{"id":160,"date":"2025-10-13T11:15:23","date_gmt":"2025-10-13T03:15:23","guid":{"rendered":"http:\/\/47.95.221.121\/?p=160"},"modified":"2025-10-14T14:54:59","modified_gmt":"2025-10-14T06:54:59","slug":"%e8%af%a2%e9%97%ae%e4%b8%8e%e5%90%a6%ef%bc%9a%e5%ad%a6%e4%b9%a0%e8%8e%b7%e5%8f%96%e4%ba%ba%e7%b1%bb%e5%8f%8d%e9%a6%88","status":"publish","type":"post","link":"https:\/\/smartaiunion.com\/index.php\/2025\/10\/13\/160\/","title":{"rendered":"\u8be2\u95ee\u4e0e\u5426\uff1a\u5b66\u4e60\u83b7\u53d6\u4eba\u7c7b\u53cd\u9988"},"content":{"rendered":"\n<p>\u6458\u8981<\/p>\n\n\n\n<p>\u5f00\u53d1\u80fd\u5728\u5206\u7c7b\u4efb\u52a1\u4e2d\u4e0e\u4eba\u7c7b\u6027\u80fd\u4e92\u8865\u7684\u51b3\u7b56\u652f\u6301\u7cfb\u7edf\uff0c\u4ecd\u662f\u4e00\u9879\u5c1a\u672a\u89e3\u51b3\u7684\u6311\u6218\u3002\u201c\u5b66\u4e60\u59d4\u6258\u201d\uff08Learning to Defer\uff0cLtD\uff09\u662f\u4e00\u79cd\u5e7f\u6cdb\u5e94\u7528\u7684\u65b9\u6cd5\uff0c\u5b83\u5141\u8bb8\u673a\u5668\u5b66\u4e60\uff08ML\uff09\u6a21\u578b\u5c06\u590d\u6742\u6848\u4f8b\u4ea4\u7531\u4eba\u7c7b\u4e13\u5bb6\u5904\u7406\u3002\u7136\u800c\uff0cLtD \u5c06\u4eba\u7c7b\u4e0e\u673a\u5668\u5b66\u4e60\u6a21\u578b\u89c6\u4e3a\u76f8\u4e92\u6392\u65a5\u7684\u51b3\u7b56\u8005\uff0c\u4ec5\u5c06\u4e13\u5bb6\u7684\u4f5c\u7528\u5c40\u9650\u4e8e\u63d0\u4f9b\u9884\u6d4b\u7ed3\u679c\uff0c\u8fd9\u4e00\u5c40\u9650\u6781\u5927\u5730\u9650\u5236\u4e86\u4e13\u5bb6\u7684\u8d21\u732e\u3002\u4e3a\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u672c\u6587\u63d0\u51fa \u201c\u5b66\u4e60\u8be2\u95ee\u201d\uff08Learning to Ask\uff0cLtA\uff09\u8fd9\u4e00\u5168\u65b0\u6846\u67b6\uff0c\u8be5\u6846\u67b6\u4e0d\u4ec5\u80fd\u786e\u5b9a\u4f55\u65f6\u9700\u8981\u7eb3\u5165\u4e13\u5bb6\u8f93\u5165\uff0c\u8fd8\u80fd\u660e\u786e\u5982\u4f55\u5c06\u4e13\u5bb6\u8f93\u5165\u878d\u5165\u673a\u5668\u5b66\u4e60\u6a21\u578b\u3002<\/p>\n\n\n\n<p>LtA \u57fa\u4e8e\u53cc\u7ec4\u4ef6\u67b6\u6784\uff1a\u4e00\u4e2a\u6807\u51c6\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u4ee5\u53ca\u4e00\u4e2a\u5229\u7528\u989d\u5916\u4eba\u7c7b\u4e13\u5bb6\u53cd\u9988\u8bad\u7ec3\u7684\u589e\u5f3a\u6a21\u578b\uff08enriched model\uff09\uff0c\u540c\u65f6\u8fd8\u5305\u542b\u4e00\u5957\u7528\u4e8e\u786e\u5b9a\u4f55\u65f6\u67e5\u8be2\u589e\u5f3a\u6a21\u578b\u7684\u7406\u8bba\u6700\u4f18\u7b56\u7565\u3002\u672c\u6587\u63d0\u4f9b\u4e86\u4e24\u79cd LtA \u7684\u5b9e\u9645\u5b9e\u73b0\u65b9\u5f0f\uff1a\u4e00\u79cd\u662f\u5e8f\u8d2f\u65b9\u6cd5\uff08sequential approach\uff09\uff0c\u5206\u9636\u6bb5\u8bad\u7ec3\u6a21\u578b\uff1b\u53e6\u4e00\u79cd\u662f\u8054\u5408\u65b9\u6cd5\uff08joint approach\uff09\uff0c\u5bf9\u6a21\u578b\u8fdb\u884c\u540c\u6b65\u4f18\u5316\u3002\u9488\u5bf9\u8054\u5408\u65b9\u6cd5\uff0c\u672c\u6587\u8bbe\u8ba1\u4e86\u5177\u6709\u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\uff08realisable-consistency\uff09\u4fdd\u969c\u7684\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff08surrogate losses\uff09\u3002\u5728\u5408\u6210\u6570\u636e\u548c\u771f\u5b9e\u4e13\u5bb6\u6570\u636e\u4e0a\u7684\u5b9e\u9a8c\u8868\u660e\uff0cLtA \u4e3a\u5b9e\u73b0\u9ad8\u6548\u7684\u4eba\u7c7b &#8211; \u4eba\u5de5\u667a\u80fd\u534f\u4f5c\u63d0\u4f9b\u4e86\u66f4\u7075\u6d3b\u3001\u66f4\u5f3a\u5927\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1 \u5f15\u8a00<\/h2>\n\n\n\n<p>\u8fc7\u53bb\u51e0\u5e74\uff0c\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u8fdb\u6b65\u63a8\u52a8\u4e86\u5404\u7c7b\u4efb\u52a1\u6027\u80fd\u7684\u5927\u5e45\u63d0\u5347\uff0c\u4f7f\u5f97\u6a21\u578b\u5728\u7279\u5b9a\u9886\u57df\u7684\u80fd\u529b\u751a\u81f3\u8d85\u8d8a\u4e86\u4eba\u7c7b\u7684\u7406\u89e3\u4e0e\u8868\u73b0 [11,13,38,45,35,24,32]\u3002\u7136\u800c\uff0c\u5728\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u573a\u666f\u4e2d\uff0c\u7531\u4e8e\u5b58\u5728\u7cfb\u7edf\u6027\u504f\u5dee [25]\u3001\u95ee\u8d23\u7f3a\u5931 [14] \u4ee5\u53ca\u6cdb\u5316\u80fd\u529b\u6709\u9650 [17] \u7b49\u95ee\u9898\uff0c\u5b8c\u5168\u81ea\u52a8\u5316\u5e76\u4e0d\u53ef\u53d6\u3002\u56e0\u6b64\uff0c\u5982\u4f55\u6784\u5efa\u878d\u5408\u4eba\u7c7b\u4e13\u5bb6\u53cd\u9988\u3001\u5b9e\u73b0\u6027\u80fd\u4e92\u8865\u7684\u4eba\u7c7b &#8211; \u4eba\u5de5\u667a\u80fd\u534f\u4f5c\u6846\u67b6\uff0c\u9010\u6e10\u6210\u4e3a\u7814\u7a76\u70ed\u70b9 [3]\u3002<\/p>\n\n\n\n<p>\u4ee5\u6025\u8bca\u5ba4\u5206\u8bca\u573a\u666f\u4e3a\u4f8b\uff0c\u533b\u7597\u4eba\u5458\u9700\u8981\u5bf9\u60a3\u8005\u8fdb\u884c\u8bc4\u4f30\u5e76\u786e\u5b9a\u4f18\u5148\u6551\u6cbb\u987a\u5e8f\u3002\u5c3d\u7ba1\u6570\u636e\u9a71\u52a8\u7684\u51b3\u7b56\u652f\u6301\u7cfb\u7edf\u5df2\u5c55\u73b0\u51fa\u51fa\u8272\u7684\u6027\u80fd [9,28]\uff0c\u4f46\u4e0e\u51b3\u7b56\u8005\uff08\u533b\u7597\u4eba\u5458\uff09\u76f8\u6bd4\uff0c\u8fd9\u4e9b\u7cfb\u7edf\u83b7\u53d6\u7684\u60a3\u8005\u4fe1\u606f\u5f80\u5f80\u66f4\u4e3a\u6709\u9650\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5728\u67d0\u4e9b\u4efb\u52a1\u4e2d\uff0c\u6709\u7814\u7a76\u8868\u660e\u4e13\u4e1a\u533b\u751f\u80fd\u591f\u5229\u7528\u51b3\u7b56\u652f\u6301\u7cfb\u7edf\u65e0\u6cd5\u83b7\u53d6\u7684\u4fe1\u606f\uff08\u5982\u60a3\u8005\u7684\u53e3\u8ff0\u75c5\u53f2\uff09\u6765\u505a\u51fa\u51b3\u7b56 [1]\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u4f8b\u5982\uff0c\u6709\u7814\u7a76\u53d1\u73b0\uff0c\u533b\u751f\u5728\u8bca\u65ad\u6025\u6027\u4e0a\u6d88\u5316\u9053\u51fa\u8840\uff08AGIB\uff09\u65f6\uff0c\u4f1a\u8003\u8651\u6297\u51dd\u836f\u7269\u4f7f\u7528\u60c5\u51b5\u7b49\u989d\u5916\u56e0\u7d20\uff0c\u800c\u8fd9\u4e9b\u56e0\u7d20\u5e76\u672a\u5305\u542b\u5728\u7528\u4e8e\u8bc4\u4f30 AGIB \u98ce\u9669\u7684\u6807\u51c6\u683c\u62c9\u65af\u54e5 &#8211; \u5e03\u62c9\u5947\u798f\u5fb7\u8bc4\u5206\uff08Glasgow-Blatchford Score\uff09[16] \u4e2d\uff08\u8be5\u8bc4\u5206\u5305\u542b 9 \u4e2a\u53d8\u91cf\uff09\u3002\u56e0\u6b64\uff0c\u533b\u751f\u7684\u51b3\u7b56\u6240\u4ea7\u751f\u7684\u5165\u9662 \/ \u51fa\u9662\u5224\u65ad\u5f71\u54cd\uff0c\u8d85\u51fa\u4e86\u4ec5\u57fa\u4e8e\u8fd9\u4e9b\u53d8\u91cf\u8bad\u7ec3\u7684\u7b97\u6cd5\u6240\u80fd\u8986\u76d6\u7684\u8303\u56f4 [1]\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u7531\u6b64\u53ef\u89c1\uff0c\u878d\u5165\u4e13\u5bb6\u53cd\u9988\u80fd\u591f\u63d0\u5347\u6a21\u578b\u7684\u51c6\u786e\u8bca\u65ad\u80fd\u529b\uff0c\u5c24\u5176\u662f\u5728\u9700\u8981\u4e34\u5e8a\u5224\u65ad\u7684\u573a\u666f\u4e2d\u3002<\/p>\n\n\n\n<p>\uff08\u5de6\u56fe\uff09\u5728\u4f20\u7edf LtD \u4efb\u52a1\u4e2d\uff0c\u7ed9\u5b9a\u6837\u672c<strong>x<\/strong>\u2208X\uff0c\u901a\u8fc7\u9009\u62e9\u7b56\u7565<em>s<\/em>(<strong>x<\/strong>)\u51b3\u5b9a\u5c06\u6700\u7ec8\u9884\u6d4b\u4efb\u52a1\u4ea4\u7531\u4eba\u7c7b\u4e13\u5bb6\u8fd8\u662f\u673a\u5668\u5b66\u4e60\u9884\u6d4b\u5668\u5b8c\u6210\u3002\u7136\u800c\uff0c\u4e13\u5bb6\u4e0e\u9884\u6d4b\u5668\u53ef\u80fd\u5206\u522b\u638c\u63e1\u76f8\u4e92\u72ec\u7acb\u7684\u6709\u6548\u7279\u5f81\uff08\u4f8b\u5982\uff0c\u590d\u6742\u7684\u533b\u7597\u4fe1\u53f7\u4e0e\u60a3\u8005\u7684\u53e3\u8ff0\u75c5\u53f2\uff09\u3002\uff08\u53f3\u56fe\uff09\u672c\u6587\u63d0\u51fa\u7684 LtA \u6846\u67b6\uff08\u7b2c 4 \u8282\uff09\u5219\u805a\u7126\u4e8e\u4e24\u4e2a\u6838\u5fc3\u95ee\u9898\uff1a\u4f55\u65f6\u9700\u8981\u83b7\u53d6\u4eba\u7c7b\u8f93\u5165\uff0c\u4ee5\u53ca\u5982\u4f55\u5c06\u8fd9\u4e9b\u4e92\u8865\u4fe1\u606f<em>h<\/em>\u2208H\u878d\u5165\u589e\u5f3a\u9884\u6d4b\u5668<em>g<\/em>:X\u00d7H\u2192Y\u3002<\/p>\n\n\n\n<p>\u201c\u6027\u80fd\u4e92\u8865\u201d \u7684\u6982\u5ff5\u5df2\u6210\u4e3a\u4eba\u673a\u4ea4\u4e92\uff08HCI\uff09[15] \u4ee5\u53ca\u8fd1\u5e74\u6765\u6df7\u5408\u51b3\u7b56\uff08Hybrid Decision Making\uff0cHDM\uff09\u9886\u57df\u7684\u91cd\u70b9\u7814\u7a76\u65b9\u5411\u3002\u5176\u6838\u5fc3\u52a8\u56e0\u5728\u4e8e\uff0c\u4eba\u7c7b\u63a8\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u7cfb\u7edf\u5b58\u5728\u672c\u8d28\u5dee\u5f02\uff0c\u4e8c\u8005\u5728\u4efb\u52a1\u7684\u4e0d\u540c\u5b50\u96c6\u4e0a\u5404\u6709\u6240\u957f\u3002\u7136\u800c\uff0c\u5982\u4f55\u786e\u5b9a\u4eba\u7c7b\u4e0e\u673a\u5668\u5b66\u4e60\u7cfb\u7edf\u4f55\u65f6\u4ee5\u53ca\u5982\u4f55\u5b9e\u73b0\u6709\u6548\u4e92\u8865\uff0c\u4ecd\u662f\u4e00\u4e2a\u4e9f\u5f85\u89e3\u51b3\u7684\u6311\u6218 [36]\u3002\u8fd9\u4e00\u95ee\u9898\u5728\u9ad8\u98ce\u9669\u573a\u666f\u4e2d\u5c24\u4e3a\u5173\u952e \u2014\u2014 \u5728\u8fd9\u7c7b\u573a\u666f\u4e2d\uff0c\u7cfb\u7edf\u5fc5\u987b\u80fd\u591f\u53ef\u9760\u5730\u5224\u65ad\u662f\u4f9d\u8d56\u4eba\u7c7b\u4e13\u5bb6\u8fd8\u662f\u673a\u5668\u9884\u6d4b\uff0c\u4ee5\u5b9e\u73b0\u6574\u4f53\u6027\u80fd\u6700\u5927\u5316 [39]\u3002<\/p>\n\n\n\n<p>\u5728\u5404\u7c7b\u51b3\u7b56\u6846\u67b6\u4e2d\uff0c\u201c\u5b66\u4e60\u59d4\u6258\u201d\uff08LtD\uff09[19] \u8fd1\u5e74\u6765\u5907\u53d7\u5173\u6ce8\u3002LtD \u5728\u6807\u51c6\u76d1\u7763\u5b66\u4e60\u7684\u57fa\u7840\u4e0a\u5f15\u5165\u4e86\u59d4\u6258\u673a\u5236\uff0c\u5141\u8bb8\u673a\u5668\u5b66\u4e60\u6a21\u578b\u81ea\u4e3b\u9009\u62e9\u662f\u8fdb\u884c\u9884\u6d4b\uff0c\u8fd8\u662f\u5c06\u51b3\u7b56\u59d4\u6258\u7ed9\u4eba\u7c7b\u4e13\u5bb6 [33]\u3002\u8be5\u6846\u67b6\u4e3a\u6784\u5efa\u66f4\u5177\u9002\u5e94\u6027\u7684\u534f\u4f5c\u7cfb\u7edf\u63d0\u4f9b\u4e86\u53ef\u80fd\uff0c\u5c24\u5176\u5728\u4eba\u7c7b\u4e13\u4e1a\u77e5\u8bc6\u80fd\u591f\u8865\u5145\u7b97\u6cd5\u9884\u6d4b\u7684\u573a\u666f\u4e2d\u6548\u679c\u663e\u8457\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u82e5\u4ee5 \u201c\u6027\u80fd\u4e92\u8865\u201d \u4e3a\u76ee\u6807\uff0cLtA \u65b9\u6cd5\u4ecd\u5b58\u5728\u4e24\u5927\u5173\u952e\u7f3a\u9677\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u53cd\u9988\u5f62\u5f0f\u5c40\u9650<\/strong>\uff1aLtD \u8981\u6c42\u4eba\u7c7b\u4e13\u5bb6\u63d0\u4f9b\u7279\u5b9a\u4e8e\u4efb\u52a1\u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u5374\u5ffd\u7565\u4e86\u5176\u4ed6\u5f62\u5f0f\u7684\u4e13\u5bb6\u53cd\u9988\uff08\u5982\u6982\u5ff5\u6807\u6ce8\u3001\u90e8\u5206\u7279\u5f81\u63cf\u8ff0\u7b49\uff09\uff0c\u800c\u8fd9\u4e9b\u53cd\u9988\u540c\u6837\u80fd\u7528\u4e8e\u63d0\u5347\u6700\u7ec8\u9884\u6d4b\u6027\u80fd\u3002<\/li>\n\n\n\n<li><strong>\u534f\u4f5c\u6a21\u5f0f\u5355\u4e00<\/strong>\uff1aLtD \u5c06\u4e13\u5bb6\u4e0e\u673a\u5668\u89c6\u4e3a\u72ec\u7acb\u7684\u51b3\u7b56\u8005\uff0c\u672a\u80fd\u5229\u7528\u4e8c\u8005\u95f4\u6f5c\u5728\u7684\u534f\u540c\u6548\u5e94\uff0c\u5f80\u5f80\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u6027\u6b20\u62df\u5408 [18]\uff0c\u8fdb\u800c\u6d6a\u8d39\u5b9d\u8d35\u7684\u4fe1\u606f\u8d44\u6e90\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e3a\u6b64\uff0c\u672c\u6587\u63d0\u51fa\u5168\u65b0\u7684 \u201c\u5b66\u4e60\u8be2\u95ee\u201d\uff08LtA\uff09\u6846\u67b6\u3002\u8be5\u6846\u67b6\u5728\u4fdd\u7559 LtD \u7075\u6d3b\u6027\u7684\u540c\u65f6\uff0c\u89e3\u51b3\u4e86\u73b0\u6709\u65b9\u6cd5\u7684\u6838\u5fc3\u5c40\u9650\u3002\u4e0e LtD \u4f18\u5316 \u201c\u4f55\u65f6\u5c06\u5b8c\u6574\u51b3\u7b56\u59d4\u6258\u7ed9\u673a\u5668\u6216\u4eba\u7c7b\u201d \u4e0d\u540c\uff0cLtA \u805a\u7126\u4e8e \u201c\u5728\u9884\u6d4b\u8fc7\u7a0b\u4e2d\u4f55\u65f6\u9700\u8981\u83b7\u53d6\u4e13\u5bb6\u53cd\u9988\u201d\u3002\u8fd9\u4e00\u76ee\u6807\u901a\u8fc7\u53cc\u7ec4\u4ef6\u67b6\u6784\u5b9e\u73b0\uff1a\u4e00\u4e2a\u6807\u51c6\u5206\u7c7b\u5668\uff0c\u4ee5\u53ca\u4e00\u4e2a\u5728\u9700\u8981\u65f6\u80fd\u878d\u5165\u4e13\u5bb6\u8f93\u5165\u7684\u589e\u5f3a\u6a21\u578b\uff08\u89c1\u56fe 1\uff09\u3002\u8be5\u8bbe\u8ba1\u4e0d\u4ec5\u80fd\u6355\u6349\u4eba\u7c7b\u4e0e\u673a\u5668\u4e4b\u95f4\u7684\u6f5c\u5728\u4e92\u8865\u6027\uff0c\u8fd8\u80fd\u5b9e\u73b0\u534f\u540c\u534f\u4f5c\uff0c\u8ba9\u4e8c\u8005\u540c\u65f6\u4e3a\u9884\u6d4b\u4efb\u52a1\u505a\u51fa\u8d21\u732e\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u672c\u6587\u8d21\u732e<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u7406\u8bba\u5206\u6790<\/strong>\uff1a\u8bc1\u660e\u5b58\u5728\uff08\u4e14\u53ef\u80fd\u5927\u91cf\u5b58\u5728\uff09\u8fd9\u6837\u7684\u6570\u636e\u5206\u5e03 \u2014\u2014 \u5728\u8fd9\u4e9b\u5206\u5e03\u4e0b\uff0cLtD \u65b9\u6cd5\u5177\u6709\u7406\u8bba\u4e0a\u7684\u6b21\u4f18\u6027\uff0c\u5373\u5355\u7eaf\u5c06\u51b3\u7b56\u59d4\u6258\u7ed9\u4e13\u5bb6\u6216\u673a\u5668\u65e0\u6cd5\u63d0\u5347\u671f\u671b\u51c6\u786e\u7387\uff08\u7b2c 3 \u8282\uff09\u3002<\/li>\n\n\n\n<li><strong>\u6846\u67b6\u6784\u5efa<\/strong>\uff1a\u63d0\u51fa\u7528\u4e8e\u8bad\u7ec3 \u201c\u80fd\u5224\u65ad\u4f55\u65f6\u83b7\u53d6\u4e13\u5bb6\u53cd\u9988\u201d \u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u5f62\u5f0f\u5316\u6846\u67b6\uff0c\u8be5\u6846\u67b6\u652f\u6301\u4e00\u822c\u5f62\u5f0f\u7684\u989d\u5916\u8f93\u5165\uff0c\u5e76\u63a8\u5bfc\u4e86 LtA \u7684\u7406\u8bba\u6700\u4f18\u9009\u62e9\u7b56\u7565\uff08\u5b9a\u7406 1\uff09\u3002<\/li>\n\n\n\n<li><strong>\u65b9\u6cd5\u5b9e\u73b0<\/strong>\uff1a\u63d0\u51fa\u4e24\u79cd LtA \u7684\u5b66\u4e60\u7b56\u7565\uff1a\n<ul class=\"wp-block-list\">\n<li>\uff08i\uff09\u5e8f\u8d2f\u6a21\u578b\uff08sequential model\uff09\uff1a\u5148\u8bad\u7ec3\u589e\u5f3a\u6a21\u578b\uff0c\u518d\u5229\u7528\u6210\u719f\u7684 LtD \u635f\u5931\u51fd\u6570\u8bad\u7ec3\u6807\u51c6\u6a21\u578b\u4e0e\u9009\u62e9\u7b56\u7565\uff1b<\/li>\n\n\n\n<li>\uff08ii\uff09\u8054\u5408\u6a21\u578b\uff08joint model\uff09\uff1a\u8bbe\u8ba1\u5168\u65b0\u7684\u5177\u6709\u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u7684\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff0c\u652f\u6301 LtA \u6846\u67b6\u4e0b\u7684\u8054\u5408\u4f18\u5316\uff08\u5b9a\u7406 2\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u5b9e\u9a8c\u9a8c\u8bc1<\/strong>\uff1a\u5728\u5408\u6210\u6570\u636e\u4e0e\u771f\u5b9e\u5206\u7c7b\u4efb\u52a1\u4e0a\u5bf9\u6240\u63d0\u7b56\u7565\u8fdb\u884c\u5b9e\u8bc1\u9a8c\u8bc1\uff08\u7b2c 5 \u8282\uff09\uff0c\u7ed3\u679c\u8868\u660e\uff0c\u5f53\u63d0\u4f9b\u66f4\u4e30\u5bcc\u7684\u53cd\u9988\u65f6\uff0cLtA \u7684\u6027\u80fd\u4f18\u4e8e LtD\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u672c\u6587\u5df2\u5c06\u5b9e\u9a8c\u6240\u7528\u6e90\u4ee3\u7801\u53ca\u539f\u59cb\u7ed3\u679c\u5f00\u6e90\uff0c\u53ef\u901a\u8fc7\u4ee5\u4e0b\u94fe\u63a5\u83b7\u53d6\uff1a<a href=\"https:\/\/github.com\/andrepugni\/LearningToAsk\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/github.com\/andrepugni\/LearningToAsk<\/a>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2 \u7814\u7a76\u80cc\u666f<\/h2>\n\n\n\n<p>\u8bbeX\u4e3a\u7279\u5f81\u7a7a\u95f4\uff0cY\u4e3a\u76ee\u6807\u7a7a\u95f4\u3002\u5728 LtD \u4e2d\uff0c\u76ee\u6807\u662f\u5b66\u4e60\u4e00\u4e2a\u6a21\u578b<em>f<\/em>:X\u2192Y\uff08\u7528\u4e8e\u9884\u6d4b\u76ee\u6807\u53d8\u91cf\uff09\u548c\u4e00\u4e2a\u9009\u62e9\u5668<em>s<\/em>:X\u2192{0,1}\uff08\u7528\u4e8e\u51b3\u5b9a\u4f55\u65f6\u5c06\u51b3\u7b56\u59d4\u6258\u7ed9\u4eba\u7c7b\u4e13\u5bb6\uff09\u3002\u9884\u6d4b\u5668\u4e0e\u9009\u62e9\u7b56\u7565\u7684\u5047\u8bbe\u7a7a\u95f4\u8bb0\u4e3aF\u00d7S\u3002\u672c\u6587\u5c06\u4eba\u7c7b\u4e13\u5bb6\u89c6\u4e3a\u53e6\u4e00\u4e2a\u56fa\u5b9a\u7684\u9884\u6d4b\u5668<em>f<\/em>\u2032\u2208F\u2032\u3002<\/p>\n\n\n\n<p>\u7ed9\u5b9aX\u00d7Y\u00d7F\u2032\u4e0a\u7684\u672a\u77e5\u6982\u7387\u5206\u5e03<em>P<\/em>\u2032\uff0cLtD \u7684\u76ee\u6807\u662f\u6700\u5c0f\u5316\u4ee5\u4e0b\u76ee\u6807\u51fd\u6570\uff1a&lt;sup&gt;[2]&lt;\/sup&gt;<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>&lt;sup&gt;[2]&lt;\/sup&gt; \u4e3a\u7b80\u5316\u7b26\u53f7\uff0c\u7528E<em>v<\/em>\u200b\u8868\u793a\u5bf9\u670d\u4ece\u67d0\u5206\u5e03<em>P<\/em><em>V<\/em>\u200b\u7684\u968f\u673a\u53d8\u91cf<em>V<\/em>\u6c42\u671f\u671b\uff0c\u4f8b\u5982E(<strong>x<\/strong>,<em>y<\/em>,<em>f<\/em>\u2032)\u200b[\u22c5]=E(<strong>x<\/strong>,<em>y<\/em>,<em>f<\/em>\u2032)\u223c<em>P<\/em>\u2032\u200b[\u22c5]\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>(<em>f<\/em>,<em>s<\/em>)\u2208F\u00d7Smin\u200bE(<strong>x<\/strong>,<em>y<\/em>,<em>f<\/em>\u2032)\u200b[<em>L<\/em>0\u22121<em>d<\/em><em>e<\/em><em>f<\/em>\u200b(<em>f<\/em>(<strong>x<\/strong>),<em>s<\/em>(<strong>x<\/strong>),<em>f<\/em>\u2032,<em>y<\/em>)](1)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c<em>L<\/em>0\u22121<em>d<\/em><em>e<\/em><em>f<\/em>\u200b(<em>f<\/em>(<strong>x<\/strong>),<em>s<\/em>(<strong>x<\/strong>),<em>f<\/em>\u2032,<em>y<\/em>)=I{<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>}\u200bI{<em>s<\/em>(<strong>x<\/strong>)=0}\u200b+(<em>\u03b1<\/em>I{<em>f<\/em>\u2032\ue020=<em>y<\/em>}\u200b+<em>\u03b4<\/em>)I{<em>s<\/em>(<strong>x<\/strong>)=1}\u200b&nbsp;\u662f\u59d4\u6258 0-1 \u635f\u5931\u51fd\u6570\u3002<em>\u03b1<\/em>\u2208[0,1]\u4e3a\u5f52\u4e00\u5316\u56e0\u5b50\uff0c<em>\u03b4<\/em>\u2208[0,1]\u4e3a\u59d4\u6258\u6210\u672c\uff08\u7528\u4e8e\u8861\u91cf\u67e5\u8be2\u4eba\u7c7b\u4e13\u5bb6\u7684\u4ee3\u4ef7\uff09\u3002\u9664\u975e\u7279\u522b\u8bf4\u660e\uff0c\u672c\u6587\u9ed8\u8ba4<em>\u03b1<\/em>=1\u4e14<em>\u03b4<\/em>=0\uff0c\u8fd9\u4e0e\u5927\u591a\u6570 LtD \u76f8\u5173\u6587\u732e\u7684\u8bbe\u5b9a\u4e00\u81f4 [26,27,22]\u3002<\/p>\n\n\n\n<p>\u5f0f\uff081\uff09\u4e2d\u7684\u635f\u5931\u51fd\u6570\u901a\u5e38\u96be\u4ee5\u76f4\u63a5\u4f18\u5316\uff0c\u56e0\u6b64\u8bb8\u591a\u7814\u7a76\u91c7\u7528\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff08surrogate losses\uff09\u3002\u5f62\u5f0f\u4e0a\uff0c\u8bbeE<em>L<\/em>\u200b(<em>q<\/em>)\u8868\u793a\u5047\u8bbe<em>q<\/em>\u2208Q\u5728\u635f\u5931<em>L<\/em>\u4e0b\u7684\u6cdb\u5316\u8bef\u5dee\uff0c\u5373E<em>L<\/em>\u200b(<em>q<\/em>)=E<strong>x<\/strong>,<em>y<\/em>,<em>f<\/em>\u2032\u200b[<em>L<\/em>(<em>q<\/em>(<strong>x<\/strong>),<em>y<\/em>,<em>f<\/em>\u2032)]\uff1bE<em>L<\/em>\u2217\u200b\u8868\u793a\u6700\u4f18\u6cdb\u5316\u8bef\u5dee\uff0c\u5373E<em>L<\/em>\u2217\u200b=inf<em>q<\/em>\u2208Q\u200bE<strong>x<\/strong>,<em>y<\/em>,<em>f<\/em>\u2032\u200b[<em>L<\/em>(<em>q<\/em>(<strong>x<\/strong>),<em>y<\/em>,<em>f<\/em>\u2032)]\u3002\u5728 LtD \u573a\u666f\u4e2d\uff0c\u5047\u8bbe\u7a7a\u95f4Q\u7531\u6240\u6709\u9884\u6d4b\u5668<em>f<\/em>\u4e0e\u9009\u62e9\u7b56\u7565<em>s<\/em>\u7684\u7ec4\u5408\u6784\u6210\u3002<\/p>\n\n\n\n<p>\u66ff\u4ee3\u635f\u5931\u51fd\u6570\u7684\u4e00\u4e2a\u7406\u60f3\u6027\u8d28\u662f<strong>\u8d1d\u53f6\u65af\u4e00\u81f4\u6027<\/strong>\uff08Bayes-consistency\uff09\uff1a\u5728\u6e10\u8fd1\u60c5\u51b5\u4e0b\uff0c\u5bf9\u6574\u4e2a\u5047\u8bbe\u7c7b\uff08\u5982 LtD \u4e2d\u7684<em>f<\/em>\u548c<em>s<\/em>\uff09\u6700\u5c0f\u5316\u66ff\u4ee3\u635f\u5931<em>L<\/em><em>s<\/em><em>u<\/em><em>rr<\/em>\u200b\uff0c\u80fd\u591f\u4fdd\u8bc1\u5bf9\u540c\u4e00\u5047\u8bbe\u7c7b\u6700\u5c0f\u5316\u539f\u59cb\u7684\u96be\u4f18\u5316\u635f\u5931<em>L<\/em><em>or<\/em><em>i<\/em><em>g<\/em>\u200b[23]\uff0c\u5373\uff1a<\/p>\n\n\n\n<p><em>n<\/em>\u2192\u221elim\u200bE<em>L<\/em><em>s<\/em><em>u<\/em><em>rr<\/em>\u200b\u200b(<em>q<\/em><em>n<\/em>\u200b)\u2212E<em>L<\/em><em>s<\/em><em>u<\/em><em>rr<\/em>\u200b\u2217\u200b=0\u27f9<em>n<\/em>\u2192\u221elim\u200bE<em>L<\/em><em>or<\/em><em>i<\/em><em>g<\/em>\u200b\u200b(<em>q<\/em><em>n<\/em>\u200b)\u2212E<em>L<\/em><em>or<\/em><em>i<\/em><em>g<\/em>\u200b\u2217\u200b=0(2)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c<em>q<\/em><em>n<\/em>\u200b\u662f\u4ece<em>n<\/em>\u4e2a\u6837\u672c\u4e2d\u5b66\u4e60\u5f97\u5230\u7684\u5047\u8bbe\u5e8f\u5217\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u5f0f\uff082\uff09\u6240\u5b9a\u4e49\u7684\u4e00\u81f4\u6027\u662f\u57fa\u4e8e\u6240\u6709\u53ef\u6d4b\u51fd\u6570\u65cf\u7684\uff0c\u5728\u5b9e\u9645\u573a\u666f\u4e2d\uff08\u5b66\u4e60\u901a\u5e38\u5c40\u9650\u4e8e\u6709\u9650\u5047\u8bbe\u7c7b\uff09\u5e76\u4e0d\u5b9e\u7528\u3002\u4e3a\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u66ff\u4ee3\u635f\u5931\u51fd\u6570\u9700\u6ee1\u8db3<strong>\u53ef\u5b9e\u73b0Q\u4e00\u81f4\u6027<\/strong>\uff08realisable&nbsp;Q-consistency\uff09\uff1a\u82e5\u5b58\u5728\u5047\u8bbe<em>q<\/em>\u2217\u2208Q\u4f7f\u5f97E<em>L<\/em><em>or<\/em><em>i<\/em><em>g<\/em>\u200b\u200b(<em>q<\/em>\u2217)=0\uff0c\u4e14<em>q<\/em>\u2032=argmin<em>q<\/em>\u2208Q\u200bE<em>L<\/em><em>s<\/em><em>u<\/em><em>rr<\/em>\u200b\u200b(<em>q<\/em>)\uff0c\u5219E<em>L<\/em><em>s<\/em><em>u<\/em><em>rr<\/em>\u200b\u200b(<em>q<\/em>\u2032)=0\u3002\u901a\u4fd7\u5730\u8bf4\uff0c\u82e5 \u201c\u5b8c\u7f8e\u5047\u8bbe\u201d\uff08\u5982 LtD \u4e2d\u7684(<em>f<\/em>,<em>s<\/em>)\u2217\uff09\u5b58\u5728\u4e8e\u7ed9\u5b9a\u5047\u8bbe\u7c7b\u4e2d\uff0c\u90a3\u4e48\u6700\u5c0f\u5316\u66ff\u4ee3\u635f\u5931\u5c06\u80fd\u6e10\u8fd1\u5730\u627e\u5230\u8be5\u5b8c\u7f8e\u5047\u8bbe [23]\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff0cMadras \u7b49\u4eba [19] \u63d0\u51fa\u7684\u4e00\u79cd\u9002\u7528\u4e8e LtD \u7684\u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u66ff\u4ee3\u635f\u5931\uff0c\u7528\u4ea4\u53c9\u71b5\u9879\u7684\u7ec4\u5408\u66ff\u4ee3\u4e86\u4e0d\u8fde\u7eed\u7684\u59d4\u6258\u635f\u5931\uff1a<\/p>\n\n\n\n<p>(1\u2212<em>s<\/em>(<strong>x<\/strong>))\u22c5\u2113<em>CE<\/em>\u200b(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)+<em>s<\/em>(<strong>x<\/strong>)\u22c5\u2113<em>CE<\/em>\u200b(<em>f<\/em>\u2032,<em>y<\/em>)(3)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c\u2113<em>CE<\/em>\u200b\u8868\u793a\u6807\u51c6\u4ea4\u53c9\u71b5\u635f\u5931\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u66f4\u591a\u76f8\u5173\u7814\u7a76<\/h3>\n\n\n\n<p>LtD \u662f\u6df7\u5408\u51b3\u7b56\u7684\u4e00\u79cd\u5178\u578b\u5f62\u5f0f\uff0c\u5176\u6838\u5fc3\u662f\u8ba9\u81ea\u52a8\u5316\u9884\u6d4b\u5668\u5b66\u4e60\u4f55\u65f6\u5c06\u9884\u6d4b\u4efb\u52a1\u59d4\u6258\u7ed9\u4eba\u7c7b\u4e13\u5bb6\u3002\u7531\u4e8e\u76f4\u63a5\u4f18\u5316\u5f0f\uff081\uff09\u5b58\u5728\u56f0\u96be\uff0c\u5df2\u6709\u7814\u7a76\u63d0\u51fa\u4e86\u5177\u6709\u4e00\u81f4\u6027\u7684\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff0c\u7528\u4e8e\u540c\u65f6\u5b66\u4e60\u9009\u62e9\u51fd\u6570\u4e0e\u9884\u6d4b\u5668 [26,29,5,40,27,4,18,43]\u3002\u8fd1\u5e74\u6765\uff0c\u76f8\u5173\u7814\u7a76\u8fdb\u4e00\u6b65\u62d3\u5c55\u4e86 LtD \u7684\u5e94\u7528\u573a\u666f\uff0c\u5305\u62ec\u591a\u4eba\u7c7b\u4e13\u5bb6\u534f\u4f5c [41,20]\u3001\u673a\u5668\u5b66\u4e60\u6a21\u578b\u5df2\u56fa\u5b9a\u4e14\u65e0\u9700\u8054\u5408\u8bad\u7ec3 [20]\uff0c\u4ee5\u53ca\u8bc4\u4f30\u5f15\u5165 LtD \u65b9\u6cd5\u7684\u56e0\u679c\u6548\u5e94 [30] \u7b49\u3002<\/p>\n\n\n\n<p>\u672c\u6587\u5de5\u4f5c\u4e0e Wilder \u7b49\u4eba [44] \u548c Charusaie \u7b49\u4eba [6] \u7684\u7814\u7a76\u5bc6\u5207\u76f8\u5173\u3002\u8fd9\u4e24\u9879\u7814\u7a76\u540c\u6837\u8003\u8651\u5c06\u4eba\u7c7b\u4e13\u5bb6\u7684\u53cd\u9988\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u878d\u5165\u6700\u7ec8\u9884\u6d4b\u4efb\u52a1\uff0c\u4f46\u4e0e\u672c\u6587\u5b58\u5728\u4e24\u70b9\u5173\u952e\u5dee\u5f02\uff1a\uff08i\uff09\u5b83\u4eec\u5c06\u4eba\u7c7b\u53cd\u9988\u5c40\u9650\u4e8e\u4e13\u5bb6\u7684\u9884\u6d4b\u7ed3\u679c\uff1b\uff08ii\uff09\u672a\u660e\u786e\u8003\u8651 \u201c\u9884\u7b97\u611f\u77e5\u7684\u4e13\u5bb6\u53cd\u9988\u67e5\u8be2\u201d\uff08\u8fd9\u662f\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u6838\u5fc3\u9700\u6c42\uff09\u3002\u6b64\u5916\uff0c\u8fd9\u4e24\u9879\u7814\u7a76\u7f3a\u4e4f\u5bf9\u5b66\u4e60\u65b9\u6cd5\u7684\u5f62\u5f0f\u5316\u5206\u6790\uff0c\u800c\u672c\u6587\u4e3a\u6700\u4f18\u9009\u62e9\u7b56\u7565\uff08\u5b9a\u7406 1\uff09\u548c\u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\uff08\u5b9a\u7406 2\uff09\u63d0\u4f9b\u4e86\u5168\u65b0\u7684\u7406\u8bba\u7ed3\u679c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5176\u4ed6\u4eba\u7c7b &#8211; \u4eba\u5de5\u667a\u80fd\u6846\u67b6<\/h3>\n\n\n\n<p>\u5df2\u6709\u5927\u91cf\u7814\u7a76\u81f4\u529b\u4e8e\u6539\u8fdb\u4eba\u7c7b &#8211; \u4eba\u5de5\u667a\u80fd\u534f\u4f5c\u3002\u4f8b\u5982\uff0c\u8fd1\u671f\u7814\u7a76\u805a\u7126\u4e8e\u5982\u4f55\u5229\u7528\u4fdd\u5f62\u9884\u6d4b\uff08conformal prediction\uff09[34] \u63d0\u5347\u4eba\u7c7b &#8211; \u4eba\u5de5\u667a\u80fd\u56e2\u961f\u7684\u8054\u5408\u51b3\u7b56\u80fd\u529b [37,10]\u3002Alur \u7b49\u4eba [1] \u63d0\u51fa\u4e86\u4e00\u4e2a\u7edf\u8ba1\u6846\u67b6\uff0c\u7528\u4e8e\u5224\u65ad\u4eba\u7c7b\u4e13\u5bb6\u662f\u5426\u80fd\u4e3a\u7279\u5b9a\u9884\u6d4b\u4efb\u52a1\u5e26\u6765\u4ef7\u503c\uff0c\u5e76\u63d0\u4f9b\u4e86\u6570\u636e\u9a71\u52a8\u7684\u9a8c\u8bc1\u6d41\u7a0b\u3002\u5728 Alur \u7b49\u4eba [2] \u7684\u7814\u7a76\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u8bc6\u522b\u673a\u5668\u5b66\u4e60\u6a21\u578b\u5c40\u9650\u6027\u7684\u65b9\u6cd5\uff0c\u5e76\u57fa\u4e8e\u89c2\u5bdf\u5230\u7684\u4e92\u8865\u6027\uff08\u4e8b\u540e\u5206\u6790\uff09\u8bc4\u4f30\u4eba\u7c7b\u4e13\u5bb6\u53cd\u9988\u662f\u5426\u80fd\u63d0\u5347\u6a21\u578b\u6027\u80fd\u3002<\/p>\n\n\n\n<p>\u672c\u6587\u4e0e\u4e0a\u8ff0\u7814\u7a76\u7684\u6838\u5fc3\u5dee\u5f02\u5728\u4e8e\uff1a\u672c\u6587\u805a\u7126\u4e8e \u201c\u5b66\u4e60\u6784\u5efa\u80fd\u5224\u65ad\u4f55\u65f6\u83b7\u53d6\u4e13\u5bb6\u53cd\u9988\u7684\u6a21\u578b\u201d\uff0c\u800c Alur \u7b49\u4eba [2] \u7684\u7814\u7a76\u4ec5\u5173\u6ce8 \u201c\u4e8b\u540e\u9a8c\u8bc1\u4e13\u5bb6\u53cd\u9988\u662f\u5426\u80fd\u63d0\u5347\u9884\u6d4b\u6027\u80fd\u201d\uff0c\u5e76\u672a\u6d89\u53ca\u4efb\u4f55\u5b66\u4e60\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"997\" height=\"332\" src=\"http:\/\/47.95.221.121\/wp-content\/uploads\/2025\/10\/x1.png\" alt=\"\" class=\"wp-image-163\" srcset=\"https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/x1.png 997w, https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/x1-300x100.png 300w, https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/x1-768x256.png 768w\" sizes=\"auto, (max-width: 997px) 100vw, 997px\" \/><\/figure>\n\n\n\n<p>\uff08\u4e0a\u56fe\uff09\u5408\u6210\u5206\u7c7b\u4efb\u52a1\u5305\u542b\u4e24\u4e2a\u4e8c\u5143\u7279\u5f81<em>x<\/em>1\u200b,<em>x<\/em>2\u200b\u2208{0,1}\u548c\u56db\u4e2a\u7c7b\u522b<em>Y<\/em>\u2208{0,1,2,3}\u3002\u901a\u8fc7\u8c03\u6574\u6bcf\u4e2a\u7279\u5f81\u7684\u4fe1\u606f\u6027\uff08\u5373\u7279\u5f81\u5bf9\u9884\u6d4b\u771f\u5b9e\u6807\u7b7e\u7684\u533a\u5206\u80fd\u529b\uff09\uff0c\u6784\u5efa\u4e09\u79cd\u573a\u666f\uff0c\u5206\u522b\u5bf9\u5e94\u4e13\u5bb6\u51c6\u786e\u7387\uff08<em>A<\/em><em>c<\/em><em>c<\/em><em>H<\/em>\u200b\uff09\u4e0e\u673a\u5668\u51c6\u786e\u7387\uff08<em>A<\/em><em>c<\/em><em>c<\/em><em>M<\/em>\u200b\uff09\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u4e0d\u540c\u8868\u73b0\u3002\uff08\u4e0b\u56fe\uff09\u5728\u6bcf\u79cd\u573a\u666f\u4e2d\uff0c\u4ec5\u57fa\u4e8e\u5355\u4e00\u7279\u5f81\u7684\u673a\u5668\u9884\u6d4b\u5668<em>f<\/em>(<em>x<\/em>1\u200b)\uff08\u5bf9\u5e94\u56fe\u4f8b\uff09\u548c\u4eba\u7c7b\u4e13\u5bb6\u9884\u6d4b\u5668<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\uff08\u5bf9\u5e94\u56fe\u4f8b\uff09\u5747\u65e0\u6cd5\u5355\u72ec\u5b8c\u7f8e\u9884\u6d4b<em>Y<\/em>\u3002\u5373\u4f7f\u662f \u201c\u6700\u4f18\u59d4\u6258\u7b56\u7565\u201d LtD*\uff08\u5bf9\u5e94\u56fe\u4f8b\uff0c\u5728\u53ef\u80fd\u7684\u60c5\u51b5\u4e0b\u59cb\u7ec8\u9009\u62e9\u6b63\u786e\u9884\u6d4b\uff09\uff0c\u4e5f\u4f1a\u53d7\u9650\u4e8e\u5355\u4e00\u7279\u5f81\u7684\u4fe1\u606f\u4e0d\u8db3\u3002\u53ea\u6709\u878d\u5408\u4e24\u79cd\u4fe1\u53f7\u7684\u7b56\u7565 LtA*\uff08\u5bf9\u5e94\u56fe\u4f8b\uff09\u624d\u80fd\u5b9e\u73b0\u5b8c\u7f8e\u5206\u7c7b\u3002\u6bcf\u4e2a\u573a\u666f\u7684\u7ed3\u679c\u5747\u62a5\u544a\u4e94\u6b21\u5b9e\u9a8c\u7684\u6807\u51c6\u5dee\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3 \u8bba \u201c\u5b66\u4e60\u59d4\u6258\u201d\uff08LtD\uff09\u7684\u6b21\u4f18\u6027<\/h2>\n\n\n\n<p>\u4e0a\u4e00\u8282\u5df2\u8bf4\u660e\uff0cLtD \u53ef\u901a\u8fc7\u5b9e\u7528\u4e14\u5177\u6709\u4e00\u81f4\u6027\u7684\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff0c\u5728\u6709\u9650\u6837\u672c\u4fdd\u8bc1\u4e0b\u6700\u5c0f\u5316\u5f0f\uff081\uff09\u7684\u76ee\u6807\u51fd\u6570\u3002\u7136\u800c\uff0c\u5728\u67d0\u4e9b\u6570\u636e\u5206\u5e03\u4e0b\uff0cLtD \u7684\u6700\u4f18\u59d4\u6258\u7b56\u7565\u53ef\u80fd\u5177\u6709\u6b21\u4f18\u6027\u3002<\/p>\n\n\n\n<p>\u8003\u8651\u4e00\u4e2a\u7b80\u5316\u7684\u5206\u7c7b\u4efb\u52a1\uff1a\u79bb\u6563\u968f\u673a\u53d8\u91cf<strong>X<\/strong>=(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)\uff08\u5176\u4e2d<em>x<\/em>1\u200b,<em>x<\/em>2\u200b\u2208{0,1}\uff09\uff0c\u6807\u7b7e\u53d8\u91cf<em>Y<\/em>\u2208{0,1,2,3}\u3002\u6bcf\u4e2a\u6807\u7b7e<em>y<\/em>\u2208<em>Y<\/em>\u5747\u4e0e<em>x<\/em>1\u200b\u548c<em>x<\/em>2\u200b\u7684\u552f\u4e00\u7ec4\u5408\u5b58\u5728\u786e\u5b9a\u6027\u5bf9\u5e94\u5173\u7cfb\u3002\u8bbe<em>x<\/em>1\u200b\u4e3a\u81ea\u52a8\u5316\u51b3\u7b56\u652f\u6301\u7cfb\u7edf\u4f7f\u7528\u7684\u7279\u5f81\uff08\u5982\u7531\u751f\u547d\u4f53\u5f81\u6784\u6210\u7684\u590d\u6742\u51fd\u6570\uff09\uff0c<em>x<\/em>2\u200b\u4e3a\u9700\u901a\u8fc7\u4eba\u7c7b\u4e13\u5bb6\u989d\u5916\u4fe1\u606f\u5904\u7406\u624d\u80fd\u83b7\u53d6\u7684\u9ad8\u6210\u672c\u7279\u5f81\uff08\u5982\u60a3\u8005\u7684\u53e3\u8ff0\u75c5\u53f2\uff09\u3002<\/p>\n\n\n\n<p>\u673a\u5668\u9884\u6d4b<em>f<\/em>(<em>x<\/em>1\u200b)\u4ec5\u57fa\u4e8e<em>x<\/em>1\u200b\uff0c\u4e13\u5bb6\u9884\u6d4b<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\u4ec5\u57fa\u4e8e<em>x<\/em>2\u200b\uff0c\u4e14\u4e8c\u8005\u5747\u4e3a\u8d1d\u53f6\u65af\u6700\u4f18\u9884\u6d4b\u5668\u3002\u82e5\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4ec5\u80fd\u89c2\u6d4b<em>x<\/em>1\u200b\uff0c\u5219\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53<em>x<\/em>1\u200b=0\u65f6\uff0c<em>P<\/em>(<em>f<\/em>(<em>x<\/em>1\u200b)\u2223<em>x<\/em>1\u200b=0)=21\u200b\uff08<em>f<\/em>(<em>x<\/em>1\u200b)\u2208{0,2}\uff09\uff1b<\/li>\n\n\n\n<li>\u5f53<em>x<\/em>1\u200b=1\u65f6\uff0c<em>P<\/em>(<em>f<\/em>(<em>x<\/em>1\u200b)\u2223<em>x<\/em>1\u200b=1)=21\u200b\uff08<em>f<\/em>(<em>x<\/em>1\u200b)\u2208{1,3}\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u53cd\u4e4b\uff0c\u5bf9\u4e8e\u4e13\u5bb6\u9884\u6d4b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53<em>x<\/em>2\u200b=0\u65f6\uff0c<em>P<\/em>(<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\u2223<em>x<\/em>2\u200b=0)=21\u200b\uff08<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\u2208{0,1}\uff09\uff1b<\/li>\n\n\n\n<li>\u5f53<em>x<\/em>2\u200b=1\u65f6\uff0c<em>P<\/em>(<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\u2223<em>x<\/em>2\u200b=1)=21\u200b\uff08<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\u2208{2,3}\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u7ed9\u5b9a\u6837\u672c<strong>x<\/strong>\uff0c\u91c7\u7528\u7b56\u7565<em>s<\/em>(<em>x<\/em>1\u200b)\u7684 LtD \u7cfb\u7edf\u7684\u671f\u671b\u51c6\u786e\u7387\u662f\u4e13\u5bb6\u51c6\u786e\u7387\u4e0e\u673a\u5668\u51c6\u786e\u7387\u7684\u51f8\u7ec4\u5408\uff1a<\/p>\n\n\n\n<p>E<em>y<\/em>\u200b[<em>s<\/em>(<em>x<\/em>1\u200b)I{<em>f<\/em>(<em>x<\/em>1\u200b)=<em>y<\/em>}\u200b+(1\u2212<em>s<\/em>(<em>x<\/em>1\u200b))I{<em>f<\/em>\u2032(<em>x<\/em>2\u200b)=<em>y<\/em>}\u200b](4)<\/p>\n\n\n\n<p>\u5728\u8be5\u8bbe\u5b9a\u4e0b\uff0c\u4efb\u4f55\u9009\u62e9\u5668<em>s<\/em>(\u22c5)\u7684\u671f\u671b\u51c6\u786e\u7387\u90fd\u65e0\u6cd5\u8d85\u8fc721\u200b\u3002\u8fd9\u662f\u56e0\u4e3a LtD \u7cfb\u7edf\u672a\u80fd\u5229\u7528\u4e13\u5bb6\u4e0e\u673a\u5668\u5b66\u4e60\u6a21\u578b\u5404\u81ea\u638c\u63e1\u7684\u4e92\u8865\u4fe1\u606f\uff08\u5982\u672c\u4f8b\u4e2d\u7684<em>x<\/em>2\u200b\uff09\u3002<\/p>\n\n\n\n<p>\u82e5\u6362\u7528\u4e00\u79cd \u201c\u5c06\u4e13\u5bb6\u8f93\u5165\u878d\u5165\u5206\u7c7b\u5668\u201d \u7684\u66ff\u4ee3\u6a21\u578b\uff08\u4f8b\u5982\uff0c\u4e13\u5bb6\u5c06\u6536\u96c6\u5230\u7684\u7279\u5f81<em>x<\/em>2\u200b\u63d0\u4f9b\u7ed9\u4e00\u4e2a\u7edf\u4e00\u6a21\u578b\uff09\uff0c\u8bbe\u8be5\u878d\u5408\u7cfb\u7edf\u7684\u9884\u6d4b\u4e3a<em>g<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)\u3002\u7531\u4e8e\u80fd\u540c\u65f6\u83b7\u53d6<em>x<\/em>1\u200b\u548c<em>x<\/em>2\u200b\uff0c\u8be5\u6a21\u578b\u53ef\u5b8c\u7f8e\u9884\u6d4b\u771f\u5b9e\u6807\u7b7e<em>Y<\/em>\uff0c\u5b9e\u73b0\u6700\u4f18\u51c6\u786e\u7387\u3002\u6b64\u65f6\uff0c\u53ea\u8981<em>s<\/em>(<em>x<\/em>1\u200b)&gt;0\uff0c\u4f7f\u7528<em>g<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)\u7684\u589e\u5f3a\u7cfb\u7edf\u7684\u51c6\u786e\u7387\u5c31\u4f1a\u4e25\u683c\u9ad8\u4e8e21\u200b\u3002<\/p>\n\n\n\n<p>\u56fe 2 \u901a\u8fc7\u5b9e\u8bc1\u5c55\u793a\u4e86\u5728\u4e09\u79cd\u4e0d\u540c\u573a\u666f\uff08\u57fa\u4e8e\u9884\u6d4b\u5668\u4e0e\u4eba\u7c7b\u4e13\u5bb6\u7684\u57fa\u7840\u51c6\u786e\u7387\uff0c\u7531\u7279\u5f81\u4fe1\u606f\u6027\u51b3\u5b9a\uff09\u4e0b\uff0c\u201c\u6700\u4f18 LtD\u201d \u7684\u6b21\u4f18\u6027\u3002\u5b8c\u6574\u63a8\u5bfc\u4e0e\u5b9e\u9a8c\u8bbe\u7f6e\u8be6\u89c1\u9644\u5f55 A.1\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4e3a\u6bcf\u4e2a\u6837\u672c\u83b7\u53d6\u5728\u7ebf\u4e13\u5bb6\u53cd\u9988\uff08\u65e0\u8bba\u662f\u9884\u6d4b\u7ed3\u679c\u8fd8\u662f\u989d\u5916\u7279\u5f81\uff09\u90fd\u53ef\u80fd\u9700\u8981\u9ad8\u6602\u6210\u672c\uff0c\u4e14\u5e76\u975e\u603b\u80fd\u5b9e\u73b0\u3002&lt;sup&gt;[3]&lt;\/sup&gt;<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>&lt;sup&gt;[3]&lt;\/sup&gt; \u4f8b\u5982\uff0c\u5728\u6025\u8bca\u5ba4\uff08ED\uff09\u5206\u8bca\u51b3\u7b56\u652f\u6301\u7cfb\u7edf\u4e2d\uff0c\u6025\u8bca\u533b\u751f\u5e38\u9762\u4e34\u9891\u7e41\u7684\u5de5\u4f5c\u4e2d\u65ad\u4e0e\u9ad8\u5f3a\u5ea6\u5de5\u4f5c\u8d1f\u8377 [7]\u3002\u56e0\u6b64\uff0c\u81ea\u52a8\u5316\u7cfb\u7edf\u5fc5\u987b\u8c28\u614e\u4f18\u5316 \u201c\u4f55\u65f6\u8bf7\u6c42\u4e13\u5bb6\u63d0\u4f9b\u989d\u5916\u53cd\u9988\u201d\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u4e3a\u6b64\uff0c\u4e0b\u4e00\u8282\u5c06\u805a\u7126\u4e8e \u201c\u5728\u9884\u7b97\u7ea6\u675f\u4e0b\u523b\u753b\u6700\u4f18\u9009\u62e9\u7b56\u7565\u201d\uff0c\u5e73\u8861 \u201c\u83b7\u53d6\u4e13\u5bb6\u989d\u5916\u53cd\u9988\u7684\u9700\u6c42\u201d \u4e0e \u201c\u6700\u5927\u5316\u7cfb\u7edf\u51c6\u786e\u7387\u7684\u76ee\u6807\u201d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4 \u201c\u5b66\u4e60\u8be2\u95ee\u201d\uff08LtA\uff09<\/h2>\n\n\n\n<p>\u672c\u6587\u65e8\u5728\u6269\u5c55\u5f0f\uff081\uff09\uff0c\u5c06<em>f<\/em>\u2032\u660e\u786e\u5efa\u6a21\u4e3a\u4e00\u4e2a\u4e0d\u540c\u7684\u51fd\u6570<em>g<\/em>:X\u00d7H\u2192Y\uff0c\u5176\u4e2dH\u2286R<em>d<\/em>\uff08<em>d<\/em>&gt;0\uff09\u4e3a\u4e13\u5bb6\u53cd\u9988\u7a7a\u95f4\u3002\u76f4\u89c2\u4e0a\uff0cH\u53ef\u89c6\u4e3a\u9664X\u4e4b\u5916\u7684\u9ad8\u6210\u672c\u7279\u5f81\u96c6\u5408\uff0c\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e13\u5bb6\u5bf9\u4efb\u52a1\u7684\u9884\u6d4b\u7ed3\u679c\uff08\u4e0e LtD \u4e00\u81f4\uff09\uff1b<\/li>\n\n\n\n<li>\u4e13\u5bb6\u7684\u4e0d\u786e\u5b9a\u6027\u9884\u6d4b\uff08\u5982\u533b\u751f\u5bf9\u8bca\u65ad\u7ed3\u679c\u7684\u7f6e\u4fe1\u5ea6\uff09\uff1b<\/li>\n\n\n\n<li>\u989d\u5916\u7279\u5f81\uff08\u5982\u533b\u751f\u5b89\u6392\u7684\u989d\u5916\u68c0\u67e5\uff09\uff1b<\/li>\n\n\n\n<li>\u975e\u7ed3\u6784\u5316\u6807\u6ce8\uff08\u5982\u5b8c\u6574\u7684\u533b\u7597\u62a5\u544a\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u672c\u6587\u5c06<em>g<\/em>\u79f0\u4e3a<strong>\u589e\u5f3a\u9884\u6d4b\u5668<\/strong>\uff08enriched predictor\uff09\uff0c\u5c06<em>f<\/em>\u79f0\u4e3a<strong>\u6807\u51c6\u9884\u6d4b\u5668<\/strong>\uff08standard predictor\uff09\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cLtD \u662f LtA \u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5 \u2014\u2014 \u5f53H=Y\u4e14<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>)=<em>h<\/em>\u65f6\uff0cLtA \u9000\u5316\u4e3a LtD\u3002<\/p>\n\n\n\n<p>\u5b9a\u4e49<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u635f\u5931\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p><em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(<em>f<\/em>(<strong>x<\/strong>),<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>s<\/em>(<strong>x<\/strong>),<em>y<\/em>)=I{<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>}\u200bI{<em>s<\/em>(<strong>x<\/strong>)=0}\u200b+I{<em>g<\/em>(<em>x<\/em>,<em>h<\/em>)\ue020=<em>y<\/em>}\u200bI{<em>s<\/em>(<strong>x<\/strong>)=1}\u200b(5)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c<em>s<\/em>(<strong>x<\/strong>):X\u2192{0,1}\u4e3a\u9009\u62e9\u51fd\u6570\uff0c\u7528\u4e8e\u51b3\u5b9a\u7531\u54ea\u4e2a\u6a21\u578b\u63d0\u4f9b\u6700\u7ec8\u9884\u6d4b\uff1a\u5f53<em>s<\/em>(<strong>x<\/strong>)=0\u65f6\uff0c\u7531\u6807\u51c6\u6a21\u578b\u9884\u6d4b\uff1b\u5f53<em>s<\/em>(<strong>x<\/strong>)=1\u65f6\uff0c\u7531\u589e\u5f3a\u6a21\u578b\u9884\u6d4b\u3002<\/p>\n\n\n\n<p>\u7531\u4e8e\u8be5\u635f\u5931\u540c\u6837\u96be\u4ee5\u76f4\u63a5\u4f18\u5316\uff0c\u672c\u6587\u91c7\u7528\u5982\u4e0b\u5b9a\u4e49\u7684\u66ff\u4ee3\u635f\u5931<em>L<\/em><em>a<\/em><em>s<\/em><em>k<\/em>\uff1a<\/p>\n\n\n\n<p><em>L<\/em><em>a<\/em><em>s<\/em><em>k<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>s<\/em>(<strong>x<\/strong>),<em>y<\/em>)=\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)(1\u2212<em>s<\/em>(<strong>x<\/strong>))+\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)<em>s<\/em>(<strong>x<\/strong>)(6)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c\u2113<em>f<\/em>\u662f\u6807\u51c6\u9884\u6d4b\u5668\u7684\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff0c\u2113<em>g<\/em>\u662f\u589e\u5f3a\u6a21\u578b<em>g<\/em>\u7684\u66ff\u4ee3\u635f\u5931\u51fd\u6570\uff08\u4e8c\u8005\u53ef\u4e0d\u540c\uff09\u3002<\/p>\n\n\n\n<p>\u7ed9\u5b9aX\u00d7Y\u00d7H\u4e0a\u7684\u5206\u5e03<em>P<\/em>\uff0cLtA \u7684\u76ee\u6807\u51fd\u6570\u4e3a\uff1a<\/p>\n\n\n\n<p><em>f<\/em>,<em>g<\/em>,<em>s<\/em>\u2208F\u00d7G\u00d7Smin\u200bE(<strong>x<\/strong>,<em>y<\/em>,<em>h<\/em>)\u200b[<em>L<\/em><em>a<\/em><em>s<\/em><em>k<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>s<\/em>(<strong>x<\/strong>),<em>y<\/em>)](7)<\/p>\n\n\n\n<p>\u4e3a\u907f\u514d\u8fc7\u5ea6\u4f9d\u8d56\u4e13\u5bb6\uff0c\u672c\u6587\u5728\u5f0f\uff087\uff09\u4e2d\u52a0\u5165\u9884\u7b97\u7ea6\u675f<em>\u03b2<\/em>\uff1a\u8981\u6c42\u6807\u51c6\u6a21\u578b<em>f<\/em>\u8986\u76d6(1\u2212<em>\u03b2<\/em>)%\u7684\u6837\u672c\uff0c\u800c\u67e5\u8be2\u4e13\u5bb6\u7684\u6b21\u6570\u4e0d\u8d85\u8fc7<em>\u03b2<\/em>%\u3002&lt;sup&gt;[4]&lt;\/sup&gt;<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>&lt;sup&gt;[4]&lt;\/sup&gt; \u5728 \u201c\u5f03\u6743\u5b66\u4e60\u201d\uff08abstention learning\uff09\u6587\u732e\u4e2d\uff0c\u7528\u9884\u7b97\u7ea6\u675f<em>\u03b2<\/em>\u6216\u53c2\u6570<em>\u03b1<\/em>\u3001<em>\u03b4<\/em>\u5efa\u6a21\u4e13\u5bb6\u6210\u672c\u7684\u65b9\u6cd5\u5df2\u6709\u60a0\u4e45\u5386\u53f2\u3002\u8be6\u89c1 Franc \u7b49\u4eba [12]\u3001Ruggieri \u4e0e Pugnana [33] \u7684\u76f8\u5173\u8ba8\u8bba\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u56e0\u6b64\uff0c\u4f18\u5316\u95ee\u9898\u53d8\u4e3a\uff1a<\/p>\n\n\n\n<p><em>f<\/em>,<em>g<\/em>,<em>s<\/em>\u2208F\u00d7G\u00d7Smin\u200bE(<strong>x<\/strong>,<em>h<\/em>,<em>y<\/em>)\u200b[<em>L<\/em><em>a<\/em><em>s<\/em><em>k<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>s<\/em>(<strong>x<\/strong>),<em>y<\/em>)]s.t.E<strong>x<\/strong>\u200b[<em>s<\/em>(<strong>x<\/strong>)]\u2264<em>\u03b2<\/em>(8)<\/p>\n\n\n\n<p>\u4e0e Okati \u7b49\u4eba [29] \u7684\u7814\u7a76\u7c7b\u4f3c\uff0c\u7ed9\u5b9a\u4efb\u610f\u9884\u6d4b\u5668<em>f<\/em>\u2208F\u548c\u589e\u5f3a\u9884\u6d4b\u5668<em>g<\/em>\u2208G\uff0c\u53ef\u5c06\u6700\u4f18\u9009\u62e9\u51fd\u6570<em>s<\/em>\u2217\u2208S\u523b\u753b\u4e3a\u5982\u4e0b\u5b9a\u7406\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u7406 1<\/h3>\n\n\n\n<p>\u8bbe<em>f<\/em>\u2208F\u4e3a\u6807\u51c6\u9884\u6d4b\u5668\uff0c<em>g<\/em>\u2208G\u4e3a\u56fa\u5b9a\u589e\u5f3a\u9884\u6d4b\u5668\u3002\u5b9a\u4e49\u0394E(\u2113<em>f<\/em>,\u2113<em>g<\/em>)=E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)]\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]\uff08\u8868\u793a<em>f<\/em>\u4e0e<em>g<\/em>\u7684\u671f\u671b\u6761\u4ef6\u98ce\u9669\u4e4b\u5dee\uff09\uff0c\u4e14\u5047\u8bbe\u8be5\u5dee\u503c\u8fde\u7eed\u3002\u5219\u5f0f\uff088\uff09\u4f18\u5316\u95ee\u9898\u7684\u6700\u4f18\u9009\u62e9\u51fd\u6570<em>s<\/em>\u2217\u53ef\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n<p><em>s<\/em>\u2217(<strong>x<\/strong>)={1\u82e5\u0394E(\u2113<em>f<\/em>,\u2113<em>g<\/em>)&gt;<em>\u03c4<\/em><em>\u03b2<\/em>\u2217\u200b0\u5176\u4ed6\u60c5\u51b5\u200b(9)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c<em>\u03c4<\/em><em>\u03b2<\/em>\u2217\u200b=inf<em>\u03bb<\/em>\u200b{<em>\u03bb<\/em>\u22650:<em>P<\/em>(E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)]\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]&gt;<em>\u03bb<\/em>)\u2264<em>\u03b2<\/em>}\u3002<\/p>\n\n\n\n<p><strong>\u5b9a\u7406 1 \u89e3\u8bfb<\/strong>\uff1a\u5728\u9884\u7b97<em>\u03b2<\/em>\u7ea6\u675f\u4e0b\uff0c\u6700\u4f18\u9009\u62e9\u7b56\u7565\u4e3a \u2014\u2014 \u4ec5\u5f53 \u201c\u6807\u51c6\u9884\u6d4b\u5668\u7684\u671f\u671b\u635f\u5931\u4e0e\u589e\u5f3a\u6a21\u578b\u7684\u671f\u671b\u635f\u5931\u4e4b\u5dee\u201d \u5927\u4e8e\u8be5\u5dee\u503c\u7684(1\u2212<em>\u03b2<\/em>)\u5206\u4f4d\u6570\u65f6\uff0c\u624d\u67e5\u8be2\u589e\u5f3a\u9884\u6d4b\u5668\u3002\u5b8c\u6574\u8bc1\u660e\u8be6\u89c1\u9644\u5f55 A.3\u3002<\/p>\n\n\n\n<p>\u4e0b\u4e00\u8282\u5c06\u8bf4\u660e\u5982\u4f55\u901a\u8fc7\u5b9a\u5236\u5316\u7684\u66ff\u4ee3\u51fd\u6570\u5b9e\u9645\u5b66\u4e60 LtA \u65b9\u6cd5\uff0c\u540c\u65f6\u8bc1\u660e\u8fd9\u4e9b\u66ff\u4ee3\u51fd\u6570\u5177\u6709\u53ef\u5b9e\u73b0\u6027\u4e0e\u4e00\u81f4\u6027\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 \u5982\u4f55\u5b9e\u9645\u5b66\u4e60 LtA \u65b9\u6cd5<\/h3>\n\n\n\n<p>\u90e8\u7f72 LtA \u65b9\u6cd5\u9700\u5b66\u4e60\u4e09\u4e2a\u6a21\u578b\uff1a\u9884\u6d4b\u5668\uff08<em>f<\/em>\uff09\u3001\u589e\u5f3a\u9884\u6d4b\u5668\uff08<em>g<\/em>\uff09\u4e0e\u9009\u62e9\u7b56\u7565\uff08<em>s<\/em>\uff09\u3002\u672c\u6587\u63d0\u51fa\u4e24\u79cd\u5b9e\u73b0\u65b9\u6cd5\uff1a<strong>LtA &#8211; \u5e8f\u8d2f\u8bad\u7ec3<\/strong>\uff08LtA-Seq\uff0c\u5206\u9636\u6bb5\u8bad\u7ec3\u6a21\u578b\uff09\u4e0e<strong>LtA &#8211; \u8054\u5408\u8bad\u7ec3<\/strong>\uff08LtA-Joint\uff0c\u540c\u6b65\u8bad\u7ec3\u6240\u6709\u6a21\u578b\uff09\u3002\u5bf9\u4e8e\u524d\u8005\uff0c\u672c\u6587\u5229\u7528 LtD \u6587\u732e\u4e2d\u5df2\u6709\u7684\u7406\u8bba\u4fdd\u8bc1 [26,23]\uff1b\u5bf9\u4e8e\u540e\u8005\uff0c\u672c\u6587\u63d0\u51fa\u5168\u65b0\u7684\u5177\u6709\u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u7684\u66ff\u4ee3\u635f\u5931\uff08\u53c2\u89c1\u5b9a\u7406 2\uff09\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5e8f\u8d2f\u8bad\u7ec3\uff08LtA-Seq\uff09<\/h4>\n\n\n\n<p>\u5e8f\u8d2f\u8bad\u7ec3\u5c06\u6a21\u578b\u5b66\u4e60\u5206\u4e3a\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u9996\u5148\u8bad\u7ec3\u9700\u8981\u989d\u5916\u4eba\u7c7b\u4e13\u5bb6\u53cd\u9988\u7684\u589e\u5f3a\u6a21\u578b<em>g<\/em>\uff1b<\/li>\n\n\n\n<li>\u968f\u540e\u8bad\u7ec3\u6807\u51c6\u6a21\u578b<em>f<\/em>\u4e0e\u9009\u62e9\u7b56\u7565<em>s<\/em>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8be5\u7b56\u7565\u7684\u4f18\u52bf\u5728\u4e8e\uff0c\u5b83\u53ef\u5229\u7528 LtD \u6587\u732e\u4e2d\u5df2\u6709\u7684\u7406\u8bba\u4fdd\u8bc1\uff0c\u5c06\u9884\u6d4b\u5668<em>f<\/em>\u4e0e\u9009\u62e9\u5668<em>s<\/em>\u4f5c\u4e3a\u4e00\u4e2a\u7edf\u4e00\u6a21\u578b\u8fdb\u884c\u5b66\u4e60\uff08\u8fd9\u4e0e\u57fa\u4e8e\u5206\u6570\u7684 LtD \u65b9\u6cd5 [20] \u7684\u5e38\u89c1\u505a\u6cd5\u4e00\u81f4\uff09\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e00\u65e6\u589e\u5f3a\u6a21\u578b<em>g<\/em>\u56fa\u5b9a\uff0c\u5373\u53ef\u5c06\u5176\u89c6\u4e3a LtD \u8303\u5f0f\u4e2d \u201c\u4e13\u5bb6\u9884\u6d4b\u201d \u7684\u6765\u6e90\uff0c\u8fdb\u800c\u8bad\u7ec3\u59d4\u6258\u6a21\u578b\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u53ef\u76f4\u63a5\u5229\u7528 LtD \u9886\u57df\u5df2\u6709\u7684\u7406\u8bba\u4fdd\u969c\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8054\u5408\u8bad\u7ec3\uff08LtA-Joint\uff09<\/h4>\n\n\n\n<p>\u53e6\u4e00\u79cd\u65b9\u6848\u662f\u5bf9\u4e09\u4e2a\u6a21\u578b\u8fdb\u884c\u8054\u5408\u8bad\u7ec3\u3002\u7136\u800c\uff0c\u73b0\u6709 LtD \u65b9\u6cd5\u5e76\u672a\u8003\u8651 \u201c\u4e13\u5bb6\uff08\u6b64\u5904\u6307\u589e\u5f3a\u6a21\u578b<em>g<\/em>\uff09\u4e0e\u59d4\u6258\u6a21\u578b\u8054\u5408\u8bad\u7ec3\u201d \u7684\u573a\u666f\u3002\u501f\u9274 \u201c\u9009\u62e9\u5668 &#8211; \u9884\u6d4b\u5668\u6846\u67b6\u201d[20] \u7684\u601d\u8def\uff0c\u672c\u6587\u91c7\u7528\u66ff\u4ee3\u635f\u5931\u2113<em>s<\/em>\u5b66\u4e60\u5f0f\uff086\uff09\u4e2d\u7684\u9009\u62e9\u5668\uff0c\u6700\u7ec8\u5f97\u5230\u5982\u4e0b\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n<p><em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(<em>f<\/em>~\u200b(<strong>x<\/strong>),<em>g<\/em>~\u200b(<strong>x<\/strong>,<em>h<\/em>),<em>s<\/em>~(<strong>x<\/strong>),<em>y<\/em>)=\u2113<em>f<\/em>(<em>f<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>),<em>y<\/em>)\u2113<em>s<\/em>(\u2212<em>s<\/em>~(<strong>x<\/strong>))+\u2113<em>g<\/em>(<em>g<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)\u2113<em>s<\/em>(<em>s<\/em>~(<strong>x<\/strong>))(10)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>f<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>):X\u2192R\u8868\u793a\u6807\u51c6\u6a21\u578b<em>f<\/em>\u5bf9\u5e94\u7c7b\u522b<em>y<\/em>\u7684\u5bf9\u6570\u51e0\u7387\uff08logit\uff09\uff1b<\/li>\n\n\n\n<li><em>g<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>,<em>h<\/em>):X\u00d7H\u2192R\u8868\u793a\u589e\u5f3a\u6a21\u578b<em>g<\/em>\u5bf9\u5e94\u7c7b\u522b<em>y<\/em>\u7684\u5bf9\u6570\u51e0\u7387\uff1b<\/li>\n\n\n\n<li><em>s<\/em>~(<strong>x<\/strong>):X\u2192R+\u8868\u793a\u9009\u62e9\u51fd\u6570\u5bf9\u5e94\u7684\u5bf9\u6570\u51e0\u7387\uff0c\u6ee1\u8db3<em>s<\/em>(<strong>x<\/strong>)=I{<em>s<\/em>~(<strong>x<\/strong>)&gt;0}\u200b\uff08\u5373\u5f53<em>s<\/em>~(<strong>x<\/strong>)&gt;0\u65f6\uff0c\u9009\u62e9\u589e\u5f3a\u6a21\u578b\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728\u5bf9\u66ff\u4ee3\u635f\u5931\u2113<em>f<\/em>\u3001\u2113<em>g<\/em>\u548c\u2113<em>s<\/em>\u65bd\u52a0\u4e00\u5b9a\u5047\u8bbe\u7684\u524d\u63d0\u4e0b\uff0c\u672c\u6587\u8bc1\u660e\u5f0f\uff0810\uff09\u4e2d\u7684\u66ff\u4ee3\u635f\u5931<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u5177\u6709F\u00d7G\u00d7S- \u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\uff0c\u5177\u4f53\u5982\u4ee5\u4e0b\u5b9a\u7406\u6240\u793a\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u7406 2<\/h3>\n\n\n\n<p>\u5047\u8bbeF\u3001G\u548cS\u5bf9\u7f29\u653e\u64cd\u4f5c\u5c01\u95ed\uff0c\u5e76\u8003\u8651\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u7684\u66ff\u4ee3\u635f\u5931\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uff08a\uff09\u2113<em>f<\/em>=\u2113<em>g<\/em>=\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>\u4e3a \u201c\u7ec4\u5408\u548c\u635f\u5931\u201d\uff08comp-sum loss\uff09[21]\uff0c\u5373\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>:[0,1]\u00d7Y\u2192[0,1]\uff0c\u4e14\u5bf9\u4e8e\u56fa\u5b9a\u7684<em>y<\/em>\uff0c\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>\u5173\u4e8e\u7b2c\u4e00\u4e2a\u53c2\u6570\u975e\u9012\u589e\uff0c\u540c\u65f6\u6ee1\u8db3\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b,<em>y<\/em>)&gt;0\u4e14lim<em>v<\/em>\u21921\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>v<\/em>,<em>y<\/em>)=0\uff1b<\/li>\n\n\n\n<li>\uff08b\uff09\u2113<em>s<\/em>\u4e3a\u57fa\u4e8e\u8fb9\u9645\u7684\u5355\u8c03\u635f\u5931\uff0c\u6ee1\u8db3lim<em>v<\/em>\u2192\u221e\u200b\u2113<em>s<\/em>(<em>v<\/em>)=1\u3001lim<em>v<\/em>\u2192\u2212\u221e\u200b\u2113<em>s<\/em>(<em>v<\/em>)=0\uff0c\u4e14\u2113<em>s<\/em>(\u2212<em>s<\/em>~(<strong>x<\/strong>))+\u2113<em>s<\/em>(<em>s<\/em>~(<strong>x<\/strong>))=1\uff1b<\/li>\n<\/ul>\n\n\n\n<p>\u5219\u66ff\u4ee3\u635f\u5931<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\uff08\u5f0f 10\uff09\u5173\u4e8e<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u5177\u6709F\u00d7G\u00d7S- \u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u3002<\/p>\n\n\n\n<p><strong>\u5b9a\u7406 2 \u89e3\u8bfb<\/strong>\uff1a\u82e5\u66ff\u4ee3\u635f\u5931\u6ee1\u8db3\u6761\u4ef6\uff08a\uff09\u548c\uff08b\uff09\uff0c\u5219<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u662f\u5177\u6709F\u00d7G\u00d7S- \u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u7684\u66ff\u4ee3\u635f\u5931\u3002\u9700\u6ce8\u610f\uff0c\u6761\u4ef6\uff08a\uff09\u8981\u6c42\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>\u7684\u8f93\u5165\u7a7a\u95f4\u4e3a[0,1]\u00d7Y\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u901a\u8fc7\u5bf9\u5bf9\u6570\u51e0\u7387\u53d6 softmax \u8f7b\u677e\u6ee1\u8db3\u8fd9\u4e00\u8981\u6c42 \u2014\u2014 \u8bb0<em>\u03c3<\/em><em>y<\/em><em>f<\/em>~\u200b\u200b(<strong>x<\/strong>)=\u2211<em>y<\/em>\u2032\u2208Y\u200bexp<em>f<\/em>~\u200b<em>y<\/em>\u2032\u200b(<strong>x<\/strong>)exp<em>f<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>)\u200b\uff08\u6807\u51c6\u6a21\u578b\u7684 softmax \u8f93\u51fa\uff09\uff0c<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b(<strong>x<\/strong>,<em>h<\/em>)=\u2211<em>y<\/em>\u2032\u2208Y\u200bexp<em>g<\/em>~\u200b<em>y<\/em>\u2032\u200b(<strong>x<\/strong>,<em>h<\/em>)exp<em>g<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>,<em>h<\/em>)\u200b\uff08\u589e\u5f3a\u6a21\u578b\u7684 softmax \u8f93\u51fa\uff09\u3002<\/p>\n\n\n\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u91c7\u7528\u4ee5\u4e0b\u635f\u5931\u51fd\u6570\u6ee1\u8db3\u5b9a\u7406 2 \u7684\u8981\u6c42\uff1a\u5bf9\u2113<em>f<\/em>\u548c\u2113<em>g<\/em>\u4f7f\u7528\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee\uff08MAE\uff09\u635f\u5931\uff0c\u5bf9\u2113<em>s<\/em>\u4f7f\u7528 SIG \u635f\u5931\uff08sigmoid-based loss\uff09\uff1a<\/p>\n\n\n\n<p>\u2113<em>M<\/em><em>A<\/em><em>E<\/em><em>f<\/em>\u200b(<em>\u03c3<\/em><em>y<\/em><em>f<\/em>~\u200b\u200b(<strong>x<\/strong>),<em>y<\/em>)=1\u2212\u2211<em>y<\/em>\u2032\u2208Y\u200bexp<em>f<\/em>~\u200b<em>y<\/em>\u2032\u200b(<strong>x<\/strong>)exp<em>f<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>)\u200b(11)<\/p>\n\n\n\n<p>\u2113<em>M<\/em><em>A<\/em><em>E<\/em><em>g<\/em>\u200b(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)=1\u2212\u2211<em>y<\/em>\u2032\u2208Y\u200bexp<em>g<\/em>~\u200b<em>y<\/em>\u2032\u200b(<strong>x<\/strong>,<em>h<\/em>)exp<em>g<\/em>~\u200b<em>y<\/em>\u200b(<strong>x<\/strong>,<em>h<\/em>)\u200b(12)<\/p>\n\n\n\n<p><em>L<\/em><em>S<\/em><em>I<\/em><em>G<\/em><em>s<\/em>\u200b(<em>s<\/em>~(<strong>x<\/strong>))=21\u200b(1\u2212tanh<em>s<\/em>~(<strong>x<\/strong>))(13)<\/p>\n\n\n\n<p>\u663e\u7136\uff0c\u4e0a\u8ff0\u635f\u5931\u51fd\u6570\u5747\u6ee1\u8db3\u5b9a\u7406 2 \u7684\u8981\u6c42\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">5 \u5b9e\u9a8c\u8bc4\u4f30<\/h2>\n\n\n\n<p>\u672c\u8282\u901a\u8fc7\u5408\u6210\u6570\u636e\u4e0e\u771f\u5b9e\u4e13\u5bb6\u6570\u636e\u7684\u6a21\u62df\u51b3\u7b56\u4efb\u52a1\uff0c\u5728\u4e0d\u540c\u53cd\u9988\u7b56\u7565\u4e0b\u5b9e\u8bc1\u8bc4\u4f30 LtA \u7684\u6709\u6548\u6027\u3002\u5b9e\u9a8c\u65e8\u5728\u56de\u7b54\u4ee5\u4e0b\u7814\u7a76\u95ee\u9898\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u95ee\u9898 1\uff08Q1\uff09<\/strong>\uff1aLtA \u7b56\u7565\u4e0e LtD \u5728\u51c6\u786e\u7387\u548c\u4eba\u7c7b &#8211; \u4eba\u5de5\u667a\u80fd\u4e92\u8865\u6027\u65b9\u9762\u7684\u8868\u73b0\u5982\u4f55\uff1f<\/li>\n\n\n\n<li><strong>\u95ee\u9898 2\uff08Q2\uff09<\/strong>\uff1a\u4e13\u5bb6\u53cd\u9988\u7c7b\u578b\u5bf9\u6027\u80fd\u4e0e\u4e92\u8865\u6027\u7684\u5f71\u54cd\u7a0b\u5ea6\u5982\u4f55\uff1f<\/li>\n\n\n\n<li><strong>\u95ee\u9898 3\uff08Q3\uff09<\/strong>\uff1a\u59d4\u6258\u6210\u672c<em>\u03b4<\/em>\u5728\u7f13\u89e3\u6b20\u62df\u5408\u4e0e\u5e73\u8861\u6027\u80fd\u65b9\u9762\u7684\u4f5c\u7528\u662f\u4ec0\u4e48\uff1f<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u6570\u636e\u96c6\u4e0e\u6a21\u578b<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5408\u6210\u6570\u636e\u96c6\uff08Synth\uff09<\/strong>\uff1a\u6784\u5efa\u591a\u5206\u7c7b\u4efb\u52a1\uff0c\u5305\u542b 4 \u4e2a\u7279\u5f81\u548c 4 \u4e2a\u7c7b\u522b\uff0c\u6240\u6709\u7279\u5f81\u5747\u5177\u6709\u4fe1\u606f\u6027\u3002\u4e3a\u6a21\u62df\u4eba\u7c7b\u4e13\u5bb6\uff0c\u4f7f\u7528\u4ec5\u542b 2 \u4e2a\u7279\u5f81\u7684\u51b3\u7b56\u6811\u8bad\u7ec3\u4e13\u5bb6\u9884\u6d4b\u5668<em>f<\/em>\u2032(<strong>x<\/strong>)\uff1b\u673a\u5668\u5b66\u4e60\u6a21\u578b\u5219\u91c7\u7528\u4ec5\u57fa\u4e8e\u5269\u4f59 2 \u4e2a\u7279\u5f81\u8bad\u7ec3\u7684\u4e24\u5c42\u611f\u77e5\u673a\u3002\u8be5\u8bbe\u7f6e\u6a21\u62df\u4e86 \u201c\u4e13\u5bb6\u638c\u63e1\u673a\u5668\u5b66\u4e60\u6a21\u578b\u65e0\u6cd5\u83b7\u53d6\u7684\u4e92\u8865\u4fe1\u606f\u201d \u7684\u573a\u666f\uff08\u4e0e\u7b2c 3 \u8282\u7684\u793a\u4f8b\u4e00\u81f4\uff09\u3002<\/li>\n\n\n\n<li><strong>NIH \u8c37\u6b4c\u80f8\u90e8 X \u5149\u6570\u636e\u96c6\uff08X-Rays\uff09<\/strong>\uff1a\u8be5\u6570\u636e\u96c6 [42] \u5305\u542b\u7ea6 4400 \u5f20\u533f\u540d\u80f8\u90e8 X \u5149\u56fe\u50cf\u53ca\u4e13\u5bb6\u6807\u6ce8\u3002\u6bcf\u5f20\u56fe\u50cf\u7531\u81f3\u5c11 3 \u540d\u533b\u751f\u8bc4\u4f30 4 \u79cd\u75c5\u75c7\uff08<em>c<\/em><em>i<\/em>\u200b\uff09\uff1a\u7ed3\u8282 \/ \u80bf\u5757\u3001\u6c14\u8154\u6df7\u6d4a\u3001\u6c14\u80f8\u548c\u9aa8\u6298\u3002\u5bf9\u4e8e\u6bcf\u79cd\u75c5\u75c7<em>i<\/em>\u2208[4]\uff0c\u56fe\u50cf\u88ab\u8d4b\u4e88\u4e8c\u5143\u771f\u503c\u6807\u7b7e\uff08<em>c<\/em><em>i<\/em>\u200b=1\u8868\u793a\u5b58\u5728\u8be5\u75c5\u75c7\uff0c<em>c<\/em><em>i<\/em>\u200b=0\u8868\u793a\u4e0d\u5b58\u5728\uff09\u3002\u5b9a\u4e49\u6574\u4f53\u4e8c\u5143\u6807\u7b7e<em>Y<\/em>\u2208{0,1}\uff1a<em>Y<\/em>=1\u8868\u793a\u5065\u5eb7\uff08\u6240\u6709<em>c<\/em><em>i<\/em>\u200b=0\uff09\uff0c<em>Y<\/em>=0\u8868\u793a\u975e\u5065\u5eb7\uff08\u81f3\u5c11\u4e00\u4e2a<em>c<\/em><em>i<\/em>\u200b=1\uff09\u3002\u5bf9\u4e8e\u6bcf\u79cd\u75c5\u75c7<em>c<\/em><em>i<\/em>\u200b\uff0c\u5c06\u4e13\u5bb6\u5171\u8bc6<em>p<\/em><em>i<\/em>\u200b\u5b9a\u4e49\u4e3a \u201c\u62a5\u544a\u8be5\u75c5\u75c7\u7684\u533b\u751f\u6bd4\u4f8b\u201d\uff0c\u5373<em>p<\/em><em>i<\/em>\u200b=<em>N<\/em>1\u200b\u2211<em>j<\/em>\u2208<em>N<\/em>\u200b<em>c<\/em><em>ij<\/em>\u200b\uff08\u5176\u4e2d<em>c<\/em><em>ij<\/em>\u200b\u4e3a\u4e13\u5bb6<em>j<\/em>\u7684\u4e8c\u5143\u6807\u6ce8\uff0c<em>N<\/em>\u4e3a\u6807\u6ce8\u4e13\u5bb6\u6570\u91cf\uff09\u3002\u4e3a\u6a21\u62df\u4e13\u5bb6\u9884\u6d4b<em>Y<\/em><em>H<\/em>\u200b\uff0c\u6309<em>c<\/em><em>i<\/em>\u200b\u223c\u4f2f\u52aa\u5229\u5206\u5e03(<em>p<\/em><em>i<\/em>\u200b)\u91c7\u6837\u75c5\u75c7\u6807\u7b7e\uff0c\u82e5\u6240\u6709<em>c<\/em><em>i<\/em>\u200b=0\u5219\u8d4b\u503c<em>Y<\/em><em>H<\/em>\u200b=1\u3002\u8be5\u8fc7\u7a0b\u53cd\u6620\u4e86\u4e13\u5bb6\u5728\u5224\u65ad\u60a3\u8005\u5065\u5eb7\u72b6\u6001\u65f6\u7684\u610f\u89c1\u5dee\u5f02\u3002\u673a\u5668\u5b66\u4e60\u6a21\u578b\u91c7\u7528\u9884\u8bad\u7ec3\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc DenseNet [8]\u3002&lt;sup&gt;[5]&lt;\/sup&gt; \u589e\u5f3a\u6a21\u578b<em>g<\/em>\u540c\u6837\u91c7\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff0c\u901a\u8fc7 FiLM \u67b6\u6784 [31]\uff08\u4e00\u79cd\u6210\u719f\u7684\u89c6\u89c9\u63a8\u7406\u65b9\u6cd5\uff09\u6ce8\u5165\u4eba\u7c7b\u4e13\u5bb6\u53cd\u9988\u3002&lt;sup&gt;[5]&lt;\/sup&gt; \u5728\u5b9e\u9645\u5b9e\u9a8c\u4e2d\uff0c\u65e0\u8bba\u662f LtA \u8fd8\u662f LtD\uff0c\u5747\u6309\u7167\u6587\u732e\u4e2d\u7684\u6807\u51c6\u505a\u6cd5\uff0c\u5728 X-Rays \u6570\u636e\u96c6\u4e0a\u5bf9 DenseNet \u6a21\u578b\u8fdb\u884c\u5fae\u8c03\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e13\u5bb6\u53cd\u9988<\/h3>\n\n\n\n<p>\u5b9a\u4e49\u4e24\u79cd\u53cd\u9988\u7b56\u7565\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>LtD-Feedback<\/strong>\uff1a<em>h<\/em>=<em>f<\/em>\u2032(<strong>x<\/strong>)\uff08\u5408\u6210\u6570\u636e\u96c6\uff09\u6216<em>h<\/em>=<em>Y<\/em><em>H<\/em>\u200b\uff08X-Rays \u6570\u636e\u96c6\uff09\uff0c\u6a21\u62df\u4e13\u5bb6\u4ec5\u5411\u589e\u5f3a\u6a21\u578b\u63d0\u4f9b\u9884\u6d4b\u5065\u5eb7\u6807\u7b7e\u7684\u573a\u666f\u3002<\/li>\n\n\n\n<li><strong>Unc-Feedback<\/strong>\uff1a\u4ec5\u9002\u7528\u4e8e X-Rays \u6570\u636e\u96c6\uff0c<em>h<\/em>=(<em>p<\/em>1\u200b,<em>p<\/em>2\u200b,<em>p<\/em>3\u200b,<em>p<\/em>4\u200b)\uff0c\u6a21\u62df\u4e13\u5bb6\u5411\u589e\u5f3a\u6a21\u578b\u63d0\u4f9b\u6bcf\u79cd\u75c5\u75c7\u7684\u5171\u8bc6\u6982\u7387\uff08\u53cd\u6620\u4e13\u5bb6\u5bf9\u75c5\u75c7\u5b58\u5728\u4e0e\u5426\u7684\u4e0d\u786e\u5b9a\u6027\uff09\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5728 LtD \u4e2d\uff0c\u4ec5\u8003\u8651 LtD-Feedback\uff08\u56e0 LtD \u8981\u6c42\u4e13\u5bb6\u76f4\u63a5\u63d0\u4f9b\u9884\u6d4b\u7ed3\u679c\uff09\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9e\u9a8c\u8bbe\u7f6e<\/h3>\n\n\n\n<p>\u5bf9\u4e24\u4e2a\u6570\u636e\u96c6\u5747\u91c7\u7528 70:10:20 \u7684\u6bd4\u4f8b\u5212\u5206\u8bad\u7ec3\u96c6\u3001\u6821\u51c6\u96c6\u4e0e\u6d4b\u8bd5\u96c6\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8bad\u7ec3\u96c6\uff1a\u7528\u4e8e\u8bad\u7ec3 LtD\u3001LtA-Seq \u548c LtA-Joint \u7b56\u7565\u4e0b\u7684\u6807\u51c6\u6a21\u578b\u4e0e\u589e\u5f3a\u6a21\u578b\u3002\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u6807\u51c6 LtD \u548c LtA-Seq\uff1a\u91c7\u7528 Mozannar \u7b49\u4eba [27] \u548c Mao \u7b49\u4eba [22] \u63d0\u51fa\u7684\u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u635f\u5931\uff08\u8be5\u635f\u5931\u5728 LtD \u4e2d\u8fbe\u5230\u5f53\u524d\u6700\u4f18\u6027\u80fd\uff09\u3002<\/li>\n\n\n\n<li>\u5bf9\u4e8e LtA-Joint\uff1a\u4f7f\u7528\u5f0f\uff0811\uff09\u3001\uff0812\uff09\u3001\uff0813\uff09\u5206\u522b\u8bad\u7ec3\u673a\u5668\u6a21\u578b<em>f<\/em>\u3001\u589e\u5f3a\u6a21\u578b<em>g<\/em>\u4e0e\u9009\u62e9\u5668\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6821\u51c6\u96c6\uff1a\u6309\u7167\u6587\u732e [27,30] \u7684\u6807\u51c6\u505a\u6cd5\uff0c\u7528\u4e8e\u4f30\u8ba1\u4e0d\u540c\u8986\u76d6\u7387<em>\u03b2<\/em>\u2208{0.0,\u2026,1.0}\u4e0b\u7684\u59d4\u6258\u9608\u503c<em>\u03c4<\/em><em>\u03b2<\/em>\u200b\u3002<\/li>\n\n\n\n<li>\u6d4b\u8bd5\u96c6\uff1a\u7528\u4e8e\u8ba1\u7b97\u5404\u65b9\u6cd5\u5728\u4e0d\u540c\u9608\u503c\u4e0b\u7684\u5b9e\u8bc1\u51c6\u786e\u7387\u3002<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"460\" src=\"http:\/\/47.95.221.121\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-13-11.11.53-1024x460.png\" alt=\"\" class=\"wp-image-164\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"818\" src=\"http:\/\/47.95.221.121\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-13-11.12.10-1024x818.png\" alt=\"\" class=\"wp-image-165\"\/><\/figure>\n\n\n\n<p>\u4e3a\u8bc4\u4f30\u4e92\u8865\u6027\uff08\u5373\u4eba\u7c7b &#8211; \u673a\u5668\u56e2\u961f\u662f\u5426\u4f18\u4e8e\u5355\u72ec\u7684\u4eba\u7c7b\u6216\u673a\u5668 [36]\uff09\uff0c\u8fd8\u9700\u6d4b\u91cf\uff08\u6a21\u62df\uff09\u4e13\u5bb6\u4e0e\u5355\u72ec\u6a21\u578b\u7684\u51c6\u786e\u7387\u3002\u5b9e\u9a8c\u91cd\u590d 5 \u6b21\uff0c\u6bcf\u6b21\u5747\u91cd\u65b0\u91c7\u6837\u8bad\u7ec3\u96c6\u3001\u6821\u51c6\u96c6\u4e0e\u6d4b\u8bd5\u96c6\u3002\u66f4\u591a\u7ec6\u8282\u8be6\u89c1\u9644\u5f55 B\u3002<\/p>\n\n\n\n<p>\uff08a\uff09\u5408\u6210\u6570\u636e\u96c6\uff08Synth\uff09\u7684\u7ed3\u679c\uff1b\uff08b\uff09X-Rays \u6570\u636e\u96c6\u91c7\u7528 LtD-Feedback \u7684\u7ed3\u679c\uff1b\uff08c\uff09X-Rays \u6570\u636e\u96c6\u91c7\u7528 Unc-Feedback \u7684\u7ed3\u679c\u3002\u56fe\uff08c\uff09\u4e2d\u540c\u6837\u5305\u542b LtD \u57fa\u7ebf\u6a21\u578b\u3002\u865a\u7ebf\u5206\u522b\u8868\u793a\u4e13\u5bb6\u5355\u72ec\u9884\u6d4b\u4e0e\u673a\u5668\u5355\u72ec\u9884\u6d4b\u7684\u5b9e\u8bc1\u51c6\u786e\u7387\u3002\u9634\u5f71\u533a\u57df\u8868\u793a 5 \u6b21\u5b9e\u9a8c\u7684\u6807\u51c6\u5dee\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 \u5b9e\u9a8c\u7ed3\u679c<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u95ee\u9898 1\uff1aLtA-Joint \u548c LtA-Seq \u7684\u6027\u80fd\u4f18\u4e8e\u4f20\u7edf LtD\uff0c\u4e14 LtA-Seq \u5bf9\u6b20\u62df\u5408\u8f83\u4e3a\u654f\u611f<\/h4>\n\n\n\n<p>\u9996\u5148\u5728\u5408\u6210\u5206\u7c7b\u4efb\u52a1\uff08Synth\uff09\u4e0a\u6bd4\u8f83 LtA-Seq\u3001LtA-Joint \u4e0e\u6807\u51c6 LtD \u7684\u6027\u80fd\u3002\u7ed3\u679c\u8868\u660e\uff0c\u5141\u8bb8\u83b7\u53d6\u66f4\u591a\u4eba\u7c7b\u53cd\u9988\u4f7f LtA \u5177\u6709\u660e\u663e\u4f18\u52bf\uff1a\u5f531\u2212<em>\u03b2<\/em>&lt;.50\uff08\u5373\u4e13\u5bb6\u67e5\u8be2\u9884\u7b97\u8f83\u9ad8\uff09\u65f6\uff0cLtA-Seq \u548c LtA-Joint \u5747\u663e\u8457\u4f18\u4e8e LtD\uff1b\u5176\u4e2d\uff0cLtA-Joint \u5728\u6240\u6709\u8986\u76d6\u7387\u4e0b\u5747\u6301\u7eed\u4f18\u4e8e LtD\uff0c\u800c LtA-Seq \u57281\u2212<em>\u03b2<\/em>\u2265.70\uff08\u5373\u4e13\u5bb6\u67e5\u8be2\u9884\u7b97\u8f83\u4f4e\uff09\u65f6\u51c6\u786e\u7387\u4f4e\u4e8e LtD\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u66f4\u6709\u6548\u5730\u5229\u7528\u53cd\u9988\uff0cLtA \u7684\u4e92\u8865\u6027\u5f3a\u4e8e LtD\uff0c\u5176\u51c6\u786e\u7387\u8d85\u8fc7\u4e86\u5355\u72ec\u7684\u6a21\u62df\u4e13\u5bb6\u4e0e\u5355\u72ec\u7684\u673a\u5668\u9884\u6d4b\u3002<\/p>\n\n\n\n<p>LtA-Seq \u4e0e LtA-Joint \u5728\u9ad8\u8986\u76d6\u7387\u4e0b\u7684\u6027\u80fd\u5dee\u8ddd\u53ef\u5f52\u56e0\u4e8e\u4e8c\u8005\u7684\u8bad\u7ec3\u6d41\u7a0b\uff1a\u5982\u7b2c 4.1 \u8282\u6240\u8ff0\uff0cLtA-Seq \u5148\u8bad\u7ec3\u589e\u5f3a\u6a21\u578b<em>g<\/em>\uff0c\u4e14\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u672a\u5bf9\u4e13\u5bb6\u67e5\u8be2\u65bd\u52a0\u60e9\u7f5a\uff08<em>\u03b4<\/em>=0\uff09\u3002\u57281\u2212<em>\u03b2<\/em>=0\uff08\u5b8c\u5168\u4f9d\u8d56\u4e13\u5bb6\uff09\u65f6\uff0c<em>g<\/em>\u7684\u51c6\u786e\u7387\u6bd4\u6a21\u62df\u4e13\u5bb6\u9ad8\u7ea6 20%\uff0c\u8fd9\u5bfc\u81f4 LtA-Seq \u8fc7\u5ea6\u4f9d\u8d56<em>g<\/em>\uff0c\u8fdb\u800c\u5f15\u53d1\u5176\u4ed6\u6a21\u578b\u5934\uff08\u5982\u6807\u51c6\u6a21\u578b<em>f<\/em>\uff09\u7684\u6b20\u62df\u5408 \u2014\u2014 \u8fd9\u662f LtD \u4e2d\u5df2\u77e5\u7684\u95ee\u9898 [18]\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u56fe 4 \u8868\u660e\uff0c\u53ea\u9700\u589e\u52a0\u59d4\u6258\u6210\u672c\uff0c\u5373\u53ef\u5728\u771f\u5b9e\u4e13\u5bb6\u6570\u636e\u4e0a\u7f13\u89e3\u8fd9\u4e00\u95ee\u9898\uff0c\u4f7f LtA-Seq \u7684\u6027\u80fd\u63a5\u8fd1 LtA-Joint\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cLtA-Joint \u901a\u8fc7\u8054\u5408\u8bad\u7ec3\u81ea\u7136\u907f\u514d\u4e86\u8fc7\u5ea6\u4f9d\u8d56\uff1a\u5176\u8054\u5408\u8bad\u7ec3\u8fc7\u7a0b\u8d77\u5230\u4e86\u6b63\u5219\u5316\u4f5c\u7528\uff0c\u4ec5\u5728\u6709\u76ca\u65f6\u624d\u5229\u7528\u4e13\u5bb6\u53cd\u9988\uff0c\u4ece\u800c\u9650\u5236\u4e86\u4e13\u5bb6\u67e5\u8be2\u7684\u9891\u7387\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u95ee\u9898 2\uff1a\u5728\u771f\u5b9e\u6570\u636e\u4e0a\uff0c\u5f53\u53cd\u9988\u5f62\u5f0f\u4e3a\u786c\u9884\u6d4b\u65f6\uff0cLtA \u4e0e LtD \u6027\u80fd\u76f8\u5f53\uff1b\u5f53\u53cd\u9988\u5f62\u5f0f\u66f4\u4e30\u5bcc\u65f6\uff0cLtA \u6027\u80fd\u663e\u8457\u63d0\u5347<\/h4>\n\n\n\n<p>\u5728 X-Rays \u6570\u636e\u96c6\u4e0a\u8bc4\u4f30\u4e0d\u540c\u53cd\u9988\u7b56\u7565\uff08LtD-Feedback \u4e0e Unc-Feedback\uff09\u7684\u5f71\u54cd\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>LtD-Feedback\uff08\u786c\u9884\u6d4b\uff09<\/strong>\uff1aLtA-Joint \u4e0e LtA-Seq \u7684\u6027\u80fd\u4e0e LtD \u57fa\u672c\u6301\u5e73\uff0c\u6574\u4f53\u4e92\u8865\u6027\u6709\u9650\uff0c\u6240\u6709\u65b9\u6cd5\u7684\u51c6\u786e\u7387\u4ec5\u7565\u9ad8\u4e8e\u5355\u72ec\u4e13\u5bb6\u7684\u9884\u6d4b\uff08\u56fe 3\uff08b\uff09\uff09\u3002<\/li>\n\n\n\n<li><strong>Unc-Feedback\uff08\u4e0d\u786e\u5b9a\u6027\u53cd\u9988\uff09<\/strong>\uff1aLtA \u5c55\u73b0\u51fa\u660e\u663e\u4f18\u52bf \u2014\u2014LtA-Seq \u4e0e LtA-Joint \u5747\u4f18\u4e8e LtD\uff0c\u57281\u2212<em>\u03b2<\/em>=.10\u65f6\u51c6\u786e\u7387\u63d0\u5347\u7ea6 5%\uff08\u56fe 3\uff08c\uff09\uff09\u3002\u901a\u8fc7\u5229\u7528\u66f4\u4e30\u5bcc\u7684\u53cd\u9988\uff0cLtA \u7684\u4e92\u8865\u6027\u663e\u8457\u589e\u5f3a\uff1a\u5f531\u2212<em>\u03b2<\/em>\u2264.05\u65f6\uff0c\u5176\u51c6\u786e\u7387\u8d85\u8fc7\u4e86\u5355\u72ec\u4e13\u5bb6\u4e0e\u5355\u72ec\u673a\u5668\u7684\u9884\u6d4b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4e0e\u9884\u671f\u4e00\u81f4\uff0c\u91c7\u7528 Unc-Feedback \u65f6\uff0cLtA-Seq \u57281\u2212<em>\u03b2<\/em>\u2265.50\u65f6\u4ecd\u5b58\u5728\u6b20\u62df\u5408\u95ee\u9898 \u2014\u2014 \u8fd9\u662f\u56e0\u4e3a\u4e0e\u786c\u9884\u6d4b\u76f8\u6bd4\uff0c\u4e0d\u786e\u5b9a\u6027\u53cd\u9988\u7684\u590d\u6742\u5ea6\u66f4\u9ad8\uff0c\u8fdb\u4e00\u6b65\u52a0\u5267\u4e86 LtA-Seq \u7684\u8fc7\u5ea6\u4f9d\u8d56\u503e\u5411\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u95ee\u9898 3\uff1a\u589e\u52a0\u59d4\u6258\u6210\u672c\u53ef\u51cf\u5c11 LtA-Seq \u7684\u6b20\u62df\u5408\uff0c\u4f7f\u5176\u6027\u80fd\u5411 LtA-Joint \u9760\u62e2<\/h4>\n\n\n\n<p>\u6700\u540e\uff0c\u7814\u7a76\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u59d4\u6258\u6210\u672c<em>\u03b4<\/em>\u5bf9\u7f13\u89e3\u4f20\u7edf LtD \u6b20\u62df\u5408\u95ee\u9898 [27,18] \u7684\u4f5c\u7528\u3002\u56fe 4 \u62a5\u544a\u4e86 X-Rays \u5206\u7c7b\u4efb\u52a1\u4e2d\uff0c\u4e0d\u540c<em>\u03b4<\/em>\u503c\u5bf9\u5404\u65b9\u6cd5\u6027\u80fd\u7684\u5f71\u54cd\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>LtD<\/strong>\uff1a\u5f15\u5165\u59d4\u6258\u6210\u672c\u5728\u9ad8\u8986\u76d6\u7387\u4e0b\u4ec5\u5e26\u6765\u5c0f\u5e45\u63d0\u5347 \u2014\u2014 \u5f531\u2212<em>\u03b2<\/em>\u2208{.80,.90}\u65f6\uff0c\u8bbe\u7f6e<em>\u03b4<\/em>=0.2\u53ef\u4f7f\u51c6\u786e\u7387\u63d0\u5347\u7ea6 3%\uff08\u56fe 4\uff08a\uff09\uff09\u3002<\/li>\n\n\n\n<li><strong>LtA-Seq<\/strong>\uff1a\u59d4\u6258\u6210\u672c\u7684\u5f71\u54cd\u66f4\u4e3a\u663e\u8457\uff08\u56fe 4\uff08b\uff09\uff09\u2014\u2014 \u5f531\u2212<em>\u03b2<\/em>&gt;.50\u65f6\uff0c\u51c6\u786e\u7387\u5927\u5e45\u63d0\u5347\uff1b\u5f53<em>\u03b4<\/em>=0.2\u4e141\u2212<em>\u03b2<\/em>=.90\u65f6\uff0c\u51c6\u786e\u7387\u6700\u9ad8\u63d0\u5347\u7ea6 16%\u3002\u8fd9\u8868\u660e\uff0c\u5f15\u5165\u59d4\u6258\u6210\u672c\u80fd\u6709\u6548\u51cf\u5c11\u5bf9\u4e13\u5bb6\u7ec4\u4ef6\u7684\u8fc7\u5ea6\u4f9d\u8d56\uff0c\u7f13\u89e3\u6b20\u62df\u5408\u95ee\u9898\u3002<\/li>\n\n\n\n<li><strong>LtA-Joint<\/strong>\uff1a\u589e\u52a0<em>\u03b4<\/em>\u4f1a\u7565\u5fae\u964d\u4f4e\u6027\u80fd\uff08\u56fe 4\uff08c\uff09\uff09\u3002\u539f\u56e0\u5728\u4e8e\uff0c\u5bf9\u4e13\u5bb6\u53cd\u9988\u65bd\u52a0\u60e9\u7f5a\u4f1a\u589e\u52a0\u8054\u5408\u7b56\u7565\u4f18\u5316\u589e\u5f3a\u6a21\u578b\u7684\u96be\u5ea6\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u7efc\u4e0a\uff0c\u5c3d\u7ba1\u59d4\u6258\u6210\u672c\u5bf9 LtD \u7684\u63d0\u5347\u6709\u9650\uff08\u4e14 LtD \u5728\u53cd\u9988\u4e30\u5bcc\u65f6\u6027\u80fd\u4ecd\u4f4e\u4e8e LtA\uff09\uff0c\u4f46\u5bf9 LtA-Seq \u800c\u8a00\uff0c\u5408\u9002\u7684\u59d4\u6258\u6210\u672c\u53ef\u4f7f\u5176\u6027\u80fd\u63a5\u8fd1 LtA-Joint\uff0c\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86 LtA 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class=\"has-fixed-layout\"><thead><tr><th><em>x<\/em>1\u200b<\/th><th><em>x<\/em>2\u200b<\/th><th><em>P<\/em>(<em>Y<\/em>=<em>y<\/em>\u2223<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)<\/th><th><\/th><th><\/th><th><\/th><\/tr><\/thead><tbody><tr><td><\/td><td><\/td><td><em>y<\/em>=0<\/td><td><em>y<\/em>=1<\/td><td><em>y<\/em>=2<\/td><td><em>y<\/em>=3<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u56e0\u6b64\uff0c\u7ed9\u5b9a\u56fa\u5b9a\u6837\u672c<strong>x<\/strong>\uff0c\u4eba\u7c7b\u4e13\u5bb6\u4e0e\u673a\u5668\u7684\u671f\u671b\u51c6\u786e\u7387\u53ef\u8868\u793a\u4e3a\uff1aE<em>y<\/em>\u200b[I{<em>f<\/em>(<em>x<\/em>1\u200b)=<em>y<\/em>}\u200b]\u200b=<em>y<\/em>\u2208<em>Y<\/em>\u2211\u200b<em>P<\/em>(<em>Y<\/em>=<em>y<\/em>\u2223<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)<em>P<\/em>(<em>f<\/em>(<em>x<\/em>1\u200b)=<em>y<\/em>\u2223<em>x<\/em>1\u200b)=0\u22c50+0\u22c50+0\u22c521\u200b+1\u22c521\u200b=21\u200b\u200b<\/p>\n\n\n\n<p>\u7531\u4e8e<em>s<\/em>(<em>x<\/em>1\u200b)\u2208(0,1)\uff0cLtD 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\u7684\u6a21\u5f0f\uff0c\u800c\u662f\u4f7f\u7528\u8d1d\u53f6\u65af\u6700\u4f18\u589e\u5f3a\u9884\u6d4b\u5668\uff08\u878d\u5408\u673a\u5668\u4fe1\u53f7\u4e0e\u4e13\u5bb6\u63d0\u4f9b\u7684\u7279\u5f81<em>x<\/em>2\u200b\uff09\uff0c\u5219\u51c6\u786e\u7387\u4f1a\u663e\u8457\u63d0\u9ad8\uff1aE<em>y<\/em>\u200b[I{<em>g<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)=<em>y<\/em>}\u200b]\u200b=<em>y<\/em>\u2208<em>Y<\/em>\u2211\u200b<em>P<\/em>(<em>Y<\/em>=<em>y<\/em>\u2223<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)<em>P<\/em>(<em>g<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)=<em>y<\/em>\u2223<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)=0\u22c50+0\u22c50+0\u22c50+1\u22c51=1\u200b<\/p>\n\n\n\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u53ea\u8981<em>s<\/em>(<em>x<\/em>1\u200b)&gt;0\uff0c\u589e\u5f3a\u7cfb\u7edf\u7684\u51c6\u786e\u7387\u5c31\u6ee1\u8db3\uff1a<\/p>\n\n\n\n<p><em>s<\/em>(<em>x<\/em>1\u200b)E<em>y<\/em>,<em>f<\/em>\u200b[I{<em>f<\/em>(<em>x<\/em>1\u200b)=<em>y<\/em>}\u200b]+(1\u2212<em>s<\/em>(<em>x<\/em>1\u200b))E<em>y<\/em>,<em>f<\/em>\u2032\u200b[I{<em>g<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)=<em>y<\/em>}\u200b]=<em>s<\/em>(<em>x<\/em>1\u200b)21\u200b+(1\u2212<em>s<\/em>(<em>x<\/em>1\u200b))1\u226521\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">A.2 \u56fe 2 \u7684\u5b9e\u9a8c\u8bbe\u7f6e<\/h3>\n\n\n\n<p>\u6784\u5efa\u5408\u6210\u5206\u7c7b\u4efb\u52a1\uff1a\u5305\u542b 4 \u4e2a\u7c7b\u522b<em>Y<\/em>\u2208{0,1,2,3}\uff0c\u6bcf\u4e2a\u7c7b\u522b\u7531\u4e00\u5bf9\u4e8c\u5143\u6f5c\u5728\u7279\u5f81(<em>b<\/em>1\u200b,<em>b<\/em>2\u200b)\u2208{0,1}2\u5b9a\u4e49\u3002\u6bcf\u4e2a\u7c7b\u522b\u6620\u5c04\u5230\u4e24\u4e2a\u89c2\u6d4b\u7279\u5f81(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)\uff0c\u5176\u4e2d\u5fc3\u4f4d\u4e8e(\u00b1sep,\u00b1sep)\uff0c\u5e76\u52a0\u5165\u9ad8\u65af\u566a\u58f0\u6270\u52a8\u3002<\/p>\n\n\n\n<p>\u4e3a\u63a7\u5236\u7279\u5f81\u4fe1\u606f\u6027\uff0c\u53ef\u9009\u62e9\u6027\u5730\u6cbf<em>x<\/em>1\u200b\u8f74\uff08\u673a\u5668\u7279\u5f81\uff09\u6216<em>x<\/em>2\u200b\u8f74\uff08\u4e13\u5bb6\u7279\u5f81\uff09\u79fb\u52a8\u4e2d\u5fc3\uff1a\u6cbf<em>x<\/em>1\u200b\u8f74\u589e\u52a0\u5206\u79bb\u5ea6\u4f1a\u63d0\u9ad8\u673a\u5668\u7684\u51c6\u786e\u7387\uff0c\u6cbf<em>x<\/em>2\u200b\u8f74\u589e\u52a0\u5206\u79bb\u5ea6\u5219\u4f1a\u63d0\u9ad8\u4e13\u5bb6\u7684\u51c6\u786e\u7387\u3002<\/p>\n\n\n\n<p>\u751f\u6210 4000 \u4e2a\u6837\u672c\uff0c\u6309 60:40 \u7684\u6bd4\u4f8b\u5212\u5206\u4e3a\u8bad\u7ec3\u96c6\u4e0e\u6d4b\u8bd5\u96c6\u3002\u5206\u522b\u8bad\u7ec3\u4e09\u79cd\u903b\u8f91\u56de\u5f52\u6a21\u578b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4ec5\u57fa\u4e8e<em>x<\/em>1\u200b\uff08\u673a\u5668\u9884\u6d4b\u5668<em>f<\/em>(<em>x<\/em>1\u200b)\uff09\uff1b<\/li>\n\n\n\n<li>\u4ec5\u57fa\u4e8e<em>x<\/em>2\u200b\uff08\u4e13\u5bb6\u9884\u6d4b\u5668<em>f<\/em>\u2032(<em>x<\/em>2\u200b)\uff09\uff1b<\/li>\n\n\n\n<li>\u57fa\u4e8e\u4e24\u4e2a\u7279\u5f81\uff08\u589e\u5f3a\u9884\u6d4b\u5668<em>g<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b)\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8bc4\u4f30\u4e24\u79cd \u201c\u6700\u4f18\u7b56\u7565\u201d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b66\u4e60\u59d4\u6258\uff08LtD\uff09\uff1a\u52a8\u6001\u9009\u62e9\u673a\u5668\u6216\u4e13\u5bb6\u7684\u9884\u6d4b\u7ed3\u679c\uff1b<\/li>\n\n\n\n<li>\u5b66\u4e60\u8be2\u95ee\uff08LtA\uff09\uff1a\u4f18\u5316 \u201c\u4f55\u65f6\u67e5\u8be2\u4e13\u5bb6\u53cd\u9988\u201d \u7684\u7b56\u7565\uff08\u672c\u573a\u666f\u4e2d\uff0c\u4e13\u5bb6\u53cd\u9988\u5373\u4e13\u5bb6\u7279\u5f81<em>x<\/em>2\u200b\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6700\u7ec8\u7ed3\u679c\u5982\u56fe 2 \u6240\u793a\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">A.3 \u5b9a\u7406 1 \u7684\u8bc1\u660e<\/h3>\n\n\n\n<p><strong>\u8bc1\u660e<\/strong>\uff1a<\/p>\n\n\n\n<p>\u9996\u5148\u8003\u8651\u65e0\u7ea6\u675f\u60c5\u51b5\uff0c\u5373\u6700\u5c0f\u5316\u4ee5\u4e0b\u76ee\u6807\u51fd\u6570\uff1a<\/p>\n\n\n\n<p><em>s<\/em>\u2208Smin\u200bE(<strong>x<\/strong>,<em>y<\/em>,<em>h<\/em>)\u200b[(1\u2212<em>s<\/em>(<strong>x<\/strong>))\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)+<em>s<\/em>(<strong>x<\/strong>)\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)](14)<\/p>\n\n\n\n<p>\u5c06\u76ee\u6807\u51fd\u6570\u91cd\u5199\u4e3a\uff1a\u200bE(<strong>x<\/strong>,<em>y<\/em>,<em>h<\/em>)\u200b[(1\u2212<em>s<\/em>(<strong>x<\/strong>))\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)+<em>s<\/em>(<strong>x<\/strong>)\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]=E<strong>x<\/strong>\u200b[(1\u2212<em>s<\/em>(<strong>x<\/strong>))E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)]+<em>s<\/em>(<strong>x<\/strong>)E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]]=E<strong>x<\/strong>\u200b[E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)]]+E<strong>x<\/strong>\u200b[<em>s<\/em>(<strong>x<\/strong>)(E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]\u2212E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)])]\u200b<\/p>\n\n\n\n<p>\u7531\u4e8e\u7b2c\u4e00\u9879\u4e0e<em>s<\/em>\u65e0\u5173\uff0c\u4f18\u5316\u95ee\u9898\u53ef\u7b80\u5316\u4e3a\uff1a<\/p>\n\n\n\n<p><em>s<\/em>\u2208[0,1]\u2200<strong>x<\/strong>\u2208Xmin\u200bE<strong>x<\/strong>\u200b[<em>s<\/em>(<strong>x<\/strong>)(E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]\u2212E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)])](15)<\/p>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u5173\u4e8e<strong>x<\/strong>\u7684\u53ef\u5206\u79bb\u7ebf\u6027\u4f18\u5316\u95ee\u9898\uff0c\u56e0\u6b64\u5bf9\u4efb\u610f<strong>x<\/strong>\u2208X\uff0c\u6700\u4f18\u9009\u62e9\u5668\u4e3a\uff1a<\/p>\n\n\n\n<p><em>s<\/em>\u2217(<strong>x<\/strong>)={1\u82e5E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)]\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]&gt;00\u5176\u4ed6\u60c5\u51b5\u200b(16)<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\u8003\u8651\u5e26\u9884\u7b97\u7ea6\u675f\u7684\u60c5\u51b5\uff0c\u5373\u4f18\u5316\u95ee\u9898\u53d8\u4e3a\uff1a<em>s<\/em>\u2208[0,1]\u2200<strong>x<\/strong>\u2208Xmin\u200bs.t.\u200bE(<strong>x<\/strong>,<em>h<\/em>,<em>y<\/em>)\u200b[(1\u2212<em>s<\/em>(<strong>x<\/strong>))\u2113<em>f<\/em>(<em>f<\/em>(<strong>x<\/strong>),<em>y<\/em>)+<em>s<\/em>(<strong>x<\/strong>)\u2113<em>g<\/em>(<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>),<em>y<\/em>)]E<strong>X<\/strong>\u200b[<em>s<\/em>(<strong>x<\/strong>)]\u2264<em>\u03b2<\/em>\u200b(17)<\/p>\n\n\n\n<p>\u6784\u5efa\u5bf9\u5076\u95ee\u9898\uff1a<em>\u03bb<\/em>\u22650max\u200b<em>s<\/em>\u2208[0,1]\u2200<strong>x<\/strong>\u2208Xmin\u200bE(<strong>x<\/strong>,<em>h<\/em>,<em>y<\/em>)\u200b[(1\u2212<em>s<\/em>(<strong>x<\/strong>))\u2113<em>f<\/em>+<em>\u03bb<\/em>(<em>s<\/em>(<strong>x<\/strong>)\u2212<em>\u03b2<\/em>)](18)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c<em>\u03bb<\/em>\u4e3a\u9884\u7b97\u7ea6\u675f\u7684\u62c9\u683c\u6717\u65e5\u4e58\u5b50\u3002\u4e0e\u65e0\u7ea6\u675f\u60c5\u51b5\u7c7b\u4f3c\uff0c\u5185\u5c42\u4f18\u5316\u7684\u6700\u4f18\u9009\u62e9\u5668\u4e3a\uff1a<\/p>\n\n\n\n<p><em>s<\/em><em>\u03bb<\/em>\u2217\u200b(<strong>x<\/strong>)={1\u82e5E<em>y<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>f<\/em>]\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b[\u2113<em>g<\/em>]&gt;<em>\u03bb<\/em>0\u5176\u4ed6\u60c5\u51b5\u200b(19)<\/p>\n\n\n\n<p>\u6ce8\u610f\u5230\uff1aE<strong>x<\/strong>\u200b[<em>s<\/em><em>\u03bb<\/em>\u2217\u200b(<strong>x<\/strong>)]\u200b=E<strong>x<\/strong>\u200b[I{E<em>y<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>f<\/em>\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>g<\/em>&gt;<em>\u03bb<\/em>}\u200b]=<em>P<\/em><strong>x<\/strong>\u200b(E<em>y<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>f<\/em>\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>g<\/em>&gt;<em>\u03bb<\/em>)=1\u2212<em>P<\/em><strong>x<\/strong>\u200b(E<em>y<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>f<\/em>\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>g<\/em>\u2264<em>\u03bb<\/em>)\u200b<\/p>\n\n\n\n<p>\u5728\u6700\u4f18\u89e3<em>\u03bb<\/em>\u2217\u5904\uff0c\u7ea6\u675f\u6761\u4ef6E<strong>x<\/strong>\u200b[<em>s<\/em>(<strong>x<\/strong>)]\u2264<em>\u03b2<\/em>\u53d6\u7b49\u53f7\uff0c\u5373<em>\u03bb<\/em>\u2217\u6ee1\u8db3\uff1a<\/p>\n\n\n\n<p><em>P<\/em><strong>x<\/strong>\u200b(E<em>y<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>f<\/em>\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>g<\/em>\u2264<em>\u03bb<\/em>\u2217)=1\u2212<em>\u03b2<\/em><\/p>\n\n\n\n<p>\u7531\u8fde\u7eed\u6027\u5047\u8bbe\u53ef\u77e5\uff0c<em>\u03bb<\/em>\u2217\u662f \u201c\u671f\u671b\u5dee\u503cE<em>y<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>f<\/em>\u2212E<em>y<\/em>,<em>h<\/em>\u2223<strong>x<\/strong>\u200b\u2113<em>g<\/em>\u201d \u7684(1\u2212<em>\u03b2<\/em>)\u5206\u4f4d\u6570\u3002<\/p>\n\n\n\n<p>\u8bc1\u6bd5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">A.4 \u5b9a\u7406 2 \u7684\u8bc1\u660e<\/h3>\n\n\n\n<p>\u4e3a\u8bc1\u660e\u5b9a\u7406 2\uff0c\u91c7\u7528\u4e0e Mao \u7b49\u4eba [22] \u7c7b\u4f3c\u7684\u601d\u8def\uff1a\u9996\u5148\u8bc1\u660e\u66ff\u4ee3\u635f\u5931\u4e0a\u754c\u4f18\u4e8e<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\uff0c\u518d\u8bc1\u660e\u5728\u53ef\u5b9e\u73b0\u6027\u5047\u8bbe\u4e0b\u635f\u5931\u6536\u655b\u81f3\u96f6\u3002<\/p>\n\n\n\n<p>\u4e3a\u7b80\u5316\u7b26\u53f7\uff0c\u8bb0\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>v<\/em>)\u4e3a \u201c\u5bf9\u6570\u51e0\u7387\u7684 softmax \u503c\u4e3a<em>v<\/em>\u65f6\u7684\u635f\u5931\u201d\uff08\u5373\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>v<\/em>)=\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>v<\/em>,<em>y<\/em>)\uff09\u3002\u9996\u5148\u8bc1\u660e\uff0c\u5bf9\u4efb\u610f<strong>x<\/strong>,<em>h<\/em>,<em>y<\/em>\u53ca\u4efb\u610f<em>f<\/em>,<em>g<\/em>,<em>s<\/em>\u2208F\u00d7G\u00d7S\uff0c\u5747\u6709\uff1a<\/p>\n\n\n\n<p><em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(<em>f<\/em>,<em>g<\/em>,<em>s<\/em>,<em>y<\/em>)\u226421\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(<em>f<\/em>~\u200b,<em>g<\/em>~\u200b,<em>s<\/em>~,<em>y<\/em>)\u200b(20)<\/p>\n\n\n\n<p>\u5206\u516d\u79cd\u60c5\u51b5\u8ba8\u8bba\uff1a<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u60c5\u51b5 1\uff1a\u4e24\u4e2a\u9884\u6d4b\u5668\u5747\u9519\u8bef\uff08<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>\u4e14<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>)\ue020=<em>y<\/em>\uff09<\/h4>\n\n\n\n<p>\u6b64\u65f6<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)=1\u3002\u5bf9\u4e8e<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(\u22c5)\uff0c\u6709\uff1a<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b=(1\u2212\u2113<em>s<\/em>(<em>s<\/em>~))\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>f<\/em>~\u200b\u200b)+\u2113<em>s<\/em>(<em>s<\/em>~)\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b)\u2265(1\u2212\u2113<em>s<\/em>(<em>s<\/em>~))\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(21\u200b)+\u2113<em>s<\/em>(<em>s<\/em>~)\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(21\u200b)\u2265(1\u2212\u2113<em>s<\/em>(<em>s<\/em>~))\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)+\u2113<em>s<\/em>(<em>s<\/em>~)\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)\u200b(21)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u7b49\u5f0f\u7531\u5047\u8bbe\uff08b\uff09\u6210\u7acb\uff1b\u7b2c\u4e00\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\u7684\u539f\u56e0\u662f\uff1a\u82e5<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>\uff0c\u5219<em>\u03c3<\/em>(<em>f<\/em>~\u200b<em>y<\/em>\u200b)&lt;21\u200b\uff08\u6839\u636e\u8d1d\u53f6\u65af\u6cd5\u5219\uff0c\u9884\u6d4b\u7ed3\u679c\u5bf9\u5e94\u6700\u5927\u5bf9\u6570\u51e0\u7387\uff09\uff0c\u540c\u7406<em>\u03c3<\/em>(<em>g<\/em>~\u200b<em>y<\/em>\u200b)&lt;21\u200b\uff1b\u7b2c\u4e8c\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\u7684\u539f\u56e0\u662f\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>\u975e\u9012\u589e\u3002<\/p>\n\n\n\n<p>\u4e24\u8fb9\u540c\u65f6\u9664\u4ee5\u6b63\u657021\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)\uff1a21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b\u226521\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)(1\u2212\u2113<em>s<\/em>(<em>s<\/em>~))\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)+\u2113<em>s<\/em>(<em>s<\/em>~)\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)\u200b\u2265\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)(1\u2212\u2113<em>s<\/em>(<em>s<\/em>~))\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)+\u2113<em>s<\/em>(<em>s<\/em>~)\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)\u200b=1=<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b(22)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c\u7b2c\u4e8c\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\u7684\u539f\u56e0\u662f\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)&gt;21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u60c5\u51b5 2\uff1a\u4e24\u4e2a\u9884\u6d4b\u5668\u5747\u6b63\u786e<\/h4>\n\n\n\n<p>\u6b64\u65f6<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)=0\uff0c\u4e14<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(\u22c5)\u22650\uff0c\u56e0\u6b64\u4e0d\u7b49\u5f0f\uff0820\uff09\u6210\u7acb\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u60c5\u51b5 3\uff1a\u9009\u62e9\u5668<em>s<\/em>(<strong>x<\/strong>)=0\uff0c<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>\u4e14<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>)=<em>y<\/em><\/h4>\n\n\n\n<p>\u6b64\u65f6<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)=1\u3002\u5bf9\u4e8e<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(\u22c5)\uff0c\u6709\uff1a<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b=(1\u2212\u2113<em>s<\/em>(<em>s<\/em>~))\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>f<\/em>~\u200b\u200b)+\u2113<em>s<\/em>(<em>s<\/em>~)\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b)\u226521\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>f<\/em>~\u200b\u200b)+21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b)\u226521\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)+21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b)\u200b(23)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\u7684\u539f\u56e0\u662f\uff1a<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>\u4e14<em>s<\/em>(<strong>x<\/strong>)=0\uff08\u5373<em>s<\/em>~&lt;0\uff09\uff0c\u56e0\u6b64\u2113<em>s<\/em>(<em>s<\/em>~)&lt;21\u200b\uff1b\u7b2c\u4e8c\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\u7684\u539f\u56e0\u662f<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>\uff08\u5373<em>\u03c3<\/em><em>y<\/em><em>f<\/em>~\u200b\u200b&lt;21\u200b\uff09\u3002<\/p>\n\n\n\n<p>\u4e24\u8fb9\u540c\u65f6\u9664\u4ee521\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)\uff1a21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b\u226521\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)+21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b)\u200b\u22651+21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(<em>\u03c3<\/em><em>y<\/em><em>g<\/em>~\u200b\u200b)\u200b\u22651=<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b(24)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u60c5\u51b5 4\uff1a\u9009\u62e9\u5668<em>s<\/em>(<strong>x<\/strong>)=1\uff0c<em>f<\/em>(<strong>x<\/strong>)=<em>y<\/em>\u4e14<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>)\ue020=<em>y<\/em><\/h4>\n\n\n\n<p>\u6b64\u65f6<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)=1\uff0c\u4e0e\u60c5\u51b5 3 \u5bf9\u79f0\uff0c\u53ef\u8bc1\u660e\u4e0d\u7b49\u5f0f\uff0820\uff09\u6210\u7acb\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u60c5\u51b5 5\uff1a\u9009\u62e9\u5668<em>s<\/em>(<strong>x<\/strong>)=1\uff0c<em>f<\/em>(<strong>x<\/strong>)\ue020=<em>y<\/em>\u4e14<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>)=<em>y<\/em><\/h4>\n\n\n\n<p>\u6b64\u65f6<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)=0\uff0c\u4e14<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(\u22c5)\u22650\uff0c\u4e0d\u7b49\u5f0f\uff0820\uff09\u6210\u7acb\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u60c5\u51b5 6\uff1a\u9009\u62e9\u5668<em>s<\/em>(<strong>x<\/strong>)=0\uff0c<em>f<\/em>(<strong>x<\/strong>)=<em>y<\/em>\u4e14<em>g<\/em>(<strong>x<\/strong>,<em>h<\/em>)\ue020=<em>y<\/em><\/h4>\n\n\n\n<p>\u6b64\u65f6<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)=0\uff0c\u4e14<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(\u22c5)\u22650\uff0c\u4e0d\u7b49\u5f0f\uff0820\uff09\u6210\u7acb\u3002<\/p>\n\n\n\n<p>\u7efc\u4e0a\uff0c\u516d\u79cd\u60c5\u51b5\u5747\u8bc1\u660e21\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>(\u22c5)\u200b\u2265<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(\u22c5)\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u5047\u8bbe\u5b58\u5728\u96f6\u8bef\u5dee\u89e3<em>f<\/em>\u2217,<em>g<\/em>\u2217,<em>s<\/em>\u2217\u2208F\u00d7G\u00d7S\uff08\u5373E<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b=0\uff09\uff0c\u8bbe<em>f<\/em>^\u200b,<em>g<\/em>^\u200b,<em>s<\/em>^\u4e3a\u66ff\u4ee3\u635f\u5931<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u7684\u6700\u5c0f\u503c\u70b9\uff08\u5373<em>f<\/em>^\u200b,<em>g<\/em>^\u200b,<em>s<\/em>^=argminE<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\uff09\u3002\u5219\u6709\uff1aE<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b(<em>f<\/em>^\u200b,<em>g<\/em>^\u200b,<em>s<\/em>^)\u200b\u226421\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)E<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(<em>f<\/em>^\u200b,<em>g<\/em>^\u200b,<em>s<\/em>^)\u200b\u226421\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)E<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(<em>\u03b1<\/em><em>f<\/em>\u2217,<em>\u03b1<\/em>\u2032<em>g<\/em>\u2217,<em>s<\/em>\u2217)\u200b\u200b<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u4e0d\u7b49\u5f0f\u753121\u200b\u2113<em>s<\/em><em>u<\/em><em>rr<\/em>(32\u200b)<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u2265<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u6210\u7acb\uff1b\u7b2c\u4e8c\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\u7684\u539f\u56e0\u662f<em>f<\/em>^\u200b,<em>g<\/em>^\u200b,<em>s<\/em>^\u662f\u6700\u5c0f\u503c\u70b9\uff0c\u4e14F\u3001G\u5bf9\u7f29\u653e\u5c01\u95ed\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u5355\u8c03\u6536\u655b\u5b9a\u7406\u53ef\u8bc1\u660e\uff0c\u5f53<em>\u03b1<\/em>,<em>\u03b1<\/em>\u2032,<em>\u03b3<\/em>\u2192\u221e\u65f6\uff0cE<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u200b(<em>\u03b1<\/em><em>f<\/em>\u2217,<em>\u03b1<\/em>\u2032<em>g<\/em>\u2217,<em>\u03b3<\/em><em>s<\/em>\u2217)\u21920\uff0c\u56e0\u6b64E<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u200b(<em>f<\/em>^\u200b,<em>g<\/em>^\u200b,<em>s<\/em>^)=0\uff0c\u5373<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u5173\u4e8e<em>L<\/em>0\u22121<em>a<\/em><em>s<\/em><em>k<\/em>\u200b\u5177\u6709F\u00d7G\u00d7S- \u53ef\u5b9e\u73b0\u4e00\u81f4\u6027\u3002<\/p>\n\n\n\n<p>\u8bc1\u6bd5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u9644\u5f55 B \u989d\u5916\u5b9e\u9a8c\u7ec6\u8282<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u8bad\u7ec3\u7ec6\u8282<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5408\u6210\u6570\u636e\u96c6\uff08Synth\uff09<\/strong>\uff1a\u6240\u6709\u65b9\u6cd5\u5747\u8bad\u7ec3 150 \u4e2a epoch\u3002\u5177\u4f53\u800c\u8a00\uff1a\n<ul class=\"wp-block-list\">\n<li>LtD\uff1a\u4ec5\u8bad\u7ec3\u6a21\u578b<em>f<\/em>\uff0c\u5171 150 \u4e2a epoch\uff1b<\/li>\n\n\n\n<li>LtA-Seq\uff1a\u5148\u8bad\u7ec3\u589e\u5f3a\u6a21\u578b<em>g<\/em>\uff0850 \u4e2a epoch\uff09\uff0c\u518d\u8bad\u7ec3\u6807\u51c6\u6a21\u578b<em>f<\/em>\uff08100 \u4e2a epoch\uff09\uff1b<\/li>\n\n\n\n<li>LtA-Joint\uff1a\u5148\u5206\u522b\u7528\u4ea4\u53c9\u71b5\u635f\u5931\u9884\u8bad\u7ec3<em>f<\/em>\u548c<em>g<\/em>\uff08\u5404 50 \u4e2a epoch\uff09\uff0c\u518d\u7528<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u8054\u5408\u8bad\u7ec3<em>f<\/em>\u3001<em>g<\/em>\u548c<em>s<\/em>\uff08100 \u4e2a epoch\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>X-Rays \u6570\u636e\u96c6\uff08\u4e24\u79cd\u53cd\u9988\u7b56\u7565\uff09<\/strong>\uff1a\u6240\u6709\u65b9\u6cd5\u5747\u8bad\u7ec3 300 \u4e2a epoch\u3002\u5177\u4f53\u800c\u8a00\uff1a\n<ul class=\"wp-block-list\">\n<li>LtD\uff1a\u4ec5\u8bad\u7ec3\u6a21\u578b<em>f<\/em>\uff0c\u5171 300 \u4e2a epoch\uff1b<\/li>\n\n\n\n<li>LtA-Seq\uff1a\u5148\u8bad\u7ec3\u589e\u5f3a\u6a21\u578b<em>g<\/em>\uff08200 \u4e2a epoch\uff09\uff0c\u518d\u8bad\u7ec3\u6807\u51c6\u6a21\u578b<em>f<\/em>\uff08100 \u4e2a epoch\uff09\uff1b<\/li>\n\n\n\n<li>LtA-Joint\uff1a\u5148\u5206\u522b\u7528\u4ea4\u53c9\u71b5\u635f\u5931\u9884\u8bad\u7ec3<em>f<\/em>\u548c<em>g<\/em>\uff08\u5404 200 \u4e2a epoch\uff09\uff0c\u518d\u7528<em>L<\/em>~<em>a<\/em><em>s<\/em><em>k<\/em>\u8054\u5408\u8bad\u7ec3<em>f<\/em>\u3001<em>g<\/em>\u548c<em>s<\/em>\uff08100 \u4e2a epoch\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u4e24\u4e2a\u6570\u636e\u96c6\u5747\u91c7\u7528\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08SGD\uff09\u4f18\u5316\u5668\uff0c\u521d\u59cb\u5b66\u4e60\u7387\u8bbe\u4e3a 0.001\u3002LtA-Joint \u7684\u72ec\u7acb\u9884\u8bad\u7ec3\u9636\u6bb5\u53ef\u907f\u514d \u201c\u4ec5\u8bad\u7ec3<em>f<\/em>\u6216\u4ec5\u8bad\u7ec3<em>g<\/em>\u201d \u7684\u8bad\u7ec3\u5d29\u6e83\u95ee\u9898\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u786c\u4ef6\u4e0e\u8bad\u7ec3\u65f6\u95f4<\/h3>\n\n\n\n<p>\u5b9e\u9a8c\u4f7f\u7528 224 \u6838\u673a\u5668\uff0c\u914d\u7f6e\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>CPU\uff1aIntel(R) Xeon(R) Platinum 8480CL\uff1b<\/li>\n\n\n\n<li>GPU\uff1a8 \u5757 NVIDIA H100 80GB HBM3\uff1b<\/li>\n\n\n\n<li>\u64cd\u4f5c\u7cfb\u7edf\uff1aUbuntu 22.04.3 LTS\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8bad\u7ec3\u65f6\u95f4\u7edf\u8ba1\uff08\u5e73\u5747\u503c \u00b1 \u6807\u51c6\u5dee\uff09\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5408\u6210\u6570\u636e\u96c6<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>LtD\uff1a\u224840\u00b10.60 \u79d2\uff1b<\/li>\n\n\n\n<li>LtA-Seq\uff1a\u224848\u00b10.37 \u79d2\uff1b<\/li>\n\n\n\n<li>LtA-Joint\uff1a\u224875\u00b13 \u79d2\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>X-Rays \u6570\u636e\u96c6\uff08Unc-Feedback\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>LtD\uff1a\u22484860\u00b150 \u79d2\uff1b<\/li>\n\n\n\n<li>LtA-Seq\uff1a\u22485010\u00b1289 \u79d2\uff1b<\/li>\n\n\n\n<li>LtA-Joint\uff1a\u22485956\u00b1130 \u79d2\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>X-Rays \u6570\u636e\u96c6\uff08LtD-Feedback\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>LtD\uff1a\u22484860\u00b150 \u79d2\uff1b<\/li>\n\n\n\n<li>LtA-Seq\uff1a\u22485967\u00b1298 \u79d2\uff1b<\/li>\n\n\n\n<li>LtA-Joint\uff1a\u22486602\u00b1207 \u79d2\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u6587\u7ae0\u6765\u6e90\uff1a<\/p>\n\n\n\n<p><a href=\"https:\/\/arxiv.org\/html\/2510.08314v1\">https:\/\/arxiv.org\/html\/2510.08314v1<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6458\u8981 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