[{"data":1,"prerenderedAt":74860},["ShallowReactive",2],{"blog-post-/blogs/ppo":3,"all-blogs-for-navigation":31437},{"id":4,"title":5,"body":6,"description":31422,"extension":31423,"meta":31424,"navigation":31432,"ogImage":31426,"path":31433,"seo":31434,"stem":31435,"__hash__":31436},"content/blogs/2. PPO学习笔记.md","零基础速通 PPO 学习笔记",{"type":7,"value":8,"toc":31406},"minimark",[9,13,17,20,575,889,1348,1351,1354,1418,1773,5781,6386,6906,6910,6986,7651,7896,8017,8346,8349,9035,10175,10277,10280,12913,13020,14892,14897,14900,14935,17724,17727,17730,17733,19220,19223,19227,19230,19233,19371,21038,21041,21045,21689,21880,26405,26408,27453,27456,27461,27497,28791,28795,28798,29408,31395,31398],[10,11,12],"h2",{"id":12},"学习背景",[14,15,16],"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。",[10,18,19],{"id":19},"符号定义",[14,21,22,23,129,130,159,160,231,232,260,261,293,294,439,440,513,514,542,543,574],{},"在强化学习中，",[24,25,28,57],"span",{"className":26},[27],"katex",[24,29,32],{"className":30},[31],"katex-mathml",[33,34,36],"math",{"xmlns":35},"http://www.w3.org/1998/Math/MathML",[37,38,39,52],"semantics",{},[40,41,42],"mrow",{},[43,44,45,49],"msub",{},[46,47,48],"mi",{},"a",[46,50,51],{},"t",[53,54,56],"annotation",{"encoding":55},"application/x-tex","a_t",[24,58,62],{"className":59,"ariaHidden":61},[60],"katex-html","true",[24,63,66,71],{"className":64},[65],"base",[24,67],{"className":68,"style":70},[69],"strut","height:0.5806em;vertical-align:-0.15em;",[24,72,75,79],{"className":73},[74],"mord",[24,76,48],{"className":77},[74,78],"mathnormal",[24,80,83],{"className":81},[82],"msupsub",[24,84,88,120],{"className":85},[86,87],"vlist-t","vlist-t2",[24,89,92,115],{"className":90},[91],"vlist-r",[24,93,97],{"className":94,"style":96},[95],"vlist","height:0.2806em;",[24,98,100,105],{"style":99},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[24,101],{"className":102,"style":104},[103],"pstrut","height:2.7em;",[24,106,112],{"className":107},[108,109,110,111],"sizing","reset-size6","size3","mtight",[24,113,51],{"className":114},[74,78,111],[24,116,119],{"className":117},[118],"vlist-s","​",[24,121,123],{"className":122},[91],[24,124,127],{"className":125,"style":126},[95],"height:0.15em;",[24,128],{}," 一般表示 ",[24,131,133,146],{"className":132},[27],[24,134,136],{"className":135},[31],[33,137,138],{"xmlns":35},[37,139,140,144],{},[40,141,142],{},[46,143,51],{},[53,145,51],{"encoding":55},[24,147,149],{"className":148,"ariaHidden":61},[60],[24,150,152,156],{"className":151},[65],[24,153],{"className":154,"style":155},[69],"height:0.6151em;",[24,157,51],{"className":158},[74,78]," 时刻 Agent 采取的动作（action）；",[24,161,163,182],{"className":162},[27],[24,164,166],{"className":165},[31],[33,167,168],{"xmlns":35},[37,169,170,179],{},[40,171,172],{},[43,173,174,177],{},[46,175,176],{},"s",[46,178,51],{},[53,180,181],{"encoding":55},"s_t",[24,183,185],{"className":184,"ariaHidden":61},[60],[24,186,188,191],{"className":187},[65],[24,189],{"className":190,"style":70},[69],[24,192,194,197],{"className":193},[74],[24,195,176],{"className":196},[74,78],[24,198,200],{"className":199},[82],[24,201,203,223],{"className":202},[86,87],[24,204,206,220],{"className":205},[91],[24,207,209],{"className":208,"style":96},[95],[24,210,211,214],{"style":99},[24,212],{"className":213,"style":104},[103],[24,215,217],{"className":216},[108,109,110,111],[24,218,51],{"className":219},[74,78,111],[24,221,119],{"className":222},[118],[24,224,226],{"className":225},[91],[24,227,229],{"className":228,"style":126},[95],[24,230],{}," 表示 ",[24,233,235,248],{"className":234},[27],[24,236,238],{"className":237},[31],[33,239,240],{"xmlns":35},[37,241,242,246],{},[40,243,244],{},[46,245,51],{},[53,247,51],{"encoding":55},[24,249,251],{"className":250,"ariaHidden":61},[60],[24,252,254,257],{"className":253},[65],[24,255],{"className":256,"style":155},[69],[24,258,51],{"className":259},[74,78]," 时刻 Agent 所处的状态（state）；",[24,262,264,279],{"className":263},[27],[24,265,267],{"className":266},[31],[33,268,269],{"xmlns":35},[37,270,271,276],{},[40,272,273],{},[46,274,275],{},"π",[53,277,278],{"encoding":55},"\\pi",[24,280,282],{"className":281,"ariaHidden":61},[60],[24,283,285,289],{"className":284},[65],[24,286],{"className":287,"style":288},[69],"height:0.4306em;",[24,290,275],{"className":291,"style":292},[74,78],"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 ",[24,295,297,335],{"className":296},[27],[24,298,300],{"className":299},[31],[33,301,302],{"xmlns":35},[37,303,304,332],{},[40,305,306,308,313,319,323,329],{},[46,307,275],{},[309,310,312],"mo",{"stretchy":311},"false","(",[43,314,315,317],{},[46,316,48],{},[46,318,51],{},[46,320,322],{"mathvariant":321},"normal","∣",[43,324,325,327],{},[46,326,176],{},[46,328,51],{},[309,330,331],{"stretchy":311},")",[53,333,334],{"encoding":55},"\\pi(a_t|s_t)",[24,336,338],{"className":337,"ariaHidden":61},[60],[24,339,341,345,348,352,392,395,435],{"className":340},[65],[24,342],{"className":343,"style":344},[69],"height:1em;vertical-align:-0.25em;",[24,346,275],{"className":347,"style":292},[74,78],[24,349,312],{"className":350},[351],"mopen",[24,353,355,358],{"className":354},[74],[24,356,48],{"className":357},[74,78],[24,359,361],{"className":360},[82],[24,362,364,384],{"className":363},[86,87],[24,365,367,381],{"className":366},[91],[24,368,370],{"className":369,"style":96},[95],[24,371,372,375],{"style":99},[24,373],{"className":374,"style":104},[103],[24,376,378],{"className":377},[108,109,110,111],[24,379,51],{"className":380},[74,78,111],[24,382,119],{"className":383},[118],[24,385,387],{"className":386},[91],[24,388,390],{"className":389,"style":126},[95],[24,391],{},[24,393,322],{"className":394},[74],[24,396,398,401],{"className":397},[74],[24,399,176],{"className":400},[74,78],[24,402,404],{"className":403},[82],[24,405,407,427],{"className":406},[86,87],[24,408,410,424],{"className":409},[91],[24,411,413],{"className":412,"style":96},[95],[24,414,415,418],{"style":99},[24,416],{"className":417,"style":104},[103],[24,419,421],{"className":420},[108,109,110,111],[24,422,51],{"className":423},[74,78,111],[24,425,119],{"className":426},[118],[24,428,430],{"className":429},[91],[24,431,433],{"className":432,"style":126},[95],[24,434],{},[24,436,331],{"className":437},[438],"mclose","；",[24,441,443,462],{"className":442},[27],[24,444,446],{"className":445},[31],[33,447,448],{"xmlns":35},[37,449,450,459],{},[40,451,452],{},[43,453,454,457],{},[46,455,456],{},"r",[46,458,51],{},[53,460,461],{"encoding":55},"r_t",[24,463,465],{"className":464,"ariaHidden":61},[60],[24,466,468,471],{"className":467},[65],[24,469],{"className":470,"style":70},[69],[24,472,474,478],{"className":473},[74],[24,475,456],{"className":476,"style":477},[74,78],"margin-right:0.02778em;",[24,479,481],{"className":480},[82],[24,482,484,505],{"className":483},[86,87],[24,485,487,502],{"className":486},[91],[24,488,490],{"className":489,"style":96},[95],[24,491,493,496],{"style":492},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[24,494],{"className":495,"style":104},[103],[24,497,499],{"className":498},[108,109,110,111],[24,500,51],{"className":501},[74,78,111],[24,503,119],{"className":504},[118],[24,506,508],{"className":507},[91],[24,509,511],{"className":510,"style":126},[95],[24,512],{}," 一边表示 ",[24,515,517,530],{"className":516},[27],[24,518,520],{"className":519},[31],[33,521,522],{"xmlns":35},[37,523,524,528],{},[40,525,526],{},[46,527,51],{},[53,529,51],{"encoding":55},[24,531,533],{"className":532,"ariaHidden":61},[60],[24,534,536,539],{"className":535},[65],[24,537],{"className":538,"style":155},[69],[24,540,51],{"className":541},[74,78]," 时刻 Agent 采取行动获得的奖励（Reward）；",[24,544,546,561],{"className":545},[27],[24,547,549],{"className":548},[31],[33,550,551],{"xmlns":35},[37,552,553,558],{},[40,554,555],{},[46,556,557],{},"τ",[53,559,560],{"encoding":55},"\\tau",[24,562,564],{"className":563,"ariaHidden":61},[60],[24,565,567,570],{"className":566},[65],[24,568],{"className":569,"style":288},[69],[24,571,557],{"className":572,"style":573},[74,78],"margin-right:0.1132em;"," 表示轨迹（Trajectory），Episode 指一次完整的交互过程：从环境开始，到终止结束。Rollout 指按某个策略实际“跑出来”的一段轨迹数据。它不一定非得是完整的一局，也可以只是中间截取的一段。",[14,576,577],{},[24,578,580,640],{"className":579},[27],[24,581,583],{"className":582},[31],[33,584,585],{"xmlns":35},[37,586,587,637],{},[40,588,589,591,599,602,608,610,617,619,625,628,635],{},[309,590,312],{"stretchy":311},[43,592,593,595],{},[46,594,176],{},[596,597,598],"mn",{},"0",[309,600,601],{"separator":61},",",[43,603,604,606],{},[46,605,48],{},[596,607,598],{},[309,609,601],{"separator":61},[43,611,612,614],{},[46,613,176],{},[596,615,616],{},"1",[309,618,601],{"separator":61},[43,620,621,623],{},[46,622,48],{},[596,624,616],{},[309,626,627],{},"…",[43,629,630,632],{},[46,631,176],{},[46,633,634],{},"T",[309,636,331],{"stretchy":311},[53,638,639],{"encoding":55},"(s_0,a_0,s_1,a_1 \\dots s_T)",[24,641,643],{"className":642,"ariaHidden":61},[60],[24,644,646,649,652,693,697,702,742,745,748,788,791,794,834,837,841,844,886],{"className":645},[65],[24,647],{"className":648,"style":344},[69],[24,650,312],{"className":651},[351],[24,653,655,658],{"className":654},[74],[24,656,176],{"className":657},[74,78],[24,659,661],{"className":660},[82],[24,662,664,685],{"className":663},[86,87],[24,665,667,682],{"className":666},[91],[24,668,671],{"className":669,"style":670},[95],"height:0.3011em;",[24,672,673,676],{"style":99},[24,674],{"className":675,"style":104},[103],[24,677,679],{"className":678},[108,109,110,111],[24,680,598],{"className":681},[74,111],[24,683,119],{"className":684},[118],[24,686,688],{"className":687},[91],[24,689,691],{"className":690,"style":126},[95],[24,692],{},[24,694,601],{"className":695},[696],"mpunct",[24,698],{"className":699,"style":701},[700],"mspace","margin-right:0.1667em;",[24,703,705,708],{"className":704},[74],[24,706,48],{"className":707},[74,78],[24,709,711],{"className":710},[82],[24,712,714,734],{"className":713},[86,87],[24,715,717,731],{"className":716},[91],[24,718,720],{"className":719,"style":670},[95],[24,721,722,725],{"style":99},[24,723],{"className":724,"style":104},[103],[24,726,728],{"className":727},[108,109,110,111],[24,729,598],{"className":730},[74,111],[24,732,119],{"className":733},[118],[24,735,737],{"className":736},[91],[24,738,740],{"className":739,"style":126},[95],[24,741],{},[24,743,601],{"className":744},[696],[24,746],{"className":747,"style":701},[700],[24,749,751,754],{"className":750},[74],[24,752,176],{"className":753},[74,78],[24,755,757],{"className":756},[82],[24,758,760,780],{"className":759},[86,87],[24,761,763,777],{"className":762},[91],[24,764,766],{"className":765,"style":670},[95],[24,767,768,771],{"style":99},[24,769],{"className":770,"style":104},[103],[24,772,774],{"className":773},[108,109,110,111],[24,775,616],{"className":776},[74,111],[24,778,119],{"className":779},[118],[24,781,783],{"className":782},[91],[24,784,786],{"className":785,"style":126},[95],[24,787],{},[24,789,601],{"className":790},[696],[24,792],{"className":793,"style":701},[700],[24,795,797,800],{"className":796},[74],[24,798,48],{"className":799},[74,78],[24,801,803],{"className":802},[82],[24,804,806,826],{"className":805},[86,87],[24,807,809,823],{"className":808},[91],[24,810,812],{"className":811,"style":670},[95],[24,813,814,817],{"style":99},[24,815],{"className":816,"style":104},[103],[24,818,820],{"className":819},[108,109,110,111],[24,821,616],{"className":822},[74,111],[24,824,119],{"className":825},[118],[24,827,829],{"className":828},[91],[24,830,832],{"className":831,"style":126},[95],[24,833],{},[24,835],{"className":836,"style":701},[700],[24,838,627],{"className":839},[840],"minner",[24,842],{"className":843,"style":701},[700],[24,845,847,850],{"className":846},[74],[24,848,176],{"className":849},[74,78],[24,851,853],{"className":852},[82],[24,854,856,878],{"className":855},[86,87],[24,857,859,875],{"className":858},[91],[24,860,863],{"className":861,"style":862},[95],"height:0.3283em;",[24,864,865,868],{"style":99},[24,866],{"className":867,"style":104},[103],[24,869,871],{"className":870},[108,109,110,111],[24,872,634],{"className":873,"style":874},[74,78,111],"margin-right:0.13889em;",[24,876,119],{"className":877},[118],[24,879,881],{"className":880},[91],[24,882,884],{"className":883,"style":126},[95],[24,885],{},[24,887,331],{"className":888},[438],[14,890,891,1117,1118,1347],{},[24,892,894,943],{"className":893},[27],[24,895,897],{"className":896},[31],[33,898,899],{"xmlns":35},[37,900,901,940],{},[40,902,903,916,919,922,924,930,932,938],{},[43,904,905,907],{},[46,906,176],{},[40,908,909,911,914],{},[46,910,51],{},[309,912,913],{},"+",[596,915,616],{},[309,917,918],{},"=",[46,920,921],{},"f",[309,923,312],{"stretchy":311},[43,925,926,928],{},[46,927,176],{},[46,929,51],{},[309,931,601],{"separator":61},[43,933,934,936],{},[46,935,48],{},[46,937,51],{},[309,939,331],{"stretchy":311},[53,941,942],{"encoding":55}," s_{t+1} = f(s_t,a_t)",[24,944,946,1015],{"className":945,"ariaHidden":61},[60],[24,947,949,953,1004,1008,1012],{"className":948},[65],[24,950],{"className":951,"style":952},[69],"height:0.6389em;vertical-align:-0.2083em;",[24,954,956,959],{"className":955},[74],[24,957,176],{"className":958},[74,78],[24,960,962],{"className":961},[82],[24,963,965,995],{"className":964},[86,87],[24,966,968,992],{"className":967},[91],[24,969,971],{"className":970,"style":670},[95],[24,972,973,976],{"style":99},[24,974],{"className":975,"style":104},[103],[24,977,979],{"className":978},[108,109,110,111],[24,980,982,985,989],{"className":981},[74,111],[24,983,51],{"className":984},[74,78,111],[24,986,913],{"className":987},[988,111],"mbin",[24,990,616],{"className":991},[74,111],[24,993,119],{"className":994},[118],[24,996,998],{"className":997},[91],[24,999,1002],{"className":1000,"style":1001},[95],"height:0.2083em;",[24,1003],{},[24,1005],{"className":1006,"style":1007},[700],"margin-right:0.2778em;",[24,1009,918],{"className":1010},[1011],"mrel",[24,1013],{"className":1014,"style":1007},[700],[24,1016,1018,1021,1025,1028,1068,1071,1074,1114],{"className":1017},[65],[24,1019],{"className":1020,"style":344},[69],[24,1022,921],{"className":1023,"style":1024},[74,78],"margin-right:0.10764em;",[24,1026,312],{"className":1027},[351],[24,1029,1031,1034],{"className":1030},[74],[24,1032,176],{"className":1033},[74,78],[24,1035,1037],{"className":1036},[82],[24,1038,1040,1060],{"className":1039},[86,87],[24,1041,1043,1057],{"className":1042},[91],[24,1044,1046],{"className":1045,"style":96},[95],[24,1047,1048,1051],{"style":99},[24,1049],{"className":1050,"style":104},[103],[24,1052,1054],{"className":1053},[108,109,110,111],[24,1055,51],{"className":1056},[74,78,111],[24,1058,119],{"className":1059},[118],[24,1061,1063],{"className":1062},[91],[24,1064,1066],{"className":1065,"style":126},[95],[24,1067],{},[24,1069,601],{"className":1070},[696],[24,1072],{"className":1073,"style":701},[700],[24,1075,1077,1080],{"className":1076},[74],[24,1078,48],{"className":1079},[74,78],[24,1081,1083],{"className":1082},[82],[24,1084,1086,1106],{"className":1085},[86,87],[24,1087,1089,1103],{"className":1088},[91],[24,1090,1092],{"className":1091,"style":96},[95],[24,1093,1094,1097],{"style":99},[24,1095],{"className":1096,"style":104},[103],[24,1098,1100],{"className":1099},[108,109,110,111],[24,1101,51],{"className":1102},[74,78,111],[24,1104,119],{"className":1105},[118],[24,1107,1109],{"className":1108},[91],[24,1110,1112],{"className":1111,"style":126},[95],[24,1113],{},[24,1115,331],{"className":1116},[438]," 或者 ",[24,1119,1121,1173],{"className":1120},[27],[24,1122,1124],{"className":1123},[31],[33,1125,1126],{"xmlns":35},[37,1127,1128,1170],{},[40,1129,1130,1142,1144,1147,1149,1152,1154,1160,1162,1168],{},[43,1131,1132,1134],{},[46,1133,176],{},[40,1135,1136,1138,1140],{},[46,1137,51],{},[309,1139,913],{},[596,1141,616],{},[309,1143,918],{},[46,1145,1146],{},"P",[309,1148,312],{"stretchy":311},[309,1150,1151],{},"⋅",[46,1153,322],{"mathvariant":321},[43,1155,1156,1158],{},[46,1157,176],{},[46,1159,51],{},[309,1161,601],{"separator":61},[43,1163,1164,1166],{},[46,1165,48],{},[46,1167,51],{},[309,1169,331],{"stretchy":311},[53,1171,1172],{"encoding":55},"s_{t+1} = P(\\cdot|s_t,a_t)",[24,1174,1176,1240],{"className":1175,"ariaHidden":61},[60],[24,1177,1179,1182,1231,1234,1237],{"className":1178},[65],[24,1180],{"className":1181,"style":952},[69],[24,1183,1185,1188],{"className":1184},[74],[24,1186,176],{"className":1187},[74,78],[24,1189,1191],{"className":1190},[82],[24,1192,1194,1223],{"className":1193},[86,87],[24,1195,1197,1220],{"className":1196},[91],[24,1198,1200],{"className":1199,"style":670},[95],[24,1201,1202,1205],{"style":99},[24,1203],{"className":1204,"style":104},[103],[24,1206,1208],{"className":1207},[108,109,110,111],[24,1209,1211,1214,1217],{"className":1210},[74,111],[24,1212,51],{"className":1213},[74,78,111],[24,1215,913],{"className":1216},[988,111],[24,1218,616],{"className":1219},[74,111],[24,1221,119],{"className":1222},[118],[24,1224,1226],{"className":1225},[91],[24,1227,1229],{"className":1228,"style":1001},[95],[24,1230],{},[24,1232],{"className":1233,"style":1007},[700],[24,1235,918],{"className":1236},[1011],[24,1238],{"className":1239,"style":1007},[700],[24,1241,1243,1246,1249,1252,1255,1258,1298,1301,1304,1344],{"className":1242},[65],[24,1244],{"className":1245,"style":344},[69],[24,1247,1146],{"className":1248,"style":874},[74,78],[24,1250,312],{"className":1251},[351],[24,1253,1151],{"className":1254},[74],[24,1256,322],{"className":1257},[74],[24,1259,1261,1264],{"className":1260},[74],[24,1262,176],{"className":1263},[74,78],[24,1265,1267],{"className":1266},[82],[24,1268,1270,1290],{"className":1269},[86,87],[24,1271,1273,1287],{"className":1272},[91],[24,1274,1276],{"className":1275,"style":96},[95],[24,1277,1278,1281],{"style":99},[24,1279],{"className":1280,"style":104},[103],[24,1282,1284],{"className":1283},[108,109,110,111],[24,1285,51],{"className":1286},[74,78,111],[24,1288,119],{"className":1289},[118],[24,1291,1293],{"className":1292},[91],[24,1294,1296],{"className":1295,"style":126},[95],[24,1297],{},[24,1299,601],{"className":1300},[696],[24,1302],{"className":1303,"style":701},[700],[24,1305,1307,1310],{"className":1306},[74],[24,1308,48],{"className":1309},[74,78],[24,1311,1313],{"className":1312},[82],[24,1314,1316,1336],{"className":1315},[86,87],[24,1317,1319,1333],{"className":1318},[91],[24,1320,1322],{"className":1321,"style":96},[95],[24,1323,1324,1327],{"style":99},[24,1325],{"className":1326,"style":104},[103],[24,1328,1330],{"className":1329},[108,109,110,111],[24,1331,51],{"className":1332},[74,78,111],[24,1334,119],{"className":1335},[118],[24,1337,1339],{"className":1338},[91],[24,1340,1342],{"className":1341,"style":126},[95],[24,1343],{},[24,1345,331],{"className":1346},[438],"。",[14,1349,1350],{},"Return 一般表示回报，指从当前时间点到游戏结束时奖励的累积和或者加权累积和。",[10,1352,1353],{"id":1353},"训练目标",[14,1355,1356,1357,1385,1386,1417],{},"训练一个 Policy 神经网络 ",[24,1358,1360,1373],{"className":1359},[27],[24,1361,1363],{"className":1362},[31],[33,1364,1365],{"xmlns":35},[37,1366,1367,1371],{},[40,1368,1369],{},[46,1370,275],{},[53,1372,278],{"encoding":55},[24,1374,1376],{"className":1375,"ariaHidden":61},[60],[24,1377,1379,1382],{"className":1378},[65],[24,1380],{"className":1381,"style":288},[69],[24,1383,275],{"className":1384,"style":292},[74,78],"，在所有状态 ",[24,1387,1389,1403],{"className":1388},[27],[24,1390,1392],{"className":1391},[31],[33,1393,1394],{"xmlns":35},[37,1395,1396,1401],{},[40,1397,1398],{},[46,1399,1400],{},"S",[53,1402,1400],{"encoding":55},[24,1404,1406],{"className":1405,"ariaHidden":61},[60],[24,1407,1409,1413],{"className":1408},[65],[24,1410],{"className":1411,"style":1412},[69],"height:0.6833em;",[24,1414,1400],{"className":1415,"style":1416},[74,78],"margin-right:0.05764em;"," 下，给出相应的 Action，得到的 Return 的期望最大。",[14,1419,1420],{},[24,1421,1423,1503],{"className":1422},[27],[24,1424,1426],{"className":1425},[31],[33,1427,1428],{"xmlns":35},[37,1429,1430,1500],{},[40,1431,1432,1435,1437,1440,1442,1444,1446,1470,1472,1480,1482,1484,1486,1488,1494,1496,1498],{},[46,1433,1434],{},"E",[309,1436,312],{"stretchy":311},[46,1438,1439],{},"R",[309,1441,312],{"stretchy":311},[46,1443,557],{},[309,1445,331],{"stretchy":311},[43,1447,1448,1450],{},[309,1449,331],{"stretchy":311},[40,1451,1452,1454,1457,1464,1466,1468],{},[46,1453,557],{},[309,1455,1456],{},"∼",[43,1458,1459,1461],{},[46,1460,1146],{},[46,1462,1463],{},"θ",[309,1465,312],{"stretchy":311},[46,1467,557],{},[309,1469,331],{"stretchy":311},[309,1471,918],{},[1473,1474,1475,1478],"munder",{},[309,1476,1477],{},"∑",[46,1479,557],{},[46,1481,1439],{},[309,1483,312],{"stretchy":311},[46,1485,557],{},[309,1487,331],{"stretchy":311},[43,1489,1490,1492],{},[46,1491,1146],{},[46,1493,1463],{},[309,1495,312],{"stretchy":311},[46,1497,557],{},[309,1499,331],{"stretchy":311},[53,1501,1502],{"encoding":55}," E (R(\\tau))_{\\tau \\sim P_{\\theta}(\\tau)} = \\sum\\limits_\\tau R(\\tau)P_\\theta(\\tau)",[24,1504,1506,1647],{"className":1505,"ariaHidden":61},[60],[24,1507,1509,1513,1516,1519,1523,1526,1529,1532,1638,1641,1644],{"className":1508},[65],[24,1510],{"className":1511,"style":1512},[69],"height:1.1052em;vertical-align:-0.3552em;",[24,1514,1434],{"className":1515,"style":1416},[74,78],[24,1517,312],{"className":1518},[351],[24,1520,1439],{"className":1521,"style":1522},[74,78],"margin-right:0.00773em;",[24,1524,312],{"className":1525},[351],[24,1527,557],{"className":1528,"style":573},[74,78],[24,1530,331],{"className":1531},[438],[24,1533,1535,1538],{"className":1534},[438],[24,1536,331],{"className":1537},[438],[24,1539,1541],{"className":1540},[82],[24,1542,1544,1629],{"className":1543},[86,87],[24,1545,1547,1626],{"className":1546},[91],[24,1548,1551],{"className":1549,"style":1550},[95],"height:0.3448em;",[24,1552,1554,1557],{"style":1553},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[24,1555],{"className":1556,"style":104},[103],[24,1558,1560],{"className":1559},[108,109,110,111],[24,1561,1563,1566,1569,1617,1620,1623],{"className":1562},[74,111],[24,1564,557],{"className":1565,"style":573},[74,78,111],[24,1567,1456],{"className":1568},[1011,111],[24,1570,1572,1575],{"className":1571},[74,111],[24,1573,1146],{"className":1574,"style":874},[74,78,111],[24,1576,1578],{"className":1577},[82],[24,1579,1581,1608],{"className":1580},[86,87],[24,1582,1584,1605],{"className":1583},[91],[24,1585,1587],{"className":1586,"style":1550},[95],[24,1588,1590,1594],{"style":1589},"top:-2.3488em;margin-left:-0.1389em;margin-right:0.0714em;",[24,1591],{"className":1592,"style":1593},[103],"height:2.5em;",[24,1595,1599],{"className":1596},[108,1597,1598,111],"reset-size3","size1",[24,1600,1602],{"className":1601},[74,111],[24,1603,1463],{"className":1604,"style":477},[74,78,111],[24,1606,119],{"className":1607},[118],[24,1609,1611],{"className":1610},[91],[24,1612,1615],{"className":1613,"style":1614},[95],"height:0.1512em;",[24,1616],{},[24,1618,312],{"className":1619},[351,111],[24,1621,557],{"className":1622,"style":573},[74,78,111],[24,1624,331],{"className":1625},[438,111],[24,1627,119],{"className":1628},[118],[24,1630,1632],{"className":1631},[91],[24,1633,1636],{"className":1634,"style":1635},[95],"height:0.3552em;",[24,1637],{},[24,1639],{"className":1640,"style":1007},[700],[24,1642,918],{"className":1643},[1011],[24,1645],{"className":1646,"style":1007},[700],[24,1648,1650,1654,1707,1710,1713,1716,1719,1722,1764,1767,1770],{"className":1649},[65],[24,1651],{"className":1652,"style":1653},[69],"height:1.7em;vertical-align:-0.95em;",[24,1655,1659],{"className":1656},[1657,1658],"mop","op-limits",[24,1660,1662,1698],{"className":1661},[86,87],[24,1663,1665,1695],{"className":1664},[91],[24,1666,1669,1682],{"className":1667,"style":1668},[95],"height:0.75em;",[24,1670,1672,1676],{"style":1671},"top:-2.15em;margin-left:0em;",[24,1673],{"className":1674,"style":1675},[103],"height:3em;",[24,1677,1679],{"className":1678},[108,109,110,111],[24,1680,557],{"className":1681,"style":573},[74,78,111],[24,1683,1685,1688],{"style":1684},"top:-3em;",[24,1686],{"className":1687,"style":1675},[103],[24,1689,1690],{},[24,1691,1477],{"className":1692},[1657,1693,1694],"op-symbol","small-op",[24,1696,119],{"className":1697},[118],[24,1699,1701],{"className":1700},[91],[24,1702,1705],{"className":1703,"style":1704},[95],"height:0.95em;",[24,1706],{},[24,1708],{"className":1709,"style":701},[700],[24,1711,1439],{"className":1712,"style":1522},[74,78],[24,1714,312],{"className":1715},[351],[24,1717,557],{"className":1718,"style":573},[74,78],[24,1720,331],{"className":1721},[438],[24,1723,1725,1728],{"className":1724},[74],[24,1726,1146],{"className":1727,"style":874},[74,78],[24,1729,1731],{"className":1730},[82],[24,1732,1734,1756],{"className":1733},[86,87],[24,1735,1737,1753],{"className":1736},[91],[24,1738,1741],{"className":1739,"style":1740},[95],"height:0.3361em;",[24,1742,1744,1747],{"style":1743},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[24,1745],{"className":1746,"style":104},[103],[24,1748,1750],{"className":1749},[108,109,110,111],[24,1751,1463],{"className":1752,"style":477},[74,78,111],[24,1754,119],{"className":1755},[118],[24,1757,1759],{"className":1758},[91],[24,1760,1762],{"className":1761,"style":126},[95],[24,1763],{},[24,1765,312],{"className":1766},[351],[24,1768,557],{"className":1769,"style":573},[74,78],[24,1771,331],{"className":1772},[438],[24,1774,1777],{"className":1775},[1776],"katex-display",[24,1778,1780,2567],{"className":1779},[27],[24,1781,1783],{"className":1782},[31],[33,1784,1786],{"xmlns":35,"display":1785},"block",[37,1787,1788,2564],{},[1789,1790,1794,1880,1926,2007,2085,2182,2256,2360,2462],"mtable",{"rowspacing":1791,"columnalign":1792,"columnspacing":1793},"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",[14,6911,6912,6913,6985],{},"为了衡量每个动作的相对好坏的情况，我们令奖励 ",[24,6914,6916,6934],{"className":6915},[27],[24,6917,6919],{"className":6918},[31],[33,6920,6921],{"xmlns":35},[37,6922,6923,6931],{},[40,6924,6925],{},[43,6926,6927,6929],{},[46,6928,1439],{},[46,6930,51],{},[53,6932,6933],{"encoding":55},"R_t",[24,6935,6937],{"className":6936,"ariaHidden":61},[60],[24,6938,6940,6944],{"className":6939},[65],[24,6941],{"className":6942,"style":6943},[69],"height:0.8333em;vertical-align:-0.15em;",[24,6945,6947,6950],{"className":6946},[74],[24,6948,1439],{"className":6949,"style":1522},[74,78],[24,6951,6953],{"className":6952},[82],[24,6954,6956,6977],{"className":6955},[86,87],[24,6957,6959,6974],{"className":6958},[91],[24,6960,6962],{"className":6961,"style":96},[95],[24,6963,6965,6968],{"style":6964},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[24,6966],{"className":6967,"style":104},[103],[24,6969,6971],{"className":6970},[108,109,110,111],[24,6972,51],{"className":6973},[74,78,111],[24,6975,119],{"className":6976},[118],[24,6978,6980],{"className":6979},[91],[24,6981,6983],{"className":6982,"style":126},[95],[24,6984],{}," 减去一个基准值。",[14,6987,6988],{},[24,6989,6991,7104],{"className":6990},[27],[24,6992,6994],{"className":6993},[31],[33,6995,6996],{"xmlns":35},[37,6997,6998,7101],{},[40,6999,7000,7006,7020,7038,7040,7048,7050,7053,7055,7063,7065,7067,7069,7071,7073,7079,7081,7089,7091,7099],{},[1977,7001,7002,7004],{},[596,7003,616],{},[46,7005,2110],{},[2340,7007,7008,7010,7018],{},[309,7009,1477],{},[40,7011,7012,7014,7016],{},[46,7013,2120],{},[309,7015,918],{},[596,7017,616],{},[46,7019,2110],{},[2340,7021,7022,7024,7032],{},[309,7023,1477],{},[40,7025,7026,7028,7030],{},[46,7027,51],{},[309,7029,918],{},[596,7031,616],{},[43,7033,7034,7036],{},[46,7035,634],{},[46,7037,2120],{},[309,7039,312],{"stretchy":311},[2340,7041,7042,7044,7046],{},[46,7043,1439],{},[46,7045,51],{},[46,7047,2120],{},[309,7049,5809],{},[46,7051,7052],{},"B",[309,7054,312],{"stretchy":311},[2340,7056,7057,7059,7061],{},[46,7058,176],{},[46,7060,51],{},[46,7062,2120],{},[309,7064,331],{"stretchy":311},[309,7066,331],{"stretchy":311},[46,7068,1807],{"mathvariant":321},[46,7070,2236],{},[309,7072,2239],{},[43,7074,7075,7077],{},[46,7076,1146],{},[46,7078,1463],{},[309,7080,312],{"stretchy":311},[2340,7082,7083,7085,7087],{},[46,7084,48],{},[46,7086,51],{},[46,7088,2120],{},[46,7090,322],{"mathvariant":321},[2340,7092,7093,7095,7097],{},[46,7094,176],{},[46,7096,51],{},[46,7098,2120],{},[309,7100,331],{"stretchy":311},[53,7102,7103],{"encoding":55}," \\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)",[24,7105,7107,7418],{"className":7106,"ariaHidden":61},[60],[24,7108,7110,7113,7181,7184,7248,7251,7355,7358,7409,7412,7415],{"className":7109},[65],[24,7111],{"className":7112,"style":5926},[69],[24,7114,7116,7119,7178],{"className":7115},[74],[24,7117],{"className":7118},[351,3238],[24,7120,7122],{"className":7121},[1977],[24,7123,7125,7170],{"className":7124},[86,87],[24,7126,7128,7167],{"className":7127},[91],[24,7129,7131,7145,7153],{"className":7130,"style":5948},[95],[24,7132,7133,7136],{"style":5951},[24,7134],{"className":7135,"style":1675},[103],[24,7137,7139],{"className":7138},[108,109,110,111],[24,7140,7142],{"className":7141},[74,111],[24,7143,2110],{"className":7144,"style":3729},[74,78,111],[24,7146,7147,7150],{"style":3312},[24,7148],{"className":7149,"style":1675},[103],[24,7151],{"className":7152,"style":3320},[3319],[24,7154,7155,7158],{"style":5974},[24,7156],{"className":7157,"style":1675},[103],[24,7159,7161],{"className":7160},[108,109,110,111],[24,7162,7164],{"className":7163},[74,111],[24,7165,616],{"className":7166},[74,111],[24,7168,119],{"className":7169},[118],[24,7171,7173],{"className":7172},[91],[24,7174,7176],{"className":7175,"style":5996},[95],[24,7177],{},[24,7179],{"className":7180},[438,3238],[24,7182],{"className":7183,"style":701},[700],[24,7185,7187],{"className":7186},[1657,1658],[24,7188,7190,7240],{"className":7189},[86,87],[24,7191,7193,7237],{"className":7192},[91],[24,7194,7196,7216,7226],{"className":7195,"style":6017},[95],[24,7197,7198,7201],{"style":6020},[24,7199],{"className":7200,"style":1675},[103],[24,7202,7204],{"className":7203},[108,109,110,111],[24,7205,7207,7210,7213],{"className":7206},[74,111],[24,7208,2120],{"className":7209},[74,78,111],[24,7211,918],{"className":7212},[1011,111],[24,7214,616],{"className":7215},[74,111],[24,7217,7218,7221],{"style":1684},[24,7219],{"className":7220,"style":1675},[103],[24,7222,7223],{},[24,7224,1477],{"className":7225},[1657,1693,1694],[24,7227,7228,7231],{"style":6051},[24,7229],{"className":7230,"style":1675},[103],[24,7232,7234],{"className":7233},[108,109,110,111],[24,7235,2110],{"className":7236,"style":3729},[74,78,111],[24,7238,119],{"className":7239},[118],[24,7241,7243],{"className":7242},[91],[24,7244,7246],{"className":7245,"style":6070},[95],[24,7247],{},[24,7249],{"className":7250,"style":701},[700],[24,7252,7254],{"className":7253},[1657,1658],[24,7255,7257,7347],{"className":7256},[86,87],[24,7258,7260,7344],{"className":7259},[91],[24,7261,7263,7283,7293],{"className":7262,"style":6088},[95],[24,7264,7265,7268],{"style":6020},[24,7266],{"className":7267,"style":1675},[103],[24,7269,7271],{"className":7270},[108,109,110,111],[24,7272,7274,7277,7280],{"className":7273},[74,111],[24,7275,51],{"className":7276},[74,78,111],[24,7278,918],{"className":7279},[1011,111],[24,7281,616],{"className":7282},[74,111],[24,7284,7285,7288],{"style":1684},[24,7286],{"className":7287,"style":1675},[103],[24,7289,7290],{},[24,7291,1477],{"className":7292},[1657,1693,1694],[24,7294,7295,7298],{"style":6121},[24,7296],{"className":7297,"style":1675},[103],[24,7299,7301],{"className":7300},[108,109,110,111],[24,7302,7304],{"className":7303},[74,111],[24,7305,7307,7310],{"className":7306},[74,111],[24,7308,634],{"className":7309,"style":874},[74,78,111],[24,7311,7313],{"className":7312},[82],[24,7314,7316,7336],{"className":7315},[86,87],[24,7317,7319,7333],{"className":7318},[91],[24,7320,7322],{"className":7321,"style":4650},[95],[24,7323,7324,7327],{"style":4653},[24,7325],{"className":7326,"style":1593},[103],[24,7328,7330],{"className":7329},[108,1597,1598,111],[24,7331,2120],{"className":7332},[74,78,111],[24,7334,119],{"className":7335},[118],[24,7337,7339],{"className":7338},[91],[24,7340,7342],{"className":7341,"style":4672},[95],[24,7343],{},[24,7345,119],{"className":7346},[118],[24,7348,7350],{"className":7349},[91],[24,7351,7353],{"className":7352,"style":6070},[95],[24,7354],{},[24,7356,312],{"className":7357},[351],[24,7359,7361,7364],{"className":7360},[74],[24,7362,1439],{"className":7363,"style":1522},[74,78],[24,7365,7367],{"className":7366},[82],[24,7368,7370,7401],{"className":7369},[86,87],[24,7371,7373,7398],{"className":7372},[91],[24,7374,7376,7387],{"className":7375,"style":4061},[95],[24,7377,7378,7381],{"style":6874},[24,7379],{"className":7380,"style":104},[103],[24,7382,7384],{"className":7383},[108,109,110,111],[24,7385,51],{"className":7386},[74,78,111],[24,7388,7389,7392],{"style":4064},[24,7390],{"className":7391,"style":104},[103],[24,7393,7395],{"className":7394},[108,109,110,111],[24,7396,2120],{"className":7397},[74,78,111],[24,7399,119],{"className":7400},[118],[24,7402,7404],{"className":7403},[91],[24,7405,7407],{"className":7406,"style":4783},[95],[24,7408],{},[24,7410],{"className":7411,"style":3225},[700],[24,7413,5809],{"className":7414},[988],[24,7416],{"className":7417,"style":3225},[700],[24,7419,7421,7424,7428,7431,7482,7486,7489,7492,7497,7500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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 ",[24,7739,7741,7770],{"className":7740},[27],[24,7742,7744],{"className":7743},[31],[33,7745,7746],{"xmlns":35},[37,7747,7748,7767],{},[40,7749,7750,7757,7759,7761,7763,7765],{},[43,7751,7752,7755],{},[46,7753,7754],{},"Q",[46,7756,1463],{},[309,7758,312],{"stretchy":311},[46,7760,176],{},[309,7762,601],{"separator":61},[46,7764,48],{},[309,7766,331],{"stretchy":311},[53,7768,7769],{"encoding":55},"Q_\\theta(s,a)",[24,7771,7773],{"className":7772,"ariaHidden":61},[60],[24,7774,7776,7779,7819,7822,7825,7828,7831,7834],{"className":7775},[65],[24,7777],{"className":7778,"style":344},[69],[24,7780,7782,7785],{"className":7781},[74],[24,7783,7754],{"className":7784},[74,78],[24,7786,7788],{"className":7787},[82],[24,7789,7791,7811],{"className":7790},[86,87],[24,7792,7794,7808],{"className":7793},[91],[24,7795,7797],{"className":7796,"style":1740},[95],[24,7798,7799,7802],{"style":99},[24,7800],{"className":7801,"style":104},[103],[24,7803,7805],{"className":7804},[108,109,110,111],[24,7806,1463],{"className":7807,"style":477},[74,78,111],[24,7809,119],{"className":7810},[118],[24,7812,7814],{"className":7813},[91],[24,7815,7817],{"className":7816,"style":126},[95],[24,7818],{},[24,7820,312],{"className":7821},[351],[24,7823,176],{"className":7824},[74,78],[24,7826,601],{"className":7827},[696],[24,7829],{"className":7830,"style":701},[700],[24,7832,48],{"className":7833},[74,78],[24,7835,331],{"className":7836},[438],"，表示在状态 ",[24,7839,7841,7854],{"className":7840},[27],[24,7842,7844],{"className":7843},[31],[33,7845,7846],{"xmlns":35},[37,7847,7848,7852],{},[40,7849,7850],{},[46,7851,176],{},[53,7853,176],{"encoding":55},[24,7855,7857],{"className":7856,"ariaHidden":61},[60],[24,7858,7860,7863],{"className":7859},[65],[24,7861],{"className":7862,"style":288},[69],[24,7864,176],{"className":7865},[74,78],"，下，做出动作 ",[24,7868,7870,7883],{"className":7869},[27],[24,7871,7873],{"className":7872},[31],[33,7874,7875],{"xmlns":35},[37,7876,7877,7881],{},[40,7878,7879],{},[46,7880,48],{},[53,7882,48],{"encoding":55},[24,7884,7886],{"className":7885,"ariaHidden":61},[60],[24,7887,7889,7892],{"className":7888},[65],[24,7890],{"className":7891,"style":288},[69],[24,7893,48],{"className":7894},[74,78]," 后期望的回报，即动作价值函数。",[14,7897,7898,7899,7987,7988,8016],{},"令 ",[24,7900,7902,7927],{"className":7901},[27],[24,7903,7905],{"className":7904},[31],[33,7906,7907],{"xmlns":35},[37,7908,7909,7924],{},[40,7910,7911,7918,7920,7922],{},[43,7912,7913,7916],{},[46,7914,7915],{},"V",[46,7917,1463],{},[309,7919,312],{"stretchy":311},[46,7921,176],{},[309,7923,331],{"stretchy":311},[53,7925,7926],{"encoding":55},"V_\\theta(s)",[24,7928,7930],{"className":7929,"ariaHidden":61},[60],[24,7931,7933,7936,7978,7981,7984],{"className":7932},[65],[24,7934],{"className":7935,"style":344},[69],[24,7937,7939,7943],{"className":7938},[74],[24,7940,7915],{"className":7941,"style":7942},[74,78],"margin-right:0.22222em;",[24,7944,7946],{"className":7945},[82],[24,7947,7949,7970],{"className":7948},[86,87],[24,7950,7952,7967],{"className":7951},[91],[24,7953,7955],{"className":7954,"style":1740},[95],[24,7956,7958,7961],{"style":7957},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[24,7959],{"className":7960,"style":104},[103],[24,7962,7964],{"className":7963},[108,109,110,111],[24,7965,1463],{"className":7966,"style":477},[74,78,111],[24,7968,119],{"className":7969},[118],[24,7971,7973],{"className":7972},[91],[24,7974,7976],{"className":7975,"style":126},[95],[24,7977],{},[24,7979,312],{"className":7980},[351],[24,7982,176],{"className":7983},[74,78],[24,7985,331],{"className":7986},[438]," 在状态 ",[24,7989,7991,8004],{"className":7990},[27],[24,7992,7994],{"className":7993},[31],[33,7995,7996],{"xmlns":35},[37,7997,7998,8002],{},[40,7999,8000],{},[46,8001,176],{},[53,8003,176],{"encoding":55},[24,8005,8007],{"className":8006,"ariaHidden":61},[60],[24,8008,8010,8013],{"className":8009},[65],[24,8011],{"className":8012,"style":288},[69],[24,8014,176],{"className":8015},[74,78]," 下期望的回报，即状态价值函数",[14,8018,8019,8287,8288,8316,8317,8345],{},[24,8020,8022,8083],{"className":8021},[27],[24,8023,8025],{"className":8024},[31],[33,8026,8027],{"xmlns":35},[37,8028,8029,8080],{},[40,8030,8031,8038,8040,8042,8044,8046,8048,8050,8056,8058,8060,8062,8064,8066,8068,8074,8076,8078],{},[43,8032,8033,8036],{},[46,8034,8035],{},"A",[46,8037,1463],{},[309,8039,312],{"stretchy":311},[46,8041,176],{},[309,8043,601],{"separator":61},[46,8045,48],{},[309,8047,331],{"stretchy":311},[309,8049,918],{},[43,8051,8052,8054],{},[46,8053,7754],{},[46,8055,1463],{},[309,8057,312],{"stretchy":311},[46,8059,176],{},[309,8061,601],{"separator":61},[46,8063,48],{},[309,8065,331],{"stretchy":311},[309,8067,5809],{},[43,8069,8070,8072],{},[46,8071,7915],{},[46,8073,1463],{},[309,8075,312],{"stretchy":311},[46,8077,176],{},[309,8079,331],{"stretchy":311},[53,8081,8082],{"encoding":55},"A_\\theta(s,a) = Q_\\theta(s,a) - V_\\theta(s)",[24,8084,8086,8159,8232],{"className":8085,"ariaHidden":61},[60],[24,8087,8089,8092,8132,8135,8138,8141,8144,8147,8150,8153,8156],{"className":8088},[65],[24,8090],{"className":8091,"style":344},[69],[24,8093,8095,8098],{"className":8094},[74],[24,8096,8035],{"className":8097},[74,78],[24,8099,8101],{"className":8100},[82],[24,8102,8104,8124],{"className":8103},[86,87],[24,8105,8107,8121],{"className":8106},[91],[24,8108,8110],{"className":8109,"style":1740},[95],[24,8111,8112,8115],{"style":99},[24,8113],{"className":8114,"style":104},[103],[24,8116,8118],{"className":8117},[108,109,110,111],[24,8119,1463],{"className":8120,"style":477},[74,78,111],[24,8122,119],{"className":8123},[118],[24,8125,8127],{"className":8126},[91],[24,8128,8130],{"className":8129,"style":126},[95],[24,8131],{},[24,8133,312],{"className":8134},[351],[24,8136,176],{"className":8137},[74,78],[24,8139,601],{"className":8140},[696],[24,8142],{"className":8143,"style":701},[700],[24,8145,48],{"className":8146},[74,78],[24,8148,331],{"className":8149},[438],[24,8151],{"className":8152,"style":1007},[700],[24,8154,918],{"className":8155},[1011],[24,8157],{"className":8158,"style":1007},[700],[24,8160,8162,8165,8205,8208,8211,8214,8217,8220,8223,8226,8229],{"className":8161},[65],[24,8163],{"className":8164,"style":344},[69],[24,8166,8168,8171],{"className":8167},[74],[24,8169,7754],{"className":8170},[74,78],[24,8172,8174],{"className":8173},[82],[24,8175,8177,8197],{"className":8176},[86,87],[24,8178,8180,8194],{"className":8179},[91],[24,8181,8183],{"className":8182,"style":1740},[95],[24,8184,8185,8188],{"style":99},[24,8186],{"className":8187,"style":104},[103],[24,8189,8191],{"className":8190},[108,109,110,111],[24,8192,1463],{"className":8193,"style":477},[74,78,111],[24,8195,119],{"className":8196},[118],[24,8198,8200],{"className":8199},[91],[24,8201,8203],{"className":8202,"style":126},[95],[24,8204],{},[24,8206,312],{"className":8207},[351],[24,8209,176],{"className":8210},[74,78],[24,8212,601],{"className":8213},[696],[24,8215],{"className":8216,"style":701},[700],[24,8218,48],{"className":8219},[74,78],[24,8221,331],{"className":8222},[438],[24,8224],{"className":8225,"style":3225},[700],[24,8227,5809],{"className":8228},[988],[24,8230],{"className":8231,"style":3225},[700],[24,8233,8235,8238,8278,8281,8284],{"className":8234},[65],[24,8236],{"className":8237,"style":344},[69],[24,8239,8241,8244],{"className":8240},[74],[24,8242,7915],{"className":8243,"style":7942},[74,78],[24,8245,8247],{"className":8246},[82],[24,8248,8250,8270],{"className":8249},[86,87],[24,8251,8253,8267],{"className":8252},[91],[24,8254,8256],{"className":8255,"style":1740},[95],[24,8257,8258,8261],{"style":7957},[24,8259],{"className":8260,"style":104},[103],[24,8262,8264],{"className":8263},[108,109,110,111],[24,8265,1463],{"className":8266,"style":477},[74,78,111],[24,8268,119],{"className":8269},[118],[24,8271,8273],{"className":8272},[91],[24,8274,8276],{"className":8275,"style":126},[95],[24,8277],{},[24,8279,312],{"className":8280},[351],[24,8282,176],{"className":8283},[74,78],[24,8285,331],{"className":8286},[438]," 表示优势函数（Advantage Function），衡量在状态 ",[24,8289,8291,8304],{"className":8290},[27],[24,8292,8294],{"className":8293},[31],[33,8295,8296],{"xmlns":35},[37,8297,8298,8302],{},[40,8299,8300],{},[46,8301,176],{},[53,8303,176],{"encoding":55},[24,8305,8307],{"className":8306,"ariaHidden":61},[60],[24,8308,8310,8313],{"className":8309},[65],[24,8311],{"className":8312,"style":288},[69],[24,8314,176],{"className":8315},[74,78]," 下，动作 ",[24,8318,8320,8333],{"className":8319},[27],[24,8321,8323],{"className":8322},[31],[33,8324,8325],{"xmlns":35},[37,8326,8327,8331],{},[40,8328,8329],{},[46,8330,48],{},[53,8332,48],{"encoding":55},[24,8334,8336],{"className":8335,"ariaHidden":61},[60],[24,8337,8339,8342],{"className":8338},[65],[24,8340],{"className":8341,"style":288},[69],[24,8343,48],{"className":8344},[74,78]," 相对于平均水平的优势。",[14,8347,8348],{},"讲上述的公式改写为",[14,8350,8351],{},[24,8352,8354,8468],{"className":8353},[27],[24,8355,8357],{"className":8356},[31],[33,8358,8359],{"xmlns":35},[37,8360,8361,8465],{},[40,8362,8363,8371,8385,8403,8409,8411,8419,8421,8429,8431,8433,8435,8437,8443,8445,8453,8455,8463],{},[1801,8364,8365],{"scriptlevel":598,"displaystyle":61},[1977,8366,8367,8369],{},[596,8368,616],{},[46,8370,2110],{},[2340,8372,8373,8375,8383],{},[309,8374,1477],{},[40,8376,8377,8379,8381],{},[46,8378,2120],{},[309,8380,918],{},[596,8382,616],{},[46,8384,2110],{},[2340,8386,8387,8389,8397],{},[309,8388,1477],{},[40,8390,8391,8393,8395],{},[46,8392,51],{},[309,8394,918],{},[596,8396,616],{},[43,8398,8399,8401],{},[46,8400,634],{},[46,8402,2120],{},[43,8404,8405,8407],{},[46,8406,8035],{},[46,8408,1463],{},[309,8410,312],{"stretchy":311},[2340,8412,8413,8415,8417],{},[46,8414,176],{},[46,8416,51],{},[46,8418,2120],{},[309,8420,601],{"separator":61},[2340,8422,8423,8425,8427],{},[46,8424,48],{},[46,8426,51],{},[46,8428,2120],{},[309,8430,331],{"stretchy":311},[46,8432,1807],{"mathvariant":321},[46,8434,2236],{},[309,8436,2239],{},[43,8438,8439,8441],{},[46,8440,1146],{},[46,8442,1463],{},[309,8444,312],{"stretchy":311},[2340,8446,8447,8449,8451],{},[46,8448,48],{},[46,8450,51],{},[46,8452,2120],{},[46,8454,322],{"mathvariant":321},[2340,8456,8457,8459,8461],{},[46,8458,176],{},[46,8460,51],{},[46,8462,2120],{},[309,8464,331],{"stretchy":311},[53,8466,8467],{"encoding":55},"\\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。",[14,10278,10279],{},"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。",[24,10281,10283],{"className":10282},[1776],[24,10284,10286,10737],{"className":10285},[27],[24,10287,10289],{"className":10288},[31],[33,10290,10291],{"xmlns":35,"display":1785},[37,10292,10293,10734],{},[40,10294,10295,10303,10305,10311,10313,10315,10317,10319,10325,10327,10329,10335,10337,10349,10351,10353,10359,10361,10367,10369,10371,10379,10381,10387,10389,10391,10393,10395,10401,10403,10405,10417,10419,10425,10431,10433,10445,10447,10449,10455,10457,10463,10465,10467,10476,10478,10484,10486,10488,10490,10492,10498,10500,10502,10505,10517,10519,10525,10527,10539,10541,10547,10553,10555,10567,10569,10571,10577,10579,10585,10587,10589,10601,10603,10611,10613,10619,10621,10623,10625,10627,10633,10635,10637,10639,10651,10653,10659,10661,10673,10675,10681,10683,10695,10697,10700,10702,10708,10710,10716,10718,10724,10726,10732],{},[2340,10296,10297,10299,10301],{},[46,10298,8035],{},[46,10300,1463],{},[596,10302,616],{},[309,10304,312],{"stretchy":311},[43,10306,10307,10309],{},[46,10308,176],{},[46,10310,51],{},[309,10312,601],{"separator":61},[46,10314,48],{},[309,10316,331],{"stretchy":311},[309,10318,918],{},[43,10320,10321,10323],{},[46,10322,456],{},[46,10324,51],{},[309,10326,913],{},[46,10328,6441],{},[43,10330,10331,10333],{},[46,10332,7915],{},[46,10334,1463],{},[309,10336,312],{"stretchy":311},[43,10338,10339,10341],{},[46,10340,176],{},[40,10342,10343,10345,10347],{},[46,10344,51],{},[309,10346,913],{},[596,10348,616],{},[309,10350,331],{"stretchy":311},[309,10352,5809],{},[43,10354,10355,10357],{},[46,10356,7915],{},[46,10358,1463],{},[309,10360,312],{"stretchy":311},[43,10362,10363,10365],{},[46,10364,176],{},[46,10366,51],{},[309,10368,331],{"stretchy":311},[700,10370],{"linebreak":9106},[2340,10372,10373,10375,10377],{},[46,10374,8035],{},[46,10376,1463],{},[596,10378,9241],{},[309,10380,312],{"stretchy":311},[43,10382,10383,10385],{},[46,10384,176],{},[46,10386,51],{},[309,10388,601],{"separator":61},[46,10390,48],{},[309,10392,331],{"stretchy":311},[309,10394,918],{},[43,10396,10397,10399],{},[46,10398,456],{},[46,10400,51],{},[309,10402,913],{},[46,10404,6441],{},[43,10406,10407,10409],{},[46,10408,456],{},[40,10410,10411,10413,10415],{},[46,10412,51],{},[309,10414,913],{},[596,10416,616],{},[309,10418,913],{},[2132,10420,10421,10423],{},[46,10422,6441],{},[596,10424,9241],{},[43,10426,10427,10429],{},[46,10428,7915],{},[46,10430,1463],{},[309,10432,312],{"stretchy":311},[43,10434,10435,10437],{},[46,10436,176],{},[40,10438,10439,10441,10443],{},[46,10440,51],{},[309,10442,913],{},[596,10444,9241],{},[309,10446,331],{"stretchy":311},[309,10448,5809],{},[43,10450,10451,10453],{},[46,10452,7915],{},[46,10454,1463],{},[309,10456,312],{"stretchy":311},[43,10458,10459,10461],{},[46,10460,176],{},[46,10462,51],{},[309,10464,331],{"stretchy":311},[700,10466],{"linebreak":9106},[2340,10468,10469,10471,10473],{},[46,10470,8035],{},[46,10472,1463],{},[596,10474,10475],{},"3",[309,10477,312],{"stretchy":311},[43,10479,10480,10482],{},[46,10481,176],{},[46,10483,51],{},[309,10485,601],{"separator":61},[46,10487,48],{},[309,10489,331],{"stretchy":311},[309,10491,918],{},[43,10493,10494,10496],{},[46,10495,456],{},[46,10497,51],{},[309,10499,913],{},[46,10501,6441],{},[309,10503,10504],{},"∗",[43,10506,10507,10509],{},[46,10508,456],{},[40,10510,10511,10513,10515],{},[46,10512,51],{},[309,10514,913],{},[596,10516,616],{},[309,10518,913],{},[2132,10520,10521,10523],{},[46,10522,6441],{},[596,10524,9241],{},[309,10526,10504],{},[43,10528,10529,10531],{},[46,10530,456],{},[40,10532,10533,10535,10537],{},[46,10534,51],{},[309,10536,913],{},[596,10538,9241],{},[309,10540,913],{},[2132,10542,10543,10545],{},[46,10544,6441],{},[596,10546,10475],{},[43,10548,10549,10551],{},[46,10550,7915],{},[46,10552,1463],{},[309,10554,312],{"stretchy":311},[43,10556,10557,10559],{},[46,10558,176],{},[40,10560,10561,10563,10565],{},[46,10562,51],{},[309,10564,913],{},[596,10566,10475],{},[309,10568,331],{"stretchy":311},[309,10570,5809],{},[43,10572,10573,10575],{},[46,10574,7915],{},[46,10576,1463],{},[309,10578,312],{"stretchy":311},[43,10580,10581,10583],{},[46,10582,176],{},[46,10584,51],{},[309,10586,331],{"stretchy":311},[700,10588],{"linebreak":9106},[40,10590,10591,10594],{},[46,10592,10593],{"mathvariant":321},"⋮",[10595,10596,10597],"mpadded",{"height":1793,"voffset":1793},[700,10598],{"mathbackground":10599,"width":1793,"height":10600},"black","1.5em",[700,10602],{"linebreak":9106},[2340,10604,10605,10607,10609],{},[46,10606,8035],{},[46,10608,1463],{},[46,10610,634],{},[309,10612,312],{"stretchy":311},[43,10614,10615,10617],{},[46,10616,176],{},[46,10618,51],{},[309,10620,601],{"separator":61},[46,10622,48],{},[309,10624,331],{"stretchy":311},[309,10626,918],{},[43,10628,10629,10631],{},[46,10630,456],{},[46,10632,51],{},[309,10634,913],{},[46,10636,6441],{},[309,10638,10504],{},[43,10640,10641,10643],{},[46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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 ",[24,12992,12994,13007],{"className":12993},[27],[24,12995,12997],{"className":12996},[31],[33,12998,12999],{"xmlns":35},[37,13000,13001,13005],{},[40,13002,13003],{},[46,13004,51],{},[53,13006,51],{"encoding":55},[24,13008,13010],{"className":13009,"ariaHidden":61},[60],[24,13011,13013,13016],{"className":13012},[65],[24,13014],{"className":13015,"style":155},[69],[24,13017,51],{"className":13018},[74,78]," 步采取特定动作带来的优势。",[24,13021,13023],{"className":13022},[1776],[24,13024,13026,13352],{"className":13025},[27],[24,13027,13029],{"className":13028},[31],[33,13030,13031],{"xmlns":35,"display":1785},[37,13032,13033,13349],{},[40,13034,13035,13043,13045,13051,13053,13055,13057,13063,13065,13077,13079,13081,13087,13089,13095,13097,13099,13113,13115,13127,13129,13131,13133,13139,13141,13153,13155,13157,13163,13165,13177,13179,13181,13189,13191,13197,13199,13201,13203,13205,13213,13215,13223,13225,13231,13233,13235,13237,13239,13247,13249,13251,13265,13267,13275,13277,13283,13285,13287,13289,13291,13299,13301,13303,13317,13319,13325,13339,13341],{},[2340,13036,13037,13039,13041],{},[46,13038,12932],{},[46,13040,51],{},[46,13042,7915],{},[309,13044,918],{},[43,13046,13047,13049],{},[46,13048,456],{},[46,13050,51],{},[309,13052,913],{},[46,13054,6441],{},[309,13056,10504],{},[43,13058,13059,13061],{},[46,13060,7915],{},[46,13062,1463],{},[309,13064,312],{"stretchy":311},[43,13066,13067,13069],{},[46,13068,176],{},[40,13070,13071,13073,13075],{},[46,13072,51],{},[309,13074,913],{},[596,13076,616],{},[309,13078,331],{"stretchy":311},[309,13080,5809],{},[43,13082,13083,13085],{},[46,13084,7915],{},[46,13086,1463],{},[309,13088,312],{"stretchy":311},[43,13090,13091,13093],{},[46,13092,176],{},[46,13094,51],{},[309,13096,331],{"stretchy":311},[700,13098],{"linebreak":9106},[2340,13100,13101,13103,13111],{},[46,13102,12932],{},[40,13104,13105,13107,13109],{},[46,13106,51],{},[309,13108,913],{},[596,13110,616],{},[46,13112,7915],{},[309,13114,918],{},[43,13116,13117,13119],{},[46,13118,456],{},[40,13120,13121,13123,13125],{},[46,13122,51],{},[309,13124,913],{},[596,13126,616],{},[309,13128,913],{},[46,13130,6441],{},[309,13132,10504],{},[43,13134,13135,13137],{},[46,13136,7915],{},[46,13138,1463],{},[309,13140,312],{"stretchy":311},[43,13142,13143,13145],{},[46,13144,176],{},[40,13146,13147,13149,13151],{},[46,13148,51],{},[309,13150,913],{},[596,13152,9241],{},[309,13154,331],{"stretchy":311},[309,13156,5809],{},[43,13158,13159,13161],{},[46,13160,7915],{},[46,13162,1463],{},[309,13164,312],{"stretchy":311},[43,13166,13167,13169],{},[46,13168,176],{},[40,13170,13171,13173,13175],{},[46,13172,51],{},[309,13174,913],{},[596,13176,616],{},[309,13178,331],{"stretchy":311},[700,13180],{"linebreak":9106},[2340,13182,13183,13185,13187],{},[46,13184,8035],{},[46,13186,1463],{},[596,13188,616],{},[309,13190,312],{"stretchy":311},[43,13192,13193,13195],{},[46,13194,176],{},[46,13196,51],{},[309,13198,601],{"separator":61},[46,13200,48],{},[309,13202,331],{"stretchy":311},[309,13204,918],{},[2340,13206,13207,13209,13211],{},[46,13208,12932],{},[46,13210,51],{},[46,13212,7915],{},[700,13214],{"linebreak":9106},[2340,13216,13217,13219,13221],{},[46,13218,8035],{},[46,13220,1463],{},[596,13222,9241],{},[309,13224,312],{"stretchy":311},[43,13226,13227,13229],{},[46,13228,176],{},[46,13230,51],{},[309,13232,601],{"separator":61},[46,13234,48],{},[309,13236,331],{"stretchy":311},[309,13238,918],{},[2340,13240,13241,13243,13245],{},[46,13242,12932],{},[46,13244,51],{},[46,13246,7915],{},[309,13248,913],{},[46,13250,6441],{},[2340,13252,13253,13255,13263],{},[46,13254,12932],{},[40,13256,13257,13259,13261],{},[46,13258,51],{},[309,13260,913],{},[596,13262,616],{},[46,13264,7915],{},[700,13266],{"linebreak":9106},[2340,13268,13269,13271,13273],{},[46,13270,8035],{},[46,13272,1463],{},[596,13274,10475],{},[309,13276,312],{"stretchy":311},[43,13278,13279,13281],{},[46,13280,176],{},[46,13282,51],{},[309,13284,601],{"separator":61},[46,13286,48],{},[309,13288,331],{"stretchy":311},[309,13290,918],{},[2340,13292,13293,13295,13297],{},[46,13294,12932],{},[46,13296,51],{},[46,13298,7915],{},[309,13300,913],{},[46,13302,6441],{},[2340,13304,13305,13307,13315],{},[46,13306,12932],{},[40,13308,13309,13311,13313],{},[46,13310,51],{},[309,13312,913],{},[596,13314,616],{},[46,13316,7915],{},[309,13318,913],{},[2132,13320,13321,13323],{},[46,13322,6441],{},[596,13324,9241],{},[2340,13326,13327,13329,13337],{},[46,13328,12932],{},[40,13330,13331,13333,13335],{},[46,13332,51],{},[309,13334,913],{},[596,13336,9241],{},[46,13338,7915],{},[700,13340],{"linebreak":9106},[40,13342,13343,13345],{},[46,13344,10593],{"mathvariant":321},[10595,13346,13347],{"height":1793,"voffset":1793},[700,13348],{"mathbackground":10599,"width":1793,"height":10600},[53,13350,13351],{"encoding":55},"\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",[24,13353,13355,13423,13478,13496,13606,13698,13701,13778,13842,13860,13970,14071,14074,14195,14252,14255,14376,14442,14511,14514,14635,14701,14779,14874,14877],{"className":13354,"ariaHidden":61},[60],[24,13356,13358,13362,13414,13417,13420],{"className":13357},[65],[24,13359],{"className":13360,"style":13361},[69],"height:1.1383em;vertical-align:-0.247em;",[24,13363,13365,13368],{"className":13364},[74],[24,13366,12932],{"className":13367,"style":12954},[74,78],[24,13369,13371],{"className":13370},[82],[24,13372,13374,13406],{"className":13373},[86,87],[24,13375,13377,13403],{"className":13376},[91],[24,13378,13380,13392],{"className":13379,"style":12251},[95],[24,13381,13383,13386],{"style":13382},"top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;",[24,13384],{"className":13385,"style":104},[103],[24,13387,13389],{"className":13388},[108,109,110,111],[24,13390,51],{"className":13391},[74,78,111],[24,13393,13394,13397],{"style":3865},[24,13395],{"className":13396,"style":104},[103],[24,13398,13400],{"className":13399},[108,109,110,111],[24,13401,7915],{"className":13402,"style":7942},[74,78,111],[24,13404,119],{"className":13405},[118],[24,13407,13409],{"className":13408},[91],[24,13410,13412],{"className":13411,"style":4783},[95],[24,13413],{},[24,13415],{"className":13416,"style":1007},[700],[24,13418,918],{"className":13419},[1011],[24,13421],{"className":13422,"style":1007},[700],[24,13424,13426,13429,13469,13472,13475],{"className":13425},[65],[24,13427],{"className":13428,"style":9366},[69],[24,13430,13432,13435],{"className":13431},[74],[24,13433,456],{"className":13434,"style":477},[74,78],[24,13436,13438],{"className":13437},[82],[24,13439,13441,13461],{"className":13440},[86,87],[24,13442,13444,13458],{"className":13443},[91],[24,13445,13447],{"className":13446,"style":96},[95],[24,13448,13449,13452],{"style":492},[24,13450],{"className":13451,"style":104},[103],[24,13453,13455],{"className":13454},[108,109,110,111],[24,13456,51],{"className":13457},[74,78,111],[24,13459,119],{"className":13460},[118],[24,13462,13464],{"className":13463},[91],[24,13465,13467],{"className":13466,"style":126},[95],[24,13468],{},[24,13470],{"className":13471,"style":3225},[700],[24,13473,913],{"className":13474},[988],[24,13476],{"className":13477,"style":3225},[700],[24,13479,13481,13484,13487,13490,13493],{"className":13480},[65],[24,13482],{"className":13483,"style":11785},[69],[24,13485,6441],{"className":13486,"style":6688},[74,78],[24,13488],{"className":13489,"style":3225},[700],[24,13491,10504],{"className":13492},[988],[24,13494],{"className":13495,"style":3225},[700],[24,13497,13499,13502,13542,13545,13594,13597,13600,13603],{"className":13498},[65],[24,13500],{"className":13501,"style":344},[69],[24,13503,13505,13508],{"className":13504},[74],[24,13506,7915],{"className":13507,"style":7942},[74,78],[24,13509,13511],{"className":13510},[82],[24,13512,13514,13534],{"className":13513},[86,87],[24,13515,13517,13531],{"className":13516},[91],[24,13518,13520],{"className":13519,"style":1740},[95],[24,13521,13522,13525],{"style":7957},[24,13523],{"className":13524,"style":104},[103],[24,13526,13528],{"className":13527},[108,109,110,111],[24,13529,1463],{"className":13530,"style":477},[74,78,111],[24,13532,119],{"className":13533},[118],[24,13535,13537],{"className":13536},[91],[24,13538,13540],{"className":13539,"style":126},[95],[24,13541],{},[24,13543,312],{"className":13544},[351],[24,13546,13548,13551],{"className":13547},[74],[24,13549,176],{"className":13550},[74,78],[24,13552,13554],{"className":13553},[82],[24,13555,13557,13586],{"className":13556},[86,87],[24,13558,13560,13583],{"className":13559},[91],[24,13561,13563],{"className":13562,"style":670},[95],[24,13564,13565,13568],{"style":99},[24,13566],{"className":13567,"style":104},[103],[24,13569,13571],{"className":13570},[108,109,110,111],[24,13572,13574,13577,13580],{"className":13573},[74,111],[24,13575,51],{"className":13576},[74,78,111],[24,13578,913],{"className":13579},[988,111],[24,13581,616],{"className":13582},[74,111],[24,13584,119],{"className":13585},[118],[24,13587,13589],{"className":13588},[91],[24,13590,13592],{"className":13591,"style":1001},[95],[24,13593],{},[24,13595,331],{"className":13596},[438],[24,13598],{"className":13599,"style":3225},[700],[24,13601,5809],{"className":13602},[988],[24,13604],{"className":13605,"style":3225},[700],[24,13607,13609,13612,13652,13655,13695],{"className":13608},[65],[24,13610],{"className":13611,"style":344},[69],[24,13613,13615,13618],{"className":13614},[74],[24,13616,7915],{"className":13617,"style":7942},[74,78],[24,13619,13621],{"className":13620},[82],[24,13622,13624,13644],{"className":13623},[86,87],[24,13625,13627,13641],{"className":13626},[91],[24,13628,13630],{"className":13629,"style":1740},[95],[24,13631,13632,13635],{"style":7957},[24,13633],{"className":13634,"style":104},[103],[24,13636,13638],{"className":13637},[108,109,110,111],[24,1363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Advantage Estimation (GAE)",[14,14898,14899],{},"这时我们考虑，在运行时我们应该向后采样几步呢？GAE 的答案是，小孩子才做选择，我全都要！",[14,14901,14902,14903,14934],{},"GAE考虑全部的采样结果，并引入一个衰减因子 ",[24,14904,14906,14921],{"className":14905},[27],[24,14907,14909],{"className":14908},[31],[33,14910,14911],{"xmlns":35},[37,14912,14913,14918],{},[40,14914,14915],{},[46,14916,14917],{},"λ",[53,14919,14920],{"encoding":55},"\\lambda",[24,14922,14924],{"className":14923,"ariaHidden":61},[60],[24,14925,14927,14931],{"className":14926},[65],[24,14928],{"className":14929,"style":14930},[69],"height:0.6944em;",[24,14932,14917],{"className":14933},[74,78]," 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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。",[14,17728,17729],{},"GAE 优势函数平衡了采样不同步带来的方差和偏差的问题。",[14,17731,17732],{},"现在我们来看上面得之不易的三个表达式：",[24,17734,17736],{"className":17735},[1776],[24,17737,17739,17995],{"className":17738},[27],[24,17740,17742],{"className":17741},[31],[33,17743,17744],{"xmlns":35,"display":1785},[37,17745,17746,17992],{},[40,17747,17748,17756,17758,17764,17766,17768,17774,17776,17788,17790,17792,17798,17800,17806,17808,17810,17824,17826,17832,17834,17836,17838,17840,17854,17856,17858,17860,17866,17880,17882,17888,17902,17920,17934,17936,17944,17946,17954,17956,17958,17960,17962,17964,17970,17972,17980,17982,17990],{},[2340,17749,17750,17752,17754],{},[46,17751,12932],{},[46,17753,51],{},[46,17755,7915],{},[309,17757,918],{},[43,17759,17760,17762],{},[46,17761,456],{},[46,17763,51],{},[309,17765,913],{},[46,17767,6441],{},[43,17769,17770,17772],{},[46,17771,7915],{},[46,17773,1463],{},[309,17775,312],{"stretchy":311},[43,17777,17778,17780],{},[46,17779,176],{},[40,17781,17782,17784,17786],{},[46,17783,51],{},[309,17785,913],{},[596,17787,616],{},[309,17789,331],{"stretchy":311},[309,17791,5809],{},[43,17793,17794,17796],{},[46,17795,7915],{},[46,17797,1463],{},[309,17799,312],{"stretchy":311},[43,17801,17802,17804],{},[46,17803,176],{},[46,17805,51],{},[309,17807,331],{"stretchy":311},[700,17809],{"linebreak":9106},[2340,17811,17812,17814,17816],{},[46,17813,8035],{},[46,17815,1463],{},[40,17817,17818,17820,17822],{},[46,17819,14968],{},[46,17821,8035],{},[46,17823,1434],{},[309,17825,312],{"stretchy":311},[43,17827,17828,17830],{},[46,17829,176],{},[46,17831,51],{},[309,17833,601],{"separator":61},[46,17835,48],{},[309,17837,331],{"stretchy":311},[309,17839,918],{},[2112,17841,17842,17844,17852],{},[309,17843,1477],{},[40,17845,17846,17848,17850],{},[46,17847,15499],{},[309,17849,918],{},[596,17851,598],{},[46,17853,15506],{"mathvariant":321},[309,17855,312],{"stretchy":311},[46,17857,6441],{},[46,17859,14917],{},[2132,17861,17862,17864],{},[309,17863,331],{"stretchy":311},[46,17865,15499],{},[2340,17867,17868,17870,17878],{},[46,17869,12932],{},[40,17871,17872,17874,17876],{},[46,17873,51],{},[309,17875,913],{},[46,17877,15499],{},[46,17879,7915],{},[700,17881],{"linebreak":9106},[1977,17883,17884,17886],{},[596,17885,616],{},[46,17887,2110],{},[2112,17889,17890,17892,17900],{},[309,17891,1477],{},[40,17893,17894,17896,17898],{},[46,17895,2120],{},[309,17897,918],{},[596,17899,616],{},[46,17901,2110],{},[2112,17903,17904,17906,17914],{},[309,17905,1477],{},[40,17907,17908,17910,17912],{},[46,17909,51],{},[309,17911,918],{},[596,17913,616],{},[43,17915,17916,17918],{},[46,17917,634],{},[46,17919,2120],{},[2340,17921,17922,17924,17926],{},[46,17923,8035],{},[46,17925,1463],{},[40,17927,17928,17930,17932],{},[46,17929,14968],{},[46,17931,8035],{},[46,17933,1434],{},[309,17935,312],{"stretchy":311},[2340,17937,17938,17940,17942],{},[46,17939,176],{},[46,17941,2120],{},[46,17943,51],{},[309,17945,601],{"separator":61},[2340,17947,17948,17950,17952],{},[46,17949,48],{},[46,17951,2120],{},[46,17953,51],{},[309,17955,331],{"stretchy":311},[15052,17957,15054],{},[46,17959,1807],{"mathvariant":321},[46,17961,2236],{},[309,17963,2239],{},[43,17965,17966,17968],{},[46,17967,1146],{},[46,17969,1463],{},[309,17971,312],{"stretchy":311},[2340,17973,17974,17976,17978],{},[46,17975,48],{},[46,17977,2120],{},[46,17979,51],{},[46,17981,322],{"mathvariant":321},[2340,17983,17984,17986,17988],{},[46,17985,176],{},[46,17987,2120],{},[46,17989,51],{},[309,17991,331],{"stretchy":311},[53,17993,17994],{"encoding":55},"\\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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assName":19202},[108,109,110,111],[24,19204,51],{"className":19205},[74,78,111],[24,19207,119],{"className":19208},[118],[24,19210,19212],{"className":19211},[91],[24,19213,19215],{"className":19214,"style":4783},[95],[24,19216],{},[24,19218,331],{"className":19219},[438],[14,19221,19222],{},"这里的价值状态函数我们一般用一个神经网路进行拟合，一般可以和策略网络公用参数，只是最后一层不同。",[10,19224,19226],{"id":19225},"proximal-policy-optimization-ppo-近邻策略优化算法","Proximal Policy Optimization (PPO) 近邻策略优化算法",[14,19228,19229],{},"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。",[14893,19231,19232],{"id":19232},"重要性采样",[14,19234,19235,19236,19281,19282,19311,19312,19341,19342,19370],{},"将 ",[24,19237,19239,19260],{"className":19238},[27],[24,19240,19242],{"className":19241},[31],[33,19243,19244],{"xmlns":35},[37,19245,19246,19257],{},[40,19247,19248,19250,19252,19255],{},[46,19249,921],{},[309,19251,312],{"stretchy":311},[46,19253,19254],{},"x",[309,19256,331],{"stretchy":311},[53,19258,19259],{"encoding":55},"f(x)",[24,19261,19263],{"className":19262,"ariaHidden":61},[60],[24,19264,19266,19269,19272,19275,19278],{"className":19265},[65],[24,19267],{"className":19268,"style":344},[69],[24,19270,921],{"className":19271,"style":1024},[74,78],[24,19273,312],{"className":19274},[351],[24,19276,19254],{"className":19277},[74,78],[24,19279,331],{"className":19280},[438]," 在分布 ",[24,19283,19285,19298],{"className":19284},[27],[24,19286,19288],{"className":19287},[31],[33,19289,19290],{"xmlns":35},[37,19291,19292,19296],{},[40,19293,19294],{},[46,19295,14],{},[53,19297,14],{"encoding":55},[24,19299,19301],{"className":19300,"ariaHidden":61},[60],[24,19302,19304,19308],{"className":19303},[65],[24,19305],{"className":19306,"style":19307},[69],"height:0.625em;vertical-align:-0.1944em;",[24,19309,14],{"className":19310},[74,78]," 下的期望改写为在另一分布 ",[24,19313,19315,19329],{"className":19314},[27],[24,19316,19318],{"className":19317},[31],[33,19319,19320],{"xmlns":35},[37,19321,19322,19327],{},[40,19323,19324],{},[46,19325,19326],{},"q",[53,19328,19326],{"encoding":55},[24,19330,19332],{"className":19331,"ariaHidden":61},[60],[24,19333,19335,19338],{"className":19334},[65],[24,19336],{"className":19337,"style":19307},[69],[24,19339,19326],{"className":19340,"style":292},[74,78],"（proposal）下的期望，从而可用从 ",[24,19343,19345,19358],{"className":19344},[27],[24,19346,19348],{"className":19347},[31],[33,19349,19350],{"xmlns":35},[37,19351,19352,19356],{},[40,19353,19354],{},[46,19355,19326],{},[53,19357,19326],{"encoding":55},[24,19359,19361],{"className":19360,"ariaHidden":61},[60],[24,19362,19364,19367],{"className":19363},[65],[24,19365],{"className":19366,"style":19307},[69],[24,19368,19326],{"className":19369,"style":292},[74,78]," 采样的数据估计：",[24,19372,19374],{"className":19373},[1776],[24,19375,19377,19762],{"className":19376},[27],[24,19378,19380],{"className":19379},[31],[33,19381,19382],{"xmlns":35,"display":1785},[37,19383,19384,19759],{},[1789,19385,19386,19459,19523,19587,19659],{"rowspacing":1791,"columnalign":1792,"columnspacing":1793},[1795,19387,19388,19425],{},[1798,19389,19390],{},[1801,19391,19392],{"scriptlevel":598,"displaystyle":61},[40,19393,19394,19397,19399,19401,19403,19405,19407],{},[46,19395,1434],{"mathvariant":19396},"double-struck",[309,19398,312],{"stretchy":311},[46,19400,921],{},[309,19402,312],{"stretchy":311},[46,19404,19254],{},[309,19406,331],{"stretchy":311},[43,19408,19409,19411],{},[309,19410,331],{"stretchy":311},[40,19412,19413,19415,19417,19419,19421,19423],{},[46,19414,19254],{},[309,19416,1456],{},[46,19418,14],{},[309,19420,312],{"stretchy":311},[46,19422,19254],{},[309,19424,331],{"stretchy":311},[1798,19426,19427],{},[1801,19428,19429],{"scriptlevel":598,"displaystyle":61},[40,19430,19431,19433,19435,19441,19443,19445,19447,19449,19451,19453,19455,19457],{},[40,19432],{},[309,19434,918],{},[1473,19436,19437,19439],{},[309,19438,1477],{},[46,19440,19254],{},[46,19442,921],{},[309,19444,312],{"stretchy":311},[46,19446,19254],{},[309,19448,331],{"stretchy":311},[309,19450,1151],{},[46,19452,14],{},[309,19454,312],{"stretchy":311},[46,19456,19254],{},[309,19458,331],{"stretchy":311},[1795,19460,19461,19467],{},[1798,19462,19463],{},[1801,19464,19465],{"scriptlevel":598,"displaystyle":61},[40,19466],{},[1798,19468,19469],{},[1801,19470,19471],{"scriptlevel":598,"displaystyle":61},[40,19472,19473,19475,19477,19483,19485,19487,19489,19491,19493,19495,19497,19499,19501],{},[40,19474],{},[309,19476,918],{},[1473,19478,19479,19481],{},[309,19480,1477],{},[46,19482,19254],{},[46,19484,921],{},[309,19486,312],{"stretchy":311},[46,19488,19254],{},[309,19490,331],{"stretchy":311},[309,19492,1151],{},[46,19494,14],{},[309,19496,312],{"stretchy":311},[46,19498,19254],{},[309,19500,331],{"stretchy":311},[1977,19502,19503,19513],{},[40,19504,19505,19507,19509,19511],{},[46,19506,19326],{},[309,19508,312],{"stretchy":311},[46,19510,19254],{},[309,19512,331],{"stretchy":311},[40,19514,19515,19517,19519,19521],{},[46,19516,19326],{},[309,19518,312],{"stretchy":311},[46,19520,19254],{},[309,19522,331],{"stretchy":311},[1795,19524,19525,19531],{},[1798,19526,19527],{},[1801,19528,19529],{"scriptlevel":598,"displaystyle":61},[40,19530],{},[1798,19532,19533],{},[1801,19534,19535],{"scriptlevel":598,"displaystyle":61},[40,19536,19537,19539,19541,19547,19549,19551,19553,19555,19577,19579,19581,19583,19585],{},[40,19538],{},[309,19540,918],{},[1473,19542,19543,19545],{},[309,19544,1477],{},[46,19546,19254],{},[46,19548,921],{},[309,19550,312],{"stretchy":311},[46,19552,19254],{},[309,19554,331],{"stretchy":311},[1977,19556,19557,19567],{},[40,19558,19559,19561,19563,19565],{},[46,19560,14],{},[309,19562,312],{"stretchy":311},[46,19564,19254],{},[309,19566,331],{"stretchy":311},[40,19568,19569,19571,19573,19575],{},[46,19570,19326],{},[309,19572,312],{"stretchy":311},[46,19574,19254],{},[309,19576,331],{"stretchy":311},[309,19578,1151],{},[46,19580,19326],{},[309,19582,312],{"stretchy":311},[46,19584,19254],{},[309,19586,331],{"stretchy":311},[1795,19588,19589,19595],{},[1798,19590,19591],{},[1801,19592,19593],{"scriptlevel":598,"displaystyle":61},[40,19594],{},[1798,19596,19597],{},[1801,19598,19599],{"scriptlevel":598,"displaystyle":61},[40,19600,19601,19603,19605,19607],{},[40,19602],{},[309,19604,918],{},[46,19606,1434],{"mathvariant":19396},[43,19608,19609,19645],{},[40,19610,19611,19613,19615,19617,19619,19621,19643],{},[309,19612,312],{"fence":61},[46,19614,921],{},[309,19616,312],{"stretchy":311},[46,19618,19254],{},[309,19620,331],{"stretchy":311},[1977,19622,19623,19633],{},[40,19624,19625,19627,19629,19631],{},[46,19626,14],{},[309,19628,312],{"stretchy":311},[46,19630,19254],{},[309,19632,331],{"stretchy":311},[40,19634,19635,19637,19639,19641],{},[46,19636,19326],{},[309,19638,312],{"stretchy":311},[46,19640,19254],{},[309,19642,331],{"stretchy":311},[309,19644,331],{"fence":61},[40,19646,19647,19649,19651,19653,19655,19657],{},[46,19648,19254],{},[309,19650,1456],{},[46,19652,19326],{},[309,19654,312],{"stretchy":311},[46,19656,19254],{},[309,19658,331],{"stretchy":311},[1795,19660,19661,19667],{},[1798,19662,19663],{},[1801,19664,19665],{"scriptlevel":598,"displaystyle":61},[40,19666],{},[1798,19668,19669],{},[1801,19670,19671],{"scriptlevel":598,"displaystyle":61},[40,19672,19673,19675,19677,19683,19697,19699,19701,19707,19709,19739,19741,19743,19749,19751,19753,19755,19757],{},[40,19674],{},[309,19676,2103],{},[1977,19678,19679,19681],{},[596,19680,616],{},[46,19682,2110],{},[2112,19684,19685,19687,19695],{},[309,19686,1477],{},[40,19688,19689,19691,19693],{},[46,19690,2120],{},[309,19692,918],{},[596,19694,616],{},[46,19696,2110],{},[46,19698,921],{},[309,19700,312],{"stretchy":311},[43,19702,19703,19705],{},[46,19704,19254],{},[46,19706,2120],{},[309,19708,331],{"stretchy":311},[1977,19710,19711,19725],{},[40,19712,19713,19715,19717,19723],{},[46,19714,14],{},[309,19716,312],{"stretchy":311},[43,19718,19719,19721],{},[46,19720,19254],{},[46,19722,2120],{},[309,19724,331],{"stretchy":311},[40,19726,19727,19729,19731,19737],{},[46,19728,19326],{},[309,19730,312],{"stretchy":311},[43,19732,19733,19735],{},[46,19734,19254],{},[46,19736,2120],{},[309,19738,331],{"stretchy":311},[309,19740,601],{"separator":61},[700,19742],{"width":15059},[43,19744,19745,19747],{},[46,19746,19254],{},[46,19748,2120],{},[309,19750,1456],{},[46,19752,19326],{},[309,19754,312],{"stretchy":311},[46,19756,19254],{},[309,19758,331],{"stretchy":311},[53,19760,19761],{"encoding":55},"\\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}",[24,19763,19765],{"className":19764,"ariaHidden":61},[60],[24,19766,19768,19772],{"className":19767},[65],[24,19769],{"className":19770,"style":19771},[69],"height:14.8742em;vertical-align:-7.1871em;",[24,19773,19775],{"className":19774},[74],[24,19776,19778,19926],{"className":19777},[1789],[24,19779,19781],{"className":19780},[2586],[24,19782,19784,19917],{"className":19783},[86,87],[24,19785,19787,19914],{"className":19786},[91],[24,19788,19791,19878,19887,19896,19905],{"className":19789,"style":19790},[95],"height:7.6871em;",[24,19792,19794,19798],{"style":19793},"top:-10.4654em;",[24,19795],{"className":19796,"style":19797},[103],"height:3.8283em;",[24,19799,19801,19805,19808,19811,19814,19817,19820],{"className":19800},[74],[24,19802,1434],{"className":19803},[74,19804],"mathbb",[24,19806,312],{"className":19807},[351],[24,19809,921],{"className":19810,"style":1024},[74,78],[24,19812,312],{"className":19813},[351],[24,19815,19254],{"className":19816},[74,78],[24,19818,331],{"className":19819},[438],[24,19821,19823,19826],{"className":19822},[438],[24,19824,331],{"className":19825},[438],[24,19827,19829],{"className":19828},[82],[24,19830,19832,19870],{"className":19831},[86,87],[24,19833,19835,19867],{"className":19834},[91],[24,19836,19838],{"className":19837,"style":1550},[95],[24,19839,19840,19843],{"style":1553},[24,19841],{"className":19842,"style":104},[103],[24,19844,19846],{"className":19845},[108,109,110,111],[24,19847,19849,19852,19855,19858,19861,19864],{"className":19848},[74,111],[24,19850,19254],{"className":19851},[74,78,111],[24,19853,1456],{"className":19854},[1011,111],[24,19856,14],{"className":19857},[74,78,111],[24,19859,312],{"className":19860},[351,111],[24,19862,19254],{"className":19863},[74,78,111],[24,19865,331],{"className":19866},[438,111],[24,19868,119],{"className":19869},[118],[24,19871,19873],{"className":19872},[91],[24,19874,19876],{"className":19875,"style":1635},[95],[24,19877],{},[24,19879,19881,19884],{"style":19880},"top:-7.4884em;",[24,19882],{"className":19883,"style":19797},[103],[24,19885],{"className":19886},[74],[24,19888,19890,19893],{"style":19889},"top:-4.5114em;",[24,19891],{"className":19892,"style":19797},[103],[24,19894],{"className":19895},[74],[24,19897,19899,19902],{"style":19898},"top:-1.5114em;",[24,19900],{"className":19901,"style":19797},[103],[24,19903],{"className":19904},[74],[24,19906,19908,19911],{"style":19907},"top:1.7917em;",[24,19909],{"className":19910,"style":19797},[103],[24,19912],{"className":19913},[74],[24,19915,119],{"className":19916},[118],[24,19918,19920],{"className":19919},[91],[24,19921,19924],{"className":19922,"style":19923},[95],"height:7.1871em;",[24,19925],{},[24,19927,19929],{"className":19928},[2810],[24,19930,19932,21030],{"className":19931},[86,87],[24,19933,19935,21027],{"className":19934},[91],[24,19936,19938,20041,20224,20407,20598],{"className":19937,"style":19790},[95],[24,19939,19940,19943],{"style":19793},[24,19941],{"className":19942,"style":19797},[103],[24,19944,19946,19949,19952,19955,19958,20005,20008,20011,20014,20017,20020,20023,20026,20029,20032,20035,20038],{"className":19945},[74],[24,19947],{"className":19948},[74],[24,19950],{"className":19951,"style":1007},[700],[24,19953,918],{"className":19954},[1011],[24,19956],{"className":19957,"style":1007},[700],[24,19959,19961],{"className":19960},[1657,1658],[24,19962,19964,19997],{"className":19963},[86,87],[24,19965,19967,19994],{"className":19966},[91],[24,19968,19970,19984],{"className":19969,"style":2858},[95],[24,19971,19972,19975],{"style":2861},[24,19973],{"className":19974,"style":2865},[103],[24,19976,19978],{"className":19977},[108,109,110,111],[24,19979,19981],{"className":19980},[74,111],[24,19982,19254],{"className":19983},[74,78,111],[24,19985,19986,19989],{"style":2874},[24,19987],{"className":19988,"style":2865},[103],[24,19990,19991],{},[24,19992,1477],{"className":19993},[1657,1693,2883],[24,19995,119],{"className":19996},[118],[24,19998,20000],{"className":19999},[91],[24,20001,20003],{"className":20002,"style":2893},[95],[24,20004],{},[24,20006],{"className":20007,"style":701},[700],[24,20009,921],{"className":20010,"style":1024},[74,78],[24,20012,312],{"className":20013},[351],[24,20015,19254],{"className":20016},[74,78],[24,20018,331],{"className":20019},[438],[24,20021],{"className":20022,"style":3225},[700],[24,20024,1151],{"className":20025},[988],[24,20027],{"className":20028,"style":3225},[700],[24,20030,14],{"className":20031},[74,78],[24,20033,312],{"className":20034},[351],[24,20036,19254],{"className":20037},[74,78],[24,20039,331],{"className":20040},[438],[24,20042,20043,20046],{"style":19880},[24,20044],{"className":20045,"style":19797},[103],[24,20047,20049,20052,20055,20058,20061,20108,20111,20114,20117,20120,20123,20126,20129,20132,20135,20138,20141,20144],{"className":20048},[74],[24,20050],{"className":20051},[74],[24,20053],{"className":20054,"style":1007},[700],[24,20056,918],{"className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on-policy 的训练改为 off-policy 的训练。",[14893,21042,21044],{"id":21043},"off-policy","Off-policy",[14,21046,21047,21048,21111,21112,21141,21142,21280,21281,21472,21473,21688],{},"记 ",[24,21049,21051,21069],{"className":21050},[27],[24,21052,21054],{"className":21053},[31],[33,21055,21056],{"xmlns":35},[37,21057,21058,21066],{},[40,21059,21060],{},[2132,21061,21062,21064],{},[46,21063,1463],{},[309,21065,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[53,21067,21068],{"encoding":55},"\\theta'",[24,21070,21072],{"className":21071,"ariaHidden":61},[60],[24,21073,21075,21079],{"className":21074},[65],[24,21076],{"className":21077,"style":21078},[69],"height:0.7519em;",[24,21080,21082,21085],{"className":21081},[74],[24,21083,1463],{"className":21084,"style":477},[74,78],[24,21086,21088],{"className":21087},[82],[24,21089,21091],{"className":21090},[86],[24,21092,21094],{"className":21093},[91],[24,21095,21097],{"className":21096,"style":21078},[95],[24,21098,21099,21102],{"style":4064},[24,21100],{"className":21101,"style":104},[103],[24,21103,21105],{"className":21104},[108,109,110,111],[24,21106,21108],{"className":21107},[74,111],[24,21109,6430],{"className":21110},[74,111]," 为采集数据时的旧策略，",[24,21113,21115,21129],{"className":21114},[27],[24,21116,21118],{"className":21117},[31],[33,21119,21120],{"xmlns":35},[37,21121,21122,21126],{},[40,21123,21124],{},[46,21125,1463],{},[53,21127,21128],{"encoding":55},"\\theta",[24,21130,21132],{"className":21131,"ariaHidden":61},[60],[24,21133,21135,21138],{"className":21134},[65],[24,21136],{"className":21137,"style":14930},[69],[24,21139,1463],{"className":21140,"style":477},[74,78]," 为当前要优化的策略；优势 ",[24,21143,21145,21175],{"className":21144},[27],[24,21146,21148],{"className":21147},[31],[33,21149,21150],{"xmlns":35},[37,21151,21152,21172],{},[40,21153,21154],{},[2340,21155,21156,21158,21164],{},[46,21157,8035],{},[2132,21159,21160,21162],{},[46,21161,1463],{},[309,21163,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[40,21165,21166,21168,21170],{},[46,21167,14968],{},[46,21169,8035],{},[46,21171,1434],{},[53,21173,21174],{"encoding":55},"A_{\\theta'}^{GAE}",[24,21176,21178],{"className":21177,"ariaHidden":61},[60],[24,21179,21181,21185],{"className":21180},[65],[24,21182],{"className":21183,"style":21184},[69],"height:1.1244em;vertical-align:-0.2831em;",[24,21186,21188,21191],{"className":21187},[74],[24,21189,8035],{"className":21190},[74,78],[24,21192,21194],{"className":21193},[82],[24,21195,21197,21271],{"className":21196},[86,87],[24,21198,21200,21268],{"className":21199},[91],[24,21201,21204,21248],{"className":21202,"style":21203},[95],"height:0.8413em;",[24,21205,21207,21210],{"style":21206},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[24,21208],{"className":21209,"style":104},[103],[24,21211,21213],{"className":21212},[108,109,110,111],[24,21214,21216],{"className":21215},[74,111],[24,21217,21219,21222],{"className":21218},[74,111],[24,21220,1463],{"className":21221,"style":477},[74,78,111],[24,21223,21225],{"className":21224},[82],[24,21226,21228],{"className":21227},[86],[24,21229,21231],{"className":21230},[91],[24,21232,21234],{"className":21233,"style":6590},[95],[24,21235,21236,21239],{"style":6593},[24,21237],{"className":21238,"style":1593},[103],[24,21240,21242],{"className":21241},[108,1597,1598,111],[24,21243,21245],{"className":21244},[74,111],[24,21246,6430],{"className":21247},[74,111],[24,21249,21250,21253],{"style":4064},[24,21251],{"className":21252,"style":104},[103],[24,21254,21256],{"className":21255},[108,109,110,111],[24,21257,21259,21262,21265],{"className":21258},[74,111],[24,21260,14968],{"className":21261},[74,78,111],[24,21263,8035],{"className":21264},[74,78,111],[24,21266,1434],{"className":21267,"style":1416},[74,78,111],[24,21269,119],{"className":21270},[118],[24,21272,21274],{"className":21273},[91],[24,21275,21278],{"className":21276,"style":21277},[95],"height:0.2831em;",[24,21279],{}," 由旧策略下的价值网络估计。利用恒等式 ",[24,21282,21284,21338],{"className":21283},[27],[24,21285,21287],{"className":21286},[31],[33,21288,21289],{"xmlns":35},[37,21290,21291,21335],{},[40,21292,21293,21295,21297,21299,21301,21303,21305,21307,21309],{},[46,21294,1807],{"mathvariant":321},[46,21296,2236],{},[309,21298,2239],{},[46,21300,921],{},[309,21302,312],{"stretchy":311},[46,21304,19254],{},[309,21306,331],{"stretchy":311},[309,21308,918],{},[1801,21310,21311],{"scriptlevel":598,"displaystyle":61},[1977,21312,21313,21325],{},[40,21314,21315,21317,21319,21321,21323],{},[46,21316,1807],{"mathvariant":321},[46,21318,921],{},[309,21320,312],{"stretchy":311},[46,21322,19254],{},[309,21324,331],{"stretchy":311},[40,21326,21327,21329,21331,21333],{},[46,21328,921],{},[309,21330,312],{"stretchy":311},[46,21332,19254],{},[309,21334,331],{"stretchy":311},[53,21336,21337],{"encoding":55},"\\nabla \\log f(x) = \\dfrac{\\nabla f(x)}{f(x)}",[24,21339,21341,21382],{"className":21340,"ariaHidden":61},[60],[24,21342,21344,21347,21350,21353,21358,21361,21364,21367,21370,21373,21376,21379],{"className":21343},[65],[24,21345],{"className":21346,"style":344},[69],[24,21348,1807],{"className":21349},[74],[24,21351],{"className":21352,"style":701},[700],[24,21354,4290,21356],{"className":21355},[1657],[24,21357,4294],{"style":4293},[24,21359],{"className":21360,"style":701},[700],[24,21362,921],{"className":21363,"style":1024},[74,78],[24,21365,312],{"className":21366},[351],[24,21368,19254],{"className":21369},[74,78],[24,21371,331],{"className":21372},[438],[24,21374],{"className":21375,"style":1007},[700],[24,21377,918],{"className":21378},[1011],[24,21380],{"className":21381,"style":1007},[700],[24,21383,21385,21389],{"className":21384},[65],[24,21386],{"className":21387,"style":21388},[69],"height:2.363em;vertical-align:-0.936em;",[24,21390,21392,21395,21469],{"className":21391},[74],[24,21393],{"className":21394},[351,3238],[24,21396,21398],{"className":21397},[1977],[24,21399,21401,21461],{"className":21400},[86,87],[24,21402,21404,21458],{"className":21403},[91],[24,21405,21407,21427,21435],{"className":21406,"style":3251},[95],[24,21408,21409,21412],{"style":3254},[24,21410],{"className":21411,"style":1675},[103],[24,21413,21415,21418,21421,21424],{"className":21414},[74],[24,21416,921],{"className":21417,"style":1024},[74,78],[24,21419,312],{"className":21420},[351],[24,21422,19254],{"className":21423},[74,78],[24,21425,331],{"className":21426},[438],[24,21428,21429,21432],{"style":3312},[24,21430],{"className":21431,"style":1675},[103],[24,21433],{"className":21434,"style":3320},[3319],[24,21436,21437,21440],{"style":3323},[24,21438],{"className":21439,"style":1675},[103],[24,21441,21443,21446,21449,21452,21455],{"className":21442},[74],[24,21444,1807],{"className":21445},[74],[24,21447,921],{"className":21448,"style":1024},[74,78],[24,21450,312],{"className":21451},[351],[24,21453,19254],{"className":21454},[74,78],[24,21456,331],{"className":21457},[438],[24,21459,119],{"className":21460},[118],[24,21462,21464],{"className":21463},[91],[24,21465,21467],{"className":21466,"style":3388},[95],[24,21468],{},[24,21470],{"className":21471},[438,3238],"，可将策略梯度写成重要性采样比 ",[24,21474,21476,21508],{"className":21475},[27],[24,21477,21479],{"className":21478},[31],[33,21480,21481],{"xmlns":35},[37,21482,21483,21505],{},[40,21484,21485],{},[1801,21486,21487],{"scriptlevel":598,"displaystyle":61},[1977,21488,21489,21495],{},[43,21490,21491,21493],{},[46,21492,1146],{},[46,21494,1463],{},[43,21496,21497,21499],{},[46,21498,1146],{},[2132,21500,21501,21503],{},[46,21502,1463],{},[309,21504,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[53,21506,21507],{"encoding":55},"\\dfrac{P_\\theta}{P_{\\theta'}}",[24,21509,21511],{"className":21510,"ariaHidden":61},[60],[24,21512,21514,21518],{"className":21513},[65],[24,21515],{"className":21516,"style":21517},[69],"height:2.1963em;vertical-align:-0.836em;",[24,21519,21521,21524,21685],{"className":21520},[74],[24,21522],{"className":21523},[351,3238],[24,21525,21527],{"className":21526},[1977],[24,21528,21530,21676],{"className":21529},[86,87],[24,21531,21533,21673],{"className":21532},[91],[24,21534,21537,21617,21625],{"className":21535,"style":21536},[95],"height:1.3603em;",[24,21538,21539,21542],{"style":3254},[24,21540],{"className":21541,"style":1675},[103],[24,21543,21545],{"className":21544},[74],[24,21546,21548,21551],{"className":21547},[74],[24,21549,1146],{"className":21550,"style":874},[74,78],[24,21552,21554],{"className":21553},[82],[24,21555,21557,21609],{"className":21556},[86,87],[24,21558,21560,21606],{"className":21559},[91],[24,21561,21563],{"className":21562,"style":1740},[95],[24,21564,21565,21568],{"style":1743},[24,21566],{"className":21567,"style":104},[103],[24,21569,21571],{"className":21570},[108,109,110,111],[24,21572,21574],{"className":21573},[74,111],[24,21575,21577,21580],{"className":21576},[74,111],[24,21578,1463],{"className":21579,"style":477},[74,78,111],[24,21581,21583],{"className":21582},[82],[24,21584,21586],{"className":21585},[86],[24,21587,21589],{"className":21588},[91],[24,21590,21592],{"className":21591,"style":6590},[95],[24,21593,21594,21597],{"style":6593},[24,21595],{"className":21596,"style":1593},[103],[24,21598,21600],{"className":21599},[108,1597,1598,111],[24,21601,21603],{"className":21602},[74,111],[24,21604,6430],{"className":21605},[74,111],[24,21607,119],{"className":21608},[118],[24,21610,21612],{"className":21611},[91],[24,21613,21615],{"className":21614,"style":126},[95],[24,21616],{},[24,21618,21619,21622],{"style":3312},[24,21620],{"className":21621,"style":1675},[103],[24,21623],{"className":21624,"style":3320},[3319],[24,21626,21627,21630],{"style":3323},[24,21628],{"className":21629,"style":1675},[103],[24,21631,21633],{"className":21632},[74],[24,21634,21636,21639],{"className":21635},[74],[24,21637,1146],{"className":21638,"style":874},[74,78],[24,21640,21642],{"className":21641},[82],[24,21643,21645,21665],{"className":21644},[86,87],[24,21646,21648,21662],{"className":21647},[91],[24,21649,21651],{"className":21650,"style":1740},[95],[24,21652,21653,21656],{"style":1743},[24,21654],{"className":21655,"style":104},[103],[24,21657,21659],{"className":21658},[108,109,110,111],[24,21660,1463],{"className":21661,"style":477},[74,78,111],[24,21663,119],{"className":21664},[118],[24,21666,21668],{"className":21667},[91],[24,21669,21671],{"className":21670,"style":126},[95],[24,21672],{},[24,21674,119],{"className":21675},[118],[24,21677,21679],{"className":21678},[91],[24,21680,21683],{"className":21681,"style":21682},[95],"height:0.836em;",[24,21684],{},[24,21686],{"className":21687},[438,3238]," 的形式：",[24,21690,21692],{"className":21691},[1776],[24,21693,21695,21747],{"className":21694},[27],[24,21696,21698],{"className":21697},[31],[33,21699,21700],{"xmlns":35,"display":1785},[37,21701,21702,21744],{},[40,21703,21704,21706,21708,21710,21712,21714,21716,21718,21720],{},[46,21705,1807],{"mathvariant":321},[46,21707,2236],{},[309,21709,2239],{},[46,21711,921],{},[309,21713,312],{"stretchy":311},[46,21715,19254],{},[309,21717,331],{"stretchy":311},[309,21719,918],{},[1977,21721,21722,21734],{},[40,21723,21724,21726,21728,21730,21732],{},[46,21725,1807],{"mathvariant":321},[46,21727,921],{},[309,21729,312],{"stretchy":311},[46,21731,19254],{},[309,21733,331],{"stretchy":311},[40,21735,21736,21738,21740,21742],{},[46,21737,921],{},[309,21739,312],{"stretchy":311},[46,21741,19254],{},[309,21743,331],{"stretchy":311},[53,21745,21746],{"encoding":55},"\\nabla \\log f(x) = \\frac{\\nabla f(x)}{f(x)}",[24,21748,21750,21791],{"className":21749,"ariaHidden":61},[60],[24,21751,21753,21756,21759,21762,21767,21770,21773,21776,21779,21782,21785,21788],{"className":21752},[65],[24,21754],{"className":21755,"style":344},[69],[24,21757,1807],{"className":21758},[74],[24,21760],{"className":21761,"style":701},[700],[24,21763,4290,21765],{"className":21764},[1657],[24,21766,4294],{"style":4293},[24,21768],{"className":21769,"style":701},[700],[24,21771,921],{"className":21772,"style":1024},[74,78],[24,21774,312],{"className":21775},[351],[24,21777,19254],{"className":21778},[74,78],[24,21780,331],{"className":21781},[438],[24,21783],{"className":21784,"style":1007},[700],[24,21786,918],{"className":21787},[1011],[24,21789],{"className":21790,"style":1007},[700],[24,21792,21794,21797],{"className":21793},[65],[24,21795],{"className":21796,"style":21388},[69],[24,21798,21800,21803,21877],{"className":21799},[74],[24,21801],{"className":21802},[351,3238],[24,21804,21806],{"className":21805},[1977],[24,21807,21809,21869],{"className":21808},[86,87],[24,21810,21812,21866],{"className":21811},[91],[24,21813,21815,21835,21843],{"className":21814,"style":3251},[95],[24,21816,21817,21820],{"style":3254},[24,21818],{"className":21819,"style":1675},[103],[24,21821,21823,21826,21829,21832],{"className":21822},[74],[24,21824,921],{"className":21825,"style":1024},[74,78],[24,21827,312],{"className":21828},[351],[24,21830,19254],{"className":21831},[74,78],[24,21833,331],{"className":21834},[438],[24,21836,21837,21840],{"style":3312},[24,21838],{"className":21839,"style":1675},[103],[24,21841],{"className":21842,"style":3320},[3319],[24,21844,21845,21848],{"style":3323},[24,21846],{"className":21847,"style":1675},[103],[24,21849,21851,21854,21857,21860,21863],{"className":21850},[74],[24,21852,1807],{"className":21853},[74],[24,21855,921],{"className":21856,"style":1024},[74,78],[24,21858,312],{"className":21859},[351],[24,21861,19254],{"className":21862},[74,78],[24,21864,331],{"className":21865},[438],[24,21867,119],{"className":21868},[118],[24,21870,21872],{"className":21871},[91],[24,21873,21875],{"className":21874,"style":3388},[95],[24,21876],{},[24,21878],{"className":21879},[438,3238],[24,21881,21883],{"className":21882},[1776],[24,21884,21886,22608],{"className":21885},[27],[24,21887,21889],{"className":21888},[31],[33,21890,21891],{"xmlns":35,"display":1785},[37,21892,21893,22605],{},[1789,21894,21895,22019,22215,22441],{"rowspacing":1791,"columnalign":1792,"columnspacing":1793},[1795,21896,21897,21903],{},[1798,21898,21899],{},[1801,21900,21901],{"scriptlevel":598,"displaystyle":61},[40,21902],{},[1798,21904,21905],{},[1801,21906,21907],{"scriptlevel":598,"displaystyle":61},[40,21908,21909,21911,21917,21931,21949,21963,21965,21973,21975,21983,21985,21987,21989,21991,21997,21999,22007,22009,22017],{},[40,21910],{},[1977,21912,21913,21915],{},[596,21914,616],{},[46,21916,2110],{},[2112,21918,21919,21921,21929],{},[309,21920,1477],{},[40,21922,21923,21925,21927],{},[46,21924,2120],{},[309,21926,918],{},[596,21928,616],{},[46,21930,2110],{},[2112,21932,21933,21935,21943],{},[309,21934,1477],{},[40,21936,21937,21939,21941],{},[46,21938,51],{},[309,21940,918],{},[596,21942,616],{},[43,21944,21945,21947],{},[46,21946,634],{},[46,21948,2120],{},[2340,21950,21951,21953,21955],{},[46,21952,8035],{},[46,21954,1463],{},[40,21956,21957,21959,21961],{},[46,21958,14968],{},[46,21960,8035],{},[46,21962,1434],{},[309,21964,312],{"stretchy":311},[2340,21966,21967,21969,21971],{},[46,21968,176],{},[46,21970,2120],{},[46,21972,51],{},[309,21974,601],{"separator":61},[2340,21976,21977,21979,21981],{},[46,21978,48],{},[46,21980,2120],{},[46,21982,51],{},[309,21984,331],{"stretchy":311},[46,21986,1807],{"mathvariant":321},[46,21988,2236],{},[309,21990,2239],{},[43,21992,21993,21995],{},[46,21994,1146],{},[46,21996,1463],{},[309,21998,312],{"stretchy":311},[2340,22000,22001,22003,22005],{},[46,22002,48],{},[46,22004,2120],{},[46,22006,51],{},[46,22008,322],{"mathvariant":321},[2340,22010,22011,22013,22015],{},[46,22012,176],{},[46,22014,2120],{},[46,22016,51],{},[309,22018,331],{"stretchy":311},[1795,22020,22021,22027],{},[1798,22022,22023],{},[1801,22024,22025],{"scriptlevel":598,"displaystyle":61},[40,22026],{},[1798,22028,22029],{},[1801,22030,22031],{"scriptlevel":598,"displaystyle":61},[40,22032,22033,22035,22037,22043,22057,22075,22093,22095,22103,22105,22113,22115,22181,22183,22185,22187,22193,22195,22203,22205,22213],{},[40,22034],{},[309,22036,918],{},[1977,22038,22039,22041],{},[596,22040,616],{},[46,22042,2110],{},[2112,22044,22045,22047,22055],{},[309,22046,1477],{},[40,22048,22049,22051,22053],{},[46,22050,2120],{},[309,22052,918],{},[596,22054,616],{},[46,22056,2110],{},[2112,22058,22059,22061,22069],{},[309,22060,1477],{},[40,22062,22063,22065,22067],{},[46,22064,51],{},[309,22066,918],{},[596,22068,616],{},[43,22070,22071,22073],{},[46,22072,634],{},[46,22074,2120],{},[2340,22076,22077,22079,22085],{},[46,22078,8035],{},[2132,22080,22081,22083],{},[46,22082,1463],{},[309,22084,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[40,22086,22087,22089,22091],{},[46,22088,14968],{},[46,22090,8035],{},[46,22092,1434],{},[309,22094,312],{"stretchy":311},[2340,22096,22097,22099,22101],{},[46,22098,176],{},[46,22100,2120],{},[46,22102,51],{},[309,22104,601],{"separator":61},[2340,22106,22107,22109,22111],{},[46,22108,48],{},[46,22110,2120],{},[46,22112,51],{},[309,22114,331],{"stretchy":311},[1977,22116,22117,22147],{},[40,22118,22119,22125,22127,22135,22137,22145],{},[43,22120,22121,22123],{},[46,22122,1146],{},[46,22124,1463],{},[309,22126,312],{"stretchy":311},[2340,22128,22129,22131,22133],{},[46,22130,48],{},[46,22132,2120],{},[46,22134,51],{},[46,22136,322],{"mathvariant":321},[2340,22138,22139,22141,22143],{},[46,22140,176],{},[46,22142,2120],{},[46,22144,51],{},[309,22146,331],{"stretchy":311},[40,22148,22149,22159,22161,22169,22171,22179],{},[43,22150,22151,22153],{},[46,22152,1146],{},[2132,22154,22155,22157],{},[46,22156,1463],{},[309,22158,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[309,22160,312],{"stretchy":311},[2340,22162,22163,22165,22167],{},[46,22164,48],{},[46,22166,2120],{},[46,22168,51],{},[46,22170,322],{"mathvariant":321},[2340,22172,22173,22175,22177],{},[46,22174,176],{},[46,22176,2120],{},[46,22178,51],{},[309,22180,331],{"stretchy":311},[46,22182,1807],{"mathvariant":321},[46,22184,2236],{},[309,22186,2239],{},[43,22188,22189,22191],{},[46,22190,1146],{},[46,22192,1463],{},[309,22194,312],{"stretchy":311},[2340,22196,22197,22199,22201],{},[46,22198,48],{},[46,22200,2120],{},[46,22202,51],{},[46,22204,322],{"mathvariant":321},[2340,22206,22207,22209,22211],{},[46,22208,176],{},[46,22210,2120],{},[46,22212,51],{},[309,22214,331],{"stretchy":311},[1795,22216,22217,22223],{},[1798,22218,22219],{},[1801,22220,22221],{"scriptlevel":598,"displaystyle":61},[40,22222],{},[1798,22224,22225],{},[1801,22226,22227],{"scriptlevel":598,"displaystyle":61},[40,22228,22229,22231,22233,22239,22253,22271,22289,22291,22299,22301,22309,22311,22377],{},[40,22230],{},[309,22232,918],{},[1977,22234,22235,22237],{},[596,22236,616],{},[46,22238,2110],{},[2112,22240,22241,22243,22251],{},[309,22242,1477],{},[40,22244,22245,22247,22249],{},[46,22246,2120],{},[309,22248,918],{},[596,22250,616],{},[46,22252,2110],{},[2112,22254,22255,22257,22265],{},[309,22256,1477],{},[40,22258,22259,22261,22263],{},[46,22260,51],{},[309,22262,918],{},[596,22264,616],{},[43,22266,22267,22269],{},[46,22268,634],{},[46,22270,2120],{},[2340,22272,22273,22275,22281],{},[46,22274,8035],{},[2132,22276,22277,22279],{},[46,22278,1463],{},[309,22280,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[40,22282,22283,22285,22287],{},[46,22284,14968],{},[46,22286,8035],{},[46,22288,1434],{},[309,22290,312],{"stretchy":311},[2340,22292,22293,22295,22297],{},[46,22294,176],{},[46,22296,2120],{},[46,22298,51],{},[309,22300,601],{"separator":61},[2340,22302,22303,22305,22307],{},[46,22304,48],{},[46,22306,2120],{},[46,22308,51],{},[309,22310,331],{"stretchy":311},[1977,22312,22313,22343],{},[40,22314,22315,22321,22323,22331,22333,22341],{},[43,22316,22317,22319],{},[46,22318,1146],{},[46,22320,1463],{},[309,22322,312],{"stretchy":311},[2340,22324,22325,22327,22329],{},[46,22326,48],{},[46,22328,2120],{},[46,22330,51],{},[46,22332,322],{"mathvariant":321},[2340,22334,22335,22337,22339],{},[46,22336,176],{},[46,22338,2120],{},[46,22340,51],{},[309,22342,331],{"stretchy":311},[40,22344,22345,22355,22357,22365,22367,22375],{},[43,22346,22347,22349],{},[46,22348,1146],{},[2132,22350,22351,22353],{},[46,22352,1463],{},[309,22354,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[309,22356,312],{"stretchy":311},[2340,22358,22359,22361,22363],{},[46,22360,48],{},[46,22362,2120],{},[46,22364,51],{},[46,22366,322],{"mathvariant":321},[2340,22368,22369,22371,22373],{},[46,22370,176],{},[46,22372,2120],{},[46,22374,51],{},[309,22376,331],{"stretchy":311},[1977,22378,22379,22411],{},[40,22380,22381,22383,22389,22391,22399,22401,22409],{},[46,22382,1807],{"mathvariant":321},[43,22384,22385,22387],{},[46,22386,1146],{},[46,22388,1463],{},[309,22390,312],{"stretchy":311},[2340,22392,22393,22395,22397],{},[46,22394,48],{},[46,22396,2120],{},[46,22398,51],{},[46,22400,322],{"mathvariant":321},[2340,22402,22403,22405,22407],{},[46,22404,176],{},[46,22406,2120],{},[46,22408,51],{},[309,22410,331],{"stretchy":311},[40,22412,22413,22419,22421,22429,22431,22439],{},[43,22414,22415,22417],{},[46,22416,1146],{},[46,22418,1463],{},[309,22420,312],{"stretchy":311},[2340,22422,22423,22425,22427],{},[46,22424,48],{},[46,22426,2120],{},[46,22428,51],{},[46,22430,322],{"mathvariant":321},[2340,22432,22433,22435,22437],{},[46,22434,176],{},[46,22436,2120],{},[46,22438,51],{},[309,22440,331],{"stretchy":311},[1795,22442,22443,22449],{},[1798,22444,22445],{},[1801,22446,22447],{"scriptlevel":598,"displaystyle":61},[40,22448],{},[1798,22450,22451],{},[1801,22452,22453],{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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}",[24,22609,22611],{"className":22610,"ariaHidden":61},[60],[24,22612,22614,22618],{"className":22613},[65],[24,22615],{"className":22616,"style":22617},[69],"height:13.6262em;vertical-align:-6.5631em;",[24,22619,22621],{"className":22620},[74],[24,22622,22624,22685],{"className":22623},[1789],[24,22625,22627],{"className":22626},[2586],[24,22628,22630,22676],{"className":22629},[86,87],[24,22631,22633,22673],{"className":22632},[91],[24,22634,22637,22646,22655,22664],{"className":22635,"style":22636},[95],"height:7.0631em;",[24,22638,22640,22643],{"style":22639},"top:-9.0631em;",[24,22641],{"className":22642,"style":2603},[103],[24,22644],{"className":22645},[74],[24,22647,22649,22652],{"style":22648},"top:-5.6565em;",[24,22650],{"className":22651,"style":2603},[103],[24,22653],{"className":22654},[74],[24,22656,22658,22661],{"style":22657},"top:-2.25em;",[24,22659],{"className":22660,"style":2603},[103],[24,22662],{"className":22663},[74],[24,22665,22667,22670],{"style":22666},"top:1.1565em;",[24,22668],{"className":22669,"style":2603},[103],[24,22671],{"className":22672},[74],[24,22674,119],{"className":22675},[118],[24,22677,22679],{"className":22678},[91],[24,22680,22683],{"className":22681,"style":22682},[95],"height:6.5631em;",[24,22684],{},[24,22686,22688],{"className":22687},[2810],[24,22689,22691,26397],{"className":22690},[86,87],[24,22692,22694,26394],{"className":22693},[91],[24,22695,22697,23289,24314,25533],{"className":22696,"style":22636},[95],[24,22698,22699,22702],{"style":22639},[24,22700],{"className":22701,"style":2603},[103],[24,22703,22705,22708,22770,22773,22840,22843,22947,22950,23010,23013,23064,23067,23070,23121,23124,23127,23130,23135,23138,23178,23181,23232,23235,23286],{"className":22704},[74],[24,22706],{"className":22707},[74],[24,22709,22711,22714,22767],{"className":22710},[74],[24,22712],{"className":22713},[351,3238],[24,22715,22717],{"className":22716},[1977],[24,22718,22720,22759],{"className":22719},[86,87],[24,22721,22723,22756],{"className":22722},[91],[24,22724,22726,22737,22745],{"className":22725,"style":3717},[95],[24,22727,22728,22731],{"style":3254},[24,22729],{"className":22730,"style":1675},[103],[24,22732,22734],{"className":22733},[74],[24,22735,2110],{"className":22736,"style":3729},[74,78],[24,22738,22739,22742],{"style":3312},[24,22740],{"className":22741,"style":1675},[103],[24,22743],{"className":22744,"style":3320},[3319],[24,22746,22747,22750],{"style":3323},[24,22748],{"className":22749,"style":1675},[103],[24,22751,22753],{"className":22752},[74],[24,22754,616],{"className":22755},[74],[24,22757,119],{"className":22758},[118],[24,22760,22762],{"className":22761},[91],[24,22763,22765],{"className":22764,"style":3758},[95],[24,22766],{},[24,22768],{"className":22769},[438,3238],[24,22771],{"className":22772,"style":701},[700],[24,22774,22776],{"className":22775},[1657,1658],[24,22777,22779,22832],{"className":22778},[86,87],[24,22780,22782,22829],{"className":22781},[91],[24,22783,22785,22805,22815],{"className":22784,"style":3779},[95],[24,22786,22787,22790],{"style":3782},[24,22788],{"className":22789,"style":2865},[103],[24,22791,22793],{"className":22792},[108,109,110,111],[24,22794,22796,22799,22802],{"className":22795},[74,111],[24,22797,2120],{"className":22798},[74,78,111],[24,22800,918],{"className":22801},[1011,111],[24,22803,616],{"className":22804},[74,111],[24,22806,22807,22810],{"style":2874},[24,22808],{"className":22809,"style":2865},[103],[24,22811,22812],{},[24,22813,1477],{"className":22814},[1657,1693,2883],[24,22816,22817,22820],{"style":3813},[24,22818],{"className":22819,"style":2865},[103],[24,22821,22823],{"className":22822},[108,109,110,111],[24,22824,22826],{"className":22825},[74,111],[24,22827,2110],{"className":22828,"style":3729},[74,78,111],[24,22830,119],{"className":22831},[118],[24,22833,22835],{"className":22834},[91],[24,22836,22838],{"className":22837,"style":3832},[95],[24,22839],{},[24,22841],{"className":22842,"style":701},[700],[24,22844,22846],{"className":22845},[1657,1658],[24,22847,22849,22939],{"className":22848},[86,87],[24,22850,22852,22936],{"className":22851},[91],[24,22853,22855,22875,22885],{"className":22854,"style":4589},[95],[24,22856,22857,22860],{"style":3782},[24,22858],{"className":22859,"style":2865},[103],[24,22861,22863],{"className":22862},[108,109,110,111],[24,22864,22866,22869,22872],{"className":22865},[74,111],[24,22867,51],{"className":22868},[74,78,111],[24,22870,918],{"className":22871},[1011,111],[24,22873,616],{"className":22874},[74,111],[24,22876,22877,22880],{"style":2874},[24,22878],{"className":22879,"style":2865},[103],[24,22881,22882],{},[24,22883,1477],{"className":22884},[1657,1693,2883],[24,22886,22887,22890],{"style":4622},[24,22888],{"className":22889,"style":2865},[103],[24,22891,22893],{"className":22892},[108,109,110,111],[24,22894,22896],{"className":22895},[74,111],[24,22897,22899,22902],{"className":22898},[74,111],[24,22900,634],{"class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= -\\frac{1}{N} \\sum_{n=1}^{N} \\sum_{t=1}^{T_n} A_{\\theta'}^{GAE}(s_n^t, a_n^t) \\frac{P_\\theta(a_n^t | s_n^t)}{P_{\\theta'}(a_n^t | 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surrogate 上加 KL 惩罚",[14,27462,27463,27464,27496],{},"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 ",[24,27465,27467,27482],{"className":27466},[27],[24,27468,27470],{"className":27469},[31],[33,27471,27472],{"xmlns":35},[37,27473,27474,27479],{},[40,27475,27476],{},[46,27477,27478],{},"β",[53,27480,27481],{"encoding":55},"\\beta",[24,27483,27485],{"className":27484,"ariaHidden":61},[60],[24,27486,27488,27492],{"className":27487},[65],[24,27489],{"className":27490,"style":27491},[69],"height:0.8889em;vertical-align:-0.1944em;",[24,27493,27478],{"className":27494,"style":27495},[74,78],"margin-right:0.05278em;"," 来调整 KL 散度影响的大小。",[24,27498,27500],{"className":27499},[1776],[24,27501,27503,27711],{"className":27502},[27],[24,27504,27506],{"className":27505},[31],[33,27507,27508],{"xmlns":35,"display":1785},[37,27509,27510,27708],{},[40,27511,27512,27514,27516,27518,27525,27527,27529,27535,27549,27567,27585,27587,27595,27597,27605,27607,27673,27675,27677,27679,27686,27688,27694,27696,27706],{},[46,27513,5797],{},[46,27515,5800],{},[46,27517,176],{},[43,27519,27520,27522],{},[46,27521,176],{},[15052,27523,27524],{},"ppo",[309,27526,918],{},[309,27528,5809],{},[1977,27530,27531,27533],{},[596,27532,616],{},[46,27534,2110],{},[2112,27536,27537,27539,27547],{},[309,27538,1477],{},[40,27540,27541,27543,27545],{},[46,27542,2120],{},[309,27544,918],{},[596,27546,616],{},[46,27548,2110],{},[2112,27550,27551,27553,27561],{},[309,27552,1477],{},[40,27554,27555,27557,27559],{},[46,27556,51],{},[309,27558,918],{},[596,27560,616],{},[43,27562,27563,27565],{},[46,27564,634],{},[46,27566,2120],{},[2340,27568,27569,27571,27577],{},[46,27570,8035],{},[2132,27572,27573,27575],{},[46,27574,1463],{},[309,27576,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[40,27578,27579,27581,27583],{},[46,27580,14968],{},[46,27582,8035],{},[46,27584,1434],{},[309,27586,312],{"stretchy":311},[2340,27588,27589,27591,27593],{},[46,27590,176],{},[46,27592,2120],{},[46,27594,51],{},[309,27596,601],{"separator":61},[2340,27598,27599,27601,27603],{},[46,27600,48],{},[46,27602,2120],{},[46,27604,51],{},[309,27606,331],{"stretchy":311},[1977,27608,27609,27639],{},[40,27610,27611,27617,27619,27627,27629,27637],{},[43,27612,27613,27615],{},[46,27614,1146],{},[46,27616,1463],{},[309,27618,312],{"stretchy":311},[2340,27620,27621,27623,27625],{},[46,27622,48],{},[46,27624,2120],{},[46,27626,51],{},[46,27628,322],{"mathvariant":321},[2340,27630,27631,27633,27635],{},[46,27632,176],{},[46,27634,2120],{},[46,27636,51],{},[309,27638,331],{"stretchy":311},[40,27640,27641,27651,27653,27661,27663,27671],{},[43,27642,27643,27645],{},[46,27644,1146],{},[2132,27646,27647,27649],{},[46,27648,1463],{},[309,27650,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[309,27652,312],{"stretchy":311},[2340,27654,27655,27657,27659],{},[46,27656,48],{},[46,27658,2120],{},[46,27660,51],{},[46,27662,322],{"mathvariant":321},[2340,27664,27665,27667,27669],{},[46,27666,176],{},[46,27668,2120],{},[46,27670,51],{},[309,27672,331],{"stretchy":311},[309,27674,913],{},[46,27676,27478],{},[15052,27678,15054],{},[40,27680,27681,27684],{},[46,27682,27683],{"mathvariant":321},"K",[46,27685,5797],{"mathvariant":321},[309,27687,312],{"stretchy":311},[43,27689,27690,27692],{},[46,27691,1146],{},[46,27693,1463],{},[309,27695,601],{"separator":61},[43,27697,27698,27700],{},[46,27699,1146],{},[2132,27701,27702,27704],{},[46,27703,1463],{},[309,27705,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[309,27707,331],{"stretchy":311},[53,27709,27710],{"encoding":55},"Loss_{\\text{ppo}} 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还有一种实现，是通过截断函数来替代 KL 散度，防止训练的策略和参考的策略偏差过大，可以看出它是由红色和蓝色两个部分构成，取两个部分的最小值。",[14,28799,28800,28801,29301,29302,29355,29356,29407],{},"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 ",[24,29303,29305,29324],{"className":29304},[27],[24,29306,29308],{"className":29307},[31],[33,29309,29310],{"xmlns":35},[37,29311,29312,29321],{},[40,29313,29314,29316,29318],{},[596,29315,616],{},[309,29317,5809],{},[46,29319,29320],{},"ϵ",[53,29322,29323],{"encoding":55},"1-\\epsilon",[24,29325,29327,29346],{"className":29326,"ariaHidden":61},[60],[24,29328,29330,29334,29337,29340,29343],{"className":29329},[65],[24,29331],{"className":29332,"style":29333},[69],"height:0.7278em;vertical-align:-0.0833em;",[24,29335,616],{"className":29336},[74],[24,29338],{"className":29339,"style":3225},[700],[24,29341,5809],{"className":29342},[988],[24,29344],{"className":29345,"style":3225},[700],[24,29347,29349,29352],{"className":29348},[65],[24,29350],{"className":29351,"style":288},[69],[24,29353,29320],{"className":29354},[74,78]," 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。",[24,29409,29411],{"className":29410},[1776],[24,29412,29414,29753],{"className":29413},[27],[24,29415,29417],{"className":29416},[31],[33,29418,29419],{"xmlns":35,"display":1785},[37,29420,29421,29750],{},[40,29422,29423,29425,29427,29429,29436,29438,29440,29446,29460,29478,29481,29483],{},[46,29424,5797],{},[46,29426,5800],{},[46,29428,176],{},[43,29430,29431,29433],{},[46,29432,176],{},[15052,29434,29435],{},"ppo2",[309,29437,918],{},[309,29439,5809],{},[1977,29441,29442,29444],{},[596,29443,616],{},[46,29445,2110],{},[2112,29447,29448,29450,29458],{},[309,29449,1477],{},[40,29451,29452,29454,29456],{},[46,29453,2120],{},[309,29455,918],{},[596,29457,616],{},[46,29459,2110],{},[2112,29461,29462,29464,29472],{},[309,29463,1477],{},[40,29465,29466,29468,29470],{},[46,29467,51],{},[309,29469,918],{},[596,29471,616],{},[43,29473,29474,29476],{},[46,29475,634],{},[46,29477,2120],{},[46,29479,29480],{},"min",[309,29482,2239],{},[40,29484,29485,29487,29596,29598,29600,29748],{},[309,29486,312],{"fence":61},[1801,29488,29490,29508,29510,29518,29520,29528,29530],{"mathcolor":29489},"red",[2340,29491,29492,29494,29500],{},[46,29493,8035],{},[2132,29495,29496,29498],{},[46,29497,1463],{},[309,29499,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[40,29501,29502,29504,29506],{},[46,29503,14968],{},[46,29505,8035],{},[46,29507,1434],{},[309,29509,312],{"stretchy":311},[2340,29511,29512,29514,29516],{},[46,29513,176],{},[46,29515,2120],{},[46,29517,51],{},[309,29519,601],{"separator":61},[2340,29521,29522,29524,29526],{},[46,29523,48],{},[46,29525,2120],{},[46,29527,51],{},[309,29529,331],{"stretchy":311},[1977,29531,29532,29562],{},[40,29533,29534,29540,29542,29550,29552,29560],{},[43,29535,29536,29538],{},[46,29537,1146],{},[46,29539,1463],{},[309,29541,312],{"stretchy":311},[2340,29543,29544,29546,29548],{},[46,29545,48],{},[46,29547,2120],{},[46,29549,51],{},[46,29551,322],{"mathvariant":321},[2340,29553,29554,29556,29558],{},[46,29555,176],{},[46,29557,2120],{},[46,29559,51],{},[309,29561,331],{"stretchy":311},[40,29563,29564,29574,29576,29584,29586,29594],{},[43,29565,29566,29568],{},[46,29567,1146],{},[2132,29569,29570,29572],{},[46,29571,1463],{},[309,29573,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[309,29575,312],{"stretchy":311},[2340,29577,29578,29580,29582],{},[46,29579,48],{},[46,29581,2120],{},[46,29583,51],{},[46,29585,322],{"mathvariant":321},[2340,29587,29588,29590,29592],{},[46,29589,176],{},[46,29591,2120],{},[46,29593,51],{},[309,29595,331],{"stretchy":311},[309,29597,601],{"separator":61},[15052,29599,15054],{},[1801,29601,29603,29616,29708,29726,29728,29736,29738,29746],{"mathcolor":29602},"skyblue",[40,29604,29605,29608,29611,29614],{},[46,29606,29607],{"mathvariant":321},"c",[46,29609,29610],{"mathvariant":321},"l",[46,29612,29613],{"mathvariant":321},"i",[46,29615,14],{"mathvariant":321},[40,29617,29618,29620,29686,29688,29690,29692,29694,29696,29698,29700,29702,29704,29706],{},[309,29619,312],{"fence":61},[1977,29621,29622,29652],{},[40,29623,29624,29630,29632,29640,29642,29650],{},[43,29625,29626,29628],{},[46,29627,1146],{},[46,29629,1463],{},[309,29631,312],{"stretchy":311},[2340,29633,29634,29636,29638],{},[46,29635,48],{},[46,29637,2120],{},[46,29639,51],{},[46,29641,322],{"mathvariant":321},[2340,29643,29644,29646,29648],{},[46,29645,176],{},[46,29647,2120],{},[46,29649,51],{},[309,29651,331],{"stretchy":311},[40,29653,29654,29664,29666,29674,29676,29684],{},[43,29655,29656,29658],{},[46,29657,1146],{},[2132,29659,29660,29662],{},[46,29661,1463],{},[309,29663,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[309,29665,312],{"stretchy":311},[2340,29667,29668,29670,29672],{},[46,29669,48],{},[46,29671,2120],{},[46,29673,51],{},[46,29675,322],{"mathvariant":321},[2340,29677,29678,29680,29682],{},[46,29679,176],{},[46,29681,2120],{},[46,29683,51],{},[309,29685,331],{"stretchy":311},[309,29687,601],{"separator":61},[15052,29689,15054],{},[596,29691,616],{},[309,29693,5809],{},[46,29695,29320],{},[309,29697,601],{"separator":61},[15052,29699,15054],{},[596,29701,616],{},[309,29703,913],{},[46,29705,29320],{},[309,29707,331],{"fence":61},[2340,29709,29710,29712,29718],{},[46,29711,8035],{},[2132,29713,29714,29716],{},[46,29715,1463],{},[309,29717,6430],{"mathvariant":321,"lspace":1793,"rspace":1793},[40,29719,29720,29722,29724],{},[46,29721,14968],{},[46,29723,8035],{},[46,29725,1434],{},[309,29727,312],{"stretchy":311},[2340,29729,29730,29732,29734],{},[46,29731,176],{},[46,29733,2120],{},[46,29735,51],{},[309,29737,601],{"separator":61},[2340,29739,29740,29742,29744],{},[46,29741,48],{},[46,29743,2120],{},[46,29745,51],{},[309,29747,331],{"stretchy":311},[309,29749,331],{"fence":61},[53,29751,29752],{"encoding":55},"Loss_{\\text{ppo2}} 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PPO学习笔记","ngXl85tXoyEZC4uVOAWn1IScbiXzrl-vgx3OlmObKkM",[31438,43951],{"id":31439,"title":31440,"body":31441,"description":43941,"extension":31423,"meta":43942,"navigation":31432,"ogImage":43944,"path":43947,"seo":43948,"stem":43949,"__hash__":43950},"content/blogs/1. transformer复习笔记.md","transformer 复习笔记",{"type":7,"value":31442,"toc":43925},[31443,31446,31449,31464,31467,31474,31477,31480,31483,31695,31698,31818,32119,32530,32536,32802,33712,33715,33941,33944,34182,34189,34192,34195,34200,34525,35869,35886,36111,36570,36573,36668,36671,37255,37614,37970,38323,38595,38598,38601,38929,39086,39089,39092,39280,39419,39422,39934,40333,40337,40340,40951,40955,40958,41958,41961,41964,42255,42258,42415,42426,43019,43022,43728,43731,43908,43911,43916,43921],[10,31444,31445],{"id":31445},"背景",[14,31447,31448],{},"距离首次学习 transformer 已经过去一年，最近在回忆 transformer 的相关内容，发现相关内容忘的差不多了，于是决定复习一下并记录下来。",[14,31450,31451,31452,31457,31458,31463],{},"本文主要记录对transformer的理解和思考，代码实现完全参考 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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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",[24,31702,31704,31717],{"className":31703},[27],[24,31705,31707],{"className":31706},[31],[33,31708,31709],{"xmlns":35},[37,31710,31711,31715],{},[40,31712,31713],{},[46,31714,2120],{},[53,31716,2120],{"encoding":55},[24,31718,31720],{"className":31719,"ariaHidden":61},[60],[24,31721,31723,31726],{"className":31722},[65],[24,31724],{"className":31725,"style":288},[69],[24,31727,2120],{"className":31728},[74,78]," 个查询和 ",[24,31731,31733,31747],{"className":31732},[27],[24,31734,31736],{"className":31735},[31],[33,31737,31738],{"xmlns":35},[37,31739,31740,31745],{},[40,31741,31742],{},[46,31743,31744],{},"m",[53,31746,31744],{"encoding":55},[24,31748,31750],{"className":31749,"ariaHidden":61},[60],[24,31751,31753,31756],{"className":31752},[65],[24,31754],{"className":31755,"style":288},[69],[24,31757,31744],{"className":31758},[74,78]," 个键-值对计算注意力，其中查询和键的长度为 ",[24,31761,31763,31776],{"className":31762},[27],[24,31764,31766],{"className":31765},[31],[33,31767,31768],{"xmlns":35},[37,31769,31770,31774],{},[40,31771,31772],{},[46,31773,31509],{},[53,31775,31509],{"encoding":55},[24,31777,31779],{"className":31778,"ariaHidden":61},[60],[24,31780,31782,31785],{"className":31781},[65],[24,31783],{"className":31784,"style":14930},[69],[24,31786,31509],{"className":31787},[74,78],"，值的长度为 ",[24,31790,31792,31806],{"className":31791},[27],[24,31793,31795],{"className":31794},[31],[33,31796,31797],{"xmlns":35},[37,31798,31799,31804],{},[40,31800,31801],{},[46,31802,31803],{},"v",[53,31805,31803],{"encoding":55},[24,31807,31809],{"className":31808,"ariaHidden":61},[60],[24,31810,31812,31815],{"className":31811},[65],[24,31813],{"className":31814,"style":288},[69],[24,31816,31803],{"className":31817,"style":292},[74,78],[14,31819,31820,31821,31921,31922,32020,32021,32118],{},"查询 ",[24,31822,31824,31854],{"className":31823},[27],[24,31825,31827],{"className":31826},[31],[33,31828,31829],{"xmlns":35},[37,31830,31831,31851],{},[40,31832,31833,31835,31838],{},[46,31834,7754],{},[309,31836,31837],{},"∈",[2132,31839,31840,31842],{},[46,31841,1439],{"mathvariant":19396},[40,31843,31844,31846,31849],{},[46,31845,2120],{},[309,31847,31848],{},"×",[46,31850,31509],{},[53,31852,31853],{"encoding":55},"Q \\in \\mathbb{R}^{n \\times d}",[24,31855,31857,31876],{"className":31856,"ariaHidden":61},[60],[24,31858,31860,31864,31867,31870,31873],{"className":31859},[65],[24,31861],{"className":31862,"style":31863},[69],"height:0.8778em;vertical-align:-0.1944em;",[24,31865,7754],{"className":31866},[74,78],[24,31868],{"className":31869,"style":1007},[700],[24,31871,31837],{"className":31872},[1011],[24,31874],{"className":31875,"style":1007},[700],[24,31877,31879,31883],{"className":31878},[65],[24,31880],{"className":31881,"style":31882},[69],"height:0.8491em;",[24,31884,31886,31889],{"className":31885},[74],[24,31887,1439],{"className":31888},[74,19804],[24,31890,31892],{"className":31891},[82],[24,31893,31895],{"className":31894},[86],[24,31896,31898],{"className":31897},[91],[24,31899,31901],{"className":31900,"style":31882},[95],[24,31902,31903,31906],{"style":4064},[24,31904],{"className":31905,"style":104},[103],[24,31907,31909],{"className":31908},[108,109,110,111],[24,31910,31912,31915,31918],{"className":31911},[74,111],[24,31913,2120],{"className":31914},[74,78,111],[24,31916,31848],{"className":31917},[988,111],[24,31919,31509],{"className":31920},[74,78,111],"、键 ",[24,31923,31925,31953],{"className":31924},[27],[24,31926,31928],{"className":31927},[31],[33,31929,31930],{"xmlns":35},[37,31931,31932,31950],{},[40,31933,31934,31936,31938],{},[46,31935,27683],{},[309,31937,31837],{},[2132,31939,31940,31942],{},[46,31941,1439],{"mathvariant":19396},[40,31943,31944,31946,31948],{},[46,31945,31744],{},[309,31947,31848],{},[46,31949,31509],{},[53,31951,31952],{"encoding":55},"K \\in \\mathbb{R}^{m \\times 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和值 ",[24,32022,32024,32052],{"className":32023},[27],[24,32025,32027],{"className":32026},[31],[33,32028,32029],{"xmlns":35},[37,32030,32031,32049],{},[40,32032,32033,32035,32037],{},[46,32034,7915],{},[309,32036,31837],{},[2132,32038,32039,32041],{},[46,32040,1439],{"mathvariant":19396},[40,32042,32043,32045,32047],{},[46,32044,31744],{},[309,32046,31848],{},[46,32048,31803],{},[53,32050,32051],{"encoding":55},"V \\in \\mathbb{R}^{m \\times v}",[24,32053,32055,32073],{"className":32054,"ariaHidden":61},[60],[24,32056,32058,32061,32064,32067,32070],{"className":32057},[65],[24,32059],{"className":32060,"style":31962},[69],[24,32062,7915],{"className":32063,"style":7942},[74,78],[24,32065],{"className":32066,"style":1007},[700],[24,32068,31837],{"className":32069},[1011],[24,32071],{"className":32072,"style":1007},[700],[24,32074,32076,32080],{"className":32075},[65],[24,32077],{"className":32078,"style":32079},[69],"height:0.7713em;",[24,32081,32083,32086],{"className":32082},[74],[24,32084,1439],{"className":32085},[74,19804],[24,32087,32089],{"className":32088},[82],[24,32090,32092],{"className":32091},[86],[24,32093,32095],{"className":32094},[91],[24,32096,32098],{"className":32097,"style":32079},[95],[24,32099,32100,32103],{"style":4064},[24,32101],{"className":32102,"style":104},[103],[24,32104,32106],{"className":32105},[108,109,110,111],[24,32107,32109,32112,32115],{"className":32108},[74,111],[24,32110,31744],{"className":32111},[74,78,111],[24,32113,31848],{"className":32114},[988,111],[24,32116,31803],{"className":32117,"style":292},[74,78,111]," 的缩放点积注意力是：",[14,32120,32121],{},[24,32122,32124,32218],{"className":32123},[27],[24,32125,32127],{"className":32126},[31],[33,32128,32129],{"xmlns":35},[37,32130,32131,32215],{},[40,32132,32133,32135,32137,32139,32142,32144,32146,32148,32150,32152,32154,32156,32158,32160,32162,32164,32166,32168,32171,32173,32196,32198,32200,32212],{},[46,32134,8035],{},[46,32136,51],{},[46,32138,51],{},[46,32140,32141],{},"e",[46,32143,2120],{},[46,32145,51],{},[46,32147,29613],{},[46,32149,5800],{},[46,32151,2120],{},[309,32153,312],{"stretchy":311},[46,32155,7754],{},[309,32157,601],{"separator":61},[46,32159,27683],{},[309,32161,601],{"separator":61},[46,32163,7915],{},[309,32165,331],{"stretchy":311},[309,32167,918],{},[46,32169,32170],{"mathvariant":321},"softmax",[309,32172,2239],{},[40,32174,32175,32177,32194],{},[309,32176,312],{"fence":61},[1977,32178,32179,32190],{},[40,32180,32181,32183],{},[46,32182,7754],{},[2132,32184,32185,32187],{},[46,32186,27683],{},[46,32188,32189],{"mathvariant":321},"⊤",[31503,32191,32192],{},[46,32193,31509],{},[309,32195,331],{"fence":61},[46,32197,7915],{},[309,32199,31837],{},[2132,32201,32202,32204],{},[46,32203,1439],{"mathvariant":19396},[40,32205,32206,32208,32210],{},[46,32207,2120],{},[309,32209,31848],{},[46,32211,31803],{},[46,32213,32214],{"mathvariant":321},".",[53,32216,32217],{"encoding":55}," Attention(Q,K,V) = \\operatorname{softmax}\\left(\\frac{QK^\\top}{\\sqrt{d}}\\right)V \\in \\mathbb{R}^{n \\times v}.",[24,32219,32221,32288,32483],{"className":32220,"ariaHidden":61},[60],[24,32222,32224,32227,32230,32234,32237,32240,32243,32246,32249,32252,32255,32258,32261,32264,32267,32270,32273,32276,32279,32282,32285],{"className":32223},[65],[24,32225],{"className":32226,"style":344},[69],[24,32228,8035],{"className":32229},[74,78],[24,32231,32233],{"className":32232},[74,78],"tt",[24,32235,32141],{"className":32236},[74,78],[24,32238,2120],{"className":32239},[74,78],[24,32241,51],{"className":32242},[74,78],[24,32244,29613],{"className":32245},[74,78],[24,32247,5800],{"className":32248},[74,78],[24,32250,2120],{"className":32251},[74,78],[24,32253,312],{"className":32254},[351],[24,32256,7754],{"className":32257},[74,78],[24,32259,601],{"className":32260},[696],[24,32262],{"className":32263,"style":701},[700],[24,32265,27683],{"className":32266,"style":31966},[74,78],[24,32268,601],{"className":32269},[696],[24,32271],{"className":32272,"style":701},[700],[24,32274,7915],{"className":32275,"style":7942},[74,78],[24,32277,331],{"className":32278},[438],[24,32280],{"className":32281,"style":1007},[700],[24,32283,918],{"className":32284},[1011],[24,32286],{"className":32287,"style":1007},[700],[24,32289,32291,32295,32301,32304,32468,32471,32474,32477,32480],{"className":32290},[65],[24,32292],{"className":32293,"style":32294},[69],"height:1.8em;vertical-align:-0.65em;",[24,32296,32298],{"className":32297},[1657],[24,32299,32170],{"className":32300},[74,28662],[24,32302],{"className":32303,"style":701},[700],[24,32305,32307,32314,32462],{"className":32306},[840],[24,32308,32310],{"className":32309,"style":17228},[351,17227],[24,32311,312],{"className":32312},[17232,32313],"size2",[24,32315,32317,32320,32459],{"className":32316},[74],[24,32318],{"className":32319},[351,3238],[24,32321,32323],{"className":32322},[1977],[24,32324,32326,32451],{"className":32325},[86,87],[24,32327,32329,32448],{"className":32328},[91],[24,32330,32333,32395,32403],{"className":32331,"style":32332},[95],"height:1.095em;",[24,32334,32336,32339],{"style":32335},"top:-2.5335em;",[24,32337],{"className":32338,"style":1675},[103],[24,32340,32342],{"className":32341},[108,109,110,111],[24,32343,32345],{"className":32344},[74,111],[24,32346,32348],{"className":32347},[74,31559,111],[24,32349,32351,32386],{"className":32350},[86,87],[24,32352,32354,32383],{"className":32353},[91],[24,32355,32358,32370],{"className":32356,"style":32357},[95],"height:0.9378em;",[24,32359,32361,32364],{"className":32360,"style":1684},[31573],[24,32362],{"className":32363,"style":1675},[103],[24,32365,32367],{"className":32366,"style":31580},[74,111],[24,32368,31509],{"className":32369},[74,78,111],[24,32371,32373,32376],{"style":32372},"top:-2.8978em;",[24,32374],{"className":32375,"style":1675},[103],[24,32377,32379],{"className":32378,"style":31633},[31632,111],[31635,32380,32381],{"xmlns":31637,"width":31638,"height":31639,"viewBox":31640,"preserveAspectRatio":31641},[31643,32382],{"d":31645},[24,32384,119],{"className":32385},[118],[24,32387,32389],{"className":32388},[91],[24,32390,32393],{"className":32391,"style":32392},[95],"height:0.1022em;",[24,32394],{},[24,32396,32397,32400],{"style":3312},[24,32398],{"className":32399,"style":1675},[103],[24,32401],{"className":32402,"style":3320},[3319],[24,32404,32406,32409],{"style":32405},"top:-3.4461em;",[24,32407],{"className":32408,"style":1675},[103],[24,32410,32412],{"className":32411},[108,109,110,111],[24,32413,32415,32418],{"className":32414},[74,111],[24,32416,7754],{"className":32417},[74,78,111],[24,32419,32421,32424],{"className":32420},[74,111],[24,32422,27683],{"className":32423,"style":31966},[74,78,111],[24,32425,32427],{"className":32426},[82],[24,32428,32430],{"className":32429},[86],[24,32431,32433],{"className":32432},[91],[24,32434,32437],{"className":32435,"style":32436},[95],"height:0.927em;",[24,32438,32439,32442],{"style":6740},[24,32440],{"className":32441,"style":1593},[103],[24,32443,32445],{"className":32444},[108,1597,1598,111],[24,32446,32189],{"className":32447},[74,111],[24,32449,119],{"className":32450},[118],[24,32452,32454],{"className":32453},[91],[24,32455,32457],{"className":32456,"style":31689},[95],[24,32458],{},[24,32460],{"className":32461},[438,3238],[24,32463,32465],{"className":32464,"style":17228},[438,17227],[24,32466,331],{"className":32467},[17232,32313],[24,32469],{"className":32470,"style":701},[700],[24,32472,7915],{"className":32473,"style":7942},[74,78],[24,32475],{"className":32476,"style":1007},[700],[24,32478,31837],{"className":32479},[1011],[24,32481],{"className":32482,"style":1007},[700],[24,32484,32486,32489,32527],{"className":32485},[65],[24,32487],{"className":32488,"style":32079},[69],[24,32490,32492,32495],{"className":32491},[74],[24,32493,1439],{"className":32494},[74,19804],[24,32496,32498],{"className":32497},[82],[24,32499,32501],{"className":32500},[86],[24,32502,32504],{"className":32503},[91],[24,32505,32507],{"className":32506,"style":32079},[95],[24,32508,32509,32512],{"style":4064},[24,32510],{"className":32511,"style":104},[103],[24,32513,32515],{"className":32514},[108,109,110,111],[24,32516,32518,32521,32524],{"className":32517},[74,111],[24,32519,2120],{"className":32520},[74,78,111],[24,32522,31848],{"className":32523},[988,111],[24,32525,31803],{"className":32526,"style":292},[74,78,111],[24,32528,32214],{"className":32529},[74],[14,32531,32532],{},[31470,32533],{"alt":32534,"src":32535},"注意力","transformer/attention.png",[14,32537,32538,32539,32609,32610,32680,32681,32801],{},"缩放点积注意力的输入由维度为 ",[24,32540,32542,32560],{"className":32541},[27],[24,32543,32545],{"className":32544},[31],[33,32546,32547],{"xmlns":35},[37,32548,32549,32557],{},[40,32550,32551],{},[43,32552,32553,32555],{},[46,32554,31509],{},[46,32556,31512],{},[53,32558,32559],{"encoding":55},"d_k",[24,32561,32563],{"className":32562,"ariaHidden":61},[60],[24,32564,32566,32569],{"className":32565},[65],[24,32567],{"className":32568,"style":12947},[69],[24,32570,32572,32575],{"className":32571},[74],[24,32573,31509],{"className":32574},[74,78],[24,32576,32578],{"className":32577},[82],[24,32579,32581,32601],{"className":32580},[86,87],[24,32582,32584,32598],{"className":32583},[91],[24,32585,32587],{"className":32586,"style":1740},[95],[24,32588,32589,32592],{"style":99},[24,32590],{"className":32591,"style":104},[103],[24,32593,32595],{"className":32594},[108,109,110,111],[24,32596,31512],{"className":32597,"style":31611},[74,78,111],[24,32599,119],{"className":32600},[118],[24,32602,32604],{"className":32603},[91],[24,32605,32607],{"className":32606,"style":126},[95],[24,32608],{}," ​的查询和键以及维度为 ",[24,32611,32613,32631],{"className":32612},[27],[24,32614,32616],{"className":32615},[31],[33,32617,32618],{"xmlns":35},[37,32619,32620,32628],{},[40,32621,32622],{},[43,32623,32624,32626],{},[46,32625,31509],{},[46,32627,31803],{},[53,32629,32630],{"encoding":55},"d_v",[24,32632,32634],{"className":32633,"ariaHidden":61},[60],[24,32635,32637,32640],{"className":32636},[65],[24,32638],{"className":32639,"style":12947},[69],[24,32641,32643,32646],{"className":32642},[74],[24,32644,31509],{"className":32645},[74,78],[24,32647,32649],{"className":32648},[82],[24,32650,32652,32672],{"className":32651},[86,87],[24,32653,32655,32669],{"className":32654},[91],[24,32656,32658],{"className":32657,"style":20777},[95],[24,32659,32660,32663],{"style":99},[24,32661],{"className":32662,"style":104},[103],[24,32664,32666],{"className":32665},[108,109,110,111],[24,32667,31803],{"className":32668,"style":292},[74,78,111],[24,32670,119],{"className":32671},[118],[24,32673,32675],{"className":32674},[91],[24,32676,32678],{"className":32677,"style":126},[95],[24,32679],{}," ​的值组成。我们计算查询与所有键的点积，将每个点积除以 ",[24,32682,32684,32704],{"className":32683},[27],[24,32685,32687],{"className":32686},[31],[33,32688,32689],{"xmlns":35},[37,32690,32691,32701],{},[40,32692,32693],{},[31503,32694,32695],{},[43,32696,32697,32699],{},[46,32698,31509],{},[46,32700,31512],{},[53,32702,32703],{"encoding":55},"\\sqrt{d_k}",[24,32705,32707],{"className":32706,"ariaHidden":61},[60],[24,32708,32710,32714],{"className":32709},[65],[24,32711],{"className":32712,"style":32713},[69],"height:1.04em;vertical-align:-0.1828em;",[24,32715,32717],{"className":32716},[74,31559],[24,32718,32720,32792],{"className":32719},[86,87],[24,32721,32723,32789],{"className":32722},[91],[24,32724,32727,32776],{"className":32725,"style":32726},[95],"height:0.8572em;",[24,32728,32730,32733],{"className":32729,"style":1684},[31573],[24,32731],{"className":32732,"style":1675},[103],[24,32734,32736],{"className":32735,"style":31580},[74],[24,32737,32739,32742],{"className":32738},[74],[24,32740,31509],{"className":32741},[74,78],[24,32743,32745],{"className":32744},[82],[24,32746,32748,32768],{"className":32747},[86,87],[24,32749,32751,32765],{"className":32750},[91],[24,32752,32754],{"className":32753,"style":1740},[95],[24,32755,32756,32759],{"style":99},[24,32757],{"className":32758,"style":104},[103],[24,32760,32762],{"className":32761},[108,109,110,111],[24,32763,31512],{"className":32764,"style":31611},[74,78,111],[24,32766,119],{"className":32767},[118],[24,32769,32771],{"className":32770},[91],[24,32772,32774],{"className":32773,"style":126},[95],[24,32775],{},[24,32777,32779,32782],{"style":32778},"top:-2.8172em;",[24,32780],{"className":32781,"style":1675},[103],[24,32783,32785],{"className":32784,"style":31633},[31632],[31635,32786,32787],{"xmlns":31637,"width":31638,"height":31639,"viewBox":31640,"preserveAspectRatio":31641},[31643,32788],{"d":31645},[24,32790,119],{"className":32791},[118],[24,32793,32795],{"className":32794},[91],[24,32796,32799],{"className":32797,"style":32798},[95],"height:0.1828em;",[24,32800],{},"​​，并应用softmax函数以获得值上的权重。",[14,32803,32804,32805,32874,32875,32944,32945,33014,33015,33043,33044,33072,33073,33102,33103,33131,33132,33429,33430,33102,33458,33527,33528,1347],{},"对于较小的 ",[24,32806,32808,32825],{"className":32807},[27],[24,32809,32811],{"className":32810},[31],[33,32812,32813],{"xmlns":35},[37,32814,32815,32823],{},[40,32816,32817],{},[43,32818,32819,32821],{},[46,32820,31509],{},[46,32822,31512],{},[53,32824,32559],{"encoding":55},[24,32826,32828],{"className":32827,"ariaHidden":61},[60],[24,32829,32831,32834],{"className":32830},[65],[24,32832],{"className":32833,"style":12947},[69],[24,32835,32837,32840],{"className":32836},[74],[24,32838,31509],{"className":32839},[74,78],[24,32841,32843],{"className":32842},[82],[24,32844,32846,32866],{"className":32845},[86,87],[24,32847,32849,32863],{"className":32848},[91],[24,32850,32852],{"className":32851,"style":1740},[95],[24,32853,32854,32857],{"style":99},[24,32855],{"className":32856,"style":104},[103],[24,32858,32860],{"className":32859},[108,109,110,111],[24,32861,31512],{"className":32862,"style":31611},[74,78,111],[24,32864,119],{"className":32865},[118],[24,32867,32869],{"className":32868},[91],[24,32870,32872],{"className":32871,"style":126},[95],[24,32873],{}," 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 ",[24,32876,32878,32895],{"className":32877},[27],[24,32879,32881],{"className":32880},[31],[33,32882,32883],{"xmlns":35},[37,32884,32885,32893],{},[40,32886,32887],{},[43,32888,32889,32891],{},[46,32890,31509],{},[46,32892,31512],{},[53,32894,32559],{"encoding":55},[24,32896,32898],{"className":32897,"ariaHidden":61},[60],[24,32899,32901,32904],{"className":32900},[65],[24,32902],{"className":32903,"style":12947},[69],[24,32905,32907,32910],{"className":32906},[74],[24,32908,31509],{"className":32909},[74,78],[24,32911,32913],{"className":32912},[82],[24,32914,32916,32936],{"className":32915},[86,87],[24,32917,32919,32933],{"className":32918},[91],[24,32920,32922],{"className":32921,"style":1740},[95],[24,32923,32924,32927],{"style":99},[24,32925],{"className":32926,"style":104},[103],[24,32928,32930],{"className":32929},[108,109,110,111],[24,32931,31512],{"className":32932,"style":31611},[74,78,111],[24,32934,119],{"className":32935},[118],[24,32937,32939],{"className":32938},[91],[24,32940,32942],{"className":32941,"style":126},[95],[24,32943],{}," 值较大时会优于点积注意力。我们怀疑在 ",[24,32946,32948,32965],{"className":32947},[27],[24,32949,32951],{"className":32950},[31],[33,32952,32953],{"xmlns":35},[37,32954,32955,32963],{},[40,32956,32957],{},[43,32958,32959,32961],{},[46,32960,31509],{},[46,32962,31512],{},[53,32964,32559],{"encoding":55},[24,32966,32968],{"className":32967,"ariaHidden":61},[60],[24,32969,32971,32974],{"className":32970},[65],[24,32972],{"className":32973,"style":12947},[69],[24,32975,32977,32980],{"className":32976},[74],[24,32978,31509],{"className":32979},[74,78],[24,32981,32983],{"className":32982},[82],[24,32984,32986,33006],{"className":32985},[86,87],[24,32987,32989,33003],{"className":32988},[91],[24,32990,32992],{"className":32991,"style":1740},[95],[24,32993,32994,32997],{"style":99},[24,32995],{"className":32996,"style":104},[103],[24,32998,33000],{"className":32999},[108,109,110,111],[24,33001,31512],{"className":33002,"style":31611},[74,78,111],[24,33004,119],{"className":33005},[118],[24,33007,33009],{"className":33008},[91],[24,33010,33012],{"className":33011,"style":126},[95],[24,33013],{}," 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 ",[24,33016,33018,33031],{"className":33017},[27],[24,33019,33021],{"className":33020},[31],[33,33022,33023],{"xmlns":35},[37,33024,33025,33029],{},[40,33026,33027],{},[46,33028,19326],{},[53,33030,19326],{"encoding":55},[24,33032,33034],{"className":33033,"ariaHidden":61},[60],[24,33035,33037,33040],{"className":33036},[65],[24,33038],{"className":33039,"style":19307},[69],[24,33041,19326],{"className":33042,"style":292},[74,78]," 和键 ",[24,33045,33047,33060],{"className":33046},[27],[24,33048,33050],{"className":33049},[31],[33,33051,33052],{"xmlns":35},[37,33053,33054,33058],{},[40,33055,33056],{},[46,33057,31512],{},[53,33059,31512],{"encoding":55},[24,33061,33063],{"className":33062,"ariaHidden":61},[60],[24,33064,33066,33069],{"className":33065},[65],[24,33067],{"className":33068,"style":14930},[69],[24,33070,31512],{"className":33071,"style":31611},[74,78]," 都符合一个均值为 ",[24,33074,33076,33089],{"className":33075},[27],[24,33077,33079],{"className":33078},[31],[33,33080,33081],{"xmlns":35},[37,33082,33083,33087],{},[40,33084,33085],{},[596,33086,598],{},[53,33088,598],{"encoding":55},[24,33090,33092],{"className":33091,"ariaHidden":61},[60],[24,33093,33095,33099],{"className":33094},[65],[24,33096],{"className":33097,"style":33098},[69],"height:0.6444em;",[24,33100,598],{"className":33101},[74],"，方差为 ",[24,33104,33106,33119],{"className":33105},[27],[24,33107,33109],{"className":33108},[31],[33,33110,33111],{"xmlns":35},[37,33112,33113,33117],{},[40,33114,33115],{},[596,33116,616],{},[53,33118,616],{"encoding":55},[24,33120,33122],{"className":33121,"ariaHidden":61},[60],[24,33123,33125,33128],{"className":33124},[65],[24,33126],{"className":33127,"style":33098},[69],[24,33129,616],{"className":33130},[74]," 的随机变量。他们点积的结果 ",[24,33133,33135,33185],{"className":33134},[27],[24,33136,33138],{"className":33137},[31],[33,33139,33140],{"xmlns":35},[37,33141,33142,33182],{},[40,33143,33144,33146,33148,33150,33152,33170,33176],{},[46,33145,19326],{},[309,33147,1151],{},[46,33149,31512],{},[309,33151,918],{},[2340,33153,33154,33156,33164],{},[309,33155,1477],{},[40,33157,33158,33160,33162],{},[46,33159,29613],{},[309,33161,918],{},[596,33163,616],{},[43,33165,33166,33168],{},[46,33167,31509],{},[46,33169,31512],{},[43,33171,33172,33174],{},[46,33173,19326],{},[46,33175,29613],{},[43,33177,33178,33180],{},[46,33179,31512],{},[46,33181,29613],{},[53,33183,33184],{"encoding":55},"q \\cdot k = \\sum_{i=1}^{d_k}q_{i}k_{i}",[24,33186,33188,33207,33225],{"className":33187,"ariaHidden":61},[60],[24,33189,33191,33195,33198,33201,33204],{"className":33190},[65],[24,33192],{"className":33193,"style":33194},[69],"height:0.6389em;vertical-align:-0.1944em;",[24,33196,19326],{"className":33197,"style":292},[74,78],[24,33199],{"className":33200,"style":3225},[700],[24,33202,1151],{"className":33203},[988],[24,33205],{"className":33206,"style":3225},[700],[24,33208,33210,33213,33216,33219,33222],{"className":33209},[65],[24,33211],{"className":33212,"style":14930},[69],[24,33214,31512],{"className":33215,"style":31611},[74,78],[24,33217],{"className":33218,"style":1007},[700],[24,33220,918],{"className":33221},[1011],[24,33223],{"className":33224,"style":1007},[700],[24,33226,33228,33232,33337,33340,33385],{"className":33227},[65],[24,33229],{"className":33230,"style":33231},[69],"height:1.2887em;vertical-align:-0.2997em;",[24,33233,33235,33239],{"className":33234},[1657],[24,33236,1477],{"className":33237,"style":33238},[1657,1693,1694],"position:relative;top:0em;",[24,33240,33242],{"className":33241},[82],[24,33243,33245,33328],{"className":33244},[86,87],[24,33246,33248,33325],{"className":33247},[91],[24,33249,33252,33273],{"className":33250,"style":33251},[95],"height:0.989em;",[24,33253,33255,33258],{"style":33254},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[24,33256],{"className":33257,"style":104},[103],[24,33259,33261],{"className":33260},[108,109,110,111],[24,33262,33264,33267,33270],{"className":33263},[74,111],[24,33265,29613],{"className":33266},[74,78,111],[24,33268,918],{"className":33269},[1011,111],[24,33271,616],{"className":33272},[74,111],[24,33274,33276,33279],{"style":33275},"top:-3.2029em;margin-right:0.05em;",[24,33277],{"className":33278,"style":104},[103],[24,33280,33282],{"className":33281},[108,109,110,111],[24,33283,33285],{"className":33284},[74,111],[24,33286,33288,33291],{"className":33287},[74,111],[24,33289,31509],{"className":33290},[74,78,111],[24,33292,33294],{"className":33293},[82],[24,33295,33297,33317],{"className":33296},[86,87],[24,33298,33300,33314],{"className":33299},[91],[24,33301,33303],{"className":33302,"style":1550},[95],[24,33304,33305,33308],{"style":31601},[24,33306],{"className":33307,"style":1593},[103],[24,33309,33311],{"className":33310},[108,1597,1598,111],[24,33312,31512],{"className":33313,"style":31611},[74,78,111],[24,33315,119],{"className":33316},[118],[24,33318,33320],{"className":33319},[91],[24,33321,33323],{"className":33322,"style":1614},[95],[24,33324],{},[24,33326,119],{"className":33327},[118],[24,33329,33331],{"className":33330},[91],[24,33332,33335],{"className":33333,"style":33334},[95],"height:0.2997em;",[24,33336],{},[24,33338],{"className":33339,"style":701},[700],[24,33341,33343,33346],{"className":33342},[74],[24,33344,19326],{"className":33345,"style":292},[74,78],[24,33347,33349],{"className":33348},[82],[24,33350,33352,33377],{"className":33351},[86,87],[24,33353,33355,33374],{"className":33354},[91],[24,33356,33359],{"className":33357,"style":33358},[95],"height:0.3117em;",[24,33360,33362,33365],{"style":33361},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[24,33363],{"className":33364,"style":104},[103],[24,33366,33368],{"className":33367},[108,109,110,111],[24,33369,33371],{"className":33370},[74,111],[24,33372,29613],{"className":33373},[74,78,111],[24,33375,119],{"className":33376},[118],[24,33378,33380],{"className":33379},[91],[24,33381,33383],{"className":33382,"style":126},[95],[24,33384],{},[24,33386,33388,33391],{"className":33387},[74],[24,33389,31512],{"className":33390,"style":31611},[74,78],[24,33392,33394],{"className":33393},[82],[24,33395,33397,33421],{"className":33396},[86,87],[24,33398,33400,33418],{"className":33399},[91],[24,33401,33403],{"className":33402,"style":33358},[95],[24,33404,33406,33409],{"style":33405},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[24,33407],{"className":33408,"style":104},[103],[24,33410,33412],{"className":33411},[108,109,110,111],[24,33413,33415],{"className":33414},[74,111],[24,33416,29613],{"className":33417},[74,78,111],[24,33419,119],{"className":33420},[118],[24,33422,33424],{"className":33423},[91],[24,33425,33427],{"className":33426,"style":126},[95],[24,33428],{}," 的均值为 ",[24,33431,33433,33446],{"className":33432},[27],[24,33434,33436],{"className":33435},[31],[33,33437,33438],{"xmlns":35},[37,33439,33440,33444],{},[40,33441,33442],{},[596,33443,598],{},[53,33445,598],{"encoding":55},[24,33447,33449],{"className":33448,"ariaHidden":61},[60],[24,33450,33452,33455],{"className":33451},[65],[24,33453],{"className":33454,"style":33098},[69],[24,33456,598],{"className":33457},[74],[24,33459,33461,33478],{"className":33460},[27],[24,33462,33464],{"className":33463},[31],[33,33465,33466],{"xmlns":35},[37,33467,33468,33476],{},[40,33469,33470],{},[43,33471,33472,33474],{},[46,33473,31509],{},[46,33475,31512],{},[53,33477,32559],{"encoding":55},[24,33479,33481],{"className":33480,"ariaHidden":61},[60],[24,33482,33484,33487],{"className":33483},[65],[24,33485],{"className":33486,"style":12947},[69],[24,33488,33490,33493],{"className":33489},[74],[24,33491,31509],{"className":33492},[74,78],[24,33494,33496],{"className":33495},[82],[24,33497,33499,33519],{"className":33498},[86,87],[24,33500,33502,33516],{"className":33501},[91],[24,33503,33505],{"className":33504,"style":1740},[95],[24,33506,33507,33510],{"style":99},[24,33508],{"className":33509,"style":104},[103],[24,33511,33513],{"className":33512},[108,109,110,111],[24,33514,31512],{"className":33515,"style":31611},[74,78,111],[24,33517,119],{"className":33518},[118],[24,33520,33522],{"className":33521},[91],[24,33523,33525],{"className":33524,"style":126},[95],[24,33526],{},"，为了抵消这种影响，我们要乘以一个缩放因子 ",[24,33529,33531,33554],{"className":33530},[27],[24,33532,33534],{"className":33533},[31],[33,33535,33536],{"xmlns":35},[37,33537,33538,33552],{},[40,33539,33540],{},[1977,33541,33542,33544],{},[596,33543,616],{},[31503,33545,33546],{},[43,33547,33548,33550],{},[46,33549,31509],{},[46,33551,31512],{},[53,33553,31515],{"encoding":55},[24,33555,33557],{"className":33556,"ariaHidden":61},[60],[24,33558,33560,33563],{"className":33559},[65],[24,33561],{"className":33562,"style":31525},[69],[24,33564,33566,33569,33709],{"className":33565},[74],[24,33567],{"className":33568},[351,3238],[24,33570,33572],{"className":33571},[1977],[24,33573,33575,33701],{"className":33574},[86,87],[24,33576,33578,33698],{"className":33577},[91],[24,33579,33581,33676,33684],{"className":33580,"style":5948},[95],[24,33582,33583,33586],{"style":31546},[24,33584],{"className":33585,"style":1675},[103],[24,33587,33589],{"className":33588},[108,109,110,111],[24,33590,33592],{"className":33591},[74,111],[24,33593,33595],{"className":33594},[74,31559,111],[24,33596,33598,33668],{"className":33597},[86,87],[24,33599,33601,33665],{"className":33600},[91],[24,33602,33604,33653],{"className":33603,"style":31569},[95],[24,33605,33607,33610],{"className":33606,"style":1684},[31573],[24,33608],{"className":33609,"style":1675},[103],[24,33611,33613],{"className":33612,"style":31580},[74,111],[24,33614,33616,33619],{"className":33615},[74,111],[24,33617,31509],{"className":33618},[74,78,111],[24,33620,33622],{"className":33621},[82],[24,33623,33625,33645],{"className":33624},[86,87],[24,33626,33628,33642],{"className":33627},[91],[24,33629,33631],{"className":33630,"style":1550},[95],[24,33632,33633,33636],{"style":31601},[24,33634],{"className":33635,"style":1593},[103],[24,33637,33639],{"className":33638},[108,1597,1598,111],[24,33640,31512],{"className":33641,"style":31611},[74,78,111],[24,33643,119],{"className":33644},[118],[24,33646,33648],{"className":33647},[91],[24,33649,33651],{"className":33650,"style":1614},[95],[24,33652],{},[24,33654,33655,33658],{"style":31625},[24,33656],{"className":33657,"style":1675},[103],[24,33659,33661],{"className":33660,"style":31633},[31632,111],[31635,33662,33663],{"xmlns":31637,"width":31638,"height":31639,"viewBox":31640,"preserveAspectRatio":31641},[31643,33664],{"d":31645},[24,33666,119],{"className":33667},[118],[24,33669,33671],{"className":33670},[91],[24,33672,33674],{"className":33673,"style":31655},[95],[24,33675],{},[24,33677,33678,33681],{"style":3312},[24,33679],{"className":33680,"style":1675},[103],[24,33682],{"className":33683,"style":3320},[3319],[24,33685,33686,33689],{"style":5974},[24,33687],{"className":33688,"style":1675},[103],[24,33690,33692],{"className":33691},[108,109,110,111],[24,33693,33695],{"className":33694},[74,111],[24,33696,616],{"className":33697},[74,111],[24,33699,119],{"className":33700},[118],[24,33702,33704],{"className":33703},[91],[24,33705,33707],{"className":33706,"style":31689},[95],[24,33708],{},[24,33710],{"className":33711},[438,3238],[14,33713,33714],{},"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":31407,"style":31407},"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":31407},[24,33725,33728,33732,33736,33739,33743,33746,33749],{"class":33726,"line":33727},"line",1,[24,33729,33731],{"class":33730},"szJfE","def",[24,33733,33735],{"class":33734},"sCLZk"," masked_softmax",[24,33737,312],{"class":33738},"scbbO",[24,33740,33742],{"class":33741},"syNf4","X",[24,33744,33745],{"class":33738},", ",[24,33747,33748],{"class":33741},"valid_lens",[24,33750,33751],{"class":33738},"):\n",[24,33753,33754],{"class":33726,"line":31408},[24,33755,33757],{"class":33756},"seLWX","    \"\"\"通过在最后一个轴上掩蔽元素来执行softmax操作\"\"\"\n",[24,33759,33760],{"class":33726,"line":31416},[24,33761,33763],{"class":33762},"sfgPZ","    # X:3D张量，valid_lens:1D或2D张量\n",[24,33765,33767,33770,33773,33776,33780],{"class":33726,"line":33766},4,[24,33768,33769],{"class":33730},"    if",[24,33771,33772],{"class":33738}," valid_lens ",[24,33774,33775],{"class":33730},"is",[24,33777,33779],{"class":33778},"soDru"," None",[24,33781,33782],{"class":33738},":\n",[24,33784,33786,33789,33792,33796,33799,33801],{"class":33726,"line":33785},5,[24,33787,33788],{"class":33730},"        return",[24,33790,33791],{"class":33738}," nn.functional.softmax(X, ",[24,33793,33795],{"class":33794},"sQkXh","dim",[24,33797,33798],{"class":33730},"=-",[24,33800,616],{"class":33778},[24,33802,33803],{"class":33738},")\n",[24,33805,33807,33810],{"class":33726,"line":33806},6,[24,33808,33809],{"class":33730},"    else",[24,33811,33782],{"class":33738},[24,33813,33815,33818,33820],{"class":33726,"line":33814},7,[24,33816,33817],{"class":33738},"        shape ",[24,33819,918],{"class":33730},[24,33821,33822],{"class":33738}," X.shape\n",[24,33824,33826,33829,33832,33835,33838],{"class":33726,"line":33825},8,[24,33827,33828],{"class":33730},"        if",[24,33830,33831],{"class":33738}," valid_lens.dim() ",[24,33833,33834],{"class":33730},"==",[24,33836,33837],{"class":33778}," 1",[24,33839,33782],{"class":33738},[24,33841,33843,33846,33848,33851,33853],{"class":33726,"line":33842},9,[24,33844,33845],{"class":33738},"            valid_lens ",[24,33847,918],{"class":33730},[24,33849,33850],{"class":33738}," torch.repeat_interleave(valid_lens, shape[",[24,33852,616],{"class":33778},[24,33854,33855],{"class":33738},"])\n",[24,33857,33859,33862],{"class":33726,"line":33858},10,[24,33860,33861],{"class":33730},"        else",[24,33863,33782],{"class":33738},[24,33865,33867,33869,33871,33874,33877,33879],{"class":33726,"line":33866},11,[24,33868,33845],{"class":33738},[24,33870,918],{"class":33730},[24,33872,33873],{"class":33738}," valid_lens.reshape(",[24,33875,33876],{"class":33730},"-",[24,33878,616],{"class":33778},[24,33880,33803],{"class":33738},[24,33882,33884],{"class":33726,"line":33883},12,[24,33885,33886],{"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",[24,33888,33890,33893,33895,33898,33900,33902,33905,33907,33909],{"class":33726,"line":33889},13,[24,33891,33892],{"class":33738},"        X ",[24,33894,918],{"class":33730},[24,33896,33897],{"class":33738}," d2l.sequence_mask(X.reshape(",[24,33899,33876],{"class":33730},[24,33901,616],{"class":33778},[24,33903,33904],{"class":33738},", shape[",[24,33906,33876],{"class":33730},[24,33908,616],{"class":33778},[24,33910,33911],{"class":33738},"]), valid_lens,\n",[24,33913,33915,33918,33920,33923],{"class":33726,"line":33914},14,[24,33916,33917],{"class":33794},"                              value",[24,33919,33798],{"class":33730},[24,33921,33922],{"class":33778},"1e6",[24,33924,33803],{"class":33738},[24,33926,33928,33930,33933,33935,33937,33939],{"class":33726,"line":33927},15,[24,33929,33788],{"class":33730},[24,33931,33932],{"class":33738}," nn.functional.softmax(X.reshape(shape), ",[24,33934,33795],{"class":33794},[24,33936,33798],{"class":33730},[24,33938,616],{"class":33778},[24,33940,33803],{"class":33738},[14,33942,33943],{},"下面实现缩放点积注意力。",[33716,33945,33947],{"className":33718,"code":33946,"language":33720,"meta":31407,"style":31407},"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":31407},[24,33950,33951,33954,33958,33960,33964,33966,33969],{"class":33726,"line":33727},[24,33952,33953],{"class":33730},"class",[24,33955,33957],{"class":33956},"skCyd"," DotProductAttention",[24,33959,312],{"class":33738},[24,33961,33963],{"class":33962},"sDP9b","nn",[24,33965,32214],{"class":33738},[24,33967,33968],{"class":33962},"Module",[24,33970,33751],{"class":33738},[24,33972,33973],{"class":33726,"line":31408},[24,33974,33975],{"class":33756},"    \"\"\"缩放点积注意力\"\"\"\n",[24,33977,33978,33981,33984,33986,33990,33992,33995,33997,34000,34003],{"class":33726,"line":31416},[24,33979,33980],{"class":33730},"    def",[24,33982,33983],{"class":33778}," __init__",[24,33985,312],{"class":33738},[24,33987,33989],{"class":33988},"sD3jg","self",[24,33991,33745],{"class":33738},[24,33993,33994],{"class":33741},"dropout",[24,33996,33745],{"class":33738},[24,33998,33999],{"class":33730},"**",[24,34001,34002],{"class":33741},"kwargs",[24,34004,33751],{"class":33738},[24,34006,34007,34011,34014,34017,34020,34023,34025,34027],{"class":33726,"line":33766},[24,34008,34010],{"class":34009},"sPGBF","        super",[24,34012,34013],{"class":33738},"(DotProductAttention, ",[24,34015,33989],{"class":34016},"sJti5",[24,34018,34019],{"class":33738},").",[24,34021,34022],{"class":33778},"__init__",[24,34024,312],{"class":33738},[24,34026,33999],{"class":33730},[24,34028,34029],{"class":33738},"kwargs)\n",[24,34031,34032,34035,34038,34040],{"class":33726,"line":33785},[24,34033,34034],{"class":34016},"        self",[24,34036,34037],{"class":33738},".dropout ",[24,34039,918],{"class":33730},[24,34041,34042],{"class":33738}," nn.Dropout(dropout)\n",[24,34044,34045],{"class":33726,"line":33806},[24,34046,34047],{"emptyLinePlaceholder":31432},"\n",[24,34049,34050],{"class":33726,"line":33814},[24,34051,34052],{"class":33762},"    # queries的形状：(batch_size，查询的个数，d)\n",[24,34054,34055],{"class":33726,"line":33825},[24,34056,34057],{"class":33762},"    # keys的形状：(batch_size，“键－值”对的个数，d)\n",[24,34059,34060],{"class":33726,"line":33842},[24,34061,34062],{"class":33762},"    # values的形状：(batch_size，“键－值”对的个数，值的维度)\n",[24,34064,34065],{"class":33726,"line":33858},[24,34066,34067],{"class":33762},"    # valid_lens的形状:(batch_size，)或者(batch_size，查询的个数)\n",[24,34069,34070,34072,34075,34077,34079,34081,34084,34086,34089,34091,34094,34096,34098,34100,34103],{"class":33726,"line":33866},[24,34071,33980],{"class":33730},[24,34073,34074],{"class":33734}," forward",[24,34076,312],{"class":33738},[24,34078,33989],{"class":33988},[24,34080,33745],{"class":33738},[24,34082,34083],{"class":33741},"queries",[24,34085,33745],{"class":33738},[24,34087,34088],{"class":33741},"keys",[24,34090,33745],{"class":33738},[24,34092,34093],{"class":33741},"values",[24,34095,33745],{"class":33738},[24,34097,33748],{"class":33741},[24,34099,918],{"class":33730},[24,34101,34102],{"class":33778},"None",[24,34104,33751],{"class":33738},[24,34106,34107,34110,34112,34115,34117,34119],{"class":33726,"line":33883},[24,34108,34109],{"class":33738},"        d ",[24,34111,918],{"class":33730},[24,34113,34114],{"class":33738}," queries.shape[",[24,34116,33876],{"class":33730},[24,34118,616],{"class":33778},[24,34120,34121],{"class":33738},"]\n",[24,34123,34124],{"class":33726,"line":33889},[24,34125,34126],{"class":33762},"        # 设置transpose_b=True为了交换keys的最后两个维度\n",[24,34128,34129,34132,34134,34137,34139,34141,34143,34146,34149],{"class":33726,"line":33914},[24,34130,34131],{"class":33738},"        scores ",[24,34133,918],{"class":33730},[24,34135,34136],{"class":33738}," torch.bmm(queries, keys.transpose(",[24,34138,616],{"class":33778},[24,34140,601],{"class":33738},[24,34142,9241],{"class":33778},[24,34144,34145],{"class":33738},")) ",[24,34147,34148],{"class":33730},"/",[24,34150,34151],{"class":33738}," math.sqrt(d)\n",[24,34153,34154,34156,34159,34161],{"class":33726,"line":33927},[24,34155,34034],{"class":34016},[24,34157,34158],{"class":33738},".attention_weights ",[24,34160,918],{"class":33730},[24,34162,34163],{"class":33738}," masked_softmax(scores, valid_lens)\n",[24,34165,34167,34169,34172,34174,34177,34179],{"class":33726,"line":34166},16,[24,34168,33788],{"class":33730},[24,34170,34171],{"class":33738}," torch.bmm(",[24,34173,33989],{"class":34016},[24,34175,34176],{"class":33738},".dropout(",[24,34178,33989],{"class":34016},[24,34180,34181],{"class":33738},".attention_weights), values)\n",[14,34183,34184,34185,34188],{},"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。",[14893,34190,34191],{"id":34191},"多头注意力",[14,34193,34194],{},"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。",[14,34196,34197],{},[31470,34198],{"alt":31407,"src":34199},"transformer/MHA.png",[14,34201,34202],{},[24,34203,34205,34318],{"className":34204},[27],[24,34206,34208],{"className":34207},[31],[33,34209,34210],{"xmlns":35},[37,34211,34212,34315],{},[40,34213,34214,34237,34239,34241,34243,34245,34247,34249,34251,34253,34268,34270,34285,34287,34289,34291,34305,34307],{},[40,34215,34216,34219,34222,34224,34226,34228,34231,34233,34235],{},[46,34217,34218],{"mathvariant":321},"M",[46,34220,34221],{"mathvariant":321},"u",[46,34223,29610],{"mathvariant":321},[46,34225,51],{"mathvariant":321},[46,34227,29613],{"mathvariant":321},[46,34229,34230],{"mathvariant":321},"H",[46,34232,32141],{"mathvariant":321},[46,34234,48],{"mathvariant":321},[46,34236,31509],{"mathvariant":321},[309,34238,312],{"stretchy":311},[46,34240,7754],{},[309,34242,601],{"separator":61},[46,34244,27683],{},[309,34246,601],{"separator":61},[46,34248,7915],{},[309,34250,331],{"stretchy":311},[309,34252,918],{},[40,34254,34255,34258,34260,34262,34264,34266],{},[46,34256,34257],{"mathvariant":321},"C",[46,34259,5800],{"mathvariant":321},[46,34261,2120],{"mathvariant":321},[46,34263,29607],{"mathvariant":321},[46,34265,48],{"mathvariant":321},[46,34267,51],{"mathvariant":321},[309,34269,312],{"stretchy":311},[43,34271,34272,34283],{},[40,34273,34274,34277,34279,34281],{},[46,34275,34276],{"mathvariant":321},"h",[46,34278,32141],{"mathvariant":321},[46,34280,48],{"mathvariant":321},[46,34282,31509],{"mathvariant":321},[596,34284,616],{},[309,34286,601],{"separator":61},[309,34288,627],{},[309,34290,601],{"separator":61},[43,34292,34293,34303],{},[40,34294,34295,34297,34299,34301],{},[46,34296,34276],{"mathvariant":321},[46,34298,32141],{"mathvariant":321},[46,34300,48],{"mathvariant":321},[46,34302,31509],{"mathvariant":321},[46,34304,34276],{},[309,34306,331],{"stretchy":311},[2132,34308,34309,34312],{},[46,34310,34311],{},"W",[46,34313,34314],{},"O",[53,34316,34317],{"encoding":55},"\\mathrm{MultiHead}(Q, K, V) = \\mathrm{Concat}(\\mathrm{head}_1, \\ldots, \\mathrm{head}_h) W^O",[24,34319,34321,34370],{"className":34320,"ariaHidden":61},[60],[24,34322,34324,34327,34334,34337,34340,34343,34346,34349,34352,34355,34358,34361,34364,34367],{"className":34323},[65],[24,34325],{"className":34326,"style":344},[69],[24,34328,34330],{"className":34329},[74],[24,34331,34333],{"className":34332},[74,28662],"MultiHead",[24,34335,312],{"className":34336},[351],[24,34338,7754],{"className":34339},[74,78],[24,34341,601],{"className":34342},[696],[24,34344],{"className":34345,"style":701},[700],[24,34347,27683],{"className":34348,"style":31966},[74,78],[24,34350,601],{"className":34351},[696],[24,34353],{"className":34354,"style":701},[700],[24,34356,7915],{"className":34357,"style":7942},[74,78],[24,34359,331],{"className":34360},[438],[24,34362],{"className":34363,"style":1007},[700],[24,34365,918],{"className":34366},[1011],[24,34368],{"className":34369,"style":1007},[700],[24,34371,34373,34377,34384,34387,34432,34435,34438,34441,34444,34447,34450,34493,34496],{"className":34372},[65],[24,34374],{"className":34375,"style":34376},[69],"height:1.0913em;vertical-align:-0.25em;",[24,34378,34380],{"className":34379},[74],[24,34381,34383],{"className":34382},[74,28662],"Concat",[24,34385,312],{"className":34386},[351],[24,34388,34390,34397],{"className":34389},[74],[24,34391,34393],{"className":34392},[74],[24,34394,34396],{"className":34395},[74,28662],"head",[24,34398,34400],{"className":34399},[82],[24,34401,34403,34424],{"className":34402},[86,87],[24,34404,34406,34421],{"className":34405},[91],[24,34407,34409],{"className":34408,"style":670},[95],[24,34410,34412,34415],{"style":34411},"top:-2.55em;margin-right:0.05em;",[24,34413],{"className":34414,"style":104},[103],[24,34416,34418],{"className":34417},[108,109,110,111],[24,34419,616],{"className":34420},[74,111],[24,34422,119],{"className":34423},[118],[24,34425,34427],{"className":34426},[91],[24,34428,34430],{"className":34429,"style":126},[95],[24,34431],{},[24,34433,601],{"className":34434},[696],[24,34436],{"className":34437,"style":701},[700],[24,34439,627],{"className":34440},[840],[24,34442],{"className":34443,"style":701},[700],[24,34445,601],{"className":34446},[696],[24,34448],{"className":34449,"style":701},[700],[24,34451,34453,34459],{"className":34452},[74],[24,34454,34456],{"className":34455},[74],[24,34457,34396],{"className":34458},[74,28662],[24,34460,34462],{"className":34461},[82],[24,34463,34465,34485],{"className":34464},[86,87],[24,34466,34468,34482],{"className":34467},[91],[24,34469,34471],{"className":34470,"style":1740},[95],[24,34472,34473,34476],{"style":34411},[24,34474],{"className":34475,"style":104},[103],[24,34477,34479],{"className":34478},[108,109,110,111],[24,34480,34276],{"className":34481},[74,78,111],[24,34483,119],{"className":34484},[118],[24,34486,34488],{"className":34487},[91],[24,34489,34491],{"className":34490,"style":126},[95],[24,34492],{},[24,34494,331],{"className":34495},[438],[24,34497,34499,34502],{"className":34498},[74],[24,34500,34311],{"className":34501,"style":874},[74,78],[24,34503,34505],{"className":34504},[82],[24,34506,34508],{"className":34507},[86],[24,34509,34511],{"className":34510},[91],[24,34512,34514],{"className":34513,"style":21203},[95],[24,34515,34516,34519],{"style":4064},[24,34517],{"className":34518,"style":104},[103],[24,34520,34522],{"className":34521},[108,109,110,111],[24,34523,34314],{"className":34524,"style":477},[74,78,111],[14,34526,34527,34528,34889,34890,35139,35140,35139,35389,35638,35639,32214],{},"其中 ",[24,34529,34531,34622],{"className":34530},[27],[24,34532,34534],{"className":34533},[31],[33,34535,34536],{"xmlns":35},[37,34537,34538,34619],{},[40,34539,34540,34554,34556,34576,34578,34580,34588,34590,34593,34595,34603,34605,34607,34609,34617],{},[43,34541,34542,34552],{},[40,34543,34544,34546,34548,34550],{},[46,34545,34276],{"mathvariant":321},[46,34547,32141],{"mathvariant":321},[46,34549,48],{"mathvariant":321},[46,34551,31509],{"mathvariant":321},[46,34553,29613],{},[309,34555,918],{},[40,34557,34558,34560,34562,34564,34566,34568,34570,34572,34574],{},[46,34559,8035],{"mathvariant":321},[46,34561,51],{"mathvariant":321},[46,34563,51],{"mathvariant":321},[46,34565,32141],{"mathvariant":321},[46,34567,2120],{"mathvariant":321},[46,34569,51],{"mathvariant":321},[46,34571,29613],{"mathvariant":321},[46,34573,5800],{"mathvariant":321},[46,34575,2120],{"mathvariant":321},[309,34577,312],{"stretchy":311},[46,34579,7754],{},[2340,34581,34582,34584,34586],{},[46,34583,34311],{},[46,34585,29613],{},[46,34587,7754],{},[309,34589,601],{"separator":61},[15052,34591,34592],{},"  ",[46,34594,27683],{},[2340,34596,34597,34599,34601],{},[46,34598,34311],{},[46,34600,29613],{},[46,34602,27683],{},[309,34604,601],{"separator":61},[15052,34606,34592],{},[46,34608,7915],{},[2340,34610,34611,34613,34615],{},[46,34612,34311],{},[46,34614,29613],{},[46,34616,7915],{},[309,34618,331],{"stretchy":311},[53,34620,34621],{"encoding":55},"\\mathrm{head}_i=\\mathrm{Attention}(QW_i^Q,\\; KW_i^K,\\; VW_i^V)",[24,34623,34625,34683],{"className":34624,"ariaHidden":61},[60],[24,34626,34628,34631,34674,34677,34680],{"className":34627},[65],[24,34629],{"className":34630,"style":12947},[69],[24,34632,34634,34640],{"className":34633},[74],[24,34635,34637],{"className":34636},[74],[24,34638,34396],{"className":34639},[74,28662],[24,34641,34643],{"className":34642},[82],[24,34644,34646,34666],{"className":34645},[86,87],[24,34647,34649,34663],{"className":34648},[91],[24,34650,34652],{"className":34651,"style":33358},[95],[24,34653,34654,34657],{"style":34411},[24,34655],{"className":34656,"style":104},[103],[24,34658,34660],{"className":34659},[108,109,110,111],[24,34661,29613],{"className":34662},[74,78,111],[24,34664,119],{"className":34665},[118],[24,34667,34669],{"className":34668},[91],[24,34670,34672],{"className":34671,"style":126},[95],[24,34673],{},[24,34675],{"className":34676,"style":1007},[700],[24,34678,918],{"className":34679},[1011],[24,34681],{"className":34682,"style":1007},[700],[24,34684,34686,34690,34697,34700,34703,34758,34761,34764,34767,34770,34823,34826,34829,34832,34835,34886],{"className":34685},[65],[24,34687],{"className":34688,"style":34689},[69],"height:1.2361em;vertical-align:-0.2769em;",[24,34691,34693],{"className":34692},[74],[24,34694,34696],{"className":34695},[74,28662],"Attention",[24,34698,312],{"className":34699},[351],[24,34701,7754],{"className":34702},[74,78],[24,34704,34706,34709],{"className":34705},[74],[24,34707,34311],{"className":34708,"style":874},[74,78],[24,34710,34712],{"className":34711},[82],[24,34713,34715,34749],{"className":34714},[86,87],[24,34716,34718,34746],{"className":34717},[91],[24,34719,34722,34734],{"className":34720,"style":34721},[95],"height:0.9592em;",[24,34723,34725,34728],{"style":34724},"top:-2.4231em;margin-left:-0.1389em;margin-right:0.05em;",[24,34726],{"className":34727,"style":104},[103],[24,34729,34731],{"className":34730},[108,109,110,111],[24,34732,29613],{"className":34733},[74,78,111],[24,34735,34737,34740],{"style":34736},"top:-3.1809em;margin-right:0.05em;",[24,34738],{"className":34739,"style":104},[103],[24,34741,34743],{"className":34742},[108,109,110,111],[24,34744,7754],{"className":34745},[74,78,111],[24,34747,119],{"className":34748},[118],[24,34750,34752],{"className":34751},[91],[24,34753,34756],{"className":34754,"style":34755},[95],"height:0.2769em;",[24,34757],{},[24,34759,601],{"className":34760},[696],[24,34762],{"className":34763,"style":1007},[700],[24,34765],{"className":34766,"style":701},[700],[24,34768,27683],{"className":34769,"style":31966},[74,78],[24,34771,34773,34776],{"className":34772},[74],[24,34774,34311],{"className":34775,"style":874},[74,78],[24,34777,34779],{"className":34778},[82],[24,34780,34782,34814],{"className":34781},[86,87],[24,34783,34785,34811],{"className":34784},[91],[24,34786,34788,34800],{"className":34787,"style":21203},[95],[24,34789,34791,34794],{"style":34790},"top:-2.4413em;margin-left:-0.1389em;margin-right:0.05em;",[24,34792],{"className":34793,"style":104},[103],[24,34795,34797],{"className":34796},[108,109,110,111],[24,34798,29613],{"className":34799},[74,78,111],[24,34801,34802,34805],{"style":4064},[24,34803],{"className":34804,"style":104},[103],[24,34806,34808],{"className":34807},[108,109,110,111],[24,34809,27683],{"className":34810,"style":31966},[74,78,111],[24,34812,119],{"className":34813},[118],[24,34815,34817],{"className":34816},[91],[24,34818,34821],{"className":34819,"style":34820},[95],"height:0.2587em;",[24,34822],{},[24,34824,601],{"className":34825},[696],[24,34827],{"className":34828,"style":1007},[700],[24,34830],{"className":34831,"style":701},[700],[24,34833,7915],{"className":34834,"style":7942},[74,78],[24,34836,34838,34841],{"className":34837},[74],[24,34839,34311],{"className":34840,"style":874},[74,78],[24,34842,34844],{"className":34843},[82],[24,34845,34847,34878],{"className":34846},[86,87],[24,34848,34850,34875],{"className":34849},[91],[24,34851,34853,34864],{"className":34852,"style":21203},[95],[24,34854,34855,34858],{"style":34790},[24,34856],{"className":34857,"style":104},[103],[24,34859,34861],{"className":34860},[108,109,110,111],[24,34862,29613],{"className":34863},[74,78,111],[24,34865,34866,34869],{"style":4064},[24,34867],{"className":34868,"style":104},[103],[24,34870,34872],{"className":34871},[108,109,110,111],[24,34873,7915],{"className":34874,"style":7942},[74,78,111],[24,34876,119],{"className":34877},[118],[24,34879,34881],{"className":34880},[91],[24,34882,34884],{"className":34883,"style":34820},[95],[24,34885],{},[24,34887,331],{"className":34888},[438],"，投影参数是矩阵\n",[24,34891,34893,34945],{"className":34892},[27],[24,34894,34896],{"className":34895},[31],[33,34897,34898],{"xmlns":35},[37,34899,34900,34942],{},[40,34901,34902,34910,34912],{},[2340,34903,34904,34906,34908],{},[46,34905,34311],{},[46,34907,29613],{},[46,34909,7754],{},[309,34911,31837],{},[2132,34913,34914,34916],{},[46,34915,1439],{"mathvariant":19396},[40,34917,34918,34934,34936],{},[43,34919,34920,34922],{},[46,34921,31509],{},[40,34923,34924,34926,34928,34930,34932],{},[46,34925,31744],{"mathvariant":321},[46,34927,5800],{"mathvariant":321},[46,34929,31509],{"mathvariant":321},[46,34931,32141],{"mathvariant":321},[46,34933,29610],{"mathvariant":321},[309,34935,31848],{},[43,34937,34938,34940],{},[46,34939,31509],{},[46,34941,31512],{},[53,34943,34944],{"encoding":55},"W_i^Q \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[24,34946,34948,35014],{"className":34947,"ariaHidden":61},[60],[24,34949,34951,34954,35005,35008,35011],{"className":34950},[65],[24,34952],{"className":34953,"style":34689},[69],[24,34955,34957,34960],{"className":34956},[74],[24,34958,34311],{"className":34959,"style":874},[74,78],[24,34961,34963],{"className":34962},[82],[24,34964,34966,34997],{"className":34965},[86,87],[24,34967,34969,34994],{"className":34968},[91],[24,34970,34972,34983],{"className":34971,"style":34721},[95],[24,34973,34974,34977],{"style":34724},[24,34975],{"className":34976,"style":104},[103],[24,34978,34980],{"className":34979},[108,109,110,111],[24,34981,29613],{"className":34982},[74,78,111],[24,34984,34985,34988],{"style":34736},[24,34986],{"className":34987,"style":104},[103],[24,34989,34991],{"className":34990},[108,109,110,111],[24,34992,7754],{"className":34993},[74,78,111],[24,34995,119],{"className":34996},[118],[24,34998,35000],{"className":34999},[91],[24,35001,35003],{"className":35002,"style":34755},[95],[24,35004],{},[24,35006],{"className":35007,"style":1007},[700],[24,35009,31837],{"className":35010},[1011],[24,35012],{"className":35013,"style":1007},[700],[24,35015,35017,35020],{"className":35016},[65],[24,35018],{"className":35019,"style":31882},[69],[24,35021,35023,35026],{"className":35022},[74],[24,35024,1439],{"className":35025},[74,19804],[24,35027,35029],{"className":35028},[82],[24,35030,35032],{"className":35031},[86],[24,35033,35035],{"className":35034},[91],[24,35036,35038],{"className":35037,"style":31882},[95],[24,35039,35040,35043],{"style":4064},[24,35041],{"className":35042,"style":104},[103],[24,35044,35046],{"className":35045},[108,109,110,111],[24,35047,35049,35096,35099],{"className":35048},[74,111],[24,35050,35052,35055],{"className":35051},[74,111],[24,35053,31509],{"className":35054},[74,78,111],[24,35056,35058],{"className":35057},[82],[24,35059,35061,35088],{"className":35060},[86,87],[24,35062,35064,35085],{"className":35063},[91],[24,35065,35067],{"className":35066,"style":1550},[95],[24,35068,35069,35072],{"style":31601},[24,35070],{"className":35071,"style":1593},[103],[24,35073,35075],{"className":35074},[108,1597,1598,111],[24,35076,35078],{"className":35077},[74,111],[24,35079,35081],{"className":35080},[74,111],[24,35082,35084],{"className":35083},[74,28662,111],"model",[24,35086,119],{"className":35087},[118],[24,35089,35091],{"className":35090},[91],[24,35092,35094],{"className":35093,"style":1614},[95],[24,35095],{},[24,35097,31848],{"className":35098},[988,111],[24,35100,35102,35105],{"className":35101},[74,111],[24,35103,31509],{"className":35104},[74,78,111],[24,35106,35108],{"className":35107},[82],[24,35109,35111,35131],{"className":35110},[86,87],[24,35112,35114,35128],{"className":35113},[91],[24,35115,35117],{"className":35116,"style":1550},[95],[24,35118,35119,35122],{"style":31601},[24,35120],{"className":35121,"style":1593},[103],[24,35123,35125],{"className":35124},[108,1597,1598,111],[24,35126,31512],{"className":35127,"style":31611},[74,78,111],[24,35129,119],{"className":35130},[118],[24,35132,35134],{"className":35133},[91],[24,35135,35137],{"className":35136,"style":1614},[95],[24,35138],{},",\n",[24,35141,35143,35195],{"className":35142},[27],[24,35144,35146],{"className":35145},[31],[33,35147,35148],{"xmlns":35},[37,35149,35150,35192],{},[40,35151,35152,35160,35162],{},[2340,35153,35154,35156,35158],{},[46,35155,34311],{},[46,35157,29613],{},[46,35159,27683],{},[309,35161,31837],{},[2132,35163,35164,35166],{},[46,35165,1439],{"mathvariant":19396},[40,35167,35168,35184,35186],{},[43,35169,35170,35172],{},[46,35171,31509],{},[40,35173,35174,35176,35178,35180,35182],{},[46,35175,31744],{"mathvariant":321},[46,35177,5800],{"mathvariant":321},[46,35179,31509],{"mathvariant":321},[46,35181,32141],{"mathvariant":321},[46,35183,29610],{"mathvariant":321},[309,35185,31848],{},[43,35187,35188,35190],{},[46,35189,31509],{},[46,35191,31512],{},[53,35193,35194],{"encoding":55},"W_i^K \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_k}",[24,35196,35198,35265],{"className":35197,"ariaHidden":61},[60],[24,35199,35201,35205,35256,35259,35262],{"className":35200},[65],[24,35202],{"className":35203,"style":35204},[69],"height:1.1em;vertical-align:-0.2587em;",[24,35206,35208,35211],{"className":35207},[74],[24,35209,34311],{"className":35210,"style":874},[74,78],[24,35212,35214],{"className":35213},[82],[24,35215,35217,35248],{"className":35216},[86,87],[24,35218,35220,35245],{"className":35219},[91],[24,35221,35223,35234],{"className":35222,"style":21203},[95],[24,35224,35225,35228],{"style":34790},[24,35226],{"className":35227,"style":104},[103],[24,35229,35231],{"className":35230},[108,109,110,111],[24,35232,29613],{"className":35233},[74,78,111],[24,35235,35236,35239],{"style":4064},[24,35237],{"className":35238,"style":104},[103],[24,35240,35242],{"className":35241},[108,109,110,111],[24,35243,27683],{"className":35244,"style":31966},[74,78,111],[24,35246,119],{"className":35247},[118],[24,35249,35251],{"className":35250},[91],[24,35252,35254],{"className":35253,"style":34820},[95],[24,35255],{},[24,35257],{"className":35258,"style":1007},[700],[24,35260,31837],{"className":35261},[1011],[24,35263],{"className":35264,"style":1007},[700],[24,35266,35268,35271],{"className":35267},[65],[24,35269],{"className":35270,"style":31882},[69],[24,35272,35274,35277],{"className":35273},[74],[24,35275,1439],{"className":35276},[74,19804],[24,35278,35280],{"className":35279},[82],[24,35281,35283],{"className":35282},[86],[24,35284,35286],{"className":35285},[91],[24,35287,35289],{"className":35288,"style":31882},[95],[24,35290,35291,35294],{"style":4064},[24,35292],{"className":35293,"style":104},[103],[24,35295,35297],{"className":35296},[108,109,110,111],[24,35298,35300,35346,35349],{"className":35299},[74,111],[24,35301,35303,35306],{"className":35302},[74,111],[24,35304,31509],{"className":35305},[74,78,111],[24,35307,35309],{"className":35308},[82],[24,35310,35312,35338],{"className":35311},[86,87],[24,35313,35315,35335],{"className":35314},[91],[24,35316,35318],{"className":35317,"style":1550},[95],[24,35319,35320,35323],{"style":31601},[24,35321],{"className":35322,"style":1593},[103],[24,35324,35326],{"className":35325},[108,1597,1598,111],[24,35327,35329],{"className":35328},[74,111],[24,35330,35332],{"className":35331},[74,111],[24,35333,35084],{"className":35334},[74,28662,111],[24,35336,119],{"className":35337},[118],[24,35339,35341],{"className":35340},[91],[24,35342,35344],{"className":35343,"style":1614},[95],[24,35345],{},[24,35347,31848],{"className":35348},[988,111],[24,35350,35352,35355],{"className":35351},[74,111],[24,35353,31509],{"className":35354},[74,78,111],[24,35356,35358],{"className":35357},[82],[24,35359,35361,35381],{"className":35360},[86,87],[24,35362,35364,35378],{"className":35363},[91],[24,35365,35367],{"className":35366,"style":1550},[95],[24,35368,35369,35372],{"style":31601},[24,35370],{"className":35371,"style":1593},[103],[24,35373,35375],{"className":35374},[108,1597,1598,111],[24,35376,31512],{"className":35377,"style":31611},[74,78,111],[24,35379,119],{"className":35380},[118],[24,35382,35384],{"className":35383},[91],[24,35385,35387],{"className":35386,"style":1614},[95],[24,35388],{},[24,35390,35392,35444],{"className":35391},[27],[24,35393,35395],{"className":35394},[31],[33,35396,35397],{"xmlns":35},[37,35398,35399,35441],{},[40,35400,35401,35409,35411],{},[2340,35402,35403,35405,35407],{},[46,35404,34311],{},[46,35406,29613],{},[46,35408,7915],{},[309,35410,31837],{},[2132,35412,35413,35415],{},[46,35414,1439],{"mathvariant":19396},[40,35416,35417,35433,35435],{},[43,35418,35419,35421],{},[46,35420,31509],{},[40,35422,35423,35425,35427,35429,35431],{},[46,35424,31744],{"mathvariant":321},[46,35426,5800],{"mathvariant":321},[46,35428,31509],{"mathvariant":321},[46,35430,32141],{"mathvariant":321},[46,35432,29610],{"mathvariant":321},[309,35434,31848],{},[43,35436,35437,35439],{},[46,35438,31509],{},[46,35440,31803],{},[53,35442,35443],{"encoding":55},"W_i^V \\in \\mathbb{R}^{d_{\\mathrm{model}} \\times d_v}",[24,35445,35447,35513],{"className":35446,"ariaHidden":61},[60],[24,35448,35450,35453,35504,35507,35510],{"className":35449},[65],[24,35451],{"className":35452,"style":35204},[69],[24,35454,35456,35459],{"className":35455},[74],[24,35457,34311],{"className":35458,"style":874},[74,78],[24,35460,35462],{"className":35461},[82],[24,35463,35465,35496],{"className":35464},[86,87],[24,35466,35468,35493],{"className":35467},[91],[24,35469,35471,35482],{"className":35470,"style":21203},[95],[24,35472,35473,35476],{"style":34790},[24,35474],{"className":35475,"style":104},[103],[24,35477,35479],{"className":35478},[108,109,110,111],[24,35480,29613],{"className":35481},[74,78,111],[24,35483,35484,35487],{"style":4064},[24,35485],{"className":35486,"style":104},[103],[24,35488,35490],{"className":35489},[108,109,110,111],[24,35491,7915],{"className":35492,"style":7942},[74,78,111],[24,35494,119],{"className":35495},[118],[24,35497,35499],{"className":35498},[91],[24,35500,35502],{"className":35501,"style":34820},[95],[24,35503],{},[24,35505],{"className":35506,"style":1007},[700],[24,35508,31837],{"className":35509},[1011],[24,35511],{"className":35512,"style":1007},[700],[24,35514,35516,35519],{"className":35515},[65],[24,35517],{"className":35518,"style":31882},[69],[24,35520,35522,35525],{"className":35521},[74],[24,35523,1439],{"className":35524},[74,19804],[24,35526,35528],{"className":35527},[82],[24,35529,35531],{"className":35530},[86],[24,35532,35534],{"className":35533},[91],[24,35535,35537],{"className":35536,"style":31882},[95],[24,35538,35539,35542],{"style":4064},[24,35540],{"className":35541,"style":104},[103],[24,35543,35545],{"className":35544},[108,109,110,111],[24,35546,35548,35594,35597],{"className":35547},[74,111],[24,35549,35551,35554],{"className":35550},[74,111],[24,35552,31509],{"className":35553},[74,78,111],[24,35555,35557],{"className":35556},[82],[24,35558,35560,35586],{"className":35559},[86,87],[24,35561,35563,35583],{"className":35562},[91],[24,35564,35566],{"className":35565,"style":1550},[95],[24,35567,35568,35571],{"style":31601},[24,35569],{"className":35570,"style":1593},[103],[24,35572,35574],{"className":35573},[108,1597,1598,111],[24,35575,35577],{"className":35576},[74,111],[24,35578,35580],{"className":35579},[74,111],[24,35581,35084],{"className":35582},[74,28662,111],[24,35584,119],{"className":35585},[118],[24,35587,35589],{"className":35588},[91],[24,35590,35592],{"className":35591,"style":1614},[95],[24,35593],{},[24,35595,31848],{"className":35596},[988,111],[24,35598,35600,35603],{"className":35599},[74,111],[24,35601,31509],{"className":35602},[74,78,111],[24,35604,35606],{"className":35605},[82],[24,35607,35609,35630],{"className":35608},[86,87],[24,35610,35612,35627],{"className":35611},[91],[24,35613,35615],{"className":35614,"style":4650},[95],[24,35616,35618,35621],{"style":35617},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[24,35619],{"className":35620,"style":1593},[103],[24,35622,35624],{"className":35623},[108,1597,1598,111],[24,35625,31803],{"className":35626,"style":292},[74,78,111],[24,35628,119],{"className":35629},[118],[24,35631,35633],{"className":35632},[91],[24,35634,35636],{"className":35635,"style":4672},[95],[24,35637],{},"\n和\n",[24,35640,35642,35694],{"className":35641},[27],[24,35643,35645],{"className":35644},[31],[33,35646,35647],{"xmlns":35},[37,35648,35649,35691],{},[40,35650,35651,35657,35659],{},[2132,35652,35653,35655],{},[46,35654,34311],{},[46,35656,34314],{},[309,35658,31837],{},[2132,35660,35661,35663],{},[46,35662,1439],{"mathvariant":19396},[40,35664,35665,35667,35673,35675],{},[46,35666,34276],{},[43,35668,35669,35671],{},[46,35670,31509],{},[46,35672,31803],{},[309,35674,31848],{},[43,35676,35677,35679],{},[46,35678,31509],{},[40,35680,35681,35683,35685,35687,35689],{},[46,35682,31744],{"mathvariant":321},[46,35684,5800],{"mathvariant":321},[46,35686,31509],{"mathvariant":321},[46,35688,32141],{"mathvariant":321},[46,35690,29610],{"mathvariant":321},[53,35692,35693],{"encoding":55},"W^O \\in \\mathbb{R}^{h d_v \\times d_{\\mathrm{model}}}",[24,35695,35697,35742],{"className":35696,"ariaHidden":61},[60],[24,35698,35700,35704,35733,35736,35739],{"className":35699},[65],[24,35701],{"className":35702,"style":35703},[69],"height:0.8804em;vertical-align:-0.0391em;",[24,35705,35707,35710],{"className":35706},[74],[24,35708,34311],{"className":35709,"style":874},[74,78],[24,35711,35713],{"className":35712},[82],[24,35714,35716],{"className":35715},[86],[24,35717,35719],{"className":35718},[91],[24,35720,35722],{"className":35721,"style":21203},[95],[24,35723,35724,35727],{"style":4064},[24,35725],{"className":35726,"style":104},[103],[24,35728,35730],{"className":35729},[108,109,110,111],[24,35731,34314],{"className":35732,"style":477},[74,78,111],[24,35734],{"className":35735,"style":1007},[700],[24,35737,31837],{"className":35738},[1011],[24,35740],{"className":35741,"style":1007},[700],[24,35743,35745,35748],{"className":35744},[65],[24,35746],{"className":35747,"style":31882},[69],[24,35749,35751,35754],{"className":35750},[74],[24,35752,1439],{"className":35753},[74,19804],[24,35755,35757],{"className":35756},[82],[24,35758,35760],{"className":35759},[86],[24,35761,35763],{"className":35762},[91],[24,35764,35766],{"className":35765,"style":31882},[95],[24,35767,35768,35771],{"style":4064},[24,35769],{"className":35770,"style":104},[103],[24,35772,35774],{"className":35773},[108,109,110,111],[24,35775,35777,35780,35820,35823],{"className":35776},[74,111],[24,35778,34276],{"className":35779},[74,78,111],[24,35781,35783,35786],{"className":35782},[74,111],[24,35784,31509],{"className":35785},[74,78,111],[24,35787,35789],{"className":35788},[82],[24,35790,35792,35812],{"className":35791},[86,87],[24,35793,35795,35809],{"className":35794},[91],[24,35796,35798],{"className":35797,"style":4650},[95],[24,35799,35800,35803],{"style":35617},[24,35801],{"className":35802,"style":1593},[103],[24,35804,35806],{"className":35805},[108,1597,1598,111],[24,35807,31803],{"className":35808,"style":292},[74,78,111],[24,35810,119],{"className":35811},[118],[24,35813,35815],{"className":35814},[91],[24,35816,35818],{"className":35817,"style":4672},[95],[24,35819],{},[24,35821,31848],{"className":35822},[988,111],[24,35824,35826,35829],{"className":35825},[74,111],[24,35827,31509],{"className":35828},[74,78,111],[24,35830,35832],{"className":35831},[82],[24,35833,35835,35861],{"className":35834},[86,87],[24,35836,35838,35858],{"className":35837},[91],[24,35839,35841],{"className":35840,"style":1550},[95],[24,35842,35843,35846],{"style":31601},[24,35844],{"className":35845,"style":1593},[103],[24,35847,35849],{"className":35848},[108,1597,1598,111],[24,35850,35852],{"className":35851},[74,111],[24,35853,35855],{"className":35854},[74,111],[24,35856,35084],{"className":35857},[74,28662,111],[24,35859,119],{"className":35860},[118],[24,35862,35864],{"className":35863},[91],[24,35865,35867],{"className":35866,"style":1614},[95],[24,35868],{},[14,35870,35871,35872,35875,35876,35879,35880,35882,35883,35885],{},"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":31407,"style":31407},"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":31407},[24,35892,35893,35895,35898,35900,35902,35904,35907],{"class":33726,"line":33727},[24,35894,33731],{"class":33730},[24,35896,35897],{"class":33734}," transpose_qkv",[24,35899,312],{"class":33738},[24,35901,33742],{"class":33741},[24,35903,33745],{"class":33738},[24,35905,35906],{"class":33741},"num_heads",[24,35908,33751],{"class":33738},[24,35910,35911],{"class":33726,"line":31408},[24,35912,35913],{"class":33756},"    \"\"\"为了多注意力头的并行计算而变换形状\"\"\"\n",[24,35915,35916],{"class":33726,"line":31416},[24,35917,35918],{"class":33762},"    # 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[24,35920,35921],{"class":33726,"line":33766},[24,35922,35923],{"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",[24,35925,35926,35929,35931,35934,35936,35939,35941,35944,35946,35948],{"class":33726,"line":33785},[24,35927,35928],{"class":33738},"    X ",[24,35930,918],{"class":33730},[24,35932,35933],{"class":33738}," X.reshape(X.shape[",[24,35935,598],{"class":33778},[24,35937,35938],{"class":33738},"], X.shape[",[24,35940,616],{"class":33778},[24,35942,35943],{"class":33738},"], num_heads, ",[24,35945,33876],{"class":33730},[24,35947,616],{"class":33778},[24,35949,33803],{"class":33738},[24,35951,35952],{"class":33726,"line":33806},[24,35953,34047],{"emptyLinePlaceholder":31432},[24,35955,35956],{"class":33726,"line":33814},[24,35957,35958],{"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",[24,35960,35961,35963,35965,35968,35970,35972,35974,35976,35978,35980,35982],{"class":33726,"line":33825},[24,35962,35928],{"class":33738},[24,35964,918],{"class":33730},[24,35966,35967],{"class":33738}," X.permute(",[24,35969,598],{"class":33778},[24,35971,33745],{"class":33738},[24,35973,9241],{"class":33778},[24,35975,33745],{"class":33738},[24,35977,616],{"class":33778},[24,35979,33745],{"class":33738},[24,35981,10475],{"class":33778},[24,35983,33803],{"class":33738},[24,35985,35986],{"class":33726,"line":33842},[24,35987,34047],{"emptyLinePlaceholder":31432},[24,35989,35990],{"class":33726,"line":33858},[24,35991,35992],{"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",[24,35994,35995,35998,36001,36003,36005,36008,36010,36012,36014],{"class":33726,"line":33866},[24,35996,35997],{"class":33730},"    return",[24,35999,36000],{"class":33738}," X.reshape(",[24,36002,33876],{"class":33730},[24,36004,616],{"class":33778},[24,36006,36007],{"class":33738},", X.shape[",[24,36009,9241],{"class":33778},[24,36011,35938],{"class":33738},[24,36013,10475],{"class":33778},[24,36015,33855],{"class":33738},[24,36017,36018],{"class":33726,"line":33883},[24,36019,34047],{"emptyLinePlaceholder":31432},[24,36021,36022,36024,36027,36029,36031,36033,36035],{"class":33726,"line":33889},[24,36023,33731],{"class":33730},[24,36025,36026],{"class":33734}," transpose_output",[24,36028,312],{"class":33738},[24,36030,33742],{"class":33741},[24,36032,33745],{"class":33738},[24,36034,35906],{"class":33741},[24,36036,33751],{"class":33738},[24,36038,36039],{"class":33726,"line":33914},[24,36040,36041],{"class":33756},"    \"\"\"逆转transpose_qkv函数的操作\"\"\"\n",[24,36043,36044,36046,36048,36050,36052,36054,36057,36059,36061,36063],{"class":33726,"line":33927},[24,36045,35928],{"class":33738},[24,36047,918],{"class":33730},[24,36049,36000],{"class":33738},[24,36051,33876],{"class":33730},[24,36053,616],{"class":33778},[24,36055,36056],{"class":33738},", num_heads, X.shape[",[24,36058,616],{"class":33778},[24,36060,35938],{"class":33738},[24,36062,9241],{"class":33778},[24,36064,33855],{"class":33738},[24,36066,36067,36069,36071,36073,36075,36077,36079,36081,36083,36085,36087],{"class":33726,"line":34166},[24,36068,35928],{"class":33738},[24,36070,918],{"class":33730},[24,36072,35967],{"class":33738},[24,36074,598],{"class":33778},[24,36076,33745],{"class":33738},[24,36078,9241],{"class":33778},[24,36080,33745],{"class":33738},[24,36082,616],{"class":33778},[24,36084,33745],{"class":33738},[24,36086,10475],{"class":33778},[24,36088,33803],{"class":33738},[24,36090,36092,36094,36096,36098,36100,36102,36105,36107,36109],{"class":33726,"line":36091},17,[24,36093,35997],{"class":33730},[24,36095,35933],{"class":33738},[24,36097,598],{"class":33778},[24,36099,35938],{"class":33738},[24,36101,616],{"class":33778},[24,36103,36104],{"class":33738},"], ",[24,36106,33876],{"class":33730},[24,36108,616],{"class":33778},[24,36110,33803],{"class":33738},[33716,36112,36114],{"className":33718,"code":36113,"language":33720,"meta":31407,"style":31407},"#@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":31407},[24,36117,36118],{"class":33726,"line":33727},[24,36119,36120],{"class":33762},"#@save\n",[24,36122,36123,36125,36128,36130,36132,36134,36136],{"class":33726,"line":31408},[24,36124,33953],{"class":33730},[24,36126,36127],{"class":33956}," MultiHeadAttention",[24,36129,312],{"class":33738},[24,36131,33963],{"class":33962},[24,36133,32214],{"class":33738},[24,36135,33968],{"class":33962},[24,36137,33751],{"class":33738},[24,36139,36140],{"class":33726,"line":31416},[24,36141,36142],{"class":33756},"    \"\"\"多头注意力\"\"\"\n",[24,36144,36145,36147,36149,36151,36153,36155,36158,36160,36163,36165,36168,36170,36173],{"class":33726,"line":33766},[24,36146,33980],{"class":33730},[24,36148,33983],{"class":33778},[24,36150,312],{"class":33738},[24,36152,33989],{"class":33988},[24,36154,33745],{"class":33738},[24,36156,36157],{"class":33741},"key_size",[24,36159,33745],{"class":33738},[24,36161,36162],{"class":33741},"query_size",[24,36164,33745],{"class":33738},[24,36166,36167],{"class":33741},"value_size",[24,36169,33745],{"class":33738},[24,36171,36172],{"class":33741},"num_hiddens",[24,36174,35139],{"class":33738},[24,36176,36177,36180,36182,36184,36186,36189,36191,36194,36196,36198,36200],{"class":33726,"line":33785},[24,36178,36179],{"class":33741},"                 num_heads",[24,36181,33745],{"class":33738},[24,36183,33994],{"class":33741},[24,36185,33745],{"class":33738},[24,36187,36188],{"class":33741},"bias",[24,36190,918],{"class":33730},[24,36192,36193],{"class":33778},"False",[24,36195,33745],{"class":33738},[24,36197,33999],{"class":33730},[24,36199,34002],{"class":33741},[24,36201,33751],{"class":33738},[24,36203,36204,36206,36209,36211,36213,36215,36217,36219],{"class":33726,"line":33806},[24,36205,34010],{"class":34009},[24,36207,36208],{"class":33738},"(MultiHeadAttention, ",[24,36210,33989],{"class":34016},[24,36212,34019],{"class":33738},[24,36214,34022],{"class":33778},[24,36216,312],{"class":33738},[24,36218,33999],{"class":33730},[24,36220,34029],{"class":33738},[24,36222,36223,36225,36228,36230],{"class":33726,"line":33814},[24,36224,34034],{"class":34016},[24,36226,36227],{"class":33738},".num_heads ",[24,36229,918],{"class":33730},[24,36231,36232],{"class":33738}," num_heads\n",[24,36234,36235,36237,36240,36242],{"class":33726,"line":33825},[24,36236,34034],{"class":34016},[24,36238,36239],{"class":33738},".attention ",[24,36241,918],{"class":33730},[24,36243,36244],{"class":33738}," d2l.DotProductAttention(dropout)\n",[24,36246,36247,36249,36252,36254,36257,36259,36261],{"class":33726,"line":33842},[24,36248,34034],{"class":34016},[24,36250,36251],{"class":33738},".W_q ",[24,36253,918],{"class":33730},[24,36255,36256],{"class":33738}," nn.Linear(query_size, num_hiddens, ",[24,36258,36188],{"class":33794},[24,36260,918],{"class":33730},[24,36262,36263],{"class":33738},"bias)\n",[24,36265,36266,36268,36271,36273,36276,36278,36280],{"class":33726,"line":33858},[24,36267,34034],{"class":34016},[24,36269,36270],{"class":33738},".W_k ",[24,36272,918],{"class":33730},[24,36274,36275],{"class":33738}," nn.Linear(key_size, num_hiddens, ",[24,36277,36188],{"class":33794},[24,36279,918],{"class":33730},[24,36281,36263],{"class":33738},[24,36283,36284,36286,36289,36291,36294,36296,36298],{"class":33726,"line":33866},[24,36285,34034],{"class":34016},[24,36287,36288],{"class":33738},".W_v ",[24,36290,918],{"class":33730},[24,36292,36293],{"class":33738}," nn.Linear(value_size, num_hiddens, ",[24,36295,36188],{"class":33794},[24,36297,918],{"class":33730},[24,36299,36263],{"class":33738},[24,36301,36302,36304,36307,36309,36312,36314,36316],{"class":33726,"line":33883},[24,36303,34034],{"class":34016},[24,36305,36306],{"class":33738},".W_o ",[24,36308,918],{"class":33730},[24,36310,36311],{"class":33738}," nn.Linear(num_hiddens, num_hiddens, ",[24,36313,36188],{"class":33794},[24,36315,918],{"class":33730},[24,36317,36263],{"class":33738},[24,36319,36320],{"class":33726,"line":33889},[24,36321,34047],{"emptyLinePlaceholder":31432},[24,36323,36324,36326,36328,36330,36332,36334,36336,36338,36340,36342,36344,36346,36348],{"class":33726,"line":33914},[24,36325,33980],{"class":33730},[24,36327,34074],{"class":33734},[24,36329,312],{"class":33738},[24,36331,33989],{"class":33988},[24,36333,33745],{"class":33738},[24,36335,34083],{"class":33741},[24,36337,33745],{"class":33738},[24,36339,34088],{"class":33741},[24,36341,33745],{"class":33738},[24,36343,34093],{"class":33741},[24,36345,33745],{"class":33738},[24,36347,33748],{"class":33741},[24,36349,33751],{"class":33738},[24,36351,36352],{"class":33726,"line":33927},[24,36353,36354],{"class":33762},"        # queries，keys，values的形状:\n",[24,36356,36357],{"class":33726,"line":34166},[24,36358,36359],{"class":33762},"        # (batch_size，查询或者“键－值”对的个数，num_hiddens)\n",[24,36361,36362],{"class":33726,"line":36091},[24,36363,36364],{"class":33762},"        # valid_lens　的形状:\n",[24,36366,36368],{"class":33726,"line":36367},18,[24,36369,36370],{"class":33762},"        # (batch_size，)或(batch_size，查询的个数)\n",[24,36372,36374],{"class":33726,"line":36373},19,[24,36375,36376],{"class":33762},"        # 经过变换后，输出的queries，keys，values 的形状:\n",[24,36378,36380],{"class":33726,"line":36379},20,[24,36381,36382],{"class":33762},"        # (batch_size*num_heads，查询或者“键－值”对的个数，num_hiddens/num_heads)\n",[24,36384,36386,36389,36391,36394,36396,36399,36401],{"class":33726,"line":36385},21,[24,36387,36388],{"class":33738},"        queries ",[24,36390,918],{"class":33730},[24,36392,36393],{"class":33738}," transpose_qkv(",[24,36395,33989],{"class":34016},[24,36397,36398],{"class":33738},".W_q(queries), ",[24,36400,33989],{"class":34016},[24,36402,36403],{"class":33738},".num_heads)\n",[24,36405,36407,36410,36412,36414,36416,36419,36421],{"class":33726,"line":36406},22,[24,36408,36409],{"class":33738},"        keys ",[24,36411,918],{"class":33730},[24,36413,36393],{"class":33738},[24,36415,33989],{"class":34016},[24,36417,36418],{"class":33738},".W_k(keys), ",[24,36420,33989],{"class":34016},[24,36422,36403],{"class":33738},[24,36424,36426,36429,36431,36433,36435,36438,36440],{"class":33726,"line":36425},23,[24,36427,36428],{"class":33738},"        values ",[24,36430,918],{"class":33730},[24,36432,36393],{"class":33738},[24,36434,33989],{"class":34016},[24,36436,36437],{"class":33738},".W_v(values), ",[24,36439,33989],{"class":34016},[24,36441,36403],{"class":33738},[24,36443,36445],{"class":33726,"line":36444},24,[24,36446,34047],{"emptyLinePlaceholder":31432},[24,36448,36450,36452,36454,36456,36459,36461],{"class":33726,"line":36449},25,[24,36451,33828],{"class":33730},[24,36453,33772],{"class":33738},[24,36455,33775],{"class":33730},[24,36457,36458],{"class":33730}," not",[24,36460,33779],{"class":33778},[24,36462,33782],{"class":33738},[24,36464,36466],{"class":33726,"line":36465},26,[24,36467,36468],{"class":33762},"            # 在轴0，将第一项（标量或者矢量）复制num_heads次，\n",[24,36470,36472],{"class":33726,"line":36471},27,[24,36473,36474],{"class":33762},"            # 然后如此复制第二项，然后诸如此类。\n",[24,36476,36478,36480,36482],{"class":33726,"line":36477},28,[24,36479,33845],{"class":33738},[24,36481,918],{"class":33730},[24,36483,36484],{"class":33738}," torch.repeat_interleave(\n",[24,36486,36488,36491,36494,36496,36498,36501,36503,36505,36507],{"class":33726,"line":36487},29,[24,36489,36490],{"class":33738},"                valid_lens, ",[24,36492,36493],{"class":33794},"repeats",[24,36495,918],{"class":33730},[24,36497,33989],{"class":34016},[24,36499,36500],{"class":33738},".num_heads, ",[24,36502,33795],{"class":33794},[24,36504,918],{"class":33730},[24,36506,598],{"class":33778},[24,36508,33803],{"class":33738},[24,36510,36512],{"class":33726,"line":36511},30,[24,36513,34047],{"emptyLinePlaceholder":31432},[24,36515,36517],{"class":33726,"line":36516},31,[24,36518,36519],{"class":33762},"        # output的形状:(batch_size*num_heads，查询的个数， num_hiddens/num_heads)\n",[24,36521,36523,36526,36528,36531],{"class":33726,"line":36522},32,[24,36524,36525],{"class":33738},"        output ",[24,36527,918],{"class":33730},[24,36529,36530],{"class":34016}," self",[24,36532,36533],{"class":33738},".attention(queries, keys, values, valid_lens)\n",[24,36535,36537],{"class":33726,"line":36536},33,[24,36538,34047],{"emptyLinePlaceholder":31432},[24,36540,36542],{"class":33726,"line":36541},34,[24,36543,36544],{"class":33762},"        # output_concat的形状:(batch_size，查询的个数，num_hiddens)\n",[24,36546,36548,36551,36553,36556,36558],{"class":33726,"line":36547},35,[24,36549,36550],{"class":33738},"        output_concat ",[24,36552,918],{"class":33730},[24,36554,36555],{"class":33738}," transpose_output(output, ",[24,36557,33989],{"class":34016},[24,36559,36403],{"class":33738},[24,36561,36563,36565,36567],{"class":33726,"line":36562},36,[24,36564,33788],{"class":33730},[24,36566,36530],{"class":34016},[24,36568,36569],{"class":33738},".W_o(output_concat)\n",[10,36571,36572],{"id":36572},"位置编码",[14,36574,36575,36576,36667],{},"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 ",[24,36577,36579,36605],{"className":36578},[27],[24,36580,36582],{"className":36581},[31],[33,36583,36584],{"xmlns":35},[37,36585,36586,36602],{},[40,36587,36588,36594,36596,36598,36600],{},[43,36589,36590,36592],{},[46,36591,31509],{},[46,36593,31744],{},[46,36595,5800],{},[46,36597,31509],{},[46,36599,32141],{},[46,36601,29610],{},[53,36603,36604],{"encoding":55},"d_model",[24,36606,36608],{"className":36607,"ariaHidden":61},[60],[24,36609,36611,36614,36654,36657,36660,36663],{"className":36610},[65],[24,36612],{"className":36613,"style":12947},[69],[24,36615,36617,36620],{"className":36616},[74],[24,36618,31509],{"className":36619},[74,78],[24,36621,36623],{"className":36622},[82],[24,36624,36626,36646],{"className":36625},[86,87],[24,36627,36629,36643],{"className":36628},[91],[24,36630,36632],{"className":36631,"style":20777},[95],[24,36633,36634,36637],{"style":99},[24,36635],{"className":36636,"style":104},[103],[24,36638,36640],{"className":36639},[108,109,110,111],[24,36641,31744],{"className":36642},[74,78,111],[24,36644,119],{"className":36645},[118],[24,36647,36649],{"className":36648},[91],[24,36650,36652],{"className":36651,"style":126},[95],[24,36653],{},[24,36655,5800],{"className":36656},[74,78],[24,36658,31509],{"className":36659},[74,78],[24,36661,32141],{"className":36662},[74,78],[24,36664,29610],{"className":36665,"style":36666},[74,78],"margin-right:0.01968em;","，因此两者可以相加。位置编码可以通过学习得到也可以直接固定得到。",[14,36669,36670],{},"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。",[14,36672,36673,36674,36839,36840,36868,36869,36897,36898,37068,37069,37129,37130,37159,37160,37197,37198,37254],{},"假设输入表示 ",[24,36675,36677,36720],{"className":36676},[27],[24,36678,36680],{"className":36679},[31],[33,36681,36682],{"xmlns":35},[37,36683,36684,36717],{},[40,36685,36686,36689,36691],{},[46,36687,33742],{"mathvariant":36688},"bold",[309,36690,31837],{},[2132,36692,36693,36695],{},[46,36694,1439],{"mathvariant":19396},[40,36696,36697,36699,36701],{},[46,36698,2120],{},[309,36700,31848],{},[43,36702,36703,36705],{},[46,36704,31509],{},[40,36706,36707,36709,36711,36713,36715],{},[46,36708,31744],{},[46,36710,5800],{},[46,36712,31509],{},[46,36714,32141],{},[46,36716,29610],{},[53,36718,36719],{"encoding":55},"\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{model}}",[24,36721,36723,36743],{"className":36722,"ariaHidden":61},[60],[24,36724,36726,36730,36734,36737,36740],{"className":36725},[65],[24,36727],{"className":36728,"style":36729},[69],"height:0.7252em;vertical-align:-0.0391em;",[24,36731,33742],{"className":36732},[74,36733],"mathbf",[24,36735],{"className":36736,"style":1007},[700],[24,36738,31837],{"className":36739},[1011],[24,36741],{"className":36742,"style":1007},[700],[24,36744,36746,36749],{"className":36745},[65],[24,36747],{"className":36748,"style":31882},[69],[24,36750,36752,36755],{"className":36751},[74],[24,36753,1439],{"className":36754},[74,19804],[24,36756,36758],{"className":36757},[82],[24,36759,36761],{"className":36760},[86],[24,36762,36764],{"className":36763},[91],[24,36765,36767],{"className":36766,"style":31882},[95],[24,36768,36769,36772],{"style":4064},[24,36770],{"className":36771,"style":104},[103],[24,36773,36775],{"className":36774},[108,109,110,111],[24,36776,36778,36781,36784],{"className":36777},[74,111],[24,36779,2120],{"className":36780},[74,78,111],[24,36782,31848],{"className":36783},[988,111],[24,36785,36787,36790],{"className":36786},[74,111],[24,36788,31509],{"className":36789},[74,78,111],[24,36791,36793],{"className":36792},[82],[24,36794,36796,36831],{"className":36795},[86,87],[24,36797,36799,36828],{"className":36798},[91],[24,36800,36802],{"className":36801,"style":1550},[95],[24,36803,36804,36807],{"style":31601},[24,36805],{"className":36806,"style":1593},[103],[24,36808,36810],{"className":36809},[108,1597,1598,111],[24,36811,36813,36816,36819,36822,36825],{"className":36812},[74,111],[24,36814,31744],{"className":36815},[74,78,111],[24,36817,5800],{"className":36818},[74,78,111],[24,36820,31509],{"className":36821},[74,78,111],[24,36823,32141],{"className":36824},[74,78,111],[24,36826,29610],{"className":36827,"style":36666},[74,78,111],[24,36829,119],{"className":36830},[118],[24,36832,36834],{"className":36833},[91],[24,36835,36837],{"className":36836,"style":1614},[95],[24,36838],{}," 包含一个序列中 ",[24,36841,36843,36856],{"className":36842},[27],[24,36844,36846],{"className":36845},[31],[33,36847,36848],{"xmlns":35},[37,36849,36850,36854],{},[40,36851,36852],{},[46,36853,2120],{},[53,36855,2120],{"encoding":55},[24,36857,36859],{"className":36858,"ariaHidden":61},[60],[24,36860,36862,36865],{"className":36861},[65],[24,36863],{"className":36864,"style":288},[69],[24,36866,2120],{"className":36867},[74,78]," 个词元的 ",[24,36870,36872,36885],{"className":36871},[27],[24,36873,36875],{"className":36874},[31],[33,36876,36877],{"xmlns":35},[37,36878,36879,36883],{},[40,36880,36881],{},[46,36882,31509],{},[53,36884,31509],{"encoding":55},[24,36886,36888],{"className":36887,"ariaHidden":61},[60],[24,36889,36891,36894],{"className":36890},[65],[24,36892],{"className":36893,"style":14930},[69],[24,36895,31509],{"className":36896},[74,78]," 维嵌入表示。位置编码使用相同形状的位置嵌入矩阵 ",[24,36899,36901,36947],{"className":36900},[27],[24,36902,36904],{"className":36903},[31],[33,36905,36906],{"xmlns":35},[37,36907,36908,36944],{},[40,36909,36910,36916,36918],{},[40,36911,36912,36914],{},[46,36913,1146],{"mathvariant":36688},[46,36915,1434],{"mathvariant":36688},[309,36917,31837],{},[2132,36919,36920,36922],{},[46,36921,1439],{"mathvariant":19396},[40,36923,36924,36926,36928],{},[46,36925,2120],{},[309,36927,31848],{},[43,36929,36930,36932],{},[46,36931,31509],{},[40,36933,36934,36936,36938,36940,36942],{},[46,36935,31744],{},[46,36937,5800],{},[46,36939,31509],{},[46,36941,32141],{},[46,36943,29610],{},[53,36945,36946],{"encoding":55},"\\mathbf{PE} \\in \\mathbb{R}^{n \\times d_{model}}",[24,36948,36950,36972],{"className":36949,"ariaHidden":61},[60],[24,36951,36953,36956,36963,36966,36969],{"className":36952},[65],[24,36954],{"className":36955,"style":36729},[69],[24,36957,36959],{"className":36958},[74],[24,36960,36962],{"className":36961},[74,36733],"PE",[24,36964],{"className":36965,"style":1007},[700],[24,36967,31837],{"className":36968},[1011],[24,36970],{"className":36971,"style":1007},[700],[24,36973,36975,36978],{"className":36974},[65],[24,36976],{"className":36977,"style":31882},[69],[24,36979,36981,36984],{"className":36980},[74],[24,36982,1439],{"className":36983},[74,19804],[24,36985,36987],{"className":36986},[82],[24,36988,36990],{"className":36989},[86],[24,36991,36993],{"className":36992},[91],[24,36994,36996],{"className":36995,"style":31882},[95],[24,36997,36998,37001],{"style":4064},[24,36999],{"className":37000,"style":104},[103],[24,37002,37004],{"className":37003},[108,109,110,111],[24,37005,37007,37010,37013],{"className":37006},[74,111],[24,37008,2120],{"className":37009},[74,78,111],[24,37011,31848],{"className":37012},[988,111],[24,37014,37016,37019],{"className":37015},[74,111],[24,37017,31509],{"className":37018},[74,78,111],[24,37020,37022],{"className":37021},[82],[24,37023,37025,37060],{"className":37024},[86,87],[24,37026,37028,37057],{"className":37027},[91],[24,37029,37031],{"className":37030,"style":1550},[95],[24,37032,37033,37036],{"style":31601},[24,37034],{"className":37035,"style":1593},[103],[24,37037,37039],{"className":37038},[108,1597,1598,111],[24,37040,37042,37045,37048,37051,37054],{"className":37041},[74,111],[24,37043,31744],{"className":37044},[74,78,111],[24,37046,5800],{"className":37047},[74,78,111],[24,37049,31509],{"className":37050},[74,78,111],[24,37052,32141],{"className":37053},[74,78,111],[24,37055,29610],{"className":37056,"style":36666},[74,78,111],[24,37058,119],{"className":37059},[118],[24,37061,37063],{"className":37062},[91],[24,37064,37066],{"className":37065,"style":1614},[95],[24,37067],{}," 输出 ",[24,37070,37072,37094],{"className":37071},[27],[24,37073,37075],{"className":37074},[31],[33,37076,37077],{"xmlns":35},[37,37078,37079,37091],{},[40,37080,37081,37083,37085],{},[46,37082,33742],{"mathvariant":36688},[309,37084,913],{},[40,37086,37087,37089],{},[46,37088,1146],{"mathvariant":36688},[46,37090,1434],{"mathvariant":36688},[53,37092,37093],{"encoding":55},"\\mathbf{X} + \\mathbf{PE}",[24,37095,37097,37116],{"className":37096,"ariaHidden":61},[60],[24,37098,37100,37104,37107,37110,37113],{"className":37099},[65],[24,37101],{"className":37102,"style":37103},[69],"height:0.7694em;vertical-align:-0.0833em;",[24,37105,33742],{"className":37106},[74,36733],[24,37108],{"className":37109,"style":3225},[700],[24,37111,913],{"className":37112},[988],[24,37114],{"className":37115,"style":3225},[700],[24,37117,37119,37123],{"className":37118},[65],[24,37120],{"className":37121,"style":37122},[69],"height:0.6861em;",[24,37124,37126],{"className":37125},[74],[24,37127,36962],{"className":37128},[74,36733],"，矩阵第 ",[24,37131,37133,37146],{"className":37132},[27],[24,37134,37136],{"className":37135},[31],[33,37137,37138],{"xmlns":35},[37,37139,37140,37144],{},[40,37141,37142],{},[46,37143,29613],{},[53,37145,29613],{"encoding":55},[24,37147,37149],{"className":37148,"ariaHidden":61},[60],[24,37150,37152,37156],{"className":37151},[65],[24,37153],{"className":37154,"style":37155},[69],"height:0.6595em;",[24,37157,29613],{"className":37158},[74,78]," 行、第 ",[24,37161,37163,37180],{"className":37162},[27],[24,37164,37166],{"className":37165},[31],[33,37167,37168],{"xmlns":35},[37,37169,37170,37177],{},[40,37171,37172,37174],{},[596,37173,9241],{},[46,37175,37176],{},"j",[53,37178,37179],{"encoding":55},"2j",[24,37181,37183],{"className":37182,"ariaHidden":61},[60],[24,37184,37186,37190,37193],{"className":37185},[65],[24,37187],{"className":37188,"style":37189},[69],"height:0.854em;vertical-align:-0.1944em;",[24,37191,9241],{"className":37192},[74],[24,37194,37176],{"className":37195,"style":37196},[74,78],"margin-right:0.05724em;"," 列和 ",[24,37199,37201,37221],{"className":37200},[27],[24,37202,37204],{"className":37203},[31],[33,37205,37206],{"xmlns":35},[37,37207,37208,37218],{},[40,37209,37210,37212,37214,37216],{},[596,37211,9241],{},[46,37213,37176],{},[309,37215,913],{},[596,37217,616],{},[53,37219,37220],{"encoding":55},"2j+1",[24,37222,37224,37245],{"className":37223,"ariaHidden":61},[60],[24,37225,37227,37230,37233,37236,37239,37242],{"className":37226},[65],[24,37228],{"className":37229,"style":37189},[69],[24,37231,9241],{"className":37232},[74],[24,37234,37176],{"className":37235,"style":37196},[74,78],[24,37237],{"className":37238,"style":3225},[700],[24,37240,913],{"className":37241},[988],[24,37243],{"className":37244,"style":3225},[700],[24,37246,37248,37251],{"className":37247},[65],[24,37249],{"className":37250,"style":33098},[69],[24,37252,616],{"className":37253},[74]," 列上的元素为：",[14,37256,37257],{},[24,37258,37260,37338],{"className":37259},[27],[24,37261,37263],{"className":37262},[31],[33,37264,37265],{"xmlns":35},[37,37266,37267,37335],{},[40,37268,37269,37271,37289,37291,37294,37296],{},[46,37270,1146],{},[43,37272,37273,37275],{},[46,37274,1434],{},[40,37276,37277,37279,37281,37283,37285,37287],{},[309,37278,312],{"stretchy":311},[46,37280,29613],{},[309,37282,601],{"separator":61},[596,37284,9241],{},[46,37286,37176],{},[309,37288,331],{"stretchy":311},[309,37290,918],{},[46,37292,37293],{},"sin",[309,37295,2239],{},[40,37297,37298,37300,37333],{},[309,37299,312],{"fence":61},[1977,37301,37302,37304],{},[46,37303,29613],{},[2132,37305,37306,37309],{},[596,37307,37308],{},"10000",[40,37310,37311,37313,37315,37317],{},[596,37312,9241],{},[46,37314,37176],{},[46,37316,34148],{"mathvariant":321},[43,37318,37319,37321],{},[46,37320,31509],{},[40,37322,37323,37325,37327,37329,37331],{},[46,37324,31744],{},[46,37326,5800],{},[46,37328,31509],{},[46,37330,32141],{},[46,37332,29610],{},[309,37334,331],{"fence":61},[53,37336,37337],{"encoding":55}," PE_{(i,2j)} = \\sin\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[24,37339,37341,37419],{"className":37340,"ariaHidden":61},[60],[24,37342,37344,37348,37351,37410,37413,37416],{"className":37343},[65],[24,37345],{"className":37346,"style":37347},[69],"height:1.0385em;vertical-align:-0.3552em;",[24,37349,1146],{"className":37350,"style":874},[74,78],[24,37352,37354,37357],{"className":37353},[74],[24,37355,1434],{"className":37356,"style":1416},[74,78],[24,37358,37360],{"className":37359},[82],[24,37361,37363,37402],{"className":37362},[86,87],[24,37364,37366,37399],{"className":37365},[91],[24,37367,37369],{"className":37368,"style":1550},[95],[24,37370,37372,37375],{"style":37371},"top:-2.5198em;margin-left:-0.0576em;margin-right:0.05em;",[24,37373],{"className":37374,"style":104},[103],[24,37376,37378],{"className":37377},[108,109,110,111],[24,37379,37381,37384,37387,37390,37393,37396],{"className":37380},[74,111],[24,37382,312],{"className":37383},[351,111],[24,37385,29613],{"className":37386},[74,78,111],[24,37388,601],{"className":37389},[696,111],[24,37391,9241],{"className":37392},[74,111],[24,37394,37176],{"className":37395,"style":37196},[74,78,111],[24,37397,331],{"className":37398},[438,111],[24,37400,119],{"className":37401},[118],[24,37403,37405],{"className":37404},[91],[24,37406,37408],{"className":37407,"style":1635},[95],[24,37409],{},[24,37411],{"className":37412,"style":1007},[700],[24,37414,918],{"className":37415},[1011],[24,37417],{"className":37418,"style":1007},[700],[24,37420,37422,37425,37428,37431],{"className":37421},[65],[24,37423],{"className":37424,"style":32294},[69],[24,37426,37293],{"className":37427},[1657],[24,37429],{"className":37430,"style":701},[700],[24,37432,37434,37440,37608],{"className":37433},[840],[24,37435,37437],{"className":37436,"style":17228},[351,17227],[24,37438,312],{"className":37439},[17232,32313],[24,37441,37443,37446,37605],{"className":37442},[74],[24,37444],{"className":37445},[351,3238],[24,37447,37449],{"className":37448},[1977],[24,37450,37452,37596],{"className":37451},[86,87],[24,37453,37455,37593],{"className":37454},[91],[24,37456,37459,37571,37579],{"className":37457,"style":37458},[95],"height:0.8557em;",[24,37460,37462,37465],{"style":37461},"top:-2.5648em;",[24,37463],{"className":37464,"style":1675},[103],[24,37466,37468],{"className":37467},[108,109,110,111],[24,37469,37471,37475],{"className":37470},[74,111],[24,37472,37474],{"className":37473},[74,111],"1000",[24,37476,37478,37481],{"className":37477},[74,111],[24,37479,598],{"className":37480},[74,111],[24,37482,37484],{"className":37483},[82],[24,37485,37487],{"className":37486},[86],[24,37488,37490],{"className":37489},[91],[24,37491,37494],{"className":37492,"style":37493},[95],"height:0.8932em;",[24,37495,37497,37501],{"style":37496},"top:-2.8932em;margin-right:0.0714em;",[24,37498],{"className":37499,"style":37500},[103],"height:2.5357em;",[24,37502,37504],{"className":37503},[108,1597,1598,111],[24,37505,37507,37510,37513,37516],{"className":37506},[74,111],[24,37508,9241],{"className":37509},[74,111],[24,37511,37176],{"className":37512,"style":37196},[74,78,111],[24,37514,34148],{"className":37515},[74,111],[24,37517,37519,37522],{"className":37518},[74,111],[24,37520,31509],{"className":37521},[74,78,111],[24,37523,37525],{"className":37524},[82],[24,37526,37528,37562],{"className":37527},[86,87],[24,37529,37531,37559],{"className":37530},[91],[24,37532,37534],{"className":37533,"style":1550},[95],[24,37535,37537,37541],{"style":37536},"top:-2.3448em;margin-left:0em;margin-right:0.1em;",[24,37538],{"className":37539,"style":37540},[103],"height:2.6944em;",[24,37542,37544,37547,37550,37553,37556],{"className":37543},[74,111],[24,37545,31744],{"className":37546},[74,78,111],[24,37548,5800],{"className":37549},[74,78,111],[24,37551,31509],{"className":37552},[74,78,111],[24,37554,32141],{"className":37555},[74,78,111],[24,37557,29610],{"className":37558,"style":36666},[74,78,111],[24,37560,119],{"className":37561},[118],[24,37563,37565],{"className":37564},[91],[24,37566,37569],{"className":37567,"style":37568},[95],"height:0.3496em;",[24,37570],{},[24,37572,37573,37576],{"style":3312},[24,37574],{"className":37575,"style":1675},[103],[24,37577],{"className":37578,"style":3320},[3319],[24,37580,37581,37584],{"style":5974},[24,37582],{"className":37583,"style":1675},[103],[24,37585,37587],{"className":37586},[108,109,110,111],[24,37588,37590],{"className":37589},[74,111],[24,37591,29613],{"className":37592},[74,78,111],[24,37594,119],{"className":37595},[118],[24,37597,37599],{"className":37598},[91],[24,37600,37603],{"className":37601,"style":37602},[95],"height:0.4352em;",[24,37604],{},[24,37606],{"className":37607},[438,3238],[24,37609,37611],{"className":37610,"style":17228},[438,17227],[24,37612,331],{"className":37613},[17232,32313],[14,37615,37616],{},[24,37617,37619,37700],{"className":37618},[27],[24,37620,37622],{"className":37621},[31],[33,37623,37624],{"xmlns":35},[37,37625,37626,37697],{},[40,37627,37628,37630,37652,37654,37657,37659],{},[46,37629,1146],{},[43,37631,37632,37634],{},[46,37633,1434],{},[40,37635,37636,37638,37640,37642,37644,37646,37648,37650],{},[309,37637,312],{"stretchy":311},[46,37639,29613],{},[309,37641,601],{"separator":61},[596,37643,9241],{},[46,37645,37176],{},[309,37647,913],{},[596,37649,616],{},[309,37651,331],{"stretchy":311},[309,37653,918],{},[46,37655,37656],{},"cos",[309,37658,2239],{},[40,37660,37661,37663,37695],{},[309,37662,312],{"fence":61},[1977,37664,37665,37667],{},[46,37666,29613],{},[2132,37668,37669,37671],{},[596,37670,37308],{},[40,37672,37673,37675,37677,37679],{},[596,37674,9241],{},[46,37676,37176],{},[46,37678,34148],{"mathvariant":321},[43,37680,37681,37683],{},[46,37682,31509],{},[40,37684,37685,37687,37689,37691,37693],{},[46,37686,31744],{},[46,37688,5800],{},[46,37690,31509],{},[46,37692,32141],{},[46,37694,29610],{},[309,37696,331],{"fence":61},[53,37698,37699],{"encoding":55}," PE_{(i,2j+1)} = \\cos\\left(\\frac{i}{10000^{2j/d_{model}}}\\right)",[24,37701,37703,37785],{"className":37702,"ariaHidden":61},[60],[24,37704,37706,37709,37712,37776,37779,37782],{"className":37705},[65],[24,37707],{"className":37708,"style":37347},[69],[24,37710,1146],{"className":37711,"style":874},[74,78],[24,37713,37715,37718],{"className":37714},[74],[24,37716,1434],{"className":37717,"style":1416},[74,78],[24,37719,37721],{"className":37720},[82],[24,37722,37724,37768],{"className":37723},[86,87],[24,37725,37727,37765],{"className":37726},[91],[24,37728,37730],{"className":37729,"style":1550},[95],[24,37731,37732,37735],{"style":37371},[24,37733],{"className":37734,"style":104},[103],[24,37736,37738],{"className":37737},[108,109,110,111],[24,37739,37741,37744,37747,37750,37753,37756,37759,37762],{"className":37740},[74,111],[24,37742,312],{"className":37743},[351,111],[24,37745,29613],{"className":37746},[74,78,111],[24,37748,601],{"className":37749},[696,111],[24,37751,9241],{"className":37752},[74,111],[24,37754,37176],{"className":37755,"style":37196},[74,78,111],[24,37757,913],{"className":37758},[988,111],[24,37760,616],{"className":37761},[74,111],[24,37763,331],{"className":37764},[438,111],[24,37766,119],{"className":37767},[118],[24,37769,37771],{"className":37770},[91],[24,37772,37774],{"className":37773,"style":1635},[95],[24,37775],{},[24,37777],{"className":37778,"style":1007},[700],[24,37780,918],{"className":37781},[1011],[24,37783],{"className":37784,"style":1007},[700],[24,37786,37788,37791,37794,37797],{"className":37787},[65],[24,37789],{"className":37790,"style":32294},[69],[24,37792,37656],{"className":37793},[1657],[24,37795],{"className":37796,"style":701},[700],[24,37798,37800,37806,37964],{"className":37799},[840],[24,37801,37803],{"className":37802,"style":17228},[351,17227],[24,37804,312],{"className":37805},[17232,32313],[24,37807,37809,37812,37961],{"className":37808},[74],[24,37810],{"className":37811},[351,3238],[24,37813,37815],{"className":37814},[1977],[24,37816,37818,37953],{"className":37817},[86,87],[24,37819,37821,37950],{"className":37820},[91],[24,37822,37824,37928,37936],{"className":37823,"style":37458},[95],[24,37825,37826,37829],{"style":37461},[24,37827],{"className":37828,"style":1675},[103],[24,37830,37832],{"className":37831},[108,109,110,111],[24,37833,37835,37838],{"className":37834},[74,111],[24,37836,37474],{"className":37837},[74,111],[24,37839,37841,37844],{"className":37840},[74,111],[24,37842,598],{"className":37843},[74,111],[24,37845,37847],{"className":37846},[82],[24,37848,37850],{"className":37849},[86],[24,37851,37853],{"className":37852},[91],[24,37854,37856],{"className":37855,"style":37493},[95],[24,37857,37858,37861],{"style":37496},[24,37859],{"className":37860,"style":37500},[103],[24,37862,37864],{"className":37863},[108,1597,1598,111],[24,37865,37867,37870,37873,37876],{"className":37866},[74,111],[24,37868,9241],{"className":37869},[74,111],[24,37871,37176],{"className":37872,"style":37196},[74,78,111],[24,37874,34148],{"className":37875},[74,111],[24,37877,37879,37882],{"className":37878},[74,111],[24,37880,31509],{"className":37881},[74,78,111],[24,37883,37885],{"className":37884},[82],[24,37886,37888,37920],{"className":37887},[86,87],[24,37889,37891,37917],{"className":37890},[91],[24,37892,37894],{"className":37893,"style":1550},[95],[24,37895,37896,37899],{"style":37536},[24,37897],{"className":37898,"style":37540},[103],[24,37900,37902,37905,37908,37911,37914],{"className":37901},[74,111],[24,37903,31744],{"className":37904},[74,78,111],[24,37906,5800],{"className":37907},[74,78,111],[24,37909,31509],{"className":37910},[74,78,111],[24,37912,32141],{"className":37913},[74,78,111],[24,37915,29610],{"className":37916,"style":36666},[74,78,111],[24,37918,119],{"className":37919},[118],[24,37921,37923],{"className":37922},[91],[24,37924,37926],{"className":37925,"style":37568},[95],[24,37927],{},[24,37929,37930,37933],{"style":3312},[24,37931],{"className":37932,"style":1675},[103],[24,37934],{"className":37935,"style":3320},[3319],[24,37937,37938,37941],{"style":5974},[24,37939],{"className":37940,"style":1675},[103],[24,37942,37944],{"className":37943},[108,109,110,111],[24,37945,37947],{"className":37946},[74,111],[24,37948,29613],{"className":37949},[74,78,111],[24,37951,119],{"className":37952},[118],[24,37954,37956],{"className":37955},[91],[24,37957,37959],{"className":37958,"style":37602},[95],[24,37960],{},[24,37962],{"className":37963},[438,3238],[24,37965,37967],{"className":37966,"style":17228},[438,17227],[24,37968,331],{"className":37969},[17232,32313],[14,37971,37972,37973,38001,38002,38030,38031,29355,38065,38121,38122,38150,38151,38243,38244,38322],{},"其中，",[24,37974,37976,37989],{"className":37975},[27],[24,37977,37979],{"className":37978},[31],[33,37980,37981],{"xmlns":35},[37,37982,37983,37987],{},[40,37984,37985],{},[46,37986,29613],{},[53,37988,29613],{"encoding":55},[24,37990,37992],{"className":37991,"ariaHidden":61},[60],[24,37993,37995,37998],{"className":37994},[65],[24,37996],{"className":37997,"style":37155},[69],[24,37999,29613],{"className":38000},[74,78]," 表示位置，",[24,38003,38005,38018],{"className":38004},[27],[24,38006,38008],{"className":38007},[31],[33,38009,38010],{"xmlns":35},[37,38011,38012,38016],{},[40,38013,38014],{},[46,38015,37176],{},[53,38017,37176],{"encoding":55},[24,38019,38021],{"className":38020,"ariaHidden":61},[60],[24,38022,38024,38027],{"className":38023},[65],[24,38025],{"className":38026,"style":37189},[69],[24,38028,37176],{"className":38029,"style":37196},[74,78]," 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 ",[24,38032,38034,38050],{"className":38033},[27],[24,38035,38037],{"className":38036},[31],[33,38038,38039],{"xmlns":35},[37,38040,38041,38047],{},[40,38042,38043,38045],{},[596,38044,9241],{},[46,38046,275],{},[53,38048,38049],{"encoding":55},"2\\pi",[24,38051,38053],{"className":38052,"ariaHidden":61},[60],[24,38054,38056,38059,38062],{"className":38055},[65],[24,38057],{"className":38058,"style":33098},[69],[24,38060,9241],{"className":38061},[74],[24,38063,275],{"className":38064,"style":292},[74,78],[24,38066,38068,38088],{"className":38067},[27],[24,38069,38071],{"className":38070},[31],[33,38072,38073],{"xmlns":35},[37,38074,38075,38085],{},[40,38076,38077,38079,38081,38083],{},[596,38078,37308],{},[309,38080,1151],{},[596,38082,9241],{},[46,38084,275],{},[53,38086,38087],{"encoding":55},"10000 \\cdot 2\\pi",[24,38089,38091,38109],{"className":38090,"ariaHidden":61},[60],[24,38092,38094,38097,38100,38103,38106],{"className":38093},[65],[24,38095],{"className":38096,"style":33098},[69],[24,38098,37308],{"className":38099},[74],[24,38101],{"className":38102,"style":3225},[700],[24,38104,1151],{"className":38105},[988],[24,38107],{"className":38108,"style":3225},[700],[24,38110,38112,38115,38118],{"className":38111},[65],[24,38113],{"className":38114,"style":33098},[69],[24,38116,9241],{"className":38117},[74],[24,38119,275],{"className":38120,"style":292},[74,78]," 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 ",[24,38123,38125,38138],{"className":38124},[27],[24,38126,38128],{"className":38127},[31],[33,38129,38130],{"xmlns":35},[37,38131,38132,38136],{},[40,38133,38134],{},[46,38135,31512],{},[53,38137,31512],{"encoding":55},[24,38139,38141],{"className":38140,"ariaHidden":61},[60],[24,38142,38144,38147],{"className":38143},[65],[24,38145],{"className":38146,"style":14930},[69],[24,38148,31512],{"className":38149,"style":31611},[74,78],"，",[24,38152,38154,38180],{"className":38153},[27],[24,38155,38157],{"className":38156},[31],[33,38158,38159],{"xmlns":35},[37,38160,38161,38177],{},[40,38162,38163,38165],{},[46,38164,1146],{},[43,38166,38167,38169],{},[46,38168,1434],{},[40,38170,38171,38173,38175],{},[46,38172,29613],{},[309,38174,913],{},[46,38176,31512],{},[53,38178,38179],{"encoding":55},"PE_{i+k}",[24,38181,38183],{"className":38182,"ariaHidden":61},[60],[24,38184,38186,38190,38193],{"className":38185},[65],[24,38187],{"className":38188,"style":38189},[69],"height:0.8917em;vertical-align:-0.2083em;",[24,38191,1146],{"className":38192,"style":874},[74,78],[24,38194,38196,38199],{"className":38195},[74],[24,38197,1434],{"className":38198,"style":1416},[74,78],[24,38200,38202],{"className":38201},[82],[24,38203,38205,38235],{"className":38204},[86,87],[24,38206,38208,38232],{"className":38207},[91],[24,38209,38211],{"className":38210,"style":1740},[95],[24,38212,38214,38217],{"style":38213},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[24,38215],{"className":38216,"style":104},[103],[24,38218,38220],{"className":38219},[108,109,110,111],[24,38221,38223,38226,38229],{"className":38222},[74,111],[24,38224,29613],{"className":38225},[74,78,111],[24,38227,913],{"className":38228},[988,111],[24,38230,31512],{"className":38231,"style":31611},[74,78,111],[24,38233,119],{"className":38234},[118],[24,38236,38238],{"className":38237},[91],[24,38239,38241],{"className":38240,"style":1001},[95],[24,38242],{}," 都可以表示为 ",[24,38245,38247,38267],{"className":38246},[27],[24,38248,38250],{"className":38249},[31],[33,38251,38252],{"xmlns":35},[37,38253,38254,38264],{},[40,38255,38256,38258],{},[46,38257,1146],{},[43,38259,38260,38262],{},[46,38261,1434],{},[46,38263,29613],{},[53,38265,38266],{"encoding":55},"PE_{i}",[24,38268,38270],{"className":38269,"ariaHidden":61},[60],[24,38271,38273,38276,38279],{"className":38272},[65],[24,38274],{"className":38275,"style":6943},[69],[24,38277,1146],{"className":38278,"style":874},[74,78],[24,38280,38282,38285],{"className":38281},[74],[24,38283,1434],{"className":38284,"style":1416},[74,78],[24,38286,38288],{"className":38287},[82],[24,38289,38291,38314],{"className":38290},[86,87],[24,38292,38294,38311],{"className":38293},[91],[24,38295,38297],{"className":38296,"style":33358},[95],[24,38298,38299,38302],{"style":38213},[24,38300],{"className":38301,"style":104},[103],[24,38303,38305],{"className":38304},[108,109,110,111],[24,38306,38308],{"className":38307},[74,111],[24,38309,29613],{"className":38310},[74,78,111],[24,38312,119],{"className":38313},[118],[24,38315,38317],{"className":38316},[91],[24,38318,38320],{"className":38319,"style":126},[95],[24,38321],{}," 的线性函数。",[33716,38324,38326],{"className":33718,"code":38325,"language":33720,"meta":31407,"style":31407},"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":31407},[24,38329,38330,38332,38335,38337,38339,38341,38344],{"class":33726,"line":33727},[24,38331,33953],{"class":33730},[24,38333,38334],{"class":33956}," PositionalEncoding",[24,38336,312],{"class":33738},[24,38338,33963],{"class":33962},[24,38340,32214],{"class":33738},[24,38342,38343],{"class":33962},"Block",[24,38345,33751],{"class":33738},[24,38347,38348],{"class":33726,"line":31408},[24,38349,38350],{"class":33756},"    \"\"\"位置编码\"\"\"\n",[24,38352,38353,38355,38357,38359,38361,38363,38365,38367,38369,38371,38374,38376,38378],{"class":33726,"line":31416},[24,38354,33980],{"class":33730},[24,38356,33983],{"class":33778},[24,38358,312],{"class":33738},[24,38360,33989],{"class":33988},[24,38362,33745],{"class":33738},[24,38364,36172],{"class":33741},[24,38366,33745],{"class":33738},[24,38368,33994],{"class":33741},[24,38370,33745],{"class":33738},[24,38372,38373],{"class":33741},"max_len",[24,38375,918],{"class":33730},[24,38377,37474],{"class":33778},[24,38379,33751],{"class":33738},[24,38381,38382,38384,38387,38389,38391,38393],{"class":33726,"line":33766},[24,38383,34010],{"class":34009},[24,38385,38386],{"class":33738},"(PositionalEncoding, ",[24,38388,33989],{"class":34016},[24,38390,34019],{"class":33738},[24,38392,34022],{"class":33778},[24,38394,38395],{"class":33738},"()\n",[24,38397,38398,38400,38402,38404],{"class":33726,"line":33785},[24,38399,34034],{"class":34016},[24,38401,34037],{"class":33738},[24,38403,918],{"class":33730},[24,38405,34042],{"class":33738},[24,38407,38408],{"class":33726,"line":33806},[24,38409,38410],{"class":33762},"        # 创建一个足够长的P\n",[24,38412,38413,38415,38418,38420,38423,38425],{"class":33726,"line":33814},[24,38414,34034],{"class":34016},[24,38416,38417],{"class":33738},".P ",[24,38419,918],{"class":33730},[24,38421,38422],{"class":33738}," np.zeros((",[24,38424,616],{"class":33778},[24,38426,38427],{"class":33738},", max_len, num_hiddens))\n",[24,38429,38430,38432,38434,38437,38439,38441,38443,38445,38448,38450],{"class":33726,"line":33825},[24,38431,33892],{"class":33738},[24,38433,918],{"class":33730},[24,38435,38436],{"class":33738}," np.arange(max_len).reshape(",[24,38438,33876],{"class":33730},[24,38440,616],{"class":33778},[24,38442,33745],{"class":33738},[24,38444,616],{"class":33778},[24,38446,38447],{"class":33738},") ",[24,38449,34148],{"class":33730},[24,38451,38452],{"class":33738}," np.power(\n",[24,38454,38455,38458,38461,38463,38466,38468,38470,38472],{"class":33726,"line":33842},[24,38456,38457],{"class":33778},"            10000",[24,38459,38460],{"class":33738},", np.arange(",[24,38462,598],{"class":33778},[24,38464,38465],{"class":33738},", num_hiddens, ",[24,38467,9241],{"class":33778},[24,38469,38447],{"class":33738},[24,38471,34148],{"class":33730},[24,38473,38474],{"class":33738}," num_hiddens)\n",[24,38476,38477,38479,38482,38485,38487,38489,38491,38493,38496,38498,38501,38503],{"class":33726,"line":33858},[24,38478,34034],{"class":34016},[24,38480,38481],{"class":33738},".P[",[24,38483,15071],{"class":38484},"sDoOe",[24,38486,33745],{"class":33738},[24,38488,15071],{"class":38484},[24,38490,33745],{"class":33738},[24,38492,598],{"class":33778},[24,38494,38495],{"class":38484},"::",[24,38497,9241],{"class":33778},[24,38499,38500],{"class":33738},"] ",[24,38502,918],{"class":33730},[24,38504,38505],{"class":33738}," np.sin(X)\n",[24,38507,38508,38510,38512,38514,38516,38518,38520,38522,38524,38526,38528,38530],{"class":33726,"line":33866},[24,38509,34034],{"class":34016},[24,38511,38481],{"class":33738},[24,38513,15071],{"class":38484},[24,38515,33745],{"class":33738},[24,38517,15071],{"class":38484},[24,38519,33745],{"class":33738},[24,38521,616],{"class":33778},[24,38523,38495],{"class":38484},[24,38525,9241],{"class":33778},[24,38527,38500],{"class":33738},[24,38529,918],{"class":33730},[24,38531,38532],{"class":33738}," np.cos(X)\n",[24,38534,38535],{"class":33726,"line":33883},[24,38536,34047],{"emptyLinePlaceholder":31432},[24,38538,38539,38541,38543,38545,38547,38549,38551],{"class":33726,"line":33889},[24,38540,33980],{"class":33730},[24,38542,34074],{"class":33734},[24,38544,312],{"class":33738},[24,38546,33989],{"class":33988},[24,38548,33745],{"class":33738},[24,38550,33742],{"class":33741},[24,38552,33751],{"class":33738},[24,38554,38555,38557,38559,38562,38564,38566,38568,38570,38572,38574,38577,38579,38581,38583],{"class":33726,"line":33914},[24,38556,33892],{"class":33738},[24,38558,918],{"class":33730},[24,38560,38561],{"class":33738}," X ",[24,38563,913],{"class":33730},[24,38565,36530],{"class":34016},[24,38567,38481],{"class":33738},[24,38569,15071],{"class":38484},[24,38571,33745],{"class":33738},[24,38573,15071],{"class":38484},[24,38575,38576],{"class":33738},"X.shape[",[24,38578,616],{"class":33778},[24,38580,36104],{"class":33738},[24,38582,15071],{"class":38484},[24,38584,38585],{"class":33738},"].as_in_ctx(X.ctx)\n",[24,38587,38588,38590,38592],{"class":33726,"line":33927},[24,38589,33788],{"class":33730},[24,38591,36530],{"class":34016},[24,38593,38594],{"class":33738},".dropout(X)\n",[10,38596,38597],{"id":38597},"前馈神经网络",[14,38599,38600],{},"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。",[14,38602,38603],{},[24,38604,38606,38676],{"className":38605},[27],[24,38607,38609],{"className":38608},[31],[33,38610,38611],{"xmlns":35},[37,38612,38613,38673],{},[40,38614,38615,38618,38620,38622,38624,38626,38628,38630,38633,38635,38637,38639,38641,38643,38649,38651,38657,38659,38665,38667],{},[46,38616,38617],{},"F",[46,38619,38617],{},[46,38621,2110],{},[309,38623,312],{"stretchy":311},[46,38625,19254],{},[309,38627,331],{"stretchy":311},[309,38629,918],{},[46,38631,38632],{},"max",[309,38634,2239],{},[309,38636,312],{"stretchy":311},[596,38638,598],{},[309,38640,601],{"separator":61},[46,38642,19254],{},[43,38644,38645,38647],{},[46,38646,34311],{},[596,38648,616],{},[309,38650,913],{},[43,38652,38653,38655],{},[46,38654,15499],{},[596,38656,616],{},[309,38658,331],{"stretchy":311},[43,38660,38661,38663],{},[46,38662,34311],{},[596,38664,9241],{},[309,38666,913],{},[43,38668,38669,38671],{},[46,38670,15499],{},[596,38672,9241],{},[53,38674,38675],{"encoding":55}," FFN(x) = \\max(0,xW_1+b_1)W_2+b_2",[24,38677,38679,38712,38785,38883],{"className":38678,"ariaHidden":61},[60],[24,38680,38682,38685,38688,38691,38694,38697,38700,38703,38706,38709],{"className":38681},[65],[24,38683],{"className":38684,"style":344},[69],[24,38686,38617],{"className":38687,"style":874},[74,78],[24,38689,38617],{"className":38690,"style":874},[74,78],[24,38692,2110],{"className":38693,"style":3729},[74,78],[24,38695,312],{"className":38696},[351],[24,38698,19254],{"className":38699},[74,78],[24,38701,331],{"className":38702},[438],[24,38704],{"className":38705,"style":1007},[700],[24,38707,918],{"className":38708},[1011],[24,38710],{"className":38711,"style":1007},[700],[24,38713,38715,38718,38721,38724,38727,38730,38733,38736,38776,38779,38782],{"className":38714},[65],[24,38716],{"className":38717,"style":344},[69],[24,38719,38632],{"className":38720},[1657],[24,38722,312],{"className":38723},[351],[24,38725,598],{"className":38726},[74],[24,38728,601],{"className":38729},[696],[24,38731],{"className":38732,"style":701},[700],[24,38734,19254],{"className":38735},[74,78],[24,38737,38739,38742],{"className":38738},[74],[24,38740,34311],{"className":38741,"style":874},[74,78],[24,38743,38745],{"className":38744},[82],[24,38746,38748,38768],{"className":38747},[86,87],[24,38749,38751,38765],{"className":38750},[91],[24,38752,38754],{"className":38753,"style":670},[95],[24,38755,38756,38759],{"style":1743},[24,38757],{"className":38758,"style":104},[103],[24,38760,38762],{"className":38761},[108,109,110,111],[24,38763,616],{"className":38764},[74,111],[24,38766,119],{"className":38767},[118],[24,38769,38771],{"className":38770},[91],[24,38772,38774],{"className":38773,"style":126},[95],[24,38775],{},[24,38777],{"className":38778,"style":3225},[700],[24,38780,913],{"className":38781},[988],[24,38783],{"className":38784,"style":3225},[700],[24,38786,38788,38791,38831,38834,38874,38877,38880],{"className":38787},[65],[24,38789],{"className":38790,"style":344},[69],[24,38792,38794,38797],{"className":38793},[74],[24,38795,15499],{"className":38796},[74,78],[24,38798,38800],{"className":38799},[82],[24,38801,38803,38823],{"className":38802},[86,87],[24,38804,38806,38820],{"className":38805},[91],[24,38807,38809],{"className":38808,"style":670},[95],[24,38810,38811,38814],{"style":99},[24,38812],{"className":38813,"style":104},[103],[24,38815,38817],{"className":38816},[108,109,110,111],[24,38818,616],{"className":38819},[74,111],[24,38821,119],{"className":38822},[118],[24,38824,38826],{"className":38825},[91],[24,38827,38829],{"className":38828,"style":126},[95],[24,38830],{},[24,38832,331],{"className":38833},[438],[24,38835,38837,38840],{"className":38836},[74],[24,38838,34311],{"className":38839,"style":874},[74,78],[24,38841,38843],{"className":38842},[82],[24,38844,38846,38866],{"className":38845},[86,87],[24,38847,38849,38863],{"className":38848},[91],[24,38850,38852],{"className":38851,"style":670},[95],[24,38853,38854,38857],{"style":1743},[24,38855],{"className":38856,"style":104},[103],[24,38858,38860],{"className":38859},[108,109,110,111],[24,38861,9241],{"className":38862},[74,111],[24,38864,119],{"className":38865},[118],[24,38867,38869],{"className":38868},[91],[24,38870,38872],{"className":38871,"style":126},[95],[24,38873],{},[24,38875],{"className":38876,"style":3225},[700],[24,38878,913],{"className":38879},[988],[24,38881],{"className":38882,"style":3225},[700],[24,38884,38886,38889],{"className":38885},[65],[24,38887],{"className":38888,"style":12947},[69],[24,38890,38892,38895],{"className":38891},[74],[24,38893,15499],{"className":38894},[74,78],[24,38896,38898],{"className":38897},[82],[24,38899,38901,38921],{"className":38900},[86,87],[24,38902,38904,38918],{"className":38903},[91],[24,38905,38907],{"className":38906,"style":670},[95],[24,38908,38909,38912],{"style":99},[24,38910],{"className":38911,"style":104},[103],[24,38913,38915],{"className":38914},[108,109,110,111],[24,38916,9241],{"className":38917},[74,111],[24,38919,119],{"className":38920},[118],[24,38922,38924],{"className":38923},[91],[24,38925,38927],{"className":38926,"style":126},[95],[24,38928],{},[33716,38930,38932],{"className":33718,"code":38931,"language":33720,"meta":31407,"style":31407},"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":31407},[24,38935,38936,38938,38941,38943,38945,38947,38949],{"class":33726,"line":33727},[24,38937,33953],{"class":33730},[24,38939,38940],{"class":33956}," PositionWiseFFN",[24,38942,312],{"class":33738},[24,38944,33963],{"class":33962},[24,38946,32214],{"class":33738},[24,38948,33968],{"class":33962},[24,38950,33751],{"class":33738},[24,38952,38953],{"class":33726,"line":31408},[24,38954,38955],{"class":33756},"    \"\"\"基于位置的前馈网络\"\"\"\n",[24,38957,38958,38960,38962,38964,38966,38968,38971,38973,38976,38978,38981],{"class":33726,"line":31416},[24,38959,33980],{"class":33730},[24,38961,33983],{"class":33778},[24,38963,312],{"class":33738},[24,38965,33989],{"class":33988},[24,38967,33745],{"class":33738},[24,38969,38970],{"class":33741},"ffn_num_input",[24,38972,33745],{"class":33738},[24,38974,38975],{"class":33741},"ffn_num_hiddens",[24,38977,33745],{"class":33738},[24,38979,38980],{"class":33741},"ffn_num_outputs",[24,38982,35139],{"class":33738},[24,38984,38985,38988,38990],{"class":33726,"line":33766},[24,38986,38987],{"class":33730},"                 **",[24,38989,34002],{"class":33741},[24,38991,33751],{"class":33738},[24,38993,38994,38996,38999,39001,39003,39005,39007,39009],{"class":33726,"line":33785},[24,38995,34010],{"class":34009},[24,38997,38998],{"class":33738},"(PositionWiseFFN, ",[24,39000,33989],{"class":34016},[24,39002,34019],{"class":33738},[24,39004,34022],{"class":33778},[24,39006,312],{"class":33738},[24,39008,33999],{"class":33730},[24,39010,34029],{"class":33738},[24,39012,39013,39015,39018,39020],{"class":33726,"line":33806},[24,39014,34034],{"class":34016},[24,39016,39017],{"class":33738},".dense1 ",[24,39019,918],{"class":33730},[24,39021,39022],{"class":33738}," nn.Linear(ffn_num_input, ffn_num_hiddens)\n",[24,39024,39025,39027,39030,39032],{"class":33726,"line":33814},[24,39026,34034],{"class":34016},[24,39028,39029],{"class":33738},".relu ",[24,39031,918],{"class":33730},[24,39033,39034],{"class":33738}," nn.ReLU()\n",[24,39036,39037,39039,39042,39044],{"class":33726,"line":33825},[24,39038,34034],{"class":34016},[24,39040,39041],{"class":33738},".dense2 ",[24,39043,918],{"class":33730},[24,39045,39046],{"class":33738}," nn.Linear(ffn_num_hiddens, ffn_num_outputs)\n",[24,39048,39049],{"class":33726,"line":33842},[24,39050,34047],{"emptyLinePlaceholder":31432},[24,39052,39053,39055,39057,39059,39061,39063,39065],{"class":33726,"line":33858},[24,39054,33980],{"class":33730},[24,39056,34074],{"class":33734},[24,39058,312],{"class":33738},[24,39060,33989],{"class":33988},[24,39062,33745],{"class":33738},[24,39064,33742],{"class":33741},[24,39066,33751],{"class":33738},[24,39068,39069,39071,39073,39076,39078,39081,39083],{"class":33726,"line":33866},[24,39070,33788],{"class":33730},[24,39072,36530],{"class":34016},[24,39074,39075],{"class":33738},".dense2(",[24,39077,33989],{"class":34016},[24,39079,39080],{"class":33738},".relu(",[24,39082,33989],{"class":34016},[24,39084,39085],{"class":33738},".dense1(X)))\n",[10,39087,39088],{"id":39088},"残差连接和层规范化",[14,39090,39091],{},"我们在每个子层之间加入了一个残差连接和层归一化。",[14,39093,39094,39095,35879,39216,39279],{},"因此，每个子层的输出都是 ",[24,39096,39098,39163],{"className":39097},[27],[24,39099,39101],{"className":39100},[31],[33,39102,39103],{"xmlns":35},[37,39104,39105,39160],{},[40,39106,39107,39128,39130,39132,39134,39152,39154,39156,39158],{},[40,39108,39109,39111,39113,39116,39118,39120,39122,39124,39126],{},[46,39110,5797],{"mathvariant":321},[46,39112,48],{"mathvariant":321},[46,39114,39115],{"mathvariant":321},"y",[46,39117,32141],{"mathvariant":321},[46,39119,456],{"mathvariant":321},[46,39121,2110],{"mathvariant":321},[46,39123,5800],{"mathvariant":321},[46,39125,456],{"mathvariant":321},[46,39127,31744],{"mathvariant":321},[309,39129,312],{"stretchy":311},[46,39131,19254],{},[309,39133,913],{},[40,39135,39136,39138,39140,39142,39144,39146,39148,39150],{},[46,39137,1400],{"mathvariant":321},[46,39139,34221],{"mathvariant":321},[46,39141,15499],{"mathvariant":321},[46,39143,29610],{"mathvariant":321},[46,39145,48],{"mathvariant":321},[46,39147,39115],{"mathvariant":321},[46,39149,32141],{"mathvariant":321},[46,39151,456],{"mathvariant":321},[309,39153,312],{"stretchy":311},[46,39155,19254],{},[309,39157,331],{"stretchy":311},[309,39159,331],{"stretchy":311},[53,39161,39162],{"encoding":55},"\\mathrm{LayerNorm}(x + \\mathrm{Sublayer}(x))",[24,39164,39166,39194],{"className":39165,"ariaHidden":61},[60],[24,39167,39169,39172,39179,39182,39185,39188,39191],{"className":39168},[65],[24,39170],{"className":39171,"style":344},[69],[24,39173,39175],{"className":39174},[74],[24,39176,39178],{"className":39177},[74,28662],"LayerNorm",[24,39180,312],{"className":39181},[351],[24,39183,19254],{"className":39184},[74,78],[24,39186],{"className":39187,"style":3225},[700],[24,39189,913],{"className":39190},[988],[24,39192],{"className":39193,"style":3225},[700],[24,39195,39197,39200,39207,39210,39213],{"className":39196},[65],[24,39198],{"className":39199,"style":344},[69],[24,39201,39203],{"className":39202},[74],[24,39204,39206],{"className":39205},[74,28662],"Sublayer",[24,39208,312],{"className":39209},[351],[24,39211,19254],{"className":39212},[74,78],[24,39214,7485],{"className":39215},[438],[24,39217,39219,39255],{"className":39218},[27],[24,39220,39222],{"className":39221},[31],[33,39223,39224],{"xmlns":35},[37,39225,39226,39252],{},[40,39227,39228,39246,39248,39250],{},[40,39229,39230,39232,39234,39236,39238,39240,39242,39244],{},[46,39231,1400],{"mathvariant":321},[46,39233,34221],{"mathvariant":321},[46,39235,15499],{"mathvariant":321},[46,39237,29610],{"mathvariant":321},[46,39239,48],{"mathvariant":321},[46,39241,39115],{"mathvariant":321},[46,39243,32141],{"mathvariant":321},[46,39245,456],{"mathvariant":321},[309,39247,312],{"stretchy":311},[46,39249,19254],{},[309,39251,331],{"stretchy":311},[53,39253,39254],{"encoding":55},"\\mathrm{Sublayer}(x)",[24,39256,39258],{"className":39257,"ariaHidden":61},[60],[24,39259,39261,39264,39270,39273,39276],{"className":39260},[65],[24,39262],{"className":39263,"style":344},[69],[24,39265,39267],{"className":39266},[74],[24,39268,39206],{"className":39269},[74,28662],[24,39271,312],{"className":39272},[351],[24,39274,19254],{"className":39275},[74,78],[24,39277,331],{"className":39278},[438]," 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":31407,"style":31407},"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":31407},[24,39286,39287,39289,39292,39294,39296,39298,39300],{"class":33726,"line":33727},[24,39288,33953],{"class":33730},[24,39290,39291],{"class":33956}," AddNorm",[24,39293,312],{"class":33738},[24,39295,33963],{"class":33962},[24,39297,32214],{"class":33738},[24,39299,33968],{"class":33962},[24,39301,33751],{"class":33738},[24,39303,39304],{"class":33726,"line":31408},[24,39305,39306],{"class":33756},"    \"\"\"残差连接后进行层规范化\"\"\"\n",[24,39308,39309,39311,39313,39315,39317,39319,39322,39324,39326,39328,39330,39332],{"class":33726,"line":31416},[24,39310,33980],{"class":33730},[24,39312,33983],{"class":33778},[24,39314,312],{"class":33738},[24,39316,33989],{"class":33988},[24,39318,33745],{"class":33738},[24,39320,39321],{"class":33741},"normalized_shape",[24,39323,33745],{"class":33738},[24,39325,33994],{"class":33741},[24,39327,33745],{"class":33738},[24,39329,33999],{"class":33730},[24,39331,34002],{"class":33741},[24,39333,33751],{"class":33738},[24,39335,39336,39338,39341,39343,39345,39347,39349,39351],{"class":33726,"line":33766},[24,39337,34010],{"class":34009},[24,39339,39340],{"class":33738},"(AddNorm, ",[24,39342,33989],{"class":34016},[24,39344,34019],{"class":33738},[24,39346,34022],{"class":33778},[24,39348,312],{"class":33738},[24,39350,33999],{"class":33730},[24,39352,34029],{"class":33738},[24,39354,39355,39357,39359,39361],{"class":33726,"line":33785},[24,39356,34034],{"class":34016},[24,39358,34037],{"class":33738},[24,39360,918],{"class":33730},[24,39362,34042],{"class":33738},[24,39364,39365,39367,39370,39372],{"class":33726,"line":33806},[24,39366,34034],{"class":34016},[24,39368,39369],{"class":33738},".ln ",[24,39371,918],{"class":33730},[24,39373,39374],{"class":33738}," nn.LayerNorm(normalized_shape)\n",[24,39376,39377],{"class":33726,"line":33814},[24,39378,34047],{"emptyLinePlaceholder":31432},[24,39380,39381,39383,39385,39387,39389,39391,39393,39395,39398],{"class":33726,"line":33825},[24,39382,33980],{"class":33730},[24,39384,34074],{"class":33734},[24,39386,312],{"class":33738},[24,39388,33989],{"class":33988},[24,39390,33745],{"class":33738},[24,39392,33742],{"class":33741},[24,39394,33745],{"class":33738},[24,39396,39397],{"class":33741},"Y",[24,39399,33751],{"class":33738},[24,39401,39402,39404,39406,39409,39411,39414,39416],{"class":33726,"line":33842},[24,39403,33788],{"class":33730},[24,39405,36530],{"class":34016},[24,39407,39408],{"class":33738},".ln(",[24,39410,33989],{"class":34016},[24,39412,39413],{"class":33738},".dropout(Y) ",[24,39415,913],{"class":33730},[24,39417,39418],{"class":33738}," X)\n",[10,39420,39421],{"id":39421},"编码器-解码器架构",[14,39423,39424,39425,39575,39576,39752,39753,39782,39783,39933],{},"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 ",[24,39426,39428,39462],{"className":39427},[27],[24,39429,39431],{"className":39430},[31],[33,39432,39433],{"xmlns":35},[37,39434,39435,39459],{},[40,39436,39437,39439,39445,39447,39449,39451,39457],{},[309,39438,312],{"stretchy":311},[43,39440,39441,39443],{},[46,39442,19254],{},[596,39444,616],{},[309,39446,601],{"separator":61},[309,39448,627],{},[309,39450,601],{"separator":61},[43,39452,39453,39455],{},[46,39454,19254],{},[46,39456,2120],{},[309,39458,331],{"stretchy":311},[53,39460,39461],{"encoding":55},"(x_1, \\ldots, x_n)",[24,39463,39465],{"className":39464,"ariaHidden":61},[60],[24,39466,39468,39471,39474,39514,39517,39520,39523,39526,39529,39532,39572],{"className":39467},[65],[24,39469],{"className":39470,"style":344},[69],[24,39472,312],{"className":39473},[351],[24,39475,39477,39480],{"className":39476},[74],[24,39478,19254],{"className":39479},[74,78],[24,39481,39483],{"className":39482},[82],[24,39484,39486,39506],{"className":39485},[86,87],[24,39487,39489,39503],{"className":39488},[91],[24,39490,39492],{"className":39491,"style":670},[95],[24,39493,39494,39497],{"style":99},[24,39495],{"className":39496,"style":104},[103],[24,39498,39500],{"className":39499},[108,109,110,111],[24,39501,616],{"className":39502},[74,111],[24,39504,119],{"className":39505},[118],[24,39507,39509],{"className":39508},[91],[24,39510,39512],{"className":39511,"style":126},[95],[24,39513],{},[24,39515,601],{"className":39516},[696],[24,39518],{"className":39519,"style":701},[700],[24,39521,627],{"className":39522},[840],[24,39524],{"className":39525,"style":701},[700],[24,39527,601],{"className":39528},[696],[24,39530],{"className":39531,"style":701},[700],[24,39533,39535,39538],{"className":39534},[74],[24,39536,19254],{"className":39537},[74,78],[24,39539,39541],{"className":39540},[82],[24,39542,39544,39564],{"className":39543},[86,87],[24,39545,39547,39561],{"className":39546},[91],[24,39548,39550],{"className":39549,"style":20777},[95],[24,39551,39552,39555],{"style":99},[24,39553],{"className":39554,"style":104},[103],[24,39556,39558],{"className":39557},[108,109,110,111],[24,39559,2120],{"className":39560},[74,78,111],[24,39562,119],{"className":39563},[118],[24,39565,39567],{"className":39566},[91],[24,39568,39570],{"className":39569,"style":126},[95],[24,39571],{},[24,39573,331],{"className":39574},[438]," 映射为连续表示序列 ",[24,39577,39579,39618],{"className":39578},[27],[24,39580,39582],{"className":39581},[31],[33,39583,39584],{"xmlns":35},[37,39585,39586,39615],{},[40,39587,39588,39591,39593,39595,39601,39603,39605,39607,39613],{},[46,39589,39590],{"mathvariant":36688},"z",[309,39592,918],{},[309,39594,312],{"stretchy":311},[43,39596,39597,39599],{},[46,39598,39590],{},[596,39600,616],{},[309,39602,601],{"separator":61},[309,39604,627],{},[309,39606,601],{"separator":61},[43,39608,39609,39611],{},[46,39610,39590],{},[46,39612,2120],{},[309,39614,331],{"stretchy":311},[53,39616,39617],{"encoding":55},"\\mathbf{z} = (z_1, \\ldots, z_n)",[24,39619,39621,39640],{"className":39620,"ariaHidden":61},[60],[24,39622,39624,39628,39631,39634,39637],{"className":39623},[65],[24,39625],{"className":39626,"style":39627},[69],"height:0.4444em;",[24,39629,39590],{"className":39630},[74,36733],[24,39632],{"className":39633,"style":1007},[700],[24,39635,918],{"className":39636},[1011],[24,39638],{"className":39639,"style":1007},[700],[24,39641,39643,39646,39649,39691,39694,39697,39700,39703,39706,39709,39749],{"className":39642},[65],[24,39644],{"className":39645,"style":344},[69],[24,39647,312],{"className":39648},[351],[24,39650,39652,39656],{"className":39651},[74],[24,39653,39590],{"className":39654,"style":39655},[74,78],"margin-right:0.04398em;",[24,39657,39659],{"className":39658},[82],[24,39660,39662,39683],{"className":39661},[86,87],[24,39663,39665,39680],{"className":39664},[91],[24,39666,39668],{"className":39667,"style":670},[95],[24,39669,39671,39674],{"style":39670},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[24,39672],{"className":39673,"style":104},[103],[24,39675,39677],{"className":39676},[108,109,110,111],[24,39678,616],{"className":39679},[74,111],[24,39681,119],{"className":39682},[118],[24,39684,39686],{"className":39685},[91],[24,39687,39689],{"className":39688,"style":126},[95],[24,39690],{},[24,39692,601],{"className":39693},[696],[24,39695],{"className":39696,"style":701},[700],[24,39698,627],{"className":39699},[840],[24,39701],{"className":39702,"style":701},[700],[24,39704,601],{"className":39705},[696],[24,39707],{"className":39708,"style":701},[700],[24,39710,39712,39715],{"className":39711},[74],[24,39713,39590],{"className":39714,"style":39655},[74,78],[24,39716,39718],{"className":39717},[82],[24,39719,39721,39741],{"className":39720},[86,87],[24,39722,39724,39738],{"className":39723},[91],[24,39725,39727],{"className":39726,"style":20777},[95],[24,39728,39729,39732],{"style":39670},[24,39730],{"className":39731,"style":104},[103],[24,39733,39735],{"className":39734},[108,109,110,111],[24,39736,2120],{"className":39737},[74,78,111],[24,39739,119],{"className":39740},[118],[24,39742,39744],{"className":39743},[91],[24,39745,39747],{"className":39746,"style":126},[95],[24,39748],{},[24,39750,331],{"className":39751},[438],"。给定 ",[24,39754,39756,39770],{"className":39755},[27],[24,39757,39759],{"className":39758},[31],[33,39760,39761],{"xmlns":35},[37,39762,39763,39767],{},[40,39764,39765],{},[46,39766,39590],{"mathvariant":36688},[53,39768,39769],{"encoding":55},"\\mathbf{z}",[24,39771,39773],{"className":39772,"ariaHidden":61},[60],[24,39774,39776,39779],{"className":39775},[65],[24,39777],{"className":39778,"style":39627},[69],[24,39780,39590],{"className":39781},[74,36733],"，解码器随后一次生成一个元素的输出符号序列 ",[24,39784,39786,39820],{"className":39785},[27],[24,39787,39789],{"className":39788},[31],[33,39790,39791],{"xmlns":35},[37,39792,39793,39817],{},[40,39794,39795,39797,39803,39805,39807,39809,39815],{},[309,39796,312],{"stretchy":311},[43,39798,39799,39801],{},[46,39800,39115],{},[596,39802,616],{},[309,39804,601],{"separator":61},[309,39806,627],{},[309,39808,601],{"separator":61},[43,39810,39811,39813],{},[46,39812,39115],{},[46,39814,31744],{},[309,39816,331],{"stretchy":311},[53,39818,39819],{"encoding":55},"(y_1, \\ldots, y_m)",[24,39821,39823],{"className":39822,"ariaHidden":61},[60],[24,39824,39826,39829,39832,39872,39875,39878,39881,39884,39887,39890,39930],{"className":39825},[65],[24,39827],{"className":39828,"style":344},[69],[24,39830,312],{"className":39831},[351],[24,39833,39835,39838],{"className":39834},[74],[24,39836,39115],{"className":39837,"style":292},[74,78],[24,39839,39841],{"className":39840},[82],[24,39842,39844,39864],{"className":39843},[86,87],[24,39845,39847,39861],{"className":39846},[91],[24,39848,39850],{"className":39849,"style":670},[95],[24,39851,39852,39855],{"style":33361},[24,39853],{"className":39854,"style":104},[103],[24,39856,39858],{"className":39857},[108,109,110,111],[24,39859,616],{"className":39860},[74,111],[24,39862,119],{"className":39863},[118],[24,39865,39867],{"className":39866},[91],[24,39868,39870],{"className":39869,"style":126},[95],[24,39871],{},[24,39873,601],{"className":39874},[696],[24,39876],{"className":39877,"style":701},[700],[24,39879,627],{"className":39880},[840],[24,39882],{"className":39883,"style":701},[700],[24,39885,601],{"className":39886},[696],[24,39888],{"className":39889,"style":701},[700],[24,39891,39893,39896],{"className":39892},[74],[24,39894,39115],{"className":39895,"style":292},[74,78],[24,39897,39899],{"className":39898},[82],[24,39900,39902,39922],{"className":39901},[86,87],[24,39903,39905,39919],{"className":39904},[91],[24,39906,39908],{"className":39907,"style":20777},[95],[24,39909,39910,39913],{"style":33361},[24,39911],{"className":39912,"style":104},[103],[24,39914,39916],{"className":39915},[108,109,110,111],[24,39917,31744],{"className":39918},[74,78,111],[24,39920,119],{"className":39921},[118],[24,39923,39925],{"className":39924},[91],[24,39926,39928],{"className":39927,"style":126},[95],[24,39929],{},[24,39931,331],{"className":39932},[438],"。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":31407,"style":31407},"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":31407},[24,39940,39941,39943,39946,39948,39950,39952,39954],{"class":33726,"line":33727},[24,39942,33953],{"class":33730},[24,39944,39945],{"class":33956}," Encoder",[24,39947,312],{"class":33738},[24,39949,33963],{"class":33962},[24,39951,32214],{"class":33738},[24,39953,33968],{"class":33962},[24,39955,33751],{"class":33738},[24,39957,39958],{"class":33726,"line":31408},[24,39959,39960],{"class":33756},"    \"\"\"编码器-解码器架构的基本编码器接口\"\"\"\n",[24,39962,39963,39965,39967,39969,39971,39973,39975,39977],{"class":33726,"line":31416},[24,39964,33980],{"class":33730},[24,39966,33983],{"class":33778},[24,39968,312],{"class":33738},[24,39970,33989],{"class":33988},[24,39972,33745],{"class":33738},[24,39974,33999],{"class":33730},[24,39976,34002],{"class":33741},[24,39978,33751],{"class":33738},[24,39980,39981,39983,39986,39988,39990,39992,39994,39996],{"class":33726,"line":33766},[24,39982,34010],{"class":34009},[24,39984,39985],{"class":33738},"(Encoder, ",[24,39987,33989],{"class":34016},[24,39989,34019],{"class":33738},[24,39991,34022],{"class":33778},[24,39993,312],{"class":33738},[24,39995,33999],{"class":33730},[24,39997,34029],{"class":33738},[24,39999,40000],{"class":33726,"line":33785},[24,40001,34047],{"emptyLinePlaceholder":31432},[24,40003,40004,40006,40008,40010,40012,40014,40016,40018,40021,40024],{"class":33726,"line":33806},[24,40005,33980],{"class":33730},[24,40007,34074],{"class":33734},[24,40009,312],{"class":33738},[24,40011,33989],{"class":33988},[24,40013,33745],{"class":33738},[24,40015,33742],{"class":33741},[24,40017,33745],{"class":33738},[24,40019,40020],{"class":33730},"*",[24,40022,40023],{"class":33741},"args",[24,40025,33751],{"class":33738},[24,40027,40028,40031],{"class":33726,"line":33814},[24,40029,40030],{"class":33730},"        raise",[24,40032,40033],{"class":34009}," NotImplementedError\n",[24,40035,40036],{"class":33726,"line":33825},[24,40037,34047],{"emptyLinePlaceholder":31432},[24,40039,40040,40042,40045,40047,40049,40051,40053],{"class":33726,"line":33842},[24,40041,33953],{"class":33730},[24,40043,40044],{"class":33956}," Decoder",[24,40046,312],{"class":33738},[24,40048,33963],{"class":33962},[24,40050,32214],{"class":33738},[24,40052,33968],{"class":33962},[24,40054,33751],{"class":33738},[24,40056,40057],{"class":33726,"line":33858},[24,40058,40059],{"class":33756},"    \"\"\"编码器-解码器架构的基本解码器接口\"\"\"\n",[24,40061,40062,40064,40066,40068,40070,40072,40074,40076],{"class":33726,"line":33866},[24,40063,33980],{"class":33730},[24,40065,33983],{"class":33778},[24,40067,312],{"class":33738},[24,40069,33989],{"class":33988},[24,40071,33745],{"class":33738},[24,40073,33999],{"class":33730},[24,40075,34002],{"class":33741},[24,40077,33751],{"class":33738},[24,40079,40080,40082,40085,40087,40089,40091,40093,40095],{"class":33726,"line":33883},[24,40081,34010],{"class":34009},[24,40083,40084],{"class":33738},"(Decoder, ",[24,40086,33989],{"class":34016},[24,40088,34019],{"class":33738},[24,40090,34022],{"class":33778},[24,40092,312],{"class":33738},[24,40094,33999],{"class":33730},[24,40096,34029],{"class":33738},[24,40098,40099],{"class":33726,"line":33889},[24,40100,34047],{"emptyLinePlaceholder":31432},[24,40102,40103,40105,40108,40110,40112,40114,40117,40119,40121,40123],{"class":33726,"line":33914},[24,40104,33980],{"class":33730},[24,40106,40107],{"class":33734}," init_state",[24,40109,312],{"class":33738},[24,40111,33989],{"class":33988},[24,40113,33745],{"class":33738},[24,40115,40116],{"class":33741},"enc_outputs",[24,40118,33745],{"class":33738},[24,40120,40020],{"class":33730},[24,40122,40023],{"class":33741},[24,40124,33751],{"class":33738},[24,40126,40127,40129],{"class":33726,"line":33927},[24,40128,40030],{"class":33730},[24,40130,40033],{"class":34009},[24,40132,40133],{"class":33726,"line":34166},[24,40134,34047],{"emptyLinePlaceholder":31432},[24,40136,40137,40139,40141,40143,40145,40147,40149,40151,40154],{"class":33726,"line":36091},[24,40138,33980],{"class":33730},[24,40140,34074],{"class":33734},[24,40142,312],{"class":33738},[24,40144,33989],{"class":33988},[24,40146,33745],{"class":33738},[24,40148,33742],{"class":33741},[24,40150,33745],{"class":33738},[24,40152,40153],{"class":33741},"state",[24,40155,33751],{"class":33738},[24,40157,40158,40160],{"class":33726,"line":36367},[24,40159,40030],{"class":33730},[24,40161,40033],{"class":34009},[24,40163,40164],{"class":33726,"line":36373},[24,40165,34047],{"emptyLinePlaceholder":31432},[24,40167,40168,40170,40173,40175,40177,40179,40181],{"class":33726,"line":36379},[24,40169,33953],{"class":33730},[24,40171,40172],{"class":33956}," EncoderDecoder",[24,40174,312],{"class":33738},[24,40176,33963],{"class":33962},[24,40178,32214],{"class":33738},[24,40180,33968],{"class":33962},[24,40182,33751],{"class":33738},[24,40184,40185],{"class":33726,"line":36385},[24,40186,40187],{"class":33756},"    \"\"\"编码器-解码器架构的基类\"\"\"\n",[24,40189,40190,40192,40194,40196,40198,40200,40203,40205,40208,40210,40212,40214],{"class":33726,"line":36406},[24,40191,33980],{"class":33730},[24,40193,33983],{"class":33778},[24,40195,312],{"class":33738},[24,40197,33989],{"class":33988},[24,40199,33745],{"class":33738},[24,40201,40202],{"class":33741},"encoder",[24,40204,33745],{"class":33738},[24,40206,40207],{"class":33741},"decoder",[24,40209,33745],{"class":33738},[24,40211,33999],{"class":33730},[24,40213,34002],{"class":33741},[24,40215,33751],{"class":33738},[24,40217,40218,40220,40223,40225,40227,40229,40231,40233],{"class":33726,"line":36425},[24,40219,34010],{"class":34009},[24,40221,40222],{"class":33738},"(EncoderDecoder, ",[24,40224,33989],{"class":34016},[24,40226,34019],{"class":33738},[24,40228,34022],{"class":33778},[24,40230,312],{"class":33738},[24,40232,33999],{"class":33730},[24,40234,34029],{"class":33738},[24,40236,40237,40239,40242,40244],{"class":33726,"line":36444},[24,40238,34034],{"class":34016},[24,40240,40241],{"class":33738},".encoder ",[24,40243,918],{"class":33730},[24,40245,40246],{"class":33738}," encoder\n",[24,40248,40249,40251,40254,40256],{"class":33726,"line":36449},[24,40250,34034],{"class":34016},[24,40252,40253],{"class":33738},".decoder ",[24,40255,918],{"class":33730},[24,40257,40258],{"class":33738}," decoder\n",[24,40260,40261],{"class":33726,"line":36465},[24,40262,34047],{"emptyLinePlaceholder":31432},[24,40264,40265,40267,40269,40271,40273,40275,40278,40280,40283,40285,40287,40289],{"class":33726,"line":36471},[24,40266,33980],{"class":33730},[24,40268,34074],{"class":33734},[24,40270,312],{"class":33738},[24,40272,33989],{"class":33988},[24,40274,33745],{"class":33738},[24,40276,40277],{"class":33741},"enc_X",[24,40279,33745],{"class":33738},[24,40281,40282],{"class":33741},"dec_X",[24,40284,33745],{"class":33738},[24,40286,40020],{"class":33730},[24,40288,40023],{"class":33741},[24,40290,33751],{"class":33738},[24,40292,40293,40296,40298,40300,40303,40305],{"class":33726,"line":36477},[24,40294,40295],{"class":33738},"        enc_outputs ",[24,40297,918],{"class":33730},[24,40299,36530],{"class":34016},[24,40301,40302],{"class":33738},".encoder(enc_X, ",[24,40304,40020],{"class":33730},[24,40306,40307],{"class":33738},"args)\n",[24,40309,40310,40313,40315,40317,40320,40322],{"class":33726,"line":36487},[24,40311,40312],{"class":33738},"        dec_state ",[24,40314,918],{"class":33730},[24,40316,36530],{"class":34016},[24,40318,40319],{"class":33738},".decoder.init_state(enc_outputs, ",[24,40321,40020],{"class":33730},[24,40323,40307],{"class":33738},[24,40325,40326,40328,40330],{"class":33726,"line":36511},[24,40327,33788],{"class":33730},[24,40329,36530],{"class":34016},[24,40331,40332],{"class":33738},".decoder(dec_X, dec_state)\n",[10,40334,40336],{"id":40335},"transformer-编码器","transformer 编码器",[14,40338,40339],{},"代码实现如下：",[33716,40341,40343],{"className":33718,"code":40342,"language":33720,"meta":31407,"style":31407},"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":31407},[24,40346,40347,40349,40352,40354,40356,40358,40360],{"class":33726,"line":33727},[24,40348,33953],{"class":33730},[24,40350,40351],{"class":33956}," EncoderBlock",[24,40353,312],{"class":33738},[24,40355,33963],{"class":33962},[24,40357,32214],{"class":33738},[24,40359,33968],{"class":33962},[24,40361,33751],{"class":33738},[24,40363,40364],{"class":33726,"line":31408},[24,40365,40366],{"class":33756},"    \"\"\"Transformer编码器块\"\"\"\n",[24,40368,40369,40371,40373,40375,40377,40379,40381,40383,40385,40387,40389,40391,40393],{"class":33726,"line":31416},[24,40370,33980],{"class":33730},[24,40372,33983],{"class":33778},[24,40374,312],{"class":33738},[24,40376,33989],{"class":33988},[24,40378,33745],{"class":33738},[24,40380,36157],{"class":33741},[24,40382,33745],{"class":33738},[24,40384,36162],{"class":33741},[24,40386,33745],{"class":33738},[24,40388,36167],{"class":33741},[24,40390,33745],{"class":33738},[24,40392,36172],{"class":33741},[24,40394,35139],{"class":33738},[24,40396,40397,40400,40402,40404,40406,40408,40410,40412],{"class":33726,"line":33766},[24,40398,40399],{"class":33741},"                 norm_shape",[24,40401,33745],{"class":33738},[24,40403,38970],{"class":33741},[24,40405,33745],{"class":33738},[24,40407,38975],{"class":33741},[24,40409,33745],{"class":33738},[24,40411,35906],{"class":33741},[24,40413,35139],{"class":33738},[24,40415,40416,40419,40421,40424,40426,40428,40430,40432,40434],{"class":33726,"line":33785},[24,40417,40418],{"class":33741},"                 dropout",[24,40420,33745],{"class":33738},[24,40422,40423],{"class":33741},"use_bias",[24,40425,918],{"class":33730},[24,40427,36193],{"class":33778},[24,40429,33745],{"class":33738},[24,40431,33999],{"class":33730},[24,40433,34002],{"class":33741},[24,40435,33751],{"class":33738},[24,40437,40438,40440,40443,40445,40447,40449,40451,40453],{"class":33726,"line":33806},[24,40439,34010],{"class":34009},[24,40441,40442],{"class":33738},"(EncoderBlock, ",[24,40444,33989],{"class":34016},[24,40446,34019],{"class":33738},[24,40448,34022],{"class":33778},[24,40450,312],{"class":33738},[24,40452,33999],{"class":33730},[24,40454,34029],{"class":33738},[24,40456,40457,40459,40461,40463],{"class":33726,"line":33814},[24,40458,34034],{"class":34016},[24,40460,36239],{"class":33738},[24,40462,918],{"class":33730},[24,40464,40465],{"class":33738}," d2l.MultiHeadAttention(\n",[24,40467,40468],{"class":33726,"line":33825},[24,40469,40470],{"class":33738},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout,\n",[24,40472,40473],{"class":33726,"line":33842},[24,40474,40475],{"class":33738},"            use_bias)\n",[24,40477,40478,40480,40483,40485],{"class":33726,"line":33858},[24,40479,34034],{"class":34016},[24,40481,40482],{"class":33738},".addnorm1 ",[24,40484,918],{"class":33730},[24,40486,40487],{"class":33738}," AddNorm(norm_shape, dropout)\n",[24,40489,40490,40492,40495,40497],{"class":33726,"line":33866},[24,40491,34034],{"class":34016},[24,40493,40494],{"class":33738},".ffn ",[24,40496,918],{"class":33730},[24,40498,40499],{"class":33738}," PositionWiseFFN(\n",[24,40501,40502],{"class":33726,"line":33883},[24,40503,40504],{"class":33738},"            ffn_num_input, ffn_num_hiddens, num_hiddens)\n",[24,40506,40507,40509,40512,40514],{"class":33726,"line":33889},[24,40508,34034],{"class":34016},[24,40510,40511],{"class":33738},".addnorm2 ",[24,40513,918],{"class":33730},[24,40515,40487],{"class":33738},[24,40517,40518],{"class":33726,"line":33914},[24,40519,34047],{"emptyLinePlaceholder":31432},[24,40521,40522,40524,40526,40528,40530,40532,40534,40536,40538],{"class":33726,"line":33927},[24,40523,33980],{"class":33730},[24,40525,34074],{"class":33734},[24,40527,312],{"class":33738},[24,40529,33989],{"class":33988},[24,40531,33745],{"class":33738},[24,40533,33742],{"class":33741},[24,40535,33745],{"class":33738},[24,40537,33748],{"class":33741},[24,40539,33751],{"class":33738},[24,40541,40542,40545,40547,40549,40552,40554],{"class":33726,"line":34166},[24,40543,40544],{"class":33738},"        Y ",[24,40546,918],{"class":33730},[24,40548,36530],{"class":34016},[24,40550,40551],{"class":33738},".addnorm1(X, ",[24,40553,33989],{"class":34016},[24,40555,40556],{"class":33738},".attention(X, X, X, valid_lens))\n",[24,40558,40559,40561,40563,40566,40568],{"class":33726,"line":36091},[24,40560,33788],{"class":33730},[24,40562,36530],{"class":34016},[24,40564,40565],{"class":33738},".addnorm2(Y, ",[24,40567,33989],{"class":34016},[24,40569,40570],{"class":33738},".ffn(Y))\n",[24,40572,40573],{"class":33726,"line":36367},[24,40574,34047],{"emptyLinePlaceholder":31432},[24,40576,40577,40579,40582,40584,40587],{"class":33726,"line":36373},[24,40578,33953],{"class":33730},[24,40580,40581],{"class":33956}," TransformerEncoder",[24,40583,312],{"class":33738},[24,40585,40586],{"class":33962},"Encoder",[24,40588,33751],{"class":33738},[24,40590,40591],{"class":33726,"line":36379},[24,40592,40593],{"class":33756},"    \"\"\"Transformer编码器\"\"\"\n",[24,40595,40596,40598,40600,40602,40604,40606,40609,40611,40613,40615,40617,40619,40621],{"class":33726,"line":36385},[24,40597,33980],{"class":33730},[24,40599,33983],{"class":33778},[24,40601,312],{"class":33738},[24,40603,33989],{"class":33988},[24,40605,33745],{"class":33738},[24,40607,40608],{"class":33741},"vocab_size",[24,40610,33745],{"class":33738},[24,40612,36157],{"class":33741},[24,40614,33745],{"class":33738},[24,40616,36162],{"class":33741},[24,40618,33745],{"class":33738},[24,40620,36167],{"class":33741},[24,40622,35139],{"class":33738},[24,40624,40625,40628,40630,40633,40635,40637,40639,40641],{"class":33726,"line":36406},[24,40626,40627],{"class":33741},"                 num_hiddens",[24,40629,33745],{"class":33738},[24,40631,40632],{"class":33741},"norm_shape",[24,40634,33745],{"class":33738},[24,40636,38970],{"class":33741},[24,40638,33745],{"class":33738},[24,40640,38975],{"class":33741},[24,40642,35139],{"class":33738},[24,40644,40645,40647,40649,40652,40654,40656,40658,40660,40662,40664,40666,40668,40670],{"class":33726,"line":36425},[24,40646,36179],{"class":33741},[24,40648,33745],{"class":33738},[24,40650,40651],{"class":33741},"num_layers",[24,40653,33745],{"class":33738},[24,40655,33994],{"class":33741},[24,40657,33745],{"class":33738},[24,40659,40423],{"class":33741},[24,40661,918],{"class":33730},[24,40663,36193],{"class":33778},[24,40665,33745],{"class":33738},[24,40667,33999],{"class":33730},[24,40669,34002],{"class":33741},[24,40671,33751],{"class":33738},[24,40673,40674,40676,40679,40681,40683,40685,40687,40689],{"class":33726,"line":36444},[24,40675,34010],{"class":34009},[24,40677,40678],{"class":33738},"(TransformerEncoder, ",[24,40680,33989],{"class":34016},[24,40682,34019],{"class":33738},[24,40684,34022],{"class":33778},[24,40686,312],{"class":33738},[24,40688,33999],{"class":33730},[24,40690,34029],{"class":33738},[24,40692,40693,40695,40698,40700],{"class":33726,"line":36449},[24,40694,34034],{"class":34016},[24,40696,40697],{"class":33738},".num_hiddens ",[24,40699,918],{"class":33730},[24,40701,40702],{"class":33738}," num_hiddens\n",[24,40704,40705,40707,40710,40712],{"class":33726,"line":36465},[24,40706,34034],{"class":34016},[24,40708,40709],{"class":33738},".embedding ",[24,40711,918],{"class":33730},[24,40713,40714],{"class":33738}," nn.Embedding(vocab_size, num_hiddens)\n",[24,40716,40717,40719,40722,40724],{"class":33726,"line":36471},[24,40718,34034],{"class":34016},[24,40720,40721],{"class":33738},".pos_encoding ",[24,40723,918],{"class":33730},[24,40725,40726],{"class":33738}," PositionalEncoding(num_hiddens, dropout)\n",[24,40728,40729,40731,40734,40736],{"class":33726,"line":36477},[24,40730,34034],{"class":34016},[24,40732,40733],{"class":33738},".blks ",[24,40735,918],{"class":33730},[24,40737,40738],{"class":33738}," nn.Sequential()\n",[24,40740,40741,40744,40747,40750,40754],{"class":33726,"line":36487},[24,40742,40743],{"class":33730},"        for",[24,40745,40746],{"class":33738}," i ",[24,40748,40749],{"class":33730},"in",[24,40751,40753],{"class":40752},"sDgm9"," range",[24,40755,40756],{"class":33738},"(num_layers):\n",[24,40758,40759,40762,40765,40769,40772,40774,40776,40779],{"class":33726,"line":36511},[24,40760,40761],{"class":34016},"            self",[24,40763,40764],{"class":33738},".blks.add_module(",[24,40766,40768],{"class":40767},"sMWOi","\"",[24,40770,1785],{"class":40771},"sEzAm",[24,40773,40768],{"class":40767},[24,40775,913],{"class":33730},[24,40777,40778],{"class":34009},"str",[24,40780,40781],{"class":33738},"(i),\n",[24,40783,40784],{"class":33726,"line":36516},[24,40785,40786],{"class":33738},"                EncoderBlock(key_size, query_size, value_size, num_hiddens,\n",[24,40788,40789],{"class":33726,"line":36522},[24,40790,40791],{"class":33738},"                             norm_shape, ffn_num_input, ffn_num_hiddens,\n",[24,40793,40794],{"class":33726,"line":36536},[24,40795,40796],{"class":33738},"                             num_heads, dropout, use_bias))\n",[24,40798,40799],{"class":33726,"line":36541},[24,40800,34047],{"emptyLinePlaceholder":31432},[24,40802,40803,40805,40807,40809,40811,40813,40815,40817,40819,40821,40823,40825],{"class":33726,"line":36547},[24,40804,33980],{"class":33730},[24,40806,34074],{"class":33734},[24,40808,312],{"class":33738},[24,40810,33989],{"class":33988},[24,40812,33745],{"class":33738},[24,40814,33742],{"class":33741},[24,40816,33745],{"class":33738},[24,40818,33748],{"class":33741},[24,40820,33745],{"class":33738},[24,40822,40020],{"class":33730},[24,40824,40023],{"class":33741},[24,40826,33751],{"class":33738},[24,40828,40829],{"class":33726,"line":36562},[24,40830,40831],{"class":33762},"        # 因为位置编码值在-1和1之间，\n",[24,40833,40835],{"class":33726,"line":40834},37,[24,40836,40837],{"class":33762},"        # 因此嵌入值乘以嵌入维度的平方根进行缩放，\n",[24,40839,40841],{"class":33726,"line":40840},38,[24,40842,40843],{"class":33762},"        # 然后再与位置编码相加。\n",[24,40845,40847,40849,40851,40853,40856,40858,40861,40863,40866,40868],{"class":33726,"line":40846},39,[24,40848,33892],{"class":33738},[24,40850,918],{"class":33730},[24,40852,36530],{"class":34016},[24,40854,40855],{"class":33738},".pos_encoding(",[24,40857,33989],{"class":34016},[24,40859,40860],{"class":33738},".embedding(X) ",[24,40862,40020],{"class":33730},[24,40864,40865],{"class":33738}," math.sqrt(",[24,40867,33989],{"class":34016},[24,40869,40870],{"class":33738},".num_hiddens))\n",[24,40872,40874,40876,40878,40880,40883,40885,40887,40889,40892,40894,40896],{"class":33726,"line":40873},40,[24,40875,34034],{"class":34016},[24,40877,34158],{"class":33738},[24,40879,918],{"class":33730},[24,40881,40882],{"class":33738}," [",[24,40884,34102],{"class":33778},[24,40886,38500],{"class":33738},[24,40888,40020],{"class":33730},[24,40890,40891],{"class":40752}," len",[24,40893,312],{"class":33738},[24,40895,33989],{"class":34016},[24,40897,40898],{"class":33738},".blks)\n",[24,40900,40902,40904,40907,40909,40912,40914,40916],{"class":33726,"line":40901},41,[24,40903,40743],{"class":33730},[24,40905,40906],{"class":33738}," i, blk ",[24,40908,40749],{"class":33730},[24,40910,40911],{"class":40752}," enumerate",[24,40913,312],{"class":33738},[24,40915,33989],{"class":34016},[24,40917,40918],{"class":33738},".blks):\n",[24,40920,40922,40925,40927],{"class":33726,"line":40921},42,[24,40923,40924],{"class":33738},"            X ",[24,40926,918],{"class":33730},[24,40928,40929],{"class":33738}," blk(X, valid_lens)\n",[24,40931,40933,40935,40938,40940],{"class":33726,"line":40932},43,[24,40934,40761],{"class":34016},[24,40936,40937],{"class":33738},".attention_weights[i] ",[24,40939,918],{"class":33730},[24,40941,40942],{"class":33738}," blk.attention.attention.attention_weights\n",[24,40944,40946,40948],{"class":33726,"line":40945},44,[24,40947,33788],{"class":33730},[24,40949,40950],{"class":33738}," X\n",[10,40952,40954],{"id":40953},"transformer-解码器","transformer 解码器",[14,40956,40957],{},"代码如下：",[33716,40959,40961],{"className":33718,"code":40960,"language":33720,"meta":31407,"style":31407},"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":31407},[24,40964,40965,40967,40970,40972,40974,40976,40978],{"class":33726,"line":33727},[24,40966,33953],{"class":33730},[24,40968,40969],{"class":33956}," DecoderBlock",[24,40971,312],{"class":33738},[24,40973,33963],{"class":33962},[24,40975,32214],{"class":33738},[24,40977,33968],{"class":33962},[24,40979,33751],{"class":33738},[24,40981,40982],{"class":33726,"line":31408},[24,40983,40984],{"class":33756},"    \"\"\"解码器中第i个块\"\"\"\n",[24,40986,40987,40989,40991,40993,40995,40997,40999,41001,41003,41005,41007,41009,41011],{"class":33726,"line":31416},[24,40988,33980],{"class":33730},[24,40990,33983],{"class":33778},[24,40992,312],{"class":33738},[24,40994,33989],{"class":33988},[24,40996,33745],{"class":33738},[24,40998,36157],{"class":33741},[24,41000,33745],{"class":33738},[24,41002,36162],{"class":33741},[24,41004,33745],{"class":33738},[24,41006,36167],{"class":33741},[24,41008,33745],{"class":33738},[24,41010,36172],{"class":33741},[24,41012,35139],{"class":33738},[24,41014,41015,41017,41019,41021,41023,41025,41027,41029],{"class":33726,"line":33766},[24,41016,40399],{"class":33741},[24,41018,33745],{"class":33738},[24,41020,38970],{"class":33741},[24,41022,33745],{"class":33738},[24,41024,38975],{"class":33741},[24,41026,33745],{"class":33738},[24,41028,35906],{"class":33741},[24,41030,35139],{"class":33738},[24,41032,41033,41035,41037,41039,41041,41043,41045],{"class":33726,"line":33785},[24,41034,40418],{"class":33741},[24,41036,33745],{"class":33738},[24,41038,29613],{"class":33741},[24,41040,33745],{"class":33738},[24,41042,33999],{"class":33730},[24,41044,34002],{"class":33741},[24,41046,33751],{"class":33738},[24,41048,41049,41051,41054,41056,41058,41060,41062,41064],{"class":33726,"line":33806},[24,41050,34010],{"class":34009},[24,41052,41053],{"class":33738},"(DecoderBlock, ",[24,41055,33989],{"class":34016},[24,41057,34019],{"class":33738},[24,41059,34022],{"class":33778},[24,41061,312],{"class":33738},[24,41063,33999],{"class":33730},[24,41065,34029],{"class":33738},[24,41067,41068,41070,41073,41075],{"class":33726,"line":33814},[24,41069,34034],{"class":34016},[24,41071,41072],{"class":33738},".i ",[24,41074,918],{"class":33730},[24,41076,41077],{"class":33738}," i\n",[24,41079,41080,41082,41085,41087],{"class":33726,"line":33825},[24,41081,34034],{"class":34016},[24,41083,41084],{"class":33738},".attention1 ",[24,41086,918],{"class":33730},[24,41088,40465],{"class":33738},[24,41090,41091],{"class":33726,"line":33842},[24,41092,41093],{"class":33738},"            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n",[24,41095,41096,41098,41100,41102],{"class":33726,"line":33858},[24,41097,34034],{"class":34016},[24,41099,40482],{"class":33738},[24,41101,918],{"class":33730},[24,41103,40487],{"class":33738},[24,41105,41106,41108,41111,41113],{"class":33726,"line":33866},[24,41107,34034],{"class":34016},[24,41109,41110],{"class":33738},".attention2 ",[24,41112,918],{"class":33730},[24,41114,40465],{"class":33738},[24,41116,41117],{"class":33726,"line":33883},[24,41118,41093],{"class":33738},[24,41120,41121,41123,41125,41127],{"class":33726,"line":33889},[24,41122,34034],{"class":34016},[24,41124,40511],{"class":33738},[24,41126,918],{"class":33730},[24,41128,40487],{"class":33738},[24,41130,41131,41133,41135,41137],{"class":33726,"line":33914},[24,41132,34034],{"class":34016},[24,41134,40494],{"class":33738},[24,41136,918],{"class":33730},[24,41138,41139],{"class":33738}," PositionWiseFFN(ffn_num_input, ffn_num_hiddens,\n",[24,41141,41142],{"class":33726,"line":33927},[24,41143,41144],{"class":33738},"                                   num_hiddens)\n",[24,41146,41147,41149,41152,41154],{"class":33726,"line":34166},[24,41148,34034],{"class":34016},[24,41150,41151],{"class":33738},".addnorm3 ",[24,41153,918],{"class":33730},[24,41155,40487],{"class":33738},[24,41157,41158],{"class":33726,"line":36091},[24,41159,34047],{"emptyLinePlaceholder":31432},[24,41161,41162,41164,41166,41168,41170,41172,41174,41176,41178],{"class":33726,"line":36367},[24,41163,33980],{"class":33730},[24,41165,34074],{"class":33734},[24,41167,312],{"class":33738},[24,41169,33989],{"class":33988},[24,41171,33745],{"class":33738},[24,41173,33742],{"class":33741},[24,41175,33745],{"class":33738},[24,41177,40153],{"class":33741},[24,41179,33751],{"class":33738},[24,41181,41182,41185,41187,41190,41192,41195,41197],{"class":33726,"line":36373},[24,41183,41184],{"class":33738},"        enc_outputs, enc_valid_lens ",[24,41186,918],{"class":33730},[24,41188,41189],{"class":33738}," state[",[24,41191,598],{"class":33778},[24,41193,41194],{"class":33738},"], state[",[24,41196,616],{"class":33778},[24,41198,34121],{"class":33738},[24,41200,41201],{"class":33726,"line":36379},[24,41202,41203],{"class":33762},"        # 训练阶段，输出序列的所有词元都在同一时间处理，\n",[24,41205,41206],{"class":33726,"line":36385},[24,41207,41208],{"class":33762},"        # 因此state[2][self.i]初始化为None。\n",[24,41210,41211],{"class":33726,"line":36406},[24,41212,41213],{"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",[24,41215,41216],{"class":33726,"line":36425},[24,41217,41218],{"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",[24,41220,41221,41223,41225,41227,41230,41232,41235,41237,41239],{"class":33726,"line":36444},[24,41222,33828],{"class":33730},[24,41224,41189],{"class":33738},[24,41226,9241],{"class":33778},[24,41228,41229],{"class":33738},"][",[24,41231,33989],{"class":34016},[24,41233,41234],{"class":33738},".i] ",[24,41236,33775],{"class":33730},[24,41238,33779],{"class":33778},[24,41240,33782],{"class":33738},[24,41242,41243,41246,41248],{"class":33726,"line":36449},[24,41244,41245],{"class":33738},"            key_values ",[24,41247,918],{"class":33730},[24,41249,40950],{"class":33738},[24,41251,41252,41254],{"class":33726,"line":36465},[24,41253,33861],{"class":33730},[24,41255,33782],{"class":33738},[24,41257,41258,41260,41262,41265,41267,41269,41271,41274,41277,41279,41281],{"class":33726,"line":36471},[24,41259,41245],{"class":33738},[24,41261,918],{"class":33730},[24,41263,41264],{"class":33738}," torch.cat((state[",[24,41266,9241],{"class":33778},[24,41268,41229],{"class":33738},[24,41270,33989],{"class":34016},[24,41272,41273],{"class":33738},".i], X), ",[24,41275,41276],{"class":33794},"axis",[24,41278,918],{"class":33730},[24,41280,616],{"class":33778},[24,41282,33803],{"class":33738},[24,41284,41285,41288,41290,41292,41294,41296,41298],{"class":33726,"line":36477},[24,41286,41287],{"class":33738},"        state[",[24,41289,9241],{"class":33778},[24,41291,41229],{"class":33738},[24,41293,33989],{"class":34016},[24,41295,41234],{"class":33738},[24,41297,918],{"class":33730},[24,41299,41300],{"class":33738}," key_values\n",[24,41302,41303,41305,41307],{"class":33726,"line":36487},[24,41304,33828],{"class":33730},[24,41306,36530],{"class":34016},[24,41308,41309],{"class":33738},".training:\n",[24,41311,41312,41315,41317],{"class":33726,"line":36511},[24,41313,41314],{"class":33738},"            batch_size, num_steps, _ ",[24,41316,918],{"class":33730},[24,41318,33822],{"class":33738},[24,41320,41321],{"class":33726,"line":36516},[24,41322,41323],{"class":33762},"            # dec_valid_lens的开头:(batch_size,num_steps),\n",[24,41325,41326],{"class":33726,"line":36522},[24,41327,41328],{"class":33762},"            # 其中每一行是[1,2,...,num_steps]\n",[24,41330,41331,41334,41336],{"class":33726,"line":36536},[24,41332,41333],{"class":33738},"            dec_valid_lens ",[24,41335,918],{"class":33730},[24,41337,41338],{"class":33738}," torch.arange(\n",[24,41340,41341,41344,41347,41349,41351,41353,41356,41358,41361,41363],{"class":33726,"line":36541},[24,41342,41343],{"class":33778},"                1",[24,41345,41346],{"class":33738},", num_steps ",[24,41348,913],{"class":33730},[24,41350,33837],{"class":33778},[24,41352,33745],{"class":33738},[24,41354,41355],{"class":33794},"device",[24,41357,918],{"class":33730},[24,41359,41360],{"class":33738},"X.device).repeat(batch_size, ",[24,41362,616],{"class":33778},[24,41364,33803],{"class":33738},[24,41366,41367,41369],{"class":33726,"line":36547},[24,41368,33861],{"class":33730},[24,41370,33782],{"class":33738},[24,41372,41373,41375,41377],{"class":33726,"line":36562},[24,41374,41333],{"class":33738},[24,41376,918],{"class":33730},[24,41378,41379],{"class":33778}," None\n",[24,41381,41382],{"class":33726,"line":40834},[24,41383,34047],{"emptyLinePlaceholder":31432},[24,41385,41386],{"class":33726,"line":40840},[24,41387,41388],{"class":33762},"        # 自注意力\n",[24,41390,41391,41394,41396,41398],{"class":33726,"line":40846},[24,41392,41393],{"class":33738},"        X2 ",[24,41395,918],{"class":33730},[24,41397,36530],{"class":34016},[24,41399,41400],{"class":33738},".attention1(X, key_values, key_values, dec_valid_lens)\n",[24,41402,41403,41405,41407,41409],{"class":33726,"line":40873},[24,41404,40544],{"class":33738},[24,41406,918],{"class":33730},[24,41408,36530],{"class":34016},[24,41410,41411],{"class":33738},".addnorm1(X, X2)\n",[24,41413,41414],{"class":33726,"line":40901},[24,41415,41416],{"class":33762},"        # 编码器－解码器注意力。\n",[24,41418,41419],{"class":33726,"line":40921},[24,41420,41421],{"class":33762},"        # enc_outputs的开头:(batch_size,num_steps,num_hiddens)\n",[24,41423,41424,41427,41429,41431],{"class":33726,"line":40932},[24,41425,41426],{"class":33738},"        Y2 ",[24,41428,918],{"class":33730},[24,41430,36530],{"class":34016},[24,41432,41433],{"class":33738},".attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n",[24,41435,41436,41439,41441,41443],{"class":33726,"line":40945},[24,41437,41438],{"class":33738},"        Z ",[24,41440,918],{"class":33730},[24,41442,36530],{"class":34016},[24,41444,41445],{"class":33738},".addnorm2(Y, Y2)\n",[24,41447,41449,41451,41453,41456,41458],{"class":33726,"line":41448},45,[24,41450,33788],{"class":33730},[24,41452,36530],{"class":34016},[24,41454,41455],{"class":33738},".addnorm3(Z, ",[24,41457,33989],{"class":34016},[24,41459,41460],{"class":33738},".ffn(Z)), state\n",[24,41462,41464],{"class":33726,"line":41463},46,[24,41465,34047],{"emptyLinePlaceholder":31432},[24,41467,41469,41471,41474,41476,41479],{"class":33726,"line":41468},47,[24,41470,33953],{"class":33730},[24,41472,41473],{"class":33956}," TransformerDecoder",[24,41475,312],{"class":33738},[24,41477,41478],{"class":33962},"AttentionDecoder",[24,41480,33751],{"class":33738},[24,41482,41484,41486,41488,41490,41492,41494,41496,41498,41500,41502,41504,41506,41508],{"class":33726,"line":41483},48,[24,41485,33980],{"class":33730},[24,41487,33983],{"class":33778},[24,41489,312],{"class":33738},[24,41491,33989],{"class":33988},[24,41493,33745],{"class":33738},[24,41495,40608],{"class":33741},[24,41497,33745],{"class":33738},[24,41499,36157],{"class":33741},[24,41501,33745],{"class":33738},[24,41503,36162],{"class":33741},[24,41505,33745],{"class":33738},[24,41507,36167],{"class":33741},[24,41509,35139],{"class":33738},[24,41511,41513,41515,41517,41519,41521,41523,41525,41527],{"class":33726,"line":41512},49,[24,41514,40627],{"class":33741},[24,41516,33745],{"class":33738},[24,41518,40632],{"class":33741},[24,41520,33745],{"class":33738},[24,41522,38970],{"class":33741},[24,41524,33745],{"class":33738},[24,41526,38975],{"class":33741},[24,41528,35139],{"class":33738},[24,41530,41532,41534,41536,41538,41540,41542,41544,41546,41548],{"class":33726,"line":41531},50,[24,41533,36179],{"class":33741},[24,41535,33745],{"class":33738},[24,41537,40651],{"class":33741},[24,41539,33745],{"class":33738},[24,41541,33994],{"class":33741},[24,41543,33745],{"class":33738},[24,41545,33999],{"class":33730},[24,41547,34002],{"class":33741},[24,41549,33751],{"class":33738},[24,41551,41553,41555,41558,41560,41562,41564,41566,41568],{"class":33726,"line":41552},51,[24,41554,34010],{"class":34009},[24,41556,41557],{"class":33738},"(TransformerDecoder, ",[24,41559,33989],{"class":34016},[24,41561,34019],{"class":33738},[24,41563,34022],{"class":33778},[24,41565,312],{"class":33738},[24,41567,33999],{"class":33730},[24,41569,34029],{"class":33738},[24,41571,41573,41575,41577,41579],{"class":33726,"line":41572},52,[24,41574,34034],{"class":34016},[24,41576,40697],{"class":33738},[24,41578,918],{"class":33730},[24,41580,40702],{"class":33738},[24,41582,41584,41586,41589,41591],{"class":33726,"line":41583},53,[24,41585,34034],{"class":34016},[24,41587,41588],{"class":33738},".num_layers ",[24,41590,918],{"class":33730},[24,41592,41593],{"class":33738}," num_layers\n",[24,41595,41597,41599,41601,41603],{"class":33726,"line":41596},54,[24,41598,34034],{"class":34016},[24,41600,40709],{"class":33738},[24,41602,918],{"class":33730},[24,41604,40714],{"class":33738},[24,41606,41608,41610,41612,41614],{"class":33726,"line":41607},55,[24,41609,34034],{"class":34016},[24,41611,40721],{"class":33738},[24,41613,918],{"class":33730},[24,41615,40726],{"class":33738},[24,41617,41619,41621,41623,41625],{"class":33726,"line":41618},56,[24,41620,34034],{"class":34016},[24,41622,40733],{"class":33738},[24,41624,918],{"class":33730},[24,41626,40738],{"class":33738},[24,41628,41630,41632,41634,41636,41638],{"class":33726,"line":41629},57,[24,41631,40743],{"class":33730},[24,41633,40746],{"class":33738},[24,41635,40749],{"class":33730},[24,41637,40753],{"class":40752},[24,41639,40756],{"class":33738},[24,41641,41643,41645,41647,41649,41651,41653,41655,41657],{"class":33726,"line":41642},58,[24,41644,40761],{"class":34016},[24,41646,40764],{"class":33738},[24,41648,40768],{"class":40767},[24,41650,1785],{"class":40771},[24,41652,40768],{"class":40767},[24,41654,913],{"class":33730},[24,41656,40778],{"class":34009},[24,41658,40781],{"class":33738},[24,41660,41662],{"class":33726,"line":41661},59,[24,41663,41664],{"class":33738},"                DecoderBlock(key_size, query_size, value_size, num_hiddens,\n",[24,41666,41668],{"class":33726,"line":41667},60,[24,41669,40791],{"class":33738},[24,41671,41673],{"class":33726,"line":41672},61,[24,41674,41675],{"class":33738},"                             num_heads, dropout, i))\n",[24,41677,41679,41681,41684,41686],{"class":33726,"line":41678},62,[24,41680,34034],{"class":34016},[24,41682,41683],{"class":33738},".dense ",[24,41685,918],{"class":33730},[24,41687,41688],{"class":33738}," nn.Linear(num_hiddens, vocab_size)\n",[24,41690,41692],{"class":33726,"line":41691},63,[24,41693,34047],{"emptyLinePlaceholder":31432},[24,41695,41697,41699,41701,41703,41705,41707,41709,41711,41714,41716,41718,41720],{"class":33726,"line":41696},64,[24,41698,33980],{"class":33730},[24,41700,40107],{"class":33734},[24,41702,312],{"class":33738},[24,41704,33989],{"class":33988},[24,41706,33745],{"class":33738},[24,41708,40116],{"class":33741},[24,41710,33745],{"class":33738},[24,41712,41713],{"class":33741},"enc_valid_lens",[24,41715,33745],{"class":33738},[24,41717,40020],{"class":33730},[24,41719,40023],{"class":33741},[24,41721,33751],{"class":33738},[24,41723,41725,41727,41730,41732,41734,41736,41738],{"class":33726,"line":41724},65,[24,41726,33788],{"class":33730},[24,41728,41729],{"class":33738}," [enc_outputs, enc_valid_lens, [",[24,41731,34102],{"class":33778},[24,41733,38500],{"class":33738},[24,41735,40020],{"class":33730},[24,41737,36530],{"class":34016},[24,41739,41740],{"class":33738},".num_layers]\n",[24,41742,41744],{"class":33726,"line":41743},66,[24,41745,34047],{"emptyLinePlaceholder":31432},[24,41747,41749,41751,41753,41755,41757,41759,41761,41763,41765],{"class":33726,"line":41748},67,[24,41750,33980],{"class":33730},[24,41752,34074],{"class":33734},[24,41754,312],{"class":33738},[24,41756,33989],{"class":33988},[24,41758,33745],{"class":33738},[24,41760,33742],{"class":33741},[24,41762,33745],{"class":33738},[24,41764,40153],{"class":33741},[24,41766,33751],{"class":33738},[24,41768,41770,41772,41774,41776,41778,41780,41782,41784,41786,41788],{"class":33726,"line":41769},68,[24,41771,33892],{"class":33738},[24,41773,918],{"class":33730},[24,41775,36530],{"class":34016},[24,41777,40855],{"class":33738},[24,41779,33989],{"class":34016},[24,41781,40860],{"class":33738},[24,41783,40020],{"class":33730},[24,41785,40865],{"class":33738},[24,41787,33989],{"class":34016},[24,41789,40870],{"class":33738},[24,41791,41793,41795,41798,41800,41803,41805,41807,41809,41811,41813,41815,41818,41821,41824,41826,41828,41831,41833],{"class":33726,"line":41792},69,[24,41794,34034],{"class":34016},[24,41796,41797],{"class":33738},"._attention_weights ",[24,41799,918],{"class":33730},[24,41801,41802],{"class":33738}," [[",[24,41804,34102],{"class":33778},[24,41806,38500],{"class":33738},[24,41808,40020],{"class":33730},[24,41810,40891],{"class":40752},[24,41812,312],{"class":33738},[24,41814,33989],{"class":34016},[24,41816,41817],{"class":33738},".blks) ",[24,41819,41820],{"class":33730},"for",[24,41822,41823],{"class":33738}," _ ",[24,41825,40749],{"class":33730},[24,41827,40753],{"class":40752},[24,41829,41830],{"class":33738}," (",[24,41832,9241],{"class":33778},[24,41834,41835],{"class":33738},")]\n",[24,41837,41839,41841,41843,41845,41847,41849,41851],{"class":33726,"line":41838},70,[24,41840,40743],{"class":33730},[24,41842,40906],{"class":33738},[24,41844,40749],{"class":33730},[24,41846,40911],{"class":40752},[24,41848,312],{"class":33738},[24,41850,33989],{"class":34016},[24,41852,40918],{"class":33738},[24,41854,41856,41859,41861],{"class":33726,"line":41855},71,[24,41857,41858],{"class":33738},"            X, state ",[24,41860,918],{"class":33730},[24,41862,41863],{"class":33738}," blk(X, state)\n",[24,41865,41867],{"class":33726,"line":41866},72,[24,41868,41869],{"class":33762},"            # 解码器自注意力权重\n",[24,41871,41873,41875,41878,41880,41883,41885],{"class":33726,"line":41872},73,[24,41874,40761],{"class":34016},[24,41876,41877],{"class":33738},"._attention_weights[",[24,41879,598],{"class":33778},[24,41881,41882],{"class":33738},"][i] ",[24,41884,918],{"class":33730},[24,41886,41887],{"class":33738}," blk.attention1.attention.attention_weights\n",[24,41889,41891],{"class":33726,"line":41890},74,[24,41892,41893],{"class":33762},"            # “编码器－解码器”自注意力权重\n",[24,41895,41897,41899,41901,41903,41905,41907],{"class":33726,"line":41896},75,[24,41898,40761],{"class":34016},[24,41900,41877],{"class":33738},[24,41902,616],{"class":33778},[24,41904,41882],{"class":33738},[24,41906,918],{"class":33730},[24,41908,41909],{"class":33738}," blk.attention2.attention.attention_weights\n",[24,41911,41913,41915,41917],{"class":33726,"line":41912},76,[24,41914,33788],{"class":33730},[24,41916,36530],{"class":34016},[24,41918,41919],{"class":33738},".dense(X), state\n",[24,41921,41923],{"class":33726,"line":41922},77,[24,41924,34047],{"emptyLinePlaceholder":31432},[24,41926,41928,41931],{"class":33726,"line":41927},78,[24,41929,41930],{"class":33734},"    @",[24,41932,41933],{"class":34009},"property\n",[24,41935,41937,41939,41942,41944,41946],{"class":33726,"line":41936},79,[24,41938,33980],{"class":33730},[24,41940,41941],{"class":33734}," attention_weights",[24,41943,312],{"class":33738},[24,41945,33989],{"class":33988},[24,41947,33751],{"class":33738},[24,41949,41951,41953,41955],{"class":33726,"line":41950},80,[24,41952,33788],{"class":33730},[24,41954,36530],{"class":34016},[24,41956,41957],{"class":33738},"._attention_weights\n",[10,41959,41960],{"id":41960},"训练",[14,41962,41963],{},"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":31407,"style":31407},"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":31407},[24,41970,41971,41973,41976,41978,41980,41982,41985,41987,41990,41992,41994],{"class":33726,"line":33727},[24,41972,33731],{"class":33730},[24,41974,41975],{"class":33734}," sequence_mask",[24,41977,312],{"class":33738},[24,41979,33742],{"class":33741},[24,41981,33745],{"class":33738},[24,41983,41984],{"class":33741},"valid_len",[24,41986,33745],{"class":33738},[24,41988,41989],{"class":33741},"value",[24,41991,918],{"class":33730},[24,41993,598],{"class":33778},[24,41995,33751],{"class":33738},[24,41997,41998],{"class":33726,"line":31408},[24,41999,42000],{"class":33756},"    \"\"\"在序列中屏蔽不相关的项\"\"\"\n",[24,42002,42003,42006,42008,42011,42013],{"class":33726,"line":31416},[24,42004,42005],{"class":33738},"    maxlen ",[24,42007,918],{"class":33730},[24,42009,42010],{"class":33738}," X.size(",[24,42012,616],{"class":33778},[24,42014,33803],{"class":33738},[24,42016,42017,42020,42022,42025,42028,42030],{"class":33726,"line":33766},[24,42018,42019],{"class":33738},"    mask ",[24,42021,918],{"class":33730},[24,42023,42024],{"class":33738}," torch.arange((maxlen), ",[24,42026,42027],{"class":33794},"dtype",[24,42029,918],{"class":33730},[24,42031,42032],{"class":33738},"torch.float32,\n",[24,42034,42035,42038,42040,42043,42045,42048,42051,42054,42056,42058,42060],{"class":33726,"line":33785},[24,42036,42037],{"class":33794},"                        device",[24,42039,918],{"class":33730},[24,42041,42042],{"class":33738},"X.device)[",[24,42044,34102],{"class":33778},[24,42046,42047],{"class":33738},", :] ",[24,42049,42050],{"class":33730},"\u003C",[24,42052,42053],{"class":33738}," valid_len[",[24,42055,15071],{"class":38484},[24,42057,33745],{"class":33738},[24,42059,34102],{"class":33778},[24,42061,34121],{"class":33738},[24,42063,42064,42067,42070,42073,42075],{"class":33726,"line":33806},[24,42065,42066],{"class":33738},"    X[",[24,42068,42069],{"class":33730},"~",[24,42071,42072],{"class":33738},"mask] ",[24,42074,918],{"class":33730},[24,42076,42077],{"class":33738}," value\n",[24,42079,42080,42082],{"class":33726,"line":33814},[24,42081,35997],{"class":33730},[24,42083,40950],{"class":33738},[24,42085,42086],{"class":33726,"line":33825},[24,42087,34047],{"emptyLinePlaceholder":31432},[24,42089,42090,42092,42095,42097,42099,42101,42104],{"class":33726,"line":33842},[24,42091,33953],{"class":33730},[24,42093,42094],{"class":33956}," MaskedSoftmaxCELoss",[24,42096,312],{"class":33738},[24,42098,33963],{"class":33962},[24,42100,32214],{"class":33738},[24,42102,42103],{"class":33962},"CrossEntropyLoss",[24,42105,33751],{"class":33738},[24,42107,42108],{"class":33726,"line":33858},[24,42109,42110],{"class":33756},"    \"\"\"带遮蔽的softmax交叉熵损失函数\"\"\"\n",[24,42112,42113],{"class":33726,"line":33866},[24,42114,42115],{"class":33762},"    # pred的形状：(batch_size,num_steps,vocab_size)\n",[24,42117,42118],{"class":33726,"line":33883},[24,42119,42120],{"class":33762},"    # label的形状：(batch_size,num_steps)\n",[24,42122,42123],{"class":33726,"line":33889},[24,42124,42125],{"class":33762},"    # valid_len的形状：(batch_size,)\n",[24,42127,42128,42130,42132,42134,42136,42138,42141,42143,42146,42148,42150],{"class":33726,"line":33914},[24,42129,33980],{"class":33730},[24,42131,34074],{"class":33734},[24,42133,312],{"class":33738},[24,42135,33989],{"class":33988},[24,42137,33745],{"class":33738},[24,42139,42140],{"class":33741},"pred",[24,42142,33745],{"class":33738},[24,42144,42145],{"class":33741},"label",[24,42147,33745],{"class":33738},[24,42149,41984],{"class":33741},[24,42151,33751],{"class":33738},[24,42153,42154,42157,42159],{"class":33726,"line":33927},[24,42155,42156],{"class":33738},"        weights ",[24,42158,918],{"class":33730},[24,42160,42161],{"class":33738}," torch.ones_like(label)\n",[24,42163,42164,42166,42168],{"class":33726,"line":34166},[24,42165,42156],{"class":33738},[24,42167,918],{"class":33730},[24,42169,42170],{"class":33738}," sequence_mask(weights, valid_len)\n",[24,42172,42173,42175,42178,42180,42183,42186],{"class":33726,"line":36091},[24,42174,34034],{"class":34016},[24,42176,42177],{"class":33738},".reduction",[24,42179,918],{"class":33730},[24,42181,42182],{"class":40767},"'",[24,42184,42185],{"class":40771},"none",[24,42187,42188],{"class":40767},"'\n",[24,42190,42191,42194,42196,42199,42202,42204],{"class":33726,"line":36367},[24,42192,42193],{"class":33738},"        unweighted_loss ",[24,42195,918],{"class":33730},[24,42197,42198],{"class":34009}," super",[24,42200,42201],{"class":33738},"(MaskedSoftmaxCELoss, ",[24,42203,33989],{"class":34016},[24,42205,42206],{"class":33738},").forward(\n",[24,42208,42209,42212,42214,42216,42218,42220,42222],{"class":33726,"line":36373},[24,42210,42211],{"class":33738},"            pred.permute(",[24,42213,598],{"class":33778},[24,42215,33745],{"class":33738},[24,42217,9241],{"class":33778},[24,42219,33745],{"class":33738},[24,42221,616],{"class":33778},[24,42223,42224],{"class":33738},"), label)\n",[24,42226,42227,42230,42232,42235,42237,42240,42242,42244,42246],{"class":33726,"line":36379},[24,42228,42229],{"class":33738},"        weighted_loss ",[24,42231,918],{"class":33730},[24,42233,42234],{"class":33738}," (unweighted_loss ",[24,42236,40020],{"class":33730},[24,42238,42239],{"class":33738}," weights).mean(",[24,42241,33795],{"class":33794},[24,42243,918],{"class":33730},[24,42245,616],{"class":33778},[24,42247,33803],{"class":33738},[24,42249,42250,42252],{"class":33726,"line":36385},[24,42251,33788],{"class":33730},[24,42253,42254],{"class":33738}," weighted_loss\n",[14,42256,42257],{},"梯度裁剪函数：",[33716,42259,42261],{"className":33718,"code":42260,"language":33720,"meta":31407,"style":31407},"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":31407},[24,42264,42265,42267,42270,42272,42275,42277,42280],{"class":33726,"line":33727},[24,42266,33731],{"class":33730},[24,42268,42269],{"class":33734}," grad_clipping",[24,42271,312],{"class":33738},[24,42273,42274],{"class":33741},"net",[24,42276,33745],{"class":33738},[24,42278,42279],{"class":33741},"theta",[24,42281,33751],{"class":33738},[24,42283,42284],{"class":33726,"line":31408},[24,42285,42286],{"class":33756},"    \"\"\"裁剪梯度\"\"\"\n",[24,42288,42289,42291,42294],{"class":33726,"line":31416},[24,42290,33769],{"class":33730},[24,42292,42293],{"class":40752}," isinstance",[24,42295,42296],{"class":33738},"(net, nn.Module):\n",[24,42298,42299,42302,42304,42307,42309,42312,42314,42317,42320],{"class":33726,"line":33766},[24,42300,42301],{"class":33738},"        params ",[24,42303,918],{"class":33730},[24,42305,42306],{"class":33738}," [p ",[24,42308,41820],{"class":33730},[24,42310,42311],{"class":33738}," p ",[24,42313,40749],{"class":33730},[24,42315,42316],{"class":33738}," net.parameters() ",[24,42318,42319],{"class":33730},"if",[24,42321,42322],{"class":33738}," p.requires_grad]\n",[24,42324,42325,42327],{"class":33726,"line":33785},[24,42326,33809],{"class":33730},[24,42328,33782],{"class":33738},[24,42330,42331,42333,42335],{"class":33726,"line":33806},[24,42332,42301],{"class":33738},[24,42334,918],{"class":33730},[24,42336,42337],{"class":33738}," net.params\n",[24,42339,42340,42343,42345,42348,42351,42354,42356,42359,42361,42363,42365,42367],{"class":33726,"line":33814},[24,42341,42342],{"class":33738},"    norm ",[24,42344,918],{"class":33730},[24,42346,42347],{"class":33738}," torch.sqrt(",[24,42349,42350],{"class":40752},"sum",[24,42352,42353],{"class":33738},"(torch.sum((p.grad ",[24,42355,33999],{"class":33730},[24,42357,42358],{"class":33778}," 2",[24,42360,34145],{"class":33738},[24,42362,41820],{"class":33730},[24,42364,42311],{"class":33738},[24,42366,40749],{"class":33730},[24,42368,42369],{"class":33738}," params))\n",[24,42371,42372,42374,42377,42380],{"class":33726,"line":33825},[24,42373,33769],{"class":33730},[24,42375,42376],{"class":33738}," norm ",[24,42378,42379],{"class":33730},">",[24,42381,42382],{"class":33738}," theta:\n",[24,42384,42385,42387,42390,42392],{"class":33726,"line":33842},[24,42386,40743],{"class":33730},[24,42388,42389],{"class":33738}," param ",[24,42391,40749],{"class":33730},[24,42393,42394],{"class":33738}," params:\n",[24,42396,42397,42400,42402,42404,42407,42410,42412],{"class":33726,"line":33858},[24,42398,42399],{"class":33738},"            param.grad[",[24,42401,15071],{"class":38484},[24,42403,38500],{"class":33738},[24,42405,42406],{"class":33730},"*=",[24,42408,42409],{"class":33738}," theta ",[24,42411,34148],{"class":33730},[24,42413,42414],{"class":33738}," norm\n",[14,42416,42417,42418],{},"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":31407,"style":31407},"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":31407},[24,42432,42433,42435,42438,42440,42442,42444,42447,42449,42452,42454,42457,42459,42462,42464,42466],{"class":33726,"line":33727},[24,42434,33731],{"class":33730},[24,42436,42437],{"class":33734}," train_seq2seq",[24,42439,312],{"class":33738},[24,42441,42274],{"class":33741},[24,42443,33745],{"class":33738},[24,42445,42446],{"class":33741},"data_iter",[24,42448,33745],{"class":33738},[24,42450,42451],{"class":33741},"lr",[24,42453,33745],{"class":33738},[24,42455,42456],{"class":33741},"num_epochs",[24,42458,33745],{"class":33738},[24,42460,42461],{"class":33741},"tgt_vocab",[24,42463,33745],{"class":33738},[24,42465,41355],{"class":33741},[24,42467,33751],{"class":33738},[24,42469,42470],{"class":33726,"line":31408},[24,42471,42472],{"class":33756},"    \"\"\"训练序列到序列模型\"\"\"\n",[24,42474,42475,42477,42480,42482,42484],{"class":33726,"line":31416},[24,42476,33980],{"class":33730},[24,42478,42479],{"class":33734}," xavier_init_weights",[24,42481,312],{"class":33738},[24,42483,31744],{"class":33741},[24,42485,33751],{"class":33738},[24,42487,42488,42490,42493,42496,42498],{"class":33726,"line":33766},[24,42489,33828],{"class":33730},[24,42491,42492],{"class":34009}," type",[24,42494,42495],{"class":33738},"(m) ",[24,42497,33834],{"class":33730},[24,42499,42500],{"class":33738}," nn.Linear:\n",[24,42502,42503],{"class":33726,"line":33785},[24,42504,42505],{"class":33738},"            nn.init.xavier_uniform_(m.weight)\n",[24,42507,42508,42510,42512,42514,42516,42519,42522],{"class":33726,"line":33806},[24,42509,33828],{"class":33730},[24,42511,42492],{"class":34009},[24,42513,42495],{"class":33738},[24,42515,33834],{"class":33730},[24,42517,42518],{"class":33738}," nn.",[24,42520,42521],{"class":33778},"GRU",[24,42523,33782],{"class":33738},[24,42525,42526,42529,42531,42533],{"class":33726,"line":33814},[24,42527,42528],{"class":33730},"            for",[24,42530,42389],{"class":33738},[24,42532,40749],{"class":33730},[24,42534,42535],{"class":33738}," m._flat_weights_names:\n",[24,42537,42538,42541,42544,42547,42549,42552],{"class":33726,"line":33825},[24,42539,42540],{"class":33730},"                if",[24,42542,42543],{"class":40767}," \"",[24,42545,42546],{"class":40771},"weight",[24,42548,40768],{"class":40767},[24,42550,42551],{"class":33730}," in",[24,42553,42554],{"class":33738}," param:\n",[24,42556,42557],{"class":33726,"line":33842},[24,42558,42559],{"class":33738},"                    nn.init.xavier_uniform_(m._parameters[param])\n",[24,42561,42562],{"class":33726,"line":33858},[24,42563,34047],{"emptyLinePlaceholder":31432},[24,42565,42566],{"class":33726,"line":33866},[24,42567,42568],{"class":33738},"    net.apply(xavier_init_weights)\n",[24,42570,42571],{"class":33726,"line":33883},[24,42572,42573],{"class":33738},"    net.to(device)\n",[24,42575,42576,42579,42581,42584,42586,42588],{"class":33726,"line":33889},[24,42577,42578],{"class":33738},"    optimizer ",[24,42580,918],{"class":33730},[24,42582,42583],{"class":33738}," torch.optim.Adam(net.parameters(), ",[24,42585,42451],{"class":33794},[24,42587,918],{"class":33730},[24,42589,42590],{"class":33738},"lr)\n",[24,42592,42593,42596,42598],{"class":33726,"line":33914},[24,42594,42595],{"class":33738},"    loss ",[24,42597,918],{"class":33730},[24,42599,42600],{"class":33738}," MaskedSoftmaxCELoss()\n",[24,42602,42603],{"class":33726,"line":33927},[24,42604,42605],{"class":33738},"    net.train()\n",[24,42607,42608,42611,42613,42616,42619,42621,42623,42626,42628,42630,42633,42635,42637,42640,42642],{"class":33726,"line":34166},[24,42609,42610],{"class":33738},"    animator ",[24,42612,918],{"class":33730},[24,42614,42615],{"class":33738}," d2l.Animator(",[24,42617,42618],{"class":33794},"xlabel",[24,42620,918],{"class":33730},[24,42622,42182],{"class":40767},[24,42624,42625],{"class":40771},"epoch",[24,42627,42182],{"class":40767},[24,42629,33745],{"class":33738},[24,42631,42632],{"class":33794},"ylabel",[24,42634,918],{"class":33730},[24,42636,42182],{"class":40767},[24,42638,42639],{"class":40771},"loss",[24,42641,42182],{"class":40767},[24,42643,35139],{"class":33738},[24,42645,42646,42649,42651,42654,42657],{"class":33726,"line":36091},[24,42647,42648],{"class":33794},"                     xlim",[24,42650,918],{"class":33730},[24,42652,42653],{"class":33738},"[",[24,42655,42656],{"class":33778},"10",[24,42658,42659],{"class":33738},", num_epochs])\n",[24,42661,42662,42665,42668,42670,42672],{"class":33726,"line":36367},[24,42663,42664],{"class":33730},"    for",[24,42666,42667],{"class":33738}," epoch ",[24,42669,40749],{"class":33730},[24,42671,40753],{"class":40752},[24,42673,42674],{"class":33738},"(num_epochs):\n",[24,42676,42677,42680,42682],{"class":33726,"line":36373},[24,42678,42679],{"class":33738},"        timer ",[24,42681,918],{"class":33730},[24,42683,42684],{"class":33738}," d2l.Timer()\n",[24,42686,42687,42690,42692,42695,42697,42700],{"class":33726,"line":36379},[24,42688,42689],{"class":33738},"        metric ",[24,42691,918],{"class":33730},[24,42693,42694],{"class":33738}," d2l.Accumulator(",[24,42696,9241],{"class":33778},[24,42698,42699],{"class":33738},")  ",[24,42701,42702],{"class":33762},"# 训练损失总和，词元数量\n",[24,42704,42705,42707,42710,42712],{"class":33726,"line":36385},[24,42706,40743],{"class":33730},[24,42708,42709],{"class":33738}," batch ",[24,42711,40749],{"class":33730},[24,42713,42714],{"class":33738}," data_iter:\n",[24,42716,42717],{"class":33726,"line":36406},[24,42718,42719],{"class":33738},"            optimizer.zero_grad()\n",[24,42721,42722,42725,42727,42730,42732,42735,42737],{"class":33726,"line":36425},[24,42723,42724],{"class":33738},"            X, X_valid_len, Y, Y_valid_len ",[24,42726,918],{"class":33730},[24,42728,42729],{"class":33738}," [x.to(device) ",[24,42731,41820],{"class":33730},[24,42733,42734],{"class":33738}," x ",[24,42736,40749],{"class":33730},[24,42738,42739],{"class":33738}," batch]\n",[24,42741,42742,42745,42747,42750,42752,42755,42757,42760,42762,42765,42767],{"class":33726,"line":36444},[24,42743,42744],{"class":33738},"            bos ",[24,42746,918],{"class":33730},[24,42748,42749],{"class":33738}," torch.tensor([tgt_vocab[",[24,42751,42182],{"class":40767},[24,42753,42754],{"class":40771},"\u003Cbos>",[24,42756,42182],{"class":40767},[24,42758,42759],{"class":33738},"]] ",[24,42761,40020],{"class":33730},[24,42763,42764],{"class":33738}," Y.shape[",[24,42766,598],{"class":33778},[24,42768,42769],{"class":33738},"],\n",[24,42771,42772,42775,42777,42780,42782,42784,42786,42788],{"class":33726,"line":36449},[24,42773,42774],{"class":33794},"                          device",[24,42776,918],{"class":33730},[24,42778,42779],{"class":33738},"device).reshape(",[24,42781,33876],{"class":33730},[24,42783,616],{"class":33778},[24,42785,33745],{"class":33738},[24,42787,616],{"class":33778},[24,42789,33803],{"class":33738},[24,42791,42792,42795,42797,42800,42802,42804,42806,42808,42810,42813,42815,42817],{"class":33726,"line":36465},[24,42793,42794],{"class":33738},"            dec_input ",[24,42796,918],{"class":33730},[24,42798,42799],{"class":33738}," torch.cat([bos, Y[",[24,42801,15071],{"class":38484},[24,42803,33745],{"class":33738},[24,42805,15071],{"class":38484},[24,42807,33876],{"class":33730},[24,42809,616],{"class":33778},[24,42811,42812],{"class":33738},"]], ",[24,42814,616],{"class":33778},[24,42816,42699],{"class":33738},[24,42818,42819],{"class":33762},"# 强制教学\n",[24,42821,42822,42825,42827],{"class":33726,"line":36471},[24,42823,42824],{"class":33738},"            Y_hat, _ ",[24,42826,918],{"class":33730},[24,42828,42829],{"class":33738}," net(X, dec_input, X_valid_len)\n",[24,42831,42832,42835,42837],{"class":33726,"line":36477},[24,42833,42834],{"class":33738},"            l ",[24,42836,918],{"class":33730},[24,42838,42839],{"class":33738}," loss(Y_hat, Y, Y_valid_len)\n",[24,42841,42842,42845],{"class":33726,"line":36487},[24,42843,42844],{"class":33738},"            l.sum().backward()      ",[24,42846,42847],{"class":33762},"# 损失函数的标量进行“反向传播”\n",[24,42849,42850,42853,42855],{"class":33726,"line":36511},[24,42851,42852],{"class":33738},"            grad_clipping(net, ",[24,42854,616],{"class":33778},[24,42856,33803],{"class":33738},[24,42858,42859,42862,42864],{"class":33726,"line":36516},[24,42860,42861],{"class":33738},"            num_tokens ",[24,42863,918],{"class":33730},[24,42865,42866],{"class":33738}," Y_valid_len.sum()\n",[24,42868,42869],{"class":33726,"line":36522},[24,42870,42871],{"class":33738},"            optimizer.step()\n",[24,42873,42874,42877],{"class":33726,"line":36536},[24,42875,42876],{"class":33730},"            with",[24,42878,42879],{"class":33738}," torch.no_grad():\n",[24,42881,42882],{"class":33726,"line":36541},[24,42883,42884],{"class":33738},"                metric.add(l.sum(), num_tokens)\n",[24,42886,42887,42889,42892,42894,42896,42898,42901,42904,42907,42910],{"class":33726,"line":36547},[24,42888,33828],{"class":33730},[24,42890,42891],{"class":33738}," (epoch ",[24,42893,913],{"class":33730},[24,42895,33837],{"class":33778},[24,42897,38447],{"class":33738},[24,42899,42900],{"class":33730},"%",[24,42902,42903],{"class":33778}," 10",[24,42905,42906],{"class":33730}," ==",[24,42908,42909],{"class":33778}," 0",[24,42911,33782],{"class":33738},[24,42913,42914,42917,42919,42921,42924,42926,42928,42930,42933,42935],{"class":33726,"line":36562},[24,42915,42916],{"class":33738},"            animator.add(epoch ",[24,42918,913],{"class":33730},[24,42920,33837],{"class":33778},[24,42922,42923],{"class":33738},", (metric[",[24,42925,598],{"class":33778},[24,42927,38500],{"class":33738},[24,42929,34148],{"class":33730},[24,42931,42932],{"class":33738}," metric[",[24,42934,616],{"class":33778},[24,42936,42937],{"class":33738},"],))\n",[24,42939,42940,42943,42945,42947,42950,42953,42956,42958,42960,42962,42964,42966,42969,42972,42975,42977,42979,42981,42983,42985,42987,42990,42993,42995],{"class":33726,"line":40834},[24,42941,42942],{"class":40752},"    print",[24,42944,312],{"class":33738},[24,42946,921],{"class":33730},[24,42948,42949],{"class":40771},"'loss ",[24,42951,42952],{"class":33778},"{",[24,42954,42955],{"class":33738},"metric[",[24,42957,598],{"class":33778},[24,42959,38500],{"class":33738},[24,42961,34148],{"class":33730},[24,42963,42932],{"class":33738},[24,42965,616],{"class":33778},[24,42967,42968],{"class":33738},"]",[24,42970,42971],{"class":33730},":.3f",[24,42973,42974],{"class":33778},"}",[24,42976,33745],{"class":40771},[24,42978,42952],{"class":33778},[24,42980,42955],{"class":33738},[24,42982,616],{"class":33778},[24,42984,38500],{"class":33738},[24,42986,34148],{"class":33730},[24,42988,42989],{"class":33738}," timer.stop()",[24,42991,42992],{"class":33730},":.1f",[24,42994,42974],{"class":33778},[24,42996,42997],{"class":40771}," '\n",[24,42999,43000,43003,43006,43008,43010,43013,43015,43017],{"class":33726,"line":40840},[24,43001,43002],{"class":33730},"        f",[24,43004,43005],{"class":40771},"'tokens/sec on ",[24,43007,42952],{"class":33778},[24,43009,40778],{"class":34009},[24,43011,43012],{"class":33738},"(device)",[24,43014,42974],{"class":33778},[24,43016,42182],{"class":40771},[24,43018,33803],{"class":33738},[14,43020,43021],{},"进行数据集的数据处理",[33716,43023,43025],{"className":33718,"code":43024,"language":33720,"meta":31407,"style":31407},"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":31407},[24,43028,43029,43031,43034],{"class":33726,"line":33727},[24,43030,33731],{"class":33730},[24,43032,43033],{"class":33734}," read_data_nmt",[24,43035,43036],{"class":33738},"():\n",[24,43038,43039],{"class":33726,"line":31408},[24,43040,43041],{"class":33756},"    \"\"\"载入“英语－法语”数据集\n",[24,43043,43044],{"class":33726,"line":31416},[24,43045,34047],{"emptyLinePlaceholder":31432},[24,43047,43048],{"class":33726,"line":33766},[24,43049,43050],{"class":33756},"    Defined in :numref:`sec_machine_translation`\"\"\"\n",[24,43052,43053,43056,43058,43061,43063,43066,43068],{"class":33726,"line":33785},[24,43054,43055],{"class":33738},"    data_dir ",[24,43057,918],{"class":33730},[24,43059,43060],{"class":33738}," d2l.download_extract(",[24,43062,42182],{"class":40767},[24,43064,43065],{"class":40771},"fra-eng",[24,43067,42182],{"class":40767},[24,43069,33803],{"class":33738},[24,43071,43072,43075,43078,43081,43083,43086,43088,43091,43093,43095,43097],{"class":33726,"line":33806},[24,43073,43074],{"class":33730},"    with",[24,43076,43077],{"class":40752}," open",[24,43079,43080],{"class":33738},"(os.path.join(data_dir, ",[24,43082,42182],{"class":40767},[24,43084,43085],{"class":40771},"fra.txt",[24,43087,42182],{"class":40767},[24,43089,43090],{"class":33738},"), ",[24,43092,42182],{"class":40767},[24,43094,456],{"class":40771},[24,43096,42182],{"class":40767},[24,43098,35139],{"class":33738},[24,43100,43101,43104,43106,43108,43111,43113,43115,43118],{"class":33726,"line":33814},[24,43102,43103],{"class":33794},"             encoding",[24,43105,918],{"class":33730},[24,43107,42182],{"class":40767},[24,43109,43110],{"class":40771},"utf-8",[24,43112,42182],{"class":40767},[24,43114,38447],{"class":33738},[24,43116,43117],{"class":33730},"as",[24,43119,43120],{"class":33738}," f:\n",[24,43122,43123,43125],{"class":33726,"line":33825},[24,43124,33788],{"class":33730},[24,43126,43127],{"class":33738}," f.read()\n",[24,43129,43130],{"class":33726,"line":33842},[24,43131,34047],{"emptyLinePlaceholder":31432},[24,43133,43134,43136,43139,43141,43143],{"class":33726,"line":33858},[24,43135,33731],{"class":33730},[24,43137,43138],{"class":33734}," preprocess_nmt",[24,43140,312],{"class":33738},[24,43142,27760],{"class":33741},[24,43144,33751],{"class":33738},[24,43146,43147],{"class":33726,"line":33866},[24,43148,43149],{"class":33756},"    \"\"\"预处理“英语－法语”数据集\n",[24,43151,43152],{"class":33726,"line":33883},[24,43153,34047],{"emptyLinePlaceholder":31432},[24,43155,43156],{"class":33726,"line":33889},[24,43157,43050],{"class":33756},[24,43159,43160,43162,43165,43167,43170,43172,43175],{"class":33726,"line":33914},[24,43161,33980],{"class":33730},[24,43163,43164],{"class":33734}," no_space",[24,43166,312],{"class":33738},[24,43168,43169],{"class":33741},"char",[24,43171,33745],{"class":33738},[24,43173,43174],{"class":33741},"prev_char",[24,43176,33751],{"class":33738},[24,43178,43179,43181,43184,43186,43189,43191,43193,43196,43198,43200,43203,43206,43209,43212],{"class":33726,"line":33927},[24,43180,33788],{"class":33730},[24,43182,43183],{"class":33738}," char ",[24,43185,40749],{"class":33730},[24,43187,43188],{"class":34009}," set",[24,43190,312],{"class":33738},[24,43192,42182],{"class":40767},[24,43194,43195],{"class":40771},",.!?",[24,43197,42182],{"class":40767},[24,43199,38447],{"class":33738},[24,43201,43202],{"class":33730},"and",[24,43204,43205],{"class":33738}," prev_char ",[24,43207,43208],{"class":33730},"!=",[24,43210,43211],{"class":40767}," '",[24,43213,42997],{"class":40767},[24,43215,43216],{"class":33726,"line":34166},[24,43217,34047],{"emptyLinePlaceholder":31432},[24,43219,43220],{"class":33726,"line":36091},[24,43221,43222],{"class":33762},"    # 使用空格替换不间断空格\n",[24,43224,43225],{"class":33726,"line":36367},[24,43226,43227],{"class":33762},"    # 使用小写字母替换大写字母\n",[24,43229,43230,43233,43235,43238,43240,43244,43246,43248,43250,43252,43255,43257,43260,43262,43264,43266,43268],{"class":33726,"line":36373},[24,43231,43232],{"class":33738},"    text ",[24,43234,918],{"class":33730},[24,43236,43237],{"class":33738}," text.replace(",[24,43239,42182],{"class":40767},[24,43241,43243],{"class":43242},"sRfyP","\\u202f",[24,43245,42182],{"class":40767},[24,43247,33745],{"class":33738},[24,43249,42182],{"class":40767},[24,43251,43211],{"class":40767},[24,43253,43254],{"class":33738},").replace(",[24,43256,42182],{"class":40767},[24,43258,43259],{"class":43242},"\\xa0",[24,43261,42182],{"class":40767},[24,43263,33745],{"class":33738},[24,43265,42182],{"class":40767},[24,43267,43211],{"class":40767},[24,43269,43270],{"class":33738},").lower()\n",[24,43272,43273],{"class":33726,"line":36379},[24,43274,43275],{"class":33762},"    # 在单词和标点符号之间插入空格\n",[24,43277,43278,43281,43283,43285,43287,43289,43292,43294,43296,43298,43300,43302,43305,43308,43310,43312,43315,43318],{"class":33726,"line":36385},[24,43279,43280],{"class":33738},"    out ",[24,43282,918],{"class":33730},[24,43284,40882],{"class":33738},[24,43286,42182],{"class":40767},[24,43288,43211],{"class":40767},[24,43290,43291],{"class":33730}," +",[24,43293,43183],{"class":33738},[24,43295,42319],{"class":33730},[24,43297,40746],{"class":33738},[24,43299,42379],{"class":33730},[24,43301,42909],{"class":33778},[24,43303,43304],{"class":33730}," and",[24,43306,43307],{"class":33738}," no_space(char, text[i ",[24,43309,33876],{"class":33730},[24,43311,33837],{"class":33778},[24,43313,43314],{"class":33738},"]) ",[24,43316,43317],{"class":33730},"else",[24,43319,43320],{"class":33738}," char\n",[24,43322,43323,43326,43329,43331,43333],{"class":33726,"line":36406},[24,43324,43325],{"class":33730},"           for",[24,43327,43328],{"class":33738}," i, char ",[24,43330,40749],{"class":33730},[24,43332,40911],{"class":40752},[24,43334,43335],{"class":33738},"(text)]\n",[24,43337,43338,43340,43343],{"class":33726,"line":36425},[24,43339,35997],{"class":33730},[24,43341,43342],{"class":40767}," ''",[24,43344,43345],{"class":33738},".join(out)\n",[24,43347,43348],{"class":33726,"line":36444},[24,43349,34047],{"emptyLinePlaceholder":31432},[24,43351,43352,43354,43357,43359,43361,43363,43366,43368,43370],{"class":33726,"line":36449},[24,43353,33731],{"class":33730},[24,43355,43356],{"class":33734}," tokenize_nmt",[24,43358,312],{"class":33738},[24,43360,27760],{"class":33741},[24,43362,33745],{"class":33738},[24,43364,43365],{"class":33741},"num_examples",[24,43367,918],{"class":33730},[24,43369,34102],{"class":33778},[24,43371,33751],{"class":33738},[24,43373,43374],{"class":33726,"line":36465},[24,43375,43376],{"class":33756},"    \"\"\"词元化“英语－法语”数据数据集\n",[24,43378,43379],{"class":33726,"line":36471},[24,43380,34047],{"emptyLinePlaceholder":31432},[24,43382,43383],{"class":33726,"line":36477},[24,43384,43050],{"class":33756},[24,43386,43387,43390,43392],{"class":33726,"line":36487},[24,43388,43389],{"class":33738},"    source, target ",[24,43391,918],{"class":33730},[24,43393,43394],{"class":33738}," [], []\n",[24,43396,43397,43399,43402,43404,43406,43409,43411,43414,43416],{"class":33726,"line":36511},[24,43398,42664],{"class":33730},[24,43400,43401],{"class":33738}," i, line ",[24,43403,40749],{"class":33730},[24,43405,40911],{"class":40752},[24,43407,43408],{"class":33738},"(text.split(",[24,43410,42182],{"class":40767},[24,43412,43413],{"class":43242},"\\n",[24,43415,42182],{"class":40767},[24,43417,43418],{"class":33738},")):\n",[24,43420,43421,43423,43426,43428,43430,43432],{"class":33726,"line":36516},[24,43422,33828],{"class":33730},[24,43424,43425],{"class":33738}," num_examples ",[24,43427,43202],{"class":33730},[24,43429,40746],{"class":33738},[24,43431,42379],{"class":33730},[24,43433,43434],{"class":33738}," num_examples:\n",[24,43436,43437],{"class":33726,"line":36522},[24,43438,43439],{"class":33730},"            break\n",[24,43441,43442,43445,43447,43450,43452,43455,43457],{"class":33726,"line":36536},[24,43443,43444],{"class":33738},"        parts ",[24,43446,918],{"class":33730},[24,43448,43449],{"class":33738}," line.split(",[24,43451,42182],{"class":40767},[24,43453,43454],{"class":43242},"\\t",[24,43456,42182],{"class":40767},[24,43458,33803],{"class":33738},[24,43460,43461,43463,43465,43468,43470,43472],{"class":33726,"line":36541},[24,43462,33828],{"class":33730},[24,43464,40891],{"class":40752},[24,43466,43467],{"class":33738},"(parts) ",[24,43469,33834],{"class":33730},[24,43471,42358],{"class":33778},[24,43473,33782],{"class":33738},[24,43475,43476,43479,43481,43484,43486,43488],{"class":33726,"line":36547},[24,43477,43478],{"class":33738},"            source.append(parts[",[24,43480,598],{"class":33778},[24,43482,43483],{"class":33738},"].split(",[24,43485,42182],{"class":40767},[24,43487,43211],{"class":40767},[24,43489,43490],{"class":33738},"))\n",[24,43492,43493,43496,43498,43500,43502,43504],{"class":33726,"line":36562},[24,43494,43495],{"class":33738},"            target.append(parts[",[24,43497,616],{"class":33778},[24,43499,43483],{"class":33738},[24,43501,42182],{"class":40767},[24,43503,43211],{"class":40767},[24,43505,43490],{"class":33738},[24,43507,43508,43510],{"class":33726,"line":40834},[24,43509,35997],{"class":33730},[24,43511,43512],{"class":33738}," source, target\n",[24,43514,43515],{"class":33726,"line":40840},[24,43516,34047],{"emptyLinePlaceholder":31432},[24,43518,43519,43521,43524,43526,43529,43531,43534,43536,43538,43540,43543],{"class":33726,"line":40846},[24,43520,33731],{"class":33730},[24,43522,43523],{"class":33734}," load_data_nmt",[24,43525,312],{"class":33738},[24,43527,43528],{"class":33741},"batch_size",[24,43530,33745],{"class":33738},[24,43532,43533],{"class":33741},"num_steps",[24,43535,33745],{"class":33738},[24,43537,43365],{"class":33741},[24,43539,918],{"class":33730},[24,43541,43542],{"class":33778},"600",[24,43544,33751],{"class":33738},[24,43546,43547],{"class":33726,"line":40873},[24,43548,43549],{"class":33756},"    \"\"\"返回翻译数据集的迭代器和词表\n",[24,43551,43552],{"class":33726,"line":40901},[24,43553,34047],{"emptyLinePlaceholder":31432},[24,43555,43556],{"class":33726,"line":40921},[24,43557,43558],{"class":33756},"    Defined in :numref:`subsec_mt_data_loading`\"\"\"\n",[24,43560,43561,43563,43565],{"class":33726,"line":40932},[24,43562,43232],{"class":33738},[24,43564,918],{"class":33730},[24,43566,43567],{"class":33738}," preprocess_nmt(read_data_nmt())\n",[24,43569,43570,43572,43574],{"class":33726,"line":40945},[24,43571,43389],{"class":33738},[24,43573,918],{"class":33730},[24,43575,43576],{"class":33738}," tokenize_nmt(text, num_examples)\n",[24,43578,43579,43582,43584,43587,43590,43592,43594],{"class":33726,"line":41448},[24,43580,43581],{"class":33738},"    src_vocab ",[24,43583,918],{"class":33730},[24,43585,43586],{"class":33738}," d2l.Vocab(source, ",[24,43588,43589],{"class":33794},"min_freq",[24,43591,918],{"class":33730},[24,43593,9241],{"class":33778},[24,43595,35139],{"class":33738},[24,43597,43598,43601,43603,43605,43607,43610,43612,43614,43616,43618,43620,43622,43624,43627,43629],{"class":33726,"line":41463},[24,43599,43600],{"class":33794},"                          reserved_tokens",[24,43602,918],{"class":33730},[24,43604,42653],{"class":33738},[24,43606,42182],{"class":40767},[24,43608,43609],{"class":40771},"\u003Cpad>",[24,43611,42182],{"class":40767},[24,43613,33745],{"class":33738},[24,43615,42182],{"class":40767},[24,43617,42754],{"class":40771},[24,43619,42182],{"class":40767},[24,43621,33745],{"class":33738},[24,43623,42182],{"class":40767},[24,43625,43626],{"class":40771},"\u003Ceos>",[24,43628,42182],{"class":40767},[24,43630,33855],{"class":33738},[24,43632,43633,43636,43638,43641,43643,43645,43647],{"class":33726,"line":41468},[24,43634,43635],{"class":33738},"    tgt_vocab ",[24,43637,918],{"class":33730},[24,43639,43640],{"class":33738}," d2l.Vocab(target, 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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":31432},"30st Jan 2026","/blogs-img/blog1.jpg",[43946,31430],"deep-learning","/blogs/transformer",{"title":31440,"description":43941},"blogs/1. 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