{"id":8167,"date":"2024-06-20T16:01:01","date_gmt":"2024-06-20T08:01:01","guid":{"rendered":""},"modified":"2024-06-20T16:01:01","modified_gmt":"2024-06-20T08:01:01","slug":"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention","status":"publish","type":"post","link":"https:\/\/mushiming.com\/8167.html","title":{"rendered":"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<h2>\u4e00\u3001Seq2Seq<\/h2>\n<h3>1.1 Seq2Seq(Encoder-Decoder)<\/h3>\n<ul>\n<li>\u7b80\u4ecb\uff1a\u4f7f\u7528Encoder\u5c06input\u7f16\u7801\u4e3a\u4e00\u4e2a<strong>\u56fa\u5b9a\u957f\u5ea6<\/strong>\u7684context\u5411\u91cf\uff0c\u4f7f\u7528Decoder\u5c06context\u89e3\u7801\u4e3aoutput\u3002input\u3001output\u957f\u5ea6\u4e0d\u4e00\u5b9a\u76f8\u540c\u3002<\/li>\n<li>\u5960\u57fa\u8bba\u6587\uff1aSequence to Sequence Learning with Neural Networks<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/e28759148cce41e7a0b51163a3f98db5.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<\/ul>\n<h3>1.2 Seq2Seq(Decoder\u8fc7\u7a0b)<\/h3>\n<ul>\n<li>\u89e3\u7801\u8fc7\u7a0b\uff1a\u6839\u636eEncoder\u83b7\u5f97\u4e0a\u4e0b\u6587\u5411\u91cfcontext\uff0c\u5728\u4ee5\u540e\u7684\u6bcf\u4e2a\u89e3\u7801\u7684\u65f6\u95f4\u6b65\uff0c\u90fd\u8981\u7528\u5230\u8fd9\u4e2a\u7edf\u4e00\u7684context\u3001\u4e0a\u4e00\u65f6\u95f4\u6b65\u7684\u8f93\u51fa\u3001\u5f53\u524d\u65f6\u95f4\u6b65\u7684\u9690\u85cf\u72b6\u6001\uff0c\u8fd93\u4e2a\u4fe1\u606f\u4f5c\u4e3a\u8f93\u5165\u8ba1\u7b97\u5f53\u524d\u65f6\u95f4\u6b65\u7684\u8f93\u51fa\u3002<br \/> <mark>\u4e0eAttention\u673a\u5236\u8fa8\u6790\uff1a\u666e\u901aSeq2Seq\u7684context\u8ba1\u7b97\u662f\u524d\u9762\u6240\u6709\u8f93\u5165\u7684\u7f16\u7801\uff0c\u4e5f\u5c31\u662f\u8bf4\u5728Decoder\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e00\u4e2a\u65f6\u95f4\u6b65\u7684context\u90fd\u662f\u76f8\u540c\u7684\uff0c\u4e5f\u5c31\u662f\u6240\u6709\u8f93\u5165\u90e8\u5206\u7684attention\u662f\u76f8\u540c\u7684\u3002\u5f15\u5165Attention\u673a\u5236\u540e\uff0cDecoder\u8fc7\u7a0b\u4e2d\u6bcf\u4e00\u4e2a\u65f6\u95f4\u6b65\u7684context\u90fd\u4f1a\u4e0d\u4e00\u6837\u4e86\uff0c\u4f1a\u5173\u6ce8\u5230\u8f93\u5165\u5e8f\u5217\u7684\u4e0d\u540c\u90e8\u5206\u3002<\/mark><\/li>\n<li>\u89e3\u7801\u65b9\u5f0f\uff1a\u8d2a\u5fc3\u6cd5\u3001beam search(k=1\u65f6\u9000\u5316\u4e3a\u8d2a\u5fc3\u6cd5)\u3002<\/li>\n<\/ul>\n<h3>1.3 Seq2Seq\u5b58\u5728\u95ee\u9898<\/h3>\n<ul>\n<li>\u5ffd\u7565\u4e86\u8f93\u5165\u5e8f\u5217\u7684\u957f\u5ea6\uff1a\u5f53\u8f93\u5165\u5e8f\u5217\u5f88\u957f\u65f6\uff0c\u6a21\u578b\u80fd\u529b\u6025\u5267\u4e0b\u964d\u3002<\/li>\n<li>\u7f3a\u5c11\u8f93\u5165\u5e8f\u5217\u7684\u533a\u5206\u5ea6\uff1a\u7f16\u7801\u6210\u56fa\u5b9a\u4e0a\u4e0b\u6587\u5411\u91cfcontext\u65f6\uff0c\u53e5\u5b50\u4e2d\u6bcf\u4e2a\u8bcd\u90fd\u8d4b\u4e88\u76f8\u540c\u7684\u6743\u91cd\uff0c\u6ca1\u6709\u533a\u5206\u5ea6\u3002<\/li>\n<\/ul>\n<h3>1.4 Seq2Seq\u6539\u8fdb<\/h3>\n<ul>\n<li>\u957f\u5e8f\u5217\u7684\u95ee\u9898\uff1a\u968f\u7740\u5e8f\u5217\u589e\u957f\uff0c\u53e5\u5b50\u8d8a\u524d\u9762\u7684\u4fe1\u606f\u4e22\u5931\u5c31\u8d8a\u4e25\u91cd\u3002\u6bd4\u5982\u4e00\u4e2a\u6e90\u5e8f\u5217\u6709100\u4e2a\u8bcd\uff0c\u89e3\u7801\u65f6\u76ee\u6807\u5e8f\u5217\u7684\u7b2c\u4e00\u4e2a\u8bcd\u5f88\u5927\u6982\u7387\u4e0a\u5c31\u548c\u6e90\u5e8f\u5217\u7684\u7b2c\u4e00\u4e2a\u8bcd\u76f8\u5bf9\u5e94\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u7b2c\u4e00\u6b65\u7684\u89e3\u7801\u8981\u8003\u8651\u5230100\u6b65\u4e4b\u524d\u7684\u4fe1\u606f\u3002<\/li>\n<li>\u6539\u8fdb\uff1a\u9006\u5e8f\u8f93\u5165(\u53cc\u5411\u5e8f\u5217)\u3001\u91cd\u590d\u5e8f\u5217\u8f93\u5165\u3001LSTM\/GRU\u3001Attention\u673a\u5236<\/li>\n<\/ul>\n<h2>\u4e8c\u3001Attention\u673a\u5236<\/h2>\n<h3>2.1 Attention\u673a\u5236\u4f5c\u7528<\/h3>\n<ul>\n<li>\u5e2e\u52a9\u6a21\u578b\u5bf9\u8f93\u5165\u5e8f\u5217\u7684\u6bcf\u90e8\u5206\u8d4b\u4e88\u4e0d\u540c\u7684\u6743\u91cd\uff0c\u4e5f\u5c31\u662f\u533a\u5206\u8f93\u5165\u7684\u4e0d\u540c\u90e8\u5206\u5bf9\u8f93\u51fa\u7684\u5f71\u54cd\u3002<\/li>\n<\/ul>\n<h3>2.2 Attention\u8ba1\u7b97\u8fc7\u7a0b<\/h3>\n<ul>\n<li>\u53c2\u8003\u6587\u7ae0\uff1a\u904d\u5730\u5f00\u82b1\u7684 Attention \uff0c\u4f60\u771f\u7684\u61c2\u5417\uff1f<\/li>\n<li>\u53ef\u4ee5\u628aAttention\u8ba1\u7b97\u8fc7\u7a0b\u62bd\u8c61\u4e3a\u4ee5\u4e0b3\u4e2a\u6b65\u9aa4\uff1a<br \/> 1\u3001<mark>\u8ba1\u7b97\u76f8\u4f3c\u6027<\/mark> score function\uff1a\u6253\u5206\u51fd\u6570\uff0c\u5ea6\u91cf\u8f93\u5165\u5e8f\u5217\u9690\u85cf\u72b6\u6001\u4e0e\u5f53\u524d\u89e3\u7801\u65f6\u95f4\u6b65\u7684\u9690\u85cf\u72b6\u6001\u7684\u76f8\u4f3c\u6027<br \/> 2\u3001<mark>\u5f52\u4e00\u5316<\/mark> alignment function\uff1a\u5bf9\u9f50\u51fd\u6570(\u901a\u5e38\u4f7f\u7528softmax\u5f52\u4e00\u5316)\uff0c\u5f97\u5230\u5f53\u524d\u89e3\u7801\u65f6\u95f4\u6b65\u7684\u8f93\u51fa\u5bf9\u5e94\u8f93\u5165\u5e8f\u5217\u9690\u85cf\u72b6\u6001\u7684\u6743\u91cd\uff0c\u603b\u548c\u4e3a1<br \/> 3\u3001<mark>\u5f97\u5230Attention<\/mark> context function\uff1a\u8f93\u5165\u7684\u9690\u85cf\u72b6\u6001\u4e0e\u5f53\u524d\u65f6\u523b\u7684\u6743\u91cd\u52a0\u6743\u6c42\u548c\uff0c\u5f97\u5230\u5f53\u524d\u89e3\u7801\u65f6\u95f4\u6b65\u7684context<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/5e42c8e7677d4502b2c566502ac29bdf.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<\/ul>\n<h2>\u4e09\u3001Attention\u79cd\u7c7b<\/h2>\n<h3>3.1 Bahdanau Attention\/Additive Attention<\/h3>\n<p>\u7531\u4e0a\u56fe\u6240\u793a\uff0c\u6e90\u5e8f\u5217\u957f\u5ea6\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> N N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault\">N<\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.61508em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span>\u9488\u5bf9\u7684\u662f\u76ee\u6807\u5e8f\u5217\u89e3\u7801\u8fc7\u7a0b\u4e2d\u7684\u6bcf\u4e2a\u65f6\u95f4\u6b65\u3002<br \/> 1\u3001score function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> e t , i = a ( s t \u2212 1 , h i ) = v a T t a n h ( W a \u2217 s t \u2212 1 + U a \u2217 h i ) e_{t,i}=a(s_{t-1,h_i})=v_a^Ttanh(W_a*s_{t-1}+U_a*h_i) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328086em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.09133em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -2.453em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault mtight\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.13889em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2217<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.791661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10903em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2217<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u8ba1\u7b97\u76f8\u4f3c\u7a0b\u5ea6<br \/> 2\u3001alignment function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b1 t , i = e x p ( e t , i ) \u2211 k = 1 N e x p ( e t , k ) \\alpha_{t,i}=\\frac{exp(e_{t,i})}{\\sum_{k=1}^{N}{exp(e_{t,k})}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0037em;\" class=\"mord mathdefault\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.0037em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.68699em; vertical-align: -0.654672em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.03232em;\"><span class=\"\" style=\"top: -2.57034em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mop op-symbol small-op mtight\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.885236em;\"><span class=\"\" style=\"top: -2.17856em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.89714em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault mtight\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.321439em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace mtight\" style=\"margin-right: 0.195167em;\"><\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">x<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.34877em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.290114em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.50732em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">x<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328086em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.281886em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.654672em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br \/> 3\u3001context function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c t = \u2211 i N \u03b1 t , i h i c_t=\\sum_i^N\\alpha_{t,i}h_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.28094em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.981231em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault mtight\">N<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0037em;\" class=\"mord mathdefault\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.0037em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u8fd9\u91cc\u53ef\u4ee5\u548c\u4f20\u7edfseq2seq\u67b6\u6784\u8fdb\u884c\u5bf9\u6bd4\uff0c\u5982\u679c\u4e0d\u5f15\u5165Attention\u673a\u5236\uff0c\u5219<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y t y_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6761\u4ef6\u6982\u7387\u516c\u5f0f\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( y t \u2223 y 1 , . . . , y t \u2212 1 , c ) = g ( y t \u2212 1 , s t , c ) p(y_t|y_1,...,y_{t-1},c)=g(y_{t-1},s_t,c) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">c<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">c<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u5f15\u5165Attention\u4e4b\u540e\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( y t \u2223 y 1 , . . . , y t \u2212 1 , X ) = g ( y t \u2212 1 , s t , c t ) p(y_t|y_1,...,y_{t-1},X)=g(y_{t-1},s_t,c_t) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u4e5f\u5c31\u662f\u89e3\u7801\u8fc7\u7a0b\u4e2d\u6bcf\u4e2a\u65f6\u95f4\u6b65\u7684context\u90fd\u4e0d\u4e00\u6837\u3002<\/p>\n<h3>3.2 Loung Attention\/Multiplication Attention<\/h3>\n<p>\u7531\u4e0a\u56fe\u6240\u793a\uff0c\u6e90\u5e8f\u5217\u957f\u5ea6\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> N N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault\">N<\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> t t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.61508em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span>\u9488\u5bf9\u7684\u662f\u76ee\u6807\u5e8f\u5217\u89e3\u7801\u8fc7\u7a0b\u4e2d\u7684\u6bcf\u4e2a\u65f6\u95f4\u6b65\u3002<br \/> 1\u3001score function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> e t , i = a ( s t \u2212 1 , h i ) = s t \u2212 1 T W a h i e_{t,i}=a(s_{t-1,h_i})=s_{t-1}^TW_ah_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328086em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.14777em; vertical-align: -0.306439em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -2.45189em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault mtight\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.306439em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.13889em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> 2\u3001alignment function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b1 t , i = e x p ( e t , i ) \u2211 k = 1 N e x p ( e t , k ) \\alpha_{t,i}=\\frac{exp(e_{t,i})}{\\sum_{k=1}^{N}{exp(e_{t,k})}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0037em;\" class=\"mord mathdefault\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.0037em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.68699em; vertical-align: -0.654672em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.03232em;\"><span class=\"\" style=\"top: -2.57034em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mop op-symbol small-op mtight\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.885236em;\"><span class=\"\" style=\"top: -2.17856em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.89714em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault mtight\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.321439em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace mtight\" style=\"margin-right: 0.195167em;\"><\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">x<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.34877em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.290114em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.50732em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">x<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328086em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.281886em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.654672em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br \/> 3\u3001context function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c t = \u2211 i N \u03b1 t , i h i c_t=\\sum_i^N\\alpha_{t,i}h_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.28094em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.981231em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault mtight\">N<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0037em;\" class=\"mord mathdefault\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.0037em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u52a0\u6027\u6ce8\u610f\u529b\u548c\u4e58\u6cd5\u6ce8\u610f\u529b\u5728\u590d\u6742\u5ea6\u4e0a\u662f\u76f8\u4f3c\u7684\uff0c\u4f46\u662f\u4e58\u6cd5\u6ce8\u610f\u529b\u5728\u5b9e\u8df5\u4e2d\u5f80\u5f80\u8981\u66f4\u5feb\u901f\u3001\u5177\u6709\u66f4\u9ad8\u6548\u7684\u5b58\u50a8\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u4f7f\u7528\u77e9\u9635\u64cd\u4f5c\u66f4\u9ad8\u6548\u5730\u5b9e\u73b0\u3002<\/p>\n<h3>3.3 Scaled dot-product Attention<\/h3>\n<p>Transformer\u91c7\u7528\u8fd9\u79cd\u65b9\u5f0f\u6784\u5efaSelf-Attention\u6a21\u5757\u3002KV\u4ee3\u8868Key-Value\uff0c\u4e0d\u540c\u7684Key\u5bf9\u5e94\u4e0d\u540c\u7684Value\u3002Q\u4e3aQuery\u5411\u91cf\uff0cQuery\u4e0e\u6240\u6709\u7684Key\u5ea6\u91cf\u4e00\u4e2a\u76f8\u4f3c\u6027\uff0c\u627e\u5230\u548c\u5b83\u6700\u76f8\u4f3c\u7684Key\uff0c\u4eff\u7167\u8fd9\u4e2aKey\u5bf9\u5e94\u7684Value\uff0c\u4ea7\u751f\u8fd9\u4e2aQuery\u5bf9\u5e94\u7684Value\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/86759a4b00ed4932827a6f1da72dc6f7.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >Scaled dot-product Attention\u8ba1\u7b97\u516c\u5f0f\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> s o f t m a x ( Q K T i n _ d i m ) V softmax(\\frac{QK^T}{\\sqrt {in\\_dim}})V <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.64833em; vertical-align: -1.13em;\"><\/span><span class=\"mord mathdefault\">s<\/span><span class=\"mord mathdefault\">o<\/span><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.51833em;\"><span class=\"\" style=\"top: -2.23278em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.87722em;\"><span class=\"svg-align\" style=\"top: -3.2em;\"><span class=\"pstrut\" style=\"height: 3.2em;\"><\/span><span class=\"mord\" style=\"padding-left: 1em;\"><span class=\"mord mathdefault\">i<\/span><span class=\"mord mathdefault\">n<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord\">_<\/span><span class=\"mord mathdefault\">d<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -2.83722em;\"><span class=\"pstrut\" style=\"height: 3.2em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em; height: 1.28em;\"><br \/>\n                   <svg width=\"400em\" height=\"1.28em\" viewbox=\"0 0 400000 1296\" preserveaspectratio=\"xMinYMin slice\"> \n                    <path d=\"M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167,\n158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067\nc4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,\n175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71\nc-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,\n-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26\ns76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z\"><\/path> \n                   <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.36278em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">Q<\/span><span class=\"mord\"><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.13em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">V<\/span><\/span><\/span><\/span><\/span><\/span>\u4e5f\u53ef\u4ee5\u7c7b\u4f3c\u5730\u62c6\u6210\u4ee5\u4e0b\u4e09\u6b65\uff1a<br \/> \u5148\u8981\u660e\u786e\u4e00\u4e0b\u6e90\u5e8f\u5217\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 , x 2 , . . . , x m x_1,x_2,...,x_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u800c\u76ee\u6807\u5e8f\u5217\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y 1 , y 2 , . . . , y t , . . . , y n y_1,y_2,...,y_t,...,y_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<br \/> \u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Q = ( q 1 , q 2 , . . . , q m ) , 1 \u2264 i \u2264 m , 1 \u2264 j \u2264 n Q=(q_1,q_2,...,q_m),1\u2264i\u2264m,1\u2264j\u2264n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.79549em; vertical-align: -0.13597em;\"><\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault\">j<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">n<\/span><\/span><\/span><\/span><\/span><br \/> 1\u3001score function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> e i , j = a ( q i , k j ) e_{i,j}=a(q_i,k_j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br \/> 2\u3001alignment function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b1 i , j = e x p ( e i , j ) \u2211 k = 1 n e x p ( e i , k ) \\alpha_{i,j}=\\frac{exp(e_{i,j})}{\\sum_{k=1}^{n}{exp(e_{i,k})}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0037em;\" class=\"mord mathdefault\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.0037em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.60233em; vertical-align: -0.570007em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.03232em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mop op-symbol small-op mtight\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.704686em;\"><span class=\"\" style=\"top: -2.17856em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.89714em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.321439em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace mtight\" style=\"margin-right: 0.195167em;\"><\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">x<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em;\"><span class=\"\" style=\"top: -2.34877em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.290114em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.50732em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">x<\/span><span class=\"mord mathdefault mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328086em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.281886em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.570007em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br \/> 3\u3001context function\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c i = \u2211 k = 1 n \u03b1 i , k v k c_i=\\sum_{k=1}^n\\alpha_{i,k}v_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0037em;\" class=\"mord mathdefault\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.0037em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u9996\u5148\u5b8f\u89c2\u4e0a\u4ed6\u4e5f\u662f<mark>\u8ba1\u7b97\u76f8\u4f3c\u6027\u3001\u5f52\u4e00\u5316\u3001Attention\u8ba1\u7b97<\/mark>\u8fd9\u4e09\u4e2a\u6b65\u9aa4\u3002<br \/> \u4f46\u548c\u524d\u9762\u4f20\u7edfAttention\u8ba1\u7b97\u6709\u4e00\u4e9b\u4e0d\u540c\uff0c\u4f46\u4e5f\u53ea\u662f\u8ba1\u7b97\u7684\u5148\u540e\u987a\u5e8f\u4e0d\u540c\uff0c\u5b8f\u89c2\u4e0a\u90fd\u662f\u4e00\u56de\u4e8b\u3002<\/p>\n<ul>\n<li>\u4f20\u7edfAttention\uff1a\u56fa\u5b9a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y t y_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,\u5c06\u5b83\u4e0e\u6e90\u5e8f\u5217\u6240\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 , x 2 , . . . , x m x_1,x_2,...,x_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u505a\u76f8\u4f3c\u6027\u8ba1\u7b97\uff0c\u8fd9\u91cc\u7528\u7684\u662f\u5bf9\u5e94\u7684\u9690\u85cf\u72b6\u6001\u3002<mark>\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u91cc\u4f60\u8981\u8ba1\u7b97\u591a\u5c11\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c t c_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1f\u662f\u4e0d\u662f\u4f60\u7684\u76ee\u6807\u5e8f\u5217\u6709\u591a\u5c11\u4e2a\u89e3\u7801\u7684\u65f6\u95f4\u6b65\uff1f\u7406\u60f3\u60c5\u51b5\u5982\u679c\u4f60\u90fd\u7ffb\u8bd1\u5bf9\u4e86\uff0c\u90a3\u4f60\u9700\u8981<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u65f6\u95f4\u6b65\u7684\u4e0a\u4e0b\u6587\u5411\u91cf\u3002<\/mark><\/li>\n<li>Scaled dot-product Attention\uff1a\u56fa\u5b9a\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x i x_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5c06\u5b83\u4e0e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y 1 , y 2 , . . . , y n y_1,y_2,...,y_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u505a\u76f8\u4f3c\u6027\u8ba1\u7b97\uff0c\u8fd9\u91cc\u7528\u5230\u7684\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Q K V QKV <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">Q<\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">K<\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">V<\/span><\/span><\/span><\/span><\/span>\u77e9\u9635\u3002<mark>\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u91cc\u4f60\u8ba1\u7b97\u51fa\u6765\u4e86\u591a\u5c11\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c t c_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1f\u662f\u4e0d\u662f\u6e90\u5e8f\u5217\u6709\u591a\u957f\uff0c\u4f60\u5c31\u8ba1\u7b97\u51fa\u4e86\u51e0\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> c t c_t <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1f\u4e5f\u5c31\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">m<\/span><\/span><\/span><\/span><\/span>\u4e2a\u4e0a\u4e0b\u6587\u5411\u91cf\u3002<\/mark><\/li>\n<\/ul>\n<h3>3.4 Self-Attention<\/h3>\n<p>Self-Attention\u5c31\u662fScaled dot-product Attention\u3002\u533a\u522b\u5c31\u662f\u6b64\u65f6\u7684<mark>\u6e90\u5e8f\u5217\u5c31\u662f\u76ee\u6807\u5e8f\u5217<\/mark>\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/b3b9a7e80e52440ebb9e443b57e69e5f.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u518d\u6b21\u660e\u786e\u4e00\u4e0b\u6e90\u5e8f\u5217\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 , x 2 , . . . , x m x_1,x_2,...,x_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u800c\u76ee\u6807\u5e8f\u5217\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y 1 , y 2 , . . . , y t , . . . , y n y_1,y_2,...,y_t,...,y_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.280556em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<ul>\n<li>Scaled dot-product Attention\uff1a\u6e90\u5e8f\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 , x 2 , . . . , x m x_1,x_2,...,x_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u90a3\u4e48\u5bf9\u5e94\u7684Q\u77e9\u9635\u5c31\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> q 1 , q 2 , . . . , q m q_1,q_2,...,q_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u76ee\u6807\u5e8f\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y 1 , y 2 , . . . , y n y_1,y_2,...,y_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u90a3\u4e48\u5bf9\u5e94\u7684K\u77e9\u9635\u3001V\u77e9\u9635\u957f\u5ea6\u90fd\u662f\u76f8\u540c\u7684\uff0c\u4e5f\u5c31\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k 1 , k 2 , . . . , k n k_1,k_2,...,k_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4ee5\u53ca<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> v 1 , v 2 , . . . , v n v_1,v_2,...,v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>Self-Attention\uff1a\u5e8f\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x 1 , x 2 , . . . , x m x_1,x_2,...,x_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u65e2\u662f\u6e90\u5e8f\u5217\u53c8\u662f\u76ee\u6807\u5e8f\u5217\uff0c\u56e0\u4e3a\u662f\u81ea\u5df1\u548c\u81ea\u5df1\u505aAttention\u7684\u8ba1\u7b97\u3002\u90a3\u4e48\u5bf9\u5e94\u7684Q\u77e9\u9635\u3001K\u77e9\u9635\u3001V\u77e9\u9635\u957f\u5ea6\u90fd\u662f\u76f8\u540c\u7684\uff0c\u4e5f\u5c31\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> q 1 , q 2 , . . . , q m q_1,q_2,...,q_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k 1 , k 2 , . . . , k m k_1,k_2,...,k_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03148em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> v 1 , v 2 , . . . , v m v_1,v_2,...,v_m <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u4e8c\u8005\u533a\u522b\uff1aScaled dot-product Attention\u3001Self-Attention\u8fa8\u6790<\/li>\n<\/ul>\n<h3>3.5 Multi-head Self-Attention<\/h3>\n<p>\u5c31\u662f\u5c06Self-Attention\u4e2d\u914d\u5957\u7684QKV\u6620\u5c04\u5230\u4e86\u4e0d\u540c\u7684\u5b50\u7a7a\u95f4\u5f53\u4e2d\u3002\u5047\u8bbehead=2\uff0c\u8ba1\u7b97\u65f6\u6bcf\u4e2ahead\u4e4b\u95f4\u7684\u6570\u636e\u72ec\u7acb\uff0c\u4e0d\u4ea7\u751f\u4ea4\u53c9\u3002\u6700\u7ec8<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> b i b_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u8f93\u51fa\u9700\u8981\u4e00\u4e2a\u6743\u91cd\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> W O W^O <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.841331em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault mtight\">O<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6a21\u578b\u5b66\u4e60\u5f97\u5230\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/d1fb4ca08e4f4ba99afbfd29f42f850d.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention (https:\/\/mushiming.com\/)  \u7b2c5\u5f20\" title=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention  \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5f53head=h\u65f6\uff0c\u6700\u7ec8Output\u7531h\u4e2ahead\u4ea7\u751f\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> O u t p u t i Output_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">O<\/span><span class=\"mord mathdefault\">u<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mord mathdefault\">u<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e\u6743\u91cd\u77e9\u9635\u76f8\u4e58\u5f97\u5230\uff1a<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/afcc7584f8894606ade73fb271321f91.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention (https:\/\/mushiming.com\/)  \u7b2c6\u5f20\" title=\"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention  \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<ul>\n<li>\u4e8c\u8005\u8fa8\u6790\uff1aSelf-Attention\u539f\u7406\u3001Multi-head Self-Attention\u539f\u7406\u53caPytorch\u5b9e\u73b0<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"Attention\u7684\u6c47\u603b\u4e0e\u8fa8\u6790_Additive\u3001Multiplication\u3001Scaled dot-product\u3001Self Attention\u3001Multi-head Self-Attention\u4e00\u3001Seq2...","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/8167"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=8167"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/8167\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=8167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=8167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=8167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}