{"id":40846,"date":"2026-02-26T21:06:28","date_gmt":"2026-02-26T13:06:28","guid":{"rendered":"https:\/\/17aitech.com\/?p=40846"},"modified":"2026-02-26T21:06:28","modified_gmt":"2026-02-26T13:06:28","slug":"%e5%8c%97%e5%a4%a7%e6%9e%97%e5%ae%99%e8%be%b0%e5%9b%a2%e9%98%9f%ef%bc%9a%e4%bb%8e%e6%9c%80%e4%bc%98%e4%bc%a0%e8%be%93%e8%a7%92%e5%ba%a6%e8%ae%ad%e7%bb%83%e6%97%b6%e5%ba%8f%e9%a2%84%e6%b5%8b%e6%a8%a1","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=40846","title":{"rendered":"\u5317\u5927\u6797\u5b99\u8fb0\u56e2\u961f\uff1a\u4ece\u6700\u4f18\u4f20\u8f93\u89d2\u5ea6\u8bad\u7ec3\u65f6\u5e8f\u9884\u6d4b\u6a21\u578b \u4e28ICLR 2026"},"content":{"rendered":"<p><\/p>\n<p>\u5728\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u7814\u7a76\u4e2d\uff0c\u4e00\u4e2a\u8010\u4eba\u5bfb\u5473\u7684\u73b0\u8c61\u957f\u671f\u5b58\u5728\uff1a<\/p>\n<p>\u4e00\u65b9\u9762\uff0c\u6a21\u578b\u7ed3\u6784\u4e0d\u65ad\u6f14\u8fdb\uff0c\u4ece\u5faa\u73af\u7f51\u7edc\u5230 Transformer\uff0c\u518d\u5230\u9891\u57df\u4e0e\u6df7\u5408\u7ed3\u6784\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u51e0\u4e4e\u6240\u6709\u65b9\u6cd5\u5728\u8bad\u7ec3\u9636\u6bb5\u4f9d\u8d56\u540c\u4e00\u7c7b\u635f\u5931\u51fd\u6570\uff0c\u5373\u4ee5\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u4e3a\u4ee3\u8868\u7684\u70b9\u5bf9\u70b9\u8bef\u5dee\u3002<\/p>\n<p>\u8fd9\u4f7f\u5f97\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u5728\u65b9\u6cd5\u8bba\u5c42\u9762\u5448\u73b0\u51fa\u4e00\u79cd\u9690\u6027\u7684\u505c\u6ede\uff0c\u5373\u7814\u7a76\u91cd\u5fc3\u6301\u7eed\u5411\u6a21\u578b\u8868\u8fbe\u80fd\u529b\u503e\u659c\uff0c\u800c\u5bf9\u635f\u5931\u51fd\u6570\u6240\u9690\u542b\u7684\u7edf\u8ba1\u5047\u8bbe\u7f3a\u4e4f\u7cfb\u7edf\u53cd\u601d\u3002<\/p>\n<p>\u70b9\u5bf9\u70b9\u8bef\u5dee\u7684\u6838\u5fc3\u5047\u8bbe\u5728\u4e8e\uff0c\u6807\u7b7e\u5e8f\u5217\u4e2d\u7684\u5404\u65f6\u95f4\u6b65\u53ef\u88ab\u89c6\u4e3a\u7ed9\u5b9a\u5386\u53f2\u6761\u4ef6\u4e0b\u76f8\u4e92\u72ec\u7acb\u7684\u9884\u6d4b\u5bf9\u8c61\u3002\u7136\u800c\uff0c\u8fd9\u4e00\u5047\u8bbe\u4e0e\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u7684\u751f\u6210\u673a\u5236\u4e4b\u95f4\u59cb\u7ec8\u5b58\u5728\u5f20\u529b\u3002<\/p>\n<p>\u771f\u5b9e\u4e16\u754c\u4e2d\u7684\u65f6\u95f4\u5e8f\u5217\u7531\u968f\u673a\u8fc7\u7a0b\u6f14\u5316\u800c\u6765\uff0c\u4e0d\u540c\u65f6\u95f4\u70b9\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u7684\u76f8\u5173\u5173\u7cfb\u3002\u5c06\u591a\u6b65\u9884\u6d4b\u95ee\u9898\u62c6\u89e3\u4e3a\u4e00\u7ec4\u72ec\u7acb\u7684\u56de\u5f52\u4efb\u52a1\uff0c\u4e0d\u53ef\u907f\u514d\u5730\u4e3a\u635f\u5931\u51fd\u6570\u5f15\u5165\u4e86\u7ed3\u6784\u6027\u504f\u5dee\uff0c\u4f7f\u6a21\u578b\u96be\u4ee5\u5b66\u4e60\u6807\u7b7e\u5e8f\u5217\u7684\u6574\u4f53\u5f62\u6001\u3001\u76f8\u5173\u7ed3\u6784\u4ee5\u53ca\u6761\u4ef6\u4f9d\u8d56\u5173\u7cfb\u3002<\/p>\n<p>\u9488\u5bf9\u8fd9\u4e00\u95ee\u9898\uff0c\u5317\u4eac\u5927\u5b66\u6797\u5b99\u8fb0\u56e2\u961f\u6df1\u5165\u5256\u6790\u4e86\u6b64\u7c7b\u7ed3\u6784\u6027\u504f\u5dee\u7684\u6210\u56e0\u3002\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u56e2\u961f\u63d0\u51fa\u4e86 DistDF\uff1a\u4e00\u79cd\u901a\u8fc7\u8054\u5408\u5206\u5e03\u5bf9\u9f50\u8bad\u7ec3\u9884\u6d4b\u6a21\u578b\u7684\u635f\u5931\u51fd\u6570\u3002DistDF \u7684\u63d0\u51fa\u4e0d\u4ec5\u4e3a\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u63d0\u4f9b\u4e86\u4e00\u79cd\u65b0\u7684\u635f\u5931\u51fd\u6570\u8bbe\u8ba1\u601d\u8def\uff0c\u4e5f\u5728\u66f4\u4e00\u822c\u7684\u610f\u4e49\u4e0a\uff0c\u5bf9\u5e8f\u5217\u5efa\u6a21\u4e2d\u201c\u5e94\u5f53\u4f18\u5316\u4ec0\u4e48\u201d\u8fd9\u4e00\u957f\u671f\u88ab\u9ed8\u8ba4\u7684\u95ee\u9898\u7ed9\u51fa\u4e86\u65b0\u7684\u56de\u7b54\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-e98b79ba151ee3b0dc50d871e0042427.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-e98b79ba151ee3b0dc50d871e0042427.png\"><\/a><\/p>\n<p>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2510.24574v1<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_78 ez-toc-wrap-left-text counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u6587\u7ae0\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/17aitech.com\/?p=40846\/#%E5%BD%93%E7%8B%AC%E7%AB%8B%E6%80%A7%E5%81%87%E8%AE%BE%E8%A2%AB%E5%AE%9E%E9%AA%8C%E8%AF%81%E4%BC%AA%E4%B9%8B%E5%90%8E\" >\u5f53\u72ec\u7acb\u6027\u5047\u8bbe\u88ab\u5b9e\u9a8c\u8bc1\u4f2a\u4e4b\u540e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/17aitech.com\/?p=40846\/#DistDF%EF%BC%9A%E5%9F%BA%E4%BA%8E%E5%88%86%E5%B8%83%E5%AF%B9%E9%BD%90%E7%9A%84%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E6%8D%9F%E5%A4%B1%E5%87%BD%E6%95%B0\" >DistDF\uff1a\u57fa\u4e8e\u5206\u5e03\u5bf9\u9f50\u7684\u65f6\u95f4\u5e8f\u5217\u635f\u5931\u51fd\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/17aitech.com\/?p=40846\/#%E5%9C%A8%E5%A4%A7%E9%87%8F%E5%AE%9E%E9%AA%8C%E4%B8%AD%EF%BC%8C%E4%B8%80%E8%87%B4%E9%AA%8C%E8%AF%81%E4%BC%98%E5%8A%BF\" >\u5728\u5927\u91cf\u5b9e\u9a8c\u4e2d\uff0c\u4e00\u81f4\u9a8c\u8bc1\u4f18\u52bf<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/17aitech.com\/?p=40846\/#%E3%80%8C%E5%A4%9A%E4%BB%BB%E5%8A%A1%E5%AD%A6%E4%B9%A0%E3%80%8D%E9%9C%80%E8%A6%81%E5%88%86%E5%B8%83%E5%AF%B9%E9%BD%90\" >\u300c\u591a\u4efb\u52a1\u5b66\u4e60\u300d\u9700\u8981\u5206\u5e03\u5bf9\u9f50<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E5%BD%93%E7%8B%AC%E7%AB%8B%E6%80%A7%E5%81%87%E8%AE%BE%E8%A2%AB%E5%AE%9E%E9%AA%8C%E8%AF%81%E4%BC%AA%E4%B9%8B%E5%90%8E\"><\/span>\u5f53\u72ec\u7acb\u6027\u5047\u8bbe\u88ab\u5b9e\u9a8c\u8bc1\u4f2a\u4e4b\u540e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5f53\u524d\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u9886\u57df\u7684\u4e3b\u6d41\u65b9\u6cd5\u666e\u904d\u91c7\u7528\u9010\u65f6\u95f4\u70b9\u7684\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u4f5c\u4e3a\u635f\u5931\u51fd\u6570\uff1a<\/p>\n<p>$$mathcal{L}_{text{MSE}} = |mathbf{y} &#8211; g_theta(mathbf{x})|^2=sum_{t=1}^mathrm{T}left(y_t-g_{theta,t}(mathbf{x})right)$$<\/p>\n<p>$$mathcal{L}_mathrm{MSE}$$\u9690\u5f0f\u5730\u505a\u4e86\u72ec\u7acb\u6027\u5047\u8bbe\uff1a\u5728\u7ed9\u5b9a\u5386\u53f2\u5e8f\u5217\u7684\u6761\u4ef6\u4e0b\uff0c\u6807\u7b7e\u5e8f\u5217\u5404\u65f6\u95f4\u70b9\u7684\u89c2\u6d4b\u76f8\u4e92\u72ec\u7acb\u3002\u7136\u800c\uff0c\u771f\u5b9e\u65f6\u95f4\u5e8f\u5217\u5b58\u5728\u663e\u8457\u7684\u6807\u7b7e\u81ea\u76f8\u5173\uff1a\u6807\u7b7e\u5e8f\u5217\u5404\u65f6\u95f4\u70b9\u7684\u89c2\u6d4b\u5f80\u5f80\u5b58\u5728\u663e\u8457\u7684\u76f8\u5173\u6027\u3002\u56e0\u6b64\uff0c$$mathcal{L}_mathrm{MSE}$$\u7684\u72ec\u7acb\u6027\u5047\u8bbe\u4e0e\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u7684\u751f\u6210\u673a\u5236\u76f8\u6096\uff0c\u5bfc\u81f4\u5176\u4f5c\u4e3a\u635f\u5931\u51fd\u6570\u662f\u6709\u504f\u7684\uff08\u5177\u4f53\u89c1\u5b9a\u74061\uff09\u3002<\/p>\n<p>[\u5b9a\u74061] \u8003\u8651\u5355\u53d8\u91cf\u6807\u7b7e\u5e8f\u5217$$mathbf{y}inmathbb{R}^{Ttimes 1}$$\uff0c\u5176\u6761\u4ef6\u81ea\u76f8\u5173\u77e9\u9635\u4e3a$$mathbf{Sigma}_mathbf{x}inmathbb{R}^{Ttimes T}$$\uff0c\u5219\u6807\u7b7e\u5e8f\u5217\u7684\u5b9e\u7528\u8d1f\u5bf9\u6570\u4f3c\u7136\u53ef\u8868\u793a\u4e3a\uff1a$$mathcal{L}_mathrm{NLL} = left|mathbf{y}-hat{mathbf{y}}right|_{mathbf{Sigma}^{-1}}^2$$\u3002\u663e\u7136\uff0c\u4ec5\u5f53$$mathbf{Sigma}_mathbf{x}$$\u662f\u5355\u4f4d\u9635\uff0c\u5373\u6807\u7b7e\u81ea\u76f8\u5173\u4e0d\u5b58\u5728\u65f6\uff0c\u624d\u6709$$mathcal{L}_mathrm{NLL} = mathcal{L}_mathrm{MSE}$$\u3002<\/p>\n<p>\u7814\u7a76\u56e2\u961f\u901a\u8fc7\u5b9e\u8bc1\u5206\u6790\u9a8c\u8bc1\u4e86\u8fd9\u4e00\u77db\u76fe\uff1a\u5728\u7ed9\u5b9a\u5386\u53f2\u5e8f\u5217$$mathbf{x}$$\u7684\u6761\u4ef6\u4e0b\uff0c\u6807\u7b7e\u5e8f\u5217\u4ecd\u5448\u73b0\u663e\u8457\u7684\u6761\u4ef6\u76f8\u5173\u7ed3\u6784\uff0c\u4ece\u800c\u5728\u5b9e\u8bc1\u610f\u4e49\u4e0a\u8bc1\u4f2a\u4e86\u72ec\u7acb\u6027\u5047\u8bbe\u3002\u5b9e\u9a8c\u8fdb\u4e00\u6b65\u8868\u660e\uff0c\u5373\u4f7f\u91c7\u7528\u9891\u57df\u53d8\u6362\u6216\u4e3b\u6210\u5206\u5206\u89e3\u7b49\u6807\u7b7e\u53d8\u6362\u65b9\u6cd5\uff0c\u53d8\u6362\u540e\u7684\u6807\u7b7e\u5e8f\u5217\u4f9d\u7136\u5b58\u5728\u6b8b\u4f59\u76f8\u5173\u6027\uff1b\u56e0\u6b64\uff0c\u5728\u53d8\u6362\u540e\u7684\u6807\u7b7e\u5e94\u7528\u5747\u65b9\u8bef\u5dee\u4f5c\u4e3a\u635f\u5931\u51fd\u6570\u4ecd\u4f1a\u5bfc\u81f4\u7ed3\u6784\u6027\u504f\u5dee\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-c80125f892b1124a43ecf1116b7d1695.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-c80125f892b1124a43ecf1116b7d1695.png\"><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"DistDF%EF%BC%9A%E5%9F%BA%E4%BA%8E%E5%88%86%E5%B8%83%E5%AF%B9%E9%BD%90%E7%9A%84%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E6%8D%9F%E5%A4%B1%E5%87%BD%E6%95%B0\"><\/span>DistDF\uff1a\u57fa\u4e8e\u5206\u5e03\u5bf9\u9f50\u7684\u65f6\u95f4\u5e8f\u5217\u635f\u5931\u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u89c4\u907f\u4f20\u7edf\u65b9\u6cd5\u4e2d\u7684\u72ec\u7acb\u6027\u5047\u8bbe\uff0cDistDF \u63d0\u51fa\u76f4\u63a5\u5bf9\u9f50\u9884\u6d4b\u5e8f\u5217\u7684\u6761\u4ef6\u5206\u5e03$$mathbb{P}(hat{mathbf{y}}|mathbf{x})$$\u4e0e\u771f\u5b9e\u6807\u7b7e\u7684\u6761\u4ef6\u5206\u5e03$$mathbb{P}(mathbf{y}|mathbf{x})$$\u3002\u76f4\u89c2\u4e0a\uff0c\u8be5\u76ee\u6807\u53ef\u901a\u8fc7\u6700\u5c0f\u5316\u4e24\u4e2a\u6761\u4ef6\u5206\u5e03\u95f4\u7684\u8ddd\u79bb$$mathrm{Disc}(mathbb{P}(hat{mathbf{y}}|mathbf{x}),mathbb{P}(mathbf{y}|mathbf{x}))$$\u6765\u5b9e\u73b0\u3002<\/p>\n<p>\u7136\u800c\uff0c\u76f4\u63a5\u5c06\u5176\u4f5c\u4e3a\u635f\u5931\u51fd\u6570\u9762\u4e34\u4e25\u91cd\u7684\u6837\u672c\u7a00\u7f3a\u95ee\u9898\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u5386\u53f2\u5e8f\u5217$$mathbf{x}$$\uff0c\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u96c6\u901a\u5e38\u4ec5\u5305\u542b\u552f\u4e00\u7684\u6807\u7b7e\u5e8f\u5217$$mathbf{y}$$\uff0c\u6a21\u578b\u4e5f\u4ec5\u4ea7\u751f\u5355\u4e00\u9884\u6d4b$$hat{mathbf{y}}$$\u3002\u8fd9\u79cd\u201c\u5355\u6837\u672c\u201d\u60c5\u5f62\u5bfc\u81f4\u76f4\u63a5\u4f30\u8ba1\u6761\u4ef6\u5206\u5e03\u8ddd\u79bb$$mathrm{Disc}(mathbb{P}(hat{mathbf{y}}|mathbf{x}),mathbb{P}(mathbf{y}|mathbf{x}))$$\u5728\u7edf\u8ba1\u4e0a\u4e0d\u53ef\u9760\u3002<\/p>\n<p>\u4e3a\u89e3\u51b3\u8fd9\u4e00\u96be\u9898\uff0c\u6211\u4eec\u5229\u7528\u6982\u7387\u6052\u7b49\u5f0f$$mathbb{P}(mathbf{y},mathbf{x}) = mathbb{P}(mathbf{y}|mathbf{x})mathbb{P}(mathbf{x})$$\u3002\u56e0\u4e3a\u8fb9\u7f18\u5206\u5e03$$mathbb{P}(mathbf{x})$$\u662f\u5171\u4eab\u7684\uff0c\u82e5\u8054\u5408\u5206\u5e03\u5bf9\u9f50\uff0c\u5219\u6761\u4ef6\u5206\u5e03\u5fc5\u7136\u5bf9\u9f50\u3002\u57fa\u4e8e\u6b64\uff0c\u6211\u4eec\u5c06\u6761\u4ef6\u5206\u5e03\u5339\u914d\u95ee\u9898\u8f6c\u5316\u4e3a\u8054\u5408\u5206\u5e03\u5339\u914d\u95ee\u9898\u3002<\/p>\n<p>\u8fdb\u4e00\u6b65\u7ed3\u5408\u6700\u4f18\u4f20\u8f93\u7406\u8bba\uff0c\u672c\u6587\u8bc1\u660e\u4e86\u8054\u5408\u5206\u5e03\u7684 Wasserstein \u8ddd\u79bb\u6784\u6210\u4e86\u6761\u4ef6\u5206\u5e03 Wasserstein \u8ddd\u79bb\u671f\u671b\u7684\u4e0a\u754c\uff1a<\/p>\n<p>$$int mathcal{W}_pleft(mathbb{P}(mathbf{y}|mathbf{x}), mathbb{P}(hat{mathbf{y}}|mathbf{x})right) dmathbb{P}(mathbf{x}) leq mathcal{W}_p left(mathbb{P}(mathbf{y},mathbf{x}), mathbb{P}(hat{mathbf{y}},mathbf{x})right)$$<\/p>\n<p>\u56e0\u6b64\uff0c\u901a\u8fc7\u6700\u5c0f\u5316\u5386\u53f2-\u9884\u6d4b\u8054\u5408\u5206\u5e03$$mathbb{P}(hat{mathbf{y}},mathbf{x})$$\u4e0e\u5386\u53f2-\u6807\u7b7e\u8054\u5408\u5206\u5e03$$mathbb{P}(mathbf{y},mathbf{x})$$\u4e4b\u95f4\u7684 Wasserstein \u8ddd\u79bb\uff0c\u53ef\u6709\u6548\u5b9e\u73b0\u6761\u4ef6\u5206\u5e03\u5bf9\u9f50\uff0c\u8fdb\u4e00\u6b65\u5b9e\u73b0\u9884\u6d4b\u6a21\u578b\u7684\u65e0\u504f\u8bad\u7ec3\u3002\u540c\u65f6\uff0c\u8fd9\u4e00\u8f6c\u6362\u5141\u8bb8\u5229\u7528\u6574\u4e2a\u6570\u636e\u96c6\u7684\u6837\u672c\u6765\u4f30\u8ba1\u8054\u5408\u5206\u5e03\u8ddd\u79bb\uff0c\u663e\u8457\u63d0\u5347\u4e86\u5206\u5e03\u8ddd\u79bb\u4f30\u8ba1\u7684\u53ef\u9760\u6027\u3002\u96f7\u5cf0\u7f51<span style=\"color:#FD5D3C\">(\u516c\u4f17\u53f7\uff1a\u96f7\u5cf0\u7f51)<\/span><\/p>\n<p>DistDF \u7684\u5b9e\u73b0\u6d41\u7a0b\u5982\u4e0b\uff1a<\/p>\n<p>\u9996\u5148\uff0c\u6784\u9020\u8054\u5408\u5e8f\u5217\uff1a$$mathbf{z}=[mathbf{y},mathbf{x}]$$\u548c$$hat{mathbf{z}}=[hat{mathbf{y}},mathbf{x}]$$\uff1b<\/p>\n<p>\u63a5\u7740\uff0c\u8ba1\u7b97\u4e24\u4e2a\u8054\u5408\u5e8f\u5217\u4e4b\u95f4\u7684Wasserstein\u8ddd\u79bb\uff1a$$mathcal{L}_mathrm{dist}=mathcal{W}_p left(mathbb{P}(mathbf{z}), mathbb{P}(hat{mathbf{z}})right)$$\uff0c<\/p>\n<p>\u6700\u540e\uff0c\u4e0e MSE \u635f\u5931\u52a0\u6743\u878d\u5408\uff1a$$mathcal{L}_{alpha} = alpha cdot mathcal{L}_mathrm{dist} + (1-alpha) cdot mathcal{L}_mathrm{MSE}$$<\/p>\n<p>DistDF \u4f5c\u4e3a\u6a21\u578b\u65e0\u5173\u7684\u635f\u5931\u51fd\u6570\uff0c\u53ef\u9002\u914d\u5404\u7c7b\u9884\u6d4b\u6a21\u578b\u67b6\u6784\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%9C%A8%E5%A4%A7%E9%87%8F%E5%AE%9E%E9%AA%8C%E4%B8%AD%EF%BC%8C%E4%B8%80%E8%87%B4%E9%AA%8C%E8%AF%81%E4%BC%98%E5%8A%BF\"><\/span>\u5728\u5927\u91cf\u5b9e\u9a8c\u4e2d\uff0c\u4e00\u81f4\u9a8c\u8bc1\u4f18\u52bf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8bba\u6587\u9996\u5148\u5c06DistDF\u4e0e\u73b0\u6709\u635f\u5931\u51fd\u6570\u8fdb\u884c\u4e86\u6bd4\u8f83\uff0c\u5305\u62ec\u901a\u8fc7\u6807\u7b7e\u53d8\u6362\u524a\u5f31\u6807\u7b7e\u76f8\u5173\u6027\u7684 FreDF \u548c Time-o1\u3002\u7ed3\u679c\u8868\u660e\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u867d\u7136\u51cf\u5c11\u4e86\u4f3c\u7136\u4f30\u8ba1\u7684\u504f\u5dee\u5e76\u63d0\u5347\u4e86\u6027\u80fd\uff0c\u4f46\u6b8b\u5dee\u504f\u5dee\u4ecd\u7136\u5b58\u5728\uff0c\u56e0\u6b64\u6027\u80fd\u4ecd\u6709\u6539\u8fdb\u7a7a\u95f4\u3002\u800cDistDF\u901a\u8fc7\u6700\u5c0f\u5316\u6761\u4ef6\u5206\u5e03\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u5b9e\u73b0\u4e86\u9884\u6d4b\u6a21\u578b\u7684\u65e0\u504f\u8bad\u7ec3\uff0c\u53d6\u5f97\u4e86\u6700\u4f73\u7684\u9884\u6d4b\u6027\u80fd\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-bc52d064bb6b54623e2d10884d0193eb.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-bc52d064bb6b54623e2d10884d0193eb.png\"><\/a><\/p>\n<p>\u5176\u6b21\uff0c\u8bba\u6587\u901a\u8fc7\u6d88\u878d\u5b9e\u9a8c\u5bf9\u4e24\u4e2a\u5173\u952e\u56e0\u7d20\u8fdb\u884c\u4e86\u9a8c\u8bc1\uff1b\u5206\u522b\u8003\u5bdf\u5728DF\u7684\u57fa\u7840\u4e0a\uff0c\u4ec5\u5bf9\u9f50\u5747\u503c\u3001\u4ec5\u5bf9\u9f50\u534f\u65b9\u5dee\u4ee5\u53ca\u540c\u65f6\u5bf9\u9f50\u4e8c\u8005\u7684\u60c5\u5f62\u3002\u7ed3\u679c\u8868\u660e\uff0c\u4e24\u79cd\u56e0\u7d20\u5355\u72ec\u5bf9\u9f50\u65f6\u5747\u80fd\u5e26\u6765\u6027\u80fd\u63d0\u5347\uff0c\u800c\u4e8c\u8005\u540c\u65f6\u5bf9\u9f50\u65f6\u6548\u679c\u6700\u4e3a\u663e\u8457\u3002\u96f7\u5cf0\u7f51<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-3f60ce292c370d25a58bf1e5515ad7c1.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-3f60ce292c370d25a58bf1e5515ad7c1.png\"><\/a><\/p>\n<p>\u63a5\u7740\uff0c\u8bba\u6587\u4e5f\u5bf9\u6a21\u578b\u8f93\u51fa\u7684\u9884\u6d4b\u5e8f\u5217\u8fdb\u884c\u4e86\u53ef\u89c6\u5316\u5206\u6790\u3002\u7ed3\u679c\u8868\u660e\uff0c\u91c7\u7528 DistDF \u8bad\u7ec3\u7684\u6a21\u578b\u80fd\u591f\u8f83\u597d\u5730\u8ddf\u968f\u5e8f\u5217\u4e2d\u7684\u7a81\u53d1\u53d8\u5316\uff0c\u4f7f\u5f97\u9884\u6d4b\u5e8f\u5217\u5728\u6574\u4f53\u5f62\u6001\u4e0a\u66f4\u52a0\u63a5\u8fd1\u771f\u5b9e\u6570\u636e\u3002\u8fd9\u8fdb\u4e00\u6b65\u8868\u660e\uff0cDistDF \u7684\u4f5c\u7528\u4e0d\u4ec5\u4f53\u73b0\u5728\u964d\u4f4e\u6570\u503c\u8bef\u5dee\u4e0a\uff0c\u66f4\u91cd\u8981\u7684\u662f\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5f15\u5bfc\u6a21\u578b\u5b66\u4e60\u5230\u4e86\u771f\u5b9e\u672a\u6765\u65f6\u95f4\u5e8f\u5217\u7684\u6574\u4f53\u5206\u5e03\u5f62\u6001\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-5b65e03e8353356c56c9bf8e5ce47088.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-5b65e03e8353356c56c9bf8e5ce47088.png\"><\/a><\/p>\n<p>\u6700\u540e\uff0c\u8bba\u6587\u5bf9DistDF\u4e0e\u4e0d\u540c\u9884\u6d4b\u6a21\u578b\u7684\u517c\u5bb9\u6027\u8fdb\u884c\u4e86\u9a8c\u8bc1\u3002\u7ed3\u679c\u8868\u660e\uff0c\u65e0\u8bba\u6a21\u578b\u672c\u8eab\u7684\u590d\u6742\u5ea6\u548c\u5efa\u6a21\u65b9\u5f0f\u5982\u4f55\uff0c\u5f15\u5165 DistDF \u8bad\u7ec3\u7b56\u7565\u540e\uff0c\u6a21\u578b\u9884\u6d4b\u6027\u80fd\u51e0\u4e4e\u90fd\u80fd\u591f\u83b7\u5f97\u8fdb\u4e00\u6b65\u63d0\u5347\u3002\u8fd9\u4e00\u7ed3\u679c\u8868\u660e\uff0cDistDF \u7684\u4f5c\u7528\u5e76\u975e\u5f25\u8865\u6a21\u578b\u7ed3\u6784\u672c\u8eab\u7684\u4e0d\u8db3\uff0c\u800c\u662f\u63d0\u4f9b\u4e86\u66f4\u597d\u7684\u8bad\u7ec3\u4fe1\u53f7\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%80%8C%E5%A4%9A%E4%BB%BB%E5%8A%A1%E5%AD%A6%E4%B9%A0%E3%80%8D%E9%9C%80%E8%A6%81%E5%88%86%E5%B8%83%E5%AF%B9%E9%BD%90\"><\/span>\u300c\u591a\u4efb\u52a1\u5b66\u4e60\u300d\u9700\u8981\u5206\u5e03\u5bf9\u9f50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6574\u4f53\u6765\u770b\uff0c\u8fd9\u9879\u7814\u7a76\u91cd\u65b0\u5ba1\u89c6\u4e86\u591a\u4efb\u52a1\u5b66\u4e60\u573a\u666f\u4e2d\u7684\u635f\u5931\u51fd\u6570\u8bbe\u8ba1\u3002\u7814\u7a76\u56e2\u961f\u5f3a\u8c03\uff1a\u591a\u4efb\u52a1\u5b66\u4e60\u7684\u6838\u5fc3\u76ee\u6807\u4e0d\u5e94\u5c40\u9650\u4e8e\u5bf9 T\u4e2a\u6807\u7b7e\u7684\u9010\u70b9\u5efa\u6a21\uff0c\u800c\u5e94\u8f6c\u5411\u5bf9\u4e00\u4e2a\u5728\u4efb\u52a1\u7ef4\u5ea6\u4e0a\u5177\u6709\u5185\u5728\u76f8\u5173\u7ed3\u6784\u7684\u968f\u673a\u8fc7\u7a0b\u8fdb\u884c\u6574\u4f53\u5efa\u6a21\u3002<\/p>\n<p>\u5728\u8fd9\u4e00\u89c6\u89d2\u4e0b\uff0c\u4f20\u7edf\u635f\u5931\u51fd\u6570\uff08\u5982MSE\uff09\u9690\u542b\u4e86\u201c\u7ed9\u5b9a\u8f93\u5165\u6761\u4ef6\u4e0b\u5404\u4efb\u52a1\u6807\u7b7e\u76f8\u4e92\u72ec\u7acb\u201d\u7684\u5047\u8bbe\uff0c\u4ece\u800c\u5c06\u4e00\u4e2a\u9ad8\u7ef4\u3001\u76f8\u5173\u7684\u968f\u673a\u8fc7\u7a0b\u5efa\u6a21\u4efb\u52a1\u9000\u5316\u4e3a\u4e00\u7ec4\u5f7c\u6b64\u72ec\u7acb\u7684\u6807\u91cf\u56de\u5f52\u4efb\u52a1\u3002\u56e0\u8be5\u5047\u8bbe\u5ffd\u7565\u4e86\u6807\u7b7e\u5e8f\u5217\u7684\u5185\u751f\u7ed3\u6784\uff0c\u8fd9\u4e9b\u635f\u5931\u51fd\u6570\u5f80\u5f80\u662f\u6709\u504f\u7684\u3002<\/p>\n<p>DistDF 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