梯度裁剪函数：",[2389,10968,10970],{"className":2391,"code":10969,"language":2393,"meta":2394,"style":2394},"def grad_clipping(net, theta):\n    \"\"\"裁剪梯度\"\"\"\n    if isinstance(net, nn.Module):\n        params = [p for p in net.parameters() if p.requires_grad]\n    else:\n        params = net.params\n    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))\n    if norm > theta:\n        for param in params:\n            param.grad[:] *= theta / norm\n",[2396,10971,10972,10991,10996,11006,11032,11038,11047,11079,11092,11104],{"__ignoreMap":2394},[58,10973,10974,10976,10979,10981,10984,10986,10989],{"class":2400,"line":2401},[58,10975,2405],{"class":2404},[58,10977,10978],{"class":2408}," grad_clipping",[58,10980,797],{"class":2412},[58,10982,10983],{"class":2415},"net",[58,10985,2419],{"class":2412},[58,10987,10988],{"class":2415},"theta",[58,10990,2425],{"class":2412},[58,10992,10993],{"class":2400,"line":2428},[58,10994,10995],{"class":2431},"    \"\"\"裁剪梯度\"\"\"\n",[58,10997,10998,11000,11003],{"class":2400,"line":2435},[58,10999,2445],{"class":2404},[58,11001,11002],{"class":9460}," isinstance",[58,11004,11005],{"class":2412},"(net, nn.Module):\n",[58,11007,11008,11011,11013,11016,11018,11021,11023,11026,11029],{"class":2400,"line":2442},[58,11009,11010],{"class":2412},"        params ",[58,11012,814],{"class":2404},[58,11014,11015],{"class":2412}," [p ",[58,11017,10529],{"class":2404},[58,11019,11020],{"class":2412}," p ",[58,11022,9457],{"class":2404},[58,11024,11025],{"class":2412}," net.parameters() ",[58,11027,11028],{"class":2404},"if",[58,11030,11031],{"class":2412}," p.requires_grad]\n",[58,11033,11034,11036],{"class":2400,"line":2461},[58,11035,2485],{"class":2404},[58,11037,2458],{"class":2412},[58,11039,11040,11042,11044],{"class":2400,"line":2482},[58,11041,11010],{"class":2412},[58,11043,814],{"class":2404},[58,11045,11046],{"class":2412}," net.params\n",[58,11048,11049,11052,11054,11057,11060,11063,11065,11068,11070,11072,11074,11076],{"class":2400,"line":2490},[58,11050,11051],{"class":2412},"    norm ",[58,11053,814],{"class":2404},[58,11055,11056],{"class":2412}," torch.sqrt(",[58,11058,11059],{"class":9460},"sum",[58,11061,11062],{"class":2412},"(torch.sum((p.grad ",[58,11064,2675],{"class":2404},[58,11066,11067],{"class":2454}," 2",[58,11069,2823],{"class":2412},[58,11071,10529],{"class":2404},[58,11073,11020],{"class":2412},[58,11075,9457],{"class":2404},[58,11077,11078],{"class":2412}," params))\n",[58,11080,11081,11083,11086,11089],{"class":2400,"line":2501},[58,11082,2445],{"class":2404},[58,11084,11085],{"class":2412}," norm ",[58,11087,11088],{"class":2404},">",[58,11090,11091],{"class":2412}," theta:\n",[58,11093,11094,11096,11099,11101],{"class":2400,"line":2518},[58,11095,9451],{"class":2404},[58,11097,11098],{"class":2412}," param ",[58,11100,9457],{"class":2404},[58,11102,11103],{"class":2412}," params:\n",[58,11105,11106,11109,11111,11113,11116,11119,11121],{"class":2400,"line":2534},[58,11107,11108],{"class":2412},"            param.grad[",[58,11110,7183],{"class":7182},[58,11112,7199],{"class":2412},[58,11114,11115],{"class":2404},"*=",[58,11117,11118],{"class":2412}," theta ",[58,11120,2826],{"class":2404},[58,11122,11123],{"class":2412}," norm\n",[14,11125,11126,11127],{},"之后，在训练时，特定的序列开始词元（“",[11128,11129,11130,11131],"bos",{},"”）和 原始的输出序列（不包括序列结束词元“",[11132,11133,11134],"eos",{},"”） 拼接在一起作为解码器的输入。 这被称为强制教学（teacher forcing）， 因为原始的输出序列（词元的标签）被送入解码器。 或者，将来自上一个时间步的预测得到的词元作为解码器的当前输入。",[2389,11136,11138],{"className":2391,"code":11137,"language":2393,"meta":2394,"style":2394},"def train_seq2seq(net, data_iter, lr, num_epochs, tgt_vocab, device):\n    \"\"\"训练序列到序列模型\"\"\"\n    def xavier_init_weights(m):\n        if type(m) == nn.Linear:\n            nn.init.xavier_uniform_(m.weight)\n        if type(m) == nn.GRU:\n            for param in m._flat_weights_names:\n                if \"weight\" in param:\n                    nn.init.xavier_uniform_(m._parameters[param])\n\n    net.apply(xavier_init_weights)\n    net.to(device)\n    optimizer = torch.optim.Adam(net.parameters(), lr=lr)\n    loss = MaskedSoftmaxCELoss()\n    net.train()\n    animator = d2l.Animator(xlabel='epoch', ylabel='loss',\n                     xlim=[10, num_epochs])\n    for epoch in range(num_epochs):\n        timer = d2l.Timer()\n        metric = d2l.Accumulator(2)  # 训练损失总和，词元数量\n        for batch in data_iter:\n            optimizer.zero_grad()\n            X, X_valid_len, Y, Y_valid_len = [x.to(device) for x in batch]\n            bos = torch.tensor([tgt_vocab['\u003Cbos>']] * Y.shape[0],\n                          device=device).reshape(-1, 1)\n            dec_input = torch.cat([bos, Y[:, :-1]], 1)  # 强制教学\n            Y_hat, _ = net(X, dec_input, X_valid_len)\n            l = loss(Y_hat, Y, Y_valid_len)\n            l.sum().backward()      # 损失函数的标量进行“反向传播”\n            grad_clipping(net, 1)\n            num_tokens = Y_valid_len.sum()\n            optimizer.step()\n            with torch.no_grad():\n                metric.add(l.sum(), num_tokens)\n        if (epoch + 1) % 10 == 0:\n            animator.add(epoch + 1, (metric[0] / metric[1],))\n    print(f'loss {metric[0] / metric[1]:.3f}, {metric[1] / timer.stop():.1f} '\n        f'tokens/sec on {str(device)}')\n",[2396,11139,11140,11177,11182,11195,11210,11215,11233,11245,11264,11269,11273,11278,11283,11300,11310,11315,11353,11369,11384,11394,11412,11424,11429,11449,11479,11499,11529,11539,11549,11557,11566,11576,11581,11589,11594,11621,11647,11708],{"__ignoreMap":2394},[58,11141,11142,11144,11147,11149,11151,11153,11156,11158,11161,11163,11166,11168,11171,11173,11175],{"class":2400,"line":2401},[58,11143,2405],{"class":2404},[58,11145,11146],{"class":2408}," train_seq2seq",[58,11148,797],{"class":2412},[58,11150,10983],{"class":2415},[58,11152,2419],{"class":2412},[58,11154,11155],{"class":2415},"data_iter",[58,11157,2419],{"class":2412},[58,11159,11160],{"class":2415},"lr",[58,11162,2419],{"class":2412},[58,11164,11165],{"class":2415},"num_epochs",[58,11167,2419],{"class":2412},[58,11169,11170],{"class":2415},"tgt_vocab",[58,11172,2419],{"class":2412},[58,11174,10064],{"class":2415},[58,11176,2425],{"class":2412},[58,11178,11179],{"class":2400,"line":2428},[58,11180,11181],{"class":2431},"    \"\"\"训练序列到序列模型\"\"\"\n",[58,11183,11184,11186,11189,11191,11193],{"class":2400,"line":2435},[58,11185,2656],{"class":2404},[58,11187,11188],{"class":2408}," xavier_init_weights",[58,11190,797],{"class":2412},[58,11192,365],{"class":2415},[58,11194,2425],{"class":2412},[58,11196,11197,11199,11202,11205,11207],{"class":2400,"line":2442},[58,11198,2504],{"class":2404},[58,11200,11201],{"class":2685}," type",[58,11203,11204],{"class":2412},"(m) ",[58,11206,2510],{"class":2404},[58,11208,11209],{"class":2412}," nn.Linear:\n",[58,11211,11212],{"class":2400,"line":2461},[58,11213,11214],{"class":2412},"            nn.init.xavier_uniform_(m.weight)\n",[58,11216,11217,11219,11221,11223,11225,11228,11231],{"class":2400,"line":2482},[58,11218,2504],{"class":2404},[58,11220,11201],{"class":2685},[58,11222,11204],{"class":2412},[58,11224,2510],{"class":2404},[58,11226,11227],{"class":2412}," nn.",[58,11229,11230],{"class":2454},"GRU",[58,11232,2458],{"class":2412},[58,11234,11235,11238,11240,11242],{"class":2400,"line":2490},[58,11236,11237],{"class":2404},"            for",[58,11239,11098],{"class":2412},[58,11241,9457],{"class":2404},[58,11243,11244],{"class":2412}," m._flat_weights_names:\n",[58,11246,11247,11250,11253,11256,11258,11261],{"class":2400,"line":2501},[58,11248,11249],{"class":2404},"                if",[58,11251,11252],{"class":9475}," \"",[58,11254,11255],{"class":9479},"weight",[58,11257,9476],{"class":9475},[58,11259,11260],{"class":2404}," in",[58,11262,11263],{"class":2412}," param:\n",[58,11265,11266],{"class":2400,"line":2518},[58,11267,11268],{"class":2412},"                    nn.init.xavier_uniform_(m._parameters[param])\n",[58,11270,11271],{"class":2400,"line":2534},[58,11272,2724],{"emptyLinePlaceholder":2723},[58,11274,11275],{"class":2400,"line":2542},[58,11276,11277],{"class":2412},"    net.apply(xavier_init_weights)\n",[58,11279,11280],{"class":2400,"line":2559},[58,11281,11282],{"class":2412},"    net.to(device)\n",[58,11284,11285,11288,11290,11293,11295,11297],{"class":2400,"line":2565},[58,11286,11287],{"class":2412},"    optimizer ",[58,11289,814],{"class":2404},[58,11291,11292],{"class":2412}," torch.optim.Adam(net.parameters(), ",[58,11294,11160],{"class":2470},[58,11296,814],{"class":2404},[58,11298,11299],{"class":2412},"lr)\n",[58,11301,11302,11305,11307],{"class":2400,"line":2590},[58,11303,11304],{"class":2412},"    loss ",[58,11306,814],{"class":2404},[58,11308,11309],{"class":2412}," MaskedSoftmaxCELoss()\n",[58,11311,11312],{"class":2400,"line":2603},[58,11313,11314],{"class":2412},"    net.train()\n",[58,11316,11317,11320,11322,11325,11328,11330,11332,11335,11337,11339,11342,11344,11346,11349,11351],{"class":2400,"line":2844},[58,11318,11319],{"class":2412},"    animator ",[58,11321,814],{"class":2404},[58,11323,11324],{"class":2412}," d2l.Animator(",[58,11326,11327],{"class":2470},"xlabel",[58,11329,814],{"class":2404},[58,11331,10891],{"class":9475},[58,11333,11334],{"class":9479},"epoch",[58,11336,10891],{"class":9475},[58,11338,2419],{"class":2412},[58,11340,11341],{"class":2470},"ylabel",[58,11343,814],{"class":2404},[58,11345,10891],{"class":9475},[58,11347,11348],{"class":9479},"loss",[58,11350,10891],{"class":9475},[58,11352,3825],{"class":2412},[58,11354,11355,11358,11360,11363,11366],{"class":2400,"line":4780},[58,11356,11357],{"class":2470},"                     xlim",[58,11359,814],{"class":2404},[58,11361,11362],{"class":2412},"[",[58,11364,11365],{"class":2454},"10",[58,11367,11368],{"class":2412},", num_epochs])\n",[58,11370,11371,11374,11377,11379,11381],{"class":2400,"line":5056},[58,11372,11373],{"class":2404},"    for",[58,11375,11376],{"class":2412}," epoch ",[58,11378,9457],{"class":2404},[58,11380,9461],{"class":9460},[58,11382,11383],{"class":2412},"(num_epochs):\n",[58,11385,11386,11389,11391],{"class":2400,"line":5062},[58,11387,11388],{"class":2412},"        timer ",[58,11390,814],{"class":2404},[58,11392,11393],{"class":2412}," d2l.Timer()\n",[58,11395,11396,11399,11401,11404,11406,11409],{"class":2400,"line":5068},[58,11397,11398],{"class":2412},"        metric ",[58,11400,814],{"class":2404},[58,11402,11403],{"class":2412}," d2l.Accumulator(",[58,11405,2820],{"class":2454},[58,11407,11408],{"class":2412},")  ",[58,11410,11411],{"class":2438},"# 训练损失总和，词元数量\n",[58,11413,11414,11416,11419,11421],{"class":2400,"line":5074},[58,11415,9451],{"class":2404},[58,11417,11418],{"class":2412}," batch ",[58,11420,9457],{"class":2404},[58,11422,11423],{"class":2412}," data_iter:\n",[58,11425,11426],{"class":2400,"line":5095},[58,11427,11428],{"class":2412},"            optimizer.zero_grad()\n",[58,11430,11431,11434,11436,11439,11441,11444,11446],{"class":2400,"line":5114},[58,11432,11433],{"class":2412},"            X, X_valid_len, Y, Y_valid_len ",[58,11435,814],{"class":2404},[58,11437,11438],{"class":2412}," [x.to(device) ",[58,11440,10529],{"class":2404},[58,11442,11443],{"class":2412}," x ",[58,11445,9457],{"class":2404},[58,11447,11448],{"class":2412}," batch]\n",[58,11450,11451,11454,11456,11459,11461,11464,11466,11469,11471,11474,11476],{"class":2400,"line":5133},[58,11452,11453],{"class":2412},"            bos ",[58,11455,814],{"class":2404},[58,11457,11458],{"class":2412}," torch.tensor([tgt_vocab[",[58,11460,10891],{"class":9475},[58,11462,11463],{"class":9479},"\u003Cbos>",[58,11465,10891],{"class":9475},[58,11467,11468],{"class":2412},"]] ",[58,11470,8728],{"class":2404},[58,11472,11473],{"class":2412}," Y.shape[",[58,11475,1753],{"class":2454},[58,11477,11478],{"class":2412},"],\n",[58,11480,11481,11484,11486,11489,11491,11493,11495,11497],{"class":2400,"line":5138},[58,11482,11483],{"class":2470},"                          device",[58,11485,814],{"class":2404},[58,11487,11488],{"class":2412},"device).reshape(",[58,11490,2552],{"class":2404},[58,11492,82],{"class":2454},[58,11494,2419],{"class":2412},[58,11496,82],{"class":2454},[58,11498,2479],{"class":2412},[58,11500,11501,11504,11506,11509,11511,11513,11515,11517,11519,11522,11524,11526],{"class":2400,"line":5154},[58,11502,11503],{"class":2412},"            dec_input ",[58,11505,814],{"class":2404},[58,11507,11508],{"class":2412}," torch.cat([bos, Y[",[58,11510,7183],{"class":7182},[58,11512,2419],{"class":2412},[58,11514,7183],{"class":7182},[58,11516,2552],{"class":2404},[58,11518,82],{"class":2454},[58,11520,11521],{"class":2412},"]], ",[58,11523,82],{"class":2454},[58,11525,11408],{"class":2412},[58,11527,11528],{"class":2438},"# 强制教学\n",[58,11530,11531,11534,11536],{"class":2400,"line":5160},[58,11532,11533],{"class":2412},"            Y_hat, _ ",[58,11535,814],{"class":2404},[58,11537,11538],{"class":2412}," net(X, dec_input, X_valid_len)\n",[58,11540,11541,11544,11546],{"class":2400,"line":5166},[58,11542,11543],{"class":2412},"            l ",[58,11545,814],{"class":2404},[58,11547,11548],{"class":2412}," loss(Y_hat, Y, Y_valid_len)\n",[58,11550,11551,11554],{"class":2400,"line":5176},[58,11552,11553],{"class":2412},"            l.sum().backward()      ",[58,11555,11556],{"class":2438},"# 损失函数的标量进行“反向传播”\n",[58,11558,11559,11562,11564],{"class":2400,"line":5200},[58,11560,11561],{"class":2412},"            grad_clipping(net, ",[58,11563,82],{"class":2454},[58,11565,2479],{"class":2412},[58,11567,11568,11571,11573],{"class":2400,"line":5205},[58,11569,11570],{"class":2412},"            num_tokens ",[58,11572,814],{"class":2404},[58,11574,11575],{"class":2412}," Y_valid_len.sum()\n",[58,11577,11578],{"class":2400,"line":5211},[58,11579,11580],{"class":2412},"            optimizer.step()\n",[58,11582,11583,11586],{"class":2400,"line":5225},[58,11584,11585],{"class":2404},"            with",[58,11587,11588],{"class":2412}," torch.no_grad():\n",[58,11590,11591],{"class":2400,"line":5230},[58,11592,11593],{"class":2412},"                metric.add(l.sum(), num_tokens)\n",[58,11595,11596,11598,11601,11603,11605,11607,11610,11613,11616,11619],{"class":2400,"line":5236},[58,11597,2504],{"class":2404},[58,11599,11600],{"class":2412}," (epoch ",[58,11602,5776],{"class":2404},[58,11604,2513],{"class":2454},[58,11606,7145],{"class":2412},[58,11608,11609],{"class":2404},"%",[58,11611,11612],{"class":2454}," 10",[58,11614,11615],{"class":2404}," ==",[58,11617,11618],{"class":2454}," 0",[58,11620,2458],{"class":2412},[58,11622,11623,11626,11628,11630,11633,11635,11637,11639,11642,11644],{"class":2400,"line":5251},[58,11624,11625],{"class":2412},"            animator.add(epoch ",[58,11627,5776],{"class":2404},[58,11629,2513],{"class":2454},[58,11631,11632],{"class":2412},", (metric[",[58,11634,1753],{"class":2454},[58,11636,7199],{"class":2412},[58,11638,2826],{"class":2404},[58,11640,11641],{"class":2412}," metric[",[58,11643,82],{"class":2454},[58,11645,11646],{"class":2412},"],))\n",[58,11648,11649,11652,11654,11657,11660,11663,11666,11668,11670,11672,11674,11676,11679,11682,11685,11687,11689,11691,11693,11695,11697,11700,11703,11705],{"class":2400,"line":9543},[58,11650,11651],{"class":9460},"    print",[58,11653,797],{"class":2412},[58,11655,11656],{"class":2404},"f",[58,11658,11659],{"class":9479},"'loss ",[58,11661,11662],{"class":2454},"{",[58,11664,11665],{"class":2412},"metric[",[58,11667,1753],{"class":2454},[58,11669,7199],{"class":2412},[58,11671,2826],{"class":2404},[58,11673,11641],{"class":2412},[58,11675,82],{"class":2454},[58,11677,11678],{"class":2412},"]",[58,11680,11681],{"class":2404},":.3f",[58,11683,11684],{"class":2454},"}",[58,11686,2419],{"class":9479},[58,11688,11662],{"class":2454},[58,11690,11665],{"class":2412},[58,11692,82],{"class":2454},[58,11694,7199],{"class":2412},[58,11696,2826],{"class":2404},[58,11698,11699],{"class":2412}," timer.stop()",[58,11701,11702],{"class":2404},":.1f",[58,11704,11684],{"class":2454},[58,11706,11707],{"class":9479}," '\n",[58,11709,11710,11713,11716,11718,11720,11723,11725,11727],{"class":2400,"line":9549},[58,11711,11712],{"class":2404},"        f",[58,11714,11715],{"class":9479},"'tokens/sec on ",[58,11717,11662],{"class":2454},[58,11719,9487],{"class":2685},[58,11721,11722],{"class":2412},"(device)",[58,11724,11684],{"class":2454},[58,11726,10891],{"class":9479},[58,11728,2479],{"class":2412},[14,11730,11731],{},"进行数据集的数据处理",[2389,11733,11735],{"className":2391,"code":11734,"language":2393,"meta":2394,"style":2394},"def read_data_nmt():\n    \"\"\"载入“英语－法语”数据集\n\n    Defined in :numref:`sec_machine_translation`\"\"\"\n    data_dir = d2l.download_extract('fra-eng')\n    with open(os.path.join(data_dir, 'fra.txt'), 'r',\n             encoding='utf-8') as f:\n        return f.read()\n\ndef preprocess_nmt(text):\n    \"\"\"预处理“英语－法语”数据集\n\n    Defined in :numref:`sec_machine_translation`\"\"\"\n    def no_space(char, prev_char):\n        return char in set(',.!?') and prev_char != ' '\n\n    # 使用空格替换不间断空格\n    # 使用小写字母替换大写字母\n    text = text.replace('\\u202f', ' ').replace('\\xa0', ' ').lower()\n    # 在单词和标点符号之间插入空格\n    out = [' ' + char if i > 0 and no_space(char, text[i - 1]) else char\n           for i, char in enumerate(text)]\n    return ''.join(out)\n\ndef tokenize_nmt(text, num_examples=None):\n    \"\"\"词元化“英语－法语”数据数据集\n\n    Defined in :numref:`sec_machine_translation`\"\"\"\n    source, target = [], []\n    for i, line in enumerate(text.split('\\n')):\n        if num_examples and i > num_examples:\n            break\n        parts = line.split('\\t')\n        if len(parts) == 2:\n            source.append(parts[0].split(' '))\n            target.append(parts[1].split(' '))\n    return source, target\n\ndef load_data_nmt(batch_size, num_steps, num_examples=600):\n    \"\"\"返回翻译数据集的迭代器和词表\n\n    Defined in :numref:`subsec_mt_data_loading`\"\"\"\n    text = preprocess_nmt(read_data_nmt())\n    source, target = tokenize_nmt(text, num_examples)\n    src_vocab = d2l.Vocab(source, min_freq=2,\n                          reserved_tokens=['\u003Cpad>', '\u003Cbos>', '\u003Ceos>'])\n    tgt_vocab = d2l.Vocab(target, min_freq=2,\n                          reserved_tokens=['\u003Cpad>', '\u003Cbos>', '\u003Ceos>'])\n    src_array, src_valid_len = build_array_nmt(source, src_vocab, num_steps)\n    tgt_array, tgt_valid_len = build_array_nmt(target, tgt_vocab, num_steps)\n    data_arrays = (src_array, src_valid_len, tgt_array, tgt_valid_len)\n    data_iter = d2l.load_array(data_arrays, batch_size)\n    return data_iter, src_vocab, tgt_vocab\n",[2396,11736,11737,11747,11752,11756,11761,11780,11809,11831,11838,11842,11856,11861,11865,11869,11888,11925,11929,11934,11939,11982,11987,12032,12047,12057,12061,12083,12088,12092,12096,12106,12130,12146,12151,12170,12185,12202,12217,12224,12228,12256,12261,12265,12270,12279,12288,12307,12342,12360,12392,12402,12412,12422,12432],{"__ignoreMap":2394},[58,11738,11739,11741,11744],{"class":2400,"line":2401},[58,11740,2405],{"class":2404},[58,11742,11743],{"class":2408}," read_data_nmt",[58,11745,11746],{"class":2412},"():\n",[58,11748,11749],{"class":2400,"line":2428},[58,11750,11751],{"class":2431},"    \"\"\"载入“英语－法语”数据集\n",[58,11753,11754],{"class":2400,"line":2435},[58,11755,2724],{"emptyLinePlaceholder":2723},[58,11757,11758],{"class":2400,"line":2442},[58,11759,11760],{"class":2431},"    Defined in :numref:`sec_machine_translation`\"\"\"\n",[58,11762,11763,11766,11768,11771,11773,11776,11778],{"class":2400,"line":2461},[58,11764,11765],{"class":2412},"    data_dir ",[58,11767,814],{"class":2404},[58,11769,11770],{"class":2412}," d2l.download_extract(",[58,11772,10891],{"class":9475},[58,11774,11775],{"class":9479},"fra-eng",[58,11777,10891],{"class":9475},[58,11779,2479],{"class":2412},[58,11781,11782,11785,11788,11791,11793,11796,11798,11801,11803,11805,11807],{"class":2400,"line":2482},[58,11783,11784],{"class":2404},"    with",[58,11786,11787],{"class":9460}," open",[58,11789,11790],{"class":2412},"(os.path.join(data_dir, ",[58,11792,10891],{"class":9475},[58,11794,11795],{"class":9479},"fra.txt",[58,11797,10891],{"class":9475},[58,11799,11800],{"class":2412},"), ",[58,11802,10891],{"class":9475},[58,11804,7825],{"class":9479},[58,11806,10891],{"class":9475},[58,11808,3825],{"class":2412},[58,11810,11811,11814,11816,11818,11821,11823,11825,11828],{"class":2400,"line":2490},[58,11812,11813],{"class":2470},"             encoding",[58,11815,814],{"class":2404},[58,11817,10891],{"class":9475},[58,11819,11820],{"class":9479},"utf-8",[58,11822,10891],{"class":9475},[58,11824,7145],{"class":2412},[58,11826,11827],{"class":2404},"as",[58,11829,11830],{"class":2412}," f:\n",[58,11832,11833,11835],{"class":2400,"line":2501},[58,11834,2464],{"class":2404},[58,11836,11837],{"class":2412}," f.read()\n",[58,11839,11840],{"class":2400,"line":2518},[58,11841,2724],{"emptyLinePlaceholder":2723},[58,11843,11844,11846,11849,11851,11854],{"class":2400,"line":2534},[58,11845,2405],{"class":2404},[58,11847,11848],{"class":2408}," preprocess_nmt",[58,11850,797],{"class":2412},[58,11852,11853],{"class":2415},"text",[58,11855,2425],{"class":2412},[58,11857,11858],{"class":2400,"line":2542},[58,11859,11860],{"class":2431},"    \"\"\"预处理“英语－法语”数据集\n",[58,11862,11863],{"class":2400,"line":2559},[58,11864,2724],{"emptyLinePlaceholder":2723},[58,11866,11867],{"class":2400,"line":2565},[58,11868,11760],{"class":2431},[58,11870,11871,11873,11876,11878,11881,11883,11886],{"class":2400,"line":2590},[58,11872,2656],{"class":2404},[58,11874,11875],{"class":2408}," no_space",[58,11877,797],{"class":2412},[58,11879,11880],{"class":2415},"char",[58,11882,2419],{"class":2412},[58,11884,11885],{"class":2415},"prev_char",[58,11887,2425],{"class":2412},[58,11889,11890,11892,11895,11897,11900,11902,11904,11907,11909,11911,11914,11917,11920,11923],{"class":2400,"line":2603},[58,11891,2464],{"class":2404},[58,11893,11894],{"class":2412}," char ",[58,11896,9457],{"class":2404},[58,11898,11899],{"class":2685}," set",[58,11901,797],{"class":2412},[58,11903,10891],{"class":9475},[58,11905,11906],{"class":9479},",.!?",[58,11908,10891],{"class":9475},[58,11910,7145],{"class":2412},[58,11912,11913],{"class":2404},"and",[58,11915,11916],{"class":2412}," prev_char ",[58,11918,11919],{"class":2404},"!=",[58,11921,11922],{"class":9475}," '",[58,11924,11707],{"class":9475},[58,11926,11927],{"class":2400,"line":2844},[58,11928,2724],{"emptyLinePlaceholder":2723},[58,11930,11931],{"class":2400,"line":4780},[58,11932,11933],{"class":2438},"    # 使用空格替换不间断空格\n",[58,11935,11936],{"class":2400,"line":5056},[58,11937,11938],{"class":2438},"    # 使用小写字母替换大写字母\n",[58,11940,11941,11944,11946,11949,11951,11955,11957,11959,11961,11963,11966,11968,11971,11973,11975,11977,11979],{"class":2400,"line":5062},[58,11942,11943],{"class":2412},"    text ",[58,11945,814],{"class":2404},[58,11947,11948],{"class":2412}," text.replace(",[58,11950,10891],{"class":9475},[58,11952,11954],{"class":11953},"sRfyP","\\u202f",[58,11956,10891],{"class":9475},[58,11958,2419],{"class":2412},[58,11960,10891],{"class":9475},[58,11962,11922],{"class":9475},[58,11964,11965],{"class":2412},").replace(",[58,11967,10891],{"class":9475},[58,11969,11970],{"class":11953},"\\xa0",[58,11972,10891],{"class":9475},[58,11974,2419],{"class":2412},[58,11976,10891],{"class":9475},[58,11978,11922],{"class":9475},[58,11980,11981],{"class":2412},").lower()\n",[58,11983,11984],{"class":2400,"line":5068},[58,11985,11986],{"class":2438},"    # 在单词和标点符号之间插入空格\n",[58,11988,11989,11992,11994,11996,11998,12000,12003,12005,12007,12009,12011,12013,12016,12019,12021,12023,12026,12029],{"class":2400,"line":5074},[58,11990,11991],{"class":2412},"    out ",[58,11993,814],{"class":2404},[58,11995,9591],{"class":2412},[58,11997,10891],{"class":9475},[58,11999,11922],{"class":9475},[58,12001,12002],{"class":2404}," +",[58,12004,11894],{"class":2412},[58,12006,11028],{"class":2404},[58,12008,9454],{"class":2412},[58,12010,11088],{"class":2404},[58,12012,11618],{"class":2454},[58,12014,12015],{"class":2404}," and",[58,12017,12018],{"class":2412}," no_space(char, text[i ",[58,12020,2552],{"class":2404},[58,12022,2513],{"class":2454},[58,12024,12025],{"class":2412},"]) ",[58,12027,12028],{"class":2404},"else",[58,12030,12031],{"class":2412}," char\n",[58,12033,12034,12037,12040,12042,12044],{"class":2400,"line":5095},[58,12035,12036],{"class":2404},"           for",[58,12038,12039],{"class":2412}," i, char ",[58,12041,9457],{"class":2404},[58,12043,9620],{"class":9460},[58,12045,12046],{"class":2412},"(text)]\n",[58,12048,12049,12051,12054],{"class":2400,"line":5114},[58,12050,4686],{"class":2404},[58,12052,12053],{"class":9475}," ''",[58,12055,12056],{"class":2412},".join(out)\n",[58,12058,12059],{"class":2400,"line":5133},[58,12060,2724],{"emptyLinePlaceholder":2723},[58,12062,12063,12065,12068,12070,12072,12074,12077,12079,12081],{"class":2400,"line":5138},[58,12064,2405],{"class":2404},[58,12066,12067],{"class":2408}," tokenize_nmt",[58,12069,797],{"class":2412},[58,12071,11853],{"class":2415},[58,12073,2419],{"class":2412},[58,12075,12076],{"class":2415},"num_examples",[58,12078,814],{"class":2404},[58,12080,2779],{"class":2454},[58,12082,2425],{"class":2412},[58,12084,12085],{"class":2400,"line":5154},[58,12086,12087],{"class":2431},"    \"\"\"词元化“英语－法语”数据数据集\n",[58,12089,12090],{"class":2400,"line":5160},[58,12091,2724],{"emptyLinePlaceholder":2723},[58,12093,12094],{"class":2400,"line":5166},[58,12095,11760],{"class":2431},[58,12097,12098,12101,12103],{"class":2400,"line":5176},[58,12099,12100],{"class":2412},"    source, target ",[58,12102,814],{"class":2404},[58,12104,12105],{"class":2412}," [], []\n",[58,12107,12108,12110,12113,12115,12117,12120,12122,12125,12127],{"class":2400,"line":5200},[58,12109,11373],{"class":2404},[58,12111,12112],{"class":2412}," i, line ",[58,12114,9457],{"class":2404},[58,12116,9620],{"class":9460},[58,12118,12119],{"class":2412},"(text.split(",[58,12121,10891],{"class":9475},[58,12123,12124],{"class":11953},"\\n",[58,12126,10891],{"class":9475},[58,12128,12129],{"class":2412},")):\n",[58,12131,12132,12134,12137,12139,12141,12143],{"class":2400,"line":5205},[58,12133,2504],{"class":2404},[58,12135,12136],{"class":2412}," num_examples ",[58,12138,11913],{"class":2404},[58,12140,9454],{"class":2412},[58,12142,11088],{"class":2404},[58,12144,12145],{"class":2412}," num_examples:\n",[58,12147,12148],{"class":2400,"line":5211},[58,12149,12150],{"class":2404},"            break\n",[58,12152,12153,12156,12158,12161,12163,12166,12168],{"class":2400,"line":5225},[58,12154,12155],{"class":2412},"        parts ",[58,12157,814],{"class":2404},[58,12159,12160],{"class":2412}," line.split(",[58,12162,10891],{"class":9475},[58,12164,12165],{"class":11953},"\\t",[58,12167,10891],{"class":9475},[58,12169,2479],{"class":2412},[58,12171,12172,12174,12176,12179,12181,12183],{"class":2400,"line":5230},[58,12173,2504],{"class":2404},[58,12175,9600],{"class":9460},[58,12177,12178],{"class":2412},"(parts) ",[58,12180,2510],{"class":2404},[58,12182,11067],{"class":2454},[58,12184,2458],{"class":2412},[58,12186,12187,12190,12192,12195,12197,12199],{"class":2400,"line":5236},[58,12188,12189],{"class":2412},"            source.append(parts[",[58,12191,1753],{"class":2454},[58,12193,12194],{"class":2412},"].split(",[58,12196,10891],{"class":9475},[58,12198,11922],{"class":9475},[58,12200,12201],{"class":2412},"))\n",[58,12203,12204,12207,12209,12211,12213,12215],{"class":2400,"line":5251},[58,12205,12206],{"class":2412},"            target.append(parts[",[58,12208,82],{"class":2454},[58,12210,12194],{"class":2412},[58,12212,10891],{"class":9475},[58,12214,11922],{"class":9475},[58,12216,12201],{"class":2412},[58,12218,12219,12221],{"class":2400,"line":9543},[58,12220,4686],{"class":2404},[58,12222,12223],{"class":2412}," source, target\n",[58,12225,12226],{"class":2400,"line":9549},[58,12227,2724],{"emptyLinePlaceholder":2723},[58,12229,12230,12232,12235,12237,12240,12242,12245,12247,12249,12251,12254],{"class":2400,"line":9555},[58,12231,2405],{"class":2404},[58,12233,12234],{"class":2408}," load_data_nmt",[58,12236,797],{"class":2412},[58,12238,12239],{"class":2415},"batch_size",[58,12241,2419],{"class":2412},[58,12243,12244],{"class":2415},"num_steps",[58,12246,2419],{"class":2412},[58,12248,12076],{"class":2415},[58,12250,814],{"class":2404},[58,12252,12253],{"class":2454},"600",[58,12255,2425],{"class":2412},[58,12257,12258],{"class":2400,"line":9582},[58,12259,12260],{"class":2431},"    \"\"\"返回翻译数据集的迭代器和词表\n",[58,12262,12263],{"class":2400,"line":9610},[58,12264,2724],{"emptyLinePlaceholder":2723},[58,12266,12267],{"class":2400,"line":9630},[58,12268,12269],{"class":2431},"    Defined in :numref:`subsec_mt_data_loading`\"\"\"\n",[58,12271,12272,12274,12276],{"class":2400,"line":9641},[58,12273,11943],{"class":2412},[58,12275,814],{"class":2404},[58,12277,12278],{"class":2412}," preprocess_nmt(read_data_nmt())\n",[58,12280,12281,12283,12285],{"class":2400,"line":9654},[58,12282,12100],{"class":2412},[58,12284,814],{"class":2404},[58,12286,12287],{"class":2412}," tokenize_nmt(text, num_examples)\n",[58,12289,12290,12293,12295,12298,12301,12303,12305],{"class":2400,"line":10157},[58,12291,12292],{"class":2412},"    src_vocab ",[58,12294,814],{"class":2404},[58,12296,12297],{"class":2412}," d2l.Vocab(source, ",[58,12299,12300],{"class":2470},"min_freq",[58,12302,814],{"class":2404},[58,12304,2820],{"class":2454},[58,12306,3825],{"class":2412},[58,12308,12309,12312,12314,12316,12318,12321,12323,12325,12327,12329,12331,12333,12335,12338,12340],{"class":2400,"line":10172},[58,12310,12311],{"class":2470},"                          reserved_tokens",[58,12313,814],{"class":2404},[58,12315,11362],{"class":2412},[58,12317,10891],{"class":9475},[58,12319,12320],{"class":9479},"\u003Cpad>",[58,12322,10891],{"class":9475},[58,12324,2419],{"class":2412},[58,12326,10891],{"class":9475},[58,12328,11463],{"class":9479},[58,12330,10891],{"class":9475},[58,12332,2419],{"class":2412},[58,12334,10891],{"class":9475},[58,12336,12337],{"class":9479},"\u003Ceos>",[58,12339,10891],{"class":9475},[58,12341,2531],{"class":2412},[58,12343,12344,12347,12349,12352,12354,12356,12358],{"class":2400,"line":10177},[58,12345,12346],{"class":2412},"    tgt_vocab ",[58,12348,814],{"class":2404},[58,12350,12351],{"class":2412}," d2l.Vocab(target, ",[58,12353,12300],{"class":2470},[58,12355,814],{"class":2404},[58,12357,2820],{"class":2454},[58,12359,3825],{"class":2412},[58,12361,12362,12364,12366,12368,12370,12372,12374,12376,12378,12380,12382,12384,12386,12388,12390],{"class":2400,"line":10192},[58,12363,12311],{"class":2470},[58,12365,814],{"class":2404},[58,12367,11362],{"class":2412},[58,12369,10891],{"class":9475},[58,12371,12320],{"class":9479},[58,12373,10891],{"class":9475},[58,12375,2419],{"class":2412},[58,12377,10891],{"class":9475},[58,12379,11463],{"class":9479},[58,12381,10891],{"class":9475},[58,12383,2419],{"class":2412},[58,12385,10891],{"class":9475},[58,12387,12337],{"class":9479},[58,12389,10891],{"class":9475},[58,12391,2531],{"class":2412},[58,12393,12394,12397,12399],{"class":2400,"line":10221},[58,12395,12396],{"class":2412},"    src_array, src_valid_len ",[58,12398,814],{"class":2404},[58,12400,12401],{"class":2412}," build_array_nmt(source, src_vocab, num_steps)\n",[58,12403,12404,12407,12409],{"class":2400,"line":10240},[58,12405,12406],{"class":2412},"    tgt_array, tgt_valid_len ",[58,12408,814],{"class":2404},[58,12410,12411],{"class":2412}," build_array_nmt(target, tgt_vocab, num_steps)\n",[58,12413,12414,12417,12419],{"class":2400,"line":10261},[58,12415,12416],{"class":2412},"    data_arrays ",[58,12418,814],{"class":2404},[58,12420,12421],{"class":2412}," (src_array, src_valid_len, tgt_array, tgt_valid_len)\n",[58,12423,12424,12427,12429],{"class":2400,"line":10281},[58,12425,12426],{"class":2412},"    data_iter ",[58,12428,814],{"class":2404},[58,12430,12431],{"class":2412}," d2l.load_array(data_arrays, batch_size)\n",[58,12433,12434,12436],{"class":2400,"line":10292},[58,12435,4686],{"class":2404},[58,12437,12438],{"class":2412}," data_iter, src_vocab, tgt_vocab\n",[14,12440,12441],{},"之后按照 transformer 架构创建编码器-解码器架构，",[2389,12443,12445],{"className":2391,"code":12444,"language":2393,"meta":2394,"style":2394},"num_hiddens, num_layers, dropout, batch_size, num_steps = 32, 2, 0.1, 64, 10\nlr, num_epochs, device = 0.005, 200, torch.device('cuda:0') if torch.cuda.device_count() >= 1 else torch.device('cpu')\nffn_num_hiddens, num_heads = 64, 4\n\ntrain_iter, src_vocab, tgt_vocab = d2l.load_data_nmt(batch_size, num_steps)\n\nencoder = TransformerEncoder(\n    len(src_vocab), num_hiddens, ffn_num_hiddens, num_heads, num_layers,\n    dropout)\ndecoder = TransformerDecoder(\n    len(tgt_vocab), num_hiddens, ffn_num_hiddens, num_heads, num_layers,\n    dropout)\nnet = EncoderDecoder(encoder, decoder)\ntrain_seq2seq(net, train_iter, lr, num_epochs, tgt_vocab, 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PPO学习笔记.md","零基础速通 PPO 学习笔记",{"type":7,"value":24104,"toc":55360},[24105,24108,24111,24114,24622,24925,25374,25377,25380,25442,25781,29773,30374,30893,30897,30972,31636,31880,31999,32327,32330,33016,34155,34257,34260,36892,36998,38870,38874,38877,38911,41693,41696,41699,41702,43189,43192,43196,43199,43202,43337,45001,45004,45008,45651,45842,50367,50370,51415,51418,51423,51459,52750,52754,52757,53366,55350,55353],[10,24106,24107],{"id":24107},"学习背景",[14,24109,24110],{},"最近陶瓷到了港科的一个 RA，组里在做 Agent 强化学习相关内容，听从学长的指导来学习 PPO 算法相关知识。",[10,24112,24113],{"id":24113},"符号定义",[14,24115,24116,24117,24189,24190,24219,24220,24291,24292,24320,24321,24350,24351,24488,24489,24560,24561,24589,24590,24621],{},"在强化学习中，",[58,24118,24120,24138],{"className":24119},[61],[58,24121,24123],{"className":24122},[65],[67,24124,24125],{"xmlns":69},[71,24126,24127,24135],{},[74,24128,24129],{},[87,24130,24131,24133],{},[90,24132,21],{},[90,24134,776],{},[97,24136,24137],{"encoding":99},"a_t",[58,24139,24141],{"className":24140,"ariaHidden":105},[104],[58,24142,24144,24148],{"className":24143},[109],[58,24145],{"className":24146,"style":24147},[113],"height:0.5806em;vertical-align:-0.15em;",[58,24149,24151,24154],{"className":24150},[118],[58,24152,21],{"className":24153},[118,191],[58,24155,24157],{"className":24156},[195],[58,24158,24160,24181],{"className":24159},[130,131],[58,24161,24163,24178],{"className":24162},[135],[58,24164,24167],{"className":24165,"style":24166},[139],"height:0.2806em;",[58,24168,24169,24172],{"style":1250},[58,24170],{"className":24171,"style":539},[147],[58,24173,24175],{"className":24174},[152,153,154,155],[58,24176,776],{"className":24177},[118,191,155],[58,24179,226],{"className":24180},[225],[58,24182,24184],{"className":24183},[135],[58,24185,24187],{"className":24186,"style":1269},[139],[58,24188],{}," 一般表示 ",[58,24191,24193,24206],{"className":24192},[61],[58,24194,24196],{"className":24195},[65],[67,24197,24198],{"xmlns":69},[71,24199,24200,24204],{},[74,24201,24202],{},[90,24203,776],{},[97,24205,776],{"encoding":99},[58,24207,24209],{"className":24208,"ariaHidden":105},[104],[58,24210,24212,24216],{"className":24211},[109],[58,24213],{"className":24214,"style":24215},[113],"height:0.6151em;",[58,24217,776],{"className":24218},[118,191]," 时刻 Agent 采取的动作（action）；",[58,24221,24223,24242],{"className":24222},[61],[58,24224,24226],{"className":24225},[65],[67,24227,24228],{"xmlns":69},[71,24229,24230,24239],{},[74,24231,24232],{},[87,24233,24234,24237],{},[90,24235,24236],{},"s",[90,24238,776],{},[97,24240,24241],{"encoding":99},"s_t",[58,24243,24245],{"className":24244,"ariaHidden":105},[104],[58,24246,24248,24251],{"className":24247},[109],[58,24249],{"className":24250,"style":24147},[113],[58,24252,24254,24257],{"className":24253},[118],[58,24255,24236],{"className":24256},[118,191],[58,24258,24260],{"className":24259},[195],[58,24261,24263,24283],{"className":24262},[130,131],[58,24264,24266,24280],{"className":24265},[135],[58,24267,24269],{"className":24268,"style":24166},[139],[58,24270,24271,24274],{"style":1250},[58,24272],{"className":24273,"style":539},[147],[58,24275,24277],{"className":24276},[152,153,154,155],[58,24278,776],{"className":24279},[118,191,155],[58,24281,226],{"className":24282},[225],[58,24284,24286],{"className":24285},[135],[58,24287,24289],{"className":24288,"style":1269},[139],[58,24290],{}," 表示 ",[58,24293,24295,24308],{"className":24294},[61],[58,24296,24298],{"className":24297},[65],[67,24299,24300],{"xmlns":69},[71,24301,24302,24306],{},[74,24303,24304],{},[90,24305,776],{},[97,24307,776],{"encoding":99},[58,24309,24311],{"className":24310,"ariaHidden":105},[104],[58,24312,24314,24317],{"className":24313},[109],[58,24315],{"className":24316,"style":24215},[113],[58,24318,776],{"className":24319},[118,191]," 时刻 Agent 所处的状态（state）；",[58,24322,24324,24338],{"className":24323},[61],[58,24325,24327],{"className":24326},[65],[67,24328,24329],{"xmlns":69},[71,24330,24331,24335],{},[74,24332,24333],{},[90,24334,6741],{},[97,24336,24337],{"encoding":99},"\\pi",[58,24339,24341],{"className":24340,"ariaHidden":105},[104],[58,24342,24344,24347],{"className":24343},[109],[58,24345],{"className":24346,"style":346},[113],[58,24348,6741],{"className":24349,"style":440},[118,191]," 表示 Agent的策略函数（policy），输入状态，输入采取每个动作的概率分布 ",[58,24352,24354,24387],{"className":24353},[61],[58,24355,24357],{"className":24356},[65],[67,24358,24359],{"xmlns":69},[71,24360,24361,24384],{},[74,24362,24363,24365,24367,24373,24376,24382],{},[90,24364,6741],{},[460,24366,797],{"stretchy":796},[87,24368,24369,24371],{},[90,24370,21],{},[90,24372,776],{},[90,24374,24375],{"mathvariant":817},"∣",[87,24377,24378,24380],{},[90,24379,24236],{},[90,24381,776],{},[460,24383,811],{"stretchy":796},[97,24385,24386],{"encoding":99},"\\pi(a_t|s_t)",[58,24388,24390],{"className":24389,"ariaHidden":105},[104],[58,24391,24393,24396,24399,24402,24442,24445,24485],{"className":24392},[109],[58,24394],{"className":24395,"style":876},[113],[58,24397,6741],{"className":24398,"style":440},[118,191],[58,24400,797],{"className":24401},[122],[58,24403,24405,24408],{"className":24404},[118],[58,24406,21],{"className":24407},[118,191],[58,24409,24411],{"className":24410},[195],[58,24412,24414,24434],{"className":24413},[130,131],[58,24415,24417,24431],{"className":24416},[135],[58,24418,24420],{"className":24419,"style":24166},[139],[58,24421,24422,24425],{"style":1250},[58,24423],{"className":24424,"style":539},[147],[58,24426,24428],{"className":24427},[152,153,154,155],[58,24429,776],{"className":24430},[118,191,155],[58,24432,226],{"className":24433},[225],[58,24435,24437],{"className":24436},[135],[58,24438,24440],{"className":24439,"style":1269},[139],[58,24441],{},[58,24443,24375],{"className":24444},[118],[58,24446,24448,24451],{"className":24447},[118],[58,24449,24236],{"className":24450},[118,191],[58,24452,24454],{"className":24453},[195],[58,24455,24457,24477],{"className":24456},[130,131],[58,24458,24460,24474],{"className":24459},[135],[58,24461,24463],{"className":24462,"style":24166},[139],[58,24464,24465,24468],{"style":1250},[58,24466],{"className":24467,"style":539},[147],[58,24469,24471],{"className":24470},[152,153,154,155],[58,24472,776],{"className":24473},[118,191,155],[58,24475,226],{"className":24476},[225],[58,24478,24480],{"className":24479},[135],[58,24481,24483],{"className":24482,"style":1269},[139],[58,24484],{},[58,24486,811],{"className":24487},[312],"；",[58,24490,24492,24510],{"className":24491},[61],[58,24493,24495],{"className":24494},[65],[67,24496,24497],{"xmlns":69},[71,24498,24499,24507],{},[74,24500,24501],{},[87,24502,24503,24505],{},[90,24504,7825],{},[90,24506,776],{},[97,24508,24509],{"encoding":99},"r_t",[58,24511,24513],{"className":24512,"ariaHidden":105},[104],[58,24514,24516,24519],{"className":24515},[109],[58,24517],{"className":24518,"style":24147},[113],[58,24520,24522,24525],{"className":24521},[118],[58,24523,7825],{"className":24524,"style":3209},[118,191],[58,24526,24528],{"className":24527},[195],[58,24529,24531,24552],{"className":24530},[130,131],[58,24532,24534,24549],{"className":24533},[135],[58,24535,24537],{"className":24536,"style":24166},[139],[58,24538,24540,24543],{"style":24539},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[58,24541],{"className":24542,"style":539},[147],[58,24544,24546],{"className":24545},[152,153,154,155],[58,24547,776],{"className":24548},[118,191,155],[58,24550,226],{"className":24551},[225],[58,24553,24555],{"className":24554},[135],[58,24556,24558],{"className":24557,"style":1269},[139],[58,24559],{}," 一边表示 ",[58,24562,24564,24577],{"className":24563},[61],[58,24565,24567],{"className":24566},[65],[67,24568,24569],{"xmlns":69},[71,24570,24571,24575],{},[74,24572,24573],{},[90,24574,776],{},[97,24576,776],{"encoding":99},[58,24578,24580],{"className":24579,"ariaHidden":105},[104],[58,24581,24583,24586],{"className":24582},[109],[58,24584],{"className":24585,"style":24215},[113],[58,24587,776],{"className":24588},[118,191]," 时刻 Agent 采取行动获得的奖励（Reward）；",[58,24591,24593,24608],{"className":24592},[61],[58,24594,24596],{"className":24595},[65],[67,24597,24598],{"xmlns":69},[71,24599,24600,24605],{},[74,24601,24602],{},[90,24603,24604],{},"τ",[97,24606,24607],{"encoding":99},"\\tau",[58,24609,24611],{"className":24610,"ariaHidden":105},[104],[58,24612,24614,24617],{"className":24613},[109],[58,24615],{"className":24616,"style":346},[113],[58,24618,24604],{"className":24619,"style":24620},[118,191],"margin-right:0.1132em;"," 表示轨迹（Trajectory），Episode 指一次完整的交互过程：从环境开始，到终止结束。Rollout 指按某个策略实际“跑出来”的一段轨迹数据。它不一定非得是完整的一局，也可以只是中间截取的一段。",[14,24623,24624],{},[58,24625,24627,24682],{"className":24626},[61],[58,24628,24630],{"className":24629},[65],[67,24631,24632],{"xmlns":69},[71,24633,24634,24679],{},[74,24635,24636,24638,24644,24646,24652,24654,24660,24662,24668,24670,24677],{},[460,24637,797],{"stretchy":796},[87,24639,24640,24642],{},[90,24641,24236],{},[80,24643,1753],{},[460,24645,802],{"separator":105},[87,24647,24648,24650],{},[90,24649,21],{},[80,24651,1753],{},[460,24653,802],{"separator":105},[87,24655,24656,24658],{},[90,24657,24236],{},[80,24659,82],{},[460,24661,802],{"separator":105},[87,24663,24664,24666],{},[90,24665,21],{},[80,24667,82],{},[460,24669,2969],{},[87,24671,24672,24674],{},[90,24673,24236],{},[90,24675,24676],{},"T",[460,24678,811],{"stretchy":796},[97,24680,24681],{"encoding":99},"(s_0,a_0,s_1,a_1 \\dots s_T)",[58,24683,24685],{"className":24684,"ariaHidden":105},[104],[58,24686,24688,24691,24694,24734,24737,24740,24780,24783,24786,24826,24829,24832,24872,24875,24878,24881,24922],{"className":24687},[109],[58,24689],{"className":24690,"style":876},[113],[58,24692,797],{"className":24693},[122],[58,24695,24697,24700],{"className":24696},[118],[58,24698,24236],{"className":24699},[118,191],[58,24701,24703],{"className":24702},[195],[58,24704,24706,24726],{"className":24705},[130,131],[58,24707,24709,24723],{"className":24708},[135],[58,24710,24712],{"className":24711,"style":3090},[139],[58,24713,24714,24717],{"style":1250},[58,24715],{"className":24716,"style":539},[147],[58,24718,24720],{"className":24719},[152,153,154,155],[58,24721,1753],{"className":24722},[118,155],[58,24724,226],{"className":24725},[225],[58,24727,24729],{"className":24728},[135],[58,24730,24732],{"className":24731,"style":1269},[139],[58,24733],{},[58,24735,802],{"className":24736},[911],[58,24738],{"className":24739,"style":915},[498],[58,24741,24743,24746],{"className":24742},[118],[58,24744,21],{"className":24745},[118,191],[58,24747,24749],{"className":24748},[195],[58,24750,24752,24772],{"className":24751},[130,131],[58,24753,24755,24769],{"className":24754},[135],[58,24756,24758],{"className":24757,"style":3090},[139],[58,24759,24760,24763],{"style":1250},[58,24761],{"className":24762,"style":539},[147],[58,24764,24766],{"className":24765},[152,153,154,155],[58,24767,1753],{"className":24768},[118,155],[58,24770,226],{"className":24771},[225],[58,24773,24775],{"className":24774},[135],[58,24776,24778],{"className":24777,"style":1269},[139],[58,24779],{},[58,24781,802],{"className":24782},[911],[58,24784],{"className":24785,"style":915},[498],[58,24787,24789,24792],{"className":24788},[118],[58,24790,24236],{"className":24791},[118,191],[58,24793,24795],{"className":24794},[195],[58,24796,24798,24818],{"className":24797},[130,131],[58,24799,24801,24815],{"className":24800},[135],[58,24802,24804],{"className":24803,"style":3090},[139],[58,24805,24806,24809],{"style":1250},[58,24807],{"className":24808,"style":539},[147],[58,24810,24812],{"className":24811},[152,153,154,155],[58,24813,82],{"className":24814},[118,155],[58,24816,226],{"className":24817},[225],[58,24819,24821],{"className":24820},[135],[58,24822,24824],{"className":24823,"style":1269},[139],[58,24825],{},[58,24827,802],{"className":24828},[911],[58,24830],{"className":24831,"style":915},[498],[58,24833,24835,24838],{"className":24834},[118],[58,24836,21],{"className":24837},[118,191],[58,24839,24841],{"className":24840},[195],[58,24842,24844,24864],{"className":24843},[130,131],[58,24845,24847,24861],{"className":24846},[135],[58,24848,24850],{"className":24849,"style":3090},[139],[58,24851,24852,24855],{"style":1250},[58,24853],{"className":24854,"style":539},[147],[58,24856,24858],{"className":24857},[152,153,154,155],[58,24859,82],{"className":24860},[118,155],[58,24862,226],{"className":24863},[225],[58,24865,24867],{"className":24866},[135],[58,24868,24870],{"className":24869,"style":1269},[139],[58,24871],{},[58,24873],{"className":24874,"style":915},[498],[58,24876,2969],{"className":24877},[961],[58,24879],{"className":24880,"style":915},[498],[58,24882,24884,24887],{"className":24883},[118],[58,24885,24236],{"className":24886},[118,191],[58,24888,24890],{"className":24889},[195],[58,24891,24893,24914],{"className":24892},[130,131],[58,24894,24896,24911],{"className":24895},[135],[58,24897,24900],{"className":24898,"style":24899},[139],"height:0.3283em;",[58,24901,24902,24905],{"style":1250},[58,24903],{"className":24904,"style":539},[147],[58,24906,24908],{"className":24907},[152,153,154,155],[58,24909,24676],{"className":24910,"style":3184},[118,191,155],[58,24912,226],{"className":24913},[225],[58,24915,24917],{"className":24916},[135],[58,24918,24920],{"className":24919,"style":1269},[139],[58,24921],{},[58,24923,811],{"className":24924},[312],[14,24926,24927,25146,25147,313],{},[58,24928,24930,24976],{"className":24929},[61],[58,24931,24933],{"className":24932},[65],[67,24934,24935],{"xmlns":69},[71,24936,24937,24973],{},[74,24938,24939,24951,24953,24955,24957,24963,24965,24971],{},[87,24940,24941,24943],{},[90,24942,24236],{},[74,24944,24945,24947,24949],{},[90,24946,776],{},[460,24948,5776],{},[80,24950,82],{},[460,24952,814],{},[90,24954,11656],{},[460,24956,797],{"stretchy":796},[87,24958,24959,24961],{},[90,24960,24236],{},[90,24962,776],{},[460,24964,802],{"separator":105},[87,24966,24967,24969],{},[90,24968,21],{},[90,24970,776],{},[460,24972,811],{"stretchy":796},[97,24974,24975],{"encoding":99}," s_{t+1} = f(s_t,a_t)",[58,24977,24979,25044],{"className":24978,"ariaHidden":105},[104],[58,24980,24982,24986,25035,25038,25041],{"className":24981},[109],[58,24983],{"className":24984,"style":24985},[113],"height:0.6389em;vertical-align:-0.2083em;",[58,24987,24989,24992],{"className":24988},[118],[58,24990,24236],{"className":24991},[118,191],[58,24993,24995],{"className":24994},[195],[58,24996,24998,25027],{"className":24997},[130,131],[58,24999,25001,25024],{"className":25000},[135],[58,25002,25004],{"className":25003,"style":3090},[139],[58,25005,25006,25009],{"style":1250},[58,25007],{"className":25008,"style":539},[147],[58,25010,25012],{"className":25011},[152,153,154,155],[58,25013,25015,25018,25021],{"className":25014},[118,155],[58,25016,776],{"className":25017},[118,191,155],[58,25019,5776],{"className":25020},[552,155],[58,25022,82],{"className":25023},[118,155],[58,25025,226],{"className":25026},[225],[58,25028,25030],{"className":25029},[135],[58,25031,25033],{"className":25032,"style":6937},[139],[58,25034],{},[58,25036],{"className":25037,"style":499},[498],[58,25039,814],{"className":25040},[503],[58,25042],{"className":25043,"style":499},[498],[58,25045,25047,25050,25054,25057,25097,25100,25103,25143],{"className":25046},[109],[58,25048],{"className":25049,"style":876},[113],[58,25051,11656],{"className":25052,"style":25053},[118,191],"margin-right:0.10764em;",[58,25055,797],{"className":25056},[122],[58,25058,25060,25063],{"className":25059},[118],[58,25061,24236],{"className":25062},[118,191],[58,25064,25066],{"className":25065},[195],[58,25067,25069,25089],{"className":25068},[130,131],[58,25070,25072,25086],{"className":25071},[135],[58,25073,25075],{"className":25074,"style":24166},[139],[58,25076,25077,25080],{"style":1250},[58,25078],{"className":25079,"style":539},[147],[58,25081,25083],{"className":25082},[152,153,154,155],[58,25084,776],{"className":25085},[118,191,155],[58,25087,226],{"className":25088},[225],[58,25090,25092],{"className":25091},[135],[58,25093,25095],{"className":25094,"style":1269},[139],[58,25096],{},[58,25098,802],{"className":25099},[911],[58,25101],{"className":25102,"style":915},[498],[58,25104,25106,25109],{"className":25105},[118],[58,25107,21],{"className":25108},[118,191],[58,25110,25112],{"className":25111},[195],[58,25113,25115,25135],{"className":25114},[130,131],[58,25116,25118,25132],{"className":25117},[135],[58,25119,25121],{"className":25120,"style":24166},[139],[58,25122,25123,25126],{"style":1250},[58,25124],{"className":25125,"style":539},[147],[58,25127,25129],{"className":25128},[152,153,154,155],[58,25130,776],{"className":25131},[118,191,155],[58,25133,226],{"className":25134},[225],[58,25136,25138],{"className":25137},[135],[58,25139,25141],{"className":25140,"style":1269},[139],[58,25142],{},[58,25144,811],{"className":25145},[312]," 或者 ",[58,25148,25150,25200],{"className":25149},[61],[58,25151,25153],{"className":25152},[65],[67,25154,25155],{"xmlns":69},[71,25156,25157,25197],{},[74,25158,25159,25171,25173,25175,25177,25179,25181,25187,25189,25195],{},[87,25160,25161,25163],{},[90,25162,24236],{},[74,25164,25165,25167,25169],{},[90,25166,776],{},[460,25168,5776],{},[80,25170,82],{},[460,25172,814],{},[90,25174,5603],{},[460,25176,797],{"stretchy":796},[460,25178,1815],{},[90,25180,24375],{"mathvariant":817},[87,25182,25183,25185],{},[90,25184,24236],{},[90,25186,776],{},[460,25188,802],{"separator":105},[87,25190,25191,25193],{},[90,25192,21],{},[90,25194,776],{},[460,25196,811],{"stretchy":796},[97,25198,25199],{"encoding":99},"s_{t+1} = P(\\cdot|s_t,a_t)",[58,25201,25203,25267],{"className":25202,"ariaHidden":105},[104],[58,25204,25206,25209,25258,25261,25264],{"className":25205},[109],[58,25207],{"className":25208,"style":24985},[113],[58,25210,25212,25215],{"className":25211},[118],[58,25213,24236],{"className":25214},[118,191],[58,25216,25218],{"className":25217},[195],[58,25219,25221,25250],{"className":25220},[130,131],[58,25222,25224,25247],{"className":25223},[135],[58,25225,25227],{"className":25226,"style":3090},[139],[58,25228,25229,25232],{"style":1250},[58,25230],{"className":25231,"style":539},[147],[58,25233,25235],{"className":25234},[152,153,154,155],[58,25236,25238,25241,25244],{"className":25237},[118,155],[58,25239,776],{"className":25240},[118,191,155],[58,25242,5776],{"className":25243},[552,155],[58,25245,82],{"className":25246},[118,155],[58,25248,226],{"className":25249},[225],[58,25251,25253],{"className":25252},[135],[58,25254,25256],{"className":25255,"style":6937},[139],[58,25257],{},[58,25259],{"className":25260,"style":499},[498],[58,25262,814],{"className":25263},[503],[58,25265],{"className":25266,"style":499},[498],[58,25268,25270,25273,25276,25279,25282,25285,25325,25328,25331,25371],{"className":25269},[109],[58,25271],{"className":25272,"style":876},[113],[58,25274,5603],{"className":25275,"style":3184},[118,191],[58,25277,797],{"className":25278},[122],[58,25280,1815],{"className":25281},[118],[58,25283,24375],{"className":25284},[118],[58,25286,25288,25291],{"className":25287},[118],[58,25289,24236],{"className":25290},[118,191],[58,25292,25294],{"className":25293},[195],[58,25295,25297,25317],{"className":25296},[130,131],[58,25298,25300,25314],{"className":25299},[135],[58,25301,25303],{"className":25302,"style":24166},[139],[58,25304,25305,25308],{"style":1250},[58,25306],{"className":25307,"style":539},[147],[58,25309,25311],{"className":25310},[152,153,154,155],[58,25312,776],{"className":25313},[118,191,155],[58,25315,226],{"className":25316},[225],[58,25318,25320],{"className":25319},[135],[58,25321,25323],{"className":25322,"style":1269},[139],[58,25324],{},[58,25326,802],{"className":25327},[911],[58,25329],{"className":25330,"style":915},[498],[58,25332,25334,25337],{"className":25333},[118],[58,25335,21],{"className":25336},[118,191],[58,25338,25340],{"className":25339},[195],[58,25341,25343,25363],{"className":25342},[130,131],[58,25344,25346,25360],{"className":25345},[135],[58,25347,25349],{"className":25348,"style":24166},[139],[58,25350,25351,25354],{"style":1250},[58,25352],{"className":25353,"style":539},[147],[58,25355,25357],{"className":25356},[152,153,154,155],[58,25358,776],{"className":25359},[118,191,155],[58,25361,226],{"className":25362},[225],[58,25364,25366],{"className":25365},[135],[58,25367,25369],{"className":25368,"style":1269},[139],[58,25370],{},[58,25372,811],{"className":25373},[312],[14,25375,25376],{},"Return 一般表示回报，指从当前时间点到游戏结束时奖励的累积和或者加权累积和。",[10,25378,25379],{"id":25379},"训练目标",[14,25381,25382,25383,25411,25412,25441],{},"训练一个 Policy 神经网络 ",[58,25384,25386,25399],{"className":25385},[61],[58,25387,25389],{"className":25388},[65],[67,25390,25391],{"xmlns":69},[71,25392,25393,25397],{},[74,25394,25395],{},[90,25396,6741],{},[97,25398,24337],{"encoding":99},[58,25400,25402],{"className":25401,"ariaHidden":105},[104],[58,25403,25405,25408],{"className":25404},[109],[58,25406],{"className":25407,"style":346},[113],[58,25409,6741],{"className":25410,"style":440},[118,191],"，在所有状态 ",[58,25413,25415,25428],{"className":25414},[61],[58,25416,25418],{"className":25417},[65],[67,25419,25420],{"xmlns":69},[71,25421,25422,25426],{},[74,25423,25424],{},[90,25425,7844],{},[97,25427,7844],{"encoding":99},[58,25429,25431],{"className":25430,"ariaHidden":105},[104],[58,25432,25434,25438],{"className":25433},[109],[58,25435],{"className":25436,"style":25437},[113],"height:0.6833em;",[58,25439,7844],{"className":25440,"style":6049},[118,191]," 下，给出相应的 Action，得到的 Return 的期望最大。",[14,25443,25444],{},[58,25445,25447,25524],{"className":25446},[61],[58,25448,25450],{"className":25449},[65],[67,25451,25452],{"xmlns":69},[71,25453,25454,25521],{},[74,25455,25456,25458,25460,25462,25464,25466,25468,25492,25494,25501,25503,25505,25507,25509,25515,25517,25519],{},[90,25457,5606],{},[460,25459,797],{"stretchy":796},[90,25461,469],{},[460,25463,797],{"stretchy":796},[90,25465,24604],{},[460,25467,811],{"stretchy":796},[87,25469,25470,25472],{},[460,25471,811],{"stretchy":796},[74,25473,25474,25476,25479,25486,25488,25490],{},[90,25475,24604],{},[460,25477,25478],{},"∼",[87,25480,25481,25483],{},[90,25482,5603],{},[90,25484,25485],{},"θ",[460,25487,797],{"stretchy":796},[90,25489,24604],{},[460,25491,811],{"stretchy":796},[460,25493,814],{},[25495,25496,25497,25499],"munder",{},[460,25498,1825],{},[90,25500,24604],{},[90,25502,469],{},[460,25504,797],{"stretchy":796},[90,25506,24604],{},[460,25508,811],{"stretchy":796},[87,25510,25511,25513],{},[90,25512,5603],{},[90,25514,25485],{},[460,25516,797],{"stretchy":796},[90,25518,24604],{},[460,25520,811],{"stretchy":796},[97,25522,25523],{"encoding":99}," E (R(\\tau))_{\\tau \\sim P_{\\theta}(\\tau)} = \\sum\\limits_\\tau R(\\tau)P_\\theta(\\tau)",[58,25525,25527,25662],{"className":25526,"ariaHidden":105},[104],[58,25528,25530,25534,25537,25540,25544,25547,25550,25553,25653,25656,25659],{"className":25529},[109],[58,25531],{"className":25532,"style":25533},[113],"height:1.1052em;vertical-align:-0.3552em;",[58,25535,5606],{"className":25536,"style":6049},[118,191],[58,25538,797],{"className":25539},[122],[58,25541,469],{"className":25542,"style":25543},[118,191],"margin-right:0.00773em;",[58,25545,797],{"className":25546},[122],[58,25548,24604],{"className":25549,"style":24620},[118,191],[58,25551,811],{"className":25552},[312],[58,25554,25556,25559],{"className":25555},[312],[58,25557,811],{"className":25558},[312],[58,25560,25562],{"className":25561},[195],[58,25563,25565,25645],{"className":25564},[130,131],[58,25566,25568,25642],{"className":25567},[135],[58,25569,25571],{"className":25570,"style":205},[139],[58,25572,25574,25577],{"style":25573},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[58,25575],{"className":25576,"style":539},[147],[58,25578,25580],{"className":25579},[152,153,154,155],[58,25581,25583,25586,25589,25633,25636,25639],{"className":25582},[118,155],[58,25584,24604],{"className":25585,"style":24620},[118,191,155],[58,25587,25478],{"className":25588},[503,155],[58,25590,25592,25595],{"className":25591},[118,155],[58,25593,5603],{"className":25594,"style":3184},[118,191,155],[58,25596,25598],{"className":25597},[195],[58,25599,25601,25625],{"className":25600},[130,131],[58,25602,25604,25622],{"className":25603},[135],[58,25605,25607],{"className":25606,"style":205},[139],[58,25608,25610,25613],{"style":25609},"top:-2.3488em;margin-left:-0.1389em;margin-right:0.0714em;",[58,25611],{"className":25612,"style":212},[147],[58,25614,25616],{"className":25615},[152,216,217,155],[58,25617,25619],{"className":25618},[118,155],[58,25620,25485],{"className":25621,"style":3209},[118,191,155],[58,25623,226],{"className":25624},[225],[58,25626,25628],{"className":25627},[135],[58,25629,25631],{"className":25630,"style":233},[139],[58,25632],{},[58,25634,797],{"className":25635},[122,155],[58,25637,24604],{"className":25638,"style":24620},[118,191,155],[58,25640,811],{"className":25641},[312,155],[58,25643,226],{"className":25644},[225],[58,25646,25648],{"className":25647},[135],[58,25649,25651],{"className":25650,"style":6101},[139],[58,25652],{},[58,25654],{"className":25655,"style":499},[498],[58,25657,814],{"className":25658},[503],[58,25660],{"className":25661,"style":499},[498],[58,25663,25665,25669,25717,25720,25723,25726,25729,25732,25772,25775,25778],{"className":25664},[109],[58,25666],{"className":25667,"style":25668},[113],"height:1.7em;vertical-align:-0.95em;",[58,25670,25673],{"className":25671},[950,25672],"op-limits",[58,25674,25676,25708],{"className":25675},[130,131],[58,25677,25679,25705],{"className":25678},[135],[58,25680,25683,25695],{"className":25681,"style":25682},[139],"height:0.75em;",[58,25684,25686,25689],{"style":25685},"top:-2.15em;margin-left:0em;",[58,25687],{"className":25688,"style":148},[147],[58,25690,25692],{"className":25691},[152,153,154,155],[58,25693,24604],{"className":25694,"style":24620},[118,191,155],[58,25696,25697,25700],{"style":177},[58,25698],{"className":25699,"style":148},[147],[58,25701,25702],{},[58,25703,1825],{"className":25704},[950,1909,1910],[58,25706,226],{"className":25707},[225],[58,25709,25711],{"className":25710},[135],[58,25712,25715],{"className":25713,"style":25714},[139],"height:0.95em;",[58,25716],{},[58,25718],{"className":25719,"style":915},[498],[58,25721,469],{"className":25722,"style":25543},[118,191],[58,25724,797],{"className":25725},[122],[58,25727,24604],{"className":25728,"style":24620},[118,191],[58,25730,811],{"className":25731},[312],[58,25733,25735,25738],{"className":25734},[118],[58,25736,5603],{"className":25737,"style":3184},[118,191],[58,25739,25741],{"className":25740},[195],[58,25742,25744,25764],{"className":25743},[130,131],[58,25745,25747,25761],{"className":25746},[135],[58,25748,25750],{"className":25749,"style":1247},[139],[58,25751,25752,25755],{"style":7459},[58,25753],{"className":25754,"style":539},[147],[58,25756,25758],{"className":25757},[152,153,154,155],[58,25759,25485],{"className":25760,"style":3209},[118,191,155],[58,25762,226],{"className":25763},[225],[58,25765,25767],{"className":25766},[135],[58,25768,25770],{"className":25769,"style":1269},[139],[58,25771],{},[58,25773,797],{"className":25774},[122],[58,25776,24604],{"className":25777,"style":24620},[118,191],[58,25779,811],{"className":25780},[312],[58,25782,25785],{"className":25783},[25784],"katex-display",[58,25786,25788,26568],{"className":25787},[61],[58,25789,25791],{"className":25790},[65],[67,25792,25793],{"xmlns":69,"display":9480},[71,25794,25795,26565],{},[25796,25797,25801,25887,25933,26013,26091,26185,26258,26361,26463],"mtable",{"rowspacing":25798,"columnalign":25799,"columnspacing":25800},"0.25em","right 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,[25808,26144,26145],{"scriptlevel":1753,"displaystyle":105},[77,26146,26147,26167],{},[74,26148,26149,26151,26157,26159,26165],{},[90,26150,25814],{"mathvariant":817},[87,26152,26153,26155],{},[90,26154,14],{},[90,26156,25485],{},[460,26158,797],{"stretchy":796},[464,26160,26161,26163],{},[90,26162,24604],{},[90,26164,334],{},[460,26166,811],{"stretchy":796},[74,26168,26169,26175,26177,26183],{},[87,26170,26171,26173],{},[90,26172,5603],{},[90,26174,25485],{},[460,26176,797],{"stretchy":796},[464,26178,26179,26181],{},[90,26180,24604],{},[90,26182,334],{},[460,26184,811],{"stretchy":796},[25802,26186,26187,26193],{},[25805,26188,26189],{},[25808,26190,26191],{"scriptlevel":1753,"displaystyle":105},[74,26192],{},[25805,26194,26195],{},[25808,26196,26197],{"scriptlevel":1753,"displaystyle":105},[74,26198,26199,26201,26203,26209,26223,26225,26227,26233,26235,26237,26240,26242,26248,26250,26256],{},[74,26200],{},[460,26202,814],{},[77,26204,26205,26207],{},[80,26206,82],{},[90,26208,7321],{},[26117,26210,26211,26213,26221],{},[460,26212,1825],{},[74,26214,26215,26217,26219],{},[90,26216,334],{},[460,26218,814],{},[80,26220,82],{},[90,26222,7321],{},[90,26224,469],{},[460,26226,797],{"stretchy":796},[464,26228,26229,26231],{},[90,26230,24604],{},[90,26232,334],{},[460,26234,811],{"stretchy":796},[90,26236,25814],{"mathvariant":817},[90,26238,26239],{},"log",[460,26241,821],{},[87,26243,26244,26246],{},[90,26245,5603],{},[90,26247,25485],{},[460,26249,797],{"stretchy":796},[464,26251,26252,26254],{},[90,26253,24604],{},[90,26255,334],{},[460,26257,811],{"stretchy":796},[25802,26259,26260,26266],{},[25805,26261,26262],{},[25808,26263,26264],{"scriptlevel":1753,"displaystyle":105},[74,26265],{},[25805,26267,26268],{},[25808,26269,26270],{"scriptlevel":1753,"displaystyle":105},[74,26271,26272,26274,26276,26282,26296,26298,26300,26306,26308,26310,26312,26314,26333,26339,26341,26349,26351,26359],{},[74,26273],{},[460,26275,814],{},[77,26277,26278,26280],{},[80,26279,82],{},[90,26281,7321],{},[26117,26283,26284,26286,26294],{},[460,26285,1825],{},[74,26287,26288,26290,26292],{},[90,26289,334],{},[460,26291,814],{},[80,26293,82],{},[90,26295,7321],{},[90,26297,469],{},[460,26299,797],{"stretchy":796},[464,26301,26302,26304],{},[90,26303,24604],{},[90,26305,334],{},[460,26307,811],{"stretchy":796},[90,26309,25814],{"mathvariant":817},[90,26311,26239],{},[460,26313,821],{},[26117,26315,26316,26319,26327],{},[460,26317,26318],{},"∏",[74,26320,26321,26323,26325],{},[90,26322,776],{},[460,26324,814],{},[80,26326,82],{},[87,26328,26329,26331],{},[90,26330,24676],{},[90,26332,334],{},[87,26334,26335,26337],{},[90,26336,5603],{},[90,26338,25485],{},[460,26340,797],{"stretchy":796},[1821,26342,26343,26345,26347],{},[90,26344,21],{},[90,26346,334],{},[90,26348,776],{},[90,26350,24375],{"mathvariant":817},[1821,26352,26353,26355,26357],{},[90,26354,24236],{},[90,26356,334],{},[90,26358,776],{},[460,26360,811],{"stretchy":796},[25802,26362,26363,26369],{},[25805,26364,26365],{},[25808,26366,26367],{"scriptlevel":1753,"displaystyle":105},[74,26368],{},[25805,26370,26371],{},[25808,26372,26373],{"scriptlevel":1753,"displaystyle":105},[74,26374,26375,26377,26379,26385,26399,26401,26403,26409,26411,26429,26431,26433,26435,26441,26443,26451,26453,26461],{},[74,26376],{},[460,26378,814],{},[77,26380,26381,26383],{},[80,26382,82],{},[90,26384,7321],{},[26117,26386,26387,26389,26397],{},[460,26388,1825],{},[74,26390,26391,26393,26395],{},[90,26392,334],{},[460,26394,814],{},[80,26396,82],{},[90,26398,7321],{},[90,26400,469],{},[460,26402,797],{"stretchy":796},[464,26404,26405,26407],{},[90,26406,24604],{},[90,26408,334],{},[460,26410,811],{"stretchy":796},[26117,26412,26413,26415,26423],{},[460,26414,1825],{},[74,26416,26417,26419,26421],{},[90,26418,776],{},[460,26420,814],{},[80,26422,82],{},[87,26424,26425,26427],{},[90,26426,24676],{},[90,26428,334],{},[90,26430,25814],{"mathvariant":817},[90,26432,26239],{},[460,26434,821],{},[87,26436,26437,26439],{},[90,26438,5603],{},[90,26440,25485],{},[460,26442,797],{"stretchy":796},[1821,26444,26445,26447,26449],{},[90,26446,21],{},[90,26448,334],{},[90,26450,776],{},[90,26452,24375],{"mathvariant":817},[1821,26454,26455,26457,26459],{},[90,26456,24236],{},[90,26458,334],{},[90,26460,776],{},[460,26462,811],{"stretchy":796},[25802,26464,26465,26471],{},[25805,26466,26467],{},[25808,26468,26469],{"scriptlevel":1753,"displaystyle":105},[74,26470],{},[25805,26472,26473],{},[25808,26474,26475],{"scriptlevel":1753,"displaystyle":105},[74,26476,26477,26479,26481,26487,26501,26519,26521,26523,26529,26531,26533,26535,26537,26543,26545,26553,26555,26563],{},[74,26478],{},[460,26480,814],{},[77,26482,26483,26485],{},[80,26484,82],{},[90,26486,7321],{},[26117,26488,26489,26491,26499],{},[460,26490,1825],{},[74,26492,26493,26495,26497],{},[90,26494,334],{},[460,26496,814],{},[80,26498,82],{},[90,26500,7321],{},[26117,26502,26503,26505,26513],{},[460,26504,1825],{},[74,26506,26507,26509,26511],{},[90,26508,776],{},[460,26510,814],{},[80,26512,82],{},[87,26514,26515,26517],{},[90,26516,24676],{},[90,26518,334],{},[90,26520,469],{},[460,26522,797],{"stretchy":796},[464,26524,26525,26527],{},[90,26526,24604],{},[90,26528,334],{},[460,26530,811],{"stretchy":796},[90,26532,25814],{"mathvariant":817},[90,26534,26239],{},[460,26536,821],{},[87,26538,26539,26541],{},[90,26540,5603],{},[90,26542,25485],{},[460,26544,797],{"stretchy":796},[1821,26546,26547,26549,26551],{},[90,26548,21],{},[90,26550,334],{},[90,26552,776],{},[90,26554,24375],{"mathvariant":817},[1821,26556,26557,26559,26561],{},[90,26558,24236],{},[90,26560,334],{},[90,26562,776],{},[460,26564,811],{"stretchy":796},[97,26566,26567],{"encoding":99},"\\begin{aligned}\n\\nabla E(R(\\tau))_{\\tau \\sim P_\\theta(\\tau)} &= \\nabla \\sum_\\tau R(\\tau)P_\\theta(\\tau)\\\\\n&= \\sum_\\tau R(\\tau)\\nabla P_\\theta(\\tau)\\\\\n&= \\sum_\\tau R(\\tau)\\nabla P_\\theta(\\tau) \\cdot \\dfrac{P_\\theta(\\tau)}{P_\\theta(\\tau)}\\\\\n&= \\sum_\\tau P_\\theta(\\tau)R(\\tau) \\dfrac{\\nabla P_\\theta(\\tau)}{P_\\theta(\\tau)}\\\\\n&\\approx \\frac{1}{N}\\sum\\limits_{n=1}^N R(\\tau^n)\\dfrac{\\nabla p_\\theta(\\tau^n)}{P_\\theta(\\tau^n)}\\\\\n&= \\frac{1}{N}\\sum\\limits_{n=1}^N R(\\tau^n)\\nabla \\log P_\\theta(\\tau^n)\\\\\n&= \\frac{1}{N}\\sum\\limits_{n=1}^N R(\\tau^n)\\nabla \\log \\prod\\limits_{t=1}^{T_n}P_\\theta(a_n^t|s_n^t)\\\\\n&= \\frac{1}{N}\\sum\\limits_{n=1}^N R(\\tau^n)\\sum\\limits_{t=1}^{T_n}\\nabla \\log P_\\theta(a_n^t|s_n^t)\\\\\n&= \\frac{1}{N}\\sum\\limits_{n=1}^N \\sum\\limits_{t=1}^{T_n} R(\\tau^n)\\nabla \\log P_\\theta(a_n^t|s_n^t)\\\\\n\\end{aligned}",[58,26569,26571],{"className":26570,"ariaHidden":105},[104],[58,26572,26574,26578],{"className":26573},[109],[58,26575],{"className":26576,"style":26577},[113],"height:28.1646em;vertical-align:-13.8323em;",[58,26579,26581],{"className":26580},[118],[58,26582,26584,26808],{"className":26583},[25796],[58,26585,26588],{"className":26586},[26587],"col-align-r",[58,26589,26591,26799],{"className":26590},[130,131],[58,26592,26594,26796],{"className":26593},[135],[58,26595,26598,26724,26733,26742,26751,26760,26769,26778,26787],{"className":26596,"style":26597},[139],"height:14.3323em;",[58,26599,26601,26605],{"style":26600},"top:-17.1217em;",[58,26602],{"className":26603,"style":26604},[147],"height:3.8394em;",[58,26606,26608,26611,26614,26617,26620,26623,26626,26629],{"className":26607},[118],[58,26609,25814],{"className":26610},[118],[58,26612,5606],{"className":26613,"style":6049},[118,191],[58,26615,797],{"className":26616},[122],[58,26618,469],{"className":26619,"style":25543},[118,191],[58,26621,797],{"className":26622},[122],[58,26624,24604],{"className":26625,"style":24620},[118,191],[58,26627,811],{"className":26628},[312],[58,26630,26632,26635],{"className":26631},[312],[58,26633,811],{"className":26634},[312],[58,26636,26638],{"className":26637},[195],[58,26639,26641,26716],{"className":26640},[130,131],[58,26642,26644,26713],{"className":26643},[135],[58,26645,26647],{"className":26646,"style":205},[139],[58,26648,26649,26652],{"style":25573},[58,26650],{"className":26651,"style":539},[147],[58,26653,26655],{"className":26654},[152,153,154,155],[58,26656,26658,26661,26664,26704,26707,26710],{"className":26657},[118,155],[58,26659,24604],{"className":26660,"style":24620},[118,191,155],[58,26662,25478],{"className":26663},[503,155],[58,26665,26667,26670],{"className":26666},[118,155],[58,26668,5603],{"className":26669,"style":3184},[118,191,155],[58,26671,26673],{"className":26672},[195],[58,26674,26676,26696],{"className":26675},[130,131],[58,26677,26679,26693],{"className":26678},[135],[58,26680,26682],{"className":26681,"style":205},[139],[58,26683,26684,26687],{"style":25609},[58,26685],{"className":26686,"style":212},[147],[58,26688,26690],{"className":26689},[152,216,217,155],[58,26691,25485],{"className":26692,"style":3209},[118,191,155],[58,26694,226],{"className":26695},[225],[58,26697,26699],{"className":26698},[135],[58,26700,26702],{"className":26701,"style":233},[139],[58,26703],{},[58,26705,797],{"className":26706},[122,155],[58,26708,24604],{"className":26709,"style":24620},[118,191,155],[58,26711,811],{"className":26712},[312,155],[58,26714,226],{"className":26715},[225],[58,26717,26719],{"className":26718},[135],[58,26720,26722],{"className":26721,"style":6101},[139],[58,26723],{},[58,26725,26727,26730],{"style":26726},"top:-14.5217em;",[58,26728],{"className":26729,"style":26604},[147],[58,26731],{"className":26732},[118],[58,26734,26736,26739],{"style":26735},"top:-11.5447em;",[58,26737],{"className":26738,"style":26604},[147],[58,26740],{"className":26741},[118],[58,26743,26745,26748],{"style":26744},"top:-8.5677em;",[58,26746],{"className":26747,"style":26604},[147],[58,26749],{"className":26750},[118],[58,26752,26754,26757],{"style":26753},"top:-5.1894em;",[58,26755],{"className":26756,"style":26604},[147],[58,26758],{"className":26759},[118],[58,26761,26763,26766],{"style":26762},"top:-1.7939em;",[58,26764],{"className":26765,"style":26604},[147],[58,26767],{"className":26768},[118],[58,26770,26772,26775],{"style":26771},"top:1.6126em;",[58,26773],{"className":26774,"style":26604},[147],[58,26776],{"className":26777},[118],[58,26779,26781,26784],{"style":26780},"top:5.0192em;",[58,26782],{"className":26783,"style":26604},[147],[58,26785],{"className":26786},[118],[58,26788,26790,26793],{"style":26789},"top:8.4257em;",[58,26791],{"className":26792,"style":26604},[147],[58,26794],{"className":26795},[118],[58,26797,226],{"className":26798},[225],[58,26800,26802],{"className":26801},[135],[58,26803,26806],{"className":26804,"style":26805},[139],"height:13.8323em;",[58,26807],{},[58,26809,26812],{"className":26810},[26811],"col-align-l",[58,26813,26815,29765],{"className":26814},[130,131],[58,26816,26818,29762],{"className":26817},[135],[58,26819,26821,26961,27092,27390,27675,28085,28367,28835,29300],{"className":26820,"style":26597},[139],[58,26822,26823,26826],{"style":26600},[58,26824],{"className":26825,"style":26604},[147],[58,26827,26829,26832,26835,26838,26841,26844,26847,26897,26900,26903,26906,26909,26912,26952,26955,26958],{"className":26828},[118],[58,26830],{"className":26831},[118],[58,26833],{"className":26834,"style":499},[498],[58,26836,814],{"className":26837},[503],[58,26839],{"className":26840,"style":499},[498],[58,26842,25814],{"className":26843},[118],[58,26845],{"className":26846,"style":915},[498],[58,26848,26850],{"className":26849},[950,25672],[58,26851,26853,26888],{"className":26852},[130,131],[58,26854,26856,26885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演员-评论家算法",[14,30898,30899,30900,30971],{},"为了衡量每个动作的相对好坏的情况，我们令奖励 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减去一个基准值。",[14,30973,30974],{},[58,30975,30977,31090],{"className":30976},[61],[58,30978,30980],{"className":30979},[65],[67,30981,30982],{"xmlns":69},[71,30983,30984,31087],{},[74,30985,30986,30992,31006,31024,31026,31034,31036,31039,31041,31049,31051,31053,31055,31057,31059,31065,31067,31075,31077,31085],{},[77,30987,30988,30990],{},[80,30989,82],{},[90,30991,7321],{},[1821,30993,30994,30996,31004],{},[460,30995,1825],{},[74,30997,30998,31000,31002],{},[90,30999,334],{},[460,31001,814],{},[80,31003,82],{},[90,31005,7321],{},[1821,31007,31008,31010,31018],{},[460,31009,1825],{},[74,31011,31012,31014,31016],{},[90,31013,776],{},[460,31015,814],{},[80,31017,82],{},[87,31019,31020,31022],{},[90,31021,24676],{},[90,31023,334],{},[460,31025,797],{"stretchy":796},[1821,31027,31028,31030,31032],{},[90,31029,469],{},[90,31031,776],{},[90,31033,334],{},[460,31035,29799],{},[90,31037,31038],{},"B",[460,31040,797],{"stretchy":796},[1821,31042,31043,31045,31047],{},[90,31044,24236],{},[90,31046,776],{},[90,31048,334],{},[460,31050,811],{"stretchy":796},[460,31052,811],{"stretchy":796},[90,31054,25814],{"mathvariant":817},[90,31056,26239],{},[460,31058,821],{},[87,31060,31061,31063],{},[90,31062,5603],{},[90,31064,25485],{},[460,31066,797],{"stretchy":796},[1821,31068,31069,31071,31073],{},[90,31070,21],{},[90,31072,776],{},[90,31074,334],{},[90,31076,24375],{"mathvariant":817},[1821,31078,31079,31081,31083],{},[90,31080,24236],{},[90,31082,776],{},[90,31084,334],{},[460,31086,811],{"stretchy":796},[97,31088,31089],{"encoding":99}," \\frac{1}{N} \\sum\\limits_{n=1}^N \\sum\\limits_{t=1}^{T_n} (R_t^n - B(s_t^n))\\nabla \\log P_\\theta(a_t^n|s_t^n)",[58,31091,31093,31404],{"className":31092,"ariaHidden":105},[104],[58,31094,31096,31099,31167,31170,31234,31237,31341,31344,31395,31398,31401],{"className":31095},[109],[58,31097],{"className":31098,"style":29916},[113],[58,31100,31102,31105,31164],{"className":31101},[118],[58,31103],{"className":31104},[122,123],[58,31106,31108],{"className":31107},[77],[58,31109,31111,31156],{"className":31110},[130,131],[58,31112,31114,31153],{"className":31113},[135],[58,31115,31117,31131,31139],{"className":31116,"style":140},[139],[58,31118,31119,31122],{"style":29940},[58,31120],{"className":31121,"style":148},[147],[58,31123,31125],{"className":31124},[152,153,154,155],[58,31126,31128],{"className":31127},[118,155],[58,31129,7321],{"className":31130,"style":7396},[118,191,155],[58,31132,31133,31136],{"style":273},[58,31134],{"className":31135,"style":148},[147],[58,31137],{"className":31138,"style":281},[280],[58,31140,31141,31144],{"style":284},[58,31142],{"className":31143,"style":148},[147],[58,31145,31147],{"className":31146},[152,153,154,155],[58,31148,31150],{"className":31149},[118,155],[58,31151,82],{"className":31152},[118,155],[58,31154,226],{"className":31155},[225],[58,31157,31159],{"className":31158},[135],[58,31160,31162],{"className":31161,"style":29984},[139],[58,31163],{},[58,31165],{"className":31166},[312,123],[58,31168],{"className":31169,"style":915},[498],[58,31171,31173],{"className":31172},[950,25672],[58,31174,31176,31226],{"className":31175},[130,131],[58,31177,31179,31223],{"className":31178},[135],[58,31180,31182,31202,31212],{"className":31181,"style":30005},[139],[58,31183,31184,31187],{"style":30008},[58,31185],{"className":31186,"style":148},[147],[58,31188,31190],{"className":31189},[152,153,154,155],[58,31191,31193,31196,31199],{"className":31192},[118,155],[58,31194,334],{"className":31195},[118,191,155],[58,31197,814],{"className":31198},[503,155],[58,31200,82],{"className":31201},[118,155],[58,31203,31204,31207],{"style":177},[58,31205],{"className":31206,"style":148},[147],[58,31208,31209],{},[58,31210,1825],{"className":31211},[950,1909,1910],[58,31213,31214,31217],{"style":30039},[58,31215],{"className":31216,"style":148},[147],[58,31218,31220],{"className":31219},[152,153,154,155],[58,31221,7321],{"className":31222,"style":7396},[118,191,155],[58,31224,226],{"className":31225},[225],[58,31227,31229],{"className":31228},[135],[58,31230,31232],{"className":31231,"style":30058},[139],[58,31233],{},[58,31235],{"className":31236,"style":915},[498],[58,31238,31240],{"className":31239},[950,25672],[58,31241,31243,31333],{"className":31242},[130,131],[58,31244,31246,31330],{"className":31245},[135],[58,31247,31249,31269,31279],{"className":31248,"style":30076},[139],[58,31250,31251,31254],{"style":30008},[58,31252],{"className":31253,"style":148},[147],[58,31255,31257],{"className":31256},[152,153,154,155],[58,31258,31260,31263,31266],{"className":31259},[118,155],[58,31261,776],{"className":31262},[118,191,155],[58,31264,814],{"className":31265},[503,155],[58,31267,82],{"className":31268},[118,155],[58,31270,31271,31274],{"style":177},[58,31272],{"className":31273,"style":148},[147],[58,31275,31276],{},[58,31277,1825],{"className":31278},[950,1909,1910],[58,31280,31281,31284],{"style":30109},[58,31282],{"className":31283,"style":148},[147],[58,31285,31287],{"className":31286},[152,153,154,155],[58,31288,31290],{"className":31289},[118,155],[58,31291,31293,31296],{"className":31292},[118,155],[58,31294,24676],{"className":31295,"style":3184},[118,191,155],[58,31297,31299],{"className":31298},[195],[58,31300,31302,31322],{"className":31301},[130,131],[58,31303,31305,31319],{"className":31304},[135],[58,31306,31308],{"className":31307,"style":4301},[139],[58,31309,31310,31313],{"style":28646},[58,31311],{"className":31312,"style":212},[147],[58,31314,31316],{"className":31315},[152,216,217,155],[58,31317,334],{"className":31318},[118,191,155],[58,31320,226],{"className":31321},[225],[58,31323,31325],{"className":31324},[135],[58,31326,31328],{"className":31327,"style":4323},[139],[58,31329],{},[58,31331,226],{"className":31332},[225],[58,31334,31336],{"className":31335},[135],[58,31337,31339],{"className":31338,"style":30058},[139],[58,31340],{},[58,31342,797],{"className":31343},[122],[58,31345,31347,31350],{"className":31346},[118],[58,31348,469],{"className":31349,"style":25543},[118,191],[58,31351,31353],{"className":31352},[195],[58,31354,31356,31387],{"className":31355},[130,131],[58,31357,31359,31384],{"className":31358},[135],[58,31360,31362,31373],{"className":31361,"style":28056},[139],[58,31363,31364,31367],{"style":30861},[58,31365],{"className":31366,"style":539},[147],[58,31368,31370],{"className":31369},[152,153,154,155],[58,31371,776],{"className":31372},[118,191,155],[58,31374,31375,31378],{"style":535},[58,31376],{"className":31377,"style":539},[147],[58,31379,31381],{"className":31380},[152,153,154,155],[58,31382,334],{"className":31383},[118,191,155],[58,31385,226],{"className":31386},[225],[58,31388,31390],{"className":31389},[135],[58,31391,31393],{"className":31392,"style":28775},[139],[58,31394],{},[58,31396],{"className":31397,"style":1871},[498],[58,31399,29799],{"className":31400},[552],[58,31402],{"className":31403,"style":1871},[498],[58,31405,31407,31410,31414,31417,31468,31471,31474,31477,31482,31485,31525,31528,31579,31582,31633],{"className":31406},[109],[58,31408],{"className":31409,"style":876},[113],[58,31411,31038],{"className":31412,"style":31413},[118,191],"margin-right:0.05017em;",[58,31415,797],{"className":31416},[122],[58,31418,31420,31423],{"className":31419},[118],[58,31421,24236],{"className":31422},[118,191],[58,31424,31426],{"className":31425},[195],[58,31427,31429,31460],{"className":31428},[130,131],[58,31430,31432,31457],{"className":31431},[135],[58,31433,31435,31446],{"className":31434,"style":28056},[139],[58,31436,31437,31440],{"style":28745},[58,31438],{"className":31439,"style":539},[147],[58,31441,31443],{"className":31442},[152,153,154,155],[58,31444,776],{"className":31445},[118,191,155],[58,31447,31448,31451],{"style":535},[58,31449],{"className":31450,"style":539},[147],[58,31452,31454],{"className":31453},[152,153,154,155],[58,31455,334],{"className":31456},[118,191,155],[58,31458,226],{"className":31459},[225],[58,31461,31463],{"className":31462},[135],[58,31464,31466],{"className":31465,"style":28775},[139],[58,31467],{},[58,31469,7923],{"className":31470},[312],[58,31472,25814],{"className":31473},[118],[58,31475],{"className":31476,"style":915},[498],[58,31478,28284,31480],{"className":31479},[950],[58,31481,28288],{"style":28287},[58,31483],{"className":31484,"style":915},[498],[58,31486,31488,31491],{"className":31487},[118],[58,31489,5603],{"className":31490,"style":3184},[118,191],[58,31492,31494],{"className":31493},[195],[58,31495,31497,31517],{"className":31496},[130,131],[58,31498,31500,31514],{"className":31499},[135],[58,31501,31503],{"className":31502,"style":1247},[139],[58,31504,31505,31508],{"style":7459},[58,31506],{"className":31507,"style":539},[147],[58,31509,31511],{"className":31510},[152,153,154,155],[58,31512,25485],{"className":31513,"style":3209},[118,191,155],[58,31515,226],{"className":31516},[225],[58,31518,31520],{"className":31519},[135],[58,31521,31523],{"className":31522,"style":1269},[139],[58,31524],{},[58,31526,797],{"className":31527},[122],[58,31529,31531,31534],{"className":31530},[118],[58,31532,21],{"className":31533},[118,191],[58,31535,31537],{"className":31536},[195],[58,31538,31540,31571],{"className":31539},[130,131],[58,31541,31543,31568],{"className":31542},[135],[58,31544,31546,31557],{"className":31545,"style":28056},[139],[58,31547,31548,31551],{"style":28745},[58,31549],{"className":31550,"style":539},[147],[58,31552,31554],{"className":31553},[152,153,154,155],[58,31555,776],{"className":31556},[118,191,155],[58,31558,31559,31562],{"style":535},[58,31560],{"className":31561,"style":539},[147],[58,31563,31565],{"className":31564},[152,153,154,155],[58,31566,334],{"className":31567},[118,191,155],[58,31569,226],{"className":31570},[225],[58,31572,31574],{"className":31573},[135],[58,31575,31577],{"className":31576,"style":28775},[139],[58,31578],{},[58,31580,24375],{"className":31581},[118],[58,31583,31585,31588],{"className":31584},[118],[58,31586,24236],{"className":31587},[118,191],[58,31589,31591],{"className":31590},[195],[58,31592,31594,31625],{"className":31593},[130,131],[58,31595,31597,31622],{"className":31596},[135],[58,31598,31600,31611],{"className":31599,"style":28056},[139],[58,31601,31602,31605],{"style":28745},[58,31603],{"className":31604,"style":539},[147],[58,31606,31608],{"className":31607},[152,153,154,155],[58,31609,776],{"className":31610},[118,191,155],[58,31612,31613,31616],{"style":535},[58,31614],{"className":31615,"style":539},[147],[58,31617,31619],{"className":31618},[152,153,154,155],[58,31620,334],{"className":31621},[118,191,155],[58,31623,226],{"className":31624},[225],[58,31626,31628],{"className":31627},[135],[58,31629,31631],{"className":31630,"style":28775},[139],[58,31632],{},[58,31634,811],{"className":31635},[312],[14,31637,31638,31639,31722,31723,31821,31822,31850,31851,31879],{},"但是，",[58,31640,31642,31662],{"className":31641},[61],[58,31643,31645],{"className":31644},[65],[67,31646,31647],{"xmlns":69},[71,31648,31649,31659],{},[74,31650,31651],{},[1821,31652,31653,31655,31657],{},[90,31654,469],{},[90,31656,776],{},[90,31658,334],{},[97,31660,31661],{"encoding":99},"R_t^n",[58,31663,31665],{"className":31664,"ariaHidden":105},[104],[58,31666,31668,31671],{"className":31667},[109],[58,31669],{"className":31670,"style":30840},[113],[58,31672,31674,31677],{"className":31673},[118],[58,31675,469],{"className":31676,"style":25543},[118,191],[58,31678,31680],{"className":31679},[195],[58,31681,31683,31714],{"className":31682},[130,131],[58,31684,31686,31711],{"className":31685},[135],[58,31687,31689,31700],{"className":31688,"style":28056},[139],[58,31690,31691,31694],{"style":30861},[58,31692],{"className":31693,"style":539},[147],[58,31695,31697],{"className":31696},[152,153,154,155],[58,31698,776],{"className":31699},[118,191,155],[58,31701,31702,31705],{"style":535},[58,31703],{"className":31704,"style":539},[147],[58,31706,31708],{"className":31707},[152,153,154,155],[58,31709,334],{"className":31710},[118,191,155],[58,31712,226],{"className":31713},[225],[58,31715,31717],{"className":31716},[135],[58,31718,31720],{"className":31719,"style":28775},[139],[58,31721],{}," 都是一次随机采样，方差很大，训练不稳定。我们引入 ",[58,31724,31726,31754],{"className":31725},[61],[58,31727,31729],{"className":31728},[65],[67,31730,31731],{"xmlns":69},[71,31732,31733,31751],{},[74,31734,31735,31741,31743,31745,31747,31749],{},[87,31736,31737,31739],{},[90,31738,458],{},[90,31740,25485],{},[460,31742,797],{"stretchy":796},[90,31744,24236],{},[460,31746,802],{"separator":105},[90,31748,21],{},[460,31750,811],{"stretchy":796},[97,31752,31753],{"encoding":99},"Q_\\theta(s,a)",[58,31755,31757],{"className":31756,"ariaHidden":105},[104],[58,31758,31760,31763,31803,31806,31809,31812,31815,31818],{"className":31759},[109],[58,31761],{"className":31762,"style":876},[113],[58,31764,31766,31769],{"className":31765},[118],[58,31767,458],{"className":31768},[118,191],[58,31770,31772],{"className":31771},[195],[58,31773,31775,31795],{"className":31774},[130,131],[58,31776,31778,31792],{"className":31777},[135],[58,31779,31781],{"className":31780,"style":1247},[139],[58,31782,31783,31786],{"style":1250},[58,31784],{"className":31785,"style":539},[147],[58,31787,31789],{"className":31788},[152,153,154,155],[58,31790,25485],{"className":31791,"style":3209},[118,191,155],[58,31793,226],{"className":31794},[225],[58,31796,31798],{"className":31797},[135],[58,31799,31801],{"className":31800,"style":1269},[139],[58,31802],{},[58,31804,797],{"className":31805},[122],[58,31807,24236],{"className":31808},[118,191],[58,31810,802],{"className":31811},[911],[58,31813],{"className":31814,"style":915},[498],[58,31816,21],{"className":31817},[118,191],[58,31819,811],{"className":31820},[312],"，表示在状态 ",[58,31823,31825,31838],{"className":31824},[61],[58,31826,31828],{"className":31827},[65],[67,31829,31830],{"xmlns":69},[71,31831,31832,31836],{},[74,31833,31834],{},[90,31835,24236],{},[97,31837,24236],{"encoding":99},[58,31839,31841],{"className":31840,"ariaHidden":105},[104],[58,31842,31844,31847],{"className":31843},[109],[58,31845],{"className":31846,"style":346},[113],[58,31848,24236],{"className":31849},[118,191],"，下，做出动作 ",[58,31852,31854,31867],{"className":31853},[61],[58,31855,31857],{"className":31856},[65],[67,31858,31859],{"xmlns":69},[71,31860,31861,31865],{},[74,31862,31863],{},[90,31864,21],{},[97,31866,21],{"encoding":99},[58,31868,31870],{"className":31869,"ariaHidden":105},[104],[58,31871,31873,31876],{"className":31872},[109],[58,31874],{"className":31875,"style":346},[113],[58,31877,21],{"className":31878},[118,191]," 后期望的回报，即动作价值函数。",[14,31881,31882,31883,31969,31970,31998],{},"令 ",[58,31884,31886,31910],{"className":31885},[61],[58,31887,31889],{"className":31888},[65],[67,31890,31891],{"xmlns":69},[71,31892,31893,31907],{},[74,31894,31895,31901,31903,31905],{},[87,31896,31897,31899],{},[90,31898,671],{},[90,31900,25485],{},[460,31902,797],{"stretchy":796},[90,31904,24236],{},[460,31906,811],{"stretchy":796},[97,31908,31909],{"encoding":99},"V_\\theta(s)",[58,31911,31913],{"className":31912,"ariaHidden":105},[104],[58,31914,31916,31919,31960,31963,31966],{"className":31915},[109],[58,31917],{"className":31918,"style":876},[113],[58,31920,31922,31925],{"className":31921},[118],[58,31923,671],{"className":31924,"style":701},[118,191],[58,31926,31928],{"className":31927},[195],[58,31929,31931,31952],{"className":31930},[130,131],[58,31932,31934,31949],{"className":31933},[135],[58,31935,31937],{"className":31936,"style":1247},[139],[58,31938,31940,31943],{"style":31939},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[58,31941],{"className":31942,"style":539},[147],[58,31944,31946],{"className":31945},[152,153,154,155],[58,31947,25485],{"className":31948,"style":3209},[118,191,155],[58,31950,226],{"className":31951},[225],[58,31953,31955],{"className":31954},[135],[58,31956,31958],{"className":31957,"style":1269},[139],[58,31959],{},[58,31961,797],{"className":31962},[122],[58,31964,24236],{"className":31965},[118,191],[58,31967,811],{"className":31968},[312]," 在状态 ",[58,31971,31973,31986],{"className":31972},[61],[58,31974,31976],{"className":31975},[65],[67,31977,31978],{"xmlns":69},[71,31979,31980,31984],{},[74,31981,31982],{},[90,31983,24236],{},[97,31985,24236],{"encoding":99},[58,31987,31989],{"className":31988,"ariaHidden":105},[104],[58,31990,31992,31995],{"className":31991},[109],[58,31993],{"className":31994,"style":346},[113],[58,31996,24236],{"className":31997},[118,191]," 下期望的回报，即状态价值函数",[14,32000,32001,32268,32269,32297,32298,32326],{},[58,32002,32004,32064],{"className":32003},[61],[58,32005,32007],{"className":32006},[65],[67,32008,32009],{"xmlns":69},[71,32010,32011,32061],{},[74,32012,32013,32019,32021,32023,32025,32027,32029,32031,32037,32039,32041,32043,32045,32047,32049,32055,32057,32059],{},[87,32014,32015,32017],{},[90,32016,773],{},[90,32018,25485],{},[460,32020,797],{"stretchy":796},[90,32022,24236],{},[460,32024,802],{"separator":105},[90,32026,21],{},[460,32028,811],{"stretchy":796},[460,32030,814],{},[87,32032,32033,32035],{},[90,32034,458],{},[90,32036,25485],{},[460,32038,797],{"stretchy":796},[90,32040,24236],{},[460,32042,802],{"separator":105},[90,32044,21],{},[460,32046,811],{"stretchy":796},[460,32048,29799],{},[87,32050,32051,32053],{},[90,32052,671],{},[90,32054,25485],{},[460,32056,797],{"stretchy":796},[90,32058,24236],{},[460,32060,811],{"stretchy":796},[97,32062,32063],{"encoding":99},"A_\\theta(s,a) = Q_\\theta(s,a) - V_\\theta(s)",[58,32065,32067,32140,32213],{"className":32066,"ariaHidden":105},[104],[58,32068,32070,32073,32113,32116,32119,32122,32125,32128,32131,32134,32137],{"className":32069},[109],[58,32071],{"className":32072,"style":876},[113],[58,32074,32076,32079],{"className":32075},[118],[58,32077,773],{"className":32078},[118,191],[58,32080,32082],{"className":32081},[195],[58,32083,32085,32105],{"className":32084},[130,131],[58,32086,32088,32102],{"className":32087},[135],[58,32089,32091],{"className":32090,"style":1247},[139],[58,32092,32093,32096],{"style":1250},[58,32094],{"className":32095,"style":539},[147],[58,32097,32099],{"className":32098},[152,153,154,155],[58,32100,25485],{"className":32101,"style":3209},[118,191,155],[58,32103,226],{"className":32104},[225],[58,32106,32108],{"className":32107},[135],[58,32109,32111],{"className":32110,"style":1269},[139],[58,32112],{},[58,32114,797],{"className":32115},[122],[58,32117,24236],{"className":32118},[118,191],[58,32120,802],{"className":32121},[911],[58,32123],{"className":32124,"style":915},[498],[58,32126,21],{"className":32127},[118,191],[58,32129,811],{"className":32130},[312],[58,32132],{"className":32133,"style":499},[498],[58,32135,814],{"className":32136},[503],[58,32138],{"className":32139,"style":499},[498],[58,32141,32143,32146,32186,32189,32192,32195,32198,32201,32204,32207,32210],{"className":32142},[109],[58,32144],{"className":32145,"style":876},[113],[58,32147,32149,32152],{"className":32148},[118],[58,32150,458],{"className":32151},[118,191],[58,32153,32155],{"className":32154},[195],[58,32156,32158,32178],{"className":32157},[130,131],[58,32159,32161,32175],{"className":32160},[135],[58,32162,32164],{"className":32163,"style":1247},[139],[58,32165,32166,32169],{"style":1250},[58,32167],{"className":32168,"style":539},[147],[58,32170,32172],{"className":32171},[152,153,154,155],[58,32173,25485],{"className":32174,"style":3209},[118,191,155],[58,32176,226],{"className":32177},[225],[58,32179,32181],{"className":32180},[135],[58,32182,32184],{"className":32183,"style":1269},[139],[58,32185],{},[58,32187,797],{"className":32188},[122],[58,32190,24236],{"className":32191},[118,191],[58,32193,802],{"className":32194},[911],[58,32196],{"className":32197,"style":915},[498],[58,32199,21],{"className":32200},[118,191],[58,32202,811],{"className":32203},[312],[58,32205],{"className":32206,"style":1871},[498],[58,32208,29799],{"className":32209},[552],[58,32211],{"className":32212,"style":1871},[498],[58,32214,32216,32219,32259,32262,32265],{"className":32215},[109],[58,32217],{"className":32218,"style":876},[113],[58,32220,32222,32225],{"className":32221},[118],[58,32223,671],{"className":32224,"style":701},[118,191],[58,32226,32228],{"className":32227},[195],[58,32229,32231,32251],{"className":32230},[130,131],[58,32232,32234,32248],{"className":32233},[135],[58,32235,32237],{"className":32236,"style":1247},[139],[58,32238,32239,32242],{"style":31939},[58,32240],{"className":32241,"style":539},[147],[58,32243,32245],{"className":32244},[152,153,154,155],[58,32246,25485],{"className":32247,"style":3209},[118,191,155],[58,32249,226],{"className":32250},[225],[58,32252,32254],{"className":32253},[135],[58,32255,32257],{"className":32256,"style":1269},[139],[58,32258],{},[58,32260,797],{"className":32261},[122],[58,32263,24236],{"className":32264},[118,191],[58,32266,811],{"className":32267},[312]," 表示优势函数（Advantage Function），衡量在状态 ",[58,32270,32272,32285],{"className":32271},[61],[58,32273,32275],{"className":32274},[65],[67,32276,32277],{"xmlns":69},[71,32278,32279,32283],{},[74,32280,32281],{},[90,32282,24236],{},[97,32284,24236],{"encoding":99},[58,32286,32288],{"className":32287,"ariaHidden":105},[104],[58,32289,32291,32294],{"className":32290},[109],[58,32292],{"className":32293,"style":346},[113],[58,32295,24236],{"className":32296},[118,191]," 下，动作 ",[58,32299,32301,32314],{"className":32300},[61],[58,32302,32304],{"className":32303},[65],[67,32305,32306],{"xmlns":69},[71,32307,32308,32312],{},[74,32309,32310],{},[90,32311,21],{},[97,32313,21],{"encoding":99},[58,32315,32317],{"className":32316,"ariaHidden":105},[104],[58,32318,32320,32323],{"className":32319},[109],[58,32321],{"className":32322,"style":346},[113],[58,32324,21],{"className":32325},[118,191]," 相对于平均水平的优势。",[14,32328,32329],{},"讲上述的公式改写为",[14,32331,32332],{},[58,32333,32335,32449],{"className":32334},[61],[58,32336,32338],{"className":32337},[65],[67,32339,32340],{"xmlns":69},[71,32341,32342,32446],{},[74,32343,32344,32352,32366,32384,32390,32392,32400,32402,32410,32412,32414,32416,32418,32424,32426,32434,32436,32444],{},[25808,32345,32346],{"scriptlevel":1753,"displaystyle":105},[77,32347,32348,32350],{},[80,32349,82],{},[90,32351,7321],{},[1821,32353,32354,32356,32364],{},[460,32355,1825],{},[74,32357,32358,32360,32362],{},[90,32359,334],{},[460,32361,814],{},[80,32363,82],{},[90,32365,7321],{},[1821,32367,32368,32370,32378],{},[460,32369,1825],{},[74,32371,32372,32374,32376],{},[90,32373,776],{},[460,32375,814],{},[80,32377,82],{},[87,32379,32380,32382],{},[90,32381,24676],{},[90,32383,334],{},[87,32385,32386,32388],{},[90,32387,773],{},[90,32389,25485],{},[460,32391,797],{"stretchy":796},[1821,32393,32394,32396,32398],{},[90,32395,24236],{},[90,32397,776],{},[90,32399,334],{},[460,32401,802],{"separator":105},[1821,32403,32404,32406,32408],{},[90,32405,21],{},[90,32407,776],{},[90,32409,334],{},[460,32411,811],{"stretchy":796},[90,32413,25814],{"mathvariant":817},[90,32415,26239],{},[460,32417,821],{},[87,32419,32420,32422],{},[90,32421,5603],{},[90,32423,25485],{},[460,32425,797],{"stretchy":796},[1821,32427,32428,32430,32432],{},[90,32429,21],{},[90,32431,776],{},[90,32433,334],{},[90,32435,24375],{"mathvariant":817},[1821,32437,32438,32440,32442],{},[90,32439,24236],{},[90,32441,776],{},[90,32443,334],{},[460,32445,811],{"stretchy":796},[97,32447,32448],{"encoding":99},"\\dfrac{1}{N}\\sum\\limits_{n=1}^N \\sum\\limits_{t=1}^{T_n} A_\\theta(s_t^n,a_t^n)\\nabla \\log 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Q_\\theta(s_t, a) = r_t + \\gamma V_\\theta(s_{t+1}) \\\\\n\n A_\\theta(s_t, a) = r_t + \\gamma V_\\theta(s_{t+1}) - V_\\theta(s_t)\\\\\n V_\\theta(s_{t+1}) \\approx r_{t+1} + \\gamma 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的推到公式仅剩一个相关变量，可以降低公式的复杂性。",[14,34258,34259],{},"之后再根据采样步数进行估算。采样越多，情况越多，整体估计的偏差就会偏小，同样的，碰到极值的概率越大，方差就越大。",[58,34261,34263],{"className":34262},[25784],[58,34264,34266,34716],{"className":34265},[61],[58,34267,34269],{"className":34268},[65],[67,34270,34271],{"xmlns":69,"display":9480},[71,34272,34273,34713],{},[74,34274,34275,34283,34285,34291,34293,34295,34297,34299,34305,34307,34309,34315,34317,34329,34331,34333,34339,34341,34347,34349,34351,34359,34361,34367,34369,34371,34373,34375,34381,34383,34385,34397,34399,34405,34411,34413,34425,34427,34429,34435,34437,34443,34445,34447,34455,34457,34463,34465,34467,34469,34471,34477,34479,34481,34484,34496,34498,34504,34506,34518,34520,34526,34532,34534,34546,34548,34550,34556,34558,34564,34566,34568,34580,34582,34590,34592,34598,34600,34602,34604,34606,34612,34614,34616,34618,34630,34632,34638,34640,34652,34654,34660,34662,34674,34676,34679,34681,34687,34689,34695,34697,34703,34705,34711],{},[1821,34276,34277,34279,34281],{},[90,34278,773],{},[90,34280,25485],{},[80,34282,82],{},[460,34284,797],{"stretchy":796},[87,34286,34287,34289],{},[90,34288,24236],{},[90,34290,776],{},[460,34292,802],{"separator":105},[90,34294,21],{},[460,34296,811],{"stretchy":796},[460,34298,814],{},[87,34300,34301,34303],{},[90,34302,7825],{},[90,34304,776],{},[460,34306,5776],{},[90,34308,30429],{},[87,34310,34311,34313],{},[90,34312,671],{},[90,34314,25485],{},[460,34316,797],{"stretchy":796},[87,34318,34319,34321],{},[90,34320,24236],{},[74,34322,34323,34325,34327],{},[90,34324,776],{},[460,34326,5776],{},[80,34328,82],{},[460,34330,811],{"stretchy":796},[460,34332,29799],{},[87,34334,34335,34337],{},[90,34336,671],{},[90,34338,25485],{},[460,34340,797],{"stretchy":796},[87,34342,34343,34345],{},[90,34344,24236],{},[90,34346,776],{},[460,34348,811],{"stretchy":796},[498,34350],{"linebreak":33087},[1821,34352,34353,34355,34357],{},[90,34354,773],{},[90,34356,25485],{},[80,34358,2820],{},[460,34360,797],{"stretchy":796},[87,34362,34363,34365],{},[90,34364,24236],{},[90,34366,776],{},[460,34368,802],{"separator":105},[90,34370,21],{},[460,34372,811],{"stretchy":796},[460,34374,814],{},[87,34376,34377,34379],{},[90,34378,7825],{},[90,34380,776],{},[460,34382,5776],{},[90,34384,30429],{},[87,34386,34387,34389],{},[90,34388,7825],{},[74,34390,34391,34393,34395],{},[90,34392,776],{},[460,34394,5776],{},[80,34396,82],{},[460,34398,5776],{},[464,34400,34401,34403],{},[90,34402,30429],{},[80,34404,2820],{},[87,34406,34407,34409],{},[90,34408,671],{},[90,34410,25485],{},[460,34412,797],{"stretchy":796},[87,34414,34415,34417],{},[90,34416,24236],{},[74,34418,34419,34421,34423],{},[90,34420,776],{},[460,34422,5776],{},[80,34424,2820],{},[460,34426,811],{"stretchy":796},[460,34428,29799],{},[87,34430,34431,34433],{},[90,34432,671],{},[90,34434,25485],{},[460,34436,797],{"stretchy":796},[87,34438,34439,34441],{},[90,34440,24236],{},[90,34442,776],{},[460,34444,811],{"stretchy":796},[498,34446],{"linebreak":33087},[1821,34448,34449,34451,34453],{},[90,34450,773],{},[90,34452,25485],{},[80,34454,4670],{},[460,34456,797],{"stretchy":796},[87,34458,34459,34461],{},[90,34460,24236],{},[90,34462,776],{},[460,34464,802],{"separator":105},[90,34466,21],{},[460,34468,811],{"stretchy":796},[460,34470,814],{},[87,34472,34473,34475],{},[90,34474,7825],{},[90,34476,776],{},[460,34478,5776],{},[90,34480,30429],{},[460,34482,34483],{},"∗",[87,34485,34486,34488],{},[90,34487,7825],{},[74,34489,34490,34492,34494],{},[90,34491,776],{},[460,34493,5776],{},[80,34495,82],{},[460,34497,5776],{},[464,34499,34500,34502],{},[90,34501,30429],{},[80,34503,2820],{},[460,34505,34483],{},[87,34507,34508,34510],{},[90,34509,7825],{},[74,34511,34512,34514,34516],{},[90,34513,776],{},[460,34515,5776],{},[80,34517,2820],{},[460,34519,5776],{},[464,34521,34522,34524],{},[90,34523,30429],{},[80,34525,4670],{},[87,34527,34528,34530],{},[90,34529,671],{},[90,34531,25485],{},[460,34533,797],{"stretchy":796},[87,34535,34536,34538],{},[90,34537,24236],{},[74,34539,34540,34542,34544],{},[90,34541,776],{},[460,34543,5776],{},[80,34545,4670],{},[460,34547,811],{"stretchy":796},[460,34549,29799],{},[87,34551,34552,34554],{},[90,34553,671],{},[90,34555,25485],{},[460,34557,797],{"stretchy":796},[87,34559,34560,34562],{},[90,34561,24236],{},[90,34563,776],{},[460,34565,811],{"stretchy":796},[498,34567],{"linebreak":33087},[74,34569,34570,34573],{},[90,34571,34572],{"mathvariant":817},"⋮",[34574,34575,34576],"mpadded",{"height":25800,"voffset":25800},[498,34577],{"mathbackground":34578,"width":25800,"height":34579},"black","1.5em",[498,34581],{"linebreak":33087},[1821,34583,34584,34586,34588],{},[90,34585,773],{},[90,34587,25485],{},[90,34589,24676],{},[460,34591,797],{"stretchy":796},[87,34593,34594,34596],{},[90,34595,24236],{},[90,34597,776],{},[460,34599,802],{"separator":105},[90,34601,21],{},[460,34603,811],{"stretchy":796},[460,34605,814],{},[87,34607,34608,34610],{},[90,34609,7825],{},[90,34611,776],{},[460,34613,5776],{},[90,34615,30429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A_\\theta^1(s_t, a) = r_t + \\gamma V_\\theta(s_{t+1}) - V_\\theta(s_t)\\\\\n A_\\theta^2(s_t, a) = r_t + \\gamma r_{t+1} + \\gamma^2 V_\\theta(s_{t+2}) - V_\\theta(s_t)\\\\\n A_\\theta^3(s_t, a) = r_t + \\gamma * r_{t+1} + \\gamma^2 * r_{t+2} + \\gamma^3 V_\\theta(s_{t+3}) - V_\\theta(s_t)\\\\\n \\vdots \\\\\n A_\\theta^T(s_t, a) = r_t + \\gamma * r_{t+1} + \\gamma^2 * r_{t+2} + \\gamma^3 * r_{t+3} + \\cdots + \\gamma^T * r_T - 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",[58,36896,36898,36917],{"className":36897},[61],[58,36899,36901],{"className":36900},[65],[67,36902,36903],{"xmlns":69},[71,36904,36905,36914],{},[74,36906,36907],{},[87,36908,36909,36912],{},[90,36910,36911],{},"δ",[90,36913,776],{},[97,36915,36916],{"encoding":99},"\\delta_t",[58,36918,36920],{"className":36919,"ariaHidden":105},[104],[58,36921,36923,36926],{"className":36922},[109],[58,36924],{"className":36925,"style":1228},[113],[58,36927,36929,36933],{"className":36928},[118],[58,36930,36911],{"className":36931,"style":36932},[118,191],"margin-right:0.03785em;",[58,36934,36936],{"className":36935},[195],[58,36937,36939,36960],{"className":36938},[130,131],[58,36940,36942,36957],{"className":36941},[135],[58,36943,36945],{"className":36944,"style":24166},[139],[58,36946,36948,36951],{"style":36947},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[58,36949],{"className":36950,"style":539},[147],[58,36952,36954],{"className":36953},[152,153,154,155],[58,36955,776],{"className":36956},[118,191,155],[58,36958,226],{"className":36959},[225],[58,36961,36963],{"className":36962},[135],[58,36964,36966],{"className":36965,"style":1269},[139],[58,36967],{}," 表示在第 ",[58,36970,36972,36985],{"className":36971},[61],[58,36973,36975],{"className":36974},[65],[67,36976,36977],{"xmlns":69},[71,36978,36979,36983],{},[74,36980,36981],{},[90,36982,776],{},[97,36984,776],{"encoding":99},[58,36986,36988],{"className":36987,"ariaHidden":105},[104],[58,36989,36991,36994],{"className":36990},[109],[58,36992],{"className":36993,"style":24215},[113],[58,36995,776],{"className":36996},[118,191]," 步采取特定动作带来的优势。",[58,36999,37001],{"className":37000},[25784],[58,37002,37004,37330],{"className":37003},[61],[58,37005,37007],{"className":37006},[65],[67,37008,37009],{"xmlns":69,"display":9480},[71,37010,37011,37327],{},[74,37012,37013,37021,37023,37029,37031,37033,37035,37041,37043,37055,37057,37059,37065,37067,37073,37075,37077,37091,37093,37105,37107,37109,37111,37117,37119,37131,37133,37135,37141,37143,37155,37157,37159,37167,37169,37175,37177,37179,37181,37183,37191,37193,37201,37203,37209,37211,37213,37215,37217,37225,37227,37229,37243,37245,37253,37255,37261,37263,37265,37267,37269,37277,37279,37281,37295,37297,37303,37317,37319],{},[1821,37014,37015,37017,37019],{},[90,37016,36911],{},[90,37018,776],{},[90,37020,671],{},[460,37022,814],{},[87,37024,37025,37027],{},[90,37026,7825],{},[90,37028,776],{},[460,37030,5776],{},[90,37032,30429],{},[460,37034,34483],{},[87,37036,37037,37039],{},[90,37038,671],{},[90,37040,25485],{},[460,37042,797],{"stretchy":796},[87,37044,37045,37047],{},[90,37046,24236],{},[74,37048,37049,37051,37053],{},[90,37050,776],{},[460,37052,5776],{},[80,37054,82],{},[460,37056,811],{"stretchy":796},[460,37058,29799],{},[87,37060,37061,37063],{},[90,37062,671],{},[90,37064,25485],{},[460,37066,797],{"stretchy":796},[87,37068,37069,37071],{},[90,37070,24236],{},[90,37072,776],{},[460,37074,811],{"stretchy":796},[498,37076],{"linebreak":33087},[1821,37078,37079,37081,37089],{},[90,37080,36911],{},[74,37082,37083,37085,37087],{},[90,37084,776],{},[460,37086,5776],{},[80,37088,82],{},[90,37090,671],{},[460,37092,814],{},[87,37094,37095,37097],{},[90,37096,7825],{},[74,37098,37099,37101,37103],{},[90,37100,776],{},[460,37102,5776],{},[80,37104,82],{},[460,37106,5776],{},[90,37108,30429],{},[460,37110,34483],{},[87,37112,37113,37115],{},[90,37114,671],{},[90,37116,25485],{},[460,37118,797],{"stretchy":796},[87,37120,37121,37123],{},[90,37122,24236],{},[74,37124,37125,37127,37129],{},[90,37126,776],{},[460,37128,5776],{},[80,37130,2820],{},[460,37132,811],{"stretchy":796},[460,37134,29799],{},[87,37136,37137,37139],{},[90,37138,671],{},[90,37140,25485],{},[460,37142,797],{"stretchy":796},[87,37144,37145,37147],{},[90,37146,24236],{},[74,37148,37149,37151,37153],{},[90,37150,776],{},[460,37152,5776],{},[80,37154,82],{},[460,37156,811],{"stretchy":796},[498,37158],{"linebreak":33087},[1821,37160,37161,37163,37165],{},[90,37162,773],{},[90,37164,25485],{},[80,37166,82],{},[460,37168,797],{"stretchy":796},[87,37170,37171,37173],{},[90,37172,24236],{},[90,37174,776],{},[460,37176,802],{"separator":105},[90,37178,21],{},[460,37180,811],{"stretchy":796},[460,37182,814],{},[1821,37184,37185,37187,37189],{},[90,37186,36911],{},[90,37188,776],{},[90,37190,671],{},[498,37192],{"linebreak":33087},[1821,37194,37195,37197,37199],{},[90,37196,773],{},[90,37198,25485],{},[80,37200,2820],{},[460,37202,797],{"stretchy":796},[87,37204,37205,37207],{},[90,37206,24236],{},[90,37208,776],{},[460,37210,802],{"separator":105},[90,37212,21],{},[460,37214,811],{"stretchy":796},[460,37216,814],{},[1821,37218,37219,37221,37223],{},[90,37220,36911],{},[90,37222,776],{},[90,37224,671],{},[460,37226,5776],{},[90,37228,30429],{},[1821,37230,37231,37233,37241],{},[90,37232,36911],{},[74,37234,37235,37237,37239],{},[90,37236,776],{},[460,37238,5776],{},[80,37240,82],{},[90,37242,671],{},[498,37244],{"linebreak":33087},[1821,37246,37247,37249,37251],{},[90,37248,773],{},[90,37250,25485],{},[80,37252,4670],{},[460,37254,797],{"stretchy":796},[87,37256,37257,37259],{},[90,37258,24236],{},[90,37260,776],{},[460,37262,802],{"separator":105},[90,37264,21],{},[460,37266,811],{"stretchy":796},[460,37268,814],{},[1821,37270,37271,37273,37275],{},[90,37272,36911],{},[90,37274,776],{},[90,37276,671],{},[460,37278,5776],{},[90,37280,30429],{},[1821,37282,37283,37285,37293],{},[90,37284,36911],{},[74,37286,37287,37289,37291],{},[90,37288,776],{},[460,37290,5776],{},[80,37292,82],{},[90,37294,671],{},[460,37296,5776],{},[464,37298,37299,37301],{},[90,37300,30429],{},[80,37302,2820],{},[1821,37304,37305,37307,37315],{},[90,37306,36911],{},[74,37308,37309,37311,37313],{},[90,37310,776],{},[460,37312,5776],{},[80,37314,2820],{},[90,37316,671],{},[498,37318],{"linebreak":33087},[74,37320,37321,37323],{},[90,37322,34572],{"mathvariant":817},[34574,37324,37325],{"height":25800,"voffset":25800},[498,37326],{"mathbackground":34578,"width":25800,"height":34579},[97,37328,37329],{"encoding":99},"\n\\delta_t^V = r_t + \\gamma * V_\\theta(s_{t+1}) - V_\\theta(s_t)\\\\\n\n\\delta_{t+1}^V = r_{t+1} + \\gamma * V_\\theta(s_{t+2}) - V_\\theta(s_{t+1})\\\\\n\nA_\\theta^1(s_t, a) = \\delta_t^V\\\\\n\nA_\\theta^2(s_t, a) = \\delta_t^V + \\gamma \\delta_{t+1}^V\\\\\n\nA_\\theta^3(s_t, a) = \\delta_t^V + \\gamma \\delta_{t+1}^V + \\gamma^2 \\delta_{t+2}^V\\\\\n\n\\vdots",[58,37331,37333,37401,37456,37474,37584,37676,37679,37756,37820,37838,37948,38049,38052,38173,38230,38233,38354,38420,38489,38492,38613,38679,38757,38852,38855],{"className":37332,"ariaHidden":105},[104],[58,37334,37336,37340,37392,37395,37398],{"className":37335},[109],[58,37337],{"className":37338,"style":37339},[113],"height:1.1383em;vertical-align:-0.247em;",[58,37341,37343,37346],{"className":37342},[118],[58,37344,36911],{"className":37345,"style":36932},[118,191],[58,37347,37349],{"className":37348},[195],[58,37350,37352,37384],{"className":37351},[130,131],[58,37353,37355,37381],{"className":37354},[135],[58,37356,37358,37370],{"className":37357,"style":36230},[139],[58,37359,37361,37364],{"style":37360},"top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;",[58,37362],{"className":37363,"style":539},[147],[58,37365,37367],{"className":37366},[152,153,154,155],[58,37368,776],{"className":37369},[118,191,155],[58,37371,37372,37375],{"style":27860},[58,37373],{"className":37374,"style":539},[147],[58,37376,37378],{"className":37377},[152,153,154,155],[58,37379,671],{"className":37380,"style":701},[118,191,155],[58,37382,226],{"className":37383},[225],[58,37385,37387],{"className":37386},[135],[58,37388,37390],{"className":37389,"style":28775},[139],[58,37391],{},[58,37393],{"className":37394,"style":499},[498],[58,37396,814],{"className":37397},[503],[58,37399],{"className":37400,"style":499},[498],[58,37402,37404,37407,37447,37450,37453],{"className":37403},[109],[58,37405],{"className":37406,"style":33346},[113],[58,37408,37410,37413],{"className":37409},[118],[58,37411,7825],{"className":37412,"style":3209},[118,191],[58,37414,37416],{"className":37415},[195],[58,37417,37419,37439],{"className":37418},[130,131],[58,37420,37422,37436],{"className":37421},[135],[58,37423,37425],{"className":37424,"style":24166},[139],[58,37426,37427,37430],{"style":24539},[58,37428],{"className":37429,"style":539},[147],[58,37431,37433],{"className":37432},[152,153,154,155],[58,37434,776],{"className":37435},[118,191,155],[58,37437,226],{"className":37438},[225],[58,37440,37442],{"className":37441},[135],[58,37443,37445],{"className":37444,"style":1269},[139],[58,37446],{},[58,37448],{"className":37449,"style":1871},[498],[58,37451,5776],{"className":37452},[552],[58,37454],{"className":37455,"style":1871},[498],[58,37457,37459,37462,37465,37468,37471],{"className":37458},[109],[58,37460],{"className":37461,"style":35764},[113],[58,37463,30429],{"className":37464,"style":30676},[118,191],[58,37466],{"className":37467,"style":1871},[498],[58,37469,34483],{"className":37470},[552],[58,37472],{"className":37473,"style":1871},[498],[58,37475,37477,37480,37520,37523,37572,37575,37578,37581],{"className":37476},[109],[58,37478],{"className":37479,"style":876},[113],[58,37481,37483,37486],{"className":37482},[118],[58,37484,671],{"className":37485,"style":701},[118,191],[58,37487,37489],{"className":37488},[195],[58,37490,37492,37512],{"className":37491},[130,131],[58,37493,37495,37509],{"className":37494},[135],[58,37496,37498],{"className":37497,"style":1247},[139],[58,37499,37500,37503],{"style":31939},[58,37501],{"className":37502,"style":539},[147],[58,37504,37506],{"className":37505},[152,153,154,155],[58,37507,25485],{"className":37508,"style":3209},[118,191,155],[58,37510,226],{"className":37511},[225],[58,37513,37515],{"className":37514},[135],[58,37516,37518],{"className":37517,"style":1269},[139],[58,37519],{},[58,37521,797],{"className":37522},[122],[58,37524,37526,37529],{"className":37525},[118],[58,37527,24236],{"className":37528},[118,191],[58,37530,37532],{"className":37531},[195],[58,37533,37535,37564],{"className":37534},[130,131],[58,37536,37538,37561],{"className":37537},[135],[58,37539,37541],{"className":37540,"style":3090},[139],[58,37542,37543,37546],{"style":1250},[58,37544],{"className":37545,"style":539},[147],[58,37547,37549],{"className":37548},[152,153,154,155],[58,37550,37552,37555,37558],{"className":37551},[118,155],[58,37553,776],{"className":37554},[118,191,155],[58,37556,5776],{"className":37557},[552,155],[58,37559,82],{"className":37560},[118,155],[58,37562,226],{"className":37563},[225],[58,37565,37567],{"className":37566},[135],[58,37568,37570],{"className":37569,"style":6937},[139],[58,37571],{},[58,37573,811],{"className":37574},[312],[58,37576],{"className":37577,"style":1871},[498],[58,37579,29799],{"className":37580},[552],[58,37582],{"className":37583,"style":1871},[498],[58,37585,37587,37590,37630,37633,37673],{"className":37586},[109],[58,37588],{"className":37589,"style":876},[113],[58,37591,37593,37596],{"className":37592},[118],[58,37594,671],{"className":37595,"style":701},[118,191],[58,37597,37599],{"className":37598},[195],[58,37600,37602,37622],{"className":37601},[130,131],[58,37603,37605,37619],{"className":37604},[135],[58,37606,37608],{"className":37607,"style":1247},[139],[58,37609,37610,37613],{"style":31939},[58,37611],{"classN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Advantage Estimation (GAE)",[14,38875,38876],{},"这时我们考虑，在运行时我们应该向后采样几步呢？GAE 的答案是，小孩子才做选择，我全都要！",[14,38878,38879,38880,38910],{},"GAE考虑全部的采样结果，并引入一个衰减因子 ",[58,38881,38883,38898],{"className":38882},[61],[58,38884,38886],{"className":38885},[65],[67,38887,38888],{"xmlns":69},[71,38889,38890,38895],{},[74,38891,38892],{},[90,38893,38894],{},"λ",[97,38896,38897],{"encoding":99},"\\lambda",[58,38899,38901],{"className":38900,"ariaHidden":105},[104],[58,38902,38904,38907],{"className":38903},[109],[58,38905],{"className":38906,"style":406},[113],[58,38908,38894],{"className":38909},[118,191]," 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a) &= (1 - \\lambda)(A_\\theta^1 + \\lambda * A_\\theta^2 + \\lambda^2 A_\\theta^3 + \\cdots) \\quad\\quad \\lambda = 0.9: \\quad A_\\theta^{GAE} = 0.1A_\\theta^1 + 0.09A_\\theta^2 + 0.081A_\\theta^3 + \\cdots \\\\\n&= (1 - \\lambda)(\\delta_t^V + \\lambda * (\\delta_t^V + \\gamma \\delta_{t+1}^V) + \\lambda^2 (\\delta_t^V + \\gamma \\delta_{t+1}^V + \\gamma^2 \\delta_{t+2}^V) + \\cdots) \\\\\n&= (1 - \\lambda)(\\delta_t^V (1 + \\lambda + \\lambda^2 + \\cdots) + \\gamma \\delta_{t+1}^V * (\\lambda + \\lambda^2 + \\cdots) + \\cdots) \\\\\n&= (1 - \\lambda)\\left(\\delta_t^V \\frac{1}{1 - \\lambda} + \\gamma \\delta_{t+1}^V \\frac{\\lambda}{1 - \\lambda} + \\cdots\\right) \\\\\n&= \\sum\\limits_{b=0}^\\infty (\\gamma\\lambda)^b 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{"style":27808},[58,41563],{"className":41564,"style":26866},[147],[58,41566,41568],{"className":41567},[152,153,154,155],[58,41569,39478],{"className":41570},[118,155],[58,41572,226],{"className":41573},[225],[58,41575,41577],{"className":41576},[135],[58,41578,41581],{"className":41579,"style":41580},[139],"height:1.3021em;",[58,41582],{},[58,41584,797],{"className":41585},[122],[58,41587,30429],{"className":41588,"style":30676},[118,191],[58,41590,38894],{"className":41591},[118,191],[58,41593,41595,41598],{"className":41594},[312],[58,41596,811],{"className":41597},[312],[58,41599,41601],{"className":41600},[195],[58,41602,41604],{"className":41603},[130],[58,41605,41607],{"className":41606},[135],[58,41608,41611],{"className":41609,"style":41610},[139],"height:0.8991em;",[58,41612,41613,41616],{"style":27860},[58,41614],{"className":41615,"style":539},[147],[58,41617,41619],{"className":41618},[152,153,154,155],[58,41620,7356],{"className":41621},[118,191,155],[58,41623,41625,41628],{"className":41624},[118],[58,41626,36911],{"className":41627,"style":36932},[118,191],[58,41629,41631],{"className":41630},[195],[58,41632,41634,41674],{"className":41633},[130,131],[58,41635,41637,41671],{"className":41636},[135],[58,41638,41640,41660],{"className":41639,"style":36230},[139],[58,41641,41642,41645],{"style":37360},[58,41643],{"className":41644,"style":539},[147],[58,41646,41648],{"className":41647},[152,153,154,155],[58,41649,41651,41654,41657],{"className":41650},[118,155],[58,41652,776],{"className":41653},[118,191,155],[58,41655,5776],{"className":41656},[552,155],[58,41658,7356],{"className":41659},[118,191,155],[58,41661,41662,41665],{"style":27860},[58,41663],{"className":41664,"style":539},[147],[58,41666,41668],{"className":41667},[152,153,154,155],[58,41669,671],{"className":41670,"style":701},[118,191,155],[58,41672,226],{"className":41673},[225],[58,41675,41677],{"className":41676},[135],[58,41678,41680],{"className":41679,"style":37744},[139],[58,41681],{},[58,41683,226],{"className":41684},[225],[58,41686,41688],{"className":41687},[135],[58,41689,41691],{"className":41690,"style":39707},[139],[58,41692],{},[14,41694,41695],{},"整理后发现其中有等比数列，利用等比数列求和得到最终的 GAE 优势函数的表达式。",[14,41697,41698],{},"GAE 优势函数平衡了采样不同步带来的方差和偏差的问题。",[14,41700,41701],{},"现在我们来看上面得之不易的三个表达式：",[58,41703,41705],{"className":41704},[25784],[58,41706,41708,41964],{"className":41707},[61],[58,41709,41711],{"className":41710},[65],[67,41712,41713],{"xmlns":69,"display":9480},[71,41714,41715,41961],{},[74,41716,41717,41725,41727,41733,41735,41737,41743,41745,41757,41759,41761,41767,41769,41775,41777,41779,41793,41795,41801,41803,41805,41807,41809,41823,41825,41827,41829,41835,41849,41851,41857,41871,41889,41903,41905,41913,41915,41923,41925,41927,41929,41931,41933,41939,41941,41949,41951,41959],{},[1821,41718,41719,41721,41723],{},[90,41720,36911],{},[90,41722,776],{},[90,41724,671],{},[460,41726,814],{},[87,41728,41729,41731],{},[90,41730,7825],{},[90,41732,776],{},[460,41734,5776],{},[90,41736,30429],{},[87,41738,41739,41741],{},[90,41740,671],{},[90,41742,25485],{},[460,41744,797],{"stretchy":796},[87,41746,41747,41749],{},[90,41748,24236],{},[74,41750,41751,41753,41755],{},[90,41752,776],{},[460,41754,5776],{},[80,41756,82],{},[460,41758,811],{"stretchy":796},[460,41760,29799],{},[87,41762,41763,41765],{},[90,41764,671],{},[90,41766,25485],{},[460,41768,797],{"stretchy":796},[87,41770,41771,41773],{},[90,41772,24236],{},[90,41774,776],{},[460,41776,811],{"stretchy":796},[498,41778],{"linebreak":33087},[1821,41780,41781,41783,41785],{},[90,41782,773],{},[90,41784,25485],{},[74,41786,41787,41789,41791],{},[90,41788,38944],{},[90,41790,773],{},[90,41792,5606],{},[460,41794,797],{"stretchy":796},[87,41796,41797,41799],{},[90,41798,24236],{},[90,41800,776],{},[460,41802,802],{"separator":105},[90,41804,21],{},[460,41806,811],{"stretchy":796},[460,41808,814],{},[26117,41810,41811,41813,41821],{},[460,41812,1825],{},[74,41814,41815,41817,41819],{},[90,41816,7356],{},[460,41818,814],{},[80,41820,1753],{},[90,41822,39478],{"mathvariant":817},[460,41824,797],{"stretchy":796},[90,41826,30429],{},[90,41828,38894],{},[464,41830,41831,41833],{},[460,41832,811],{"stretchy":796},[90,41834,7356],{},[1821,41836,41837,41839,41847],{},[90,41838,36911],{},[74,41840,41841,41843,41845],{},[90,41842,776],{},[460,41844,5776],{},[90,41846,7356],{},[90,41848,671],{},[498,41850],{"linebreak":33087},[77,41852,41853,41855],{},[80,41854,82],{},[90,41856,7321],{},[26117,41858,41859,41861,41869],{},[460,41860,1825],{},[74,41862,41863,41865,41867],{},[90,41864,334],{},[460,41866,814],{},[80,41868,82],{},[90,41870,7321],{},[26117,41872,41873,41875,41883],{},[460,41874,1825],{},[74,41876,41877,41879,41881],{},[90,41878,776],{},[460,41880,814],{},[80,41882,82],{},[87,41884,41885,41887],{},[90,41886,24676],{},[90,41888,334],{},[1821,41890,41891,41893,41895],{},[90,41892,773],{},[90,41894,25485],{},[74,41896,41897,41899,41901],{},[90,41898,38944],{},[90,41900,773],{},[90,41902,5606],{},[460,41904,797],{"stretchy":796},[1821,41906,41907,41909,41911],{},[90,41908,24236],{},[90,41910,334],{},[90,41912,776],{},[460,41914,802],{"separator":105},[1821,41916,41917,41919,41921],{},[90,41918,21],{},[90,41920,334],{},[90,41922,776],{},[460,41924,811],{"stretchy":796},[3276,41926,39029],{},[90,41928,25814],{"mathvariant":817},[90,41930,26239],{},[460,41932,821],{},[87,41934,41935,41937],{},[90,41936,5603],{},[90,41938,25485],{},[460,41940,797],{"stretchy":796},[1821,41942,41943,41945,41947],{},[90,41944,21],{},[90,41946,334],{},[90,41948,776],{},[90,41950,24375],{"mathvariant":817},[1821,41952,41953,41955,41957],{},[90,41954,24236],{},[90,41956,334],{},[90,41958,776],{},[460,41960,811],{"stretchy":796},[97,41962,41963],{"encoding":99},"\\delta_t^V = r_t + \\gamma V_\\theta(s_{t+1}) - V_\\theta(s_t) \\\\\nA_\\theta^{GAE}(s_t, a) = \\sum_{b=0}^{\\infty} (\\gamma\\lambda)^b \\delta_{t+b}^V \\\\\n\\frac{1}{N}\\sum_{n=1}^N\\sum_{t=1}^{T_n} A_\\theta^{GAE}(s_n^t, a_n^t)\\, \\nabla \\log 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me":43149},[135],[58,43151,43153,43164],{"className":43152,"style":28742},[139],[58,43154,43155,43158],{"style":28745},[58,43156],{"className":43157,"style":539},[147],[58,43159,43161],{"className":43160},[152,153,154,155],[58,43162,334],{"className":43163},[118,191,155],[58,43165,43166,43169],{"style":27860},[58,43167],{"className":43168,"style":539},[147],[58,43170,43172],{"className":43171},[152,153,154,155],[58,43173,776],{"className":43174},[118,191,155],[58,43176,226],{"className":43177},[225],[58,43179,43181],{"className":43180},[135],[58,43182,43184],{"className":43183,"style":28775},[139],[58,43185],{},[58,43187,811],{"className":43188},[312],[14,43190,43191],{},"这里的价值状态函数我们一般用一个神经网路进行拟合，一般可以和策略网络公用参数，只是最后一层不同。",[10,43193,43195],{"id":43194},"proximal-policy-optimization-ppo-近邻策略优化算法","Proximal Policy Optimization (PPO) 近邻策略优化算法",[14,43197,43198],{},"在经典的强化学习环境中，我们一般是一边采集数据，一边进行训练模型，采集完的数据用完就会丢掉。这导致我们采集的数据发生了一定的浪费，且模型训练的成本也会增高。但如果我们有一种方法，能让模型在其他模型的表现中学习自己的表现，参考其他数据就能实现自身的更新，这样我们的训练成本就会大大减少。",[48,43200,43201],{"id":43201},"重要性采样",[14,43203,43204,43205,43249,43250,43278,43279,43307,43308,43336],{},"将 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",[58,43251,43253,43266],{"className":43252},[61],[58,43254,43256],{"className":43255},[65],[67,43257,43258],{"xmlns":69},[71,43259,43260,43264],{},[74,43261,43262],{},[90,43263,14],{},[97,43265,14],{"encoding":99},[58,43267,43269],{"className":43268,"ariaHidden":105},[104],[58,43270,43272,43275],{"className":43271},[109],[58,43273],{"className":43274,"style":1705},[113],[58,43276,14],{"className":43277},[118,191]," 下的期望改写为在另一分布 ",[58,43280,43282,43295],{"className":43281},[61],[58,43283,43285],{"className":43284},[65],[67,43286,43287],{"xmlns":69},[71,43288,43289,43293],{},[74,43290,43291],{},[90,43292,1693],{},[97,43294,1693],{"encoding":99},[58,43296,43298],{"className":43297,"ariaHidden":105},[104],[58,43299,43301,43304],{"className":43300},[109],[58,43302],{"className":43303,"style":1705},[113],[58,43305,1693],{"className":43306,"style":440},[118,191],"（proposal）下的期望，从而可用从 ",[58,43309,43311,43324],{"className":43310},[61],[58,43312,43314],{"className":43313},[65],[67,43315,43316],{"xmlns":69},[71,43317,43318,43322],{},[74,43319,43320],{},[90,43321,1693],{},[97,43323,1693],{"encoding":99},[58,43325,43327],{"className":43326,"ariaHidden":105},[104],[58,43328,43330,43333],{"className":43329},[109],[58,43331],{"className":43332,"style":1705},[113],[58,43334,1693],{"className":43335,"style":440},[118,191]," 采样的数据估计：",[58,43338,43340],{"className":43339},[25784],[58,43341,43343,43727],{"className":43342},[61],[58,43344,43346],{"className":43345},[65],[67,43347,43348],{"xmlns":69,"display":9480},[71,43349,43350,43724],{},[25796,43351,43352,43424,43488,43552,43624],{"rowspacing":25798,"columnalign":25799,"columnspacing":25800},[25802,43353,43354,43390],{},[25805,43355,43356],{},[25808,43357,43358],{"scriptlevel":1753,"displaystyle":105},[74,43359,43360,43362,43364,43366,43368,43370,43372],{},[90,43361,5606],{"mathvariant":468},[460,43363,797],{"stretchy":796},[90,43365,11656],{},[460,43367,797],{"stretchy":796},[90,43369,7326],{},[460,43371,811],{"stretchy":796},[87,43373,43374,43376],{},[460,43375,811],{"stretchy":796},[74,43377,43378,43380,43382,43384,43386,43388],{},[90,43379,7326],{},[460,43381,25478],{},[90,43383,14],{},[460,43385,797],{"stretchy":796},[90,43387,7326],{},[460,43389,811],{"stretchy":796},[25805,43391,43392],{},[25808,43393,43394],{"scriptlevel":1753,"displaystyle":105},[74,43395,43396,43398,43400,43406,43408,43410,43412,43414,43416,43418,43420,43422],{},[74,43397],{},[460,43399,814],{},[25495,43401,43402,43404],{},[460,43403,1825],{},[90,43405,7326],{},[90,43407,11656],{},[460,43409,797],{"stretchy":796},[90,43411,7326],{},[460,43413,811],{"stretchy":796},[460,43415,1815],{},[90,43417,14],{},[460,43419,797],{"stretchy":796},[90,43421,7326],{},[460,43423,811],{"stretchy":796},[25802,43425,43426,43432],{},[25805,43427,43428],{},[25808,43429,43430],{"scriptlevel":1753,"displaystyle":105},[74,43431],{},[25805,43433,43434],{},[25808,43435,43436],{"scriptlevel":1753,"displaystyle":105},[74,43437,43438,43440,43442,43448,43450,43452,43454,43456,43458,43460,43462,43464,43466],{},[74,43439],{},[460,43441,814],{},[25495,43443,43444,43446],{},[460,43445,1825],{},[90,43447,7326],{},[90,43449,11656],{},[460,43451,797],{"stretchy":796},[90,43453,7326],{},[460,43455,811],{"stretchy":796},[460,43457,1815],{},[90,43459,14],{},[460,43461,797],{"stretchy":796},[90,43463,7326],{},[460,43465,811],{"stretchy":796},[77,43467,43468,43478],{},[74,43469,43470,43472,43474,43476],{},[90,43471,1693],{},[460,43473,797],{"stretchy":796},[90,43475,7326],{},[460,43477,811],{"stretchy":796},[74,43479,43480,43482,43484,43486],{},[90,43481,1693],{},[460,43483,797],{"stretchy":796},[90,43485,7326],{},[460,43487,811],{"stretchy":796},[25802,43489,43490,43496],{},[25805,43491,43492],{},[25808,43493,43494],{"scriptlevel":1753,"displaystyle":105},[74,43495],{},[25805,43497,43498],{},[25808,43499,43500],{"scriptlevel":1753,"displaystyle":105},[74,43501,43502,43504,43506,43512,43514,43516,43518,43520,43542,43544,43546,43548,43550],{},[74,43503],{},[460,43505,814],{},[25495,43507,43508,43510],{},[460,43509,1825],{},[90,43511,7326],{},[90,43513,11656],{},[460,43515,797],{"stretchy":796},[90,43517,7326],{},[460,43519,811],{"stretchy":796},[77,43521,43522,43532],{},[74,43523,43524,43526,43528,43530],{},[90,43525,14],{},[460,43527,797],{"stretchy":796},[90,43529,7326],{},[460,43531,811],{"stretchy":796},[74,43533,43534,43536,43538,43540],{},[90,43535,1693],{},[460,43537,797],{"stretchy":796},[90,43539,7326],{},[460,43541,811],{"stretchy":796},[460,43543,1815],{},[90,43545,1693],{},[460,43547,797],{"stretchy":796},[90,43549,7326],{},[460,43551,811],{"stretchy":796},[25802,43553,43554,43560],{},[25805,43555,43556],{},[25808,43557,43558],{"scriptlevel":1753,"displaystyle":105},[74,43559],{},[25805,43561,43562],{},[25808,43563,43564],{"scriptlevel":1753,"displaystyle":105},[74,43565,43566,43568,43570,43572],{},[74,43567],{},[460,43569,814],{},[90,43571,5606],{"mathvariant":468},[87,43573,43574,43610],{},[74,43575,43576,43578,43580,43582,43584,43586,43608],{},[460,43577,797],{"fence":105},[90,43579,11656],{},[460,43581,797],{"stretchy":796},[90,43583,7326],{},[460,43585,811],{"stretchy":796},[77,43587,43588,43598],{},[74,43589,43590,43592,43594,43596],{},[90,43591,14],{},[460,43593,797],{"stretchy":796},[90,43595,7326],{},[460,43597,811],{"stretchy":796},[74,43599,43600,43602,43604,43606],{},[90,43601,1693],{},[460,43603,797],{"stretchy":796},[90,43605,7326],{},[460,43607,811],{"stretchy":796},[460,43609,811],{"fence":105},[74,43611,43612,43614,43616,43618,43620,43622],{},[90,43613,7326],{},[460,43615,25478],{},[90,43617,1693],{},[460,43619,797],{"stretchy":796},[90,43621,7326],{},[460,43623,811],{"stretchy":796},[25802,43625,43626,43632],{},[25805,43627,43628],{},[25808,43629,43630],{"scriptlevel":1753,"displaystyle":105},[74,43631],{},[25805,43633,43634],{},[25808,43635,43636],{"scriptlevel":1753,"displaystyle":105},[74,43637,43638,43640,43642,43648,43662,43664,43666,43672,43674,43704,43706,43708,43714,43716,43718,43720,43722],{},[74,43639],{},[460,43641,26109],{},[77,43643,43644,43646],{},[80,43645,82],{},[90,43647,7321],{},[26117,43649,43650,43652,43660],{},[460,43651,1825],{},[74,43653,43654,43656,43658],{},[90,43655,334],{},[460,43657,814],{},[80,43659,82],{},[90,43661,7321],{},[90,43663,11656],{},[460,43665,797],{"stretchy":796},[87,43667,43668,43670],{},[90,43669,7326],{},[90,43671,334],{},[460,43673,811],{"stretchy":796},[77,43675,43676,43690],{},[74,43677,43678,43680,43682,43688],{},[90,43679,14],{},[460,43681,797],{"stretchy":796},[87,43683,43684,43686],{},[90,43685,7326],{},[90,43687,334],{},[460,43689,811],{"stretchy":796},[74,43691,43692,43694,43696,43702],{},[90,43693,1693],{},[460,43695,797],{"stretchy":796},[87,43697,43698,43700],{},[90,43699,7326],{},[90,43701,334],{},[460,43703,811],{"stretchy":796},[460,43705,802],{"separator":105},[498,43707],{"width":39034},[87,43709,43710,43712],{},[90,43711,7326],{},[90,43713,334],{},[460,43715,25478],{},[90,43717,1693],{},[460,43719,797],{"stretchy":796},[90,43721,7326],{},[460,43723,811],{"stretchy":796},[97,43725,43726],{"encoding":99},"\\begin{aligned}\n\\mathbb{E}(f(x))_{x \\sim p(x)} &= \\sum_{x} f(x) \\cdot p(x) \\\\\n&= \\sum_{x} f(x) \\cdot p(x) \\frac{q(x)}{q(x)} \\\\\n&= \\sum_{x} f(x) \\frac{p(x)}{q(x)} \\cdot q(x) \\\\\n&= \\mathbb{E}\\left(f(x) \\frac{p(x)}{q(x)}\\right)_{x \\sim q(x)} \\\\\n&\\approx \\frac{1}{N} \\sum_{n=1}^{N} f(x_n) \\frac{p(x_n)}{q(x_n)}, \\quad x_n \\sim q(x)\n\\end{aligned}",[58,43728,43730],{"className":43729,"ariaHidden":105},[104],[58,43731,43733,43737],{"className":43732},[109],[58,43734],{"className":43735,"style":43736},[113],"height:14.8742em;vertical-align:-7.1871em;",[58,43738,43740],{"className":43739},[118],[58,43741,43743,43890],{"className":43742},[25796],[58,43744,43746],{"className":43745},[26587],[58,43747,43749,43881],{"className":43748},[130,131],[58,43750,43752,43878],{"className":43751},[135],[58,43753,43756,43842,43851,43860,43869],{"className":43754,"style":43755},[139],"height:7.6871em;",[58,43757,43759,43763],{"style":43758},"top:-10.4654em;",[58,43760],{"className":43761,"style":43762},[147],"height:3.8283em;",[58,43764,43766,43769,43772,43775,43778,43781,43784],{"className":43765},[118],[58,43767,5606],{"className":43768},[118,520],[58,43770,797],{"className":43771},[122],[58,43773,11656],{"className":43774,"style":25053},[118,191],[58,43776,797],{"className":43777},[122],[58,43779,7326],{"className":43780},[118,191],[58,43782,811],{"className":43783},[312],[58,43785,43787,43790],{"className":43786},[312],[58,43788,811],{"className":43789},[312],[58,43791,43793],{"className":43792},[195],[58,43794,43796,43834],{"className":43795},[130,131],[58,43797,43799,43831],{"className":43798},[135],[58,43800,43802],{"className":43801,"style":205},[139],[58,43803,43804,43807],{"style":25573},[58,43805],{"className":43806,"style":539},[147],[58,43808,43810],{"className":43809},[152,153,154,155],[58,43811,43813,43816,43819,43822,43825,43828],{"className":43812},[118,155],[58,43814,7326],{"className":43815},[118,191,155],[58,43817,25478],{"className":43818},[503,155],[58,43820,14],{"className":43821},[118,191,155],[58,43823,797],{"className":43824},[122,155],[58,43826,7326],{"className":43827},[118,191,155],[58,43829,811],{"className":43830},[312,155],[58,43832,226],{"className":43833},[225],[58,43835,43837],{"className":43836},[135],[58,43838,43840],{"className":43839,"style":6101},[139],[58,43841],{},[58,43843,43845,43848],{"style":43844},"top:-7.4884em;",[58,43846],{"className":43847,"style":43762},[147],[58,43849],{"className":43850},[118],[58,43852,43854,43857],{"style":43853},"top:-4.5114em;",[58,43855],{"className":43856,"style":43762},[147],[58,43858],{"className":43859},[118],[58,43861,43863,43866],{"style":43862},"top:-1.5114em;",[58,43864],{"className":43865,"style":43762},[147],[58,43867],{"className":43868},[118],[58,43870,43872,43875],{"style":43871},"top:1.7917em;",[58,43873],{"className":43874,"style":43762},[147],[58,43876],{"className":43877},[118],[58,43879,226],{"className":43880},[225],[58,43882,43884],{"className":43883},[135],[58,43885,43888],{"className":43886,"style":43887},[139],"height:7.1871em;",[58,43889],{},[58,43891,43893],{"className":43892},[26811],[58,43894,43896,44993],{"className":43895},[130,131],[58,43897,43899,44990],{"className":43898},[135],[58,43900,43902,44005,44188,44371,44562],{"className":43901,"style":43755},[139],[58,43903,43904,43907],{"style":43758},[58,43905],{"className":43906,"style":43762},[147],[58,43908,43910,43913,43916,43919,43922,43969,43972,43975,43978,43981,43984,43987,43990,43993,43996,43999,44002],{"className":43909},[118],[58,43911],{"className":43912},[118],[58,43914],{"className":43915,"style":499},[498],[58,43917,814],{"className":43918},[503],[58,43920],{"className":43921,"style":499},[498],[58,43923,43925],{"className":43924},[950,25672],[58,43926,43928,43961],{"className":43927},[130,131],[58,43929,43931,43958],{"className":43930},[135],[58,43932,43934,43948],{"className":43933,"style":26859},[139],[58,43935,43936,43939],{"style":26862},[58,43937],{"className":43938,"style":26866},[147],[58,43940,43942],{"className":43941},[152,153,154,155],[58,43943,43945],{"className":43944},[118,155],[58,43946,7326],{"className":43947},[118,191,155],[58,43949,43950,43953],{"style":26875},[58,43951],{"className":43952,"style":26866},[147],[58,43954,43955],{},[58,43956,1825],{"className":43957},[950,1909,26884],[58,43959,226],{"className":43960},[225],[58,43962,43964],{"className":43963},[135],[58,43965,43967],{"className":43966,"style":26894},[139],[58,43968],{},[58,43970],{"className":43971,"style":915},[498],[58,43973,11656],{"className":43974,"style":25053},[118,191],[58,43976,797],{"className":43977},[122],[58,43979,7326],{"className":43980},[118,191],[58,43982,811],{"className":43983},[312],[58,43985],{"className":43986,"style":1871},[498],[58,43988,1815],{"className":43989},[552],[58,43991],{"className":43992,"style":1871},[498],[58,43994,14],{"className":43995},[118,191],[58,43997,797],{"className":43998},[122],[58,44000,7326],{"className":44001},[118,191],[58,44003,811],{"className":44004},[312],[58,44006,44007,44010],{"style":43844},[58,44008],{"className":44009,"style":43762},[147],[58,44011,44013,44016,44019,44022,44025,44072,44075,44078,44081,44084,44087,44090,44093,44096,44099,44102,44105,44108],{"className":44012},[118],[58,44014],{"className":44015},[118],[58,44017],{"classNam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on-policy 的训练改为 off-policy 的训练。",[48,45005,45007],{"id":45006},"off-policy","Off-policy",[14,45009,45010,45011,45074,45075,45104,45105,45242,45243,45434,45435,45650],{},"记 ",[58,45012,45014,45032],{"className":45013},[61],[58,45015,45017],{"className":45016},[65],[67,45018,45019],{"xmlns":69},[71,45020,45021,45029],{},[74,45022,45023],{},[464,45024,45025,45027],{},[90,45026,25485],{},[460,45028,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[97,45030,45031],{"encoding":99},"\\theta'",[58,45033,45035],{"className":45034,"ariaHidden":105},[104],[58,45036,45038,45042],{"className":45037},[109],[58,45039],{"className":45040,"style":45041},[113],"height:0.7519em;",[58,45043,45045,45048],{"className":45044},[118],[58,45046,25485],{"className":45047,"style":3209},[118,191],[58,45049,45051],{"className":45050},[195],[58,45052,45054],{"className":45053},[130],[58,45055,45057],{"className":45056},[135],[58,45058,45060],{"className":45059,"style":45041},[139],[58,45061,45062,45065],{"style":535},[58,45063],{"className":45064,"style":539},[147],[58,45066,45068],{"className":45067},[152,153,154,155],[58,45069,45071],{"className":45070},[118,155],[58,45072,30418],{"className":45073},[118,155]," 为采集数据时的旧策略，",[58,45076,45078,45092],{"className":45077},[61],[58,45079,45081],{"className":45080},[65],[67,45082,45083],{"xmlns":69},[71,45084,45085,45089],{},[74,45086,45087],{},[90,45088,25485],{},[97,45090,45091],{"encoding":99},"\\theta",[58,45093,45095],{"className":45094,"ariaHidden":105},[104],[58,45096,45098,45101],{"className":45097},[109],[58,45099],{"className":45100,"style":406},[113],[58,45102,25485],{"className":45103,"style":3209},[118,191]," 为当前要优化的策略；优势 ",[58,45106,45108,45138],{"className":45107},[61],[58,45109,45111],{"className":45110},[65],[67,45112,45113],{"xmlns":69},[71,45114,45115,45135],{},[74,45116,45117],{},[1821,45118,45119,45121,45127],{},[90,45120,773],{},[464,45122,45123,45125],{},[90,45124,25485],{},[460,45126,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[74,45128,45129,45131,45133],{},[90,45130,38944],{},[90,45132,773],{},[90,45134,5606],{},[97,45136,45137],{"encoding":99},"A_{\\theta'}^{GAE}",[58,45139,45141],{"className":45140,"ariaHidden":105},[104],[58,45142,45144,45148],{"className":45143},[109],[58,45145],{"className":45146,"style":45147},[113],"height:1.1244em;vertical-align:-0.2831em;",[58,45149,45151,45154],{"className":45150},[118],[58,45152,773],{"className":45153},[118,191],[58,45155,45157],{"className":45156},[195],[58,45158,45160,45233],{"className":45159},[130,131],[58,45161,45163,45230],{"className":45162},[135],[58,45164,45166,45210],{"className":45165,"style":3197},[139],[58,45167,45169,45172],{"style":45168},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[58,45170],{"className":45171,"style":539},[147],[58,45173,45175],{"className":45174},[152,153,154,155],[58,45176,45178],{"className":45177},[118,155],[58,45179,45181,45184],{"className":45180},[118,155],[58,45182,25485],{"className":45183,"style":3209},[118,191,155],[58,45185,45187],{"className":45186},[195],[58,45188,45190],{"className":45189},[130],[58,45191,45193],{"className":45192},[135],[58,45194,45196],{"className":45195,"style":30578},[139],[58,45197,45198,45201],{"style":30581},[58,45199],{"className":45200,"style":212},[147],[58,45202,45204],{"className":45203},[152,216,217,155],[58,45205,45207],{"className":45206},[118,155],[58,45208,30418],{"className":45209},[118,155],[58,45211,45212,45215],{"style":535},[58,45213],{"className":45214,"style":539},[147],[58,45216,45218],{"className":45217},[152,153,154,155],[58,45219,45221,45224,45227],{"className":45220},[118,155],[58,45222,38944],{"className":45223},[118,191,155],[58,45225,773],{"className":45226},[118,191,155],[58,45228,5606],{"className":45229,"style":6049},[118,191,155],[58,45231,226],{"className":45232},[225],[58,45234,45236],{"className":45235},[135],[58,45237,45240],{"className":45238,"style":45239},[139],"height:0.2831em;",[58,45241],{}," 由旧策略下的价值网络估计。利用恒等式 ",[58,45244,45246,45300],{"className":45245},[61],[58,45247,45249],{"className":45248},[65],[67,45250,45251],{"xmlns":69},[71,45252,45253,45297],{},[74,45254,45255,45257,45259,45261,45263,45265,45267,45269,45271],{},[90,45256,25814],{"mathvariant":817},[90,45258,26239],{},[460,45260,821],{},[90,45262,11656],{},[460,45264,797],{"stretchy":796},[90,45266,7326],{},[460,45268,811],{"stretchy":796},[460,45270,814],{},[25808,45272,45273],{"scriptlevel":1753,"displaystyle":105},[77,45274,45275,45287],{},[74,45276,45277,45279,45281,45283,45285],{},[90,45278,25814],{"mathvariant":817},[90,45280,11656],{},[460,45282,797],{"stretchy":796},[90,45284,7326],{},[460,45286,811],{"stretchy":796},[74,45288,45289,45291,45293,45295],{},[90,45290,11656],{},[460,45292,797],{"stretchy":796},[90,45294,7326],{},[460,45296,811],{"stretchy":796},[97,45298,45299],{"encoding":99},"\\nabla \\log f(x) = \\dfrac{\\nabla f(x)}{f(x)}",[58,45301,45303,45344],{"className":45302,"ariaHidden":105},[104],[58,45304,45306,45309,45312,45315,45320,45323,45326,45329,45332,45335,45338,45341],{"className":45305},[109],[58,45307],{"className":45308,"style":876},[113],[58,45310,25814],{"className":45311},[118],[58,45313],{"className":45314,"style":915},[498],[58,45316,28284,45318],{"className":45317},[950],[58,45319,28288],{"style":28287},[58,45321],{"className":45322,"style":915},[498],[58,45324,11656],{"className":45325,"style":25053},[118,191],[58,45327,797],{"className":45328},[122],[58,45330,7326],{"className":45331},[118,191],[58,45333,811],{"className":45334},[312],[58,45336],{"className":45337,"style":499},[498],[58,45339,814],{"className":45340},[503],[58,45342],{"className":45343,"style":499},[498],[58,45345,45347,45351],{"className":45346},[109],[58,45348],{"className":45349,"style":45350},[113],"height:2.363em;vertical-align:-0.936em;",[58,45352,45354,45357,45431],{"className":45353},[118],[58,45355],{"className":45356},[122,123],[58,45358,45360],{"className":45359},[77],[58,45361,45363,45423],{"className":45362},[130,131],[58,45364,45366,45420],{"className":45365},[135],[58,45367,45369,45389,45397],{"className":45368,"style":27250},[139],[58,45370,45371,45374],{"style":27253},[58,45372],{"className":45373,"style":148},[147],[58,45375,45377,45380,45383,45386],{"className":45376},[118],[58,45378,11656],{"className":45379,"style":25053},[118,191],[58,45381,797],{"className":45382},[122],[58,45384,7326],{"className":45385},[118,191],[58,45387,811],{"className":45388},[312],[58,45390,45391,45394],{"style":273},[58,45392],{"className":45393,"style":148},[147],[58,45395],{"className":45396,"style":281},[280],[58,45398,45399,45402],{"style":27319},[58,45400],{"className":45401,"style":148},[147],[58,45403,45405,45408,45411,45414,45417],{"className":45404},[118],[58,45406,25814],{"className":45407},[118],[58,45409,11656],{"className":45410,"style":25053},[118,191],[58,45412,797],{"className":45413},[122],[58,45415,7326],{"className":45416},[118,191],[58,45418,811],{"className":45419},[312],[58,45421,226],{"className":45422},[225],[58,45424,45426],{"className":45425},[135],[58,45427,45429],{"className":45428,"style":27384},[139],[58,45430],{},[58,45432],{"className":45433},[312,123],"，可将策略梯度写成重要性采样比 ",[58,45436,45438,45470],{"className":45437},[61],[58,45439,45441],{"className":45440},[65],[67,45442,45443],{"xmlns":69},[71,45444,45445,45467],{},[74,45446,45447],{},[25808,45448,45449],{"scriptlevel":1753,"displaystyle":105},[77,45450,45451,45457],{},[87,45452,45453,45455],{},[90,45454,5603],{},[90,45456,25485],{},[87,45458,45459,45461],{},[90,45460,5603],{},[464,45462,45463,45465],{},[90,45464,25485],{},[460,45466,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[97,45468,45469],{"encoding":99},"\\dfrac{P_\\theta}{P_{\\theta'}}",[58,45471,45473],{"className":45472,"ariaHidden":105},[104],[58,45474,45476,45480],{"className":45475},[109],[58,45477],{"className":45478,"style":45479},[113],"height:2.1963em;vertical-align:-0.836em;",[58,45481,45483,45486,45647],{"className":45482},[118],[58,45484],{"className":45485},[122,123],[58,45487,45489],{"className":45488},[77],[58,45490,45492,45638],{"className":45491},[130,131],[58,45493,45495,45635],{"className":45494},[135],[58,45496,45499,45579,45587],{"className":45497,"style":45498},[139],"height:1.3603em;",[58,45500,45501,45504],{"style":27253},[58,45502],{"className":45503,"style":148},[147],[58,45505,45507],{"className":45506},[118],[58,45508,45510,45513],{"className":45509},[118],[58,45511,5603],{"className":45512,"style":3184},[118,191],[58,45514,45516],{"className":45515},[195],[58,45517,45519,45571],{"className":45518},[130,131],[58,45520,45522,45568],{"className":45521},[135],[58,45523,45525],{"className":45524,"style":1247},[139],[58,45526,45527,45530],{"style":7459},[58,45528],{"className":45529,"style":539},[147],[58,45531,45533],{"className":45532},[152,153,154,155],[58,45534,45536],{"className":45535},[118,155],[58,45537,45539,45542],{"className":45538},[118,155],[58,45540,25485],{"className":45541,"style":3209},[118,191,155],[58,45543,45545],{"className":45544},[195],[58,45546,45548],{"className":45547},[130],[58,45549,45551],{"className":45550},[135],[58,45552,45554],{"className":45553,"style":30578},[139],[58,45555,45556,45559],{"style":30581},[58,45557],{"className":45558,"style":212},[147],[58,45560,45562],{"className":45561},[152,216,217,155],[58,45563,45565],{"className":45564},[118,155],[58,45566,30418],{"className":45567},[118,155],[58,45569,226],{"className":45570},[225],[58,45572,45574],{"className":45573},[135],[58,45575,45577],{"className":45576,"style":1269},[139],[58,45578],{},[58,45580,45581,45584],{"style":273},[58,45582],{"className":45583,"style":148},[147],[58,45585],{"className":45586,"style":281},[280],[58,45588,45589,45592],{"style":27319},[58,45590],{"className":45591,"style":148},[147],[58,45593,45595],{"className":45594},[118],[58,45596,45598,45601],{"className":45597},[118],[58,45599,5603],{"className":45600,"style":3184},[118,191],[58,45602,45604],{"className":45603},[195],[58,45605,45607,45627],{"className":45606},[130,131],[58,45608,45610,45624],{"className":45609},[135],[58,45611,45613],{"className":45612,"style":1247},[139],[58,45614,45615,45618],{"style":7459},[58,45616],{"className":45617,"style":539},[147],[58,45619,45621],{"className":45620},[152,153,154,155],[58,45622,25485],{"className":45623,"style":3209},[118,191,155],[58,45625,226],{"className":45626},[225],[58,45628,45630],{"className":45629},[135],[58,45631,45633],{"className":45632,"style":1269},[139],[58,45634],{},[58,45636,226],{"className":45637},[225],[58,45639,45641],{"className":45640},[135],[58,45642,45645],{"className":45643,"style":45644},[139],"height:0.836em;",[58,45646],{},[58,45648],{"className":45649},[312,123]," 的形式：",[58,45652,45654],{"className":45653},[25784],[58,45655,45657,45709],{"className":45656},[61],[58,45658,45660],{"className":45659},[65],[67,45661,45662],{"xmlns":69,"display":9480},[71,45663,45664,45706],{},[74,45665,45666,45668,45670,45672,45674,45676,45678,45680,45682],{},[90,45667,25814],{"mathvariant":817},[90,45669,26239],{},[460,45671,821],{},[90,45673,11656],{},[460,45675,797],{"stretchy":796},[90,45677,7326],{},[460,45679,811],{"stretchy":796},[460,45681,814],{},[77,45683,45684,45696],{},[74,45685,45686,45688,45690,45692,45694],{},[90,45687,25814],{"mathvariant":817},[90,45689,11656],{},[460,45691,797],{"stretchy":796},[90,45693,7326],{},[460,45695,811],{"stretchy":796},[74,45697,45698,45700,45702,45704],{},[90,45699,11656],{},[460,45701,797],{"stretchy":796},[90,45703,7326],{},[460,45705,811],{"stretchy":796},[97,45707,45708],{"encoding":99},"\\nabla \\log f(x) = \\frac{\\nabla f(x)}{f(x)}",[58,45710,45712,45753],{"className":45711,"ariaHidden":105},[104],[58,45713,45715,45718,45721,45724,45729,45732,45735,45738,45741,45744,45747,45750],{"className":45714},[109],[58,45716],{"className":45717,"style":876},[113],[58,45719,25814],{"className":45720},[118],[58,45722],{"className":45723,"style":915},[498],[58,45725,28284,45727],{"className":45726},[950],[58,45728,28288],{"style":28287},[58,45730],{"className":45731,"style":915},[498],[58,45733,11656],{"className":45734,"style":25053},[118,191],[58,45736,797],{"className":45737},[122],[58,45739,7326],{"className":45740},[118,191],[58,45742,811],{"className":45743},[312],[58,45745],{"className":45746,"style":499},[498],[58,45748,814],{"className":45749},[503],[58,45751],{"className":45752,"style":499},[498],[58,45754,45756,45759],{"className":45755},[109],[58,45757],{"className":45758,"style":45350},[113],[58,45760,45762,45765,45839],{"className":45761},[118],[58,45763],{"className":45764},[122,123],[58,45766,45768],{"className":45767},[77],[58,45769,45771,45831],{"className":45770},[130,131],[58,45772,45774,45828],{"className":45773},[135],[58,45775,45777,45797,45805],{"className":45776,"style":27250},[139],[58,45778,45779,45782],{"style":27253},[58,45780],{"className":45781,"style":148},[147],[58,45783,45785,45788,45791,45794],{"className":45784},[118],[58,45786,11656],{"className":45787,"style":25053},[118,191],[58,45789,797],{"className":45790},[122],[58,45792,7326],{"className":45793},[118,191],[58,45795,811],{"className":45796},[312],[58,45798,45799,45802],{"style":273},[58,45800],{"className":45801,"style":148},[147],[58,45803],{"className":45804,"style":281},[280],[58,45806,45807,45810],{"style":27319},[58,45808],{"className":45809,"style":148},[147],[58,45811,45813,45816,45819,45822,45825],{"className":45812},[118],[58,45814,25814],{"className":45815},[118],[58,45817,11656],{"className":45818,"style":25053},[118,191],[58,45820,797],{"className":45821},[122],[58,45823,7326],{"className":45824},[118,191],[58,45826,811],{"className":45827},[312],[58,45829,226],{"className":45830},[225],[58,45832,45834],{"className":45833},[135],[58,45835,45837],{"className":45836,"style":27384},[139],[58,45838],{},[58,45840],{"className":45841},[312,123],[58,45843,45845],{"className":45844},[25784],[58,45846,45848,46570],{"className":45847},[61],[58,45849,45851],{"className":45850},[65],[67,45852,45853],{"xmlns":69,"display":9480},[71,45854,45855,46567],{},[25796,45856,45857,45981,46177,46403],{"rowspacing":25798,"columnalign":25799,"columnspacing":25800},[25802,45858,45859,45865],{},[25805,45860,45861],{},[25808,45862,45863],{"scriptlevel":1753,"displaystyle":105},[74,45864],{},[25805,45866,45867],{},[25808,45868,45869],{"scriptlevel":1753,"displaystyle":105},[74,45870,45871,45873,45879,45893,45911,45925,45927,45935,45937,45945,45947,45949,45951,45953,45959,45961,45969,45971,45979],{},[74,45872],{},[77,45874,45875,45877],{},[80,45876,82],{},[90,45878,7321],{},[26117,45880,45881,45883,45891],{},[460,45882,1825],{},[74,45884,45885,45887,45889],{},[90,45886,334],{},[460,45888,814],{},[80,45890,82],{},[90,45892,7321],{},[26117,45894,45895,45897,45905],{},[460,45896,1825],{},[74,45898,45899,45901,45903],{},[90,45900,776],{},[460,45902,814],{},[80,45904,82],{},[87,45906,45907,45909],{},[90,45908,24676],{},[90,45910,334],{},[1821,45912,45913,45915,45917],{},[90,45914,773],{},[90,45916,25485],{},[74,45918,45919,45921,45923],{},[90,45920,38944],{},[90,45922,773],{},[90,45924,5606],{},[460,45926,797],{"stretchy":796},[1821,45928,45929,45931,45933],{},[90,45930,24236],{},[90,45932,334],{},[90,45934,776],{},[460,45936,802],{"separator":105},[1821,45938,45939,45941,45943],{},[90,45940,21],{},[90,45942,334],{},[90,45944,776],{},[460,45946,811],{"stretchy":796},[90,45948,25814],{"mathvariant":817},[90,45950,26239],{},[460,45952,821],{},[87,45954,45955,45957],{},[90,45956,5603],{},[90,45958,25485],{},[460,45960,797],{"stretchy":796},[1821,45962,45963,45965,45967],{},[90,45964,21],{},[90,45966,334],{},[90,45968,776],{},[90,45970,24375],{"mathvariant":817},[1821,45972,45973,45975,45977],{},[90,45974,24236],{},[90,45976,334],{},[90,45978,776],{},[460,45980,811],{"stretchy":796},[25802,45982,45983,45989],{},[25805,45984,45985],{},[25808,45986,45987],{"scriptlevel":1753,"displaystyle":105},[74,45988],{},[25805,45990,45991],{},[25808,45992,45993],{"scriptlevel":1753,"displaystyle":105},[74,45994,45995,45997,45999,46005,46019,46037,46055,46057,46065,46067,46075,46077,46143,46145,46147,46149,46155,46157,46165,46167,46175],{},[74,45996],{},[460,45998,814],{},[77,46000,46001,46003],{},[80,46002,82],{},[90,46004,7321],{},[26117,46006,46007,46009,46017],{},[460,46008,1825],{},[74,46010,46011,46013,46015],{},[90,46012,334],{},[460,46014,814],{},[80,46016,82],{},[90,46018,7321],{},[26117,46020,46021,46023,46031],{},[460,46022,1825],{},[74,46024,46025,46027,46029],{},[90,46026,776],{},[460,46028,814],{},[80,46030,82],{},[87,46032,46033,46035],{},[90,46034,24676],{},[90,46036,33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\\sum_{n=1}^{N} \\sum_{t=1}^{T_n} A_\\theta^{GAE}(s_n^t, a_n^t) \\nabla \\log P_\\theta(a_n^t | s_n^t) \\\\\n&= \\frac{1}{N} \\sum_{n=1}^{N} \\sum_{t=1}^{T_n} A_{\\theta'}^{GAE}(s_n^t, a_n^t) \\frac{P_\\theta(a_n^t | s_n^t)}{P_{\\theta'}(a_n^t | s_n^t)} \\nabla \\log P_\\theta(a_n^t | s_n^t) \\\\\n&= \\frac{1}{N} \\sum_{n=1}^{N} \\sum_{t=1}^{T_n} A_{\\theta'}^{GAE}(s_n^t, a_n^t) \\frac{P_\\theta(a_n^t | s_n^t)}{P_{\\theta'}(a_n^t | s_n^t)} \\frac{\\nabla P_\\theta(a_n^t | s_n^t)}{P_\\theta(a_n^t | s_n^t)} \\\\\n&= \\frac{1}{N} \\sum_{n=1}^{N} \\sum_{t=1}^{T_n} A_{\\theta'}^{GAE}(s_n^t, a_n^t) \\frac{\\nabla P_\\theta(a_n^t | s_n^t)}{P_{\\theta'}(a_n^t | 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surrogate 上加 KL 惩罚",[14,51424,51425,51426,51458],{},"如何给我们训练的策略和参考的策略增加相差不能过大这个约束呢？那就是加上 KL 散度的约束。KL 散度就是衡量两个分布差异大小的指标。两个分布差异越小，KL散度越小，分布差异越大，KL散度越大。通过因子 ",[58,51427,51429,51444],{"className":51428},[61],[58,51430,51432],{"className":51431},[65],[67,51433,51434],{"xmlns":69},[71,51435,51436,51441],{},[74,51437,51438],{},[90,51439,51440],{},"β",[97,51442,51443],{"encoding":99},"\\beta",[58,51445,51447],{"className":51446,"ariaHidden":105},[104],[58,51448,51450,51454],{"className":51449},[109],[58,51451],{"className":51452,"style":51453},[113],"height:0.8889em;vertical-align:-0.1944em;",[58,51455,51440],{"className":51456,"style":51457},[118,191],"margin-right:0.05278em;"," 来调整 KL 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还有一种实现，是通过截断函数来替代 KL 散度，防止训练的策略和参考的策略偏差过大，可以看出它是由红色和蓝色两个部分构成，取两个部分的最小值。",[14,52758,52759,52760,53260,53261,6760,53314,53365],{},"其中红色部分是原始公式，蓝色部分是一个截断函数，截断函数内由三个部分组成。如果 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的值介于 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之间，就返回原值，否则返回其中更接近的一个。这就限制的参考模型和训练模型差异的值不能太大。",[58,53367,53369],{"className":53368},[25784],[58,53370,53372,53708],{"className":53371},[61],[58,53373,53375],{"className":53374},[65],[67,53376,53377],{"xmlns":69,"display":9480},[71,53378,53379,53705],{},[74,53380,53381,53383,53385,53387,53394,53396,53398,53404,53418,53436,53439,53441],{},[90,53382,7815],{},[90,53384,791],{},[90,53386,24236],{},[87,53388,53389,53391],{},[90,53390,24236],{},[3276,53392,53393],{},"ppo2",[460,53395,814],{},[460,53397,29799],{},[77,53399,53400,53402],{},[80,53401,82],{},[90,53403,7321],{},[26117,53405,53406,53408,53416],{},[460,53407,1825],{},[74,53409,53410,53412,53414],{},[90,53411,334],{},[460,53413,814],{},[80,53415,82],{},[90,53417,7321],{},[26117,53419,53420,53422,53430],{},[460,53421,1825],{},[74,53423,53424,53426,53428],{},[90,53425,776],{},[460,53427,814],{},[80,53429,82],{},[87,53431,53432,53434],{},[90,53433,24676],{},[90,53435,334],{},[90,53437,53438],{},"min",[460,53440,821],{},[74,53442,53443,53445,53554,53556,53558,53703],{},[460,53444,797],{"fence":105},[25808,53446,53448,53466,53468,53476,53478,53486,53488],{"mathcolor":53447},"red",[1821,53449,53450,53452,53458],{},[90,53451,773],{},[464,53453,53454,53456],{},[90,53455,25485],{},[460,53457,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[74,53459,53460,53462,53464],{},[90,53461,38944],{},[90,53463,773],{},[90,53465,5606],{},[460,53467,797],{"stretchy":796},[1821,53469,53470,53472,53474],{},[90,53471,24236],{},[90,53473,334],{},[90,53475,776],{},[460,53477,802],{"separator":105},[1821,53479,53480,53482,53484],{},[90,53481,21],{},[90,53483,334],{},[90,53485,776],{},[460,53487,811],{"stretchy":796},[77,53489,53490,53520],{},[74,53491,53492,53498,53500,53508,53510,53518],{},[87,53493,53494,53496],{},[90,53495,5603],{},[90,53497,25485],{},[460,53499,797],{"stretchy":796},[1821,53501,53502,53504,53506],{},[90,53503,21],{},[90,53505,334],{},[90,53507,776],{},[90,53509,24375],{"mathvariant":817},[1821,53511,53512,53514,53516],{},[90,53513,24236],{},[90,53515,334],{},[90,53517,776],{},[460,53519,811],{"stretchy":796},[74,53521,53522,53532,53534,53542,53544,53552],{},[87,53523,53524,53526],{},[90,53525,5603],{},[464,53527,53528,53530],{},[90,53529,25485],{},[460,53531,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[460,53533,797],{"stretchy":796},[1821,53535,53536,53538,53540],{},[90,53537,21],{},[90,53539,334],{},[90,53541,776],{},[90,53543,24375],{"mathvariant":817},[1821,53545,53546,53548,53550],{},[90,53547,24236],{},[90,53549,334],{},[90,53551,776],{},[460,53553,811],{"stretchy":796},[460,53555,802],{"separator":105},[3276,53557,39029],{},[25808,53559,53561,53571,53663,53681,53683,53691,53693,53701],{"mathcolor":53560},"skyblue",[74,53562,53563,53565,53567,53569],{},[90,53564,2943],{"mathvariant":817},[90,53566,2902],{"mathvariant":817},[90,53568,788],{"mathvariant":817},[90,53570,14],{"mathvariant":817},[74,53572,53573,53575,53641,53643,53645,53647,53649,53651,53653,53655,53657,53659,53661],{},[460,53574,797],{"fence":105},[77,53576,53577,53607],{},[74,53578,53579,53585,53587,53595,53597,53605],{},[87,53580,53581,53583],{},[90,53582,5603],{},[90,53584,25485],{},[460,53586,797],{"stretchy":796},[1821,53588,53589,53591,53593],{},[90,53590,21],{},[90,53592,334],{},[90,53594,776],{},[90,53596,24375],{"mathvariant":817},[1821,53598,53599,53601,53603],{},[90,53600,24236],{},[90,53602,334],{},[90,53604,776],{},[460,53606,811],{"stretchy":796},[74,53608,53609,53619,53621,53629,53631,53639],{},[87,53610,53611,53613],{},[90,53612,5603],{},[464,53614,53615,53617],{},[90,53616,25485],{},[460,53618,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[460,53620,797],{"stretchy":796},[1821,53622,53623,53625,53627],{},[90,53624,21],{},[90,53626,334],{},[90,53628,776],{},[90,53630,24375],{"mathvariant":817},[1821,53632,53633,53635,53637],{},[90,53634,24236],{},[90,53636,334],{},[90,53638,776],{},[460,53640,811],{"stretchy":796},[460,53642,802],{"separator":105},[3276,53644,39029],{},[80,53646,82],{},[460,53648,29799],{},[90,53650,53279],{},[460,53652,802],{"separator":105},[3276,53654,39029],{},[80,53656,82],{},[460,53658,5776],{},[90,53660,53279],{},[460,53662,811],{"fence":105},[1821,53664,53665,53667,53673],{},[90,53666,773],{},[464,53668,53669,53671],{},[90,53670,25485],{},[460,53672,30418],{"mathvariant":817,"lspace":25800,"rspace":25800},[74,53674,53675,53677,53679],{},[90,53676,38944],{},[90,53678,773],{},[90,53680,5606],{},[460,53682,797],{"stretchy":796},[1821,53684,53685,53687,53689],{},[90,53686,24236],{},[90,53688,334],{},[90,53690,776],{},[460,53692,802],{"separator":105},[1821,53694,53695,53697,53699],{},[90,53696,21],{},[90,53698,334],{},[90,53700,776],{},[460,53702,811],{"stretchy":796},[460,53704,811],{"fence":105},[97,53706,53707],{"encoding":99},"Loss_{\\text{ppo2}} 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