[{"data":1,"prerenderedAt":86295},["ShallowReactive",2],{"recent-post":3,"trending-post":43951},[4,31438],{"id":5,"title":6,"body":7,"description":31423,"extension":31424,"meta":31425,"navigation":31433,"ogImage":31427,"path":31434,"seo":31435,"stem":31436,"__hash__":31437},"content/blogs/2. PPO学习笔记.md","零基础速通 PPO 学习笔记",{"type":8,"value":9,"toc":31407},"minimark",[10,14,18,21,576,890,1349,1352,1355,1419,1774,5782,6387,6907,6911,6987,7652,7897,8018,8347,8350,9036,10176,10278,10281,12914,13021,14893,14898,14901,14936,17725,17728,17731,17734,19221,19224,19228,19231,19234,19372,21039,21042,21046,21690,21881,26406,26409,27454,27457,27462,27498,28792,28796,28799,29409,31396,31399],[11,12,13],"h2",{"id":13},"学习背景",[15,16,17],"p",{},"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。",[11,19,20],{"id":20},"符号定义",[15,22,23,24,130,131,160,161,232,233,261,262,294,295,440,441,514,515,543,544,575],{},"在强化学习中，",[25,26,29,58],"span",{"className":27},[28],"katex",[25,30,33],{"className":31},[32],"katex-mathml",[34,35,37],"math",{"xmlns":36},"http://www.w3.org/1998/Math/MathML",[38,39,40,53],"semantics",{},[41,42,43],"mrow",{},[44,45,46,50],"msub",{},[47,48,49],"mi",{},"a",[47,51,52],{},"t",[54,55,57],"annotation",{"encoding":56},"application/x-tex","a_t",[25,59,63],{"className":60,"ariaHidden":62},[61],"katex-html","true",[25,64,67,72],{"className":65},[66],"base",[25,68],{"className":69,"style":71},[70],"strut","height:0.5806em;vertical-align:-0.15em;",[25,73,76,80],{"className":74},[75],"mord",[25,77,49],{"className":78},[75,79],"mathnormal",[25,81,84],{"className":82},[83],"msupsub",[25,85,89,121],{"className":86},[87,88],"vlist-t","vlist-t2",[25,90,93,116],{"className":91},[92],"vlist-r",[25,94,98],{"className":95,"style":97},[96],"vlist","height:0.2806em;",[25,99,101,106],{"style":100},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[25,102],{"className":103,"style":105},[104],"pstrut","height:2.7em;",[25,107,113],{"className":108},[109,110,111,112],"sizing","reset-size6","size3","mtight",[25,114,52],{"className":115},[75,79,112],[25,117,120],{"className":118},[119],"vlist-s","​",[25,122,124],{"className":123},[92],[25,125,128],{"className":126,"style":127},[96],"height:0.15em;",[25,129],{}," 一般表示 ",[25,132,134,147],{"className":133},[28],[25,135,137],{"className":136},[32],[34,138,139],{"xmlns":36},[38,140,141,145],{},[41,142,143],{},[47,144,52],{},[54,146,52],{"encoding":56},[25,148,150],{"className":149,"ariaHidden":62},[61],[25,151,153,157],{"className":152},[66],[25,154],{"className":155,"style":156},[70],"height:0.6151em;",[25,158,52],{"className":159},[75,79]," 时刻 Agent 采取的动作（action）；",[25,162,164,183],{"className":163},[28],[25,165,167],{"className":166},[32],[34,168,169],{"xmlns":36},[38,170,171,180],{},[41,172,173],{},[44,174,175,178],{},[47,176,177],{},"s",[47,179,52],{},[54,181,182],{"encoding":56},"s_t",[25,184,186],{"className":185,"ariaHidden":62},[61],[25,187,189,192],{"className":188},[66],[25,190],{"className":191,"style":71},[70],[25,193,195,198],{"className":194},[75],[25,196,177],{"className":197},[75,79],[25,199,201],{"className":200},[83],[25,202,204,224],{"className":203},[87,88],[25,205,207,221],{"className":206},[92],[25,208,210],{"className":209,"style":97},[96],[25,211,212,215],{"style":100},[25,213],{"className":214,"style":105},[104],[25,216,218],{"className":217},[109,110,111,112],[25,219,52],{"className":220},[75,79,112],[25,222,120],{"className":223},[119],[25,225,227],{"className":226},[92],[25,228,230],{"className":229,"style":127},[96],[25,231],{}," 表示 ",[25,234,236,249],{"className":235},[28],[25,237,239],{"className":238},[32],[34,240,241],{"xmlns":36},[38,242,243,247],{},[41,244,245],{},[47,246,52],{},[54,248,52],{"encoding":56},[25,250,252],{"className":251,"ariaHidden":62},[61],[25,253,255,258],{"className":254},[66],[25,256],{"className":257,"style":156},[70],[25,259,52],{"className":260},[75,79]," 时刻 Agent 所处的状态（state）；",[25,263,265,280],{"className":264},[28],[25,266,268],{"className":267},[32],[34,269,270],{"xmlns":36},[38,271,272,277],{},[41,273,274],{},[47,275,276],{},"π",[54,278,279],{"encoding":56},"\\pi",[25,281,283],{"className":282,"ariaHidden":62},[61],[25,284,286,290],{"className":285},[66],[25,287],{"className":288,"style":289},[70],"height:0.4306em;",[25,291,276],{"className":292,"style":293},[75,79],"margin-right:0.03588em;"," 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 ",[25,296,298,336],{"className":297},[28],[25,299,301],{"className":300},[32],[34,302,303],{"xmlns":36},[38,304,305,333],{},[41,306,307,309,314,320,324,330],{},[47,308,276],{},[310,311,313],"mo",{"stretchy":312},"false","(",[44,315,316,318],{},[47,317,49],{},[47,319,52],{},[47,321,323],{"mathvariant":322},"normal","∣",[44,325,326,328],{},[47,327,177],{},[47,329,52],{},[310,331,332],{"stretchy":312},")",[54,334,335],{"encoding":56},"\\pi(a_t|s_t)",[25,337,339],{"className":338,"ariaHidden":62},[61],[25,340,342,346,349,353,393,396,436],{"className":341},[66],[25,343],{"className":344,"style":345},[70],"height:1em;vertical-align:-0.25em;",[25,347,276],{"className":348,"style":293},[75,79],[25,350,313],{"className":351},[352],"mopen",[25,354,356,359],{"className":355},[75],[25,357,49],{"className":358},[75,79],[25,360,362],{"className":361},[83],[25,363,365,385],{"className":364},[87,88],[25,366,368,382],{"className":367},[92],[25,369,371],{"className":370,"style":97},[96],[25,372,373,376],{"style":100},[25,374],{"className":375,"style":105},[104],[25,377,379],{"className":378},[109,110,111,112],[25,380,52],{"className":381},[75,79,112],[25,383,120],{"className":384},[119],[25,386,388],{"className":387},[92],[25,389,391],{"className":390,"style":127},[96],[25,392],{},[25,394,323],{"className":395},[75],[25,397,399,402],{"className":398},[75],[25,400,177],{"className":401},[75,79],[25,403,405],{"className":404},[83],[25,406,408,428],{"className":407},[87,88],[25,409,411,425],{"className":410},[92],[25,412,414],{"className":413,"style":97},[96],[25,415,416,419],{"style":100},[25,417],{"className":418,"style":105},[104],[25,420,422],{"className":421},[109,110,111,112],[25,423,52],{"className":424},[75,79,112],[25,426,120],{"className":427},[119],[25,429,431],{"className":430},[92],[25,432,434],{"className":433,"style":127},[96],[25,435],{},[25,437,332],{"className":438},[439],"mclose","；",[25,442,444,463],{"className":443},[28],[25,445,447],{"className":446},[32],[34,448,449],{"xmlns":36},[38,450,451,460],{},[41,452,453],{},[44,454,455,458],{},[47,456,457],{},"r",[47,459,52],{},[54,461,462],{"encoding":56},"r_t",[25,464,466],{"className":465,"ariaHidden":62},[61],[25,467,469,472],{"className":468},[66],[25,470],{"className":471,"style":71},[70],[25,473,475,479],{"className":474},[75],[25,476,457],{"className":477,"style":478},[75,79],"margin-right:0.02778em;",[25,480,482],{"className":481},[83],[25,483,485,506],{"className":484},[87,88],[25,486,488,503],{"className":487},[92],[25,489,491],{"className":490,"style":97},[96],[25,492,494,497],{"style":493},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[25,495],{"className":496,"style":105},[104],[25,498,500],{"className":499},[109,110,111,112],[25,501,52],{"className":502},[75,79,112],[25,504,120],{"className":505},[119],[25,507,509],{"className":508},[92],[25,510,512],{"className":511,"style":127},[96],[25,513],{}," 一边表示 ",[25,516,518,531],{"className":517},[28],[25,519,521],{"className":520},[32],[34,522,523],{"xmlns":36},[38,524,525,529],{},[41,526,527],{},[47,528,52],{},[54,530,52],{"encoding":56},[25,532,534],{"className":533,"ariaHidden":62},[61],[25,535,537,540],{"className":536},[66],[25,538],{"className":539,"style":156},[70],[25,541,52],{"className":542},[75,79]," 时刻 Agent 采取行动获得的奖励（Reward）；",[25,545,547,562],{"className":546},[28],[25,548,550],{"className":549},[32],[34,551,552],{"xmlns":36},[38,553,554,559],{},[41,555,556],{},[47,557,558],{},"τ",[54,560,561],{"encoding":56},"\\tau",[25,563,565],{"className":564,"ariaHidden":62},[61],[25,566,568,571],{"className":567},[66],[25,569],{"className":570,"style":289},[70],[25,572,558],{"className":573,"style":574},[75,79],"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。",[15,577,578],{},[25,579,581,641],{"className":580},[28],[25,582,584],{"className":583},[32],[34,585,586],{"xmlns":36},[38,587,588,638],{},[41,589,590,592,600,603,609,611,618,620,626,629,636],{},[310,591,313],{"stretchy":312},[44,593,594,596],{},[47,595,177],{},[597,598,599],"mn",{},"0",[310,601,602],{"separator":62},",",[44,604,605,607],{},[47,606,49],{},[597,608,599],{},[310,610,602],{"separator":62},[44,612,613,615],{},[47,614,177],{},[597,616,617],{},"1",[310,619,602],{"separator":62},[44,621,622,624],{},[47,623,49],{},[597,625,617],{},[310,627,628],{},"…",[44,630,631,633],{},[47,632,177],{},[47,634,635],{},"T",[310,637,332],{"stretchy":312},[54,639,640],{"encoding":56},"(s_0,a_0,s_1,a_1 \\dots s_T)",[25,642,644],{"className":643,"ariaHidden":62},[61],[25,645,647,650,653,694,698,703,743,746,749,789,792,795,835,838,842,845,887],{"className":646},[66],[25,648],{"className":649,"style":345},[70],[25,651,313],{"className":652},[352],[25,654,656,659],{"className":655},[75],[25,657,177],{"className":658},[75,79],[25,660,662],{"className":661},[83],[25,663,665,686],{"className":664},[87,88],[25,666,668,683],{"className":667},[92],[25,669,672],{"className":670,"style":671},[96],"height:0.3011em;",[25,673,674,677],{"style":100},[25,675],{"className":676,"style":105},[104],[25,678,680],{"className":679},[109,110,111,112],[25,681,599],{"className":682},[75,112],[25,684,120],{"className":685},[119],[25,687,689],{"className":688},[92],[25,690,692],{"className":691,"style":127},[96],[25,693],{},[25,695,602],{"className":696},[697],"mpunct",[25,699],{"className":700,"style":702},[701],"mspace","margin-right:0.1667em;",[25,704,706,709],{"className":705},[75],[25,707,49],{"className":708},[75,79],[25,710,712],{"className":711},[83],[25,713,715,735],{"className":714},[87,88],[25,716,718,732],{"className":717},[92],[25,719,721],{"className":720,"style":671},[96],[25,722,723,726],{"style":100},[25,724],{"className":725,"style":105},[104],[25,727,729],{"className":728},[109,110,111,112],[25,730,599],{"className":731},[75,112],[25,733,120],{"className":734},[119],[25,736,738],{"className":737},[92],[25,739,741],{"className":740,"style":127},[96],[25,742],{},[25,744,602],{"className":745},[697],[25,747],{"className":748,"style":702},[701],[25,750,752,755],{"className":751},[75],[25,753,177],{"className":754},[75,79],[25,756,758],{"className":757},[83],[25,759,761,781],{"className":760},[87,88],[25,762,764,778],{"className":763},[92],[25,765,767],{"className":766,"style":671},[96],[25,768,769,772],{"style":100},[25,770],{"className":771,"style":105},[104],[25,773,775],{"className":774},[109,110,111,112],[25,776,617],{"className":777},[75,112],[25,779,120],{"className":780},[119],[25,782,784],{"className":783},[92],[25,785,787],{"className":786,"style":127},[96],[25,788],{},[25,790,602],{"className":791},[697],[25,793],{"className":794,"style":702},[701],[25,796,798,801],{"className":797},[75],[25,799,49],{"className":800},[75,79],[25,802,804],{"className":803},[83],[25,805,807,827],{"className":806},[87,88],[25,808,810,824],{"className":809},[92],[25,811,813],{"className":812,"style":671},[96],[25,814,815,818],{"style":100},[25,816],{"className":817,"style":105},[104],[25,819,821],{"className":820},[109,110,111,112],[25,822,617],{"className":823},[75,112],[25,825,120],{"className":826},[119],[25,828,830],{"className":829},[92],[25,831,833],{"className":832,"style":127},[96],[25,834],{},[25,836],{"className":837,"style":702},[701],[25,839,628],{"className":840},[841],"minner",[25,843],{"className":844,"style":702},[701],[25,846,848,851],{"className":847},[75],[25,849,177],{"className":850},[75,79],[25,852,854],{"className":853},[83],[25,855,857,879],{"className":856},[87,88],[25,858,860,876],{"className":859},[92],[25,861,864],{"className":862,"style":863},[96],"height:0.3283em;",[25,865,866,869],{"style":100},[25,867],{"className":868,"style":105},[104],[25,870,872],{"className":871},[109,110,111,112],[25,873,635],{"className":874,"style":875},[75,79,112],"margin-right:0.13889em;",[25,877,120],{"className":878},[119],[25,880,882],{"className":881},[92],[25,883,885],{"className":884,"style":127},[96],[25,886],{},[25,888,332],{"className":889},[439],[15,891,892,1118,1119,1348],{},[25,893,895,944],{"className":894},[28],[25,896,898],{"className":897},[32],[34,899,900],{"xmlns":36},[38,901,902,941],{},[41,903,904,917,920,923,925,931,933,939],{},[44,905,906,908],{},[47,907,177],{},[41,909,910,912,915],{},[47,911,52],{},[310,913,914],{},"+",[597,916,617],{},[310,918,919],{},"=",[47,921,922],{},"f",[310,924,313],{"stretchy":312},[44,926,927,929],{},[47,928,177],{},[47,930,52],{},[310,932,602],{"separator":62},[44,934,935,937],{},[47,936,49],{},[47,938,52],{},[310,940,332],{"stretchy":312},[54,942,943],{"encoding":56}," s_{t+1} = f(s_t,a_t)",[25,945,947,1016],{"className":946,"ariaHidden":62},[61],[25,948,950,954,1005,1009,1013],{"className":949},[66],[25,951],{"className":952,"style":953},[70],"height:0.6389em;vertical-align:-0.2083em;",[25,955,957,960],{"className":956},[75],[25,958,177],{"className":959},[75,79],[25,961,963],{"className":962},[83],[25,964,966,996],{"className":965},[87,88],[25,967,969,993],{"className":968},[92],[25,970,972],{"className":971,"style":671},[96],[25,973,974,977],{"style":100},[25,975],{"className":976,"style":105},[104],[25,978,980],{"className":979},[109,110,111,112],[25,981,983,986,990],{"className":982},[75,112],[25,984,52],{"className":985},[75,79,112],[25,987,914],{"className":988},[989,112],"mbin",[25,991,617],{"className":992},[75,112],[25,994,120],{"className":995},[119],[25,997,999],{"className":998},[92],[25,1000,1003],{"className":1001,"style":1002},[96],"height:0.2083em;",[25,1004],{},[25,1006],{"className":1007,"style":1008},[701],"margin-right:0.2778em;",[25,1010,919],{"className":1011},[1012],"mrel",[25,1014],{"className":1015,"style":1008},[701],[25,1017,1019,1022,1026,1029,1069,1072,1075,1115],{"className":1018},[66],[25,1020],{"className":1021,"style":345},[70],[25,1023,922],{"className":1024,"style":1025},[75,79],"margin-right:0.10764em;",[25,1027,313],{"className":1028},[352],[25,1030,1032,1035],{"className":1031},[75],[25,1033,177],{"className":1034},[75,79],[25,1036,1038],{"className":1037},[83],[25,1039,1041,1061],{"className":1040},[87,88],[25,1042,1044,1058],{"className":1043},[92],[25,1045,1047],{"className":1046,"style":97},[96],[25,1048,1049,1052],{"style":100},[25,1050],{"className":1051,"style":105},[104],[25,1053,1055],{"className":1054},[109,110,111,112],[25,1056,52],{"className":1057},[75,79,112],[25,1059,120],{"className":1060},[119],[25,1062,1064],{"className":1063},[92],[25,1065,1067],{"className":1066,"style":127},[96],[25,1068],{},[25,1070,602],{"className":1071},[697],[25,1073],{"className":1074,"style":702},[701],[25,1076,1078,1081],{"className":1077},[75],[25,1079,49],{"className":1080},[75,79],[25,1082,1084],{"className":1083},[83],[25,1085,1087,1107],{"className":1086},[87,88],[25,1088,1090,1104],{"className":1089},[92],[25,1091,1093],{"className":1092,"style":97},[96],[25,1094,1095,1098],{"style":100},[25,1096],{"className":1097,"style":105},[104],[25,1099,1101],{"className":1100},[109,110,111,112],[25,1102,52],{"className":1103},[75,79,112],[25,1105,120],{"className":1106},[119],[25,1108,1110],{"className":1109},[92],[25,1111,1113],{"className":1112,"style":127},[96],[25,1114],{},[25,1116,332],{"className":1117},[439]," 或者 ",[25,1120,1122,1174],{"className":1121},[28],[25,1123,1125],{"className":1124},[32],[34,1126,1127],{"xmlns":36},[38,1128,1129,1171],{},[41,1130,1131,1143,1145,1148,1150,1153,1155,1161,1163,1169],{},[44,1132,1133,1135],{},[47,1134,177],{},[41,1136,1137,1139,1141],{},[47,1138,52],{},[310,1140,914],{},[597,1142,617],{},[310,1144,919],{},[47,1146,1147],{},"P",[310,1149,313],{"stretchy":312},[310,1151,1152],{},"⋅",[47,1154,323],{"mathvariant":322},[44,1156,1157,1159],{},[47,1158,177],{},[47,1160,52],{},[310,1162,602],{"separator":62},[44,1164,1165,1167],{},[47,1166,49],{},[47,1168,52],{},[310,1170,332],{"stretchy":312},[54,1172,1173],{"encoding":56},"s_{t+1} = P(\\cdot|s_t,a_t)",[25,1175,1177,1241],{"className":1176,"ariaHidden":62},[61],[25,1178,1180,1183,1232,1235,1238],{"className":1179},[66],[25,1181],{"className":1182,"style":953},[70],[25,1184,1186,1189],{"className":1185},[75],[25,1187,177],{"className":1188},[75,79],[25,1190,1192],{"className":1191},[83],[25,1193,1195,1224],{"className":1194},[87,88],[25,1196,1198,1221],{"className":1197},[92],[25,1199,1201],{"className":1200,"style":671},[96],[25,1202,1203,1206],{"style":100},[25,1204],{"className":1205,"style":105},[104],[25,1207,1209],{"className":1208},[109,110,111,112],[25,1210,1212,1215,1218],{"className":1211},[75,112],[25,1213,52],{"className":1214},[75,79,112],[25,1216,914],{"className":1217},[989,112],[25,1219,617],{"className":1220},[75,112],[25,1222,120],{"className":1223},[119],[25,1225,1227],{"className":1226},[92],[25,1228,1230],{"className":1229,"style":1002},[96],[25,1231],{},[25,1233],{"className":1234,"style":1008},[701],[25,1236,919],{"className":1237},[1012],[25,1239],{"className":1240,"style":1008},[701],[25,1242,1244,1247,1250,1253,1256,1259,1299,1302,1305,1345],{"className":1243},[66],[25,1245],{"className":1246,"style":345},[70],[25,1248,1147],{"className":1249,"style":875},[75,79],[25,1251,313],{"className":1252},[352],[25,1254,1152],{"className":1255},[75],[25,1257,323],{"className":1258},[75],[25,1260,1262,1265],{"className":1261},[75],[25,1263,177],{"className":1264},[75,79],[25,1266,1268],{"className":1267},[83],[25,1269,1271,1291],{"className":1270},[87,88],[25,1272,1274,1288],{"className":1273},[92],[25,1275,1277],{"className":1276,"style":97},[96],[25,1278,1279,1282],{"style":100},[25,1280],{"className":1281,"style":105},[104],[25,1283,1285],{"className":1284},[109,110,111,112],[25,1286,52],{"className":1287},[75,79,112],[25,1289,120],{"className":1290},[119],[25,1292,1294],{"className":1293},[92],[25,1295,1297],{"className":1296,"style":127},[96],[25,1298],{},[25,1300,602],{"className":1301},[697],[25,1303],{"className":1304,"style":702},[701],[25,1306,1308,1311],{"className":1307},[75],[25,1309,49],{"className":1310},[75,79],[25,1312,1314],{"className":1313},[83],[25,1315,1317,1337],{"className":1316},[87,88],[25,1318,1320,1334],{"className":1319},[92],[25,1321,1323],{"className":1322,"style":97},[96],[25,1324,1325,1328],{"style":100},[25,1326],{"className":1327,"style":105},[104],[25,1329,1331],{"className":1330},[109,110,111,112],[25,1332,52],{"className":1333},[75,79,112],[25,1335,120],{"className":1336},[119],[25,1338,1340],{"className":1339},[92],[25,1341,1343],{"className":1342,"style":127},[96],[25,1344],{},[25,1346,332],{"className":1347},[439],"。",[15,1350,1351],{},"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。",[11,1353,1354],{"id":1354},"训练目标",[15,1356,1357,1358,1386,1387,1418],{},"训练一个 Policy 神经网络 ",[25,1359,1361,1374],{"className":1360},[28],[25,1362,1364],{"className":1363},[32],[34,1365,1366],{"xmlns":36},[38,1367,1368,1372],{},[41,1369,1370],{},[47,1371,276],{},[54,1373,279],{"encoding":56},[25,1375,1377],{"className":1376,"ariaHidden":62},[61],[25,1378,1380,1383],{"className":1379},[66],[25,1381],{"className":1382,"style":289},[70],[25,1384,276],{"className":1385,"style":293},[75,79],"，在所有状态 ",[25,1388,1390,1404],{"className":1389},[28],[25,1391,1393],{"className":1392},[32],[34,1394,1395],{"xmlns":36},[38,1396,1397,1402],{},[41,1398,1399],{},[47,1400,1401],{},"S",[54,1403,1401],{"encoding":56},[25,1405,1407],{"className":1406,"ariaHidden":62},[61],[25,1408,1410,1414],{"className":1409},[66],[25,1411],{"className":1412,"style":1413},[70],"height:0.6833em;",[25,1415,1401],{"className":1416,"style":1417},[75,79],"margin-right:0.05764em;"," 下，给出相应的 Action，得到的 Return 的期望最大。",[15,1420,1421],{},[25,1422,1424,1504],{"className":1423},[28],[25,1425,1427],{"className":1426},[32],[34,1428,1429],{"xmlns":36},[38,1430,1431,1501],{},[41,1432,1433,1436,1438,1441,1443,1445,1447,1471,1473,1481,1483,1485,1487,1489,1495,1497,1499],{},[47,1434,1435],{},"E",[310,1437,313],{"stretchy":312},[47,1439,1440],{},"R",[310,1442,313],{"stretchy":312},[47,1444,558],{},[310,1446,332],{"stretchy":312},[44,1448,1449,1451],{},[310,1450,332],{"stretchy":312},[41,1452,1453,1455,1458,1465,1467,1469],{},[47,1454,558],{},[310,1456,1457],{},"∼",[44,1459,1460,1462],{},[47,1461,1147],{},[47,1463,1464],{},"θ",[310,1466,313],{"stretchy":312},[47,1468,558],{},[310,1470,332],{"stretchy":312},[310,1472,919],{},[1474,1475,1476,1479],"munder",{},[310,1477,1478],{},"∑",[47,1480,558],{},[47,1482,1440],{},[310,1484,313],{"stretchy":312},[47,1486,558],{},[310,1488,332],{"stretchy":312},[44,1490,1491,1493],{},[47,1492,1147],{},[47,1494,1464],{},[310,1496,313],{"stretchy":312},[47,1498,558],{},[310,1500,332],{"stretchy":312},[54,1502,1503],{"encoding":56}," E (R(\\tau))_{\\tau \\sim P_{\\theta}(\\tau)} = \\sum\\limits_\\tau R(\\tau)P_\\theta(\\tau)",[25,1505,1507,1648],{"className":1506,"ariaHidden":62},[61],[25,1508,1510,1514,1517,1520,1524,1527,1530,1533,1639,1642,1645],{"className":1509},[66],[25,1511],{"className":1512,"style":1513},[70],"height:1.1052em;vertical-align:-0.3552em;",[25,1515,1435],{"className":1516,"style":1417},[75,79],[25,1518,313],{"className":1519},[352],[25,1521,1440],{"className":1522,"style":1523},[75,79],"margin-right:0.00773em;",[25,1525,313],{"className":1526},[352],[25,1528,558],{"className":1529,"style":574},[75,79],[25,1531,332],{"className":1532},[439],[25,1534,1536,1539],{"className":1535},[439],[25,1537,332],{"className":1538},[439],[25,1540,1542],{"className":1541},[83],[25,1543,1545,1630],{"className":1544},[87,88],[25,1546,1548,1627],{"className":1547},[92],[25,1549,1552],{"className":1550,"style":1551},[96],"height:0.3448em;",[25,1553,1555,1558],{"style":1554},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[25,1556],{"className":1557,"style":105},[104],[25,1559,1561],{"className":1560},[109,110,111,112],[25,1562,1564,1567,1570,1618,1621,1624],{"className":1563},[75,112],[25,1565,558],{"className":1566,"style":574},[75,79,112],[25,1568,1457],{"className":1569},[1012,112],[25,1571,1573,1576],{"className":1572},[75,112],[25,1574,1147],{"className":1575,"style":875},[75,79,112],[25,1577,1579],{"className":1578},[83],[25,1580,1582,1609],{"className":1581},[87,88],[25,1583,1585,1606],{"className":1584},[92],[25,1586,1588],{"className":1587,"style":1551},[96],[25,1589,1591,1595],{"style":1590},"top:-2.3488em;margin-left:-0.1389em;margin-right:0.0714em;",[25,1592],{"className":1593,"style":1594},[104],"height:2.5em;",[25,1596,1600],{"className":1597},[109,1598,1599,112],"reset-size3","size1",[25,1601,1603],{"className":1602},[75,112],[25,1604,1464],{"className":1605,"style":478},[75,79,112],[25,1607,120],{"className":1608},[119],[25,1610,1612],{"className":1611},[92],[25,1613,1616],{"className":1614,"style":1615},[96],"height:0.1512em;",[25,1617],{},[25,1619,313],{"className":1620},[352,112],[25,1622,558],{"className":1623,"style":574},[75,79,112],[25,1625,332],{"className":1626},[439,112],[25,1628,120],{"className":1629},[119],[25,1631,1633],{"className":1632},[92],[25,1634,1637],{"className":1635,"style":1636},[96],"height:0.3552em;",[25,1638],{},[25,1640],{"className":1641,"style":1008},[701],[25,1643,919],{"className":1644},[1012],[25,1646],{"className":1647,"style":1008},[701],[25,1649,1651,1655,1708,1711,1714,1717,1720,1723,1765,1768,1771],{"className":1650},[66],[25,1652],{"className":1653,"style":1654},[70],"height:1.7em;vertical-align:-0.95em;",[25,1656,1660],{"className":1657},[1658,1659],"mop","op-limits",[25,1661,1663,1699],{"className":1662},[87,88],[25,1664,1666,1696],{"className":1665},[92],[25,1667,1670,1683],{"className":1668,"style":1669},[96],"height:0.75em;",[25,1671,1673,1677],{"style":1672},"top:-2.15em;margin-left:0em;",[25,1674],{"className":1675,"style":1676},[104],"height:3em;",[25,1678,1680],{"className":1679},[109,110,111,112],[25,1681,558],{"className":1682,"style":574},[75,79,112],[25,1684,1686,1689],{"style":1685},"top:-3em;",[25,1687],{"className":1688,"style":1676},[104],[25,1690,1691],{},[25,1692,1478],{"className":1693},[1658,1694,1695],"op-symbol","small-op",[25,1697,120],{"className":1698},[119],[25,1700,1702],{"className":1701},[92],[25,1703,1706],{"className":1704,"style":1705},[96],"height:0.95em;",[25,1707],{},[25,1709],{"className":1710,"style":702},[701],[25,1712,1440],{"className":1713,"style":1523},[75,79],[25,1715,313],{"className":1716},[352],[25,1718,558],{"className":1719,"style":574},[75,79],[25,1721,332],{"className":1722},[439],[25,1724,1726,1729],{"className":1725},[75],[25,1727,1147],{"className":1728,"style":875},[75,79],[25,1730,1732],{"className":1731},[83],[25,1733,1735,1757],{"className":1734},[87,88],[25,1736,1738,1754],{"className":1737},[92],[25,1739,1742],{"className":1740,"style":1741},[96],"height:0.3361em;",[25,1743,1745,1748],{"style":1744},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[25,1746],{"className":1747,"style":105},[104],[25,1749,1751],{"className":1750},[109,110,111,112],[25,1752,1464],{"className":1753,"style":478},[75,79,112],[25,1755,120],{"className":1756},[119],[25,1758,1760],{"className":1759},[92],[25,1761,1763],{"className":1762,"style":127},[96],[25,1764],{},[25,1766,313],{"className":1767},[352],[25,1769,558],{"className":1770,"style":574},[75,79],[25,1772,332],{"className":1773},[439],[25,1775,1778],{"className":1776},[1777],"katex-display",[25,1779,1781,2568],{"className":1780},[28],[25,1782,1784],{"className":1783},[32],[34,1785,1787],{"xmlns":36,"display":1786},"block",[38,1788,1789,2565],{},[1790,1791,1795,1881,1927,2008,2086,2183,2257,2361,2463],"mtable",{"rowspacing":1792,"columnalign":1793,"columnspacing":1794},"0.25em","right 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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 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演员-评论家算法",[15,6912,6913,6914,6986],{},"为了衡量每个动作的相对好坏的情况，我们令奖励 ",[25,6915,6917,6935],{"className":6916},[28],[25,6918,6920],{"className":6919},[32],[34,6921,6922],{"xmlns":36},[38,6923,6924,6932],{},[41,6925,6926],{},[44,6927,6928,6930],{},[47,6929,1440],{},[47,6931,52],{},[54,6933,6934],{"encoding":56},"R_t",[25,6936,6938],{"className":6937,"ariaHidden":62},[61],[25,6939,6941,6945],{"className":6940},[66],[25,6942],{"className":6943,"style":6944},[70],"height:0.8333em;vertical-align:-0.15em;",[25,6946,6948,6951],{"className":6947},[75],[25,6949,1440],{"className":6950,"style":1523},[75,79],[25,6952,6954],{"className":6953},[83],[25,6955,6957,6978],{"className":6956},[87,88],[25,6958,6960,6975],{"className":6959},[92],[25,6961,6963],{"className":6962,"style":97},[96],[25,6964,6966,6969],{"style":6965},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[25,6967],{"className":6968,"style":105},[104],[25,6970,6972],{"className":6971},[109,110,111,112],[25,6973,52],{"className":6974},[75,79,112],[25,6976,120],{"className":6977},[119],[25,6979,6981],{"className":6980},[92],[25,6982,6984],{"className":6983,"style":127},[96],[25,6985],{}," 减去一个基准值。",[15,6988,6989],{},[25,6990,6992,7105],{"className":6991},[28],[25,6993,6995],{"className":6994},[32],[34,6996,6997],{"xmlns":36},[38,6998,6999,7102],{},[41,7000,7001,7007,7021,7039,7041,7049,7051,7054,7056,7064,7066,7068,7070,7072,7074,7080,7082,7090,7092,7100],{},[1978,7002,7003,7005],{},[597,7004,617],{},[47,7006,2111],{},[2341,7008,7009,7011,7019],{},[310,7010,1478],{},[41,7012,7013,7015,7017],{},[47,7014,2121],{},[310,7016,919],{},[597,7018,617],{},[47,7020,2111],{},[2341,7022,7023,7025,7033],{},[310,7024,1478],{},[41,7026,7027,7029,7031],{},[47,7028,52],{},[310,7030,919],{},[597,7032,617],{},[44,7034,7035,7037],{},[47,7036,635],{},[47,7038,2121],{},[310,7040,313],{"stretchy":312},[2341,7042,7043,7045,7047],{},[47,7044,1440],{},[47,7046,52],{},[47,7048,2121],{},[310,7050,5810],{},[47,7052,7053],{},"B",[310,7055,313],{"stretchy":312},[2341,7057,7058,7060,7062],{},[47,7059,177],{},[47,7061,52],{},[47,7063,2121],{},[310,7065,332],{"stretchy":312},[310,7067,332],{"stretchy":312},[47,7069,1808],{"mathvariant":322},[47,7071,2237],{},[310,7073,2240],{},[44,7075,7076,7078],{},[47,7077,1147],{},[47,7079,1464],{},[310,7081,313],{"stretchy":312},[2341,7083,7084,7086,7088],{},[47,7085,49],{},[47,7087,52],{},[47,7089,2121],{},[47,7091,323],{"mathvariant":322},[2341,7093,7094,7096,7098],{},[47,7095,177],{},[47,7097,52],{},[47,7099,2121],{},[310,7101,332],{"stretchy":312},[54,7103,7104],{"encoding":56}," \\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)",[25,7106,7108,7419],{"className":7107,"ariaHidden":62},[61],[25,7109,7111,7114,7182,7185,7249,7252,7356,7359,7410,7413,7416],{"className":7110},[66],[25,7112],{"className":7113,"style":5927},[70],[25,7115,7117,7120,7179],{"className":7116},[75],[25,7118],{"className":7119},[352,3239],[25,7121,7123],{"className":7122},[1978],[25,7124,7126,7171],{"className":7125},[87,88],[25,7127,7129,7168],{"className":7128},[92],[25,7130,7132,7146,7154],{"className":7131,"style":5949},[96],[25,7133,7134,7137],{"style":5952},[25,7135],{"className":7136,"style":1676},[104],[25,7138,7140],{"className":7139},[109,110,111,112],[25,7141,7143],{"className":7142},[75,112],[25,7144,2111],{"className":7145,"style":3730},[75,79,112],[25,7147,7148,7151],{"style":3313},[25,7149],{"className":7150,"style":1676},[104],[25,7152],{"className":7153,"style":3321},[3320],[25,7155,7156,7159],{"style":5975},[25,7157],{"className":7158,"style":1676},[104],[25,7160,7162],{"className":7161},[109,110,111,112],[25,7163,7165],{"className":7164},[75,112],[25,7166,617],{"className":7167},[75,112],[25,7169,120],{"className":7170},[119],[25,7172,7174],{"className":7173},[92],[25,7175,7177],{"className":7176,"style":5997},[96],[25,7178],{},[25,7180],{"className":7181},[439,3239],[25,7183],{"className":7184,"style":702},[701],[25,7186,7188],{"className":7187},[1658,1659],[25,7189,7191,7241],{"className":7190},[87,88],[25,7192,7194,7238],{"className":7193},[92],[25,7195,7197,7217,7227],{"className":7196,"style":6018},[96],[25,7198,7199,7202],{"style":6021},[25,7200],{"className":7201,"style":1676},[104],[25,7203,7205],{"className":7204},[109,110,111,112],[25,7206,7208,7211,7214],{"className":7207},[75,112],[25,7209,2121],{"className":7210},[75,79,112],[25,7212,919],{"className":7213},[1012,112],[25,7215,617],{"className":7216},[75,112],[25,7218,7219,7222],{"style":1685},[25,7220],{"className":7221,"style":1676},[104],[25,7223,7224],{},[25,7225,1478],{"className":7226},[1658,1694,1695],[25,7228,7229,7232],{"style":6052},[25,7230],{"className":7231,"style":1676},[104],[25,7233,7235],{"className":7234},[109,110,111,112],[25,7236,2111],{"className":7237,"style":3730},[75,79,112],[25,7239,120],{"className":7240},[119],[25,7242,7244],{"className":7243},[92],[25,7245,7247],{"className":7246,"style":6071},[96],[25,7248],{},[25,7250],{"className":7251,"style":702},[701],[25,7253,7255],{"className":7254},[1658,1659],[25,7256,7258,7348],{"className":7257},[87,88],[25,7259,7261,7345],{"className":7260},[92],[25,7262,7264,7284,7294],{"className":7263,"style":6089},[96],[25,7265,7266,7269],{"style":6021},[25,7267],{"className":7268,"style":1676},[104],[25,7270,7272],{"className":7271},[109,110,111,112],[25,7273,7275,7278,7281],{"className":7274},[75,112],[25,7276,52],{"className":7277},[75,79,112],[25,7279,919],{"className":7280},[1012,112],[25,7282,617],{"className":7283},[75,112],[25,7285,7286,7289],{"style":1685},[25,7287],{"className":7288,"style":1676},[104],[25,7290,7291],{},[25,7292,1478],{"className":7293},[1658,1694,1695],[25,7295,7296,7299],{"style":6122},[25,7297],{"className":7298,"style":1676},[104],[25,7300,7302],{"className":7301},[109,110,111,112],[25,7303,7305],{"className":7304},[75,112],[25,7306,7308,7311],{"className":7307},[75,112],[25,7309,635],{"className":7310,"style":875},[75,79,112],[25,7312,7314],{"className":7313},[83],[25,7315,7317,7337],{"className":7316},[87,88],[25,7318,7320,7334],{"className":7319},[92],[25,7321,7323],{"className":7322,"style":4651},[96],[25,7324,7325,7328],{"style":4654},[25,7326],{"className":7327,"style":1594},[104],[25,7329,7331],{"className":7330},[109,1598,1599,112],[25,7332,2121],{"className":7333},[75,79,112],[25,7335,120],{"className":7336},[119],[25,7338,7340],{"className":7339},[92],[25,7341,7343],{"className":7342,"style":4673},[96],[25,7344],{},[25,7346,120],{"className":7347},[119],[25,7349,7351],{"className":7350},[92],[25,7352,7354],{"className":7353,"style":6071},[96],[25,7355],{},[25,7357,313],{"className":7358},[352],[25,7360,7362,7365],{"className":7361},[75],[25,7363,1440],{"className":7364,"style":1523},[75,79],[25,7366,7368],{"className":7367},[83],[25,7369,7371,7402],{"className":7370},[87,88],[25,7372,7374,7399],{"className":7373},[92],[25,7375,7377,7388],{"className":7376,"style":4062},[96],[25,7378,7379,7382],{"style":6875},[25,7380],{"className":7381,"style":105},[104],[25,7383,7385],{"className":7384},[109,110,111,112],[25,7386,52],{"className":7387},[75,79,112],[25,7389,7390,7393],{"style":4065},[25,7391],{"className":7392,"style":105},[104],[25,7394,7396],{"className":7395},[109,110,111,112],[25,7397,2121],{"className":7398},[75,79,112],[25,7400,120],{"className":7401},[119],[25,7403,7405],{"className":7404},[92],[25,7406,7408],{"className":7407,"style":4784},[96],[25,7409],{},[25,7411],{"className":7412,"style":3226},[701],[25,7414,5810],{"className":7415},[989],[25,7417],{"className":7418,"style":3226},[701],[25,7420,7422,7425,7429,7432,7483,7487,7490,7493,7498,7501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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 ",[25,7740,7742,7771],{"className":7741},[28],[25,7743,7745],{"className":7744},[32],[34,7746,7747],{"xmlns":36},[38,7748,7749,7768],{},[41,7750,7751,7758,7760,7762,7764,7766],{},[44,7752,7753,7756],{},[47,7754,7755],{},"Q",[47,7757,1464],{},[310,7759,313],{"stretchy":312},[47,7761,177],{},[310,7763,602],{"separator":62},[47,7765,49],{},[310,7767,332],{"stretchy":312},[54,7769,7770],{"encoding":56},"Q_\\theta(s,a)",[25,7772,7774],{"className":7773,"ariaHidden":62},[61],[25,7775,7777,7780,7820,7823,7826,7829,7832,7835],{"className":7776},[66],[25,7778],{"className":7779,"style":345},[70],[25,7781,7783,7786],{"className":7782},[75],[25,7784,7755],{"className":7785},[75,79],[25,7787,7789],{"className":7788},[83],[25,7790,7792,7812],{"className":7791},[87,88],[25,7793,7795,7809],{"className":7794},[92],[25,7796,7798],{"className":7797,"style":1741},[96],[25,7799,7800,7803],{"style":100},[25,7801],{"className":7802,"style":105},[104],[25,7804,7806],{"className":7805},[109,110,111,112],[25,7807,1464],{"className":7808,"style":478},[75,79,112],[25,7810,120],{"className":7811},[119],[25,7813,7815],{"className":7814},[92],[25,7816,7818],{"className":7817,"style":127},[96],[25,7819],{},[25,7821,313],{"className":7822},[352],[25,7824,177],{"className":7825},[75,79],[25,7827,602],{"className":7828},[697],[25,7830],{"className":7831,"style":702},[701],[25,7833,49],{"className":7834},[75,79],[25,7836,332],{"className":7837},[439],"，表示在状态 ",[25,7840,7842,7855],{"className":7841},[28],[25,7843,7845],{"className":7844},[32],[34,7846,7847],{"xmlns":36},[38,7848,7849,7853],{},[41,7850,7851],{},[47,7852,177],{},[54,7854,177],{"encoding":56},[25,7856,7858],{"className":7857,"ariaHidden":62},[61],[25,7859,7861,7864],{"className":7860},[66],[25,7862],{"className":7863,"style":289},[70],[25,7865,177],{"className":7866},[75,79],"，下，做出动作 ",[25,7869,7871,7884],{"className":7870},[28],[25,7872,7874],{"className":7873},[32],[34,7875,7876],{"xmlns":36},[38,7877,7878,7882],{},[41,7879,7880],{},[47,7881,49],{},[54,7883,49],{"encoding":56},[25,7885,7887],{"className":7886,"ariaHidden":62},[61],[25,7888,7890,7893],{"className":7889},[66],[25,7891],{"className":7892,"style":289},[70],[25,7894,49],{"className":7895},[75,79]," 后期望的回报，即动作价值函数。",[15,7898,7899,7900,7988,7989,8017],{},"令 ",[25,7901,7903,7928],{"className":7902},[28],[25,7904,7906],{"className":7905},[32],[34,7907,7908],{"xmlns":36},[38,7909,7910,7925],{},[41,7911,7912,7919,7921,7923],{},[44,7913,7914,7917],{},[47,7915,7916],{},"V",[47,7918,1464],{},[310,7920,313],{"stretchy":312},[47,7922,177],{},[310,7924,332],{"stretchy":312},[54,7926,7927],{"encoding":56},"V_\\theta(s)",[25,7929,7931],{"className":7930,"ariaHidden":62},[61],[25,7932,7934,7937,7979,7982,7985],{"className":7933},[66],[25,7935],{"className":7936,"style":345},[70],[25,7938,7940,7944],{"className":7939},[75],[25,7941,7916],{"className":7942,"style":7943},[75,79],"margin-right:0.22222em;",[25,7945,7947],{"className":7946},[83],[25,7948,7950,7971],{"className":7949},[87,88],[25,7951,7953,7968],{"className":7952},[92],[25,7954,7956],{"className":7955,"style":1741},[96],[25,7957,7959,7962],{"style":7958},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[25,7960],{"className":7961,"style":105},[104],[25,7963,7965],{"className":7964},[109,110,111,112],[25,7966,1464],{"className":7967,"style":478},[75,79,112],[25,7969,120],{"className":7970},[119],[25,7972,7974],{"className":7973},[92],[25,7975,7977],{"className":7976,"style":127},[96],[25,7978],{},[25,7980,313],{"className":7981},[352],[25,7983,177],{"className":7984},[75,79],[25,7986,332],{"className":7987},[439]," 在状态 ",[25,7990,7992,8005],{"className":7991},[28],[25,7993,7995],{"className":7994},[32],[34,7996,7997],{"xmlns":36},[38,7998,7999,8003],{},[41,8000,8001],{},[47,8002,177],{},[54,8004,177],{"encoding":56},[25,8006,8008],{"className":8007,"ariaHidden":62},[61],[25,8009,8011,8014],{"className":8010},[66],[25,8012],{"className":8013,"style":289},[70],[25,8015,177],{"className":8016},[75,79]," 下期望的回报，即状态价值函数",[15,8019,8020,8288,8289,8317,8318,8346],{},[25,8021,8023,8084],{"className":8022},[28],[25,8024,8026],{"className":8025},[32],[34,8027,8028],{"xmlns":36},[38,8029,8030,8081],{},[41,8031,8032,8039,8041,8043,8045,8047,8049,8051,8057,8059,8061,8063,8065,8067,8069,8075,8077,8079],{},[44,8033,8034,8037],{},[47,8035,8036],{},"A",[47,8038,1464],{},[310,8040,313],{"stretchy":312},[47,8042,177],{},[310,8044,602],{"separator":62},[47,8046,49],{},[310,8048,332],{"stretchy":312},[310,8050,919],{},[44,8052,8053,8055],{},[47,8054,7755],{},[47,8056,1464],{},[310,8058,313],{"stretchy":312},[47,8060,177],{},[310,8062,602],{"separator":62},[47,8064,49],{},[310,8066,332],{"stretchy":312},[310,8068,5810],{},[44,8070,8071,8073],{},[47,8072,7916],{},[47,8074,1464],{},[310,8076,313],{"stretchy":312},[47,8078,177],{},[310,8080,332],{"stretchy":312},[54,8082,8083],{"encoding":56},"A_\\theta(s,a) = Q_\\theta(s,a) - V_\\theta(s)",[25,8085,8087,8160,8233],{"className":8086,"ariaHidden":62},[61],[25,8088,8090,8093,8133,8136,8139,8142,8145,8148,8151,8154,8157],{"className":8089},[66],[25,8091],{"className":8092,"style":345},[70],[25,8094,8096,8099],{"className":8095},[75],[25,8097,8036],{"className":8098},[75,79],[25,8100,8102],{"className":8101},[83],[25,8103,8105,8125],{"className":8104},[87,88],[25,8106,8108,8122],{"className":8107},[92],[25,8109,8111],{"className":8110,"style":1741},[96],[25,8112,8113,8116],{"style":100},[25,8114],{"className":8115,"style":105},[104],[25,8117,8119],{"className":8118},[109,110,111,112],[25,8120,1464],{"className":8121,"style":478},[75,79,112],[25,8123,120],{"className":8124},[119],[25,8126,8128],{"className":8127},[92],[25,8129,8131],{"className":8130,"style":127},[96],[25,8132],{},[25,8134,313],{"className":8135},[352],[25,8137,177],{"className":8138},[75,79],[25,8140,602],{"className":8141},[697],[25,8143],{"className":8144,"style":702},[701],[25,8146,49],{"className":8147},[75,79],[25,8149,332],{"className":8150},[439],[25,8152],{"className":8153,"style":1008},[701],[25,8155,919],{"className":8156},[1012],[25,8158],{"className":8159,"style":1008},[701],[25,8161,8163,8166,8206,8209,8212,8215,8218,8221,8224,8227,8230],{"className":8162},[66],[25,8164],{"className":8165,"style":345},[70],[25,8167,8169,8172],{"className":8168},[75],[25,8170,7755],{"className":8171},[75,79],[25,8173,8175],{"className":8174},[83],[25,8176,8178,8198],{"className":8177},[87,88],[25,8179,8181,8195],{"className":8180},[92],[25,8182,8184],{"className":8183,"style":1741},[96],[25,8185,8186,8189],{"style":100},[25,8187],{"className":8188,"style":105},[104],[25,8190,8192],{"className":8191},[109,110,111,112],[25,8193,1464],{"className":8194,"style":478},[75,79,112],[25,8196,120],{"className":8197},[119],[25,8199,8201],{"className":8200},[92],[25,8202,8204],{"className":8203,"style":127},[96],[25,8205],{},[25,8207,313],{"className":8208},[352],[25,8210,177],{"className":8211},[75,79],[25,8213,602],{"className":8214},[697],[25,8216],{"className":8217,"style":702},[701],[25,8219,49],{"className":8220},[75,79],[25,8222,332],{"className":8223},[439],[25,8225],{"className":8226,"style":3226},[701],[25,8228,5810],{"className":8229},[989],[25,8231],{"className":8232,"style":3226},[701],[25,8234,8236,8239,8279,8282,8285],{"className":8235},[66],[25,8237],{"className":8238,"style":345},[70],[25,8240,8242,8245],{"className":8241},[75],[25,8243,7916],{"className":8244,"style":7943},[75,79],[25,8246,8248],{"className":8247},[83],[25,8249,8251,8271],{"className":8250},[87,88],[25,8252,8254,8268],{"className":8253},[92],[25,8255,8257],{"className":8256,"style":1741},[96],[25,8258,8259,8262],{"style":7958},[25,8260],{"className":8261,"style":105},[104],[25,8263,8265],{"className":8264},[109,110,111,112],[25,8266,1464],{"className":8267,"style":478},[75,79,112],[25,8269,120],{"className":8270},[119],[25,8272,8274],{"className":8273},[92],[25,8275,8277],{"className":8276,"style":127},[96],[25,8278],{},[25,8280,313],{"className":8281},[352],[25,8283,177],{"className":8284},[75,79],[25,8286,332],{"className":8287},[439]," 表示优势函数（Advantage Function），衡量在状态 ",[25,8290,8292,8305],{"className":8291},[28],[25,8293,8295],{"className":8294},[32],[34,8296,8297],{"xmlns":36},[38,8298,8299,8303],{},[41,8300,8301],{},[47,8302,177],{},[54,8304,177],{"encoding":56},[25,8306,8308],{"className":8307,"ariaHidden":62},[61],[25,8309,8311,8314],{"className":8310},[66],[25,8312],{"className":8313,"style":289},[70],[25,8315,177],{"className":8316},[75,79]," 下，动作 ",[25,8319,8321,8334],{"className":8320},[28],[25,8322,8324],{"className":8323},[32],[34,8325,8326],{"xmlns":36},[38,8327,8328,8332],{},[41,8329,8330],{},[47,8331,49],{},[54,8333,49],{"encoding":56},[25,8335,8337],{"className":8336,"ariaHidden":62},[61],[25,8338,8340,8343],{"className":8339},[66],[25,8341],{"className":8342,"style":289},[70],[25,8344,49],{"className":8345},[75,79]," 相对于平均水平的优势。",[15,8348,8349],{},"讲上述的公式改写为",[15,8351,8352],{},[25,8353,8355,8469],{"className":8354},[28],[25,8356,8358],{"className":8357},[32],[34,8359,8360],{"xmlns":36},[38,8361,8362,8466],{},[41,8363,8364,8372,8386,8404,8410,8412,8420,8422,8430,8432,8434,8436,8438,8444,8446,8454,8456,8464],{},[1802,8365,8366],{"scriptlevel":599,"displaystyle":62},[1978,8367,8368,8370],{},[597,8369,617],{},[47,8371,2111],{},[2341,8373,8374,8376,8384],{},[310,8375,1478],{},[41,8377,8378,8380,8382],{},[47,8379,2121],{},[310,8381,919],{},[597,8383,617],{},[47,8385,2111],{},[2341,8387,8388,8390,8398],{},[310,8389,1478],{},[41,8391,8392,8394,8396],{},[47,8393,52],{},[310,8395,919],{},[597,8397,617],{},[44,8399,8400,8402],{},[47,8401,635],{},[47,8403,2121],{},[44,8405,8406,8408],{},[47,8407,8036],{},[47,8409,1464],{},[310,8411,313],{"stretchy":312},[2341,8413,8414,8416,8418],{},[47,8415,177],{},[47,8417,52],{},[47,8419,2121],{},[310,8421,602],{"separator":62},[2341,8423,8424,8426,8428],{},[47,8425,49],{},[47,8427,52],{},[47,8429,2121],{},[310,8431,332],{"stretchy":312},[47,8433,1808],{"mathvariant":322},[47,8435,2237],{},[310,8437,2240],{},[44,8439,8440,8442],{},[47,8441,1147],{},[47,8443,1464],{},[310,8445,313],{"stretchy":312},[2341,8447,8448,8450,8452],{},[47,8449,49],{},[47,8451,52],{},[47,8453,2121],{},[47,8455,323],{"mathvariant":322},[2341,8457,8458,8460,8462],{},[47,8459,177],{},[47,8461,52],{},[47,8463,2121],{},[310,8465,332],{"stretchy":312},[54,8467,8468],{"encoding":56},"\\dfrac{1}{N}\\sum\\limits_{n=1}^N 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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。",[15,10279,10280],{},"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。",[25,10282,10284],{"className":10283},[1777],[25,10285,10287,10738],{"className":10286},[28],[25,10288,10290],{"className":10289},[32],[34,10291,10292],{"xmlns":36,"display":1786},[38,10293,10294,10735],{},[41,10295,10296,10304,10306,10312,10314,10316,10318,10320,10326,10328,10330,10336,10338,10350,10352,10354,10360,10362,10368,10370,10372,10380,10382,10388,10390,10392,10394,10396,10402,10404,10406,10418,10420,10426,10432,10434,10446,10448,10450,10456,10458,10464,10466,10468,10477,10479,10485,10487,10489,10491,10493,10499,10501,10503,10506,10518,10520,10526,10528,10540,10542,10548,10554,10556,10568,10570,10572,10578,10580,10586,10588,10590,10602,10604,10612,10614,10620,10622,10624,10626,10628,10634,10636,10638,10640,10652,10654,10660,10662,10674,10676,10682,10684,10696,10698,10701,10703,10709,10711,10717,10719,10725,10727,10733],{},[2341,10297,10298,10300,10302],{},[47,10299,8036],{},[47,10301,1464],{},[597,10303,617],{},[310,10305,313],{"stretchy":312},[44,10307,10308,10310],{},[47,10309,177],{},[47,10311,52],{},[310,10313,602],{"separator":62},[47,10315,49],{},[310,10317,332],{"stretchy":312},[310,10319,919],{},[44,10321,10322,10324],{},[47,10323,457],{},[47,10325,52],{},[310,10327,914],{},[47,10329,6442],{},[44,10331,10332,10334],{},[47,10333,7916],{},[47,10335,1464],{},[310,10337,313],{"stretchy":312},[44,10339,10340,10342],{},[47,10341,177],{},[41,10343,10344,10346,10348],{},[47,10345,52],{},[310,10347,914],{},[597,10349,617],{},[310,10351,332],{"stretchy":312},[310,10353,5810],{},[44,10355,10356,10358],{},[47,10357,7916],{},[47,10359,1464],{},[310,10361,313],{"stretchy":312},[44,10363,10364,10366],{},[47,10365,177],{},[47,10367,52],{},[310,10369,332],{"stretchy":312},[701,10371],{"linebreak":9107},[2341,10373,10374,10376,10378],{},[47,10375,8036],{},[47,10377,1464],{},[597,10379,9242],{},[310,10381,313],{"stretchy":312},[44,10383,10384,10386],{},[47,10385,177],{},[47,10387,52],{},[310,10389,602],{"separator":62},[47,10391,49],{},[310,10393,332],{"stretchy":312},[310,10395,919],{},[44,10397,10398,10400],{},[47,10399,457],{},[47,10401,52],{},[310,10403,914],{},[47,10405,6442],{},[44,10407,10408,10410],{},[47,10409,457],{},[41,10411,10412,10414,10416],{},[47,10413,52],{},[310,10415,914],{},[597,10417,617],{},[310,10419,914],{},[2133,10421,10422,10424],{},[47,10423,6442],{},[597,10425,9242],{},[44,10427,10428,10430],{},[47,10429,7916],{},[47,10431,1464],{},[310,10433,313],{"stretchy":312},[44,10435,10436,10438],{},[47,10437,177],{},[41,10439,10440,10442,10444],{},[47,10441,52],{},[310,10443,914],{},[597,10445,9242],{},[310,10447,332],{"stretchy":312},[310,10449,5810],{},[44,10451,10452,10454],{},[47,10453,7916],{},[47,10455,1464],{},[310,10457,313],{"stretchy":312},[44,10459,10460,10462],{},[47,10461,177],{},[47,10463,52],{},[310,10465,332],{"stretchy":312},[701,10467],{"linebreak":9107},[2341,10469,10470,10472,10474],{},[47,10471,8036],{},[47,10473,1464],{},[597,10475,10476],{},"3",[310,10478,313],{"stretchy":312},[44,10480,10481,10483],{},[47,10482,177],{},[47,10484,52],{},[310,10486,602],{"separator":62},[47,10488,49],{},[310,10490,332],{"stretchy":312},[310,10492,919],{},[44,10494,10495,10497],{},[47,10496,457],{},[47,10498,52],{},[310,10500,914],{},[47,10502,6442],{},[310,10504,10505],{},"∗",[44,10507,10508,10510],{},[47,10509,457],{},[41,10511,10512,10514,10516],{},[47,10513,52],{},[310,10515,914],{},[597,10517,617],{},[310,10519,914],{},[2133,10521,10522,10524],{},[47,10523,6442],{},[597,10525,9242],{},[310,10527,10505],{},[44,10529,10530,10532],{},[47,10531,457],{},[41,10533,10534,10536,10538],{},[47,10535,52],{},[310,10537,914],{},[597,10539,9242],{},[310,10541,914],{},[2133,10543,10544,10546],{},[47,10545,6442],{},[597,10547,10476],{},[44,10549,10550,10552],{},[47,10551,7916],{},[47,10553,1464],{},[310,10555,313],{"stretchy":312},[44,10557,10558,10560],{},[47,10559,177],{},[41,10561,10562,10564,10566],{},[47,10563,52],{},[310,10565,914],{},[597,10567,10476],{},[310,10569,332],{"stretchy":312},[310,10571,5810],{},[44,10573,10574,10576],{},[47,10575,7916],{},[47,10577,1464],{},[310,10579,313],{"stretchy":312},[44,10581,10582,10584],{},[47,10583,177],{},[47,10585,52],{},[310,10587,332],{"stretchy":312},[701,10589],{"linebreak":9107},[41,10591,10592,10595],{},[47,10593,10594],{"mathvariant":322},"⋮",[10596,10597,10598],"mpadded",{"height":1794,"voffset":1794},[701,10599],{"mathbackground":10600,"width":1794,"height":10601},"black","1.5em",[701,10603],{"linebreak":9107},[2341,10605,10606,10608,10610],{},[47,10607,8036],{},[47,10609,1464],{},[47,10611,635],{},[310,10613,313],{"stretchy":312},[44,10615,10616,10618],{},[47,10617,177],{},[47,10619,52],{},[310,10621,602],{"separator":62},[47,10623,49],{},[310,10625,332],{"stretchy":312},[310,10627,919],{},[44,10629,10630,10632],{},[47,10631,457],{},[47,10633,52],{},[310,10635,914],{},[47,10637,6442],{},[310,10639,10505],{},[44,10641,10642,10644],{},[47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A_\\theta^1(s_t, a) = r_t + \\gamma V_\\theta(s_{t+1}) - V_\\theta(s_t)\\\\\n A_\\theta^2(s_t, a) = r_t + \\gamma r_{t+1} + \\gamma^2 V_\\theta(s_{t+2}) - V_\\theta(s_t)\\\\\n A_\\theta^3(s_t, a) = r_t + \\gamma * r_{t+1} + \\gamma^2 * r_{t+2} + \\gamma^3 V_\\theta(s_{t+3}) - V_\\theta(s_t)\\\\\n \\vdots \\\\\n A_\\theta^T(s_t, a) = r_t + \\gamma * r_{t+1} + \\gamma^2 * r_{t+2} + \\gamma^3 * r_{t+3} + \\cdots + \\gamma^T * r_T - 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表示在第 ",[25,12993,12995,13008],{"className":12994},[28],[25,12996,12998],{"className":12997},[32],[34,12999,13000],{"xmlns":36},[38,13001,13002,13006],{},[41,13003,13004],{},[47,13005,52],{},[54,13007,52],{"encoding":56},[25,13009,13011],{"className":13010,"ariaHidden":62},[61],[25,13012,13014,13017],{"className":13013},[66],[25,13015],{"className":13016,"style":156},[70],[25,13018,52],{"className":13019},[75,79]," 步采取特定动作带来的优势。",[25,13022,13024],{"className":13023},[1777],[25,13025,13027,13353],{"className":13026},[28],[25,13028,13030],{"className":13029},[32],[34,13031,13032],{"xmlns":36,"display":1786},[38,13033,13034,13350],{},[41,13035,13036,13044,13046,13052,13054,13056,13058,13064,13066,13078,13080,13082,13088,13090,13096,13098,13100,13114,13116,13128,13130,13132,13134,13140,13142,13154,13156,13158,13164,13166,13178,13180,13182,13190,13192,13198,13200,13202,13204,13206,13214,13216,13224,13226,13232,13234,13236,13238,13240,13248,13250,13252,13266,13268,13276,13278,13284,13286,13288,13290,13292,13300,13302,13304,13318,13320,13326,13340,13342],{},[2341,13037,13038,13040,13042],{},[47,13039,12933],{},[47,13041,52],{},[47,13043,7916],{},[310,13045,919],{},[44,13047,13048,13050],{},[47,13049,457],{},[47,13051,52],{},[310,13053,914],{},[47,13055,6442],{},[310,13057,10505],{},[44,13059,13060,13062],{},[47,13061,7916],{},[47,13063,1464],{},[310,13065,313],{"stretchy":312},[44,13067,13068,13070],{},[47,13069,177],{},[41,13071,13072,13074,13076],{},[47,13073,52],{},[310,13075,914],{},[597,13077,617],{},[310,13079,332],{"stretchy":312},[310,13081,5810],{},[44,13083,13084,13086],{},[47,13085,7916],{},[47,13087,1464],{},[310,13089,313],{"stretchy":312},[44,13091,13092,13094],{},[47,13093,177],{},[47,13095,52],{},[310,13097,332],{"stretchy":312},[701,13099],{"linebreak":9107},[2341,13101,13102,13104,13112],{},[47,13103,12933],{},[41,13105,13106,13108,13110],{},[47,13107,52],{},[310,13109,914],{},[597,13111,617],{},[47,13113,7916],{},[310,13115,919],{},[44,13117,13118,13120],{},[47,13119,457],{},[41,13121,13122,13124,13126],{},[47,13123,52],{},[310,13125,914],{},[597,13127,617],{},[310,13129,914],{},[47,13131,6442],{},[310,13133,10505],{},[44,13135,13136,13138],{},[47,13137,7916],{},[47,13139,1464],{},[310,13141,313],{"stretchy":312},[44,13143,13144,13146],{},[47,13145,177],{},[41,13147,13148,13150,13152],{},[47,13149,52],{},[310,13151,914],{},[597,13153,9242],{},[310,13155,332],{"stretchy":312},[310,13157,5810],{},[44,13159,13160,13162],{},[47,13161,7916],{},[47,13163,1464],{},[310,13165,313],{"stretchy":312},[44,13167,13168,13170],{},[47,13169,177],{},[41,13171,13172,13174,13176],{},[47,13173,52],{},[310,13175,914],{},[597,13177,617],{},[310,13179,332],{"stretchy":312},[701,13181],{"linebreak":9107},[2341,13183,13184,13186,13188],{},[47,13185,8036],{},[47,13187,1464],{},[597,13189,617],{},[310,13191,313],{"stretchy":312},[44,13193,13194,13196],{},[47,13195,177],{},[47,13197,52],{},[310,13199,602],{"separator":62},[47,13201,49],{},[310,13203,332],{"stretchy":312},[310,13205,919],{},[2341,13207,13208,13210,13212],{},[47,13209,12933],{},[47,13211,52],{},[47,13213,7916],{},[701,13215],{"linebreak":9107},[2341,13217,13218,13220,13222],{},[47,13219,8036],{},[47,13221,1464],{},[597,13223,9242],{},[310,13225,313],{"stretchy":312},[44,13227,13228,13230],{},[47,13229,177],{},[47,13231,52],{},[310,13233,602],{"separator":62},[47,13235,49],{},[310,13237,332],{"stretchy":312},[310,13239,919],{},[2341,13241,13242,13244,13246],{},[47,13243,12933],{},[47,13245,52],{},[47,13247,7916],{},[310,13249,914],{},[47,13251,6442],{},[2341,13253,13254,13256,13264],{},[47,13255,12933],{},[41,13257,13258,13260,13262],{},[47,13259,52],{},[310,13261,914],{},[597,13263,617],{},[47,13265,7916],{},[701,13267],{"linebreak":9107},[2341,13269,13270,13272,13274],{},[47,13271,8036],{},[47,13273,1464],{},[597,13275,10476],{},[310,13277,313],{"stretchy":312},[44,13279,13280,13282],{},[47,13281,177],{},[47,13283,52],{},[310,13285,602],{"separator":62},[47,13287,49],{},[310,13289,332],{"stretchy":312},[310,13291,919],{},[2341,13293,13294,13296,13298],{},[47,13295,12933],{},[47,13297,52],{},[47,13299,7916],{},[310,13301,914],{},[47,13303,6442],{},[2341,13305,13306,13308,13316],{},[47,13307,12933],{},[41,13309,13310,13312,13314],{},[47,13311,52],{},[310,13313,914],{},[597,13315,617],{},[47,13317,7916],{},[310,13319,914],{},[2133,13321,13322,13324],{},[47,13323,6442],{},[597,13325,9242],{},[2341,13327,13328,13330,13338],{},[47,13329,12933],{},[41,13331,13332,13334,13336],{},[47,13333,52],{},[310,13335,914],{},[597,13337,9242],{},[47,13339,7916],{},[701,13341],{"linebreak":9107},[41,13343,13344,13346],{},[47,13345,10594],{"mathvariant":322},[10596,13347,13348],{"height":1794,"voffset":1794},[701,13349],{"mathbackground":10600,"width":1794,"height":10601},[54,13351,13352],{"encoding":56},"\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",[25,13354,13356,13424,13479,13497,13607,13699,13702,13779,13843,13861,13971,14072,14075,14196,14253,14256,14377,14443,14512,14515,14636,14702,14780,14875,14878],{"className":13355,"ariaHidden":62},[61],[25,13357,13359,13363,13415,13418,13421],{"className":13358},[66],[25,13360],{"className":13361,"style":13362},[70],"height:1.1383em;vertical-align:-0.247em;",[25,13364,13366,13369],{"className":13365},[75],[25,13367,12933],{"className":13368,"style":12955},[75,79],[25,13370,13372],{"className":13371},[83],[25,13373,13375,13407],{"className":13374},[87,88],[25,13376,13378,13404],{"className":13377},[92],[25,13379,13381,13393],{"className":13380,"style":12252},[96],[25,13382,13384,13387],{"style":13383},"top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;",[25,13385],{"className":13386,"style":105},[104],[25,13388,13390],{"className":13389},[109,110,111,112],[25,13391,52],{"className":13392},[75,79,112],[25,13394,13395,13398],{"style":3866},[25,13396],{"className":13397,"style":105},[104],[25,13399,13401],{"className":13400},[109,110,111,112],[25,13402,7916],{"className":13403,"style":7943},[75,79,112],[25,13405,120],{"className":13406},[119],[25,13408,13410],{"className":13409},[92],[25,13411,13413],{"className":13412,"style":4784},[96],[25,13414],{},[25,13416],{"className":13417,"style":1008},[701],[25,13419,919],{"className":13420},[1012],[25,13422],{"className":13423,"style":1008},[701],[25,13425,13427,13430,13470,13473,13476],{"className":13426},[66],[25,13428],{"className":13429,"style":9367},[70],[25,13431,13433,13436],{"className":13432},[75],[25,13434,457],{"className":13435,"style":478},[75,79],[25,13437,13439],{"className":13438},[83],[25,13440,13442,13462],{"className":13441},[87,88],[25,13443,13445,13459],{"className":13444},[92],[25,13446,13448],{"className":13447,"style":97},[96],[25,13449,13450,13453],{"style":493},[25,13451],{"className":13452,"style":105},[104],[25,13454,13456],{"className":13455},[109,110,111,112],[25,13457,52],{"className":13458},[75,79,112],[25,13460,120],{"className":13461},[119],[25,13463,13465],{"className":13464},[92],[25,13466,13468],{"className":13467,"style":127},[96],[25,13469],{},[25,13471],{"className":13472,"style":3226},[701],[25,13474,914],{"className":13475},[989],[25,13477],{"className":13478,"style":3226},[701],[25,13480,13482,13485,13488,13491,13494],{"className":13481},[66],[25,13483],{"className":13484,"style":11786},[70],[25,13486,6442],{"className":13487,"style":6689},[75,79],[25,13489],{"className":13490,"style":3226},[701],[25,13492,10505],{"className":13493},[989],[25,13495],{"className":13496,"style":3226},[701],[25,13498,13500,13503,13543,13546,13595,13598,13601,13604],{"className":13499},[66],[25,13501],{"className":13502,"style":345},[70],[25,13504,13506,13509],{"className":13505},[75],[25,13507,7916],{"className":13508,"style":7943},[75,79],[25,13510,13512],{"className":13511},[83],[25,13513,13515,13535],{"className":13514},[87,88],[25,13516,13518,13532],{"className":13517},[92],[25,13519,13521],{"className":13520,"style":1741},[96],[25,13522,13523,13526],{"style":7958},[25,13524],{"className":13525,"style":105},[104],[25,13527,13529],{"className":13528},[109,110,111,112],[25,13530,1464],{"className":13531,"style":478},[75,79,112],[25,13533,120],{"className":13534},[119],[25,13536,13538],{"className":13537},[92],[25,13539,13541],{"className":13540,"style":127},[96],[25,13542],{},[25,13544,313],{"className":13545},[352],[25,13547,13549,13552],{"className":13548},[75],[25,13550,177],{"className":13551},[75,79],[25,13553,13555],{"className":13554},[83],[25,13556,13558,13587],{"className":13557},[87,88],[25,13559,13561,13584],{"className":13560},[92],[25,13562,13564],{"className":13563,"style":671},[96],[25,13565,13566,13569],{"style":100},[25,13567],{"className":13568,"style":105},[104],[25,13570,13572],{"className":13571},[109,110,111,112],[25,13573,13575,13578,13581],{"className":13574},[75,112],[25,13576,52],{"className":13577},[75,79,112],[25,13579,914],{"className":13580},[989,112],[25,13582,617],{"className":13583},[75,112],[25,13585,120],{"className":13586},[119],[25,13588,13590],{"className":13589},[92],[25,13591,13593],{"className":13592,"style":1002},[96],[25,13594],{},[25,13596,332],{"className":13597},[439],[25,13599],{"className":13600,"style":3226},[701],[25,13602,5810],{"className":13603},[989],[25,13605],{"className":13606,"style":3226},[701],[25,13608,13610,13613,13653,13656,13696],{"className":13609},[66],[25,13611],{"className":13612,"style":345},[70],[25,13614,13616,13619],{"className":13615},[75],[25,13617,7916],{"className":13618,"style":7943},[75,79],[25,13620,13622],{"className":13621},[83],[25,13623,13625,13645],{"className":13624},[87,88],[25,13626,13628,13642],{"className":13627},[92],[25,13629,13631],{"className":13630,"style":1741},[96],[25,13632,13633,13636],{"style":7958},[25,13634],{"className":13635,"style":105},[104],[25,13637,13639],{"className":13638},[109,110,111,112],[25,136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Advantage Estimation (GAE)",[15,14899,14900],{},"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！",[15,14902,14903,14904,14935],{},"GAE考虑全部的采样结果，并引入一个衰减因子 ",[25,14905,14907,14922],{"className":14906},[28],[25,14908,14910],{"className":14909},[32],[34,14911,14912],{"xmlns":36},[38,14913,14914,14919],{},[41,14915,14916],{},[47,14917,14918],{},"λ",[54,14920,14921],{"encoding":56},"\\lambda",[25,14923,14925],{"className":14924,"ariaHidden":62},[61],[25,14926,14928,14932],{"className":14927},[66],[25,14929],{"className":14930,"style":14931},[70],"height:0.6944em;",[25,14933,14918],{"className":14934},[75,79]," 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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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GAE 优势函数的表达式。",[15,17729,17730],{},"GAE 优势函数平衡了采样不同步带来的方差和偏差的问题。",[15,17732,17733],{},"现在我们来看上面得之不易的三个表达式：",[25,17735,17737],{"className":17736},[1777],[25,17738,17740,17996],{"className":17739},[28],[25,17741,17743],{"className":17742},[32],[34,17744,17745],{"xmlns":36,"display":1786},[38,17746,17747,17993],{},[41,17748,17749,17757,17759,17765,17767,17769,17775,17777,17789,17791,17793,17799,17801,17807,17809,17811,17825,17827,17833,17835,17837,17839,17841,17855,17857,17859,17861,17867,17881,17883,17889,17903,17921,17935,17937,17945,17947,17955,17957,17959,17961,17963,17965,17971,17973,17981,17983,17991],{},[2341,17750,17751,17753,17755],{},[47,17752,12933],{},[47,17754,52],{},[47,17756,7916],{},[310,17758,919],{},[44,17760,17761,17763],{},[47,17762,457],{},[47,17764,52],{},[310,17766,914],{},[47,17768,6442],{},[44,17770,17771,17773],{},[47,17772,7916],{},[47,17774,1464],{},[310,17776,313],{"stretchy":312},[44,17778,17779,17781],{},[47,17780,177],{},[41,17782,17783,17785,17787],{},[47,17784,52],{},[310,17786,914],{},[597,17788,617],{},[310,17790,332],{"stretchy":312},[310,17792,5810],{},[44,17794,17795,17797],{},[47,17796,7916],{},[47,17798,1464],{},[310,17800,313],{"stretchy":312},[44,17802,17803,17805],{},[47,17804,177],{},[47,17806,52],{},[310,17808,332],{"stretchy":312},[701,17810],{"linebreak":9107},[2341,17812,17813,17815,17817],{},[47,17814,8036],{},[47,17816,1464],{},[41,17818,17819,17821,17823],{},[47,17820,14969],{},[47,17822,8036],{},[47,17824,1435],{},[310,17826,313],{"stretchy":312},[44,17828,17829,17831],{},[47,17830,177],{},[47,17832,52],{},[310,17834,602],{"separator":62},[47,17836,49],{},[310,17838,332],{"stretchy":312},[310,17840,919],{},[2113,17842,17843,17845,17853],{},[310,17844,1478],{},[41,17846,17847,17849,17851],{},[47,17848,15500],{},[310,17850,919],{},[597,17852,599],{},[47,17854,15507],{"mathvariant":322},[310,17856,313],{"stretchy":312},[47,17858,6442],{},[47,17860,14918],{},[2133,17862,17863,17865],{},[310,17864,332],{"stretchy":312},[47,17866,15500],{},[2341,17868,17869,17871,17879],{},[47,17870,12933],{},[41,17872,17873,17875,17877],{},[47,17874,52],{},[310,17876,914],{},[47,17878,15500],{},[47,17880,7916],{},[701,17882],{"linebreak":9107},[1978,17884,17885,17887],{},[597,17886,617],{},[47,17888,2111],{},[2113,17890,17891,17893,17901],{},[310,17892,1478],{},[41,17894,17895,17897,17899],{},[47,17896,2121],{},[310,17898,919],{},[597,17900,617],{},[47,17902,2111],{},[2113,17904,17905,17907,17915],{},[310,17906,1478],{},[41,17908,17909,17911,17913],{},[47,17910,52],{},[310,17912,919],{},[597,17914,617],{},[44,17916,17917,17919],{},[47,17918,635],{},[47,17920,2121],{},[2341,17922,17923,17925,17927],{},[47,17924,8036],{},[47,17926,1464],{},[41,17928,17929,17931,17933],{},[47,17930,14969],{},[47,17932,8036],{},[47,17934,1435],{},[310,17936,313],{"stretchy":312},[2341,17938,17939,17941,17943],{},[47,17940,177],{},[47,17942,2121],{},[47,17944,52],{},[310,17946,602],{"separator":62},[2341,17948,17949,17951,17953],{},[47,17950,49],{},[47,17952,2121],{},[47,17954,52],{},[310,17956,332],{"stretchy":312},[15053,17958,15055],{},[47,17960,1808],{"mathvariant":322},[47,17962,2237],{},[310,17964,2240],{},[44,17966,17967,17969],{},[47,17968,1147],{},[47,17970,1464],{},[310,17972,313],{"stretchy":312},[2341,17974,17975,17977,17979],{},[47,17976,49],{},[47,17978,2121],{},[47,17980,52],{},[47,17982,323],{"mathvariant":322},[2341,17984,17985,17987,17989],{},[47,17986,177],{},[47,17988,2121],{},[47,17990,52],{},[310,17992,332],{"stretchy":312},[54,17994,17995],{"encoding":56},"\\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",[15,19229,19230],{},"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。",[14894,19232,19233],{"id":19233},"重要性采样",[15,19235,19236,19237,19282,19283,19312,19313,19342,19343,19371],{},"将 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",[25,19284,19286,19299],{"className":19285},[28],[25,19287,19289],{"className":19288},[32],[34,19290,19291],{"xmlns":36},[38,19292,19293,19297],{},[41,19294,19295],{},[47,19296,15],{},[54,19298,15],{"encoding":56},[25,19300,19302],{"className":19301,"ariaHidden":62},[61],[25,19303,19305,19309],{"className":19304},[66],[25,19306],{"className":19307,"style":19308},[70],"height:0.625em;vertical-align:-0.1944em;",[25,19310,15],{"className":19311},[75,79]," 下的期望改写为在另一分布 ",[25,19314,19316,19330],{"className":19315},[28],[25,19317,19319],{"className":19318},[32],[34,19320,19321],{"xmlns":36},[38,19322,19323,19328],{},[41,19324,19325],{},[47,19326,19327],{},"q",[54,19329,19327],{"encoding":56},[25,19331,19333],{"className":19332,"ariaHidden":62},[61],[25,19334,19336,19339],{"className":19335},[66],[25,19337],{"className":19338,"style":19308},[70],[25,19340,19327],{"className":19341,"style":293},[75,79],"（proposal）下的期望，从而可用从 ",[25,19344,19346,19359],{"className":19345},[28],[25,19347,19349],{"className":19348},[32],[34,19350,19351],{"xmlns":36},[38,19352,19353,19357],{},[41,19354,19355],{},[47,19356,19327],{},[54,19358,19327],{"encoding":56},[25,19360,19362],{"className":19361,"ariaHidden":62},[61],[25,19363,19365,19368],{"className":19364},[66],[25,19366],{"className":19367,"style":19308},[70],[25,19369,19327],{"className":19370,"style":293},[75,79]," 采样的数据估计：",[25,19373,19375],{"className":19374},[1777],[25,19376,19378,19763],{"className":19377},[28],[25,19379,19381],{"className":19380},[32],[34,19382,19383],{"xmlns":36,"display":1786},[38,19384,19385,19760],{},[1790,19386,19387,19460,19524,19588,19660],{"rowspacing":1792,"columnalign":1793,"columnspacing":1794},[1796,19388,19389,19426],{},[1799,19390,19391],{},[1802,19392,19393],{"scriptlevel":599,"displaystyle":62},[41,19394,19395,19398,19400,19402,19404,19406,19408],{},[47,19396,1435],{"mathvariant":19397},"double-struck",[310,19399,313],{"stretchy":312},[47,19401,922],{},[310,19403,313],{"stretchy":312},[47,19405,19255],{},[310,19407,332],{"stretchy":312},[44,19409,19410,19412],{},[310,19411,332],{"stretchy":312},[41,19413,19414,19416,19418,19420,19422,19424],{},[47,19415,19255],{},[310,19417,1457],{},[47,19419,15],{},[310,19421,313],{"stretchy":312},[47,19423,19255],{},[310,19425,332],{"stretchy":312},[1799,19427,19428],{},[1802,19429,19430],{"scriptlevel":599,"displaystyle":62},[41,19431,19432,19434,19436,19442,19444,19446,19448,19450,19452,19454,19456,19458],{},[41,19433],{},[310,19435,919],{},[1474,19437,19438,19440],{},[310,19439,1478],{},[47,19441,19255],{},[47,19443,922],{},[310,19445,313],{"stretchy":312},[47,19447,19255],{},[310,19449,332],{"stretchy":312},[310,19451,1152],{},[47,19453,15],{},[310,19455,313],{"stretchy":312},[47,19457,19255],{},[310,19459,332],{"stretchy":312},[1796,19461,19462,19468],{},[1799,19463,19464],{},[1802,19465,19466],{"scriptlevel":599,"displaystyle":62},[41,19467],{},[1799,19469,19470],{},[1802,19471,19472],{"scriptlevel":599,"displaystyle":62},[41,19473,19474,19476,19478,19484,19486,19488,19490,19492,19494,19496,19498,19500,19502],{},[41,19475],{},[310,19477,919],{},[1474,19479,19480,19482],{},[310,19481,1478],{},[47,19483,19255],{},[47,19485,922],{},[310,19487,313],{"stretchy":312},[47,19489,19255],{},[310,19491,332],{"stretchy":312},[310,19493,1152],{},[47,19495,15],{},[310,19497,313],{"stretchy":312},[47,19499,19255],{},[310,19501,332],{"stretchy":312},[1978,19503,19504,19514],{},[41,19505,19506,19508,19510,19512],{},[47,19507,19327],{},[310,19509,313],{"stretchy":312},[47,19511,19255],{},[310,19513,332],{"stretchy":312},[41,19515,19516,19518,19520,19522],{},[47,19517,19327],{},[310,19519,313],{"stretchy":312},[47,19521,19255],{},[310,19523,332],{"stretchy":312},[1796,19525,19526,19532],{},[1799,19527,19528],{},[1802,19529,19530],{"scriptlevel":599,"displaystyle":62},[41,19531],{},[1799,19533,19534],{},[1802,19535,19536],{"scriptlevel":599,"displaystyle":62},[41,19537,19538,19540,19542,19548,19550,19552,19554,19556,19578,19580,19582,19584,19586],{},[41,19539],{},[310,19541,919],{},[1474,19543,19544,19546],{},[310,19545,1478],{},[47,19547,19255],{},[47,19549,922],{},[310,19551,313],{"stretchy":312},[47,19553,19255],{},[310,19555,332],{"stretchy":312},[1978,19557,19558,19568],{},[41,19559,19560,19562,19564,19566],{},[47,19561,15],{},[310,19563,313],{"stretchy":312},[47,19565,19255],{},[310,19567,332],{"stretchy":312},[41,19569,19570,19572,19574,19576],{},[47,19571,19327],{},[310,19573,313],{"stretchy":312},[47,19575,19255],{},[310,19577,332],{"stretchy":312},[310,19579,1152],{},[47,19581,19327],{},[310,19583,313],{"stretchy":312},[47,19585,19255],{},[310,19587,332],{"stretchy":312},[1796,19589,19590,19596],{},[1799,19591,19592],{},[1802,19593,19594],{"scriptlevel":599,"displaystyle":62},[41,19595],{},[1799,19597,19598],{},[1802,19599,19600],{"scriptlevel":599,"displaystyle":62},[41,19601,19602,19604,19606,19608],{},[41,19603],{},[310,19605,919],{},[47,19607,1435],{"mathvariant":19397},[44,19609,19610,19646],{},[41,19611,19612,19614,19616,19618,19620,19622,19644],{},[310,19613,313],{"fence":62},[47,19615,922],{},[310,19617,313],{"stretchy":312},[47,19619,19255],{},[310,19621,332],{"stretchy":312},[1978,19623,19624,19634],{},[41,19625,19626,19628,19630,19632],{},[47,19627,15],{},[310,19629,313],{"stretchy":312},[47,19631,19255],{},[310,19633,332],{"stretchy":312},[41,19635,19636,19638,19640,19642],{},[47,19637,19327],{},[310,19639,313],{"stretchy":312},[47,19641,19255],{},[310,19643,332],{"stretchy":312},[310,19645,332],{"fence":62},[41,19647,19648,19650,19652,19654,19656,19658],{},[47,19649,19255],{},[310,19651,1457],{},[47,19653,19327],{},[310,19655,313],{"stretchy":312},[47,19657,19255],{},[310,19659,332],{"stretchy":312},[1796,19661,19662,19668],{},[1799,19663,19664],{},[1802,19665,19666],{"scriptlevel":599,"displaystyle":62},[41,19667],{},[1799,19669,19670],{},[1802,19671,19672],{"scriptlevel":599,"displaystyle":62},[41,19673,19674,19676,19678,19684,19698,19700,19702,19708,19710,19740,19742,19744,19750,19752,19754,19756,19758],{},[41,19675],{},[310,19677,2104],{},[1978,19679,19680,19682],{},[597,19681,617],{},[47,19683,2111],{},[2113,19685,19686,19688,19696],{},[310,19687,1478],{},[41,19689,19690,19692,19694],{},[47,19691,2121],{},[310,19693,919],{},[597,19695,617],{},[47,19697,2111],{},[47,19699,922],{},[310,19701,313],{"stretchy":312},[44,19703,19704,19706],{},[47,19705,19255],{},[47,19707,2121],{},[310,19709,332],{"stretchy":312},[1978,19711,19712,19726],{},[41,19713,19714,19716,19718,19724],{},[47,19715,15],{},[310,19717,313],{"stretchy":312},[44,19719,19720,19722],{},[47,19721,19255],{},[47,19723,2121],{},[310,19725,332],{"stretchy":312},[41,19727,19728,19730,19732,19738],{},[47,19729,19327],{},[310,19731,313],{"stretchy":312},[44,19733,19734,19736],{},[47,19735,19255],{},[47,19737,2121],{},[310,19739,332],{"stretchy":312},[310,19741,602],{"separator":62},[701,19743],{"width":15060},[44,19745,19746,19748],{},[47,19747,19255],{},[47,19749,2121],{},[310,19751,1457],{},[47,19753,19327],{},[310,19755,313],{"stretchy":312},[47,19757,19255],{},[310,19759,332],{"stretchy":312},[54,19761,19762],{"encoding":56},"\\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}",[25,19764,19766],{"className":19765,"ariaHidden":62},[61],[25,19767,19769,19773],{"className":19768},[66],[25,19770],{"className":19771,"style":19772},[70],"height:14.8742em;vertical-align:-7.1871em;",[25,19774,19776],{"className":19775},[75],[25,19777,19779,19927],{"className":19778},[1790],[25,19780,19782],{"className":19781},[2587],[25,19783,19785,19918],{"className":19784},[87,88],[25,19786,19788,19915],{"className":19787},[92],[25,19789,19792,19879,19888,19897,19906],{"className":19790,"style":19791},[96],"height:7.6871em;",[25,19793,19795,19799],{"style":19794},"top:-10.4654em;",[25,19796],{"className":19797,"style":19798},[104],"height:3.8283em;",[25,19800,19802,19806,19809,19812,19815,19818,19821],{"className":19801},[75],[25,19803,1435],{"className":19804},[75,19805],"mathbb",[25,19807,313],{"className":19808},[352],[25,19810,922],{"className":19811,"style":1025},[75,79],[25,19813,313],{"className":19814},[352],[25,19816,19255],{"className":19817},[75,79],[25,19819,332],{"className":19820},[439],[25,19822,19824,19827],{"className":19823},[439],[25,19825,332],{"className":19826},[439],[25,19828,19830],{"className":19829},[83],[25,19831,19833,19871],{"className":19832},[87,88],[25,19834,19836,19868],{"className":19835},[92],[25,19837,19839],{"className":19838,"style":1551},[96],[25,19840,19841,19844],{"style":1554},[25,19842],{"className":19843,"style":105},[104],[25,19845,19847],{"className":19846},[109,110,111,112],[25,19848,19850,19853,19856,19859,19862,19865],{"className":19849},[75,112],[25,19851,19255],{"className":19852},[75,79,112],[25,19854,1457],{"className":19855},[1012,112],[25,19857,15],{"className":19858},[75,79,112],[25,19860,313],{"className":19861},[352,112],[25,19863,19255],{"className":19864},[75,79,112],[25,19866,332],{"className":19867},[439,112],[25,19869,120],{"className":19870},[119],[25,19872,19874],{"className":19873},[92],[25,19875,19877],{"className":19876,"style":1636},[96],[25,19878],{},[25,19880,19882,19885],{"style":19881},"top:-7.4884em;",[25,19883],{"className":19884,"style":19798},[104],[25,19886],{"className":19887},[75],[25,19889,19891,19894],{"style":19890},"top:-4.5114em;",[25,19892],{"className":19893,"style":19798},[104],[25,19895],{"className":19896},[75],[25,19898,19900,19903],{"style":19899},"top:-1.5114em;",[25,19901],{"className":19902,"style":19798},[104],[25,19904],{"className":19905},[75],[25,19907,19909,19912],{"style":19908},"top:1.7917em;",[25,19910],{"className":19911,"style":19798},[104],[25,19913],{"className":19914},[75],[25,19916,120],{"className":19917},[119],[25,19919,19921],{"className":19920},[92],[25,19922,19925],{"className":19923,"style":19924},[96],"height:7.1871em;",[25,19926],{},[25,19928,19930],{"className":19929},[2811],[25,19931,19933,21031],{"className":19932},[87,88],[25,19934,19936,21028],{"className":19935},[92],[25,19937,19939,20042,20225,20408,20599],{"className":19938,"style":19791},[96],[25,19940,19941,19944],{"style":19794},[25,19942],{"className":19943,"style":19798},[104],[25,19945,19947,19950,19953,19956,19959,20006,20009,20012,20015,20018,20021,20024,20027,20030,20033,20036,20039],{"className":19946},[75],[25,19948],{"className":19949},[75],[25,19951],{"className":19952,"style":1008},[701],[25,19954,919],{"className":19955},[1012],[25,19957],{"className":19958,"style":1008},[701],[25,19960,19962],{"className":19961},[1658,1659],[25,19963,19965,19998],{"className":19964},[87,88],[25,19966,19968,19995],{"className":19967},[92],[25,19969,19971,19985],{"className":19970,"style":2859},[96],[25,19972,19973,19976],{"style":2862},[25,19974],{"className":19975,"style":2866},[104],[25,19977,19979],{"className":19978},[109,110,111,112],[25,19980,19982],{"className":19981},[75,112],[25,19983,19255],{"className":19984},[75,79,112],[25,19986,19987,19990],{"style":2875},[25,19988],{"className":19989,"style":2866},[104],[25,19991,19992],{},[25,19993,1478],{"className":19994},[1658,1694,2884],[25,19996,120],{"className":19997},[119],[25,19999,20001],{"className":20000},[92],[25,20002,20004],{"className":20003,"style":2894},[96],[25,20005],{},[25,20007],{"className":20008,"style":702},[701],[25,20010,922],{"className":20011,"style":1025},[75,79],[25,20013,313],{"className":20014},[352],[25,20016,19255],{"className":20017},[75,79],[25,20019,332],{"className":20020},[439],[25,20022],{"className":20023,"style":3226},[701],[25,20025,1152],{"className":20026},[989],[25,20028],{"className":20029,"style":3226},[701],[25,20031,15],{"className":20032},[75,79],[25,20034,313],{"className":20035},[352],[25,20037,19255],{"className":20038},[75,79],[25,20040,332],{"className":20041},[439],[25,20043,20044,20047],{"style":19881},[25,20045],{"className":20046,"style":19798},[104],[25,20048,20050,20053,20056,20059,20062,20109,20112,20115,20118,20121,20124,20127,20130,20133,20136,20139,20142,20145],{"className":20049},[75],[25,20051],{"className":20052},[75],[25,20054],{"className":20055,"style":1008},[701],[25,20057,919],{"className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on-policy 的训练改为 off-policy 的训练。",[14894,21043,21045],{"id":21044},"off-policy","Off-policy",[15,21047,21048,21049,21112,21113,21142,21143,21281,21282,21473,21474,21689],{},"记 ",[25,21050,21052,21070],{"className":21051},[28],[25,21053,21055],{"className":21054},[32],[34,21056,21057],{"xmlns":36},[38,21058,21059,21067],{},[41,21060,21061],{},[2133,21062,21063,21065],{},[47,21064,1464],{},[310,21066,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[54,21068,21069],{"encoding":56},"\\theta'",[25,21071,21073],{"className":21072,"ariaHidden":62},[61],[25,21074,21076,21080],{"className":21075},[66],[25,21077],{"className":21078,"style":21079},[70],"height:0.7519em;",[25,21081,21083,21086],{"className":21082},[75],[25,21084,1464],{"className":21085,"style":478},[75,79],[25,21087,21089],{"className":21088},[83],[25,21090,21092],{"className":21091},[87],[25,21093,21095],{"className":21094},[92],[25,21096,21098],{"className":21097,"style":21079},[96],[25,21099,21100,21103],{"style":4065},[25,21101],{"className":21102,"style":105},[104],[25,21104,21106],{"className":21105},[109,110,111,112],[25,21107,21109],{"className":21108},[75,112],[25,21110,6431],{"className":21111},[75,112]," 为采集数据时的旧策略，",[25,21114,21116,21130],{"className":21115},[28],[25,21117,21119],{"className":21118},[32],[34,21120,21121],{"xmlns":36},[38,21122,21123,21127],{},[41,21124,21125],{},[47,21126,1464],{},[54,21128,21129],{"encoding":56},"\\theta",[25,21131,21133],{"className":21132,"ariaHidden":62},[61],[25,21134,21136,21139],{"className":21135},[66],[25,21137],{"className":21138,"style":14931},[70],[25,21140,1464],{"className":21141,"style":478},[75,79]," 为当前要优化的策略；优势 ",[25,21144,21146,21176],{"className":21145},[28],[25,21147,21149],{"className":21148},[32],[34,21150,21151],{"xmlns":36},[38,21152,21153,21173],{},[41,21154,21155],{},[2341,21156,21157,21159,21165],{},[47,21158,8036],{},[2133,21160,21161,21163],{},[47,21162,1464],{},[310,21164,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[41,21166,21167,21169,21171],{},[47,21168,14969],{},[47,21170,8036],{},[47,21172,1435],{},[54,21174,21175],{"encoding":56},"A_{\\theta'}^{GAE}",[25,21177,21179],{"className":21178,"ariaHidden":62},[61],[25,21180,21182,21186],{"className":21181},[66],[25,21183],{"className":21184,"style":21185},[70],"height:1.1244em;vertical-align:-0.2831em;",[25,21187,21189,21192],{"className":21188},[75],[25,21190,8036],{"className":21191},[75,79],[25,21193,21195],{"className":21194},[83],[25,21196,21198,21272],{"className":21197},[87,88],[25,21199,21201,21269],{"className":21200},[92],[25,21202,21205,21249],{"className":21203,"style":21204},[96],"height:0.8413em;",[25,21206,21208,21211],{"style":21207},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[25,21209],{"className":21210,"style":105},[104],[25,21212,21214],{"className":21213},[109,110,111,112],[25,21215,21217],{"className":21216},[75,112],[25,21218,21220,21223],{"className":21219},[75,112],[25,21221,1464],{"className":21222,"style":478},[75,79,112],[25,21224,21226],{"className":21225},[83],[25,21227,21229],{"className":21228},[87],[25,21230,21232],{"className":21231},[92],[25,21233,21235],{"className":21234,"style":6591},[96],[25,21236,21237,21240],{"style":6594},[25,21238],{"className":21239,"style":1594},[104],[25,21241,21243],{"className":21242},[109,1598,1599,112],[25,21244,21246],{"className":21245},[75,112],[25,21247,6431],{"className":21248},[75,112],[25,21250,21251,21254],{"style":4065},[25,21252],{"className":21253,"style":105},[104],[25,21255,21257],{"className":21256},[109,110,111,112],[25,21258,21260,21263,21266],{"className":21259},[75,112],[25,21261,14969],{"className":21262},[75,79,112],[25,21264,8036],{"className":21265},[75,79,112],[25,21267,1435],{"className":21268,"style":1417},[75,79,112],[25,21270,120],{"className":21271},[119],[25,21273,21275],{"className":21274},[92],[25,21276,21279],{"className":21277,"style":21278},[96],"height:0.2831em;",[25,21280],{}," 由旧策略下的价值网络估计。利用恒等式 ",[25,21283,21285,21339],{"className":21284},[28],[25,21286,21288],{"className":21287},[32],[34,21289,21290],{"xmlns":36},[38,21291,21292,21336],{},[41,21293,21294,21296,21298,21300,21302,21304,21306,21308,21310],{},[47,21295,1808],{"mathvariant":322},[47,21297,2237],{},[310,21299,2240],{},[47,21301,922],{},[310,21303,313],{"stretchy":312},[47,21305,19255],{},[310,21307,332],{"stretchy":312},[310,21309,919],{},[1802,21311,21312],{"scriptlevel":599,"displaystyle":62},[1978,21313,21314,21326],{},[41,21315,21316,21318,21320,21322,21324],{},[47,21317,1808],{"mathvariant":322},[47,21319,922],{},[310,21321,313],{"stretchy":312},[47,21323,19255],{},[310,21325,332],{"stretchy":312},[41,21327,21328,21330,21332,21334],{},[47,21329,922],{},[310,21331,313],{"stretchy":312},[47,21333,19255],{},[310,21335,332],{"stretchy":312},[54,21337,21338],{"encoding":56},"\\nabla \\log f(x) = \\dfrac{\\nabla f(x)}{f(x)}",[25,21340,21342,21383],{"className":21341,"ariaHidden":62},[61],[25,21343,21345,21348,21351,21354,21359,21362,21365,21368,21371,21374,21377,21380],{"className":21344},[66],[25,21346],{"className":21347,"style":345},[70],[25,21349,1808],{"className":21350},[75],[25,21352],{"className":21353,"style":702},[701],[25,21355,4291,21357],{"className":21356},[1658],[25,21358,4295],{"style":4294},[25,21360],{"className":21361,"style":702},[701],[25,21363,922],{"className":21364,"style":1025},[75,79],[25,21366,313],{"className":21367},[352],[25,21369,19255],{"className":21370},[75,79],[25,21372,332],{"className":21373},[439],[25,21375],{"className":21376,"style":1008},[701],[25,21378,919],{"className":21379},[1012],[25,21381],{"className":21382,"style":1008},[701],[25,21384,21386,21390],{"className":21385},[66],[25,21387],{"className":21388,"style":21389},[70],"height:2.363em;vertical-align:-0.936em;",[25,21391,21393,21396,21470],{"className":21392},[75],[25,21394],{"className":21395},[352,3239],[25,21397,21399],{"className":21398},[1978],[25,21400,21402,21462],{"className":21401},[87,88],[25,21403,21405,21459],{"className":21404},[92],[25,21406,21408,21428,21436],{"className":21407,"style":3252},[96],[25,21409,21410,21413],{"style":3255},[25,21411],{"className":21412,"style":1676},[104],[25,21414,21416,21419,21422,21425],{"className":21415},[75],[25,21417,922],{"className":21418,"style":1025},[75,79],[25,21420,313],{"className":21421},[352],[25,21423,19255],{"className":21424},[75,79],[25,21426,332],{"className":21427},[439],[25,21429,21430,21433],{"style":3313},[25,21431],{"className":21432,"style":1676},[104],[25,21434],{"className":21435,"style":3321},[3320],[25,21437,21438,21441],{"style":3324},[25,21439],{"className":21440,"style":1676},[104],[25,21442,21444,21447,21450,21453,21456],{"className":21443},[75],[25,21445,1808],{"className":21446},[75],[25,21448,922],{"className":21449,"style":1025},[75,79],[25,21451,313],{"className":21452},[352],[25,21454,19255],{"className":21455},[75,79],[25,21457,332],{"className":21458},[439],[25,21460,120],{"className":21461},[119],[25,21463,21465],{"className":21464},[92],[25,21466,21468],{"className":21467,"style":3389},[96],[25,21469],{},[25,21471],{"className":21472},[439,3239],"，可将策略梯度写成重要性采样比 ",[25,21475,21477,21509],{"className":21476},[28],[25,21478,21480],{"className":21479},[32],[34,21481,21482],{"xmlns":36},[38,21483,21484,21506],{},[41,21485,21486],{},[1802,21487,21488],{"scriptlevel":599,"displaystyle":62},[1978,21489,21490,21496],{},[44,21491,21492,21494],{},[47,21493,1147],{},[47,21495,1464],{},[44,21497,21498,21500],{},[47,21499,1147],{},[2133,21501,21502,21504],{},[47,21503,1464],{},[310,21505,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[54,21507,21508],{"encoding":56},"\\dfrac{P_\\theta}{P_{\\theta'}}",[25,21510,21512],{"className":21511,"ariaHidden":62},[61],[25,21513,21515,21519],{"className":21514},[66],[25,21516],{"className":21517,"style":21518},[70],"height:2.1963em;vertical-align:-0.836em;",[25,21520,21522,21525,21686],{"className":21521},[75],[25,21523],{"className":21524},[352,3239],[25,21526,21528],{"className":21527},[1978],[25,21529,21531,21677],{"className":21530},[87,88],[25,21532,21534,21674],{"className":21533},[92],[25,21535,21538,21618,21626],{"className":21536,"style":21537},[96],"height:1.3603em;",[25,21539,21540,21543],{"style":3255},[25,21541],{"className":21542,"style":1676},[104],[25,21544,21546],{"className":21545},[75],[25,21547,21549,21552],{"className":21548},[75],[25,21550,1147],{"className":21551,"style":875},[75,79],[25,21553,21555],{"className":21554},[83],[25,21556,21558,21610],{"className":21557},[87,88],[25,21559,21561,21607],{"className":21560},[92],[25,21562,21564],{"className":21563,"style":1741},[96],[25,21565,21566,21569],{"style":1744},[25,21567],{"className":21568,"style":105},[104],[25,21570,21572],{"className":21571},[109,110,111,112],[25,21573,21575],{"className":21574},[75,112],[25,21576,21578,21581],{"className":21577},[75,112],[25,21579,1464],{"className":21580,"style":478},[75,79,112],[25,21582,21584],{"className":21583},[83],[25,21585,21587],{"className":21586},[87],[25,21588,21590],{"className":21589},[92],[25,21591,21593],{"className":21592,"style":6591},[96],[25,21594,21595,21598],{"style":6594},[25,21596],{"className":21597,"style":1594},[104],[25,21599,21601],{"className":21600},[109,1598,1599,112],[25,21602,21604],{"className":21603},[75,112],[25,21605,6431],{"className":21606},[75,112],[25,21608,120],{"className":21609},[119],[25,21611,21613],{"className":21612},[92],[25,21614,21616],{"className":21615,"style":127},[96],[25,21617],{},[25,21619,21620,21623],{"style":3313},[25,21621],{"className":21622,"style":1676},[104],[25,21624],{"className":21625,"style":3321},[3320],[25,21627,21628,21631],{"style":3324},[25,21629],{"className":21630,"style":1676},[104],[25,21632,21634],{"className":21633},[75],[25,21635,21637,21640],{"className":21636},[75],[25,21638,1147],{"className":21639,"style":875},[75,79],[25,21641,21643],{"className":21642},[83],[25,21644,21646,21666],{"className":21645},[87,88],[25,21647,21649,21663],{"className":21648},[92],[25,21650,21652],{"className":21651,"style":1741},[96],[25,21653,21654,21657],{"style":1744},[25,21655],{"className":21656,"style":105},[104],[25,21658,21660],{"className":21659},[109,110,111,112],[25,21661,1464],{"className":21662,"style":478},[75,79,112],[25,21664,120],{"className":21665},[119],[25,21667,21669],{"className":21668},[92],[25,21670,21672],{"className":21671,"style":127},[96],[25,21673],{},[25,21675,120],{"className":21676},[119],[25,21678,21680],{"className":21679},[92],[25,21681,21684],{"className":21682,"style":21683},[96],"height:0.836em;",[25,21685],{},[25,21687],{"className":21688},[439,3239]," 的形式：",[25,21691,21693],{"className":21692},[1777],[25,21694,21696,21748],{"className":21695},[28],[25,21697,21699],{"className":21698},[32],[34,21700,21701],{"xmlns":36,"display":1786},[38,21702,21703,21745],{},[41,21704,21705,21707,21709,21711,21713,21715,21717,21719,21721],{},[47,21706,1808],{"mathvariant":322},[47,21708,2237],{},[310,21710,2240],{},[47,21712,922],{},[310,21714,313],{"stretchy":312},[47,21716,19255],{},[310,21718,332],{"stretchy":312},[310,21720,919],{},[1978,21722,21723,21735],{},[41,21724,21725,21727,21729,21731,21733],{},[47,21726,1808],{"mathvariant":322},[47,21728,922],{},[310,21730,313],{"stretchy":312},[47,21732,19255],{},[310,21734,332],{"stretchy":312},[41,21736,21737,21739,21741,21743],{},[47,21738,922],{},[310,21740,313],{"stretchy":312},[47,21742,19255],{},[310,21744,332],{"stretchy":312},[54,21746,21747],{"encoding":56},"\\nabla \\log f(x) = \\frac{\\nabla f(x)}{f(x)}",[25,21749,21751,21792],{"className":21750,"ariaHidden":62},[61],[25,21752,21754,21757,21760,21763,21768,21771,21774,21777,21780,21783,21786,21789],{"className":21753},[66],[25,21755],{"className":21756,"style":345},[70],[25,21758,1808],{"className":21759},[75],[25,21761],{"className":21762,"style":702},[701],[25,21764,4291,21766],{"className":21765},[1658],[25,21767,4295],{"style":4294},[25,21769],{"className":21770,"style":702},[701],[25,21772,922],{"className":21773,"style":1025},[75,79],[25,21775,313],{"className":21776},[352],[25,21778,19255],{"className":21779},[75,79],[25,21781,332],{"className":21782},[439],[25,21784],{"className":21785,"style":1008},[701],[25,21787,919],{"className":21788},[1012],[25,21790],{"className":21791,"style":1008},[701],[25,21793,21795,21798],{"className":21794},[66],[25,21796],{"className":21797,"style":21389},[70],[25,21799,21801,21804,21878],{"className":21800},[75],[25,21802],{"className":21803},[352,3239],[25,21805,21807],{"className":21806},[1978],[25,21808,21810,21870],{"className":21809},[87,88],[25,21811,21813,21867],{"className":21812},[92],[25,21814,21816,21836,21844],{"className":21815,"style":3252},[96],[25,21817,21818,21821],{"style":3255},[25,21819],{"className":21820,"style":1676},[104],[25,21822,21824,21827,21830,21833],{"className":21823},[75],[25,21825,922],{"className":21826,"style":1025},[75,79],[25,21828,313],{"className":21829},[352],[25,21831,19255],{"className":21832},[75,79],[25,21834,332],{"className":21835},[439],[25,21837,21838,21841],{"style":3313},[25,21839],{"className":21840,"style":1676},[104],[25,21842],{"className":21843,"style":3321},[3320],[25,21845,21846,21849],{"style":3324},[25,21847],{"className":21848,"style":1676},[104],[25,21850,21852,21855,21858,21861,21864],{"className":21851},[75],[25,21853,1808],{"className":21854},[75],[25,21856,922],{"className":21857,"style":1025},[75,79],[25,21859,313],{"className":21860},[352],[25,21862,19255],{"className":21863},[75,79],[25,21865,332],{"className":21866},[439],[25,21868,120],{"className":21869},[119],[25,21871,21873],{"className":21872},[92],[25,21874,21876],{"className":21875,"style":3389},[96],[25,21877],{},[25,21879],{"className":21880},[439,3239],[25,21882,21884],{"className":21883},[1777],[25,21885,21887,22609],{"className":21886},[28],[25,21888,21890],{"className":21889},[32],[34,21891,21892],{"xmlns":36,"display":1786},[38,21893,21894,22606],{},[1790,21895,21896,22020,22216,22442],{"rowspacing":1792,"columnalign":1793,"columnspacing":1794},[1796,21897,21898,21904],{},[1799,21899,21900],{},[1802,21901,21902],{"scriptlevel":599,"displaystyle":62},[41,21903],{},[1799,21905,21906],{},[1802,21907,21908],{"scriptlevel":599,"displaystyle":62},[41,21909,21910,21912,21918,21932,21950,21964,21966,21974,21976,21984,21986,21988,21990,21992,21998,22000,22008,22010,22018],{},[41,21911],{},[1978,21913,21914,21916],{},[597,21915,617],{},[47,21917,2111],{},[2113,21919,21920,21922,21930],{},[310,21921,1478],{},[41,21923,21924,21926,21928],{},[47,21925,2121],{},[310,21927,919],{},[597,21929,617],{},[47,21931,2111],{},[2113,21933,21934,21936,21944],{},[310,21935,1478],{},[41,21937,21938,21940,21942],{},[47,21939,52],{},[310,21941,919],{},[597,21943,617],{},[44,21945,21946,21948],{},[47,21947,635],{},[47,21949,2121],{},[2341,21951,21952,21954,21956],{},[47,21953,8036],{},[47,21955,1464],{},[41,21957,21958,21960,21962],{},[47,21959,14969],{},[47,21961,8036],{},[47,21963,1435],{},[310,21965,313],{"stretchy":312},[2341,21967,21968,21970,21972],{},[47,21969,177],{},[47,21971,2121],{},[47,21973,52],{},[310,21975,602],{"separator":62},[2341,21977,21978,21980,21982],{},[47,21979,49],{},[47,21981,2121],{},[47,21983,52],{},[310,21985,332],{"stretchy":312},[47,21987,1808],{"mathvariant":322},[47,21989,2237],{},[310,21991,2240],{},[44,21993,21994,21996],{},[47,21995,1147],{},[47,21997,1464],{},[310,21999,313],{"stretchy":312},[2341,22001,22002,22004,22006],{},[47,22003,49],{},[47,22005,2121],{},[47,22007,52],{},[47,22009,323],{"mathvariant":322},[2341,22011,22012,22014,22016],{},[47,22013,177],{},[47,22015,2121],{},[47,22017,52],{},[310,22019,332],{"stretchy":312},[1796,22021,22022,22028],{},[1799,22023,22024],{},[1802,22025,22026],{"scriptlevel":599,"displaystyle":62},[41,22027],{},[1799,22029,22030],{},[1802,22031,22032],{"scriptlevel":599,"displaystyle":62},[41,22033,22034,22036,22038,22044,22058,22076,22094,22096,22104,22106,22114,22116,22182,22184,22186,22188,22194,22196,22204,22206,22214],{},[41,22035],{},[310,22037,919],{},[1978,22039,22040,22042],{},[597,22041,617],{},[47,22043,2111],{},[2113,22045,22046,22048,22056],{},[310,22047,1478],{},[41,22049,22050,22052,22054],{},[47,22051,2121],{},[310,22053,919],{},[597,22055,617],{},[47,22057,2111],{},[2113,22059,22060,22062,22070],{},[310,22061,1478],{},[41,22063,22064,22066,22068],{},[47,22065,52],{},[310,22067,919],{},[597,22069,617],{},[44,22071,22072,22074],{},[47,22073,635],{},[47,22075,2121],{},[2341,22077,22078,22080,22086],{},[47,22079,8036],{},[2133,22081,22082,22084],{},[47,22083,1464],{},[310,22085,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[41,22087,22088,22090,22092],{},[47,22089,14969],{},[47,22091,8036],{},[47,22093,1435],{},[310,22095,313],{"stretchy":312},[2341,22097,22098,22100,22102],{},[47,22099,177],{},[47,22101,2121],{},[47,22103,52],{},[310,22105,602],{"separator":62},[2341,22107,22108,22110,22112],{},[47,22109,49],{},[47,22111,2121],{},[47,22113,52],{},[310,22115,332],{"stretchy":312},[1978,22117,22118,22148],{},[41,22119,22120,22126,22128,22136,22138,22146],{},[44,22121,22122,22124],{},[47,22123,1147],{},[47,22125,1464],{},[310,22127,313],{"stretchy":312},[2341,22129,22130,22132,22134],{},[47,22131,49],{},[47,22133,2121],{},[47,22135,52],{},[47,22137,323],{"mathvariant":322},[2341,22139,22140,22142,22144],{},[47,22141,177],{},[47,22143,2121],{},[47,22145,52],{},[310,22147,332],{"stretchy":312},[41,22149,22150,22160,22162,22170,22172,22180],{},[44,22151,22152,22154],{},[47,22153,1147],{},[2133,22155,22156,22158],{},[47,22157,1464],{},[310,22159,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[310,22161,313],{"stretchy":312},[2341,22163,22164,22166,22168],{},[47,22165,49],{},[47,22167,2121],{},[47,22169,52],{},[47,22171,323],{"mathvariant":322},[2341,22173,22174,22176,22178],{},[47,22175,177],{},[47,22177,2121],{},[47,22179,52],{},[310,22181,332],{"stretchy":312},[47,22183,1808],{"mathvariant":322},[47,22185,2237],{},[310,22187,2240],{},[44,22189,22190,22192],{},[47,22191,1147],{},[47,22193,1464],{},[310,22195,313],{"stretchy":312},[2341,22197,22198,22200,22202],{},[47,22199,49],{},[47,22201,2121],{},[47,22203,52],{},[47,22205,323],{"mathvariant":322},[2341,22207,22208,22210,22212],{},[47,22209,177],{},[47,22211,2121],{},[47,22213,52],{},[310,22215,332],{"stretchy":312},[1796,22217,22218,22224],{},[1799,22219,22220],{},[1802,22221,22222],{"scriptlevel":599,"displaystyle":62},[41,22223],{},[1799,22225,22226],{},[1802,22227,22228],{"scriptlevel":599,"displaystyle":62},[41,22229,22230,22232,22234,22240,22254,22272,22290,22292,22300,22302,22310,22312,22378],{},[41,22231],{},[310,22233,919],{},[1978,22235,22236,22238],{},[597,22237,617],{},[47,22239,2111],{},[2113,22241,22242,22244,22252],{},[310,22243,1478],{},[41,22245,22246,22248,22250],{},[47,22247,2121],{},[310,22249,919],{},[597,22251,617],{},[47,22253,2111],{},[2113,22255,22256,22258,22266],{},[310,22257,1478],{},[41,22259,22260,22262,22264],{},[47,22261,52],{},[310,22263,919],{},[597,22265,617],{},[44,22267,22268,22270],{},[47,22269,635],{},[47,22271,2121],{},[2341,22273,22274,22276,22282],{},[47,22275,8036],{},[2133,22277,22278,22280],{},[47,22279,1464],{},[310,22281,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[41,22283,22284,22286,22288],{},[47,22285,14969],{},[47,22287,8036],{},[47,22289,1435],{},[310,22291,313],{"stretchy":312},[2341,22293,22294,22296,22298],{},[47,22295,177],{},[47,22297,2121],{},[47,22299,52],{},[310,22301,602],{"separator":62},[2341,22303,22304,22306,22308],{},[47,22305,49],{},[47,22307,2121],{},[47,22309,52],{},[310,22311,332],{"stretchy":312},[1978,22313,22314,22344],{},[41,22315,22316,22322,22324,22332,22334,22342],{},[44,22317,22318,22320],{},[47,22319,1147],{},[47,22321,1464],{},[310,22323,313],{"stretchy":312},[2341,22325,22326,22328,22330],{},[47,22327,49],{},[47,22329,2121],{},[47,22331,52],{},[47,22333,323],{"mathvariant":322},[2341,22335,22336,22338,22340],{},[47,22337,177],{},[47,22339,2121],{},[47,22341,52],{},[310,22343,332],{"stretchy":312},[41,22345,22346,22356,22358,22366,22368,22376],{},[44,22347,22348,22350],{},[47,22349,1147],{},[2133,22351,22352,22354],{},[47,22353,1464],{},[310,22355,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[310,22357,313],{"stretchy":312},[2341,22359,22360,22362,22364],{},[47,22361,49],{},[47,22363,2121],{},[47,22365,52],{},[47,22367,323],{"mathvariant":322},[2341,22369,22370,22372,22374],{},[47,22371,177],{},[47,22373,2121],{},[47,22375,52],{},[310,22377,332],{"stretchy":312},[1978,22379,22380,22412],{},[41,22381,22382,22384,22390,22392,22400,22402,22410],{},[47,22383,1808],{"mathvariant":322},[44,22385,22386,22388],{},[47,22387,1147],{},[47,22389,1464],{},[310,22391,313],{"stretchy":312},[2341,22393,22394,22396,22398],{},[47,22395,49],{},[47,22397,2121],{},[47,22399,52],{},[47,22401,323],{"mathvariant":322},[2341,22403,22404,22406,22408],{},[47,22405,177],{},[47,22407,2121],{},[47,22409,52],{},[310,22411,332],{"stretchy":312},[41,22413,22414,22420,22422,22430,22432,22440],{},[44,22415,22416,22418],{},[47,22417,1147],{},[47,22419,1464],{},[310,22421,313],{"stretchy":312},[2341,22423,22424,22426,22428],{},[47,22425,49],{},[47,22427,2121],{},[47,22429,52],{},[47,22431,323],{"mathvariant":322},[2341,22433,22434,22436,22438],{},[47,22435,177],{},[47,22437,2121],{},[47,22439,52],{},[310,22441,332],{"stretchy":312},[1796,22443,22444,22450],{},[1799,22445,22446],{},[1802,22447,22448],{"scriptlevel":599,"displaystyle":62},[41,22449],{},[1799,22451,22452],{},[1802,22453,22454],{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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}",[25,22610,22612],{"className":22611,"ariaHidden":62},[61],[25,22613,22615,22619],{"className":22614},[66],[25,22616],{"className":22617,"style":22618},[70],"height:13.6262em;vertical-align:-6.5631em;",[25,22620,22622],{"className":22621},[75],[25,22623,22625,22686],{"className":22624},[1790],[25,22626,22628],{"className":22627},[2587],[25,22629,22631,22677],{"className":22630},[87,88],[25,22632,22634,22674],{"className":22633},[92],[25,22635,22638,22647,22656,22665],{"className":22636,"style":22637},[96],"height:7.0631em;",[25,22639,22641,22644],{"style":22640},"top:-9.0631em;",[25,22642],{"className":22643,"style":2604},[104],[25,22645],{"className":22646},[75],[25,22648,22650,22653],{"style":22649},"top:-5.6565em;",[25,22651],{"className":22652,"style":2604},[104],[25,22654],{"className":22655},[75],[25,22657,22659,22662],{"style":22658},"top:-2.25em;",[25,22660],{"className":22661,"style":2604},[104],[25,22663],{"className":22664},[75],[25,22666,22668,22671],{"style":22667},"top:1.1565em;",[25,22669],{"className":22670,"style":2604},[104],[25,22672],{"className":22673},[75],[25,22675,120],{"className":22676},[119],[25,22678,22680],{"className":22679},[92],[25,22681,22684],{"className":22682,"style":22683},[96],"height:6.5631em;",[25,22685],{},[25,22687,22689],{"className":22688},[2811],[25,22690,22692,26398],{"className":22691},[87,88],[25,22693,22695,26395],{"className":22694},[92],[25,22696,22698,23290,24315,25534],{"className":22697,"style":22637},[96],[25,22699,22700,22703],{"style":22640},[25,22701],{"className":22702,"style":2604},[104],[25,22704,22706,22709,22771,22774,22841,22844,22948,22951,23011,23014,23065,23068,23071,23122,23125,23128,23131,23136,23139,23179,23182,23233,23236,23287],{"className":22705},[75],[25,22707],{"className":22708},[75],[25,22710,22712,22715,22768],{"className":22711},[75],[25,22713],{"className":22714},[352,3239],[25,22716,22718],{"className":22717},[1978],[25,22719,22721,22760],{"className":22720},[87,88],[25,22722,22724,22757],{"className":22723},[92],[25,22725,22727,22738,22746],{"className":22726,"style":3718},[96],[25,22728,22729,22732],{"style":3255},[25,22730],{"className":22731,"style":1676},[104],[25,22733,22735],{"className":22734},[75],[25,22736,2111],{"className":22737,"style":3730},[75,79],[25,22739,22740,22743],{"style":3313},[25,22741],{"className":22742,"style":1676},[104],[25,22744],{"className":22745,"style":3321},[3320],[25,22747,22748,22751],{"style":3324},[25,22749],{"className":22750,"style":1676},[104],[25,22752,22754],{"className":22753},[75],[25,22755,617],{"className":22756},[75],[25,22758,120],{"className":22759},[119],[25,22761,22763],{"className":22762},[92],[25,22764,22766],{"className":22765,"style":3759},[96],[25,22767],{},[25,22769],{"className":22770},[439,3239],[25,22772],{"className":22773,"style":702},[701],[25,22775,22777],{"className":22776},[1658,1659],[25,22778,22780,22833],{"className":22779},[87,88],[25,22781,22783,22830],{"className":22782},[92],[25,22784,22786,22806,22816],{"className":22785,"style":3780},[96],[25,22787,22788,22791],{"style":3783},[25,22789],{"className":22790,"style":2866},[104],[25,22792,22794],{"className":22793},[109,110,111,112],[25,22795,22797,22800,22803],{"className":22796},[75,112],[25,22798,2121],{"className":22799},[75,79,112],[25,22801,919],{"className":22802},[1012,112],[25,22804,617],{"className":22805},[75,112],[25,22807,22808,22811],{"style":2875},[25,22809],{"className":22810,"style":2866},[104],[25,22812,22813],{},[25,22814,1478],{"className":22815},[1658,1694,2884],[25,22817,22818,22821],{"style":3814},[25,22819],{"className":22820,"style":2866},[104],[25,22822,22824],{"className":22823},[109,110,111,112],[25,22825,22827],{"className":22826},[75,112],[25,22828,2111],{"className":22829,"style":3730},[75,79,112],[25,22831,120],{"className":22832},[119],[25,22834,22836],{"className":22835},[92],[25,22837,22839],{"className":22838,"style":3833},[96],[25,22840],{},[25,22842],{"className":22843,"style":702},[701],[25,22845,22847],{"className":22846},[1658,1659],[25,22848,22850,22940],{"className":22849},[87,88],[25,22851,22853,22937],{"className":22852},[92],[25,22854,22856,22876,22886],{"className":22855,"style":4590},[96],[25,22857,22858,22861],{"style":3783},[25,22859],{"className":22860,"style":2866},[104],[25,22862,22864],{"className":22863},[109,110,111,112],[25,22865,22867,22870,22873],{"className":22866},[75,112],[25,22868,52],{"className":22869},[75,79,112],[25,22871,919],{"className":22872},[1012,112],[25,22874,617],{"className":22875},[75,112],[25,22877,22878,22881],{"style":2875},[25,22879],{"className":22880,"style":2866},[104],[25,22882,22883],{},[25,22884,1478],{"className":22885},[1658,1694,2884],[25,22887,22888,22891],{"style":4623},[25,22889],{"className":22890,"style":2866},[104],[25,22892,22894],{"className":22893},[109,110,111,112],[25,22895,22897],{"className":22896},[75,112],[25,22898,22900,22903],{"className":22899},[75,112],[25,22901,635],{"class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surrogate 上加 KL 惩罚",[15,27463,27464,27465,27497],{},"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 ",[25,27466,27468,27483],{"className":27467},[28],[25,27469,27471],{"className":27470},[32],[34,27472,27473],{"xmlns":36},[38,27474,27475,27480],{},[41,27476,27477],{},[47,27478,27479],{},"β",[54,27481,27482],{"encoding":56},"\\beta",[25,27484,27486],{"className":27485,"ariaHidden":62},[61],[25,27487,27489,27493],{"className":27488},[66],[25,27490],{"className":27491,"style":27492},[70],"height:0.8889em;vertical-align:-0.1944em;",[25,27494,27479],{"className":27495,"style":27496},[75,79],"margin-right:0.05278em;"," 来调整 KL 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还有一种实现，是通过截断函数来替代 KL 散度，防止训练的策略和参考的策略偏差过大，可以看出它是由红色和蓝色两个部分构成，取两个部分的最小值。",[15,28800,28801,28802,29302,29303,29356,29357,29408],{},"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 ",[25,29304,29306,29325],{"className":29305},[28],[25,29307,29309],{"className":29308},[32],[34,29310,29311],{"xmlns":36},[38,29312,29313,29322],{},[41,29314,29315,29317,29319],{},[597,29316,617],{},[310,29318,5810],{},[47,29320,29321],{},"ϵ",[54,29323,29324],{"encoding":56},"1-\\epsilon",[25,29326,29328,29347],{"className":29327,"ariaHidden":62},[61],[25,29329,29331,29335,29338,29341,29344],{"className":29330},[66],[25,29332],{"className":29333,"style":29334},[70],"height:0.7278em;vertical-align:-0.0833em;",[25,29336,617],{"className":29337},[75],[25,29339],{"className":29340,"style":3226},[701],[25,29342,5810],{"className":29343},[989],[25,29345],{"className":29346,"style":3226},[701],[25,29348,29350,29353],{"className":29349},[66],[25,29351],{"className":29352,"style":289},[70],[25,29354,29321],{"className":29355},[75,79]," 到 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之间，就返回原值，否则返回其中更接近的一个。这就限制的参考模型和训练模型差异的值不能太大。",[25,29410,29412],{"className":29411},[1777],[25,29413,29415,29754],{"className":29414},[28],[25,29416,29418],{"className":29417},[32],[34,29419,29420],{"xmlns":36,"display":1786},[38,29421,29422,29751],{},[41,29423,29424,29426,29428,29430,29437,29439,29441,29447,29461,29479,29482,29484],{},[47,29425,5798],{},[47,29427,5801],{},[47,29429,177],{},[44,29431,29432,29434],{},[47,29433,177],{},[15053,29435,29436],{},"ppo2",[310,29438,919],{},[310,29440,5810],{},[1978,29442,29443,29445],{},[597,29444,617],{},[47,29446,2111],{},[2113,29448,29449,29451,29459],{},[310,29450,1478],{},[41,29452,29453,29455,29457],{},[47,29454,2121],{},[310,29456,919],{},[597,29458,617],{},[47,29460,2111],{},[2113,29462,29463,29465,29473],{},[310,29464,1478],{},[41,29466,29467,29469,29471],{},[47,29468,52],{},[310,29470,919],{},[597,29472,617],{},[44,29474,29475,29477],{},[47,29476,635],{},[47,29478,2121],{},[47,29480,29481],{},"min",[310,29483,2240],{},[41,29485,29486,29488,29597,29599,29601,29749],{},[310,29487,313],{"fence":62},[1802,29489,29491,29509,29511,29519,29521,29529,29531],{"mathcolor":29490},"red",[2341,29492,29493,29495,29501],{},[47,29494,8036],{},[2133,29496,29497,29499],{},[47,29498,1464],{},[310,29500,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[41,29502,29503,29505,29507],{},[47,29504,14969],{},[47,29506,8036],{},[47,29508,1435],{},[310,29510,313],{"stretchy":312},[2341,29512,29513,29515,29517],{},[47,29514,177],{},[47,29516,2121],{},[47,29518,52],{},[310,29520,602],{"separator":62},[2341,29522,29523,29525,29527],{},[47,29524,49],{},[47,29526,2121],{},[47,29528,52],{},[310,29530,332],{"stretchy":312},[1978,29532,29533,29563],{},[41,29534,29535,29541,29543,29551,29553,29561],{},[44,29536,29537,29539],{},[47,29538,1147],{},[47,29540,1464],{},[310,29542,313],{"stretchy":312},[2341,29544,29545,29547,29549],{},[47,29546,49],{},[47,29548,2121],{},[47,29550,52],{},[47,29552,323],{"mathvariant":322},[2341,29554,29555,29557,29559],{},[47,29556,177],{},[47,29558,2121],{},[47,29560,52],{},[310,29562,332],{"stretchy":312},[41,29564,29565,29575,29577,29585,29587,29595],{},[44,29566,29567,29569],{},[47,29568,1147],{},[2133,29570,29571,29573],{},[47,29572,1464],{},[310,29574,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[310,29576,313],{"stretchy":312},[2341,29578,29579,29581,29583],{},[47,29580,49],{},[47,29582,2121],{},[47,29584,52],{},[47,29586,323],{"mathvariant":322},[2341,29588,29589,29591,29593],{},[47,29590,177],{},[47,29592,2121],{},[47,29594,52],{},[310,29596,332],{"stretchy":312},[310,29598,602],{"separator":62},[15053,29600,15055],{},[1802,29602,29604,29617,29709,29727,29729,29737,29739,29747],{"mathcolor":29603},"skyblue",[41,29605,29606,29609,29612,29615],{},[47,29607,29608],{"mathvariant":322},"c",[47,29610,29611],{"mathvariant":322},"l",[47,29613,29614],{"mathvariant":322},"i",[47,29616,15],{"mathvariant":322},[41,29618,29619,29621,29687,29689,29691,29693,29695,29697,29699,29701,29703,29705,29707],{},[310,29620,313],{"fence":62},[1978,29622,29623,29653],{},[41,29624,29625,29631,29633,29641,29643,29651],{},[44,29626,29627,29629],{},[47,29628,1147],{},[47,29630,1464],{},[310,29632,313],{"stretchy":312},[2341,29634,29635,29637,29639],{},[47,29636,49],{},[47,29638,2121],{},[47,29640,52],{},[47,29642,323],{"mathvariant":322},[2341,29644,29645,29647,29649],{},[47,29646,177],{},[47,29648,2121],{},[47,29650,52],{},[310,29652,332],{"stretchy":312},[41,29654,29655,29665,29667,29675,29677,29685],{},[44,29656,29657,29659],{},[47,29658,1147],{},[2133,29660,29661,29663],{},[47,29662,1464],{},[310,29664,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[310,29666,313],{"stretchy":312},[2341,29668,29669,29671,29673],{},[47,29670,49],{},[47,29672,2121],{},[47,29674,52],{},[47,29676,323],{"mathvariant":322},[2341,29678,29679,29681,29683],{},[47,29680,177],{},[47,29682,2121],{},[47,29684,52],{},[310,29686,332],{"stretchy":312},[310,29688,602],{"separator":62},[15053,29690,15055],{},[597,29692,617],{},[310,29694,5810],{},[47,29696,29321],{},[310,29698,602],{"separator":62},[15053,29700,15055],{},[597,29702,617],{},[310,29704,914],{},[47,29706,29321],{},[310,29708,332],{"fence":62},[2341,29710,29711,29713,29719],{},[47,29712,8036],{},[2133,29714,29715,29717],{},[47,29716,1464],{},[310,29718,6431],{"mathvariant":322,"lspace":1794,"rspace":1794},[41,29720,29721,29723,29725],{},[47,29722,14969],{},[47,29724,8036],{},[47,29726,1435],{},[310,29728,313],{"stretchy":312},[2341,29730,29731,29733,29735],{},[47,29732,177],{},[47,29734,2121],{},[47,29736,52],{},[310,29738,602],{"separator":62},[2341,29740,29741,29743,29745],{},[47,29742,49],{},[47,29744,2121],{},[47,29746,52],{},[310,29748,332],{"stretchy":312},[310,29750,332],{"fence":62},[54,29752,29753],{"encoding":56},"Loss_{\\text{ppo2}} 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0 400000 1080","xMinYMin slice",[31643,31644],"path",{"d":31645},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 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",[25,31761,31763,31776],{"className":31762},[28],[25,31764,31766],{"className":31765},[32],[34,31767,31768],{"xmlns":36},[38,31769,31770,31774],{},[41,31771,31772],{},[47,31773,31509],{},[54,31775,31509],{"encoding":56},[25,31777,31779],{"className":31778,"ariaHidden":62},[61],[25,31780,31782,31785],{"className":31781},[66],[25,31783],{"className":31784,"style":14931},[70],[25,31786,31509],{"className":31787},[75,79],"，值的长度为 ",[25,31790,31792,31806],{"className":31791},[28],[25,31793,31795],{"className":31794},[32],[34,31796,31797],{"xmlns":36},[38,31798,31799,31804],{},[41,31800,31801],{},[47,31802,31803],{},"v",[54,31805,31803],{"encoding":56},[25,31807,31809],{"className":31808,"ariaHidden":62},[61],[25,31810,31812,31815],{"className":31811},[66],[25,31813],{"className":31814,"style":289},[70],[25,31816,31803],{"className":31817,"style":293},[75,79],[15,31819,31820,31821,31921,31922,32020,32021,32118],{},"查询 ",[25,31822,31824,31854],{"className":31823},[28],[25,31825,31827],{"className":31826},[32],[34,31828,31829],{"xmlns":36},[38,31830,31831,31851],{},[41,31832,31833,31835,31838],{},[47,31834,7755],{},[310,31836,31837],{},"∈",[2133,31839,31840,31842],{},[47,31841,1440],{"mathvariant":19397},[41,31843,31844,31846,31849],{},[47,31845,2121],{},[310,31847,31848],{},"×",[47,31850,31509],{},[54,31852,31853],{"encoding":56},"Q \\in \\mathbb{R}^{n \\times d}",[25,31855,31857,31876],{"className":31856,"ariaHidden":62},[61],[25,31858,31860,31864,31867,31870,31873],{"className":31859},[66],[25,31861],{"className":31862,"style":31863},[70],"height:0.8778em;vertical-align:-0.1944em;",[25,31865,7755],{"className":31866},[75,79],[25,31868],{"className":31869,"style":1008},[701],[25,31871,31837],{"className":31872},[1012],[25,31874],{"className":31875,"style":1008},[701],[25,31877,31879,31883],{"className":31878},[66],[25,31880],{"className":31881,"style":31882},[70],"height:0.8491em;",[25,31884,31886,31889],{"className":31885},[75],[25,31887,1440],{"className":31888},[75,19805],[25,31890,31892],{"className":31891},[83],[25,31893,31895],{"className":31894},[87],[25,31896,31898],{"className":31897},[92],[25,31899,31901],{"className":31900,"style":31882},[96],[25,31902,31903,31906],{"style":4065},[25,31904],{"className":31905,"style":105},[104],[25,31907,31909],{"className":31908},[109,110,111,112],[25,31910,31912,31915,31918],{"className":31911},[75,112],[25,31913,2121],{"className":31914},[75,79,112],[25,31916,31848],{"className":31917},[989,112],[25,31919,31509],{"className":31920},[75,79,112],"、键 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和值 ",[25,32022,32024,32052],{"className":32023},[28],[25,32025,32027],{"className":32026},[32],[34,32028,32029],{"xmlns":36},[38,32030,32031,32049],{},[41,32032,32033,32035,32037],{},[47,32034,7916],{},[310,32036,31837],{},[2133,32038,32039,32041],{},[47,32040,1440],{"mathvariant":19397},[41,32042,32043,32045,32047],{},[47,32044,31744],{},[310,32046,31848],{},[47,32048,31803],{},[54,32050,32051],{"encoding":56},"V \\in \\mathbb{R}^{m \\times v}",[25,32053,32055,32073],{"className":32054,"ariaHidden":62},[61],[25,32056,32058,32061,32064,32067,32070],{"className":32057},[66],[25,32059],{"className":32060,"style":31962},[70],[25,32062,7916],{"className":32063,"style":7943},[75,79],[25,32065],{"className":32066,"style":1008},[701],[25,32068,31837],{"className":32069},[1012],[25,32071],{"className":32072,"style":1008},[701],[25,32074,32076,32080],{"className":32075},[66],[25,32077],{"className":32078,"style":32079},[70],"height:0.7713em;",[25,32081,32083,32086],{"className":32082},[75],[25,32084,1440],{"className":32085},[75,19805],[25,32087,32089],{"className":32088},[83],[25,32090,32092],{"className":32091},[87],[25,32093,32095],{"className":32094},[92],[25,32096,32098],{"className":32097,"style":32079},[96],[25,32099,32100,32103],{"style":4065},[25,32101],{"className":32102,"style":105},[104],[25,32104,32106],{"className":32105},[109,110,111,112],[25,32107,32109,32112,32115],{"className":32108},[75,112],[25,32110,31744],{"className":32111},[75,79,112],[25,32113,31848],{"className":32114},[989,112],[25,32116,31803],{"className":32117,"style":293},[75,79,112]," 的缩放点积注意力是：",[15,32120,32121],{},[25,32122,32124,32218],{"className":32123},[28],[25,32125,32127],{"className":32126},[32],[34,32128,32129],{"xmlns":36},[38,32130,32131,32215],{},[41,32132,32133,32135,32137,32139,32142,32144,32146,32148,32150,32152,32154,32156,32158,32160,32162,32164,32166,32168,32171,32173,32196,32198,32200,32212],{},[47,32134,8036],{},[47,32136,52],{},[47,32138,52],{},[47,32140,32141],{},"e",[47,32143,2121],{},[47,32145,52],{},[47,32147,29614],{},[47,32149,5801],{},[47,32151,2121],{},[310,32153,313],{"stretchy":312},[47,32155,7755],{},[310,32157,602],{"separator":62},[47,32159,27684],{},[310,32161,602],{"separator":62},[47,32163,7916],{},[310,32165,332],{"stretchy":312},[310,32167,919],{},[47,32169,32170],{"mathvariant":322},"softmax",[310,32172,2240],{},[41,32174,32175,32177,32194],{},[310,32176,313],{"fence":62},[1978,32178,32179,32190],{},[41,32180,32181,32183],{},[47,32182,7755],{},[2133,32184,32185,32187],{},[47,32186,27684],{},[47,32188,32189],{"mathvariant":322},"⊤",[31503,32191,32192],{},[47,32193,31509],{},[310,32195,332],{"fence":62},[47,32197,7916],{},[310,32199,31837],{},[2133,32201,32202,32204],{},[47,32203,1440],{"mathvariant":19397},[41,32205,32206,32208,32210],{},[47,32207,2121],{},[310,32209,31848],{},[47,32211,31803],{},[47,32213,32214],{"mathvariant":322},".",[54,32216,32217],{"encoding":56}," Attention(Q,K,V) = \\operatorname{softmax}\\left(\\frac{QK^\\top}{\\sqrt{d}}\\right)V \\in \\mathbb{R}^{n \\times v}.",[25,32219,32221,32288,32483],{"className":32220,"ariaHidden":62},[61],[25,32222,32224,32227,32230,32234,32237,32240,32243,32246,32249,32252,32255,32258,32261,32264,32267,32270,32273,32276,32279,32282,32285],{"className":32223},[66],[25,32225],{"className":32226,"style":345},[70],[25,32228,8036],{"className":32229},[75,79],[25,32231,32233],{"className":32232},[75,79],"tt",[25,32235,32141],{"className":32236},[75,79],[25,32238,2121],{"className":32239},[75,79],[25,32241,52],{"className":32242},[75,79],[25,32244,29614],{"className":32245},[75,79],[25,32247,5801],{"className":32248},[75,79],[25,32250,2121],{"className":32251},[75,79],[25,32253,313],{"className":32254},[352],[25,32256,7755],{"className":32257},[75,79],[25,32259,602],{"className":32260},[697],[25,32262],{"className":32263,"style":702},[701],[25,32265,27684],{"className":32266,"style":31966},[75,79],[25,32268,602],{"className":32269},[697],[25,32271],{"className":32272,"style":702},[701],[25,32274,7916],{"className":32275,"style":7943},[75,79],[25,32277,332],{"className":32278},[439],[25,32280],{"className":32281,"style":1008},[701],[25,32283,919],{"className":32284},[1012],[25,32286],{"className":32287,"style":1008},[701],[25,32289,32291,32295,32301,32304,32468,32471,32474,32477,32480],{"className":32290},[66],[25,32292],{"className":32293,"style":32294},[70],"height:1.8em;vertical-align:-0.65em;",[25,32296,32298],{"className":32297},[1658],[25,32299,32170],{"className":32300},[75,28663],[25,32302],{"className":32303,"style":702},[701],[25,32305,32307,32314,32462],{"className":32306},[841],[25,32308,32310],{"className":32309,"style":17229},[352,17228],[25,32311,313],{"className":32312},[17233,32313],"size2",[25,32315,32317,32320,32459],{"className":32316},[75],[25,32318],{"className":32319},[352,3239],[25,32321,32323],{"className":32322},[1978],[25,32324,32326,32451],{"className":32325},[87,88],[25,32327,32329,32448],{"className":32328},[92],[25,32330,32333,32395,32403],{"className":32331,"style":32332},[96],"height:1.095em;",[25,32334,32336,32339],{"style":32335},"top:-2.5335em;",[25,32337],{"className":32338,"style":1676},[104],[25,32340,32342],{"className":32341},[109,110,111,112],[25,32343,32345],{"className":32344},[75,112],[25,32346,32348],{"className":32347},[75,31559,112],[25,32349,32351,32386],{"className":32350},[87,88],[25,32352,32354,32383],{"className":32353},[92],[25,32355,32358,32370],{"className":32356,"style":32357},[96],"height:0.9378em;",[25,32359,32361,32364],{"className":32360,"style":1685},[31573],[25,32362],{"className":32363,"style":1676},[104],[25,32365,32367],{"className":32366,"style":31580},[75,112],[25,32368,31509],{"className":32369},[75,79,112],[25,32371,32373,32376],{"style":32372},"top:-2.8978em;",[25,32374],{"className":32375,"style":1676},[104],[25,32377,32379],{"className":32378,"style":31633},[31632,112],[31635,32380,32381],{"xmlns":31637,"width":31638,"height":31639,"viewBox":31640,"preserveAspectRatio":31641},[31643,32382],{"d":31645},[25,32384,120],{"className":32385},[119],[25,32387,32389],{"className":32388},[92],[25,32390,32393],{"className":32391,"style":32392},[96],"height:0.1022em;",[25,32394],{},[25,32396,32397,32400],{"style":3313},[25,32398],{"className":32399,"style":1676},[104],[25,32401],{"className":32402,"style":3321},[3320],[25,32404,32406,32409],{"style":32405},"top:-3.4461em;",[25,32407],{"className":32408,"style":1676},[104],[25,32410,32412],{"className":32411},[109,110,111,112],[25,32413,32415,32418],{"className":32414},[75,112],[25,32416,7755],{"className":32417},[75,79,112],[25,32419,32421,32424],{"className":32420},[75,112],[25,32422,27684],{"className":32423,"style":31966},[75,79,112],[25,32425,32427],{"className":32426},[83],[25,32428,32430],{"className":32429},[87],[25,32431,32433],{"className":32432},[92],[25,32434,32437],{"className":32435,"style":32436},[96],"height:0.927em;",[25,32438,32439,32442],{"style":6741},[25,32440],{"className":32441,"style":1594},[104],[25,32443,32445],{"className":32444},[109,1598,1599,112],[25,32446,32189],{"className":32447},[75,112],[25,32449,120],{"className":32450},[119],[25,32452,32454],{"className":32453},[92],[25,32455,32457],{"className":32456,"style":31689},[96],[25,32458],{},[25,32460],{"className":32461},[439,3239],[25,32463,32465],{"className":32464,"style":17229},[439,17228],[25,32466,332],{"className":32467},[17233,32313],[25,32469],{"className":32470,"style":702},[701],[25,32472,7916],{"className":32473,"style":7943},[75,79],[25,32475],{"className":32476,"style":1008},[701],[25,32478,31837],{"className":32479},[1012],[25,32481],{"className":32482,"style":1008},[701],[25,32484,32486,32489,32527],{"className":32485},[66],[25,32487],{"className":32488,"style":32079},[70],[25,32490,32492,32495],{"className":32491},[75],[25,32493,1440],{"className":32494},[75,19805],[25,32496,32498],{"className":32497},[83],[25,32499,32501],{"className":32500},[87],[25,32502,32504],{"className":32503},[92],[25,32505,32507],{"className":32506,"style":32079},[96],[25,32508,32509,32512],{"style":4065},[25,32510],{"className":32511,"style":105},[104],[25,32513,32515],{"className":32514},[109,110,111,112],[25,32516,32518,32521,32524],{"className":32517},[75,112],[25,32519,2121],{"className":32520},[75,79,112],[25,32522,31848],{"className":32523},[989,112],[25,32525,31803],{"className":32526,"style":293},[75,79,112],[25,32528,32214],{"className":32529},[75],[15,32531,32532],{},[31470,32533],{"alt":32534,"src":32535},"注意力","transformer/attention.png",[15,32537,32538,32539,32609,32610,32680,32681,32801],{},"缩放点积注意力的输入由维度为 ",[25,32540,32542,32560],{"className":32541},[28],[25,32543,32545],{"className":32544},[32],[34,32546,32547],{"xmlns":36},[38,32548,32549,32557],{},[41,32550,32551],{},[44,32552,32553,32555],{},[47,32554,31509],{},[47,32556,31512],{},[54,32558,32559],{"encoding":56},"d_k",[25,32561,32563],{"className":32562,"ariaHidden":62},[61],[25,32564,32566,32569],{"className":32565},[66],[25,32567],{"className":32568,"style":12948},[70],[25,32570,32572,32575],{"className":32571},[75],[25,32573,31509],{"className":32574},[75,79],[25,32576,32578],{"className":32577},[83],[25,32579,32581,32601],{"className":32580},[87,88],[25,32582,32584,32598],{"className":32583},[92],[25,32585,32587],{"className":32586,"style":1741},[96],[25,32588,32589,32592],{"style":100},[25,32590],{"className":32591,"style":105},[104],[25,32593,32595],{"className":32594},[109,110,111,112],[25,32596,31512],{"className":32597,"style":31611},[75,79,112],[25,32599,120],{"className":32600},[119],[25,32602,32604],{"className":32603},[92],[25,32605,32607],{"className":32606,"style":127},[96],[25,32608],{}," ​的查询和键以及维度为 ",[25,32611,32613,32631],{"className":32612},[28],[25,32614,32616],{"className":32615},[32],[34,32617,32618],{"xmlns":36},[38,32619,32620,32628],{},[41,32621,32622],{},[44,32623,32624,32626],{},[47,32625,31509],{},[47,32627,31803],{},[54,32629,32630],{"encoding":56},"d_v",[25,32632,32634],{"className":32633,"ariaHidden":62},[61],[25,32635,32637,32640],{"className":32636},[66],[25,32638],{"className":32639,"style":12948},[70],[25,32641,32643,32646],{"className":32642},[75],[25,32644,31509],{"className":32645},[75,79],[25,32647,32649],{"className":32648},[83],[25,32650,32652,32672],{"className":32651},[87,88],[25,32653,32655,32669],{"className":32654},[92],[25,32656,32658],{"className":32657,"style":20778},[96],[25,32659,32660,32663],{"style":100},[25,32661],{"className":32662,"style":105},[104],[25,32664,32666],{"className":32665},[109,110,111,112],[25,32667,31803],{"className":32668,"style":293},[75,79,112],[25,32670,120],{"className":32671},[119],[25,32673,32675],{"className":32674},[92],[25,32676,32678],{"className":32677,"style":127},[96],[25,32679],{}," ​的值组成。我们计算查询与所有键的点积，将每个点积除以 ",[25,32682,32684,32704],{"className":32683},[28],[25,32685,32687],{"className":32686},[32],[34,32688,32689],{"xmlns":36},[38,32690,32691,32701],{},[41,32692,32693],{},[31503,32694,32695],{},[44,32696,32697,32699],{},[47,32698,31509],{},[47,32700,31512],{},[54,32702,32703],{"encoding":56},"\\sqrt{d_k}",[25,32705,32707],{"className":32706,"ariaHidden":62},[61],[25,32708,32710,32714],{"className":32709},[66],[25,32711],{"className":32712,"style":32713},[70],"height:1.04em;vertical-align:-0.1828em;",[25,32715,32717],{"className":32716},[75,31559],[25,32718,32720,32792],{"className":32719},[87,88],[25,32721,32723,32789],{"className":32722},[92],[25,32724,32727,32776],{"className":32725,"style":32726},[96],"height:0.8572em;",[25,32728,32730,32733],{"className":32729,"style":1685},[31573],[25,32731],{"className":32732,"style":1676},[104],[25,32734,32736],{"className":32735,"style":31580},[75],[25,32737,32739,32742],{"className":32738},[75],[25,32740,31509],{"className":32741},[75,79],[25,32743,32745],{"className":32744},[83],[25,32746,32748,32768],{"className":32747},[87,88],[25,32749,32751,32765],{"className":32750},[92],[25,32752,32754],{"className":32753,"style":1741},[96],[25,32755,32756,32759],{"style":100},[25,32757],{"className":32758,"style":105},[104],[25,32760,32762],{"className":32761},[109,110,111,112],[25,32763,31512],{"className":32764,"style":31611},[75,79,112],[25,32766,120],{"className":32767},[119],[25,32769,32771],{"className":32770},[92],[25,32772,32774],{"className":32773,"style":127},[96],[25,32775],{},[25,32777,32779,32782],{"style":32778},"top:-2.8172em;",[25,32780],{"className":32781,"style":1676},[104],[25,32783,32785],{"className":32784,"style":31633},[31632],[31635,32786,32787],{"xmlns":31637,"width":31638,"height":31639,"viewBox":31640,"preserveAspectRatio":31641},[31643,32788],{"d":31645},[25,32790,120],{"className":32791},[119],[25,32793,32795],{"className":32794},[92],[25,32796,32799],{"className":32797,"style":32798},[96],"height:0.1828em;",[25,32800],{},"​​，并应用softmax函数以获得值上的权重。",[15,32803,32804,32805,32874,32875,32944,32945,33014,33015,33043,33044,33072,33073,33102,33103,33131,33132,33429,33430,33102,33458,33527,33528,1348],{},"对于较小的 ",[25,32806,32808,32825],{"className":32807},[28],[25,32809,32811],{"className":32810},[32],[34,32812,32813],{"xmlns":36},[38,32814,32815,32823],{},[41,32816,32817],{},[44,32818,32819,32821],{},[47,32820,31509],{},[47,32822,31512],{},[54,32824,32559],{"encoding":56},[25,32826,32828],{"className":32827,"ariaHidden":62},[61],[25,32829,32831,32834],{"className":32830},[66],[25,32832],{"className":32833,"style":12948},[70],[25,32835,32837,32840],{"className":32836},[75],[25,32838,31509],{"className":32839},[75,79],[25,32841,32843],{"className":32842},[83],[25,32844,32846,32866],{"className":32845},[87,88],[25,32847,32849,32863],{"className":32848},[92],[25,32850,32852],{"className":32851,"style":1741},[96],[25,32853,32854,32857],{"style":100},[25,32855],{"className":32856,"style":105},[104],[25,32858,32860],{"className":32859},[109,110,111,112],[25,32861,31512],{"className":32862,"style":31611},[75,79,112],[25,32864,120],{"className":32865},[119],[25,32867,32869],{"className":32868},[92],[25,32870,32872],{"className":32871,"style":127},[96],[25,32873],{}," 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 ",[25,32876,32878,32895],{"className":32877},[28],[25,32879,32881],{"className":32880},[32],[34,32882,32883],{"xmlns":36},[38,32884,32885,32893],{},[41,32886,32887],{},[44,32888,32889,32891],{},[47,32890,31509],{},[47,32892,31512],{},[54,32894,32559],{"encoding":56},[25,32896,32898],{"className":32897,"ariaHidden":62},[61],[25,32899,32901,32904],{"className":32900},[66],[25,32902],{"className":32903,"style":12948},[70],[25,32905,32907,32910],{"className":32906},[75],[25,32908,31509],{"className":32909},[75,79],[25,32911,32913],{"className":32912},[83],[25,32914,32916,32936],{"className":32915},[87,88],[25,32917,32919,32933],{"className":32918},[92],[25,32920,32922],{"className":32921,"style":1741},[96],[25,32923,32924,32927],{"style":100},[25,32925],{"className":32926,"style":105},[104],[25,32928,32930],{"className":32929},[109,110,111,112],[25,32931,31512],{"className":32932,"style":31611},[75,79,112],[25,32934,120],{"className":32935},[119],[25,32937,32939],{"className":32938},[92],[25,32940,32942],{"className":32941,"style":127},[96],[25,32943],{}," 值较大时会优于点积注意力。我们怀疑在 ",[25,32946,32948,32965],{"className":32947},[28],[25,32949,32951],{"className":32950},[32],[34,32952,32953],{"xmlns":36},[38,32954,32955,32963],{},[41,32956,32957],{},[44,32958,32959,32961],{},[47,32960,31509],{},[47,32962,31512],{},[54,32964,32559],{"encoding":56},[25,32966,32968],{"className":32967,"ariaHidden":62},[61],[25,32969,32971,32974],{"className":32970},[66],[25,32972],{"className":32973,"style":12948},[70],[25,32975,32977,32980],{"className":32976},[75],[25,32978,31509],{"className":32979},[75,79],[25,32981,32983],{"className":32982},[83],[25,32984,32986,33006],{"className":32985},[87,88],[25,32987,32989,33003],{"className":32988},[92],[25,32990,32992],{"className":32991,"style":1741},[96],[25,32993,32994,32997],{"style":100},[25,32995],{"className":32996,"style":105},[104],[25,32998,33000],{"className":32999},[109,110,111,112],[25,33001,31512],{"className":33002,"style":31611},[75,79,112],[25,33004,120],{"className":33005},[119],[25,33007,33009],{"className":33008},[92],[25,33010,33012],{"className":33011,"style":127},[96],[25,33013],{}," 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 ",[25,33016,33018,33031],{"className":33017},[28],[25,33019,33021],{"className":33020},[32],[34,33022,33023],{"xmlns":36},[38,33024,33025,33029],{},[41,33026,33027],{},[47,33028,19327],{},[54,33030,19327],{"encoding":56},[25,33032,33034],{"className":33033,"ariaHidden":62},[61],[25,33035,33037,33040],{"className":33036},[66],[25,33038],{"className":33039,"style":19308},[70],[25,33041,19327],{"className":33042,"style":293},[75,79]," 和键 ",[25,33045,33047,33060],{"className":33046},[28],[25,33048,33050],{"className":33049},[32],[34,33051,33052],{"xmlns":36},[38,33053,33054,33058],{},[41,33055,33056],{},[47,33057,31512],{},[54,33059,31512],{"encoding":56},[25,33061,33063],{"className":33062,"ariaHidden":62},[61],[25,33064,33066,33069],{"className":33065},[66],[25,33067],{"className":33068,"style":14931},[70],[25,33070,31512],{"className":33071,"style":31611},[75,79]," 都符合一个均值为 ",[25,33074,33076,33089],{"className":33075},[28],[25,33077,33079],{"className":33078},[32],[34,33080,33081],{"xmlns":36},[38,33082,33083,33087],{},[41,33084,33085],{},[597,33086,599],{},[54,33088,599],{"encoding":56},[25,33090,33092],{"className":33091,"ariaHidden":62},[61],[25,33093,33095,33099],{"className":33094},[66],[25,33096],{"className":33097,"style":33098},[70],"height:0.6444em;",[25,33100,599],{"className":33101},[75],"，方差为 ",[25,33104,33106,33119],{"className":33105},[28],[25,33107,33109],{"className":33108},[32],[34,33110,33111],{"xmlns":36},[38,33112,33113,33117],{},[41,33114,33115],{},[597,33116,617],{},[54,33118,617],{"encoding":56},[25,33120,33122],{"className":33121,"ariaHidden":62},[61],[25,33123,33125,33128],{"className":33124},[66],[25,33126],{"className":33127,"style":33098},[70],[25,33129,617],{"className":33130},[75]," 的随机变量。他们点积的结果 ",[25,33133,33135,33185],{"className":33134},[28],[25,33136,33138],{"className":33137},[32],[34,33139,33140],{"xmlns":36},[38,33141,33142,33182],{},[41,33143,33144,33146,33148,33150,33152,33170,33176],{},[47,33145,19327],{},[310,33147,1152],{},[47,33149,31512],{},[310,33151,919],{},[2341,33153,33154,33156,33164],{},[310,33155,1478],{},[41,33157,33158,33160,33162],{},[47,33159,29614],{},[310,33161,919],{},[597,33163,617],{},[44,33165,33166,33168],{},[47,33167,31509],{},[47,33169,31512],{},[44,33171,33172,33174],{},[47,33173,19327],{},[47,33175,29614],{},[44,33177,33178,33180],{},[47,33179,31512],{},[47,33181,29614],{},[54,33183,33184],{"encoding":56},"q \\cdot k = \\sum_{i=1}^{d_k}q_{i}k_{i}",[25,33186,33188,33207,33225],{"className":33187,"ariaHidden":62},[61],[25,33189,33191,33195,33198,33201,33204],{"className":33190},[66],[25,33192],{"className":33193,"style":33194},[70],"height:0.6389em;vertical-align:-0.1944em;",[25,33196,19327],{"className":33197,"style":293},[75,79],[25,33199],{"className":33200,"style":3226},[701],[25,33202,1152],{"className":33203},[989],[25,33205],{"className":33206,"style":3226},[701],[25,33208,33210,33213,33216,33219,33222],{"className":33209},[66],[25,33211],{"className":33212,"style":14931},[70],[25,33214,31512],{"className":33215,"style":31611},[75,79],[25,33217],{"className":33218,"style":1008},[701],[25,33220,919],{"className":33221},[1012],[25,33223],{"className":33224,"style":1008},[701],[25,33226,33228,33232,33337,33340,33385],{"className":33227},[66],[25,33229],{"className":33230,"style":33231},[70],"height:1.2887em;vertical-align:-0.2997em;",[25,33233,33235,33239],{"className":33234},[1658],[25,33236,1478],{"className":33237,"style":33238},[1658,1694,1695],"position:relative;top:0em;",[25,33240,33242],{"className":33241},[83],[25,33243,33245,33328],{"className":33244},[87,88],[25,33246,33248,33325],{"className":33247},[92],[25,33249,33252,33273],{"className":33250,"style":33251},[96],"height:0.989em;",[25,33253,33255,33258],{"style":33254},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[25,33256],{"className":33257,"style":105},[104],[25,33259,33261],{"className":33260},[109,110,111,112],[25,33262,33264,33267,33270],{"className":33263},[75,112],[25,33265,29614],{"className":33266},[75,79,112],[25,33268,919],{"className":33269},[1012,112],[25,33271,617],{"className":33272},[75,112],[25,33274,33276,33279],{"style":33275},"top:-3.2029em;margin-right:0.05em;",[25,33277],{"className":33278,"style":105},[104],[25,33280,33282],{"className":33281},[109,110,111,112],[25,33283,33285],{"className":33284},[75,112],[25,33286,33288,33291],{"className":33287},[75,112],[25,33289,31509],{"className":33290},[75,79,112],[25,33292,33294],{"className":33293},[83],[25,33295,33297,33317],{"className":33296},[87,88],[25,33298,33300,33314],{"className":33299},[92],[25,33301,33303],{"className":33302,"style":1551},[96],[25,33304,33305,33308],{"style":31601},[25,33306],{"className":33307,"style":1594},[104],[25,33309,33311],{"className":33310},[109,1598,1599,112],[25,33312,31512],{"className":33313,"style":31611},[75,79,112],[25,33315,120],{"className":33316},[119],[25,33318,33320],{"className":33319},[92],[25,33321,33323],{"className":33322,"style":1615},[96],[25,33324],{},[25,33326,120],{"className":33327},[119],[25,33329,33331],{"className":33330},[92],[25,33332,33335],{"className":33333,"style":33334},[96],"height:0.2997em;",[25,33336],{},[25,33338],{"className":33339,"style":702},[701],[25,33341,33343,33346],{"className":33342},[75],[25,33344,19327],{"className":33345,"style":293},[75,79],[25,33347,33349],{"className":33348},[83],[25,33350,33352,33377],{"className":33351},[87,88],[25,33353,33355,33374],{"className":33354},[92],[25,33356,33359],{"className":33357,"style":33358},[96],"height:0.3117em;",[25,33360,33362,33365],{"style":33361},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[25,33363],{"className":33364,"style":105},[104],[25,33366,33368],{"className":33367},[109,110,111,112],[25,33369,33371],{"className":33370},[75,112],[25,33372,29614],{"className":33373},[75,79,112],[25,33375,120],{"className":33376},[119],[25,33378,33380],{"className":33379},[92],[25,33381,33383],{"className":33382,"style":127},[96],[25,33384],{},[25,33386,33388,33391],{"className":33387},[75],[25,33389,31512],{"className":33390,"style":31611},[75,79],[25,33392,33394],{"className":33393},[83],[25,33395,33397,33421],{"className":33396},[87,88],[25,33398,33400,33418],{"className":33399},[92],[25,33401,33403],{"className":33402,"style":33358},[96],[25,33404,33406,33409],{"style":33405},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[25,33407],{"className":33408,"style":105},[104],[25,33410,33412],{"className":33411},[109,110,111,112],[25,33413,33415],{"className":33414},[75,112],[25,33416,29614],{"className":33417},[75,79,112],[25,33419,120],{"className":33420},[119],[25,33422,33424],{"className":33423},[92],[25,33425,33427],{"className":33426,"style":127},[96],[25,33428],{}," 的均值为 ",[25,33431,33433,33446],{"className":33432},[28],[25,33434,33436],{"className":33435},[32],[34,33437,33438],{"xmlns":36},[38,33439,33440,33444],{},[41,33441,33442],{},[597,33443,599],{},[54,33445,599],{"encoding":56},[25,33447,33449],{"className":33448,"ariaHidden":62},[61],[25,33450,33452,33455],{"className":33451},[66],[25,33453],{"className":33454,"style":33098},[70],[25,33456,599],{"className":33457},[75],[25,33459,33461,33478],{"className":33460},[28],[25,33462,33464],{"className":33463},[32],[34,33465,33466],{"xmlns":36},[38,33467,33468,33476],{},[41,33469,33470],{},[44,33471,33472,33474],{},[47,33473,31509],{},[47,33475,31512],{},[54,33477,32559],{"encoding":56},[25,33479,33481],{"className":33480,"ariaHidden":62},[61],[25,33482,33484,33487],{"className":33483},[66],[25,33485],{"className":33486,"style":12948},[70],[25,33488,33490,33493],{"className":33489},[75],[25,33491,31509],{"className":33492},[75,79],[25,33494,33496],{"className":33495},[83],[25,33497,33499,33519],{"className":33498},[87,88],[25,33500,33502,33516],{"className":33501},[92],[25,33503,33505],{"className":33504,"style":1741},[96],[25,33506,33507,33510],{"style":100},[25,33508],{"className":33509,"style":105},[104],[25,33511,33513],{"className":33512},[109,110,111,112],[25,33514,31512],{"className":33515,"style":31611},[75,79,112],[25,33517,120],{"className":33518},[119],[25,33520,33522],{"className":33521},[92],[25,33523,33525],{"className":33524,"style":127},[96],[25,33526],{},"，为了抵消这种影响，我们要乘以一个缩放因子 ",[25,33529,33531,33554],{"className":33530},[28],[25,33532,33534],{"className":33533},[32],[34,33535,33536],{"xmlns":36},[38,33537,33538,33552],{},[41,33539,33540],{},[1978,33541,33542,33544],{},[597,33543,617],{},[31503,33545,33546],{},[44,33547,33548,33550],{},[47,33549,31509],{},[47,33551,31512],{},[54,33553,31515],{"encoding":56},[25,33555,33557],{"className":33556,"ariaHidden":62},[61],[25,33558,33560,33563],{"className":33559},[66],[25,33561],{"className":33562,"style":31525},[70],[25,33564,33566,33569,33709],{"className":33565},[75],[25,33567],{"className":33568},[352,3239],[25,33570,33572],{"className":33571},[1978],[25,33573,33575,33701],{"className":33574},[87,88],[25,33576,33578,33698],{"className":33577},[92],[25,33579,33581,33676,33684],{"className":33580,"style":5949},[96],[25,33582,33583,33586],{"style":31546},[25,33584],{"className":33585,"style":1676},[104],[25,33587,33589],{"className":33588},[109,110,111,112],[25,33590,33592],{"className":33591},[75,112],[25,33593,33595],{"className":33594},[75,31559,112],[25,33596,33598,33668],{"className":33597},[87,88],[25,33599,33601,33665],{"className":33600},[92],[25,33602,33604,33653],{"className":33603,"style":31569},[96],[25,33605,33607,33610],{"className":33606,"style":1685},[31573],[25,33608],{"className":33609,"style":1676},[104],[25,33611,33613],{"className":33612,"style":31580},[75,112],[25,33614,33616,33619],{"className":33615},[75,112],[25,33617,31509],{"className":33618},[75,79,112],[25,33620,33622],{"className":33621},[83],[25,33623,33625,33645],{"className":33624},[87,88],[25,33626,33628,33642],{"className":33627},[92],[25,33629,33631],{"className":33630,"style":1551},[96],[25,33632,33633,33636],{"style":31601},[25,33634],{"className":33635,"style":1594},[104],[25,33637,33639],{"className":33638},[109,1598,1599,112],[25,33640,31512],{"className":33641,"style":31611},[75,79,112],[25,33643,120],{"className":33644},[119],[25,33646,33648],{"className":33647},[92],[25,33649,33651],{"className":33650,"style":1615},[96],[25,33652],{},[25,33654,33655,33658],{"style":31625},[25,33656],{"className":33657,"style":1676},[104],[25,33659,33661],{"className":33660,"style":31633},[31632,112],[31635,33662,33663],{"xmlns":31637,"width":31638,"height":31639,"viewBox":31640,"preserveAspectRatio":31641},[31643,33664],{"d":31645},[25,33666,120],{"className":33667},[119],[25,33669,33671],{"className":33670},[92],[25,33672,33674],{"className":33673,"style":31655},[96],[25,33675],{},[25,33677,33678,33681],{"style":3313},[25,33679],{"className":33680,"style":1676},[104],[25,33682],{"className":33683,"style":3321},[3320],[25,33685,33686,33689],{"style":5975},[25,33687],{"className":33688,"style":1676},[104],[25,33690,33692],{"className":33691},[109,110,111,112],[25,33693,33695],{"className":33694},[75,112],[25,33696,617],{"className":33697},[75,112],[25,33699,120],{"className":33700},[119],[25,33702,33704],{"className":33703},[92],[25,33705,33707],{"className":33706,"style":31689},[96],[25,33708],{},[25,33710],{"className":33711},[439,3239],[15,33713,33714],{},"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。",[33716,33717,33721],"pre",{"className":33718,"code":33719,"language":33720,"meta":31408,"style":31408},"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",[33722,33723,33724,33752,33758,33764,33783,33804,33812,33823,33840,33856,33864,33881,33887,33912,33925],"code",{"__ignoreMap":31408},[25,33725,33728,33732,33736,33739,33743,33746,33749],{"class":33726,"line":33727},"line",1,[25,33729,33731],{"class":33730},"szJfE","def",[25,33733,33735],{"class":33734},"sCLZk"," masked_softmax",[25,33737,313],{"class":33738},"scbbO",[25,33740,33742],{"class":33741},"syNf4","X",[25,33744,33745],{"class":33738},", ",[25,33747,33748],{"class":33741},"valid_lens",[25,33750,33751],{"class":33738},"):\n",[25,33753,33754],{"class":33726,"line":31409},[25,33755,33757],{"class":33756},"seLWX","    \"\"\"通过在最后一个轴上掩蔽元素来执行softmax操作\"\"\"\n",[25,33759,33760],{"class":33726,"line":31417},[25,33761,33763],{"class":33762},"sfgPZ","    # X:3D张量，valid_lens:1D或2D张量\n",[25,33765,33767,33770,33773,33776,33780],{"class":33726,"line":33766},4,[25,33768,33769],{"class":33730},"    if",[25,33771,33772],{"class":33738}," valid_lens ",[25,33774,33775],{"class":33730},"is",[25,33777,33779],{"class":33778},"soDru"," None",[25,33781,33782],{"class":33738},":\n",[25,33784,33786,33789,33792,33796,33799,33801],{"class":33726,"line":33785},5,[25,33787,33788],{"class":33730},"        return",[25,33790,33791],{"class":33738}," nn.functional.softmax(X, ",[25,33793,33795],{"class":33794},"sQkXh","dim",[25,33797,33798],{"class":33730},"=-",[25,33800,617],{"class":33778},[25,33802,33803],{"class":33738},")\n",[25,33805,33807,33810],{"class":33726,"line":33806},6,[25,33808,33809],{"class":33730},"    else",[25,33811,33782],{"class":33738},[25,33813,33815,33818,33820],{"class":33726,"line":33814},7,[25,33816,33817],{"class":33738},"        shape ",[25,33819,919],{"class":33730},[25,33821,33822],{"class":33738}," X.shape\n",[25,33824,33826,33829,33832,33835,33838],{"class":33726,"line":33825},8,[25,33827,33828],{"class":33730},"        if",[25,33830,33831],{"class":33738}," valid_lens.dim() ",[25,33833,33834],{"class":33730},"==",[25,33836,33837],{"class":33778}," 1",[25,33839,33782],{"class":33738},[25,33841,33843,33846,33848,33851,33853],{"class":33726,"line":33842},9,[25,33844,33845],{"class":33738},"            valid_lens ",[25,33847,919],{"class":33730},[25,33849,33850],{"class":33738}," torch.repeat_interleave(valid_lens, shape[",[25,33852,617],{"class":33778},[25,33854,33855],{"class":33738},"])\n",[25,33857,33859,33862],{"class":33726,"line":33858},10,[25,33860,33861],{"class":33730},"        else",[25,33863,33782],{"class":33738},[25,33865,33867,33869,33871,33874,33877,33879],{"class":33726,"line":33866},11,[25,33868,33845],{"class":33738},[25,33870,919],{"class":33730},[25,33872,33873],{"class":33738}," valid_lens.reshape(",[25,33875,33876],{"class":33730},"-",[25,33878,617],{"class":33778},[25,33880,33803],{"class":33738},[25,33882,33884],{"class":33726,"line":33883},12,[25,33885,33886],{"class":33762},"        # 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",[25,33888,33890,33893,33895,33898,33900,33902,33905,33907,33909],{"class":33726,"line":33889},13,[25,33891,33892],{"class":33738},"        X ",[25,33894,919],{"class":33730},[25,33896,33897],{"class":33738}," d2l.sequence_mask(X.reshape(",[25,33899,33876],{"class":33730},[25,33901,617],{"class":33778},[25,33903,33904],{"class":33738},", shape[",[25,33906,33876],{"class":33730},[25,33908,617],{"class":33778},[25,33910,33911],{"class":33738},"]), valid_lens,\n",[25,33913,33915,33918,33920,33923],{"class":33726,"line":33914},14,[25,33916,33917],{"class":33794},"                              value",[25,33919,33798],{"class":33730},[25,33921,33922],{"class":33778},"1e6",[25,33924,33803],{"class":33738},[25,33926,33928,33930,33933,33935,33937,33939],{"class":33726,"line":33927},15,[25,33929,33788],{"class":33730},[25,33931,33932],{"class":33738}," nn.functional.softmax(X.reshape(shape), ",[25,33934,33795],{"class":33794},[25,33936,33798],{"class":33730},[25,33938,617],{"class":33778},[25,33940,33803],{"class":33738},[15,33942,33943],{},"下面实现缩放点积注意力。",[33716,33945,33947],{"className":33718,"code":33946,"language":33720,"meta":31408,"style":31408},"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",[33722,33948,33949,33971,33976,34005,34030,34043,34048,34053,34058,34063,34068,34105,34122,34127,34152,34164],{"__ignoreMap":31408},[25,33950,33951,33954,33958,33960,33964,33966,33969],{"class":33726,"line":33727},[25,33952,33953],{"class":33730},"class",[25,33955,33957],{"class":33956},"skCyd"," DotProductAttention",[25,33959,313],{"class":33738},[25,33961,33963],{"class":33962},"sDP9b","nn",[25,33965,32214],{"class":33738},[25,33967,33968],{"class":33962},"Module",[25,33970,33751],{"class":33738},[25,33972,33973],{"class":33726,"line":31409},[25,33974,33975],{"class":33756},"    \"\"\"缩放点积注意力\"\"\"\n",[25,33977,33978,33981,33984,33986,33990,33992,33995,33997,34000,34003],{"class":33726,"line":31417},[25,33979,33980],{"class":33730},"    def",[25,33982,33983],{"class":33778}," __init__",[25,33985,313],{"class":33738},[25,33987,33989],{"class":33988},"sD3jg","self",[25,33991,33745],{"class":33738},[25,33993,33994],{"class":33741},"dropout",[25,33996,33745],{"class":33738},[25,33998,33999],{"class":33730},"**",[25,34001,34002],{"class":33741},"kwargs",[25,34004,33751],{"class":33738},[25,34006,34007,34011,34014,34017,34020,34023,34025,34027],{"class":33726,"line":33766},[25,34008,34010],{"class":34009},"sPGBF","        super",[25,34012,34013],{"class":33738},"(DotProductAttention, ",[25,34015,33989],{"class":34016},"sJti5",[25,34018,34019],{"class":33738},").",[25,34021,34022],{"class":33778},"__init__",[25,34024,313],{"class":33738},[25,34026,33999],{"class":33730},[25,34028,34029],{"class":33738},"kwargs)\n",[25,34031,34032,34035,34038,34040],{"class":33726,"line":33785},[25,34033,34034],{"class":34016},"        self",[25,34036,34037],{"class":33738},".dropout ",[25,34039,919],{"class":33730},[25,34041,34042],{"class":33738}," nn.Dropout(dropout)\n",[25,34044,34045],{"class":33726,"line":33806},[25,34046,34047],{"emptyLinePlaceholder":31433},"\n",[25,34049,34050],{"class":33726,"line":33814},[25,34051,34052],{"class":33762},"    # queries的形状：(batch_size，查询的个数，d)\n",[25,34054,34055],{"class":33726,"line":33825},[25,34056,34057],{"class":33762},"    # keys的形状：(batch_size，“键－值”对的个数，d)\n",[25,34059,34060],{"class":33726,"line":33842},[25,34061,34062],{"class":33762},"    # values的形状：(batch_size，“键－值”对的个数，值的维度)\n",[25,34064,34065],{"class":33726,"line":33858},[25,34066,34067],{"class":33762},"    # valid_lens的形状:(batch_size，)或者(batch_size，查询的个数)\n",[25,34069,34070,34072,34075,34077,34079,34081,34084,34086,34089,34091,34094,34096,34098,34100,34103],{"class":33726,"line":33866},[25,34071,33980],{"class":33730},[25,34073,34074],{"class":33734}," forward",[25,34076,313],{"class":33738},[25,34078,33989],{"class":33988},[25,34080,33745],{"class":33738},[25,34082,34083],{"class":33741},"queries",[25,34085,33745],{"class":33738},[25,34087,34088],{"class":33741},"keys",[25,34090,33745],{"class":33738},[25,34092,34093],{"class":33741},"values",[25,34095,33745],{"class":33738},[25,34097,33748],{"class":33741},[25,34099,919],{"class":33730},[25,34101,34102],{"class":33778},"None",[25,34104,33751],{"class":33738},[25,34106,34107,34110,34112,34115,34117,34119],{"class":33726,"line":33883},[25,34108,34109],{"class":33738},"        d ",[25,34111,919],{"class":33730},[25,34113,34114],{"class":33738}," queries.shape[",[25,34116,33876],{"class":33730},[25,34118,617],{"class":33778},[25,34120,34121],{"class":33738},"]\n",[25,34123,34124],{"class":33726,"line":33889},[25,34125,34126],{"class":33762},"        # 设置transpose_b=True为了交换keys的最后两个维度\n",[25,34128,34129,34132,34134,34137,34139,34141,34143,34146,34149],{"class":33726,"line":33914},[25,34130,34131],{"class":33738},"        scores ",[25,34133,919],{"class":33730},[25,34135,34136],{"class":33738}," torch.bmm(queries, keys.transpose(",[25,34138,617],{"class":33778},[25,34140,602],{"class":33738},[25,34142,9242],{"class":33778},[25,34144,34145],{"class":33738},")) ",[25,34147,34148],{"class":33730},"/",[25,34150,34151],{"class":33738}," math.sqrt(d)\n",[25,34153,34154,34156,34159,34161],{"class":33726,"line":33927},[25,34155,34034],{"class":34016},[25,34157,34158],{"class":33738},".attention_weights ",[25,34160,919],{"class":33730},[25,34162,34163],{"class":33738}," masked_softmax(scores, valid_lens)\n",[25,34165,34167,34169,34172,34174,34177,34179],{"class":33726,"line":34166},16,[25,34168,33788],{"class":33730},[25,34170,34171],{"class":33738}," torch.bmm(",[25,34173,33989],{"class":34016},[25,34175,34176],{"class":33738},".dropout(",[25,34178,33989],{"class":34016},[25,34180,34181],{"class":33738},".attention_weights), values)\n",[15,34183,34184,34185,34188],{},"代码中函数的 ",[33722,34186,34187],{},"**kwargs","表示任意关键字参数，为了符合 Pytorch 的继承约定。",[14894,34190,34191],{"id":34191},"多头注意力",[15,34193,34194],{},"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。",[15,34196,34197],{},[31470,34198],{"alt":31408,"src":34199},"transformer/MHA.png",[15,34201,34202],{},[25,34203,34205,34318],{"className":34204},[28],[25,34206,34208],{"className":34207},[32],[34,34209,34210],{"xmlns":36},[38,34211,34212,34315],{},[41,34213,34214,34237,34239,34241,34243,34245,34247,34249,34251,34253,34268,34270,34285,34287,34289,34291,34305,34307],{},[41,34215,34216,34219,34222,34224,34226,34228,34231,34233,34235],{},[47,34217,34218],{"mathvariant":322},"M",[47,34220,34221],{"mathvariant":322},"u",[47,34223,29611],{"mathvariant":322},[47,34225,52],{"mathvariant":322},[47,34227,29614],{"mathvariant":322},[47,34229,34230],{"mathvariant":322},"H",[47,34232,32141],{"mathvariant":322},[47,34234,49],{"mathvariant":322},[47,34236,31509],{"mathvariant":322},[310,34238,313],{"stretchy":312},[47,34240,7755],{},[310,34242,602],{"separator":62},[47,34244,27684],{},[310,34246,602],{"separator":62},[47,34248,7916],{},[310,34250,332],{"stretchy":312},[310,34252,919],{},[41,34254,34255,34258,34260,34262,34264,34266],{},[47,34256,34257],{"mathvariant":322},"C",[47,34259,5801],{"mathvariant":322},[47,34261,2121],{"mathvariant":322},[47,34263,29608],{"mathvariant":322},[47,34265,49],{"mathvariant":322},[47,34267,52],{"mathvariant":322},[310,34269,313],{"stretchy":312},[44,34271,34272,34283],{},[41,34273,34274,34277,34279,34281],{},[47,34275,34276],{"mathvariant":322},"h",[47,34278,32141],{"mathvariant":322},[47,34280,49],{"mathvariant":322},[47,34282,31509],{"mathvariant":322},[597,34284,617],{},[310,34286,602],{"separator":62},[310,34288,628],{},[310,34290,602],{"separator":62},[44,34292,34293,34303],{},[41,34294,34295,34297,34299,34301],{},[47,34296,34276],{"mathvariant":322},[47,34298,32141],{"mathvariant":322},[47,34300,49],{"mathvariant":322},[47,34302,31509],{"mathvariant":322},[47,34304,34276],{},[310,34306,332],{"stretchy":312},[2133,34308,34309,34312],{},[47,34310,34311],{},"W",[47,34313,34314],{},"O",[54,34316,34317],{"encoding":56},"\\mathrm{MultiHead}(Q, K, V) = \\mathrm{Concat}(\\mathrm{head}_1, \\ldots, \\mathrm{head}_h) W^O",[25,34319,34321,34370],{"className":34320,"ariaHidden":62},[61],[25,34322,34324,34327,34334,34337,34340,34343,34346,34349,34352,34355,34358,34361,34364,34367],{"className":34323},[66],[25,34325],{"className":34326,"style":345},[70],[25,34328,34330],{"className":34329},[75],[25,34331,34333],{"className":34332},[75,28663],"MultiHead",[25,34335,313],{"className":34336},[352],[25,34338,7755],{"className":34339},[75,79],[25,34341,602],{"className":34342},[697],[25,34344],{"className":34345,"style":702},[701],[25,34347,27684],{"className":34348,"style":31966},[75,79],[25,34350,602],{"className":34351},[697],[25,34353],{"className":34354,"style":702},[701],[25,34356,7916],{"className":34357,"style":7943},[75,79],[25,34359,332],{"className":34360},[439],[25,34362],{"className":34363,"style":1008},[701],[25,34365,919],{"className":34366},[1012],[25,34368],{"className":34369,"style":1008},[701],[25,34371,34373,34377,34384,34387,34432,34435,34438,34441,34444,34447,34450,34493,34496],{"className":34372},[66],[25,34374],{"className":34375,"style":34376},[70],"height:1.0913em;vertical-align:-0.25em;",[25,34378,34380],{"className":34379},[75],[25,34381,34383],{"className":34382},[75,28663],"Concat",[25,34385,313],{"className":34386},[352],[25,34388,34390,34397],{"className":34389},[75],[25,34391,34393],{"className":34392},[75],[25,34394,34396],{"className":34395},[75,28663],"head",[25,34398,34400],{"className":34399},[83],[25,34401,34403,34424],{"className":34402},[87,88],[25,34404,34406,34421],{"className":34405},[92],[25,34407,34409],{"className":34408,"style":671},[96],[25,34410,34412,34415],{"style":34411},"top:-2.55em;margin-right:0.05em;",[25,34413],{"className":34414,"style":105},[104],[25,34416,34418],{"className":34417},[109,110,111,112],[25,34419,617],{"className":34420},[75,112],[25,34422,120],{"className":34423},[119],[25,34425,34427],{"className":34426},[92],[25,34428,34430],{"className":34429,"style":127},[96],[25,34431],{},[25,34433,602],{"className":34434},[697],[25,34436],{"className":34437,"style":702},[701],[25,34439,628],{"className":34440},[841],[25,34442],{"className":34443,"style":702},[701],[25,34445,602],{"className":34446},[697],[25,34448],{"className":34449,"style":702},[701],[25,34451,34453,34459],{"className":34452},[75],[25,34454,34456],{"className":34455},[75],[25,34457,34396],{"className":34458},[75,28663],[25,34460,34462],{"className":34461},[83],[25,34463,34465,34485],{"className":34464},[87,88],[25,34466,34468,34482],{"className":34467},[92],[25,34469,34471],{"className":34470,"style":1741},[96],[25,34472,34473,34476],{"style":34411},[25,34474],{"className":34475,"style":105},[104],[25,34477,34479],{"className":34478},[109,110,111,112],[25,34480,34276],{"className":34481},[75,79,112],[25,34483,120],{"className":34484},[119],[25,34486,34488],{"className":34487},[92],[25,34489,34491],{"className":34490,"style":127},[96],[25,34492],{},[25,34494,332],{"className":34495},[439],[25,34497,34499,34502],{"className":34498},[75],[25,34500,34311],{"className":34501,"style":875},[75,79],[25,34503,34505],{"className":34504},[83],[25,34506,34508],{"className":34507},[87],[25,34509,34511],{"className":34510},[92],[25,34512,34514],{"className":34513,"style":21204},[96],[25,34515,34516,34519],{"style":4065},[25,34517],{"className":34518,"style":105},[104],[25,34520,34522],{"className":34521},[109,110,111,112],[25,34523,34314],{"className":34524,"style":478},[75,79,112],[15,34526,34527,34528,34889,34890,35139,35140,35139,35389,35638,35639,32214],{},"其中 ",[25,34529,34531,34622],{"className":34530},[28],[25,34532,34534],{"className":34533},[32],[34,34535,34536],{"xmlns":36},[38,34537,34538,34619],{},[41,34539,34540,34554,34556,34576,34578,34580,34588,34590,34593,34595,34603,34605,34607,34609,34617],{},[44,34541,34542,34552],{},[41,34543,34544,34546,34548,34550],{},[47,34545,34276],{"mathvariant":322},[47,34547,32141],{"mathvariant":322},[47,34549,49],{"mathvariant":322},[47,34551,31509],{"mathvariant":322},[47,34553,29614],{},[310,34555,919],{},[41,34557,34558,34560,34562,34564,34566,34568,34570,34572,34574],{},[47,34559,8036],{"mathvariant":322},[47,34561,52],{"mathvariant":322},[47,34563,52],{"mathvariant":322},[47,34565,32141],{"mathvariant":322},[47,34567,2121],{"mathvariant":322},[47,34569,52],{"mathvariant":322},[47,34571,29614],{"mathvariant":322},[47,34573,5801],{"mathvariant":322},[47,34575,2121],{"mathvariant":322},[310,34577,313],{"stretchy":312},[47,34579,7755],{},[2341,34581,34582,34584,34586],{},[47,34583,34311],{},[47,34585,29614],{},[47,34587,7755],{},[310,34589,602],{"separator":62},[15053,34591,34592],{},"  ",[47,34594,27684],{},[2341,34596,34597,34599,34601],{},[47,34598,34311],{},[47,34600,29614],{},[47,34602,27684],{},[310,34604,602],{"separator":62},[15053,34606,34592],{},[47,34608,7916],{},[2341,34610,34611,34613,34615],{},[47,34612,34311],{},[47,34614,29614],{},[47,34616,7916],{},[310,34618,332],{"stretchy":312},[54,34620,34621],{"encoding":56},"\\mathrm{head}_i=\\mathrm{Attention}(QW_i^Q,\\; KW_i^K,\\; VW_i^V)",[25,34623,34625,34683],{"className":34624,"ariaHidden":62},[61],[25,34626,34628,34631,34674,34677,34680],{"className":34627},[66],[25,34629],{"className":34630,"style":12948},[70],[25,34632,34634,34640],{"className":34633},[75],[25,34635,34637],{"className":34636},[75],[25,34638,34396],{"className":34639},[75,28663],[25,34641,34643],{"className":34642},[83],[25,34644,34646,34666],{"className":34645},[87,88],[25,34647,34649,34663],{"className":34648},[92],[25,34650,34652],{"className":34651,"style":33358},[96],[25,34653,34654,34657],{"style":34411},[25,34655],{"className":34656,"style":105},[104],[25,34658,34660],{"className":34659},[109,110,111,112],[25,34661,29614],{"className":34662},[75,79,112],[25,34664,120],{"className":34665},[119],[25,34667,34669],{"className":34668},[92],[25,34670,34672],{"className":34671,"style":127},[96],[25,34673],{},[25,34675],{"className":34676,"style":1008},[701],[25,34678,919],{"className":34679},[1012],[25,34681],{"className":34682,"style":1008},[701],[25,34684,34686,34690,34697,34700,34703,34758,34761,34764,34767,34770,34823,34826,34829,34832,34835,34886],{"className":34685},[66],[25,34687],{"className":34688,"style":34689},[70],"height:1.2361em;vertical-align:-0.2769em;",[25,34691,34693],{"className":34692},[75],[25,34694,34696],{"className":34695},[75,28663],"Attention",[25,34698,313],{"className":34699},[352],[25,34701,7755],{"className":34702},[75,79],[25,34704,34706,34709],{"className":34705},[75],[25,34707,34311],{"className":34708,"style":875},[75,79],[25,34710,34712],{"className":34711},[83],[25,34713,34715,34749],{"className":34714},[87,88],[25,34716,34718,34746],{"className":34717},[92],[25,34719,34722,34734],{"className":34720,"style":34721},[96],"height:0.9592em;",[25,34723,34725,34728],{"style":34724},"top:-2.4231em;margin-left:-0.1389em;margin-right:0.05em;",[25,34726],{"className":34727,"style":105},[104],[25,34729,34731],{"className":34730},[109,110,111,112],[25,34732,29614],{"className":34733},[75,79,112],[25,34735,34737,34740],{"style":34736},"top:-3.1809em;margin-right:0.05em;",[25,34738],{"className":34739,"style":105},[104],[25,34741,34743],{"className":34742},[109,110,111,112],[25,34744,7755],{"className":34745},[75,79,112],[25,34747,120],{"className":34748},[119],[25,34750,34752],{"className":34751},[92],[25,34753,34756],{"className":34754,"style":34755},[96],"height:0.2769em;",[25,34757],{},[25,34759,602],{"className":34760},[697],[25,34762],{"className":34763,"style":1008},[701],[25,34765],{"className":34766,"style":702},[701],[25,34768,27684],{"className":34769,"style":31966},[75,79],[25,34771,34773,34776],{"className":34772},[75],[25,34774,34311],{"className":34775,"style":875},[75,79],[25,34777,34779],{"className":34778},[83],[25,34780,34782,34814],{"className":34781},[87,88],[25,34783,34785,34811],{"className":34784},[92],[25,34786,34788,34800],{"className":34787,"style":21204},[96],[25,34789,34791,34794],{"style":34790},"top:-2.4413em;margin-left:-0.1389em;margin-right:0.05em;",[25,34792],{"className":34793,"style":105},[104],[25,34795,34797],{"className":34796},[109,110,111,112],[25,34798,29614],{"className":34799},[75,79,112],[25,34801,34802,34805],{"style":4065},[25,34803],{"className":34804,"style":105},[104],[25,34806,34808],{"className":34807},[109,110,111,112],[25,34809,27684],{"className":34810,"style":31966},[75,79,112],[25,34812,120],{"className":34813},[119],[25,34815,34817],{"className":34816},[92],[25,34818,34821],{"className":34819,"style":34820},[96],"height:0.2587em;",[25,34822],{},[25,34824,602],{"className":34825},[697],[25,34827],{"className":34828,"style":1008},[701],[25,34830],{"className":34831,"style":702},[701],[25,34833,7916],{"className":34834,"style":7943},[75,79],[25,34836,34838,34841],{"className":34837},[75],[25,34839,34311],{"className":34840,"style":875},[75,79],[25,34842,34844],{"className":34843},[83],[25,34845,34847,34878],{"className":34846},[87,88],[25,34848,34850,34875],{"className":34849},[92],[25,34851,34853,34864],{"className":34852,"style":21204},[96],[25,34854,34855,34858],{"style":34790},[25,34856],{"className":34857,"style":105},[104],[25,34859,34861],{"className":34860},[109,110,111,112],[25,34862,29614],{"className":34863},[75,79,112],[25,34865,34866,34869],{"style":4065},[25,34867],{"className":34868,"style":105},[104],[25,34870,34872],{"className":34871},[109,110,111,112],[25,34873,7916],{"className":34874,"style":7943},[75,79,112],[25,34876,120],{"className":34877},[119],[25,34879,34881],{"className":34880},[92],[25,34882,34884],{"className":34883,"style":34820},[96],[25,34885],{},[25,34887,332],{"className":34888},[439],"，投影参数是矩阵\n",[25,34891,34893,34945],{"className":34892},[28],[25,34894,34896],{"className":34895},[32],[34,34897,34898],{"xmlns":36},[38,34899,34900,34942],{},[41,34901,34902,34910,34912],{},[2341,34903,34904,34906,34908],{},[47,34905,34311],{},[47,34907,29614],{},[47,34909,7755],{},[310,34911,31837],{},[2133,34913,34914,34916],{},[47,34915,1440],{"mathvariant":19397},[41,34917,34918,34934,34936],{},[44,34919,34920,34922],{},[47,34921,31509],{},[41,34923,34924,34926,34928,34930,34932],{},[47,34925,31744],{"mathvariant":322},[47,34927,5801],{"mathvariant":322},[47,34929,31509],{"mathvariant":322},[47,34931,32141],{"mathvariant":322},[47,34933,29611],{"mathvariant":322},[310,34935,31848],{},[44,34937,34938,34940],{},[47,34939,31509],{},[47,34941,31512],{},[54,34943,34944],{"encoding":56},"W_i^Q \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[25,34946,34948,35014],{"className":34947,"ariaHidden":62},[61],[25,34949,34951,34954,35005,35008,35011],{"className":34950},[66],[25,34952],{"className":34953,"style":34689},[70],[25,34955,34957,34960],{"className":34956},[75],[25,34958,34311],{"className":34959,"style":875},[75,79],[25,34961,34963],{"className":34962},[83],[25,34964,34966,34997],{"className":34965},[87,88],[25,34967,34969,34994],{"className":34968},[92],[25,34970,34972,34983],{"className":34971,"style":34721},[96],[25,34973,34974,34977],{"style":34724},[25,34975],{"className":34976,"style":105},[104],[25,34978,34980],{"className":34979},[109,110,111,112],[25,34981,29614],{"className":34982},[75,79,112],[25,34984,34985,34988],{"style":34736},[25,34986],{"className":34987,"style":105},[104],[25,34989,34991],{"className":34990},[109,110,111,112],[25,34992,7755],{"className":34993},[75,79,112],[25,34995,120],{"className":34996},[119],[25,34998,35000],{"className":34999},[92],[25,35001,35003],{"className":35002,"style":34755},[96],[25,35004],{},[25,35006],{"className":35007,"style":1008},[701],[25,35009,31837],{"className":35010},[1012],[25,35012],{"className":35013,"style":1008},[701],[25,35015,35017,35020],{"className":35016},[66],[25,35018],{"className":35019,"style":31882},[70],[25,35021,35023,35026],{"className":35022},[75],[25,35024,1440],{"className":35025},[75,19805],[25,35027,35029],{"className":35028},[83],[25,35030,35032],{"className":35031},[87],[25,35033,35035],{"className":35034},[92],[25,35036,35038],{"className":35037,"style":31882},[96],[25,35039,35040,35043],{"style":4065},[25,35041],{"className":35042,"style":105},[104],[25,35044,35046],{"className":35045},[109,110,111,112],[25,35047,35049,35096,35099],{"className":35048},[75,112],[25,35050,35052,35055],{"className":35051},[75,112],[25,35053,31509],{"className":35054},[75,79,112],[25,35056,35058],{"className":35057},[83],[25,35059,35061,35088],{"className":35060},[87,88],[25,35062,35064,35085],{"className":35063},[92],[25,35065,35067],{"className":35066,"style":1551},[96],[25,35068,35069,35072],{"style":31601},[25,35070],{"className":35071,"style":1594},[104],[25,35073,35075],{"className":35074},[109,1598,1599,112],[25,35076,35078],{"className":35077},[75,112],[25,35079,35081],{"className":35080},[75,112],[25,35082,35084],{"className":35083},[75,28663,112],"model",[25,35086,120],{"className":35087},[119],[25,35089,35091],{"className":35090},[92],[25,35092,35094],{"className":35093,"style":1615},[96],[25,35095],{},[25,35097,31848],{"className":35098},[989,112],[25,35100,35102,35105],{"className":35101},[75,112],[25,35103,31509],{"className":35104},[75,79,112],[25,35106,35108],{"className":35107},[83],[25,35109,35111,35131],{"className":35110},[87,88],[25,35112,35114,35128],{"className":35113},[92],[25,35115,35117],{"className":35116,"style":1551},[96],[25,35118,35119,35122],{"style":31601},[25,35120],{"className":35121,"style":1594},[104],[25,35123,35125],{"className":35124},[109,1598,1599,112],[25,35126,31512],{"className":35127,"style":31611},[75,79,112],[25,35129,120],{"className":35130},[119],[25,35132,35134],{"className":35133},[92],[25,35135,35137],{"className":35136,"style":1615},[96],[25,35138],{},",\n",[25,35141,35143,35195],{"className":35142},[28],[25,35144,35146],{"className":35145},[32],[34,35147,35148],{"xmlns":36},[38,35149,35150,35192],{},[41,35151,35152,35160,35162],{},[2341,35153,35154,35156,35158],{},[47,35155,34311],{},[47,35157,29614],{},[47,35159,27684],{},[310,35161,31837],{},[2133,35163,35164,35166],{},[47,35165,1440],{"mathvariant":19397},[41,35167,35168,35184,35186],{},[44,35169,35170,35172],{},[47,35171,31509],{},[41,35173,35174,35176,35178,35180,35182],{},[47,35175,31744],{"mathvariant":322},[47,35177,5801],{"mathvariant":322},[47,35179,31509],{"mathvariant":322},[47,35181,32141],{"mathvariant":322},[47,35183,29611],{"mathvariant":322},[310,35185,31848],{},[44,35187,35188,35190],{},[47,35189,31509],{},[47,35191,31512],{},[54,35193,35194],{"encoding":56},"W_i^K \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[25,35196,35198,35265],{"className":35197,"ariaHidden":62},[61],[25,35199,35201,35205,35256,35259,35262],{"className":35200},[66],[25,35202],{"className":35203,"style":35204},[70],"height:1.1em;vertical-align:-0.2587em;",[25,35206,35208,35211],{"className":35207},[75],[25,35209,34311],{"className":35210,"style":875},[75,79],[25,35212,35214],{"className":35213},[83],[25,35215,35217,35248],{"className":35216},[87,88],[25,35218,35220,35245],{"className":35219},[92],[25,35221,35223,35234],{"className":35222,"style":21204},[96],[25,35224,35225,35228],{"style":34790},[25,35226],{"className":35227,"style":105},[104],[25,35229,35231],{"className":35230},[109,110,111,112],[25,35232,29614],{"className":35233},[75,79,112],[25,35235,35236,35239],{"style":4065},[25,35237],{"className":35238,"style":105},[104],[25,35240,35242],{"className":35241},[109,110,111,112],[25,35243,27684],{"className":35244,"style":31966},[75,79,112],[25,35246,120],{"className":35247},[119],[25,35249,35251],{"className":35250},[92],[25,35252,35254],{"className":35253,"style":34820},[96],[25,35255],{},[25,35257],{"className":35258,"style":1008},[701],[25,35260,31837],{"className":35261},[1012],[25,35263],{"className":35264,"style":1008},[701],[25,35266,35268,35271],{"className":35267},[66],[25,35269],{"className":35270,"style":31882},[70],[25,35272,35274,35277],{"className":35273},[75],[25,35275,1440],{"className":35276},[75,19805],[25,35278,35280],{"className":35279},[83],[25,35281,35283],{"className":35282},[87],[25,35284,35286],{"className":35285},[92],[25,35287,35289],{"className":35288,"style":31882},[96],[25,35290,35291,35294],{"style":4065},[25,35292],{"className":35293,"style":105},[104],[25,35295,35297],{"className":35296},[109,110,111,112],[25,35298,35300,35346,35349],{"className":35299},[75,112],[25,35301,35303,35306],{"className":35302},[75,112],[25,35304,31509],{"className":35305},[75,79,112],[25,35307,35309],{"className":35308},[83],[25,35310,35312,35338],{"className":35311},[87,88],[25,35313,35315,35335],{"className":35314},[92],[25,35316,35318],{"className":35317,"style":1551},[96],[25,35319,35320,35323],{"style":31601},[25,35321],{"className":35322,"style":1594},[104],[25,35324,35326],{"className":35325},[109,1598,1599,112],[25,35327,35329],{"className":35328},[75,112],[25,35330,35332],{"className":35331},[75,112],[25,35333,35084],{"className":35334},[75,28663,112],[25,35336,120],{"className":35337},[119],[25,35339,35341],{"className":35340},[92],[25,35342,35344],{"className":35343,"style":1615},[96],[25,35345],{},[25,35347,31848],{"className":35348},[989,112],[25,35350,35352,35355],{"className":35351},[75,112],[25,35353,31509],{"className":35354},[75,79,112],[25,35356,35358],{"className":35357},[83],[25,35359,35361,35381],{"className":35360},[87,88],[25,35362,35364,35378],{"className":35363},[92],[25,35365,35367],{"className":35366,"style":1551},[96],[25,35368,35369,35372],{"style":31601},[25,35370],{"className":35371,"style":1594},[104],[25,35373,35375],{"className":35374},[109,1598,1599,112],[25,35376,31512],{"className":35377,"style":31611},[75,79,112],[25,35379,120],{"className":35380},[119],[25,35382,35384],{"className":35383},[92],[25,35385,35387],{"className":35386,"style":1615},[96],[25,35388],{},[25,35390,35392,35444],{"className":35391},[28],[25,35393,35395],{"className":35394},[32],[34,35396,35397],{"xmlns":36},[38,35398,35399,35441],{},[41,35400,35401,35409,35411],{},[2341,35402,35403,35405,35407],{},[47,35404,34311],{},[47,35406,29614],{},[47,35408,7916],{},[310,35410,31837],{},[2133,35412,35413,35415],{},[47,35414,1440],{"mathvariant":19397},[41,35416,35417,35433,35435],{},[44,35418,35419,35421],{},[47,35420,31509],{},[41,35422,35423,35425,35427,35429,35431],{},[47,35424,31744],{"mathvariant":322},[47,35426,5801],{"mathvariant":322},[47,35428,31509],{"mathvariant":322},[47,35430,32141],{"mathvariant":322},[47,35432,29611],{"mathvariant":322},[310,35434,31848],{},[44,35436,35437,35439],{},[47,35438,31509],{},[47,35440,31803],{},[54,35442,35443],{"encoding":56},"W_i^V \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_v}",[25,35445,35447,35513],{"className":35446,"ariaHidden":62},[61],[25,35448,35450,35453,35504,35507,35510],{"className":35449},[66],[25,35451],{"className":35452,"style":35204},[70],[25,35454,35456,35459],{"className":35455},[75],[25,35457,34311],{"className":35458,"style":875},[75,79],[25,35460,35462],{"className":35461},[83],[25,35463,35465,35496],{"className":35464},[87,88],[25,35466,35468,35493],{"className":35467},[92],[25,35469,35471,35482],{"className":35470,"style":21204},[96],[25,35472,35473,35476],{"style":34790},[25,35474],{"className":35475,"style":105},[104],[25,35477,35479],{"className":35478},[109,110,111,112],[25,35480,29614],{"className":35481},[75,79,112],[25,35483,35484,35487],{"style":4065},[25,35485],{"className":35486,"style":105},[104],[25,35488,35490],{"className":35489},[109,110,111,112],[25,35491,7916],{"className":35492,"style":7943},[75,79,112],[25,35494,120],{"className":35495},[119],[25,35497,35499],{"className":35498},[92],[25,35500,35502],{"className":35501,"style":34820},[96],[25,35503],{},[25,35505],{"className":35506,"style":1008},[701],[25,35508,31837],{"className":35509},[1012],[25,35511],{"className":35512,"style":1008},[701],[25,35514,35516,35519],{"className":35515},[66],[25,35517],{"className":35518,"style":31882},[70],[25,35520,35522,35525],{"className":35521},[75],[25,35523,1440],{"className":35524},[75,19805],[25,35526,35528],{"className":35527},[83],[25,35529,35531],{"className":35530},[87],[25,35532,35534],{"className":35533},[92],[25,35535,35537],{"className":35536,"style":31882},[96],[25,35538,35539,35542],{"style":4065},[25,35540],{"className":35541,"style":105},[104],[25,35543,35545],{"className":35544},[109,110,111,112],[25,35546,35548,35594,35597],{"className":35547},[75,112],[25,35549,35551,35554],{"className":35550},[75,112],[25,35552,31509],{"className":35553},[75,79,112],[25,35555,35557],{"className":35556},[83],[25,35558,35560,35586],{"className":35559},[87,88],[25,35561,35563,35583],{"className":35562},[92],[25,35564,35566],{"className":35565,"style":1551},[96],[25,35567,35568,35571],{"style":31601},[25,35569],{"className":35570,"style":1594},[104],[25,35572,35574],{"className":35573},[109,1598,1599,112],[25,35575,35577],{"className":35576},[75,112],[25,35578,35580],{"className":35579},[75,112],[25,35581,35084],{"className":35582},[75,28663,112],[25,35584,120],{"className":35585},[119],[25,35587,35589],{"className":35588},[92],[25,35590,35592],{"className":35591,"style":1615},[96],[25,35593],{},[25,35595,31848],{"className":35596},[989,112],[25,35598,35600,35603],{"className":35599},[75,112],[25,35601,31509],{"className":35602},[75,79,112],[25,35604,35606],{"className":35605},[83],[25,35607,35609,35630],{"className":35608},[87,88],[25,35610,35612,35627],{"className":35611},[92],[25,35613,35615],{"className":35614,"style":4651},[96],[25,35616,35618,35621],{"style":35617},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[25,35619],{"className":35620,"style":1594},[104],[25,35622,35624],{"className":35623},[109,1598,1599,112],[25,35625,31803],{"className":35626,"style":293},[75,79,112],[25,35628,120],{"className":35629},[119],[25,35631,35633],{"className":35632},[92],[25,35634,35636],{"className":35635,"style":4673},[96],[25,35637],{},"\n和\n",[25,35640,35642,35694],{"className":35641},[28],[25,35643,35645],{"className":35644},[32],[34,35646,35647],{"xmlns":36},[38,35648,35649,35691],{},[41,35650,35651,35657,35659],{},[2133,35652,35653,35655],{},[47,35654,34311],{},[47,35656,34314],{},[310,35658,31837],{},[2133,35660,35661,35663],{},[47,35662,1440],{"mathvariant":19397},[41,35664,35665,35667,35673,35675],{},[47,35666,34276],{},[44,35668,35669,35671],{},[47,35670,31509],{},[47,35672,31803],{},[310,35674,31848],{},[44,35676,35677,35679],{},[47,35678,31509],{},[41,35680,35681,35683,35685,35687,35689],{},[47,35682,31744],{"mathvariant":322},[47,35684,5801],{"mathvariant":322},[47,35686,31509],{"mathvariant":322},[47,35688,32141],{"mathvariant":322},[47,35690,29611],{"mathvariant":322},[54,35692,35693],{"encoding":56},"W^O \\in \\mathbb{R}^{h d_v \\times d_{\\mathrm{model}}}",[25,35695,35697,35742],{"className":35696,"ariaHidden":62},[61],[25,35698,35700,35704,35733,35736,35739],{"className":35699},[66],[25,35701],{"className":35702,"style":35703},[70],"height:0.8804em;vertical-align:-0.0391em;",[25,35705,35707,35710],{"className":35706},[75],[25,35708,34311],{"className":35709,"style":875},[75,79],[25,35711,35713],{"className":35712},[83],[25,35714,35716],{"className":35715},[87],[25,35717,35719],{"className":35718},[92],[25,35720,35722],{"className":35721,"style":21204},[96],[25,35723,35724,35727],{"style":4065},[25,35725],{"className":35726,"style":105},[104],[25,35728,35730],{"className":35729},[109,110,111,112],[25,35731,34314],{"className":35732,"style":478},[75,79,112],[25,35734],{"className":35735,"style":1008},[701],[25,35737,31837],{"className":35738},[1012],[25,35740],{"className":35741,"style":1008},[701],[25,35743,35745,35748],{"className":35744},[66],[25,35746],{"className":35747,"style":31882},[70],[25,35749,35751,35754],{"className":35750},[75],[25,35752,1440],{"className":35753},[75,19805],[25,35755,35757],{"className":35756},[83],[25,35758,35760],{"className":35759},[87],[25,35761,35763],{"className":35762},[92],[25,35764,35766],{"className":35765,"style":31882},[96],[25,35767,35768,35771],{"style":4065},[25,35769],{"className":35770,"style":105},[104],[25,35772,35774],{"className":35773},[109,110,111,112],[25,35775,35777,35780,35820,35823],{"className":35776},[75,112],[25,35778,34276],{"className":35779},[75,79,112],[25,35781,35783,35786],{"className":35782},[75,112],[25,35784,31509],{"className":35785},[75,79,112],[25,35787,35789],{"className":35788},[83],[25,35790,35792,35812],{"className":35791},[87,88],[25,35793,35795,35809],{"className":35794},[92],[25,35796,35798],{"className":35797,"style":4651},[96],[25,35799,35800,35803],{"style":35617},[25,35801],{"className":35802,"style":1594},[104],[25,35804,35806],{"className":35805},[109,1598,1599,112],[25,35807,31803],{"className":35808,"style":293},[75,79,112],[25,35810,120],{"className":35811},[119],[25,35813,35815],{"className":35814},[92],[25,35816,35818],{"className":35817,"style":4673},[96],[25,35819],{},[25,35821,31848],{"className":35822},[989,112],[25,35824,35826,35829],{"className":35825},[75,112],[25,35827,31509],{"className":35828},[75,79,112],[25,35830,35832],{"className":35831},[83],[25,35833,35835,35861],{"className":35834},[87,88],[25,35836,35838,35858],{"className":35837},[92],[25,35839,35841],{"className":35840,"style":1551},[96],[25,35842,35843,35846],{"style":31601},[25,35844],{"className":35845,"style":1594},[104],[25,35847,35849],{"className":35848},[109,1598,1599,112],[25,35850,35852],{"className":35851},[75,112],[25,35853,35855],{"className":35854},[75,112],[25,35856,35084],{"className":35857},[75,28663,112],[25,35859,120],{"className":35860},[119],[25,35862,35864],{"className":35863},[92],[25,35865,35867],{"className":35866,"style":1615},[96],[25,35868],{},[15,35870,35871,35872,35875,35876,35879,35880,35882,35883,35885],{},"为了能使多个头并行计算，我们定义两个转置函数 ",[33722,35873,35874],{},"transpose_output"," 和 ",[33722,35877,35878],{},"transpose_qkv","，其中 ",[33722,35881,35874],{}," 还原了 ",[33722,35884,35878],{}," 的结果。",[33716,35887,35889],{"className":33718,"code":35888,"language":33720,"meta":31408,"style":31408},"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",[33722,35890,35891,35909,35914,35919,35924,35950,35954,35959,35984,35988,35993,36016,36020,36037,36042,36065,36089],{"__ignoreMap":31408},[25,35892,35893,35895,35898,35900,35902,35904,35907],{"class":33726,"line":33727},[25,35894,33731],{"class":33730},[25,35896,35897],{"class":33734}," transpose_qkv",[25,35899,313],{"class":33738},[25,35901,33742],{"class":33741},[25,35903,33745],{"class":33738},[25,35905,35906],{"class":33741},"num_heads",[25,35908,33751],{"class":33738},[25,35910,35911],{"class":33726,"line":31409},[25,35912,35913],{"class":33756},"    \"\"\"为了多注意力头的并行计算而变换形状\"\"\"\n",[25,35915,35916],{"class":33726,"line":31417},[25,35917,35918],{"class":33762},"    # 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[25,35920,35921],{"class":33726,"line":33766},[25,35922,35923],{"class":33762},"    # 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",[25,35925,35926,35929,35931,35934,35936,35939,35941,35944,35946,35948],{"class":33726,"line":33785},[25,35927,35928],{"class":33738},"    X ",[25,35930,919],{"class":33730},[25,35932,35933],{"class":33738}," X.reshape(X.shape[",[25,35935,599],{"class":33778},[25,35937,35938],{"class":33738},"], X.shape[",[25,35940,617],{"class":33778},[25,35942,35943],{"class":33738},"], num_heads, ",[25,35945,33876],{"class":33730},[25,35947,617],{"class":33778},[25,35949,33803],{"class":33738},[25,35951,35952],{"class":33726,"line":33806},[25,35953,34047],{"emptyLinePlaceholder":31433},[25,35955,35956],{"class":33726,"line":33814},[25,35957,35958],{"class":33762},"    # 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",[25,35960,35961,35963,35965,35968,35970,35972,35974,35976,35978,35980,35982],{"class":33726,"line":33825},[25,35962,35928],{"class":33738},[25,35964,919],{"class":33730},[25,35966,35967],{"class":33738}," X.permute(",[25,35969,599],{"class":33778},[25,35971,33745],{"class":33738},[25,35973,9242],{"class":33778},[25,35975,33745],{"class":33738},[25,35977,617],{"class":33778},[25,35979,33745],{"class":33738},[25,35981,10476],{"class":33778},[25,35983,33803],{"class":33738},[25,35985,35986],{"class":33726,"line":33842},[25,35987,34047],{"emptyLinePlaceholder":31433},[25,35989,35990],{"class":33726,"line":33858},[25,35991,35992],{"class":33762},"    # 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",[25,35994,35995,35998,36001,36003,36005,36008,36010,36012,36014],{"class":33726,"line":33866},[25,35996,35997],{"class":33730},"    return",[25,35999,36000],{"class":33738}," X.reshape(",[25,36002,33876],{"class":33730},[25,36004,617],{"class":33778},[25,36006,36007],{"class":33738},", X.shape[",[25,36009,9242],{"class":33778},[25,36011,35938],{"class":33738},[25,36013,10476],{"class":33778},[25,36015,33855],{"class":33738},[25,36017,36018],{"class":33726,"line":33883},[25,36019,34047],{"emptyLinePlaceholder":31433},[25,36021,36022,36024,36027,36029,36031,36033,36035],{"class":33726,"line":33889},[25,36023,33731],{"class":33730},[25,36025,36026],{"class":33734}," transpose_output",[25,36028,313],{"class":33738},[25,36030,33742],{"class":33741},[25,36032,33745],{"class":33738},[25,36034,35906],{"class":33741},[25,36036,33751],{"class":33738},[25,36038,36039],{"class":33726,"line":33914},[25,36040,36041],{"class":33756},"    \"\"\"逆转transpose_qkv函数的操作\"\"\"\n",[25,36043,36044,36046,36048,36050,36052,36054,36057,36059,36061,36063],{"class":33726,"line":33927},[25,36045,35928],{"class":33738},[25,36047,919],{"class":33730},[25,36049,36000],{"class":33738},[25,36051,33876],{"class":33730},[25,36053,617],{"class":33778},[25,36055,36056],{"class":33738},", num_heads, X.shape[",[25,36058,617],{"class":33778},[25,36060,35938],{"class":33738},[25,36062,9242],{"class":33778},[25,36064,33855],{"class":33738},[25,36066,36067,36069,36071,36073,36075,36077,36079,36081,36083,36085,36087],{"class":33726,"line":34166},[25,36068,35928],{"class":33738},[25,36070,919],{"class":33730},[25,36072,35967],{"class":33738},[25,36074,599],{"class":33778},[25,36076,33745],{"class":33738},[25,36078,9242],{"class":33778},[25,36080,33745],{"class":33738},[25,36082,617],{"class":33778},[25,36084,33745],{"class":33738},[25,36086,10476],{"class":33778},[25,36088,33803],{"class":33738},[25,36090,36092,36094,36096,36098,36100,36102,36105,36107,36109],{"class":33726,"line":36091},17,[25,36093,35997],{"class":33730},[25,36095,35933],{"class":33738},[25,36097,599],{"class":33778},[25,36099,35938],{"class":33738},[25,36101,617],{"class":33778},[25,36103,36104],{"class":33738},"], ",[25,36106,33876],{"class":33730},[25,36108,617],{"class":33778},[25,36110,33803],{"class":33738},[33716,36112,36114],{"className":33718,"code":36113,"language":33720,"meta":31408,"style":31408},"#@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",[33722,36115,36116,36121,36138,36143,36175,36202,36221,36233,36245,36264,36282,36300,36318,36322,36350,36355,36360,36365,36371,36377,36383,36404,36423,36442,36447,36463,36469,36475,36485,36509,36514,36520,36534,36539,36545,36560],{"__ignoreMap":31408},[25,36117,36118],{"class":33726,"line":33727},[25,36119,36120],{"class":33762},"#@save\n",[25,36122,36123,36125,36128,36130,36132,36134,36136],{"class":33726,"line":31409},[25,36124,33953],{"class":33730},[25,36126,36127],{"class":33956}," MultiHeadAttention",[25,36129,313],{"class":33738},[25,36131,33963],{"class":33962},[25,36133,32214],{"class":33738},[25,36135,33968],{"class":33962},[25,36137,33751],{"class":33738},[25,36139,36140],{"class":33726,"line":31417},[25,36141,36142],{"class":33756},"    \"\"\"多头注意力\"\"\"\n",[25,36144,36145,36147,36149,36151,36153,36155,36158,36160,36163,36165,36168,36170,36173],{"class":33726,"line":33766},[25,36146,33980],{"class":33730},[25,36148,33983],{"class":33778},[25,36150,313],{"class":33738},[25,36152,33989],{"class":33988},[25,36154,33745],{"class":33738},[25,36156,36157],{"class":33741},"key_size",[25,36159,33745],{"class":33738},[25,36161,36162],{"class":33741},"query_size",[25,36164,33745],{"class":33738},[25,36166,36167],{"class":33741},"value_size",[25,36169,33745],{"class":33738},[25,36171,36172],{"class":33741},"num_hiddens",[25,36174,35139],{"class":33738},[25,36176,36177,36180,36182,36184,36186,36189,36191,36194,36196,36198,36200],{"class":33726,"line":33785},[25,36178,36179],{"class":33741},"                 num_heads",[25,36181,33745],{"class":33738},[25,36183,33994],{"class":33741},[25,36185,33745],{"class":33738},[25,36187,36188],{"class":33741},"bias",[25,36190,919],{"class":33730},[25,36192,36193],{"class":33778},"False",[25,36195,33745],{"class":33738},[25,36197,33999],{"class":33730},[25,36199,34002],{"class":33741},[25,36201,33751],{"class":33738},[25,36203,36204,36206,36209,36211,36213,36215,36217,36219],{"class":33726,"line":33806},[25,36205,34010],{"class":34009},[25,36207,36208],{"class":33738},"(MultiHeadAttention, ",[25,36210,33989],{"class":34016},[25,36212,34019],{"class":33738},[25,36214,34022],{"class":33778},[25,36216,313],{"class":33738},[25,36218,33999],{"class":33730},[25,36220,34029],{"class":33738},[25,36222,36223,36225,36228,36230],{"class":33726,"line":33814},[25,36224,34034],{"class":34016},[25,36226,36227],{"class":33738},".num_heads ",[25,36229,919],{"class":33730},[25,36231,36232],{"class":33738}," num_heads\n",[25,36234,36235,36237,36240,36242],{"class":33726,"line":33825},[25,36236,34034],{"class":34016},[25,36238,36239],{"class":33738},".attention ",[25,36241,919],{"class":33730},[25,36243,36244],{"class":33738}," d2l.DotProductAttention(dropout)\n",[25,36246,36247,36249,36252,36254,36257,36259,36261],{"class":33726,"line":33842},[25,36248,34034],{"class":34016},[25,36250,36251],{"class":33738},".W_q ",[25,36253,919],{"class":33730},[25,36255,36256],{"class":33738}," nn.Linear(query_size, num_hiddens, ",[25,36258,36188],{"class":33794},[25,36260,919],{"class":33730},[25,36262,36263],{"class":33738},"bias)\n",[25,36265,36266,36268,36271,36273,36276,36278,36280],{"class":33726,"line":33858},[25,36267,34034],{"class":34016},[25,36269,36270],{"class":33738},".W_k ",[25,36272,919],{"class":33730},[25,36274,36275],{"class":33738}," nn.Linear(key_size, num_hiddens, ",[25,36277,36188],{"class":33794},[25,36279,919],{"class":33730},[25,36281,36263],{"class":33738},[25,36283,36284,36286,36289,36291,36294,36296,36298],{"class":33726,"line":33866},[25,36285,34034],{"class":34016},[25,36287,36288],{"class":33738},".W_v ",[25,36290,919],{"class":33730},[25,36292,36293],{"class":33738}," nn.Linear(value_size, num_hiddens, ",[25,36295,36188],{"class":33794},[25,36297,919],{"class":33730},[25,36299,36263],{"class":33738},[25,36301,36302,36304,36307,36309,36312,36314,36316],{"class":33726,"line":33883},[25,36303,34034],{"class":34016},[25,36305,36306],{"class":33738},".W_o ",[25,36308,919],{"class":33730},[25,36310,36311],{"class":33738}," nn.Linear(num_hiddens, num_hiddens, ",[25,36313,36188],{"class":33794},[25,36315,919],{"class":33730},[25,36317,36263],{"class":33738},[25,36319,36320],{"class":33726,"line":33889},[25,36321,34047],{"emptyLinePlaceholder":31433},[25,36323,36324,36326,36328,36330,36332,36334,36336,36338,36340,36342,36344,36346,36348],{"class":33726,"line":33914},[25,36325,33980],{"class":33730},[25,36327,34074],{"class":33734},[25,36329,313],{"class":33738},[25,36331,33989],{"class":33988},[25,36333,33745],{"class":33738},[25,36335,34083],{"class":33741},[25,36337,33745],{"class":33738},[25,36339,34088],{"class":33741},[25,36341,33745],{"class":33738},[25,36343,34093],{"class":33741},[25,36345,33745],{"class":33738},[25,36347,33748],{"class":33741},[25,36349,33751],{"class":33738},[25,36351,36352],{"class":33726,"line":33927},[25,36353,36354],{"class":33762},"        # queries，keys，values的形状:\n",[25,36356,36357],{"class":33726,"line":34166},[25,36358,36359],{"class":33762},"        # (batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[25,36361,36362],{"class":33726,"line":36091},[25,36363,36364],{"class":33762},"        # valid_lens　的形状:\n",[25,36366,36368],{"class":33726,"line":36367},18,[25,36369,36370],{"class":33762},"        # (batch_size，)或(batch_size，查询的个数)\n",[25,36372,36374],{"class":33726,"line":36373},19,[25,36375,36376],{"class":33762},"        # 经过变换后，输出的queries，keys，values 的形状:\n",[25,36378,36380],{"class":33726,"line":36379},20,[25,36381,36382],{"class":33762},"        # (batch_size*num_heads，查询或者“键－值”对的个数，num_hiddens/num_heads)\n",[25,36384,36386,36389,36391,36394,36396,36399,36401],{"class":33726,"line":36385},21,[25,36387,36388],{"class":33738},"        queries ",[25,36390,919],{"class":33730},[25,36392,36393],{"class":33738}," transpose_qkv(",[25,36395,33989],{"class":34016},[25,36397,36398],{"class":33738},".W_q(queries), ",[25,36400,33989],{"class":34016},[25,36402,36403],{"class":33738},".num_heads)\n",[25,36405,36407,36410,36412,36414,36416,36419,36421],{"class":33726,"line":36406},22,[25,36408,36409],{"class":33738},"        keys ",[25,36411,919],{"class":33730},[25,36413,36393],{"class":33738},[25,36415,33989],{"class":34016},[25,36417,36418],{"class":33738},".W_k(keys), ",[25,36420,33989],{"class":34016},[25,36422,36403],{"class":33738},[25,36424,36426,36429,36431,36433,36435,36438,36440],{"class":33726,"line":36425},23,[25,36427,36428],{"class":33738},"        values ",[25,36430,919],{"class":33730},[25,36432,36393],{"class":33738},[25,36434,33989],{"class":34016},[25,36436,36437],{"class":33738},".W_v(values), ",[25,36439,33989],{"class":34016},[25,36441,36403],{"class":33738},[25,36443,36445],{"class":33726,"line":36444},24,[25,36446,34047],{"emptyLinePlaceholder":31433},[25,36448,36450,36452,36454,36456,36459,36461],{"class":33726,"line":36449},25,[25,36451,33828],{"class":33730},[25,36453,33772],{"class":33738},[25,36455,33775],{"class":33730},[25,36457,36458],{"class":33730}," not",[25,36460,33779],{"class":33778},[25,36462,33782],{"class":33738},[25,36464,36466],{"class":33726,"line":36465},26,[25,36467,36468],{"class":33762},"            # 在轴0，将第一项（标量或者矢量）复制num_heads次，\n",[25,36470,36472],{"class":33726,"line":36471},27,[25,36473,36474],{"class":33762},"            # 然后如此复制第二项，然后诸如此类。\n",[25,36476,36478,36480,36482],{"class":33726,"line":36477},28,[25,36479,33845],{"class":33738},[25,36481,919],{"class":33730},[25,36483,36484],{"class":33738}," torch.repeat_interleave(\n",[25,36486,36488,36491,36494,36496,36498,36501,36503,36505,36507],{"class":33726,"line":36487},29,[25,36489,36490],{"class":33738},"                valid_lens, ",[25,36492,36493],{"class":33794},"repeats",[25,36495,919],{"class":33730},[25,36497,33989],{"class":34016},[25,36499,36500],{"class":33738},".num_heads, ",[25,36502,33795],{"class":33794},[25,36504,919],{"class":33730},[25,36506,599],{"class":33778},[25,36508,33803],{"class":33738},[25,36510,36512],{"class":33726,"line":36511},30,[25,36513,34047],{"emptyLinePlaceholder":31433},[25,36515,36517],{"class":33726,"line":36516},31,[25,36518,36519],{"class":33762},"        # output的形状:(batch_size*num_heads，查询的个数， num_hiddens/num_heads)\n",[25,36521,36523,36526,36528,36531],{"class":33726,"line":36522},32,[25,36524,36525],{"class":33738},"        output ",[25,36527,919],{"class":33730},[25,36529,36530],{"class":34016}," self",[25,36532,36533],{"class":33738},".attention(queries, keys, values, valid_lens)\n",[25,36535,36537],{"class":33726,"line":36536},33,[25,36538,34047],{"emptyLinePlaceholder":31433},[25,36540,36542],{"class":33726,"line":36541},34,[25,36543,36544],{"class":33762},"        # output_concat的形状:(batch_size，查询的个数，num_hiddens)\n",[25,36546,36548,36551,36553,36556,36558],{"class":33726,"line":36547},35,[25,36549,36550],{"class":33738},"        output_concat ",[25,36552,919],{"class":33730},[25,36554,36555],{"class":33738}," transpose_output(output, ",[25,36557,33989],{"class":34016},[25,36559,36403],{"class":33738},[25,36561,36563,36565,36567],{"class":33726,"line":36562},36,[25,36564,33788],{"class":33730},[25,36566,36530],{"class":34016},[25,36568,36569],{"class":33738},".W_o(output_concat)\n",[11,36571,36572],{"id":36572},"位置编码",[15,36574,36575,36576,36667],{},"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 ",[25,36577,36579,36605],{"className":36578},[28],[25,36580,36582],{"className":36581},[32],[34,36583,36584],{"xmlns":36},[38,36585,36586,36602],{},[41,36587,36588,36594,36596,36598,36600],{},[44,36589,36590,36592],{},[47,36591,31509],{},[47,36593,31744],{},[47,36595,5801],{},[47,36597,31509],{},[47,36599,32141],{},[47,36601,29611],{},[54,36603,36604],{"encoding":56},"d_model",[25,36606,36608],{"className":36607,"ariaHidden":62},[61],[25,36609,36611,36614,36654,36657,36660,36663],{"className":36610},[66],[25,36612],{"className":36613,"style":12948},[70],[25,36615,36617,36620],{"className":36616},[75],[25,36618,31509],{"className":36619},[75,79],[25,36621,36623],{"className":36622},[83],[25,36624,36626,36646],{"className":36625},[87,88],[25,36627,36629,36643],{"className":36628},[92],[25,36630,36632],{"className":36631,"style":20778},[96],[25,36633,36634,36637],{"style":100},[25,36635],{"className":36636,"style":105},[104],[25,36638,36640],{"className":36639},[109,110,111,112],[25,36641,31744],{"className":36642},[75,79,112],[25,36644,120],{"className":36645},[119],[25,36647,36649],{"className":36648},[92],[25,36650,36652],{"className":36651,"style":127},[96],[25,36653],{},[25,36655,5801],{"className":36656},[75,79],[25,36658,31509],{"className":36659},[75,79],[25,36661,32141],{"className":36662},[75,79],[25,36664,29611],{"className":36665,"style":36666},[75,79],"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。",[15,36669,36670],{},"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。",[15,36672,36673,36674,36839,36840,36868,36869,36897,36898,37068,37069,37129,37130,37159,37160,37197,37198,37254],{},"假设输入表示 ",[25,36675,36677,36720],{"className":36676},[28],[25,36678,36680],{"className":36679},[32],[34,36681,36682],{"xmlns":36},[38,36683,36684,36717],{},[41,36685,36686,36689,36691],{},[47,36687,33742],{"mathvariant":36688},"bold",[310,36690,31837],{},[2133,36692,36693,36695],{},[47,36694,1440],{"mathvariant":19397},[41,36696,36697,36699,36701],{},[47,36698,2121],{},[310,36700,31848],{},[44,36702,36703,36705],{},[47,36704,31509],{},[41,36706,36707,36709,36711,36713,36715],{},[47,36708,31744],{},[47,36710,5801],{},[47,36712,31509],{},[47,36714,32141],{},[47,36716,29611],{},[54,36718,36719],{"encoding":56},"\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{model}}",[25,36721,36723,36743],{"className":36722,"ariaHidden":62},[61],[25,36724,36726,36730,36734,36737,36740],{"className":36725},[66],[25,36727],{"className":36728,"style":36729},[70],"height:0.7252em;vertical-align:-0.0391em;",[25,36731,33742],{"className":36732},[75,36733],"mathbf",[25,36735],{"className":36736,"style":1008},[701],[25,36738,31837],{"className":36739},[1012],[25,36741],{"className":36742,"style":1008},[701],[25,36744,36746,36749],{"className":36745},[66],[25,36747],{"className":36748,"style":31882},[70],[25,36750,36752,36755],{"className":36751},[75],[25,36753,1440],{"className":36754},[75,19805],[25,36756,36758],{"className":36757},[83],[25,36759,36761],{"className":36760},[87],[25,36762,36764],{"className":36763},[92],[25,36765,36767],{"className":36766,"style":31882},[96],[25,36768,36769,36772],{"style":4065},[25,36770],{"className":36771,"style":105},[104],[25,36773,36775],{"className":36774},[109,110,111,112],[25,36776,36778,36781,36784],{"className":36777},[75,112],[25,36779,2121],{"className":36780},[75,79,112],[25,36782,31848],{"className":36783},[989,112],[25,36785,36787,36790],{"className":36786},[75,112],[25,36788,31509],{"className":36789},[75,79,112],[25,36791,36793],{"className":36792},[83],[25,36794,36796,36831],{"className":36795},[87,88],[25,36797,36799,36828],{"className":36798},[92],[25,36800,36802],{"className":36801,"style":1551},[96],[25,36803,36804,36807],{"style":31601},[25,36805],{"className":36806,"style":1594},[104],[25,36808,36810],{"className":36809},[109,1598,1599,112],[25,36811,36813,36816,36819,36822,36825],{"className":36812},[75,112],[25,36814,31744],{"className":36815},[75,79,112],[25,36817,5801],{"className":36818},[75,79,112],[25,36820,31509],{"className":36821},[75,79,112],[25,36823,32141],{"className":36824},[75,79,112],[25,36826,29611],{"className":36827,"style":36666},[75,79,112],[25,36829,120],{"className":36830},[119],[25,36832,36834],{"className":36833},[92],[25,36835,36837],{"className":36836,"style":1615},[96],[25,36838],{}," 包含一个序列中 ",[25,36841,36843,36856],{"className":36842},[28],[25,36844,36846],{"className":36845},[32],[34,36847,36848],{"xmlns":36},[38,36849,36850,36854],{},[41,36851,36852],{},[47,36853,2121],{},[54,36855,2121],{"encoding":56},[25,36857,36859],{"className":36858,"ariaHidden":62},[61],[25,36860,36862,36865],{"className":36861},[66],[25,36863],{"className":36864,"style":289},[70],[25,36866,2121],{"className":36867},[75,79]," 个词元的 ",[25,36870,36872,36885],{"className":36871},[28],[25,36873,36875],{"className":36874},[32],[34,36876,36877],{"xmlns":36},[38,36878,36879,36883],{},[41,36880,36881],{},[47,36882,31509],{},[54,36884,31509],{"encoding":56},[25,36886,36888],{"className":36887,"ariaHidden":62},[61],[25,36889,36891,36894],{"className":36890},[66],[25,36892],{"className":36893,"style":14931},[70],[25,36895,31509],{"className":36896},[75,79]," 维嵌入表示。位置编码使用相同形状的位置嵌入矩阵 ",[25,36899,36901,36947],{"className":36900},[28],[25,36902,36904],{"className":36903},[32],[34,36905,36906],{"xmlns":36},[38,36907,36908,36944],{},[41,36909,36910,36916,36918],{},[41,36911,36912,36914],{},[47,36913,1147],{"mathvariant":36688},[47,36915,1435],{"mathvariant":36688},[310,36917,31837],{},[2133,36919,36920,36922],{},[47,36921,1440],{"mathvariant":19397},[41,36923,36924,36926,36928],{},[47,36925,2121],{},[310,36927,31848],{},[44,36929,36930,36932],{},[47,36931,31509],{},[41,36933,36934,36936,36938,36940,36942],{},[47,36935,31744],{},[47,36937,5801],{},[47,36939,31509],{},[47,36941,32141],{},[47,36943,29611],{},[54,36945,36946],{"encoding":56},"\\mathbf{PE} \\in \\mathbb{R}^{n \\times d_{model}}",[25,36948,36950,36972],{"className":36949,"ariaHidden":62},[61],[25,36951,36953,36956,36963,36966,36969],{"className":36952},[66],[25,36954],{"className":36955,"style":36729},[70],[25,36957,36959],{"className":36958},[75],[25,36960,36962],{"className":36961},[75,36733],"PE",[25,36964],{"className":36965,"style":1008},[701],[25,36967,31837],{"className":36968},[1012],[25,36970],{"className":36971,"style":1008},[701],[25,36973,36975,36978],{"className":36974},[66],[25,36976],{"className":36977,"style":31882},[70],[25,36979,36981,36984],{"className":36980},[75],[25,36982,1440],{"className":36983},[75,19805],[25,36985,36987],{"className":36986},[83],[25,36988,36990],{"className":36989},[87],[25,36991,36993],{"className":36992},[92],[25,36994,36996],{"className":36995,"style":31882},[96],[25,36997,36998,37001],{"style":4065},[25,36999],{"className":37000,"style":105},[104],[25,37002,37004],{"className":37003},[109,110,111,112],[25,37005,37007,37010,37013],{"className":37006},[75,112],[25,37008,2121],{"className":37009},[75,79,112],[25,37011,31848],{"className":37012},[989,112],[25,37014,37016,37019],{"className":37015},[75,112],[25,37017,31509],{"className":37018},[75,79,112],[25,37020,37022],{"className":37021},[83],[25,37023,37025,37060],{"className":37024},[87,88],[25,37026,37028,37057],{"className":37027},[92],[25,37029,37031],{"className":37030,"style":1551},[96],[25,37032,37033,37036],{"style":31601},[25,37034],{"className":37035,"style":1594},[104],[25,37037,37039],{"className":37038},[109,1598,1599,112],[25,37040,37042,37045,37048,37051,37054],{"className":37041},[75,112],[25,37043,31744],{"className":37044},[75,79,112],[25,37046,5801],{"className":37047},[75,79,112],[25,37049,31509],{"className":37050},[75,79,112],[25,37052,32141],{"className":37053},[75,79,112],[25,37055,29611],{"className":37056,"style":36666},[75,79,112],[25,37058,120],{"className":37059},[119],[25,37061,37063],{"className":37062},[92],[25,37064,37066],{"className":37065,"style":1615},[96],[25,37067],{}," 输出 ",[25,37070,37072,37094],{"className":37071},[28],[25,37073,37075],{"className":37074},[32],[34,37076,37077],{"xmlns":36},[38,37078,37079,37091],{},[41,37080,37081,37083,37085],{},[47,37082,33742],{"mathvariant":36688},[310,37084,914],{},[41,37086,37087,37089],{},[47,37088,1147],{"mathvariant":36688},[47,37090,1435],{"mathvariant":36688},[54,37092,37093],{"encoding":56},"\\mathbf{X} + \\mathbf{PE}",[25,37095,37097,37116],{"className":37096,"ariaHidden":62},[61],[25,37098,37100,37104,37107,37110,37113],{"className":37099},[66],[25,37101],{"className":37102,"style":37103},[70],"height:0.7694em;vertical-align:-0.0833em;",[25,37105,33742],{"className":37106},[75,36733],[25,37108],{"className":37109,"style":3226},[701],[25,37111,914],{"className":37112},[989],[25,37114],{"className":37115,"style":3226},[701],[25,37117,37119,37123],{"className":37118},[66],[25,37120],{"className":37121,"style":37122},[70],"height:0.6861em;",[25,37124,37126],{"className":37125},[75],[25,37127,36962],{"className":37128},[75,36733],"，矩阵第 ",[25,37131,37133,37146],{"className":37132},[28],[25,37134,37136],{"className":37135},[32],[34,37137,37138],{"xmlns":36},[38,37139,37140,37144],{},[41,37141,37142],{},[47,37143,29614],{},[54,37145,29614],{"encoding":56},[25,37147,37149],{"className":37148,"ariaHidden":62},[61],[25,37150,37152,37156],{"className":37151},[66],[25,37153],{"className":37154,"style":37155},[70],"height:0.6595em;",[25,37157,29614],{"className":37158},[75,79]," 行、第 ",[25,37161,37163,37180],{"className":37162},[28],[25,37164,37166],{"className":37165},[32],[34,37167,37168],{"xmlns":36},[38,37169,37170,37177],{},[41,37171,37172,37174],{},[597,37173,9242],{},[47,37175,37176],{},"j",[54,37178,37179],{"encoding":56},"2j",[25,37181,37183],{"className":37182,"ariaHidden":62},[61],[25,37184,37186,37190,37193],{"className":37185},[66],[25,37187],{"className":37188,"style":37189},[70],"height:0.854em;vertical-align:-0.1944em;",[25,37191,9242],{"className":37192},[75],[25,37194,37176],{"className":37195,"style":37196},[75,79],"margin-right:0.05724em;"," 列和 ",[25,37199,37201,37221],{"className":37200},[28],[25,37202,37204],{"className":37203},[32],[34,37205,37206],{"xmlns":36},[38,37207,37208,37218],{},[41,37209,37210,37212,37214,37216],{},[597,37211,9242],{},[47,37213,37176],{},[310,37215,914],{},[597,37217,617],{},[54,37219,37220],{"encoding":56},"2j+1",[25,37222,37224,37245],{"className":37223,"ariaHidden":62},[61],[25,37225,37227,37230,37233,37236,37239,37242],{"className":37226},[66],[25,37228],{"className":37229,"style":37189},[70],[25,37231,9242],{"className":37232},[75],[25,37234,37176],{"className":37235,"style":37196},[75,79],[25,37237],{"className":37238,"style":3226},[701],[25,37240,914],{"className":37241},[989],[25,37243],{"className":37244,"style":3226},[701],[25,37246,37248,37251],{"className":37247},[66],[25,37249],{"className":37250,"style":33098},[70],[25,37252,617],{"className":37253},[75]," 列上的元素为：",[15,37256,37257],{},[25,37258,37260,37338],{"className":37259},[28],[25,37261,37263],{"className":37262},[32],[34,37264,37265],{"xmlns":36},[38,37266,37267,37335],{},[41,37268,37269,37271,37289,37291,37294,37296],{},[47,37270,1147],{},[44,37272,37273,37275],{},[47,37274,1435],{},[41,37276,37277,37279,37281,37283,37285,37287],{},[310,37278,313],{"stretchy":312},[47,37280,29614],{},[310,37282,602],{"separator":62},[597,37284,9242],{},[47,37286,37176],{},[310,37288,332],{"stretchy":312},[310,37290,919],{},[47,37292,37293],{},"sin",[310,37295,2240],{},[41,37297,37298,37300,37333],{},[310,37299,313],{"fence":62},[1978,37301,37302,37304],{},[47,37303,29614],{},[2133,37305,37306,37309],{},[597,37307,37308],{},"10000",[41,37310,37311,37313,37315,37317],{},[597,37312,9242],{},[47,37314,37176],{},[47,37316,34148],{"mathvariant":322},[44,37318,37319,37321],{},[47,37320,31509],{},[41,37322,37323,37325,37327,37329,37331],{},[47,37324,31744],{},[47,37326,5801],{},[47,37328,31509],{},[47,37330,32141],{},[47,37332,29611],{},[310,37334,332],{"fence":62},[54,37336,37337],{"encoding":56}," PE_{(i,2j)} = \\sin\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[25,37339,37341,37419],{"className":37340,"ariaHidden":62},[61],[25,37342,37344,37348,37351,37410,37413,37416],{"className":37343},[66],[25,37345],{"className":37346,"style":37347},[70],"height:1.0385em;vertical-align:-0.3552em;",[25,37349,1147],{"className":37350,"style":875},[75,79],[25,37352,37354,37357],{"className":37353},[75],[25,37355,1435],{"className":37356,"style":1417},[75,79],[25,37358,37360],{"className":37359},[83],[25,37361,37363,37402],{"className":37362},[87,88],[25,37364,37366,37399],{"className":37365},[92],[25,37367,37369],{"className":37368,"style":1551},[96],[25,37370,37372,37375],{"style":37371},"top:-2.5198em;margin-left:-0.0576em;margin-right:0.05em;",[25,37373],{"className":37374,"style":105},[104],[25,37376,37378],{"className":37377},[109,110,111,112],[25,37379,37381,37384,37387,37390,37393,37396],{"className":37380},[75,112],[25,37382,313],{"className":37383},[352,112],[25,37385,29614],{"className":37386},[75,79,112],[25,37388,602],{"className":37389},[697,112],[25,37391,9242],{"className":37392},[75,112],[25,37394,37176],{"className":37395,"style":37196},[75,79,112],[25,37397,332],{"className":37398},[439,112],[25,37400,120],{"className":37401},[119],[25,37403,37405],{"className":37404},[92],[25,37406,37408],{"className":37407,"style":1636},[96],[25,37409],{},[25,37411],{"className":37412,"style":1008},[701],[25,37414,919],{"className":37415},[1012],[25,37417],{"className":37418,"style":1008},[701],[25,37420,37422,37425,37428,37431],{"className":37421},[66],[25,37423],{"className":37424,"style":32294},[70],[25,37426,37293],{"className":37427},[1658],[25,37429],{"className":37430,"style":702},[701],[25,37432,37434,37440,37608],{"className":37433},[841],[25,37435,37437],{"className":37436,"style":17229},[352,17228],[25,37438,313],{"className":37439},[17233,32313],[25,37441,37443,37446,37605],{"className":37442},[75],[25,37444],{"className":37445},[352,3239],[25,37447,37449],{"className":37448},[1978],[25,37450,37452,37596],{"className":37451},[87,88],[25,37453,37455,37593],{"className":37454},[92],[25,37456,37459,37571,37579],{"className":37457,"style":37458},[96],"height:0.8557em;",[25,37460,37462,37465],{"style":37461},"top:-2.5648em;",[25,37463],{"className":37464,"style":1676},[104],[25,37466,37468],{"className":37467},[109,110,111,112],[25,37469,37471,37475],{"className":37470},[75,112],[25,37472,37474],{"className":37473},[75,112],"1000",[25,37476,37478,37481],{"className":37477},[75,112],[25,37479,599],{"className":37480},[75,112],[25,37482,37484],{"className":37483},[83],[25,37485,37487],{"className":37486},[87],[25,37488,37490],{"className":37489},[92],[25,37491,37494],{"className":37492,"style":37493},[96],"height:0.8932em;",[25,37495,37497,37501],{"style":37496},"top:-2.8932em;margin-right:0.0714em;",[25,37498],{"className":37499,"style":37500},[104],"height:2.5357em;",[25,37502,37504],{"className":37503},[109,1598,1599,112],[25,37505,37507,37510,37513,37516],{"className":37506},[75,112],[25,37508,9242],{"className":37509},[75,112],[25,37511,37176],{"className":37512,"style":37196},[75,79,112],[25,37514,34148],{"className":37515},[75,112],[25,37517,37519,37522],{"className":37518},[75,112],[25,37520,31509],{"className":37521},[75,79,112],[25,37523,37525],{"className":37524},[83],[25,37526,37528,37562],{"className":37527},[87,88],[25,37529,37531,37559],{"className":37530},[92],[25,37532,37534],{"className":37533,"style":1551},[96],[25,37535,37537,37541],{"style":37536},"top:-2.3448em;margin-left:0em;margin-right:0.1em;",[25,37538],{"className":37539,"style":37540},[104],"height:2.6944em;",[25,37542,37544,37547,37550,37553,37556],{"className":37543},[75,112],[25,37545,31744],{"className":37546},[75,79,112],[25,37548,5801],{"className":37549},[75,79,112],[25,37551,31509],{"className":37552},[75,79,112],[25,37554,32141],{"className":37555},[75,79,112],[25,37557,29611],{"className":37558,"style":36666},[75,79,112],[25,37560,120],{"className":37561},[119],[25,37563,37565],{"className":37564},[92],[25,37566,37569],{"className":37567,"style":37568},[96],"height:0.3496em;",[25,37570],{},[25,37572,37573,37576],{"style":3313},[25,37574],{"className":37575,"style":1676},[104],[25,37577],{"className":37578,"style":3321},[3320],[25,37580,37581,37584],{"style":5975},[25,37582],{"className":37583,"style":1676},[104],[25,37585,37587],{"className":37586},[109,110,111,112],[25,37588,37590],{"className":37589},[75,112],[25,37591,29614],{"className":37592},[75,79,112],[25,37594,120],{"className":37595},[119],[25,37597,37599],{"className":37598},[92],[25,37600,37603],{"className":37601,"style":37602},[96],"height:0.4352em;",[25,37604],{},[25,37606],{"className":37607},[439,3239],[25,37609,37611],{"className":37610,"style":17229},[439,17228],[25,37612,332],{"className":37613},[17233,32313],[15,37615,37616],{},[25,37617,37619,37700],{"className":37618},[28],[25,37620,37622],{"className":37621},[32],[34,37623,37624],{"xmlns":36},[38,37625,37626,37697],{},[41,37627,37628,37630,37652,37654,37657,37659],{},[47,37629,1147],{},[44,37631,37632,37634],{},[47,37633,1435],{},[41,37635,37636,37638,37640,37642,37644,37646,37648,37650],{},[310,37637,313],{"stretchy":312},[47,37639,29614],{},[310,37641,602],{"separator":62},[597,37643,9242],{},[47,37645,37176],{},[310,37647,914],{},[597,37649,617],{},[310,37651,332],{"stretchy":312},[310,37653,919],{},[47,37655,37656],{},"cos",[310,37658,2240],{},[41,37660,37661,37663,37695],{},[310,37662,313],{"fence":62},[1978,37664,37665,37667],{},[47,37666,29614],{},[2133,37668,37669,37671],{},[597,37670,37308],{},[41,37672,37673,37675,37677,37679],{},[597,37674,9242],{},[47,37676,37176],{},[47,37678,34148],{"mathvariant":322},[44,37680,37681,37683],{},[47,37682,31509],{},[41,37684,37685,37687,37689,37691,37693],{},[47,37686,31744],{},[47,37688,5801],{},[47,37690,31509],{},[47,37692,32141],{},[47,37694,29611],{},[310,37696,332],{"fence":62},[54,37698,37699],{"encoding":56}," PE_{(i,2j+1)} = \\cos\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[25,37701,37703,37785],{"className":37702,"ariaHidden":62},[61],[25,37704,37706,37709,37712,37776,37779,37782],{"className":37705},[66],[25,37707],{"className":37708,"style":37347},[70],[25,37710,1147],{"className":37711,"style":875},[75,79],[25,37713,37715,37718],{"className":37714},[75],[25,37716,1435],{"className":37717,"style":1417},[75,79],[25,37719,37721],{"className":37720},[83],[25,37722,37724,37768],{"className":37723},[87,88],[25,37725,37727,37765],{"className":37726},[92],[25,37728,37730],{"className":37729,"style":1551},[96],[25,37731,37732,37735],{"style":37371},[25,37733],{"className":37734,"style":105},[104],[25,37736,37738],{"className":37737},[109,110,111,112],[25,37739,37741,37744,37747,37750,37753,37756,37759,37762],{"className":37740},[75,112],[25,37742,313],{"className":37743},[352,112],[25,37745,29614],{"className":37746},[75,79,112],[25,37748,602],{"className":37749},[697,112],[25,37751,9242],{"className":37752},[75,112],[25,37754,37176],{"className":37755,"style":37196},[75,79,112],[25,37757,914],{"className":37758},[989,112],[25,37760,617],{"className":37761},[75,112],[25,37763,332],{"className":37764},[439,112],[25,37766,120],{"className":37767},[119],[25,37769,37771],{"className":37770},[92],[25,37772,37774],{"className":37773,"style":1636},[96],[25,37775],{},[25,37777],{"className":37778,"style":1008},[701],[25,37780,919],{"className":37781},[1012],[25,37783],{"className":37784,"style":1008},[701],[25,37786,37788,37791,37794,37797],{"className":37787},[66],[25,37789],{"className":37790,"style":32294},[70],[25,37792,37656],{"className":37793},[1658],[25,37795],{"className":37796,"style":702},[701],[25,37798,37800,37806,37964],{"className":37799},[841],[25,37801,37803],{"className":37802,"style":17229},[352,17228],[25,37804,313],{"className":37805},[17233,32313],[25,37807,37809,37812,37961],{"className":37808},[75],[25,37810],{"className":37811},[352,3239],[25,37813,37815],{"className":37814},[1978],[25,37816,37818,37953],{"className":37817},[87,88],[25,37819,37821,37950],{"className":37820},[92],[25,37822,37824,37928,37936],{"className":37823,"style":37458},[96],[25,37825,37826,37829],{"style":37461},[25,37827],{"className":37828,"style":1676},[104],[25,37830,37832],{"className":37831},[109,110,111,112],[25,37833,37835,37838],{"className":37834},[75,112],[25,37836,37474],{"className":37837},[75,112],[25,37839,37841,37844],{"className":37840},[75,112],[25,37842,599],{"className":37843},[75,112],[25,37845,37847],{"className":37846},[83],[25,37848,37850],{"className":37849},[87],[25,37851,37853],{"className":37852},[92],[25,37854,37856],{"className":37855,"style":37493},[96],[25,37857,37858,37861],{"style":37496},[25,37859],{"className":37860,"style":37500},[104],[25,37862,37864],{"className":37863},[109,1598,1599,112],[25,37865,37867,37870,37873,37876],{"className":37866},[75,112],[25,37868,9242],{"className":37869},[75,112],[25,37871,37176],{"className":37872,"style":37196},[75,79,112],[25,37874,34148],{"className":37875},[75,112],[25,37877,37879,37882],{"className":37878},[75,112],[25,37880,31509],{"className":37881},[75,79,112],[25,37883,37885],{"className":37884},[83],[25,37886,37888,37920],{"className":37887},[87,88],[25,37889,37891,37917],{"className":37890},[92],[25,37892,37894],{"className":37893,"style":1551},[96],[25,37895,37896,37899],{"style":37536},[25,37897],{"className":37898,"style":37540},[104],[25,37900,37902,37905,37908,37911,37914],{"className":37901},[75,112],[25,37903,31744],{"className":37904},[75,79,112],[25,37906,5801],{"className":37907},[75,79,112],[25,37909,31509],{"className":37910},[75,79,112],[25,37912,32141],{"className":37913},[75,79,112],[25,37915,29611],{"className":37916,"style":36666},[75,79,112],[25,37918,120],{"className":37919},[119],[25,37921,37923],{"className":37922},[92],[25,37924,37926],{"className":37925,"style":37568},[96],[25,37927],{},[25,37929,37930,37933],{"style":3313},[25,37931],{"className":37932,"style":1676},[104],[25,37934],{"className":37935,"style":3321},[3320],[25,37937,37938,37941],{"style":5975},[25,37939],{"className":37940,"style":1676},[104],[25,37942,37944],{"className":37943},[109,110,111,112],[25,37945,37947],{"className":37946},[75,112],[25,37948,29614],{"className":37949},[75,79,112],[25,37951,120],{"className":37952},[119],[25,37954,37956],{"className":37955},[92],[25,37957,37959],{"className":37958,"style":37602},[96],[25,37960],{},[25,37962],{"className":37963},[439,3239],[25,37965,37967],{"className":37966,"style":17229},[439,17228],[25,37968,332],{"className":37969},[17233,32313],[15,37971,37972,37973,38001,38002,38030,38031,29356,38065,38121,38122,38150,38151,38243,38244,38322],{},"其中，",[25,37974,37976,37989],{"className":37975},[28],[25,37977,37979],{"className":37978},[32],[34,37980,37981],{"xmlns":36},[38,37982,37983,37987],{},[41,37984,37985],{},[47,37986,29614],{},[54,37988,29614],{"encoding":56},[25,37990,37992],{"className":37991,"ariaHidden":62},[61],[25,37993,37995,37998],{"className":37994},[66],[25,37996],{"className":37997,"style":37155},[70],[25,37999,29614],{"className":38000},[75,79]," 表示位置，",[25,38003,38005,38018],{"className":38004},[28],[25,38006,38008],{"className":38007},[32],[34,38009,38010],{"xmlns":36},[38,38011,38012,38016],{},[41,38013,38014],{},[47,38015,37176],{},[54,38017,37176],{"encoding":56},[25,38019,38021],{"className":38020,"ariaHidden":62},[61],[25,38022,38024,38027],{"className":38023},[66],[25,38025],{"className":38026,"style":37189},[70],[25,38028,37176],{"className":38029,"style":37196},[75,79]," 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 ",[25,38032,38034,38050],{"className":38033},[28],[25,38035,38037],{"className":38036},[32],[34,38038,38039],{"xmlns":36},[38,38040,38041,38047],{},[41,38042,38043,38045],{},[597,38044,9242],{},[47,38046,276],{},[54,38048,38049],{"encoding":56},"2\\pi",[25,38051,38053],{"className":38052,"ariaHidden":62},[61],[25,38054,38056,38059,38062],{"className":38055},[66],[25,38057],{"className":38058,"style":33098},[70],[25,38060,9242],{"className":38061},[75],[25,38063,276],{"className":38064,"style":293},[75,79],[25,38066,38068,38088],{"className":38067},[28],[25,38069,38071],{"className":38070},[32],[34,38072,38073],{"xmlns":36},[38,38074,38075,38085],{},[41,38076,38077,38079,38081,38083],{},[597,38078,37308],{},[310,38080,1152],{},[597,38082,9242],{},[47,38084,276],{},[54,38086,38087],{"encoding":56},"10000 \\cdot 2\\pi",[25,38089,38091,38109],{"className":38090,"ariaHidden":62},[61],[25,38092,38094,38097,38100,38103,38106],{"className":38093},[66],[25,38095],{"className":38096,"style":33098},[70],[25,38098,37308],{"className":38099},[75],[25,38101],{"className":38102,"style":3226},[701],[25,38104,1152],{"className":38105},[989],[25,38107],{"className":38108,"style":3226},[701],[25,38110,38112,38115,38118],{"className":38111},[66],[25,38113],{"className":38114,"style":33098},[70],[25,38116,9242],{"className":38117},[75],[25,38119,276],{"className":38120,"style":293},[75,79]," 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 ",[25,38123,38125,38138],{"className":38124},[28],[25,38126,38128],{"className":38127},[32],[34,38129,38130],{"xmlns":36},[38,38131,38132,38136],{},[41,38133,38134],{},[47,38135,31512],{},[54,38137,31512],{"encoding":56},[25,38139,38141],{"className":38140,"ariaHidden":62},[61],[25,38142,38144,38147],{"className":38143},[66],[25,38145],{"className":38146,"style":14931},[70],[25,38148,31512],{"className":38149,"style":31611},[75,79],"，",[25,38152,38154,38180],{"className":38153},[28],[25,38155,38157],{"className":38156},[32],[34,38158,38159],{"xmlns":36},[38,38160,38161,38177],{},[41,38162,38163,38165],{},[47,38164,1147],{},[44,38166,38167,38169],{},[47,38168,1435],{},[41,38170,38171,38173,38175],{},[47,38172,29614],{},[310,38174,914],{},[47,38176,31512],{},[54,38178,38179],{"encoding":56},"PE_{i+k}",[25,38181,38183],{"className":38182,"ariaHidden":62},[61],[25,38184,38186,38190,38193],{"className":38185},[66],[25,38187],{"className":38188,"style":38189},[70],"height:0.8917em;vertical-align:-0.2083em;",[25,38191,1147],{"className":38192,"style":875},[75,79],[25,38194,38196,38199],{"className":38195},[75],[25,38197,1435],{"className":38198,"style":1417},[75,79],[25,38200,38202],{"className":38201},[83],[25,38203,38205,38235],{"className":38204},[87,88],[25,38206,38208,38232],{"className":38207},[92],[25,38209,38211],{"className":38210,"style":1741},[96],[25,38212,38214,38217],{"style":38213},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[25,38215],{"className":38216,"style":105},[104],[25,38218,38220],{"className":38219},[109,110,111,112],[25,38221,38223,38226,38229],{"className":38222},[75,112],[25,38224,29614],{"className":38225},[75,79,112],[25,38227,914],{"className":38228},[989,112],[25,38230,31512],{"className":38231,"style":31611},[75,79,112],[25,38233,120],{"className":38234},[119],[25,38236,38238],{"className":38237},[92],[25,38239,38241],{"className":38240,"style":1002},[96],[25,38242],{}," 都可以表示为 ",[25,38245,38247,38267],{"className":38246},[28],[25,38248,38250],{"className":38249},[32],[34,38251,38252],{"xmlns":36},[38,38253,38254,38264],{},[41,38255,38256,38258],{},[47,38257,1147],{},[44,38259,38260,38262],{},[47,38261,1435],{},[47,38263,29614],{},[54,38265,38266],{"encoding":56},"PE_{i}",[25,38268,38270],{"className":38269,"ariaHidden":62},[61],[25,38271,38273,38276,38279],{"className":38272},[66],[25,38274],{"className":38275,"style":6944},[70],[25,38277,1147],{"className":38278,"style":875},[75,79],[25,38280,38282,38285],{"className":38281},[75],[25,38283,1435],{"className":38284,"style":1417},[75,79],[25,38286,38288],{"className":38287},[83],[25,38289,38291,38314],{"className":38290},[87,88],[25,38292,38294,38311],{"className":38293},[92],[25,38295,38297],{"className":38296,"style":33358},[96],[25,38298,38299,38302],{"style":38213},[25,38300],{"className":38301,"style":105},[104],[25,38303,38305],{"className":38304},[109,110,111,112],[25,38306,38308],{"className":38307},[75,112],[25,38309,29614],{"className":38310},[75,79,112],[25,38312,120],{"className":38313},[119],[25,38315,38317],{"className":38316},[92],[25,38318,38320],{"className":38319,"style":127},[96],[25,38321],{}," 的线性函数。",[33716,38324,38326],{"className":33718,"code":38325,"language":33720,"meta":31408,"style":31408},"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",[33722,38327,38328,38346,38351,38380,38396,38406,38411,38428,38453,38475,38506,38533,38537,38553,38586],{"__ignoreMap":31408},[25,38329,38330,38332,38335,38337,38339,38341,38344],{"class":33726,"line":33727},[25,38331,33953],{"class":33730},[25,38333,38334],{"class":33956}," PositionalEncoding",[25,38336,313],{"class":33738},[25,38338,33963],{"class":33962},[25,38340,32214],{"class":33738},[25,38342,38343],{"class":33962},"Block",[25,38345,33751],{"class":33738},[25,38347,38348],{"class":33726,"line":31409},[25,38349,38350],{"class":33756},"    \"\"\"位置编码\"\"\"\n",[25,38352,38353,38355,38357,38359,38361,38363,38365,38367,38369,38371,38374,38376,38378],{"class":33726,"line":31417},[25,38354,33980],{"class":33730},[25,38356,33983],{"class":33778},[25,38358,313],{"class":33738},[25,38360,33989],{"class":33988},[25,38362,33745],{"class":33738},[25,38364,36172],{"class":33741},[25,38366,33745],{"class":33738},[25,38368,33994],{"class":33741},[25,38370,33745],{"class":33738},[25,38372,38373],{"class":33741},"max_len",[25,38375,919],{"class":33730},[25,38377,37474],{"class":33778},[25,38379,33751],{"class":33738},[25,38381,38382,38384,38387,38389,38391,38393],{"class":33726,"line":33766},[25,38383,34010],{"class":34009},[25,38385,38386],{"class":33738},"(PositionalEncoding, ",[25,38388,33989],{"class":34016},[25,38390,34019],{"class":33738},[25,38392,34022],{"class":33778},[25,38394,38395],{"class":33738},"()\n",[25,38397,38398,38400,38402,38404],{"class":33726,"line":33785},[25,38399,34034],{"class":34016},[25,38401,34037],{"class":33738},[25,38403,919],{"class":33730},[25,38405,34042],{"class":33738},[25,38407,38408],{"class":33726,"line":33806},[25,38409,38410],{"class":33762},"        # 创建一个足够长的P\n",[25,38412,38413,38415,38418,38420,38423,38425],{"class":33726,"line":33814},[25,38414,34034],{"class":34016},[25,38416,38417],{"class":33738},".P ",[25,38419,919],{"class":33730},[25,38421,38422],{"class":33738}," np.zeros((",[25,38424,617],{"class":33778},[25,38426,38427],{"class":33738},", max_len, num_hiddens))\n",[25,38429,38430,38432,38434,38437,38439,38441,38443,38445,38448,38450],{"class":33726,"line":33825},[25,38431,33892],{"class":33738},[25,38433,919],{"class":33730},[25,38435,38436],{"class":33738}," np.arange(max_len).reshape(",[25,38438,33876],{"class":33730},[25,38440,617],{"class":33778},[25,38442,33745],{"class":33738},[25,38444,617],{"class":33778},[25,38446,38447],{"class":33738},") ",[25,38449,34148],{"class":33730},[25,38451,38452],{"class":33738}," np.power(\n",[25,38454,38455,38458,38461,38463,38466,38468,38470,38472],{"class":33726,"line":33842},[25,38456,38457],{"class":33778},"            10000",[25,38459,38460],{"class":33738},", np.arange(",[25,38462,599],{"class":33778},[25,38464,38465],{"class":33738},", num_hiddens, ",[25,38467,9242],{"class":33778},[25,38469,38447],{"class":33738},[25,38471,34148],{"class":33730},[25,38473,38474],{"class":33738}," num_hiddens)\n",[25,38476,38477,38479,38482,38485,38487,38489,38491,38493,38496,38498,38501,38503],{"class":33726,"line":33858},[25,38478,34034],{"class":34016},[25,38480,38481],{"class":33738},".P[",[25,38483,15072],{"class":38484},"sDoOe",[25,38486,33745],{"class":33738},[25,38488,15072],{"class":38484},[25,38490,33745],{"class":33738},[25,38492,599],{"class":33778},[25,38494,38495],{"class":38484},"::",[25,38497,9242],{"class":33778},[25,38499,38500],{"class":33738},"] ",[25,38502,919],{"class":33730},[25,38504,38505],{"class":33738}," np.sin(X)\n",[25,38507,38508,38510,38512,38514,38516,38518,38520,38522,38524,38526,38528,38530],{"class":33726,"line":33866},[25,38509,34034],{"class":34016},[25,38511,38481],{"class":33738},[25,38513,15072],{"class":38484},[25,38515,33745],{"class":33738},[25,38517,15072],{"class":38484},[25,38519,33745],{"class":33738},[25,38521,617],{"class":33778},[25,38523,38495],{"class":38484},[25,38525,9242],{"class":33778},[25,38527,38500],{"class":33738},[25,38529,919],{"class":33730},[25,38531,38532],{"class":33738}," np.cos(X)\n",[25,38534,38535],{"class":33726,"line":33883},[25,38536,34047],{"emptyLinePlaceholder":31433},[25,38538,38539,38541,38543,38545,38547,38549,38551],{"class":33726,"line":33889},[25,38540,33980],{"class":33730},[25,38542,34074],{"class":33734},[25,38544,313],{"class":33738},[25,38546,33989],{"class":33988},[25,38548,33745],{"class":33738},[25,38550,33742],{"class":33741},[25,38552,33751],{"class":33738},[25,38554,38555,38557,38559,38562,38564,38566,38568,38570,38572,38574,38577,38579,38581,38583],{"class":33726,"line":33914},[25,38556,33892],{"class":33738},[25,38558,919],{"class":33730},[25,38560,38561],{"class":33738}," X ",[25,38563,914],{"class":33730},[25,38565,36530],{"class":34016},[25,38567,38481],{"class":33738},[25,38569,15072],{"class":38484},[25,38571,33745],{"class":33738},[25,38573,15072],{"class":38484},[25,38575,38576],{"class":33738},"X.shape[",[25,38578,617],{"class":33778},[25,38580,36104],{"class":33738},[25,38582,15072],{"class":38484},[25,38584,38585],{"class":33738},"].as_in_ctx(X.ctx)\n",[25,38587,38588,38590,38592],{"class":33726,"line":33927},[25,38589,33788],{"class":33730},[25,38591,36530],{"class":34016},[25,38593,38594],{"class":33738},".dropout(X)\n",[11,38596,38597],{"id":38597},"前馈神经网络",[15,38599,38600],{},"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。",[15,38602,38603],{},[25,38604,38606,38676],{"className":38605},[28],[25,38607,38609],{"className":38608},[32],[34,38610,38611],{"xmlns":36},[38,38612,38613,38673],{},[41,38614,38615,38618,38620,38622,38624,38626,38628,38630,38633,38635,38637,38639,38641,38643,38649,38651,38657,38659,38665,38667],{},[47,38616,38617],{},"F",[47,38619,38617],{},[47,38621,2111],{},[310,38623,313],{"stretchy":312},[47,38625,19255],{},[310,38627,332],{"stretchy":312},[310,38629,919],{},[47,38631,38632],{},"max",[310,38634,2240],{},[310,38636,313],{"stretchy":312},[597,38638,599],{},[310,38640,602],{"separator":62},[47,38642,19255],{},[44,38644,38645,38647],{},[47,38646,34311],{},[597,38648,617],{},[310,38650,914],{},[44,38652,38653,38655],{},[47,38654,15500],{},[597,38656,617],{},[310,38658,332],{"stretchy":312},[44,38660,38661,38663],{},[47,38662,34311],{},[597,38664,9242],{},[310,38666,914],{},[44,38668,38669,38671],{},[47,38670,15500],{},[597,38672,9242],{},[54,38674,38675],{"encoding":56}," FFN(x) = \\max(0,xW_1+b_1)W_2+b_2",[25,38677,38679,38712,38785,38883],{"className":38678,"ariaHidden":62},[61],[25,38680,38682,38685,38688,38691,38694,38697,38700,38703,38706,38709],{"className":38681},[66],[25,38683],{"className":38684,"style":345},[70],[25,38686,38617],{"className":38687,"style":875},[75,79],[25,38689,38617],{"className":38690,"style":875},[75,79],[25,38692,2111],{"className":38693,"style":3730},[75,79],[25,38695,313],{"className":38696},[352],[25,38698,19255],{"className":38699},[75,79],[25,38701,332],{"className":38702},[439],[25,38704],{"className":38705,"style":1008},[701],[25,38707,919],{"className":38708},[1012],[25,38710],{"className":38711,"style":1008},[701],[25,38713,38715,38718,38721,38724,38727,38730,38733,38736,38776,38779,38782],{"className":38714},[66],[25,38716],{"className":38717,"style":345},[70],[25,38719,38632],{"className":38720},[1658],[25,38722,313],{"className":38723},[352],[25,38725,599],{"className":38726},[75],[25,38728,602],{"className":38729},[697],[25,38731],{"className":38732,"style":702},[701],[25,38734,19255],{"className":38735},[75,79],[25,38737,38739,38742],{"className":38738},[75],[25,38740,34311],{"className":38741,"style":875},[75,79],[25,38743,38745],{"className":38744},[83],[25,38746,38748,38768],{"className":38747},[87,88],[25,38749,38751,38765],{"className":38750},[92],[25,38752,38754],{"className":38753,"style":671},[96],[25,38755,38756,38759],{"style":1744},[25,38757],{"className":38758,"style":105},[104],[25,38760,38762],{"className":38761},[109,110,111,112],[25,38763,617],{"className":38764},[75,112],[25,38766,120],{"className":38767},[119],[25,38769,38771],{"className":38770},[92],[25,38772,38774],{"className":38773,"style":127},[96],[25,38775],{},[25,38777],{"className":38778,"style":3226},[701],[25,38780,914],{"className":38781},[989],[25,38783],{"className":38784,"style":3226},[701],[25,38786,38788,38791,38831,38834,38874,38877,38880],{"className":38787},[66],[25,38789],{"className":38790,"style":345},[70],[25,38792,38794,38797],{"className":38793},[75],[25,38795,15500],{"className":38796},[75,79],[25,38798,38800],{"className":38799},[83],[25,38801,38803,38823],{"className":38802},[87,88],[25,38804,38806,38820],{"className":38805},[92],[25,38807,38809],{"className":38808,"style":671},[96],[25,38810,38811,38814],{"style":100},[25,38812],{"className":38813,"style":105},[104],[25,38815,38817],{"className":38816},[109,110,111,112],[25,38818,617],{"className":38819},[75,112],[25,38821,120],{"className":38822},[119],[25,38824,38826],{"className":38825},[92],[25,38827,38829],{"className":38828,"style":127},[96],[25,38830],{},[25,38832,332],{"className":38833},[439],[25,38835,38837,38840],{"className":38836},[75],[25,38838,34311],{"className":38839,"style":875},[75,79],[25,38841,38843],{"className":38842},[83],[25,38844,38846,38866],{"className":38845},[87,88],[25,38847,38849,38863],{"className":38848},[92],[25,38850,38852],{"className":38851,"style":671},[96],[25,38853,38854,38857],{"style":1744},[25,38855],{"className":38856,"style":105},[104],[25,38858,38860],{"className":38859},[109,110,111,112],[25,38861,9242],{"className":38862},[75,112],[25,38864,120],{"className":38865},[119],[25,38867,38869],{"className":38868},[92],[25,38870,38872],{"className":38871,"style":127},[96],[25,38873],{},[25,38875],{"className":38876,"style":3226},[701],[25,38878,914],{"className":38879},[989],[25,38881],{"className":38882,"style":3226},[701],[25,38884,38886,38889],{"className":38885},[66],[25,38887],{"className":38888,"style":12948},[70],[25,38890,38892,38895],{"className":38891},[75],[25,38893,15500],{"className":38894},[75,79],[25,38896,38898],{"className":38897},[83],[25,38899,38901,38921],{"className":38900},[87,88],[25,38902,38904,38918],{"className":38903},[92],[25,38905,38907],{"className":38906,"style":671},[96],[25,38908,38909,38912],{"style":100},[25,38910],{"className":38911,"style":105},[104],[25,38913,38915],{"className":38914},[109,110,111,112],[25,38916,9242],{"className":38917},[75,112],[25,38919,120],{"className":38920},[119],[25,38922,38924],{"className":38923},[92],[25,38925,38927],{"className":38926,"style":127},[96],[25,38928],{},[33716,38930,38932],{"className":33718,"code":38931,"language":33720,"meta":31408,"style":31408},"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",[33722,38933,38934,38951,38956,38983,38992,39011,39023,39035,39047,39051,39067],{"__ignoreMap":31408},[25,38935,38936,38938,38941,38943,38945,38947,38949],{"class":33726,"line":33727},[25,38937,33953],{"class":33730},[25,38939,38940],{"class":33956}," PositionWiseFFN",[25,38942,313],{"class":33738},[25,38944,33963],{"class":33962},[25,38946,32214],{"class":33738},[25,38948,33968],{"class":33962},[25,38950,33751],{"class":33738},[25,38952,38953],{"class":33726,"line":31409},[25,38954,38955],{"class":33756},"    \"\"\"基于位置的前馈网络\"\"\"\n",[25,38957,38958,38960,38962,38964,38966,38968,38971,38973,38976,38978,38981],{"class":33726,"line":31417},[25,38959,33980],{"class":33730},[25,38961,33983],{"class":33778},[25,38963,313],{"class":33738},[25,38965,33989],{"class":33988},[25,38967,33745],{"class":33738},[25,38969,38970],{"class":33741},"ffn_num_input",[25,38972,33745],{"class":33738},[25,38974,38975],{"class":33741},"ffn_num_hiddens",[25,38977,33745],{"class":33738},[25,38979,38980],{"class":33741},"ffn_num_outputs",[25,38982,35139],{"class":33738},[25,38984,38985,38988,38990],{"class":33726,"line":33766},[25,38986,38987],{"class":33730},"                 **",[25,38989,34002],{"class":33741},[25,38991,33751],{"class":33738},[25,38993,38994,38996,38999,39001,39003,39005,39007,39009],{"class":33726,"line":33785},[25,38995,34010],{"class":34009},[25,38997,38998],{"class":33738},"(PositionWiseFFN, ",[25,39000,33989],{"class":34016},[25,39002,34019],{"class":33738},[25,39004,34022],{"class":33778},[25,39006,313],{"class":33738},[25,39008,33999],{"class":33730},[25,39010,34029],{"class":33738},[25,39012,39013,39015,39018,39020],{"class":33726,"line":33806},[25,39014,34034],{"class":34016},[25,39016,39017],{"class":33738},".dense1 ",[25,39019,919],{"class":33730},[25,39021,39022],{"class":33738}," nn.Linear(ffn_num_input, ffn_num_hiddens)\n",[25,39024,39025,39027,39030,39032],{"class":33726,"line":33814},[25,39026,34034],{"class":34016},[25,39028,39029],{"class":33738},".relu ",[25,39031,919],{"class":33730},[25,39033,39034],{"class":33738}," nn.ReLU()\n",[25,39036,39037,39039,39042,39044],{"class":33726,"line":33825},[25,39038,34034],{"class":34016},[25,39040,39041],{"class":33738},".dense2 ",[25,39043,919],{"class":33730},[25,39045,39046],{"class":33738}," nn.Linear(ffn_num_hiddens, ffn_num_outputs)\n",[25,39048,39049],{"class":33726,"line":33842},[25,39050,34047],{"emptyLinePlaceholder":31433},[25,39052,39053,39055,39057,39059,39061,39063,39065],{"class":33726,"line":33858},[25,39054,33980],{"class":33730},[25,39056,34074],{"class":33734},[25,39058,313],{"class":33738},[25,39060,33989],{"class":33988},[25,39062,33745],{"class":33738},[25,39064,33742],{"class":33741},[25,39066,33751],{"class":33738},[25,39068,39069,39071,39073,39076,39078,39081,39083],{"class":33726,"line":33866},[25,39070,33788],{"class":33730},[25,39072,36530],{"class":34016},[25,39074,39075],{"class":33738},".dense2(",[25,39077,33989],{"class":34016},[25,39079,39080],{"class":33738},".relu(",[25,39082,33989],{"class":34016},[25,39084,39085],{"class":33738},".dense1(X)))\n",[11,39087,39088],{"id":39088},"残差连接和层规范化",[15,39090,39091],{},"我们在每个子层之间加入了一个残差连接和层归一化。",[15,39093,39094,39095,35879,39216,39279],{},"因此，每个子层的输出都是 ",[25,39096,39098,39163],{"className":39097},[28],[25,39099,39101],{"className":39100},[32],[34,39102,39103],{"xmlns":36},[38,39104,39105,39160],{},[41,39106,39107,39128,39130,39132,39134,39152,39154,39156,39158],{},[41,39108,39109,39111,39113,39116,39118,39120,39122,39124,39126],{},[47,39110,5798],{"mathvariant":322},[47,39112,49],{"mathvariant":322},[47,39114,39115],{"mathvariant":322},"y",[47,39117,32141],{"mathvariant":322},[47,39119,457],{"mathvariant":322},[47,39121,2111],{"mathvariant":322},[47,39123,5801],{"mathvariant":322},[47,39125,457],{"mathvariant":322},[47,39127,31744],{"mathvariant":322},[310,39129,313],{"stretchy":312},[47,39131,19255],{},[310,39133,914],{},[41,39135,39136,39138,39140,39142,39144,39146,39148,39150],{},[47,39137,1401],{"mathvariant":322},[47,39139,34221],{"mathvariant":322},[47,39141,15500],{"mathvariant":322},[47,39143,29611],{"mathvariant":322},[47,39145,49],{"mathvariant":322},[47,39147,39115],{"mathvariant":322},[47,39149,32141],{"mathvariant":322},[47,39151,457],{"mathvariant":322},[310,39153,313],{"stretchy":312},[47,39155,19255],{},[310,39157,332],{"stretchy":312},[310,39159,332],{"stretchy":312},[54,39161,39162],{"encoding":56},"\\mathrm{LayerNorm}(x + \\mathrm{Sublayer}(x))",[25,39164,39166,39194],{"className":39165,"ariaHidden":62},[61],[25,39167,39169,39172,39179,39182,39185,39188,39191],{"className":39168},[66],[25,39170],{"className":39171,"style":345},[70],[25,39173,39175],{"className":39174},[75],[25,39176,39178],{"className":39177},[75,28663],"LayerNorm",[25,39180,313],{"className":39181},[352],[25,39183,19255],{"className":39184},[75,79],[25,39186],{"className":39187,"style":3226},[701],[25,39189,914],{"className":39190},[989],[25,39192],{"className":39193,"style":3226},[701],[25,39195,39197,39200,39207,39210,39213],{"className":39196},[66],[25,39198],{"className":39199,"style":345},[70],[25,39201,39203],{"className":39202},[75],[25,39204,39206],{"className":39205},[75,28663],"Sublayer",[25,39208,313],{"className":39209},[352],[25,39211,19255],{"className":39212},[75,79],[25,39214,7486],{"className":39215},[439],[25,39217,39219,39255],{"className":39218},[28],[25,39220,39222],{"className":39221},[32],[34,39223,39224],{"xmlns":36},[38,39225,39226,39252],{},[41,39227,39228,39246,39248,39250],{},[41,39229,39230,39232,39234,39236,39238,39240,39242,39244],{},[47,39231,1401],{"mathvariant":322},[47,39233,34221],{"mathvariant":322},[47,39235,15500],{"mathvariant":322},[47,39237,29611],{"mathvariant":322},[47,39239,49],{"mathvariant":322},[47,39241,39115],{"mathvariant":322},[47,39243,32141],{"mathvariant":322},[47,39245,457],{"mathvariant":322},[310,39247,313],{"stretchy":312},[47,39249,19255],{},[310,39251,332],{"stretchy":312},[54,39253,39254],{"encoding":56},"\\mathrm{Sublayer}(x)",[25,39256,39258],{"className":39257,"ariaHidden":62},[61],[25,39259,39261,39264,39270,39273,39276],{"className":39260},[66],[25,39262],{"className":39263,"style":345},[70],[25,39265,39267],{"className":39266},[75],[25,39268,39206],{"className":39269},[75,28663],[25,39271,313],{"className":39272},[352],[25,39274,19255],{"className":39275},[75,79],[25,39277,332],{"className":39278},[439]," 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。",[33716,39281,39283],{"className":33718,"code":39282,"language":33720,"meta":31408,"style":31408},"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",[33722,39284,39285,39302,39307,39334,39353,39363,39375,39379,39400],{"__ignoreMap":31408},[25,39286,39287,39289,39292,39294,39296,39298,39300],{"class":33726,"line":33727},[25,39288,33953],{"class":33730},[25,39290,39291],{"class":33956}," AddNorm",[25,39293,313],{"class":33738},[25,39295,33963],{"class":33962},[25,39297,32214],{"class":33738},[25,39299,33968],{"class":33962},[25,39301,33751],{"class":33738},[25,39303,39304],{"class":33726,"line":31409},[25,39305,39306],{"class":33756},"    \"\"\"残差连接后进行层规范化\"\"\"\n",[25,39308,39309,39311,39313,39315,39317,39319,39322,39324,39326,39328,39330,39332],{"class":33726,"line":31417},[25,39310,33980],{"class":33730},[25,39312,33983],{"class":33778},[25,39314,313],{"class":33738},[25,39316,33989],{"class":33988},[25,39318,33745],{"class":33738},[25,39320,39321],{"class":33741},"normalized_shape",[25,39323,33745],{"class":33738},[25,39325,33994],{"class":33741},[25,39327,33745],{"class":33738},[25,39329,33999],{"class":33730},[25,39331,34002],{"class":33741},[25,39333,33751],{"class":33738},[25,39335,39336,39338,39341,39343,39345,39347,39349,39351],{"class":33726,"line":33766},[25,39337,34010],{"class":34009},[25,39339,39340],{"class":33738},"(AddNorm, ",[25,39342,33989],{"class":34016},[25,39344,34019],{"class":33738},[25,39346,34022],{"class":33778},[25,39348,313],{"class":33738},[25,39350,33999],{"class":33730},[25,39352,34029],{"class":33738},[25,39354,39355,39357,39359,39361],{"class":33726,"line":33785},[25,39356,34034],{"class":34016},[25,39358,34037],{"class":33738},[25,39360,919],{"class":33730},[25,39362,34042],{"class":33738},[25,39364,39365,39367,39370,39372],{"class":33726,"line":33806},[25,39366,34034],{"class":34016},[25,39368,39369],{"class":33738},".ln ",[25,39371,919],{"class":33730},[25,39373,39374],{"class":33738}," nn.LayerNorm(normalized_shape)\n",[25,39376,39377],{"class":33726,"line":33814},[25,39378,34047],{"emptyLinePlaceholder":31433},[25,39380,39381,39383,39385,39387,39389,39391,39393,39395,39398],{"class":33726,"line":33825},[25,39382,33980],{"class":33730},[25,39384,34074],{"class":33734},[25,39386,313],{"class":33738},[25,39388,33989],{"class":33988},[25,39390,33745],{"class":33738},[25,39392,33742],{"class":33741},[25,39394,33745],{"class":33738},[25,39396,39397],{"class":33741},"Y",[25,39399,33751],{"class":33738},[25,39401,39402,39404,39406,39409,39411,39414,39416],{"class":33726,"line":33842},[25,39403,33788],{"class":33730},[25,39405,36530],{"class":34016},[25,39407,39408],{"class":33738},".ln(",[25,39410,33989],{"class":34016},[25,39412,39413],{"class":33738},".dropout(Y) ",[25,39415,914],{"class":33730},[25,39417,39418],{"class":33738}," X)\n",[11,39420,39421],{"id":39421},"编码器-解码器架构",[15,39423,39424,39425,39575,39576,39752,39753,39782,39783,39933],{},"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 ",[25,39426,39428,39462],{"className":39427},[28],[25,39429,39431],{"className":39430},[32],[34,39432,39433],{"xmlns":36},[38,39434,39435,39459],{},[41,39436,39437,39439,39445,39447,39449,39451,39457],{},[310,39438,313],{"stretchy":312},[44,39440,39441,39443],{},[47,39442,19255],{},[597,39444,617],{},[310,39446,602],{"separator":62},[310,39448,628],{},[310,39450,602],{"separator":62},[44,39452,39453,39455],{},[47,39454,19255],{},[47,39456,2121],{},[310,39458,332],{"stretchy":312},[54,39460,39461],{"encoding":56},"(x_1, \\ldots, x_n)",[25,39463,39465],{"className":39464,"ariaHidden":62},[61],[25,39466,39468,39471,39474,39514,39517,39520,39523,39526,39529,39532,39572],{"className":39467},[66],[25,39469],{"className":39470,"style":345},[70],[25,39472,313],{"className":39473},[352],[25,39475,39477,39480],{"className":39476},[75],[25,39478,19255],{"className":39479},[75,79],[25,39481,39483],{"className":39482},[83],[25,39484,39486,39506],{"className":39485},[87,88],[25,39487,39489,39503],{"className":39488},[92],[25,39490,39492],{"className":39491,"style":671},[96],[25,39493,39494,39497],{"style":100},[25,39495],{"className":39496,"style":105},[104],[25,39498,39500],{"className":39499},[109,110,111,112],[25,39501,617],{"className":39502},[75,112],[25,39504,120],{"className":39505},[119],[25,39507,39509],{"className":39508},[92],[25,39510,39512],{"className":39511,"style":127},[96],[25,39513],{},[25,39515,602],{"className":39516},[697],[25,39518],{"className":39519,"style":702},[701],[25,39521,628],{"className":39522},[841],[25,39524],{"className":39525,"style":702},[701],[25,39527,602],{"className":39528},[697],[25,39530],{"className":39531,"style":702},[701],[25,39533,39535,39538],{"className":39534},[75],[25,39536,19255],{"className":39537},[75,79],[25,39539,39541],{"className":39540},[83],[25,39542,39544,39564],{"className":39543},[87,88],[25,39545,39547,39561],{"className":39546},[92],[25,39548,39550],{"className":39549,"style":20778},[96],[25,39551,39552,39555],{"style":100},[25,39553],{"className":39554,"style":105},[104],[25,39556,39558],{"className":39557},[109,110,111,112],[25,39559,2121],{"className":39560},[75,79,112],[25,39562,120],{"className":39563},[119],[25,39565,39567],{"className":39566},[92],[25,39568,39570],{"className":39569,"style":127},[96],[25,39571],{},[25,39573,332],{"className":39574},[439]," 映射为连续表示序列 ",[25,39577,39579,39618],{"className":39578},[28],[25,39580,39582],{"className":39581},[32],[34,39583,39584],{"xmlns":36},[38,39585,39586,39615],{},[41,39587,39588,39591,39593,39595,39601,39603,39605,39607,39613],{},[47,39589,39590],{"mathvariant":36688},"z",[310,39592,919],{},[310,39594,313],{"stretchy":312},[44,39596,39597,39599],{},[47,39598,39590],{},[597,39600,617],{},[310,39602,602],{"separator":62},[310,39604,628],{},[310,39606,602],{"separator":62},[44,39608,39609,39611],{},[47,39610,39590],{},[47,39612,2121],{},[310,39614,332],{"stretchy":312},[54,39616,39617],{"encoding":56},"\\mathbf{z} = (z_1, \\ldots, z_n)",[25,39619,39621,39640],{"className":39620,"ariaHidden":62},[61],[25,39622,39624,39628,39631,39634,39637],{"className":39623},[66],[25,39625],{"className":39626,"style":39627},[70],"height:0.4444em;",[25,39629,39590],{"className":39630},[75,36733],[25,39632],{"className":39633,"style":1008},[701],[25,39635,919],{"className":39636},[1012],[25,39638],{"className":39639,"style":1008},[701],[25,39641,39643,39646,39649,39691,39694,39697,39700,39703,39706,39709,39749],{"className":39642},[66],[25,39644],{"className":39645,"style":345},[70],[25,39647,313],{"className":39648},[352],[25,39650,39652,39656],{"className":39651},[75],[25,39653,39590],{"className":39654,"style":39655},[75,79],"margin-right:0.04398em;",[25,39657,39659],{"className":39658},[83],[25,39660,39662,39683],{"className":39661},[87,88],[25,39663,39665,39680],{"className":39664},[92],[25,39666,39668],{"className":39667,"style":671},[96],[25,39669,39671,39674],{"style":39670},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[25,39672],{"className":39673,"style":105},[104],[25,39675,39677],{"className":39676},[109,110,111,112],[25,39678,617],{"className":39679},[75,112],[25,39681,120],{"className":39682},[119],[25,39684,39686],{"className":39685},[92],[25,39687,39689],{"className":39688,"style":127},[96],[25,39690],{},[25,39692,602],{"className":39693},[697],[25,39695],{"className":39696,"style":702},[701],[25,39698,628],{"className":39699},[841],[25,39701],{"className":39702,"style":702},[701],[25,39704,602],{"className":39705},[697],[25,39707],{"className":39708,"style":702},[701],[25,39710,39712,39715],{"className":39711},[75],[25,39713,39590],{"className":39714,"style":39655},[75,79],[25,39716,39718],{"className":39717},[83],[25,39719,39721,39741],{"className":39720},[87,88],[25,39722,39724,39738],{"className":39723},[92],[25,39725,39727],{"className":39726,"style":20778},[96],[25,39728,39729,39732],{"style":39670},[25,39730],{"className":39731,"style":105},[104],[25,39733,39735],{"className":39734},[109,110,111,112],[25,39736,2121],{"className":39737},[75,79,112],[25,39739,120],{"className":39740},[119],[25,39742,39744],{"className":39743},[92],[25,39745,39747],{"className":39746,"style":127},[96],[25,39748],{},[25,39750,332],{"className":39751},[439],"。给定 ",[25,39754,39756,39770],{"className":39755},[28],[25,39757,39759],{"className":39758},[32],[34,39760,39761],{"xmlns":36},[38,39762,39763,39767],{},[41,39764,39765],{},[47,39766,39590],{"mathvariant":36688},[54,39768,39769],{"encoding":56},"\\mathbf{z}",[25,39771,39773],{"className":39772,"ariaHidden":62},[61],[25,39774,39776,39779],{"className":39775},[66],[25,39777],{"className":39778,"style":39627},[70],[25,39780,39590],{"className":39781},[75,36733],"，解码器随后一次生成一个元素的输出符号序列 ",[25,39784,39786,39820],{"className":39785},[28],[25,39787,39789],{"className":39788},[32],[34,39790,39791],{"xmlns":36},[38,39792,39793,39817],{},[41,39794,39795,39797,39803,39805,39807,39809,39815],{},[310,39796,313],{"stretchy":312},[44,39798,39799,39801],{},[47,39800,39115],{},[597,39802,617],{},[310,39804,602],{"separator":62},[310,39806,628],{},[310,39808,602],{"separator":62},[44,39810,39811,39813],{},[47,39812,39115],{},[47,39814,31744],{},[310,39816,332],{"stretchy":312},[54,39818,39819],{"encoding":56},"(y_1, \\ldots, y_m)",[25,39821,39823],{"className":39822,"ariaHidden":62},[61],[25,39824,39826,39829,39832,39872,39875,39878,39881,39884,39887,39890,39930],{"className":39825},[66],[25,39827],{"className":39828,"style":345},[70],[25,39830,313],{"className":39831},[352],[25,39833,39835,39838],{"className":39834},[75],[25,39836,39115],{"className":39837,"style":293},[75,79],[25,39839,39841],{"className":39840},[83],[25,39842,39844,39864],{"className":39843},[87,88],[25,39845,39847,39861],{"className":39846},[92],[25,39848,39850],{"className":39849,"style":671},[96],[25,39851,39852,39855],{"style":33361},[25,39853],{"className":39854,"style":105},[104],[25,39856,39858],{"className":39857},[109,110,111,112],[25,39859,617],{"className":39860},[75,112],[25,39862,120],{"className":39863},[119],[25,39865,39867],{"className":39866},[92],[25,39868,39870],{"className":39869,"style":127},[96],[25,39871],{},[25,39873,602],{"className":39874},[697],[25,39876],{"className":39877,"style":702},[701],[25,39879,628],{"className":39880},[841],[25,39882],{"className":39883,"style":702},[701],[25,39885,602],{"className":39886},[697],[25,39888],{"className":39889,"style":702},[701],[25,39891,39893,39896],{"className":39892},[75],[25,39894,39115],{"className":39895,"style":293},[75,79],[25,39897,39899],{"className":39898},[83],[25,39900,39902,39922],{"className":39901},[87,88],[25,39903,39905,39919],{"className":39904},[92],[25,39906,39908],{"className":39907,"style":20778},[96],[25,39909,39910,39913],{"style":33361},[25,39911],{"className":39912,"style":105},[104],[25,39914,39916],{"className":39915},[109,110,111,112],[25,39917,31744],{"className":39918},[75,79,112],[25,39920,120],{"className":39921},[119],[25,39923,39925],{"className":39924},[92],[25,39926,39928],{"className":39927,"style":127},[96],[25,39929],{},[25,39931,332],{"className":39932},[439],"。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。",[33716,39935,39937],{"className":33718,"code":39936,"language":33720,"meta":31408,"style":31408},"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",[33722,39938,39939,39956,39961,39979,39998,40002,40026,40034,40038,40055,40060,40078,40097,40101,40125,40131,40135,40156,40162,40166,40183,40188,40216,40235,40247,40259,40263,40291,40308,40324],{"__ignoreMap":31408},[25,39940,39941,39943,39946,39948,39950,39952,39954],{"class":33726,"line":33727},[25,39942,33953],{"class":33730},[25,39944,39945],{"class":33956}," Encoder",[25,39947,313],{"class":33738},[25,39949,33963],{"class":33962},[25,39951,32214],{"class":33738},[25,39953,33968],{"class":33962},[25,39955,33751],{"class":33738},[25,39957,39958],{"class":33726,"line":31409},[25,39959,39960],{"class":33756},"    \"\"\"编码器-解码器架构的基本编码器接口\"\"\"\n",[25,39962,39963,39965,39967,39969,39971,39973,39975,39977],{"class":33726,"line":31417},[25,39964,33980],{"class":33730},[25,39966,33983],{"class":33778},[25,39968,313],{"class":33738},[25,39970,33989],{"class":33988},[25,39972,33745],{"class":33738},[25,39974,33999],{"class":33730},[25,39976,34002],{"class":33741},[25,39978,33751],{"class":33738},[25,39980,39981,39983,39986,39988,39990,39992,39994,39996],{"class":33726,"line":33766},[25,39982,34010],{"class":34009},[25,39984,39985],{"class":33738},"(Encoder, ",[25,39987,33989],{"class":34016},[25,39989,34019],{"class":33738},[25,39991,34022],{"class":33778},[25,39993,313],{"class":33738},[25,39995,33999],{"class":33730},[25,39997,34029],{"class":33738},[25,39999,40000],{"class":33726,"line":33785},[25,40001,34047],{"emptyLinePlaceholder":31433},[25,40003,40004,40006,40008,40010,40012,40014,40016,40018,40021,40024],{"class":33726,"line":33806},[25,40005,33980],{"class":33730},[25,40007,34074],{"class":33734},[25,40009,313],{"class":33738},[25,40011,33989],{"class":33988},[25,40013,33745],{"class":33738},[25,40015,33742],{"class":33741},[25,40017,33745],{"class":33738},[25,40019,40020],{"class":33730},"*",[25,40022,40023],{"class":33741},"args",[25,40025,33751],{"class":33738},[25,40027,40028,40031],{"class":33726,"line":33814},[25,40029,40030],{"class":33730},"        raise",[25,40032,40033],{"class":34009}," NotImplementedError\n",[25,40035,40036],{"class":33726,"line":33825},[25,40037,34047],{"emptyLinePlaceholder":31433},[25,40039,40040,40042,40045,40047,40049,40051,40053],{"class":33726,"line":33842},[25,40041,33953],{"class":33730},[25,40043,40044],{"class":33956}," Decoder",[25,40046,313],{"class":33738},[25,40048,33963],{"class":33962},[25,40050,32214],{"class":33738},[25,40052,33968],{"class":33962},[25,40054,33751],{"class":33738},[25,40056,40057],{"class":33726,"line":33858},[25,40058,40059],{"class":33756},"    \"\"\"编码器-解码器架构的基本解码器接口\"\"\"\n",[25,40061,40062,40064,40066,40068,40070,40072,40074,40076],{"class":33726,"line":33866},[25,40063,33980],{"class":33730},[25,40065,33983],{"class":33778},[25,40067,313],{"class":33738},[25,40069,33989],{"class":33988},[25,40071,33745],{"class":33738},[25,40073,33999],{"class":33730},[25,40075,34002],{"class":33741},[25,40077,33751],{"class":33738},[25,40079,40080,40082,40085,40087,40089,40091,40093,40095],{"class":33726,"line":33883},[25,40081,34010],{"class":34009},[25,40083,40084],{"class":33738},"(Decoder, ",[25,40086,33989],{"class":34016},[25,40088,34019],{"class":33738},[25,40090,34022],{"class":33778},[25,40092,313],{"class":33738},[25,40094,33999],{"class":33730},[25,40096,34029],{"class":33738},[25,40098,40099],{"class":33726,"line":33889},[25,40100,34047],{"emptyLinePlaceholder":31433},[25,40102,40103,40105,40108,40110,40112,40114,40117,40119,40121,40123],{"class":33726,"line":33914},[25,40104,33980],{"class":33730},[25,40106,40107],{"class":33734}," init_state",[25,40109,313],{"class":33738},[25,40111,33989],{"class":33988},[25,40113,33745],{"class":33738},[25,40115,40116],{"class":33741},"enc_outputs",[25,40118,33745],{"class":33738},[25,40120,40020],{"class":33730},[25,40122,40023],{"class":33741},[25,40124,33751],{"class":33738},[25,40126,40127,40129],{"class":33726,"line":33927},[25,40128,40030],{"class":33730},[25,40130,40033],{"class":34009},[25,40132,40133],{"class":33726,"line":34166},[25,40134,34047],{"emptyLinePlaceholder":31433},[25,40136,40137,40139,40141,40143,40145,40147,40149,40151,40154],{"class":33726,"line":36091},[25,40138,33980],{"class":33730},[25,40140,34074],{"class":33734},[25,40142,313],{"class":33738},[25,40144,33989],{"class":33988},[25,40146,33745],{"class":33738},[25,40148,33742],{"class":33741},[25,40150,33745],{"class":33738},[25,40152,40153],{"class":33741},"state",[25,40155,33751],{"class":33738},[25,40157,40158,40160],{"class":33726,"line":36367},[25,40159,40030],{"class":33730},[25,40161,40033],{"class":34009},[25,40163,40164],{"class":33726,"line":36373},[25,40165,34047],{"emptyLinePlaceholder":31433},[25,40167,40168,40170,40173,40175,40177,40179,40181],{"class":33726,"line":36379},[25,40169,33953],{"class":33730},[25,40171,40172],{"class":33956}," EncoderDecoder",[25,40174,313],{"class":33738},[25,40176,33963],{"class":33962},[25,40178,32214],{"class":33738},[25,40180,33968],{"class":33962},[25,40182,33751],{"class":33738},[25,40184,40185],{"class":33726,"line":36385},[25,40186,40187],{"class":33756},"    \"\"\"编码器-解码器架构的基类\"\"\"\n",[25,40189,40190,40192,40194,40196,40198,40200,40203,40205,40208,40210,40212,40214],{"class":33726,"line":36406},[25,40191,33980],{"class":33730},[25,40193,33983],{"class":33778},[25,40195,313],{"class":33738},[25,40197,33989],{"class":33988},[25,40199,33745],{"class":33738},[25,40201,40202],{"class":33741},"encoder",[25,40204,33745],{"class":33738},[25,40206,40207],{"class":33741},"decoder",[25,40209,33745],{"class":33738},[25,40211,33999],{"class":33730},[25,40213,34002],{"class":33741},[25,40215,33751],{"class":33738},[25,40217,40218,40220,40223,40225,40227,40229,40231,40233],{"class":33726,"line":36425},[25,40219,34010],{"class":34009},[25,40221,40222],{"class":33738},"(EncoderDecoder, ",[25,40224,33989],{"class":34016},[25,40226,34019],{"class":33738},[25,40228,34022],{"class":33778},[25,40230,313],{"class":33738},[25,40232,33999],{"class":33730},[25,40234,34029],{"class":33738},[25,40236,40237,40239,40242,40244],{"class":33726,"line":36444},[25,40238,34034],{"class":34016},[25,40240,40241],{"class":33738},".encoder ",[25,40243,919],{"class":33730},[25,40245,40246],{"class":33738}," encoder\n",[25,40248,40249,40251,40254,40256],{"class":33726,"line":36449},[25,40250,34034],{"class":34016},[25,40252,40253],{"class":33738},".decoder ",[25,40255,919],{"class":33730},[25,40257,40258],{"class":33738}," decoder\n",[25,40260,40261],{"class":33726,"line":36465},[25,40262,34047],{"emptyLinePlaceholder":31433},[25,40264,40265,40267,40269,40271,40273,40275,40278,40280,40283,40285,40287,40289],{"class":33726,"line":36471},[25,40266,33980],{"class":33730},[25,40268,34074],{"class":33734},[25,40270,313],{"class":33738},[25,40272,33989],{"class":33988},[25,40274,33745],{"class":33738},[25,40276,40277],{"class":33741},"enc_X",[25,40279,33745],{"class":33738},[25,40281,40282],{"class":33741},"dec_X",[25,40284,33745],{"class":33738},[25,40286,40020],{"class":33730},[25,40288,40023],{"class":33741},[25,40290,33751],{"class":33738},[25,40292,40293,40296,40298,40300,40303,40305],{"class":33726,"line":36477},[25,40294,40295],{"class":33738},"        enc_outputs ",[25,40297,919],{"class":33730},[25,40299,36530],{"class":34016},[25,40301,40302],{"class":33738},".encoder(enc_X, ",[25,40304,40020],{"class":33730},[25,40306,40307],{"class":33738},"args)\n",[25,40309,40310,40313,40315,40317,40320,40322],{"class":33726,"line":36487},[25,40311,40312],{"class":33738},"        dec_state ",[25,40314,919],{"class":33730},[25,40316,36530],{"class":34016},[25,40318,40319],{"class":33738},".decoder.init_state(enc_outputs, ",[25,40321,40020],{"class":33730},[25,40323,40307],{"class":33738},[25,40325,40326,40328,40330],{"class":33726,"line":36511},[25,40327,33788],{"class":33730},[25,40329,36530],{"class":34016},[25,40331,40332],{"class":33738},".decoder(dec_X, dec_state)\n",[11,40334,40336],{"id":40335},"transformer-编码器","transformer 编码器",[15,40338,40339],{},"代码实现如下：",[33716,40341,40343],{"className":33718,"code":40342,"language":33720,"meta":31408,"style":31408},"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",[33722,40344,40345,40362,40367,40395,40414,40436,40455,40466,40471,40476,40488,40500,40505,40516,40520,40540,40557,40571,40575,40589,40594,40623,40643,40672,40691,40703,40715,40727,40739,40757,40782,40787,40792,40797,40801,40827,40832,40838,40844,40871,40899,40919,40930,40943],{"__ignoreMap":31408},[25,40346,40347,40349,40352,40354,40356,40358,40360],{"class":33726,"line":33727},[25,40348,33953],{"class":33730},[25,40350,40351],{"class":33956}," EncoderBlock",[25,40353,313],{"class":33738},[25,40355,33963],{"class":33962},[25,40357,32214],{"class":33738},[25,40359,33968],{"class":33962},[25,40361,33751],{"class":33738},[25,40363,40364],{"class":33726,"line":31409},[25,40365,40366],{"class":33756},"    \"\"\"Transformer编码器块\"\"\"\n",[25,40368,40369,40371,40373,40375,40377,40379,40381,40383,40385,40387,40389,40391,40393],{"class":33726,"line":31417},[25,40370,33980],{"class":33730},[25,40372,33983],{"class":33778},[25,40374,313],{"class":33738},[25,40376,33989],{"class":33988},[25,40378,33745],{"class":33738},[25,40380,36157],{"class":33741},[25,40382,33745],{"class":33738},[25,40384,36162],{"class":33741},[25,40386,33745],{"class":33738},[25,40388,36167],{"class":33741},[25,40390,33745],{"class":33738},[25,40392,36172],{"class":33741},[25,40394,35139],{"class":33738},[25,40396,40397,40400,40402,40404,40406,40408,40410,40412],{"class":33726,"line":33766},[25,40398,40399],{"class":33741},"                 norm_shape",[25,40401,33745],{"class":33738},[25,40403,38970],{"class":33741},[25,40405,33745],{"class":33738},[25,40407,38975],{"class":33741},[25,40409,33745],{"class":33738},[25,40411,35906],{"class":33741},[25,40413,35139],{"class":33738},[25,40415,40416,40419,40421,40424,40426,40428,40430,40432,40434],{"class":33726,"line":33785},[25,40417,40418],{"class":33741},"                 dropout",[25,40420,33745],{"class":33738},[25,40422,40423],{"class":33741},"use_bias",[25,40425,919],{"class":33730},[25,40427,36193],{"class":33778},[25,40429,33745],{"class":33738},[25,40431,33999],{"class":33730},[25,40433,34002],{"class":33741},[25,40435,33751],{"class":33738},[25,40437,40438,40440,40443,40445,40447,40449,40451,40453],{"class":33726,"line":33806},[25,40439,34010],{"class":34009},[25,40441,40442],{"class":33738},"(EncoderBlock, ",[25,40444,33989],{"class":34016},[25,40446,34019],{"class":33738},[25,40448,34022],{"class":33778},[25,40450,313],{"class":33738},[25,40452,33999],{"class":33730},[25,40454,34029],{"class":33738},[25,40456,40457,40459,40461,40463],{"class":33726,"line":33814},[25,40458,34034],{"class":34016},[25,40460,36239],{"class":33738},[25,40462,919],{"class":33730},[25,40464,40465],{"class":33738}," d2l.MultiHeadAttention(\n",[25,40467,40468],{"class":33726,"line":33825},[25,40469,40470],{"class":33738},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout,\n",[25,40472,40473],{"class":33726,"line":33842},[25,40474,40475],{"class":33738},"            use_bias)\n",[25,40477,40478,40480,40483,40485],{"class":33726,"line":33858},[25,40479,34034],{"class":34016},[25,40481,40482],{"class":33738},".addnorm1 ",[25,40484,919],{"class":33730},[25,40486,40487],{"class":33738}," AddNorm(norm_shape, dropout)\n",[25,40489,40490,40492,40495,40497],{"class":33726,"line":33866},[25,40491,34034],{"class":34016},[25,40493,40494],{"class":33738},".ffn ",[25,40496,919],{"class":33730},[25,40498,40499],{"class":33738}," PositionWiseFFN(\n",[25,40501,40502],{"class":33726,"line":33883},[25,40503,40504],{"class":33738},"            ffn_num_input, ffn_num_hiddens, num_hiddens)\n",[25,40506,40507,40509,40512,40514],{"class":33726,"line":33889},[25,40508,34034],{"class":34016},[25,40510,40511],{"class":33738},".addnorm2 ",[25,40513,919],{"class":33730},[25,40515,40487],{"class":33738},[25,40517,40518],{"class":33726,"line":33914},[25,40519,34047],{"emptyLinePlaceholder":31433},[25,40521,40522,40524,40526,40528,40530,40532,40534,40536,40538],{"class":33726,"line":33927},[25,40523,33980],{"class":33730},[25,40525,34074],{"class":33734},[25,40527,313],{"class":33738},[25,40529,33989],{"class":33988},[25,40531,33745],{"class":33738},[25,40533,33742],{"class":33741},[25,40535,33745],{"class":33738},[25,40537,33748],{"class":33741},[25,40539,33751],{"class":33738},[25,40541,40542,40545,40547,40549,40552,40554],{"class":33726,"line":34166},[25,40543,40544],{"class":33738},"        Y ",[25,40546,919],{"class":33730},[25,40548,36530],{"class":34016},[25,40550,40551],{"class":33738},".addnorm1(X, ",[25,40553,33989],{"class":34016},[25,40555,40556],{"class":33738},".attention(X, X, X, valid_lens))\n",[25,40558,40559,40561,40563,40566,40568],{"class":33726,"line":36091},[25,40560,33788],{"class":33730},[25,40562,36530],{"class":34016},[25,40564,40565],{"class":33738},".addnorm2(Y, ",[25,40567,33989],{"class":34016},[25,40569,40570],{"class":33738},".ffn(Y))\n",[25,40572,40573],{"class":33726,"line":36367},[25,40574,34047],{"emptyLinePlaceholder":31433},[25,40576,40577,40579,40582,40584,40587],{"class":33726,"line":36373},[25,40578,33953],{"class":33730},[25,40580,40581],{"class":33956}," TransformerEncoder",[25,40583,313],{"class":33738},[25,40585,40586],{"class":33962},"Encoder",[25,40588,33751],{"class":33738},[25,40590,40591],{"class":33726,"line":36379},[25,40592,40593],{"class":33756},"    \"\"\"Transformer编码器\"\"\"\n",[25,40595,40596,40598,40600,40602,40604,40606,40609,40611,40613,40615,40617,40619,40621],{"class":33726,"line":36385},[25,40597,33980],{"class":33730},[25,40599,33983],{"class":33778},[25,40601,313],{"class":33738},[25,40603,33989],{"class":33988},[25,40605,33745],{"class":33738},[25,40607,40608],{"class":33741},"vocab_size",[25,40610,33745],{"class":33738},[25,40612,36157],{"class":33741},[25,40614,33745],{"class":33738},[25,40616,36162],{"class":33741},[25,40618,33745],{"class":33738},[25,40620,36167],{"class":33741},[25,40622,35139],{"class":33738},[25,40624,40625,40628,40630,40633,40635,40637,40639,40641],{"class":33726,"line":36406},[25,40626,40627],{"class":33741},"                 num_hiddens",[25,40629,33745],{"class":33738},[25,40631,40632],{"class":33741},"norm_shape",[25,40634,33745],{"class":33738},[25,40636,38970],{"class":33741},[25,40638,33745],{"class":33738},[25,40640,38975],{"class":33741},[25,40642,35139],{"class":33738},[25,40644,40645,40647,40649,40652,40654,40656,40658,40660,40662,40664,40666,40668,40670],{"class":33726,"line":36425},[25,40646,36179],{"class":33741},[25,40648,33745],{"class":33738},[25,40650,40651],{"class":33741},"num_layers",[25,40653,33745],{"class":33738},[25,40655,33994],{"class":33741},[25,40657,33745],{"class":33738},[25,40659,40423],{"class":33741},[25,40661,919],{"class":33730},[25,40663,36193],{"class":33778},[25,40665,33745],{"class":33738},[25,40667,33999],{"class":33730},[25,40669,34002],{"class":33741},[25,40671,33751],{"class":33738},[25,40673,40674,40676,40679,40681,40683,40685,40687,40689],{"class":33726,"line":36444},[25,40675,34010],{"class":34009},[25,40677,40678],{"class":33738},"(TransformerEncoder, ",[25,40680,33989],{"class":34016},[25,40682,34019],{"class":33738},[25,40684,34022],{"class":33778},[25,40686,313],{"class":33738},[25,40688,33999],{"class":33730},[25,40690,34029],{"class":33738},[25,40692,40693,40695,40698,40700],{"class":33726,"line":36449},[25,40694,34034],{"class":34016},[25,40696,40697],{"class":33738},".num_hiddens ",[25,40699,919],{"class":33730},[25,40701,40702],{"class":33738}," num_hiddens\n",[25,40704,40705,40707,40710,40712],{"class":33726,"line":36465},[25,40706,34034],{"class":34016},[25,40708,40709],{"class":33738},".embedding ",[25,40711,919],{"class":33730},[25,40713,40714],{"class":33738}," nn.Embedding(vocab_size, num_hiddens)\n",[25,40716,40717,40719,40722,40724],{"class":33726,"line":36471},[25,40718,34034],{"class":34016},[25,40720,40721],{"class":33738},".pos_encoding ",[25,40723,919],{"class":33730},[25,40725,40726],{"class":33738}," PositionalEncoding(num_hiddens, dropout)\n",[25,40728,40729,40731,40734,40736],{"class":33726,"line":36477},[25,40730,34034],{"class":34016},[25,40732,40733],{"class":33738},".blks ",[25,40735,919],{"class":33730},[25,40737,40738],{"class":33738}," nn.Sequential()\n",[25,40740,40741,40744,40747,40750,40754],{"class":33726,"line":36487},[25,40742,40743],{"class":33730},"        for",[25,40745,40746],{"class":33738}," i ",[25,40748,40749],{"class":33730},"in",[25,40751,40753],{"class":40752},"sDgm9"," range",[25,40755,40756],{"class":33738},"(num_layers):\n",[25,40758,40759,40762,40765,40769,40772,40774,40776,40779],{"class":33726,"line":36511},[25,40760,40761],{"class":34016},"            self",[25,40763,40764],{"class":33738},".blks.add_module(",[25,40766,40768],{"class":40767},"sMWOi","\"",[25,40770,1786],{"class":40771},"sEzAm",[25,40773,40768],{"class":40767},[25,40775,914],{"class":33730},[25,40777,40778],{"class":34009},"str",[25,40780,40781],{"class":33738},"(i),\n",[25,40783,40784],{"class":33726,"line":36516},[25,40785,40786],{"class":33738},"                EncoderBlock(key_size, query_size, value_size, num_hiddens,\n",[25,40788,40789],{"class":33726,"line":36522},[25,40790,40791],{"class":33738},"                             norm_shape, ffn_num_input, ffn_num_hiddens,\n",[25,40793,40794],{"class":33726,"line":36536},[25,40795,40796],{"class":33738},"                             num_heads, dropout, use_bias))\n",[25,40798,40799],{"class":33726,"line":36541},[25,40800,34047],{"emptyLinePlaceholder":31433},[25,40802,40803,40805,40807,40809,40811,40813,40815,40817,40819,40821,40823,40825],{"class":33726,"line":36547},[25,40804,33980],{"class":33730},[25,40806,34074],{"class":33734},[25,40808,313],{"class":33738},[25,40810,33989],{"class":33988},[25,40812,33745],{"class":33738},[25,40814,33742],{"class":33741},[25,40816,33745],{"class":33738},[25,40818,33748],{"class":33741},[25,40820,33745],{"class":33738},[25,40822,40020],{"class":33730},[25,40824,40023],{"class":33741},[25,40826,33751],{"class":33738},[25,40828,40829],{"class":33726,"line":36562},[25,40830,40831],{"class":33762},"        # 因为位置编码值在-1和1之间，\n",[25,40833,40835],{"class":33726,"line":40834},37,[25,40836,40837],{"class":33762},"        # 因此嵌入值乘以嵌入维度的平方根进行缩放，\n",[25,40839,40841],{"class":33726,"line":40840},38,[25,40842,40843],{"class":33762},"        # 然后再与位置编码相加。\n",[25,40845,40847,40849,40851,40853,40856,40858,40861,40863,40866,40868],{"class":33726,"line":40846},39,[25,40848,33892],{"class":33738},[25,40850,919],{"class":33730},[25,40852,36530],{"class":34016},[25,40854,40855],{"class":33738},".pos_encoding(",[25,40857,33989],{"class":34016},[25,40859,40860],{"class":33738},".embedding(X) ",[25,40862,40020],{"class":33730},[25,40864,40865],{"class":33738}," math.sqrt(",[25,40867,33989],{"class":34016},[25,40869,40870],{"class":33738},".num_hiddens))\n",[25,40872,40874,40876,40878,40880,40883,40885,40887,40889,40892,40894,40896],{"class":33726,"line":40873},40,[25,40875,34034],{"class":34016},[25,40877,34158],{"class":33738},[25,40879,919],{"class":33730},[25,40881,40882],{"class":33738}," [",[25,40884,34102],{"class":33778},[25,40886,38500],{"class":33738},[25,40888,40020],{"class":33730},[25,40890,40891],{"class":40752}," len",[25,40893,313],{"class":33738},[25,40895,33989],{"class":34016},[25,40897,40898],{"class":33738},".blks)\n",[25,40900,40902,40904,40907,40909,40912,40914,40916],{"class":33726,"line":40901},41,[25,40903,40743],{"class":33730},[25,40905,40906],{"class":33738}," i, blk ",[25,40908,40749],{"class":33730},[25,40910,40911],{"class":40752}," enumerate",[25,40913,313],{"class":33738},[25,40915,33989],{"class":34016},[25,40917,40918],{"class":33738},".blks):\n",[25,40920,40922,40925,40927],{"class":33726,"line":40921},42,[25,40923,40924],{"class":33738},"            X ",[25,40926,919],{"class":33730},[25,40928,40929],{"class":33738}," blk(X, valid_lens)\n",[25,40931,40933,40935,40938,40940],{"class":33726,"line":40932},43,[25,40934,40761],{"class":34016},[25,40936,40937],{"class":33738},".attention_weights[i] ",[25,40939,919],{"class":33730},[25,40941,40942],{"class":33738}," blk.attention.attention.attention_weights\n",[25,40944,40946,40948],{"class":33726,"line":40945},44,[25,40947,33788],{"class":33730},[25,40949,40950],{"class":33738}," X\n",[11,40952,40954],{"id":40953},"transformer-解码器","transformer 解码器",[15,40956,40957],{},"代码如下：",[33716,40959,40961],{"className":33718,"code":40960,"language":33720,"meta":31408,"style":31408},"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",[33722,40962,40963,40980,40985,41013,41031,41047,41066,41078,41089,41094,41104,41115,41119,41129,41140,41145,41156,41160,41180,41199,41204,41209,41214,41219,41241,41250,41256,41283,41301,41310,41319,41324,41329,41339,41365,41371,41380,41384,41389,41401,41412,41417,41422,41434,41446,41461,41466,41481,41510,41529,41550,41570,41581,41594,41605,41616,41627,41640,41659,41665,41670,41676,41689,41694,41722,41741,41746,41767,41790,41836,41853,41864,41870,41888,41894,41910,41920,41925,41934,41948],{"__ignoreMap":31408},[25,40964,40965,40967,40970,40972,40974,40976,40978],{"class":33726,"line":33727},[25,40966,33953],{"class":33730},[25,40968,40969],{"class":33956}," DecoderBlock",[25,40971,313],{"class":33738},[25,40973,33963],{"class":33962},[25,40975,32214],{"class":33738},[25,40977,33968],{"class":33962},[25,40979,33751],{"class":33738},[25,40981,40982],{"class":33726,"line":31409},[25,40983,40984],{"class":33756},"    \"\"\"解码器中第i个块\"\"\"\n",[25,40986,40987,40989,40991,40993,40995,40997,40999,41001,41003,41005,41007,41009,41011],{"class":33726,"line":31417},[25,40988,33980],{"class":33730},[25,40990,33983],{"class":33778},[25,40992,313],{"class":33738},[25,40994,33989],{"class":33988},[25,40996,33745],{"class":33738},[25,40998,36157],{"class":33741},[25,41000,33745],{"class":33738},[25,41002,36162],{"class":33741},[25,41004,33745],{"class":33738},[25,41006,36167],{"class":33741},[25,41008,33745],{"class":33738},[25,41010,36172],{"class":33741},[25,41012,35139],{"class":33738},[25,41014,41015,41017,41019,41021,41023,41025,41027,41029],{"class":33726,"line":33766},[25,41016,40399],{"class":33741},[25,41018,33745],{"class":33738},[25,41020,38970],{"class":33741},[25,41022,33745],{"class":33738},[25,41024,38975],{"class":33741},[25,41026,33745],{"class":33738},[25,41028,35906],{"class":33741},[25,41030,35139],{"class":33738},[25,41032,41033,41035,41037,41039,41041,41043,41045],{"class":33726,"line":33785},[25,41034,40418],{"class":33741},[25,41036,33745],{"class":33738},[25,41038,29614],{"class":33741},[25,41040,33745],{"class":33738},[25,41042,33999],{"class":33730},[25,41044,34002],{"class":33741},[25,41046,33751],{"class":33738},[25,41048,41049,41051,41054,41056,41058,41060,41062,41064],{"class":33726,"line":33806},[25,41050,34010],{"class":34009},[25,41052,41053],{"class":33738},"(DecoderBlock, ",[25,41055,33989],{"class":34016},[25,41057,34019],{"class":33738},[25,41059,34022],{"class":33778},[25,41061,313],{"class":33738},[25,41063,33999],{"class":33730},[25,41065,34029],{"class":33738},[25,41067,41068,41070,41073,41075],{"class":33726,"line":33814},[25,41069,34034],{"class":34016},[25,41071,41072],{"class":33738},".i ",[25,41074,919],{"class":33730},[25,41076,41077],{"class":33738}," i\n",[25,41079,41080,41082,41085,41087],{"class":33726,"line":33825},[25,41081,34034],{"class":34016},[25,41083,41084],{"class":33738},".attention1 ",[25,41086,919],{"class":33730},[25,41088,40465],{"class":33738},[25,41090,41091],{"class":33726,"line":33842},[25,41092,41093],{"class":33738},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n",[25,41095,41096,41098,41100,41102],{"class":33726,"line":33858},[25,41097,34034],{"class":34016},[25,41099,40482],{"class":33738},[25,41101,919],{"class":33730},[25,41103,40487],{"class":33738},[25,41105,41106,41108,41111,41113],{"class":33726,"line":33866},[25,41107,34034],{"class":34016},[25,41109,41110],{"class":33738},".attention2 ",[25,41112,919],{"class":33730},[25,41114,40465],{"class":33738},[25,41116,41117],{"class":33726,"line":33883},[25,41118,41093],{"class":33738},[25,41120,41121,41123,41125,41127],{"class":33726,"line":33889},[25,41122,34034],{"class":34016},[25,41124,40511],{"class":33738},[25,41126,919],{"class":33730},[25,41128,40487],{"class":33738},[25,41130,41131,41133,41135,41137],{"class":33726,"line":33914},[25,41132,34034],{"class":34016},[25,41134,40494],{"class":33738},[25,41136,919],{"class":33730},[25,41138,41139],{"class":33738}," PositionWiseFFN(ffn_num_input, ffn_num_hiddens,\n",[25,41141,41142],{"class":33726,"line":33927},[25,41143,41144],{"class":33738},"                                   num_hiddens)\n",[25,41146,41147,41149,41152,41154],{"class":33726,"line":34166},[25,41148,34034],{"class":34016},[25,41150,41151],{"class":33738},".addnorm3 ",[25,41153,919],{"class":33730},[25,41155,40487],{"class":33738},[25,41157,41158],{"class":33726,"line":36091},[25,41159,34047],{"emptyLinePlaceholder":31433},[25,41161,41162,41164,41166,41168,41170,41172,41174,41176,41178],{"class":33726,"line":36367},[25,41163,33980],{"class":33730},[25,41165,34074],{"class":33734},[25,41167,313],{"class":33738},[25,41169,33989],{"class":33988},[25,41171,33745],{"class":33738},[25,41173,33742],{"class":33741},[25,41175,33745],{"class":33738},[25,41177,40153],{"class":33741},[25,41179,33751],{"class":33738},[25,41181,41182,41185,41187,41190,41192,41195,41197],{"class":33726,"line":36373},[25,41183,41184],{"class":33738},"        enc_outputs, enc_valid_lens ",[25,41186,919],{"class":33730},[25,41188,41189],{"class":33738}," state[",[25,41191,599],{"class":33778},[25,41193,41194],{"class":33738},"], state[",[25,41196,617],{"class":33778},[25,41198,34121],{"class":33738},[25,41200,41201],{"class":33726,"line":36379},[25,41202,41203],{"class":33762},"        # 训练阶段，输出序列的所有词元都在同一时间处理，\n",[25,41205,41206],{"class":33726,"line":36385},[25,41207,41208],{"class":33762},"        # 因此state[2][self.i]初始化为None。\n",[25,41210,41211],{"class":33726,"line":36406},[25,41212,41213],{"class":33762},"        # 预测阶段，输出序列是通过词元一个接着一个解码的，\n",[25,41215,41216],{"class":33726,"line":36425},[25,41217,41218],{"class":33762},"        # 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",[25,41220,41221,41223,41225,41227,41230,41232,41235,41237,41239],{"class":33726,"line":36444},[25,41222,33828],{"class":33730},[25,41224,41189],{"class":33738},[25,41226,9242],{"class":33778},[25,41228,41229],{"class":33738},"][",[25,41231,33989],{"class":34016},[25,41233,41234],{"class":33738},".i] ",[25,41236,33775],{"class":33730},[25,41238,33779],{"class":33778},[25,41240,33782],{"class":33738},[25,41242,41243,41246,41248],{"class":33726,"line":36449},[25,41244,41245],{"class":33738},"            key_values ",[25,41247,919],{"class":33730},[25,41249,40950],{"class":33738},[25,41251,41252,41254],{"class":33726,"line":36465},[25,41253,33861],{"class":33730},[25,41255,33782],{"class":33738},[25,41257,41258,41260,41262,41265,41267,41269,41271,41274,41277,41279,41281],{"class":33726,"line":36471},[25,41259,41245],{"class":33738},[25,41261,919],{"class":33730},[25,41263,41264],{"class":33738}," torch.cat((state[",[25,41266,9242],{"class":33778},[25,41268,41229],{"class":33738},[25,41270,33989],{"class":34016},[25,41272,41273],{"class":33738},".i], X), ",[25,41275,41276],{"class":33794},"axis",[25,41278,919],{"class":33730},[25,41280,617],{"class":33778},[25,41282,33803],{"class":33738},[25,41284,41285,41288,41290,41292,41294,41296,41298],{"class":33726,"line":36477},[25,41286,41287],{"class":33738},"        state[",[25,41289,9242],{"class":33778},[25,41291,41229],{"class":33738},[25,41293,33989],{"class":34016},[25,41295,41234],{"class":33738},[25,41297,919],{"class":33730},[25,41299,41300],{"class":33738}," key_values\n",[25,41302,41303,41305,41307],{"class":33726,"line":36487},[25,41304,33828],{"class":33730},[25,41306,36530],{"class":34016},[25,41308,41309],{"class":33738},".training:\n",[25,41311,41312,41315,41317],{"class":33726,"line":36511},[25,41313,41314],{"class":33738},"            batch_size, num_steps, _ ",[25,41316,919],{"class":33730},[25,41318,33822],{"class":33738},[25,41320,41321],{"class":33726,"line":36516},[25,41322,41323],{"class":33762},"            # dec_valid_lens的开头:(batch_size,num_steps),\n",[25,41325,41326],{"class":33726,"line":36522},[25,41327,41328],{"class":33762},"            # 其中每一行是[1,2,...,num_steps]\n",[25,41330,41331,41334,41336],{"class":33726,"line":36536},[25,41332,41333],{"class":33738},"            dec_valid_lens ",[25,41335,919],{"class":33730},[25,41337,41338],{"class":33738}," torch.arange(\n",[25,41340,41341,41344,41347,41349,41351,41353,41356,41358,41361,41363],{"class":33726,"line":36541},[25,41342,41343],{"class":33778},"                1",[25,41345,41346],{"class":33738},", num_steps ",[25,41348,914],{"class":33730},[25,41350,33837],{"class":33778},[25,41352,33745],{"class":33738},[25,41354,41355],{"class":33794},"device",[25,41357,919],{"class":33730},[25,41359,41360],{"class":33738},"X.device).repeat(batch_size, ",[25,41362,617],{"class":33778},[25,41364,33803],{"class":33738},[25,41366,41367,41369],{"class":33726,"line":36547},[25,41368,33861],{"class":33730},[25,41370,33782],{"class":33738},[25,41372,41373,41375,41377],{"class":33726,"line":36562},[25,41374,41333],{"class":33738},[25,41376,919],{"class":33730},[25,41378,41379],{"class":33778}," None\n",[25,41381,41382],{"class":33726,"line":40834},[25,41383,34047],{"emptyLinePlaceholder":31433},[25,41385,41386],{"class":33726,"line":40840},[25,41387,41388],{"class":33762},"        # 自注意力\n",[25,41390,41391,41394,41396,41398],{"class":33726,"line":40846},[25,41392,41393],{"class":33738},"        X2 ",[25,41395,919],{"class":33730},[25,41397,36530],{"class":34016},[25,41399,41400],{"class":33738},".attention1(X, key_values, key_values, dec_valid_lens)\n",[25,41402,41403,41405,41407,41409],{"class":33726,"line":40873},[25,41404,40544],{"class":33738},[25,41406,919],{"class":33730},[25,41408,36530],{"class":34016},[25,41410,41411],{"class":33738},".addnorm1(X, X2)\n",[25,41413,41414],{"class":33726,"line":40901},[25,41415,41416],{"class":33762},"        # 编码器－解码器注意力。\n",[25,41418,41419],{"class":33726,"line":40921},[25,41420,41421],{"class":33762},"        # enc_outputs的开头:(batch_size,num_steps,num_hiddens)\n",[25,41423,41424,41427,41429,41431],{"class":33726,"line":40932},[25,41425,41426],{"class":33738},"        Y2 ",[25,41428,919],{"class":33730},[25,41430,36530],{"class":34016},[25,41432,41433],{"class":33738},".attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n",[25,41435,41436,41439,41441,41443],{"class":33726,"line":40945},[25,41437,41438],{"class":33738},"        Z ",[25,41440,919],{"class":33730},[25,41442,36530],{"class":34016},[25,41444,41445],{"class":33738},".addnorm2(Y, Y2)\n",[25,41447,41449,41451,41453,41456,41458],{"class":33726,"line":41448},45,[25,41450,33788],{"class":33730},[25,41452,36530],{"class":34016},[25,41454,41455],{"class":33738},".addnorm3(Z, ",[25,41457,33989],{"class":34016},[25,41459,41460],{"class":33738},".ffn(Z)), state\n",[25,41462,41464],{"class":33726,"line":41463},46,[25,41465,34047],{"emptyLinePlaceholder":31433},[25,41467,41469,41471,41474,41476,41479],{"class":33726,"line":41468},47,[25,41470,33953],{"class":33730},[25,41472,41473],{"class":33956}," TransformerDecoder",[25,41475,313],{"class":33738},[25,41477,41478],{"class":33962},"AttentionDecoder",[25,41480,33751],{"class":33738},[25,41482,41484,41486,41488,41490,41492,41494,41496,41498,41500,41502,41504,41506,41508],{"class":33726,"line":41483},48,[25,41485,33980],{"class":33730},[25,41487,33983],{"class":33778},[25,41489,313],{"class":33738},[25,41491,33989],{"class":33988},[25,41493,33745],{"class":33738},[25,41495,40608],{"class":33741},[25,41497,33745],{"class":33738},[25,41499,36157],{"class":33741},[25,41501,33745],{"class":33738},[25,41503,36162],{"class":33741},[25,41505,33745],{"class":33738},[25,41507,36167],{"class":33741},[25,41509,35139],{"class":33738},[25,41511,41513,41515,41517,41519,41521,41523,41525,41527],{"class":33726,"line":41512},49,[25,41514,40627],{"class":33741},[25,41516,33745],{"class":33738},[25,41518,40632],{"class":33741},[25,41520,33745],{"class":33738},[25,41522,38970],{"class":33741},[25,41524,33745],{"class":33738},[25,41526,38975],{"class":33741},[25,41528,35139],{"class":33738},[25,41530,41532,41534,41536,41538,41540,41542,41544,41546,41548],{"class":33726,"line":41531},50,[25,41533,36179],{"class":33741},[25,41535,33745],{"class":33738},[25,41537,40651],{"class":33741},[25,41539,33745],{"class":33738},[25,41541,33994],{"class":33741},[25,41543,33745],{"class":33738},[25,41545,33999],{"class":33730},[25,41547,34002],{"class":33741},[25,41549,33751],{"class":33738},[25,41551,41553,41555,41558,41560,41562,41564,41566,41568],{"class":33726,"line":41552},51,[25,41554,34010],{"class":34009},[25,41556,41557],{"class":33738},"(TransformerDecoder, ",[25,41559,33989],{"class":34016},[25,41561,34019],{"class":33738},[25,41563,34022],{"class":33778},[25,41565,313],{"class":33738},[25,41567,33999],{"class":33730},[25,41569,34029],{"class":33738},[25,41571,41573,41575,41577,41579],{"class":33726,"line":41572},52,[25,41574,34034],{"class":34016},[25,41576,40697],{"class":33738},[25,41578,919],{"class":33730},[25,41580,40702],{"class":33738},[25,41582,41584,41586,41589,41591],{"class":33726,"line":41583},53,[25,41585,34034],{"class":34016},[25,41587,41588],{"class":33738},".num_layers ",[25,41590,919],{"class":33730},[25,41592,41593],{"class":33738}," num_layers\n",[25,41595,41597,41599,41601,41603],{"class":33726,"line":41596},54,[25,41598,34034],{"class":34016},[25,41600,40709],{"class":33738},[25,41602,919],{"class":33730},[25,41604,40714],{"class":33738},[25,41606,41608,41610,41612,41614],{"class":33726,"line":41607},55,[25,41609,34034],{"class":34016},[25,41611,40721],{"class":33738},[25,41613,919],{"class":33730},[25,41615,40726],{"class":33738},[25,41617,41619,41621,41623,41625],{"class":33726,"line":41618},56,[25,41620,34034],{"class":34016},[25,41622,40733],{"class":33738},[25,41624,919],{"class":33730},[25,41626,40738],{"class":33738},[25,41628,41630,41632,41634,41636,41638],{"class":33726,"line":41629},57,[25,41631,40743],{"class":33730},[25,41633,40746],{"class":33738},[25,41635,40749],{"class":33730},[25,41637,40753],{"class":40752},[25,41639,40756],{"class":33738},[25,41641,41643,41645,41647,41649,41651,41653,41655,41657],{"class":33726,"line":41642},58,[25,41644,40761],{"class":34016},[25,41646,40764],{"class":33738},[25,41648,40768],{"class":40767},[25,41650,1786],{"class":40771},[25,41652,40768],{"class":40767},[25,41654,914],{"class":33730},[25,41656,40778],{"class":34009},[25,41658,40781],{"class":33738},[25,41660,41662],{"class":33726,"line":41661},59,[25,41663,41664],{"class":33738},"                DecoderBlock(key_size, query_size, value_size, num_hiddens,\n",[25,41666,41668],{"class":33726,"line":41667},60,[25,41669,40791],{"class":33738},[25,41671,41673],{"class":33726,"line":41672},61,[25,41674,41675],{"class":33738},"                             num_heads, dropout, i))\n",[25,41677,41679,41681,41684,41686],{"class":33726,"line":41678},62,[25,41680,34034],{"class":34016},[25,41682,41683],{"class":33738},".dense ",[25,41685,919],{"class":33730},[25,41687,41688],{"class":33738}," nn.Linear(num_hiddens, vocab_size)\n",[25,41690,41692],{"class":33726,"line":41691},63,[25,41693,34047],{"emptyLinePlaceholder":31433},[25,41695,41697,41699,41701,41703,41705,41707,41709,41711,41714,41716,41718,41720],{"class":33726,"line":41696},64,[25,41698,33980],{"class":33730},[25,41700,40107],{"class":33734},[25,41702,313],{"class":33738},[25,41704,33989],{"class":33988},[25,41706,33745],{"class":33738},[25,41708,40116],{"class":33741},[25,41710,33745],{"class":33738},[25,41712,41713],{"class":33741},"enc_valid_lens",[25,41715,33745],{"class":33738},[25,41717,40020],{"class":33730},[25,41719,40023],{"class":33741},[25,41721,33751],{"class":33738},[25,41723,41725,41727,41730,41732,41734,41736,41738],{"class":33726,"line":41724},65,[25,41726,33788],{"class":33730},[25,41728,41729],{"class":33738}," [enc_outputs, enc_valid_lens, [",[25,41731,34102],{"class":33778},[25,41733,38500],{"class":33738},[25,41735,40020],{"class":33730},[25,41737,36530],{"class":34016},[25,41739,41740],{"class":33738},".num_layers]\n",[25,41742,41744],{"class":33726,"line":41743},66,[25,41745,34047],{"emptyLinePlaceholder":31433},[25,41747,41749,41751,41753,41755,41757,41759,41761,41763,41765],{"class":33726,"line":41748},67,[25,41750,33980],{"class":33730},[25,41752,34074],{"class":33734},[25,41754,313],{"class":33738},[25,41756,33989],{"class":33988},[25,41758,33745],{"class":33738},[25,41760,33742],{"class":33741},[25,41762,33745],{"class":33738},[25,41764,40153],{"class":33741},[25,41766,33751],{"class":33738},[25,41768,41770,41772,41774,41776,41778,41780,41782,41784,41786,41788],{"class":33726,"line":41769},68,[25,41771,33892],{"class":33738},[25,41773,919],{"class":33730},[25,41775,36530],{"class":34016},[25,41777,40855],{"class":33738},[25,41779,33989],{"class":34016},[25,41781,40860],{"class":33738},[25,41783,40020],{"class":33730},[25,41785,40865],{"class":33738},[25,41787,33989],{"class":34016},[25,41789,40870],{"class":33738},[25,41791,41793,41795,41798,41800,41803,41805,41807,41809,41811,41813,41815,41818,41821,41824,41826,41828,41831,41833],{"class":33726,"line":41792},69,[25,41794,34034],{"class":34016},[25,41796,41797],{"class":33738},"._attention_weights ",[25,41799,919],{"class":33730},[25,41801,41802],{"class":33738}," [[",[25,41804,34102],{"class":33778},[25,41806,38500],{"class":33738},[25,41808,40020],{"class":33730},[25,41810,40891],{"class":40752},[25,41812,313],{"class":33738},[25,41814,33989],{"class":34016},[25,41816,41817],{"class":33738},".blks) ",[25,41819,41820],{"class":33730},"for",[25,41822,41823],{"class":33738}," _ ",[25,41825,40749],{"class":33730},[25,41827,40753],{"class":40752},[25,41829,41830],{"class":33738}," (",[25,41832,9242],{"class":33778},[25,41834,41835],{"class":33738},")]\n",[25,41837,41839,41841,41843,41845,41847,41849,41851],{"class":33726,"line":41838},70,[25,41840,40743],{"class":33730},[25,41842,40906],{"class":33738},[25,41844,40749],{"class":33730},[25,41846,40911],{"class":40752},[25,41848,313],{"class":33738},[25,41850,33989],{"class":34016},[25,41852,40918],{"class":33738},[25,41854,41856,41859,41861],{"class":33726,"line":41855},71,[25,41857,41858],{"class":33738},"            X, state ",[25,41860,919],{"class":33730},[25,41862,41863],{"class":33738}," blk(X, state)\n",[25,41865,41867],{"class":33726,"line":41866},72,[25,41868,41869],{"class":33762},"            # 解码器自注意力权重\n",[25,41871,41873,41875,41878,41880,41883,41885],{"class":33726,"line":41872},73,[25,41874,40761],{"class":34016},[25,41876,41877],{"class":33738},"._attention_weights[",[25,41879,599],{"class":33778},[25,41881,41882],{"class":33738},"][i] ",[25,41884,919],{"class":33730},[25,41886,41887],{"class":33738}," blk.attention1.attention.attention_weights\n",[25,41889,41891],{"class":33726,"line":41890},74,[25,41892,41893],{"class":33762},"            # “编码器－解码器”自注意力权重\n",[25,41895,41897,41899,41901,41903,41905,41907],{"class":33726,"line":41896},75,[25,41898,40761],{"class":34016},[25,41900,41877],{"class":33738},[25,41902,617],{"class":33778},[25,41904,41882],{"class":33738},[25,41906,919],{"class":33730},[25,41908,41909],{"class":33738}," blk.attention2.attention.attention_weights\n",[25,41911,41913,41915,41917],{"class":33726,"line":41912},76,[25,41914,33788],{"class":33730},[25,41916,36530],{"class":34016},[25,41918,41919],{"class":33738},".dense(X), state\n",[25,41921,41923],{"class":33726,"line":41922},77,[25,41924,34047],{"emptyLinePlaceholder":31433},[25,41926,41928,41931],{"class":33726,"line":41927},78,[25,41929,41930],{"class":33734},"    @",[25,41932,41933],{"class":34009},"property\n",[25,41935,41937,41939,41942,41944,41946],{"class":33726,"line":41936},79,[25,41938,33980],{"class":33730},[25,41940,41941],{"class":33734}," attention_weights",[25,41943,313],{"class":33738},[25,41945,33989],{"class":33988},[25,41947,33751],{"class":33738},[25,41949,41951,41953,41955],{"class":33726,"line":41950},80,[25,41952,33788],{"class":33730},[25,41954,36530],{"class":34016},[25,41956,41957],{"class":33738},"._attention_weights\n",[11,41959,41960],{"id":41960},"训练",[15,41962,41963],{},"同样，训练时需要屏蔽部分不需要的内容：",[33716,41965,41967],{"className":33718,"code":41966,"language":33720,"meta":31408,"style":31408},"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",[33722,41968,41969,41996,42001,42015,42033,42062,42078,42084,42088,42106,42111,42116,42121,42126,42152,42162,42171,42189,42207,42225,42248],{"__ignoreMap":31408},[25,41970,41971,41973,41976,41978,41980,41982,41985,41987,41990,41992,41994],{"class":33726,"line":33727},[25,41972,33731],{"class":33730},[25,41974,41975],{"class":33734}," sequence_mask",[25,41977,313],{"class":33738},[25,41979,33742],{"class":33741},[25,41981,33745],{"class":33738},[25,41983,41984],{"class":33741},"valid_len",[25,41986,33745],{"class":33738},[25,41988,41989],{"class":33741},"value",[25,41991,919],{"class":33730},[25,41993,599],{"class":33778},[25,41995,33751],{"class":33738},[25,41997,41998],{"class":33726,"line":31409},[25,41999,42000],{"class":33756},"    \"\"\"在序列中屏蔽不相关的项\"\"\"\n",[25,42002,42003,42006,42008,42011,42013],{"class":33726,"line":31417},[25,42004,42005],{"class":33738},"    maxlen ",[25,42007,919],{"class":33730},[25,42009,42010],{"class":33738}," X.size(",[25,42012,617],{"class":33778},[25,42014,33803],{"class":33738},[25,42016,42017,42020,42022,42025,42028,42030],{"class":33726,"line":33766},[25,42018,42019],{"class":33738},"    mask ",[25,42021,919],{"class":33730},[25,42023,42024],{"class":33738}," torch.arange((maxlen), ",[25,42026,42027],{"class":33794},"dtype",[25,42029,919],{"class":33730},[25,42031,42032],{"class":33738},"torch.float32,\n",[25,42034,42035,42038,42040,42043,42045,42048,42051,42054,42056,42058,42060],{"class":33726,"line":33785},[25,42036,42037],{"class":33794},"                        device",[25,42039,919],{"class":33730},[25,42041,42042],{"class":33738},"X.device)[",[25,42044,34102],{"class":33778},[25,42046,42047],{"class":33738},", :] ",[25,42049,42050],{"class":33730},"\u003C",[25,42052,42053],{"class":33738}," valid_len[",[25,42055,15072],{"class":38484},[25,42057,33745],{"class":33738},[25,42059,34102],{"class":33778},[25,42061,34121],{"class":33738},[25,42063,42064,42067,42070,42073,42075],{"class":33726,"line":33806},[25,42065,42066],{"class":33738},"    X[",[25,42068,42069],{"class":33730},"~",[25,42071,42072],{"class":33738},"mask] ",[25,42074,919],{"class":33730},[25,42076,42077],{"class":33738}," value\n",[25,42079,42080,42082],{"class":33726,"line":33814},[25,42081,35997],{"class":33730},[25,42083,40950],{"class":33738},[25,42085,42086],{"class":33726,"line":33825},[25,42087,34047],{"emptyLinePlaceholder":31433},[25,42089,42090,42092,42095,42097,42099,42101,42104],{"class":33726,"line":33842},[25,42091,33953],{"class":33730},[25,42093,42094],{"class":33956}," MaskedSoftmaxCELoss",[25,42096,313],{"class":33738},[25,42098,33963],{"class":33962},[25,42100,32214],{"class":33738},[25,42102,42103],{"class":33962},"CrossEntropyLoss",[25,42105,33751],{"class":33738},[25,42107,42108],{"class":33726,"line":33858},[25,42109,42110],{"class":33756},"    \"\"\"带遮蔽的softmax交叉熵损失函数\"\"\"\n",[25,42112,42113],{"class":33726,"line":33866},[25,42114,42115],{"class":33762},"    # pred的形状：(batch_size,num_steps,vocab_size)\n",[25,42117,42118],{"class":33726,"line":33883},[25,42119,42120],{"class":33762},"    # label的形状：(batch_size,num_steps)\n",[25,42122,42123],{"class":33726,"line":33889},[25,42124,42125],{"class":33762},"    # valid_len的形状：(batch_size,)\n",[25,42127,42128,42130,42132,42134,42136,42138,42141,42143,42146,42148,42150],{"class":33726,"line":33914},[25,42129,33980],{"class":33730},[25,42131,34074],{"class":33734},[25,42133,313],{"class":33738},[25,42135,33989],{"class":33988},[25,42137,33745],{"class":33738},[25,42139,42140],{"class":33741},"pred",[25,42142,33745],{"class":33738},[25,42144,42145],{"class":33741},"label",[25,42147,33745],{"class":33738},[25,42149,41984],{"class":33741},[25,42151,33751],{"class":33738},[25,42153,42154,42157,42159],{"class":33726,"line":33927},[25,42155,42156],{"class":33738},"        weights ",[25,42158,919],{"class":33730},[25,42160,42161],{"class":33738}," torch.ones_like(label)\n",[25,42163,42164,42166,42168],{"class":33726,"line":34166},[25,42165,42156],{"class":33738},[25,42167,919],{"class":33730},[25,42169,42170],{"class":33738}," sequence_mask(weights, valid_len)\n",[25,42172,42173,42175,42178,42180,42183,42186],{"class":33726,"line":36091},[25,42174,34034],{"class":34016},[25,42176,42177],{"class":33738},".reduction",[25,42179,919],{"class":33730},[25,42181,42182],{"class":40767},"'",[25,42184,42185],{"class":40771},"none",[25,42187,42188],{"class":40767},"'\n",[25,42190,42191,42194,42196,42199,42202,42204],{"class":33726,"line":36367},[25,42192,42193],{"class":33738},"        unweighted_loss ",[25,42195,919],{"class":33730},[25,42197,42198],{"class":34009}," super",[25,42200,42201],{"class":33738},"(MaskedSoftmaxCELoss, ",[25,42203,33989],{"class":34016},[25,42205,42206],{"class":33738},").forward(\n",[25,42208,42209,42212,42214,42216,42218,42220,42222],{"class":33726,"line":36373},[25,42210,42211],{"class":33738},"            pred.permute(",[25,42213,599],{"class":33778},[25,42215,33745],{"class":33738},[25,42217,9242],{"class":33778},[25,42219,33745],{"class":33738},[25,42221,617],{"class":33778},[25,42223,42224],{"class":33738},"), label)\n",[25,42226,42227,42230,42232,42235,42237,42240,42242,42244,42246],{"class":33726,"line":36379},[25,42228,42229],{"class":33738},"        weighted_loss ",[25,42231,919],{"class":33730},[25,42233,42234],{"class":33738}," (unweighted_loss ",[25,42236,40020],{"class":33730},[25,42238,42239],{"class":33738}," weights).mean(",[25,42241,33795],{"class":33794},[25,42243,919],{"class":33730},[25,42245,617],{"class":33778},[25,42247,33803],{"class":33738},[25,42249,42250,42252],{"class":33726,"line":36385},[25,42251,33788],{"class":33730},[25,42253,42254],{"class":33738}," weighted_loss\n",[15,42256,42257],{},"梯度裁剪函数：",[33716,42259,42261],{"className":33718,"code":42260,"language":33720,"meta":31408,"style":31408},"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",[33722,42262,42263,42282,42287,42297,42323,42329,42338,42370,42383,42395],{"__ignoreMap":31408},[25,42264,42265,42267,42270,42272,42275,42277,42280],{"class":33726,"line":33727},[25,42266,33731],{"class":33730},[25,42268,42269],{"class":33734}," grad_clipping",[25,42271,313],{"class":33738},[25,42273,42274],{"class":33741},"net",[25,42276,33745],{"class":33738},[25,42278,42279],{"class":33741},"theta",[25,42281,33751],{"class":33738},[25,42283,42284],{"class":33726,"line":31409},[25,42285,42286],{"class":33756},"    \"\"\"裁剪梯度\"\"\"\n",[25,42288,42289,42291,42294],{"class":33726,"line":31417},[25,42290,33769],{"class":33730},[25,42292,42293],{"class":40752}," isinstance",[25,42295,42296],{"class":33738},"(net, nn.Module):\n",[25,42298,42299,42302,42304,42307,42309,42312,42314,42317,42320],{"class":33726,"line":33766},[25,42300,42301],{"class":33738},"        params ",[25,42303,919],{"class":33730},[25,42305,42306],{"class":33738}," [p ",[25,42308,41820],{"class":33730},[25,42310,42311],{"class":33738}," p ",[25,42313,40749],{"class":33730},[25,42315,42316],{"class":33738}," net.parameters() ",[25,42318,42319],{"class":33730},"if",[25,42321,42322],{"class":33738}," p.requires_grad]\n",[25,42324,42325,42327],{"class":33726,"line":33785},[25,42326,33809],{"class":33730},[25,42328,33782],{"class":33738},[25,42330,42331,42333,42335],{"class":33726,"line":33806},[25,42332,42301],{"class":33738},[25,42334,919],{"class":33730},[25,42336,42337],{"class":33738}," net.params\n",[25,42339,42340,42343,42345,42348,42351,42354,42356,42359,42361,42363,42365,42367],{"class":33726,"line":33814},[25,42341,42342],{"class":33738},"    norm ",[25,42344,919],{"class":33730},[25,42346,42347],{"class":33738}," torch.sqrt(",[25,42349,42350],{"class":40752},"sum",[25,42352,42353],{"class":33738},"(torch.sum((p.grad ",[25,42355,33999],{"class":33730},[25,42357,42358],{"class":33778}," 2",[25,42360,34145],{"class":33738},[25,42362,41820],{"class":33730},[25,42364,42311],{"class":33738},[25,42366,40749],{"class":33730},[25,42368,42369],{"class":33738}," params))\n",[25,42371,42372,42374,42377,42380],{"class":33726,"line":33825},[25,42373,33769],{"class":33730},[25,42375,42376],{"class":33738}," norm ",[25,42378,42379],{"class":33730},">",[25,42381,42382],{"class":33738}," theta:\n",[25,42384,42385,42387,42390,42392],{"class":33726,"line":33842},[25,42386,40743],{"class":33730},[25,42388,42389],{"class":33738}," param ",[25,42391,40749],{"class":33730},[25,42393,42394],{"class":33738}," params:\n",[25,42396,42397,42400,42402,42404,42407,42410,42412],{"class":33726,"line":33858},[25,42398,42399],{"class":33738},"            param.grad[",[25,42401,15072],{"class":38484},[25,42403,38500],{"class":33738},[25,42405,42406],{"class":33730},"*=",[25,42408,42409],{"class":33738}," theta ",[25,42411,34148],{"class":33730},[25,42413,42414],{"class":33738}," norm\n",[15,42416,42417,42418],{},"之后，在训练时，特定的序列开始词元（“",[42419,42420,42421,42422],"bos",{},"”）和 原始的输出序列（不包括序列结束词元“",[42423,42424,42425],"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。",[33716,42427,42429],{"className":33718,"code":42428,"language":33720,"meta":31408,"style":31408},"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",[33722,42430,42431,42468,42473,42486,42501,42506,42524,42536,42555,42560,42564,42569,42574,42591,42601,42606,42644,42660,42675,42685,42703,42715,42720,42740,42770,42790,42820,42830,42840,42848,42857,42867,42872,42880,42885,42912,42938,42998],{"__ignoreMap":31408},[25,42432,42433,42435,42438,42440,42442,42444,42447,42449,42452,42454,42457,42459,42462,42464,42466],{"class":33726,"line":33727},[25,42434,33731],{"class":33730},[25,42436,42437],{"class":33734}," train_seq2seq",[25,42439,313],{"class":33738},[25,42441,42274],{"class":33741},[25,42443,33745],{"class":33738},[25,42445,42446],{"class":33741},"data_iter",[25,42448,33745],{"class":33738},[25,42450,42451],{"class":33741},"lr",[25,42453,33745],{"class":33738},[25,42455,42456],{"class":33741},"num_epochs",[25,42458,33745],{"class":33738},[25,42460,42461],{"class":33741},"tgt_vocab",[25,42463,33745],{"class":33738},[25,42465,41355],{"class":33741},[25,42467,33751],{"class":33738},[25,42469,42470],{"class":33726,"line":31409},[25,42471,42472],{"class":33756},"    \"\"\"训练序列到序列模型\"\"\"\n",[25,42474,42475,42477,42480,42482,42484],{"class":33726,"line":31417},[25,42476,33980],{"class":33730},[25,42478,42479],{"class":33734}," xavier_init_weights",[25,42481,313],{"class":33738},[25,42483,31744],{"class":33741},[25,42485,33751],{"class":33738},[25,42487,42488,42490,42493,42496,42498],{"class":33726,"line":33766},[25,42489,33828],{"class":33730},[25,42491,42492],{"class":34009}," type",[25,42494,42495],{"class":33738},"(m) ",[25,42497,33834],{"class":33730},[25,42499,42500],{"class":33738}," nn.Linear:\n",[25,42502,42503],{"class":33726,"line":33785},[25,42504,42505],{"class":33738},"            nn.init.xavier_uniform_(m.weight)\n",[25,42507,42508,42510,42512,42514,42516,42519,42522],{"class":33726,"line":33806},[25,42509,33828],{"class":33730},[25,42511,42492],{"class":34009},[25,42513,42495],{"class":33738},[25,42515,33834],{"class":33730},[25,42517,42518],{"class":33738}," nn.",[25,42520,42521],{"class":33778},"GRU",[25,42523,33782],{"class":33738},[25,42525,42526,42529,42531,42533],{"class":33726,"line":33814},[25,42527,42528],{"class":33730},"            for",[25,42530,42389],{"class":33738},[25,42532,40749],{"class":33730},[25,42534,42535],{"class":33738}," m._flat_weights_names:\n",[25,42537,42538,42541,42544,42547,42549,42552],{"class":33726,"line":33825},[25,42539,42540],{"class":33730},"                if",[25,42542,42543],{"class":40767}," \"",[25,42545,42546],{"class":40771},"weight",[25,42548,40768],{"class":40767},[25,42550,42551],{"class":33730}," in",[25,42553,42554],{"class":33738}," param:\n",[25,42556,42557],{"class":33726,"line":33842},[25,42558,42559],{"class":33738},"                    nn.init.xavier_uniform_(m._parameters[param])\n",[25,42561,42562],{"class":33726,"line":33858},[25,42563,34047],{"emptyLinePlaceholder":31433},[25,42565,42566],{"class":33726,"line":33866},[25,42567,42568],{"class":33738},"    net.apply(xavier_init_weights)\n",[25,42570,42571],{"class":33726,"line":33883},[25,42572,42573],{"class":33738},"    net.to(device)\n",[25,42575,42576,42579,42581,42584,42586,42588],{"class":33726,"line":33889},[25,42577,42578],{"class":33738},"    optimizer ",[25,42580,919],{"class":33730},[25,42582,42583],{"class":33738}," torch.optim.Adam(net.parameters(), ",[25,42585,42451],{"class":33794},[25,42587,919],{"class":33730},[25,42589,42590],{"class":33738},"lr)\n",[25,42592,42593,42596,42598],{"class":33726,"line":33914},[25,42594,42595],{"class":33738},"    loss ",[25,42597,919],{"class":33730},[25,42599,42600],{"class":33738}," MaskedSoftmaxCELoss()\n",[25,42602,42603],{"class":33726,"line":33927},[25,42604,42605],{"class":33738},"    net.train()\n",[25,42607,42608,42611,42613,42616,42619,42621,42623,42626,42628,42630,42633,42635,42637,42640,42642],{"class":33726,"line":34166},[25,42609,42610],{"class":33738},"    animator ",[25,42612,919],{"class":33730},[25,42614,42615],{"class":33738}," d2l.Animator(",[25,42617,42618],{"class":33794},"xlabel",[25,42620,919],{"class":33730},[25,42622,42182],{"class":40767},[25,42624,42625],{"class":40771},"epoch",[25,42627,42182],{"class":40767},[25,42629,33745],{"class":33738},[25,42631,42632],{"class":33794},"ylabel",[25,42634,919],{"class":33730},[25,42636,42182],{"class":40767},[25,42638,42639],{"class":40771},"loss",[25,42641,42182],{"class":40767},[25,42643,35139],{"class":33738},[25,42645,42646,42649,42651,42654,42657],{"class":33726,"line":36091},[25,42647,42648],{"class":33794},"                     xlim",[25,42650,919],{"class":33730},[25,42652,42653],{"class":33738},"[",[25,42655,42656],{"class":33778},"10",[25,42658,42659],{"class":33738},", num_epochs])\n",[25,42661,42662,42665,42668,42670,42672],{"class":33726,"line":36367},[25,42663,42664],{"class":33730},"    for",[25,42666,42667],{"class":33738}," epoch ",[25,42669,40749],{"class":33730},[25,42671,40753],{"class":40752},[25,42673,42674],{"class":33738},"(num_epochs):\n",[25,42676,42677,42680,42682],{"class":33726,"line":36373},[25,42678,42679],{"class":33738},"        timer ",[25,42681,919],{"class":33730},[25,42683,42684],{"class":33738}," d2l.Timer()\n",[25,42686,42687,42690,42692,42695,42697,42700],{"class":33726,"line":36379},[25,42688,42689],{"class":33738},"        metric ",[25,42691,919],{"class":33730},[25,42693,42694],{"class":33738}," d2l.Accumulator(",[25,42696,9242],{"class":33778},[25,42698,42699],{"class":33738},")  ",[25,42701,42702],{"class":33762},"# 训练损失总和，词元数量\n",[25,42704,42705,42707,42710,42712],{"class":33726,"line":36385},[25,42706,40743],{"class":33730},[25,42708,42709],{"class":33738}," batch ",[25,42711,40749],{"class":33730},[25,42713,42714],{"class":33738}," data_iter:\n",[25,42716,42717],{"class":33726,"line":36406},[25,42718,42719],{"class":33738},"            optimizer.zero_grad()\n",[25,42721,42722,42725,42727,42730,42732,42735,42737],{"class":33726,"line":36425},[25,42723,42724],{"class":33738},"            X, X_valid_len, Y, Y_valid_len ",[25,42726,919],{"class":33730},[25,42728,42729],{"class":33738}," [x.to(device) ",[25,42731,41820],{"class":33730},[25,42733,42734],{"class":33738}," x ",[25,42736,40749],{"class":33730},[25,42738,42739],{"class":33738}," batch]\n",[25,42741,42742,42745,42747,42750,42752,42755,42757,42760,42762,42765,42767],{"class":33726,"line":36444},[25,42743,42744],{"class":33738},"            bos ",[25,42746,919],{"class":33730},[25,42748,42749],{"class":33738}," torch.tensor([tgt_vocab[",[25,42751,42182],{"class":40767},[25,42753,42754],{"class":40771},"\u003Cbos>",[25,42756,42182],{"class":40767},[25,42758,42759],{"class":33738},"]] ",[25,42761,40020],{"class":33730},[25,42763,42764],{"class":33738}," Y.shape[",[25,42766,599],{"class":33778},[25,42768,42769],{"class":33738},"],\n",[25,42771,42772,42775,42777,42780,42782,42784,42786,42788],{"class":33726,"line":36449},[25,42773,42774],{"class":33794},"                          device",[25,42776,919],{"class":33730},[25,42778,42779],{"class":33738},"device).reshape(",[25,42781,33876],{"class":33730},[25,42783,617],{"class":33778},[25,42785,33745],{"class":33738},[25,42787,617],{"class":33778},[25,42789,33803],{"class":33738},[25,42791,42792,42795,42797,42800,42802,42804,42806,42808,42810,42813,42815,42817],{"class":33726,"line":36465},[25,42793,42794],{"class":33738},"            dec_input ",[25,42796,919],{"class":33730},[25,42798,42799],{"class":33738}," torch.cat([bos, Y[",[25,42801,15072],{"class":38484},[25,42803,33745],{"class":33738},[25,42805,15072],{"class":38484},[25,42807,33876],{"class":33730},[25,42809,617],{"class":33778},[25,42811,42812],{"class":33738},"]], ",[25,42814,617],{"class":33778},[25,42816,42699],{"class":33738},[25,42818,42819],{"class":33762},"# 强制教学\n",[25,42821,42822,42825,42827],{"class":33726,"line":36471},[25,42823,42824],{"class":33738},"            Y_hat, _ ",[25,42826,919],{"class":33730},[25,42828,42829],{"class":33738}," net(X, dec_input, X_valid_len)\n",[25,42831,42832,42835,42837],{"class":33726,"line":36477},[25,42833,42834],{"class":33738},"            l ",[25,42836,919],{"class":33730},[25,42838,42839],{"class":33738}," loss(Y_hat, Y, Y_valid_len)\n",[25,42841,42842,42845],{"class":33726,"line":36487},[25,42843,42844],{"class":33738},"            l.sum().backward()      ",[25,42846,42847],{"class":33762},"# 损失函数的标量进行“反向传播”\n",[25,42849,42850,42853,42855],{"class":33726,"line":36511},[25,42851,42852],{"class":33738},"            grad_clipping(net, ",[25,42854,617],{"class":33778},[25,42856,33803],{"class":33738},[25,42858,42859,42862,42864],{"class":33726,"line":36516},[25,42860,42861],{"class":33738},"            num_tokens ",[25,42863,919],{"class":33730},[25,42865,42866],{"class":33738}," Y_valid_len.sum()\n",[25,42868,42869],{"class":33726,"line":36522},[25,42870,42871],{"class":33738},"            optimizer.step()\n",[25,42873,42874,42877],{"class":33726,"line":36536},[25,42875,42876],{"class":33730},"            with",[25,42878,42879],{"class":33738}," torch.no_grad():\n",[25,42881,42882],{"class":33726,"line":36541},[25,42883,42884],{"class":33738},"                metric.add(l.sum(), num_tokens)\n",[25,42886,42887,42889,42892,42894,42896,42898,42901,42904,42907,42910],{"class":33726,"line":36547},[25,42888,33828],{"class":33730},[25,42890,42891],{"class":33738}," (epoch ",[25,42893,914],{"class":33730},[25,42895,33837],{"class":33778},[25,42897,38447],{"class":33738},[25,42899,42900],{"class":33730},"%",[25,42902,42903],{"class":33778}," 10",[25,42905,42906],{"class":33730}," ==",[25,42908,42909],{"class":33778}," 0",[25,42911,33782],{"class":33738},[25,42913,42914,42917,42919,42921,42924,42926,42928,42930,42933,42935],{"class":33726,"line":36562},[25,42915,42916],{"class":33738},"            animator.add(epoch ",[25,42918,914],{"class":33730},[25,42920,33837],{"class":33778},[25,42922,42923],{"class":33738},", (metric[",[25,42925,599],{"class":33778},[25,42927,38500],{"class":33738},[25,42929,34148],{"class":33730},[25,42931,42932],{"class":33738}," metric[",[25,42934,617],{"class":33778},[25,42936,42937],{"class":33738},"],))\n",[25,42939,42940,42943,42945,42947,42950,42953,42956,42958,42960,42962,42964,42966,42969,42972,42975,42977,42979,42981,42983,42985,42987,42990,42993,42995],{"class":33726,"line":40834},[25,42941,42942],{"class":40752},"    print",[25,42944,313],{"class":33738},[25,42946,922],{"class":33730},[25,42948,42949],{"class":40771},"'loss ",[25,42951,42952],{"class":33778},"{",[25,42954,42955],{"class":33738},"metric[",[25,42957,599],{"class":33778},[25,42959,38500],{"class":33738},[25,42961,34148],{"class":33730},[25,42963,42932],{"class":33738},[25,42965,617],{"class":33778},[25,42967,42968],{"class":33738},"]",[25,42970,42971],{"class":33730},":.3f",[25,42973,42974],{"class":33778},"}",[25,42976,33745],{"class":40771},[25,42978,42952],{"class":33778},[25,42980,42955],{"class":33738},[25,42982,617],{"class":33778},[25,42984,38500],{"class":33738},[25,42986,34148],{"class":33730},[25,42988,42989],{"class":33738}," timer.stop()",[25,42991,42992],{"class":33730},":.1f",[25,42994,42974],{"class":33778},[25,42996,42997],{"class":40771}," '\n",[25,42999,43000,43003,43006,43008,43010,43013,43015,43017],{"class":33726,"line":40840},[25,43001,43002],{"class":33730},"        f",[25,43004,43005],{"class":40771},"'tokens/sec on ",[25,43007,42952],{"class":33778},[25,43009,40778],{"class":34009},[25,43011,43012],{"class":33738},"(device)",[25,43014,42974],{"class":33778},[25,43016,42182],{"class":40771},[25,43018,33803],{"class":33738},[15,43020,43021],{},"进行数据集的数据处理",[33716,43023,43025],{"className":33718,"code":43024,"language":33720,"meta":31408,"style":31408},"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",[33722,43026,43027,43037,43042,43046,43051,43070,43099,43121,43128,43132,43145,43150,43154,43158,43177,43214,43218,43223,43228,43271,43276,43321,43336,43346,43350,43372,43377,43381,43385,43395,43419,43435,43440,43459,43474,43491,43506,43513,43517,43545,43550,43554,43559,43568,43577,43596,43631,43649,43681,43691,43701,43711,43721],{"__ignoreMap":31408},[25,43028,43029,43031,43034],{"class":33726,"line":33727},[25,43030,33731],{"class":33730},[25,43032,43033],{"class":33734}," read_data_nmt",[25,43035,43036],{"class":33738},"():\n",[25,43038,43039],{"class":33726,"line":31409},[25,43040,43041],{"class":33756},"    \"\"\"载入“英语－法语”数据集\n",[25,43043,43044],{"class":33726,"line":31417},[25,43045,34047],{"emptyLinePlaceholder":31433},[25,43047,43048],{"class":33726,"line":33766},[25,43049,43050],{"class":33756},"    Defined in :numref:`sec_machine_translation`\"\"\"\n",[25,43052,43053,43056,43058,43061,43063,43066,43068],{"class":33726,"line":33785},[25,43054,43055],{"class":33738},"    data_dir ",[25,43057,919],{"class":33730},[25,43059,43060],{"class":33738}," d2l.download_extract(",[25,43062,42182],{"class":40767},[25,43064,43065],{"class":40771},"fra-eng",[25,43067,42182],{"class":40767},[25,43069,33803],{"class":33738},[25,43071,43072,43075,43078,43081,43083,43086,43088,43091,43093,43095,43097],{"class":33726,"line":33806},[25,43073,43074],{"class":33730},"    with",[25,43076,43077],{"class":40752}," open",[25,43079,43080],{"class":33738},"(os.path.join(data_dir, ",[25,43082,42182],{"class":40767},[25,43084,43085],{"class":40771},"fra.txt",[25,43087,42182],{"class":40767},[25,43089,43090],{"class":33738},"), ",[25,43092,42182],{"class":40767},[25,43094,457],{"class":40771},[25,43096,42182],{"class":40767},[25,43098,35139],{"class":33738},[25,43100,43101,43104,43106,43108,43111,43113,43115,43118],{"class":33726,"line":33814},[25,43102,43103],{"class":33794},"             encoding",[25,43105,919],{"class":33730},[25,43107,42182],{"class":40767},[25,43109,43110],{"class":40771},"utf-8",[25,43112,42182],{"class":40767},[25,43114,38447],{"class":33738},[25,43116,43117],{"class":33730},"as",[25,43119,43120],{"class":33738}," f:\n",[25,43122,43123,43125],{"class":33726,"line":33825},[25,43124,33788],{"class":33730},[25,43126,43127],{"class":33738}," f.read()\n",[25,43129,43130],{"class":33726,"line":33842},[25,43131,34047],{"emptyLinePlaceholder":31433},[25,43133,43134,43136,43139,43141,43143],{"class":33726,"line":33858},[25,43135,33731],{"class":33730},[25,43137,43138],{"class":33734}," preprocess_nmt",[25,43140,313],{"class":33738},[25,43142,27761],{"class":33741},[25,43144,33751],{"class":33738},[25,43146,43147],{"class":33726,"line":33866},[25,43148,43149],{"class":33756},"    \"\"\"预处理“英语－法语”数据集\n",[25,43151,43152],{"class":33726,"line":33883},[25,43153,34047],{"emptyLinePlaceholder":31433},[25,43155,43156],{"class":33726,"line":33889},[25,43157,43050],{"class":33756},[25,43159,43160,43162,43165,43167,43170,43172,43175],{"class":33726,"line":33914},[25,43161,33980],{"class":33730},[25,43163,43164],{"class":33734}," no_space",[25,43166,313],{"class":33738},[25,43168,43169],{"class":33741},"char",[25,43171,33745],{"class":33738},[25,43173,43174],{"class":33741},"prev_char",[25,43176,33751],{"class":33738},[25,43178,43179,43181,43184,43186,43189,43191,43193,43196,43198,43200,43203,43206,43209,43212],{"class":33726,"line":33927},[25,43180,33788],{"class":33730},[25,43182,43183],{"class":33738}," char ",[25,43185,40749],{"class":33730},[25,43187,43188],{"class":34009}," set",[25,43190,313],{"class":33738},[25,43192,42182],{"class":40767},[25,43194,43195],{"class":40771},",.!?",[25,43197,42182],{"class":40767},[25,43199,38447],{"class":33738},[25,43201,43202],{"class":33730},"and",[25,43204,43205],{"class":33738}," prev_char ",[25,43207,43208],{"class":33730},"!=",[25,43210,43211],{"class":40767}," '",[25,43213,42997],{"class":40767},[25,43215,43216],{"class":33726,"line":34166},[25,43217,34047],{"emptyLinePlaceholder":31433},[25,43219,43220],{"class":33726,"line":36091},[25,43221,43222],{"class":33762},"    # 使用空格替换不间断空格\n",[25,43224,43225],{"class":33726,"line":36367},[25,43226,43227],{"class":33762},"    # 使用小写字母替换大写字母\n",[25,43229,43230,43233,43235,43238,43240,43244,43246,43248,43250,43252,43255,43257,43260,43262,43264,43266,43268],{"class":33726,"line":36373},[25,43231,43232],{"class":33738},"    text ",[25,43234,919],{"class":33730},[25,43236,43237],{"class":33738}," text.replace(",[25,43239,42182],{"class":40767},[25,43241,43243],{"class":43242},"sRfyP","\\u202f",[25,43245,42182],{"class":40767},[25,43247,33745],{"class":33738},[25,43249,42182],{"class":40767},[25,43251,43211],{"class":40767},[25,43253,43254],{"class":33738},").replace(",[25,43256,42182],{"class":40767},[25,43258,43259],{"class":43242},"\\xa0",[25,43261,42182],{"class":40767},[25,43263,33745],{"class":33738},[25,43265,42182],{"class":40767},[25,43267,43211],{"class":40767},[25,43269,43270],{"class":33738},").lower()\n",[25,43272,43273],{"class":33726,"line":36379},[25,43274,43275],{"class":33762},"    # 在单词和标点符号之间插入空格\n",[25,43277,43278,43281,43283,43285,43287,43289,43292,43294,43296,43298,43300,43302,43305,43308,43310,43312,43315,43318],{"class":33726,"line":36385},[25,43279,43280],{"class":33738},"    out ",[25,43282,919],{"class":33730},[25,43284,40882],{"class":33738},[25,43286,42182],{"class":40767},[25,43288,43211],{"class":40767},[25,43290,43291],{"class":33730}," +",[25,43293,43183],{"class":33738},[25,43295,42319],{"class":33730},[25,43297,40746],{"class":33738},[25,43299,42379],{"class":33730},[25,43301,42909],{"class":33778},[25,43303,43304],{"class":33730}," and",[25,43306,43307],{"class":33738}," no_space(char, text[i ",[25,43309,33876],{"class":33730},[25,43311,33837],{"class":33778},[25,43313,43314],{"class":33738},"]) ",[25,43316,43317],{"class":33730},"else",[25,43319,43320],{"class":33738}," char\n",[25,43322,43323,43326,43329,43331,43333],{"class":33726,"line":36406},[25,43324,43325],{"class":33730},"           for",[25,43327,43328],{"class":33738}," i, char ",[25,43330,40749],{"class":33730},[25,43332,40911],{"class":40752},[25,43334,43335],{"class":33738},"(text)]\n",[25,43337,43338,43340,43343],{"class":33726,"line":36425},[25,43339,35997],{"class":33730},[25,43341,43342],{"class":40767}," ''",[25,43344,43345],{"class":33738},".join(out)\n",[25,43347,43348],{"class":33726,"line":36444},[25,43349,34047],{"emptyLinePlaceholder":31433},[25,43351,43352,43354,43357,43359,43361,43363,43366,43368,43370],{"class":33726,"line":36449},[25,43353,33731],{"class":33730},[25,43355,43356],{"class":33734}," tokenize_nmt",[25,43358,313],{"class":33738},[25,43360,27761],{"class":33741},[25,43362,33745],{"class":33738},[25,43364,43365],{"class":33741},"num_examples",[25,43367,919],{"class":33730},[25,43369,34102],{"class":33778},[25,43371,33751],{"class":33738},[25,43373,43374],{"class":33726,"line":36465},[25,43375,43376],{"class":33756},"    \"\"\"词元化“英语－法语”数据数据集\n",[25,43378,43379],{"class":33726,"line":36471},[25,43380,34047],{"emptyLinePlaceholder":31433},[25,43382,43383],{"class":33726,"line":36477},[25,43384,43050],{"class":33756},[25,43386,43387,43390,43392],{"class":33726,"line":36487},[25,43388,43389],{"class":33738},"    source, target ",[25,43391,919],{"class":33730},[25,43393,43394],{"class":33738}," [], []\n",[25,43396,43397,43399,43402,43404,43406,43409,43411,43414,43416],{"class":33726,"line":36511},[25,43398,42664],{"class":33730},[25,43400,43401],{"class":33738}," i, line ",[25,43403,40749],{"class":33730},[25,43405,40911],{"class":40752},[25,43407,43408],{"class":33738},"(text.split(",[25,43410,42182],{"class":40767},[25,43412,43413],{"class":43242},"\\n",[25,43415,42182],{"class":40767},[25,43417,43418],{"class":33738},")):\n",[25,43420,43421,43423,43426,43428,43430,43432],{"class":33726,"line":36516},[25,43422,33828],{"class":33730},[25,43424,43425],{"class":33738}," num_examples ",[25,43427,43202],{"class":33730},[25,43429,40746],{"class":33738},[25,43431,42379],{"class":33730},[25,43433,43434],{"class":33738}," num_examples:\n",[25,43436,43437],{"class":33726,"line":36522},[25,43438,43439],{"class":33730},"            break\n",[25,43441,43442,43445,43447,43450,43452,43455,43457],{"class":33726,"line":36536},[25,43443,43444],{"class":33738},"        parts ",[25,43446,919],{"class":33730},[25,43448,43449],{"class":33738}," line.split(",[25,43451,42182],{"class":40767},[25,43453,43454],{"class":43242},"\\t",[25,43456,42182],{"class":40767},[25,43458,33803],{"class":33738},[25,43460,43461,43463,43465,43468,43470,43472],{"class":33726,"line":36541},[25,43462,33828],{"class":33730},[25,43464,40891],{"class":40752},[25,43466,43467],{"class":33738},"(parts) ",[25,43469,33834],{"class":33730},[25,43471,42358],{"class":33778},[25,43473,33782],{"class":33738},[25,43475,43476,43479,43481,43484,43486,43488],{"class":33726,"line":36547},[25,43477,43478],{"class":33738},"            source.append(parts[",[25,43480,599],{"class":33778},[25,43482,43483],{"class":33738},"].split(",[25,43485,42182],{"class":40767},[25,43487,43211],{"class":40767},[25,43489,43490],{"class":33738},"))\n",[25,43492,43493,43496,43498,43500,43502,43504],{"class":33726,"line":36562},[25,43494,43495],{"class":33738},"            target.append(parts[",[25,43497,617],{"class":33778},[25,43499,43483],{"class":33738},[25,43501,42182],{"class":40767},[25,43503,43211],{"class":40767},[25,43505,43490],{"class":33738},[25,43507,43508,43510],{"class":33726,"line":40834},[25,43509,35997],{"class":33730},[25,43511,43512],{"class":33738}," source, target\n",[25,43514,43515],{"class":33726,"line":40840},[25,43516,34047],{"emptyLinePlaceholder":31433},[25,43518,43519,43521,43524,43526,43529,43531,43534,43536,43538,43540,43543],{"class":33726,"line":40846},[25,43520,33731],{"class":33730},[25,43522,43523],{"class":33734}," load_data_nmt",[25,43525,313],{"class":33738},[25,43527,43528],{"class":33741},"batch_size",[25,43530,33745],{"class":33738},[25,43532,43533],{"class":33741},"num_steps",[25,43535,33745],{"class":33738},[25,43537,43365],{"class":33741},[25,43539,919],{"class":33730},[25,43541,43542],{"class":33778},"600",[25,43544,33751],{"class":33738},[25,43546,43547],{"class":33726,"line":40873},[25,43548,43549],{"class":33756},"    \"\"\"返回翻译数据集的迭代器和词表\n",[25,43551,43552],{"class":33726,"line":40901},[25,43553,34047],{"emptyLinePlaceholder":31433},[25,43555,43556],{"class":33726,"line":40921},[25,43557,43558],{"class":33756},"    Defined in :numref:`subsec_mt_data_loading`\"\"\"\n",[25,43560,43561,43563,43565],{"class":33726,"line":40932},[25,43562,43232],{"class":33738},[25,43564,919],{"class":33730},[25,43566,43567],{"class":33738}," preprocess_nmt(read_data_nmt())\n",[25,43569,43570,43572,43574],{"class":33726,"line":40945},[25,43571,43389],{"class":33738},[25,43573,919],{"class":33730},[25,43575,43576],{"class":33738}," tokenize_nmt(text, num_examples)\n",[25,43578,43579,43582,43584,43587,43590,43592,43594],{"class":33726,"line":41448},[25,43580,43581],{"class":33738},"    src_vocab ",[25,43583,919],{"class":33730},[25,43585,43586],{"class":33738}," d2l.Vocab(source, ",[25,43588,43589],{"class":33794},"min_freq",[25,43591,919],{"class":33730},[25,43593,9242],{"class":33778},[25,43595,35139],{"class":33738},[25,43597,43598,43601,43603,43605,43607,43610,43612,43614,43616,43618,43620,43622,43624,43627,43629],{"class":33726,"line":41463},[25,43599,43600],{"class":33794},"                          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已经过去一年，内容忘的差不多了，决定复习一下。",{"date":43943,"image":43944,"alt":31440,"tags":43945,"published":31433},"30st Jan 2026","/blogs-img/blog1.jpg",[43946,31431],"deep-learning","/blogs/transformer",{"title":31440,"description":43941},"blogs/1. 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