{"id":104214,"date":"2026-09-12T02:33:07","date_gmt":"2026-09-11T18:33:07","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/104214.html"},"modified":"2026-09-12T02:33:07","modified_gmt":"2026-09-11T18:33:07","slug":"%e8%ae%ba%e6%96%87%e5%ad%a6%e4%b9%a0%e6%8b%9c%e5%8d%a0%e5%ba%ad%e6%95%85%e9%9a%9c%e4%b8%8b%e7%9a%84robust%e5%a4%9a%e6%99%ba%e8%83%bd%e4%bd%93llm%e7%b3%bb%e7%bb%9f%ef%bc%9aself-anchored-consensus","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/104214.html","title":{"rendered":"[\u8bba\u6587\u5b66\u4e60]\u62dc\u5360\u5ead\u6545\u969c\u4e0b\u7684Robust\u591a\u667a\u80fd\u4f53LLM\u7cfb\u7edf\uff1aSelf-Anchored Consensus\uff08SAC\uff09\u6df1\u5ea6\u89e3\u6790"},"content":{"rendered":"<h2>Robust Multi-Agent LLMs under Byzantine Faults (SAC)<\/h2>\n<h3>\u8bba\u6587\u91cd\u70b9<\/h3>\n<p>\u8fd9\u7bc7\u8bba\u6587\u7814\u7a76\u7684\u662f\u53bb\u4e2d\u5fc3\u5316LLM\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\u5728\u62dc\u5360\u5ead\u6545\u969c\u4e0b\u7684\u9c81\u68d2\u6027\u95ee\u9898\u3002\u6838\u5fc3\u4e3b\u5f20\u5f88\u76f4\u63a5&#xff1a;\u73b0\u6709\u65b9\u6cd5\u8981\u4e48\u4f9d\u8d56leader\u534f\u8c03\u3001\u8981\u4e48\u4f9d\u8d56\u667a\u80fd\u4f53\u81ea\u62a5\u7684\u7f6e\u4fe1\u5ea6&#xff0c;\u8fd9\u4e24\u6761\u8def\u5728\u5bf9\u6297\u73af\u5883\u4e0b\u90fd\u5bb9\u6613\u88ab\u6253\u7a7f\u3002\u4f5c\u8005\u63d0\u51fa\u4e86Self-Anchored Consensus&#xff08;SAC&#xff09;&#xff0c;\u4e00\u4e2a\u5b8c\u5168\u53bb\u4e2d\u5fc3\u5316\u7684\u8fed\u4ee3\u201c\u8fc7\u6ee4-\u7cbe\u70bc\u201d\u534f\u8bae&#xff0c;\u8ba9\u6bcf\u4e2a\u667a\u80fd\u4f53\u5728\u63a5\u6536\u7aef\u72ec\u7acb\u8bc4\u4f30\u90bb\u5c45\u54cd\u5e94\u7684\u53ef\u9760\u6027&#xff0c;\u518d\u636e\u6b64\u8fc7\u6ee4\u548c\u66f4\u65b0\u81ea\u5df1\u7684\u8f93\u51fa&#xff0c;\u914d\u5408(F&#043;1)-\u9c81\u68d2\u901a\u4fe1\u56fe\u6761\u4ef6&#xff0c;\u5b9e\u73b0\u62dc\u5360\u5ead\u5bb9\u9519\u3002<\/p>\n<h3>\u6838\u5fc3\u7814\u7a76\u5185\u5bb9<\/h3>\n<h4>\u95ee\u9898\u5b9a\u4e49<\/h4>\n<p>LLM\u667a\u80fd\u4f53\u901a\u8fc7P2P\u7f51\u7edc\u534f\u4f5c\u5df2\u7ecf\u6210\u4e3a\u63d0\u5347\u53ef\u9760\u6027\u7684\u4e3b\u6d41\u8303\u5f0f&#xff0c;\u4f46\u8fd9\u4e5f\u6253\u5f00\u4e86\u4e00\u4e2a\u653b\u51fb\u9762&#xff1a;\u4e0d\u53ef\u9760\u6216\u6076\u610f&#xff08;\u62dc\u5360\u5ead&#xff09;\u667a\u80fd\u4f53\u53ef\u4ee5\u901a\u8fc7\u5bf9\u8bdd\u5f71\u54cd\u90bb\u5c45&#xff0c;\u628a\u9519\u8bef\u7ed3\u8bba\u201c\u4f20\u67d3\u201d\u7ed9\u539f\u672c\u53ef\u9760\u7684\u8282\u70b9\u3002\u4ece\u5176\u4ed6\u667a\u80fd\u4f53\u7684\u89c6\u89d2\u770b&#xff0c;\u4e00\u4e2a\u56e0\u5e7b\u89c9\u7ed9\u51fa\u9519\u8bef\u7b54\u6848\u7684\u667a\u80fd\u4f53\u548c\u4e00\u4e2a\u6545\u610f\u6ce8\u5165\u5bf9\u6297\u5185\u5bb9\u7684\u667a\u80fd\u4f53&#xff0c;\u5728\u5c40\u90e8\u4fe1\u606f\u4e0a\u662f\u4e0d\u53ef\u533a\u5206\u7684\u2014\u2014\u4e24\u8005\u90fd\u662f\u201c\u62dc\u5360\u5ead\u6545\u969c\u201d\u3002<\/p>\n<p>\u8bba\u6587\u805a\u7126\u4e24\u4e2a\u7ed3\u6784\u6027\u95ee\u9898&#xff1a;\u7b2c\u4e00&#xff0c;\u6bcf\u4e2a\u667a\u80fd\u4f53\u5982\u4f55\u5728\u6bcf\u4e00\u8f6e\u4e2d\u5224\u65ad\u54ea\u4e9b\u90bb\u5c45\u7684\u54cd\u5e94\u503c\u5f97\u4fe1\u4efb&#xff1b;\u7b2c\u4e8c&#xff0c;\u901a\u4fe1\u56fe\u7684\u62d3\u6251\u5e94\u8be5\u6ee1\u8db3\u4ec0\u4e48\u6761\u4ef6&#xff0c;\u624d\u80fd\u628a\u62dc\u5360\u5ead\u5f71\u54cd\u9650\u5236\u5728\u53ef\u63a7\u8303\u56f4\u5185\u3002<\/p>\n<h4>\u521b\u65b0\u65b9\u6cd5<\/h4>\n<p>SAC\u7684\u6838\u5fc3\u521b\u65b0\u70b9\u6709\u4e24\u4e2a\u5c42\u9762\u3002<\/p>\n<p>\u534f\u8bae\u5c42\u9762&#xff0c;SAC\u662f\u4e00\u4e2a\u56db\u9636\u6bb5\u7684\u8fed\u4ee3\u6d41\u7a0b&#xff1a;<\/p>\n<li>\u5e7f\u64ad&#xff1a;\u6bcf\u4e2a\u667a\u80fd\u4f53\u5c06\u5f53\u524d\u54cd\u5e94\u53d1\u9001\u7ed9\u90bb\u5c45\u3002<\/li>\n<li>\u8bc4\u5206&#xff1a;\u6bcf\u4e2a\u667a\u80fd\u4f53\u5728\u63a5\u6536\u7aef\u7528\u81ea\u5df1LLM\u7684\u9a8c\u8bc1\u63d0\u793a&#xff08;verification prompt&#xff09;\u5bf9\u6bcf\u6761\u90bb\u5c45\u54cd\u5e94\u6253\u5206&#xff0c;\u5f97\u5206\u5728[0,1]\u533a\u95f4\u3002\u5173\u952e\u5728\u4e8e\u8fd9\u4e2a\u5206\u6570\u7531\u63a5\u6536\u65b9\u81ea\u5df1\u8ba1\u7b97&#xff0c;\u5b8c\u5168\u4e0d\u4f9d\u8d56\u90bb\u5c45\u81ea\u62a5\u7684\u7f6e\u4fe1\u5ea6\u2014\u2014\u8fd9\u5c31\u5835\u6b7b\u4e86\u62dc\u5360\u5ead\u667a\u80fd\u4f53\u901a\u8fc7\u865a\u62a5\u7f6e\u4fe1\u5ea6\u6765\u64cd\u7eb5\u81ea\u8eab\u6743\u91cd\u7684\u8def\u5f84\u3002<\/li>\n<li>\u8fc7\u6ee4&#xff1a;\u6bcf\u4e2a\u667a\u80fd\u4f53\u5c06\u90bb\u5c45\u5f97\u5206\u4e0e\u81ea\u5df1\u7684\u81ea\u8bc4\u5f97\u5206\u6bd4\u8f83&#xff0c;\u4e22\u5f03\u5f97\u5206\u4f4e\u4e8e\u81ea\u8bc4\u7684\u90bb\u5c45\u4e2d\u6700\u4f4e\u7684F\u4e2a&#xff08;F\u4e3a\u62dc\u5360\u5ead\u8282\u70b9\u4e0a\u754c&#xff09;\u3002<\/li>\n<li>\u7cbe\u70bc&#xff1a;\u667a\u80fd\u4f53\u5c06\u81ea\u5df1\u7684\u5f53\u524d\u54cd\u5e94\u548c\u4fdd\u7559\u7684\u90bb\u5c45\u54cd\u5e94\u91cd\u65b0\u7ec4\u88c5\u6210\u63d0\u793a&#xff0c;\u8ba9LLM\u91cd\u65b0\u751f\u6210\u8f93\u51fa\u3002<\/li>\n<p>\u8fd9\u4e2a\u8bbe\u8ba1\u501f\u9274\u4e86\u7ecf\u5178\u5206\u5e03\u5f0f\u7cfb\u7edf\u4e2d\u7684Mean-Subsequence-Reduced&#xff08;MSR&#xff09;\u7b97\u6cd5\u601d\u60f3&#xff0c;\u4f46\u505a\u4e86\u9762\u5411\u81ea\u7136\u8bed\u8a00\u4ea4\u4e92\u7684\u5173\u952e\u6539\u9020&#xff1a;\u7528\u63a5\u6536\u7aefLLM\u7684\u8bed\u4e49\u5224\u65ad\u66ff\u4ee3\u6570\u503c\u578b\u805a\u5408&#xff0c;\u7528filter-and-refine\u66ff\u4ee3\u786c\u6295\u7968\u3002<\/p>\n<p>\u7406\u8bba\u5c42\u9762&#xff0c;\u8bba\u6587\u7ed9\u51fa\u4e86\u901a\u4fe1\u56fe\u7684(F&#043;1)-\u9c81\u68d2\u6027\u6761\u4ef6\u3002\u8fd9\u4e2a\u6761\u4ef6\u7684\u76f4\u89c9\u662f&#xff1a;\u5728\u6bcf\u4e2a\u8bda\u5b9e\u8282\u70b9\u7684\u90bb\u5c45\u96c6\u5408\u4e2d&#xff0c;\u8bda\u5b9e\u8282\u70b9\u7684\u6570\u91cf\u8981\u4e25\u683c\u591a\u4e8e\u62dc\u5360\u5ead\u8282\u70b9\u7684\u6570\u91cf\u81f3\u5c111\u4e2a&#xff0c;\u8fd9\u6837\u8fc7\u6ee4\u64cd\u4f5c\u603b\u80fd\u4fdd\u8bc1\u4fdd\u7559\u7684\u96c6\u5408\u4e2d\u8bda\u5b9e\u54cd\u5e94\u5360\u591a\u6570\u3002\u8bba\u6587\u8bc1\u660e\u5728\u8be5\u6761\u4ef6\u4e0b&#xff0c;\u8bda\u5b9e\u667a\u80fd\u4f53\u80fd\u591f\u4fdd\u6301\u5e76\u4f20\u64ad\u53ef\u9760\u4fe1\u606f&#xff0c;\u4e0d\u4f1a\u88ab\u62dc\u5360\u5ead\u5f71\u54cd\u201c\u62c9\u504f\u201d\u3002<\/p>\n<h4>\u7814\u7a76\u6210\u679c<\/h4>\n<p>\u5b9e\u9a8c\u8986\u76d6\u4e86\u4e24\u4e2a\u5c42\u9762\u7684\u57fa\u51c6&#xff1a;\u95ed\u6e90\u6a21\u578b\u7528Hendrycks MATH\u7684100\u9053Level 4\u9898\u76ee\u548cCommonsense170k\u768430\u4e2a\u6837\u672c&#xff1b;\u5f00\u6e90\u6a21\u578b\u7528Qwen2.5-1.5B-Instruct&#xff08;\u5f31&#xff09;\u548cQwen3-4B&#xff08;\u5f3a&#xff09;\u5728\u4e94\u4e2a\u5e38\u8bc6\u63a8\u7406\u57fa\u51c6\u4e0a\u6d4b\u8bd5&#xff08;ARC-C\u3001HellaSwag\u3001BoolQ\u3001OBQA\u3001RTE&#xff09;&#xff0c;\u6bcf\u4e2a50\u9898\u3002<\/p>\n<p>\u7f51\u7edc\u914d\u7f6e\u4e3a7\u4e2a\u667a\u80fd\u4f53&#xff1a;4\u4e2a\u5f3a\u8bda\u5b9e\u30012\u4e2a\u5f31\u8bda\u5b9e&#xff08;\u89c6\u4e3a\u6545\u969c\u62dc\u5360\u5ead&#xff09;\u30011\u4e2a\u5bf9\u6297\u62dc\u5360\u5ead&#xff0c;F&#061;3&#xff0c;\u8bc4\u4f30\u4e09\u79cd(F&#043;1)-\u9c81\u68d2\u62d3\u6251&#xff1a;\u03b3-MERG\u3001\u5b8c\u5168\u56fe\u3001Erd\u0151s\u2013R\u00e9nyi\u3002<\/p>\n<p>\u6700\u76f4\u63a5\u7684\u5bf9\u6bd4\u6765\u81ea\u5e38\u8bc6\u63a8\u7406\u4efb\u52a1\u4e0a\u7684\u6bcf\u8f6e\u51c6\u786e\u7387\u3002CP-WBFT\u7684\u521d\u59cb\u51c6\u786e\u7387\u7ea666.6\/69.9&#xff08;\u5f31\/\u5f3a\u8bda\u5b9e&#xff09;&#xff0c;\u4f46\u7ecf\u8fc71-6\u8f6e\u8fed\u4ee3\u540e\u5927\u5e45\u5d29\u6e83\u523054.6\/47.1\u751a\u81f3\u66f4\u4f4e\u2014\u2014\u8fed\u4ee3\u975e\u4f46\u6ca1\u6709\u6539\u5584&#xff0c;\u53cd\u800c\u8ba9\u62dc\u5360\u5ead\u5f71\u54cd\u6269\u6563\u4e86\u3002SAC\u7684\u521d\u59cb\u51c6\u786e\u7387\u76f8\u8fd1&#xff08;\u7ea666.8\/70.1&#xff09;&#xff0c;\u4f46\u7b2c\u4e00\u8f6e\u5c31\u8df3\u5347\u523061.6\/74.2&#xff0c;\u7b2c\u4e8c\u8f6e\u8fbe\u5230\u5cf0\u503c64.8\/77.6&#xff0c;\u4e4b\u540e\u572864\/76\u9644\u8fd1\u6ce2\u52a8&#xff0c;\u59cb\u7ec8\u7ef4\u6301\u5728\u663e\u8457\u9ad8\u4e8e\u57fa\u7ebf\u7684\u6c34\u5e73\u3002\u8fd9\u8bf4\u660eSAC\u7684\u8fc7\u6ee4\u673a\u5236\u786e\u5b9e\u5728\u8fed\u4ee3\u4e2d\u8d77\u5230\u4e86\u201c\u63d0\u7eaf\u201d\u4f5c\u7528\u3002<\/p>\n<h4>\u5b9e\u9645\u843d\u5730\u5e94\u7528\u7684\u53ef\u80fd\u6027<\/h4>\n<p>SAC\u7684\u534f\u8bae\u5c42\u8bbe\u8ba1\u662f\u5185\u5bb9\u65e0\u5173\u7684\u2014\u2014\u5b83\u4e0d\u5173\u5fc3\u667a\u80fd\u4f53\u8ba8\u8bba\u7684\u662f\u6570\u5b66\u9898\u3001\u4ee3\u7801\u5ba1\u67e5\u8fd8\u662f\u533b\u7597\u8bca\u65ad&#xff0c;\u53ea\u4f9d\u8d56\u63a5\u6536\u7aef\u7684\u9a8c\u8bc1\u63d0\u793a\u6765\u8bc4\u4f30\u54cd\u5e94\u8d28\u91cf\u3002\u8fd9\u610f\u5473\u7740\u53ea\u8981\u6709\u529e\u6cd5\u6784\u9020\u51fa\u9488\u5bf9\u7279\u5b9a\u4efb\u52a1\u7684\u9a8c\u8bc1\u63d0\u793a&#xff0c;SAC\u5c31\u53ef\u4ee5\u8fc1\u79fb\u5230\u4efb\u4f55\u9700\u8981\u591a\u667a\u80fd\u4f53\u534f\u4f5c\u4e14\u5b58\u5728\u8282\u70b9\u4e0d\u53ef\u9760\u98ce\u9669\u7684\u573a\u666f\u3002\u5de5\u7a0b\u4e0a\u6700\u5927\u7684\u6210\u672c\u5728\u4e8e\u9a8c\u8bc1\u63d0\u793a\u7684\u8c03\u4f18\u548c\u901a\u4fe1\u5f00\u9500&#xff08;\u6bcf\u8f6e\u9700\u8981\u5e7f\u64ad\u5b8c\u6574\u54cd\u5e94&#xff09;&#xff0c;\u4f46\u5728\u5bf9\u53ef\u9760\u6027\u8981\u6c42\u9ad8\u4e8e\u6548\u7387\u7684\u573a\u666f\u4e2d&#xff0c;\u8fd9\u4e2a\u4ee3\u4ef7\u662f\u5408\u7406\u7684\u3002<\/p>\n<h3>\u6280\u672f\u7ec6\u8282<\/h3>\n<p>SAC\u7684\u6bcf\u8f6e\u66f4\u65b0\u89c4\u5219\u53ef\u4ee5\u5f62\u5f0f\u5316\u8868\u8ff0\u5982\u4e0b\u3002<\/p>\n<p>\u667a\u80fd\u4f53 (i) \u5728\u7b2c (t) \u8f6e\u7684\u54cd\u5e94\u8bb0\u4e3a (r_i^{(t)})\u3002\u90bb\u5c45\u96c6\u5408\u4e3a (\\\\mathcal{N}_i)\u3002\u63a5\u6536\u7aef\u8bc4\u5206\u51fd\u6570\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">si\u2192j(t)&#061;\u03d5i(x,rj(t))\u2208[0,1]s_{i\\\\to j}^{(t)} &#061; \\\\phi_i(x, r_j^{(t)}) \\\\in [0,1]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.4578em;vertical-align: -0.413em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.413em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.4578em;vertical-align: -0.413em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.413em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d (\\\\phi_i) \u7531\u667a\u80fd\u4f53 (i) \u7684LLM\u901a\u8fc7\u9a8c\u8bc1\u63d0\u793a\u5b9e\u73b0&#xff0c;\u8981\u6c42LLM\u5224\u65ad\u54cd\u5e94 (r_j^{(t)}) \u76f8\u5bf9\u4e8e\u67e5\u8be2 (x) \u7684\u6b63\u786e\u6027\u5e76\u7ed9\u51fa\u6821\u51c6\u5206\u6570\u3002<\/p>\n<p>\u8fc7\u6ee4\u89c4\u5219\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Li(t)&#061;{j\u2208Ni\u2223si\u2192j(t)&lt;si\u2192i(t)}\\\\mathcal{L}_i^{(t)} &#061; \\\\{j \\\\in \\\\mathcal{N}_i \\\\mid s_{i\\\\to j}^{(t)} &lt; s_{i\\\\to i}^{(t)}\\\\}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3217em;vertical-align: -0.2769em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.1474em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1474em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.4578em;vertical-align: -0.413em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.413em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3217em;vertical-align: -0.2769em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Ri(t)&#061;Ni\u2216\u6700\u4f4e\u5206\u7684min\u2061(F,\u2223Li(t)\u2223)\u4e2a\u5143\u7d20\\\\mathcal{R}_i^{(t)} &#061; \\\\mathcal{N}_i \\\\setminus \\\\text{\u6700\u4f4e\u5206\u7684} \\\\min(F, |\\\\mathcal{L}_i^{(t)}|) \\\\text{\u4e2a\u5143\u7d20}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3217em;vertical-align: -0.2769em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.1474em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1474em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2216<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3217em;vertical-align: -0.2769em\"><\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u6700\u4f4e\u5206\u7684<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u4e2a\u5143\u7d20<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5373&#xff0c;\u53ea\u6709\u5728\u63a5\u6536\u7aef\u8bc4\u5206\u4f4e\u4e8e\u81ea\u8bc4\u5206\u7684\u90bb\u5c45\u624d\u4f1a\u8fdb\u5165\u201c\u5019\u9009\u4e22\u5f03\u96c6\u201d&#xff0c;\u7136\u540e\u4ece\u4e2d\u4e22\u5f03\u6700\u4f4e\u7684F\u4e2a\u3002\u8fd9\u4e2a\u8bbe\u8ba1\u6bd4\u7b80\u5355\u4e22\u5f03\u6700\u4f4e\u5206\u90bb\u5c45\u66f4\u4fdd\u5b88\u2014\u2014\u5b83\u4fdd\u7559\u4e86\u90a3\u4e9b\u5f97\u5206\u9ad8\u4e8e\u6216\u7b49\u4e8e\u81ea\u8bc4\u5206\u7684\u90bb\u5c45&#xff0c;\u907f\u514d\u8fc7\u5ea6\u8fc7\u6ee4\u3002<\/p>\n<p>\u7cbe\u70bc\u9636\u6bb5&#xff0c;\u667a\u80fd\u4f53\u7528\u4fdd\u7559\u96c6 (\\\\mathcal{R}_i^{(t)}) \u7684\u54cd\u5e94\u548c\u81ea\u8eab\u5f53\u524d\u8f93\u51fa\u91cd\u65b0prompt\u5176LLM&#xff0c;\u751f\u6210 (r_i^{(t&#043;1)})\u3002\u6574\u4e2a\u6d41\u7a0b\u8fed\u4ee3T\u8f6e\u3002<\/p>\n<p>(F&#043;1)-\u9c81\u68d2\u6027\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49\u5728\u8bba\u6587\u7684\u56fe\u8bba\u90e8\u5206\u7ed9\u51fa&#xff1a;\u5bf9\u4efb\u610f\u8282\u70b9\u5b50\u96c6&#xff0c;\u5176\u90bb\u57df\u4e2d\u7684\u8bda\u5b9e\u8282\u70b9\u6570\u81f3\u5c11\u6bd4\u62dc\u5360\u5ead\u8282\u70b9\u6570\u591a1\u3002\u76f4\u89c2\u4e0a&#xff0c;\u8fd9\u4fdd\u8bc1\u4e86\u5728\u4efb\u4f55\u8bda\u5b9e\u8282\u70b9\u7684\u201c\u5c40\u90e8\u89c6\u91ce\u201d\u4e2d&#xff0c;\u8bda\u5b9e\u54cd\u5e94\u5728\u6570\u91cf\u4e0a\u59cb\u7ec8\u5360\u4f18&#xff0c;\u8fc7\u6ee4\u540e\u4fdd\u7559\u7684\u96c6\u5408\u4e0d\u4f1a\u4ee5\u62dc\u5360\u5ead\u54cd\u5e94\u4e3a\u4e3b\u3002<\/p>\n<h3>\u7814\u7a76\u8bbe\u5b9a<\/h3>\n<p>\u8f6f\u4ef6\u6808&#xff1a;\u95ed\u6e90\u5b9e\u9a8c\u4f7f\u7528gpt-3.5-turbo\u548cgpt-4o-mini&#xff08;MATH\u4efb\u52a1&#xff09;&#xff0c;gpt-4o\u548cgpt-5&#xff08;\u5e38\u8bc6\u63a8\u7406\u4efb\u52a1&#xff09;&#xff1b;\u5f00\u6e90\u5b9e\u9a8c\u4f7f\u7528Qwen2.5-1.5B-Instruct\u548cQwen3-4B&#xff0c;\u5728\u672c\u5730\u63a8\u7406\u3002\u9a8c\u8bc1\u63d0\u793a\u7684\u5177\u4f53\u6a21\u677f\u5728\u8bba\u6587\u9644\u5f55B\u4e2d\u3002<\/p>\n<p>\u786c\u4ef6\u9700\u6c42&#xff1a;\u95ed\u6e90\u6a21\u578b\u5b9e\u9a8c\u53ea\u9700\u8981API\u8c03\u7528&#xff0c;\u5bf9\u672c\u5730\u786c\u4ef6\u6ca1\u6709\u7279\u6b8a\u8981\u6c42\u3002\u5f00\u6e90\u6a21\u578b\u5b9e\u9a8c\u9700\u8981\u80fd\u8fd0\u884c4B\u53c2\u6570\u6a21\u578b\u7684GPU&#xff08;\u5355\u5f20\u6d88\u8d39\u7ea7\u663e\u5361\u5373\u53ef&#xff09;\u3002\u901a\u4fe1\u62d3\u6251\u7684\u6a21\u62df\u5728CPU\u4e0a\u5b8c\u6210\u3002<\/p>\n<p>\u62d3\u6251\u914d\u7f6e&#xff1a;\u4e09\u79cd(F&#043;1)-\u9c81\u68d2\u56fe\u2014\u2014\u03b3-MERG\u662f\u4e00\u79cd\u9488\u5bf9\u62dc\u5360\u5ead\u5bb9\u9519\u8bbe\u8ba1\u7684\u7a00\u758f\u56fe\u6784\u9020\u65b9\u6cd5&#xff0c;\u5b8c\u5168\u56fe\u63d0\u4f9b\u6700\u5f3a\u7684\u8fde\u63a5\u5197\u4f59\u4f46\u901a\u4fe1\u5f00\u9500\u6700\u5927&#xff0c;Erd\u0151s\u2013R\u00e9nyi\u968f\u673a\u56fe\u5219\u68c0\u9a8c\u65b9\u6cd5\u5728\u975e\u7ed3\u6784\u5316\u62d3\u6251\u4e0b\u7684\u9c81\u68d2\u6027\u3002<\/p>\n<p>\u62dc\u5360\u5ead\u6a21\u578b&#xff1a;\u8bba\u6587\u533a\u5206\u4e86\u201c\u6545\u969c\u62dc\u5360\u5ead\u201d\u548c\u201c\u5bf9\u6297\u62dc\u5360\u5ead\u201d\u4e24\u7c7b\u3002\u6545\u969c\u62dc\u5360\u5ead&#xff08;\u5373\u5f31\u8bda\u5b9e\u667a\u80fd\u4f53&#xff09;\u6267\u884c\u534f\u8bae\u4f46\u521d\u59cb\u8f93\u51fa\u4e0d\u53ef\u9760&#xff0c;SAC\u7684\u8fed\u4ee3\u7cbe\u70bc\u7406\u8bba\u4e0a\u53ef\u4ee5\u201c\u6cbb\u6108\u201d\u8fd9\u7c7b\u8282\u70b9&#xff1b;\u5bf9\u6297\u62dc\u5360\u5ead\u5219\u53ef\u80fd\u4efb\u610f\u504f\u79bb\u534f\u8bae&#xff0c;SAC\u7684\u76ee\u6807\u4e0d\u662f\u7ea0\u6b63\u5b83\u4eec&#xff0c;\u800c\u662f\u9632\u6b62\u5b83\u4eec\u6c61\u67d3\u8bda\u5b9e\u8282\u70b9\u3002\u8fd9\u4e2a\u533a\u5206\u5f88\u91cd\u8981&#xff1a;\u5b83\u610f\u5473\u7740SAC\u5728\u201c\u53ef\u4fee\u590d\u6545\u969c\u201d\u548c\u201c\u4e0d\u53ef\u4fee\u590d\u5bf9\u6297\u201d\u4e4b\u95f4\u505a\u4e86\u52a1\u5b9e\u7684\u6743\u8861\u3002<\/p>\n<h3>\u7efc\u5408\u5206\u6790<\/h3>\n<p>\u8fd9\u7bc7\u8bba\u6587\u7684\u4ef7\u503c\u5728\u4e8e\u628a\u5206\u5e03\u5f0f\u7cfb\u7edf\u91cc\u6210\u719f\u7684\u62dc\u5360\u5ead\u5bb9\u9519\u6846\u67b6\u7cfb\u7edf\u5730\u5f15\u5165LLM\u591a\u667a\u80fd\u4f53\u7cfb\u7edf&#xff0c;\u800c\u4e14\u4e0d\u662f\u7b80\u5355\u7167\u642c&#xff0c;\u505a\u4e86\u51e0\u4e2a\u5173\u952e\u7684\u6982\u5ff5\u8fc1\u79fb\u3002<\/p>\n<p>\u63a5\u6536\u7aef\u8bc4\u4f30 vs \u81ea\u62a5\u7f6e\u4fe1\u5ea6\u3002CP-WBFT\u7684\u6838\u5fc3\u673a\u5236\u662f\u8ba9\u667a\u80fd\u4f53\u81ea\u62a5\u7f6e\u4fe1\u5ea6&#xff0c;\u7136\u540e\u52a0\u6743\u805a\u5408\u3002\u8bba\u6587\u5728LinkedIn\u7684\u5206\u4eab\u4e2d\u8bf4\u5f97\u5f88\u76f4\u767d&#xff1a;\u201c\u5f53\u7f6e\u4fe1\u5ea6\u4fe1\u53f7\u672c\u8eab\u53ef\u4ee5\u88ab\u64cd\u7eb5\u65f6&#xff0c;\u57fa\u4e8e\u7f6e\u4fe1\u5ea6\u7684\u805a\u5408\u4f1a\u53d8\u5f97\u9ad8\u5ea6\u8106\u5f31\u201d\u3002SAC\u7684\u63a5\u6536\u7aef\u8bc4\u5206\u4ece\u6839\u672c\u4e0a\u79fb\u9664\u4e86\u8fd9\u4e2a\u653b\u51fb\u9762\u2014\u2014\u62dc\u5360\u5ead\u667a\u80fd\u4f53\u53ef\u4ee5\u6492\u8c0e\u8bf4\u81ea\u5df1\u5f88\u786e\u4fe1&#xff0c;\u4f46\u5b83\u65e0\u6cd5\u63a7\u5236\u90bb\u5c45\u5982\u4f55\u8bc4\u4ef7\u5b83\u7684\u8f93\u51fa\u5185\u5bb9\u3002\u8fd9\u4e2a\u8bbe\u8ba1\u51b3\u7b56\u5728\u5de5\u7a0b\u4e0a\u770b\u4f3c\u7b80\u5355&#xff0c;\u5728\u5b89\u5168\u8bed\u4e49\u4e0a\u5374\u662f\u672c\u8d28\u6027\u7684\u3002<\/p>\n<p>filter-and-refine 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