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的缩放点积注意力是：",[14,835,836],{},[135,837,839,944],{"className":838},[138],[135,840,842],{"className":841},[142],[144,843,844],{"xmlns":146},[148,845,846,941],{},[151,847,848,851,854,856,859,861,863,866,869,871,875,877,880,882,884,886,889,892,896,899,922,924,926,938],{},[167,849,850],{},"A",[167,852,853],{},"t",[167,855,853],{},[167,857,858],{},"e",[167,860,411],{},[167,862,853],{},[167,864,865],{},"i",[167,867,868],{},"o",[167,870,411],{},[537,872,874],{"stretchy":873},"false","(",[167,876,535],{},[537,878,879],{"separator":182},",",[167,881,648],{},[537,883,879],{"separator":182},[167,885,748],{},[537,887,888],{"stretchy":873},")",[537,890,891],{},"=",[167,893,895],{"mathvariant":894},"normal","softmax",[537,897,898],{},"⁡",[151,900,901,903,920],{},[537,902,874],{"fence":182},[154,904,905,916],{},[151,906,907,909],{},[167,908,535],{},[541,910,911,913],{},[167,912,648],{},[167,914,915],{"mathvariant":894},"⊤",[161,917,918],{},[167,919,169],{},[537,921,888],{"fence":182},[167,923,748],{},[537,925,539],{},[541,927,928,930],{},[167,929,546],{"mathvariant":545},[151,931,932,934,936],{},[167,933,411],{},[537,935,553],{},[167,937,502],{},[167,939,940],{"mathvariant":894},".",[174,942,943],{"encoding":176}," Attention(Q,K,V) = \\operatorname{softmax}\\left(\\frac{QK^\\top}{\\sqrt{d}}\\right)V \\in \\mathbb{R}^{n \\times v}.",[135,945,947,1017,1219],{"className":946,"ariaHidden":182},[181],[135,948,950,954,957,961,964,967,970,973,976,979,982,985,989,993,996,999,1002,1005,1008,1011,1014],{"className":949},[186],[135,951],{"className":952,"style":953},[190],"height:1em;vertical-align:-0.25em;",[135,955,850],{"className":956},[195,268],[135,958,960],{"className":959},[195,268],"tt",[135,962,858],{"className":963},[195,268],[135,965,411],{"className":966},[195,268],[135,968,853],{"className":969},[195,268],[135,971,865],{"className":972},[195,268],[135,974,868],{"className":975},[195,268],[135,977,411],{"className":978},[195,268],[135,980,874],{"className":981},[199],[135,983,535],{"className":984},[195,268],[135,986,879],{"className":987},[988],"mpunct",[135,990],{"className":991,"style":992},[575],"margin-right:0.1667em;",[135,994,648],{"className":995,"style":679},[195,268],[135,997,879],{"className":998},[988],[135,1000],{"className":1001,"style":992},[575],[135,1003,748],{"className":1004,"style":778},[195,268],[135,1006,888],{"className":1007},[389],[135,1009],{"className":1010,"style":576},[575],[135,1012,891],{"className":1013},[580],[135,1015],{"className":1016,"style":576},[575],[135,1018,1020,1024,1032,1035,1204,1207,1210,1213,1216],{"className":1019},[186],[135,1021],{"className":1022,"style":1023},[190],"height:1.8em;vertical-align:-0.65em;",[135,1025,1028],{"className":1026},[1027],"mop",[135,1029,895],{"className":1030},[195,1031],"mathrm",[135,1033],{"className":1034,"style":992},[575],[135,1036,1039,1049,1198],{"className":1037},[1038],"minner",[135,1040,1044],{"className":1041,"style":1043},[199,1042],"delimcenter","top:0em;",[135,1045,874],{"className":1046},[1047,1048],"delimsizing","size2",[135,1050,1052,1055,1195],{"className":1051},[195],[135,1053],{"className":1054},[199,200],[135,1056,1058],{"className":1057},[154],[135,1059,1061,1187],{"className":1060},[207,208],[135,1062,1064,1184],{"className":1063},[212],[135,1065,1068,1130,1138],{"className":1066,"style":1067},[216],"height:1.095em;",[135,1069,1071,1074],{"style":1070},"top:-2.5335em;",[135,1072],{"className":1073,"style":225},[224],[135,1075,1077],{"className":1076},[229,230,231,232],[135,1078,1080],{"className":1079},[195,232],[135,1081,1083],{"className":1082},[195,239,232],[135,1084,1086,1121],{"className":1085},[207,208],[135,1087,1089,1118],{"className":1088},[212],[135,1090,1093,1105],{"className":1091,"style":1092},[216],"height:0.9378em;",[135,1094,1096,1099],{"className":1095,"style":254},[253],[135,1097],{"className":1098,"style":225},[224],[135,1100,1102],{"className":1101,"style":261},[195,232],[135,1103,169],{"className":1104},[195,268,232],[135,1106,1108,1111],{"style":1107},"top:-2.8978em;",[135,1109],{"className":1110,"style":225},[224],[135,1112,1114],{"className":1113,"style":323},[322,232],[325,1115,1116],{"xmlns":327,"width":328,"height":329,"viewBox":330,"preserveAspectRatio":331},[333,1117],{"d":335},[135,1119,303],{"className":1120},[302],[135,1122,1124],{"className":1123},[212],[135,1125,1128],{"className":1126,"style":1127},[216],"height:0.1022em;",[135,1129],{},[135,1131,1132,1135],{"style":350},[135,1133],{"className":1134,"style":225},[224],[135,1136],{"className":1137,"style":358},[357],[135,1139,1141,1144],{"style":1140},"top:-3.4461em;",[135,1142],{"className":1143,"style":225},[224],[135,1145,1147],{"className":1146},[229,230,231,232],[135,1148,1150,1153],{"className":1149},[195,232],[135,1151,535],{"className":1152},[195,268,232],[135,1154,1156,1159],{"className":1155},[195,232],[135,1157,648],{"className":1158,"style":679},[195,268,232],[135,1160,1162],{"className":1161},[272],[135,1163,1165],{"className":1164},[207],[135,1166,1168],{"className":1167},[212],[135,1169,1172],{"className":1170,"style":1171},[216],"height:0.927em;",[135,1173,1175,1178],{"style":1174},"top:-2.931em;margin-right:0.0714em;",[135,1176],{"className":1177,"style":289},[224],[135,1179,1181],{"className":1180},[229,293,294,232],[135,1182,915],{"className":1183},[195,232],[135,1185,303],{"className":1186},[302],[135,1188,1190],{"className":1189},[212],[135,1191,1193],{"className":1192,"style":383},[216],[135,1194],{},[135,1196],{"className":1197},[389,200],[135,1199,1201],{"className":1200,"style":1043},[389,1042],[135,1202,888],{"className":1203},[1047,1048],[135,1205],{"className":1206,"style":992},[575],[135,1208,748],{"className":1209,"style":778},[195,268],[135,1211],{"className":1212,"style":576},[575],[135,1214,539],{"className":1215},[580],[135,1217],{"className":1218,"style":576},[575],[135,1220,1222,1225,1263],{"className":1221},[186],[135,1223],{"className":1224,"style":794},[190],[135,1226,1228,1231],{"className":1227},[195],[135,1229,546],{"className":1230},[195,597],[135,1232,1234],{"className":1233},[272],[135,1235,1237],{"className":1236},[207],[135,1238,1240],{"className":1239},[212],[135,1241,1243],{"className":1242,"style":794},[216],[135,1244,1245,1248],{"style":612},[135,1246],{"className":1247,"style":616},[224],[135,1249,1251],{"className":1250},[229,230,231,232],[135,1252,1254,1257,1260],{"className":1253},[195,232],[135,1255,411],{"className":1256},[195,268,232],[135,1258,553],{"className":1259},[629,232],[135,1261,502],{"className":1262,"style":517},[195,268,232],[135,1264,940],{"className":1265},[195],[14,1267,1268],{},[117,1269],{"alt":1270,"src":1271},"注意力","transformer/attention.png",[14,1273,1274,1275,1349,1350,1421,1422,1542],{},"缩放点积注意力的输入由维度为 ",[135,1276,1278,1296],{"className":1277},[138],[135,1279,1281],{"className":1280},[142],[144,1282,1283],{"xmlns":146},[148,1284,1285,1293],{},[151,1286,1287],{},[164,1288,1289,1291],{},[167,1290,169],{},[167,1292,172],{},[174,1294,1295],{"encoding":176},"d_k",[135,1297,1299],{"className":1298,"ariaHidden":182},[181],[135,1300,1302,1306],{"className":1301},[186],[135,1303],{"className":1304,"style":1305},[190],"height:0.8444em;vertical-align:-0.15em;",[135,1307,1309,1312],{"className":1308},[195],[135,1310,169],{"className":1311},[195,268],[135,1313,1315],{"className":1314},[272],[135,1316,1318,1340],{"className":1317},[207,208],[135,1319,1321,1337],{"className":1320},[212],[135,1322,1325],{"className":1323,"style":1324},[216],"height:0.3361em;",[135,1326,1328,1331],{"style":1327},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[135,1329],{"className":1330,"style":616},[224],[135,1332,1334],{"className":1333},[229,230,231,232],[135,1335,172],{"className":1336,"style":298},[195,268,232],[135,1338,303],{"className":1339},[302],[135,1341,1343],{"className":1342},[212],[135,1344,1347],{"className":1345,"style":1346},[216],"height:0.15em;",[135,1348],{}," ​的查询和键以及维度为 ",[135,1351,1353,1371],{"className":1352},[138],[135,1354,1356],{"className":1355},[142],[144,1357,1358],{"xmlns":146},[148,1359,1360,1368],{},[151,1361,1362],{},[164,1363,1364,1366],{},[167,1365,169],{},[167,1367,502],{},[174,1369,1370],{"encoding":176},"d_v",[135,1372,1374],{"className":1373,"ariaHidden":182},[181],[135,1375,1377,1380],{"className":1376},[186],[135,1378],{"className":1379,"style":1305},[190],[135,1381,1383,1386],{"className":1382},[195],[135,1384,169],{"className":1385},[195,268],[135,1387,1389],{"className":1388},[272],[135,1390,1392,1413],{"className":1391},[207,208],[135,1393,1395,1410],{"className":1394},[212],[135,1396,1399],{"className":1397,"style":1398},[216],"height:0.1514em;",[135,1400,1401,1404],{"style":1327},[135,1402],{"className":1403,"style":616},[224],[135,1405,1407],{"className":1406},[229,230,231,232],[135,1408,502],{"className":1409,"style":517},[195,268,232],[135,1411,303],{"className":1412},[302],[135,1414,1416],{"className":1415},[212],[135,1417,1419],{"className":1418,"style":1346},[216],[135,1420],{}," ​的值组成。我们计算查询与所有键的点积，将每个点积除以 ",[135,1423,1425,1445],{"className":1424},[138],[135,1426,1428],{"className":1427},[142],[144,1429,1430],{"xmlns":146},[148,1431,1432,1442],{},[151,1433,1434],{},[161,1435,1436],{},[164,1437,1438,1440],{},[167,1439,169],{},[167,1441,172],{},[174,1443,1444],{"encoding":176},"\\sqrt{d_k}",[135,1446,1448],{"className":1447,"ariaHidden":182},[181],[135,1449,1451,1455],{"className":1450},[186],[135,1452],{"className":1453,"style":1454},[190],"height:1.04em;vertical-align:-0.1828em;",[135,1456,1458],{"className":1457},[195,239],[135,1459,1461,1533],{"className":1460},[207,208],[135,1462,1464,1530],{"className":1463},[212],[135,1465,1468,1517],{"className":1466,"style":1467},[216],"height:0.8572em;",[135,1469,1471,1474],{"className":1470,"style":254},[253],[135,1472],{"className":1473,"style":225},[224],[135,1475,1477],{"className":1476,"style":261},[195],[135,1478,1480,1483],{"className":1479},[195],[135,1481,169],{"className":1482},[195,268],[135,1484,1486],{"className":1485},[272],[135,1487,1489,1509],{"className":1488},[207,208],[135,1490,1492,1506],{"className":1491},[212],[135,1493,1495],{"className":1494,"style":1324},[216],[135,1496,1497,1500],{"style":1327},[135,1498],{"className":1499,"style":616},[224],[135,1501,1503],{"className":1502},[229,230,231,232],[135,1504,172],{"className":1505,"style":298},[195,268,232],[135,1507,303],{"className":1508},[302],[135,1510,1512],{"className":1511},[212],[135,1513,1515],{"className":1514,"style":1346},[216],[135,1516],{},[135,1518,1520,1523],{"style":1519},"top:-2.8172em;",[135,1521],{"className":1522,"style":225},[224],[135,1524,1526],{"className":1525,"style":323},[322],[325,1527,1528],{"xmlns":327,"width":328,"height":329,"viewBox":330,"preserveAspectRatio":331},[333,1529],{"d":335},[135,1531,303],{"className":1532},[302],[135,1534,1536],{"className":1535},[212],[135,1537,1540],{"className":1538,"style":1539},[216],"height:0.1828em;",[135,1541],{},"​​，并应用softmax函数以获得值上的权重。",[14,1544,1545,1546,1615,1616,1685,1686,1755,1756,1786,1787,1815,1816,1846,1847,1875,1876,2179,2180,1846,2208,2277,2278,390],{},"对于较小的 ",[135,1547,1549,1566],{"className":1548},[138],[135,1550,1552],{"className":1551},[142],[144,1553,1554],{"xmlns":146},[148,1555,1556,1564],{},[151,1557,1558],{},[164,1559,1560,1562],{},[167,1561,169],{},[167,1563,172],{},[174,1565,1295],{"encoding":176},[135,1567,1569],{"className":1568,"ariaHidden":182},[181],[135,1570,1572,1575],{"className":1571},[186],[135,1573],{"className":1574,"style":1305},[190],[135,1576,1578,1581],{"className":1577},[195],[135,1579,169],{"className":1580},[195,268],[135,1582,1584],{"className":1583},[272],[135,1585,1587,1607],{"className":1586},[207,208],[135,1588,1590,1604],{"className":1589},[212],[135,1591,1593],{"className":1592,"style":1324},[216],[135,1594,1595,1598],{"style":1327},[135,1596],{"className":1597,"style":616},[224],[135,1599,1601],{"className":1600},[229,230,231,232],[135,1602,172],{"className":1603,"style":298},[195,268,232],[135,1605,303],{"className":1606},[302],[135,1608,1610],{"className":1609},[212],[135,1611,1613],{"className":1612,"style":1346},[216],[135,1614],{}," 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 ",[135,1617,1619,1636],{"className":1618},[138],[135,1620,1622],{"className":1621},[142],[144,1623,1624],{"xmlns":146},[148,1625,1626,1634],{},[151,1627,1628],{},[164,1629,1630,1632],{},[167,1631,169],{},[167,1633,172],{},[174,1635,1295],{"encoding":176},[135,1637,1639],{"className":1638,"ariaHidden":182},[181],[135,1640,1642,1645],{"className":1641},[186],[135,1643],{"className":1644,"style":1305},[190],[135,1646,1648,1651],{"className":1647},[195],[135,1649,169],{"className":1650},[195,268],[135,1652,1654],{"className":1653},[272],[135,1655,1657,1677],{"className":1656},[207,208],[135,1658,1660,1674],{"className":1659},[212],[135,1661,1663],{"className":1662,"style":1324},[216],[135,1664,1665,1668],{"style":1327},[135,1666],{"className":1667,"style":616},[224],[135,1669,1671],{"className":1670},[229,230,231,232],[135,1672,172],{"className":1673,"style":298},[195,268,232],[135,1675,303],{"className":1676},[302],[135,1678,1680],{"className":1679},[212],[135,1681,1683],{"className":1682,"style":1346},[216],[135,1684],{}," 值较大时会优于点积注意力。我们怀疑在 ",[135,1687,1689,1706],{"className":1688},[138],[135,1690,1692],{"className":1691},[142],[144,1693,1694],{"xmlns":146},[148,1695,1696,1704],{},[151,1697,1698],{},[164,1699,1700,1702],{},[167,1701,169],{},[167,1703,172],{},[174,1705,1295],{"encoding":176},[135,1707,1709],{"className":1708,"ariaHidden":182},[181],[135,1710,1712,1715],{"className":1711},[186],[135,1713],{"className":1714,"style":1305},[190],[135,1716,1718,1721],{"className":1717},[195],[135,1719,169],{"className":1720},[195,268],[135,1722,1724],{"className":1723},[272],[135,1725,1727,1747],{"className":1726},[207,208],[135,1728,1730,1744],{"className":1729},[212],[135,1731,1733],{"className":1732,"style":1324},[216],[135,1734,1735,1738],{"style":1327},[135,1736],{"className":1737,"style":616},[224],[135,1739,1741],{"className":1740},[229,230,231,232],[135,1742,172],{"className":1743,"style":298},[195,268,232],[135,1745,303],{"className":1746},[302],[135,1748,1750],{"className":1749},[212],[135,1751,1753],{"className":1752,"style":1346},[216],[135,1754],{}," 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 ",[135,1757,1759,1773],{"className":1758},[138],[135,1760,1762],{"className":1761},[142],[144,1763,1764],{"xmlns":146},[148,1765,1766,1771],{},[151,1767,1768],{},[167,1769,1770],{},"q",[174,1772,1770],{"encoding":176},[135,1774,1776],{"className":1775,"ariaHidden":182},[181],[135,1777,1779,1783],{"className":1778},[186],[135,1780],{"className":1781,"style":1782},[190],"height:0.625em;vertical-align:-0.1944em;",[135,1784,1770],{"className":1785,"style":517},[195,268]," 和键 ",[135,1788,1790,1803],{"className":1789},[138],[135,1791,1793],{"className":1792},[142],[144,1794,1795],{"xmlns":146},[148,1796,1797,1801],{},[151,1798,1799],{},[167,1800,172],{},[174,1802,172],{"encoding":176},[135,1804,1806],{"className":1805,"ariaHidden":182},[181],[135,1807,1809,1812],{"className":1808},[186],[135,1810],{"className":1811,"style":483},[190],[135,1813,172],{"className":1814,"style":298},[195,268]," 都符合一个均值为 ",[135,1817,1819,1833],{"className":1818},[138],[135,1820,1822],{"className":1821},[142],[144,1823,1824],{"xmlns":146},[148,1825,1826,1831],{},[151,1827,1828],{},[157,1829,1830],{},"0",[174,1832,1830],{"encoding":176},[135,1834,1836],{"className":1835,"ariaHidden":182},[181],[135,1837,1839,1843],{"className":1838},[186],[135,1840],{"className":1841,"style":1842},[190],"height:0.6444em;",[135,1844,1830],{"className":1845},[195],"，方差为 ",[135,1848,1850,1863],{"className":1849},[138],[135,1851,1853],{"className":1852},[142],[144,1854,1855],{"xmlns":146},[148,1856,1857,1861],{},[151,1858,1859],{},[157,1860,159],{},[174,1862,159],{"encoding":176},[135,1864,1866],{"className":1865,"ariaHidden":182},[181],[135,1867,1869,1872],{"className":1868},[186],[135,1870],{"className":1871,"style":1842},[190],[135,1873,159],{"className":1874},[195]," 的随机变量。他们点积的结果 ",[135,1877,1879,1932],{"className":1878},[138],[135,1880,1882],{"className":1881},[142],[144,1883,1884],{"xmlns":146},[148,1885,1886,1929],{},[151,1887,1888,1890,1893,1895,1897,1917,1923],{},[167,1889,1770],{},[537,1891,1892],{},"⋅",[167,1894,172],{},[537,1896,891],{},[1898,1899,1900,1903,1911],"msubsup",{},[537,1901,1902],{},"∑",[151,1904,1905,1907,1909],{},[167,1906,865],{},[537,1908,891],{},[157,1910,159],{},[164,1912,1913,1915],{},[167,1914,169],{},[167,1916,172],{},[164,1918,1919,1921],{},[167,1920,1770],{},[167,1922,865],{},[164,1924,1925,1927],{},[167,1926,172],{},[167,1928,865],{},[174,1930,1931],{"encoding":176},"q \\cdot k = \\sum_{i=1}^{d_k}q_{i}k_{i}",[135,1933,1935,1955,1973],{"className":1934,"ariaHidden":182},[181],[135,1936,1938,1942,1945,1949,1952],{"className":1937},[186],[135,1939],{"className":1940,"style":1941},[190],"height:0.6389em;vertical-align:-0.1944em;",[135,1943,1770],{"className":1944,"style":517},[195,268],[135,1946],{"className":1947,"style":1948},[575],"margin-right:0.2222em;",[135,1950,1892],{"className":1951},[629],[135,1953],{"className":1954,"style":1948},[575],[135,1956,1958,1961,1964,1967,1970],{"className":1957},[186],[135,1959],{"className":1960,"style":483},[190],[135,1962,172],{"className":1963,"style":298},[195,268],[135,1965],{"className":1966,"style":576},[575],[135,1968,891],{"className":1969},[580],[135,1971],{"className":1972,"style":576},[575],[135,1974,1976,1980,2087,2090,2135],{"className":1975},[186],[135,1977],{"className":1978,"style":1979},[190],"height:1.2887em;vertical-align:-0.2997em;",[135,1981,1983,1989],{"className":1982},[1027],[135,1984,1902],{"className":1985,"style":1988},[1027,1986,1987],"op-symbol","small-op","position:relative;top:0em;",[135,1990,1992],{"className":1991},[272],[135,1993,1995,2078],{"className":1994},[207,208],[135,1996,1998,2075],{"className":1997},[212],[135,1999,2002,2023],{"className":2000,"style":2001},[216],"height:0.989em;",[135,2003,2005,2008],{"style":2004},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[135,2006],{"className":2007,"style":616},[224],[135,2009,2011],{"className":2010},[229,230,231,232],[135,2012,2014,2017,2020],{"className":2013},[195,232],[135,2015,865],{"className":2016},[195,268,232],[135,2018,891],{"className":2019},[580,232],[135,2021,159],{"className":2022},[195,232],[135,2024,2026,2029],{"style":2025},"top:-3.2029em;margin-right:0.05em;",[135,2027],{"className":2028,"style":616},[224],[135,2030,2032],{"className":2031},[229,230,231,232],[135,2033,2035],{"className":2034},[195,232],[135,2036,2038,2041],{"className":2037},[195,232],[135,2039,169],{"className":2040},[195,268,232],[135,2042,2044],{"className":2043},[272],[135,2045,2047,2067],{"className":2046},[207,208],[135,2048,2050,2064],{"className":2049},[212],[135,2051,2053],{"className":2052,"style":282},[216],[135,2054,2055,2058],{"style":285},[135,2056],{"className":2057,"style":289},[224],[135,2059,2061],{"className":2060},[229,293,294,232],[135,2062,172],{"className":2063,"style":298},[195,268,232],[135,2065,303],{"className":2066},[302],[135,2068,2070],{"className":2069},[212],[135,2071,2073],{"className":2072,"style":310},[216],[135,2074],{},[135,2076,303],{"className":2077},[302],[135,2079,2081],{"className":2080},[212],[135,2082,2085],{"className":2083,"style":2084},[216],"height:0.2997em;",[135,2086],{},[135,2088],{"className":2089,"style":992},[575],[135,2091,2093,2096],{"className":2092},[195],[135,2094,1770],{"className":2095,"style":517},[195,268],[135,2097,2099],{"className":2098},[272],[135,2100,2102,2127],{"className":2101},[207,208],[135,2103,2105,2124],{"className":2104},[212],[135,2106,2109],{"className":2107,"style":2108},[216],"height:0.3117em;",[135,2110,2112,2115],{"style":2111},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[135,2113],{"className":2114,"style":616},[224],[135,2116,2118],{"className":2117},[229,230,231,232],[135,2119,2121],{"className":2120},[195,232],[135,2122,865],{"className":2123},[195,268,232],[135,2125,303],{"className":2126},[302],[135,2128,2130],{"className":2129},[212],[135,2131,2133],{"className":2132,"style":1346},[216],[135,2134],{},[135,2136,2138,2141],{"className":2137},[195],[135,2139,172],{"className":2140,"style":298},[195,268],[135,2142,2144],{"className":2143},[272],[135,2145,2147,2171],{"className":2146},[207,208],[135,2148,2150,2168],{"className":2149},[212],[135,2151,2153],{"className":2152,"style":2108},[216],[135,2154,2156,2159],{"style":2155},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[135,2157],{"className":2158,"style":616},[224],[135,2160,2162],{"className":2161},[229,230,231,232],[135,2163,2165],{"className":2164},[195,232],[135,2166,865],{"className":2167},[195,268,232],[135,2169,303],{"className":2170},[302],[135,2172,2174],{"className":2173},[212],[135,2175,2177],{"className":2176,"style":1346},[216],[135,2178],{}," 的均值为 ",[135,2181,2183,2196],{"className":2182},[138],[135,2184,2186],{"className":2185},[142],[144,2187,2188],{"xmlns":146},[148,2189,2190,2194],{},[151,2191,2192],{},[157,2193,1830],{},[174,2195,1830],{"encoding":176},[135,2197,2199],{"className":2198,"ariaHidden":182},[181],[135,2200,2202,2205],{"className":2201},[186],[135,2203],{"className":2204,"style":1842},[190],[135,2206,1830],{"className":2207},[195],[135,2209,2211,2228],{"className":2210},[138],[135,2212,2214],{"className":2213},[142],[144,2215,2216],{"xmlns":146},[148,2217,2218,2226],{},[151,2219,2220],{},[164,2221,2222,2224],{},[167,2223,169],{},[167,2225,172],{},[174,2227,1295],{"encoding":176},[135,2229,2231],{"className":2230,"ariaHidden":182},[181],[135,2232,2234,2237],{"className":2233},[186],[135,2235],{"className":2236,"style":1305},[190],[135,2238,2240,2243],{"className":2239},[195],[135,2241,169],{"className":2242},[195,268],[135,2244,2246],{"className":2245},[272],[135,2247,2249,2269],{"className":2248},[207,208],[135,2250,2252,2266],{"className":2251},[212],[135,2253,2255],{"className":2254,"style":1324},[216],[135,2256,2257,2260],{"style":1327},[135,2258],{"className":2259,"style":616},[224],[135,2261,2263],{"className":2262},[229,230,231,232],[135,2264,172],{"className":2265,"style":298},[195,268,232],[135,2267,303],{"className":2268},[302],[135,2270,2272],{"className":2271},[212],[135,2273,2275],{"className":2274,"style":1346},[216],[135,2276],{},"，为了抵消这种影响，我们要乘以一个缩放因子 ",[135,2279,2281,2304],{"className":2280},[138],[135,2282,2284],{"className":2283},[142],[144,2285,2286],{"xmlns":146},[148,2287,2288,2302],{},[151,2289,2290],{},[154,2291,2292,2294],{},[157,2293,159],{},[161,2295,2296],{},[164,2297,2298,2300],{},[167,2299,169],{},[167,2301,172],{},[174,2303,177],{"encoding":176},[135,2305,2307],{"className":2306,"ariaHidden":182},[181],[135,2308,2310,2313],{"className":2309},[186],[135,2311],{"className":2312,"style":191},[190],[135,2314,2316,2319,2459],{"className":2315},[195],[135,2317],{"className":2318},[199,200],[135,2320,2322],{"className":2321},[154],[135,2323,2325,2451],{"className":2324},[207,208],[135,2326,2328,2448],{"className":2327},[212],[135,2329,2331,2426,2434],{"className":2330,"style":217},[216],[135,2332,2333,2336],{"style":220},[135,2334],{"className":2335,"style":225},[224],[135,2337,2339],{"className":2338},[229,230,231,232],[135,2340,2342],{"className":2341},[195,232],[135,2343,2345],{"className":2344},[195,239,232],[135,2346,2348,2418],{"className":2347},[207,208],[135,2349,2351,2415],{"className":2350},[212],[135,2352,2354,2403],{"className":2353,"style":249},[216],[135,2355,2357,2360],{"className":2356,"style":254},[253],[135,2358],{"className":2359,"style":225},[224],[135,2361,2363],{"className":2362,"style":261},[195,232],[135,2364,2366,2369],{"className":2365},[195,232],[135,2367,169],{"className":2368},[195,268,232],[135,2370,2372],{"className":2371},[272],[135,2373,2375,2395],{"className":2374},[207,208],[135,2376,2378,2392],{"className":2377},[212],[135,2379,2381],{"className":2380,"style":282},[216],[135,2382,2383,2386],{"style":285},[135,2384],{"className":2385,"style":289},[224],[135,2387,2389],{"className":2388},[229,293,294,232],[135,2390,172],{"className":2391,"style":298},[195,268,232],[135,2393,303],{"className":2394},[302],[135,2396,2398],{"className":2397},[212],[135,2399,2401],{"className":2400,"style":310},[216],[135,2402],{},[135,2404,2405,2408],{"style":315},[135,2406],{"className":2407,"style":225},[224],[135,2409,2411],{"className":2410,"style":323},[322,232],[325,2412,2413],{"xmlns":327,"width":328,"height":329,"viewBox":330,"preserveAspectRatio":331},[333,2414],{"d":335},[135,2416,303],{"className":2417},[302],[135,2419,2421],{"className":2420},[212],[135,2422,2424],{"className":2423,"style":345},[216],[135,2425],{},[135,2427,2428,2431],{"style":350},[135,2429],{"className":2430,"style":225},[224],[135,2432],{"className":2433,"style":358},[357],[135,2435,2436,2439],{"style":361},[135,2437],{"className":2438,"style":225},[224],[135,2440,2442],{"className":2441},[229,230,231,232],[135,2443,2445],{"className":2444},[195,232],[135,2446,159],{"className":2447},[195,232],[135,2449,303],{"className":2450},[302],[135,2452,2454],{"className":2453},[212],[135,2455,2457],{"className":2456,"style":383},[216],[135,2458],{},[135,2460],{"className":2461},[389,200],[14,2463,2464],{},"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。",[2466,2467,2471],"pre",{"className":2468,"code":2469,"language":2470,"meta":65,"style":65},"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",[2472,2473,2474,2502,2508,2515,2534,2555,2563,2574,2591,2607,2615,2632,2638,2663,2676],"code",{"__ignoreMap":65},[135,2475,2478,2482,2486,2489,2493,2496,2499],{"class":2476,"line":2477},"line",1,[135,2479,2481],{"class":2480},"szJfE","def",[135,2483,2485],{"class":2484},"sCLZk"," masked_softmax",[135,2487,874],{"class":2488},"scbbO",[135,2490,2492],{"class":2491},"syNf4","X",[135,2494,2495],{"class":2488},", ",[135,2497,2498],{"class":2491},"valid_lens",[135,2500,2501],{"class":2488},"):\n",[135,2503,2504],{"class":2476,"line":66},[135,2505,2507],{"class":2506},"seLWX","    \"\"\"通过在最后一个轴上掩蔽元素来执行softmax操作\"\"\"\n",[135,2509,2511],{"class":2476,"line":2510},3,[135,2512,2514],{"class":2513},"sfgPZ","    # X:3D张量，valid_lens:1D或2D张量\n",[135,2516,2518,2521,2524,2527,2531],{"class":2476,"line":2517},4,[135,2519,2520],{"class":2480},"    if",[135,2522,2523],{"class":2488}," valid_lens ",[135,2525,2526],{"class":2480},"is",[135,2528,2530],{"class":2529},"soDru"," None",[135,2532,2533],{"class":2488},":\n",[135,2535,2537,2540,2543,2547,2550,2552],{"class":2476,"line":2536},5,[135,2538,2539],{"class":2480},"        return",[135,2541,2542],{"class":2488}," nn.functional.softmax(X, ",[135,2544,2546],{"class":2545},"sQkXh","dim",[135,2548,2549],{"class":2480},"=-",[135,2551,159],{"class":2529},[135,2553,2554],{"class":2488},")\n",[135,2556,2558,2561],{"class":2476,"line":2557},6,[135,2559,2560],{"class":2480},"    else",[135,2562,2533],{"class":2488},[135,2564,2566,2569,2571],{"class":2476,"line":2565},7,[135,2567,2568],{"class":2488},"        shape ",[135,2570,891],{"class":2480},[135,2572,2573],{"class":2488}," X.shape\n",[135,2575,2577,2580,2583,2586,2589],{"class":2476,"line":2576},8,[135,2578,2579],{"class":2480},"        if",[135,2581,2582],{"class":2488}," valid_lens.dim() ",[135,2584,2585],{"class":2480},"==",[135,2587,2588],{"class":2529}," 1",[135,2590,2533],{"class":2488},[135,2592,2594,2597,2599,2602,2604],{"class":2476,"line":2593},9,[135,2595,2596],{"class":2488},"            valid_lens ",[135,2598,891],{"class":2480},[135,2600,2601],{"class":2488}," torch.repeat_interleave(valid_lens, shape[",[135,2603,159],{"class":2529},[135,2605,2606],{"class":2488},"])\n",[135,2608,2610,2613],{"class":2476,"line":2609},10,[135,2611,2612],{"class":2480},"        else",[135,2614,2533],{"class":2488},[135,2616,2618,2620,2622,2625,2628,2630],{"class":2476,"line":2617},11,[135,2619,2596],{"class":2488},[135,2621,891],{"class":2480},[135,2623,2624],{"class":2488}," valid_lens.reshape(",[135,2626,2627],{"class":2480},"-",[135,2629,159],{"class":2529},[135,2631,2554],{"class":2488},[135,2633,2635],{"class":2476,"line":2634},12,[135,2636,2637],{"class":2513},"        # 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",[135,2639,2641,2644,2646,2649,2651,2653,2656,2658,2660],{"class":2476,"line":2640},13,[135,2642,2643],{"class":2488},"        X ",[135,2645,891],{"class":2480},[135,2647,2648],{"class":2488}," d2l.sequence_mask(X.reshape(",[135,2650,2627],{"class":2480},[135,2652,159],{"class":2529},[135,2654,2655],{"class":2488},", shape[",[135,2657,2627],{"class":2480},[135,2659,159],{"class":2529},[135,2661,2662],{"class":2488},"]), valid_lens,\n",[135,2664,2666,2669,2671,2674],{"class":2476,"line":2665},14,[135,2667,2668],{"class":2545},"                              value",[135,2670,2549],{"class":2480},[135,2672,2673],{"class":2529},"1e6",[135,2675,2554],{"class":2488},[135,2677,2679,2681,2684,2686,2688,2690],{"class":2476,"line":2678},15,[135,2680,2539],{"class":2480},[135,2682,2683],{"class":2488}," nn.functional.softmax(X.reshape(shape), ",[135,2685,2546],{"class":2545},[135,2687,2549],{"class":2480},[135,2689,159],{"class":2529},[135,2691,2554],{"class":2488},[14,2693,2694],{},"下面实现缩放点积注意力。",[2466,2696,2698],{"className":2468,"code":2697,"language":2470,"meta":65,"style":65},"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",[2472,2699,2700,2722,2727,2756,2781,2794,2799,2804,2809,2814,2819,2856,2873,2878,2904,2916],{"__ignoreMap":65},[135,2701,2702,2705,2709,2711,2715,2717,2720],{"class":2476,"line":2477},[135,2703,2704],{"class":2480},"class",[135,2706,2708],{"class":2707},"skCyd"," DotProductAttention",[135,2710,874],{"class":2488},[135,2712,2714],{"class":2713},"sDP9b","nn",[135,2716,940],{"class":2488},[135,2718,2719],{"class":2713},"Module",[135,2721,2501],{"class":2488},[135,2723,2724],{"class":2476,"line":66},[135,2725,2726],{"class":2506},"    \"\"\"缩放点积注意力\"\"\"\n",[135,2728,2729,2732,2735,2737,2741,2743,2746,2748,2751,2754],{"class":2476,"line":2510},[135,2730,2731],{"class":2480},"    def",[135,2733,2734],{"class":2529}," __init__",[135,2736,874],{"class":2488},[135,2738,2740],{"class":2739},"sD3jg","self",[135,2742,2495],{"class":2488},[135,2744,2745],{"class":2491},"dropout",[135,2747,2495],{"class":2488},[135,2749,2750],{"class":2480},"**",[135,2752,2753],{"class":2491},"kwargs",[135,2755,2501],{"class":2488},[135,2757,2758,2762,2765,2768,2771,2774,2776,2778],{"class":2476,"line":2517},[135,2759,2761],{"class":2760},"sPGBF","        super",[135,2763,2764],{"class":2488},"(DotProductAttention, ",[135,2766,2740],{"class":2767},"sJti5",[135,2769,2770],{"class":2488},").",[135,2772,2773],{"class":2529},"__init__",[135,2775,874],{"class":2488},[135,2777,2750],{"class":2480},[135,2779,2780],{"class":2488},"kwargs)\n",[135,2782,2783,2786,2789,2791],{"class":2476,"line":2536},[135,2784,2785],{"class":2767},"        self",[135,2787,2788],{"class":2488},".dropout ",[135,2790,891],{"class":2480},[135,2792,2793],{"class":2488}," nn.Dropout(dropout)\n",[135,2795,2796],{"class":2476,"line":2557},[135,2797,2798],{"emptyLinePlaceholder":80},"\n",[135,2800,2801],{"class":2476,"line":2565},[135,2802,2803],{"class":2513},"    # queries的形状：(batch_size，查询的个数，d)\n",[135,2805,2806],{"class":2476,"line":2576},[135,2807,2808],{"class":2513},"    # keys的形状：(batch_size，“键－值”对的个数，d)\n",[135,2810,2811],{"class":2476,"line":2593},[135,2812,2813],{"class":2513},"    # values的形状：(batch_size，“键－值”对的个数，值的维度)\n",[135,2815,2816],{"class":2476,"line":2609},[135,2817,2818],{"class":2513},"    # valid_lens的形状:(batch_size，)或者(batch_size，查询的个数)\n",[135,2820,2821,2823,2826,2828,2830,2832,2835,2837,2840,2842,2845,2847,2849,2851,2854],{"class":2476,"line":2617},[135,2822,2731],{"class":2480},[135,2824,2825],{"class":2484}," forward",[135,2827,874],{"class":2488},[135,2829,2740],{"class":2739},[135,2831,2495],{"class":2488},[135,2833,2834],{"class":2491},"queries",[135,2836,2495],{"class":2488},[135,2838,2839],{"class":2491},"keys",[135,2841,2495],{"class":2488},[135,2843,2844],{"class":2491},"values",[135,2846,2495],{"class":2488},[135,2848,2498],{"class":2491},[135,2850,891],{"class":2480},[135,2852,2853],{"class":2529},"None",[135,2855,2501],{"class":2488},[135,2857,2858,2861,2863,2866,2868,2870],{"class":2476,"line":2634},[135,2859,2860],{"class":2488},"        d ",[135,2862,891],{"class":2480},[135,2864,2865],{"class":2488}," queries.shape[",[135,2867,2627],{"class":2480},[135,2869,159],{"class":2529},[135,2871,2872],{"class":2488},"]\n",[135,2874,2875],{"class":2476,"line":2640},[135,2876,2877],{"class":2513},"        # 设置transpose_b=True为了交换keys的最后两个维度\n",[135,2879,2880,2883,2885,2888,2890,2892,2895,2898,2901],{"class":2476,"line":2665},[135,2881,2882],{"class":2488},"        scores ",[135,2884,891],{"class":2480},[135,2886,2887],{"class":2488}," torch.bmm(queries, keys.transpose(",[135,2889,159],{"class":2529},[135,2891,879],{"class":2488},[135,2893,2894],{"class":2529},"2",[135,2896,2897],{"class":2488},")) ",[135,2899,2900],{"class":2480},"/",[135,2902,2903],{"class":2488}," math.sqrt(d)\n",[135,2905,2906,2908,2911,2913],{"class":2476,"line":2678},[135,2907,2785],{"class":2767},[135,2909,2910],{"class":2488},".attention_weights ",[135,2912,891],{"class":2480},[135,2914,2915],{"class":2488}," masked_softmax(scores, valid_lens)\n",[135,2917,2919,2921,2924,2926,2929,2931],{"class":2476,"line":2918},16,[135,2920,2539],{"class":2480},[135,2922,2923],{"class":2488}," torch.bmm(",[135,2925,2740],{"class":2767},[135,2927,2928],{"class":2488},".dropout(",[135,2930,2740],{"class":2767},[135,2932,2933],{"class":2488},".attention_weights), values)\n",[14,2935,2936,2937,2940],{},"代码中函数的 ",[2472,2938,2939],{},"**kwargs","表示任意关键字参数，为了符合 Pytorch 的继承约定。",[125,2942,2943],{"id":2943},"多头注意力",[14,2945,2946],{},"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。",[14,2948,2949],{},[117,2950],{"alt":65,"src":2951},"transformer/MHA.png",[14,2953,2954],{},[135,2955,2957,3073],{"className":2956},[138],[135,2958,2960],{"className":2959},[142],[144,2961,2962],{"xmlns":146},[148,2963,2964,3070],{},[151,2965,2966,2990,2992,2994,2996,2998,3000,3002,3004,3006,3022,3024,3039,3041,3044,3046,3060,3062],{},[151,2967,2968,2971,2974,2977,2979,2981,2984,2986,2988],{},[167,2969,2970],{"mathvariant":894},"M",[167,2972,2973],{"mathvariant":894},"u",[167,2975,2976],{"mathvariant":894},"l",[167,2978,853],{"mathvariant":894},[167,2980,865],{"mathvariant":894},[167,2982,2983],{"mathvariant":894},"H",[167,2985,858],{"mathvariant":894},[167,2987,31],{"mathvariant":894},[167,2989,169],{"mathvariant":894},[537,2991,874],{"stretchy":873},[167,2993,535],{},[537,2995,879],{"separator":182},[167,2997,648],{},[537,2999,879],{"separator":182},[167,3001,748],{},[537,3003,888],{"stretchy":873},[537,3005,891],{},[151,3007,3008,3011,3013,3015,3018,3020],{},[167,3009,3010],{"mathvariant":894},"C",[167,3012,868],{"mathvariant":894},[167,3014,411],{"mathvariant":894},[167,3016,3017],{"mathvariant":894},"c",[167,3019,31],{"mathvariant":894},[167,3021,853],{"mathvariant":894},[537,3023,874],{"stretchy":873},[164,3025,3026,3037],{},[151,3027,3028,3031,3033,3035],{},[167,3029,3030],{"mathvariant":894},"h",[167,3032,858],{"mathvariant":894},[167,3034,31],{"mathvariant":894},[167,3036,169],{"mathvariant":894},[157,3038,159],{},[537,3040,879],{"separator":182},[537,3042,3043],{},"…",[537,3045,879],{"separator":182},[164,3047,3048,3058],{},[151,3049,3050,3052,3054,3056],{},[167,3051,3030],{"mathvariant":894},[167,3053,858],{"mathvariant":894},[167,3055,31],{"mathvariant":894},[167,3057,169],{"mathvariant":894},[167,3059,3030],{},[537,3061,888],{"stretchy":873},[541,3063,3064,3067],{},[167,3065,3066],{},"W",[167,3068,3069],{},"O",[174,3071,3072],{"encoding":176},"\\mathrm{MultiHead}(Q, K, V) = \\mathrm{Concat}(\\mathrm{head}_1, \\ldots, \\mathrm{head}_h) W^O",[135,3074,3076,3125],{"className":3075,"ariaHidden":182},[181],[135,3077,3079,3082,3089,3092,3095,3098,3101,3104,3107,3110,3113,3116,3119,3122],{"className":3078},[186],[135,3080],{"className":3081,"style":953},[190],[135,3083,3085],{"className":3084},[195],[135,3086,3088],{"className":3087},[195,1031],"MultiHead",[135,3090,874],{"className":3091},[199],[135,3093,535],{"className":3094},[195,268],[135,3096,879],{"className":3097},[988],[135,3099],{"className":3100,"style":992},[575],[135,3102,648],{"className":3103,"style":679},[195,268],[135,3105,879],{"className":3106},[988],[135,3108],{"className":3109,"style":992},[575],[135,3111,748],{"className":3112,"style":778},[195,268],[135,3114,888],{"className":3115},[389],[135,3117],{"className":3118,"style":576},[575],[135,3120,891],{"className":3121},[580],[135,3123],{"className":3124,"style":576},[575],[135,3126,3128,3132,3139,3142,3188,3191,3194,3197,3200,3203,3206,3249,3252],{"className":3127},[186],[135,3129],{"className":3130,"style":3131},[190],"height:1.0913em;vertical-align:-0.25em;",[135,3133,3135],{"className":3134},[195],[135,3136,3138],{"className":3137},[195,1031],"Concat",[135,3140,874],{"className":3141},[199],[135,3143,3145,3152],{"className":3144},[195],[135,3146,3148],{"className":3147},[195],[135,3149,3151],{"className":3150},[195,1031],"head",[135,3153,3155],{"className":3154},[272],[135,3156,3158,3180],{"className":3157},[207,208],[135,3159,3161,3177],{"className":3160},[212],[135,3162,3165],{"className":3163,"style":3164},[216],"height:0.3011em;",[135,3166,3168,3171],{"style":3167},"top:-2.55em;margin-right:0.05em;",[135,3169],{"className":3170,"style":616},[224],[135,3172,3174],{"className":3173},[229,230,231,232],[135,3175,159],{"className":3176},[195,232],[135,3178,303],{"className":3179},[302],[135,3181,3183],{"className":3182},[212],[135,3184,3186],{"className":3185,"style":1346},[216],[135,3187],{},[135,3189,879],{"className":3190},[988],[135,3192],{"className":3193,"style":992},[575],[135,3195,3043],{"className":3196},[1038],[135,3198],{"className":3199,"style":992},[575],[135,3201,879],{"className":3202},[988],[135,3204],{"className":3205,"style":992},[575],[135,3207,3209,3215],{"className":3208},[195],[135,3210,3212],{"className":3211},[195],[135,3213,3151],{"className":3214},[195,1031],[135,3216,3218],{"className":3217},[272],[135,3219,3221,3241],{"className":3220},[207,208],[135,3222,3224,3238],{"className":3223},[212],[135,3225,3227],{"className":3226,"style":1324},[216],[135,3228,3229,3232],{"style":3167},[135,3230],{"className":3231,"style":616},[224],[135,3233,3235],{"className":3234},[229,230,231,232],[135,3236,3030],{"className":3237},[195,268,232],[135,3239,303],{"className":3240},[302],[135,3242,3244],{"className":3243},[212],[135,3245,3247],{"className":3246,"style":1346},[216],[135,3248],{},[135,3250,888],{"className":3251},[389],[135,3253,3255,3259],{"className":3254},[195],[135,3256,3066],{"className":3257,"style":3258},[195,268],"margin-right:0.13889em;",[135,3260,3262],{"className":3261},[272],[135,3263,3265],{"className":3264},[207],[135,3266,3268],{"className":3267},[212],[135,3269,3272],{"className":3270,"style":3271},[216],"height:0.8413em;",[135,3273,3274,3277],{"style":612},[135,3275],{"className":3276,"style":616},[224],[135,3278,3280],{"className":3279},[229,230,231,232],[135,3281,3069],{"className":3282,"style":3283},[195,268,232],"margin-right:0.02778em;",[14,3285,3286,3287,3649,3650,3899,3900,3899,4149,4400,4401,940],{},"其中 ",[135,3288,3290,3382],{"className":3289},[138],[135,3291,3293],{"className":3292},[142],[144,3294,3295],{"xmlns":146},[148,3296,3297,3379],{},[151,3298,3299,3313,3315,3335,3337,3339,3347,3349,3353,3355,3363,3365,3367,3369,3377],{},[164,3300,3301,3311],{},[151,3302,3303,3305,3307,3309],{},[167,3304,3030],{"mathvariant":894},[167,3306,858],{"mathvariant":894},[167,3308,31],{"mathvariant":894},[167,3310,169],{"mathvariant":894},[167,3312,865],{},[537,3314,891],{},[151,3316,3317,3319,3321,3323,3325,3327,3329,3331,3333],{},[167,3318,850],{"mathvariant":894},[167,3320,853],{"mathvariant":894},[167,3322,853],{"mathvariant":894},[167,3324,858],{"mathvariant":894},[167,3326,411],{"mathvariant":894},[167,3328,853],{"mathvariant":894},[167,3330,865],{"mathvariant":894},[167,3332,868],{"mathvariant":894},[167,3334,411],{"mathvariant":894},[537,3336,874],{"stretchy":873},[167,3338,535],{},[1898,3340,3341,3343,3345],{},[167,3342,3066],{},[167,3344,865],{},[167,3346,535],{},[537,3348,879],{"separator":182},[3350,3351,3352],"mtext",{},"  ",[167,3354,648],{},[1898,3356,3357,3359,3361],{},[167,3358,3066],{},[167,3360,865],{},[167,3362,648],{},[537,3364,879],{"separator":182},[3350,3366,3352],{},[167,3368,748],{},[1898,3370,3371,3373,3375],{},[167,3372,3066],{},[167,3374,865],{},[167,3376,748],{},[537,3378,888],{"stretchy":873},[174,3380,3381],{"encoding":176},"\\mathrm{head}_i=\\mathrm{Attention}(QW_i^Q,\\; KW_i^K,\\; VW_i^V)",[135,3383,3385,3443],{"className":3384,"ariaHidden":182},[181],[135,3386,3388,3391,3434,3437,3440],{"className":3387},[186],[135,3389],{"className":3390,"style":1305},[190],[135,3392,3394,3400],{"className":3393},[195],[135,3395,3397],{"className":3396},[195],[135,3398,3151],{"className":3399},[195,1031],[135,3401,3403],{"className":3402},[272],[135,3404,3406,3426],{"className":3405},[207,208],[135,3407,3409,3423],{"className":3408},[212],[135,3410,3412],{"className":3411,"style":2108},[216],[135,3413,3414,3417],{"style":3167},[135,3415],{"className":3416,"style":616},[224],[135,3418,3420],{"className":3419},[229,230,231,232],[135,3421,865],{"className":3422},[195,268,232],[135,3424,303],{"className":3425},[302],[135,3427,3429],{"className":3428},[212],[135,3430,3432],{"className":3431,"style":1346},[216],[135,3433],{},[135,3435],{"className":3436,"style":576},[575],[135,3438,891],{"className":3439},[580],[135,3441],{"className":3442,"style":576},[575],[135,3444,3446,3450,3457,3460,3463,3518,3521,3524,3527,3530,3583,3586,3589,3592,3595,3646],{"className":3445},[186],[135,3447],{"className":3448,"style":3449},[190],"height:1.2361em;vertical-align:-0.2769em;",[135,3451,3453],{"className":3452},[195],[135,3454,3456],{"className":3455},[195,1031],"Attention",[135,3458,874],{"className":3459},[199],[135,3461,535],{"className":3462},[195,268],[135,3464,3466,3469],{"className":3465},[195],[135,3467,3066],{"className":3468,"style":3258},[195,268],[135,3470,3472],{"className":3471},[272],[135,3473,3475,3509],{"className":3474},[207,208],[135,3476,3478,3506],{"className":3477},[212],[135,3479,3482,3494],{"className":3480,"style":3481},[216],"height:0.9592em;",[135,3483,3485,3488],{"style":3484},"top:-2.4231em;margin-left:-0.1389em;margin-right:0.05em;",[135,3486],{"className":3487,"style":616},[224],[135,3489,3491],{"className":3490},[229,230,231,232],[135,3492,865],{"className":3493},[195,268,232],[135,3495,3497,3500],{"style":3496},"top:-3.1809em;margin-right:0.05em;",[135,3498],{"className":3499,"style":616},[224],[135,3501,3503],{"className":3502},[229,230,231,232],[135,3504,535],{"className":3505},[195,268,232],[135,3507,303],{"className":3508},[302],[135,3510,3512],{"className":3511},[212],[135,3513,3516],{"className":3514,"style":3515},[216],"height:0.2769em;",[135,3517],{},[135,3519,879],{"className":3520},[988],[135,3522],{"className":3523,"style":576},[575],[135,3525],{"className":3526,"style":992},[575],[135,3528,648],{"className":3529,"style":679},[195,268],[135,3531,3533,3536],{"className":3532},[195],[135,3534,3066],{"className":3535,"style":3258},[195,268],[135,3537,3539],{"className":3538},[272],[135,3540,3542,3574],{"className":3541},[207,208],[135,3543,3545,3571],{"className":3544},[212],[135,3546,3548,3560],{"className":3547,"style":3271},[216],[135,3549,3551,3554],{"style":3550},"top:-2.4413em;margin-left:-0.1389em;margin-right:0.05em;",[135,3552],{"className":3553,"style":616},[224],[135,3555,3557],{"className":3556},[229,230,231,232],[135,3558,865],{"className":3559},[195,268,232],[135,3561,3562,3565],{"style":612},[135,3563],{"className":3564,"style":616},[224],[135,3566,3568],{"className":3567},[229,230,231,232],[135,3569,648],{"className":3570,"style":679},[195,268,232],[135,3572,303],{"className":3573},[302],[135,3575,3577],{"className":3576},[212],[135,3578,3581],{"className":3579,"style":3580},[216],"height:0.2587em;",[135,3582],{},[135,3584,879],{"className":3585},[988],[135,3587],{"className":3588,"style":576},[575],[135,3590],{"className":3591,"style":992},[575],[135,3593,748],{"className":3594,"style":778},[195,268],[135,3596,3598,3601],{"className":3597},[195],[135,3599,3066],{"className":3600,"style":3258},[195,268],[135,3602,3604],{"className":3603},[272],[135,3605,3607,3638],{"className":3606},[207,208],[135,3608,3610,3635],{"className":3609},[212],[135,3611,3613,3624],{"className":3612,"style":3271},[216],[135,3614,3615,3618],{"style":3550},[135,3616],{"className":3617,"style":616},[224],[135,3619,3621],{"className":3620},[229,230,231,232],[135,3622,865],{"className":3623},[195,268,232],[135,3625,3626,3629],{"style":612},[135,3627],{"className":3628,"style":616},[224],[135,3630,3632],{"className":3631},[229,230,231,232],[135,3633,748],{"className":3634,"style":778},[195,268,232],[135,3636,303],{"className":3637},[302],[135,3639,3641],{"className":3640},[212],[135,3642,3644],{"className":3643,"style":3580},[216],[135,3645],{},[135,3647,888],{"className":3648},[389],"，投影参数是矩阵\n",[135,3651,3653,3705],{"className":3652},[138],[135,3654,3656],{"className":3655},[142],[144,3657,3658],{"xmlns":146},[148,3659,3660,3702],{},[151,3661,3662,3670,3672],{},[1898,3663,3664,3666,3668],{},[167,3665,3066],{},[167,3667,865],{},[167,3669,535],{},[537,3671,539],{},[541,3673,3674,3676],{},[167,3675,546],{"mathvariant":545},[151,3677,3678,3694,3696],{},[164,3679,3680,3682],{},[167,3681,169],{},[151,3683,3684,3686,3688,3690,3692],{},[167,3685,442],{"mathvariant":894},[167,3687,868],{"mathvariant":894},[167,3689,169],{"mathvariant":894},[167,3691,858],{"mathvariant":894},[167,3693,2976],{"mathvariant":894},[537,3695,553],{},[164,3697,3698,3700],{},[167,3699,169],{},[167,3701,172],{},[174,3703,3704],{"encoding":176},"W_i^Q \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[135,3706,3708,3774],{"className":3707,"ariaHidden":182},[181],[135,3709,3711,3714,3765,3768,3771],{"className":3710},[186],[135,3712],{"className":3713,"style":3449},[190],[135,3715,3717,3720],{"className":3716},[195],[135,3718,3066],{"className":3719,"style":3258},[195,268],[135,3721,3723],{"className":3722},[272],[135,3724,3726,3757],{"className":3725},[207,208],[135,3727,3729,3754],{"className":3728},[212],[135,3730,3732,3743],{"className":3731,"style":3481},[216],[135,3733,3734,3737],{"style":3484},[135,3735],{"className":3736,"style":616},[224],[135,3738,3740],{"className":3739},[229,230,231,232],[135,3741,865],{"className":3742},[195,268,232],[135,3744,3745,3748],{"style":3496},[135,3746],{"className":3747,"style":616},[224],[135,3749,3751],{"className":3750},[229,230,231,232],[135,3752,535],{"className":3753},[195,268,232],[135,3755,303],{"className":3756},[302],[135,3758,3760],{"className":3759},[212],[135,3761,3763],{"className":3762,"style":3515},[216],[135,3764],{},[135,3766],{"className":3767,"style":576},[575],[135,3769,539],{"className":3770},[580],[135,3772],{"className":3773,"style":576},[575],[135,3775,3777,3780],{"className":3776},[186],[135,3778],{"className":3779,"style":590},[190],[135,3781,3783,3786],{"className":3782},[195],[135,3784,546],{"className":3785},[195,597],[135,3787,3789],{"className":3788},[272],[135,3790,3792],{"className":3791},[207],[135,3793,3795],{"className":3794},[212],[135,3796,3798],{"className":3797,"style":590},[216],[135,3799,3800,3803],{"style":612},[135,3801],{"className":3802,"style":616},[224],[135,3804,3806],{"className":3805},[229,230,231,232],[135,3807,3809,3856,3859],{"className":3808},[195,232],[135,3810,3812,3815],{"className":3811},[195,232],[135,3813,169],{"className":3814},[195,268,232],[135,3816,3818],{"className":3817},[272],[135,3819,3821,3848],{"className":3820},[207,208],[135,3822,3824,3845],{"className":3823},[212],[135,3825,3827],{"className":3826,"style":282},[216],[135,3828,3829,3832],{"style":285},[135,3830],{"className":3831,"style":289},[224],[135,3833,3835],{"className":3834},[229,293,294,232],[135,3836,3838],{"className":3837},[195,232],[135,3839,3841],{"className":3840},[195,232],[135,3842,3844],{"className":3843},[195,1031,232],"model",[135,3846,303],{"className":3847},[302],[135,3849,3851],{"className":3850},[212],[135,3852,3854],{"className":3853,"style":310},[216],[135,3855],{},[135,3857,553],{"className":3858},[629,232],[135,3860,3862,3865],{"className":3861},[195,232],[135,3863,169],{"className":3864},[195,268,232],[135,3866,3868],{"className":3867},[272],[135,3869,3871,3891],{"className":3870},[207,208],[135,3872,3874,3888],{"className":3873},[212],[135,3875,3877],{"className":3876,"style":282},[216],[135,3878,3879,3882],{"style":285},[135,3880],{"className":3881,"style":289},[224],[135,3883,3885],{"className":3884},[229,293,294,232],[135,3886,172],{"className":3887,"style":298},[195,268,232],[135,3889,303],{"className":3890},[302],[135,3892,3894],{"className":3893},[212],[135,3895,3897],{"className":3896,"style":310},[216],[135,3898],{},",\n",[135,3901,3903,3955],{"className":3902},[138],[135,3904,3906],{"className":3905},[142],[144,3907,3908],{"xmlns":146},[148,3909,3910,3952],{},[151,3911,3912,3920,3922],{},[1898,3913,3914,3916,3918],{},[167,3915,3066],{},[167,3917,865],{},[167,3919,648],{},[537,3921,539],{},[541,3923,3924,3926],{},[167,3925,546],{"mathvariant":545},[151,3927,3928,3944,3946],{},[164,3929,3930,3932],{},[167,3931,169],{},[151,3933,3934,3936,3938,3940,3942],{},[167,3935,442],{"mathvariant":894},[167,3937,868],{"mathvariant":894},[167,3939,169],{"mathvariant":894},[167,3941,858],{"mathvariant":894},[167,3943,2976],{"mathvariant":894},[537,3945,553],{},[164,3947,3948,3950],{},[167,3949,169],{},[167,3951,172],{},[174,3953,3954],{"encoding":176},"W_i^K \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[135,3956,3958,4025],{"className":3957,"ariaHidden":182},[181],[135,3959,3961,3965,4016,4019,4022],{"className":3960},[186],[135,3962],{"className":3963,"style":3964},[190],"height:1.1em;vertical-align:-0.2587em;",[135,3966,3968,3971],{"className":3967},[195],[135,3969,3066],{"className":3970,"style":3258},[195,268],[135,3972,3974],{"className":3973},[272],[135,3975,3977,4008],{"className":3976},[207,208],[135,3978,3980,4005],{"className":3979},[212],[135,3981,3983,3994],{"className":3982,"style":3271},[216],[135,3984,3985,3988],{"style":3550},[135,3986],{"className":3987,"style":616},[224],[135,3989,3991],{"className":3990},[229,230,231,232],[135,3992,865],{"className":3993},[195,268,232],[135,3995,3996,3999],{"style":612},[135,3997],{"className":3998,"style":616},[224],[135,4000,4002],{"className":4001},[229,230,231,232],[135,4003,648],{"className":4004,"style":679},[195,268,232],[135,4006,303],{"className":4007},[302],[135,4009,4011],{"className":4010},[212],[135,4012,4014],{"className":4013,"style":3580},[216],[135,4015],{},[135,4017],{"className":4018,"style":576},[575],[135,4020,539],{"className":4021},[580],[135,4023],{"className":4024,"style":576},[575],[135,4026,4028,4031],{"className":4027},[186],[135,4029],{"className":4030,"style":590},[190],[135,4032,4034,4037],{"className":4033},[195],[135,4035,546],{"className":4036},[195,597],[135,4038,4040],{"className":4039},[272],[135,4041,4043],{"className":4042},[207],[135,4044,4046],{"className":4045},[212],[135,4047,4049],{"className":4048,"style":590},[216],[135,4050,4051,4054],{"style":612},[135,4052],{"className":4053,"style":616},[224],[135,4055,4057],{"className":4056},[229,230,231,232],[135,4058,4060,4106,4109],{"className":4059},[195,232],[135,4061,4063,4066],{"className":4062},[195,232],[135,4064,169],{"className":4065},[195,268,232],[135,4067,4069],{"className":4068},[272],[135,4070,4072,4098],{"className":4071},[207,208],[135,4073,4075,4095],{"className":4074},[212],[135,4076,4078],{"className":4077,"style":282},[216],[135,4079,4080,4083],{"style":285},[135,4081],{"className":4082,"style":289},[224],[135,4084,4086],{"className":4085},[229,293,294,232],[135,4087,4089],{"className":4088},[195,232],[135,4090,4092],{"className":4091},[195,232],[135,4093,3844],{"className":4094},[195,1031,232],[135,4096,303],{"className":4097},[302],[135,4099,4101],{"className":4100},[212],[135,4102,4104],{"className":4103,"style":310},[216],[135,4105],{},[135,4107,553],{"className":4108},[629,232],[135,4110,4112,4115],{"className":4111},[195,232],[135,4113,169],{"className":4114},[195,268,232],[135,4116,4118],{"className":4117},[272],[135,4119,4121,4141],{"className":4120},[207,208],[135,4122,4124,4138],{"className":4123},[212],[135,4125,4127],{"className":4126,"style":282},[216],[135,4128,4129,4132],{"style":285},[135,4130],{"className":4131,"style":289},[224],[135,4133,4135],{"className":4134},[229,293,294,232],[135,4136,172],{"className":4137,"style":298},[195,268,232],[135,4139,303],{"className":4140},[302],[135,4142,4144],{"className":4143},[212],[135,4145,4147],{"className":4146,"style":310},[216],[135,4148],{},[135,4150,4152,4204],{"className":4151},[138],[135,4153,4155],{"className":4154},[142],[144,4156,4157],{"xmlns":146},[148,4158,4159,4201],{},[151,4160,4161,4169,4171],{},[1898,4162,4163,4165,4167],{},[167,4164,3066],{},[167,4166,865],{},[167,4168,748],{},[537,4170,539],{},[541,4172,4173,4175],{},[167,4174,546],{"mathvariant":545},[151,4176,4177,4193,4195],{},[164,4178,4179,4181],{},[167,4180,169],{},[151,4182,4183,4185,4187,4189,4191],{},[167,4184,442],{"mathvariant":894},[167,4186,868],{"mathvariant":894},[167,4188,169],{"mathvariant":894},[167,4190,858],{"mathvariant":894},[167,4192,2976],{"mathvariant":894},[537,4194,553],{},[164,4196,4197,4199],{},[167,4198,169],{},[167,4200,502],{},[174,4202,4203],{"encoding":176},"W_i^V \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_v}",[135,4205,4207,4273],{"className":4206,"ariaHidden":182},[181],[135,4208,4210,4213,4264,4267,4270],{"className":4209},[186],[135,4211],{"className":4212,"style":3964},[190],[135,4214,4216,4219],{"className":4215},[195],[135,4217,3066],{"className":4218,"style":3258},[195,268],[135,4220,4222],{"className":4221},[272],[135,4223,4225,4256],{"className":4224},[207,208],[135,4226,4228,4253],{"className":4227},[212],[135,4229,4231,4242],{"className":4230,"style":3271},[216],[135,4232,4233,4236],{"style":3550},[135,4234],{"className":4235,"style":616},[224],[135,4237,4239],{"className":4238},[229,230,231,232],[135,4240,865],{"className":4241},[195,268,232],[135,4243,4244,4247],{"style":612},[135,4245],{"className":4246,"style":616},[224],[135,4248,4250],{"className":4249},[229,230,231,232],[135,4251,748],{"className":4252,"style":778},[195,268,232],[135,4254,303],{"className":4255},[302],[135,4257,4259],{"className":4258},[212],[135,4260,4262],{"className":4261,"style":3580},[216],[135,4263],{},[135,4265],{"className":4266,"style":576},[575],[135,4268,539],{"className":4269},[580],[135,4271],{"className":4272,"style":576},[575],[135,4274,4276,4279],{"className":4275},[186],[135,4277],{"className":4278,"style":590},[190],[135,4280,4282,4285],{"className":4281},[195],[135,4283,546],{"className":4284},[195,597],[135,4286,4288],{"className":4287},[272],[135,4289,4291],{"className":4290},[207],[135,4292,4294],{"className":4293},[212],[135,4295,4297],{"className":4296,"style":590},[216],[135,4298,4299,4302],{"style":612},[135,4300],{"className":4301,"style":616},[224],[135,4303,4305],{"className":4304},[229,230,231,232],[135,4306,4308,4354,4357],{"className":4307},[195,232],[135,4309,4311,4314],{"className":4310},[195,232],[135,4312,169],{"className":4313},[195,268,232],[135,4315,4317],{"className":4316},[272],[135,4318,4320,4346],{"className":4319},[207,208],[135,4321,4323,4343],{"className":4322},[212],[135,4324,4326],{"className":4325,"style":282},[216],[135,4327,4328,4331],{"style":285},[135,4329],{"className":4330,"style":289},[224],[135,4332,4334],{"className":4333},[229,293,294,232],[135,4335,4337],{"className":4336},[195,232],[135,4338,4340],{"className":4339},[195,232],[135,4341,3844],{"className":4342},[195,1031,232],[135,4344,303],{"className":4345},[302],[135,4347,4349],{"className":4348},[212],[135,4350,4352],{"className":4351,"style":310},[216],[135,4353],{},[135,4355,553],{"className":4356},[629,232],[135,4358,4360,4363],{"className":4359},[195,232],[135,4361,169],{"className":4362},[195,268,232],[135,4364,4366],{"className":4365},[272],[135,4367,4369,4391],{"className":4368},[207,208],[135,4370,4372,4388],{"className":4371},[212],[135,4373,4376],{"className":4374,"style":4375},[216],"height:0.1645em;",[135,4377,4379,4382],{"style":4378},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[135,4380],{"className":4381,"style":289},[224],[135,4383,4385],{"className":4384},[229,293,294,232],[135,4386,502],{"className":4387,"style":517},[195,268,232],[135,4389,303],{"className":4390},[302],[135,4392,4394],{"className":4393},[212],[135,4395,4398],{"className":4396,"style":4397},[216],"height:0.143em;",[135,4399],{},"\n和\n",[135,4402,4404,4456],{"className":4403},[138],[135,4405,4407],{"className":4406},[142],[144,4408,4409],{"xmlns":146},[148,4410,4411,4453],{},[151,4412,4413,4419,4421],{},[541,4414,4415,4417],{},[167,4416,3066],{},[167,4418,3069],{},[537,4420,539],{},[541,4422,4423,4425],{},[167,4424,546],{"mathvariant":545},[151,4426,4427,4429,4435,4437],{},[167,4428,3030],{},[164,4430,4431,4433],{},[167,4432,169],{},[167,4434,502],{},[537,4436,553],{},[164,4438,4439,4441],{},[167,4440,169],{},[151,4442,4443,4445,4447,4449,4451],{},[167,4444,442],{"mathvariant":894},[167,4446,868],{"mathvariant":894},[167,4448,169],{"mathvariant":894},[167,4450,858],{"mathvariant":894},[167,4452,2976],{"mathvariant":894},[174,4454,4455],{"encoding":176},"W^O \\in \\mathbb{R}^{h d_v \\times d_{\\mathrm{model}}}",[135,4457,4459,4504],{"className":4458,"ariaHidden":182},[181],[135,4460,4462,4466,4495,4498,4501],{"className":4461},[186],[135,4463],{"className":4464,"style":4465},[190],"height:0.8804em;vertical-align:-0.0391em;",[135,4467,4469,4472],{"className":4468},[195],[135,4470,3066],{"className":4471,"style":3258},[195,268],[135,4473,4475],{"className":4474},[272],[135,4476,4478],{"className":4477},[207],[135,4479,4481],{"className":4480},[212],[135,4482,4484],{"className":4483,"style":3271},[216],[135,4485,4486,4489],{"style":612},[135,4487],{"className":4488,"style":616},[224],[135,4490,4492],{"className":4491},[229,230,231,232],[135,4493,3069],{"className":4494,"style":3283},[195,268,232],[135,4496],{"className":4497,"style":576},[575],[135,4499,539],{"className":4500},[580],[135,4502],{"className":4503,"style":576},[575],[135,4505,4507,4510],{"className":4506},[186],[135,4508],{"className":4509,"style":590},[190],[135,4511,4513,4516],{"className":4512},[195],[135,4514,546],{"className":4515},[195,597],[135,4517,4519],{"className":4518},[272],[135,4520,4522],{"className":4521},[207],[135,4523,4525],{"className":4524},[212],[135,4526,4528],{"className":4527,"style":590},[216],[135,4529,4530,4533],{"style":612},[135,4531],{"className":4532,"style":616},[224],[135,4534,4536],{"className":4535},[229,230,231,232],[135,4537,4539,4542,4582,4585],{"className":4538},[195,232],[135,4540,3030],{"className":4541},[195,268,232],[135,4543,4545,4548],{"className":4544},[195,232],[135,4546,169],{"className":4547},[195,268,232],[135,4549,4551],{"className":4550},[272],[135,4552,4554,4574],{"className":4553},[207,208],[135,4555,4557,4571],{"className":4556},[212],[135,4558,4560],{"className":4559,"style":4375},[216],[135,4561,4562,4565],{"style":4378},[135,4563],{"className":4564,"style":289},[224],[135,4566,4568],{"className":4567},[229,293,294,232],[135,4569,502],{"className":4570,"style":517},[195,268,232],[135,4572,303],{"className":4573},[302],[135,4575,4577],{"className":4576},[212],[135,4578,4580],{"className":4579,"style":4397},[216],[135,4581],{},[135,4583,553],{"className":4584},[629,232],[135,4586,4588,4591],{"className":4587},[195,232],[135,4589,169],{"className":4590},[195,268,232],[135,4592,4594],{"className":4593},[272],[135,4595,4597,4623],{"className":4596},[207,208],[135,4598,4600,4620],{"className":4599},[212],[135,4601,4603],{"className":4602,"style":282},[216],[135,4604,4605,4608],{"style":285},[135,4606],{"className":4607,"style":289},[224],[135,4609,4611],{"className":4610},[229,293,294,232],[135,4612,4614],{"className":4613},[195,232],[135,4615,4617],{"className":4616},[195,232],[135,4618,3844],{"className":4619},[195,1031,232],[135,4621,303],{"className":4622},[302],[135,4624,4626],{"className":4625},[212],[135,4627,4629],{"className":4628,"style":310},[216],[135,4630],{},[14,4632,4633,4634,4637,4638,4641,4642,4644,4645,4647],{},"为了能使多个头并行计算，我们定义两个转置函数 ",[2472,4635,4636],{},"transpose_output"," 和 ",[2472,4639,4640],{},"transpose_qkv","，其中 ",[2472,4643,4636],{}," 还原了 ",[2472,4646,4640],{}," 的结果。",[2466,4649,4651],{"className":2468,"code":4650,"language":2470,"meta":65,"style":65},"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",[2472,4652,4653,4671,4676,4681,4686,4712,4716,4721,4747,4751,4756,4779,4783,4800,4805,4828,4852],{"__ignoreMap":65},[135,4654,4655,4657,4660,4662,4664,4666,4669],{"class":2476,"line":2477},[135,4656,2481],{"class":2480},[135,4658,4659],{"class":2484}," transpose_qkv",[135,4661,874],{"class":2488},[135,4663,2492],{"class":2491},[135,4665,2495],{"class":2488},[135,4667,4668],{"class":2491},"num_heads",[135,4670,2501],{"class":2488},[135,4672,4673],{"class":2476,"line":66},[135,4674,4675],{"class":2506},"    \"\"\"为了多注意力头的并行计算而变换形状\"\"\"\n",[135,4677,4678],{"class":2476,"line":2510},[135,4679,4680],{"class":2513},"    # 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[135,4682,4683],{"class":2476,"line":2517},[135,4684,4685],{"class":2513},"    # 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",[135,4687,4688,4691,4693,4696,4698,4701,4703,4706,4708,4710],{"class":2476,"line":2536},[135,4689,4690],{"class":2488},"    X ",[135,4692,891],{"class":2480},[135,4694,4695],{"class":2488}," X.reshape(X.shape[",[135,4697,1830],{"class":2529},[135,4699,4700],{"class":2488},"], X.shape[",[135,4702,159],{"class":2529},[135,4704,4705],{"class":2488},"], num_heads, ",[135,4707,2627],{"class":2480},[135,4709,159],{"class":2529},[135,4711,2554],{"class":2488},[135,4713,4714],{"class":2476,"line":2557},[135,4715,2798],{"emptyLinePlaceholder":80},[135,4717,4718],{"class":2476,"line":2565},[135,4719,4720],{"class":2513},"    # 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",[135,4722,4723,4725,4727,4730,4732,4734,4736,4738,4740,4742,4745],{"class":2476,"line":2576},[135,4724,4690],{"class":2488},[135,4726,891],{"class":2480},[135,4728,4729],{"class":2488}," X.permute(",[135,4731,1830],{"class":2529},[135,4733,2495],{"class":2488},[135,4735,2894],{"class":2529},[135,4737,2495],{"class":2488},[135,4739,159],{"class":2529},[135,4741,2495],{"class":2488},[135,4743,4744],{"class":2529},"3",[135,4746,2554],{"class":2488},[135,4748,4749],{"class":2476,"line":2593},[135,4750,2798],{"emptyLinePlaceholder":80},[135,4752,4753],{"class":2476,"line":2609},[135,4754,4755],{"class":2513},"    # 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",[135,4757,4758,4761,4764,4766,4768,4771,4773,4775,4777],{"class":2476,"line":2617},[135,4759,4760],{"class":2480},"    return",[135,4762,4763],{"class":2488}," X.reshape(",[135,4765,2627],{"class":2480},[135,4767,159],{"class":2529},[135,4769,4770],{"class":2488},", X.shape[",[135,4772,2894],{"class":2529},[135,4774,4700],{"class":2488},[135,4776,4744],{"class":2529},[135,4778,2606],{"class":2488},[135,4780,4781],{"class":2476,"line":2634},[135,4782,2798],{"emptyLinePlaceholder":80},[135,4784,4785,4787,4790,4792,4794,4796,4798],{"class":2476,"line":2640},[135,4786,2481],{"class":2480},[135,4788,4789],{"class":2484}," transpose_output",[135,4791,874],{"class":2488},[135,4793,2492],{"class":2491},[135,4795,2495],{"class":2488},[135,4797,4668],{"class":2491},[135,4799,2501],{"class":2488},[135,4801,4802],{"class":2476,"line":2665},[135,4803,4804],{"class":2506},"    \"\"\"逆转transpose_qkv函数的操作\"\"\"\n",[135,4806,4807,4809,4811,4813,4815,4817,4820,4822,4824,4826],{"class":2476,"line":2678},[135,4808,4690],{"class":2488},[135,4810,891],{"class":2480},[135,4812,4763],{"class":2488},[135,4814,2627],{"class":2480},[135,4816,159],{"class":2529},[135,4818,4819],{"class":2488},", num_heads, X.shape[",[135,4821,159],{"class":2529},[135,4823,4700],{"class":2488},[135,4825,2894],{"class":2529},[135,4827,2606],{"class":2488},[135,4829,4830,4832,4834,4836,4838,4840,4842,4844,4846,4848,4850],{"class":2476,"line":2918},[135,4831,4690],{"class":2488},[135,4833,891],{"class":2480},[135,4835,4729],{"class":2488},[135,4837,1830],{"class":2529},[135,4839,2495],{"class":2488},[135,4841,2894],{"class":2529},[135,4843,2495],{"class":2488},[135,4845,159],{"class":2529},[135,4847,2495],{"class":2488},[135,4849,4744],{"class":2529},[135,4851,2554],{"class":2488},[135,4853,4855,4857,4859,4861,4863,4865,4868,4870,4872],{"class":2476,"line":4854},17,[135,4856,4760],{"class":2480},[135,4858,4695],{"class":2488},[135,4860,1830],{"class":2529},[135,4862,4700],{"class":2488},[135,4864,159],{"class":2529},[135,4866,4867],{"class":2488},"], ",[135,4869,2627],{"class":2480},[135,4871,159],{"class":2529},[135,4873,2554],{"class":2488},[2466,4875,4877],{"className":2468,"code":4876,"language":2470,"meta":65,"style":65},"#@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",[2472,4878,4879,4884,4901,4906,4938,4965,4984,4996,5008,5027,5045,5063,5081,5085,5113,5118,5123,5128,5134,5140,5146,5167,5186,5205,5210,5226,5232,5238,5248,5272,5277,5283,5297,5302,5308,5323],{"__ignoreMap":65},[135,4880,4881],{"class":2476,"line":2477},[135,4882,4883],{"class":2513},"#@save\n",[135,4885,4886,4888,4891,4893,4895,4897,4899],{"class":2476,"line":66},[135,4887,2704],{"class":2480},[135,4889,4890],{"class":2707}," MultiHeadAttention",[135,4892,874],{"class":2488},[135,4894,2714],{"class":2713},[135,4896,940],{"class":2488},[135,4898,2719],{"class":2713},[135,4900,2501],{"class":2488},[135,4902,4903],{"class":2476,"line":2510},[135,4904,4905],{"class":2506},"    \"\"\"多头注意力\"\"\"\n",[135,4907,4908,4910,4912,4914,4916,4918,4921,4923,4926,4928,4931,4933,4936],{"class":2476,"line":2517},[135,4909,2731],{"class":2480},[135,4911,2734],{"class":2529},[135,4913,874],{"class":2488},[135,4915,2740],{"class":2739},[135,4917,2495],{"class":2488},[135,4919,4920],{"class":2491},"key_size",[135,4922,2495],{"class":2488},[135,4924,4925],{"class":2491},"query_size",[135,4927,2495],{"class":2488},[135,4929,4930],{"class":2491},"value_size",[135,4932,2495],{"class":2488},[135,4934,4935],{"class":2491},"num_hiddens",[135,4937,3899],{"class":2488},[135,4939,4940,4943,4945,4947,4949,4952,4954,4957,4959,4961,4963],{"class":2476,"line":2536},[135,4941,4942],{"class":2491},"                 num_heads",[135,4944,2495],{"class":2488},[135,4946,2745],{"class":2491},[135,4948,2495],{"class":2488},[135,4950,4951],{"class":2491},"bias",[135,4953,891],{"class":2480},[135,4955,4956],{"class":2529},"False",[135,4958,2495],{"class":2488},[135,4960,2750],{"class":2480},[135,4962,2753],{"class":2491},[135,4964,2501],{"class":2488},[135,4966,4967,4969,4972,4974,4976,4978,4980,4982],{"class":2476,"line":2557},[135,4968,2761],{"class":2760},[135,4970,4971],{"class":2488},"(MultiHeadAttention, ",[135,4973,2740],{"class":2767},[135,4975,2770],{"class":2488},[135,4977,2773],{"class":2529},[135,4979,874],{"class":2488},[135,4981,2750],{"class":2480},[135,4983,2780],{"class":2488},[135,4985,4986,4988,4991,4993],{"class":2476,"line":2565},[135,4987,2785],{"class":2767},[135,4989,4990],{"class":2488},".num_heads ",[135,4992,891],{"class":2480},[135,4994,4995],{"class":2488}," num_heads\n",[135,4997,4998,5000,5003,5005],{"class":2476,"line":2576},[135,4999,2785],{"class":2767},[135,5001,5002],{"class":2488},".attention ",[135,5004,891],{"class":2480},[135,5006,5007],{"class":2488}," d2l.DotProductAttention(dropout)\n",[135,5009,5010,5012,5015,5017,5020,5022,5024],{"class":2476,"line":2593},[135,5011,2785],{"class":2767},[135,5013,5014],{"class":2488},".W_q ",[135,5016,891],{"class":2480},[135,5018,5019],{"class":2488}," nn.Linear(query_size, num_hiddens, ",[135,5021,4951],{"class":2545},[135,5023,891],{"class":2480},[135,5025,5026],{"class":2488},"bias)\n",[135,5028,5029,5031,5034,5036,5039,5041,5043],{"class":2476,"line":2609},[135,5030,2785],{"class":2767},[135,5032,5033],{"class":2488},".W_k ",[135,5035,891],{"class":2480},[135,5037,5038],{"class":2488}," nn.Linear(key_size, num_hiddens, ",[135,5040,4951],{"class":2545},[135,5042,891],{"class":2480},[135,5044,5026],{"class":2488},[135,5046,5047,5049,5052,5054,5057,5059,5061],{"class":2476,"line":2617},[135,5048,2785],{"class":2767},[135,5050,5051],{"class":2488},".W_v ",[135,5053,891],{"class":2480},[135,5055,5056],{"class":2488}," nn.Linear(value_size, num_hiddens, ",[135,5058,4951],{"class":2545},[135,5060,891],{"class":2480},[135,5062,5026],{"class":2488},[135,5064,5065,5067,5070,5072,5075,5077,5079],{"class":2476,"line":2634},[135,5066,2785],{"class":2767},[135,5068,5069],{"class":2488},".W_o ",[135,5071,891],{"class":2480},[135,5073,5074],{"class":2488}," nn.Linear(num_hiddens, num_hiddens, ",[135,5076,4951],{"class":2545},[135,5078,891],{"class":2480},[135,5080,5026],{"class":2488},[135,5082,5083],{"class":2476,"line":2640},[135,5084,2798],{"emptyLinePlaceholder":80},[135,5086,5087,5089,5091,5093,5095,5097,5099,5101,5103,5105,5107,5109,5111],{"class":2476,"line":2665},[135,5088,2731],{"class":2480},[135,5090,2825],{"class":2484},[135,5092,874],{"class":2488},[135,5094,2740],{"class":2739},[135,5096,2495],{"class":2488},[135,5098,2834],{"class":2491},[135,5100,2495],{"class":2488},[135,5102,2839],{"class":2491},[135,5104,2495],{"class":2488},[135,5106,2844],{"class":2491},[135,5108,2495],{"class":2488},[135,5110,2498],{"class":2491},[135,5112,2501],{"class":2488},[135,5114,5115],{"class":2476,"line":2678},[135,5116,5117],{"class":2513},"        # queries，keys，values的形状:\n",[135,5119,5120],{"class":2476,"line":2918},[135,5121,5122],{"class":2513},"        # (batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[135,5124,5125],{"class":2476,"line":4854},[135,5126,5127],{"class":2513},"        # valid_lens　的形状:\n",[135,5129,5131],{"class":2476,"line":5130},18,[135,5132,5133],{"class":2513},"        # (batch_size，)或(batch_size，查询的个数)\n",[135,5135,5137],{"class":2476,"line":5136},19,[135,5138,5139],{"class":2513},"        # 经过变换后，输出的queries，keys，values 的形状:\n",[135,5141,5143],{"class":2476,"line":5142},20,[135,5144,5145],{"class":2513},"        # (batch_size*num_heads，查询或者“键－值”对的个数，num_hiddens/num_heads)\n",[135,5147,5149,5152,5154,5157,5159,5162,5164],{"class":2476,"line":5148},21,[135,5150,5151],{"class":2488},"        queries ",[135,5153,891],{"class":2480},[135,5155,5156],{"class":2488}," transpose_qkv(",[135,5158,2740],{"class":2767},[135,5160,5161],{"class":2488},".W_q(queries), ",[135,5163,2740],{"class":2767},[135,5165,5166],{"class":2488},".num_heads)\n",[135,5168,5170,5173,5175,5177,5179,5182,5184],{"class":2476,"line":5169},22,[135,5171,5172],{"class":2488},"        keys ",[135,5174,891],{"class":2480},[135,5176,5156],{"class":2488},[135,5178,2740],{"class":2767},[135,5180,5181],{"class":2488},".W_k(keys), ",[135,5183,2740],{"class":2767},[135,5185,5166],{"class":2488},[135,5187,5189,5192,5194,5196,5198,5201,5203],{"class":2476,"line":5188},23,[135,5190,5191],{"class":2488},"        values ",[135,5193,891],{"class":2480},[135,5195,5156],{"class":2488},[135,5197,2740],{"class":2767},[135,5199,5200],{"class":2488},".W_v(values), ",[135,5202,2740],{"class":2767},[135,5204,5166],{"class":2488},[135,5206,5208],{"class":2476,"line":5207},24,[135,5209,2798],{"emptyLinePlaceholder":80},[135,5211,5213,5215,5217,5219,5222,5224],{"class":2476,"line":5212},25,[135,5214,2579],{"class":2480},[135,5216,2523],{"class":2488},[135,5218,2526],{"class":2480},[135,5220,5221],{"class":2480}," not",[135,5223,2530],{"class":2529},[135,5225,2533],{"class":2488},[135,5227,5229],{"class":2476,"line":5228},26,[135,5230,5231],{"class":2513},"            # 在轴0，将第一项（标量或者矢量）复制num_heads次，\n",[135,5233,5235],{"class":2476,"line":5234},27,[135,5236,5237],{"class":2513},"            # 然后如此复制第二项，然后诸如此类。\n",[135,5239,5241,5243,5245],{"class":2476,"line":5240},28,[135,5242,2596],{"class":2488},[135,5244,891],{"class":2480},[135,5246,5247],{"class":2488}," torch.repeat_interleave(\n",[135,5249,5251,5254,5257,5259,5261,5264,5266,5268,5270],{"class":2476,"line":5250},29,[135,5252,5253],{"class":2488},"                valid_lens, ",[135,5255,5256],{"class":2545},"repeats",[135,5258,891],{"class":2480},[135,5260,2740],{"class":2767},[135,5262,5263],{"class":2488},".num_heads, ",[135,5265,2546],{"class":2545},[135,5267,891],{"class":2480},[135,5269,1830],{"class":2529},[135,5271,2554],{"class":2488},[135,5273,5275],{"class":2476,"line":5274},30,[135,5276,2798],{"emptyLinePlaceholder":80},[135,5278,5280],{"class":2476,"line":5279},31,[135,5281,5282],{"class":2513},"        # output的形状:(batch_size*num_heads，查询的个数， num_hiddens/num_heads)\n",[135,5284,5286,5289,5291,5294],{"class":2476,"line":5285},32,[135,5287,5288],{"class":2488},"        output ",[135,5290,891],{"class":2480},[135,5292,5293],{"class":2767}," self",[135,5295,5296],{"class":2488},".attention(queries, keys, values, valid_lens)\n",[135,5298,5300],{"class":2476,"line":5299},33,[135,5301,2798],{"emptyLinePlaceholder":80},[135,5303,5305],{"class":2476,"line":5304},34,[135,5306,5307],{"class":2513},"        # output_concat的形状:(batch_size，查询的个数，num_hiddens)\n",[135,5309,5311,5314,5316,5319,5321],{"class":2476,"line":5310},35,[135,5312,5313],{"class":2488},"        output_concat ",[135,5315,891],{"class":2480},[135,5317,5318],{"class":2488}," transpose_output(output, ",[135,5320,2740],{"class":2767},[135,5322,5166],{"class":2488},[135,5324,5326,5328,5330],{"class":2476,"line":5325},36,[135,5327,2539],{"class":2480},[135,5329,5293],{"class":2767},[135,5331,5332],{"class":2488},".W_o(output_concat)\n",[10,5334,5335],{"id":5335},"位置编码",[14,5337,5338,5339,5430],{},"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 ",[135,5340,5342,5368],{"className":5341},[138],[135,5343,5345],{"className":5344},[142],[144,5346,5347],{"xmlns":146},[148,5348,5349,5365],{},[151,5350,5351,5357,5359,5361,5363],{},[164,5352,5353,5355],{},[167,5354,169],{},[167,5356,442],{},[167,5358,868],{},[167,5360,169],{},[167,5362,858],{},[167,5364,2976],{},[174,5366,5367],{"encoding":176},"d_model",[135,5369,5371],{"className":5370,"ariaHidden":182},[181],[135,5372,5374,5377,5417,5420,5423,5426],{"className":5373},[186],[135,5375],{"className":5376,"style":1305},[190],[135,5378,5380,5383],{"className":5379},[195],[135,5381,169],{"className":5382},[195,268],[135,5384,5386],{"className":5385},[272],[135,5387,5389,5409],{"className":5388},[207,208],[135,5390,5392,5406],{"className":5391},[212],[135,5393,5395],{"className":5394,"style":1398},[216],[135,5396,5397,5400],{"style":1327},[135,5398],{"className":5399,"style":616},[224],[135,5401,5403],{"className":5402},[229,230,231,232],[135,5404,442],{"className":5405},[195,268,232],[135,5407,303],{"className":5408},[302],[135,5410,5412],{"className":5411},[212],[135,5413,5415],{"className":5414,"style":1346},[216],[135,5416],{},[135,5418,868],{"className":5419},[195,268],[135,5421,169],{"className":5422},[195,268],[135,5424,858],{"className":5425},[195,268],[135,5427,2976],{"className":5428,"style":5429},[195,268],"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。",[14,5432,5433],{},"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。",[14,5435,5436,5437,5602,5603,5631,5632,5660,5661,5833,5834,5895,5896,5925,5926,5963,5964,6020],{},"假设输入表示 ",[135,5438,5440,5483],{"className":5439},[138],[135,5441,5443],{"className":5442},[142],[144,5444,5445],{"xmlns":146},[148,5446,5447,5480],{},[151,5448,5449,5452,5454],{},[167,5450,2492],{"mathvariant":5451},"bold",[537,5453,539],{},[541,5455,5456,5458],{},[167,5457,546],{"mathvariant":545},[151,5459,5460,5462,5464],{},[167,5461,411],{},[537,5463,553],{},[164,5465,5466,5468],{},[167,5467,169],{},[151,5469,5470,5472,5474,5476,5478],{},[167,5471,442],{},[167,5473,868],{},[167,5475,169],{},[167,5477,858],{},[167,5479,2976],{},[174,5481,5482],{"encoding":176},"\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{model}}",[135,5484,5486,5506],{"className":5485,"ariaHidden":182},[181],[135,5487,5489,5493,5497,5500,5503],{"className":5488},[186],[135,5490],{"className":5491,"style":5492},[190],"height:0.7252em;vertical-align:-0.0391em;",[135,5494,2492],{"className":5495},[195,5496],"mathbf",[135,5498],{"className":5499,"style":576},[575],[135,5501,539],{"className":5502},[580],[135,5504],{"className":5505,"style":576},[575],[135,5507,5509,5512],{"className":5508},[186],[135,5510],{"className":5511,"style":590},[190],[135,5513,5515,5518],{"className":5514},[195],[135,5516,546],{"className":5517},[195,597],[135,5519,5521],{"className":5520},[272],[135,5522,5524],{"className":5523},[207],[135,5525,5527],{"className":5526},[212],[135,5528,5530],{"className":5529,"style":590},[216],[135,5531,5532,5535],{"style":612},[135,5533],{"className":5534,"style":616},[224],[135,5536,5538],{"className":5537},[229,230,231,232],[135,5539,5541,5544,5547],{"className":5540},[195,232],[135,5542,411],{"className":5543},[195,268,232],[135,5545,553],{"className":5546},[629,232],[135,5548,5550,5553],{"className":5549},[195,232],[135,5551,169],{"className":5552},[195,268,232],[135,5554,5556],{"className":5555},[272],[135,5557,5559,5594],{"className":5558},[207,208],[135,5560,5562,5591],{"className":5561},[212],[135,5563,5565],{"className":5564,"style":282},[216],[135,5566,5567,5570],{"style":285},[135,5568],{"className":5569,"style":289},[224],[135,5571,5573],{"className":5572},[229,293,294,232],[135,5574,5576,5579,5582,5585,5588],{"className":5575},[195,232],[135,5577,442],{"className":5578},[195,268,232],[135,5580,868],{"className":5581},[195,268,232],[135,5583,169],{"className":5584},[195,268,232],[135,5586,858],{"className":5587},[195,268,232],[135,5589,2976],{"className":5590,"style":5429},[195,268,232],[135,5592,303],{"className":5593},[302],[135,5595,5597],{"className":5596},[212],[135,5598,5600],{"className":5599,"style":310},[216],[135,5601],{}," 包含一个序列中 ",[135,5604,5606,5619],{"className":5605},[138],[135,5607,5609],{"className":5608},[142],[144,5610,5611],{"xmlns":146},[148,5612,5613,5617],{},[151,5614,5615],{},[167,5616,411],{},[174,5618,411],{"encoding":176},[135,5620,5622],{"className":5621,"ariaHidden":182},[181],[135,5623,5625,5628],{"className":5624},[186],[135,5626],{"className":5627,"style":423},[190],[135,5629,411],{"className":5630},[195,268]," 个词元的 ",[135,5633,5635,5648],{"className":5634},[138],[135,5636,5638],{"className":5637},[142],[144,5639,5640],{"xmlns":146},[148,5641,5642,5646],{},[151,5643,5644],{},[167,5645,169],{},[174,5647,169],{"encoding":176},[135,5649,5651],{"className":5650,"ariaHidden":182},[181],[135,5652,5654,5657],{"className":5653},[186],[135,5655],{"className":5656,"style":483},[190],[135,5658,169],{"className":5659},[195,268]," 维嵌入表示。位置编码使用相同形状的位置嵌入矩阵 ",[135,5662,5664,5712],{"className":5663},[138],[135,5665,5667],{"className":5666},[142],[144,5668,5669],{"xmlns":146},[148,5670,5671,5709],{},[151,5672,5673,5681,5683],{},[151,5674,5675,5678],{},[167,5676,5677],{"mathvariant":5451},"P",[167,5679,5680],{"mathvariant":5451},"E",[537,5682,539],{},[541,5684,5685,5687],{},[167,5686,546],{"mathvariant":545},[151,5688,5689,5691,5693],{},[167,5690,411],{},[537,5692,553],{},[164,5694,5695,5697],{},[167,5696,169],{},[151,5698,5699,5701,5703,5705,5707],{},[167,5700,442],{},[167,5702,868],{},[167,5704,169],{},[167,5706,858],{},[167,5708,2976],{},[174,5710,5711],{"encoding":176},"\\mathbf{PE} \\in \\mathbb{R}^{n \\times d_{model}}",[135,5713,5715,5737],{"className":5714,"ariaHidden":182},[181],[135,5716,5718,5721,5728,5731,5734],{"className":5717},[186],[135,5719],{"className":5720,"style":5492},[190],[135,5722,5724],{"className":5723},[195],[135,5725,5727],{"className":5726},[195,5496],"PE",[135,5729],{"className":5730,"style":576},[575],[135,5732,539],{"className":5733},[580],[135,5735],{"className":5736,"style":576},[575],[135,5738,5740,5743],{"className":5739},[186],[135,5741],{"className":5742,"style":590},[190],[135,5744,5746,5749],{"className":5745},[195],[135,5747,546],{"className":5748},[195,597],[135,5750,5752],{"className":5751},[272],[135,5753,5755],{"className":5754},[207],[135,5756,5758],{"className":5757},[212],[135,5759,5761],{"className":5760,"style":590},[216],[135,5762,5763,5766],{"style":612},[135,5764],{"className":5765,"style":616},[224],[135,5767,5769],{"className":5768},[229,230,231,232],[135,5770,5772,5775,5778],{"className":5771},[195,232],[135,5773,411],{"className":5774},[195,268,232],[135,5776,553],{"className":5777},[629,232],[135,5779,5781,5784],{"className":5780},[195,232],[135,5782,169],{"className":5783},[195,268,232],[135,5785,5787],{"className":5786},[272],[135,5788,5790,5825],{"className":5789},[207,208],[135,5791,5793,5822],{"className":5792},[212],[135,5794,5796],{"className":5795,"style":282},[216],[135,5797,5798,5801],{"style":285},[135,5799],{"className":5800,"style":289},[224],[135,5802,5804],{"className":5803},[229,293,294,232],[135,5805,5807,5810,5813,5816,5819],{"className":5806},[195,232],[135,5808,442],{"className":5809},[195,268,232],[135,5811,868],{"className":5812},[195,268,232],[135,5814,169],{"className":5815},[195,268,232],[135,5817,858],{"className":5818},[195,268,232],[135,5820,2976],{"className":5821,"style":5429},[195,268,232],[135,5823,303],{"className":5824},[302],[135,5826,5828],{"className":5827},[212],[135,5829,5831],{"className":5830,"style":310},[216],[135,5832],{}," 输出 ",[135,5835,5837,5860],{"className":5836},[138],[135,5838,5840],{"className":5839},[142],[144,5841,5842],{"xmlns":146},[148,5843,5844,5857],{},[151,5845,5846,5848,5851],{},[167,5847,2492],{"mathvariant":5451},[537,5849,5850],{},"+",[151,5852,5853,5855],{},[167,5854,5677],{"mathvariant":5451},[167,5856,5680],{"mathvariant":5451},[174,5858,5859],{"encoding":176},"\\mathbf{X} + \\mathbf{PE}",[135,5861,5863,5882],{"className":5862,"ariaHidden":182},[181],[135,5864,5866,5870,5873,5876,5879],{"className":5865},[186],[135,5867],{"className":5868,"style":5869},[190],"height:0.7694em;vertical-align:-0.0833em;",[135,5871,2492],{"className":5872},[195,5496],[135,5874],{"className":5875,"style":1948},[575],[135,5877,5850],{"className":5878},[629],[135,5880],{"className":5881,"style":1948},[575],[135,5883,5885,5889],{"className":5884},[186],[135,5886],{"className":5887,"style":5888},[190],"height:0.6861em;",[135,5890,5892],{"className":5891},[195],[135,5893,5727],{"className":5894},[195,5496],"，矩阵第 ",[135,5897,5899,5912],{"className":5898},[138],[135,5900,5902],{"className":5901},[142],[144,5903,5904],{"xmlns":146},[148,5905,5906,5910],{},[151,5907,5908],{},[167,5909,865],{},[174,5911,865],{"encoding":176},[135,5913,5915],{"className":5914,"ariaHidden":182},[181],[135,5916,5918,5922],{"className":5917},[186],[135,5919],{"className":5920,"style":5921},[190],"height:0.6595em;",[135,5923,865],{"className":5924},[195,268]," 行、第 ",[135,5927,5929,5946],{"className":5928},[138],[135,5930,5932],{"className":5931},[142],[144,5933,5934],{"xmlns":146},[148,5935,5936,5943],{},[151,5937,5938,5940],{},[157,5939,2894],{},[167,5941,5942],{},"j",[174,5944,5945],{"encoding":176},"2j",[135,5947,5949],{"className":5948,"ariaHidden":182},[181],[135,5950,5952,5956,5959],{"className":5951},[186],[135,5953],{"className":5954,"style":5955},[190],"height:0.854em;vertical-align:-0.1944em;",[135,5957,2894],{"className":5958},[195],[135,5960,5942],{"className":5961,"style":5962},[195,268],"margin-right:0.05724em;"," 列和 ",[135,5965,5967,5987],{"className":5966},[138],[135,5968,5970],{"className":5969},[142],[144,5971,5972],{"xmlns":146},[148,5973,5974,5984],{},[151,5975,5976,5978,5980,5982],{},[157,5977,2894],{},[167,5979,5942],{},[537,5981,5850],{},[157,5983,159],{},[174,5985,5986],{"encoding":176},"2j+1",[135,5988,5990,6011],{"className":5989,"ariaHidden":182},[181],[135,5991,5993,5996,5999,6002,6005,6008],{"className":5992},[186],[135,5994],{"className":5995,"style":5955},[190],[135,5997,2894],{"className":5998},[195],[135,6000,5942],{"className":6001,"style":5962},[195,268],[135,6003],{"className":6004,"style":1948},[575],[135,6006,5850],{"className":6007},[629],[135,6009],{"className":6010,"style":1948},[575],[135,6012,6014,6017],{"className":6013},[186],[135,6015],{"className":6016,"style":1842},[190],[135,6018,159],{"className":6019},[195]," 列上的元素为：",[14,6022,6023],{},[135,6024,6026,6104],{"className":6025},[138],[135,6027,6029],{"className":6028},[142],[144,6030,6031],{"xmlns":146},[148,6032,6033,6101],{},[151,6034,6035,6037,6055,6057,6060,6062],{},[167,6036,5677],{},[164,6038,6039,6041],{},[167,6040,5680],{},[151,6042,6043,6045,6047,6049,6051,6053],{},[537,6044,874],{"stretchy":873},[167,6046,865],{},[537,6048,879],{"separator":182},[157,6050,2894],{},[167,6052,5942],{},[537,6054,888],{"stretchy":873},[537,6056,891],{},[167,6058,6059],{},"sin",[537,6061,898],{},[151,6063,6064,6066,6099],{},[537,6065,874],{"fence":182},[154,6067,6068,6070],{},[167,6069,865],{},[541,6071,6072,6075],{},[157,6073,6074],{},"10000",[151,6076,6077,6079,6081,6083],{},[157,6078,2894],{},[167,6080,5942],{},[167,6082,2900],{"mathvariant":894},[164,6084,6085,6087],{},[167,6086,169],{},[151,6088,6089,6091,6093,6095,6097],{},[167,6090,442],{},[167,6092,868],{},[167,6094,169],{},[167,6096,858],{},[167,6098,2976],{},[537,6100,888],{"fence":182},[174,6102,6103],{"encoding":176}," PE_{(i,2j)} = \\sin\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[135,6105,6107,6187],{"className":6106,"ariaHidden":182},[181],[135,6108,6110,6114,6117,6178,6181,6184],{"className":6109},[186],[135,6111],{"className":6112,"style":6113},[190],"height:1.0385em;vertical-align:-0.3552em;",[135,6115,5677],{"className":6116,"style":3258},[195,268],[135,6118,6120,6124],{"className":6119},[195],[135,6121,5680],{"className":6122,"style":6123},[195,268],"margin-right:0.05764em;",[135,6125,6127],{"className":6126},[272],[135,6128,6130,6169],{"className":6129},[207,208],[135,6131,6133,6166],{"className":6132},[212],[135,6134,6136],{"className":6135,"style":282},[216],[135,6137,6139,6142],{"style":6138},"top:-2.5198em;margin-left:-0.0576em;margin-right:0.05em;",[135,6140],{"className":6141,"style":616},[224],[135,6143,6145],{"className":6144},[229,230,231,232],[135,6146,6148,6151,6154,6157,6160,6163],{"className":6147},[195,232],[135,6149,874],{"className":6150},[199,232],[135,6152,865],{"className":6153},[195,268,232],[135,6155,879],{"className":6156},[988,232],[135,6158,2894],{"className":6159},[195,232],[135,6161,5942],{"className":6162,"style":5962},[195,268,232],[135,6164,888],{"className":6165},[389,232],[135,6167,303],{"className":6168},[302],[135,6170,6172],{"className":6171},[212],[135,6173,6176],{"className":6174,"style":6175},[216],"height:0.3552em;",[135,6177],{},[135,6179],{"className":6180,"style":576},[575],[135,6182,891],{"className":6183},[580],[135,6185],{"className":6186,"style":576},[575],[135,6188,6190,6193,6196,6199],{"className":6189},[186],[135,6191],{"className":6192,"style":1023},[190],[135,6194,6059],{"className":6195},[1027],[135,6197],{"className":6198,"style":992},[575],[135,6200,6202,6208,6376],{"className":6201},[1038],[135,6203,6205],{"className":6204,"style":1043},[199,1042],[135,6206,874],{"className":6207},[1047,1048],[135,6209,6211,6214,6373],{"className":6210},[195],[135,6212],{"className":6213},[199,200],[135,6215,6217],{"className":6216},[154],[135,6218,6220,6364],{"className":6219},[207,208],[135,6221,6223,6361],{"className":6222},[212],[135,6224,6227,6339,6347],{"className":6225,"style":6226},[216],"height:0.8557em;",[135,6228,6230,6233],{"style":6229},"top:-2.5648em;",[135,6231],{"className":6232,"style":225},[224],[135,6234,6236],{"className":6235},[229,230,231,232],[135,6237,6239,6243],{"className":6238},[195,232],[135,6240,6242],{"className":6241},[195,232],"1000",[135,6244,6246,6249],{"className":6245},[195,232],[135,6247,1830],{"className":6248},[195,232],[135,6250,6252],{"className":6251},[272],[135,6253,6255],{"className":6254},[207],[135,6256,6258],{"className":6257},[212],[135,6259,6262],{"className":6260,"style":6261},[216],"height:0.8932em;",[135,6263,6265,6269],{"style":6264},"top:-2.8932em;margin-right:0.0714em;",[135,6266],{"className":6267,"style":6268},[224],"height:2.5357em;",[135,6270,6272],{"className":6271},[229,293,294,232],[135,6273,6275,6278,6281,6284],{"className":6274},[195,232],[135,6276,2894],{"className":6277},[195,232],[135,6279,5942],{"className":6280,"style":5962},[195,268,232],[135,6282,2900],{"className":6283},[195,232],[135,6285,6287,6290],{"className":6286},[195,232],[135,6288,169],{"className":6289},[195,268,232],[135,6291,6293],{"className":6292},[272],[135,6294,6296,6330],{"className":6295},[207,208],[135,6297,6299,6327],{"className":6298},[212],[135,6300,6302],{"className":6301,"style":282},[216],[135,6303,6305,6309],{"style":6304},"top:-2.3448em;margin-left:0em;margin-right:0.1em;",[135,6306],{"className":6307,"style":6308},[224],"height:2.6944em;",[135,6310,6312,6315,6318,6321,6324],{"className":6311},[195,232],[135,6313,442],{"className":6314},[195,268,232],[135,6316,868],{"className":6317},[195,268,232],[135,6319,169],{"className":6320},[195,268,232],[135,6322,858],{"className":6323},[195,268,232],[135,6325,2976],{"className":6326,"style":5429},[195,268,232],[135,6328,303],{"className":6329},[302],[135,6331,6333],{"className":6332},[212],[135,6334,6337],{"className":6335,"style":6336},[216],"height:0.3496em;",[135,6338],{},[135,6340,6341,6344],{"style":350},[135,6342],{"className":6343,"style":225},[224],[135,6345],{"className":6346,"style":358},[357],[135,6348,6349,6352],{"style":361},[135,6350],{"className":6351,"style":225},[224],[135,6353,6355],{"className":6354},[229,230,231,232],[135,6356,6358],{"className":6357},[195,232],[135,6359,865],{"className":6360},[195,268,232],[135,6362,303],{"className":6363},[302],[135,6365,6367],{"className":6366},[212],[135,6368,6371],{"className":6369,"style":6370},[216],"height:0.4352em;",[135,6372],{},[135,6374],{"className":6375},[389,200],[135,6377,6379],{"className":6378,"style":1043},[389,1042],[135,6380,888],{"className":6381},[1047,1048],[14,6383,6384],{},[135,6385,6387,6468],{"className":6386},[138],[135,6388,6390],{"className":6389},[142],[144,6391,6392],{"xmlns":146},[148,6393,6394,6465],{},[151,6395,6396,6398,6420,6422,6425,6427],{},[167,6397,5677],{},[164,6399,6400,6402],{},[167,6401,5680],{},[151,6403,6404,6406,6408,6410,6412,6414,6416,6418],{},[537,6405,874],{"stretchy":873},[167,6407,865],{},[537,6409,879],{"separator":182},[157,6411,2894],{},[167,6413,5942],{},[537,6415,5850],{},[157,6417,159],{},[537,6419,888],{"stretchy":873},[537,6421,891],{},[167,6423,6424],{},"cos",[537,6426,898],{},[151,6428,6429,6431,6463],{},[537,6430,874],{"fence":182},[154,6432,6433,6435],{},[167,6434,865],{},[541,6436,6437,6439],{},[157,6438,6074],{},[151,6440,6441,6443,6445,6447],{},[157,6442,2894],{},[167,6444,5942],{},[167,6446,2900],{"mathvariant":894},[164,6448,6449,6451],{},[167,6450,169],{},[151,6452,6453,6455,6457,6459,6461],{},[167,6454,442],{},[167,6456,868],{},[167,6458,169],{},[167,6460,858],{},[167,6462,2976],{},[537,6464,888],{"fence":182},[174,6466,6467],{"encoding":176}," PE_{(i,2j+1)} = \\cos\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[135,6469,6471,6553],{"className":6470,"ariaHidden":182},[181],[135,6472,6474,6477,6480,6544,6547,6550],{"className":6473},[186],[135,6475],{"className":6476,"style":6113},[190],[135,6478,5677],{"className":6479,"style":3258},[195,268],[135,6481,6483,6486],{"className":6482},[195],[135,6484,5680],{"className":6485,"style":6123},[195,268],[135,6487,6489],{"className":6488},[272],[135,6490,6492,6536],{"className":6491},[207,208],[135,6493,6495,6533],{"className":6494},[212],[135,6496,6498],{"className":6497,"style":282},[216],[135,6499,6500,6503],{"style":6138},[135,6501],{"className":6502,"style":616},[224],[135,6504,6506],{"className":6505},[229,230,231,232],[135,6507,6509,6512,6515,6518,6521,6524,6527,6530],{"className":6508},[195,232],[135,6510,874],{"className":6511},[199,232],[135,6513,865],{"className":6514},[195,268,232],[135,6516,879],{"className":6517},[988,232],[135,6519,2894],{"className":6520},[195,232],[135,6522,5942],{"className":6523,"style":5962},[195,268,232],[135,6525,5850],{"className":6526},[629,232],[135,6528,159],{"className":6529},[195,232],[135,6531,888],{"className":6532},[389,232],[135,6534,303],{"className":6535},[302],[135,6537,6539],{"className":6538},[212],[135,6540,6542],{"className":6541,"style":6175},[216],[135,6543],{},[135,6545],{"className":6546,"style":576},[575],[135,6548,891],{"className":6549},[580],[135,6551],{"className":6552,"style":576},[575],[135,6554,6556,6559,6562,6565],{"className":6555},[186],[135,6557],{"className":6558,"style":1023},[190],[135,6560,6424],{"className":6561},[1027],[135,6563],{"className":6564,"style":992},[575],[135,6566,6568,6574,6732],{"className":6567},[1038],[135,6569,6571],{"className":6570,"style":1043},[199,1042],[135,6572,874],{"className":6573},[1047,1048],[135,6575,6577,6580,6729],{"className":6576},[195],[135,6578],{"className":6579},[199,200],[135,6581,6583],{"className":6582},[154],[135,6584,6586,6721],{"className":6585},[207,208],[135,6587,6589,6718],{"className":6588},[212],[135,6590,6592,6696,6704],{"className":6591,"style":6226},[216],[135,6593,6594,6597],{"style":6229},[135,6595],{"className":6596,"style":225},[224],[135,6598,6600],{"className":6599},[229,230,231,232],[135,6601,6603,6606],{"className":6602},[195,232],[135,6604,6242],{"className":6605},[195,232],[135,6607,6609,6612],{"className":6608},[195,232],[135,6610,1830],{"className":6611},[195,232],[135,6613,6615],{"className":6614},[272],[135,6616,6618],{"className":6617},[207],[135,6619,6621],{"className":6620},[212],[135,6622,6624],{"className":6623,"style":6261},[216],[135,6625,6626,6629],{"style":6264},[135,6627],{"className":6628,"style":6268},[224],[135,6630,6632],{"className":6631},[229,293,294,232],[135,6633,6635,6638,6641,6644],{"className":6634},[195,232],[135,6636,2894],{"className":6637},[195,232],[135,6639,5942],{"className":6640,"style":5962},[195,268,232],[135,6642,2900],{"className":6643},[195,232],[135,6645,6647,6650],{"className":6646},[195,232],[135,6648,169],{"className":6649},[195,268,232],[135,6651,6653],{"className":6652},[272],[135,6654,6656,6688],{"className":6655},[207,208],[135,6657,6659,6685],{"className":6658},[212],[135,6660,6662],{"className":6661,"style":282},[216],[135,6663,6664,6667],{"style":6304},[135,6665],{"className":6666,"style":6308},[224],[135,6668,6670,6673,6676,6679,6682],{"className":6669},[195,232],[135,6671,442],{"className":6672},[195,268,232],[135,6674,868],{"className":6675},[195,268,232],[135,6677,169],{"className":6678},[195,268,232],[135,6680,858],{"className":6681},[195,268,232],[135,6683,2976],{"className":6684,"style":5429},[195,268,232],[135,6686,303],{"className":6687},[302],[135,6689,6691],{"className":6690},[212],[135,6692,6694],{"className":6693,"style":6336},[216],[135,6695],{},[135,6697,6698,6701],{"style":350},[135,6699],{"className":6700,"style":225},[224],[135,6702],{"className":6703,"style":358},[357],[135,6705,6706,6709],{"style":361},[135,6707],{"className":6708,"style":225},[224],[135,6710,6712],{"className":6711},[229,230,231,232],[135,6713,6715],{"className":6714},[195,232],[135,6716,865],{"className":6717},[195,268,232],[135,6719,303],{"className":6720},[302],[135,6722,6724],{"className":6723},[212],[135,6725,6727],{"className":6726,"style":6370},[216],[135,6728],{},[135,6730],{"className":6731},[389,200],[135,6733,6735],{"className":6734,"style":1043},[389,1042],[135,6736,888],{"className":6737},[1047,1048],[14,6739,6740,6741,6769,6770,6798,6799,6834,6835,6891,6892,6920,6921,7014,7015,7094],{},"其中，",[135,6742,6744,6757],{"className":6743},[138],[135,6745,6747],{"className":6746},[142],[144,6748,6749],{"xmlns":146},[148,6750,6751,6755],{},[151,6752,6753],{},[167,6754,865],{},[174,6756,865],{"encoding":176},[135,6758,6760],{"className":6759,"ariaHidden":182},[181],[135,6761,6763,6766],{"className":6762},[186],[135,6764],{"className":6765,"style":5921},[190],[135,6767,865],{"className":6768},[195,268]," 表示位置，",[135,6771,6773,6786],{"className":6772},[138],[135,6774,6776],{"className":6775},[142],[144,6777,6778],{"xmlns":146},[148,6779,6780,6784],{},[151,6781,6782],{},[167,6783,5942],{},[174,6785,5942],{"encoding":176},[135,6787,6789],{"className":6788,"ariaHidden":182},[181],[135,6790,6792,6795],{"className":6791},[186],[135,6793],{"className":6794,"style":5955},[190],[135,6796,5942],{"className":6797,"style":5962},[195,268]," 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 ",[135,6800,6802,6819],{"className":6801},[138],[135,6803,6805],{"className":6804},[142],[144,6806,6807],{"xmlns":146},[148,6808,6809,6816],{},[151,6810,6811,6813],{},[157,6812,2894],{},[167,6814,6815],{},"π",[174,6817,6818],{"encoding":176},"2\\pi",[135,6820,6822],{"className":6821,"ariaHidden":182},[181],[135,6823,6825,6828,6831],{"className":6824},[186],[135,6826],{"className":6827,"style":1842},[190],[135,6829,2894],{"className":6830},[195],[135,6832,6815],{"className":6833,"style":517},[195,268]," 到 ",[135,6836,6838,6858],{"className":6837},[138],[135,6839,6841],{"className":6840},[142],[144,6842,6843],{"xmlns":146},[148,6844,6845,6855],{},[151,6846,6847,6849,6851,6853],{},[157,6848,6074],{},[537,6850,1892],{},[157,6852,2894],{},[167,6854,6815],{},[174,6856,6857],{"encoding":176},"10000 \\cdot 2\\pi",[135,6859,6861,6879],{"className":6860,"ariaHidden":182},[181],[135,6862,6864,6867,6870,6873,6876],{"className":6863},[186],[135,6865],{"className":6866,"style":1842},[190],[135,6868,6074],{"className":6869},[195],[135,6871],{"className":6872,"style":1948},[575],[135,6874,1892],{"className":6875},[629],[135,6877],{"className":6878,"style":1948},[575],[135,6880,6882,6885,6888],{"className":6881},[186],[135,6883],{"className":6884,"style":1842},[190],[135,6886,2894],{"className":6887},[195],[135,6889,6815],{"className":6890,"style":517},[195,268]," 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 ",[135,6893,6895,6908],{"className":6894},[138],[135,6896,6898],{"className":6897},[142],[144,6899,6900],{"xmlns":146},[148,6901,6902,6906],{},[151,6903,6904],{},[167,6905,172],{},[174,6907,172],{"encoding":176},[135,6909,6911],{"className":6910,"ariaHidden":182},[181],[135,6912,6914,6917],{"className":6913},[186],[135,6915],{"className":6916,"style":483},[190],[135,6918,172],{"className":6919,"style":298},[195,268],"，",[135,6922,6924,6950],{"className":6923},[138],[135,6925,6927],{"className":6926},[142],[144,6928,6929],{"xmlns":146},[148,6930,6931,6947],{},[151,6932,6933,6935],{},[167,6934,5677],{},[164,6936,6937,6939],{},[167,6938,5680],{},[151,6940,6941,6943,6945],{},[167,6942,865],{},[537,6944,5850],{},[167,6946,172],{},[174,6948,6949],{"encoding":176},"PE_{i+k}",[135,6951,6953],{"className":6952,"ariaHidden":182},[181],[135,6954,6956,6960,6963],{"className":6955},[186],[135,6957],{"className":6958,"style":6959},[190],"height:0.8917em;vertical-align:-0.2083em;",[135,6961,5677],{"className":6962,"style":3258},[195,268],[135,6964,6966,6969],{"className":6965},[195],[135,6967,5680],{"className":6968,"style":6123},[195,268],[135,6970,6972],{"className":6971},[272],[135,6973,6975,7005],{"className":6974},[207,208],[135,6976,6978,7002],{"className":6977},[212],[135,6979,6981],{"className":6980,"style":1324},[216],[135,6982,6984,6987],{"style":6983},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[135,6985],{"className":6986,"style":616},[224],[135,6988,6990],{"className":6989},[229,230,231,232],[135,6991,6993,6996,6999],{"className":6992},[195,232],[135,6994,865],{"className":6995},[195,268,232],[135,6997,5850],{"className":6998},[629,232],[135,7000,172],{"className":7001,"style":298},[195,268,232],[135,7003,303],{"className":7004},[302],[135,7006,7008],{"className":7007},[212],[135,7009,7012],{"className":7010,"style":7011},[216],"height:0.2083em;",[135,7013],{}," 都可以表示为 ",[135,7016,7018,7038],{"className":7017},[138],[135,7019,7021],{"className":7020},[142],[144,7022,7023],{"xmlns":146},[148,7024,7025,7035],{},[151,7026,7027,7029],{},[167,7028,5677],{},[164,7030,7031,7033],{},[167,7032,5680],{},[167,7034,865],{},[174,7036,7037],{"encoding":176},"PE_{i}",[135,7039,7041],{"className":7040,"ariaHidden":182},[181],[135,7042,7044,7048,7051],{"className":7043},[186],[135,7045],{"className":7046,"style":7047},[190],"height:0.8333em;vertical-align:-0.15em;",[135,7049,5677],{"className":7050,"style":3258},[195,268],[135,7052,7054,7057],{"className":7053},[195],[135,7055,5680],{"className":7056,"style":6123},[195,268],[135,7058,7060],{"className":7059},[272],[135,7061,7063,7086],{"className":7062},[207,208],[135,7064,7066,7083],{"className":7065},[212],[135,7067,7069],{"className":7068,"style":2108},[216],[135,7070,7071,7074],{"style":6983},[135,7072],{"className":7073,"style":616},[224],[135,7075,7077],{"className":7076},[229,230,231,232],[135,7078,7080],{"className":7079},[195,232],[135,7081,865],{"className":7082},[195,268,232],[135,7084,303],{"className":7085},[302],[135,7087,7089],{"className":7088},[212],[135,7090,7092],{"className":7091,"style":1346},[216],[135,7093],{}," 的线性函数。",[2466,7096,7098],{"className":2468,"code":7097,"language":2470,"meta":65,"style":65},"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",[2472,7099,7100,7118,7123,7152,7168,7178,7183,7200,7225,7247,7279,7306,7310,7326,7359],{"__ignoreMap":65},[135,7101,7102,7104,7107,7109,7111,7113,7116],{"class":2476,"line":2477},[135,7103,2704],{"class":2480},[135,7105,7106],{"class":2707}," PositionalEncoding",[135,7108,874],{"class":2488},[135,7110,2714],{"class":2713},[135,7112,940],{"class":2488},[135,7114,7115],{"class":2713},"Block",[135,7117,2501],{"class":2488},[135,7119,7120],{"class":2476,"line":66},[135,7121,7122],{"class":2506},"    \"\"\"位置编码\"\"\"\n",[135,7124,7125,7127,7129,7131,7133,7135,7137,7139,7141,7143,7146,7148,7150],{"class":2476,"line":2510},[135,7126,2731],{"class":2480},[135,7128,2734],{"class":2529},[135,7130,874],{"class":2488},[135,7132,2740],{"class":2739},[135,7134,2495],{"class":2488},[135,7136,4935],{"class":2491},[135,7138,2495],{"class":2488},[135,7140,2745],{"class":2491},[135,7142,2495],{"class":2488},[135,7144,7145],{"class":2491},"max_len",[135,7147,891],{"class":2480},[135,7149,6242],{"class":2529},[135,7151,2501],{"class":2488},[135,7153,7154,7156,7159,7161,7163,7165],{"class":2476,"line":2517},[135,7155,2761],{"class":2760},[135,7157,7158],{"class":2488},"(PositionalEncoding, ",[135,7160,2740],{"class":2767},[135,7162,2770],{"class":2488},[135,7164,2773],{"class":2529},[135,7166,7167],{"class":2488},"()\n",[135,7169,7170,7172,7174,7176],{"class":2476,"line":2536},[135,7171,2785],{"class":2767},[135,7173,2788],{"class":2488},[135,7175,891],{"class":2480},[135,7177,2793],{"class":2488},[135,7179,7180],{"class":2476,"line":2557},[135,7181,7182],{"class":2513},"        # 创建一个足够长的P\n",[135,7184,7185,7187,7190,7192,7195,7197],{"class":2476,"line":2565},[135,7186,2785],{"class":2767},[135,7188,7189],{"class":2488},".P ",[135,7191,891],{"class":2480},[135,7193,7194],{"class":2488}," np.zeros((",[135,7196,159],{"class":2529},[135,7198,7199],{"class":2488},", max_len, num_hiddens))\n",[135,7201,7202,7204,7206,7209,7211,7213,7215,7217,7220,7222],{"class":2476,"line":2576},[135,7203,2643],{"class":2488},[135,7205,891],{"class":2480},[135,7207,7208],{"class":2488}," np.arange(max_len).reshape(",[135,7210,2627],{"class":2480},[135,7212,159],{"class":2529},[135,7214,2495],{"class":2488},[135,7216,159],{"class":2529},[135,7218,7219],{"class":2488},") ",[135,7221,2900],{"class":2480},[135,7223,7224],{"class":2488}," np.power(\n",[135,7226,7227,7230,7233,7235,7238,7240,7242,7244],{"class":2476,"line":2593},[135,7228,7229],{"class":2529},"            10000",[135,7231,7232],{"class":2488},", np.arange(",[135,7234,1830],{"class":2529},[135,7236,7237],{"class":2488},", num_hiddens, ",[135,7239,2894],{"class":2529},[135,7241,7219],{"class":2488},[135,7243,2900],{"class":2480},[135,7245,7246],{"class":2488}," num_hiddens)\n",[135,7248,7249,7251,7254,7258,7260,7262,7264,7266,7269,7271,7274,7276],{"class":2476,"line":2609},[135,7250,2785],{"class":2767},[135,7252,7253],{"class":2488},".P[",[135,7255,7257],{"class":7256},"sDoOe",":",[135,7259,2495],{"class":2488},[135,7261,7257],{"class":7256},[135,7263,2495],{"class":2488},[135,7265,1830],{"class":2529},[135,7267,7268],{"class":7256},"::",[135,7270,2894],{"class":2529},[135,7272,7273],{"class":2488},"] ",[135,7275,891],{"class":2480},[135,7277,7278],{"class":2488}," np.sin(X)\n",[135,7280,7281,7283,7285,7287,7289,7291,7293,7295,7297,7299,7301,7303],{"class":2476,"line":2617},[135,7282,2785],{"class":2767},[135,7284,7253],{"class":2488},[135,7286,7257],{"class":7256},[135,7288,2495],{"class":2488},[135,7290,7257],{"class":7256},[135,7292,2495],{"class":2488},[135,7294,159],{"class":2529},[135,7296,7268],{"class":7256},[135,7298,2894],{"class":2529},[135,7300,7273],{"class":2488},[135,7302,891],{"class":2480},[135,7304,7305],{"class":2488}," np.cos(X)\n",[135,7307,7308],{"class":2476,"line":2634},[135,7309,2798],{"emptyLinePlaceholder":80},[135,7311,7312,7314,7316,7318,7320,7322,7324],{"class":2476,"line":2640},[135,7313,2731],{"class":2480},[135,7315,2825],{"class":2484},[135,7317,874],{"class":2488},[135,7319,2740],{"class":2739},[135,7321,2495],{"class":2488},[135,7323,2492],{"class":2491},[135,7325,2501],{"class":2488},[135,7327,7328,7330,7332,7335,7337,7339,7341,7343,7345,7347,7350,7352,7354,7356],{"class":2476,"line":2665},[135,7329,2643],{"class":2488},[135,7331,891],{"class":2480},[135,7333,7334],{"class":2488}," X ",[135,7336,5850],{"class":2480},[135,7338,5293],{"class":2767},[135,7340,7253],{"class":2488},[135,7342,7257],{"class":7256},[135,7344,2495],{"class":2488},[135,7346,7257],{"class":7256},[135,7348,7349],{"class":2488},"X.shape[",[135,7351,159],{"class":2529},[135,7353,4867],{"class":2488},[135,7355,7257],{"class":7256},[135,7357,7358],{"class":2488},"].as_in_ctx(X.ctx)\n",[135,7360,7361,7363,7365],{"class":2476,"line":2678},[135,7362,2539],{"class":2480},[135,7364,5293],{"class":2767},[135,7366,7367],{"class":2488},".dropout(X)\n",[10,7369,7370],{"id":7370},"前馈神经网络",[14,7372,7373],{},"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。",[14,7375,7376],{},[135,7377,7379,7452],{"className":7378},[138],[135,7380,7382],{"className":7381},[142],[144,7383,7384],{"xmlns":146},[148,7385,7386,7449],{},[151,7387,7388,7391,7393,7396,7398,7401,7403,7405,7408,7410,7412,7414,7416,7418,7424,7426,7433,7435,7441,7443],{},[167,7389,7390],{},"F",[167,7392,7390],{},[167,7394,7395],{},"N",[537,7397,874],{"stretchy":873},[167,7399,7400],{},"x",[537,7402,888],{"stretchy":873},[537,7404,891],{},[167,7406,7407],{},"max",[537,7409,898],{},[537,7411,874],{"stretchy":873},[157,7413,1830],{},[537,7415,879],{"separator":182},[167,7417,7400],{},[164,7419,7420,7422],{},[167,7421,3066],{},[157,7423,159],{},[537,7425,5850],{},[164,7427,7428,7431],{},[167,7429,7430],{},"b",[157,7432,159],{},[537,7434,888],{"stretchy":873},[164,7436,7437,7439],{},[167,7438,3066],{},[157,7440,2894],{},[537,7442,5850],{},[164,7444,7445,7447],{},[167,7446,7430],{},[157,7448,2894],{},[174,7450,7451],{"encoding":176}," FFN(x) = \\max(0,xW_1+b_1)W_2+b_2",[135,7453,7455,7489,7563,7661],{"className":7454,"ariaHidden":182},[181],[135,7456,7458,7461,7464,7467,7471,7474,7477,7480,7483,7486],{"className":7457},[186],[135,7459],{"className":7460,"style":953},[190],[135,7462,7390],{"className":7463,"style":3258},[195,268],[135,7465,7390],{"className":7466,"style":3258},[195,268],[135,7468,7395],{"className":7469,"style":7470},[195,268],"margin-right:0.10903em;",[135,7472,874],{"className":7473},[199],[135,7475,7400],{"className":7476},[195,268],[135,7478,888],{"className":7479},[389],[135,7481],{"className":7482,"style":576},[575],[135,7484,891],{"className":7485},[580],[135,7487],{"className":7488,"style":576},[575],[135,7490,7492,7495,7498,7501,7504,7507,7510,7513,7554,7557,7560],{"className":7491},[186],[135,7493],{"className":7494,"style":953},[190],[135,7496,7407],{"className":7497},[1027],[135,7499,874],{"className":7500},[199],[135,7502,1830],{"className":7503},[195],[135,7505,879],{"className":7506},[988],[135,7508],{"className":7509,"style":992},[575],[135,7511,7400],{"className":7512},[195,268],[135,7514,7516,7519],{"className":7515},[195],[135,7517,3066],{"className":7518,"style":3258},[195,268],[135,7520,7522],{"className":7521},[272],[135,7523,7525,7546],{"className":7524},[207,208],[135,7526,7528,7543],{"className":7527},[212],[135,7529,7531],{"className":7530,"style":3164},[216],[135,7532,7534,7537],{"style":7533},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[135,7535],{"className":7536,"style":616},[224],[135,7538,7540],{"className":7539},[229,230,231,232],[135,7541,159],{"className":7542},[195,232],[135,7544,303],{"className":7545},[302],[135,7547,7549],{"className":7548},[212],[135,7550,7552],{"className":7551,"style":1346},[216],[135,7553],{},[135,7555],{"className":7556,"style":1948},[575],[135,7558,5850],{"className":7559},[629],[135,7561],{"className":7562,"style":1948},[575],[135,7564,7566,7569,7609,7612,7652,7655,7658],{"className":7565},[186],[135,7567],{"className":7568,"style":953},[190],[135,7570,7572,7575],{"className":7571},[195],[135,7573,7430],{"className":7574},[195,268],[135,7576,7578],{"className":7577},[272],[135,7579,7581,7601],{"className":7580},[207,208],[135,7582,7584,7598],{"className":7583},[212],[135,7585,7587],{"className":7586,"style":3164},[216],[135,7588,7589,7592],{"style":1327},[135,7590],{"className":7591,"style":616},[224],[135,7593,7595],{"className":7594},[229,230,231,232],[135,7596,159],{"className":7597},[195,232],[135,7599,303],{"className":7600},[302],[135,7602,7604],{"className":7603},[212],[135,7605,7607],{"className":7606,"style":1346},[216],[135,7608],{},[135,7610,888],{"className":7611},[389],[135,7613,7615,7618],{"className":7614},[195],[135,7616,3066],{"className":7617,"style":3258},[195,268],[135,7619,7621],{"className":7620},[272],[135,7622,7624,7644],{"className":7623},[207,208],[135,7625,7627,7641],{"className":7626},[212],[135,7628,7630],{"className":7629,"style":3164},[216],[135,7631,7632,7635],{"style":7533},[135,7633],{"className":7634,"style":616},[224],[135,7636,7638],{"className":7637},[229,230,231,232],[135,7639,2894],{"className":7640},[195,232],[135,7642,303],{"className":7643},[302],[135,7645,7647],{"className":7646},[212],[135,7648,7650],{"className":7649,"style":1346},[216],[135,7651],{},[135,7653],{"className":7654,"style":1948},[575],[135,7656,5850],{"className":7657},[629],[135,7659],{"className":7660,"style":1948},[575],[135,7662,7664,7667],{"className":7663},[186],[135,7665],{"className":7666,"style":1305},[190],[135,7668,7670,7673],{"className":7669},[195],[135,7671,7430],{"className":7672},[195,268],[135,7674,7676],{"className":7675},[272],[135,7677,7679,7699],{"className":7678},[207,208],[135,7680,7682,7696],{"className":7681},[212],[135,7683,7685],{"className":7684,"style":3164},[216],[135,7686,7687,7690],{"style":1327},[135,7688],{"className":7689,"style":616},[224],[135,7691,7693],{"className":7692},[229,230,231,232],[135,7694,2894],{"className":7695},[195,232],[135,7697,303],{"className":7698},[302],[135,7700,7702],{"className":7701},[212],[135,7703,7705],{"className":7704,"style":1346},[216],[135,7706],{},[2466,7708,7710],{"className":2468,"code":7709,"language":2470,"meta":65,"style":65},"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",[2472,7711,7712,7729,7734,7761,7770,7789,7801,7813,7825,7829,7845],{"__ignoreMap":65},[135,7713,7714,7716,7719,7721,7723,7725,7727],{"class":2476,"line":2477},[135,7715,2704],{"class":2480},[135,7717,7718],{"class":2707}," PositionWiseFFN",[135,7720,874],{"class":2488},[135,7722,2714],{"class":2713},[135,7724,940],{"class":2488},[135,7726,2719],{"class":2713},[135,7728,2501],{"class":2488},[135,7730,7731],{"class":2476,"line":66},[135,7732,7733],{"class":2506},"    \"\"\"基于位置的前馈网络\"\"\"\n",[135,7735,7736,7738,7740,7742,7744,7746,7749,7751,7754,7756,7759],{"class":2476,"line":2510},[135,7737,2731],{"class":2480},[135,7739,2734],{"class":2529},[135,7741,874],{"class":2488},[135,7743,2740],{"class":2739},[135,7745,2495],{"class":2488},[135,7747,7748],{"class":2491},"ffn_num_input",[135,7750,2495],{"class":2488},[135,7752,7753],{"class":2491},"ffn_num_hiddens",[135,7755,2495],{"class":2488},[135,7757,7758],{"class":2491},"ffn_num_outputs",[135,7760,3899],{"class":2488},[135,7762,7763,7766,7768],{"class":2476,"line":2517},[135,7764,7765],{"class":2480},"                 **",[135,7767,2753],{"class":2491},[135,7769,2501],{"class":2488},[135,7771,7772,7774,7777,7779,7781,7783,7785,7787],{"class":2476,"line":2536},[135,7773,2761],{"class":2760},[135,7775,7776],{"class":2488},"(PositionWiseFFN, ",[135,7778,2740],{"class":2767},[135,7780,2770],{"class":2488},[135,7782,2773],{"class":2529},[135,7784,874],{"class":2488},[135,7786,2750],{"class":2480},[135,7788,2780],{"class":2488},[135,7790,7791,7793,7796,7798],{"class":2476,"line":2557},[135,7792,2785],{"class":2767},[135,7794,7795],{"class":2488},".dense1 ",[135,7797,891],{"class":2480},[135,7799,7800],{"class":2488}," nn.Linear(ffn_num_input, ffn_num_hiddens)\n",[135,7802,7803,7805,7808,7810],{"class":2476,"line":2565},[135,7804,2785],{"class":2767},[135,7806,7807],{"class":2488},".relu ",[135,7809,891],{"class":2480},[135,7811,7812],{"class":2488}," nn.ReLU()\n",[135,7814,7815,7817,7820,7822],{"class":2476,"line":2576},[135,7816,2785],{"class":2767},[135,7818,7819],{"class":2488},".dense2 ",[135,7821,891],{"class":2480},[135,7823,7824],{"class":2488}," nn.Linear(ffn_num_hiddens, ffn_num_outputs)\n",[135,7826,7827],{"class":2476,"line":2593},[135,7828,2798],{"emptyLinePlaceholder":80},[135,7830,7831,7833,7835,7837,7839,7841,7843],{"class":2476,"line":2609},[135,7832,2731],{"class":2480},[135,7834,2825],{"class":2484},[135,7836,874],{"class":2488},[135,7838,2740],{"class":2739},[135,7840,2495],{"class":2488},[135,7842,2492],{"class":2491},[135,7844,2501],{"class":2488},[135,7846,7847,7849,7851,7854,7856,7859,7861],{"class":2476,"line":2617},[135,7848,2539],{"class":2480},[135,7850,5293],{"class":2767},[135,7852,7853],{"class":2488},".dense2(",[135,7855,2740],{"class":2767},[135,7857,7858],{"class":2488},".relu(",[135,7860,2740],{"class":2767},[135,7862,7863],{"class":2488},".dense1(X)))\n",[10,7865,7866],{"id":7866},"残差连接和层规范化",[14,7868,7869],{},"我们在每个子层之间加入了一个残差连接和层归一化。",[14,7871,7872,7873,4641,7998,8061],{},"因此，每个子层的输出都是 ",[135,7874,7876,7944],{"className":7875},[138],[135,7877,7879],{"className":7878},[142],[144,7880,7881],{"xmlns":146},[148,7882,7883,7941],{},[151,7884,7885,7908,7910,7912,7914,7933,7935,7937,7939],{},[151,7886,7887,7890,7892,7895,7897,7900,7902,7904,7906],{},[167,7888,7889],{"mathvariant":894},"L",[167,7891,31],{"mathvariant":894},[167,7893,7894],{"mathvariant":894},"y",[167,7896,858],{"mathvariant":894},[167,7898,7899],{"mathvariant":894},"r",[167,7901,7395],{"mathvariant":894},[167,7903,868],{"mathvariant":894},[167,7905,7899],{"mathvariant":894},[167,7907,442],{"mathvariant":894},[537,7909,874],{"stretchy":873},[167,7911,7400],{},[537,7913,5850],{},[151,7915,7916,7919,7921,7923,7925,7927,7929,7931],{},[167,7917,7918],{"mathvariant":894},"S",[167,7920,2973],{"mathvariant":894},[167,7922,7430],{"mathvariant":894},[167,7924,2976],{"mathvariant":894},[167,7926,31],{"mathvariant":894},[167,7928,7894],{"mathvariant":894},[167,7930,858],{"mathvariant":894},[167,7932,7899],{"mathvariant":894},[537,7934,874],{"stretchy":873},[167,7936,7400],{},[537,7938,888],{"stretchy":873},[537,7940,888],{"stretchy":873},[174,7942,7943],{"encoding":176},"\\mathrm{LayerNorm}(x + \\mathrm{Sublayer}(x))",[135,7945,7947,7975],{"className":7946,"ariaHidden":182},[181],[135,7948,7950,7953,7960,7963,7966,7969,7972],{"className":7949},[186],[135,7951],{"className":7952,"style":953},[190],[135,7954,7956],{"className":7955},[195],[135,7957,7959],{"className":7958},[195,1031],"LayerNorm",[135,7961,874],{"className":7962},[199],[135,7964,7400],{"className":7965},[195,268],[135,7967],{"className":7968,"style":1948},[575],[135,7970,5850],{"className":7971},[629],[135,7973],{"className":7974,"style":1948},[575],[135,7976,7978,7981,7988,7991,7994],{"className":7977},[186],[135,7979],{"className":7980,"style":953},[190],[135,7982,7984],{"className":7983},[195],[135,7985,7987],{"className":7986},[195,1031],"Sublayer",[135,7989,874],{"className":7990},[199],[135,7992,7400],{"className":7993},[195,268],[135,7995,7997],{"className":7996},[389],"))",[135,7999,8001,8037],{"className":8000},[138],[135,8002,8004],{"className":8003},[142],[144,8005,8006],{"xmlns":146},[148,8007,8008,8034],{},[151,8009,8010,8028,8030,8032],{},[151,8011,8012,8014,8016,8018,8020,8022,8024,8026],{},[167,8013,7918],{"mathvariant":894},[167,8015,2973],{"mathvariant":894},[167,8017,7430],{"mathvariant":894},[167,8019,2976],{"mathvariant":894},[167,8021,31],{"mathvariant":894},[167,8023,7894],{"mathvariant":894},[167,8025,858],{"mathvariant":894},[167,8027,7899],{"mathvariant":894},[537,8029,874],{"stretchy":873},[167,8031,7400],{},[537,8033,888],{"stretchy":873},[174,8035,8036],{"encoding":176},"\\mathrm{Sublayer}(x)",[135,8038,8040],{"className":8039,"ariaHidden":182},[181],[135,8041,8043,8046,8052,8055,8058],{"className":8042},[186],[135,8044],{"className":8045,"style":953},[190],[135,8047,8049],{"className":8048},[195],[135,8050,7987],{"className":8051},[195,1031],[135,8053,874],{"className":8054},[199],[135,8056,7400],{"className":8057},[195,268],[135,8059,888],{"className":8060},[389]," 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。",[2466,8063,8065],{"className":2468,"code":8064,"language":2470,"meta":65,"style":65},"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",[2472,8066,8067,8084,8089,8116,8135,8145,8157,8161,8182],{"__ignoreMap":65},[135,8068,8069,8071,8074,8076,8078,8080,8082],{"class":2476,"line":2477},[135,8070,2704],{"class":2480},[135,8072,8073],{"class":2707}," AddNorm",[135,8075,874],{"class":2488},[135,8077,2714],{"class":2713},[135,8079,940],{"class":2488},[135,8081,2719],{"class":2713},[135,8083,2501],{"class":2488},[135,8085,8086],{"class":2476,"line":66},[135,8087,8088],{"class":2506},"    \"\"\"残差连接后进行层规范化\"\"\"\n",[135,8090,8091,8093,8095,8097,8099,8101,8104,8106,8108,8110,8112,8114],{"class":2476,"line":2510},[135,8092,2731],{"class":2480},[135,8094,2734],{"class":2529},[135,8096,874],{"class":2488},[135,8098,2740],{"class":2739},[135,8100,2495],{"class":2488},[135,8102,8103],{"class":2491},"normalized_shape",[135,8105,2495],{"class":2488},[135,8107,2745],{"class":2491},[135,8109,2495],{"class":2488},[135,8111,2750],{"class":2480},[135,8113,2753],{"class":2491},[135,8115,2501],{"class":2488},[135,8117,8118,8120,8123,8125,8127,8129,8131,8133],{"class":2476,"line":2517},[135,8119,2761],{"class":2760},[135,8121,8122],{"class":2488},"(AddNorm, ",[135,8124,2740],{"class":2767},[135,8126,2770],{"class":2488},[135,8128,2773],{"class":2529},[135,8130,874],{"class":2488},[135,8132,2750],{"class":2480},[135,8134,2780],{"class":2488},[135,8136,8137,8139,8141,8143],{"class":2476,"line":2536},[135,8138,2785],{"class":2767},[135,8140,2788],{"class":2488},[135,8142,891],{"class":2480},[135,8144,2793],{"class":2488},[135,8146,8147,8149,8152,8154],{"class":2476,"line":2557},[135,8148,2785],{"class":2767},[135,8150,8151],{"class":2488},".ln ",[135,8153,891],{"class":2480},[135,8155,8156],{"class":2488}," nn.LayerNorm(normalized_shape)\n",[135,8158,8159],{"class":2476,"line":2565},[135,8160,2798],{"emptyLinePlaceholder":80},[135,8162,8163,8165,8167,8169,8171,8173,8175,8177,8180],{"class":2476,"line":2576},[135,8164,2731],{"class":2480},[135,8166,2825],{"class":2484},[135,8168,874],{"class":2488},[135,8170,2740],{"class":2739},[135,8172,2495],{"class":2488},[135,8174,2492],{"class":2491},[135,8176,2495],{"class":2488},[135,8178,8179],{"class":2491},"Y",[135,8181,2501],{"class":2488},[135,8183,8184,8186,8188,8191,8193,8196,8198],{"class":2476,"line":2593},[135,8185,2539],{"class":2480},[135,8187,5293],{"class":2767},[135,8189,8190],{"class":2488},".ln(",[135,8192,2740],{"class":2767},[135,8194,8195],{"class":2488},".dropout(Y) ",[135,8197,5850],{"class":2480},[135,8199,8200],{"class":2488}," X)\n",[10,8202,8203],{"id":8203},"编码器-解码器架构",[14,8205,8206,8207,8357,8358,8534,8535,8564,8565,8715],{},"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 ",[135,8208,8210,8244],{"className":8209},[138],[135,8211,8213],{"className":8212},[142],[144,8214,8215],{"xmlns":146},[148,8216,8217,8241],{},[151,8218,8219,8221,8227,8229,8231,8233,8239],{},[537,8220,874],{"stretchy":873},[164,8222,8223,8225],{},[167,8224,7400],{},[157,8226,159],{},[537,8228,879],{"separator":182},[537,8230,3043],{},[537,8232,879],{"separator":182},[164,8234,8235,8237],{},[167,8236,7400],{},[167,8238,411],{},[537,8240,888],{"stretchy":873},[174,8242,8243],{"encoding":176},"(x_1, \\ldots, x_n)",[135,8245,8247],{"className":8246,"ariaHidden":182},[181],[135,8248,8250,8253,8256,8296,8299,8302,8305,8308,8311,8314,8354],{"className":8249},[186],[135,8251],{"className":8252,"style":953},[190],[135,8254,874],{"className":8255},[199],[135,8257,8259,8262],{"className":8258},[195],[135,8260,7400],{"className":8261},[195,268],[135,8263,8265],{"className":8264},[272],[135,8266,8268,8288],{"className":8267},[207,208],[135,8269,8271,8285],{"className":8270},[212],[135,8272,8274],{"className":8273,"style":3164},[216],[135,8275,8276,8279],{"style":1327},[135,8277],{"className":8278,"style":616},[224],[135,8280,8282],{"className":8281},[229,230,231,232],[135,8283,159],{"className":8284},[195,232],[135,8286,303],{"className":8287},[302],[135,8289,8291],{"className":8290},[212],[135,8292,8294],{"className":8293,"style":1346},[216],[135,8295],{},[135,8297,879],{"className":8298},[988],[135,8300],{"className":8301,"style":992},[575],[135,8303,3043],{"className":8304},[1038],[135,8306],{"className":8307,"style":992},[575],[135,8309,879],{"className":8310},[988],[135,8312],{"className":8313,"style":992},[575],[135,8315,8317,8320],{"className":8316},[195],[135,8318,7400],{"className":8319},[195,268],[135,8321,8323],{"className":8322},[272],[135,8324,8326,8346],{"className":8325},[207,208],[135,8327,8329,8343],{"className":8328},[212],[135,8330,8332],{"className":8331,"style":1398},[216],[135,8333,8334,8337],{"style":1327},[135,8335],{"className":8336,"style":616},[224],[135,8338,8340],{"className":8339},[229,230,231,232],[135,8341,411],{"className":8342},[195,268,232],[135,8344,303],{"className":8345},[302],[135,8347,8349],{"className":8348},[212],[135,8350,8352],{"className":8351,"style":1346},[216],[135,8353],{},[135,8355,888],{"className":8356},[389]," 映射为连续表示序列 ",[135,8359,8361,8400],{"className":8360},[138],[135,8362,8364],{"className":8363},[142],[144,8365,8366],{"xmlns":146},[148,8367,8368,8397],{},[151,8369,8370,8373,8375,8377,8383,8385,8387,8389,8395],{},[167,8371,8372],{"mathvariant":5451},"z",[537,8374,891],{},[537,8376,874],{"stretchy":873},[164,8378,8379,8381],{},[167,8380,8372],{},[157,8382,159],{},[537,8384,879],{"separator":182},[537,8386,3043],{},[537,8388,879],{"separator":182},[164,8390,8391,8393],{},[167,8392,8372],{},[167,8394,411],{},[537,8396,888],{"stretchy":873},[174,8398,8399],{"encoding":176},"\\mathbf{z} = (z_1, \\ldots, z_n)",[135,8401,8403,8422],{"className":8402,"ariaHidden":182},[181],[135,8404,8406,8410,8413,8416,8419],{"className":8405},[186],[135,8407],{"className":8408,"style":8409},[190],"height:0.4444em;",[135,8411,8372],{"className":8412},[195,5496],[135,8414],{"className":8415,"style":576},[575],[135,8417,891],{"className":8418},[580],[135,8420],{"className":8421,"style":576},[575],[135,8423,8425,8428,8431,8473,8476,8479,8482,8485,8488,8491,8531],{"className":8424},[186],[135,8426],{"className":8427,"style":953},[190],[135,8429,874],{"className":8430},[199],[135,8432,8434,8438],{"className":8433},[195],[135,8435,8372],{"className":8436,"style":8437},[195,268],"margin-right:0.04398em;",[135,8439,8441],{"className":8440},[272],[135,8442,8444,8465],{"className":8443},[207,208],[135,8445,8447,8462],{"className":8446},[212],[135,8448,8450],{"className":8449,"style":3164},[216],[135,8451,8453,8456],{"style":8452},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[135,8454],{"className":8455,"style":616},[224],[135,8457,8459],{"className":8458},[229,230,231,232],[135,8460,159],{"className":8461},[195,232],[135,8463,303],{"className":8464},[302],[135,8466,8468],{"className":8467},[212],[135,8469,8471],{"className":8470,"style":1346},[216],[135,8472],{},[135,8474,879],{"className":8475},[988],[135,8477],{"className":8478,"style":992},[575],[135,8480,3043],{"className":8481},[1038],[135,8483],{"className":8484,"style":992},[575],[135,8486,879],{"className":8487},[988],[135,8489],{"className":8490,"style":992},[575],[135,8492,8494,8497],{"className":8493},[195],[135,8495,8372],{"className":8496,"style":8437},[195,268],[135,8498,8500],{"className":8499},[272],[135,8501,8503,8523],{"className":8502},[207,208],[135,8504,8506,8520],{"className":8505},[212],[135,8507,8509],{"className":8508,"style":1398},[216],[135,8510,8511,8514],{"style":8452},[135,8512],{"className":8513,"style":616},[224],[135,8515,8517],{"className":8516},[229,230,231,232],[135,8518,411],{"className":8519},[195,268,232],[135,8521,303],{"className":8522},[302],[135,8524,8526],{"className":8525},[212],[135,8527,8529],{"className":8528,"style":1346},[216],[135,8530],{},[135,8532,888],{"className":8533},[389],"。给定 ",[135,8536,8538,8552],{"className":8537},[138],[135,8539,8541],{"className":8540},[142],[144,8542,8543],{"xmlns":146},[148,8544,8545,8549],{},[151,8546,8547],{},[167,8548,8372],{"mathvariant":5451},[174,8550,8551],{"encoding":176},"\\mathbf{z}",[135,8553,8555],{"className":8554,"ariaHidden":182},[181],[135,8556,8558,8561],{"className":8557},[186],[135,8559],{"className":8560,"style":8409},[190],[135,8562,8372],{"className":8563},[195,5496],"，解码器随后一次生成一个元素的输出符号序列 ",[135,8566,8568,8602],{"className":8567},[138],[135,8569,8571],{"className":8570},[142],[144,8572,8573],{"xmlns":146},[148,8574,8575,8599],{},[151,8576,8577,8579,8585,8587,8589,8591,8597],{},[537,8578,874],{"stretchy":873},[164,8580,8581,8583],{},[167,8582,7894],{},[157,8584,159],{},[537,8586,879],{"separator":182},[537,8588,3043],{},[537,8590,879],{"separator":182},[164,8592,8593,8595],{},[167,8594,7894],{},[167,8596,442],{},[537,8598,888],{"stretchy":873},[174,8600,8601],{"encoding":176},"(y_1, \\ldots, y_m)",[135,8603,8605],{"className":8604,"ariaHidden":182},[181],[135,8606,8608,8611,8614,8654,8657,8660,8663,8666,8669,8672,8712],{"className":8607},[186],[135,8609],{"className":8610,"style":953},[190],[135,8612,874],{"className":8613},[199],[135,8615,8617,8620],{"className":8616},[195],[135,8618,7894],{"className":8619,"style":517},[195,268],[135,8621,8623],{"className":8622},[272],[135,8624,8626,8646],{"className":8625},[207,208],[135,8627,8629,8643],{"className":8628},[212],[135,8630,8632],{"className":8631,"style":3164},[216],[135,8633,8634,8637],{"style":2111},[135,8635],{"className":8636,"style":616},[224],[135,8638,8640],{"className":8639},[229,230,231,232],[135,8641,159],{"className":8642},[195,232],[135,8644,303],{"className":8645},[302],[135,8647,8649],{"className":8648},[212],[135,8650,8652],{"className":8651,"style":1346},[216],[135,8653],{},[135,8655,879],{"className":8656},[988],[135,8658],{"className":8659,"style":992},[575],[135,8661,3043],{"className":8662},[1038],[135,8664],{"className":8665,"style":992},[575],[135,8667,879],{"className":8668},[988],[135,8670],{"className":8671,"style":992},[575],[135,8673,8675,8678],{"className":8674},[195],[135,8676,7894],{"className":8677,"style":517},[195,268],[135,8679,8681],{"className":8680},[272],[135,8682,8684,8704],{"className":8683},[207,208],[135,8685,8687,8701],{"className":8686},[212],[135,8688,8690],{"className":8689,"style":1398},[216],[135,8691,8692,8695],{"style":2111},[135,8693],{"className":8694,"style":616},[224],[135,8696,8698],{"className":8697},[229,230,231,232],[135,8699,442],{"className":8700},[195,268,232],[135,8702,303],{"className":8703},[302],[135,8705,8707],{"className":8706},[212],[135,8708,8710],{"className":8709,"style":1346},[216],[135,8711],{},[135,8713,888],{"className":8714},[389],"。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。",[2466,8717,8719],{"className":2468,"code":8718,"language":2470,"meta":65,"style":65},"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",[2472,8720,8721,8738,8743,8761,8780,8784,8808,8816,8820,8837,8842,8860,8879,8883,8907,8913,8917,8938,8944,8948,8965,8970,8998,9017,9029,9041,9045,9073,9090,9106],{"__ignoreMap":65},[135,8722,8723,8725,8728,8730,8732,8734,8736],{"class":2476,"line":2477},[135,8724,2704],{"class":2480},[135,8726,8727],{"class":2707}," Encoder",[135,8729,874],{"class":2488},[135,8731,2714],{"class":2713},[135,8733,940],{"class":2488},[135,8735,2719],{"class":2713},[135,8737,2501],{"class":2488},[135,8739,8740],{"class":2476,"line":66},[135,8741,8742],{"class":2506},"    \"\"\"编码器-解码器架构的基本编码器接口\"\"\"\n",[135,8744,8745,8747,8749,8751,8753,8755,8757,8759],{"class":2476,"line":2510},[135,8746,2731],{"class":2480},[135,8748,2734],{"class":2529},[135,8750,874],{"class":2488},[135,8752,2740],{"class":2739},[135,8754,2495],{"class":2488},[135,8756,2750],{"class":2480},[135,8758,2753],{"class":2491},[135,8760,2501],{"class":2488},[135,8762,8763,8765,8768,8770,8772,8774,8776,8778],{"class":2476,"line":2517},[135,8764,2761],{"class":2760},[135,8766,8767],{"class":2488},"(Encoder, ",[135,8769,2740],{"class":2767},[135,8771,2770],{"class":2488},[135,8773,2773],{"class":2529},[135,8775,874],{"class":2488},[135,8777,2750],{"class":2480},[135,8779,2780],{"class":2488},[135,8781,8782],{"class":2476,"line":2536},[135,8783,2798],{"emptyLinePlaceholder":80},[135,8785,8786,8788,8790,8792,8794,8796,8798,8800,8803,8806],{"class":2476,"line":2557},[135,8787,2731],{"class":2480},[135,8789,2825],{"class":2484},[135,8791,874],{"class":2488},[135,8793,2740],{"class":2739},[135,8795,2495],{"class":2488},[135,8797,2492],{"class":2491},[135,8799,2495],{"class":2488},[135,8801,8802],{"class":2480},"*",[135,8804,8805],{"class":2491},"args",[135,8807,2501],{"class":2488},[135,8809,8810,8813],{"class":2476,"line":2565},[135,8811,8812],{"class":2480},"        raise",[135,8814,8815],{"class":2760}," NotImplementedError\n",[135,8817,8818],{"class":2476,"line":2576},[135,8819,2798],{"emptyLinePlaceholder":80},[135,8821,8822,8824,8827,8829,8831,8833,8835],{"class":2476,"line":2593},[135,8823,2704],{"class":2480},[135,8825,8826],{"class":2707}," Decoder",[135,8828,874],{"class":2488},[135,8830,2714],{"class":2713},[135,8832,940],{"class":2488},[135,8834,2719],{"class":2713},[135,8836,2501],{"class":2488},[135,8838,8839],{"class":2476,"line":2609},[135,8840,8841],{"class":2506},"    \"\"\"编码器-解码器架构的基本解码器接口\"\"\"\n",[135,8843,8844,8846,8848,8850,8852,8854,8856,8858],{"class":2476,"line":2617},[135,8845,2731],{"class":2480},[135,8847,2734],{"class":2529},[135,8849,874],{"class":2488},[135,8851,2740],{"class":2739},[135,8853,2495],{"class":2488},[135,8855,2750],{"class":2480},[135,8857,2753],{"class":2491},[135,8859,2501],{"class":2488},[135,8861,8862,8864,8867,8869,8871,8873,8875,8877],{"class":2476,"line":2634},[135,8863,2761],{"class":2760},[135,8865,8866],{"class":2488},"(Decoder, ",[135,8868,2740],{"class":2767},[135,8870,2770],{"class":2488},[135,8872,2773],{"class":2529},[135,8874,874],{"class":2488},[135,8876,2750],{"class":2480},[135,8878,2780],{"class":2488},[135,8880,8881],{"class":2476,"line":2640},[135,8882,2798],{"emptyLinePlaceholder":80},[135,8884,8885,8887,8890,8892,8894,8896,8899,8901,8903,8905],{"class":2476,"line":2665},[135,8886,2731],{"class":2480},[135,8888,8889],{"class":2484}," init_state",[135,8891,874],{"class":2488},[135,8893,2740],{"class":2739},[135,8895,2495],{"class":2488},[135,8897,8898],{"class":2491},"enc_outputs",[135,8900,2495],{"class":2488},[135,8902,8802],{"class":2480},[135,8904,8805],{"class":2491},[135,8906,2501],{"class":2488},[135,8908,8909,8911],{"class":2476,"line":2678},[135,8910,8812],{"class":2480},[135,8912,8815],{"class":2760},[135,8914,8915],{"class":2476,"line":2918},[135,8916,2798],{"emptyLinePlaceholder":80},[135,8918,8919,8921,8923,8925,8927,8929,8931,8933,8936],{"class":2476,"line":4854},[135,8920,2731],{"class":2480},[135,8922,2825],{"class":2484},[135,8924,874],{"class":2488},[135,8926,2740],{"class":2739},[135,8928,2495],{"class":2488},[135,8930,2492],{"class":2491},[135,8932,2495],{"class":2488},[135,8934,8935],{"class":2491},"state",[135,8937,2501],{"class":2488},[135,8939,8940,8942],{"class":2476,"line":5130},[135,8941,8812],{"class":2480},[135,8943,8815],{"class":2760},[135,8945,8946],{"class":2476,"line":5136},[135,8947,2798],{"emptyLinePlaceholder":80},[135,8949,8950,8952,8955,8957,8959,8961,8963],{"class":2476,"line":5142},[135,8951,2704],{"class":2480},[135,8953,8954],{"class":2707}," EncoderDecoder",[135,8956,874],{"class":2488},[135,8958,2714],{"class":2713},[135,8960,940],{"class":2488},[135,8962,2719],{"class":2713},[135,8964,2501],{"class":2488},[135,8966,8967],{"class":2476,"line":5148},[135,8968,8969],{"class":2506},"    \"\"\"编码器-解码器架构的基类\"\"\"\n",[135,8971,8972,8974,8976,8978,8980,8982,8985,8987,8990,8992,8994,8996],{"class":2476,"line":5169},[135,8973,2731],{"class":2480},[135,8975,2734],{"class":2529},[135,8977,874],{"class":2488},[135,8979,2740],{"class":2739},[135,8981,2495],{"class":2488},[135,8983,8984],{"class":2491},"encoder",[135,8986,2495],{"class":2488},[135,8988,8989],{"class":2491},"decoder",[135,8991,2495],{"class":2488},[135,8993,2750],{"class":2480},[135,8995,2753],{"class":2491},[135,8997,2501],{"class":2488},[135,8999,9000,9002,9005,9007,9009,9011,9013,9015],{"class":2476,"line":5188},[135,9001,2761],{"class":2760},[135,9003,9004],{"class":2488},"(EncoderDecoder, ",[135,9006,2740],{"class":2767},[135,9008,2770],{"class":2488},[135,9010,2773],{"class":2529},[135,9012,874],{"class":2488},[135,9014,2750],{"class":2480},[135,9016,2780],{"class":2488},[135,9018,9019,9021,9024,9026],{"class":2476,"line":5207},[135,9020,2785],{"class":2767},[135,9022,9023],{"class":2488},".encoder ",[135,9025,891],{"class":2480},[135,9027,9028],{"class":2488}," encoder\n",[135,9030,9031,9033,9036,9038],{"class":2476,"line":5212},[135,9032,2785],{"class":2767},[135,9034,9035],{"class":2488},".decoder ",[135,9037,891],{"class":2480},[135,9039,9040],{"class":2488}," decoder\n",[135,9042,9043],{"class":2476,"line":5228},[135,9044,2798],{"emptyLinePlaceholder":80},[135,9046,9047,9049,9051,9053,9055,9057,9060,9062,9065,9067,9069,9071],{"class":2476,"line":5234},[135,9048,2731],{"class":2480},[135,9050,2825],{"class":2484},[135,9052,874],{"class":2488},[135,9054,2740],{"class":2739},[135,9056,2495],{"class":2488},[135,9058,9059],{"class":2491},"enc_X",[135,9061,2495],{"class":2488},[135,9063,9064],{"class":2491},"dec_X",[135,9066,2495],{"class":2488},[135,9068,8802],{"class":2480},[135,9070,8805],{"class":2491},[135,9072,2501],{"class":2488},[135,9074,9075,9078,9080,9082,9085,9087],{"class":2476,"line":5240},[135,9076,9077],{"class":2488},"        enc_outputs ",[135,9079,891],{"class":2480},[135,9081,5293],{"class":2767},[135,9083,9084],{"class":2488},".encoder(enc_X, ",[135,9086,8802],{"class":2480},[135,9088,9089],{"class":2488},"args)\n",[135,9091,9092,9095,9097,9099,9102,9104],{"class":2476,"line":5250},[135,9093,9094],{"class":2488},"        dec_state ",[135,9096,891],{"class":2480},[135,9098,5293],{"class":2767},[135,9100,9101],{"class":2488},".decoder.init_state(enc_outputs, ",[135,9103,8802],{"class":2480},[135,9105,9089],{"class":2488},[135,9107,9108,9110,9112],{"class":2476,"line":5274},[135,9109,2539],{"class":2480},[135,9111,5293],{"class":2767},[135,9113,9114],{"class":2488},".decoder(dec_X, dec_state)\n",[10,9116,9118],{"id":9117},"transformer-编码器","transformer 编码器",[14,9120,9121],{},"代码实现如下：",[2466,9123,9125],{"className":2468,"code":9124,"language":2470,"meta":65,"style":65},"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",[2472,9126,9127,9144,9149,9177,9196,9218,9237,9248,9253,9258,9270,9282,9287,9298,9302,9322,9339,9353,9357,9371,9376,9405,9425,9454,9473,9485,9497,9509,9521,9539,9565,9570,9575,9580,9584,9610,9615,9621,9627,9654,9682,9702,9713,9726],{"__ignoreMap":65},[135,9128,9129,9131,9134,9136,9138,9140,9142],{"class":2476,"line":2477},[135,9130,2704],{"class":2480},[135,9132,9133],{"class":2707}," EncoderBlock",[135,9135,874],{"class":2488},[135,9137,2714],{"class":2713},[135,9139,940],{"class":2488},[135,9141,2719],{"class":2713},[135,9143,2501],{"class":2488},[135,9145,9146],{"class":2476,"line":66},[135,9147,9148],{"class":2506},"    \"\"\"Transformer编码器块\"\"\"\n",[135,9150,9151,9153,9155,9157,9159,9161,9163,9165,9167,9169,9171,9173,9175],{"class":2476,"line":2510},[135,9152,2731],{"class":2480},[135,9154,2734],{"class":2529},[135,9156,874],{"class":2488},[135,9158,2740],{"class":2739},[135,9160,2495],{"class":2488},[135,9162,4920],{"class":2491},[135,9164,2495],{"class":2488},[135,9166,4925],{"class":2491},[135,9168,2495],{"class":2488},[135,9170,4930],{"class":2491},[135,9172,2495],{"class":2488},[135,9174,4935],{"class":2491},[135,9176,3899],{"class":2488},[135,9178,9179,9182,9184,9186,9188,9190,9192,9194],{"class":2476,"line":2517},[135,9180,9181],{"class":2491},"                 norm_shape",[135,9183,2495],{"class":2488},[135,9185,7748],{"class":2491},[135,9187,2495],{"class":2488},[135,9189,7753],{"class":2491},[135,9191,2495],{"class":2488},[135,9193,4668],{"class":2491},[135,9195,3899],{"class":2488},[135,9197,9198,9201,9203,9206,9208,9210,9212,9214,9216],{"class":2476,"line":2536},[135,9199,9200],{"class":2491},"                 dropout",[135,9202,2495],{"class":2488},[135,9204,9205],{"class":2491},"use_bias",[135,9207,891],{"class":2480},[135,9209,4956],{"class":2529},[135,9211,2495],{"class":2488},[135,9213,2750],{"class":2480},[135,9215,2753],{"class":2491},[135,9217,2501],{"class":2488},[135,9219,9220,9222,9225,9227,9229,9231,9233,9235],{"class":2476,"line":2557},[135,9221,2761],{"class":2760},[135,9223,9224],{"class":2488},"(EncoderBlock, ",[135,9226,2740],{"class":2767},[135,9228,2770],{"class":2488},[135,9230,2773],{"class":2529},[135,9232,874],{"class":2488},[135,9234,2750],{"class":2480},[135,9236,2780],{"class":2488},[135,9238,9239,9241,9243,9245],{"class":2476,"line":2565},[135,9240,2785],{"class":2767},[135,9242,5002],{"class":2488},[135,9244,891],{"class":2480},[135,9246,9247],{"class":2488}," d2l.MultiHeadAttention(\n",[135,9249,9250],{"class":2476,"line":2576},[135,9251,9252],{"class":2488},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout,\n",[135,9254,9255],{"class":2476,"line":2593},[135,9256,9257],{"class":2488},"            use_bias)\n",[135,9259,9260,9262,9265,9267],{"class":2476,"line":2609},[135,9261,2785],{"class":2767},[135,9263,9264],{"class":2488},".addnorm1 ",[135,9266,891],{"class":2480},[135,9268,9269],{"class":2488}," AddNorm(norm_shape, dropout)\n",[135,9271,9272,9274,9277,9279],{"class":2476,"line":2617},[135,9273,2785],{"class":2767},[135,9275,9276],{"class":2488},".ffn ",[135,9278,891],{"class":2480},[135,9280,9281],{"class":2488}," PositionWiseFFN(\n",[135,9283,9284],{"class":2476,"line":2634},[135,9285,9286],{"class":2488},"            ffn_num_input, ffn_num_hiddens, num_hiddens)\n",[135,9288,9289,9291,9294,9296],{"class":2476,"line":2640},[135,9290,2785],{"class":2767},[135,9292,9293],{"class":2488},".addnorm2 ",[135,9295,891],{"class":2480},[135,9297,9269],{"class":2488},[135,9299,9300],{"class":2476,"line":2665},[135,9301,2798],{"emptyLinePlaceholder":80},[135,9303,9304,9306,9308,9310,9312,9314,9316,9318,9320],{"class":2476,"line":2678},[135,9305,2731],{"class":2480},[135,9307,2825],{"class":2484},[135,9309,874],{"class":2488},[135,9311,2740],{"class":2739},[135,9313,2495],{"class":2488},[135,9315,2492],{"class":2491},[135,9317,2495],{"class":2488},[135,9319,2498],{"class":2491},[135,9321,2501],{"class":2488},[135,9323,9324,9327,9329,9331,9334,9336],{"class":2476,"line":2918},[135,9325,9326],{"class":2488},"        Y ",[135,9328,891],{"class":2480},[135,9330,5293],{"class":2767},[135,9332,9333],{"class":2488},".addnorm1(X, ",[135,9335,2740],{"class":2767},[135,9337,9338],{"class":2488},".attention(X, X, X, valid_lens))\n",[135,9340,9341,9343,9345,9348,9350],{"class":2476,"line":4854},[135,9342,2539],{"class":2480},[135,9344,5293],{"class":2767},[135,9346,9347],{"class":2488},".addnorm2(Y, ",[135,9349,2740],{"class":2767},[135,9351,9352],{"class":2488},".ffn(Y))\n",[135,9354,9355],{"class":2476,"line":5130},[135,9356,2798],{"emptyLinePlaceholder":80},[135,9358,9359,9361,9364,9366,9369],{"class":2476,"line":5136},[135,9360,2704],{"class":2480},[135,9362,9363],{"class":2707}," TransformerEncoder",[135,9365,874],{"class":2488},[135,9367,9368],{"class":2713},"Encoder",[135,9370,2501],{"class":2488},[135,9372,9373],{"class":2476,"line":5142},[135,9374,9375],{"class":2506},"    \"\"\"Transformer编码器\"\"\"\n",[135,9377,9378,9380,9382,9384,9386,9388,9391,9393,9395,9397,9399,9401,9403],{"class":2476,"line":5148},[135,9379,2731],{"class":2480},[135,9381,2734],{"class":2529},[135,9383,874],{"class":2488},[135,9385,2740],{"class":2739},[135,9387,2495],{"class":2488},[135,9389,9390],{"class":2491},"vocab_size",[135,9392,2495],{"class":2488},[135,9394,4920],{"class":2491},[135,9396,2495],{"class":2488},[135,9398,4925],{"class":2491},[135,9400,2495],{"class":2488},[135,9402,4930],{"class":2491},[135,9404,3899],{"class":2488},[135,9406,9407,9410,9412,9415,9417,9419,9421,9423],{"class":2476,"line":5169},[135,9408,9409],{"class":2491},"                 num_hiddens",[135,9411,2495],{"class":2488},[135,9413,9414],{"class":2491},"norm_shape",[135,9416,2495],{"class":2488},[135,9418,7748],{"class":2491},[135,9420,2495],{"class":2488},[135,9422,7753],{"class":2491},[135,9424,3899],{"class":2488},[135,9426,9427,9429,9431,9434,9436,9438,9440,9442,9444,9446,9448,9450,9452],{"class":2476,"line":5188},[135,9428,4942],{"class":2491},[135,9430,2495],{"class":2488},[135,9432,9433],{"class":2491},"num_layers",[135,9435,2495],{"class":2488},[135,9437,2745],{"class":2491},[135,9439,2495],{"class":2488},[135,9441,9205],{"class":2491},[135,9443,891],{"class":2480},[135,9445,4956],{"class":2529},[135,9447,2495],{"class":2488},[135,9449,2750],{"class":2480},[135,9451,2753],{"class":2491},[135,9453,2501],{"class":2488},[135,9455,9456,9458,9461,9463,9465,9467,9469,9471],{"class":2476,"line":5207},[135,9457,2761],{"class":2760},[135,9459,9460],{"class":2488},"(TransformerEncoder, ",[135,9462,2740],{"class":2767},[135,9464,2770],{"class":2488},[135,9466,2773],{"class":2529},[135,9468,874],{"class":2488},[135,9470,2750],{"class":2480},[135,9472,2780],{"class":2488},[135,9474,9475,9477,9480,9482],{"class":2476,"line":5212},[135,9476,2785],{"class":2767},[135,9478,9479],{"class":2488},".num_hiddens ",[135,9481,891],{"class":2480},[135,9483,9484],{"class":2488}," num_hiddens\n",[135,9486,9487,9489,9492,9494],{"class":2476,"line":5228},[135,9488,2785],{"class":2767},[135,9490,9491],{"class":2488},".embedding ",[135,9493,891],{"class":2480},[135,9495,9496],{"class":2488}," nn.Embedding(vocab_size, num_hiddens)\n",[135,9498,9499,9501,9504,9506],{"class":2476,"line":5234},[135,9500,2785],{"class":2767},[135,9502,9503],{"class":2488},".pos_encoding ",[135,9505,891],{"class":2480},[135,9507,9508],{"class":2488}," PositionalEncoding(num_hiddens, dropout)\n",[135,9510,9511,9513,9516,9518],{"class":2476,"line":5240},[135,9512,2785],{"class":2767},[135,9514,9515],{"class":2488},".blks ",[135,9517,891],{"class":2480},[135,9519,9520],{"class":2488}," nn.Sequential()\n",[135,9522,9523,9526,9529,9532,9536],{"class":2476,"line":5250},[135,9524,9525],{"class":2480},"        for",[135,9527,9528],{"class":2488}," i ",[135,9530,9531],{"class":2480},"in",[135,9533,9535],{"class":9534},"sDgm9"," range",[135,9537,9538],{"class":2488},"(num_layers):\n",[135,9540,9541,9544,9547,9551,9555,9557,9559,9562],{"class":2476,"line":5274},[135,9542,9543],{"class":2767},"            self",[135,9545,9546],{"class":2488},".blks.add_module(",[135,9548,9550],{"class":9549},"sMWOi","\"",[135,9552,9554],{"class":9553},"sEzAm","block",[135,9556,9550],{"class":9549},[135,9558,5850],{"class":2480},[135,9560,9561],{"class":2760},"str",[135,9563,9564],{"class":2488},"(i),\n",[135,9566,9567],{"class":2476,"line":5279},[135,9568,9569],{"class":2488},"                EncoderBlock(key_size, query_size, value_size, num_hiddens,\n",[135,9571,9572],{"class":2476,"line":5285},[135,9573,9574],{"class":2488},"                             norm_shape, ffn_num_input, ffn_num_hiddens,\n",[135,9576,9577],{"class":2476,"line":5299},[135,9578,9579],{"class":2488},"                             num_heads, dropout, use_bias))\n",[135,9581,9582],{"class":2476,"line":5304},[135,9583,2798],{"emptyLinePlaceholder":80},[135,9585,9586,9588,9590,9592,9594,9596,9598,9600,9602,9604,9606,9608],{"class":2476,"line":5310},[135,9587,2731],{"class":2480},[135,9589,2825],{"class":2484},[135,9591,874],{"class":2488},[135,9593,2740],{"class":2739},[135,9595,2495],{"class":2488},[135,9597,2492],{"class":2491},[135,9599,2495],{"class":2488},[135,9601,2498],{"class":2491},[135,9603,2495],{"class":2488},[135,9605,8802],{"class":2480},[135,9607,8805],{"class":2491},[135,9609,2501],{"class":2488},[135,9611,9612],{"class":2476,"line":5325},[135,9613,9614],{"class":2513},"        # 因为位置编码值在-1和1之间，\n",[135,9616,9618],{"class":2476,"line":9617},37,[135,9619,9620],{"class":2513},"        # 因此嵌入值乘以嵌入维度的平方根进行缩放，\n",[135,9622,9624],{"class":2476,"line":9623},38,[135,9625,9626],{"class":2513},"        # 然后再与位置编码相加。\n",[135,9628,9630,9632,9634,9636,9639,9641,9644,9646,9649,9651],{"class":2476,"line":9629},39,[135,9631,2643],{"class":2488},[135,9633,891],{"class":2480},[135,9635,5293],{"class":2767},[135,9637,9638],{"class":2488},".pos_encoding(",[135,9640,2740],{"class":2767},[135,9642,9643],{"class":2488},".embedding(X) ",[135,9645,8802],{"class":2480},[135,9647,9648],{"class":2488}," math.sqrt(",[135,9650,2740],{"class":2767},[135,9652,9653],{"class":2488},".num_hiddens))\n",[135,9655,9657,9659,9661,9663,9666,9668,9670,9672,9675,9677,9679],{"class":2476,"line":9656},40,[135,9658,2785],{"class":2767},[135,9660,2910],{"class":2488},[135,9662,891],{"class":2480},[135,9664,9665],{"class":2488}," [",[135,9667,2853],{"class":2529},[135,9669,7273],{"class":2488},[135,9671,8802],{"class":2480},[135,9673,9674],{"class":9534}," len",[135,9676,874],{"class":2488},[135,9678,2740],{"class":2767},[135,9680,9681],{"class":2488},".blks)\n",[135,9683,9685,9687,9690,9692,9695,9697,9699],{"class":2476,"line":9684},41,[135,9686,9525],{"class":2480},[135,9688,9689],{"class":2488}," i, blk ",[135,9691,9531],{"class":2480},[135,9693,9694],{"class":9534}," enumerate",[135,9696,874],{"class":2488},[135,9698,2740],{"class":2767},[135,9700,9701],{"class":2488},".blks):\n",[135,9703,9705,9708,9710],{"class":2476,"line":9704},42,[135,9706,9707],{"class":2488},"            X ",[135,9709,891],{"class":2480},[135,9711,9712],{"class":2488}," blk(X, valid_lens)\n",[135,9714,9716,9718,9721,9723],{"class":2476,"line":9715},43,[135,9717,9543],{"class":2767},[135,9719,9720],{"class":2488},".attention_weights[i] ",[135,9722,891],{"class":2480},[135,9724,9725],{"class":2488}," blk.attention.attention.attention_weights\n",[135,9727,9729,9731],{"class":2476,"line":9728},44,[135,9730,2539],{"class":2480},[135,9732,9733],{"class":2488}," X\n",[10,9735,9737],{"id":9736},"transformer-解码器","transformer 解码器",[14,9739,9740],{},"代码如下：",[2466,9742,9744],{"className":2468,"code":9743,"language":2470,"meta":65,"style":65},"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",[2472,9745,9746,9763,9768,9796,9814,9830,9849,9861,9872,9877,9887,9898,9902,9912,9923,9928,9939,9943,9963,9982,9987,9992,9997,10002,10024,10033,10039,10066,10084,10093,10102,10107,10112,10122,10148,10154,10163,10167,10172,10184,10195,10200,10205,10217,10229,10244,10249,10264,10293,10312,10333,10353,10364,10377,10388,10399,10410,10423,10442,10448,10453,10459,10472,10477,10505,10524,10529,10550,10573,10619,10636,10647,10653,10671,10677,10693,10703,10708,10717,10731],{"__ignoreMap":65},[135,9747,9748,9750,9753,9755,9757,9759,9761],{"class":2476,"line":2477},[135,9749,2704],{"class":2480},[135,9751,9752],{"class":2707}," DecoderBlock",[135,9754,874],{"class":2488},[135,9756,2714],{"class":2713},[135,9758,940],{"class":2488},[135,9760,2719],{"class":2713},[135,9762,2501],{"class":2488},[135,9764,9765],{"class":2476,"line":66},[135,9766,9767],{"class":2506},"    \"\"\"解码器中第i个块\"\"\"\n",[135,9769,9770,9772,9774,9776,9778,9780,9782,9784,9786,9788,9790,9792,9794],{"class":2476,"line":2510},[135,9771,2731],{"class":2480},[135,9773,2734],{"class":2529},[135,9775,874],{"class":2488},[135,9777,2740],{"class":2739},[135,9779,2495],{"class":2488},[135,9781,4920],{"class":2491},[135,9783,2495],{"class":2488},[135,9785,4925],{"class":2491},[135,9787,2495],{"class":2488},[135,9789,4930],{"class":2491},[135,9791,2495],{"class":2488},[135,9793,4935],{"class":2491},[135,9795,3899],{"class":2488},[135,9797,9798,9800,9802,9804,9806,9808,9810,9812],{"class":2476,"line":2517},[135,9799,9181],{"class":2491},[135,9801,2495],{"class":2488},[135,9803,7748],{"class":2491},[135,9805,2495],{"class":2488},[135,9807,7753],{"class":2491},[135,9809,2495],{"class":2488},[135,9811,4668],{"class":2491},[135,9813,3899],{"class":2488},[135,9815,9816,9818,9820,9822,9824,9826,9828],{"class":2476,"line":2536},[135,9817,9200],{"class":2491},[135,9819,2495],{"class":2488},[135,9821,865],{"class":2491},[135,9823,2495],{"class":2488},[135,9825,2750],{"class":2480},[135,9827,2753],{"class":2491},[135,9829,2501],{"class":2488},[135,9831,9832,9834,9837,9839,9841,9843,9845,9847],{"class":2476,"line":2557},[135,9833,2761],{"class":2760},[135,9835,9836],{"class":2488},"(DecoderBlock, ",[135,9838,2740],{"class":2767},[135,9840,2770],{"class":2488},[135,9842,2773],{"class":2529},[135,9844,874],{"class":2488},[135,9846,2750],{"class":2480},[135,9848,2780],{"class":2488},[135,9850,9851,9853,9856,9858],{"class":2476,"line":2565},[135,9852,2785],{"class":2767},[135,9854,9855],{"class":2488},".i ",[135,9857,891],{"class":2480},[135,9859,9860],{"class":2488}," i\n",[135,9862,9863,9865,9868,9870],{"class":2476,"line":2576},[135,9864,2785],{"class":2767},[135,9866,9867],{"class":2488},".attention1 ",[135,9869,891],{"class":2480},[135,9871,9247],{"class":2488},[135,9873,9874],{"class":2476,"line":2593},[135,9875,9876],{"class":2488},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n",[135,9878,9879,9881,9883,9885],{"class":2476,"line":2609},[135,9880,2785],{"class":2767},[135,9882,9264],{"class":2488},[135,9884,891],{"class":2480},[135,9886,9269],{"class":2488},[135,9888,9889,9891,9894,9896],{"class":2476,"line":2617},[135,9890,2785],{"class":2767},[135,9892,9893],{"class":2488},".attention2 ",[135,9895,891],{"class":2480},[135,9897,9247],{"class":2488},[135,9899,9900],{"class":2476,"line":2634},[135,9901,9876],{"class":2488},[135,9903,9904,9906,9908,9910],{"class":2476,"line":2640},[135,9905,2785],{"class":2767},[135,9907,9293],{"class":2488},[135,9909,891],{"class":2480},[135,9911,9269],{"class":2488},[135,9913,9914,9916,9918,9920],{"class":2476,"line":2665},[135,9915,2785],{"class":2767},[135,9917,9276],{"class":2488},[135,9919,891],{"class":2480},[135,9921,9922],{"class":2488}," PositionWiseFFN(ffn_num_input, ffn_num_hiddens,\n",[135,9924,9925],{"class":2476,"line":2678},[135,9926,9927],{"class":2488},"                                   num_hiddens)\n",[135,9929,9930,9932,9935,9937],{"class":2476,"line":2918},[135,9931,2785],{"class":2767},[135,9933,9934],{"class":2488},".addnorm3 ",[135,9936,891],{"class":2480},[135,9938,9269],{"class":2488},[135,9940,9941],{"class":2476,"line":4854},[135,9942,2798],{"emptyLinePlaceholder":80},[135,9944,9945,9947,9949,9951,9953,9955,9957,9959,9961],{"class":2476,"line":5130},[135,9946,2731],{"class":2480},[135,9948,2825],{"class":2484},[135,9950,874],{"class":2488},[135,9952,2740],{"class":2739},[135,9954,2495],{"class":2488},[135,9956,2492],{"class":2491},[135,9958,2495],{"class":2488},[135,9960,8935],{"class":2491},[135,9962,2501],{"class":2488},[135,9964,9965,9968,9970,9973,9975,9978,9980],{"class":2476,"line":5136},[135,9966,9967],{"class":2488},"        enc_outputs, enc_valid_lens ",[135,9969,891],{"class":2480},[135,9971,9972],{"class":2488}," state[",[135,9974,1830],{"class":2529},[135,9976,9977],{"class":2488},"], state[",[135,9979,159],{"class":2529},[135,9981,2872],{"class":2488},[135,9983,9984],{"class":2476,"line":5142},[135,9985,9986],{"class":2513},"        # 训练阶段，输出序列的所有词元都在同一时间处理，\n",[135,9988,9989],{"class":2476,"line":5148},[135,9990,9991],{"class":2513},"        # 因此state[2][self.i]初始化为None。\n",[135,9993,9994],{"class":2476,"line":5169},[135,9995,9996],{"class":2513},"        # 预测阶段，输出序列是通过词元一个接着一个解码的，\n",[135,9998,9999],{"class":2476,"line":5188},[135,10000,10001],{"class":2513},"        # 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",[135,10003,10004,10006,10008,10010,10013,10015,10018,10020,10022],{"class":2476,"line":5207},[135,10005,2579],{"class":2480},[135,10007,9972],{"class":2488},[135,10009,2894],{"class":2529},[135,10011,10012],{"class":2488},"][",[135,10014,2740],{"class":2767},[135,10016,10017],{"class":2488},".i] ",[135,10019,2526],{"class":2480},[135,10021,2530],{"class":2529},[135,10023,2533],{"class":2488},[135,10025,10026,10029,10031],{"class":2476,"line":5212},[135,10027,10028],{"class":2488},"            key_values ",[135,10030,891],{"class":2480},[135,10032,9733],{"class":2488},[135,10034,10035,10037],{"class":2476,"line":5228},[135,10036,2612],{"class":2480},[135,10038,2533],{"class":2488},[135,10040,10041,10043,10045,10048,10050,10052,10054,10057,10060,10062,10064],{"class":2476,"line":5234},[135,10042,10028],{"class":2488},[135,10044,891],{"class":2480},[135,10046,10047],{"class":2488}," torch.cat((state[",[135,10049,2894],{"class":2529},[135,10051,10012],{"class":2488},[135,10053,2740],{"class":2767},[135,10055,10056],{"class":2488},".i], X), ",[135,10058,10059],{"class":2545},"axis",[135,10061,891],{"class":2480},[135,10063,159],{"class":2529},[135,10065,2554],{"class":2488},[135,10067,10068,10071,10073,10075,10077,10079,10081],{"class":2476,"line":5240},[135,10069,10070],{"class":2488},"        state[",[135,10072,2894],{"class":2529},[135,10074,10012],{"class":2488},[135,10076,2740],{"class":2767},[135,10078,10017],{"class":2488},[135,10080,891],{"class":2480},[135,10082,10083],{"class":2488}," key_values\n",[135,10085,10086,10088,10090],{"class":2476,"line":5250},[135,10087,2579],{"class":2480},[135,10089,5293],{"class":2767},[135,10091,10092],{"class":2488},".training:\n",[135,10094,10095,10098,10100],{"class":2476,"line":5274},[135,10096,10097],{"class":2488},"            batch_size, num_steps, _ ",[135,10099,891],{"class":2480},[135,10101,2573],{"class":2488},[135,10103,10104],{"class":2476,"line":5279},[135,10105,10106],{"class":2513},"            # dec_valid_lens的开头:(batch_size,num_steps),\n",[135,10108,10109],{"class":2476,"line":5285},[135,10110,10111],{"class":2513},"            # 其中每一行是[1,2,...,num_steps]\n",[135,10113,10114,10117,10119],{"class":2476,"line":5299},[135,10115,10116],{"class":2488},"            dec_valid_lens ",[135,10118,891],{"class":2480},[135,10120,10121],{"class":2488}," torch.arange(\n",[135,10123,10124,10127,10130,10132,10134,10136,10139,10141,10144,10146],{"class":2476,"line":5304},[135,10125,10126],{"class":2529},"                1",[135,10128,10129],{"class":2488},", num_steps ",[135,10131,5850],{"class":2480},[135,10133,2588],{"class":2529},[135,10135,2495],{"class":2488},[135,10137,10138],{"class":2545},"device",[135,10140,891],{"class":2480},[135,10142,10143],{"class":2488},"X.device).repeat(batch_size, ",[135,10145,159],{"class":2529},[135,10147,2554],{"class":2488},[135,10149,10150,10152],{"class":2476,"line":5310},[135,10151,2612],{"class":2480},[135,10153,2533],{"class":2488},[135,10155,10156,10158,10160],{"class":2476,"line":5325},[135,10157,10116],{"class":2488},[135,10159,891],{"class":2480},[135,10161,10162],{"class":2529}," None\n",[135,10164,10165],{"class":2476,"line":9617},[135,10166,2798],{"emptyLinePlaceholder":80},[135,10168,10169],{"class":2476,"line":9623},[135,10170,10171],{"class":2513},"        # 自注意力\n",[135,10173,10174,10177,10179,10181],{"class":2476,"line":9629},[135,10175,10176],{"class":2488},"        X2 ",[135,10178,891],{"class":2480},[135,10180,5293],{"class":2767},[135,10182,10183],{"class":2488},".attention1(X, key_values, key_values, dec_valid_lens)\n",[135,10185,10186,10188,10190,10192],{"class":2476,"line":9656},[135,10187,9326],{"class":2488},[135,10189,891],{"class":2480},[135,10191,5293],{"class":2767},[135,10193,10194],{"class":2488},".addnorm1(X, X2)\n",[135,10196,10197],{"class":2476,"line":9684},[135,10198,10199],{"class":2513},"        # 编码器－解码器注意力。\n",[135,10201,10202],{"class":2476,"line":9704},[135,10203,10204],{"class":2513},"        # enc_outputs的开头:(batch_size,num_steps,num_hiddens)\n",[135,10206,10207,10210,10212,10214],{"class":2476,"line":9715},[135,10208,10209],{"class":2488},"        Y2 ",[135,10211,891],{"class":2480},[135,10213,5293],{"class":2767},[135,10215,10216],{"class":2488},".attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n",[135,10218,10219,10222,10224,10226],{"class":2476,"line":9728},[135,10220,10221],{"class":2488},"        Z ",[135,10223,891],{"class":2480},[135,10225,5293],{"class":2767},[135,10227,10228],{"class":2488},".addnorm2(Y, Y2)\n",[135,10230,10232,10234,10236,10239,10241],{"class":2476,"line":10231},45,[135,10233,2539],{"class":2480},[135,10235,5293],{"class":2767},[135,10237,10238],{"class":2488},".addnorm3(Z, ",[135,10240,2740],{"class":2767},[135,10242,10243],{"class":2488},".ffn(Z)), state\n",[135,10245,10247],{"class":2476,"line":10246},46,[135,10248,2798],{"emptyLinePlaceholder":80},[135,10250,10252,10254,10257,10259,10262],{"class":2476,"line":10251},47,[135,10253,2704],{"class":2480},[135,10255,10256],{"class":2707}," TransformerDecoder",[135,10258,874],{"class":2488},[135,10260,10261],{"class":2713},"AttentionDecoder",[135,10263,2501],{"class":2488},[135,10265,10267,10269,10271,10273,10275,10277,10279,10281,10283,10285,10287,10289,10291],{"class":2476,"line":10266},48,[135,10268,2731],{"class":2480},[135,10270,2734],{"class":2529},[135,10272,874],{"class":2488},[135,10274,2740],{"class":2739},[135,10276,2495],{"class":2488},[135,10278,9390],{"class":2491},[135,10280,2495],{"class":2488},[135,10282,4920],{"class":2491},[135,10284,2495],{"class":2488},[135,10286,4925],{"class":2491},[135,10288,2495],{"class":2488},[135,10290,4930],{"class":2491},[135,10292,3899],{"class":2488},[135,10294,10296,10298,10300,10302,10304,10306,10308,10310],{"class":2476,"line":10295},49,[135,10297,9409],{"class":2491},[135,10299,2495],{"class":2488},[135,10301,9414],{"class":2491},[135,10303,2495],{"class":2488},[135,10305,7748],{"class":2491},[135,10307,2495],{"class":2488},[135,10309,7753],{"class":2491},[135,10311,3899],{"class":2488},[135,10313,10315,10317,10319,10321,10323,10325,10327,10329,10331],{"class":2476,"line":10314},50,[135,10316,4942],{"class":2491},[135,10318,2495],{"class":2488},[135,10320,9433],{"class":2491},[135,10322,2495],{"class":2488},[135,10324,2745],{"class":2491},[135,10326,2495],{"class":2488},[135,10328,2750],{"class":2480},[135,10330,2753],{"class":2491},[135,10332,2501],{"class":2488},[135,10334,10336,10338,10341,10343,10345,10347,10349,10351],{"class":2476,"line":10335},51,[135,10337,2761],{"class":2760},[135,10339,10340],{"class":2488},"(TransformerDecoder, ",[135,10342,2740],{"class":2767},[135,10344,2770],{"class":2488},[135,10346,2773],{"class":2529},[135,10348,874],{"class":2488},[135,10350,2750],{"class":2480},[135,10352,2780],{"class":2488},[135,10354,10356,10358,10360,10362],{"class":2476,"line":10355},52,[135,10357,2785],{"class":2767},[135,10359,9479],{"class":2488},[135,10361,891],{"class":2480},[135,10363,9484],{"class":2488},[135,10365,10367,10369,10372,10374],{"class":2476,"line":10366},53,[135,10368,2785],{"class":2767},[135,10370,10371],{"class":2488},".num_layers ",[135,10373,891],{"class":2480},[135,10375,10376],{"class":2488}," num_layers\n",[135,10378,10380,10382,10384,10386],{"class":2476,"line":10379},54,[135,10381,2785],{"class":2767},[135,10383,9491],{"class":2488},[135,10385,891],{"class":2480},[135,10387,9496],{"class":2488},[135,10389,10391,10393,10395,10397],{"class":2476,"line":10390},55,[135,10392,2785],{"class":2767},[135,10394,9503],{"class":2488},[135,10396,891],{"class":2480},[135,10398,9508],{"class":2488},[135,10400,10402,10404,10406,10408],{"class":2476,"line":10401},56,[135,10403,2785],{"class":2767},[135,10405,9515],{"class":2488},[135,10407,891],{"class":2480},[135,10409,9520],{"class":2488},[135,10411,10413,10415,10417,10419,10421],{"class":2476,"line":10412},57,[135,10414,9525],{"class":2480},[135,10416,9528],{"class":2488},[135,10418,9531],{"class":2480},[135,10420,9535],{"class":9534},[135,10422,9538],{"class":2488},[135,10424,10426,10428,10430,10432,10434,10436,10438,10440],{"class":2476,"line":10425},58,[135,10427,9543],{"class":2767},[135,10429,9546],{"class":2488},[135,10431,9550],{"class":9549},[135,10433,9554],{"class":9553},[135,10435,9550],{"class":9549},[135,10437,5850],{"class":2480},[135,10439,9561],{"class":2760},[135,10441,9564],{"class":2488},[135,10443,10445],{"class":2476,"line":10444},59,[135,10446,10447],{"class":2488},"                DecoderBlock(key_size, query_size, value_size, num_hiddens,\n",[135,10449,10451],{"class":2476,"line":10450},60,[135,10452,9574],{"class":2488},[135,10454,10456],{"class":2476,"line":10455},61,[135,10457,10458],{"class":2488},"                             num_heads, dropout, i))\n",[135,10460,10462,10464,10467,10469],{"class":2476,"line":10461},62,[135,10463,2785],{"class":2767},[135,10465,10466],{"class":2488},".dense ",[135,10468,891],{"class":2480},[135,10470,10471],{"class":2488}," nn.Linear(num_hiddens, vocab_size)\n",[135,10473,10475],{"class":2476,"line":10474},63,[135,10476,2798],{"emptyLinePlaceholder":80},[135,10478,10480,10482,10484,10486,10488,10490,10492,10494,10497,10499,10501,10503],{"class":2476,"line":10479},64,[135,10481,2731],{"class":2480},[135,10483,8889],{"class":2484},[135,10485,874],{"class":2488},[135,10487,2740],{"class":2739},[135,10489,2495],{"class":2488},[135,10491,8898],{"class":2491},[135,10493,2495],{"class":2488},[135,10495,10496],{"class":2491},"enc_valid_lens",[135,10498,2495],{"class":2488},[135,10500,8802],{"class":2480},[135,10502,8805],{"class":2491},[135,10504,2501],{"class":2488},[135,10506,10508,10510,10513,10515,10517,10519,10521],{"class":2476,"line":10507},65,[135,10509,2539],{"class":2480},[135,10511,10512],{"class":2488}," [enc_outputs, enc_valid_lens, [",[135,10514,2853],{"class":2529},[135,10516,7273],{"class":2488},[135,10518,8802],{"class":2480},[135,10520,5293],{"class":2767},[135,10522,10523],{"class":2488},".num_layers]\n",[135,10525,10527],{"class":2476,"line":10526},66,[135,10528,2798],{"emptyLinePlaceholder":80},[135,10530,10532,10534,10536,10538,10540,10542,10544,10546,10548],{"class":2476,"line":10531},67,[135,10533,2731],{"class":2480},[135,10535,2825],{"class":2484},[135,10537,874],{"class":2488},[135,10539,2740],{"class":2739},[135,10541,2495],{"class":2488},[135,10543,2492],{"class":2491},[135,10545,2495],{"class":2488},[135,10547,8935],{"class":2491},[135,10549,2501],{"class":2488},[135,10551,10553,10555,10557,10559,10561,10563,10565,10567,10569,10571],{"class":2476,"line":10552},68,[135,10554,2643],{"class":2488},[135,10556,891],{"class":2480},[135,10558,5293],{"class":2767},[135,10560,9638],{"class":2488},[135,10562,2740],{"class":2767},[135,10564,9643],{"class":2488},[135,10566,8802],{"class":2480},[135,10568,9648],{"class":2488},[135,10570,2740],{"class":2767},[135,10572,9653],{"class":2488},[135,10574,10576,10578,10581,10583,10586,10588,10590,10592,10594,10596,10598,10601,10604,10607,10609,10611,10614,10616],{"class":2476,"line":10575},69,[135,10577,2785],{"class":2767},[135,10579,10580],{"class":2488},"._attention_weights ",[135,10582,891],{"class":2480},[135,10584,10585],{"class":2488}," [[",[135,10587,2853],{"class":2529},[135,10589,7273],{"class":2488},[135,10591,8802],{"class":2480},[135,10593,9674],{"class":9534},[135,10595,874],{"class":2488},[135,10597,2740],{"class":2767},[135,10599,10600],{"class":2488},".blks) ",[135,10602,10603],{"class":2480},"for",[135,10605,10606],{"class":2488}," _ ",[135,10608,9531],{"class":2480},[135,10610,9535],{"class":9534},[135,10612,10613],{"class":2488}," (",[135,10615,2894],{"class":2529},[135,10617,10618],{"class":2488},")]\n",[135,10620,10622,10624,10626,10628,10630,10632,10634],{"class":2476,"line":10621},70,[135,10623,9525],{"class":2480},[135,10625,9689],{"class":2488},[135,10627,9531],{"class":2480},[135,10629,9694],{"class":9534},[135,10631,874],{"class":2488},[135,10633,2740],{"class":2767},[135,10635,9701],{"class":2488},[135,10637,10639,10642,10644],{"class":2476,"line":10638},71,[135,10640,10641],{"class":2488},"            X, state ",[135,10643,891],{"class":2480},[135,10645,10646],{"class":2488}," blk(X, state)\n",[135,10648,10650],{"class":2476,"line":10649},72,[135,10651,10652],{"class":2513},"            # 解码器自注意力权重\n",[135,10654,10656,10658,10661,10663,10666,10668],{"class":2476,"line":10655},73,[135,10657,9543],{"class":2767},[135,10659,10660],{"class":2488},"._attention_weights[",[135,10662,1830],{"class":2529},[135,10664,10665],{"class":2488},"][i] ",[135,10667,891],{"class":2480},[135,10669,10670],{"class":2488}," blk.attention1.attention.attention_weights\n",[135,10672,10674],{"class":2476,"line":10673},74,[135,10675,10676],{"class":2513},"            # “编码器－解码器”自注意力权重\n",[135,10678,10680,10682,10684,10686,10688,10690],{"class":2476,"line":10679},75,[135,10681,9543],{"class":2767},[135,10683,10660],{"class":2488},[135,10685,159],{"class":2529},[135,10687,10665],{"class":2488},[135,10689,891],{"class":2480},[135,10691,10692],{"class":2488}," blk.attention2.attention.attention_weights\n",[135,10694,10696,10698,10700],{"class":2476,"line":10695},76,[135,10697,2539],{"class":2480},[135,10699,5293],{"class":2767},[135,10701,10702],{"class":2488},".dense(X), state\n",[135,10704,10706],{"class":2476,"line":10705},77,[135,10707,2798],{"emptyLinePlaceholder":80},[135,10709,10711,10714],{"class":2476,"line":10710},78,[135,10712,10713],{"class":2484},"    @",[135,10715,10716],{"class":2760},"property\n",[135,10718,10720,10722,10725,10727,10729],{"class":2476,"line":10719},79,[135,10721,2731],{"class":2480},[135,10723,10724],{"class":2484}," attention_weights",[135,10726,874],{"class":2488},[135,10728,2740],{"class":2739},[135,10730,2501],{"class":2488},[135,10732,10734,10736,10738],{"class":2476,"line":10733},80,[135,10735,2539],{"class":2480},[135,10737,5293],{"class":2767},[135,10739,10740],{"class":2488},"._attention_weights\n",[10,10742,10743],{"id":10743},"训练",[14,10745,10746],{},"同样，训练时需要屏蔽部分不需要的内容：",[2466,10748,10750],{"className":2468,"code":10749,"language":2470,"meta":65,"style":65},"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",[2472,10751,10752,10779,10784,10798,10816,10845,10861,10867,10871,10889,10894,10899,10904,10909,10935,10945,10954,10972,10990,11008,11031],{"__ignoreMap":65},[135,10753,10754,10756,10759,10761,10763,10765,10768,10770,10773,10775,10777],{"class":2476,"line":2477},[135,10755,2481],{"class":2480},[135,10757,10758],{"class":2484}," sequence_mask",[135,10760,874],{"class":2488},[135,10762,2492],{"class":2491},[135,10764,2495],{"class":2488},[135,10766,10767],{"class":2491},"valid_len",[135,10769,2495],{"class":2488},[135,10771,10772],{"class":2491},"value",[135,10774,891],{"class":2480},[135,10776,1830],{"class":2529},[135,10778,2501],{"class":2488},[135,10780,10781],{"class":2476,"line":66},[135,10782,10783],{"class":2506},"    \"\"\"在序列中屏蔽不相关的项\"\"\"\n",[135,10785,10786,10789,10791,10794,10796],{"class":2476,"line":2510},[135,10787,10788],{"class":2488},"    maxlen ",[135,10790,891],{"class":2480},[135,10792,10793],{"class":2488}," X.size(",[135,10795,159],{"class":2529},[135,10797,2554],{"class":2488},[135,10799,10800,10803,10805,10808,10811,10813],{"class":2476,"line":2517},[135,10801,10802],{"class":2488},"    mask ",[135,10804,891],{"class":2480},[135,10806,10807],{"class":2488}," torch.arange((maxlen), ",[135,10809,10810],{"class":2545},"dtype",[135,10812,891],{"class":2480},[135,10814,10815],{"class":2488},"torch.float32,\n",[135,10817,10818,10821,10823,10826,10828,10831,10834,10837,10839,10841,10843],{"class":2476,"line":2536},[135,10819,10820],{"class":2545},"                        device",[135,10822,891],{"class":2480},[135,10824,10825],{"class":2488},"X.device)[",[135,10827,2853],{"class":2529},[135,10829,10830],{"class":2488},", :] ",[135,10832,10833],{"class":2480},"\u003C",[135,10835,10836],{"class":2488}," valid_len[",[135,10838,7257],{"class":7256},[135,10840,2495],{"class":2488},[135,10842,2853],{"class":2529},[135,10844,2872],{"class":2488},[135,10846,10847,10850,10853,10856,10858],{"class":2476,"line":2557},[135,10848,10849],{"class":2488},"    X[",[135,10851,10852],{"class":2480},"~",[135,10854,10855],{"class":2488},"mask] ",[135,10857,891],{"class":2480},[135,10859,10860],{"class":2488}," value\n",[135,10862,10863,10865],{"class":2476,"line":2565},[135,10864,4760],{"class":2480},[135,10866,9733],{"class":2488},[135,10868,10869],{"class":2476,"line":2576},[135,10870,2798],{"emptyLinePlaceholder":80},[135,10872,10873,10875,10878,10880,10882,10884,10887],{"class":2476,"line":2593},[135,10874,2704],{"class":2480},[135,10876,10877],{"class":2707}," MaskedSoftmaxCELoss",[135,10879,874],{"class":2488},[135,10881,2714],{"class":2713},[135,10883,940],{"class":2488},[135,10885,10886],{"class":2713},"CrossEntropyLoss",[135,10888,2501],{"class":2488},[135,10890,10891],{"class":2476,"line":2609},[135,10892,10893],{"class":2506},"    \"\"\"带遮蔽的softmax交叉熵损失函数\"\"\"\n",[135,10895,10896],{"class":2476,"line":2617},[135,10897,10898],{"class":2513},"    # pred的形状：(batch_size,num_steps,vocab_size)\n",[135,10900,10901],{"class":2476,"line":2634},[135,10902,10903],{"class":2513},"    # label的形状：(batch_size,num_steps)\n",[135,10905,10906],{"class":2476,"line":2640},[135,10907,10908],{"class":2513},"    # valid_len的形状：(batch_size,)\n",[135,10910,10911,10913,10915,10917,10919,10921,10924,10926,10929,10931,10933],{"class":2476,"line":2665},[135,10912,2731],{"class":2480},[135,10914,2825],{"class":2484},[135,10916,874],{"class":2488},[135,10918,2740],{"class":2739},[135,10920,2495],{"class":2488},[135,10922,10923],{"class":2491},"pred",[135,10925,2495],{"class":2488},[135,10927,10928],{"class":2491},"label",[135,10930,2495],{"class":2488},[135,10932,10767],{"class":2491},[135,10934,2501],{"class":2488},[135,10936,10937,10940,10942],{"class":2476,"line":2678},[135,10938,10939],{"class":2488},"        weights ",[135,10941,891],{"class":2480},[135,10943,10944],{"class":2488}," torch.ones_like(label)\n",[135,10946,10947,10949,10951],{"class":2476,"line":2918},[135,10948,10939],{"class":2488},[135,10950,891],{"class":2480},[135,10952,10953],{"class":2488}," sequence_mask(weights, valid_len)\n",[135,10955,10956,10958,10961,10963,10966,10969],{"class":2476,"line":4854},[135,10957,2785],{"class":2767},[135,10959,10960],{"class":2488},".reduction",[135,10962,891],{"class":2480},[135,10964,10965],{"class":9549},"'",[135,10967,10968],{"class":9553},"none",[135,10970,10971],{"class":9549},"'\n",[135,10973,10974,10977,10979,10982,10985,10987],{"class":2476,"line":5130},[135,10975,10976],{"class":2488},"        unweighted_loss ",[135,10978,891],{"class":2480},[135,10980,10981],{"class":2760}," super",[135,10983,10984],{"class":2488},"(MaskedSoftmaxCELoss, ",[135,10986,2740],{"class":2767},[135,10988,10989],{"class":2488},").forward(\n",[135,10991,10992,10995,10997,10999,11001,11003,11005],{"class":2476,"line":5136},[135,10993,10994],{"class":2488},"            pred.permute(",[135,10996,1830],{"class":2529},[135,10998,2495],{"class":2488},[135,11000,2894],{"class":2529},[135,11002,2495],{"class":2488},[135,11004,159],{"class":2529},[135,11006,11007],{"class":2488},"), label)\n",[135,11009,11010,11013,11015,11018,11020,11023,11025,11027,11029],{"class":2476,"line":5142},[135,11011,11012],{"class":2488},"        weighted_loss ",[135,11014,891],{"class":2480},[135,11016,11017],{"class":2488}," (unweighted_loss ",[135,11019,8802],{"class":2480},[135,11021,11022],{"class":2488}," weights).mean(",[135,11024,2546],{"class":2545},[135,11026,891],{"class":2480},[135,11028,159],{"class":2529},[135,11030,2554],{"class":2488},[135,11032,11033,11035],{"class":2476,"line":5148},[135,11034,2539],{"class":2480},[135,11036,11037],{"class":2488}," weighted_loss\n",[14,11039,11040],{},"梯度裁剪函数：",[2466,11042,11044],{"className":2468,"code":11043,"language":2470,"meta":65,"style":65},"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",[2472,11045,11046,11065,11070,11080,11106,11112,11121,11153,11166,11178],{"__ignoreMap":65},[135,11047,11048,11050,11053,11055,11058,11060,11063],{"class":2476,"line":2477},[135,11049,2481],{"class":2480},[135,11051,11052],{"class":2484}," grad_clipping",[135,11054,874],{"class":2488},[135,11056,11057],{"class":2491},"net",[135,11059,2495],{"class":2488},[135,11061,11062],{"class":2491},"theta",[135,11064,2501],{"class":2488},[135,11066,11067],{"class":2476,"line":66},[135,11068,11069],{"class":2506},"    \"\"\"裁剪梯度\"\"\"\n",[135,11071,11072,11074,11077],{"class":2476,"line":2510},[135,11073,2520],{"class":2480},[135,11075,11076],{"class":9534}," isinstance",[135,11078,11079],{"class":2488},"(net, nn.Module):\n",[135,11081,11082,11085,11087,11090,11092,11095,11097,11100,11103],{"class":2476,"line":2517},[135,11083,11084],{"class":2488},"        params ",[135,11086,891],{"class":2480},[135,11088,11089],{"class":2488}," [p ",[135,11091,10603],{"class":2480},[135,11093,11094],{"class":2488}," p ",[135,11096,9531],{"class":2480},[135,11098,11099],{"class":2488}," net.parameters() ",[135,11101,11102],{"class":2480},"if",[135,11104,11105],{"class":2488}," p.requires_grad]\n",[135,11107,11108,11110],{"class":2476,"line":2536},[135,11109,2560],{"class":2480},[135,11111,2533],{"class":2488},[135,11113,11114,11116,11118],{"class":2476,"line":2557},[135,11115,11084],{"class":2488},[135,11117,891],{"class":2480},[135,11119,11120],{"class":2488}," net.params\n",[135,11122,11123,11126,11128,11131,11134,11137,11139,11142,11144,11146,11148,11150],{"class":2476,"line":2565},[135,11124,11125],{"class":2488},"    norm ",[135,11127,891],{"class":2480},[135,11129,11130],{"class":2488}," torch.sqrt(",[135,11132,11133],{"class":9534},"sum",[135,11135,11136],{"class":2488},"(torch.sum((p.grad ",[135,11138,2750],{"class":2480},[135,11140,11141],{"class":2529}," 2",[135,11143,2897],{"class":2488},[135,11145,10603],{"class":2480},[135,11147,11094],{"class":2488},[135,11149,9531],{"class":2480},[135,11151,11152],{"class":2488}," params))\n",[135,11154,11155,11157,11160,11163],{"class":2476,"line":2576},[135,11156,2520],{"class":2480},[135,11158,11159],{"class":2488}," norm ",[135,11161,11162],{"class":2480},">",[135,11164,11165],{"class":2488}," theta:\n",[135,11167,11168,11170,11173,11175],{"class":2476,"line":2593},[135,11169,9525],{"class":2480},[135,11171,11172],{"class":2488}," param ",[135,11174,9531],{"class":2480},[135,11176,11177],{"class":2488}," params:\n",[135,11179,11180,11183,11185,11187,11190,11193,11195],{"class":2476,"line":2609},[135,11181,11182],{"class":2488},"            param.grad[",[135,11184,7257],{"class":7256},[135,11186,7273],{"class":2488},[135,11188,11189],{"class":2480},"*=",[135,11191,11192],{"class":2488}," theta ",[135,11194,2900],{"class":2480},[135,11196,11197],{"class":2488}," norm\n",[14,11199,11200,11201],{},"之后，在训练时，特定的序列开始词元（“",[11202,11203,11204,11205],"bos",{},"”）和 原始的输出序列（不包括序列结束词元“",[11206,11207,11208],"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。",[2466,11210,11212],{"className":2468,"code":11211,"language":2470,"meta":65,"style":65},"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",[2472,11213,11214,11251,11256,11269,11284,11289,11307,11319,11338,11343,11347,11352,11357,11374,11384,11389,11427,11443,11458,11468,11486,11498,11503,11523,11553,11573,11603,11613,11623,11631,11640,11650,11655,11663,11668,11695,11721,11782],{"__ignoreMap":65},[135,11215,11216,11218,11221,11223,11225,11227,11230,11232,11235,11237,11240,11242,11245,11247,11249],{"class":2476,"line":2477},[135,11217,2481],{"class":2480},[135,11219,11220],{"class":2484}," train_seq2seq",[135,11222,874],{"class":2488},[135,11224,11057],{"class":2491},[135,11226,2495],{"class":2488},[135,11228,11229],{"class":2491},"data_iter",[135,11231,2495],{"class":2488},[135,11233,11234],{"class":2491},"lr",[135,11236,2495],{"class":2488},[135,11238,11239],{"class":2491},"num_epochs",[135,11241,2495],{"class":2488},[135,11243,11244],{"class":2491},"tgt_vocab",[135,11246,2495],{"class":2488},[135,11248,10138],{"class":2491},[135,11250,2501],{"class":2488},[135,11252,11253],{"class":2476,"line":66},[135,11254,11255],{"class":2506},"    \"\"\"训练序列到序列模型\"\"\"\n",[135,11257,11258,11260,11263,11265,11267],{"class":2476,"line":2510},[135,11259,2731],{"class":2480},[135,11261,11262],{"class":2484}," xavier_init_weights",[135,11264,874],{"class":2488},[135,11266,442],{"class":2491},[135,11268,2501],{"class":2488},[135,11270,11271,11273,11276,11279,11281],{"class":2476,"line":2517},[135,11272,2579],{"class":2480},[135,11274,11275],{"class":2760}," type",[135,11277,11278],{"class":2488},"(m) ",[135,11280,2585],{"class":2480},[135,11282,11283],{"class":2488}," nn.Linear:\n",[135,11285,11286],{"class":2476,"line":2536},[135,11287,11288],{"class":2488},"            nn.init.xavier_uniform_(m.weight)\n",[135,11290,11291,11293,11295,11297,11299,11302,11305],{"class":2476,"line":2557},[135,11292,2579],{"class":2480},[135,11294,11275],{"class":2760},[135,11296,11278],{"class":2488},[135,11298,2585],{"class":2480},[135,11300,11301],{"class":2488}," nn.",[135,11303,11304],{"class":2529},"GRU",[135,11306,2533],{"class":2488},[135,11308,11309,11312,11314,11316],{"class":2476,"line":2565},[135,11310,11311],{"class":2480},"            for",[135,11313,11172],{"class":2488},[135,11315,9531],{"class":2480},[135,11317,11318],{"class":2488}," m._flat_weights_names:\n",[135,11320,11321,11324,11327,11330,11332,11335],{"class":2476,"line":2576},[135,11322,11323],{"class":2480},"                if",[135,11325,11326],{"class":9549}," \"",[135,11328,11329],{"class":9553},"weight",[135,11331,9550],{"class":9549},[135,11333,11334],{"class":2480}," in",[135,11336,11337],{"class":2488}," param:\n",[135,11339,11340],{"class":2476,"line":2593},[135,11341,11342],{"class":2488},"                    nn.init.xavier_uniform_(m._parameters[param])\n",[135,11344,11345],{"class":2476,"line":2609},[135,11346,2798],{"emptyLinePlaceholder":80},[135,11348,11349],{"class":2476,"line":2617},[135,11350,11351],{"class":2488},"    net.apply(xavier_init_weights)\n",[135,11353,11354],{"class":2476,"line":2634},[135,11355,11356],{"class":2488},"    net.to(device)\n",[135,11358,11359,11362,11364,11367,11369,11371],{"class":2476,"line":2640},[135,11360,11361],{"class":2488},"    optimizer ",[135,11363,891],{"class":2480},[135,11365,11366],{"class":2488}," torch.optim.Adam(net.parameters(), ",[135,11368,11234],{"class":2545},[135,11370,891],{"class":2480},[135,11372,11373],{"class":2488},"lr)\n",[135,11375,11376,11379,11381],{"class":2476,"line":2665},[135,11377,11378],{"class":2488},"    loss ",[135,11380,891],{"class":2480},[135,11382,11383],{"class":2488}," MaskedSoftmaxCELoss()\n",[135,11385,11386],{"class":2476,"line":2678},[135,11387,11388],{"class":2488},"    net.train()\n",[135,11390,11391,11394,11396,11399,11402,11404,11406,11409,11411,11413,11416,11418,11420,11423,11425],{"class":2476,"line":2918},[135,11392,11393],{"class":2488},"    animator ",[135,11395,891],{"class":2480},[135,11397,11398],{"class":2488}," d2l.Animator(",[135,11400,11401],{"class":2545},"xlabel",[135,11403,891],{"class":2480},[135,11405,10965],{"class":9549},[135,11407,11408],{"class":9553},"epoch",[135,11410,10965],{"class":9549},[135,11412,2495],{"class":2488},[135,11414,11415],{"class":2545},"ylabel",[135,11417,891],{"class":2480},[135,11419,10965],{"class":9549},[135,11421,11422],{"class":9553},"loss",[135,11424,10965],{"class":9549},[135,11426,3899],{"class":2488},[135,11428,11429,11432,11434,11437,11440],{"class":2476,"line":4854},[135,11430,11431],{"class":2545},"                     xlim",[135,11433,891],{"class":2480},[135,11435,11436],{"class":2488},"[",[135,11438,11439],{"class":2529},"10",[135,11441,11442],{"class":2488},", num_epochs])\n",[135,11444,11445,11448,11451,11453,11455],{"class":2476,"line":5130},[135,11446,11447],{"class":2480},"    for",[135,11449,11450],{"class":2488}," epoch ",[135,11452,9531],{"class":2480},[135,11454,9535],{"class":9534},[135,11456,11457],{"class":2488},"(num_epochs):\n",[135,11459,11460,11463,11465],{"class":2476,"line":5136},[135,11461,11462],{"class":2488},"        timer ",[135,11464,891],{"class":2480},[135,11466,11467],{"class":2488}," d2l.Timer()\n",[135,11469,11470,11473,11475,11478,11480,11483],{"class":2476,"line":5142},[135,11471,11472],{"class":2488},"        metric ",[135,11474,891],{"class":2480},[135,11476,11477],{"class":2488}," d2l.Accumulator(",[135,11479,2894],{"class":2529},[135,11481,11482],{"class":2488},")  ",[135,11484,11485],{"class":2513},"# 训练损失总和，词元数量\n",[135,11487,11488,11490,11493,11495],{"class":2476,"line":5148},[135,11489,9525],{"class":2480},[135,11491,11492],{"class":2488}," batch ",[135,11494,9531],{"class":2480},[135,11496,11497],{"class":2488}," data_iter:\n",[135,11499,11500],{"class":2476,"line":5169},[135,11501,11502],{"class":2488},"            optimizer.zero_grad()\n",[135,11504,11505,11508,11510,11513,11515,11518,11520],{"class":2476,"line":5188},[135,11506,11507],{"class":2488},"            X, X_valid_len, Y, Y_valid_len ",[135,11509,891],{"class":2480},[135,11511,11512],{"class":2488}," [x.to(device) ",[135,11514,10603],{"class":2480},[135,11516,11517],{"class":2488}," x ",[135,11519,9531],{"class":2480},[135,11521,11522],{"class":2488}," batch]\n",[135,11524,11525,11528,11530,11533,11535,11538,11540,11543,11545,11548,11550],{"class":2476,"line":5207},[135,11526,11527],{"class":2488},"            bos ",[135,11529,891],{"class":2480},[135,11531,11532],{"class":2488}," torch.tensor([tgt_vocab[",[135,11534,10965],{"class":9549},[135,11536,11537],{"class":9553},"\u003Cbos>",[135,11539,10965],{"class":9549},[135,11541,11542],{"class":2488},"]] ",[135,11544,8802],{"class":2480},[135,11546,11547],{"class":2488}," Y.shape[",[135,11549,1830],{"class":2529},[135,11551,11552],{"class":2488},"],\n",[135,11554,11555,11558,11560,11563,11565,11567,11569,11571],{"class":2476,"line":5212},[135,11556,11557],{"class":2545},"                          device",[135,11559,891],{"class":2480},[135,11561,11562],{"class":2488},"device).reshape(",[135,11564,2627],{"class":2480},[135,11566,159],{"class":2529},[135,11568,2495],{"class":2488},[135,11570,159],{"class":2529},[135,11572,2554],{"class":2488},[135,11574,11575,11578,11580,11583,11585,11587,11589,11591,11593,11596,11598,11600],{"class":2476,"line":5228},[135,11576,11577],{"class":2488},"            dec_input ",[135,11579,891],{"class":2480},[135,11581,11582],{"class":2488}," torch.cat([bos, Y[",[135,11584,7257],{"class":7256},[135,11586,2495],{"class":2488},[135,11588,7257],{"class":7256},[135,11590,2627],{"class":2480},[135,11592,159],{"class":2529},[135,11594,11595],{"class":2488},"]], ",[135,11597,159],{"class":2529},[135,11599,11482],{"class":2488},[135,11601,11602],{"class":2513},"# 强制教学\n",[135,11604,11605,11608,11610],{"class":2476,"line":5234},[135,11606,11607],{"class":2488},"            Y_hat, _ ",[135,11609,891],{"class":2480},[135,11611,11612],{"class":2488}," net(X, dec_input, X_valid_len)\n",[135,11614,11615,11618,11620],{"class":2476,"line":5240},[135,11616,11617],{"class":2488},"            l ",[135,11619,891],{"class":2480},[135,11621,11622],{"class":2488}," loss(Y_hat, Y, Y_valid_len)\n",[135,11624,11625,11628],{"class":2476,"line":5250},[135,11626,11627],{"class":2488},"            l.sum().backward()      ",[135,11629,11630],{"class":2513},"# 损失函数的标量进行“反向传播”\n",[135,11632,11633,11636,11638],{"class":2476,"line":5274},[135,11634,11635],{"class":2488},"            grad_clipping(net, ",[135,11637,159],{"class":2529},[135,11639,2554],{"class":2488},[135,11641,11642,11645,11647],{"class":2476,"line":5279},[135,11643,11644],{"class":2488},"            num_tokens ",[135,11646,891],{"class":2480},[135,11648,11649],{"class":2488}," Y_valid_len.sum()\n",[135,11651,11652],{"class":2476,"line":5285},[135,11653,11654],{"class":2488},"            optimizer.step()\n",[135,11656,11657,11660],{"class":2476,"line":5299},[135,11658,11659],{"class":2480},"            with",[135,11661,11662],{"class":2488}," torch.no_grad():\n",[135,11664,11665],{"class":2476,"line":5304},[135,11666,11667],{"class":2488},"                metric.add(l.sum(), num_tokens)\n",[135,11669,11670,11672,11675,11677,11679,11681,11684,11687,11690,11693],{"class":2476,"line":5310},[135,11671,2579],{"class":2480},[135,11673,11674],{"class":2488}," (epoch ",[135,11676,5850],{"class":2480},[135,11678,2588],{"class":2529},[135,11680,7219],{"class":2488},[135,11682,11683],{"class":2480},"%",[135,11685,11686],{"class":2529}," 10",[135,11688,11689],{"class":2480}," ==",[135,11691,11692],{"class":2529}," 0",[135,11694,2533],{"class":2488},[135,11696,11697,11700,11702,11704,11707,11709,11711,11713,11716,11718],{"class":2476,"line":5325},[135,11698,11699],{"class":2488},"            animator.add(epoch ",[135,11701,5850],{"class":2480},[135,11703,2588],{"class":2529},[135,11705,11706],{"class":2488},", (metric[",[135,11708,1830],{"class":2529},[135,11710,7273],{"class":2488},[135,11712,2900],{"class":2480},[135,11714,11715],{"class":2488}," metric[",[135,11717,159],{"class":2529},[135,11719,11720],{"class":2488},"],))\n",[135,11722,11723,11726,11728,11731,11734,11737,11740,11742,11744,11746,11748,11750,11753,11756,11759,11761,11763,11765,11767,11769,11771,11774,11777,11779],{"class":2476,"line":9617},[135,11724,11725],{"class":9534},"    print",[135,11727,874],{"class":2488},[135,11729,11730],{"class":2480},"f",[135,11732,11733],{"class":9553},"'loss ",[135,11735,11736],{"class":2529},"{",[135,11738,11739],{"class":2488},"metric[",[135,11741,1830],{"class":2529},[135,11743,7273],{"class":2488},[135,11745,2900],{"class":2480},[135,11747,11715],{"class":2488},[135,11749,159],{"class":2529},[135,11751,11752],{"class":2488},"]",[135,11754,11755],{"class":2480},":.3f",[135,11757,11758],{"class":2529},"}",[135,11760,2495],{"class":9553},[135,11762,11736],{"class":2529},[135,11764,11739],{"class":2488},[135,11766,159],{"class":2529},[135,11768,7273],{"class":2488},[135,11770,2900],{"class":2480},[135,11772,11773],{"class":2488}," timer.stop()",[135,11775,11776],{"class":2480},":.1f",[135,11778,11758],{"class":2529},[135,11780,11781],{"class":9553}," '\n",[135,11783,11784,11787,11790,11792,11794,11797,11799,11801],{"class":2476,"line":9623},[135,11785,11786],{"class":2480},"        f",[135,11788,11789],{"class":9553},"'tokens/sec on ",[135,11791,11736],{"class":2529},[135,11793,9561],{"class":2760},[135,11795,11796],{"class":2488},"(device)",[135,11798,11758],{"class":2529},[135,11800,10965],{"class":9553},[135,11802,2554],{"class":2488},[14,11804,11805],{},"进行数据集的数据处理",[2466,11807,11809],{"className":2468,"code":11808,"language":2470,"meta":65,"style":65},"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",[2472,11810,11811,11821,11826,11830,11835,11854,11883,11905,11912,11916,11930,11935,11939,11943,11962,11999,12003,12008,12013,12056,12061,12106,12121,12131,12135,12157,12162,12166,12170,12180,12204,12220,12225,12244,12259,12276,12291,12298,12302,12330,12335,12339,12344,12353,12362,12381,12416,12434,12466,12476,12486,12496,12506],{"__ignoreMap":65},[135,11812,11813,11815,11818],{"class":2476,"line":2477},[135,11814,2481],{"class":2480},[135,11816,11817],{"class":2484}," read_data_nmt",[135,11819,11820],{"class":2488},"():\n",[135,11822,11823],{"class":2476,"line":66},[135,11824,11825],{"class":2506},"    \"\"\"载入“英语－法语”数据集\n",[135,11827,11828],{"class":2476,"line":2510},[135,11829,2798],{"emptyLinePlaceholder":80},[135,11831,11832],{"class":2476,"line":2517},[135,11833,11834],{"class":2506},"    Defined in :numref:`sec_machine_translation`\"\"\"\n",[135,11836,11837,11840,11842,11845,11847,11850,11852],{"class":2476,"line":2536},[135,11838,11839],{"class":2488},"    data_dir ",[135,11841,891],{"class":2480},[135,11843,11844],{"class":2488}," d2l.download_extract(",[135,11846,10965],{"class":9549},[135,11848,11849],{"class":9553},"fra-eng",[135,11851,10965],{"class":9549},[135,11853,2554],{"class":2488},[135,11855,11856,11859,11862,11865,11867,11870,11872,11875,11877,11879,11881],{"class":2476,"line":2557},[135,11857,11858],{"class":2480},"    with",[135,11860,11861],{"class":9534}," open",[135,11863,11864],{"class":2488},"(os.path.join(data_dir, ",[135,11866,10965],{"class":9549},[135,11868,11869],{"class":9553},"fra.txt",[135,11871,10965],{"class":9549},[135,11873,11874],{"class":2488},"), ",[135,11876,10965],{"class":9549},[135,11878,7899],{"class":9553},[135,11880,10965],{"class":9549},[135,11882,3899],{"class":2488},[135,11884,11885,11888,11890,11892,11895,11897,11899,11902],{"class":2476,"line":2565},[135,11886,11887],{"class":2545},"             encoding",[135,11889,891],{"class":2480},[135,11891,10965],{"class":9549},[135,11893,11894],{"class":9553},"utf-8",[135,11896,10965],{"class":9549},[135,11898,7219],{"class":2488},[135,11900,11901],{"class":2480},"as",[135,11903,11904],{"class":2488}," f:\n",[135,11906,11907,11909],{"class":2476,"line":2576},[135,11908,2539],{"class":2480},[135,11910,11911],{"class":2488}," f.read()\n",[135,11913,11914],{"class":2476,"line":2593},[135,11915,2798],{"emptyLinePlaceholder":80},[135,11917,11918,11920,11923,11925,11928],{"class":2476,"line":2609},[135,11919,2481],{"class":2480},[135,11921,11922],{"class":2484}," preprocess_nmt",[135,11924,874],{"class":2488},[135,11926,11927],{"class":2491},"text",[135,11929,2501],{"class":2488},[135,11931,11932],{"class":2476,"line":2617},[135,11933,11934],{"class":2506},"    \"\"\"预处理“英语－法语”数据集\n",[135,11936,11937],{"class":2476,"line":2634},[135,11938,2798],{"emptyLinePlaceholder":80},[135,11940,11941],{"class":2476,"line":2640},[135,11942,11834],{"class":2506},[135,11944,11945,11947,11950,11952,11955,11957,11960],{"class":2476,"line":2665},[135,11946,2731],{"class":2480},[135,11948,11949],{"class":2484}," no_space",[135,11951,874],{"class":2488},[135,11953,11954],{"class":2491},"char",[135,11956,2495],{"class":2488},[135,11958,11959],{"class":2491},"prev_char",[135,11961,2501],{"class":2488},[135,11963,11964,11966,11969,11971,11974,11976,11978,11981,11983,11985,11988,11991,11994,11997],{"class":2476,"line":2678},[135,11965,2539],{"class":2480},[135,11967,11968],{"class":2488}," char ",[135,11970,9531],{"class":2480},[135,11972,11973],{"class":2760}," set",[135,11975,874],{"class":2488},[135,11977,10965],{"class":9549},[135,11979,11980],{"class":9553},",.!?",[135,11982,10965],{"class":9549},[135,11984,7219],{"class":2488},[135,11986,11987],{"class":2480},"and",[135,11989,11990],{"class":2488}," prev_char ",[135,11992,11993],{"class":2480},"!=",[135,11995,11996],{"class":9549}," '",[135,11998,11781],{"class":9549},[135,12000,12001],{"class":2476,"line":2918},[135,12002,2798],{"emptyLinePlaceholder":80},[135,12004,12005],{"class":2476,"line":4854},[135,12006,12007],{"class":2513},"    # 使用空格替换不间断空格\n",[135,12009,12010],{"class":2476,"line":5130},[135,12011,12012],{"class":2513},"    # 使用小写字母替换大写字母\n",[135,12014,12015,12018,12020,12023,12025,12029,12031,12033,12035,12037,12040,12042,12045,12047,12049,12051,12053],{"class":2476,"line":5136},[135,12016,12017],{"class":2488},"    text ",[135,12019,891],{"class":2480},[135,12021,12022],{"class":2488}," text.replace(",[135,12024,10965],{"class":9549},[135,12026,12028],{"class":12027},"sRfyP","\\u202f",[135,12030,10965],{"class":9549},[135,12032,2495],{"class":2488},[135,12034,10965],{"class":9549},[135,12036,11996],{"class":9549},[135,12038,12039],{"class":2488},").replace(",[135,12041,10965],{"class":9549},[135,12043,12044],{"class":12027},"\\xa0",[135,12046,10965],{"class":9549},[135,12048,2495],{"class":2488},[135,12050,10965],{"class":9549},[135,12052,11996],{"class":9549},[135,12054,12055],{"class":2488},").lower()\n",[135,12057,12058],{"class":2476,"line":5142},[135,12059,12060],{"class":2513},"    # 在单词和标点符号之间插入空格\n",[135,12062,12063,12066,12068,12070,12072,12074,12077,12079,12081,12083,12085,12087,12090,12093,12095,12097,12100,12103],{"class":2476,"line":5148},[135,12064,12065],{"class":2488},"    out ",[135,12067,891],{"class":2480},[135,12069,9665],{"class":2488},[135,12071,10965],{"class":9549},[135,12073,11996],{"class":9549},[135,12075,12076],{"class":2480}," +",[135,12078,11968],{"class":2488},[135,12080,11102],{"class":2480},[135,12082,9528],{"class":2488},[135,12084,11162],{"class":2480},[135,12086,11692],{"class":2529},[135,12088,12089],{"class":2480}," and",[135,12091,12092],{"class":2488}," no_space(char, text[i ",[135,12094,2627],{"class":2480},[135,12096,2588],{"class":2529},[135,12098,12099],{"class":2488},"]) ",[135,12101,12102],{"class":2480},"else",[135,12104,12105],{"class":2488}," char\n",[135,12107,12108,12111,12114,12116,12118],{"class":2476,"line":5169},[135,12109,12110],{"class":2480},"           for",[135,12112,12113],{"class":2488}," i, char ",[135,12115,9531],{"class":2480},[135,12117,9694],{"class":9534},[135,12119,12120],{"class":2488},"(text)]\n",[135,12122,12123,12125,12128],{"class":2476,"line":5188},[135,12124,4760],{"class":2480},[135,12126,12127],{"class":9549}," ''",[135,12129,12130],{"class":2488},".join(out)\n",[135,12132,12133],{"class":2476,"line":5207},[135,12134,2798],{"emptyLinePlaceholder":80},[135,12136,12137,12139,12142,12144,12146,12148,12151,12153,12155],{"class":2476,"line":5212},[135,12138,2481],{"class":2480},[135,12140,12141],{"class":2484}," tokenize_nmt",[135,12143,874],{"class":2488},[135,12145,11927],{"class":2491},[135,12147,2495],{"class":2488},[135,12149,12150],{"class":2491},"num_examples",[135,12152,891],{"class":2480},[135,12154,2853],{"class":2529},[135,12156,2501],{"class":2488},[135,12158,12159],{"class":2476,"line":5228},[135,12160,12161],{"class":2506},"    \"\"\"词元化“英语－法语”数据数据集\n",[135,12163,12164],{"class":2476,"line":5234},[135,12165,2798],{"emptyLinePlaceholder":80},[135,12167,12168],{"class":2476,"line":5240},[135,12169,11834],{"class":2506},[135,12171,12172,12175,12177],{"class":2476,"line":5250},[135,12173,12174],{"class":2488},"    source, target ",[135,12176,891],{"class":2480},[135,12178,12179],{"class":2488}," [], []\n",[135,12181,12182,12184,12187,12189,12191,12194,12196,12199,12201],{"class":2476,"line":5274},[135,12183,11447],{"class":2480},[135,12185,12186],{"class":2488}," i, line ",[135,12188,9531],{"class":2480},[135,12190,9694],{"class":9534},[135,12192,12193],{"class":2488},"(text.split(",[135,12195,10965],{"class":9549},[135,12197,12198],{"class":12027},"\\n",[135,12200,10965],{"class":9549},[135,12202,12203],{"class":2488},")):\n",[135,12205,12206,12208,12211,12213,12215,12217],{"class":2476,"line":5279},[135,12207,2579],{"class":2480},[135,12209,12210],{"class":2488}," num_examples ",[135,12212,11987],{"class":2480},[135,12214,9528],{"class":2488},[135,12216,11162],{"class":2480},[135,12218,12219],{"class":2488}," num_examples:\n",[135,12221,12222],{"class":2476,"line":5285},[135,12223,12224],{"class":2480},"            break\n",[135,12226,12227,12230,12232,12235,12237,12240,12242],{"class":2476,"line":5299},[135,12228,12229],{"class":2488},"        parts ",[135,12231,891],{"class":2480},[135,12233,12234],{"class":2488}," line.split(",[135,12236,10965],{"class":9549},[135,12238,12239],{"class":12027},"\\t",[135,12241,10965],{"class":9549},[135,12243,2554],{"class":2488},[135,12245,12246,12248,12250,12253,12255,12257],{"class":2476,"line":5304},[135,12247,2579],{"class":2480},[135,12249,9674],{"class":9534},[135,12251,12252],{"class":2488},"(parts) ",[135,12254,2585],{"class":2480},[135,12256,11141],{"class":2529},[135,12258,2533],{"class":2488},[135,12260,12261,12264,12266,12269,12271,12273],{"class":2476,"line":5310},[135,12262,12263],{"class":2488},"            source.append(parts[",[135,12265,1830],{"class":2529},[135,12267,12268],{"class":2488},"].split(",[135,12270,10965],{"class":9549},[135,12272,11996],{"class":9549},[135,12274,12275],{"class":2488},"))\n",[135,12277,12278,12281,12283,12285,12287,12289],{"class":2476,"line":5325},[135,12279,12280],{"class":2488},"            target.append(parts[",[135,12282,159],{"class":2529},[135,12284,12268],{"class":2488},[135,12286,10965],{"class":9549},[135,12288,11996],{"class":9549},[135,12290,12275],{"class":2488},[135,12292,12293,12295],{"class":2476,"line":9617},[135,12294,4760],{"class":2480},[135,12296,12297],{"class":2488}," source, target\n",[135,12299,12300],{"class":2476,"line":9623},[135,12301,2798],{"emptyLinePlaceholder":80},[135,12303,12304,12306,12309,12311,12314,12316,12319,12321,12323,12325,12328],{"class":2476,"line":9629},[135,12305,2481],{"class":2480},[135,12307,12308],{"class":2484}," load_data_nmt",[135,12310,874],{"class":2488},[135,12312,12313],{"class":2491},"batch_size",[135,12315,2495],{"class":2488},[135,12317,12318],{"class":2491},"num_steps",[135,12320,2495],{"class":2488},[135,12322,12150],{"class":2491},[135,12324,891],{"class":2480},[135,12326,12327],{"class":2529},"600",[135,12329,2501],{"class":2488},[135,12331,12332],{"class":2476,"line":9656},[135,12333,12334],{"class":2506},"    \"\"\"返回翻译数据集的迭代器和词表\n",[135,12336,12337],{"class":2476,"line":9684},[135,12338,2798],{"emptyLinePlaceholder":80},[135,12340,12341],{"class":2476,"line":9704},[135,12342,12343],{"class":2506},"    Defined in :numref:`subsec_mt_data_loading`\"\"\"\n",[135,12345,12346,12348,12350],{"class":2476,"line":9715},[135,12347,12017],{"class":2488},[135,12349,891],{"class":2480},[135,12351,12352],{"class":2488}," preprocess_nmt(read_data_nmt())\n",[135,12354,12355,12357,12359],{"class":2476,"line":9728},[135,12356,12174],{"class":2488},[135,12358,891],{"class":2480},[135,12360,12361],{"class":2488}," tokenize_nmt(text, num_examples)\n",[135,12363,12364,12367,12369,12372,12375,12377,12379],{"class":2476,"line":10231},[135,12365,12366],{"class":2488},"    src_vocab ",[135,12368,891],{"class":2480},[135,12370,12371],{"class":2488}," d2l.Vocab(source, ",[135,12373,12374],{"class":2545},"min_freq",[135,12376,891],{"class":2480},[135,12378,2894],{"class":2529},[135,12380,3899],{"class":2488},[135,12382,12383,12386,12388,12390,12392,12395,12397,12399,12401,12403,12405,12407,12409,12412,12414],{"class":2476,"line":10246},[135,12384,12385],{"class":2545},"                          reserved_tokens",[135,12387,891],{"class":2480},[135,12389,11436],{"class":2488},[135,12391,10965],{"class":9549},[135,12393,12394],{"class":9553},"\u003Cpad>",[135,12396,10965],{"class":9549},[135,12398,2495],{"class":2488},[135,12400,10965],{"class":9549},[135,12402,11537],{"class":9553},[135,12404,10965],{"class":9549},[135,12406,2495],{"class":2488},[135,12408,10965],{"class":9549},[135,12410,12411],{"class":9553},"\u003Ceos>",[135,12413,10965],{"class":9549},[135,12415,2606],{"class":2488},[135,12417,12418,12421,12423,12426,12428,12430,12432],{"class":2476,"line":10251},[135,12419,12420],{"class":2488},"    tgt_vocab ",[135,12422,891],{"class":2480},[135,12424,12425],{"class":2488}," d2l.Vocab(target, ",[135,12427,12374],{"class":2545},[135,12429,891],{"class":2480},[135,12431,2894],{"class":2529},[135,12433,3899],{"class":2488},[135,12435,12436,12438,12440,12442,12444,12446,12448,12450,12452,12454,12456,12458,12460,12462,12464],{"class":2476,"line":10266},[135,12437,12385],{"class":2545},[135,12439,891],{"class":2480},[135,12441,11436],{"class":2488},[135,12443,10965],{"class":9549},[135,12445,12394],{"class":9553},[135,12447,10965],{"class":9549},[135,12449,2495],{"class":2488},[135,12451,10965],{"class":9549},[135,12453,11537],{"class":9553},[135,12455,10965],{"class":9549},[135,12457,2495],{"class":2488},[135,12459,10965],{"class":9549},[135,12461,12411],{"class":9553},[135,12463,10965],{"class":9549},[135,12465,2606],{"class":2488},[135,12467,12468,12471,12473],{"class":2476,"line":10295},[135,12469,12470],{"class":2488},"    src_array, src_valid_len ",[135,12472,891],{"class":2480},[135,12474,12475],{"class":2488}," build_array_nmt(source, src_vocab, num_steps)\n",[135,12477,12478,12481,12483],{"class":2476,"line":10314},[135,12479,12480],{"class":2488},"    tgt_array, tgt_valid_len ",[135,12482,891],{"class":2480},[135,12484,12485],{"class":2488}," build_array_nmt(target, tgt_vocab, num_steps)\n",[135,12487,12488,12491,12493],{"class":2476,"line":10335},[135,12489,12490],{"class":2488},"    data_arrays ",[135,12492,891],{"class":2480},[135,12494,12495],{"class":2488}," (src_array, src_valid_len, tgt_array, tgt_valid_len)\n",[135,12497,12498,12501,12503],{"class":2476,"line":10355},[135,12499,12500],{"class":2488},"    data_iter ",[135,12502,891],{"class":2480},[135,12504,12505],{"class":2488}," d2l.load_array(data_arrays, batch_size)\n",[135,12507,12508,12510],{"class":2476,"line":10366},[135,12509,4760],{"class":2480},[135,12511,12512],{"class":2488}," data_iter, src_vocab, tgt_vocab\n",[14,12514,12515],{},"之后按照 transformer 架构创建编码器-解码器架构，",[2466,12517,12519],{"className":2468,"code":12518,"language":2470,"meta":65,"style":65},"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, device)\n",[2472,12520,12521,12550,12602,12617,12621,12631,12635,12645,12653,12658,12668,12675,12679,12689],{"__ignoreMap":65},[135,12522,12523,12526,12528,12531,12533,12535,12537,12540,12542,12545,12547],{"class":2476,"line":2477},[135,12524,12525],{"class":2488},"num_hiddens, num_layers, dropout, batch_size, num_steps ",[135,12527,891],{"class":2480},[135,12529,12530],{"class":2529}," 32",[135,12532,2495],{"class":2488},[135,12534,2894],{"class":2529},[135,12536,2495],{"class":2488},[135,12538,12539],{"class":2529},"0.1",[135,12541,2495],{"class":2488},[135,12543,12544],{"class":2529},"64",[135,12546,2495],{"class":2488},[135,12548,12549],{"class":2529},"10\n",[135,12551,12552,12555,12557,12560,12562,12565,12568,12570,12573,12575,12577,12579,12582,12585,12587,12590,12593,12595,12598,12600],{"class":2476,"line":66},[135,12553,12554],{"class":2488},"lr, num_epochs, device ",[135,12556,891],{"class":2480},[135,12558,12559],{"class":2529}," 0.005",[135,12561,2495],{"class":2488},[135,12563,12564],{"class":2529},"200",[135,12566,12567],{"class":2488},", torch.device(",[135,12569,10965],{"class":9549},[135,12571,12572],{"class":9553},"cuda:0",[135,12574,10965],{"class":9549},[135,12576,7219],{"class":2488},[135,12578,11102],{"class":2480},[135,12580,12581],{"class":2488}," torch.cuda.device_count() ",[135,12583,12584],{"class":2480},">=",[135,12586,2588],{"class":2529},[135,12588,12589],{"class":2480}," else",[135,12591,12592],{"class":2488}," torch.device(",[135,12594,10965],{"class":9549},[135,12596,12597],{"class":9553},"cpu",[135,12599,10965],{"class":9549},[135,12601,2554],{"class":2488},[135,12603,12604,12607,12609,12612,12614],{"class":2476,"line":2510},[135,12605,12606],{"class":2488},"ffn_num_hiddens, num_heads ",[135,12608,891],{"class":2480},[135,12610,12611],{"class":2529}," 64",[135,12613,2495],{"class":2488},[135,12615,12616],{"class":2529},"4\n",[135,12618,12619],{"class":2476,"line":2517},[135,12620,2798],{"emptyLinePlaceholder":80},[135,12622,12623,12626,12628],{"class":2476,"line":2536},[135,12624,12625],{"class":2488},"train_iter, src_vocab, tgt_vocab ",[135,12627,891],{"class":2480},[135,12629,12630],{"class":2488}," d2l.load_data_nmt(batch_size, num_steps)\n",[135,12632,12633],{"class":2476,"line":2557},[135,12634,2798],{"emptyLinePlaceholder":80},[135,12636,12637,12640,12642],{"class":2476,"line":2565},[135,12638,12639],{"class":2488},"encoder ",[135,12641,891],{"class":2480},[135,12643,12644],{"class":2488}," TransformerEncoder(\n",[135,12646,12647,12650],{"class":2476,"line":2576},[135,12648,12649],{"class":9534},"    len",[135,12651,12652],{"class":2488},"(src_vocab), num_hiddens, ffn_num_hiddens, num_heads, num_layers,\n",[135,12654,12655],{"class":2476,"line":2593},[135,12656,12657],{"class":2488},"    dropout)\n",[135,12659,12660,12663,12665],{"class":2476,"line":2609},[135,12661,12662],{"class":2488},"decoder ",[135,12664,891],{"class":2480},[135,12666,12667],{"class":2488}," TransformerDecoder(\n",[135,12669,12670,12672],{"class":2476,"line":2617},[135,12671,12649],{"class":9534},[135,12673,12674],{"class":2488},"(tgt_vocab), num_hiddens, ffn_num_hiddens, num_heads, num_layers,\n",[135,12676,12677],{"class":2476,"line":2634},[135,12678,12657],{"class":2488},[135,12680,12681,12684,12686],{"class":2476,"line":2640},[135,12682,12683],{"class":2488},"net ",[135,12685,891],{"class":2480},[135,12687,12688],{"class":2488}," EncoderDecoder(encoder, decoder)\n",[135,12690,12691],{"class":2476,"line":2665},[135,12692,12693],{"class":2488},"train_seq2seq(net, train_iter, lr, num_epochs, tgt_vocab, device)\n",[10,12695,12696],{"id":12696},"参考文献",[14,12698,12699],{},[31,12700,109],{"href":107,"rel":12701},[35],[14,12703,12704],{},[31,12705,103],{"href":101,"rel":12706},[35],[12708,12709,12710],"style",{},"html pre.shiki code .szJfE, html code.shiki .szJfE{--shiki-default:#D73A49;--shiki-dark:#FF79C6}html pre.shiki code .sCLZk, html code.shiki .sCLZk{--shiki-default:#6F42C1;--shiki-dark:#50FA7B}html pre.shiki code .scbbO, html code.shiki .scbbO{--shiki-default:#24292E;--shiki-dark:#F8F8F2}html pre.shiki code .syNf4, html code.shiki .syNf4{--shiki-default:#24292E;--shiki-default-font-style:inherit;--shiki-dark:#FFB86C;--shiki-dark-font-style:italic}html pre.shiki code .seLWX, html code.shiki .seLWX{--shiki-default:#032F62;--shiki-dark:#6272A4}html pre.shiki code .sfgPZ, html code.shiki .sfgPZ{--shiki-default:#6A737D;--shiki-dark:#6272A4}html pre.shiki code .soDru, html code.shiki .soDru{--shiki-default:#005CC5;--shiki-dark:#BD93F9}html pre.shiki code .sQkXh, html code.shiki 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html code.shiki .sMWOi{--shiki-default:#032F62;--shiki-dark:#E9F284}html pre.shiki code .sEzAm, html code.shiki .sEzAm{--shiki-default:#032F62;--shiki-dark:#F1FA8C}html pre.shiki code .sRfyP, html code.shiki .sRfyP{--shiki-default:#005CC5;--shiki-dark:#FF79C6}",{"title":65,"searchDepth":66,"depth":66,"links":12712},[12713,12714,12715,12719,12720,12721,12722,12723,12724,12725,12726],{"id":12,"depth":66,"text":12},{"id":113,"depth":66,"text":113},{"id":123,"depth":66,"text":123,"children":12716},[12717,12718],{"id":127,"depth":2510,"text":127},{"id":2943,"depth":2510,"text":2943},{"id":5335,"depth":66,"text":5335},{"id":7370,"depth":66,"text":7370},{"id":7866,"depth":66,"text":7866},{"id":8203,"depth":66,"text":8203},{"id":9117,"depth":66,"text":9118},{"id":9736,"depth":66,"text":9737},{"id":10743,"depth":66,"text":10743},{"id":12696,"depth":66,"text":12696},"距离首次学习 transformer 已经过去一年，内容忘的差不多了，决定复习一下。",{"date":12729,"image":12730,"alt":88,"tags":12731,"published":80},"30st Jan 2026","/blogs-img/blog1.jpg",[12732,12733],"deep-learning","学习笔记","/blogs/transformer",{"title":88,"description":12727},"blogs/1. transformer复习笔记","59tIbWfqdpJGJRh5PHVoEHC170F6vnech8kVXdG8MGw",{"id":12739,"title":12740,"body":12741,"description":44010,"extension":72,"meta":44011,"navigation":80,"ogImage":44013,"path":44017,"seo":44018,"stem":44019,"__hash__":44020},"content/blogs/2. PPO学习笔记.md","零基础速通 PPO 学习笔记",{"type":7,"value":12742,"toc":43997},[12743,12746,12749,12752,13260,13563,14012,14015,14018,14080,14419,18411,19012,19531,19535,19610,20274,20518,20637,20965,20968,21654,22793,22895,22898,25530,25636,27508,27512,27515,27549,30331,30334,30337,30340,31827,31830,31834,31837,31840,31975,33639,33642,33646,34289,34480,39005,39008,40053,40056,40061,40097,41388,41392,41395,42004,43988,43990],[10,12744,12745],{"id":12745},"学习背景",[14,12747,12748],{},"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。",[10,12750,12751],{"id":12751},"符号定义",[14,12753,12754,12755,12827,12828,12857,12858,12929,12930,12958,12959,12988,12989,13126,13127,13198,13199,13227,13228,13259],{},"在强化学习中，",[135,12756,12758,12776],{"className":12757},[138],[135,12759,12761],{"className":12760},[142],[144,12762,12763],{"xmlns":146},[148,12764,12765,12773],{},[151,12766,12767],{},[164,12768,12769,12771],{},[167,12770,31],{},[167,12772,853],{},[174,12774,12775],{"encoding":176},"a_t",[135,12777,12779],{"className":12778,"ariaHidden":182},[181],[135,12780,12782,12786],{"className":12781},[186],[135,12783],{"className":12784,"style":12785},[190],"height:0.5806em;vertical-align:-0.15em;",[135,12787,12789,12792],{"className":12788},[195],[135,12790,31],{"className":12791},[195,268],[135,12793,12795],{"className":12794},[272],[135,12796,12798,12819],{"className":12797},[207,208],[135,12799,12801,12816],{"className":12800},[212],[135,12802,12805],{"className":12803,"style":12804},[216],"height:0.2806em;",[135,12806,12807,12810],{"style":1327},[135,12808],{"className":12809,"style":616},[224],[135,12811,12813],{"className":12812},[229,230,231,232],[135,12814,853],{"className":12815},[195,268,232],[135,12817,303],{"className":12818},[302],[135,12820,12822],{"className":12821},[212],[135,12823,12825],{"className":12824,"style":1346},[216],[135,12826],{}," 一般表示 ",[135,12829,12831,12844],{"className":12830},[138],[135,12832,12834],{"className":12833},[142],[144,12835,12836],{"xmlns":146},[148,12837,12838,12842],{},[151,12839,12840],{},[167,12841,853],{},[174,12843,853],{"encoding":176},[135,12845,12847],{"className":12846,"ariaHidden":182},[181],[135,12848,12850,12854],{"className":12849},[186],[135,12851],{"className":12852,"style":12853},[190],"height:0.6151em;",[135,12855,853],{"className":12856},[195,268]," 时刻 Agent 采取的动作（action）；",[135,12859,12861,12880],{"className":12860},[138],[135,12862,12864],{"className":12863},[142],[144,12865,12866],{"xmlns":146},[148,12867,12868,12877],{},[151,12869,12870],{},[164,12871,12872,12875],{},[167,12873,12874],{},"s",[167,12876,853],{},[174,12878,12879],{"encoding":176},"s_t",[135,12881,12883],{"className":12882,"ariaHidden":182},[181],[135,12884,12886,12889],{"className":12885},[186],[135,12887],{"className":12888,"style":12785},[190],[135,12890,12892,12895],{"className":12891},[195],[135,12893,12874],{"className":12894},[195,268],[135,12896,12898],{"className":12897},[272],[135,12899,12901,12921],{"className":12900},[207,208],[135,12902,12904,12918],{"className":12903},[212],[135,12905,12907],{"className":12906,"style":12804},[216],[135,12908,12909,12912],{"style":1327},[135,12910],{"className":12911,"style":616},[224],[135,12913,12915],{"className":12914},[229,230,231,232],[135,12916,853],{"className":12917},[195,268,232],[135,12919,303],{"className":12920},[302],[135,12922,12924],{"className":12923},[212],[135,12925,12927],{"className":12926,"style":1346},[216],[135,12928],{}," 表示 ",[135,12931,12933,12946],{"className":12932},[138],[135,12934,12936],{"className":12935},[142],[144,12937,12938],{"xmlns":146},[148,12939,12940,12944],{},[151,12941,12942],{},[167,12943,853],{},[174,12945,853],{"encoding":176},[135,12947,12949],{"className":12948,"ariaHidden":182},[181],[135,12950,12952,12955],{"className":12951},[186],[135,12953],{"className":12954,"style":12853},[190],[135,12956,853],{"className":12957},[195,268]," 时刻 Agent 所处的状态（state）；",[135,12960,12962,12976],{"className":12961},[138],[135,12963,12965],{"className":12964},[142],[144,12966,12967],{"xmlns":146},[148,12968,12969,12973],{},[151,12970,12971],{},[167,12972,6815],{},[174,12974,12975],{"encoding":176},"\\pi",[135,12977,12979],{"className":12978,"ariaHidden":182},[181],[135,12980,12982,12985],{"className":12981},[186],[135,12983],{"className":12984,"style":423},[190],[135,12986,6815],{"className":12987,"style":517},[195,268]," 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 ",[135,12990,12992,13025],{"className":12991},[138],[135,12993,12995],{"className":12994},[142],[144,12996,12997],{"xmlns":146},[148,12998,12999,13022],{},[151,13000,13001,13003,13005,13011,13014,13020],{},[167,13002,6815],{},[537,13004,874],{"stretchy":873},[164,13006,13007,13009],{},[167,13008,31],{},[167,13010,853],{},[167,13012,13013],{"mathvariant":894},"∣",[164,13015,13016,13018],{},[167,13017,12874],{},[167,13019,853],{},[537,13021,888],{"stretchy":873},[174,13023,13024],{"encoding":176},"\\pi(a_t|s_t)",[135,13026,13028],{"className":13027,"ariaHidden":182},[181],[135,13029,13031,13034,13037,13040,13080,13083,13123],{"className":13030},[186],[135,13032],{"className":13033,"style":953},[190],[135,13035,6815],{"className":13036,"style":517},[195,268],[135,13038,874],{"className":13039},[199],[135,13041,13043,13046],{"className":13042},[195],[135,13044,31],{"className":13045},[195,268],[135,13047,13049],{"className":13048},[272],[135,13050,13052,13072],{"className":13051},[207,208],[135,13053,13055,13069],{"className":13054},[212],[135,13056,13058],{"className":13057,"style":12804},[216],[135,13059,13060,13063],{"style":1327},[135,13061],{"className":13062,"style":616},[224],[135,13064,13066],{"className":13065},[229,230,231,232],[135,13067,853],{"className":13068},[195,268,232],[135,13070,303],{"className":13071},[302],[135,13073,13075],{"className":13074},[212],[135,13076,13078],{"className":13077,"style":1346},[216],[135,13079],{},[135,13081,13013],{"className":13082},[195],[135,13084,13086,13089],{"className":13085},[195],[135,13087,12874],{"className":13088},[195,268],[135,13090,13092],{"className":13091},[272],[135,13093,13095,13115],{"className":13094},[207,208],[135,13096,13098,13112],{"className":13097},[212],[135,13099,13101],{"className":13100,"style":12804},[216],[135,13102,13103,13106],{"style":1327},[135,13104],{"className":13105,"style":616},[224],[135,13107,13109],{"className":13108},[229,230,231,232],[135,13110,853],{"className":13111},[195,268,232],[135,13113,303],{"className":13114},[302],[135,13116,13118],{"className":13117},[212],[135,13119,13121],{"className":13120,"style":1346},[216],[135,13122],{},[135,13124,888],{"className":13125},[389],"；",[135,13128,13130,13148],{"className":13129},[138],[135,13131,13133],{"className":13132},[142],[144,13134,13135],{"xmlns":146},[148,13136,13137,13145],{},[151,13138,13139],{},[164,13140,13141,13143],{},[167,13142,7899],{},[167,13144,853],{},[174,13146,13147],{"encoding":176},"r_t",[135,13149,13151],{"className":13150,"ariaHidden":182},[181],[135,13152,13154,13157],{"className":13153},[186],[135,13155],{"className":13156,"style":12785},[190],[135,13158,13160,13163],{"className":13159},[195],[135,13161,7899],{"className":13162,"style":3283},[195,268],[135,13164,13166],{"className":13165},[272],[135,13167,13169,13190],{"className":13168},[207,208],[135,13170,13172,13187],{"className":13171},[212],[135,13173,13175],{"className":13174,"style":12804},[216],[135,13176,13178,13181],{"style":13177},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[135,13179],{"className":13180,"style":616},[224],[135,13182,13184],{"className":13183},[229,230,231,232],[135,13185,853],{"className":13186},[195,268,232],[135,13188,303],{"className":13189},[302],[135,13191,13193],{"className":13192},[212],[135,13194,13196],{"className":13195,"style":1346},[216],[135,13197],{}," 一边表示 ",[135,13200,13202,13215],{"className":13201},[138],[135,13203,13205],{"className":13204},[142],[144,13206,13207],{"xmlns":146},[148,13208,13209,13213],{},[151,13210,13211],{},[167,13212,853],{},[174,13214,853],{"encoding":176},[135,13216,13218],{"className":13217,"ariaHidden":182},[181],[135,13219,13221,13224],{"className":13220},[186],[135,13222],{"className":13223,"style":12853},[190],[135,13225,853],{"className":13226},[195,268]," 时刻 Agent 采取行动获得的奖励（Reward）；",[135,13229,13231,13246],{"className":13230},[138],[135,13232,13234],{"className":13233},[142],[144,13235,13236],{"xmlns":146},[148,13237,13238,13243],{},[151,13239,13240],{},[167,13241,13242],{},"τ",[174,13244,13245],{"encoding":176},"\\tau",[135,13247,13249],{"className":13248,"ariaHidden":182},[181],[135,13250,13252,13255],{"className":13251},[186],[135,13253],{"className":13254,"style":423},[190],[135,13256,13242],{"className":13257,"style":13258},[195,268],"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。",[14,13261,13262],{},[135,13263,13265,13320],{"className":13264},[138],[135,13266,13268],{"className":13267},[142],[144,13269,13270],{"xmlns":146},[148,13271,13272,13317],{},[151,13273,13274,13276,13282,13284,13290,13292,13298,13300,13306,13308,13315],{},[537,13275,874],{"stretchy":873},[164,13277,13278,13280],{},[167,13279,12874],{},[157,13281,1830],{},[537,13283,879],{"separator":182},[164,13285,13286,13288],{},[167,13287,31],{},[157,13289,1830],{},[537,13291,879],{"separator":182},[164,13293,13294,13296],{},[167,13295,12874],{},[157,13297,159],{},[537,13299,879],{"separator":182},[164,13301,13302,13304],{},[167,13303,31],{},[157,13305,159],{},[537,13307,3043],{},[164,13309,13310,13312],{},[167,13311,12874],{},[167,13313,13314],{},"T",[537,13316,888],{"stretchy":873},[174,13318,13319],{"encoding":176},"(s_0,a_0,s_1,a_1 \\dots s_T)",[135,13321,13323],{"className":13322,"ariaHidden":182},[181],[135,13324,13326,13329,13332,13372,13375,13378,13418,13421,13424,13464,13467,13470,13510,13513,13516,13519,13560],{"className":13325},[186],[135,13327],{"className":13328,"style":953},[190],[135,13330,874],{"className":13331},[199],[135,13333,13335,13338],{"className":13334},[195],[135,13336,12874],{"className":13337},[195,268],[135,13339,13341],{"className":13340},[272],[135,13342,13344,13364],{"className":13343},[207,208],[135,13345,13347,13361],{"className":13346},[212],[135,13348,13350],{"className":13349,"style":3164},[216],[135,13351,13352,13355],{"style":1327},[135,13353],{"className":13354,"style":616},[224],[135,13356,13358],{"className":13357},[229,230,231,232],[135,13359,1830],{"className":13360},[195,232],[135,13362,303],{"className":13363},[302],[135,13365,13367],{"className":13366},[212],[135,13368,13370],{"className":13369,"style":1346},[216],[135,13371],{},[135,13373,879],{"className":13374},[988],[135,13376],{"className":13377,"style":992},[575],[135,13379,13381,13384],{"className":13380},[195],[135,13382,31],{"className":13383},[195,268],[135,13385,13387],{"className":13386},[272],[135,13388,13390,13410],{"className":13389},[207,208],[135,13391,13393,13407],{"className":13392},[212],[135,13394,13396],{"className":13395,"style":3164},[216],[135,13397,13398,13401],{"style":1327},[135,13399],{"className":13400,"style":616},[224],[135,13402,13404],{"className":13403},[229,230,231,232],[135,13405,1830],{"className":13406},[195,232],[135,13408,303],{"className":13409},[302],[135,13411,13413],{"className":13412},[212],[135,13414,13416],{"className":13415,"style":1346},[216],[135,13417],{},[135,13419,879],{"className":13420},[988],[135,13422],{"className":13423,"style":992},[575],[135,13425,13427,13430],{"className":13426},[195],[135,13428,12874],{"className":13429},[195,268],[135,13431,13433],{"className":13432},[272],[135,13434,13436,13456],{"className":13435},[207,208],[135,13437,13439,13453],{"className":13438},[212],[135,13440,13442],{"className":13441,"style":3164},[216],[135,13443,13444,13447],{"style":1327},[135,13445],{"className":13446,"style":616},[224],[135,13448,13450],{"className":13449},[229,230,231,232],[135,13451,159],{"className":13452},[195,232],[135,13454,303],{"className":13455},[302],[135,13457,13459],{"className":13458},[212],[135,13460,13462],{"className":13461,"style":1346},[216],[135,13463],{},[135,13465,879],{"className":13466},[988],[135,13468],{"className":13469,"style":992},[575],[135,13471,13473,13476],{"className":13472},[195],[135,13474,31],{"className":13475},[195,268],[135,13477,13479],{"className":13478},[272],[135,13480,13482,13502],{"className":13481},[207,208],[135,13483,13485,13499],{"className":13484},[212],[135,13486,13488],{"className":13487,"style":3164},[216],[135,13489,13490,13493],{"style":1327},[135,13491],{"className":13492,"style":616},[224],[135,13494,13496],{"className":13495},[229,230,231,232],[135,13497,159],{"className":13498},[195,232],[135,13500,303],{"className":13501},[302],[135,13503,13505],{"className":13504},[212],[135,13506,13508],{"className":13507,"style":1346},[216],[135,13509],{},[135,13511],{"className":13512,"style":992},[575],[135,13514,3043],{"className":13515},[1038],[135,13517],{"className":13518,"style":992},[575],[135,13520,13522,13525],{"className":13521},[195],[135,13523,12874],{"className":13524},[195,268],[135,13526,13528],{"className":13527},[272],[135,13529,13531,13552],{"className":13530},[207,208],[135,13532,13534,13549],{"className":13533},[212],[135,13535,13538],{"className":13536,"style":13537},[216],"height:0.3283em;",[135,13539,13540,13543],{"style":1327},[135,13541],{"className":13542,"style":616},[224],[135,13544,13546],{"className":13545},[229,230,231,232],[135,13547,13314],{"className":13548,"style":3258},[195,268,232],[135,13550,303],{"className":13551},[302],[135,13553,13555],{"className":13554},[212],[135,13556,13558],{"className":13557,"style":1346},[216],[135,13559],{},[135,13561,888],{"className":13562},[389],[14,13564,13565,13784,13785,390],{},[135,13566,13568,13614],{"className":13567},[138],[135,13569,13571],{"className":13570},[142],[144,13572,13573],{"xmlns":146},[148,13574,13575,13611],{},[151,13576,13577,13589,13591,13593,13595,13601,13603,13609],{},[164,13578,13579,13581],{},[167,13580,12874],{},[151,13582,13583,13585,13587],{},[167,13584,853],{},[537,13586,5850],{},[157,13588,159],{},[537,13590,891],{},[167,13592,11730],{},[537,13594,874],{"stretchy":873},[164,13596,13597,13599],{},[167,13598,12874],{},[167,13600,853],{},[537,13602,879],{"separator":182},[164,13604,13605,13607],{},[167,13606,31],{},[167,13608,853],{},[537,13610,888],{"stretchy":873},[174,13612,13613],{"encoding":176}," s_{t+1} = f(s_t,a_t)",[135,13615,13617,13682],{"className":13616,"ariaHidden":182},[181],[135,13618,13620,13624,13673,13676,13679],{"className":13619},[186],[135,13621],{"className":13622,"style":13623},[190],"height:0.6389em;vertical-align:-0.2083em;",[135,13625,13627,13630],{"className":13626},[195],[135,13628,12874],{"className":13629},[195,268],[135,13631,13633],{"className":13632},[272],[135,13634,13636,13665],{"className":13635},[207,208],[135,13637,13639,13662],{"className":13638},[212],[135,13640,13642],{"className":13641,"style":3164},[216],[135,13643,13644,13647],{"style":1327},[135,13645],{"className":13646,"style":616},[224],[135,13648,13650],{"className":13649},[229,230,231,232],[135,13651,13653,13656,13659],{"className":13652},[195,232],[135,13654,853],{"className":13655},[195,268,232],[135,13657,5850],{"className":13658},[629,232],[135,13660,159],{"className":13661},[195,232],[135,13663,303],{"className":13664},[302],[135,13666,13668],{"className":13667},[212],[135,13669,13671],{"className":13670,"style":7011},[216],[135,13672],{},[135,13674],{"className":13675,"style":576},[575],[135,13677,891],{"className":13678},[580],[135,13680],{"className":13681,"style":576},[575],[135,13683,13685,13688,13692,13695,13735,13738,13741,13781],{"className":13684},[186],[135,13686],{"className":13687,"style":953},[190],[135,13689,11730],{"className":13690,"style":13691},[195,268],"margin-right:0.10764em;",[135,13693,874],{"className":13694},[199],[135,13696,13698,13701],{"className":13697},[195],[135,13699,12874],{"className":13700},[195,268],[135,13702,13704],{"className":13703},[272],[135,13705,13707,13727],{"className":13706},[207,208],[135,13708,13710,13724],{"className":13709},[212],[135,13711,13713],{"className":13712,"style":12804},[216],[135,13714,13715,13718],{"style":1327},[135,13716],{"className":13717,"style":616},[224],[135,13719,13721],{"className":13720},[229,230,231,232],[135,13722,853],{"className":13723},[195,268,232],[135,13725,303],{"className":13726},[302],[135,13728,13730],{"className":13729},[212],[135,13731,13733],{"className":13732,"style":1346},[216],[135,13734],{},[135,13736,879],{"className":13737},[988],[135,13739],{"className":13740,"style":992},[575],[135,13742,13744,13747],{"className":13743},[195],[135,13745,31],{"className":13746},[195,268],[135,13748,13750],{"className":13749},[272],[135,13751,13753,13773],{"className":13752},[207,208],[135,13754,13756,13770],{"className":13755},[212],[135,13757,13759],{"className":13758,"style":12804},[216],[135,13760,13761,13764],{"style":1327},[135,13762],{"className":13763,"style":616},[224],[135,13765,13767],{"className":13766},[229,230,231,232],[135,13768,853],{"className":13769},[195,268,232],[135,13771,303],{"className":13772},[302],[135,13774,13776],{"className":13775},[212],[135,13777,13779],{"className":13778,"style":1346},[216],[135,13780],{},[135,13782,888],{"className":13783},[389]," 或者 ",[135,13786,13788,13838],{"className":13787},[138],[135,13789,13791],{"className":13790},[142],[144,13792,13793],{"xmlns":146},[148,13794,13795,13835],{},[151,13796,13797,13809,13811,13813,13815,13817,13819,13825,13827,13833],{},[164,13798,13799,13801],{},[167,13800,12874],{},[151,13802,13803,13805,13807],{},[167,13804,853],{},[537,13806,5850],{},[157,13808,159],{},[537,13810,891],{},[167,13812,5677],{},[537,13814,874],{"stretchy":873},[537,13816,1892],{},[167,13818,13013],{"mathvariant":894},[164,13820,13821,13823],{},[167,13822,12874],{},[167,13824,853],{},[537,13826,879],{"separator":182},[164,13828,13829,13831],{},[167,13830,31],{},[167,13832,853],{},[537,13834,888],{"stretchy":873},[174,13836,13837],{"encoding":176},"s_{t+1} = P(\\cdot|s_t,a_t)",[135,13839,13841,13905],{"className":13840,"ariaHidden":182},[181],[135,13842,13844,13847,13896,13899,13902],{"className":13843},[186],[135,13845],{"className":13846,"style":13623},[190],[135,13848,13850,13853],{"className":13849},[195],[135,13851,12874],{"className":13852},[195,268],[135,13854,13856],{"className":13855},[272],[135,13857,13859,13888],{"className":13858},[207,208],[135,13860,13862,13885],{"className":13861},[212],[135,13863,13865],{"className":13864,"style":3164},[216],[135,13866,13867,13870],{"style":1327},[135,13868],{"className":13869,"style":616},[224],[135,13871,13873],{"className":13872},[229,230,231,232],[135,13874,13876,13879,13882],{"className":13875},[195,232],[135,13877,853],{"className":13878},[195,268,232],[135,13880,5850],{"className":13881},[629,232],[135,13883,159],{"className":13884},[195,232],[135,13886,303],{"className":13887},[302],[135,13889,13891],{"className":13890},[212],[135,13892,13894],{"className":13893,"style":7011},[216],[135,13895],{},[135,13897],{"className":13898,"style":576},[575],[135,13900,891],{"className":13901},[580],[135,13903],{"className":13904,"style":576},[575],[135,13906,13908,13911,13914,13917,13920,13923,13963,13966,13969,14009],{"className":13907},[186],[135,13909],{"className":13910,"style":953},[190],[135,13912,5677],{"className":13913,"style":3258},[195,268],[135,13915,874],{"className":13916},[199],[135,13918,1892],{"className":13919},[195],[135,13921,13013],{"className":13922},[195],[135,13924,13926,13929],{"className":13925},[195],[135,13927,12874],{"className":13928},[195,268],[135,13930,13932],{"className":13931},[272],[135,13933,13935,13955],{"className":13934},[207,208],[135,13936,13938,13952],{"className":13937},[212],[135,13939,13941],{"className":13940,"style":12804},[216],[135,13942,13943,13946],{"style":1327},[135,13944],{"className":13945,"style":616},[224],[135,13947,13949],{"className":13948},[229,230,231,232],[135,13950,853],{"className":13951},[195,268,232],[135,13953,303],{"className":13954},[302],[135,13956,13958],{"className":13957},[212],[135,13959,13961],{"className":13960,"style":1346},[216],[135,13962],{},[135,13964,879],{"className":13965},[988],[135,13967],{"className":13968,"style":992},[575],[135,13970,13972,13975],{"className":13971},[195],[135,13973,31],{"className":13974},[195,268],[135,13976,13978],{"className":13977},[272],[135,13979,13981,14001],{"className":13980},[207,208],[135,13982,13984,13998],{"className":13983},[212],[135,13985,13987],{"className":13986,"style":12804},[216],[135,13988,13989,13992],{"style":1327},[135,13990],{"className":13991,"style":616},[224],[135,13993,13995],{"className":13994},[229,230,231,232],[135,13996,853],{"className":13997},[195,268,232],[135,13999,303],{"className":14000},[302],[135,14002,14004],{"className":14003},[212],[135,14005,14007],{"className":14006,"style":1346},[216],[135,14008],{},[135,14010,888],{"className":14011},[389],[14,14013,14014],{},"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。",[10,14016,14017],{"id":14017},"训练目标",[14,14019,14020,14021,14049,14050,14079],{},"训练一个 Policy 神经网络 ",[135,14022,14024,14037],{"className":14023},[138],[135,14025,14027],{"className":14026},[142],[144,14028,14029],{"xmlns":146},[148,14030,14031,14035],{},[151,14032,14033],{},[167,14034,6815],{},[174,14036,12975],{"encoding":176},[135,14038,14040],{"className":14039,"ariaHidden":182},[181],[135,14041,14043,14046],{"className":14042},[186],[135,14044],{"className":14045,"style":423},[190],[135,14047,6815],{"className":14048,"style":517},[195,268],"，在所有状态 ",[135,14051,14053,14066],{"className":14052},[138],[135,14054,14056],{"className":14055},[142],[144,14057,14058],{"xmlns":146},[148,14059,14060,14064],{},[151,14061,14062],{},[167,14063,7918],{},[174,14065,7918],{"encoding":176},[135,14067,14069],{"className":14068,"ariaHidden":182},[181],[135,14070,14072,14076],{"className":14071},[186],[135,14073],{"className":14074,"style":14075},[190],"height:0.6833em;",[135,14077,7918],{"className":14078,"style":6123},[195,268]," 下，给出相应的 Action，得到的 Return 的期望最大。",[14,14081,14082],{},[135,14083,14085,14162],{"className":14084},[138],[135,14086,14088],{"className":14087},[142],[144,14089,14090],{"xmlns":146},[148,14091,14092,14159],{},[151,14093,14094,14096,14098,14100,14102,14104,14106,14130,14132,14139,14141,14143,14145,14147,14153,14155,14157],{},[167,14095,5680],{},[537,14097,874],{"stretchy":873},[167,14099,546],{},[537,14101,874],{"stretchy":873},[167,14103,13242],{},[537,14105,888],{"stretchy":873},[164,14107,14108,14110],{},[537,14109,888],{"stretchy":873},[151,14111,14112,14114,14117,14124,14126,14128],{},[167,14113,13242],{},[537,14115,14116],{},"∼",[164,14118,14119,14121],{},[167,14120,5677],{},[167,14122,14123],{},"θ",[537,14125,874],{"stretchy":873},[167,14127,13242],{},[537,14129,888],{"stretchy":873},[537,14131,891],{},[14133,14134,14135,14137],"munder",{},[537,14136,1902],{},[167,14138,13242],{},[167,14140,546],{},[537,14142,874],{"stretchy":873},[167,14144,13242],{},[537,14146,888],{"stretchy":873},[164,14148,14149,14151],{},[167,14150,5677],{},[167,14152,14123],{},[537,14154,874],{"stretchy":873},[167,14156,13242],{},[537,14158,888],{"stretchy":873},[174,14160,14161],{"encoding":176}," E (R(\\tau))_{\\tau \\sim P_{\\theta}(\\tau)} = \\sum\\limits_\\tau 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},[151,15130,15131,15133,15135],{},[167,15132,411],{},[537,15134,891],{},[157,15136,159],{},[167,15138,7395],{},[14755,15140,15141,15143,15151],{},[537,15142,1902],{},[151,15144,15145,15147,15149],{},[167,15146,853],{},[537,15148,891],{},[157,15150,159],{},[164,15152,15153,15155],{},[167,15154,13314],{},[167,15156,411],{},[167,15158,546],{},[537,15160,874],{"stretchy":873},[541,15162,15163,15165],{},[167,15164,13242],{},[167,15166,411],{},[537,15168,888],{"stretchy":873},[167,15170,14452],{"mathvariant":894},[167,15172,14877],{},[537,15174,898],{},[164,15176,15177,15179],{},[167,15178,5677],{},[167,15180,14123],{},[537,15182,874],{"stretchy":873},[1898,15184,15185,15187,15189],{},[167,15186,31],{},[167,15188,411],{},[167,15190,853],{},[167,15192,13013],{"mathvariant":894},[1898,15194,15195,15197,15199],{},[167,15196,12874],{},[167,15198,411],{},[167,15200,853],{},[537,15202,888],{"stretchy":873},[174,15204,15205],{"encoding":176},"\\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}",[135,15207,15209],{"className":15208,"ariaHidden":182},[181],[135,15210,15212,15216],{"className":15211},[186],[135,15213],{"className":15214,"style":15215},[190],"height:28.1646em;vertical-align:-13.8323em;",[135,15217,15219],{"className":15218},[195],[135,15220,15222,15446],{"className":15221},[14434],[135,15223,15226],{"className":15224},[15225],"col-align-r",[135,15227,15229,15437],{"className":15228},[207,208],[135,15230,15232,15434],{"className":15231},[212],[135,15233,15236,15362,15371,15380,15389,15398,15407,15416,15425],{"className":15234,"style":15235},[216],"height:14.3323em;",[135,15237,15239,15243],{"style":15238},"top:-17.1217em;",[135,15240],{"className":15241,"style":15242},[224],"height:3.8394em;",[135,15244,15246,15249,15252,15255,15258,15261,15264,15267],{"className":15245},[195],[135,15247,14452],{"className":15248},[195],[135,15250,5680],{"className":15251,"style":6123},[195,268],[135,15253,874],{"className":15254},[199],[135,15256,546],{"className":15257,"style":14181},[195,268],[135,15259,874],{"className":15260},[199],[135,15262,13242],{"className":15263,"style":13258},[195,268],[135,15265,888],{"className":15266},[389],[135,15268,15270,15273],{"className":15269},[389],[135,15271,888],{"className":15272},[389],[135,15274,15276],{"className":15275},[272],[135,15277,15279,15354],{"className":15278},[207,208],[135,15280,15282,15351],{"className":15281},[212],[135,15283,15285],{"className":15284,"style":282},[216],[135,15286,15287,15290],{"style":14211},[135,15288],{"className":15289,"style":616},[224],[135,15291,15293],{"className":15292},[229,230,231,232],[135,15294,15296,15299,15302,15342,15345,15348],{"className":15295},[195,232],[135,15297,13242],{"className":15298,"style":13258},[195,268,232],[135,15300,14116],{"className":15301},[580,232],[135,15303,15305,15308],{"className":15304},[195,232],[135,15306,5677],{"className":15307,"style":3258},[195,268,232],[135,15309,15311],{"className":15310},[272],[135,15312,15314,15334],{"className":15313},[207,208],[135,15315,15317,15331],{"className":15316},[212],[135,15318,15320],{"className":15319,"style":282},[216],[135,15321,15322,15325],{"style":14247},[135,15323],{"className":15324,"style":289},[224],[135,15326,15328],{"className":15327},[229,293,294,232],[135,15329,14123],{"className":15330,"style":3283},[195,268,232],[135,15332,303],{"className":15333},[302],[135,15335,15337],{"className":15336},[212],[135,15338,15340],{"className":15339,"style":310},[216],[135,15341],{},[135,15343,874],{"className":15344},[199,232],[135,15346,13242],{"className":15347,"style":13258},[195,268,232],[135,15349,888],{"className":15350},[389,232],[135,15352,303],{"className":15353},[302],[135,15355,15357],{"className":15356},[212],[135,15358,15360],{"className":15359,"style":6175},[216],[135,15361],{},[135,15363,15365,15368],{"style":15364},"top:-14.5217em;",[135,15366],{"className":15367,"style":15242},[224],[135,15369],{"className":15370},[195],[135,15372,15374,15377],{"style":15373},"top:-11.5447em;",[135,15375],{"className":15376,"style":15242},[224],[135,15378],{"className":15379},[195],[135,15381,15383,15386],{"style":15382},"top:-8.5677em;",[135,15384],{"className":15385,"style":15242},[224],[135,15387],{"className":15388},[195],[135,15390,15392,15395],{"style":15391},"top:-5.1894em;",[135,15393],{"className":15394,"style":15242},[224],[135,15396],{"className":15397},[195],[135,15399,15401,15404],{"style":15400},"top:-1.7939em;",[135,15402],{"className":15403,"style":15242},[224],[135,15405],{"className":15406},[195],[135,15408,15410,15413],{"style":15409},"top:1.6126em;",[135,15411],{"className":15412,"style":15242},[224],[135,15414],{"className":15415},[195],[135,15417,15419,15422],{"style":15418},"top:5.0192em;",[135,15420],{"className":15421,"style":15242},[224],[135,15423],{"className":15424},[195],[135,15426,15428,15431],{"style":15427},"top:8.4257em;",[135,15429],{"className":15430,"style":15242},[224],[135,15432],{"className":15433},[195],[135,15435,303],{"className":15436},[302],[135,15438,15440],{"className":15439},[212],[135,15441,15444],{"className":15442,"style":15443},[216],"height:13.8323em;",[135,15445],{},[135,15447,15450],{"className":15448},[15449],"col-align-l",[135,15451,15453,18403],{"className":15452},[207,208],[135,15454,15456,18400],{"className":15455},[212],[135,15457,15459,15599,15730,16028,16313,16723,17005,17473,17938],{"className":15458,"style":15235},[216],[135,15460,15461,15464],{"style":15238},[135,15462],{"className":15463,"style":15242},[224],[135,15465,15467,15470,15473,15476,15479,15482,15485,15535,15538,15541,15544,15547,15550,15590,15593,15596],{"className":15466},[195],[135,15468],{"className":15469},[195],[135,15471],{"className":15472,"style":576},[575],[135,15474,891],{"className":15475},[580],[135,15477],{"className":15478,"style":576},[575],[135,15480,14452],{"className":15481},[195],[135,15483],{"className":15484,"style":992},[575],[135,15486,15488],{"className"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= \\sum\\limits_{t=t'}^{T_n} \\gamma^{t-t'} r_{t'}^n = R_t^n",[135,19106,19108,19161,19472],{"className":19107,"ariaHidden":182},[181],[135,19109,19111,19114,19117,19120,19149,19152,19155,19158],{"className":19110},[186],[135,19112],{"className":19113,"style":953},[190],[135,19115,546],{"className":19116,"style":14181},[195,268],[135,19118,874],{"className":19119},[199],[135,19121,19123,19126],{"className":19122},[195],[135,19124,13242],{"className":19125,"style":13258},[195,268],[135,19127,19129],{"className":19128},[272],[135,19130,19132],{"className":19131},[207],[135,19133,19135],{"className":19134},[212],[135,19136,19138],{"className":19137,"style":16694},[216],[135,19139,19140,19143],{"style":612},[135,19141],{"className":19142,"style":616},[224],[135,19144,19146],{"className":19145},[229,230,231,232],[135,19147,411],{"className":19148},[195,268,232],[135,19150,888],{"className":19151},[389],[135,19153],{"className":19154,"style":576},[575],[135,19156,891],{"className":19157},[580],[135,19159],{"className":19160,"style":576},[575],[135,19162,19164,19168,19305,19308,19378,19463,19466,19469],{"className":19163},[186],[135,19165],{"className":19166,"style":19167},[190],"height:2.5334em;vertical-align:-0.994em;",[135,19169,19171],{"className":19170},[1027,14310],[135,19172,19174,19296],{"className":19173},[207,208],[135,19175,19177,19293],{"className":19176},[212],[135,19178,19180,19232,19242],{"className":19179,"style":18714},[216],[135,19181,19183,19186],{"style":19182},"top:-2.106em;margin-left:0em;",[135,19184],{"className":19185,"style":225},[224],[135,19187,19189],{"className":19188},[229,230,231,232],[135,19190,19192,19195,19198],{"className":19191},[195,232],[135,19193,853],{"className":19194},[195,268,232],[135,19196,891],{"className":19197},[580,232],[135,19199,19201,19204],{"className":19200},[195,232],[135,19202,853],{"className":19203},[195,268,232],[135,19205,19207],{"className":19206},[272],[135,19208,19210],{"className":19209},[207],[135,19211,19213],{"className":19212},[212],[135,19214,19217],{"className":19215,"style":19216},[216],"height:0.6828em;",[135,19218,19220,19223],{"style":19219},"top:-2.786em;margin-right:0.0714em;",[135,19221],{"className":19222,"style":289},[224],[135,19224,19226],{"className":19225},[229,293,294,232],[135,19227,19229],{"className":19228},[195,232],[135,19230,19056],{"className":19231},[195,232],[135,19233,19234,19237],{"style":254},[135,19235],{"className":19236,"style":225},[224],[135,19238,19239],{},[135,19240,1902],{"className":19241},[1027,1986,1987],[135,19243,19244,19247],{"style":18747},[135,19245],{"className":19246,"style":225},[224],[135,19248,19250],{"className":19249},[229,230,231,232],[135,19251,19253],{"className":19252},[195,232],[135,19254,19256,19259],{"className":19255},[195,232],[135,19257,13314],{"className":19258,"style":3258},[195,268,232],[135,19260,19262],{"className":19261},[272],[135,19263,19265,19285],{"className":19264},[207,208],[135,19266,19268,19282],{"className":19267},[212],[135,19269,19271],{"className":19270,"style":4375},[216],[135,19272,19273,19276],{"style":17284},[135,19274],{"className":19275,"style":289},[224],[135,19277,19279],{"className":19278},[229,293,294,232],[135,19280,411],{"className":19281},[195,268,232],[135,19283,303],{"className":19284},[302],[135,19286,19288],{"className":19287},[212],[135,19289,19291],{"className":19290,"style":4397},[216],[135,19292],{},[135,19294,303],{"className":19295},[302],[135,19297,19299],{"className":19298},[212],[135,19300,19303],{"className":19301,"style":19302},[216],"height:0.994em;",[135,19304],{},[135,19306],{"className":19307,"style":992},[575],[135,19309,19311,19315],{"className":19310},[195],[135,19312,19067],{"className":19313,"style":19314},[195,268],"margin-right:0.05556em;",[135,19316,19318],{"className":19317},[272],[135,19319,19321],{"className":19320},[207],[135,19322,19324],{"className":19323},[212],[135,19325,19328],{"className":19326,"style":19327},[216],"height:0.9425em;",[135,19329,19330,19333],{"style":612},[135,19331],{"className":19332,"style":616},[224],[135,19334,19336],{"className":19335},[229,230,231,232],[135,19337,19339,19342,19345],{"className":19338},[195,232],[135,19340,853],{"className":19341},[195,268,232],[135,19343,18437],{"className":19344},[629,232],[135,19346,19348,19351],{"className":19347},[195,232],[135,19349,853],{"className":19350},[195,268,232],[135,19352,19354],{"className":19353},[272],[135,19355,19357],{"className":19356},[207],[135,19358,19360],{"className":19359},[212],[135,19361,19364],{"className":19362,"style":19363},[216],"height:0.8278em;",[135,19365,19366,19369],{"style":1174},[135,19367],{"className":19368,"style":289},[224],[135,19370,19372],{"className":19371},[229,293,294,232],[135,19373,19375],{"className":19374},[195,232],[135,19376,19056],{"className":19377},[195,232],[135,19379,19381,19384],{"className":19380},[195],[135,19382,7899],{"className":19383,"style":3283},[195,268],[135,19385,19387],{"className":19386},[272],[135,19388,19390,19454],{"className":19389},[207,2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演员-评论家算法",[14,19536,19537,19538,19609],{},"为了衡量每个动作的相对好坏的情况，我们令奖励 ",[135,19539,19541,19559],{"className":19540},[138],[135,19542,19544],{"className":19543},[142],[144,19545,19546],{"xmlns":146},[148,19547,19548,19556],{},[151,19549,19550],{},[164,19551,19552,19554],{},[167,19553,546],{},[167,19555,853],{},[174,19557,19558],{"encoding":176},"R_t",[135,19560,19562],{"className":19561,"ariaHidden":182},[181],[135,19563,19565,19568],{"className":19564},[186],[135,19566],{"className":19567,"style":7047},[190],[135,19569,19571,19574],{"className":19570},[195],[135,19572,546],{"className":19573,"style":14181},[195,268],[135,19575,19577],{"className":19576},[272],[135,19578,19580,19601],{"className":19579},[207,208],[135,19581,19583,19598],{"className":19582},[212],[135,19584,19586],{"className":19585,"style":12804},[216],[135,19587,19589,19592],{"style":19588},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[135,19590],{"className":19591,"style":616},[224],[135,19593,19595],{"className":19594},[229,230,231,232],[135,19596,853],{"className":19597},[195,268,232],[135,19599,303],{"className":19600},[302],[135,19602,19604],{"className":19603},[212],[135,19605,19607],{"className":19606,"style":1346},[216],[135,19608],{}," 减去一个基准值。",[14,19611,19612],{},[135,19613,19615,19728],{"className":19614},[138],[135,19616,19618],{"className":19617},[142],[144,19619,19620],{"xmlns":146},[148,19621,19622,19725],{},[151,19623,19624,19630,19644,19662,19664,19672,19674,19677,19679,19687,19689,19691,19693,19695,19697,19703,19705,19713,19715,19723],{},[154,19625,19626,19628],{},[157,19627,159],{},[167,19629,7395],{},[1898,19631,19632,19634,19642],{},[537,19633,1902],{},[151,19635,19636,19638,19640],{},[167,19637,411],{},[537,19639,891],{},[157,19641,159],{},[167,19643,7395],{},[1898,19645,19646,19648,19656],{},[537,19647,1902],{},[151,19649,19650,19652,19654],{},[167,19651,853],{},[537,19653,891],{},[157,19655,159],{},[164,19657,19658,19660],{},[167,19659,13314],{},[167,19661,411],{},[537,19663,874],{"stretchy":873},[1898,19665,19666,19668,19670],{},[167,19667,546],{},[167,19669,853],{},[167,19671,411],{},[537,19673,18437],{},[167,19675,19676],{},"B",[537,19678,874],{"stretchy":873},[1898,19680,19681,19683,19685],{},[167,19682,12874],{},[167,19684,853],{},[167,19686,411],{},[537,19688,888],{"stretchy":873},[537,19690,888],{"stretchy":873},[167,19692,14452],{"mathvariant":894},[167,19694,14877],{},[537,19696,898],{},[164,19698,19699,19701],{},[167,19700,5677],{},[167,19702,14123],{},[537,19704,874],{"stretchy":873},[1898,19706,19707,19709,19711],{},[167,19708,31],{},[167,19710,853],{},[167,19712,411],{},[167,19714,13013],{"mathvariant":894},[1898,19716,19717,19719,19721],{},[167,19718,12874],{},[167,19720,853],{},[167,19722,411],{},[537,19724,888],{"stretchy":873},[174,19726,19727],{"encoding":176}," \\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)",[135,19729,19731,20042],{"className":19730,"ariaHidden":182},[181],[135,19732,19734,19737,19805,19808,19872,19875,19979,19982,20033,20036,20039],{"className":19733},[186],[135,19735],{"className":19736,"style":18554},[190],[135,19738,19740,19743,19802],{"className":19739},[195],[135,19741],{"className":19742},[199,200],[135,19744,19746],{"className":19745},[154],[135,19747,19749,19794],{"className":19748},[207,208],[135,19750,19752,19791],{"className":19751},[212],[135,19753,19755,19769,19777],{"className":19754,"style":217},[216],[135,19756,19757,19760],{"style":18578},[135,19758],{"className":19759,"style":225},[224],[135,19761,19763],{"className":19762},[229,230,231,232],[135,19764,19766],{"className":19765},[195,232],[135,19767,7395],{"className":19768,"style":7470},[195,268,232],[135,19770,19771,19774],{"style":350},[135,19772],{"className":19773,"style":225},[224],[135,19775],{"className":19776,"style":358},[357],[135,19778,19779,19782],{"style":361},[135,19780],{"className":19781,"style":225},[224],[135,19783,19785],{"className":19784},[229,230,231,232],[135,19786,19788],{"className":19787},[195,232],[135,19789,159],{"className":19790},[195,232],[135,19792,303],{"className":19793},[302],[135,19795,19797],{"className":19796},[212],[135,19798,19800],{"className":19799,"style":18622},[216],[135,19801],{},[135,19803],{"className":19804},[389,200],[135,19806],{"className":19807,"style":992},[575],[135,19809,19811],{"className":19810},[1027,14310],[135,19812,19814,19864],{"className":19813},[207,208],[135,19815,19817,19861],{"className":19816},[212],[135,19818,19820,19840,19850],{"className":19819,"style":18643},[216],[135,19821,19822,19825],{"style":18646},[135,19823],{"className":19824,"style":225},[224],[135,19826,19828],{"className":19827},[229,230,231,232],[135,19829,19831,19834,19837],{"className":19830},[195,232],[135,19832,411],{"className":19833},[195,268,232],[135,19835,891],{"className":19836},[580,232],[135,19838,159],{"className":19839},[195,232],[135,19841,19842,19845],{"style":254},[135,19843],{"className":19844,"style":225},[224],[135,19846,19847],{},[135,19848,1902],{"className":19849},[1027,1986,1987],[135,19851,19852,19855],{"style":18677},[135,19853],{"className":19854,"style":225},[224],[135,19856,19858],{"className":19857},[229,230,231,232],[135,19859,7395],{"className":19860,"style":7470},[195,268,232],[135,19862,303],{"className":19863},[302],[135,19865,19867],{"className":19866},[212],[135,19868,19870],{"className":19869,"style":18696},[216],[135,19871],{},[135,19873],{"className":19874,"style":992},[575],[135,19876,19878],{"className":19877},[1027,14310],[135,19879,19881,19971],{"className":19880},[207,208],[135,19882,19884,19968],{"className":19883},[212],[135,19885,19887,19907,19917],{"className":19886,"style":18714},[216],[135,19888,19889,19892],{"style":18646},[135,19890],{"className":19891,"style":225},[224],[135,19893,19895],{"className":19894},[229,230,231,232],[135,19896,19898,19901,19904],{"className":19897},[195,232],[135,19899,853],{"className":19900},[195,268,232],[135,19902,891],{"className":19903},[580,232],[135,19905,159],{"className":19906},[195,232],[135,19908,19909,19912],{"style":254},[135,19910],{"className":19911,"style":225},[224],[135,19913,19914],{},[135,19915,1902],{"className":19916},[1027,1986,1987],[135,19918,19919,19922],{"style":18747},[135,19920],{"className":19921,"style":225},[224],[135,19923,19925],{"className":19924},[229,230,231,232],[135,19926,19928],{"className":19927},[195,232],[135,19929,19931,19934],{"className":19930},[195,232],[135,19932,13314],{"className":19933,"style":3258},[195,268,232],[135,19935,19937],{"className":19936},[272],[135,19938,19940,19960],{"className":19939},[207,208],[135,19941,19943,19957],{"className":19942},[212],[135,19944,19946],{"className":19945,"style":4375},[216],[135,19947,19948,19951],{"style":17284},[135,19949],{"className":19950,"style":289},[224],[135,19952,19954],{"className":19953},[229,293,294,232],[135,19955,411],{"className":19956},[195,268,232],[135,19958,303],{"className":19959},[302],[135,19961,19963],{"className":19962},[212],[135,19964,19966],{"className":19965,"style":4397},[216],[135,19967],{},[135,19969,303],{"className":19970},[302],[135,19972,19974],{"className":19973},[212],[135,19975,19977],{"className":19976,"style":18696},[216],[135,19978],{},[135,19980,874],{"className":19981},[199],[135,19983,19985,19988],{"className":19984},[195],[135,19986,546],{"className":19987,"style":14181},[195,268],[135,19989,19991],{"className":19990},[272],[135,19992,19994,20025],{"className":19993},[207,208],[135,19995,19997,20022],{"className":19996},[212],[135,19998,20000,20011],{"className":19999,"style":16694},[216],[135,20001,20002,20005],{"style":19499},[135,20003],{"className":20004,"style":616},[224],[135,20006,20008],{"className":20007},[229,230,231,232],[135,20009,853],{"className":20010},[195,268,232],[135,20012,20013,20016],{"style":612},[135,20014],{"className":20015,"st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都是一次随机采样，方差很大，训练不稳定。我们引入 ",[135,20362,20364,20392],{"className":20363},[138],[135,20365,20367],{"className":20366},[142],[144,20368,20369],{"xmlns":146},[148,20370,20371,20389],{},[151,20372,20373,20379,20381,20383,20385,20387],{},[164,20374,20375,20377],{},[167,20376,535],{},[167,20378,14123],{},[537,20380,874],{"stretchy":873},[167,20382,12874],{},[537,20384,879],{"separator":182},[167,20386,31],{},[537,20388,888],{"stretchy":873},[174,20390,20391],{"encoding":176},"Q_\\theta(s,a)",[135,20393,20395],{"className":20394,"ariaHidden":182},[181],[135,20396,20398,20401,20441,20444,20447,20450,20453,20456],{"className":20397},[186],[135,20399],{"className":20400,"style":953},[190],[135,20402,20404,20407],{"className":20403},[195],[135,20405,535],{"className":20406},[195,268],[135,20408,20410],{"className":20409},[272],[135,20411,20413,20433],{"className":20412},[207,208],[135,20414,20416,20430],{"className":20415},[212],[135,20417,20419],{"className":20418,"style":1324},[216],[135,20420,20421,20424],{"style":1327},[135,20422],{"className":20423,"style":616},[224],[135,20425,20427],{"className":20426},[229,230,231,232],[135,20428,14123],{"className":20429,"style":3283},[195,268,232],[135,20431,303],{"className":20432},[302],[135,20434,20436],{"className":20435},[212],[135,20437,20439],{"className":20438,"style":1346},[216],[135,20440],{},[135,20442,874],{"className":20443},[199],[135,20445,12874],{"className":20446},[195,268],[135,20448,879],{"className":20449},[988],[135,20451],{"className":20452,"style":992},[575],[135,20454,31],{"className":20455},[195,268],[135,20457,888],{"className":20458},[389],"，表示在状态 ",[135,20461,20463,20476],{"className":20462},[138],[135,20464,20466],{"className":20465},[142],[144,20467,20468],{"xmlns":146},[148,20469,20470,20474],{},[151,20471,20472],{},[167,20473,12874],{},[174,20475,12874],{"encoding":176},[135,20477,20479],{"className":20478,"ariaHidden":182},[181],[135,20480,20482,20485],{"className":20481},[186],[135,20483],{"className":20484,"style":423},[190],[135,20486,12874],{"className":20487},[195,268],"，下，做出动作 ",[135,20490,20492,20505],{"className":20491},[138],[135,20493,20495],{"className":20494},[142],[144,20496,20497],{"xmlns":146},[148,20498,20499,20503],{},[151,20500,20501],{},[167,20502,31],{},[174,20504,31],{"encoding":176},[135,20506,20508],{"className":20507,"ariaHidden":182},[181],[135,20509,20511,20514],{"className":20510},[186],[135,20512],{"className":20513,"style":423},[190],[135,20515,31],{"className":20516},[195,268]," 后期望的回报，即动作价值函数。",[14,20519,20520,20521,20607,20608,20636],{},"令 ",[135,20522,20524,20548],{"className":20523},[138],[135,20525,20527],{"className":20526},[142],[144,20528,20529],{"xmlns":146},[148,20530,20531,20545],{},[151,20532,20533,20539,20541,20543],{},[164,20534,20535,20537],{},[167,20536,748],{},[167,20538,14123],{},[537,20540,874],{"stretchy":873},[167,20542,12874],{},[537,20544,888],{"stretchy":873},[174,20546,20547],{"encoding":176},"V_\\theta(s)",[135,20549,20551],{"className":20550,"ariaHidden":182},[181],[135,20552,20554,20557,20598,20601,20604],{"className":20553},[186],[135,20555],{"className":20556,"style":953},[190],[135,20558,20560,20563],{"className":20559},[195],[135,20561,748],{"className":20562,"style":778},[195,268],[135,20564,20566],{"className":20565},[272],[135,20567,20569,20590],{"className":20568},[207,208],[135,20570,20572,20587],{"className":20571},[212],[135,20573,20575],{"className":20574,"style":1324},[216],[135,20576,20578,20581],{"style":20577},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[135,20579],{"className":20580,"style":616},[224],[135,20582,20584],{"className":20583},[229,230,231,232],[135,20585,14123],{"className":20586,"style":3283},[195,268,232],[135,20588,303],{"className":20589},[302],[135,20591,20593],{"className":20592},[212],[135,20594,20596],{"className":20595,"style":1346},[216],[135,20597],{},[135,20599,874],{"className":20600},[199],[135,20602,12874],{"className":20603},[195,268],[135,20605,888],{"className":20606},[389]," 在状态 ",[135,20609,20611,20624],{"className":20610},[138],[135,20612,20614],{"className":20613},[142],[144,20615,20616],{"xmlns":146},[148,20617,20618,20622],{},[151,20619,20620],{},[167,20621,12874],{},[174,20623,12874],{"encoding":176},[135,20625,20627],{"className":20626,"ariaHidden":182},[181],[135,20628,20630,20633],{"className":20629},[186],[135,20631],{"className":20632,"style":423},[190],[135,20634,12874],{"className":20635},[195,268]," 下期望的回报，即状态价值函数",[14,20638,20639,20906,20907,20935,20936,20964],{},[135,20640,20642,20702],{"className":20641},[138],[135,20643,20645],{"className":20644},[142],[144,20646,20647],{"xmlns":146},[148,20648,20649,20699],{},[151,20650,20651,20657,20659,20661,20663,20665,20667,20669,20675,20677,20679,20681,20683,20685,20687,20693,20695,20697],{},[164,20652,20653,20655],{},[167,20654,850],{},[167,20656,14123],{},[537,20658,874],{"stretchy":873},[167,20660,12874],{},[537,20662,879],{"separator":182},[167,20664,31],{},[537,20666,888],{"stretchy":873},[537,20668,891],{},[164,20670,20671,20673],{},[167,20672,535],{},[167,20674,14123],{},[537,20676,874],{"stretchy":873},[167,20678,12874],{},[537,20680,879],{"separator":182},[167,20682,31],{},[537,20684,888],{"stretchy":873},[537,20686,18437],{},[164,20688,20689,20691],{},[167,20690,748],{},[167,20692,14123],{},[537,20694,874],{"stretchy":873},[167,20696,12874],{},[537,20698,888],{"stretchy":873},[174,20700,20701],{"encoding":176},"A_\\theta(s,a) = Q_\\theta(s,a) - V_\\theta(s)",[135,20703,20705,20778,20851],{"className":20704,"ariaHidden":182},[181],[135,20706,20708,20711,20751,20754,20757,20760,20763,20766,20769,20772,20775],{"className":20707},[186],[135,20709],{"className":20710,"style":953},[190],[135,20712,20714,20717],{"className":20713},[195],[135,20715,850],{"className":20716},[195,268],[135,20718,20720],{"className":20719},[272],[135,20721,20723,20743],{"className":20722},[207,208],[135,20724,20726,20740],{"className":20725},[212],[135,20727,20729],{"className":20728,"style":1324},[216],[135,20730,20731,20734],{"style":1327},[135,20732],{"className":20733,"style":616},[224],[135,20735,20737],{"className":20736},[229,230,231,232],[135,20738,14123],{"className":20739,"style":3283},[195,268,232],[135,20741,303],{"className":20742},[302],[135,20744,20746],{"className":20745},[212],[135,20747,20749],{"className":20748,"style":1346},[216],[135,20750],{},[135,20752,874],{"className":20753},[199],[135,20755,12874],{"className":20756},[195,268],[135,20758,879],{"className":20759},[988],[135,20761],{"className":20762,"style":992},[575],[135,20764,31],{"className":20765},[195,268],[135,20767,888],{"className":20768},[389],[135,20770],{"className":20771,"style":576},[575],[135,20773,891],{"className":20774},[580],[135,20776],{"className":20777,"style":576},[575],[135,20779,20781,20784,20824,20827,20830,20833,20836,20839,20842,20845,20848],{"className":20780},[186],[135,20782],{"className":20783,"style":953},[190],[135,20785,20787,20790],{"className":20786},[195],[135,20788,535],{"className":20789},[195,268],[135,20791,20793],{"className":20792},[272],[135,20794,20796,20816],{"className":20795},[207,208],[135,20797,20799,20813],{"className":20798},[212],[135,20800,20802],{"className":20801,"style":1324},[216],[135,20803,20804,20807],{"style":1327},[135,20805],{"className":20806,"style":616},[224],[135,20808,20810],{"className":20809},[229,230,231,232],[135,20811,14123],{"className":20812,"style":3283},[195,268,232],[135,20814,303],{"className":20815},[302],[135,20817,20819],{"className":20818},[212],[135,20820,20822],{"className":20821,"style":1346},[216],[135,20823],{},[135,20825,874],{"className":20826},[199],[135,20828,12874],{"className":20829},[195,268],[135,20831,879],{"className":20832},[988],[135,20834],{"className":20835,"style":992},[575],[135,20837,31],{"className":20838},[195,268],[135,20840,888],{"className":20841},[389],[135,20843],{"className":20844,"style":1948},[575],[135,20846,18437],{"className":20847},[629],[135,20849],{"className":20850,"style":1948},[575],[135,20852,20854,20857,20897,20900,20903],{"className":20853},[186],[135,20855],{"className":20856,"style":953},[190],[135,20858,20860,20863],{"className":20859},[195],[135,20861,748],{"className":20862,"style":778},[195,268],[135,20864,20866],{"className":20865},[272],[135,20867,20869,20889],{"className":20868},[207,208],[135,20870,20872,20886],{"className":20871},[212],[135,20873,20875],{"className":20874,"style":1324},[216],[135,20876,20877,20880],{"style":20577},[135,20878],{"className":20879,"style":616},[224],[135,20881,20883],{"className":20882},[229,230,231,232],[135,20884,14123],{"className":20885,"style":3283},[195,268,232],[135,20887,303],{"className":20888},[302],[135,20890,20892],{"className":20891},[212],[135,20893,20895],{"className":20894,"style":1346},[216],[135,20896],{},[135,20898,874],{"className":20899},[199],[135,20901,12874],{"className":20902},[195,268],[135,20904,888],{"className":20905},[389]," 表示优势函数（Advantage Function），衡量在状态 ",[135,20908,20910,20923],{"className":20909},[138],[135,20911,20913],{"className":20912},[142],[144,20914,20915],{"xmlns":146},[148,20916,20917,20921],{},[151,20918,20919],{},[167,20920,12874],{},[174,20922,12874],{"encoding":176},[135,20924,20926],{"className":20925,"ariaHidden":182},[181],[135,20927,20929,20932],{"className":20928},[186],[135,20930],{"className":20931,"style":423},[190],[135,20933,12874],{"className":20934},[195,268]," 下，动作 ",[135,20937,20939,20952],{"className":20938},[138],[135,20940,20942],{"className":20941},[142],[144,20943,20944],{"xmlns":146},[148,20945,20946,20950],{},[151,20947,20948],{},[167,20949,31],{},[174,20951,31],{"encoding":176},[135,20953,20955],{"className":20954,"ariaHidden":182},[181],[135,20956,20958,20961],{"className":20957},[186],[135,20959],{"className":20960,"style":423},[190],[135,20962,31],{"className":20963},[195,268]," 相对于平均水平的优势。",[14,20966,20967],{},"讲上述的公式改写为",[14,20969,20970],{},[135,20971,20973,21087],{"className":20972},[138],[135,20974,20976],{"className":20975},[142],[144,20977,20978],{"xmlns":146},[148,20979,20980,21084],{},[151,20981,20982,20990,21004,21022,21028,21030,21038,21040,21048,21050,21052,21054,21056,21062,21064,21072,21074,21082],{},[14446,20983,20984],{"scriptlevel":1830,"displaystyle":182},[154,20985,20986,20988],{},[157,20987,159],{},[167,20989,7395],{},[1898,20991,20992,20994,21002],{},[537,20993,1902],{},[151,20995,20996,20998,21000],{},[167,20997,411],{},[537,20999,891],{},[157,21001,159],{},[167,21003,7395],{},[1898,21005,21006,21008,21016],{},[537,21007,1902],{},[151,21009,21010,21012,21014],{},[167,21011,853],{},[537,21013,891],{},[157,21015,159],{},[164,21017,21018,21020],{},[167,21019,13314],{},[167,21021,411],{},[164,21023,21024,21026],{},[167,21025,850],{},[167,21027,14123],{},[537,21029,874],{"stretchy":873},[1898,21031,21032,21034,21036],{},[167,21033,12874],{},[167,21035,853],{},[167,21037,411],{},[537,21039,879],{"separator":182},[1898,21041,21042,21044,21046],{},[167,21043,31],{},[167,21045,853],{},[167,21047,411],{},[537,21049,888],{"stretchy":873},[167,21051,14452],{"mathvariant":894},[167,21053,14877],{},[537,21055,898],{},[164,21057,21058,21060],{},[167,21059,5677],{},[167,21061,14123],{},[537,21063,874],{"stretchy":873},[1898,21065,21066,21068,21070],{},[167,21067,31],{},[167,21069,853],{},[167,21071,411],{},[167,21073,13013],{"mathvariant":894},[1898,21075,21076,21078,21080],{},[167,21077,12874],{},[167,21079,853],{},[167,21081,411],{},[537,21083,888],{"stretchy":873},[174,21085,21086],{"encoding":176},"\\dfrac{1}{N}\\sum\\limits_{n=1}^N \\sum\\limits_{t=1}^{T_n} A_\\theta(s_t^n,a_t^n)\\nabla \\log P_\\theta(a_t^n|s_t^n)",[135,21088,21090],{"className":21089,"ariaHidden":182},[181],[135,21091,21093,21096,21158,21161,21225,21228,21332,21335,21375,21378,21429,21432,21435,21486,21489,21492,21495,21500,21503,21543,21546,21597,21600,21651],{"className":21092},[186],[135,21094],{"className":21095,"style":18554},[190],[135,21097,21099,21102,21155],{"className":21098},[195],[135,21100],{"className":21101},[199,200],[135,21103,21105],{"className":21104},[154],[135,21106,21108,21147],{"className":21107},[207,208],[135,21109,21111,21144],{"className":21110},[212],[135,21112,21114,21125,21133],{"className":21113,"style":16351},[216],[135,21115,21116,21119],{"style":15891},[135,21117],{"className":21118,"style":225},[224],[135,21120,21122],{"className":21121},[195],[135,21123,7395],{"className":21124,"style":7470},[195,268],[135,21126,21127,21130],{"style":350},[135,21128],{"className":21129,"style":225},[224],[135,21131],{"className":21132,"style":358},[357],[135,21134,21135,21138],{"style":15957},[135,21136],{"className":21137,"style":225},[224],[135,21139,21141],{"className":21140},[195],[135,21142,159],{"className":21143},[195],[135,21145,303],{"className":21146},[302],[135,21148,21150],{"className":21149},[212],[135,21151,21153],{"className":21152,"style":16391},[216],[135,21154],{},[135,21156],{"className":21157},[389,200],[135,21159],{"className":21160,"style":992},[575],[135,21162,21164],{"className":21163},[1027,14310],[135,21165,21167,21217],{"className":21166},[207,208],[135,21168,21170,21214],{"className":21169},[212],[135,21171,21173,21193,21203],{"className":21172,"style":18643},[216],[135,21174,21175,21178],{"style":18646},[135,21176],{"className":21177,"style":225},[224],[135,21179,21181],{"className":21180},[229,230,231,232],[135,21182,21184,21187,21190],{"className":21183},[195,232],[135,21185,411],{"className":21186},[195,268,232],[135,21188,891],{"className":21189},[580,232],[135,21191,159],{"className":21192},[195,232],[135,21194,21195,21198],{"style":254},[135,21196],{"className":21197,"style":225},[224],[135,21199,21200],{},[135,21201,1902],{"className":21202},[1027,1986,1987],[135,21204,21205,21208],{"style":18677},[135,21206],{"className":21207,"style":225},[224],[135,21209,21211],{"className":21210},[229,230,231,232],[135,21212,7395],{"className":21213,"style":7470},[195,268,232],[135,21215,303],{"className":21216},[302],[135,21218,21220],{"className":21219},[212],[135,21221,21223],{"className":21222,"style":18696},[216],[135,21224],{},[135,21226],{"className":21227,"style":992},[575],[135,21229,21231],{"className":21230},[1027,14310],[135,21232,21234,21324],{"className":21233},[207,208],[135,21235,21237,21321],{"className":21236},[212],[135,21238,21240,21260,21270],{"className":21239,"style":18714},[216],[135,21241,21242,21245],{"style":18646},[135,21243],{"className":21244,"style":225},[224],[135,21246,21248],{"className":21247},[229,230,231,232],[135,21249,21251,21254,21257],{"className":21250},[195,232],[135,21252,853],{"className":21253},[195,268,232],[135,21255,891],{"className":21256},[580,232],[135,21258,159],{"className":21259},[195,232],[135,21261,21262,21265],{"style":254},[135,21263],{"className":21264,"style":225},[224],[135,21266,21267],{},[135,21268,1902],{"className":21269},[1027,1986,1987],[135,21271,21272,21275],{"style":18747},[135,21273],{"className":21274,"style":225},[224],[135,21276,21278],{"className":21277},[229,230,231,232],[135,21279,21281],{"className":21280},[195,232],[135,21282,21284,21287],{"className":21283},[195,232],[135,21285,13314],{"className":21286,"style":3258},[195,268,232],[135,21288,21290],{"className":21289},[272],[135,21291,21293,21313],{"className":21292},[207,208],[135,21294,21296,21310],{"className":21295},[212],[135,21297,21299],{"className":21298,"style":4375},[216],[135,21300,21301,21304],{"style":17284},[135,21302],{"className":21303,"style":289},[224],[135,21305,21307],{"className":21306},[229,293,294,232],[135,21308,411],{"className":21309},[195,268,232],[135,21311,303],{"className":21312},[302],[135,21314,21316],{"className":21315},[212],[135,21317,21319],{"className":21318,"style":4397},[216],[135,21320],{},[135,21322,303],{"className":21323},[302],[135,21325,21327],{"className":21326},[212],[135,21328,21330],{"className":21329,"style":18696},[216],[135,21331],{},[135,21333],{"className":21334,"style":992},[575],[135,21336,21338,21341],{"className":21337},[195],[135,21339,850],{"className":21340},[195,268],[135,21342,21344],{"className":21343},[272],[135,21345,21347,21367],{"className":21346},[207,208],[135,21348,21350,21364],{"className":21349},[212],[135,21351,21353],{"className":21352,"style":1324},[216],[135,21354,21355,21358],{"style":1327},[135,21356],{"className":21357,"style":616},[224],[135,21359,21361],{"className":21360},[229,230,231,232],[135,21362,14123],{"className":21363,"style":3283},[195,268,232],[135,21365,303],{"className":21366},[302],[135,21368,21370],{"className":21369},[212],[135,21371,21373],{"className":21372,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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。",[14,22896,22897],{},"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。",[135,22899,22901],{"className":22900},[14422],[135,22902,22904,23354],{"className":22903},[138],[135,22905,22907],{"className":22906},[142],[144,22908,22909],{"xmlns":146,"display":9554},[148,22910,22911,23351],{},[151,22912,22913,22921,22923,22929,22931,22933,22935,22937,22943,22945,22947,22953,22955,22967,22969,22971,22977,22979,22985,22987,22989,22997,22999,23005,23007,23009,23011,23013,23019,23021,23023,23035,23037,23043,23049,23051,23063,23065,23067,23073,23075,23081,23083,23085,23093,23095,23101,23103,23105,23107,23109,23115,23117,23119,23122,23134,23136,23142,23144,23156,23158,23164,23170,23172,23184,23186,23188,23194,23196,23202,23204,23206,23218,23220,23228,23230,23236,23238,23240,23242,23244,23250,23252,23254,23256,23268,23270,23276,23278,23290,23292,23298,23300,23312,23314,23317,23319,23325,23327,23333,23335,23341,23343,23349],{},[1898,22914,22915,22917,22919],{},[167,22916,850],{},[167,22918,14123],{},[157,22920,159],{},[537,22922,874],{"stretchy":873},[164,22924,22925,22927],{},[167,22926,12874],{},[167,22928,853],{},[537,22930,879],{"separator":182},[167,22932,31],{},[537,22934,888],{"stretchy":873},[537,22936,891],{},[164,22938,22939,22941],{},[167,22940,7899],{},[167,22942,853],{},[537,22944,5850],{},[167,22946,19067],{},[164,22948,22949,22951],{},[167,22950,748],{},[167,22952,14123],{},[537,22954,874],{"stretchy":873},[164,22956,22957,22959],{},[167,22958,12874],{},[151,22960,22961,22963,22965],{},[167,22962,853],{},[537,22964,5850],{},[157,22966,159],{},[537,22968,888],{"stretchy":873},[537,22970,18437],{},[164,22972,22973,22975],{},[167,22974,748],{},[167,22976,14123],{},[537,22978,874],{"stretchy":873},[164,22980,22981,22983],{},[167,22982,12874],{},[167,22984,853],{},[537,22986,888],{"stretchy":873},[575,22988],{"linebreak":21725},[1898,22990,22991,22993,22995],{},[167,22992,850],{},[167,22994,14123],{},[157,22996,2894],{},[537,22998,874],{"stretchy":873},[164,23000,23001,23003],{},[167,23002,12874],{},[167,23004,853],{},[537,23006,879],{"separator":182},[167,23008,31],{},[537,23010,888],{"stretchy":873},[537,23012,891],{},[164,23014,23015,23017],{},[167,23016,7899],{},[167,23018,853],{},[537,23020,5850],{},[167,23022,19067],{},[164,23024,23025,23027],{},[167,23026,7899],{},[151,23028,23029,23031,23033],{},[167,23030,853],{},[537,23032,5850],{},[157,23034,159],{},[537,23036,5850],{},[541,23038,23039,23041],{},[167,23040,19067],{},[157,23042,2894],{},[164,23044,23045,23047],{},[167,23046,748],{},[167,23048,14123],{},[537,23050,874],{"stretchy":873},[164,23052,23053,23055],{},[167,23054,12874],{},[151,23056,23057,23059,23061],{},[167,23058,853],{},[537,23060,5850],{},[157,23062,2894],{},[537,23064,888],{"stretchy":873},[537,23066,18437],{},[164,23068,23069,23071],{},[167,23070,748],{},[167,23072,14123],{},[537,23074,874],{"stretchy":873},[164,23076,23077,23079],{},[167,23078,12874],{},[167,23080,853],{},[537,23082,888],{"stretchy":873},[575,23084],{"linebreak":21725},[1898,23086,23087,23089,23091],{},[167,23088,850],{},[167,23090,14123],{},[157,23092,4744],{},[537,23094,874],{"stretchy":873},[164,23096,23097,23099],{},[167,23098,12874],{},[167,23100,853],{},[537,23102,879],{"separator":182},[167,23104,31],{},[537,23106,888],{"stretchy":873},[537,23108,891],{},[164,23110,23111,23113],{},[167,23112,7899],{},[167,23114,853],{},[537,23116,5850],{},[167,23118,19067],{},[537,23120,23121],{},"∗",[164,23123,23124,23126],{},[167,23125,7899],{},[151,23127,23128,23130,23132],{},[167,23129,853],{},[537,23131,5850],{},[157,23133,159],{},[537,23135,5850],{},[541,23137,23138,23140],{},[167,23139,19067],{},[157,23141,2894],{},[537,23143,23121],{},[164,23145,23146,23148],{},[167,23147,7899],{},[151,23149,23150,23152,23154],{},[167,23151,853],{},[537,23153,5850],{},[157,23155,2894],{},[537,23157,5850],{},[541,23159,23160,23162],{},[167,23161,19067],{},[157,23163,4744],{},[164,23165,23166,23168],{},[167,23167,748],{},[167,23169,14123],{},[537,23171,874],{"stretchy":873},[164,23173,23174,23176],{},[167,23175,12874],{},[151,23177,23178,23180,23182],{},[167,23179,853],{},[537,23181,5850],{},[157,23183,4744],{},[537,23185,888],{"stretchy":873},[537,23187,18437],{},[164,23189,23190,23192],{},[167,23191,748],{},[167,23193,14123],{},[537,23195,874],{"stretchy":873},[164,23197,23198,23200],{},[167,23199,12874],{},[167,23201,853],{},[537,23203,888],{"stretchy":873},[575,23205],{"linebreak":21725},[151,23207,23208,23211],{},[167,23209,23210],{"mathvariant":894},"⋮",[23212,23213,23214],"mpadded",{"height":14438,"voffset":14438},[575,23215],{"mathbackground":23216,"width":14438,"height":23217},"black","1.5em",[575,23219],{"linebreak":21725},[1898,23221,23222,23224,23226],{},[167,23223,850],{},[167,23225,14123],{},[167,23227,13314],{},[537,23229,874],{"stretchy":873},[164,23231,23232,23234],{},[167,23233,12874],{},[167,23235,853],{},[537,23237,879],{"separator":182},[167,23239,31],{},[537,23241,888],{"stretchy":873},[537,23243,891],{},[164,23245,23246,23248],{},[167,23247,7899],{},[167,23249,853],{},[537,23251,5850],{},[167,23253,19067],{},[537,23255,23121],{},[164,23257,23258,23260],{},[167,23259,7899],{},[151,23261,23262,23264,23266],{},[167,23263,853],{},[537,23265,5850],{},[157,23267,159],{},[537,23269,5850],{},[541,23271,23272,23274],{},[167,23273,19067],{},[157,23275,2894],{},[537,23277,23121],{},[164,23279,23280,23282],{},[167,23281,7899],{},[151,23283,23284,23286,23288],{},[167,23285,853],{},[537,23287,5850],{},[157,23289,2894],{},[537,23291,5850],{},[541,23293,23294,23296],{},[167,23295,19067],{},[157,23297,4744],{},[537,23299,23121],{},[164,23301,23302,23304],{},[167,23303,7899],{},[151,23305,23306,23308,23310],{},[167,23307,853],{},[537,23309,5850],{},[157,23311,4744],{},[537,23313,5850],{},[537,23315,23316],{},"⋯",[537,23318,5850],{},[541,23320,23321,23323],{},[167,23322,19067],{},[167,23324,13314],{},[537,23326,23121],{},[164,23328,23329,23331],{},[167,23330,7899],{},[167,23332,13314],{},[537,23334,18437],{},[164,23336,23337,23339],{},[167,23338,748],{},[167,23340,14123],{},[537,23342,874],{"stretchy":873},[164,23344,23345,23347],{},[167,23346,12874],{},[167,23348,853],{},[537,23350,888],{"stretchy":873},[174,23352,23353],{"encoding":176}," 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 - V_\\theta(s_t)",[135,23355,23357,23480,23535,23648,23740,23743,23864,23919,23986,24125,24217,24220,24341,24396,24415,24479,24524,24588,24727,24819,24822,24840,24843,24966,25021,25039,25103,25147,25211,25255,25319,25338,25383,25438],{"className":23356,"ariaHidden":182},[181],[135,23358,23360,23364,23416,23419,23459,23462,23465,23468,23471,23474,23477],{"className":23359},[186],[135,23361],{"className":23362,"style":23363},[190],"height:1.1141em;vertical-align:-0.25em;",[135,23365,23367,23370],{"className":23366},[195],[135,23368,850],{"className":23369},[195,268],[135,23371,23373],{"className":23372},[272],[135,23374,23376,23408],{"className":23375},[207,208],[135,23377,23379,23405],{"className":23378},[212],[135,23380,23383,23394],{"className":23381,"style":23382},[216],"height:0.8641em;",[135,23384,23385,23388],{"style":17383},[135,23386],{"className":23387,"style":616},[224],[135,23389,23391],{"className":23390},[229,230,231,232],[135,23392,14123],{"className":23393,"style":3283},[195,268,232],[135,23395,23396,23399],{"style":16498},[135,23397],{"className":23398,"style":616},[224],[135,23400,23402],{"className":23401},[229,230,231,232],[135,23403,159],{"className":23404},[195,232],[135,23406,303],{"className":23407},[302],[135,23409,23411],{"className":23410},[212],[135,23412,23414],{"className":23413,"style":17413},[216],[135,23415],{},[135,23417,874],{"className":23418},[199],[135,23420,23422,23425],{"className":23421},[195],[135,23423,12874],{"className":23424},[195,268],[135,23426,23428],{"className":23427},[272],[135,23429,23431,23451],{"className":23430},[207,208],[135,23432,23434,23448],{"className":23433},[212],[135,23435,23437],{"className":23436,"style":12804},[216],[135,23438,23439,23442],{"style":1327},[135,23440],{"className":23441,"style":616},[224],[135,23443,23445],{"className":23444},[229,230,231,232],[135,23446,853],{"className":23447},[195,268,232],[135,23449,303],{"className":23450},[302],[135,23452,23454],{"className":23453},[212],[135,23455,23457],{"className":23456,"style":1346},[216],[135,23458],{},[135,23460,879],{"className":23461},[988],[135,23463],{"className":23464,"style":992},[575],[135,23466,31],{"className":23467},[195,268],[135,23469,888],{"className":23470},[389],[135,23472],{"className":23473,"style":576},[575],[135,23475,891],{"className":23476},[580],[135,23478],{"className":23479,"style":576},[575],[135,23481,23483,23486,23526,23529,23532],{"className":23482},[186],[135,23484],{"className":23485,"style":21984},[190],[135,23487,23489,23492],{"className":23488},[195],[135,23490,7899],{"className":23491,"style":3283},[195,268],[135,23493,23495],{"className":23494},[272],[135,23496,23498,23518],{"className":23497},[207,208],[135,23499,23501,23515],{"className":23500},[212],[135,23502,23504],{"className":23503,"style":12804},[216],[135,23505,23506,23509],{"style":13177},[135,23507],{"className":23508,"style":616},[224],[135,23510,23512],{"className":23511},[229,230,231,232],[135,23513,853],{"className":23514},[195,268,232],[135,23516,303],{"className":23517},[302],[135,23519,23521],{"className":23520},[212],[135,23522,23524],{"className":23523,"style":1346},[216],[135,23525],{},[135,23527],{"className":23528,"style":1948},[575],[135,23530,5850],{"className":23531},[629],[135,23533],{"className":23534,"style":1948},[575],[135,23536,23538,23541,23544,23584,23587,23636,23639,23642,23645],{"className":23537},[186],[135,23539],{"className":23540,"style":953},[190],[135,23542,19067],{"className":23543,"style":19314},[195,268],[135,23545,23547,23550],{"className":23546},[195],[135,23548,748],{"className":23549,"style":778},[195,268],[135,23551,23553],{"className":23552},[272],[135,23554,23556,23576],{"className":23555},[207,208],[135,23557,23559,23573],{"className":23558},[212],[135,23560,23562],{"className":23561,"style":1324},[216],[135,23563,23564,23567],{"style":20577},[135,23565],{"className":23566,"style":616},[224],[135,23568,23570],{"className":23569},[229,230,231,232],[135,23571,14123],{"className":23572,"style":3283},[195,268,232],[135,23574,303],{"className":23575},[302],[135,23577,23579],{"className":23578},[212],[135,23580,23582],{"className":23581,"style":1346},[216],[135,23583],{},[135,23585,874],{"className":23586},[199],[135,23588,23590,23593],{"className":23589},[195],[135,23591,12874],{"className":23592},[195,268],[135,23594,23596],{"className":23595},[272],[135,23597,23599,23628],{"className":23598},[207,208],[135,23600,23602,23625],{"className":23601},[212],[135,23603,23605],{"className":23604,"style":3164},[216],[135,23606,23607,23610],{"style":1327},[135,23608],{"className":23609,"style":616},[224],[135,23611,23613],{"className":23612},[229,230,231,232],[135,23614,23616,23619,23622],{"className":23615},[195,232],[135,23617,853],{"className":23618},[195,268,232],[135,23620,5850],{"className":23621},[629,232],[135,23623,159],{"className":23624},[195,232],[135,23626,303],{"className":23627},[302],[135,23629,23631],{"className":23630},[212],[135,23632,23634],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",[135,25534,25536,25555],{"className":25535},[138],[135,25537,25539],{"className":25538},[142],[144,25540,25541],{"xmlns":146},[148,25542,25543,25552],{},[151,25544,25545],{},[164,25546,25547,25550],{},[167,25548,25549],{},"δ",[167,25551,853],{},[174,25553,25554],{"encoding":176},"\\delta_t",[135,25556,25558],{"className":25557,"ariaHidden":182},[181],[135,25559,25561,25564],{"className":25560},[186],[135,25562],{"className":25563,"style":1305},[190],[135,25565,25567,25571],{"className":25566},[195],[135,25568,25549],{"className":25569,"style":25570},[195,268],"margin-right:0.03785em;",[135,25572,25574],{"className":25573},[272],[135,25575,25577,25598],{"className":25576},[207,208],[135,25578,25580,25595],{"className":25579},[212],[135,25581,25583],{"className":25582,"style":12804},[216],[135,25584,25586,25589],{"style":25585},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[135,25587],{"className":25588,"style":616},[224],[135,25590,25592],{"className":25591},[229,230,231,232],[135,25593,853],{"className":25594},[195,268,232],[135,25596,303],{"className":25597},[302],[135,25599,25601],{"className":25600},[212],[135,25602,25604],{"className":25603,"style":1346},[216],[135,25605],{}," 表示在第 ",[135,25608,25610,25623],{"className":25609},[138],[135,25611,25613],{"className":25612},[142],[144,25614,25615],{"xmlns":146},[148,25616,25617,25621],{},[151,25618,25619],{},[167,25620,853],{},[174,25622,853],{"encoding":176},[135,25624,25626],{"className":25625,"ariaHidden":182},[181],[135,25627,25629,25632],{"className":25628},[186],[135,25630],{"className":25631,"style":12853},[190],[135,25633,853],{"className":25634},[195,268]," 步采取特定动作带来的优势。",[135,25637,25639],{"className":25638},[14422],[135,25640,25642,25968],{"className":25641},[138],[135,25643,25645],{"className":25644},[142],[144,25646,25647],{"xmlns":146,"display":9554},[148,25648,25649,25965],{},[151,25650,25651,25659,25661,25667,25669,25671,25673,25679,25681,25693,25695,25697,25703,25705,25711,25713,25715,25729,25731,25743,25745,25747,25749,25755,25757,25769,25771,25773,25779,25781,25793,25795,25797,25805,25807,25813,25815,25817,25819,25821,25829,25831,25839,25841,25847,25849,25851,25853,25855,25863,25865,25867,25881,25883,25891,25893,25899,25901,25903,25905,25907,25915,25917,25919,25933,25935,25941,25955,25957],{},[1898,25652,25653,25655,25657],{},[167,25654,25549],{},[167,25656,853],{},[167,25658,748],{},[537,25660,891],{},[164,25662,25663,25665],{},[167,25664,7899],{},[167,25666,853],{},[537,25668,5850],{},[167,25670,19067],{},[537,25672,23121],{},[164,25674,25675,25677],{},[167,25676,748],{},[167,25678,14123],{},[537,25680,874],{"stretchy":873},[164,25682,25683,25685],{},[167,25684,12874],{},[151,25686,25687,25689,25691],{},[167,25688,853],{},[537,25690,5850],{},[157,25692,159],{},[537,25694,888],{"stretchy":873},[537,25696,18437],{},[164,25698,25699,25701],{},[167,25700,748],{},[167,25702,14123],{},[537,25704,874],{"stretchy":873},[164,25706,25707,25709],{},[167,25708,12874],{},[167,25710,853],{},[537,25712,888],{"stretchy":873},[575,25714],{"linebreak":21725},[1898,25716,25717,25719,25727],{},[167,25718,25549],{},[151,25720,25721,25723,25725],{},[167,25722,853],{},[537,25724,5850],{},[157,25726,159],{},[167,25728,748],{},[537,25730,891],{},[164,25732,25733,25735],{},[167,25734,7899],{},[151,25736,25737,25739,25741],{},[167,25738,853],{},[537,25740,5850],{},[157,25742,159],{},[537,25744,5850],{},[167,25746,19067],{},[537,25748,23121],{},[164,25750,25751,25753],{},[167,25752,748],{},[167,25754,14123],{},[537,25756,874],{"stretchy":873},[164,25758,25759,25761],{},[167,25760,12874],{},[151,25762,25763,25765,25767],{},[167,25764,853],{},[537,25766,5850],{},[157,25768,2894],{},[537,25770,888],{"stretchy":873},[537,25772,18437],{},[164,25774,25775,25777],{},[167,25776,748],{},[167,25778,14123],{},[537,25780,874],{"stretchy":873},[164,25782,25783,25785],{},[167,25784,12874],{},[151,25786,25787,25789,25791],{},[167,25788,853],{},[537,25790,5850],{},[157,25792,159],{},[537,25794,888],{"stretchy":873},[575,25796],{"linebreak":21725},[1898,25798,25799,25801,25803],{},[167,25800,850],{},[167,25802,14123],{},[157,25804,159],{},[537,25806,874],{"stretchy":873},[164,25808,25809,25811],{},[167,25810,12874],{},[167,25812,853],{},[537,25814,879],{"separator":182},[167,25816,31],{},[537,25818,888],{"stretchy":873},[537,25820,891],{},[1898,25822,25823,25825,25827],{},[167,25824,25549],{},[167,25826,853],{},[167,25828,748],{},[575,25830],{"linebreak":21725},[1898,25832,25833,25835,25837],{},[167,25834,850],{},[167,25836,14123],{},[157,25838,2894],{},[537,25840,874],{"stretchy":873},[164,25842,25843,25845],{},[167,25844,12874],{},[167,25846,853],{},[537,25848,879],{"separator":182},[167,25850,31],{},[537,25852,888],{"stretchy":873},[537,25854,891],{},[1898,25856,25857,25859,25861],{},[167,25858,25549],{},[167,25860,853],{},[167,25862,748],{},[537,25864,5850],{},[167,25866,19067],{},[1898,25868,25869,25871,25879],{},[167,25870,25549],{},[151,25872,25873,25875,25877],{},[167,25874,853],{},[537,25876,5850],{},[157,25878,159],{},[167,25880,748],{},[575,25882],{"linebreak":21725},[1898,25884,25885,25887,25889],{},[167,25886,850],{},[167,25888,14123],{},[157,25890,4744],{},[537,25892,874],{"stretchy":873},[164,25894,25895,25897],{},[167,25896,12874],{},[167,25898,853],{},[537,25900,879],{"separator":182},[167,25902,31],{},[537,25904,888],{"stretchy":873},[537,25906,891],{},[1898,25908,25909,25911,25913],{},[167,25910,25549],{},[167,25912,853],{},[167,25914,748],{},[537,25916,5850],{},[167,25918,19067],{},[1898,25920,25921,25923,25931],{},[167,25922,25549],{},[151,25924,25925,25927,25929],{},[167,25926,853],{},[537,25928,5850],{},[157,25930,159],{},[167,25932,748],{},[537,25934,5850],{},[541,25936,25937,25939],{},[167,25938,19067],{},[157,25940,2894],{},[1898,25942,25943,25945,25953],{},[167,25944,25549],{},[151,25946,25947,25949,25951],{},[167,25948,853],{},[537,25950,5850],{},[157,25952,2894],{},[167,25954,748],{},[575,25956],{"linebreak":21725},[151,25958,25959,25961],{},[167,25960,23210],{"mathvariant":894},[23212,25962,25963],{"height":14438,"voffset":14438},[575,25964],{"mathbackground":23216,"width":14438,"height":23217},[174,25966,25967],{"encoding":176},"\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",[135,25969,25971,26039,26094,26112,26222,26314,26317,26394,26458,26476,26586,26687,26690,26811,26868,26871,26992,27058,27127,27130,27251,27317,27395,27490,27493],{"className":25970,"ariaHidden":182},[181],[135,25972,25974,25978,26030,26033,26036],{"className":25973},[186],[135,25975],{"className":25976,"style":25977},[190],"height:1.1383em;vertical-align:-0.247em;",[135,25979,25981,25984],{"className":25980},[195],[135,25982,25549],{"className":25983,"style":25570},[195,268],[135,25985,25987],{"className":25986},[272],[135,25988,25990,26022],{"className":25989},[207,208],[135,25991,25993,26019],{"className":25992},[212],[135,25994,25996,26008],{"className":25995,"style":24868},[216],[135,25997,25999,26002],{"style":25998},"top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;",[135,26000],{"className":26001,"style":616},[224],[135,26003,26005],{"className":26004},[229,230,231,232],[135,26006,853],{"className":26007},[195,268,232],[135,26009,26010,26013],{"style":16498},[135,26011],{"className":26012,"style":616},[224],[135,26014,26016],{"className":26015},[229,230,231,232],[135,26017,748],{"className":26018,"style":778},[195,268,232],[135,26020,303],{"className":26021},[302],[135,26023,26025],{"className":26024},[212],[135,26026,26028],{"className":26027,"style":17413},[216],[135,26029],{},[135,26031],{"className":26032,"style":576},[575],[135,26034,891],{"className":26035},[580],[135,26037],{"className":26038,"style":576},[575],[135,26040,26042,26045,26085,26088,26091],{"className":26041},[186],[135,26043],{"className":26044,"style":21984},[190],[135,26046,26048,26051],{"className":26047},[195],[135,26049,7899],{"className":26050,"style":3283},[195,268],[135,26052,26054],{"className":26053},[272],[135,26055,26057,26077],{"className":26056},[207,208],[135,26058,26060,26074],{"className":26059},[212],[135,26061,26063],{"className":26062,"style":12804},[216],[135,26064,26065,26068],{"style":13177},[135,26066],{"className":26067,"style":616},[224],[135,26069,26071],{"className":26070},[229,230,231,232],[135,26072,853],{"className":26073},[195,268,232],[135,26075,303],{"className":26076},[302],[135,26078,26080],{"className":26079},[212],[135,26081,26083],{"className":26082,"style":1346},[216],[135,26084],{},[135,26086],{"className":26087,"style":1948},[575],[135,26089,5850],{"className":26090},[629],[135,26092],{"className":26093,"style":1948},[575],[135,26095,26097,26100,26103,26106,26109],{"className":26096},[186],[135,26098],{"className":26099,"style":24402},[190],[135,26101,19067],{"className":26102,"style":19314},[195,268],[135,26104],{"className":26105,"style":1948},[575],[135,26107,23121],{"className":26108},[629],[135,26110],{"className":26111,"style":1948},[575],[135,26113,26115,26118,26158,26161,26210,26213,26216,26219],{"className":26114},[186],[135,26116],{"className":26117,"style":953},[190],[135,26119,26121,26124],{"className":26120},[195],[135,26122,748],{"className":26123,"style":778},[195,268],[135,26125,26127],{"className":26126},[272],[135,26128,26130,26150],{"className":26129},[207,208],[135,26131,26133,26147],{"className":26132},[212],[135,26134,26136],{"className":26135,"style":1324},[216],[135,26137,26138,26141],{"style":20577},[135,26139],{"className":26140,"style":616},[224],[135,26142,26144],{"className":26143},[229,230,231,232],[135,26145,14123],{"className":26146,"style":3283},[195,268,232],[135,26148,303],{"className":26149},[302],[135,26151,26153],{"className":26152},[212],[135,26154,26156],{"className":26155,"style":1346},[216],[135,26157],{},[135,26159,874],{"className":26160},[199],[135,26162,26164,26167],{"className":26163},[195],[135,26165,12874],{"className":26166},[195,268],[135,26168,26170],{"className":26169},[272],[135,26171,26173,26202],{"className":26172},[207,208],[135,26174,26176,26199],{"className":26175},[212],[135,26177,26179],{"className":26178,"style":3164},[216],[135,26180,26181,26184],{"style":1327},[135,26182],{"className":26183,"style":616},[224],[135,26185,26187],{"className":26186},[229,230,231,232],[135,26188,26190,26193,26196],{"className":26189},[195,232],[135,26191,853],{"className":26192},[195,268,232],[135,26194,5850],{"className":26195},[629,232],[135,26197,159],{"className":26198},[195,232],[135,26200,303],{"className":26201},[302],[135,26203,26205],{"className":26204},[212],[135,26206,26208],{"className":26207,"style":7011},[216],[135,26209],{},[135,26211,888],{"className":26212},[389],[135,26214],{"className":26215,"style":1948},[575],[135,26217,18437],{"className":26218},[629],[135,26220],{"className":26221,"style":1948},[575],[135,26223,26225,26228,26268,26271,26311],{"className":26224},[186],[135,26226],{"className":26227,"style":953},[190],[135,26229,26231,26234],{"className":26230},[195],[135,26232,748],{"className":26233,"style":778},[195,268],[135,26235,26237],{"className":26236},[272],[135,26238,26240,26260],{"className":26239},[207,208],[135,26241,26243,26257],{"className":26242},[212],[135,26244,26246],{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Advantage Estimation (GAE)",[14,27513,27514],{},"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！",[14,27516,27517,27518,27548],{},"GAE考虑全部的采样结果，并引入一个衰减因子 ",[135,27519,27521,27536],{"className":27520},[138],[135,27522,27524],{"className":27523},[142],[144,27525,27526],{"xmlns":146},[148,27527,27528,27533],{},[151,27529,27530],{},[167,27531,27532],{},"λ",[174,27534,27535],{"encoding":176},"\\lambda",[135,27537,27539],{"className":27538,"ariaHidden":182},[181],[135,27540,27542,27545],{"className":27541},[186],[135,27543],{"className":27544,"style":483},[190],[135,27546,27532],{"className":27547},[195,268]," 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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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sName":30159},[207,208],[135,30161,30163,30209],{"className":30162},[212],[135,30164,30167,30188,30198],{"className":30165,"style":30166},[216],"height:1.6514em;",[135,30168,30170,30173],{"style":30169},"top:-1.8479em;margin-left:0em;",[135,30171],{"className":30172,"style":15504},[224],[135,30174,30176],{"className":30175},[229,230,231,232],[135,30177,30179,30182,30185],{"className":30178},[195,232],[135,30180,7430],{"className":30181},[195,268,232],[135,30183,891],{"className":30184},[580,232],[135,30186,1830],{"className":30187},[195,232],[135,30189,30190,30193],{"style":15513},[135,30191],{"className":30192,"style":15504},[224],[135,30194,30195],{},[135,30196,1902],{"className":30197},[1027,1986,15522],[135,30199,30200,30203],{"style":16446},[135,30201],{"className":30202,"style":15504},[224],[135,30204,30206],{"className":30205},[229,230,231,232],[135,30207,28116],{"className":30208},[195,232],[135,30210,303],{"className":30211},[302],[135,30213,30215],{"className":30214},[212],[135,30216,30219],{"className":30217,"style":30218},[216],"height:1.3021em;",[135,30220],{},[135,30222,874],{"className":30223},[199],[135,30225,19067],{"className":30226,"style":19314},[195,268],[135,30228,27532],{"className":30229},[195,268],[135,30231,30233,30236],{"className":30232},[389],[135,30234,888],{"className":30235},[389],[135,30237,30239],{"className":30238},[272],[135,30240,30242],{"className":30241},[207],[135,30243,30245],{"className":30244},[212],[135,30246,30249],{"className":30247,"style":30248},[216],"height:0.8991em;",[135,30250,30251,30254],{"style":16498},[135,30252],{"className":30253,"style":616},[224],[135,30255,30257],{"className":30256},[229,230,231,232],[135,30258,7430],{"className":30259},[195,268,232],[135,30261,30263,30266],{"className":30262},[195],[135,30264,25549],{"className":30265,"style":25570},[195,268],[135,30267,30269],{"className":30268},[272],[135,30270,30272,30312],{"className":30271},[207,208],[135,30273,30275,30309],{"className":30274},[212],[135,30276,30278,30298],{"className":30277,"style":24868},[216],[135,30279,30280,30283],{"style":25998},[135,30281],{"className":30282,"style":616},[224],[135,30284,30286],{"className":30285},[229,230,231,232],[135,30287,30289,30292,30295],{"className":30288},[195,232],[135,30290,853],{"className":30291},[195,268,232],[135,30293,5850],{"className":30294},[629,232],[135,30296,7430],{"className":30297},[195,268,232],[135,30299,30300,30303],{"style":16498},[135,30301],{"className":30302,"style":616},[224],[135,30304,30306],{"className":30305},[229,230,231,232],[135,30307,748],{"className":30308,"style":778},[195,268,232],[135,30310,303],{"className":30311},[302],[135,30313,30315],{"className":30314},[212],[135,30316,30318],{"className":30317,"style":26382},[216],[135,30319],{},[135,30321,303],{"className":30322},[302],[135,30324,30326],{"className":30325},[212],[135,30327,30329],{"className":30328,"style":28345},[216],[135,30330],{},[14,30332,30333],{},"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。",[14,30335,30336],{},"GAE 优势函数平衡了采样不同步带来的方差和偏差的问题。",[14,30338,30339],{},"现在我们来看上面得之不易的三个表达式：",[135,30341,30343],{"className":30342},[14422],[135,30344,30346,30602],{"className":30345},[138],[135,30347,30349],{"className":30348},[142],[144,30350,30351],{"xmlns":146,"display":9554},[148,30352,30353,30599],{},[151,30354,30355,30363,30365,30371,30373,30375,30381,30383,30395,30397,30399,30405,30407,30413,30415,30417,30431,30433,30439,30441,30443,30445,30447,30461,30463,30465,30467,30473,30487,30489,30495,30509,30527,30541,30543,30551,30553,30561,30563,30565,30567,30569,30571,30577,30579,30587,30589,30597],{},[1898,30356,30357,30359,30361],{},[167,30358,25549],{},[167,30360,853],{},[167,30362,748],{},[537,30364,891],{},[164,30366,30367,30369],{},[167,30368,7899],{},[167,30370,853],{},[537,30372,5850],{},[167,30374,19067],{},[164,30376,30377,30379],{},[167,30378,748],{},[167,30380,14123],{},[537,30382,874],{"stretchy":873},[164,30384,30385,30387],{},[167,30386,12874],{},[151,30388,30389,30391,30393],{},[167,30390,853],{},[537,30392,5850],{},[157,30394,159],{},[537,30396,888],{"stretchy":873},[537,30398,18437],{},[164,30400,30401,30403],{},[167,30402,748],{},[167,30404,14123],{},[537,30406,874],{"stretchy":873},[164,30408,30409,30411],{},[167,30410,12874],{},[167,30412,853],{},[537,30414,888],{"stretchy":873},[575,30416],{"linebreak":21725},[1898,30418,30419,30421,30423],{},[167,30420,850],{},[167,30422,14123],{},[151,30424,30425,30427,30429],{},[167,30426,27582],{},[167,30428,850],{},[167,30430,5680],{},[537,30432,874],{"stretchy":873},[164,30434,30435,30437],{},[167,30436,12874],{},[167,30438,853],{},[537,30440,879],{"separator":182},[167,30442,31],{},[537,30444,888],{"stretchy":873},[537,30446,891],{},[14755,30448,30449,30451,30459],{},[537,30450,1902],{},[151,30452,30453,30455,30457],{},[167,30454,7430],{},[537,30456,891],{},[157,30458,1830],{},[167,30460,28116],{"mathvariant":894},[537,30462,874],{"stretchy":873},[167,30464,19067],{},[167,30466,27532],{},[541,30468,30469,30471],{},[537,30470,888],{"stretchy":873},[167,30472,7430],{},[1898,30474,30475,30477,30485],{},[167,30476,25549],{},[151,30478,30479,30481,30483],{},[167,30480,853],{},[537,30482,5850],{},[167,30484,7430],{},[167,30486,748],{},[575,30488],{"linebreak":21725},[154,30490,30491,30493],{},[157,30492,159],{},[167,30494,7395],{},[14755,30496,30497,30499,30507],{},[537,30498,1902],{},[151,30500,30501,30503,30505],{},[167,30502,411],{},[537,30504,891],{},[157,30506,159],{},[167,30508,7395],{},[14755,30510,30511,30513,30521],{},[537,30512,1902],{},[151,30514,30515,30517,30519],{},[167,30516,853],{},[537,30518,891],{},[157,30520,159],{},[164,30522,30523,30525],{},[167,30524,13314],{},[167,30526,411],{},[1898,30528,30529,30531,30533],{},[167,30530,850],{},[167,30532,14123],{},[151,30534,30535,30537,30539],{},[167,30536,27582],{},[167,30538,850],{},[167,30540,5680],{},[537,30542,874],{"stretchy":873},[1898,30544,30545,30547,30549],{},[167,30546,12874],{},[167,30548,411],{},[167,30550,853],{},[537,30552,879],{"separator":182},[1898,30554,30555,30557,30559],{},[167,30556,31],{},[167,30558,411],{},[167,30560,853],{},[537,30562,888],{"stretchy":873},[3350,30564,27667],{},[167,30566,14452],{"mathvariant":894},[167,30568,14877],{},[537,30570,898],{},[164,30572,30573,30575],{},[167,30574,5677],{},[167,30576,14123],{},[537,30578,874],{"stretchy":873},[1898,30580,30581,30583,30585],{},[167,30582,31],{},[167,30584,411],{},[167,30586,853],{},[167,30588,13013],{"mathvariant":894},[1898,30590,30591,30593,30595],{},[167,30592,12874],{},[167,30594,411],{},[167,30596,853],{},[537,30598,888],{"stretchy":873},[174,30600,30601],{"encoding":176},"\\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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Policy Optimization (PPO) 近邻策略优化算法",[14,31835,31836],{},"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。",[125,31838,31839],{"id":31839},"重要性采样",[14,31841,31842,31843,31887,31888,31916,31917,31945,31946,31974],{},"将 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",[135,31889,31891,31904],{"className":31890},[138],[135,31892,31894],{"className":31893},[142],[144,31895,31896],{"xmlns":146},[148,31897,31898,31902],{},[151,31899,31900],{},[167,31901,14],{},[174,31903,14],{"encoding":176},[135,31905,31907],{"className":31906,"ariaHidden":182},[181],[135,31908,31910,31913],{"className":31909},[186],[135,31911],{"className":31912,"style":1782},[190],[135,31914,14],{"className":31915},[195,268]," 下的期望改写为在另一分布 ",[135,31918,31920,31933],{"className":31919},[138],[135,31921,31923],{"className":31922},[142],[144,31924,31925],{"xmlns":146},[148,31926,31927,31931],{},[151,31928,31929],{},[167,31930,1770],{},[174,31932,1770],{"encoding":176},[135,31934,31936],{"className":31935,"ariaHidden":182},[181],[135,31937,31939,31942],{"className":31938},[186],[135,31940],{"className":31941,"style":1782},[190],[135,31943,1770],{"className":31944,"style":517},[195,268],"（proposal）下的期望，从而可用从 ",[135,31947,31949,31962],{"className":31948},[138],[135,31950,31952],{"className":31951},[142],[144,31953,31954],{"xmlns":146},[148,31955,31956,31960],{},[151,31957,31958],{},[167,31959,1770],{},[174,31961,1770],{"encoding":176},[135,31963,31965],{"className":31964,"ariaHidden":182},[181],[135,31966,31968,31971],{"className":31967},[186],[135,31969],{"className":31970,"style":1782},[190],[135,31972,1770],{"className":31973,"style":517},[195,268]," 采样的数据估计：",[135,31976,31978],{"className":31977},[14422],[135,31979,31981,32365],{"className":31980},[138],[135,31982,31984],{"className":31983},[142],[144,31985,31986],{"xmlns":146,"display":9554},[148,31987,31988,32362],{},[14434,31989,31990,32062,32126,32190,32262],{"rowspacing":14436,"columnalign":14437,"columnspacing":14438},[14440,31991,31992,32028],{},[14443,31993,31994],{},[14446,31995,31996],{"scriptlevel":1830,"displaystyle":182},[151,31997,31998,32000,32002,32004,32006,32008,32010],{},[167,31999,5680],{"mathvariant":545},[537,32001,874],{"stretchy":873},[167,32003,11730],{},[537,32005,874],{"stretchy":873},[167,32007,7400],{},[537,32009,888],{"stretchy":873},[164,32011,32012,32014],{},[537,32013,888],{"stretchy":873},[151,32015,32016,32018,32020,32022,32024,32026],{},[167,32017,7400],{},[537,32019,14116],{},[167,32021,14],{},[537,32023,874],{"stretchy":873},[167,32025,7400],{},[537,32027,888],{"stretchy":873},[14443,32029,32030],{},[14446,32031,32032],{"scriptlevel":1830,"displaystyle":182},[151,32033,32034,32036,32038,32044,32046,32048,32050,32052,32054,32056,32058,32060],{},[151,32035],{},[537,32037,891],{},[14133,32039,32040,32042],{},[537,32041,1902],{},[167,32043,7400],{},[167,32045,11730],{},[537,32047,874],{"stretchy":873},[167,32049,7400],{},[537,32051,888],{"stretchy":873},[537,32053,1892],{},[167,32055,14],{},[537,32057,874],{"stretchy":873},[167,32059,7400],{},[537,32061,888],{"stretchy":873},[14440,32063,32064,32070],{},[14443,32065,32066],{},[14446,32067,32068],{"scriptlevel":1830,"displaystyle":182},[151,32069],{},[14443,32071,32072],{},[14446,32073,32074],{"scriptlevel":1830,"displaystyle":182},[151,32075,32076,32078,32080,32086,32088,32090,32092,32094,32096,32098,32100,32102,32104],{},[151,32077],{},[537,32079,891],{},[14133,32081,32082,32084],{},[537,32083,1902],{},[167,32085,7400],{},[167,32087,11730],{},[537,32089,874],{"stretchy":873},[167,32091,7400],{},[537,32093,888],{"stretchy":873},[537,32095,1892],{},[167,32097,14],{},[537,32099,874],{"stretchy":873},[167,32101,7400],{},[537,32103,888],{"stretchy":873},[154,32105,32106,32116],{},[151,32107,32108,32110,32112,32114],{},[167,32109,1770],{},[537,32111,874],{"stretchy":873},[167,32113,7400],{},[537,32115,888],{"stretchy":873},[151,32117,32118,32120,32122,32124],{},[167,32119,1770],{},[537,32121,874],{"stretchy":873},[167,32123,7400],{},[537,32125,888],{"stretchy":873},[14440,32127,32128,32134],{},[14443,32129,32130],{},[14446,32131,32132],{"scriptlevel":1830,"displaystyle":182},[151,32133],{},[14443,32135,32136],{},[14446,32137,32138],{"scriptlevel":1830,"displaystyle":182},[151,32139,32140,32142,32144,32150,32152,32154,32156,32158,32180,32182,32184,32186,32188],{},[151,32141],{},[537,32143,891],{},[14133,32145,32146,32148],{},[537,32147,1902],{},[167,32149,7400],{},[167,32151,11730],{},[537,32153,874],{"stretchy":873},[167,32155,7400],{},[537,32157,888],{"stretchy":873},[154,32159,32160,32170],{},[151,32161,32162,32164,32166,32168],{},[167,32163,14],{},[537,32165,874],{"stretchy":873},[167,32167,7400],{},[537,32169,888],{"stretchy":873},[151,32171,32172,32174,32176,32178],{},[167,32173,1770],{},[537,32175,874],{"stretchy":873},[167,32177,7400],{},[537,32179,888],{"stretchy":873},[537,32181,1892],{},[167,32183,1770],{},[537,32185,874],{"stretchy":873},[167,32187,7400],{},[537,32189,888],{"stretchy":873},[14440,32191,32192,32198],{},[14443,32193,32194],{},[14446,32195,32196],{"scriptlevel":1830,"displaystyle":182},[151,32197],{},[14443,32199,32200],{},[14446,32201,32202],{"scriptlevel":1830,"displaystyle":182},[151,32203,32204,32206,32208,32210],{},[151,32205],{},[537,32207,891],{},[167,32209,5680],{"mathvariant":545},[164,32211,32212,32248],{},[151,32213,32214,32216,32218,32220,32222,32224,32246],{},[537,32215,874],{"fence":182},[167,32217,11730],{},[537,32219,874],{"stretchy":873},[167,32221,7400],{},[537,32223,888],{"stretchy":873},[154,32225,32226,32236],{},[151,32227,32228,32230,32232,32234],{},[167,32229,14],{},[537,32231,874],{"stretchy":873},[167,32233,7400],{},[537,32235,888],{"stretchy":873},[151,32237,32238,32240,32242,32244],{},[167,32239,1770],{},[537,32241,874],{"stretchy":873},[167,32243,7400],{},[537,32245,888],{"stretchy":873},[537,32247,888],{"fence":182},[151,32249,32250,32252,32254,32256,32258,32260],{},[167,32251,7400],{},[537,32253,14116],{},[167,32255,1770],{},[537,32257,874],{"stretchy":873},[167,32259,7400],{},[537,32261,888],{"stretchy":873},[14440,32263,32264,32270],{},[14443,32265,32266],{},[14446,32267,32268],{"scriptlevel":1830,"displaystyle":182},[151,32269],{},[14443,32271,32272],{},[14446,32273,32274],{"scriptlevel":1830,"displaystyle":182},[151,32275,32276,32278,32280,32286,32300,32302,32304,32310,32312,32342,32344,32346,32352,32354,32356,32358,32360],{},[151,32277],{},[537,32279,14747],{},[154,32281,32282,32284],{},[157,32283,159],{},[167,32285,7395],{},[14755,32287,32288,32290,32298],{},[537,32289,1902],{},[151,32291,32292,32294,32296],{},[167,32293,411],{},[537,32295,891],{},[157,32297,159],{},[167,32299,7395],{},[167,32301,11730],{},[537,32303,874],{"stretchy":873},[164,32305,32306,32308],{},[167,32307,7400],{},[167,32309,411],{},[537,32311,888],{"stretchy":873},[154,32313,32314,32328],{},[151,32315,32316,32318,32320,32326],{},[167,32317,14],{},[537,32319,874],{"stretchy":873},[164,32321,32322,32324],{},[167,32323,7400],{},[167,32325,411],{},[537,32327,888],{"stretchy":873},[151,32329,32330,32332,32334,32340],{},[167,32331,1770],{},[537,32333,874],{"stretchy":873},[164,32335,32336,32338],{},[167,32337,7400],{},[167,32339,411],{},[537,32341,888],{"stretchy":873},[537,32343,879],{"separator":182},[575,32345],{"width":27672},[164,32347,32348,32350],{},[167,32349,7400],{},[167,32351,411],{},[537,32353,14116],{},[167,32355,1770],{},[537,32357,874],{"stretchy":873},[167,32359,7400],{},[537,32361,888],{"stretchy":873},[174,32363,32364],{"encoding":176},"\\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}",[135,32366,32368],{"className":32367,"ariaHidden":182},[181],[135,32369,32371,32375],{"className":32370},[186],[135,32372],{"className":32373,"style":32374},[190],"height:14.8742em;vertical-align:-7.1871em;",[135,32376,32378],{"className":32377},[195],[135,32379,32381,32528],{"className":32380},[14434],[135,32382,32384],{"className":32383},[15225],[135,32385,32387,32519],{"className":32386},[207,208],[135,32388,32390,32516],{"className":32389},[212],[135,32391,32394,32480,32489,32498,32507],{"className":32392,"style":32393},[216],"height:7.6871em;",[135,32395,32397,32401],{"style":32396},"top:-10.4654em;",[135,32398],{"className":32399,"style":32400},[224],"height:3.8283em;",[135,32402,32404,32407,32410,32413,32416,32419,32422],{"className":32403},[195],[135,32405,5680],{"className":32406},[195,597],[135,32408,874],{"className":32409},[199],[135,32411,11730],{"className":32412,"style":13691},[195,268],[135,32414,874],{"className":32415},[199],[135,32417,7400],{"className":32418},[195,268],[135,32420,888],{"className":32421},[389],[135,32423,32425,32428],{"className":32424},[389],[135,32426,888],{"className":32427},[389],[135,32429,32431],{"className":32430},[272],[135,32432,32434,32472],{"className":32433},[207,208],[135,32435,32437,32469],{"className":32436},[212],[135,32438,32440],{"className":32439,"style":282},[216],[135,32441,32442,32445],{"style":14211},[135,32443],{"className":32444,"style":616},[224],[135,32446,32448],{"className":32447},[229,230,231,232],[135,32449,32451,32454,32457,32460,32463,32466],{"className":32450},[195,232],[135,32452,7400],{"className":32453},[195,268,232],[135,32455,14116],{"className":32456},[580,232],[135,32458,14],{"className":32459},[195,268,232],[135,32461,874],{"className":32462},[199,232],[135,32464,7400],{"className":32465},[195,268,232],[135,32467,888],{"className":32468},[389,232],[135,32470,303],{"className":32471},[302],[135,32473,32475],{"className":32474},[212],[135,32476,32478],{"className":32477,"style":6175},[216],[135,32479],{},[135,32481,32483,32486],{"style":32482},"top:-7.4884em;",[135,32484],{"className":32485,"style":32400},[224],[135,32487],{"className":32488},[195],[135,32490,32492,32495],{"style":32491},"top:-4.5114em;",[135,32493],{"className":32494,"style":32400},[224],[135,32496],{"className":32497},[195],[135,32499,32501,32504],{"style":32500},"top:-1.5114em;",[135,32502],{"className":32503,"style":32400},[224],[135,32505],{"className":32506},[195],[135,32508,32510,32513],{"style":32509},"top:1.7917em;",[135,32511],{"className":32512,"style":32400},[224],[135,32514],{"className":32515},[195],[135,32517,303],{"className":32518},[302],[135,32520,32522],{"className":32521},[212],[135,32523,32526],{"className":32524,"style":32525},[216],"height:7.1871em;",[135,32527],{},[135,32529,32531],{"className":32530},[15449],[135,32532,32534,33631],{"className":32533},[207,208],[135,32535,32537,33628],{"className":32536},[212],[135,32538,32540,32643,32826,33009,33200],{"className":32539,"style":32393},[216],[135,32541,32542,32545],{"style":32396},[135,32543],{"className":32544,"style":32400},[224],[135,32546,32548,32551,32554,32557,32560,32607,32610,32613,32616,32619,32622,32625,32628,32631,32634,32637,32640],{"className":32547},[195],[135,32549],{"className":32550},[195],[135,32552],{"className":32553,"style":576},[575],[135,32555,891],{"className":32556},[580],[135,32558],{"className":32559,"style":576},[575],[135,32561,32563],{"className":32562},[1027,14310],[135,32564,32566,32599],{"className":32565},[207,208],[135,32567,32569,32596],{"className":32568},[212],[135,32570,32572,32586],{"className":32571,"style":15497},[216],[135,32573,32574,32577],{"style":15500},[135,32575],{"className":32576,"style":15504},[224],[135,32578,32580],{"className":32579},[229,230,231,232],[135,32581,32583],{"className":32582},[195,232],[135,32584,7400],{"className":32585},[195,268,232],[135,32587,32588,32591],{"style":15513},[135,32589],{"className":32590,"style":15504},[224],[135,32592,32593],{},[135,32594,1902],{"className":32595},[1027,1986,15522],[135,32597,303],{"className":32598},[302],[135,32600,32602],{"className":32601},[212],[135,32603,32605],{"className":32604,"style":15532},[216],[135,32606],{},[135,32608],{"className":32609,"style":992},[575],[135,32611,11730],{"className":32612,"style":13691},[195,268],[135,32614,874],{"className":32615},[199],[135,32617,7400],{"className":32618},[195,268],[135,32620,888],{"className":32621},[389],[135,32623],{"className":32624,"style":1948},[575],[135,32626,1892],{"className":32627},[629],[135,32629],{"className":32630,"style":1948},[575],[135,32632,14],{"className":32633},[195,268],[135,32635,874],{"className":32636},[199],[135,32638,7400],{"className":32639},[195,268],[135,32641,888],{"className":32642},[389],[135,32644,32645,32648],{"style":32482},[135,32646],{"className":32647,"style":32400},[224],[135,32649,32651,32654,32657,32660,32663,32710,32713,32716,32719,32722,32725,32728,32731,32734,32737,3274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on-policy 的训练改为 off-policy 的训练。",[125,33643,33645],{"id":33644},"off-policy","Off-policy",[14,33647,33648,33649,33712,33713,33742,33743,33880,33881,34072,34073,34288],{},"记 ",[135,33650,33652,33670],{"className":33651},[138],[135,33653,33655],{"className":33654},[142],[144,33656,33657],{"xmlns":146},[148,33658,33659,33667],{},[151,33660,33661],{},[541,33662,33663,33665],{},[167,33664,14123],{},[537,33666,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[174,33668,33669],{"encoding":176},"\\theta'",[135,33671,33673],{"className":33672,"ariaHidden":182},[181],[135,33674,33676,33680],{"className":33675},[186],[135,33677],{"className":33678,"style":33679},[190],"height:0.7519em;",[135,33681,33683,33686],{"className":33682},[195],[135,33684,14123],{"className":33685,"style":3283},[195,268],[135,33687,33689],{"className":33688},[272],[135,33690,33692],{"className":33691},[207],[135,33693,33695],{"className":33694},[212],[135,33696,33698],{"className":33697,"style":33679},[216],[135,33699,33700,33703],{"style":612},[135,33701],{"className":33702,"style":616},[224],[135,33704,33706],{"className":33705},[229,230,231,232],[135,33707,33709],{"className":33708},[195,232],[135,33710,19056],{"className":33711},[195,232]," 为采集数据时的旧策略，",[135,33714,33716,33730],{"className":33715},[138],[135,33717,33719],{"className":33718},[142],[144,33720,33721],{"xmlns":146},[148,33722,33723,33727],{},[151,33724,33725],{},[167,33726,14123],{},[174,33728,33729],{"encoding":176},"\\theta",[135,33731,33733],{"className":33732,"ariaHidden":182},[181],[135,33734,33736,33739],{"className":33735},[186],[135,33737],{"className":33738,"style":483},[190],[135,33740,14123],{"className":33741,"style":3283},[195,268]," 为当前要优化的策略；优势 ",[135,33744,33746,33776],{"className":33745},[138],[135,33747,33749],{"className":33748},[142],[144,33750,33751],{"xmlns":146},[148,33752,33753,33773],{},[151,33754,33755],{},[1898,33756,33757,33759,33765],{},[167,33758,850],{},[541,33760,33761,33763],{},[167,33762,14123],{},[537,33764,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[151,33766,33767,33769,33771],{},[167,33768,27582],{},[167,33770,850],{},[167,33772,5680],{},[174,33774,33775],{"encoding":176},"A_{\\theta'}^{GAE}",[135,33777,33779],{"className":33778,"ariaHidden":182},[181],[135,33780,33782,33786],{"className":33781},[186],[135,33783],{"className":33784,"style":33785},[190],"height:1.1244em;vertical-align:-0.2831em;",[135,33787,33789,33792],{"className":33788},[195],[135,33790,850],{"className":33791},[195,268],[135,33793,33795],{"className":33794},[272],[135,33796,33798,33871],{"className":33797},[207,208],[135,33799,33801,33868],{"className":33800},[212],[135,33802,33804,33848],{"className":33803,"style":3271},[216],[135,33805,33807,33810],{"style":33806},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[135,33808],{"className":33809,"style":616},[224],[135,33811,33813],{"className":33812},[229,230,231,232],[135,33814,33816],{"className":33815},[195,232],[135,33817,33819,33822],{"className":33818},[195,232],[135,33820,14123],{"className":33821,"style":3283},[195,268,232],[135,33823,33825],{"className":33824},[272],[135,33826,33828],{"className":33827},[207],[135,33829,33831],{"className":33830},[212],[135,33832,33834],{"className":33833,"style":19216},[216],[135,33835,33836,33839],{"style":19219},[135,33837],{"className":33838,"style":289},[224],[135,33840,33842],{"className":33841},[229,293,294,232],[135,33843,33845],{"className":33844},[195,232],[135,33846,19056],{"className":33847},[195,232],[135,33849,33850,33853],{"style":612},[135,33851],{"className":33852,"style":616},[224],[135,33854,33856],{"className":33855},[229,230,231,232],[135,33857,33859,33862,33865],{"className":33858},[195,232],[135,33860,27582],{"className":33861},[195,268,232],[135,33863,850],{"className":33864},[195,268,232],[135,33866,5680],{"className":33867,"style":6123},[195,268,232],[135,33869,303],{"className":33870},[302],[135,33872,33874],{"className":33873},[212],[135,33875,33878],{"className":33876,"style":33877},[216],"height:0.2831em;",[135,33879],{}," 由旧策略下的价值网络估计。利用恒等式 ",[135,33882,33884,33938],{"className":33883},[138],[135,33885,33887],{"className":33886},[142],[144,33888,33889],{"xmlns":146},[148,33890,33891,33935],{},[151,33892,33893,33895,33897,33899,33901,33903,33905,33907,33909],{},[167,33894,14452],{"mathvariant":894},[167,33896,14877],{},[537,33898,898],{},[167,33900,11730],{},[537,33902,874],{"stretchy":873},[167,33904,7400],{},[537,33906,888],{"stretchy":873},[537,33908,891],{},[14446,33910,33911],{"scriptlevel":1830,"displaystyle":182},[154,33912,33913,33925],{},[151,33914,33915,33917,33919,33921,33923],{},[167,33916,14452],{"mathvariant":894},[167,33918,11730],{},[537,33920,874],{"stretchy":873},[167,33922,7400],{},[537,33924,888],{"stretchy":873},[151,33926,33927,33929,33931,33933],{},[167,33928,11730],{},[537,33930,874],{"stretchy":873},[167,33932,7400],{},[537,33934,888],{"stretchy":873},[174,33936,33937],{"encoding":176},"\\nabla \\log f(x) = \\dfrac{\\nabla f(x)}{f(x)}",[135,33939,33941,33982],{"className":33940,"ariaHidden":182},[181],[135,33942,33944,33947,33950,33953,33958,33961,33964,33967,33970,33973,33976,33979],{"className":33943},[186],[135,33945],{"className":33946,"style":953},[190],[135,33948,14452],{"className":33949},[195],[135,33951],{"className":33952,"style":992},[575],[135,33954,16922,33956],{"className":33955},[1027],[135,33957,16926],{"style":16925},[135,33959],{"className":33960,"style":992},[575],[135,33962,11730],{"className":33963,"style":13691},[195,268],[135,33965,874],{"className":33966},[199],[135,33968,7400],{"className":33969},[195,268],[135,33971,888],{"className":33972},[389],[135,33974],{"className":33975,"style":576},[575],[135,33977,891],{"className":33978},[580],[135,33980],{"className":33981,"style":576},[575],[135,33983,33985,33989],{"className":33984},[186],[135,33986],{"className":33987,"style":33988},[190],"height:2.363em;vertical-align:-0.936em;",[135,33990,33992,33995,34069],{"className":33991},[195],[135,33993],{"className":33994},[199,200],[135,33996,33998],{"className":33997},[154],[135,33999,34001,34061],{"className":34000},[207,208],[135,34002,34004,34058],{"className":34003},[212],[135,34005,34007,34027,34035],{"className":34006,"style":15888},[216],[135,34008,34009,34012],{"style":15891},[135,34010],{"className":34011,"style":225},[224],[135,34013,34015,34018,34021,34024],{"className":34014},[195],[135,34016,11730],{"className":34017,"style":13691},[195,268],[135,34019,874],{"className":34020},[199],[135,34022,7400],{"className":34023},[195,268],[135,34025,888],{"className":34026},[389],[135,34028,34029,34032],{"style":350},[135,34030],{"className":34031,"style":225},[224],[135,34033],{"className":34034,"style":358},[357],[135,34036,34037,34040],{"style":15957},[135,34038],{"className":34039,"style":225},[224],[135,34041,34043,34046,34049,34052,34055],{"className":34042},[195],[135,34044,14452],{"className":34045},[195],[135,34047,11730],{"className":34048,"style":13691},[195,268],[135,34050,874],{"className":34051},[199],[135,34053,7400],{"className":34054},[195,268],[135,34056,888],{"className":34057},[389],[135,34059,303],{"className":34060},[302],[135,34062,34064],{"className":34063},[212],[135,34065,34067],{"className":34066,"style":16022},[216],[135,34068],{},[135,34070],{"className":34071},[389,200],"，可将策略梯度写成重要性采样比 ",[135,34074,34076,34108],{"className":34075},[138],[135,34077,34079],{"className":34078},[142],[144,34080,34081],{"xmlns":146},[148,34082,34083,34105],{},[151,34084,34085],{},[14446,34086,34087],{"scriptlevel":1830,"displaystyle":182},[154,34088,34089,34095],{},[164,34090,34091,34093],{},[167,34092,5677],{},[167,34094,14123],{},[164,34096,34097,34099],{},[167,34098,5677],{},[541,34100,34101,34103],{},[167,34102,14123],{},[537,34104,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[174,34106,34107],{"encoding":176},"\\dfrac{P_\\theta}{P_{\\theta'}}",[135,34109,34111],{"className":34110,"ariaHidden":182},[181],[135,34112,34114,34118],{"className":34113},[186],[135,34115],{"className":34116,"style":34117},[190],"height:2.1963em;vertical-align:-0.836em;",[135,34119,34121,34124,34285],{"className":34120},[195],[135,34122],{"className":34123},[199,200],[135,34125,34127],{"className":34126},[154],[135,34128,34130,34276],{"className":34129},[207,208],[135,34131,34133,34273],{"className":34132},[212],[135,34134,34137,34217,34225],{"className":34135,"style":34136},[216],"height:1.3603em;",[135,34138,34139,34142],{"style":15891},[135,34140],{"className":34141,"style":225},[224],[135,34143,34145],{"className":34144},[195],[135,34146,34148,34151],{"className":34147},[195],[135,34149,5677],{"className":34150,"style":3258},[195,268],[135,34152,34154],{"className":34153},[272],[135,34155,34157,34209],{"className":34156},[207,208],[135,34158,34160,34206],{"className":34159},[212],[135,34161,34163],{"className":34162,"style":1324},[216],[135,34164,34165,34168],{"style":7533},[135,34166],{"className":34167,"style":616},[224],[135,34169,34171],{"className":34170},[229,230,231,232],[135,34172,34174],{"className":34173},[195,232],[135,34175,34177,34180],{"className":34176},[195,232],[135,34178,14123],{"className":34179,"style":3283},[195,268,232],[135,34181,34183],{"className":34182},[272],[135,34184,34186],{"className":34185},[207],[135,34187,34189],{"className":34188},[212],[135,34190,34192],{"className":34191,"style":19216},[216],[135,34193,34194,34197],{"style":19219},[135,34195],{"className":34196,"style":289},[224],[135,34198,34200],{"className":34199},[229,293,294,232],[135,34201,34203],{"className":34202},[195,232],[135,34204,19056],{"className":34205},[195,232],[135,34207,303],{"className":34208},[302],[135,34210,34212],{"className":34211},[212],[135,34213,34215],{"className":34214,"style":1346},[216],[135,34216],{},[135,34218,34219,34222],{"style":350},[135,34220],{"className":34221,"style":225},[224],[135,34223],{"className":34224,"style":358},[357],[135,34226,34227,34230],{"style":15957},[135,34228],{"className":34229,"style":225},[224],[135,34231,34233],{"className":34232},[195],[135,34234,34236,34239],{"className":34235},[195],[135,34237,5677],{"className":34238,"style":3258},[195,268],[135,34240,34242],{"className":34241},[272],[135,34243,34245,34265],{"className":34244},[207,208],[135,34246,34248,34262],{"className":34247},[212],[135,34249,34251],{"className":34250,"style":1324},[216],[135,34252,34253,34256],{"style":7533},[135,34254],{"className":34255,"style":616},[224],[135,34257,34259],{"className":34258},[229,230,231,232],[135,34260,14123],{"className":34261,"style":3283},[195,268,232],[135,34263,303],{"className":34264},[302],[135,34266,34268],{"className":34267},[212],[135,34269,34271],{"className":34270,"style":1346},[216],[135,34272],{},[135,34274,303],{"className":34275},[302],[135,34277,34279],{"className":34278},[212],[135,34280,34283],{"className":34281,"style":34282},[216],"height:0.836em;",[135,34284],{},[135,34286],{"className":34287},[389,200]," 的形式：",[135,34290,34292],{"className":34291},[14422],[135,34293,34295,34347],{"className":34294},[138],[135,34296,34298],{"className":34297},[142],[144,34299,34300],{"xmlns":146,"display":9554},[148,34301,34302,34344],{},[151,34303,34304,34306,34308,34310,34312,34314,34316,34318,34320],{},[167,34305,14452],{"mathvariant":894},[167,34307,14877],{},[537,34309,898],{},[167,34311,11730],{},[537,34313,874],{"stretchy":873},[167,34315,7400],{},[537,34317,888],{"stretchy":873},[537,34319,891],{},[154,34321,34322,34334],{},[151,34323,34324,34326,34328,34330,34332],{},[167,34325,14452],{"mathvariant":894},[167,34327,11730],{},[537,34329,874],{"stretchy":873},[167,34331,7400],{},[537,34333,888],{"stretchy":873},[151,34335,34336,34338,34340,34342],{},[167,34337,11730],{},[537,34339,874],{"stretchy":873},[167,34341,7400],{},[537,34343,888],{"stretchy":873},[174,34345,34346],{"encoding":176},"\\nabla \\log f(x) = \\frac{\\nabla 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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 | s_n^t)}\n\\end{aligned}",[135,35209,35211],{"className":35210,"ariaHidden":182},[181],[135,35212,35214,35218],{"className":35213},[186],[135,35215],{"className":35216,"style":35217},[190],"height:13.6262em;vertical-align:-6.5631em;",[135,35219,35221],{"className":35220},[195],[135,35222,35224,35285],{"className":35223},[14434],[135,35225,35227],{"className":35226},[15225],[135,35228,35230,35276],{"className":35229},[207,208],[135,35231,35233,35273],{"className":35232},[212],[135,35234,35237,35246,35255,35264],{"className":35235,"style":35236},[216],"height:7.0631em;",[135,35238,35240,35243],{"style":35239},"top:-9.0631em;",[135,35241],{"className":35242,"style":15242},[224],[135,35244],{"className":35245},[195],[135,35247,35249,35252],{"style":35248},"top:-5.6565em;",[135,35250],{"className":35251,"style":15242},[224],[135,35253],{"className":35254},[195],[135,35256,35258,35261],{"style":35257},"top:-2.25em;",[135,35259],{"className":35260,"style":15242},[224],[135,35262],{"className":35263},[195],[135,35265,35267,35270],{"style":35266},"top:1.1565em;",[135,35268],{"className":35269,"style":15242},[224],[135,35271],{"className":35272},[195],[135,35274,303],{"className":35275},[302],[135,35277,35279],{"className":35278},[212],[135,35280,35283],{"className":35281,"style":35282},[216],"height:6.5631em;",[135,35284],{},[135,35286,35288],{"className":35287},[15449],[135,35289,35291,38997],{"className":35290},[207,208],[135,35292,35294,38994],{"className":35293},[212],[135,35295,35297,35889,36914,38133],{"className":35296,"style":35236},[216],[135,35298,35299,35302],{"style":35239},[135,35300],{"className":35301,"style":15242},[224],[135,35303,35305,35308,35370,35373,35440,35443,35547,35550,35610,35613,35664,35667,35670,35721,35724,35727,35730,35735,35738,35778,35781,35832,35835,35886],{"className":35304},[195],[135,35306],{"className":35307},[195],[135,35309,35311,35314,35367],{"className":35310},[195],[135,35312],{"className":35313},[199,200],[135,35315,35317],{"className":35316},[154],[135,35318,35320,35359],{"className":35319},[207,208],[135,35321,35323,35356],{"className":35322},[212],[135,35324,35326,35337,35345],{"className":35325,"style":16351},[216],[135,35327,35328,35331],{"style":15891},[135,35329],{"className":35330,"style":225},[224],[135,35332,35334],{"className":35333},[195],[135,35335,7395],{"className":35336,"style":7470},[195,268],[135,35338,35339,35342],{"style":350},[135,35340],{"className":35341,"style":225},[224],[135,35343],{"className":35344,"style":358},[357],[135,35346,35347,35350],{"style":15957},[135,35348],{"className":35349,"style":225},[224],[135,35351,35353],{"className":35352},[195],[135,35354,159],{"className":35355},[195],[135,35357,303],{"className":35358},[302],[135,35360,35362],{"className":35361},[212],[135,35363,35365],{"className":35364,"style":16391},[216],[135,35366],{},[135,35368],{"className":35369},[389,200],[135,35371],{"className":35372,"style":992},[575],[135,35374,35376],{"className":35375},[1027,14310],[135,35377,35379,35432],{"className":35378},[207,208],[135,35380,35382,35429],{"className":35381},[212],[135,35383,35385,35405,35415],{"className":35384,"style":16412},[216],[135,35386,35387,35390],{"style":16415},[135,35388],{"className":35389,"style":15504},[224],[135,35391,35393],{"className":35392},[229,230,231,232],[135,35394,35396,35399,35402],{"className":35395},[195,232],[135,35397,411],{"className":35398},[195,268,232],[135,35400,891],{"className":35401},[580,232],[135,35403,159],{"className":35404},[195,232],[135,35406,35407,35410],{"style":15513},[135,35408],{"className":35409,"style":15504},[224],[135,35411,35412],{},[135,35413,1902],{"className":35414},[1027,1986,15522],[135,35416,35417,35420],{"style":16446},[135,35418],{"className":35419,"style":15504},[224],[135,35421,35423],{"className":35422},[229,230,231,232],[135,35424,35426],{"className":35425},[195,232],[135,35427,7395],{"className":35428,"style":7470},[195,268,232],[135,35430,303],{"className":35431},[302],[135,35433,35435],{"className":35434},[212],[135,35436,35438],{"className":35437,"style":16465},[216],[135,35439],{},[135,35441],{"className":35442,"style":992},[575],[135,35444,35446],{"className":35445},[1027,14310],[135,35447,35449,35539],{"className":35448},[207,208],[135,35450,35452,35536],{"className":35451},[212],[135,35453,35455,35475,35485],{"className":35454,"style":17221},[216],[135,35456,35457,35460],{"style":16415},[135,35458],{"className":35459,"style":15504},[224],[135,35461,35463],{"className":35462},[229,230,231,232],[135,35464,35466,35469,35472],{"className":35465},[195,232],[135,35467,853],{"className":35468},[195,268,232],[135,35470,891],{"className":35471},[580,232],[135,35473,159],{"className":35474},[195,232],[135,35476,35477,35480],{"style":15513},[135,35478],{"className":35479,"style":15504},[224],[135,35481,35482],{},[135,35483,1902],{"className":35484},[1027,1986,15522],[135,35486,35487,35490],{"style":17254},[135,35488],{"className":35489,"style":15504},[224],[13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= -\\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 | 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surrogate 上加 KL 惩罚",[14,40062,40063,40064,40096],{},"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 ",[135,40065,40067,40082],{"className":40066},[138],[135,40068,40070],{"className":40069},[142],[144,40071,40072],{"xmlns":146},[148,40073,40074,40079],{},[151,40075,40076],{},[167,40077,40078],{},"β",[174,40080,40081],{"encoding":176},"\\beta",[135,40083,40085],{"className":40084,"ariaHidden":182},[181],[135,40086,40088,40092],{"className":40087},[186],[135,40089],{"className":40090,"style":40091},[190],"height:0.8889em;vertical-align:-0.1944em;",[135,40093,40078],{"className":40094,"style":40095},[195,268],"margin-right:0.05278em;"," 来调整 KL 散度影响的大小。",[135,40098,40100],{"className":40099},[14422],[135,40101,40103,40310],{"className":40102},[138],[135,40104,40106],{"className":40105},[142],[144,40107,40108],{"xmlns":146,"display":9554},[148,40109,40110,40307],{},[151,40111,40112,40114,40116,40118,40125,40127,40129,40135,40149,40167,40185,40187,40195,40197,40205,40207,40273,40275,40277,40279,40285,40287,40293,40295,40305],{},[167,40113,7889],{},[167,40115,868],{},[167,40117,12874],{},[164,40119,40120,40122],{},[167,40121,12874],{},[3350,40123,40124],{},"ppo",[537,40126,891],{},[537,40128,18437],{},[154,40130,40131,40133],{},[157,40132,159],{},[167,40134,7395],{},[14755,40136,40137,40139,40147],{},[537,40138,1902],{},[151,40140,40141,40143,40145],{},[167,40142,411],{},[537,40144,891],{},[157,40146,159],{},[167,40148,7395],{},[14755,40150,40151,40153,40161],{},[537,40152,1902],{},[151,40154,40155,40157,40159],{},[167,40156,853],{},[537,40158,891],{},[157,40160,159],{},[164,40162,40163,40165],{},[167,40164,13314],{},[167,40166,411],{},[1898,40168,40169,40171,40177],{},[167,40170,850],{},[541,40172,40173,40175],{},[167,40174,14123],{},[537,40176,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[151,40178,40179,40181,40183],{},[167,40180,27582],{},[167,40182,850],{},[167,40184,5680],{},[537,40186,874],{"stretchy":873},[1898,40188,40189,40191,40193],{},[167,40190,12874],{},[167,40192,411],{},[167,40194,853],{},[537,40196,879],{"separator":182},[1898,40198,40199,40201,40203],{},[167,40200,31],{},[167,40202,411],{},[167,40204,853],{},[537,40206,888],{"stretchy":873},[154,40208,40209,40239],{},[151,40210,40211,40217,40219,40227,40229,40237],{},[164,40212,40213,40215],{},[167,40214,5677],{},[167,40216,14123],{},[537,40218,874],{"stretchy":873},[1898,40220,40221,40223,40225],{},[167,40222,31],{},[167,40224,411],{},[167,40226,853],{},[167,40228,13013],{"mathvariant":894},[1898,40230,40231,40233,40235],{},[167,40232,12874],{},[167,40234,411],{},[167,40236,853],{},[537,40238,888],{"stretchy":873},[151,40240,40241,40251,40253,40261,40263,40271],{},[164,40242,40243,40245],{},[167,40244,5677],{},[541,40246,40247,40249],{},[167,40248,14123],{},[537,40250,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[537,40252,874],{"stretchy":873},[1898,40254,40255,40257,40259],{},[167,40256,31],{},[167,40258,411],{},[167,40260,853],{},[167,40262,13013],{"mathvariant":894},[1898,40264,40265,40267,40269],{},[167,40266,12874],{},[167,40268,411],{},[167,40270,853],{},[537,40272,888],{"stretchy":873},[537,40274,5850],{},[167,40276,40078],{},[3350,40278,27667],{},[151,40280,40281,40283],{},[167,40282,648],{"mathvariant":894},[167,40284,7889],{"mathvariant":894},[537,40286,874],{"stretchy":873},[164,40288,40289,40291],{},[167,40290,5677],{},[167,40292,14123],{},[537,40294,879],{"separator":182},[164,40296,40297,40299],{},[167,40298,5677],{},[541,40300,40301,40303],{},[167,40302,14123],{},[537,40304,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[537,40306,888],{"stretchy":873},[174,40308,40309],{"encoding":176},"Loss_{\\text{ppo}} = -\\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)} + \\beta\\,\\mathrm{KL}(P_{\\theta}, P_{\\theta'})",[135,40311,40313,40383,41242],{"className":40312,"ariaHidden":182},[181],[135,40314,40316,40320,40323,40327,40374,40377,40380],{"className":40315},[186],[135,40317],{"className":40318,"style":40319},[190],"height:0.9694em;vertical-align:-0.2861em;",[135,40321,7889],{"className":40322},[195,268],[135,40324,40326],{"className":40325},[195,268],"os",[135,40328,40330,40333],{"className":40329},[195],[135,40331,12874],{"className":40332},[195,268],[135,40334,40336],{"className":40335},[272],[135,40337,40339,40365],{"className":40338},[207,208],[135,40340,40342,40362],{"className":40341},[212],[135,40343,40345],{"className":40344,"style":1398},[216],[135,40346,40347,40350],{"style":1327},[135,40348],{"className":40349,"style":616},[224],[135,40351,40353],{"className":40352},[229,230,231,232],[135,40354,40356],{"className":40355},[195,232],[135,40357,40359],{"className":40358},[195,11927,232],[135,40360,40124],{"className":40361},[195,232],[135,40363,303],{"className":40364},[302],[135,40366,40368],{"className":40367},[212],[135,40369,40372],{"className":40370,"style":40371},[216],"height:0.2861em;",[135,40373],{},[135,40375],{"className":40376,"style":576},[575],[135,40378,891],{"className":40379},[580],[135,40381],{"className":40382,"style":576},[575],[135,40384,40386,40389,40392,40454,40457,40524,40527,40631,40634,40726,40729,40780,40783,40786,40837,40840,41233,41236,41239],{"className":40385},[186],[135,40387],{"className":40388,"style":31245},[190],[135,40390,18437],{"className":40391},[195],[135,40393,40395,40398,40451],{"className":40394},[195],[135,40396],{"className":40397},[199,200],[135,40399,40401],{"className":40400},[154],[135,40402,40404,40443],{"className":40403},[207,208],[135,40405,40407,40440],{"className":40406},[212],[135,40408,40410,40421,40429],{"className":40409,"style":16351},[216],[135,40411,40412,40415],{"style":15891},[135,40413],{"className":40414,"style":225},[224],[135,40416,40418],{"className":40417},[195],[135,40419,7395],{"className":40420,"style":7470},[195,268],[135,40422,40423,40426],{"style":350},[135,40424],{"className":40425,"style":225},[224],[135,40427],{"className":40428,"style":358},[357],[135,40430,40431,40434],{"style":15957},[135,40432],{"className":40433,"style":225},[224],[135,40435,40437],{"className":40436},[195],[135,40438,159],{"className":40439},[195],[135,40441,303],{"className":40442},[302],[135,40444,40446],{"className":40445},[212],[135,40447,40449],{"className":40448,"style":16391},[216],[135,40450],{},[135,40452],{"className":40453},[389,200],[135,40455],{"className":40456,"style":992},[575],[135,40458,40460],{"className":40459},[1027,14310],[135,40461,40463,40516],{"className":40462},[207,208],[135,40464,40466,40513],{"className":40465},[212],[135,40467,40469,40489,40499],{"className":40468,"style":16412},[216],[135,40470,40471,40474],{"style":16415},[135,40472],{"className":40473,"style":15504},[224],[135,40475,40477],{"className":40476},[229,230,231,232],[135,40478,40480,40483,40486],{"className":40479},[195,232],[135,40481,411],{"className":40482},[195,268,232],[135,40484,891],{"className":40485},[580,232],[135,40487,159],{"className":40488},[195,232],[135,40490,40491,40494],{"style":15513},[135,40492],{"className":40493,"style":15504},[224],[135,40495,40496],{},[135,40497,1902],{"className":40498},[1027,1986,15522],[135,40500,40501,40504],{"style":16446},[135,40502],{"className":40503,"style":15504},[224],[135,40505,40507],{"className":40506},[229,230,231,232],[135,40508,40510],{"className":40509},[195,232],[135,40511,7395],{"className":40512,"style":7470},[195,268,232],[135,40514,303],{"className":40515},[302],[135,40517,40519],{"className":40518},[212],[135,40520,40522],{"className":40521,"style":16465},[216],[135,40523],{},[135,40525],{"className":40526,"style":992},[575],[135,40528,40530],{"className":40529},[1027,14310],[135,40531,40533,40623],{"className":40532},[207,208],[135,40534,40536,40620],{"className":40535},[212],[135,40537,40539,40559,40569],{"className":40538,"style":17221},[216],[135,40540,40541,40544],{"style":16415},[135,40542],{"className":40543,"style":15504},[224],[135,40545,40547],{"className":40546},[229,230,231,232],[135,40548,40550,40553,40556],{"className":40549},[195,232],[135,40551,853],{"className":40552},[195,268,232],[135,40554,891],{"className":40555},[580,232],[135,40557,159],{"className":40558},[195,232],[135,40560,40561,40564],{"style":15513},[135,40562],{"className":40563,"style":15504},[224],[135,40565,40566],{},[135,40567,1902],{"className":40568},[1027,1986,15522],[135,40570,40571,40574],{"style":17254},[135,40572],{"className":40573,"style":15504},[224],[135,40575,40577],{"className":40576},[229,230,231,232],[135,40578,40580],{"className":40579},[195,232],[135,40581,40583,40586],{"className":40582},[195,232],[135,40584,13314],{"className":40585,"style":3258},[195,268,232],[135,40587,40589],{"className":40588},[272],[135,40590,40592,40612],{"className":40591},[207,208],[135,40593,40595,40609],{"c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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。",[14,41396,41397,41398,41898,41899,6834,41952,42003],{},"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 ",[135,41900,41902,41921],{"className":41901},[138],[135,41903,41905],{"className":41904},[142],[144,41906,41907],{"xmlns":146},[148,41908,41909,41918],{},[151,41910,41911,41913,41915],{},[157,41912,159],{},[537,41914,18437],{},[167,41916,41917],{},"ϵ",[174,41919,41920],{"encoding":176},"1-\\epsilon",[135,41922,41924,41943],{"className":41923,"ariaHidden":182},[181],[135,41925,41927,41931,41934,41937,41940],{"className":41926},[186],[135,41928],{"className":41929,"style":41930},[190],"height:0.7278em;vertical-align:-0.0833em;",[135,41932,159],{"className":41933},[195],[135,41935],{"className":41936,"style":1948},[575],[135,41938,18437],{"className":41939},[629],[135,41941],{"className":41942,"style":1948},[575],[135,41944,41946,41949],{"className":41945},[186],[135,41947],{"className":41948,"style":423},[190],[135,41950,41917],{"className":41951},[195,268],[135,41953,41955,41973],{"className":41954},[138],[135,41956,41958],{"className":41957},[142],[144,41959,41960],{"xmlns":146},[148,41961,41962,41970],{},[151,41963,41964,41966,41968],{},[157,41965,159],{},[537,41967,5850],{},[167,41969,41917],{},[174,41971,41972],{"encoding":176},"1+\\epsilon",[135,41974,41976,41994],{"className":41975,"ariaHidden":182},[181],[135,41977,41979,41982,41985,41988,41991],{"className":41978},[186],[135,41980],{"className":41981,"style":41930},[190],[135,41983,159],{"className":41984},[195],[135,41986],{"className":41987,"style":1948},[575],[135,41989,5850],{"className":41990},[629],[135,41992],{"className":41993,"style":1948},[575],[135,41995,41997,42000],{"className":41996},[186],[135,41998],{"className":41999,"style":423},[190],[135,42001,41917],{"className":42002},[195,268]," 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。",[135,42005,42007],{"className":42006},[14422],[135,42008,42010,42346],{"className":42009},[138],[135,42011,42013],{"className":42012},[142],[144,42014,42015],{"xmlns":146,"display":9554},[148,42016,42017,42343],{},[151,42018,42019,42021,42023,42025,42032,42034,42036,42042,42056,42074,42077,42079],{},[167,42020,7889],{},[167,42022,868],{},[167,42024,12874],{},[164,42026,42027,42029],{},[167,42028,12874],{},[3350,42030,42031],{},"ppo2",[537,42033,891],{},[537,42035,18437],{},[154,42037,42038,42040],{},[157,42039,159],{},[167,42041,7395],{},[14755,42043,42044,42046,42054],{},[537,42045,1902],{},[151,42047,42048,42050,42052],{},[167,42049,411],{},[537,42051,891],{},[157,42053,159],{},[167,42055,7395],{},[14755,42057,42058,42060,42068],{},[537,42059,1902],{},[151,42061,42062,42064,42066],{},[167,42063,853],{},[537,42065,891],{},[157,42067,159],{},[164,42069,42070,42072],{},[167,42071,13314],{},[167,42073,411],{},[167,42075,42076],{},"min",[537,42078,898],{},[151,42080,42081,42083,42192,42194,42196,42341],{},[537,42082,874],{"fence":182},[14446,42084,42086,42104,42106,42114,42116,42124,42126],{"mathcolor":42085},"red",[1898,42087,42088,42090,42096],{},[167,42089,850],{},[541,42091,42092,42094],{},[167,42093,14123],{},[537,42095,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[151,42097,42098,42100,42102],{},[167,42099,27582],{},[167,42101,850],{},[167,42103,5680],{},[537,42105,874],{"stretchy":873},[1898,42107,42108,42110,42112],{},[167,42109,12874],{},[167,42111,411],{},[167,42113,853],{},[537,42115,879],{"separator":182},[1898,42117,42118,42120,42122],{},[167,42119,31],{},[167,42121,411],{},[167,42123,853],{},[537,42125,888],{"stretchy":873},[154,42127,42128,42158],{},[151,42129,42130,42136,42138,42146,42148,42156],{},[164,42131,42132,42134],{},[167,42133,5677],{},[167,42135,14123],{},[537,42137,874],{"stretchy":873},[1898,42139,42140,42142,42144],{},[167,42141,31],{},[167,42143,411],{},[167,42145,853],{},[167,42147,13013],{"mathvariant":894},[1898,42149,42150,42152,42154],{},[167,42151,12874],{},[167,42153,411],{},[167,42155,853],{},[537,42157,888],{"stretchy":873},[151,42159,42160,42170,42172,42180,42182,42190],{},[164,42161,42162,42164],{},[167,42163,5677],{},[541,42165,42166,42168],{},[167,42167,14123],{},[537,42169,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[537,42171,874],{"stretchy":873},[1898,42173,42174,42176,42178],{},[167,42175,31],{},[167,42177,411],{},[167,42179,853],{},[167,42181,13013],{"mathvariant":894},[1898,42183,42184,42186,42188],{},[167,42185,12874],{},[167,42187,411],{},[167,42189,853],{},[537,42191,888],{"stretchy":873},[537,42193,879],{"separator":182},[3350,42195,27667],{},[14446,42197,42199,42209,42301,42319,42321,42329,42331,42339],{"mathcolor":42198},"skyblue",[151,42200,42201,42203,42205,42207],{},[167,42202,3017],{"mathvariant":894},[167,42204,2976],{"mathvariant":894},[167,42206,865],{"mathvariant":894},[167,42208,14],{"mathvariant":894},[151,42210,42211,42213,42279,42281,42283,42285,42287,42289,42291,42293,42295,42297,42299],{},[537,42212,874],{"fence":182},[154,42214,42215,42245],{},[151,42216,42217,42223,42225,42233,42235,42243],{},[164,42218,42219,42221],{},[167,42220,5677],{},[167,42222,14123],{},[537,42224,874],{"stretchy":873},[1898,42226,42227,42229,42231],{},[167,42228,31],{},[167,42230,411],{},[167,42232,853],{},[167,42234,13013],{"mathvariant":894},[1898,42236,42237,42239,42241],{},[167,42238,12874],{},[167,42240,411],{},[167,42242,853],{},[537,42244,888],{"stretchy":873},[151,42246,42247,42257,42259,42267,42269,42277],{},[164,42248,42249,42251],{},[167,42250,5677],{},[541,42252,42253,42255],{},[167,42254,14123],{},[537,42256,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[537,42258,874],{"stretchy":873},[1898,42260,42261,42263,42265],{},[167,42262,31],{},[167,42264,411],{},[167,42266,853],{},[167,42268,13013],{"mathvariant":894},[1898,42270,42271,42273,42275],{},[167,42272,12874],{},[167,42274,411],{},[167,42276,853],{},[537,42278,888],{"stretchy":873},[537,42280,879],{"separator":182},[3350,42282,27667],{},[157,42284,159],{},[537,42286,18437],{},[167,42288,41917],{},[537,42290,879],{"separator":182},[3350,42292,27667],{},[157,42294,159],{},[537,42296,5850],{},[167,42298,41917],{},[537,42300,888],{"fence":182},[1898,42302,42303,42305,42311],{},[167,42304,850],{},[541,42306,42307,42309],{},[167,42308,14123],{},[537,42310,19056],{"mathvariant":894,"lspace":14438,"rspace":14438},[151,42312,42313,42315,42317],{},[167,42314,27582],{},[167,42316,850],{},[167,42318,5680],{},[537,42320,874],{"stretchy":873},[1898,42322,42323,42325,42327],{},[167,42324,12874],{},[167,42326,411],{},[167,42328,853],{},[537,42330,879],{"separator":182},[1898,42332,42333,42335,42337],{},[167,42334,31],{},[167,42336,411],{},[167,42338,853],{},[537,42340,888],{"stretchy":873},[537,42342,888],{"fence":182},[174,42344,42345],{"encoding":176},"Loss_{\\text{ppo2}} = -\\frac{1}{N} \\sum_{n=1}^{N} \\sum_{t=1}^{T_n} \\min\\left(\\textcolor{red}{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)}},\\,\\textcolor{skyblue}{\\mathrm{clip}\\left(\\frac{P_{\\theta}(a_n^t|s_n^t)}{P_{\\theta'}(a_n^t|s_n^t)},\\, 1-\\epsilon,\\, 1+\\epsilon\\right) A_{\\theta'}^{GAE}(s_n^t, 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{"className":43967,"style":43298},[195,268,232],[135,43969,303],{"className":43970},[302],[135,43972,43974],{"className":43973},[212],[135,43975,43977],{"className":43976,"style":17413},[216],[135,43978],{},[135,43980,888],{"className":43981,"style":43298},[389],[135,43983,43985],{"className":43984,"style":1043},[389,1042],[135,43986,888],{"className":43987},[1047,231],[10,43989,40],{"id":40},[14,43991,43992],{},[31,43993,43996],{"href":43994,"rel":43995},"https://www.bilibili.com/video/BV1iz421h7gb/",[35],"零基础学习强化学习算法：ppo",{"title":65,"searchDepth":66,"depth":66,"links":43998},[43999,44000,44001,44002,44005,44009],{"id":12745,"depth":66,"text":12745},{"id":12751,"depth":66,"text":12751},{"id":14017,"depth":66,"text":14017},{"id":19533,"depth":66,"text":19534,"children":44003},[44004],{"id":27510,"depth":2510,"text":27511},{"id":31832,"depth":66,"text":31833,"children":44006},[44007,44008],{"id":31839,"depth":2510,"text":31839},{"id":33644,"depth":2510,"text":33645},{"id":40,"depth":66,"text":40},"记一下学习 PPO中学习到的东西",{"date":44012,"image":44013,"alt":44014,"tags":44015,"published":80},"8 Mar 2026","/blogs-img/blog2.jpg","PPO学习笔记",[44016,12733],"Reinforcement learning","/blogs/ppo",{"title":12740,"description":44010},"blogs/2. PPO学习笔记","Sx3SA-gd0nzBc5-IShm_PpZrHX9EMT8A7rF2k0GLT9I",{"id":44022,"title":44023,"body":44024,"description":44023,"extension":72,"meta":44398,"navigation":80,"ogImage":44400,"path":44404,"seo":44405,"stem":44406,"__hash__":44407},"content/blogs/3. 记录一下我的 zsh 配置.md","记录一下我的 zsh 配置",{"type":7,"value":44025,"toc":44381},[44026,44028,44031,44035,44038,44041,44044,44047,44050,44093,44096,44100,44103,44106,44172,44175,44194,44197,44200,44203,44206,44209,44229,44232,44235,44237,44256,44258,44265,44270,44273,44276,44279,44282,44289,44297,44300,44303,44306,44309,44312,44361,44367,44370,44373,44378],[10,44027,12],{"id":12},[14,44029,44030],{},"最近想写点东西记录一下自己折腾这些工具的经历，之前没想到记录什么，今年实验室的服务器迁移需要重新配置一下 zsh,于是想着干脆顺手写一下自己折腾 zsh 出来的方案。",[10,44032,44034],{"id":44033},"什么是-zsh","什么是 Zsh",[14,44036,44037],{},"Zsh 也是一种 shell 软件，可以看成是一个更好用的 Bash，目前 MacOS 中的默认 shell 已经是 Zsh 了。Zsh 完全兼容 Bash，拥有极其丰富的插件，其强大的自动补全参数、文件名以及自定义功能，可以大大提高我们使用 Linux 的效率。",[14,44039,44040],{},"Zsh 可以通过大部分主流 Linux 发行版的包管理器进行安装，若在没有 sudo 权限的服务器上也可以通过conda进行安装。",[10,44042,44043],{"id":44043},"oh-my-zsh",[14,44045,44046],{},"Zsh 固然好用，但初始时只有白板没有任何插件，距离理想的使用体验还有一些差距，这里我们介绍 oh-my-zsh。",[14,44048,44049],{},"oh-my-zsh 是社区为 zsh 收集的一个第三方插件和主题合集，我们可以通过国内镜像快速安装，这里使用了南京大学镜像站。",[2466,44051,44055],{"className":44052,"code":44053,"language":44054,"meta":65,"style":65},"language-bash shiki shiki-themes github-light dracula","git clone https://mirror.nju.edu.cn/git/ohmyzsh.git\ncd ohmyzsh/tools\nREMOTE=https://mirror.nju.edu.cn/git/ohmyzsh.git sh install.sh\n","bash",[2472,44056,44057,44068,44076],{"__ignoreMap":65},[135,44058,44059,44062,44065],{"class":2476,"line":2477},[135,44060,44061],{"class":2484},"git",[135,44063,44064],{"class":9553}," clone",[135,44066,44067],{"class":9553}," https://mirror.nju.edu.cn/git/ohmyzsh.git\n",[135,44069,44070,44073],{"class":2476,"line":66},[135,44071,44072],{"class":9534},"cd",[135,44074,44075],{"class":9553}," ohmyzsh/tools\n",[135,44077,44078,44082,44084,44087,44090],{"class":2476,"line":2510},[135,44079,44081],{"class":44080},"scEb-","REMOTE",[135,44083,891],{"class":2480},[135,44085,44086],{"class":9553},"https://mirror.nju.edu.cn/git/ohmyzsh.git",[135,44088,44089],{"class":2484}," sh",[135,44091,44092],{"class":9553}," install.sh\n",[14,44094,44095],{},"通过这三条指令可以在境内快速安装我们的 oh-my-zsh，同时也可以选择将 zsh 设置为默认 shell。",[10,44097,44099],{"id":44098},"powerlevel10k","Powerlevel10k",[14,44101,44102],{},"oh-my-zsh 中的主题我认为还是不够美观和定制，我希望有个更好的体验，这里我们引入 Powerlevel10k 主题。在众多主题中，Powerlevel10k 因其美观性和高度定制的特性脱颖而出，截止到 2026年4月28日，Powerlevel10k 在 github 已累计收获 54k 个 star。",[14,44104,44105],{},"在国内，安装 Powerlevel10k 可以使用 gitee 的镜像进行安装，安装指令如下：",[2466,44107,44109],{"className":44052,"code":44108,"language":44054,"meta":65,"style":65},"git clone --depth=1 https://gitee.com/romkatv/powerlevel10k.git \"${ZSH_CUSTOM:-$HOME/.oh-my-zsh/custom}/themes/powerlevel10k\"\necho 'source /usr/share/zsh-theme-powerlevel10k/powerlevel10k.zsh-theme' >>~/.zshrc\n",[2472,44110,44111,44154],{"__ignoreMap":65},[135,44112,44113,44115,44117,44120,44123,44125,44128,44131,44134,44137,44139,44141,44143,44145,44148,44151],{"class":2476,"line":2477},[135,44114,44061],{"class":2484},[135,44116,44064],{"class":9553},[135,44118,44119],{"class":2529}," --depth=1",[135,44121,44122],{"class":9553}," https://gitee.com/romkatv/powerlevel10k.git",[135,44124,11326],{"class":9549},[135,44126,44127],{"class":9553},"${",[135,44129,44130],{"class":44080},"ZSH_CUSTOM",[135,44132,44133],{"class":2480},":-",[135,44135,44136],{"class":44080},"$HOME",[135,44138,2900],{"class":2480},[135,44140,940],{"class":9553},[135,44142,44043],{"class":44080},[135,44144,2900],{"class":2480},[135,44146,44147],{"class":44080},"custom",[135,44149,44150],{"class":9553},"}/themes/powerlevel10k",[135,44152,44153],{"class":9549},"\"\n",[135,44155,44156,44159,44161,44164,44166,44169],{"class":2476,"line":66},[135,44157,44158],{"class":9534},"echo",[135,44160,11996],{"class":9549},[135,44162,44163],{"class":9553},"source /usr/share/zsh-theme-powerlevel10k/powerlevel10k.zsh-theme",[135,44165,10965],{"class":9549},[135,44167,44168],{"class":2480}," >>",[135,44170,44171],{"class":9553},"~/.zshrc\n",[14,44173,44174],{},"之后需要安装一款推荐字体，这里我个人使用的 0xProtoNerdFont 字体，大家也可以在其他博客或者官方仓库中使用其他人推荐的字体。",[14,44176,44177,44178,44181,44182,44185,44186,44189,44190,44193],{},"之后修改 ",[2472,44179,44180],{},"~/.zshrc"," 文件，将变量 ",[2472,44183,44184],{},"ZSH_THEME"," 修改为 ",[2472,44187,44188],{},"powerlevel10k/powerlevel10k",",即 ",[2472,44191,44192],{},"ZSH_THEME=\"powerlevel10k/powerlevel10k\""," 即可，之后重启终端即可根据个人喜好开始配置。",[10,44195,44196],{"id":44196},"插件设置",[14,44198,44199],{},"现在主题已经搞定了，下一步开始设置真正能帮助我们提高生产力的插件。",[125,44201,44202],{"id":44202},"zsh-autosuggestions",[14,44204,44205],{},"一个非常有用的插件，它根据历史记录和补全信息在输入时建议命令。",[14,44207,44208],{},"安装指令：",[2466,44210,44212],{"className":44052,"code":44211,"language":44054,"meta":65,"style":65},"git clone https://github.com/zsh-users/zsh-autosuggestions $ZSH_CUSTOM/plugins/zsh-autosuggestions\n",[2472,44213,44214],{"__ignoreMap":65},[135,44215,44216,44218,44220,44223,44226],{"class":2476,"line":2477},[135,44217,44061],{"class":2484},[135,44219,44064],{"class":9553},[135,44221,44222],{"class":9553}," https://github.com/zsh-users/zsh-autosuggestions",[135,44224,44225],{"class":44080}," $ZSH_CUSTOM",[135,44227,44228],{"class":9553},"/plugins/zsh-autosuggestions\n",[125,44230,44231],{"id":44231},"zsh-syntax-highlighting",[14,44233,44234],{},"提供指令和文件路径的高亮限制，方便你检查指令和路径的正确性。",[14,44236,44208],{},[2466,44238,44240],{"className":44052,"code":44239,"language":44054,"meta":65,"style":65},"git clone https://github.com/zsh-users/zsh-syntax-highlighting $ZSH_CUSTOM/plugins/zsh-syntax-highlighting\n",[2472,44241,44242],{"__ignoreMap":65},[135,44243,44244,44246,44248,44251,44253],{"class":2476,"line":2477},[135,44245,44061],{"class":2484},[135,44247,44064],{"class":9553},[135,44249,44250],{"class":9553}," https://github.com/zsh-users/zsh-syntax-highlighting",[135,44252,44225],{"class":44080},[135,44254,44255],{"class":9553},"/plugins/zsh-syntax-highlighting\n",[125,44257,44061],{"id":44061},[14,44259,44260,44261,44264],{},"oh-my-zsh 自带的插件，将大量常用的 git 指令简化，具体怎么使用可以参考 ",[2472,44262,44263],{},"$ZSH/plugins/git/git.plugin.zsh "," 这个文件。",[14,44266,44267],{},[117,44268],{"alt":44061,"src":44269},"zsh/git.png",[14,44271,44272],{},"如图所示 alias 表示别名，等号左边为缩写指令，右边为原指令。",[10,44274,44275],{"id":44275},"一些软件",[125,44277,44278],{"id":44278},"nvm",[14,44280,44281],{},"一个非常好用的 node.js 版本管理器，无需 sudo 权限。",[14,44283,44284,44285,44288],{},"解决使用系统级 node 时 ",[2472,44286,44287],{},"npm install -g "," 安装引起的一些问题。",[14,44290,44291,44292,44296],{},"参考 ",[31,44293,44294],{"href":44294,"rel":44295},"https://github.com/nvm-sh/nvm",[35]," 安装。",[125,44298,44299],{"id":44299},"conda",[14,44301,44302],{},"无需多言。",[125,44304,44305],{"id":44305},"fastfetch",[14,44307,44308],{},"获取本机发行版和硬件信息，比较酷炫，装逼使用。",[14,44310,44311],{},"可以进行美化，参考指令：",[2466,44313,44315],{"className":44052,"code":44314,"language":44054,"meta":65,"style":65},"cd $HOME/.config\n\n# 下载并解压然后删除\nwget https://github.com/sqlsec/fastfetch/releases/download/v0.1/fastfetch-for-Linux.zip\nunzip fastfetch-for-Linux.zip && rm fastfetch-for-Linux.zip\n",[2472,44316,44317,44327,44331,44336,44344],{"__ignoreMap":65},[135,44318,44319,44321,44324],{"class":2476,"line":2477},[135,44320,44072],{"class":9534},[135,44322,44323],{"class":44080}," $HOME",[135,44325,44326],{"class":9553},"/.config\n",[135,44328,44329],{"class":2476,"line":66},[135,44330,2798],{"emptyLinePlaceholder":80},[135,44332,44333],{"class":2476,"line":2510},[135,44334,44335],{"class":2513},"# 下载并解压然后删除\n",[135,44337,44338,44341],{"class":2476,"line":2517},[135,44339,44340],{"class":2484},"wget",[135,44342,44343],{"class":9553}," https://github.com/sqlsec/fastfetch/releases/download/v0.1/fastfetch-for-Linux.zip\n",[135,44345,44346,44349,44352,44355,44358],{"class":2476,"line":2536},[135,44347,44348],{"class":2484},"unzip",[135,44350,44351],{"class":9553}," fastfetch-for-Linux.zip",[135,44353,44354],{"class":2488}," && ",[135,44356,44357],{"class":2484},"rm",[135,44359,44360],{"class":9553}," fastfetch-for-Linux.zip\n",[14,44362,44363,44364],{},"效果如图：\n",[117,44365],{"alt":44305,"src":44366},"zsh/fastfetch.png",[125,44368,44369],{"id":44369},"onefetch",[14,44371,44372],{},"获取当前 git 项目信息，使用时需保证当前目录已经 git 初始化。",[14,44374,44363,44375],{},[117,44376],{"alt":44369,"src":44377},"zsh/onefetch.png",[12708,44379,44380],{},"html pre.shiki code .sCLZk, html code.shiki .sCLZk{--shiki-default:#6F42C1;--shiki-dark:#50FA7B}html pre.shiki code .sEzAm, html code.shiki .sEzAm{--shiki-default:#032F62;--shiki-dark:#F1FA8C}html pre.shiki code .sDgm9, html code.shiki .sDgm9{--shiki-default:#005CC5;--shiki-dark:#8BE9FD}html pre.shiki code .scEb-, html code.shiki .scEb-{--shiki-default:#24292E;--shiki-dark:#BD93F9}html pre.shiki code .szJfE, html code.shiki .szJfE{--shiki-default:#D73A49;--shiki-dark:#FF79C6}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .soDru, html code.shiki .soDru{--shiki-default:#005CC5;--shiki-dark:#BD93F9}html pre.shiki code .sMWOi, html code.shiki .sMWOi{--shiki-default:#032F62;--shiki-dark:#E9F284}html pre.shiki code .sfgPZ, html code.shiki .sfgPZ{--shiki-default:#6A737D;--shiki-dark:#6272A4}html pre.shiki code .scbbO, html code.shiki .scbbO{--shiki-default:#24292E;--shiki-dark:#F8F8F2}",{"title":65,"searchDepth":66,"depth":66,"links":44382},[44383,44384,44385,44386,44387,44392],{"id":12,"depth":66,"text":12},{"id":44033,"depth":66,"text":44034},{"id":44043,"depth":66,"text":44043},{"id":44098,"depth":66,"text":44099},{"id":44196,"depth":66,"text":44196,"children":44388},[44389,44390,44391],{"id":44202,"depth":2510,"text":44202},{"id":44231,"depth":2510,"text":44231},{"id":44061,"depth":2510,"text":44061},{"id":44275,"depth":66,"text":44275,"children":44393},[44394,44395,44396,44397],{"id":44278,"depth":2510,"text":44278},{"id":44299,"depth":2510,"text":44299},{"id":44305,"depth":2510,"text":44305},{"id":44369,"depth":2510,"text":44369},{"date":44399,"image":44400,"alt":44401,"tags":44402,"published":80},"28 April 2026","/blogs-img/blog3.jpg","Zsh 配置",[78,44403],"折腾笔记","/blogs/zsh",{"title":44023,"description":44023},"blogs/3. 记录一下我的 zsh 配置","PJV8pr0i_NIcto4IrLugXMoDWoeE7cWFgoETPzSjgXk",{"id":44409,"title":44410,"body":44411,"description":44501,"extension":72,"meta":44502,"navigation":80,"ogImage":75,"path":44508,"seo":44509,"stem":44510,"__hash__":44511},"content/blogs/4. Agent 相关的折腾记录（持续更新）.md","Agent 相关的折腾记录（持续更新）",{"type":7,"value":44412,"toc":44488},[44413,44415,44418,44421,44424,44428,44431,44435,44438,44442,44445,44449,44452,44456,44459,44463,44466,44469,44472,44476,44479,44482,44485],[10,44414,12],{"id":12},[14,44416,44417],{},"最近开始静下心来研究 Agent 生态了，之前一直没有深入研究主要是因为个人感觉生态不够成熟，技术日新月异，发展太快，还没到一个成熟稳定的阶段。最近感觉 Agent 相关概念开始趋于稳定完备，于是开始折腾。",[10,44419,44420],{"id":44420},"介绍一下我有哪些工具",[14,44422,44423],{},"截至目前，本人共尝试过 Claude Code, Codex, Cursor, 最近又刚开始体验 SOLO Trae（支持国产），先说一下体验。",[125,44425,44427],{"id":44426},"claude-code","Claude Code",[14,44429,44430],{},"夯，编程体验最好的一个，插件生态没得说，感觉聪明程度是目前其他 Coding Agent 没得比的，而且能搭配 Curosr/Vscode 之类的编辑器使用，在终端中打开 Claude Code 时可以选中 Cursor/Vscode 视图中某一部分的代码，同步给 Claude Code 作为上下文，选择是否应用修改时也能在 Cursor/Vscode 中进行检查，使用体验极好。",[125,44432,44434],{"id":44433},"codex","Codex",[14,44436,44437],{},"量大管饱，智力也相当可以，开 xhigh 写代码一点不含糊，感觉生态略差一些。",[125,44439,44441],{"id":44440},"cursor","Cursor",[14,44443,44444],{},"还可以，使用 GPT 系列经常降智， claude sonnet 和 opus 又容易过度思考，简单任务 auto 又快又省钱，Tab 补全确实惊艳，对于手写古人来说值得体验。",[125,44446,44448],{"id":44447},"solo-trae","SOLO Trae",[14,44450,44451],{},"现在模型免费，可以白嫖干点简单活，添加模型时自定义能力差，使用 skill 还要指定，用还要排大队，感觉有待提高。",[10,44453,44455],{"id":44454},"skills","Skills",[14,44457,44458],{},"最近发现 Skills 确实能极大地提高模型的能力，打算开始挖掘 Skills 的潜力。",[10,44460,44462],{"id":44461},"mcp","MCP",[14,44464,44465],{},"体验不多，目前高度使用 Notion 的 MCP，让 AI 直接把文字写入 Notion 中，非常方便。",[10,44467,44468],{"id":44468},"杂谈",[14,44470,44471],{},"目前还使用了 CC-Switch 来管理多个 api 渠道，Claude Code 主力使用公益神站 AnyRouter，这个网站唯一的缺点就是太不稳定，最近开始又恢复正常使用了，准备狠狠地用起来。",[10,44473,44475],{"id":44474},"zcf","ZCF",[14,44477,44478],{},"ZCF 全称 Zero-Config Code Flow。",[14,44480,44481],{},"ZCF（Zero-Config Code Flow）是一个面向专业开发者的 CLI 工具，目标是在几分钟内完成 Claude Code 与 Codex 的端到端环境初始化。通过 npx zcf 可以一站式完成配置目录创建、API/代理接入、MCP 服务接入、工作流导入、输出风格与记忆配置，以及常用工具安装。",[14,44483,44484],{},"最近体验了一下 zcf:init-project，发现确实不赖，比Claude Code 和 Codex 自带的 init功能要好不少。这个初始化会生成总体的和目录级的 CLAUDE.md 文件作为指导，还会生成 .claude/index.json 文件作为文件索引，同时会记录修改时间，之后每次使用 Claude Code 修改代码还会同步修改 CLAUDE.md 文件，记录自己在什么时候修改了什么代码，这样可以极大地保证代码的可维护性，防止 AI 拉了一大坨之后无法维护，虽然会加大 Token 消耗，但收益大于付出。",[14,44486,44487],{},"zcf 在安装时还可以选择性地安装部分 MCP 服务，我个人一般会安装 spec-workflow，context7 和 open-websearch 这三个 MCP 服务，不过最近 spec-workflow 总是连接不上，后面要找个时间修复一下。",{"title":65,"searchDepth":66,"depth":66,"links":44489},[44490,44491,44497,44498,44499,44500],{"id":12,"depth":66,"text":12},{"id":44420,"depth":66,"text":44420,"children":44492},[44493,44494,44495,44496],{"id":44426,"depth":2510,"text":44427},{"id":44433,"depth":2510,"text":44434},{"id":44440,"depth":2510,"text":44441},{"id":44447,"depth":2510,"text":44448},{"id":44454,"depth":66,"text":44455},{"id":44461,"depth":66,"text":44462},{"id":44468,"depth":66,"text":44468},{"id":44474,"depth":66,"text":44475},"记录自己折腾一些智能体相关技术的经历",{"date":44503,"image":75,"alt":44504,"tags":44505,"published":80},"30 April 2026","Agent",[44504,44403,44506,44462,44455,44507],"worlflow","harness","/blogs/agent",{"title":44410,"description":44501},"blogs/4. 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