{"id":34321,"date":"2024-12-04T13:56:21","date_gmt":"2024-12-04T05:56:21","guid":{"rendered":"https:\/\/17aitech.com\/?p=34321"},"modified":"2024-12-04T13:56:21","modified_gmt":"2024-12-04T05:56:21","slug":"%e7%ad%89%e4%b8%8d%e6%9d%a5openai%e7%9a%84q%ef%bc%8c%e5%8d%8e%e4%b8%ba%e8%af%ba%e4%ba%9a%e6%8e%a2%e7%b4%a2llm%e6%8e%a8%e7%90%86%e7%9a%84%e7%a7%98%e5%af%86%e6%ad%a6%e5%99%a8mindstar%e5%85%88%e6%9d%a5","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=34321","title":{"rendered":"\u7b49\u4e0d\u6765OpenAI\u7684Q*\uff0c\u534e\u4e3a\u8bfa\u4e9a\u63a2\u7d22LLM\u63a8\u7406\u7684\u79d8\u5bc6\u6b66\u5668MindStar\u5148\u6765\u4e86"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2024-07-01-9\" target=\"_blank\">\u7b49\u4e0d\u6765OpenAI\u7684Q*\uff0c\u534e\u4e3a\u8bfa\u4e9a\u63a2\u7d22LLM\u63a8\u7406\u7684\u79d8\u5bc6\u6b66\u5668MindStar\u5148\u6765\u4e86<\/a><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-02cf5ca87084e7799a9ce582b62e1833.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-02cf5ca87084e7799a9ce582b62e1833.png\"><\/a><\/section>\n<blockquote data-author-name=\"\" data-content-utf8-length=\"166\" data-source-title=\"\" data-type=\"2\" data-url=\"\">\n<section>\n<section>AIxiv\u4e13\u680f\u662f\u673a\u5668\u4e4b\u5fc3\u53d1\u5e03\u5b66\u672f\u3001\u6280\u672f\u5185\u5bb9\u7684\u680f\u76ee\u3002\u8fc7\u53bb\u6570\u5e74\uff0c\u673a\u5668\u4e4b\u5fc3AIxiv\u4e13\u680f\u63a5\u6536\u62a5\u9053\u4e862000\u591a\u7bc7\u5185\u5bb9\uff0c\u8986\u76d6\u5168\u7403\u5404\u5927\u9ad8\u6821\u4e0e\u4f01\u4e1a\u7684\u9876\u7ea7\u5b9e\u9a8c\u5ba4\uff0c\u6709\u6548\u4fc3\u8fdb\u4e86\u5b66\u672f\u4ea4\u6d41\u4e0e\u4f20\u64ad\u3002\u5982\u679c\u60a8\u6709\u4f18\u79c0\u7684\u5de5\u4f5c\u60f3\u8981\u5206\u4eab\uff0c\u6b22\u8fce\u6295\u7a3f\u6216\u8005\u8054\u7cfb\u62a5\u9053\u3002\u6295\u7a3f\u90ae\u7bb1\uff1aliyazhou@jiqizhixin.com\uff1bzhaoyunfeng@jiqizhixin.com<\/section>\n<\/section>\n<\/blockquote>\n<section><\/section>\n<section><strong>\u672c\u8bba\u6587\u4f5c\u8005\u6765\u81ea\u534e\u4e3a\u8499\u7279\u5229\u5c14\u8bfa\u4e9a\u65b9\u821f\u5b9e\u9a8c\u5ba4\u7684\u5eb7\u8ba1\u5803\uff0c\u674e\u4fe1\u62e9\uff0c\u9648\u7199\uff0c Amirreza Kazemi\uff0c\u9648\u535a\u5174\u3002<\/strong><\/section>\n<section><\/section>\n<section>\u4eba\u5de5\u667a\u80fd\uff08AI\uff09\u5728\u8fc7\u53bb\u5341\u5e74\u91cc\u53d6\u5f97\u4e86\u957f\u8db3\u8fdb\u6b65\uff0c\u7279\u522b\u662f\u5728\u81ea\u7136\u8bed\u8a00\u5904\u7406\u548c\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\u3002\u7136\u800c\uff0c\u5982\u4f55\u63d0\u5347 AI \u7684\u8ba4\u77e5\u80fd\u529b\u548c\u63a8\u7406\u80fd\u529b\uff0c\u4ecd\u7136\u662f\u4e00\u4e2a\u5de8\u5927\u7684\u6311\u6218\u3002<\/section>\n<section><\/section>\n<section>\u8fd1\u671f\uff0c\u4e00\u7bc7\u9898\u4e3a\u300aMindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time\u300b\u7684\u8bba\u6587\u63d0\u51fa\u4e86\u57fa\u4e8e\u6811\u641c\u7d22\u7684\u63a8\u7406\u65f6\u95f4\u80fd\u529b\u63d0\u5347\u65b9\u6cd5 MindStar [1]\uff0c\u8be5\u65b9\u6cd5\u5728\u5f00\u6e90\u6a21\u578b Llama-13-B \u4e0e Mistral-7B \u4e0a\u8fbe\u5230\u4e86\u8fd1\u4f3c\u95ed\u6e90\u5927\u6a21\u578b GPT-3.5 \u4e0e Grok-1 \u5728\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u63a8\u7406\u80fd\u529b\u3002<\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-629034b1bee8a3f651a057b6f715b49f.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-629034b1bee8a3f651a057b6f715b49f.png\"><\/a><\/p>\n<ul>\n<li>\n<section>\u8bba\u6587\u6807\u9898\uff1aMindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time<\/section>\n<\/li>\n<li>\n<section>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/abs\/2405.16265v2<\/section>\n<\/li>\n<\/ul>\n<section><\/section>\n<section>MindStar \u5728\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u5e94\u7528\u6548\u679c\uff1a<\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-c30000b4da55471810323e3e70b372d2.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-c30000b4da55471810323e3e70b372d2.png\"><\/a><\/p>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 1 \uff1a\u4e0d\u540c\u5927\u578b\u8bed\u8a00\u6a21\u578b\u7684\u6570\u5b66\u51c6\u786e\u7387\u3002LLaMA-2-13B \u5728\u6570\u5b66\u6027\u80fd\u4e0a\u4e0e GPT-3.5 (4-shot) \u7c7b\u4f3c\uff0c\u4f46\u8282\u7701\u4e86\u5927\u7ea6 200 \u500d\u7684\u8ba1\u7b97\u8d44\u6e90\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section><strong>1. \u5f15\u8a00<\/strong><\/section>\n<section><\/section>\n<section>\u968f\u7740\u6a21\u578b\u89c4\u6a21\u7684\u5feb\u901f\u589e\u957f\uff0c\u57fa\u4e8e Transformer \u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u5728\u6307\u4ee4\u9075\u5faa [1,2]\u3001\u7f16\u7801\u8f85\u52a9 [3,4] \u548c\u521b\u610f\u5199\u4f5c [5] \u7b49\u9886\u57df\u5c55\u793a\u4e86\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\u7684\u6210\u679c\u3002\u7136\u800c\uff0c\u89e3\u9501 LLMs \u89e3\u51b3\u590d\u6742\u63a8\u7406\u4efb\u52a1\u7684\u80fd\u529b\u4ecd\u7136\u662f\u4e00\u5927\u6311\u6218\u3002\u6700\u8fd1\u7684\u4e00\u4e9b\u7814\u7a76 [6,7] \u5c1d\u8bd5\u901a\u8fc7\u76d1\u7763\u5fae\u8c03\uff08Supervised Fine-Tuning, SFT\uff09\u6765\u89e3\u51b3\uff0c\u901a\u8fc7\u5c06\u65b0\u7684\u63a8\u7406\u6570\u636e\u6837\u672c\u4e0e\u539f\u59cb\u6570\u636e\u96c6\u6df7\u5408\uff0c\u4f7f LLMs \u5b66\u4e60\u8fd9\u4e9b\u6837\u672c\u7684\u5e95\u5c42\u5206\u5e03\uff0c\u5e76\u5c1d\u8bd5\u6a21\u4eff\u6240\u5b66\u903b\u8f91\u6765\u89e3\u51b3\u672a\u89c1\u8fc7\u7684\u63a8\u7406\u4efb\u52a1\u3002\u5c3d\u7ba1\u8fd9\u79cd\u65b9\u6cd5\u6709\u6027\u80fd\u63d0\u5347\uff0c\u4f46\u5b83\u4e25\u91cd\u4f9d\u8d56\u4e8e\u5927\u91cf\u7684\u8bad\u7ec3\u548c\u989d\u5916\u7684\u6570\u636e\u51c6\u5907 [8,9]\u3002<\/section>\n<section><\/section>\n<section>Llama-3 \u62a5\u544a [10] \u5f3a\u8c03\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u89c2\u5bdf\uff1a\u5f53\u9762\u5bf9\u4e00\u4e2a\u5177\u6709\u6311\u6218\u6027\u7684\u63a8\u7406\u95ee\u9898\u65f6\uff0c\u6a21\u578b\u6709\u65f6\u4f1a\u751f\u6210\u6b63\u786e\u7684\u63a8\u7406\u8f68\u8ff9\u3002\u8fd9\u8868\u660e\u6a21\u578b\u77e5\u9053\u5982\u4f55\u4ea7\u751f\u6b63\u786e\u7b54\u6848\uff0c\u4f46\u5728\u9009\u62e9\u4e0a\u5b58\u5728\u56f0\u96be\u3002\u57fa\u4e8e\u8fd9\u4e00\u53d1\u73b0\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u95ee\u9898\uff1a\u6211\u4eec\u80fd\u5426\u901a\u8fc7\u5e2e\u52a9 LLMs \u9009\u62e9\u6b63\u786e\u7684\u8f93\u51fa\u6765\u589e\u5f3a\u5b83\u4eec\u7684\u63a8\u7406\u80fd\u529b\uff1f\u4e3a\u63a2\u7d22\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u8fdb\u884c\u4e86\u4e00\u9879\u5b9e\u9a8c\uff0c\u5229\u7528\u4e0d\u540c\u7684\u5956\u52b1\u6a21\u578b\u8fdb\u884c LLMs \u8f93\u51fa\u9009\u62e9\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u6b65\u9aa4\u7ea7\u9009\u62e9\u663e\u8457\u4f18\u4e8e\u4f20\u7edf\u7684\u00a0CoT \u65b9\u6cd5\u3002<\/section>\n<section><\/section>\n<section><strong>2. MindStar \u65b9\u6cd5<\/strong><\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-1ccc592604ded76a144858e180856be4.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-1ccc592604ded76a144858e180856be4.png\"><\/a><\/p>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 2 MindStar \u7684\u7b97\u6cd5\u67b6\u6784\u56fe<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u65b0\u7684\u63a8\u7406\u641c\u7d22\u6846\u67b6 \u2014\u2014MindStar\uff08M*\uff09\uff0c\u901a\u8fc7\u5c06\u63a8\u7406\u4efb\u52a1\u89c6\u4e3a\u641c\u7d22\u95ee\u9898\uff0c\u5e76\u5229\u7528\u8fc7\u7a0b\u76d1\u7763\u7684\u5956\u52b1\u6a21\u578b\uff08Process-supervised Reward Model, PRM\uff09\uff0cM * \u5728\u63a8\u7406\u6811\u7a7a\u95f4\u4e2d\u6709\u6548\u5bfc\u822a\uff0c\u8bc6\u522b\u8fd1\u4f3c\u6700\u4f18\u8def\u5f84\u3002\u7ed3\u5408\u675f\u641c\u7d22\uff08Beam Search, BS\uff09\u548c Levin \u6811\u641c\u7d22\uff08Levin Tree Search, LevinTS\uff09\u7684\u601d\u60f3\uff0c\u8fdb\u4e00\u6b65\u589e\u5f3a\u4e86\u641c\u7d22\u6548\u7387\uff0c\u5e76\u4fdd\u8bc1\u5728\u6709\u9650\u8ba1\u7b97\u590d\u6742\u5ea6\u5185\u627e\u5230\u6700\u4f73\u63a8\u7406\u8def\u5f84\u3002<\/section>\n<section><\/section>\n<section><strong>2.1 \u8fc7\u7a0b\u76d1\u7763\u5956\u52b1\u6a21\u578b<\/strong><\/section>\n<section><\/section>\n<section>\u8fc7\u7a0b\u76d1\u7763\u5956\u52b1\u6a21\u578b (PRM) \u7684\u8bbe\u8ba1\u76ee\u7684\u662f\u8bc4\u4f30\u5927\u8bed\u8a00\u6a21\u578b (LLM) \u751f\u6210\u7684\u4e2d\u95f4\u6b65\u9aa4\uff0c\u4ee5\u5e2e\u52a9\u9009\u62e9\u6b63\u786e\u7684\u63a8\u7406\u8def\u5f84\u3002\u8fd9\u79cd\u65b9\u6cd5\u501f\u9274\u4e86\u5176\u4ed6\u5e94\u7528\u4e2d PRM \u7684\u6210\u529f\u7ecf\u9a8c\u3002\u5177\u4f53\u800c\u8a00\uff0cPRM \u4ee5\u5f53\u524d\u63a8\u7406\u8def\u5f84<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-c167ea0871f37b61a3d2ffed97d1bce9.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-c167ea0871f37b61a3d2ffed97d1bce9.png\"><\/a>\u548c\u6f5c\u5728\u7684\u4e0b\u4e00\u6b65<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-0ecff3702911e3d895f23859ae3374bc.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-0ecff3702911e3d895f23859ae3374bc.png\"><\/a>\u4f5c\u4e3a\u8f93\u5165\uff0c\u5e76\u8fd4\u56de\u5956\u52b1\u503c<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-c030b5ea43e7d6400b395fc1a0c091ee.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-c030b5ea43e7d6400b395fc1a0c091ee.png\"><\/a>\u3002<\/section>\n<section><\/section>\n<section>PRM \u901a\u8fc7\u8003\u8651\u6574\u4e2a\u5f53\u524d\u63a8\u7406\u8f68\u8ff9\u6765\u8bc4\u4f30\u65b0\u6b65\u9aa4\uff0c\u9f13\u52b1\u4e0e\u6574\u4f53\u8def\u5f84\u7684\u4e00\u81f4\u6027\u548c\u5fe0\u5b9e\u6027\u3002\u9ad8\u5956\u52b1\u503c\u8868\u660e\uff0c\u65b0\u7684\u6b65\u9aa4<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-113a6ae0274718d35f60d4ab62eeb931.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-113a6ae0274718d35f60d4ab62eeb931.png\"><\/a>\uff09\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u63a8\u7406\u8def\u5f84<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-6038c16cc7f445e01c703404cdabfb88.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-6038c16cc7f445e01c703404cdabfb88.png\"><\/a>\u53ef\u80fd\u662f\u6b63\u786e\u7684\uff0c\u4ece\u800c\u4f7f\u6269\u5c55\u8def\u5f84\u503c\u5f97\u8fdb\u4e00\u6b65\u63a2\u7d22\u3002\u76f8\u53cd\uff0c\u4f4e\u5956\u52b1\u503c\u5219\u8868\u793a\u65b0\u6b65\u9aa4\u53ef\u80fd\u4e0d\u6b63\u786e\uff0c\u8fd9\u610f\u5473\u7740\u9075\u5faa\u6b64\u8def\u5f84\u7684\u89e3\u51b3\u65b9\u6848\u4e5f\u53ef\u80fd\u4e0d\u6b63\u786e\u3002<\/section>\n<section><\/section>\n<section>M* \u7b97\u6cd5\u5305\u542b\u4e24\u4e2a\u4e3b\u8981\u6b65\u9aa4\uff0c\u8fed\u4ee3\u76f4\u5230\u627e\u5230\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\uff1a<\/section>\n<section><\/section>\n<section>1. \u63a8\u7406\u8def\u5f84\u6269\u5c55\uff1a\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\uff0c\u57fa\u7840 LLM \u751f\u6210\u5f53\u524d\u63a8\u7406\u8def\u5f84\u7684\u4e0b\u4e00\u6b65\u3002<\/section>\n<section>2. \u8bc4\u4f30\u548c\u9009\u62e9\uff1a\u4f7f\u7528 PRM \u8bc4\u4f30\u751f\u6210\u7684\u6b65\u9aa4\uff0c\u5e76\u6839\u636e\u8fd9\u4e9b\u8bc4\u4f30\u9009\u62e9\u4e0b\u4e00\u6b21\u8fed\u4ee3\u7684\u63a8\u7406\u8def\u5f84\u3002<\/section>\n<section><\/section>\n<section><strong>2.2 \u63a8\u7406\u8def\u5f84\u6269\u5c55<\/strong><\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-1f3b6a533d2aa60c0e3c24dd327486ad.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-1f3b6a533d2aa60c0e3c24dd327486ad.png\"><\/a><\/p>\n<section>\u5728\u9009\u62e9\u8981\u6269\u5c55\u7684\u63a8\u7406\u8def\u5f84<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-2119f50348eacab250a9c4544a83f1bd.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-2119f50348eacab250a9c4544a83f1bd.png\"><\/a>\u540e\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u63d0\u793a\u6a21\u677f\uff08Example 3.1\uff09\uff0c\u4ee5\u4ece LLM \u4e2d\u6536\u96c6\u4e0b\u4e00\u6b65\u3002\u6b63\u5982\u793a\u4f8b\u6240\u793a\uff0cLLM \u5c06\u539f\u59cb\u95ee\u9898\u4f5c\u4e3a {question}\uff0c\u5c06\u5f53\u524d\u63a8\u7406\u8def\u5f84\u4f5c\u4e3a {answer}\u3002\u6ce8\u610f\uff0c\u5728\u7b97\u6cd5\u7684\u7b2c\u4e00\u6b21\u8fed\u4ee3\u4e2d\uff0c\u6240\u9009\u62e9\u7684\u8282\u70b9\u662f\u4ec5\u5305\u542b\u95ee\u9898\u7684\u6839\u8282\u70b9\uff0c\u56e0\u6b64 {answer} \u4e3a\u7a7a\u3002\u5bf9\u4e8e\u63a8\u7406\u8def\u5f84<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-325a7b07f28a7a46201e66a3a2b145f0.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-325a7b07f28a7a46201e66a3a2b145f0.png\"><\/a>\uff0cLLM \u751f\u6210 N \u4e2a\u4e2d\u95f4\u6b65\u9aa4\uff0c\u5e76\u5c06\u5b83\u4eec\u4f5c\u4e3a\u5f53\u524d\u8282\u70b9\u7684\u5b50\u8282\u70b9\u9644\u52a0\u3002\u5728\u7b97\u6cd5\u7684\u4e0b\u4e00\u6b65\u4e2d\uff0c\u5c06\u8bc4\u4f30\u8fd9\u4e9b\u65b0\u751f\u6210\u7684\u5b50\u8282\u70b9\uff0c\u5e76\u9009\u62e9\u4e00\u4e2a\u65b0\u7684\u8282\u70b9\u8fdb\u884c\u8fdb\u4e00\u6b65\u6269\u5c55\u3002\u6211\u4eec\u8fd8\u610f\u8bc6\u5230\uff0c\u751f\u6210\u6b65\u9aa4\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u6b65\u9aa4\u6807\u8bb0\u5bf9 LLM \u8fdb\u884c\u5fae\u8c03\u3002\u7136\u800c\uff0c\u8fd9\u53ef\u80fd\u4f1a\u964d\u4f4e LLM \u7684\u63a8\u7406\u80fd\u529b\uff0c\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e0e\u672c\u6587\u7684\u91cd\u70b9 \u2014\u2014 \u5728\u4e0d\u4fee\u6539\u6743\u91cd\u7684\u60c5\u51b5\u4e0b\u589e\u5f3a LLM \u63a8\u7406\u80fd\u529b\u76f8\u6096\u3002<\/section>\n<section><\/section>\n<section><strong>2.3 \u63a8\u7406\u8def\u5f84\u9009\u62e9<\/strong><\/section>\n<section><\/section>\n<section>\u5728\u6269\u5c55\u63a8\u7406\u6811\u540e\uff0c\u6211\u4eec\u4f7f\u7528\u9884\u8bad\u7ec3\u7684\u8fc7\u7a0b\u76d1\u7763\u5956\u52b1\u6a21\u578b\uff08PRM\uff09\u6765\u8bc4\u4f30\u6bcf\u4e2a\u65b0\u751f\u6210\u7684\u6b65\u9aa4\u3002\u6b63\u5982\u524d\u9762\u63d0\u5230\u7684\uff0cPRM \u91c7\u7528\u8def\u5f84\u548c\u6b65\u9aa4 \uff0c\u5e76\u8fd4\u56de\u76f8\u5e94\u7684\u5956\u52b1\u503c\u3002\u5728\u8bc4\u4f30\u4e4b\u540e\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u6811\u641c\u7d22\u7b97\u6cd5\u6765\u9009\u62e9\u4e0b\u4e00\u4e2a\u8981\u6269\u5c55\u7684\u8282\u70b9\u3002\u6211\u4eec\u7684\u6846\u67b6\u4e0d\u4f9d\u8d56\u4e8e\u7279\u5b9a\u7684\u641c\u7d22\u7b97\u6cd5\uff0c\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u5b9e\u4f8b\u5316\u4e86\u4e24\u79cd\u6700\u4f73\u4f18\u5148\u641c\u7d22\u65b9\u6cd5\uff0c\u5373 Beam Search \u548c Levin Tree Search\u3002<\/section>\n<section><\/section>\n<section><strong>3. \u7ed3\u679c\u4e0e\u8ba8\u8bba<\/strong><\/section>\n<section><\/section>\n<section>\u5728 GSM8K \u548c MATH \u6570\u636e\u96c6\u4e0a\u7684\u5e7f\u6cdb\u8bc4\u4f30\u663e\u793a\uff0cM * \u663e\u8457\u63d0\u5347\u4e86\u5f00\u6e90\u6a21\u578b\uff08\u5982 LLaMA-2\uff09\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5176\u8868\u73b0\u53ef\u4e0e\u66f4\u5927\u89c4\u6a21\u7684\u95ed\u6e90\u6a21\u578b\uff08\u5982 GPT-3.5 \u548c Grok-1\uff09\u5ab2\u7f8e\uff0c\u540c\u65f6\u5927\u5e45\u51cf\u5c11\u4e86\u6a21\u578b\u89c4\u6a21\u548c\u8ba1\u7b97\u6210\u672c\u3002\u8fd9\u4e9b\u53d1\u73b0\u7a81\u663e\u4e86\u5c06\u8ba1\u7b97\u8d44\u6e90\u4ece\u5fae\u8c03\u8f6c\u79fb\u5230\u63a8\u7406\u65f6\u95f4\u641c\u7d22\u7684\u6f5c\u529b\uff0c\u4e3a\u672a\u6765\u9ad8\u6548\u63a8\u7406\u589e\u5f3a\u6280\u672f\u7684\u7814\u7a76\u5f00\u8f9f\u4e86\u65b0\u9014\u5f84\u3002<\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-4d1596dae6d7e1051345f0105da74fc3.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-4d1596dae6d7e1051345f0105da74fc3.png\"><\/a><\/p>\n<section>\u8868 1 \u5c55\u793a\u4e86\u5404\u79cd\u65b9\u6848\u5728 GSM8K \u548c MATH \u63a8\u7406\u57fa\u51c6\u4e0a\u7684\u5bf9\u6bd4\u7ed3\u679c\u3002\u6bcf\u4e2a\u6761\u76ee\u7684\u6570\u5b57\u8868\u793a\u95ee\u9898\u89e3\u51b3\u7684\u767e\u5206\u6bd4\u3002\u7b26\u53f7 SC@32 \u8868\u793a\u5728 32 \u4e2a\u5019\u9009\u7ed3\u679c\u4e2d\u7684\u81ea\u4e00\u81f4\u6027\uff0c\u800c n-shot \u8868\u793a\u5c11\u6837\u672c\u4f8b\u5b50\u7684\u7ed3\u679c\u3002CoT-SC@16 \u6307\u7684\u662f\u5728 16 \u4e2a\u601d\u7ef4\u94fe\uff08CoT\uff09\u5019\u9009\u7ed3\u679c\u4e2d\u7684\u81ea\u4e00\u81f4\u6027\u3002BS@16 \u4ee3\u8868\u675f\u641c\u7d22\u65b9\u6cd5\uff0c\u5373\u5728\u6bcf\u4e2a\u6b65\u9aa4\u7ea7\u522b\u6d89\u53ca 16 \u4e2a\u5019\u9009\u7ed3\u679c\uff0c\u800c LevinTS@16 \u8be6\u7ec6\u8bf4\u660e\u4e86\u4f7f\u7528\u76f8\u540c\u6570\u91cf\u5019\u9009\u7ed3\u679c\u7684 Levin \u6811\u641c\u7d22\u65b9\u6cd5\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cMATH \u6570\u636e\u96c6\u4e0a GPT-4 \u7684\u6700\u65b0\u7ed3\u679c\u4e3a GPT-4-turbo-0409\uff0c\u6211\u4eec\u7279\u522b\u5f3a\u8c03\u8fd9\u4e00\u70b9\uff0c\u56e0\u4e3a\u5b83\u4ee3\u8868\u4e86 GPT-4 \u5bb6\u65cf\u4e2d\u7684\u6700\u4f73\u6027\u80fd\u3002<\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-b23cc9e397c8fd8fa23bb41e9e2d7fae.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-b23cc9e397c8fd8fa23bb41e9e2d7fae.png\"><\/a><\/p>\n<section>\u56fe 3 \u6211\u4eec\u7814\u7a76\u4e86 M * \u6027\u80fd\u5982\u4f55\u968f\u7740\u6b65\u9aa4\u7ea7\u522b\u5019\u9009\u6570\u91cf\u7684\u53d8\u5316\u800c\u53d8\u5316\u3002\u6211\u4eec\u9009\u62e9 Llama-2-13B \u4f5c\u4e3a\u57fa\u7840\u6a21\u578b\uff0c\u5e76\u5206\u522b\u9009\u62e9\u675f\u641c\u7d22\uff08BS\uff09\u4f5c\u4e3a\u641c\u7d22\u7b97\u6cd5\u3002<\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-380cdd909ca73ec1d9e9af5e281aacb3.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-380cdd909ca73ec1d9e9af5e281aacb3.png\"><\/a><\/p>\n<section>\u56fe 4 Llama-2 \u548c Llama-3 \u6a21\u578b\u5bb6\u65cf\u5728 MATH \u6570\u636e\u96c6\u4e0a\u7684\u5c3a\u5ea6\u5b9a\u5f8b\u3002\u6240\u6709\u7ed3\u679c\u5747\u6765\u81ea\u5b83\u4eec\u7684\u539f\u59cb\u8d44\u6e90\u3002\u6211\u4eec\u4f7f\u7528 Scipy \u5de5\u5177\u548c\u5bf9\u6570\u51fd\u6570\u6765\u8ba1\u7b97\u62df\u5408\u66f2\u7ebf\u3002<\/section>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-d58001f2ed2d53e92dfdcdb42008e070.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-d58001f2ed2d53e92dfdcdb42008e070.png\"><\/a><\/p>\n<section>\u8868 2 \u4e0d\u540c\u65b9\u6cd5\u5728\u56de\u7b54\u95ee\u9898\u65f6\u7684\u5e73\u5747 token \u751f\u4ea7\u6570\u91cf<\/section>\n<section><\/section>\n<section><strong>4. \u7ed3\u8bba<\/strong><\/section>\n<section><\/section>\n<section>\u672c\u6587\u4ecb\u7ecd\u4e86 MindStar\uff08M*\uff09\uff0c\u4e00\u79cd\u65b0\u9896\u7684\u57fa\u4e8e\u641c\u7d22\u7684\u63a8\u7406\u6846\u67b6\uff0c\u7528\u4e8e\u589e\u5f3a\u9884\u8bad\u7ec3\u5927\u578b\u8bed\u8a00\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u3002\u901a\u8fc7\u5c06\u63a8\u7406\u4efb\u52a1\u89c6\u4e3a\u641c\u7d22\u95ee\u9898\u5e76\u5229\u7528\u8fc7\u7a0b\u76d1\u7763\u7684\u5956\u52b1\u6a21\u578b\uff0cM*\u00a0\u5728\u63a8\u7406\u6811\u7a7a\u95f4\u4e2d\u6709\u6548\u5bfc\u822a\uff0c\u8bc6\u522b\u8fd1\u4f3c\u6700\u4f18\u8def\u5f84\u3002\u7ed3\u5408\u675f\u641c\u7d22\u548c Levin \u6811\u641c\u7d22\u7684\u601d\u60f3\uff0c\u8fdb\u4e00\u6b65\u589e\u5f3a\u4e86\u641c\u7d22\u6548\u7387\uff0c\u5e76\u4fdd\u8bc1\u5728\u6709\u9650\u8ba1\u7b97\u590d\u6742\u5ea6\u5185\u627e\u5230\u6700\u4f73\u63a8\u7406\u8def\u5f84\u3002\u5e7f\u6cdb\u7684\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0cM*\u00a0\u663e\u8457\u63d0\u5347\u4e86\u5f00\u6e90\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5176\u8868\u73b0\u53ef\u4e0e\u66f4\u5927\u89c4\u6a21\u7684\u95ed\u6e90\u6a21\u578b\u5ab2\u7f8e\uff0c\u540c\u65f6\u5927\u5e45\u51cf\u5c11\u4e86\u6a21\u578b\u89c4\u6a21\u548c\u8ba1\u7b97\u6210\u672c\u3002<\/section>\n<section><\/section>\n<section>\u8fd9\u4e9b\u7814\u7a76\u6210\u679c\u8868\u660e\uff0c\u5c06\u8ba1\u7b97\u8d44\u6e90\u4ece\u5fae\u8c03\u8f6c\u79fb\u5230\u63a8\u7406\u65f6\u95f4\u641c\u7d22\u5177\u6709\u5de8\u5927\u7684\u6f5c\u529b\uff0c\u4e3a\u672a\u6765\u9ad8\u6548\u63a8\u7406\u589e\u5f3a\u6280\u672f\u7684\u7814\u7a76\u5f00\u8f9f\u4e86\u65b0\u9014\u5f84\u3002<\/section>\n<section><\/section>\n<section><em><sup>\u53c2\u8003\u6587\u732e\uff1a<\/sup><\/em><\/section>\n<section><sup><em>[1] Nisan Stiennon, Long Ouyang, Jeffrey Wu, Daniel Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul F Christiano. Learning to summarize with human feedback. Advances in Neural Information Processing Systems, 33:3008\u20133021, 2020.<\/em><\/sup><\/section>\n<section><sup><em>[2] Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. Advances in neural information processing systems, 35:27730\u201327744, 2022.\u00a0<\/em><\/sup><\/section>\n<section><sup><em>[3] Ziyang Luo, Can Xu, Pu Zhao, Qingfeng Sun, Xiubo Geng, Wenxiang Hu, Chongyang Tao, Jing Ma, Qingwei Lin, and Daxin Jiang. Wizardcoder: Empowering code large language models with evol-instruct. arXiv preprint arXiv:2306.08568, 2023.<\/em><\/sup><\/section>\n<section><sup><em>[4] Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, et al. Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374, 2021.<\/em><\/sup><\/section>\n<section><sup><em>[5] Carlos G\u00f3mez-Rodr\u00edguez and Paul Williams. A confederacy of models: A comprehensive evaluation of llms on creative writing. arXiv preprint arXiv:2310.08433, 2023.<\/em><\/sup><\/section>\n<section><sup><em>[6] Longhui Yu, Weisen Jiang, Han Shi, Jincheng Yu, Zhengying Liu, Yu Zhang, James T Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. Metamath: Bootstrap your own mathematical questions for large language models. arXiv preprint arXiv:2309.12284, 2023.<\/em><\/sup><\/section>\n<section><sup><em>[7] Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, YK Li, Y Wu, and Daya Guo. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024.<\/em><\/sup><\/section>\n<section><sup><em>[8] Keiran Paster, Marco Dos Santos, Zhangir Azerbayev, and Jimmy Ba. Openwebmath: An open dataset of high-quality mathematical web text. arXiv preprint arXiv:2310.06786, 2023.<\/em><\/sup><\/section>\n<section><sup><em>[9] Peiyi Wang, Lei Li, Zhihong Shao, RX Xu, Damai Dai, Yifei Li, Deli Chen, Y Wu, and Zhifang Sui. Math-shepherd: Verify and reinforce llms step-by-step without human annotations. CoRR, abs\/2312.08935, 2023.<\/em><\/sup><\/section>\n<section><em><sup>[10] Meta AI. Introducing meta llama 3: The most capable openly available llm to date, April 2024. URL https:\/\/ai.meta.com\/blog\/meta-llama-3\/. 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