{"id":55193,"date":"2025-08-13T19:04:28","date_gmt":"2025-08-13T11:04:28","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/55193.html"},"modified":"2025-08-13T19:04:28","modified_gmt":"2025-08-13T11:04:28","slug":"%e3%80%90%e8%ae%ba%e6%96%87%e9%98%85%e8%af%bb%e3%80%91bevformer%e8%ae%ba%e6%96%87%e8%a7%a3%e6%9e%90%e5%8f%8atemporal-self-attention%e3%80%81spatial-cross-attention%e6%b3%a8%e6%84%8f%e5%8a%9b%e6%9c%ba","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/55193.html","title":{"rendered":"\u3010\u8bba\u6587\u9605\u8bfb\u3011BEVFormer\u8bba\u6587\u89e3\u6790\u53caTemporal Self-Attention\u3001Spatial Cross-Attention\u6ce8\u610f\u529b\u673a\u5236\u8be6\u89e3\u53ca\u4ee3\u7801\u793a\u4f8b"},"content":{"rendered":"<h4>BEVFormer: Learning Bird\u2019s-Eye-ViewRepresentation from Multi-Camera Images via Spatiotemporal Transformers|Temporal Self-Attention\u3001Spatial Cross-Attention\u6ce8\u610f\u529b\u673a\u5236\u8be6\u89e3<\/h4>\n<p>BEVFormer&#xff08;Bird\u2019s-Eye-View Former&#xff09;\u662f\u4e00\u79cd\u5148\u8fdb\u7684\u8ba1\u7b97\u673a\u89c6\u89c9\u6a21\u578b&#xff0c;\u65e8\u5728\u4ece\u591a\u6444\u50cf\u5934\u56fe\u50cf\u5e8f\u5217\u4e2d\u751f\u6210\u9e1f\u77b0\u56fe&#xff08;BEV&#xff09;\u8868\u793a\u3002\u5b83\u901a\u8fc7\u65f6\u7a7a\u53d8\u6362\u5668\u878d\u5408\u591a\u89c6\u89d2\u548c\u65f6\u95f4\u4fe1\u606f&#xff0c;\u5b9e\u73b0\u9ad8\u6548\u76843D\u573a\u666f\u7406\u89e3\u3002\u5e7f\u6cdb\u5e94\u7528\u4e8e\u81ea\u52a8\u9a7e\u9a76\u7b49\u9886\u57df\u3002\u4ee5\u4e0b\u4ece\u6a21\u578b\u7ed3\u6784\u3001\u521b\u65b0\u70b9\u3001\u8bad\u7ec3\u65b9\u6cd5\u548c\u6a21\u578b\u5b9e\u9a8c\u56db\u4e2a\u65b9\u9762\u8fdb\u884c\u8be6\u7ec6\u603b\u7ed3\u3002<\/p>\n<h5>\u4e00. \u6a21\u578b\u7ed3\u6784<\/h5>\n<p>BEVFormer\u7684\u6574\u4f53\u67b6\u6784\u5206\u4e3a\u8f93\u5165\u5c42\u3001\u7279\u5f81\u63d0\u53d6\u5c42\u3001\u65f6\u7a7a\u53d8\u6362\u5668\u5c42\u548c\u8f93\u51fa\u5c42&#xff0c;\u5904\u7406\u591a\u6444\u50cf\u5934\u56fe\u50cf\u5e8f\u5217&#xff08;\u59826\u4e2a\u6444\u50cf\u5934&#xff09;\u4ee5\u751f\u6210BEV\u7279\u5f81\u56fe\u3002<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250813110425-689c713953c6e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li>\u8f93\u5165\u5c42&#xff1a;\u8f93\u5165\u4e3a\u591a\u6444\u50cf\u5934\u56fe\u50cf\u5e8f\u5217&#xff0c;\u8bb0\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">I&#061;{Itc\u2223c\u2208{1,2,\u2026,C},t\u2208{1,2,\u2026,T}}I &#061; \\\\{I_t^c | c \\\\in \\\\{1, 2, \\\\dots, C\\\\}, t \\\\in \\\\{1, 2, \\\\dots, T\\\\}\\\\}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0785em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/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 class=\"mord mathnormal mtight\">c<\/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\">\u2223<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mclose\">}}<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>\u662f\u6444\u50cf\u5934\u6570\u91cf&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>\u662f\u65f6\u95f4\u6b65\u957f\u3002\u4f8b\u5982&#xff0c;\u5728nuScenes\u6570\u636e\u96c6\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;6C&#061;6<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>\u901a\u5e38\u53d63-5\u5e27\u3002<\/li>\n<li>\u7279\u5f81\u63d0\u53d6\u5c42&#xff1a;\u4f7f\u7528\u5377\u79ef\u795e\u7ecf\u7f51\u7edc&#xff08;CNN&#xff09;backbone&#xff08;\u5982ResNet\u6216EfficientNet&#xff09;\u63d0\u53d6\u6bcf\u5e27\u56fe\u50cf\u76842D\u7279\u5f81\u3002\u7279\u5f81\u56fe\u8bb0\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F2DcF_{2D}^c<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9587em;vertical-align: -0.2753em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -2.4247em;margin-left: -0.1389em;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 mtight\">2<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/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 class=\"mord mathnormal mtight\">c<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2753em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7ef4\u5ea6\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">H\u00d7W\u00d7DH \\\\times W \\\\times D<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DD<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>\u662f\u7279\u5f81\u7ef4\u5ea6\u3002<\/li>\n<li>\u65f6\u7a7a\u53d8\u6362\u5668\u5c42&#xff1a;\u8fd9\u662f\u6838\u5fc3\u6a21\u5757&#xff0c;\u5305\u62ec\u7a7a\u95f4\u4ea4\u53c9\u6ce8\u610f\u529b\u548c\u65f6\u95f4\u81ea\u6ce8\u610f\u529b\u673a\u5236\u3002\u7a7a\u95f4\u4ea4\u53c9\u6ce8\u610f\u529b\u878d\u5408\u591a\u6444\u50cf\u5934\u89c6\u89d2&#xff0c;\u65f6\u95f4\u81ea\u6ce8\u610f\u529b\u5efa\u6a21\u65f6\u95f4\u4f9d\u8d56\u6027\u3002\u516c\u5f0f\u5982\u4e0b&#xff1a;\n<ul>\n<li>\u7a7a\u95f4\u4ea4\u53c9\u6ce8\u610f\u529b&#xff1a;\u5bf9\u4e8e\u6bcf\u4e2aBEV\u7f51\u683c\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u67e5\u8be2\u6240\u6709\u6444\u50cf\u5934\u7279\u5f81&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Attention(Q,K,V)&#061;softmax(QKTdk)V<br \/>\n\\\\text{Attention}(Q, K, V) &#061; \\\\text{softmax}\\\\left(\\\\frac{QK^T}{\\\\sqrt{d_k}}\\\\right)V<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attention<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4684em;vertical-align: -0.95em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/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: 1.5183em\"><span class=\"\" style=\"top: -2.2528em\"><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: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\" style=\"margin-right: 0.0315em\">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 class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><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 mathnormal\">Q<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">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: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">QQ<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span>\u662fBEV\u67e5\u8be2&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">KK<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">VV<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span>\u662f2D\u7279\u5f81\u56fe\u7684\u952e\u548c\u503c\u3002<\/li>\n<li>\u65f6\u95f4\u81ea\u6ce8\u610f\u529b&#xff1a;\u5728\u65f6\u95f4\u7ef4\u5ea6\u4e0a\u805a\u5408\u4fe1\u606f&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Attention(Qt,Kt\u22121,Vt\u22121)&#061;softmax(QtKt\u22121Tdk)Vt\u22121<br \/>\n\\\\text{Attention}(Q_t, K_{t-1}, V_{t-1}) &#061; \\\\text{softmax}\\\\left(\\\\frac{Q_t K_{t-1}^T}{\\\\sqrt{d_k}}\\\\right)V_{t-1}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attention<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><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 mathnormal 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: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;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 mathnormal 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: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;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 mathnormal 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: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4878em;vertical-align: -0.95em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/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: 1.5378em\"><span class=\"\" style=\"top: -2.2528em\"><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: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\" style=\"margin-right: 0.0315em\">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 class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><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: -3.6964em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><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 mathnormal 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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0715em;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 mathnormal 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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3064em\"><span class=\"\"><\/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: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;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 mathnormal 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: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u8fd9\u5141\u8bb8\u6a21\u578b\u4ece\u5386\u53f2\u5e27\u4e2d\u5b66\u4e60\u8fd0\u52a8\u4fe1\u606f\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u8f93\u51fa\u5c42&#xff1a;\u751f\u6210BEV\u7279\u5f81\u56fe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">FbevF_{bev}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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 mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/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>&#xff0c;\u7ef4\u5ea6\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Hbev\u00d7Wbev\u00d7DbevH_{bev} \\\\times W_{bev} \\\\times D_{bev}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0813em;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 mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/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: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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 mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/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: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;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 mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/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\u8be5\u7279\u5f81\u56fe\u53ef\u76f4\u63a5\u7528\u4e8e\u4e0b\u6e38\u4efb\u52a1&#xff0c;\u59823D\u76ee\u6807\u68c0\u6d4b\u6216\u5206\u5272\u3002<\/li>\n<\/ul>\n<p>\u6574\u4e2a\u6a21\u578b\u662f\u7aef\u5230\u7aef\u7684&#xff0c;\u8f93\u5165\u56fe\u50cf\u5e8f\u5217&#xff0c;\u8f93\u51faBEV\u8868\u793a&#xff0c;\u4e2d\u95f4\u901a\u8fc7\u591a\u5c42\u53d8\u6362\u5668\u5806\u53e0\u5b9e\u73b0\u9ad8\u6548\u878d\u5408\u3002<\/p>\n<h5>\u4e8c. \u521b\u65b0\u70b9\u8be6\u89e3&#xff1a;Temporal Self-Attention \u4e0e Spatial Cross-Attention \u6ce8\u610f\u529b\u673a\u5236<\/h5>\n<p>\u6ce8\u610f\u529b\u673a\u5236\u662f\u6df1\u5ea6\u5b66\u4e60\u4e2d\u5904\u7406\u5e8f\u5217\u6570\u636e\u7684\u5173\u952e\u6280\u672f&#xff0c;\u901a\u8fc7\u8ba1\u7b97\u8f93\u5165\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u6743\u91cd&#xff0c;\u5b9e\u73b0\u52a8\u6001\u7279\u5f81\u805a\u7126\u3002\u9010\u6b65\u89e3\u91ca Temporal Self-Attention \u548c Spatial Cross-Attention \u7684\u539f\u7406\u3001\u6570\u5b66\u8868\u8fbe\u548c\u5e94\u7528\u573a\u666f\u3002<\/p>\n<h6>1&#xff09; \u6ce8\u610f\u529b\u673a\u5236\u57fa\u7840<\/h6>\n<p>\u6ce8\u610f\u529b\u673a\u5236\u7684\u6838\u5fc3\u662f\u8ba1\u7b97\u67e5\u8be2&#xff08;Query&#xff09;\u3001\u952e&#xff08;Key&#xff09;\u548c\u503c&#xff08;Value&#xff09;\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6&#xff0c;\u751f\u6210\u52a0\u6743\u8f93\u51fa\u3002\u901a\u7528\u516c\u5f0f\u4e3a&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Attention(Q,K,V)&#061;softmax(QKTdk)V<br \/>\n\\\\text{Attention}(Q, K, V) &#061; \\\\text{softmax}\\\\left(\\\\frac{QK^T}{\\\\sqrt{d_k}}\\\\right)V<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attention<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4684em;vertical-align: -0.95em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/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: 1.5183em\"><span class=\"\" style=\"top: -2.2528em\"><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: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\" style=\"margin-right: 0.0315em\">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 class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><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 mathnormal\">Q<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">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: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Q\u2208Rn\u00d7dkQ \\\\in \\\\mathbb{R}^{n \\\\times d_k}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u67e5\u8be2\u77e9\u9635\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">K\u2208Rm\u00d7dkK \\\\in \\\\mathbb{R}^{m \\\\times d_k}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u952e\u77e9\u9635\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">V\u2208Rm\u00d7dvV \\\\in \\\\mathbb{R}^{m \\\\times d_v}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/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><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u503c\u77e9\u9635\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dkd_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\" style=\"margin-right: 0.0315em\">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> \u662f\u952e\u7684\u7ef4\u5ea6&#xff0c;\u7528\u4e8e\u7f29\u653e\u70b9\u79ef\u9632\u6b62\u68af\u5ea6\u7206\u70b8\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">softmax\\\\text{softmax}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><\/span><\/span><\/span><\/span> \u51fd\u6570\u786e\u4fdd\u6743\u91cd\u548c\u4e3a 1\u3002<\/li>\n<\/ul>\n<p>Temporal Self-Attention \u548c Spatial Cross-Attention \u662f\u8be5\u673a\u5236\u7684\u53d8\u4f53&#xff0c;\u5206\u522b\u9488\u5bf9\u65f6\u95f4\u548c\u7a7a\u95f4\u7ef4\u5ea6\u4f18\u5316\u3002<\/p>\n<h6>2&#xff09; Temporal Self-Attention \u8be6\u89e3<\/h6>\n<p>\u5b9a\u4e49&#xff1a;Temporal Self-Attention \u662f\u4e00\u79cd\u81ea\u6ce8\u610f\u529b\u673a\u5236&#xff0c;\u4e13\u6ce8\u4e8e\u65f6\u95f4\u5e8f\u5217\u6570\u636e&#xff08;\u5982\u89c6\u9891\u5e27\u3001\u4f20\u611f\u5668\u8bfb\u6570&#xff09;\u3002\u5b83\u5728\u540c\u4e00\u5e8f\u5217\u7684\u65f6\u95f4\u6b65\u4e4b\u95f4\u8ba1\u7b97\u6ce8\u610f\u529b&#xff0c;\u6355\u6349\u957f\u671f\u4f9d\u8d56\u5173\u7cfb&#xff0c;\u5ffd\u7565\u7a7a\u95f4\u4f4d\u7f6e\u4fe1\u606f\u3002<\/p>\n<p>\u6570\u5b66\u539f\u7406&#xff1a;<\/p>\n<ul>\n<li>\u8f93\u5165\u5e8f\u5217&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">X\u2208RT\u00d7dX \\\\in \\\\mathbb{R}^{T \\\\times d}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u4e3a\u65f6\u95f4\u6b65\u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dd<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7279\u5f81\u7ef4\u5ea6\u3002<\/li>\n<li>\u901a\u8fc7\u53ef\u5b66\u4e60\u6743\u91cd\u77e9\u9635\u751f\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Q,K,VQ, K, V<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span>&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Q&#061;XWQ,K&#061;XWK,V&#061;XWV<br \/>\nQ &#061; X W^Q, \\\\quad K &#061; X W^K, \\\\quad V &#061; X W^V<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0858em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0858em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8913em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">WQ,WK\u2208Rd\u00d7dkW^Q, W^K \\\\in \\\\mathbb{R}^{d \\\\times d_k}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0358em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">WV\u2208Rd\u00d7dvW^V \\\\in \\\\mathbb{R}^{d \\\\times d_v}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8804em;vertical-align: -0.0391em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/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><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u6ce8\u610f\u529b\u8ba1\u7b97&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Attention(Q,K,V)&#061;softmax(QKTdk)V<br \/>\n\\\\text{Attention}(Q, K, V) &#061; \\\\text{softmax}\\\\left(\\\\frac{QK^T}{\\\\sqrt{d_k}}\\\\right)V<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attention<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4684em;vertical-align: -0.95em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/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: 1.5183em\"><span class=\"\" style=\"top: -2.2528em\"><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: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\" style=\"margin-right: 0.0315em\">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 class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><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 mathnormal\">Q<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">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: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O\u2208RT\u00d7dvO \\\\in \\\\mathbb{R}^{T \\\\times d_v}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/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><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u4e2a\u65f6\u95f4\u6b65\u7684\u503c\u4e3a\u5176\u4ed6\u65f6\u95f4\u6b65\u7684\u52a0\u6743\u548c\u3002<\/li>\n<li>\u793a\u4f8b&#xff1a;\u5bf9\u4e8e\u65f6\u95f4\u6b65 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">tt<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">oto_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><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 mathnormal 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> \u8ba1\u7b97\u4e3a&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">ot&#061;\u2211j&#061;1T\u03b1tjvj,\u03b1tj&#061;exp\u2061(qt\u22c5kjdk)\u2211k&#061;1Texp\u2061(qt\u22c5kkdk)<br \/>\no_t &#061; \\\\sum_{j&#061;1}^{T} \\\\alpha_{tj} v_j, \\\\quad \\\\alpha_{tj} &#061; \\\\frac{\\\\exp\\\\left(\\\\frac{q_t \\\\cdot k_j}{\\\\sqrt{d_k}}\\\\right)}{\\\\sum_{k&#061;1}^{T} \\\\exp\\\\left(\\\\frac{q_t \\\\cdot k_k}{\\\\sqrt{d_k}}\\\\right)}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><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 mathnormal 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: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.2421em;vertical-align: -1.4138em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4138em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal mtight\">t<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal mtight\">t<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.88em;vertical-align: -1.69em\"><\/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: 2.19em\"><span class=\"\" style=\"top: -2.11em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;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 mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/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: 0.9322em\"><span class=\"\" style=\"top: -2.5864em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8622em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8222em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1778em\"><span class=\"\"><\/span><\/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: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/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 class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/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: -2.3488em;margin-left: -0.0315em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><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: 0.538em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.38em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -4.19em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"mord\"><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/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: 0.9934em\"><span class=\"\" style=\"top: -2.5864em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8622em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8222em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1778em\"><span class=\"\"><\/span><\/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: -3.5073em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/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 class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0315em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2819em\"><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: 0.538em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b1tj\\\\alpha_{tj}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal mtight\">t<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u65f6\u95f4\u6b65 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">tt<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">jj<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u7684\u6ce8\u610f\u529b\u6743\u91cd&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">qtq_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal 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> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kjk_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0315em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">QQ<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">KK<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span> \u7684\u884c\u5411\u91cf\u3002<\/li>\n<\/ul>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u9ad8\u6548\u5904\u7406\u957f\u5e8f\u5217&#xff0c;\u6355\u6349\u65f6\u95f4\u52a8\u6001&#xff08;\u5982\u89c6\u9891\u4e2d\u7684\u8fd0\u52a8\u6a21\u5f0f&#xff09;\u3002<\/li>\n<li>\u7f3a\u70b9&#xff1a;\u8ba1\u7b97\u590d\u6742\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(T2)O(T^2)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><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 class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5bf9\u957f\u5e8f\u5217\u53ef\u80fd\u6602\u8d35\u3002<\/li>\n<li>\u5e94\u7528\u573a\u666f&#xff1a;\u89c6\u9891\u52a8\u4f5c\u8bc6\u522b&#xff08;\u5206\u6790\u5e27\u95f4\u5173\u7cfb&#xff09;\u3001\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b&#xff08;\u5982\u80a1\u7968\u6570\u636e&#xff09;\u3001\u8bed\u97f3\u5904\u7406&#xff08;\u5efa\u6a21\u97f3\u9891\u65f6\u5e8f&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u7b80\u5355\u4ee3\u7801\u793a\u4f8b&#xff08;Python&#xff09;&#xff1a;<br \/>\n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5316\u5b9e\u73b0&#xff0c;\u5c55\u793a Temporal Self-Attention \u7684\u6838\u5fc3\u903b\u8f91&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn<span class=\"token punctuation\">.<\/span>functional <span class=\"token keyword\">as<\/span> F<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">temporal_self_attention<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># X: \u8f93\u5165\u5e8f\u5217, shape [batch_size, T, d]<\/span><br \/>\n    d_k <span class=\"token operator\">&#061;<\/span> X<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u952e\u7ef4\u5ea6<\/span><br \/>\n    Q <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> W_Q<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># W_Q \u662f\u53ef\u5b66\u4e60\u6743\u91cd<\/span><br \/>\n    K <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> W_K<span class=\"token punctuation\">)<\/span><br \/>\n    V <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> W_V<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u8ba1\u7b97\u6ce8\u610f\u529b\u5206\u6570<\/span><br \/>\n    scores <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>Q<span class=\"token punctuation\">,<\/span> K<span class=\"token punctuation\">.<\/span>transpose<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token punctuation\">(<\/span>d_k <span class=\"token operator\">**<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    attn_weights <span class=\"token operator\">&#061;<\/span> F<span class=\"token punctuation\">.<\/span>softmax<span class=\"token punctuation\">(<\/span>scores<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u52a0\u6743\u8f93\u51fa<\/span><br \/>\n    output <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>attn_weights<span class=\"token punctuation\">,<\/span> V<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> output<\/p>\n<p><span class=\"token comment\"># \u793a\u4f8b\u4f7f\u7528<\/span><br \/>\nbatch_size<span class=\"token punctuation\">,<\/span> T<span class=\"token punctuation\">,<\/span> d <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">64<\/span>  <span class=\"token comment\"># \u6279\u5927\u5c0f\u3001\u65f6\u95f4\u6b65\u3001\u7279\u5f81\u7ef4\u5ea6<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>batch_size<span class=\"token punctuation\">,<\/span> T<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\nW_Q <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\nW_K <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\nW_V <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\noutput <span class=\"token operator\">&#061;<\/span> temporal_self_attention<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8f93\u51fa: torch.Size([2, 10, 64])<\/span><\/p>\n<h6>3&#xff09; Spatial Cross-Attention \u8be6\u89e3<\/h6>\n<p>\u5b9a\u4e49&#xff1a;Spatial Cross-Attention \u662f\u4e00\u79cd\u4ea4\u53c9\u6ce8\u610f\u529b\u673a\u5236&#xff0c;\u4e13\u6ce8\u4e8e\u7a7a\u95f4\u6570\u636e&#xff08;\u5982\u56fe\u50cf\u3001\u7279\u5f81\u56fe&#xff09;\u3002\u5b83\u5728\u4e0d\u540c\u5e8f\u5217\u7684\u7a7a\u95f4\u4f4d\u7f6e\u4e4b\u95f4\u8ba1\u7b97\u6ce8\u610f\u529b&#xff0c;\u4f8b\u5982\u67e5\u8be2\u5e8f\u5217\u6765\u81ea\u4e00\u4e2a\u6a21\u6001&#xff08;\u5982\u6587\u672c&#xff09;&#xff0c;\u952e\u503c\u5e8f\u5217\u6765\u81ea\u53e6\u4e00\u4e2a\u6a21\u6001&#xff08;\u5982\u56fe\u50cf&#xff09;&#xff0c;\u5b9e\u73b0\u8de8\u6a21\u6001\u4fe1\u606f\u878d\u5408\u3002<\/p>\n<p>\u6570\u5b66\u539f\u7406&#xff1a;<\/p>\n<ul>\n<li>\u8f93\u5165&#xff1a;\u4e24\u4e2a\u72ec\u7acb\u5e8f\u5217&#xff0c;\u67e5\u8be2\u5e8f\u5217 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Qseq\u2208RN\u00d7dqQ_{\\\\text{seq}} \\\\in \\\\mathbb{R}^{N \\\\times d_q}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><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 text mtight\"><span class=\"mord mtight\">seq<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2819em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c\u952e\u503c\u5e8f\u5217 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">KVseq\u2208RM\u00d7dkvKV_{\\\\text{seq}} \\\\in \\\\mathbb{R}^{M \\\\times d_{kv}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;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 text mtight\"><span class=\"mord mtight\">seq<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">MM<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7a7a\u95f4\u4f4d\u7f6e\u6570&#xff08;\u5982\u56fe\u50cf\u50cf\u7d20\u6216\u533a\u57df&#xff09;\u3002<\/li>\n<li>\u751f\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Q,K,VQ, K, V<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span>&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Q&#061;QseqWQ,K&#061;KVseqWK,V&#061;KVseqWV<br \/>\nQ &#061; Q_{\\\\text{seq}} W^Q, \\\\quad K &#061; KV_{\\\\text{seq}} W^K, \\\\quad V &#061; KV_{\\\\text{seq}} W^V<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1774em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><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 text mtight\"><span class=\"mord mtight\">seq<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1774em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;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 text mtight\"><span class=\"mord mtight\">seq<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1774em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;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 text mtight\"><span class=\"mord mtight\">seq<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">WQ\u2208Rdq\u00d7dkW^Q \\\\in \\\\mathbb{R}^{d_q \\\\times d_k}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8804em;vertical-align: -0.0391em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2819em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">WK,WV\u2208Rdkv\u00d7dkW^K, W^V \\\\in \\\\mathbb{R}^{d_{kv} \\\\times d_k}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0358em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u6ce8\u610f\u529b\u8ba1\u7b97&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Attention(Q,K,V)&#061;softmax(QKTdk)V<br \/>\n\\\\text{Attention}(Q, K, V) &#061; \\\\text{softmax}\\\\left(\\\\frac{QK^T}{\\\\sqrt{d_k}}\\\\right)V<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attention<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4684em;vertical-align: -0.95em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/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: 1.5183em\"><span class=\"\" style=\"top: -2.2528em\"><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: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\" style=\"margin-right: 0.0315em\">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 class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><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 mathnormal\">Q<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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 class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">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: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O\u2208RN\u00d7dvO \\\\in \\\\mathbb{R}^{N \\\\times d_v}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><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 class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/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><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u4e2a\u67e5\u8be2\u4f4d\u7f6e\u7684\u503c\u662f\u952e\u503c\u5e8f\u5217\u4f4d\u7f6e\u7684\u52a0\u6743\u548c\u3002<\/li>\n<li>\u793a\u4f8b&#xff1a;\u5bf9\u4e8e\u67e5\u8be2\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">oio_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal 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> \u8ba1\u7b97\u4e3a&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">oi&#061;\u2211j&#061;1M\u03b2ijvj,\u03b2ij&#061;exp\u2061(qi\u22c5kjdk)\u2211k&#061;1Mexp\u2061(qi\u22c5kkdk)<br \/>\no_i &#061; \\\\sum_{j&#061;1}^{M} \\\\beta_{ij} v_j, \\\\quad \\\\beta_{ij} &#061; \\\\frac{\\\\exp\\\\left(\\\\frac{q_i \\\\cdot k_j}{\\\\sqrt{d_k}}\\\\right)}{\\\\sum_{k&#061;1}^{M} \\\\exp\\\\left(\\\\frac{q_i \\\\cdot k_k}{\\\\sqrt{d_k}}\\\\right)}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal 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: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.2421em;vertical-align: -1.4138em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4138em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.88em;vertical-align: -1.69em\"><\/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: 2.19em\"><span class=\"\" style=\"top: -2.11em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;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 mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/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: 0.9322em\"><span class=\"\" style=\"top: -2.5864em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8622em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8222em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1778em\"><span class=\"\"><\/span><\/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: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal 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 class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/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: -2.3488em;margin-left: -0.0315em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><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: 0.538em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.38em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -4.19em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"mord\"><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/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: 0.9934em\"><span class=\"\" style=\"top: -2.5864em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8622em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/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: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8222em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1778em\"><span class=\"\"><\/span><\/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: -3.5073em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal 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 class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0315em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2819em\"><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: 0.538em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2ij\\\\beta_{ij}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u67e5\u8be2\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u5bf9\u952e\u503c\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">jj<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u7684\u6ce8\u610f\u529b\u6743\u91cd\u3002<\/li>\n<\/ul>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u652f\u6301\u5f02\u6784\u6570\u636e\u4ea4\u4e92&#xff0c;\u589e\u5f3a\u7a7a\u95f4\u4e0a\u4e0b\u6587\u7406\u89e3&#xff08;\u5982\u7269\u4f53\u5b9a\u4f4d&#xff09;\u3002<\/li>\n<li>\u7f3a\u70b9&#xff1a;\u9700\u5bf9\u9f50\u4e0d\u540c\u5e8f\u5217\u7684\u7a7a\u95f4\u7ef4\u5ea6&#xff0c;\u8ba1\u7b97\u590d\u6742\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N\u00d7M)O(N \\\\times M)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u5e94\u7528\u573a\u666f&#xff1a;\u89c6\u89c9\u95ee\u7b54&#xff08;\u6587\u672c\u67e5\u8be2\u5173\u6ce8\u56fe\u50cf\u533a\u57df&#xff09;\u3001\u56fe\u50cf\u751f\u6210&#xff08;\u8349\u56fe\u5230\u7167\u7247\u7684\u8f6c\u6362&#xff09;\u3001\u591a\u6a21\u6001\u878d\u5408&#xff08;\u89c6\u9891\u548c\u97f3\u9891\u7684\u7a7a\u95f4\u5bf9\u9f50&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u7b80\u5355\u4ee3\u7801\u793a\u4f8b&#xff08;Python&#xff09;&#xff1a;<br \/>\n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5316\u5b9e\u73b0&#xff0c;\u5c55\u793a Spatial Cross-Attention \u7684\u6838\u5fc3\u903b\u8f91&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn<span class=\"token punctuation\">.<\/span>functional <span class=\"token keyword\">as<\/span> F<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">spatial_cross_attention<\/span><span class=\"token punctuation\">(<\/span>query_seq<span class=\"token punctuation\">,<\/span> kv_seq<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># query_seq: \u67e5\u8be2\u5e8f\u5217, shape [batch_size, N, d_q]<\/span><br \/>\n    <span class=\"token comment\"># kv_seq: \u952e\u503c\u5e8f\u5217, shape [batch_size, M, d_kv]<\/span><br \/>\n    d_k <span class=\"token operator\">&#061;<\/span> query_seq<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u952e\u7ef4\u5ea6<\/span><br \/>\n    Q <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>query_seq<span class=\"token punctuation\">,<\/span> W_Q<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># W_Q \u662f\u53ef\u5b66\u4e60\u6743\u91cd<\/span><br \/>\n    K <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>kv_seq<span class=\"token punctuation\">,<\/span> W_K<span class=\"token punctuation\">)<\/span><br \/>\n    V <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>kv_seq<span class=\"token punctuation\">,<\/span> W_V<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u8ba1\u7b97\u6ce8\u610f\u529b\u5206\u6570<\/span><br \/>\n    scores <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>Q<span class=\"token punctuation\">,<\/span> K<span class=\"token punctuation\">.<\/span>transpose<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token punctuation\">(<\/span>d_k <span class=\"token operator\">**<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    attn_weights <span class=\"token operator\">&#061;<\/span> F<span class=\"token punctuation\">.<\/span>softmax<span class=\"token punctuation\">(<\/span>scores<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u52a0\u6743\u8f93\u51fa<\/span><br \/>\n    output <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>matmul<span class=\"token punctuation\">(<\/span>attn_weights<span class=\"token punctuation\">,<\/span> V<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> output<\/p>\n<p><span class=\"token comment\"># \u793a\u4f8b\u4f7f\u7528<\/span><br \/>\nbatch_size<span class=\"token punctuation\">,<\/span> N<span class=\"token punctuation\">,<\/span> M<span class=\"token punctuation\">,<\/span> d_q<span class=\"token punctuation\">,<\/span> d_kv <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">16<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">32<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span>  <span class=\"token comment\"># N: \u67e5\u8be2\u4f4d\u7f6e\u6570, M: \u952e\u503c\u4f4d\u7f6e\u6570<\/span><br \/>\nquery_seq <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>batch_size<span class=\"token punctuation\">,<\/span> N<span class=\"token punctuation\">,<\/span> d_q<span class=\"token punctuation\">)<\/span><br \/>\nkv_seq <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>batch_size<span class=\"token punctuation\">,<\/span> M<span class=\"token punctuation\">,<\/span> d_kv<span class=\"token punctuation\">)<\/span><br \/>\nW_Q <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d_q<span class=\"token punctuation\">,<\/span> d_k<span class=\"token punctuation\">)<\/span><br \/>\nW_K <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d_kv<span class=\"token punctuation\">,<\/span> d_k<span class=\"token punctuation\">)<\/span><br \/>\nW_V <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d_kv<span class=\"token punctuation\">,<\/span> d_k<span class=\"token punctuation\">)<\/span><br \/>\noutput <span class=\"token operator\">&#061;<\/span> spatial_cross_attention<span class=\"token punctuation\">(<\/span>query_seq<span class=\"token punctuation\">,<\/span> kv_seq<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8f93\u51fa: torch.Size([2, 16, d_k])<\/span><\/p>\n<p>\u6574\u4f53\u539f\u7248\u4ee3\u7801\u63a8\u7406\u7ed3\u6784&#xff0c;\u5c06\u6b642\u79cd\u7ed3\u6784\u91cd\u590d\u53e0\u52a0\u5e76\u6267\u884c6\u6b21\u8fdb\u884cencoder\u64cd\u4f5c&#xff1a;<br \/>\noperation_order&#061;(\u2018self_attn\u2019, \u2018norm\u2019, \u2018cross_attn\u2019, \u2018norm\u2019,   \u2018ffn\u2019, \u2018norm\u2019)<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">attn_bev_encode<\/span><span class=\"token punctuation\">(<\/span><br \/>\n            self<span class=\"token punctuation\">,<\/span><br \/>\n            mlvl_feats<span class=\"token punctuation\">,<\/span><br \/>\n            bev_queries<span class=\"token punctuation\">,<\/span><br \/>\n            bev_h<span class=\"token punctuation\">,<\/span><br \/>\n            bev_w<span class=\"token punctuation\">,<\/span><br \/>\n            grid_length<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.512<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.512<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n            bev_pos<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n            prev_bev<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n            <span class=\"token operator\">**<\/span>kwargs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        bs <span class=\"token operator\">&#061;<\/span> mlvl_feats<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        bev_queries <span class=\"token operator\">&#061;<\/span> bev_queries<span class=\"token punctuation\">.<\/span>unsqueeze<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>repeat<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> bs<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        bev_pos <span class=\"token operator\">&#061;<\/span> bev_pos<span class=\"token punctuation\">.<\/span>flatten<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                    <span class=\"token comment\">#[4,256,3200]-&gt;[3200,4,256]<\/span><br \/>\n        <span class=\"token comment\"># obtain rotation angle and shift with ego motion<\/span><br \/>\n        delta_x <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>array<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>each<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;can_bus&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><br \/>\n                           <span class=\"token keyword\">for<\/span> each <span class=\"token keyword\">in<\/span> kwargs<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;img_metas&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        delta_y <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>array<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>each<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;can_bus&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><br \/>\n                           <span class=\"token keyword\">for<\/span> each <span class=\"token keyword\">in<\/span> kwargs<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;img_metas&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        ego_angle <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>array<span class=\"token punctuation\">(<\/span><br \/>\n            <span class=\"token punctuation\">[<\/span>each<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;can_bus&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">\/<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token number\">180<\/span> <span class=\"token keyword\">for<\/span> each <span class=\"token keyword\">in<\/span> kwargs<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;img_metas&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        grid_length_y <span class=\"token operator\">&#061;<\/span> grid_length<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        grid_length_x <span class=\"token operator\">&#061;<\/span> grid_length<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        translation_length <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>sqrt<span class=\"token punctuation\">(<\/span>delta_x <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">&#043;<\/span> delta_y <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        translation_angle <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>arctan2<span class=\"token punctuation\">(<\/span>delta_y<span class=\"token punctuation\">,<\/span> delta_x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token number\">180<\/span><br \/>\n        bev_angle <span class=\"token operator\">&#061;<\/span> ego_angle <span class=\"token operator\">&#8211;<\/span> translation_angle<br \/>\n        shift_y <span class=\"token operator\">&#061;<\/span> translation_length <span class=\"token operator\">*<\/span> \\\\<br \/>\n            np<span class=\"token punctuation\">.<\/span>cos<span class=\"token punctuation\">(<\/span>bev_angle <span class=\"token operator\">\/<\/span> <span class=\"token number\">180<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> grid_length_y <span class=\"token operator\">\/<\/span> bev_h<br \/>\n        shift_x <span class=\"token operator\">&#061;<\/span> translation_length <span class=\"token operator\">*<\/span> \\\\<br \/>\n            np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span>bev_angle <span class=\"token operator\">\/<\/span> <span class=\"token number\">180<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> grid_length_x <span class=\"token operator\">\/<\/span> bev_w<br \/>\n        shift_y <span class=\"token operator\">&#061;<\/span> shift_y <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>use_shift<br \/>\n        shift_x <span class=\"token operator\">&#061;<\/span> shift_x <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>use_shift<br \/>\n        shift <span class=\"token operator\">&#061;<\/span> bev_queries<span class=\"token punctuation\">.<\/span>new_tensor<span class=\"token punctuation\">(<\/span><br \/>\n            <span class=\"token punctuation\">[<\/span>shift_x<span class=\"token punctuation\">,<\/span> shift_y<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># xy, bs -&gt; bs, xy<\/span><\/p>\n<p>        <span class=\"token comment\"># \u901a\u8fc7&#096;\u65cb\u8f6c&#096;\u548c&#096;\u5e73\u79fb&#096;\u53d8\u6362\u5b9e\u73b0 BEV \u7279\u5f81\u7684\u5bf9\u9f50&#xff0c;\u5bf9\u4e8e\u5e73\u79fb\u90e8\u5206\u662f\u901a\u8fc7\u5bf9\u53c2\u8003\u70b9\u52a0\u4e0a\u504f\u79fb\u91cf&#096;shift&#096;\u4f53\u73b0\u7684<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> prev_bev <span class=\"token keyword\">is<\/span> <span class=\"token keyword\">not<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> prev_bev<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> bev_h <span class=\"token operator\">*<\/span> bev_w<span class=\"token punctuation\">:<\/span><br \/>\n                prev_bev <span class=\"token operator\">&#061;<\/span> prev_bev<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> self<span class=\"token punctuation\">.<\/span>rotate_prev_bev<span class=\"token punctuation\">:<\/span><br \/>\n                <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>bs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n                    <span class=\"token comment\"># num_prev_bev &#061; prev_bev.size(1)<\/span><br \/>\n                    rotation_angle <span class=\"token operator\">&#061;<\/span> kwargs<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;img_metas&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;can_bus&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><br \/>\n                    tmp_prev_bev <span class=\"token operator\">&#061;<\/span> prev_bev<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><br \/>\n                        bev_h<span class=\"token punctuation\">,<\/span> bev_w<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                    tmp_prev_bev <span class=\"token operator\">&#061;<\/span> rotate<span class=\"token punctuation\">(<\/span>tmp_prev_bev<span class=\"token punctuation\">,<\/span> rotation_angle<span class=\"token punctuation\">,<\/span><br \/>\n                                          center<span class=\"token operator\">&#061;<\/span>self<span class=\"token punctuation\">.<\/span>rotate_center<span class=\"token punctuation\">)<\/span><br \/>\n                    tmp_prev_bev <span class=\"token operator\">&#061;<\/span> tmp_prev_bev<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><br \/>\n                        bev_h <span class=\"token operator\">*<\/span> bev_w<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                    prev_bev<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmp_prev_bev<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<p>        <span class=\"token comment\"># add can bus signals<\/span><br \/>\n        can_bus <span class=\"token operator\">&#061;<\/span> bev_queries<span class=\"token punctuation\">.<\/span>new_tensor<span class=\"token punctuation\">(<\/span><br \/>\n            <span class=\"token punctuation\">[<\/span>each<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;can_bus&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token keyword\">for<\/span> each <span class=\"token keyword\">in<\/span> kwargs<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;img_metas&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        can_bus <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>can_bus_mlp<span class=\"token punctuation\">(<\/span>can_bus<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token comment\">#\u7f16\u7801\u4e3a\u9ad8\u7ef4\u7279\u5f81<\/span><br \/>\n        bev_queries <span class=\"token operator\">&#061;<\/span> bev_queries <span class=\"token operator\">&#043;<\/span> can_bus <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>use_can_bus<\/p>\n<p>        feat_flatten <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        spatial_shapes <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> lvl<span class=\"token punctuation\">,<\/span> feat <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">enumerate<\/span><span class=\"token punctuation\">(<\/span>mlvl_feats<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            bs<span class=\"token punctuation\">,<\/span> num_cam<span class=\"token punctuation\">,<\/span> c<span class=\"token punctuation\">,<\/span> h<span class=\"token punctuation\">,<\/span> w <span class=\"token operator\">&#061;<\/span> feat<span class=\"token punctuation\">.<\/span>shape<br \/>\n            spatial_shape <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>h<span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">)<\/span><br \/>\n            feat <span class=\"token operator\">&#061;<\/span> feat<span class=\"token punctuation\">.<\/span>flatten<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> self<span class=\"token punctuation\">.<\/span>use_cams_embeds<span class=\"token punctuation\">:<\/span><br \/>\n                feat <span class=\"token operator\">&#061;<\/span> feat <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>cams_embeds<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>to<span class=\"token punctuation\">(<\/span>feat<span class=\"token punctuation\">.<\/span>dtype<span class=\"token punctuation\">)<\/span> <span class=\"token comment\">#self.cams_embeds\u6444\u50cf\u5934\u4f4d\u7f6e\u7f16\u7801<\/span><br \/>\n            feat <span class=\"token operator\">&#061;<\/span> feat <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>level_embeds<span class=\"token punctuation\">[<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                            <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span> lvl<span class=\"token punctuation\">:<\/span>lvl <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>to<span class=\"token punctuation\">(<\/span>feat<span class=\"token punctuation\">.<\/span>dtype<span class=\"token punctuation\">)<\/span><br \/>\n            spatial_shapes<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>spatial_shape<span class=\"token punctuation\">)<\/span><br \/>\n            feat_flatten<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>feat<span class=\"token punctuation\">)<\/span><\/p>\n<p>        feat_flatten <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>cat<span class=\"token punctuation\">(<\/span>feat_flatten<span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        spatial_shapes <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>as_tensor<span class=\"token punctuation\">(<\/span><br \/>\n            spatial_shapes<span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">long<\/span><span class=\"token punctuation\">,<\/span> device<span class=\"token operator\">&#061;<\/span>bev_pos<span class=\"token punctuation\">.<\/span>device<span class=\"token punctuation\">)<\/span><br \/>\n        level_start_index <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>cat<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>spatial_shapes<span class=\"token punctuation\">.<\/span>new_zeros<span class=\"token punctuation\">(<\/span><br \/>\n            <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> spatial_shapes<span class=\"token punctuation\">.<\/span>prod<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>cumsum<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>        feat_flatten <span class=\"token operator\">&#061;<\/span> feat_flatten<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span><br \/>\n            <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># (num_cam, H*W, bs, embed_dims)<\/span><\/p>\n<p>        ret_dict <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>encoder<span class=\"token punctuation\">(<\/span><br \/>\n            bev_queries<span class=\"token punctuation\">,<\/span><br \/>\n            feat_flatten<span class=\"token punctuation\">,<\/span><br \/>\n            feat_flatten<span class=\"token punctuation\">,<\/span><br \/>\n            mlvl_feats<span class=\"token operator\">&#061;<\/span>mlvl_feats<span class=\"token punctuation\">,<\/span><br \/>\n            bev_h<span class=\"token operator\">&#061;<\/span>bev_h<span class=\"token punctuation\">,<\/span><br \/>\n            bev_w<span class=\"token operator\">&#061;<\/span>bev_w<span class=\"token punctuation\">,<\/span><br \/>\n            bev_pos<span class=\"token operator\">&#061;<\/span>bev_pos<span class=\"token punctuation\">,<\/span><br \/>\n            spatial_shapes<span class=\"token operator\">&#061;<\/span>spatial_shapes<span class=\"token punctuation\">,<\/span><br \/>\n            level_start_index<span class=\"token operator\">&#061;<\/span>level_start_index<span class=\"token punctuation\">,<\/span><br \/>\n            prev_bev<span class=\"token operator\">&#061;<\/span>prev_bev<span class=\"token punctuation\">,<\/span><br \/>\n            shift<span class=\"token operator\">&#061;<\/span>shift<span class=\"token punctuation\">,<\/span><br \/>\n            <span class=\"token operator\">**<\/span>kwargs<br \/>\n        <span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> ret_dict<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span><br \/>\n                query<span class=\"token punctuation\">,<\/span><br \/>\n                key<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                value<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                bev_pos<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                query_pos<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                key_pos<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                attn_masks<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                query_key_padding_mask<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                key_padding_mask<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                ref_2d<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                ref_3d<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                bev_h<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                bev_w<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                reference_points_cam<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                mask<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                spatial_shapes<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                level_start_index<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                prev_bev<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                <span class=\"token operator\">**<\/span>kwargs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;Forward function for &#096;TransformerDecoderLayer&#096;.<\/p>\n<p>        **kwargs contains some specific arguments of attentions.<\/p>\n<p>        Args:<br \/>\n            query (Tensor): The input query with shape<br \/>\n                [num_queries, bs, embed_dims] if<br \/>\n                self.batch_first is False, else<br \/>\n                [bs, num_queries embed_dims].<br \/>\n            key (Tensor): The key tensor with shape [num_keys, bs,<br \/>\n                embed_dims] if self.batch_first is False, else<br \/>\n                [bs, num_keys, embed_dims] .<br \/>\n            value (Tensor): The value tensor with same shape as &#096;key&#096;.<br \/>\n            query_pos (Tensor): The positional encoding for &#096;query&#096;.<br \/>\n                Default: None.<br \/>\n            key_pos (Tensor): The positional encoding for &#096;key&#096;.<br \/>\n                Default: None.<br \/>\n            attn_masks (List[Tensor] | None): 2D Tensor used in<br \/>\n                calculation of corresponding attention. The length of<br \/>\n                it should equal to the number of &#096;attention&#096; in<br \/>\n                &#096;operation_order&#096;. Default: None.<br \/>\n            query_key_padding_mask (Tensor): ByteTensor for &#096;query&#096;, with<br \/>\n                shape [bs, num_queries]. Only used in &#096;self_attn&#096; layer.<br \/>\n                Defaults to None.<br \/>\n            key_padding_mask (Tensor): ByteTensor for &#096;query&#096;, with<br \/>\n                shape [bs, num_keys]. Default: None.<\/p>\n<p>        Returns:<br \/>\n            Tensor: forwarded results with shape [num_queries, bs, embed_dims].<br \/>\n        &#034;&#034;&#034;<\/span><\/p>\n<p>        norm_index <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n        attn_index <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n        ffn_index <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n        identity <span class=\"token operator\">&#061;<\/span> query<br \/>\n        <span class=\"token keyword\">if<\/span> attn_masks <span class=\"token keyword\">is<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            attn_masks <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token boolean\">None<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>num_attn<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        <span class=\"token keyword\">elif<\/span> <span class=\"token builtin\">isinstance<\/span><span class=\"token punctuation\">(<\/span>attn_masks<span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>Tensor<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            attn_masks <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><br \/>\n                copy<span class=\"token punctuation\">.<\/span>deepcopy<span class=\"token punctuation\">(<\/span>attn_masks<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>num_attn<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token punctuation\">]<\/span><br \/>\n            warnings<span class=\"token punctuation\">.<\/span>warn<span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;Use same attn_mask in all attentions in &#039;<\/span><\/span><br \/>\n                          <span class=\"token string-interpolation\"><span class=\"token string\">f&#039;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>self<span class=\"token punctuation\">.<\/span>__class__<span class=\"token punctuation\">.<\/span>__name__<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> &#039;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">else<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            <span class=\"token keyword\">assert<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>attn_masks<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;&#061;<\/span> self<span class=\"token punctuation\">.<\/span>num_attn<span class=\"token punctuation\">,<\/span> <span class=\"token string-interpolation\"><span class=\"token string\">f&#039;The length of &#039;<\/span><\/span> \\\\<br \/>\n                                                     <span class=\"token string-interpolation\"><span class=\"token string\">f&#039;attn_masks <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span><span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>attn_masks<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> must be equal &#039;<\/span><\/span> \\\\<br \/>\n                                                     <span class=\"token string-interpolation\"><span class=\"token string\">f&#039;to the number of attention in &#039;<\/span><\/span> \\\\<br \/>\n                <span class=\"token string-interpolation\"><span class=\"token string\">f&#039;operation_order <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>self<span class=\"token punctuation\">.<\/span>num_attn<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#039;<\/span><\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> layer <span class=\"token keyword\">in<\/span> self<span class=\"token punctuation\">.<\/span>operation_order<span class=\"token punctuation\">:<\/span><br \/>\n            <span class=\"token comment\"># temporal self attention<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> layer <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;self_attn&#039;<\/span><span class=\"token punctuation\">:<\/span><\/p>\n<p>                query <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>attentions<span class=\"token punctuation\">[<\/span>attn_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">(<\/span><br \/>\n                    query<span class=\"token punctuation\">,<\/span><br \/>\n                    prev_bev<span class=\"token punctuation\">,<\/span><br \/>\n                    prev_bev<span class=\"token punctuation\">,<\/span><br \/>\n                    identity <span class=\"token keyword\">if<\/span> self<span class=\"token punctuation\">.<\/span>pre_norm <span class=\"token keyword\">else<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    query_pos<span class=\"token operator\">&#061;<\/span>bev_pos<span class=\"token punctuation\">,<\/span><br \/>\n                    key_pos<span class=\"token operator\">&#061;<\/span>bev_pos<span class=\"token punctuation\">,<\/span><br \/>\n                    attn_mask<span class=\"token operator\">&#061;<\/span>attn_masks<span class=\"token punctuation\">[<\/span>attn_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    key_padding_mask<span class=\"token operator\">&#061;<\/span>query_key_padding_mask<span class=\"token punctuation\">,<\/span><br \/>\n                    reference_points<span class=\"token operator\">&#061;<\/span>ref_2d<span class=\"token punctuation\">,<\/span><br \/>\n                    spatial_shapes<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><br \/>\n                        <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span>bev_h<span class=\"token punctuation\">,<\/span> bev_w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> device<span class=\"token operator\">&#061;<\/span>query<span class=\"token punctuation\">.<\/span>device<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    level_start_index<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> device<span class=\"token operator\">&#061;<\/span>query<span class=\"token punctuation\">.<\/span>device<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    <span class=\"token operator\">**<\/span>kwargs<span class=\"token punctuation\">)<\/span><br \/>\n                attn_index <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token number\">1<\/span><br \/>\n                identity <span class=\"token operator\">&#061;<\/span> query<\/p>\n<p>            <span class=\"token keyword\">elif<\/span> layer <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;norm&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n                query <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>norms<span class=\"token punctuation\">[<\/span>norm_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">(<\/span>query<span class=\"token punctuation\">)<\/span><br \/>\n                norm_index <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token number\">1<\/span><\/p>\n<p>            <span class=\"token comment\"># spaital cross attention<\/span><br \/>\n            <span class=\"token keyword\">elif<\/span> layer <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;cross_attn&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n                query <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>attentions<span class=\"token punctuation\">[<\/span>attn_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">(<\/span><br \/>\n                    query<span class=\"token punctuation\">,<\/span><br \/>\n                    key<span class=\"token punctuation\">,<\/span><br \/>\n                    value<span class=\"token punctuation\">,<\/span><br \/>\n                    identity <span class=\"token keyword\">if<\/span> self<span class=\"token punctuation\">.<\/span>pre_norm <span class=\"token keyword\">else<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    query_pos<span class=\"token operator\">&#061;<\/span>query_pos<span class=\"token punctuation\">,<\/span><br \/>\n                    key_pos<span class=\"token operator\">&#061;<\/span>key_pos<span class=\"token punctuation\">,<\/span><br \/>\n                    reference_points<span class=\"token operator\">&#061;<\/span>ref_3d<span class=\"token punctuation\">,<\/span><br \/>\n                    reference_points_cam<span class=\"token operator\">&#061;<\/span>reference_points_cam<span class=\"token punctuation\">,<\/span><br \/>\n                    mask<span class=\"token operator\">&#061;<\/span>mask<span class=\"token punctuation\">,<\/span><br \/>\n                    attn_mask<span class=\"token operator\">&#061;<\/span>attn_masks<span class=\"token punctuation\">[<\/span>attn_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    key_padding_mask<span class=\"token operator\">&#061;<\/span>key_padding_mask<span class=\"token punctuation\">,<\/span><br \/>\n                    spatial_shapes<span class=\"token operator\">&#061;<\/span>spatial_shapes<span class=\"token punctuation\">,<\/span><br \/>\n                    level_start_index<span class=\"token operator\">&#061;<\/span>level_start_index<span class=\"token punctuation\">,<\/span><br \/>\n                    <span class=\"token operator\">**<\/span>kwargs<span class=\"token punctuation\">)<\/span><br \/>\n                attn_index <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token number\">1<\/span><br \/>\n                identity <span class=\"token operator\">&#061;<\/span> query<\/p>\n<p>            <span class=\"token keyword\">elif<\/span> layer <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;ffn&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n                query <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>ffns<span class=\"token punctuation\">[<\/span>ffn_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">(<\/span><br \/>\n                    query<span class=\"token punctuation\">,<\/span> identity <span class=\"token keyword\">if<\/span> self<span class=\"token punctuation\">.<\/span>pre_norm <span class=\"token keyword\">else<\/span> <span class=\"token boolean\">None<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                ffn_index <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token number\">1<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> query<\/p>\n<h5>\u4e09. \u8bad\u7ec3\u65b9\u6cd5<\/h5>\n<p>BEVFormer\u91c7\u7528\u7aef\u5230\u7aef\u76d1\u7763\u5b66\u4e60&#xff0c;\u8bad\u7ec3\u8fc7\u7a0b\u5305\u62ec\u6570\u636e\u51c6\u5907\u3001\u635f\u5931\u51fd\u6570\u548c\u4f18\u5316\u7b56\u7565&#xff1a;<\/p>\n<ul>\n<li>\u6570\u636e\u51c6\u5907&#xff1a;\u4f7f\u7528\u5927\u89c4\u6a213D\u6570\u636e\u96c6&#xff08;\u5982nuScenes&#xff09;&#xff0c;\u6570\u636e\u96c6\u63d0\u4f9b\u591a\u6444\u50cf\u5934\u56fe\u50cf\u5e8f\u5217\u548c\u5bf9\u5e94\u76843D\u6807\u6ce8&#xff08;\u5982\u8fb9\u754c\u6846&#xff09;\u3002\u6570\u636e\u589e\u5f3a\u5305\u62ec\u968f\u673a\u88c1\u526a\u3001\u65cb\u8f6c\u548c\u989c\u8272\u6296\u52a8&#xff0c;\u4ee5\u63d0\u9ad8\u9c81\u68d2\u6027\u3002<\/li>\n<li>\u635f\u5931\u51fd\u6570&#xff1a;\u4e3b\u8981\u9488\u5bf9\u4e0b\u6e38\u4efb\u52a1\u8bbe\u8ba1\u3002\u4f8b\u5982&#xff0c;\u5bf9\u4e8e3D\u76ee\u6807\u68c0\u6d4b&#xff0c;\u91c7\u7528\u591a\u4efb\u52a1\u635f\u5931&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">L&#061;\u03bbclsLcls&#043;\u03bbregLreg&#043;\u03bbiouLiou<br \/>\n\\\\mathcal{L} &#061; \\\\lambda_{cls} \\\\mathcal{L}_{cls} &#043; \\\\lambda_{reg} \\\\mathcal{L}_{reg} &#043; \\\\lambda_{iou} \\\\mathcal{L}_{iou}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\">c<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/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 mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\">c<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/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: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><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 mathnormal mtight\">re<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">g<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><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 mathnormal mtight\">re<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">g<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal mtight\">i<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">u<\/span><\/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 mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal mtight\">i<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">u<\/span><\/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><\/span><br \/>\n\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Lcls\\\\mathcal{L}_{cls}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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 mathnormal mtight\">c<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/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>\u662f\u5206\u7c7b\u635f\u5931&#xff08;\u5982Focal Loss&#xff09;&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Lreg\\\\mathcal{L}_{reg}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><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 mathnormal mtight\">re<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">g<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u8fb9\u754c\u6846\u56de\u5f52\u635f\u5931&#xff08;\u5982Smooth L1&#xff09;&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Liou\\\\mathcal{L}_{iou}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><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 mathnormal mtight\">i<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">u<\/span><\/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>\u662fIoU\u635f\u5931\u3002\u6743\u91cd<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb\\\\lambda<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><\/span><\/span><\/span><\/span>\u901a\u8fc7\u7f51\u683c\u641c\u7d22\u4f18\u5316\u3002<\/li>\n<li>\u4f18\u5316\u7b56\u7565&#xff1a;\u4f7f\u7528AdamW\u4f18\u5316\u5668&#xff0c;\u5b66\u4e60\u7387\u91c7\u7528\u4f59\u5f26\u8870\u51cf\u8c03\u5ea6\u3002\u521d\u59cb\u5b66\u4e60\u7387\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">10\u2212410^{-4}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><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 class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6279\u91cf\u5927\u5c0f\u8bbe\u7f6e\u4e3a8-16&#xff08;\u53d6\u51b3\u4e8eGPU\u5185\u5b58&#xff09;\u3002\u8bad\u7ec3\u901a\u5e38\u5728100-200\u4e2aepoch\u5185\u6536\u655b&#xff0c;\u4f7f\u7528\u9884\u8bad\u7ec3CNN backbone&#xff08;\u5982ImageNet\u6743\u91cd&#xff09;\u52a0\u901f\u6536\u655b\u3002<\/li>\n<li>\u5b9e\u73b0\u7ec6\u8282&#xff1a;\u5728PyTorch\u4e2d\u5b9e\u73b0&#xff0c;\u652f\u6301\u5206\u5e03\u5f0f\u8bad\u7ec3\u3002\u6a21\u578b\u53c2\u6570\u91cf\u7ea6\u4e3a50M&#xff0c;\u8bad\u7ec3\u65f6\u9700\u6ce8\u610f\u5185\u5b58\u7ba1\u7406&#xff08;\u5982\u68af\u5ea6\u7d2f\u79ef&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u8be5\u65b9\u6cd5\u786e\u4fdd\u4e86\u6a21\u578b\u4ece\u539f\u59cb\u56fe\u50cf\u4e2d\u5b66\u4e60\u9c81\u68d2\u7684BEV\u8868\u793a&#xff0c;\u652f\u6301\u5b9e\u65f6\u63a8\u7406\u3002<\/p>\n<h5>\u56db. \u6a21\u578b\u5b9e\u9a8c<\/h5>\n<p>BEVFormer\u5728\u6807\u51c6\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u4e86\u5168\u9762\u5b9e\u9a8c&#xff0c;\u9a8c\u8bc1\u5176\u6709\u6548\u6027&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u6570\u636e\u96c6&#xff1a;\u4e3b\u8981\u5728nuScenes\u6570\u636e\u96c6\u4e0a\u8bc4\u4f30&#xff0c;\u8be5\u6570\u636e\u96c6\u5305\u542b1000\u4e2a\u9a7e\u9a76\u573a\u666f&#xff0c;\u6bcf\u4e2a\u573a\u666f\u67096\u4e2a\u6444\u50cf\u5934\u548c3D\u6807\u6ce8\u3002<\/p>\n<\/li>\n<li>\n<p>\u8bc4\u4f30\u6307\u6807&#xff1a;\u6838\u5fc3\u6307\u6807\u5305\u62ec&#xff1a;<\/p>\n<ul>\n<li>mAP&#xff08;\u5e73\u5747\u7cbe\u5ea6&#xff09;&#xff1a;\u7528\u4e8e3D\u76ee\u6807\u68c0\u6d4b&#xff0c;\u8ba1\u7b97\u4e0d\u540c\u8ddd\u79bb\u9608\u503c\u4e0b\u7684\u5e73\u5747\u7cbe\u5ea6\u3002<\/li>\n<li>NDS&#xff08;nuScenes Detection Score&#xff09;&#xff1a;\u7efc\u5408\u6307\u6807&#xff0c;\u8003\u8651mAP\u3001\u4f4d\u7f6e\u8bef\u5dee\u548c\u65b9\u5411\u8bef\u5dee\u3002<\/li>\n<li>\u63a8\u7406\u901f\u5ea6&#xff1a;FPS&#xff08;\u5e27\u6bcf\u79d2&#xff09;\u8bc4\u4f30\u5b9e\u65f6\u6027\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5b9e\u9a8c\u7ed3\u679c&#xff1a;<\/p>\n<ul>\n<li>BEVFormer\u5728nuScenes\u6d4b\u8bd5\u96c6\u4e0a\u8fbe\u5230SOTA&#xff08;state-of-the-art&#xff09;\u6027\u80fd&#xff0c;\u4f8b\u5982mAP\u4e3a48.1%&#xff0c;NDS\u4e3a53.5%&#xff0c;\u663e\u8457\u4f18\u4e8e\u57fa\u7ebf\u6a21\u578b&#xff08;\u5982LSS\u6216DETR3D&#xff09;\u3002<\/li>\n<li>\u6d88\u878d\u5b9e\u9a8c\u8bc1\u660e&#xff1a;\u65f6\u7a7a\u53d8\u6362\u5668\u8d21\u732e\u6700\u5927&#xff0c;mAP\u63d0\u5347\u7ea68%&#xff1b;\u65f6\u95f4\u5efa\u6a21\u6a21\u5757&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">T&#061;3T&#061;3<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u5e27&#xff09;\u6bd4\u5355\u5e27\u63d0\u53475%\u3002<\/li>\n<li>\u6548\u7387\u65b9\u9762&#xff1a;\u5728NVIDIA V100 GPU\u4e0a&#xff0c;\u63a8\u7406\u901f\u5ea6\u8fbe15 FPS&#xff0c;\u9002\u5408\u5b9e\u65f6\u7cfb\u7edf\u3002<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250813110426-689c713a1d735.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5bf9\u6bd4\u5206\u6790&#xff1a;\u4e0e\u540c\u7c7b\u6a21\u578b&#xff08;\u5982PolarFormer\u6216PETR&#xff09;\u76f8\u6bd4&#xff0c;BEVFormer\u5728\u590d\u6742\u573a\u666f&#xff08;\u5982\u96e8\u96fe\u5929\u6c14&#xff09;\u4e0b\u9c81\u68d2\u6027\u66f4\u5f3a&#xff0c;\u5f52\u529f\u4e8e\u5176\u65f6\u7a7a\u878d\u5408\u8bbe\u8ba1\u3002\u5b9e\u9a8c\u8fd8\u6269\u5c55\u5230\u5176\u4ed6\u4efb\u52a1&#xff08;\u5982BEV\u5206\u5272&#xff09;&#xff0c;\u6027\u80fd\u4e00\u81f4\u4f18\u5f02\u3002<\/p>\n<\/li>\n<\/ul>\n<h5>\u603b\u7ed3<\/h5>\n<p>BEVFormer\u901a\u8fc7\u521b\u65b0\u7684\u65f6\u7a7a\u53d8\u6362\u5668\u67b6\u6784&#xff0c;\u9ad8\u6548\u5730\u4ece\u591a\u6444\u50cf\u5934\u56fe\u50cf\u751f\u6210BEV\u8868\u793a&#xff0c;\u89e3\u51b3\u4e86\u81ea\u52a8\u9a7e\u9a76\u4e2d\u76843D\u611f\u77e5\u6311\u6218\u3002\u5176\u6838\u5fc3\u4f18\u52bf\u5728\u4e8e\u7aef\u5230\u7aef\u5b66\u4e60\u3001\u5b9e\u65f6\u6027\u548c\u9ad8\u7cbe\u5ea6\u3002\u5b9e\u9a8c\u8868\u660e&#xff0c;\u5b83\u5728nuScenes\u7b49\u57fa\u51c6\u4e0a\u9886\u5148&#xff0c;\u4e3a\u5b9e\u9645\u5e94\u7528\u63d0\u4f9b\u4e86\u53ef\u9760\u57fa\u7840\u3002\u672a\u6765\u5de5\u4f5c\u53ef\u63a2\u7d22\u8f7b\u91cf\u5316\u7248\u672c\u6216\u6269\u5c55\u5230\u66f4\u591a\u4f20\u611f\u5668\u878d\u5408\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb814\u6b21\uff0c\u70b9\u8d5e13\u6b21\uff0c\u6536\u85cf15\u6b21\u3002BEVFormer\u662f\u4e00\u79cd\u57fa\u4e8e\u65f6\u7a7a\u53d8\u6362\u5668\u7684\u591a\u6444\u50cf\u5934\u9e1f\u77b0\u56fe\u751f\u6210\u6a21\u578b\uff0c\u5176\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u65f6\u7a7a\u6ce8\u610f\u529b\u673a\u5236\u7684\u8bbe\u8ba1\u3002\u6a21\u578b\u901a\u8fc7\u7a7a\u95f4\u4ea4\u53c9\u6ce8\u610f\u529b\uff08Spatial Cross-Attention\uff09\u5c06\u591a\u89c6\u89d22D\u7279\u5f81\u6620\u5c04\u5230BEV\u7a7a\u95f4\uff0c\u540c\u65f6\u5229\u7528\u65f6\u95f4\u81ea\u6ce8\u610f\u529b\uff08Temporal Self-Attention\uff09\u878d\u5408\u5386\u53f2\u5e27\u4fe1\u606f\u3002\u8fd9\u4e24\u79cd\u6ce8\u610f\u529b\u673a\u5236\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u5206\u522b\u4e3aO(N\u00d7M)\u548cO(T\u00b2)\uff0c\u5206\u522b\u8d1f\u8d23\u7a7a\u95f4\u7279\u5f81\u805a\u5408\u548c\u65f6\u95f4\u8fd0\u52a8\u5efa\u6a21\u3002\u5b9e\u9a8c\u8868\u660e\uff0c\u8be5\u65b9\u6cd5\u5728nuScenes\u6570\u636e\u96c6\u4e0a\u5b9e\u73b0\u4e86SOTA\u6027\u80fd\uff0cmAP\u8fbe\u523056.9%\uff0cNDS\u6307\u6807\u8fbe62.8%\u3002\u8be5\u6280\u672f\u4e3a\u81ea\u52a8\u9a7e\u9a76<\/p>\n","protected":false},"author":2,"featured_media":55191,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[81,86,427,2051,5669,3546],"topic":[],"class_list":["post-55193","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-python","tag-86","tag-427","tag-2051","tag-5669","tag-3546"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u3010\u8bba\u6587\u9605\u8bfb\u3011BEVFormer\u8bba\u6587\u89e3\u6790\u53caTemporal Self-Attention\u3001Spatial Cross-Attention\u6ce8\u610f\u529b\u673a\u5236\u8be6\u89e3\u53ca\u4ee3\u7801\u793a\u4f8b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/55193.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010\u8bba\u6587\u9605\u8bfb\u3011BEVFormer\u8bba\u6587\u89e3\u6790\u53caTemporal Self-Attention\u3001Spatial Cross-Attention\u6ce8\u610f\u529b\u673a\u5236\u8be6\u89e3\u53ca\u4ee3\u7801\u793a\u4f8b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb814\u6b21\uff0c\u70b9\u8d5e13\u6b21\uff0c\u6536\u85cf15\u6b21\u3002BEVFormer\u662f\u4e00\u79cd\u57fa\u4e8e\u65f6\u7a7a\u53d8\u6362\u5668\u7684\u591a\u6444\u50cf\u5934\u9e1f\u77b0\u56fe\u751f\u6210\u6a21\u578b\uff0c\u5176\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u65f6\u7a7a\u6ce8\u610f\u529b\u673a\u5236\u7684\u8bbe\u8ba1\u3002\u6a21\u578b\u901a\u8fc7\u7a7a\u95f4\u4ea4\u53c9\u6ce8\u610f\u529b\uff08Spatial Cross-Attention\uff09\u5c06\u591a\u89c6\u89d22D\u7279\u5f81\u6620\u5c04\u5230BEV\u7a7a\u95f4\uff0c\u540c\u65f6\u5229\u7528\u65f6\u95f4\u81ea\u6ce8\u610f\u529b\uff08Temporal 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