{"id":40840,"date":"2026-02-18T01:06:14","date_gmt":"2026-02-17T17:06:14","guid":{"rendered":"https:\/\/17aitech.com\/?p=40840"},"modified":"2026-02-18T01:06:14","modified_gmt":"2026-02-17T17:06:14","slug":"%e5%8c%97%e5%a4%a7%e6%9e%97%e5%ae%99%e8%be%b0%e5%9b%a2%e9%98%9f%e8%ae%ba%e6%96%87%ef%bc%9a%e4%bb%8e%e6%95%b0%e6%8d%ae%e4%b8%ad%e8%87%aa%e9%80%82%e5%ba%94%e5%ad%a6%e4%b9%a0%e6%97%b6%e5%ba%8f%e9%a2%84","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=40840","title":{"rendered":"\u5317\u5927\u6797\u5b99\u8fb0\u56e2\u961f\u8bba\u6587\uff1a\u4ece\u6570\u636e\u4e2d\u81ea\u9002\u5e94\u5b66\u4e60\u65f6\u5e8f\u9884\u6d4b\u635f\u5931\u4e28ICLR 2026"},"content":{"rendered":"<p>\u5728\u591a\u6b65\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u4efb\u52a1\u4e2d\uff0c\u9884\u6d4b\u6027\u80fd\u968f\u65f6\u95f4\u6b65\u957f\u8fc5\u901f\u9000\u5316\u51e0\u4e4e\u6210\u4e3a\u4e00\u79cd\u5171\u8bc6\u3002\u4f8b\u5982\uff1a\u5728\u6c14\u8c61\u9884\u6d4b\u4e2d\uff0c\u77ed\u671f\u7684\u6e29\u5ea6\u53d8\u5316\u80fd\u591f\u8f83\u4e3a\u51c6\u786e\u5730\u523b\u753b\uff0c\u4f46\u5f53\u9884\u6d4b\u8de8\u5ea6\u6269\u5c55\u81f3\u6570\u65e5\u751a\u81f3\u4e00\u5468\u65f6\uff0c\u9884\u6d4b\u8bef\u5dee\u5c31\u4f1a\u9010\u6e10\u653e\u5927\uff0c\u5468\u671f\u4e0e\u8d8b\u52bf\u7ed3\u6784\u9010\u6e10\u504f\u79bb\u771f\u5b9e\u8f68\u8ff9\u3002\u7c7b\u4f3c\u7684\u95ee\u9898\u5728\u91d1\u878d\u4ef7\u683c\u8d70\u52bf\u548c\u7535\u529b\u8d1f\u8377\u9884\u6d4b\u7b49\u573a\u666f\u4e2d\u4e5f\u5e7f\u6cdb\u5b58\u5728\u3002<\/p>\n<p>\u65e0\u8bba\u6a21\u578b\u7ed3\u6784\u5982\u4f55\u53d8\u5316\uff0c\u5f53\u9884\u6d4b\u8303\u56f4\u4ece\u77ed\u671f\u6269\u5c55\u81f3\u4e2d\u957f\u671f\u65f6\uff0c\u8bef\u5dee\u79ef\u7d2f\u3001\u8d8b\u52bf\u6f02\u79fb\u548c\u7ed3\u6784\u5931\u771f\u5f80\u5f80\u4e0d\u53ef\u907f\u514d\u5730\u51fa\u73b0\u3002\u8fd9\u7c7b\u73b0\u8c61\u5728\u5b9e\u8df5\u4e2d\u88ab\u9891\u7e41\u89c2\u5bdf\uff0c\u5374\u901a\u5e38\u88ab\u89c6\u4e3a\u6a21\u578b\u8868\u8fbe\u80fd\u529b\u6216\u4f9d\u8d56\u5efa\u6a21\u4e0d\u8db3\u7684\u76f4\u63a5\u7ed3\u679c\u3002<\/p>\n<p>\u7136\u800c\uff0c\u4e0e\u6a21\u578b\u7ed3\u6784\u6301\u7eed\u6f14\u8fdb\u5f62\u6210\u9c9c\u660e\u5bf9\u6bd4\u7684\u662f\uff0c\u591a\u6b65\u9884\u6d4b\u5728\u8bad\u7ec3\u9636\u6bb5\u6240\u4f7f\u7528\u7684\u635f\u5931\u51fd\u6570\u5374\u957f\u671f\u4fdd\u6301\u56fa\u5b9a\u3002\u5927\u591a\u6570\u65b9\u6cd5\u4ecd\u4ee5\u9010\u65f6\u95f4\u70b9\u7684\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u4f5c\u4e3a\u4f18\u5316\u76ee\u6807\uff0c\u9ed8\u8ba4\u5c06\u672a\u6765\u4e0d\u540c\u9884\u6d4b\u6b65\u89c6\u4e3a\u76f8\u4e92\u72ec\u7acb\u4e14\u91cd\u8981\u6027\u4e00\u81f4\u7684\u9884\u6d4b\u5bf9\u8c61\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u591a\u6b65\u9884\u6d4b\u5e76\u975e\u4e00\u7ec4\u5f7c\u6b64\u72ec\u7acb\u7684\u56de\u5f52\u4efb\u52a1\uff0c\u672a\u6765\u4e0d\u540c\u65f6\u95f4\u70b9\u4e4b\u95f4\u5f80\u5f80\u5448\u73b0\u663e\u8457\u7684\u76f8\u5173\u6027\uff1b\u6b64\u5916\uff0c\u4e0d\u540c\u9884\u6d4b\u6b65\u5728\u4f18\u5316\u9636\u6bb5\u7684\u91cd\u8981\u6027\u4e5f\u5e76\u4e0d\u76f8\u540c\u3002\u82e5\u635f\u5931\u51fd\u6570\u65e0\u6cd5\u663e\u5f0f\u523b\u753b\u8fd9\u4e9b\u7ed3\u6784\u7279\u5f81\uff0c\u6a21\u578b\u5728\u957f\u671f\u9884\u6d4b\u4e2d\u51fa\u73b0\u7cfb\u7edf\u6027\u504f\u5dee\u4fbf\u5e76\u975e\u5076\u7136\uff0c\u800c\u662f\u8bad\u7ec3\u9636\u6bb5\u9519\u8bef\u5047\u8bbe\u7684\u81ea\u7136\u7ed3\u679c\u3002<\/p>\n<p>\u6b63\u662f\u5728\u8fd9\u4e00\u80cc\u666f\u4e0b\uff0c\u6797\u5b99\u8fb0\u56e2\u961f\u63d0\u51fa\u4e86\u9898\u4e3a\u300aQuadratic Direct Forecast for Training Multi-step Time-Series Forecast Models\u300b\u7684\u7814\u7a76\u5de5\u4f5c\u3002\u901a\u8fc7\u91cd\u6784\u8bad\u7ec3\u76ee\u6807\u7684\u52a0\u6743\u7ed3\u6784\uff0c\u5f15\u5165\u5bf9\u9884\u6d4b\u6b65\u76f8\u5173\u6027\u4e0e\u4e0d\u786e\u5b9a\u6027\u5dee\u5f02\u7684\u663e\u5f0f\u5efa\u6a21\u3002\u7814\u7a76\u56e2\u961f\u5c55\u793a\u4e86\u5728\u4e0d\u6539\u53d8\u6a21\u578b\u67b6\u6784\u7684\u524d\u63d0\u4e0b\uff0c\u4ec5\u901a\u8fc7\u8c03\u6574\u8bad\u7ec3\u76ee\u6807\u5373\u53ef\u663e\u8457\u6539\u5584\u591a\u6b65\u9884\u6d4b\u6027\u80fd\u7684\u53ef\u80fd\u6027\uff0c\u4ece\u800c\u4e3a\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u63d0\u4f9b\u4e86\u4e00\u79cd\u4ece\u8bad\u7ec3\u673a\u5236\u5c42\u9762\u7406\u89e3\u957f\u671f\u9884\u6d4b\u5931\u6548\u7684\u65b0\u89c6\u89d2\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-4b454f55983a7b433327096d4ea6a936.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-4b454f55983a7b433327096d4ea6a936.png\"><\/a><\/p>\n<p>\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/pdf\/2511.00053v1<\/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 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>\u95ee\u9898\u6839\u6e90\uff1a\u5747\u65b9\u8bef\u5dee\u7684\u4e24\u4e2a\u5148\u9a8c<\/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=40840\/#QDF%EF%BC%9A%E4%BB%8E%E6%95%B0%E6%8D%AE%E4%B8%AD%E8%87%AA%E9%80%82%E5%BA%94%E5%AD%A6%E4%B9%A0%E9%A2%84%E6%B5%8B%E6%8D%9F%E5%A4%B1\" >QDF\uff1a\u4ece\u6570\u636e\u4e2d\u81ea\u9002\u5e94\u5b66\u4e60\u9884\u6d4b\u635f\u5931<\/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=40840\/#%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=40840\/#%E4%B8%80%E6%AC%A1%E9%92%88%E5%AF%B9%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AE%E7%9A%84%E7%B3%BB%E7%BB%9F%E6%80%A7%E5%AE%A1%E5%88%A4\" >\u4e00\u6b21\u9488\u5bf9\u5747\u65b9\u8bef\u5dee\u7684\u7cfb\u7edf\u6027\u5ba1\u5224<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/17aitech.com\/?p=40840\/#%E4%BD%9C%E8%80%85%E4%BF%A1%E6%81%AF\" >\u4f5c\u8005\u4fe1\u606f<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E9%97%AE%E9%A2%98%E6%A0%B9%E6%BA%90%EF%BC%9A%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AE%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%85%88%E9%AA%8C\"><\/span>\u95ee\u9898\u6839\u6e90\uff1a\u5747\u65b9\u8bef\u5dee\u7684\u4e24\u4e2a\u5148\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u5f53\u4e0b\u7684\u65f6\u5e8f\u9884\u6d4b\u9886\u57df\uff0c\u7edd\u5927\u591a\u6570\u6587\u732e\u4ecd\u4ee5\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>\u8fd9\u4e2a\u635f\u5931\u51fd\u6570\u9690\u542b\u4e86\u4e24\u4e2a\u5148\u9a8c\uff1a1. \u672a\u6765\u4e0d\u540c\u65f6\u95f4\u70b9\u7684\u9884\u6d4b\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff1b2. \u6240\u6709\u9884\u6d4b\u6b65\u7684\u91cd\u8981\u6027\u662f\u76f8\u540c\u7684\u3002<\/p>\n<p>\u7136\u800c\uff0c\u73b0\u5b9e\u5e76\u975e\u5982\u6b64\uff1a\u660e\u5929\u7684\u5929\u6c14\u4e0e\u540e\u5929\u7684\u5929\u6c14\u5b58\u5728\u76f8\u5173\u6027\uff0c\u9884\u6d4b\u672a\u67651\u5c0f\u65f6\u548c1\u5468\u7684\u96be\u5ea6\u4e5f\u5b8c\u5168\u4e0d\u540c\u3002\u56e0\u6b64\uff0c\u591a\u6b65\u9884\u6d4b\u5e76\u975e\u4e00\u7ec4\u72ec\u7acb\u7684\u56de\u5f52\u4efb\u52a1\uff1b\u4e0d\u540c\u9884\u6d4b\u6b65\u5728\u4f18\u5316\u9636\u6bb5\u7684\u91cd\u8981\u6027\u4e5f\u5e76\u4e0d\u76f8\u540c\u3002\u5982\u635f\u5931\u51fd\u6570\u65e0\u6cd5\u6b63\u786e\u523b\u753b\u8fd9\u4e9b\u7ed3\u6784\u7279\u5f81\uff0c\u6a21\u578b\u5728\u957f\u671f\u9884\u6d4b\u4e2d\u51fa\u73b0\u7cfb\u7edf\u6027\u504f\u5dee\uff0c\u5c31\u5e76\u975e\u5076\u7136\uff0c\u800c\u662f\u8bad\u7ec3\u9636\u6bb5\u9519\u8bef\u5047\u8bbe\u7684\u5fc5\u7136\u7ed3\u679c\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-e2dc6f061ddb6798493c97952d3e2d0f.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-e2dc6f061ddb6798493c97952d3e2d0f.png\"><\/a><\/p>\n<p>\u7814\u7a76\u4eba\u5458\u4e0a\u8ff0\u4e24\u70b9\u5148\u9a8c\u8fdb\u884c\u4e86\u5b9e\u9a8c\u68c0\u9a8c\uff0c\u53d1\u73b0\u5b83\u4eec\u5728\u591a\u6b65\u9884\u6d4b\u573a\u666f\u4e2d\u5747\u4e0d\u6210\u7acb\u3002<\/p>\n<p>\u9996\u5148\uff0c\u5bf9\u6807\u7b7e\u5e8f\u5217\u7684\u6761\u4ef6\u534f\u65b9\u5dee\u8fdb\u884c\u4e86\u504f\u76f8\u5173\u5206\u6790\uff0c\u4ee5\u523b\u753b\u5728\u63a7\u5236\u5386\u53f2\u8f93\u5165\u7684\u5f71\u54cd\u4e4b\u540e\uff0c\u6807\u7b7e\u5e8f\u5217\u4e0d\u540c\u65f6\u95f4\u70b9 $Y_t$ \u4e0e $Y_{t&#8217;}$ \u4e4b\u95f4\u7684\u76f4\u63a5\u5173\u7cfb\u3002\u5b9e\u9a8c\u7ed3\u679c\u663e\u793a\uff0c\u672a\u6765\u65f6\u95f4\u70b9\u4e4b\u95f4\u5b58\u5728\u5927\u91cf\u975e\u96f6\u504f\u76f8\u5173\u7cfb\u6570\uff0c\u5426\u5b9a\u4e86\u5747\u65b9\u8bef\u5dee\u6240\u9690\u542b\u7684\u6761\u4ef6\u72ec\u7acb\u5047\u8bbe\u3002\u96f7\u5cf0\u7f51<span style=\"color:#FD5D3C\">(\u516c\u4f17\u53f7\uff1a\u96f7\u5cf0\u7f51)<\/span><\/p>\n<p>\u8fdb\u4e00\u6b65\uff0c\u5bf9\u6807\u7b7e\u5e8f\u5217\u7684\u6761\u4ef6\u65b9\u5dee\u8fdb\u884c\u4e86\u5206\u6790\u3002\u5b9e\u9a8c\u7ed3\u679c\u663e\u793a\uff0c\u4e0d\u540c\u65f6\u95f4\u70b9\u7684\u8bef\u5dee\u65b9\u5dee\u5b58\u5728\u663e\u8457\u5dee\u5f02\uff0c\u4e14\u968f\u7740\u9884\u6d4b\u6b65\u6574\u4f53\u589e\u5927\uff0c\u8bf4\u660e\u5c06\u6240\u6709\u9884\u6d4b\u6b65\u89c6\u4e3a\u96be\u5ea6\u4e00\u81f4\u7684\u4efb\u52a1\u5e76\u4e0d\u7b26\u5408\u6570\u636e\u7279\u6027\uff0c\u5426\u5b9a\u4e86\u5747\u65b9\u8bef\u5dee\u9690\u542b\u91cd\u8981\u6027\u4e00\u81f4\u5047\u8bbe\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"QDF%EF%BC%9A%E4%BB%8E%E6%95%B0%E6%8D%AE%E4%B8%AD%E8%87%AA%E9%80%82%E5%BA%94%E5%AD%A6%E4%B9%A0%E9%A2%84%E6%B5%8B%E6%8D%9F%E5%A4%B1\"><\/span>QDF\uff1a\u4ece\u6570\u636e\u4e2d\u81ea\u9002\u5e94\u5b66\u4e60\u9884\u6d4b\u635f\u5931<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u9488\u5bf9MSE\u5b58\u5728\u7684\u4e24\u4e2a\u4e0d\u5408\u7406\u5148\u9a8c\uff0c\u6797\u5b99\u8fb0\u6559\u6388\u56e2\u961f\u63d0\u51fa\u4e86QDF\uff08Quadratic Direct Forecast\uff09\u65b9\u6cd5\uff0c\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\uff1a\u4e0d\u518d\u5c06\u635f\u5931\u51fd\u6570\u89c6\u4e3a\u56fa\u5b9a\u4e0d\u53d8\u7684\u4f18\u5316\u76ee\u6807\uff0c\u800c\u662f\u5c06\u5176\u672c\u8eab\u4f5c\u4e3a\u53ef\u5b66\u4e60\u7684\u5bf9\u8c61\uff0c\u4ece\u800c\u81ea\u52a8\u201c\u53d1\u73b0\u201d\u6700\u9002\u5408\u7279\u5b9a\u4efb\u52a1\u6570\u636e\u7ed3\u6784\u7684\u635f\u5931\u8868\u8ff0\u3002<\/p>\n<p>\u4ece\u6982\u7387\u5efa\u6a21\u7684\u89c6\u89d2\u51fa\u53d1\uff0c\u7406\u60f3\u7684\u635f\u5931\u51fd\u6570\u5e94\u6765\u6e90\u4e8e\u8d1f\u5bf9\u6570\u4f3c\u7136\u3002\u5728\u9ad8\u65af\u8bef\u5dee\u5047\u8bbe\u4e0b\u3002\u5728\u9ad8\u65af\u8bef\u5dee\u5047\u8bbe\u4e0b\uff0c\u7ed9\u5b9a\u5386\u53f2\u5e8f\u5217 $mathbf{x}$\uff0c\u6807\u7b7e\u5e8f\u5217 $$mathbf{y}inmathbb{R}^mathrm{Ttimes 1}$$ \u7684\u6761\u4ef6\u5206\u5e03\u4e3a\u591a\u5143\u9ad8\u65af\u5206\u5e03\uff0c\u5176\u8d1f\u5bf9\u6570\u4f3c\u7136\uff08\u5ffd\u7565\u5e38\u6570\u9879\uff09\u53ef\u8868\u793a\u4e3a\uff1a<\/p>\n<p>$$mathcal{L}_{boldsymbol{Sigma}}(mathbf{x},mathbf{y};g_theta) = (mathbf{y} &#8211; g_theta(mathbf{x}))^top boldsymbol{bar{Sigma}} (mathbf{y} &#8211; g_theta(mathbf{x}))$$<\/p>\n<p>\u5176\u4e2d\uff0c$boldsymbol{Sigma} in mathbb{R}^{T times T}$\u662f\u6807\u7b7e\u5e8f\u5217\u7684\u6761\u4ef6\u534f\u65b9\u5dee\u77e9\u9635\uff0c$T$ \u4e3a\u9884\u6d4b\u6b65\u957f\uff0c$boldsymbol{bar{Sigma}} = boldsymbol{Sigma}^{-1}$\u4e3a\u8be5\u4e8c\u6b21\u578b\u7684\u6743\u91cd\u77e9\u9635\u3002\u5728\u8be5\u4e8c\u6b21\u578b\u4e2d\uff1a\u6743\u91cd\u77e9\u9635\u7684\u975e\u5bf9\u89d2\u5143\u7d20\u523b\u753b\u4e86\u672a\u6765\u4e0d\u540c\u65f6\u95f4\u70b9\u4e4b\u95f4\u7684\u6761\u4ef6\u76f8\u5173\u6027\uff0c\u4ece\u800c\u80fd\u591f\u663e\u5f0f\u5efa\u6a21\u6807\u7b7e\u81ea\u76f8\u5173\u6548\u5e94\uff0c\u6253\u7834\u4e86MSE\u6240\u9690\u542b\u7684\u6761\u4ef6\u72ec\u7acb\u5047\u8bbe\uff1b\u6743\u91cd\u77e9\u9635\u7684\u5bf9\u89d2\u5143\u7d20\u53cd\u6620\u4e86\u4e0d\u540c\u9884\u6d4b\u6b65\u7684\u4e0d\u786e\u5b9a\u6027\u5dee\u5f02\uff0c\u4f7f\u5f97\u6a21\u578b\u80fd\u591f\u4e3a\u4e0d\u540c\u96be\u5ea6\u7684\u9884\u6d4b\u4efb\u52a1\u5206\u914d\u5f02\u6784\u6743\u91cd\uff0c\u6253\u7834\u4e86MSE\u6240\u9690\u542b\u7684\u91cd\u8981\u6027\u4e00\u81f4\u5047\u8bbe\u3002\u96f7\u5cf0\u7f51<\/p>\n<p>\u56e0\u6b64\uff0c\u8be5\u4e8c\u6b21\u578b\u635f\u5931\u51fd\u6570\u5728\u7406\u8bba\u4e0a\u80fd\u591f\u540c\u65f6\u89e3\u51b3\u4f20\u7edfMSE\u635f\u5931\u5728\u591a\u6b65\u9884\u6d4b\u573a\u666f\u4e0b\u7684\u4e24\u4e2a\u7ed3\u6784\u6027\u504f\u5dee\u95ee\u9898\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5728\u5b9e\u9645\u9884\u6d4b\u4efb\u52a1\u4e2d\uff0c\u6743\u91cd\u77e9\u9635$boldsymbol{bar{Sigma}}$\u96be\u4ee5\u4f30\u8ba1\u3002\u4e3a\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u7814\u7a76\u56e2\u961f\u53d7\u5230\u5143\u5b66\u4e60\u542f\u53d1\uff0c\u5c06$boldsymbol{bar{Sigma}}$\u4f5c\u4e3a\u53ef\u5b66\u4e60\u7684\u5bf9\u8c61\uff0c\u901a\u8fc7\u4e00\u4e2a\u53cc\u5c42\u4f18\u5316\u673a\u5236\u5c06$boldsymbol{bar{Sigma}}$\u4ece\u6570\u636e\u4e2d\u201c\u5b66\u201d\u51fa\u6765\uff1a<\/p>\n<p>$$min_{boldsymbol{Sigma} succeq 0} mathcal{L}_{boldsymbol{Sigma}}(mathbf{x}_{text{out}}, mathbf{y}_{text{out}};g_{theta^*}) quad text{s.t.} quad theta^* = argmin_{theta} mathcal{L}_{boldsymbol{Sigma}}(mathbf{x}_{text{in}}, mathbf{y}_{text{in}};g_theta)$$<\/p>\n<p>\u8be5\u53cc\u5c42\u4f18\u5316\u95ee\u9898\u7684\u6c42\u89e3\u8fc7\u7a0b\u5305\u62ec\u4e24\u4e2a\u9636\u6bb5\u3002\u9996\u5148\uff0c\u5728\u7ed9\u5b9a$boldsymbol{Sigma}$ \u7684\u6761\u4ef6\u4e0b\uff0c\u901a\u8fc7\u5728\u5143\u8bad\u7ec3\u96c6$(mathbf{x}_{text{in}}, mathbf{y}_{text{in}})$\u4e0a\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570$mathcal{L}_{boldsymbol{Sigma}}$\u6765\u66f4\u65b0\u6a21\u578b\u53c2\u6570$theta$\u3002\u63a5\u7740\uff0c\u4f9d\u636e\u6a21\u578b\u5728\u5143\u9a8c\u8bc1\u96c6$(mathbf{x}_{text{out}}, mathbf{y}_{text{out}})$\u4e0a\u7684\u9884\u6d4b\u8bef\u5dee\uff0c\u53cd\u5411\u4f20\u64ad\u66f4\u65b0$boldsymbol{Sigma}$\u3002\u5176\u4e2d\uff0c\u5143\u8bad\u7ec3\u96c6\u548c\u5143\u9a8c\u8bc1\u96c6\u6765\u81ea\u5bf9\u8bad\u7ec3\u96c6\u7684\u4e0d\u540c\u5207\u7247\u3002<\/p>\n<p>\u8fd9\u79cd\u53cc\u5c42\u8bbe\u8ba1\u7684\u6838\u5fc3\u4f18\u52bf\u5728\u4e8e\uff1a\u8bad\u7ec3\u76ee\u6807\u7684\u4f18\u52a3\u4e0d\u518d\u7531\u62df\u5408\u4f18\u5ea6\u51b3\u5b9a\uff0c\u800c\u662f\u7531\u5143\u9a8c\u8bc1\u96c6\u4e0a\u7684\u6cdb\u5316\u6027\u80fd\u6765\u523b\u753b\u3002\u901a\u8fc7\u591a\u6b21\u6570\u636e\u62c6\u5206\u4e0e\u8fed\u4ee3\u66f4\u65b0\uff0c\u7b97\u6cd5\u5f97\u4ee5\u5b66\u4e60\u5230\u5728\u4e0d\u540c\u65f6\u95f4\u533a\u95f4\u5185\u4e00\u81f4\u7684\u8bef\u5dee\u76f8\u5173\u6a21\u5f0f\uff0c\u4ece\u800c\u5f62\u6210\u7a33\u5b9a\u4e14\u53ef\u6cdb\u5316\u7684\u8bad\u7ec3\u76ee\u6807\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\u5c06 QDF \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\u8fd9\u4e9b\u65b9\u6cd5\u76f8\u8f83\u4e8e\u5747\u65b9\u8bef\u5dee\u5747\u80fd\u5e26\u6765\u4e00\u5b9a\u7684\u6027\u80fd\u63d0\u5347\uff0c\u4f46\u5728\u7a33\u5b9a\u6027\u548c\u6027\u80fd\u4e0a\u9650\u65b9\u9762\u4ecd\u4e0d\u53ca QDF\u3002\u539f\u56e0\u5728\u4e8e\u8fd9\u4e9b\u65b9\u6cd5\u4ec5\u90e8\u5206\u5904\u7406\u6807\u7b7e\u4e4b\u95f4\u7684\u76f8\u5173\u6027\uff0c\u4ecd\u9690\u542b\u5730\u5047\u8bbe\u5269\u4f59\u8bef\u5dee\u53ef\u901a\u8fc7\u5747\u5300\u52a0\u6743\u65b9\u5f0f\u8fdb\u884c\u4f18\u5316\uff0c\u800c QDF \u540c\u65f6\u5efa\u6a21\u4e86\u6807\u7b7e\u95f4\u7684\u76f8\u5173\u6027\u4ee5\u53ca\u4e0d\u540c\u9884\u6d4b\u6b65\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u5e76\u901a\u8fc7\u5143\u5b66\u4e60\u5f97\u5230\u6700\u4f18\u52a0\u6743\u6743\u91cd\uff0c\u5f7b\u5e95\u89e3\u51b3\u4e86\u635f\u5931\u51fd\u6570\u4e2d\u53ef\u80fd\u5b58\u5728\u7684\u504f\u5dee\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-bd96c3b818f14fd236a9126e9c187eff.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-bd96c3b818f14fd236a9126e9c187eff.png\"><\/a><\/p>\n<p>\u5176\u6b21\uff0c\u7814\u7a76\u4eba\u5458\u901a\u8fc7\u6d88\u878d\u5b9e\u9a8c\u5bf9\u4e0a\u8ff0\u4e24\u4e2a\u5173\u952e\u56e0\u7d20\u8fdb\u884c\u4e86\u9a8c\u8bc1\u3002\u5b9e\u9a8c\u5206\u522b\u8003\u5bdf\u4ec5\u5efa\u6a21\u4e0d\u540c\u9884\u6d4b\u6b65\u6743\u91cd\u3001\u4ec5\u5efa\u6a21\u65f6\u95f4\u76f8\u5173\u6027\u4ee5\u53ca\u540c\u65f6\u5efa\u6a21\u4e8c\u8005\u7684\u60c5\u5f62\u3002\u7ed3\u679c\u663e\u793a\uff0c\u4e24\u79cd\u56e0\u7d20\u5355\u72ec\u5f15\u5165\u65f6\u5747\u80fd\u5e26\u6765\u6027\u80fd\u63d0\u5347\uff0c\u800c\u4e8c\u8005\u540c\u65f6\u4f5c\u7528\u65f6\u6548\u679c\u6700\u4e3a\u663e\u8457\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-ecfd4a7db2c0d26a0ae6efc84c9c7052.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-ecfd4a7db2c0d26a0ae6efc84c9c7052.png\"><\/a><\/p>\n<p>\u7814\u7a76\u4eba\u5458\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\u57fa\u4e8e\u5747\u65b9\u8bef\u5dee\u8bad\u7ec3\u7684\u6a21\u578b\u5728\u5468\u671f\u6027\u65f6\u95f4\u5e8f\u5217\u4e2d\u666e\u904d\u5b58\u5728\u632f\u5e45\u538b\u7f29\u3001\u5cf0\u503c\u88ab\u62b9\u5e73\u4ee5\u53ca\u62d0\u70b9\u54cd\u5e94\u6ede\u540e\u7684\u73b0\u8c61\u3002\u5f15\u5165QDF\u540e\uff0c\u6a21\u578b\u5728\u5cf0\u503c\u4f4d\u7f6e\u3001\u5468\u671f\u76f8\u4f4d\u4ee5\u53ca\u957f\u671f\u8d8b\u52bf\u7a33\u5b9a\u6027\u65b9\u9762\u5747\u8868\u73b0\u51fa\u66f4\u9ad8\u4e00\u81f4\u6027\uff0c\u65f6\u95f4\u7ed3\u6784\u5f97\u5230\u4e86\u66f4\u5b8c\u6574\u7684\u4fdd\u7559\uff0c\u8bf4\u660eQDF\u6709\u6548\u8bad\u7ec3\u6a21\u578b\u5c0a\u91cd\u672a\u6765\u4e0d\u540c\u65f6\u95f4\u70b9\u4e4b\u95f4\u7684\u6574\u4f53\u5173\u7cfb\u3002<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-2faf36985abbaadb740c85159a743a8f.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2026\/02\/frc-2faf36985abbaadb740c85159a743a8f.png\"><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E4%B8%80%E6%AC%A1%E9%92%88%E5%AF%B9%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AE%E7%9A%84%E7%B3%BB%E7%BB%9F%E6%80%A7%E5%AE%A1%E5%88%A4\"><\/span>\u4e00\u6b21\u9488\u5bf9\u5747\u65b9\u8bef\u5dee\u7684\u7cfb\u7edf\u6027\u5ba1\u5224<span 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