{"id":38217,"date":"2025-02-12T01:00:52","date_gmt":"2025-02-11T17:00:52","guid":{"rendered":"https:\/\/17aitech.com\/?p=38217"},"modified":"2025-02-12T01:00:52","modified_gmt":"2025-02-11T17:00:52","slug":"%e4%ba%ba%e5%a4%a7%e5%88%98%e5%8b%87%e5%9b%a2%e9%98%9f%e3%80%8c%e6%85%a2%e6%80%9d%e8%80%83%e3%80%8d%e6%9c%ba%e7%90%86%e5%88%86%e6%9e%90%ef%bc%9a%e4%bb%8e%e9%9b%aa%e7%90%83%e8%af%af%e5%b7%ae%e5%88%b0","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=38217","title":{"rendered":"\u4eba\u5927\u5218\u52c7\u56e2\u961f\u300c\u6162\u601d\u8003\u300d\u673a\u7406\u5206\u6790\uff1a\u4ece\u96ea\u7403\u8bef\u5dee\u5230\u6b63\u786e\u63a8\u7406\u6982\u7387"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-02-10-5\" target=\"_blank\">\u4eba\u5927\u5218\u52c7\u56e2\u961f\u300c\u6162\u601d\u8003\u300d\u673a\u7406\u5206\u6790\uff1a\u4ece\u96ea\u7403\u8bef\u5dee\u5230\u6b63\u786e\u63a8\u7406\u6982\u7387<\/a><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a5aa86fcc64ad25a8905b35e0d8b12f7.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a5aa86fcc64ad25a8905b35e0d8b12f7.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>\u5728\u5927\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u7684\u53d1\u5c55\u5386\u7a0b\u4e2d\uff0c Scaling Laws [1] \u4e00\u76f4\u662f\u63a8\u52a8\u6027\u80fd\u63d0\u5347\u7684\u6838\u5fc3\u7b56\u7565\u3002\u7814\u7a76\u8868\u660e\uff0c\u968f\u7740\u6a21\u578b\u89c4\u6a21\u548c\u8bad\u7ec3\u6570\u636e\u7684\u589e\u957f\uff0cLLMs \u7684\u8868\u73b0\u4f1a\u4e0d\u65ad\u4f18\u5316 [2]\u3002\u7136\u800c\uff0c\u968f\u7740\u8bad\u7ec3\u9636\u6bb5\u89c4\u6a21\u7684\u8fdb\u4e00\u6b65\u6269\u5927\uff0c\u6027\u80fd\u63d0\u5347\u7684\u8fb9\u9645\u6536\u76ca\u9010\u6e10\u51cf\u5c0f\uff0c\u8bad\u7ec3\u66f4\u5f3a\u5927\u7684\u6a21\u578b\u9700\u8981\u5de8\u989d\u6295\u5165\u3002\u56e0\u6b64\uff0c<strong>\u7814\u7a76\u91cd\u70b9\u9010\u6e10\u4ece\u8bad\u7ec3\u9636\u6bb5\u7684\u6269\u5c55\u8f6c\u5411\u63a8\u7406\u9636\u6bb5\u7684\u6269\u5c55 [3]<\/strong>\uff0c\u63a2\u7d22\u5728\u4e0d\u589e\u52a0\u6a21\u578b\u53c2\u6570\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u5982\u4f55\u63d0\u5347\u63a8\u7406\u8d28\u91cf\u3002<\/section>\n<section><\/section>\n<section>\u300c\u6162\u601d\u8003\u300d\uff08Slow-Thinking\uff09\uff0c\u4e5f\u88ab\u79f0\u4e3a\u6d4b\u8bd5\u65f6\u6269\u5c55\uff08Test-Time Scaling\uff09\uff0c\u6210\u4e3a\u63d0\u5347 LLM \u63a8\u7406\u80fd\u529b\u7684\u65b0\u65b9\u5411\u3002\u8fd1\u5e74\u6765\uff0cOpenAI \u7684 o1 [4]\u3001DeepSeek \u7684 R1 [5] \u4ee5\u53ca Qwen \u7684 QwQ [6] \u7b49\u9876\u5c16\u63a8\u7406\u5927\u6a21\u578b\u7684\u53d1\u5e03\uff0c\u8fdb\u4e00\u6b65\u5370\u8bc1\u4e86\u63a8\u7406\u8fc7\u7a0b\u7684\u6269\u5c55\u662f\u4f18\u5316 LLM \u903b\u8f91\u80fd\u529b\u7684\u6709\u6548\u8def\u5f84\u3002\u7814\u7a76\u53d1\u73b0\uff0c\u589e\u52a0\u63a8\u7406\u65f6\u95f4\u80fd\u591f\u663e\u8457\u63d0\u5347 LLM \u7684\u63a8\u7406\u8d28\u91cf [7]\uff0c\u8fd9\u4e00\u53d1\u73b0\u63a8\u52a8\u4e86\u5bf9 \u300c\u6162\u601d\u8003\u300d\u65b9\u6cd5\u7684\u6df1\u5165\u7814\u7a76\u3002<\/section>\n<section><\/section>\n<section><strong>\u300c\u6162\u601d\u8003\u300d\u4e3b\u8981\u53ef\u4ee5\u5206\u4e3a\u5185\u90e8\u6162\u601d\u8003\uff08Internal Slow-Thinking\uff09 \u548c \u5916\u90e8\u6162\u601d\u8003\uff08External Slow-Thinking\uff09 \u4e24\u79cd\u65b9\u5f0f<\/strong>\uff1a<\/section>\n<ul>\n<li>\n<p><strong>\u5185\u90e8\u6162\u601d\u8003<\/strong>\uff1a\u901a\u8fc7\u989d\u5916\u7684\u8bad\u7ec3\uff0c\u4f7f\u6a21\u578b\u5728\u4e13\u95e8\u7684\u63a8\u7406\u4efb\u52a1\u4e0a\u4f18\u5316\u53c2\u6570\uff0c\u63d0\u5347\u81ea\u8eab\u7684\u63a8\u7406\u6df1\u5ea6\u548c\u8f93\u51fa\u8d28\u91cf\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5916\u90e8\u6162\u601d\u8003<\/strong>\uff1a\u4e0d\u6539\u53d8\u6a21\u578b\u672c\u8eab\uff0c\u800c\u662f\u589e\u52a0\u8ba1\u7b97\u5f00\u9500\uff0c\u4f8b\u5982\u901a\u8fc7<strong>\u591a\u6b21\u91c7\u6837\u3001\u91cd\u65b0\u751f\u6210\u7b54\u6848<\/strong>\u7b49\u65b9\u5f0f\u5ef6\u957f\u63a8\u7406\u8fc7\u7a0b\uff0c\u4ece\u800c\u63d0\u9ad8\u63a8\u7406\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>\u672c\u6587\u4e3b\u8981\u5173\u6ce8\u5916\u90e8\u6162\u601d\u8003<\/strong>\u3002\u5728\u9762\u5bf9\u590d\u6742\u95ee\u9898\u65f6\uff0c\u4eba\u7c7b\u5f80\u5f80\u4f1a\u82b1\u8d39\u989d\u5916\u7684\u65f6\u95f4\u601d\u8003\u548c\u5b8c\u5584\u63a8\u7406\u7684\u4e2d\u95f4\u8fc7\u7a0b\uff0c\u4ee5\u63d0\u9ad8\u51c6\u786e\u6027\u3002\u5916\u90e8\u6162\u601d\u8003\u53d7\u8fd9\u4e00\u8ba4\u77e5\u8fc7\u7a0b\u7684\u542f\u53d1\uff0c\u901a\u8fc7\u589e\u52a0\u63a8\u7406\u6b65\u9aa4\u6765\u63d0\u5347\u5927\u8bed\u8a00\u6a21\u578b\u7684\u63a8\u7406\u8d28\u91cf [8]\u3002\u4f8b\u5982\uff0cBoN\uff08Best-of-N\uff09\u65b9\u6cd5\u4f1a\u751f\u6210\u591a\u4e2a\u7b54\u6848\uff0c\u5e76\u901a\u8fc7\u591a\u6570\u6295\u7968\u6216\u6392\u5e8f\u7b49\u7b56\u7565\u9009\u51fa\u6700\u4f18\u89e3 [9]\u3002\u6b64\u5916\uff0c\u66f4\u524d\u6cbf\u7684\u6846\u67b6 \u5982\u601d\u7ef4\u94fe\uff08CoT\uff09[10]\u3001\u601d\u7ef4\u6811\uff08ToT\uff09[11] \u4ee5\u53ca\u501f\u9274 AlphaGo [12] \u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\uff08MCTS\uff09 \u7684\u65b9\u6cd5\uff0c\u80fd\u591f\u5728\u6811\u72b6\u7ed3\u6784\u4e2d\u63a2\u7d22\u89e3\u7b54\u7a7a\u95f4\uff0c\u5bfb\u627e\u66f4\u4f18\u7684\u7b54\u6848 [13-14]\u3002<\/section>\n<section><\/section>\n<section>\u7136\u800c\uff0c\u5c3d\u7ba1\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u5c55\u73b0\u51fa\u63d0\u5347\u63a8\u7406\u8d28\u91cf\u7684\u6f5c\u529b\uff0c\u4f46\u4ecd\u9762\u4e34<strong>\u4e24\u5927\u6838\u5fc3\u6311\u6218<\/strong>\uff1a<\/section>\n<ol>\n<li>\n<p><strong>\u7f3a\u4e4f\u7406\u8bba\u652f\u6491<\/strong>\uff1a\u76ee\u524d\uff0c\u6211\u4eec\u5bf9\u8fd9\u4e9b\u65b9\u6cd5\u4e3a\u4f55\u6709\u6548\u7684\u7406\u89e3\u4ecd\u7136\u6709\u9650\uff0c\u8fd9\u963b\u788d\u4e86\u66f4\u5148\u8fdb\u7b56\u7565\u7684\u8bbe\u8ba1\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8ba1\u7b97\u8d44\u6e90\u9700\u6c42\u9ad8<\/strong>\uff1a\u590d\u6742\u7684\u6162\u601d\u8003\u6280\u672f\u5f80\u5f80\u9700\u8981\u5927\u91cf\u8ba1\u7b97\u8d44\u6e90\uff0c\u4e14\u4f18\u5316\u8bbe\u8ba1\u53c2\u6570\u7684\u96be\u5ea6\u8f83\u5927\uff0c\u5bfc\u81f4\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u8868\u73b0\u4e0d\u5c3d\u5982\u4eba\u610f\u3002<\/p>\n<\/li>\n<\/ol>\n<section>\u9488\u5bf9\u8fd9\u4e9b\u6311\u6218\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u4e00\u79cd<strong>\u57fa\u4e8e\u4fe1\u606f\u8bba\u7684\u7cfb\u7edf\u6027\u6846\u67b6<\/strong>\uff0c\u5efa\u7acb<strong>\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u4e0e LLM \u751f\u6210\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387<\/strong>\u4e4b\u95f4\u7684\u8054\u7cfb\u3002\u968f\u7740\u300c\u6162\u601d\u8003\u300d\u65b9\u6cd5\u7684\u6df1\u5165\u63a2\u7d22\uff0cLLM \u53d1\u5c55\u65b0\u7684\u8f6c\u6298\u70b9\u6b63\u5728\u5230\u6765\u3002\u672a\u6765\uff0c\u5927\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u4f18\u5316\u4e0d\u518d\u5c40\u9650\u4e8e\u6269\u5927\u6a21\u578b\u89c4\u6a21\uff0c\u800c\u662f\u901a\u8fc7\u4f18\u5316\u63a8\u7406\u8fc7\u7a0b\uff0c\u5b9e\u73b0\u66f4\u667a\u80fd\u3001\u66f4\u7cbe\u51c6\u7684\u903b\u8f91\u63a8\u7406\u3002\u672c\u7814\u7a76\u5c06\u6df1\u5165\u5256\u6790\u5916\u90e8\u6162\u601d\u8003\u7b56\u7565\u7684\u7406\u8bba\u57fa\u7840\u3001\u673a\u5236\u89e3\u6790\u4ee5\u53ca\u5176\u5bf9 LLM \u63a8\u7406\u80fd\u529b\u7684\u5f71\u54cd\uff0c\u4e3a\u4eba\u5de5\u667a\u80fd\u63a8\u7406\u80fd\u529b\u7684\u8fdb\u4e00\u6b65\u7a81\u7834\u63d0\u4f9b\u65b0\u7684\u65b9\u5411\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-ca417295fc3900e91d601170a9bfb3fd.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-ca417295fc3900e91d601170a9bfb3fd.png\"><\/a><\/section>\n<ul>\n<li>\n<p>\u8bba\u6587\u6807\u9898\uff1aRethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning<\/p>\n<\/li>\n<li>\n<p>\u8bba\u6587\u94fe\u63a5\uff1ahttp:\/\/arxiv.org\/abs\/2501.15602<\/p>\n<\/li>\n<\/ul>\n<section>\u6b64\u5de5\u4f5c\u4e3b\u8981\u4f5c\u51fa\u4e86\u5982\u4e0b\u8d21\u732e\uff1a<\/section>\n<ul>\n<li>\n<p><strong>\u5206\u6790\u4e86 LLM \u63a8\u7406\u8fc7\u7a0b\u4e2d\u7684\u96ea\u7403\u8bef\u5dee\u6548\u5e94<\/strong>\uff0c\u5e76\u8bc1\u660e\u8be5\u6548\u5e94\u4f1a\u5bfc\u81f4\u63a8\u7406\u9519\u8bef\u6982\u7387\u968f\u63a8\u7406\u8def\u5f84\u7684\u589e\u957f\u800c\u4e0a\u5347\uff0c\u5f3a\u8c03\u4e86\u6162\u601d\u8003\u7b56\u7565\u5728\u51cf\u5c11\u9519\u8bef\u4e2d\u7684\u5173\u952e\u4f5c\u7528\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u4fe1\u606f\u8bba\u7684\u7cfb\u7edf\u6027\u6846\u67b6<\/strong>\uff0c\u5efa\u7acb<strong>\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5<\/strong>\u4e0e<strong>\u63a8\u7406\u6b63\u786e\u6982\u7387<\/strong>\u4e4b\u95f4\u7684\u6570\u5b66\u8054\u7cfb\uff0c\u4e3a\u7406\u89e3\u6162\u601d\u8003\u7b56\u7565\u7684\u6709\u6548\u6027\u63d0\u4f9b\u7406\u8bba\u652f\u6491\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5bf9\u6bd4\u4e86\u4e0d\u540c\u7684\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5<\/strong>\uff0c\u5305\u62ec BoN \u548c MCTS \u7b49\uff0c\u63ed\u793a\u5b83\u4eec\u5728\u63a8\u7406\u80fd\u529b\u63d0\u5347\u65b9\u9762\u7684\u5dee\u5f02\u4e0e\u5185\u5728\u8054\u7cfb\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>1 \u5927\u6a21\u578b\u63a8\u7406\u8fc7\u7a0b\u4e2d\u7684\u300c\u96ea\u7403\u8bef\u5dee\u300d<\/strong><\/section>\n<section><\/section>\n<section>\u60f3\u8c61\u4e00\u4e0b\uff0c\u5728\u51ac\u5929\u7684\u96ea\u5730\u4e0a\u6eda\u52a8\u4e00\u4e2a\u96ea\u7403\u3002\u968f\u7740\u6eda\u52a8\u7684\u8ddd\u79bb\u589e\u52a0\uff0c\u96ea\u7403\u4f1a\u4ee5\u8d8a\u6765\u8d8a\u5feb\u7684\u901f\u5ea6\u53d8\u5927\uff0c\u8fd9\u5c31\u662f<strong>\u96ea\u7403\u6548\u5e94\uff08Snowball Effect\uff09<\/strong>\u2014\u2014 \u5c0f\u7684\u53d8\u5316\u4f1a\u968f\u7740\u65f6\u95f4\u63a8\u79fb\u4e0d\u65ad\u7d2f\u79ef\uff0c\u6700\u7ec8\u5e26\u6765\u663e\u8457\u5f71\u54cd\u3002<\/section>\n<section><\/section>\n<section>\u5728\u5927\u89c4\u6a21\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u4e2d\uff0c\u8fd9\u4e00\u6548\u5e94\u6700\u521d\u4f53\u73b0\u5728\u81ea\u56de\u5f52\u5f0f\uff08Auto-Regressive\uff09 \u7684 Next-Token Prediction\uff08NTP\uff09\u4efb\u52a1\u4e2d\uff0c\u5fae\u5c0f\u7684 token \u7ea7\u9519\u8bef\u4f1a\u4e0d\u65ad\u7d2f\u79ef\uff0c\u6700\u7ec8\u5bfc\u81f4\u6a21\u578b\u751f\u6210\u7684\u7b54\u6848\u504f\u79bb\u9884\u671f\u7684\u6b63\u786e\u7b54\u6848 [15]\u3002<strong>\u7136\u800c\uff0c\u5728\u66f4\u590d\u6742\u7684\u63a8\u7406\u4efb\u52a1\u4e2d\uff0c\u8fd9\u79cd\u9519\u8bef\u4e0d\u518d\u4ec5\u9650\u4e8e token \u7ea7\uff0c\u800c\u662f\u6269\u5c55\u5230\u53e5\u5b50\u7ea7<\/strong>\uff0c\u4f7f\u5f97\u63a8\u7406\u504f\u5dee\u66f4\u52a0\u96be\u4ee5\u8861\u91cf\u548c\u63a7\u5236\u3002<\/section>\n<section><\/section>\n<section><strong>\u4e3a\u4ec0\u4e48\u63a8\u7406\u504f\u5dee\u4f1a\u9010\u6b65\u653e\u5927\uff1f<\/strong><\/section>\n<section><\/section>\n<section>\u7814\u7a76\u8868\u660e\uff0cLLM \u7684\u63a8\u7406\u8fc7\u7a0b\u53ef\u4ee5\u770b\u4f5c\u662f<strong>\u9010\u6b65\u6267\u884c\u4e00\u7cfb\u5217\u539f\u59cb\u4efb\u52a1\uff08Primitive Tasks\uff09[16]<\/strong>\uff0c\u6bcf\u4e00\u6b65\u7684\u63a8\u7406\u7ed3\u679c\u90fd\u4f9d\u8d56\u4e8e\u524d\u9762\u7684\u8f93\u51fa\u3002\u56e0\u6b64\uff0c<strong>\u4efb\u4f55\u65e9\u671f\u7684\u5fae\u5c0f\u8bef\u5dee\u90fd\u4f1a\u5728\u63a8\u7406\u94fe\u6761\u4e2d\u4e0d\u65ad\u653e\u5927\uff0c\u6700\u7ec8\u5bfc\u81f4\u6a21\u578b\u504f\u79bb\u6b63\u786e\u7b54\u6848<\/strong>\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u66f4\u76f4\u89c2\u5730\u7406\u89e3\u8fd9\u4e00\u73b0\u8c61\uff0c\u7814\u7a76\u8005\u501f\u52a9<strong>\u67cf\u62c9\u56fe\u7684\u300c\u6d1e\u7a74\u5bd3\u8a00\u300d<\/strong>\uff08Plato\u2019s Allegory of the Cave\uff09\u3002\u5728\u8fd9\u4e2a\u5bd3\u8a00\u4e2d\uff0c\u4eba\u4eec\u53ea\u80fd\u770b\u5230\u6295\u5c04\u5728\u5899\u4e0a\u7684\u5f71\u5b50\uff0c\u800c\u65e0\u6cd5\u76f4\u63a5\u611f\u77e5\u771f\u5b9e\u4e16\u754c\uff0c\u7c7b\u4f3c\u4e8e LLM \u53ea\u80fd\u4ece\u8bad\u7ec3\u6570\u636e\u4e2d\u5b66\u4e60\u4e16\u754c\u7684\u300c\u6295\u5f71\u300d\u3002\u5982\u56fe 1 (a) \u6240\u793a\uff0c\u8bad\u7ec3\u6570\u636e\u53ea\u662f\u73b0\u5b9e\u4e16\u754c\u7684\u6620\u5c04\uff0c\u800c LLM \u751f\u6210\u7684\u63a8\u7406\u7ed3\u679c\u6b63\u5982\u56fe 1 (b) \u6240\u793a\uff0c\u4ec5\u662f\u5176\u5185\u90e8\u63a8\u7406\u8fc7\u7a0b\u7684\u300c\u5f71\u5b50\u300d\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-6bccfc574336bacb26e1e74b14993236.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-6bccfc574336bacb26e1e74b14993236.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe\u8868 1: \u5927\u6a21\u578b\u63a8\u7406\u8fc7\u7a0b\u7684\u67cf\u62c9\u56fe\u5047\u8bbe<\/sup><\/em><\/section>\n<section><\/section>\n<section><strong>\u6362\u53e5\u8bdd\u8bf4\uff0c\u6a21\u578b\u7684\u63a8\u7406\u8f93\u51fa\u5e76\u975e\u76f4\u63a5\u53cd\u6620\u5176\u601d\u7ef4\u8fc7\u7a0b\uff0c\u800c\u662f\u53d7\u9650\u4e8e\u5b83\u4ece\u8bad\u7ec3\u6570\u636e\u4e2d\u5b66\u5230\u7684\u6a21\u5f0f\u548c\u8bef\u5dee\uff0c\u5bfc\u81f4\u6eda\u96ea\u7403\u6548\u5e94\u7684\u6301\u7eed\u7d2f\u79ef<\/strong>\u3002<\/section>\n<section><\/section>\n<blockquote data-author-name=\"\" data-content-utf8-length=\"188\" data-source-title=\"\" data-type=\"2\" data-url=\"\">\n<section>\n<section>\n<section>\u4f8b\u5982\uff1a\u5728 LLM \u6267\u884c\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u65f6\uff0c\u4f8b\u5982\u89e3\u7b54\u300c\u8ba1\u7b97 3x + 2y\u300d\uff0c\u6a21\u578b\u5e76\u4e0d\u662f\u76f4\u63a5\u7ed9\u51fa\u7b54\u6848\uff0c\u800c\u662f\u9690\u5f0f\u5730\u6267\u884c\u4e00\u7cfb\u5217\u63a8\u7406\u6b65\u9aa4\uff1a<\/section>\n<section><\/section>\n<section>t\u2081: \u8ba1\u7b97 3x \u2192 t\u2082: \u8ba1\u7b97 2y \u2192 t\u2083: \u5c06 3x \u548c 2y \u76f8\u52a0\u3002<\/section>\n<section><\/section>\n<section>\u7136\u800c\uff0c\u8fd9\u4e9b\u63a8\u7406\u6b65\u9aa4\u662f\u62bd\u8c61\u7684\u3001\u4e0d\u53ef\u76f4\u63a5\u89c2\u5bdf\u7684\uff0c\u6a21\u578b\u7684\u6700\u7ec8\u8f93\u51fa\u662f\u8fd9\u4e9b\u63a8\u7406\u8fc7\u7a0b\u7684\u4e0d\u540c\u8868\u8fbe\u65b9\u5f0f\u3002\u4f8b\u5982\uff0c\u8f93\u51fa\u5e8f\u5217 r\u2081 \u2192 r\u2082 \u2192 r\u2083 \u53ef\u80fd\u6709\u591a\u79cd\u4e0d\u540c\u7684\u8868\u8fbe\u5f62\u5f0f\uff0c\u4f46\u5b83\u4eec\u5e76\u4e0d\u4e00\u5b9a\u80fd\u5b8c\u5168\u8fd8\u539f\u5bf9\u5e94\u7684\u63a8\u7406\u6b65\u9aa4 t\u2081 \u2192 t\u2082 \u2192 t\u2083\u3002<\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n<section><\/section>\n<section>\u7531\u4e8e\u5355\u4e2a\u8f93\u51fa r_l \u65e0\u6cd5\u5b8c\u5168\u8868\u8fbe\u5bf9\u5e94\u7684\u63a8\u7406\u6b65\u9aa4 t_l\uff0c\u5373\u4f7f\u521d\u59cb\u8bef\u5dee\u5fae\u5c0f\uff0c\u4e5f\u4f1a\u968f\u7740\u63a8\u7406\u94fe\u6761\u7684\u5ef6\u7eed\u9010\u6b65\u653e\u5927\uff0c\u6700\u7ec8\u5bfc\u81f4<strong>\u4e25\u91cd\u7684\u63a8\u7406\u504f\u5dee<\/strong>\u3002\u8fd9\u79cd\u8bef\u5dee\u7684\u79ef\u7d2f\uff0c\u6b63\u662f\u96ea\u7403\u6548\u5e94\u5728\u63a8\u7406\u4efb\u52a1\u4e2d\u7684\u5178\u578b\u4f53\u73b0\u3002<\/section>\n<section><\/section>\n<section>\u5728 LLM \u63a8\u7406\u8fc7\u7a0b\u4e2d\uff0c\u96ea\u7403\u8bef\u5dee\u4f1a\u5bfc\u81f4\u6a21\u578b\u7684\u63a8\u7406\u7ed3\u679c\u9010\u6b65\u504f\u79bb\u6b63\u786e\u7b54\u6848\u3002\u4e3a\u4e86\u7cbe\u51c6\u8861\u91cf\u8fd9\u4e00\u8bef\u5dee\uff0c\u672c\u7814\u7a76\u5f15\u5165<strong>\u4e92\u4fe1\u606f\uff08Mutual Information, MI\uff09<\/strong>\u8fd9\u4e00\u6570\u5b66\u5de5\u5177\uff0c\u6765<strong>\u91cf\u5316\u9690\u5f0f\u63a8\u7406\u5e8f\u5217 t \u4e0e\u6700\u7ec8\u751f\u6210\u7684\u56de\u590d\u5e8f\u5217 r\u00a0<\/strong>\u4e4b\u95f4\u7684\u5171\u4eab\u4fe1\u606f\u91cf\uff0c\u8bb0\u4f5c<strong>\u00a0I (t; r)<\/strong>\u3002\u8fd9\u4e00\u5ea6\u91cf\u5e2e\u52a9\u8bc4\u4f30\u6a21\u578b\u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\u80fd\u591f\u4fdd\u7559\u591a\u5c11\u5173\u952e\u4fe1\u606f\u3002<\/section>\n<section><\/section>\n<section>\u5177\u4f53\u800c\u8a00\uff0c\u5728\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u4e2d\uff0c\u6a21\u578b\u7684\u8f93\u51fa\u53ef\u80fd\u5b58\u5728\u7ec6\u5fae\u504f\u5dee\uff0c\u8fd9\u4e9b\u8bef\u5dee\u4f1a\u9010\u6b65\u7d2f\u79ef\u5e76\u5bfc\u81f4\u4fe1\u606f\u635f\u5931\u3002\u7814\u7a76\u8005<strong>\u5c06\u4fe1\u606f\u635f\u5931\u5b9a\u4e49\u4e3a\u4e92\u4fe1\u606f I (t; r) \u4e0e\u9690\u5f0f\u63a8\u7406\u8fc7\u7a0b\u7684\u4fe1\u606f\u71b5 H (t) \u4e4b\u95f4\u7684\u5dee\u503c<\/strong>\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-d5b9505ce8e1d64dcfaa89b3d7414798.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-d5b9505ce8e1d64dcfaa89b3d7414798.png\"><\/a><\/section>\n<section>\u800c\u6700\u7ec8\u7684\u96ea\u7403\u8bef\u5dee\u5219\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u5728\u6240\u6709\u63a8\u7406\u6b65\u9aa4\u4e0a\u4fe1\u606f\u635f\u5931\u7684\u7d2f\u79ef\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-94dc9f7e01f7710d8f77b699b1178599.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-94dc9f7e01f7710d8f77b699b1178599.png\"><\/a><\/section>\n<section><strong>2 \u4ece\u300c\u96ea\u7403\u8bef\u5dee\u300d\u5230\u63a8\u7406\u9519\u8bef\u7684\u6982\u7387<\/strong><\/section>\n<section><\/section>\n<section>\u5728 LLM \u7684\u63a8\u7406\u8fc7\u7a0b\u4e2d\uff0c<strong>\u63a8\u7406\u8def\u5f84\u8d8a\u957f\uff0c\u96ea\u7403\u8bef\u5dee\u5c31\u4f1a\u4e0d\u65ad\u7d2f\u79ef\uff0c\u6700\u7ec8\u5bfc\u81f4\u4e25\u91cd\u7684\u4e8b\u5b9e\u504f\u5dee\uff0c\u7814\u7a76\u8005\u5c06\u5176\u5b9a\u4e49\u4e3a\u63a8\u7406\u9519\u8bef\uff08Reasoning Errors\uff09<\/strong>\u3002<\/section>\n<section><\/section>\n<section><strong>\u5982\u4f55\u8861\u91cf\u63a8\u7406\u9519\u8bef\uff1f<\/strong><\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u51c6\u786e\u8bc4\u4f30\u63a8\u7406\u9519\u8bef\uff0c\u7814\u7a76\u8005\u9996\u5148\u9700\u8981\u6e05\u6670\u5730\u5b9a\u4e49\u5b83\u3002\u7531\u4e8e\u6bcf\u4e2a\u8f93\u51fa r_l \u4ee3\u8868\u9690\u5f0f\u63a8\u7406\u6b65\u9aa4 t_l\uff0c\u7814\u7a76\u8005\u901a\u8fc7\u68c0\u67e5\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u8db3\u591f\u5f3a\u5927\u7684\u6620\u5c04\u51fd\u6570 <em>f \u00a0<\/em>\u6765\u4ece r_l \u8fd8\u539f t_l\u3002\u5982\u679c\u8fd9\u79cd\u8fd8\u539f\u80fd\u529b\u8f83\u5f31\uff0c\u8bf4\u660e\u63a8\u7406\u8fc7\u7a0b\u4e2d\u4fe1\u606f\u635f\u5931\u8f83\u5927\uff0c\u8fdb\u800c\u5bfc\u81f4\u4e86\u63a8\u7406\u9519\u8bef\u7684\u53d1\u751f\u3002\u5177\u4f53\u800c\u8a00\uff0c\u7814\u7a76\u8005\u5c06\u300c\u63a8\u7406\u9519\u8bef\u300d\u8fd9\u4e00\u4e8b\u4ef6\u523b\u753b\u5982\u4e0b\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-7212262a6c17581355dc2d85aef702de.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-7212262a6c17581355dc2d85aef702de.png\"><\/a><\/section>\n<section>\u4e3a\u4e86\u66f4\u51c6\u786e\u5730<strong>\u4f30\u8ba1 LLM \u53d1\u751f\u63a8\u7406\u9519\u8bef\u7684\u6982\u7387<\/strong>\uff0c\u672c\u7814\u7a76\u63d0\u51fa\u4f7f\u7528\u4fe1\u606f\u8bba\u65b9\u6cd5\uff0c\u5efa\u7acb<strong>\u96ea\u7403\u8bef\u5dee\u4e0e\u63a8\u7406\u9519\u8bef\u53d1\u751f\u6982\u7387<\/strong>\u4e4b\u95f4\u7684\u6570\u5b66\u8054\u7cfb\u3002\u7814\u7a76\u8005\u4ece\u4e00\u4e2a\u5173\u952e\u5f15\u7406\u51fa\u53d1\uff0c\u901a\u8fc7\u7406\u8bba\u63a8\u5bfc\u63ed\u793a\u6eda\u96ea\u7403\u8bef\u5dee\u5982\u4f55\u9010\u6b65\u79ef\u7d2f\uff0c\u5e76\u6700\u7ec8\u5f71\u54cd\u6a21\u578b\u7684\u63a8\u7406\u51c6\u786e\u6027\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-6848d8cd7ad084a96b5ea1fef2c30f7d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-6848d8cd7ad084a96b5ea1fef2c30f7d.png\"><\/a><\/section>\n<section>\u57fa\u4e8e\u6b64\u5f15\u7406\uff0c\u7814\u7a76\u8005\u53ef\u4ee5\u63a8\u5bfc\u51fa\u63a8\u7406\u9519\u8bef\u53d1\u751f\u6982\u7387\u7684\u4e0b\u754c\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-900d00a0205adc3f296bee252dc90136.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-900d00a0205adc3f296bee252dc90136.png\"><\/a><\/section>\n<section>\u6b64\u5b9a\u7406\u8868\u660e\uff0c\u5728\u63a8\u7406\u7684\u7b2c l \u6b65\uff0c\u9519\u8bef\u6982\u7387\u7684\u4e0b\u754c\u53d7<strong>\u7d2f\u79ef\u4fe1\u606f\u635f\u5931 H_( \u5f71\u54cd\uff0c\u7531\u4e8e\u5176\u7d2f\u52a0\u7684\u5b9a\u4e49\uff0c\u8fd9\u4e00\u635f\u5931\u81f3\u5c11\u4f1a\u968f\u63a8\u7406\u6b65\u6570 l \u7ebf\u6027\u589e\u957f\u3002<\/strong><\/section>\n<section><\/section>\n<section>\u5f53<strong>\u96ea\u7403\u6548\u5e94<\/strong>\u51fa\u73b0\u65f6\uff0c\u7d2f\u79ef\u4fe1\u606f\u635f\u5931\u53ef\u80fd<strong>\u8d85\u8fc7\u7ebf\u6027\u589e\u957f<\/strong>\uff0c\u5bfc\u81f4\u63a8\u7406\u9519\u8bef\u6982\u7387\u968f\u63a8\u7406\u8def\u5f84\u7684\u589e\u52a0\u800c\u5feb\u901f\u4e0a\u5347\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c<strong>\u63a8\u7406\u94fe\u6761\u8d8a\u957f\uff0c\u6a21\u578b\u51fa\u9519\u7684\u53ef\u80fd\u6027\u8d8a\u5927<\/strong>\uff0c\u8fd9\u89e3\u91ca\u4e86 LLM \u5728\u957f\u94fe\u63a8\u7406\u4efb\u52a1\u4e2d\u4e3a\u4f55\u5bb9\u6613\u51fa\u73b0\u504f\u5dee\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-98e67db9e05a287117cf643a046f36b0.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-98e67db9e05a287117cf643a046f36b0.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe\u8868 2: \u4e0d\u540c LLM \u5728 GSM8k \u6570\u636e\u96c6\u4e0a\u751f\u6210\u56de\u590d\u7684\u4f30\u8ba1\u4e92\u4fe1\u606f\uff08MI\uff09\u548c\u5956\u52b1\u5206\u6570<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u4e3a\u4e86<strong>\u5b9e\u8bc1\u9a8c\u8bc1 LLM \u63a8\u7406\u4e2d\u7684\u96ea\u7403\u8bef\u5dee\u6548\u5e94<\/strong>\uff0c\u672c\u7814\u7a76\u57fa\u4e8e GSM8k \u6570\u636e\u96c6\u8fdb\u884c\u5b9e\u9a8c\uff0c\u5e76\u6d4b\u8bd5\u4e86\u4e09\u6b3e\u5148\u8fdb\u7684\u63a8\u7406 LLMs\uff1aLlama3.1-8B-Instruct\u3001Qwen2.5-7B-Instruct\u4ee5\u53ca Skywork-o1-Open-Llama-3.1-8B\u3002<\/section>\n<section><\/section>\n<section>\u7814\u7a76\u8005\u8ba1\u7b97\u4e86<strong>\u4e92\u4fe1\u606f I (t; r) \u5728\u6240\u6709 token \u4e0a\u7684\u5e73\u5747\u503c<\/strong>\uff0c\u5e76\u5206\u6790\u5176\u968f\u63a8\u7406\u8def\u5f84\u957f\u5ea6 L \u7684\u53d8\u5316\uff0c\u540c\u65f6\u8bc4\u4f30\u751f\u6210\u7ed3\u679c\u7684<strong>\u5956\u52b1\u5206\u6570\uff08reward\uff09\uff0c\u7ed3\u679c\u5982\u56fe\u8868 2 \u6240\u793a<\/strong>\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff1a<\/section>\n<ul>\n<li>\n<p><strong>\u4e92\u4fe1\u606f\u5448\u8d1f\u6307\u6570\u7ea7\u4e0b\u964d\uff0c\u6bd4\u7ebf\u6027\u8870\u51cf\u66f4\u5feb<\/strong>\uff0c\u968f\u7740\u63a8\u7406\u6b65\u6570 L \u7684\u589e\u957f\uff0c\u4fe1\u606f\u635f\u5931\u8fc5\u901f\u7d2f\u79ef\uff1b<\/p>\n<\/li>\n<li>\n<p>\u7531\u4e8e\u8ba1\u7b97\u7684\u662f<strong>\u5e73\u5747\u4e92\u4fe1\u606f\uff0c\u63a8\u7406\u94fe\u6761\u9760\u540e\u7684 token \u53ef\u80fd\u635f\u5931\u66f4\u591a\u5173\u952e\u4fe1\u606f<\/strong>\uff1b<\/p>\n<\/li>\n<li>\n<p><strong>\u5956\u52b1\u5206\u6570\u968f\u63a8\u7406\u957f\u5ea6\u589e\u52a0\u800c\u4e0b\u964d<\/strong>\uff0c\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86\u96ea\u7403\u8bef\u5dee\u5bf9 LLM \u751f\u6210\u8d28\u91cf\u7684\u5f71\u54cd\u3002<\/p>\n<\/li>\n<\/ul>\n<section>\u8fd9\u4e00\u5b9e\u9a8c\u7ed3\u679c\u4e0d\u4ec5<strong>\u9a8c\u8bc1\u4e86\u96ea\u7403\u8bef\u5dee\u7684\u5b58\u5728<\/strong>\uff0c\u4e5f\u8868\u660e\u4fe1\u606f\u635f\u5931\u7684\u7d2f\u79ef\u901f\u5ea6\u8fdc\u8d85\u7ebf\u6027\u8870\u51cf\uff0c\u76f4\u63a5\u5f71\u54cd LLM \u751f\u6210\u7684\u63a8\u7406\u8d28\u91cf\u3002\u8fd9\u4e00\u53d1\u73b0\u4e0e\u7814\u7a76\u8005\u7684\u7406\u8bba\u5206\u6790\u4e00\u81f4\u3002<\/section>\n<section><\/section>\n<section><strong>3 \u5916\u90e8\u6162\u601d\u8003\u4e2d\u7684\u6b63\u786e\u63a8\u7406\u6982\u7387<\/strong><\/section>\n<section><\/section>\n<section>\u5148\u524d\u7684\u5206\u6790\u8868\u660e\uff0c<strong>\u63a8\u7406\u9519\u8bef\u6982\u7387 P (e_l) \u00a0\u968f\u7740\u63a8\u7406\u6b65\u6570 l \u7684\u589e\u52a0\u800c\u4e0a\u5347<\/strong>\u3002\u7136\u800c\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u63a8\u7406\u9519\u8bef\u901a\u5e38\u4f53\u73b0\u5728<strong>\u6a21\u578b\u751f\u6210\u7ed3\u679c\u7684\u5956\u52b1\u5206\u6570\uff08reward\uff09<\/strong> \u4e0a\u3002\u56e0\u6b64\uff0c\u672c\u6587\u8fdb\u4e00\u6b65\u6269\u5c55\u81f3<strong>\u73b0\u5b9e\u573a\u666f<\/strong>\uff0c\u63a2\u8ba8<strong>\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u4e3a\u4f55\u6709\u6548<\/strong>\u3002<\/section>\n<section><\/section>\n<section><strong>3.1 \u4f55\u4e3a\u6b63\u786e\u63a8\u7406<\/strong><\/section>\n<section><\/section>\n<section>\u7814\u7a76\u8005\u9996\u5148\u5b9a\u4e49 LLM \u5728\u73b0\u5b9e\u573a\u666f\u4e2d\u7684\u63a8\u7406\u8fc7\u7a0b\u3002\u5bf9\u4e8e\u4e00\u4e2a\u95ee\u9898 \u00a0r_0\uff0c\u6a21\u578b\u4f1a\u901a\u8fc7<strong>\u81ea\u56de\u5f52<\/strong>\u65b9\u5f0f\u751f\u6210\u4e00\u4e2a\u5305\u542b L \u4e2a\u63a8\u7406\u6b65\u9aa4\u7684\u54cd\u5e94\u5e8f\u5217\uff1aR = [r_1,r_2,\u2026,r_L]\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u8bc4\u4f30\u6bcf\u4e00\u6b65\u63a8\u7406 r_l \u00a0\u7684\u8d28\u91cf\uff0c\u7814\u7a76\u8005\u5f15\u5165\u4e00\u4e2a\u4ef7\u503c\u51fd\u6570 \u03c6\uff0c<strong>\u7528\u4e8e\u8861\u91cf\u6bcf\u4e2a\u6b65\u9aa4\u7684\u6b63\u786e\u6027 \u03c6(r_l)\u00a0<\/strong>\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8fd9\u4e00\u8bc4\u4f30\u53ef\u4ee5\u901a\u8fc7\u4eba\u7c7b\u53cd\u9988\u6216\u5956\u52b1\u6a21\u578b\u6765\u5b9e\u73b0\u3002\u6b64\u5916\uff0c\u7814\u7a76\u8005\u5047\u8bbe\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u90fd\u6709\u4e00\u4e2a\u6807\u51c6\u7b54\u6848 r_l^*\uff0c\u4ee3\u8868 LLM \u5e94\u8be5\u751f\u6210\u7684\u6700\u51c6\u786e\u7b54\u6848\uff0c\u4e0e\u4eba\u7c7b\u7406\u60f3\u63a8\u7406\u65b9\u5f0f\u4fdd\u6301\u4e00\u81f4\u3002<\/section>\n<section><\/section>\n<section>\u57fa\u4e8e\u4e0a\u8ff0\u8bbe\u5b9a\uff0c\u7814\u7a76\u8005\u5229\u7528\u4ef7\u503c\u51fd\u6570 \u03c6 \u8bc4\u4f30\u63a8\u7406\u6b65\u9aa4\u7684\u6b63\u786e\u6027\uff0c\u5e76\u636e\u6b64<strong>\u91cf\u5316 LLM \u751f\u6210\u56de\u590d\u7684\u8d28\u91cf<\/strong>\u3002\u5177\u4f53\u800c\u8a00\uff0c\u7814\u7a76\u8005\u5206\u522b\u5c06\u5355\u6b65\u63a8\u7406\u548c\u6574\u4e2a\u63a8\u7406\u8fc7\u7a0b\u7684\u6b63\u786e\u6027\u5b9a\u4e49\u5982\u4e0b\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-2f5e58b85c0371932cb8327fac284539.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-2f5e58b85c0371932cb8327fac284539.png\"><\/a><\/section>\n<section><strong>3.2 \u6b63\u786e\u63a8\u7406\u7684\u6982\u7387<\/strong><\/section>\n<section><\/section>\n<section>\u5b9e\u9a8c\u7ed3\u679c\uff08\u56fe\u8868 2\uff09\u8868\u660e\uff0c<strong>\u5e73\u5747\u4e92\u4fe1\u606f\u4f1a\u968f\u63a8\u7406\u6b65\u6570\u5448\u8fd1\u4f3c\u6307\u6570\u7ea7\u4e0b\u964d<\/strong>\uff0c\u8fd9\u610f\u5473\u7740<strong>\u96ea\u7403\u8bef\u5dee\u968f\u7740\u63a8\u7406\u957f\u5ea6\u7684\u589e\u52a0\u5448\u6307\u6570\u7ea7\u589e\u957f<\/strong>\u3002\u7136\u800c\uff0c\u7531\u4e8e\u6982\u7387\u503c\u4e0d\u80fd\u8d85\u8fc7 1\uff0c\u7814\u7a76\u8005\u57fa\u4e8e<strong>\u5b9a\u7406 3.3<\/strong> \u63d0\u51fa\u4e00\u4e2a\u5047\u8bbe\uff1a<strong>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u63a8\u7406\u9519\u8bef\u7684\u6982\u7387\u53ef\u80fd\u9075\u5faa\u6307\u6570\u8870\u51cf\u51fd\u6570<\/strong>\uff0c\u5373\uff1aP (e_l) = 1 -\u03bbe^(-l)\uff0c\u8fd9\u4e00\u5047\u8bbe\u4f7f\u5f97\u540e\u7eed\u5206\u6790\u66f4\u52a0\u76f4\u89c2\uff0c\u5e76\u8fdb\u4e00\u6b65\u5e2e\u52a9\u63a8\u5bfc<strong>\u5728\u7b2c l \u5c42\u751f\u6210\u6b63\u786e\u63a8\u7406\u6b65\u9aa4\u7684\u6982\u7387<\/strong>\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-9bc464472efd2f215bf948458f2b021b.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-9bc464472efd2f215bf948458f2b021b.png\"><\/a><\/section>\n<section>\u7531\u6b64\u5047\u8bbe\uff0c\u7814\u7a76\u8005\u63a8\u5bfc\u51fa\u5728\u96ea\u7403\u8bef\u5dee\u5b58\u5728\u65f6\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u6b63\u786e\u7684\u5b8c\u6574\u63a8\u7406\u8fc7\u7a0b\u7684\u6982\u7387\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a66d9b23607673d6b0098f08d95368e5.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a66d9b23607673d6b0098f08d95368e5.png\"><\/a><\/section>\n<section><strong>3.3 \u5916\u90e8\u6162\u601d\u8003\u63d0\u5347\u63a8\u7406\u8d28\u91cf\u7684\u673a\u7406<\/strong><\/section>\n<section><\/section>\n<section>\u57fa\u4e8e\u524d\u9762\u7684\u5206\u6790\uff0c\u7814\u7a76\u8005\u9996\u5148\u76f4\u89c2\u4e0a\u5f97\u51fa\u8fd9\u6837\u7684\u7ed3\u8bba\uff1a\u7531\u4e8e LLM \u751f\u6210\u7684\u968f\u673a\u6027\uff0c<strong>\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u7684\u6838\u5fc3\u76ee\u6807\u662f\u5f15\u5165\u989d\u5916\u7684\u63a8\u7406\u6b65\u9aa4\u5e76\u7ed3\u5408\u591a\u6b21\u91cd\u65b0\u91c7\u6837\u7b56\u7565\uff0c\u4ece\u800c\u5bf9\u51b2\u96ea\u7403\u8bef\u5dee\uff0c\u8fdb\u800c\u63d0\u9ad8\u6a21\u578b\u751f\u6210\u7ed3\u679c\u7684\u6b63\u786e\u6027<\/strong>\u3002<\/section>\n<section><\/section>\n<section>\u63a5\u4e0b\u6765\uff0c\u7814\u7a76\u8005\u5229\u7528\u7406\u8bba\u5206\u6790\u8fdb\u4e00\u6b65\u8be6\u7ec6\u9610\u8ff0\u8fd9\u4e00\u89c2\u70b9\u3002\u9996\u5148\uff0c\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u4ece\u6839\u672c\u4e0a\u6765\u8bf4\u4e3b\u8981\u5177\u6709\u4e24\u4e2a\u7279\u70b9\uff1a<\/section>\n<ul>\n<li>\n<p><strong>\u5bbd\u5ea6\u6269\u5c55\uff08Width-Expansion\uff09\uff1a<\/strong><\/p>\n<\/li>\n<li>\n<p>\u5bf9\u4e8e\u957f\u5ea6\u4e00\u5b9a\u7684\u63a8\u7406\u5e8f\u5217\uff0c\u5927\u591a\u6570\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u90fd\u8bd5\u56fe\u6269\u5c55\u63a8\u7406\u7a7a\u95f4\u7684\u5bbd\u5ea6\u3002<\/p>\n<\/li>\n<li>\n<p>\u8fd9\u53ef\u4ee5\u901a\u8fc7\u7b80\u5355\u7684\u91cd\u65b0\u751f\u6210\uff08BoN\u3001CoT-SC\uff09\u6216\u66f4\u590d\u6742\u7684\u6811\u641c\u7d22\u65b9\u6cd5\uff08ToT\u3001MCTS\uff09 \u6765\u5b9e\u73b0\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u751f\u6210 &amp; \u9009\u62e9\uff08Generation &amp; Selection\uff09\uff1a<\/strong><\/p>\n<\/li>\n<li>\n<p>\u6269\u5c55\u63a8\u7406\u7a7a\u95f4\u540e\uff0c\u8fd8\u9700\u8981\u4ece\u591a\u4e2a\u5019\u9009\u63a8\u7406\u8def\u5f84\u4e2d\u9009\u51fa\u6700\u4f18\u89e3\u3002<\/p>\n<\/li>\n<li>\n<p>\u8bbe Pr (\u03c4_generate) \u4e3a\u751f\u6210\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387\uff0cPr (\u03c4_select) \u4e3a\u4ece\u5019\u9009\u8def\u5f84\u4e2d\u9009\u51fa\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387\uff0c\u5219\u6700\u7ec8\u83b7\u5f97\u6b63\u786e\u63a8\u7406\u7ed3\u679c\u7684\u6982\u7387\u53ef\u8868\u793a\u4e3a\uff1aPr [\u03c8(R)\u2264\u03c4 ]= Pr (\u03c4_generate )\u00d7 Pr (\u03c4_select \u00a0)\u3002<\/p>\n<\/li>\n<\/ul>\n<section>\u5916\u90e8\u6162\u601d\u8003 \u901a\u8fc7\u6269\u5c55\u63a8\u7406\u7a7a\u95f4\u6765\u63d0\u5347 LLM \u751f\u6210\u6b63\u786e\u7b54\u6848\u7684\u6982\u7387 Pr (\u03c4_generate)\uff0c\u4f46\u4e0e\u6b64\u540c\u65f6\uff0c\u989d\u5916\u7684\u63a8\u7406\u6b65\u9aa4\u4e5f\u4f1a\u589e\u52a0\u9009\u62e9\u6700\u4f18\u63a8\u7406\u8def\u5f84\u7684\u96be\u5ea6\uff0c\u4ece\u800c\u964d\u4f4e Pr (\u03c4_select)\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5728\u63d0\u5347\u63a8\u7406\u6b63\u786e\u6027\u7684\u540c\u65f6\uff0c\u4e5f\u5e26\u6765\u4e86\u66f4\u590d\u6742\u7684\u51b3\u7b56\u6311\u6218\u3002<\/section>\n<section><\/section>\n<section><strong>\u5982\u4f55\u91cf\u5316\u8fd9\u79cd\u6743\u8861\uff1f<\/strong><\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u66f4\u76f4\u89c2\u5730\u5206\u6790\u8fd9\u4e00\u73b0\u8c61\uff0c\u7814\u7a76\u8005\u4ee5 Beam Search \u4f5c\u4e3a\u57fa\u51c6\u7684\u5bbd\u5ea6\u6269\u5c55\u7b56\u7565\u3002Beam Search \u5e7f\u6cdb\u5e94\u7528\u4e8e\u6811\u641c\u7d22\u7b97\u6cd5\uff0c\u5176\u6838\u5fc3\u673a\u5236\u5982\u4e0b\uff1a<\/section>\n<ul>\n<li>\n<p>\u5728\u6bcf\u4e00\u5c42\u63a8\u7406\uff0c\u751f\u6210 k \u4e2a\u5b50\u8282\u70b9\u4ee5\u6269\u5c55\u641c\u7d22\u6811\u7684\u5bbd\u5ea6\uff1b<\/p>\n<\/li>\n<li>\n<p>\u4ec5\u4fdd\u7559 b \u4e2a\u6700\u4f18\u5019\u9009\u89e3\uff0c\u4ee5\u51cf\u5c11\u8ba1\u7b97\u590d\u6742\u5ea6\u3002<\/p>\n<\/li>\n<\/ul>\n<section>\u7814\u7a76\u8005\u5c06\u5206\u6790\u7ed3\u679c\u5f62\u5f0f\u5316\u4e3a\u4e00\u4e2a\u6570\u5b66\u5f15\u7406\uff0c\u8fdb\u4e00\u6b65\u63ed\u793a\u4e86\u63a8\u7406\u7a7a\u95f4\u6269\u5c55\u4e0e\u6700\u4f18\u8def\u5f84\u9009\u62e9\u4e4b\u95f4\u7684\u5e73\u8861\u5173\u7cfb\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-de0e8b5855af6c2a71e8e3dbc9f6f6f9.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-de0e8b5855af6c2a71e8e3dbc9f6f6f9.png\"><\/a><\/section>\n<section>\u57fa\u4e8e\u63a8\u7406\u8fc7\u7a0b\u7684\u57fa\u672c\u5047\u8bbe\uff0c\u8fd9\u4e00\u6982\u7387\u4e0a\u754c\u53ef\u4ee5\u88ab\u8fdb\u4e00\u6b65\u7b80\u5316\u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-f27908339520a0da5c11d9f8ac709511.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-f27908339520a0da5c11d9f8ac709511.png\"><\/a><\/section>\n<section>\u5f15\u7406 4.5 \u548c\u5b9a\u7406 4.6 \u9610\u8ff0\u4e86\u5916\u90e8\u6162\u601d\u8003\u6280\u672f\u7684\u672c\u8d28\u673a\u7406\u5e76\u652f\u6491\u4e86\u5982\u4e0b\u7ed3\u8bba\uff1a<\/section>\n<section><\/section>\n<section><strong>\u83b7\u5f97\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387\u4e3b\u8981\u53d7\u4ee5\u4e0b\u4e09\u4e2a\u5173\u952e\u56e0\u7d20\u5f71\u54cd\uff1a<\/strong><\/section>\n<ul>\n<li>\n<p>\u6bcf\u5c42\u751f\u6210\u7684\u5019\u9009\u6570 k \uff1a\u51b3\u5b9a\u4e86\u63a8\u7406\u7a7a\u95f4\u7684\u6269\u5c55\u5bbd\u5ea6\uff1b<\/p>\n<\/li>\n<li>\n<p>\u6bcf\u5c42\u7b5b\u9009\u7684\u6700\u4f18\u5019\u9009\u6570 b \uff1a\u5f71\u54cd\u6b63\u786e\u63a8\u7406\u8def\u5f84\u7684\u9009\u62e9\u7cbe\u5ea6\uff1b<\/p>\n<\/li>\n<li>\n<p>\u6b63\u786e\u6027\u9608\u503c \u03c4 \uff1a\u8861\u91cf\u63a8\u7406\u7ed3\u679c\u7684\u8d28\u91cf\u8981\u6c42\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>\u5bbd\u5ea6\u6269\u5c55 vs. \u9009\u62e9\u53ef\u9760\u6027\uff1a\u5982\u4f55\u627e\u5230\u5e73\u8861\uff1f<\/strong><\/section>\n<ul>\n<li>\n<p>Pr (\u03c4_select) \uff08\u9009\u62e9\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387\uff09\u4f9d\u8d56\u4e8e\u4ef7\u503c\u51fd\u6570\u7684\u53ef\u9760\u6027\uff0c\u5373 \u03f5_b \u00a0 \u76f8\u5173\u7684\u53c2\u6570\u3002<\/p>\n<\/li>\n<li>\n<p>Pr (\u03c4_generate) \uff08\u751f\u6210\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387\uff09\u53d7 \u63a8\u7406\u8def\u5f84\u957f\u5ea6 L \u548c\u6269\u5c55\u5bbd\u5ea6 k \u5f71\u54cd\u3002<\/p>\n<\/li>\n<li>\n<p>\u901a\u8fc7\u589e\u52a0\u63a8\u7406\u6b65\u9aa4\uff0c\u53ef\u4ee5\u63d0\u5347\u751f\u6210\u6b63\u786e\u63a8\u7406\u7684\u6982\u7387\uff0c\u4f46\u540c\u65f6\u4f1a\u5f15\u5165\u989d\u5916\u7684\u9009\u62e9\u4ee3\u4ef7\uff0c\u589e\u52a0\u9519\u8bef\u6982\u7387\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>\u6162\u601d\u8003\u65b9\u6cd5\u7684\u5173\u952e\u4f18\u5316\u6761\u4ef6<\/strong><\/section>\n<section><\/section>\n<section>\u5bf9\u6bd4\u5f15\u7406 4.4 \u548c\u5b9a\u7406 4.6 \u53d1\u73b0\uff0c\u6162\u601d\u8003\u65b9\u6cd5\u662f\u5426\u6709\u6548\uff0c\u8fd8\u53d6\u51b3\u4e8e\u4ef7\u503c\u51fd\u6570\u7684\u53ef\u9760\u6027\u3002\u4e3a\u4e86\u4fdd\u8bc1\u63a8\u7406\u51c6\u786e\u7387\u7684\u4e0a\u9650\u5f97\u5230\u63d0\u5347\uff0c\u4ef7\u503c\u51fd\u6570\u7684\u53ef\u9760\u6027\u5fc5\u987b\u6ee1\u8db3\uff1a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-29a3e0f5eabb130a9af544dbc94d7c1a.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-29a3e0f5eabb130a9af544dbc94d7c1a.png\"><\/a>\u3002<\/section>\n<section><\/section>\n<section>\u901a\u8fc7\u4e0a\u8ff0\u5206\u6790\uff0c\u7814\u7a76\u8005\u603b\u7ed3\u4e86\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u7684\u6838\u5fc3\u673a\u5236\u3002<strong>\u901a\u8fc7\u589e\u52a0\u63a8\u7406\u8def\u5f84\u7684\u641c\u7d22\u8303\u56f4\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u63d0\u9ad8\u4e86\u751f\u6210\u6b63\u786e\u7b54\u6848\u7684\u6982\u7387\uff0c\u6709\u6548\u51cf\u5c11\u96ea\u7403\u8bef\u5dee\u7684\u7d2f\u79ef\u3002\u540c\u65f6\u5176\u6548\u679c\u6781\u5927\u4f9d\u8d56\u4e8e\u6240\u4f7f\u7528\u7684\u4ef7\u503c\u51fd\u6570\u7684\u53ef\u9760\u6027\uff0c\u8fd9\u4e00\u56e0\u7d20\u76f4\u63a5\u5f71\u54cd\u6574\u4e2a\u65b9\u6cd5\u7684\u6700\u7ec8\u8868\u73b0<\/strong>\u3002<\/section>\n<section><\/section>\n<section><strong>4 \u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u95f4\u7684\u5bf9\u6bd4<\/strong><\/section>\n<section><\/section>\n<section>\u63a5\u4e0b\u6765\uff0c\u7814\u7a76\u8005\u5c06\u5bf9\u6bd4\u7b80\u5355\u548c\u590d\u6742\u7684\u5916\u90e8\u6162\u601d\u8003\u6846\u67b6\u4e4b\u95f4\u7684\u6838\u5fc3\u533a\u522b\uff0c\u5e76\u4ee5\u8457\u540d\u7684 BoN \u548c MCTS \u4e3a\u4f8b\u8fdb\u884c\u5206\u6790\u3002<\/section>\n<section><\/section>\n<section><strong>4.1 BoN \u4e0e MCTS \u6846\u67b6\u4e0b\u7684\u6b63\u786e\u63a8\u7406\u6982\u7387<\/strong><\/section>\n<section><\/section>\n<section>\u5bf9\u4e8e BoN \u6765\u8bf4\uff0c\u7814\u7a76\u8005\u5f88\u65b9\u4fbf\u5730\u5c06\u5176\u5efa\u6a21\u4e3a\u8fdb\u884c N \u6b21\u957f\u5ea6\u4e3a L \u7684\u63a8\u7406\uff0c\u5e76\u6700\u7ec8\u5728 N \u4e2a\u7b54\u6848\u4e2d\u9009\u62e9\u4e00\u6b21\u7684\u8fc7\u7a0b\u3002\u56e0\u6b64\uff0cBoN \u7684\u6b63\u786e\u63a8\u7406\u6982\u7387\u4e0a\u754c\u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-ccea29d51bfd584f61019237f14d9cf1.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-ccea29d51bfd584f61019237f14d9cf1.png\"><\/a><\/section>\n<section>\u5bf9\u4e8e MCTS\uff08RAP \u6a21\u5f0f\uff09\uff0c\u7531\u4e8e\u5176\u673a\u5236\u8f83\u4e3a\u590d\u6742\uff0c\u7814\u7a76\u8005\u8003\u8651\u5176\u6700\u597d\u548c\u6700\u574f\u7684\u60c5\u51b5\u3002\u5728\u6700\u597d\u7684\u60c5\u51b5\u4e0b\uff0cMCTS \u7684\u6bcf\u6b21\u8282\u70b9\u6269\u5c55\u65f6\u90fd\u53d1\u751f\u5728\u6700\u6df1\u7684\u53f6\u5b50\u8282\u70b9\u4e0a\uff0c\u5219\u5b83\u9000\u5316\u6210\u4e86\u4e00\u4e2a\u91c7\u6837\u5bbd\u5ea6\u548c\u4fdd\u7559\u5bbd\u5ea6\u90fd\u4e3a b \u7684 Beam Search\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-2a68764b1c63982ed174465b4290af7e.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-2a68764b1c63982ed174465b4290af7e.png\"><\/a><\/section>\n<section>\u800c\u5728\u6700\u5dee\u60c5\u51b5\uff0cMCTS \u9700\u8981\u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u8282\u70b9\uff0c\u4ece\u800c\u5f62\u6210\u4e00\u68f5\u5b8c\u5168 b &#8211; \u53c9\u6811\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-e9c73ced056cca283e3766b463c8970b.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-e9c73ced056cca283e3766b463c8970b.png\"><\/a><\/section>\n<section><strong>4.2 \u5bf9\u6bd4 BoN \u4e0e MCTS \u7684\u603b\u63a8\u7406\u4ee3\u4ef7<\/strong><\/section>\n<section><\/section>\n<section>\u53ef\u4ee5\u770b\u51fa\uff0cMCTS \u7531\u4e8e\u9700\u8981\u8c03\u7528\u66f4\u591a\u6b21\u7684\u9009\u62e9\u8fc7\u7a0b\uff0c\u4e00\u822c\u4f1a\u6bd4 BoN \u5bf9\u4e8e\u4ef7\u503c\u51fd\u6570\u6709\u66f4\u9ad8\u7684\u654f\u611f\u6027\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u5728\u5047\u8bbe\u4ef7\u503c\u51fd\u6570\u5b8c\u7f8e\uff08\u03f5_b=1\uff09\u7684\u60c5\u51b5\u4e0b\uff0c\u7814\u7a76\u8005\u5bf9\u9f50\u6982\u7387\u4e0a\u754c\u4e2d\u7684\u5176\u4f59\u90e8\u5206\uff0c\u53ef\u4ee5\u8ba1\u7b97\u51fa\u5f53 BoN \u548c MCTS \u5177\u6709\u76f8\u5f53\u7684\u6b63\u786e\u63a8\u7406\u6982\u7387\u4e0a\u754c\u65f6\uff0c\u6240\u9700\u8981\u5177\u5907\u7684\u603b\u63a8\u7406\u4ee3\u4ef7\u7684\u89c4\u6a21\uff0c\u5982\u56fe\u8868 3 \u6240\u793a\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-ec29be757b57c2156e0d699351a4aced.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-ec29be757b57c2156e0d699351a4aced.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe\u8868 3: \u76f8\u540c\u63a8\u7406\u6b63\u786e\u6982\u7387\u4e0b BoN \u4e0e MCTS \u603b\u63a8\u7406\u4ee3\u4ef7\u89c4\u6a21\u5bf9\u6bd4<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u7ed3\u679c\u8868\u660e\uff0c\u5f53 BoN \u4e0e MCTS \u5728\u63a8\u7406\u6b63\u786e\u7387\u4e0a\u76f8\u5f53\u65f6\uff0cBoN \u7684\u603b\u63a8\u7406\u6210\u672c\u4e0e MCTS \u63a5\u8fd1\u3002<\/section>\n<ul>\n<li>\n<p>\u6700\u4f18\u60c5\u51b5\u4e0b\uff1aBoN \u4e0e MCTS \u7684\u63a8\u7406\u6210\u672c\u8d8b\u8fd1\u76f8\u7b49\uff1b<\/p>\n<\/li>\n<li>\n<p>\u6700\u5dee\u60c5\u51b5\u4e0b\uff1a\u5f53\u63a8\u7406\u6b65\u6570 L \u00a0\u8f83\u5c0f\u65f6\uff0cBoN \u7684\u6210\u672c\u53ef\u80fd\u7565\u9ad8\u4e8e MCTS\uff0c\u4f46\u4ecd\u4fdd\u6301\u5728\u5408\u7406\u8303\u56f4\u5185\u3002\u5f53 L \u589e\u52a0\uff0cBoN \u7684\u63a8\u7406\u6210\u672c\u751a\u81f3\u53ef\u80fd\u4f4e\u4e8e MCTS\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>\u8fd9\u4e00\u7ed3\u8bba\u8868\u660e\uff0c\u63a8\u7406\u6210\u672c\u662f\u51b3\u5b9a\u51cf\u5c11\u96ea\u7403\u8bef\u5dee\u6548\u679c\u7684\u5173\u952e\u56e0\u7d20<\/strong>\uff0c\u800c\u5177\u4f53\u91c7\u7528\u54ea\u79cd\u6162\u601d\u8003\u6846\u67b6\uff08\u5982 BoN \u6216 MCTS\uff09\u5bf9\u6700\u7ec8\u7ed3\u679c\u7684\u5f71\u54cd\u7406\u8bba\u4e0a\u53ef\u80fd\u662f\u8f83\u5c0f\u7684\u3002<\/section>\n<section><\/section>\n<section><strong>4.3 \u5b9e\u9a8c\u9a8c\u8bc1<\/strong><\/section>\n<section><\/section>\n<section>\u5728 GSM8k \u548c PrOntoQA \u4e24\u4e2a\u63a8\u7406\u4efb\u52a1\u4e0a\uff0c\u5b9e\u8bc1\u5bf9\u6bd4\u4e86 BoN \u548c MCTS \u7684\u63a8\u7406\u51c6\u786e\u6027\u3002\u7814\u7a76\u8005\u91c7\u7528 [14] \u63a8\u8350\u7684 MCTS \u4f18\u5316\u914d\u7f6e\uff0c\u5e76\u8ba1\u7b97\u76f8\u5e94\u7684 N \u503c\uff0c\u4f7f BoN \u7684\u63a8\u7406\u6210\u672c\u4e0e MCTS \u5c3d\u53ef\u80fd\u63a5\u8fd1\u3002\u7531\u4e8e\u4e24\u79cd\u65b9\u6cd5\u751f\u6210\u63a8\u7406\u8def\u5f84\u7684\u65b9\u5f0f\u4e0d\u540c\uff0c\u5b8c\u5168\u5bf9\u9f50\u5e76\u4e0d\u73b0\u5b9e\uff0c\u56e0\u6b64\u7814\u7a76\u8005\u5b9a\u4e49\u5408\u7406\u7684 N \u503c\u533a\u95f4\uff1a<\/section>\n<section><\/section>\n<section><strong>N \u5408\u7406\u8303\u56f4\u7684\u4e0b\u754c\u4e0e\u4e0a\u754c\uff1a<\/strong><\/section>\n<ul>\n<li>\n<p>N \u0303_res \uff1a\u5bf9\u9f50\u63a8\u7406\u6b65\u6570\u7684 N \u503c<\/p>\n<\/li>\n<li>\n<p>N \u0303_call \uff1a\u5bf9\u9f50 LLM \u8c03\u7528\u6b21\u6570\u7684 N \u503c<\/p>\n<\/li>\n<\/ul>\n<section>\u7814\u7a76\u8005\u6d4b\u8bd5\u4e86 <strong>BoN \u7684\u4e09\u79cd\u9009\u62e9\u7b56\u7565<\/strong>\uff1a<\/section>\n<ul>\n<li>\n<p><strong>Self-Consistency<\/strong>\uff08\u81ea\u6d3d\u6027\u9009\u62e9\uff09<\/p>\n<\/li>\n<li>\n<p><strong>ORM Vote<\/strong>\uff08\u57fa\u4e8e\u5956\u52b1\u6a21\u578b\u7684\u6295\u7968\u9009\u62e9\uff09<\/p>\n<\/li>\n<li>\n<p><strong>ORM Max<\/strong>\uff08\u57fa\u4e8e\u5956\u52b1\u6a21\u578b\u7684\u6700\u5927\u503c\u9009\u62e9\uff09<\/p>\n<\/li>\n<\/ul>\n<section>\u5b9e\u9a8c\u7ed3\u679c\u5982\u56fe\u8868 4 \u6240\u793a\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a363799dbb5d83e65977dcaa2f73dcdb.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a363799dbb5d83e65977dcaa2f73dcdb.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe\u8868 4: GSM8k \u548c PrOntoQA \u4e0a BoN \u4e0e MCTS \u7684\u51c6\u786e\u6027\u5bf9\u6bd4<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u7814\u7a76\u8005\u53ef\u4ee5\u5f97\u51fa\u5982\u4e0b\u7ed3\u8bba\uff1a<\/section>\n<section><\/section>\n<section><strong>\u4e0d\u540c\u4efb\u52a1\u4e0b\u7684 BoN \u8868\u73b0<\/strong><\/section>\n<ul>\n<li>\n<p>PrOntoQA\uff08\u4e8c\u5206\u7c7b\u4efb\u52a1\uff1aTrue\/False\uff09\uff1a<\/p>\n<\/li>\n<li>\n<p>\u7531\u4e8e\u7b54\u6848\u56fa\u5b9a\uff0c\u589e\u52a0 N \u5e76\u4e0d\u4f1a\u63d0\u5347 Self-Consistency \u7b56\u7565\u4e0b\u7684 BoN \u6027\u80fd\uff0c\u9664\u975e\u5f15\u5165\u5956\u52b1\u6a21\u578b\u3002<\/p>\n<\/li>\n<li>\n<p>GSM8k\uff08\u591a\u6b65\u63a8\u7406\u4efb\u52a1\uff09\uff1a<\/p>\n<\/li>\n<li>\n<p>\u7531\u4e8e\u7b54\u6848\u591a\u6837\uff0c\u589e\u52a0 N \u5373\u4f7f\u5728\u6ca1\u6709\u5956\u52b1\u6a21\u578b\u7684\u60c5\u51b5\u4e0b\uff0c\u4e5f\u80fd\u63d0\u5347 BoN \u7684\u6027\u80fd\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>BoN \u4e0e MCTS \u7684\u5173\u952e\u5bf9\u6bd4<\/strong><\/section>\n<ul>\n<li>\n<p>ORM Vote &amp; ORM Max \u7b56\u7565\uff08\u7ed3\u5408\u5956\u52b1\u6a21\u578b\uff09\uff1a\u5f53 N \u5728 N \u0303_res \u548c N \u0303_call \u4e4b\u95f4\u65f6\uff0cBoN \u80fd\u591f\u8fbe\u5230\u4e0e MCTS \u76f8\u5f53\u7684\u63a8\u7406\u6027\u80fd\uff1b<\/p>\n<\/li>\n<li>\n<p>N \u63a5\u8fd1 N \u0303_res \u65f6\uff0cBoN \u7565\u4f4e\u4e8e MCTS\uff0c\u4f46\u5dee\u8ddd\u4e0d\u5927\uff1b<\/p>\n<\/li>\n<li>\n<p>N \u53d6\u66f4\u5927\u503c\u65f6\uff0cBoN \u80fd\u591f\u5339\u654c\u751a\u81f3\u8d85\u8d8a MCTS\uff0c\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86 MCTS \u5728 LLM \u63a8\u7406\u4e2d\u7684\u5c40\u9650\u6027\uff0c\u5e76\u652f\u6301\u7814\u7a76\u8005\u7684\u7406\u8bba\u5206\u6790\u3002<\/p>\n<\/li>\n<\/ul>\n<section><strong>\u672c\u5b9e\u9a8c\u8868\u660e\uff0c\u5728\u5408\u7406\u7684 N \u503c\u8303\u56f4\u5185\uff0cBoN \u901a\u8fc7\u9002\u5f53\u8c03\u6574\u63a8\u7406\u5bbd\u5ea6\uff0c\u53ef\u4ee5\u8fbe\u5230\u751a\u81f3\u8d85\u8d8a MCTS \u7684\u63a8\u7406\u6548\u679c\uff0c\u8fd9\u4e0e\u7814\u7a76\u8005\u7684\u7406\u8bba\u5206\u6790\u4e00\u81f4<\/strong>\u3002<\/section>\n<section><\/section>\n<section><strong>5 \u5c0f\u7ed3<\/strong><\/section>\n<section><\/section>\n<section>\u672c\u7814\u7a76\u5206\u6790\u4e86\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u7684\u6709\u6548\u6027\u673a\u5236\uff0c\u5e76\u901a\u8fc7\u4fe1\u606f\u8bba\u5efa\u7acb\u4e86 LLM \u63a8\u7406\u4e2d\u7684\u96ea\u7403\u8bef\u5dee\u4e0e\u63a8\u7406\u9519\u8bef\u4e4b\u95f4\u7684\u8054\u7cfb\u3002\u7814\u7a76\u8868\u660e\uff0c\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u901a\u8fc7\u6269\u5c55\u63a8\u7406\u7a7a\u95f4\u53ef\u4ee5\u51cf\u5c11\u63a8\u7406\u9519\u8bef\uff0c\u4f46\u540c\u65f6\u589e\u52a0\u4e86\u63a8\u7406\u6210\u672c\uff0c\u9700\u8981\u5728\u6b63\u786e\u6027\u548c\u8ba1\u7b97\u5f00\u9500\u4e4b\u95f4\u6743\u8861\u3002<\/section>\n<section><\/section>\n<section>\u5bf9\u6bd4 BoN \u548c MCTS \u7b49\u65b9\u6cd5\u540e\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u5f71\u54cd\u5176\u6709\u6548\u6027\u7684\u6838\u5fc3\u56e0\u7d20\u662f\u5956\u52b1\u51fd\u6570\u7684\u80fd\u529b\u548c\u63a8\u7406\u603b\u6210\u672c\uff0c\u800c\u5177\u4f53\u7684\u641c\u7d22\u6846\u67b6\u5f71\u54cd\u8f83\u5c0f\u3002\u56e0\u6b64\uff0c\u4f18\u5316\u5956\u52b1\u51fd\u6570\u548c\u63d0\u5347\u7b56\u7565\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u662f\u672a\u6765\u6539\u8fdb\u5916\u90e8\u6162\u601d\u8003\u65b9\u6cd5\u7684\u5173\u952e\u65b9\u5411\u3002<\/section>\n<section><\/section>\n<section><strong><sup>\u53c2\u8003\u6587\u732e<\/sup><\/strong><\/section>\n<section><sup><em>[1] Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., &#8230; &amp; Amodei, D. (2020). Scaling laws for neural language models. arXiv preprint arXiv:2001.08361.<\/em><\/sup><\/section>\n<section><sup><em>[2] Yuan, Z., Yuan, H., Li, C., Dong, G., Tan, C., &amp; Zhou, C. (2023). Scaling relationship on learning mathematical reasoning with large language models. arXiv preprint arXiv:2308.01825.<\/em><\/sup><\/section>\n<section><sup><em>[3] Snell, C., Lee, J., Xu, K., &amp; Kumar, A. (2024). Scaling llm test-time compute optimally can be more effective than scaling model parameters. arXiv preprint arXiv:2408.03314.<\/em><\/sup><\/section>\n<section><sup><em>[4] OpenAI. Learning to reason with llms, 2024. URL https:\/\/openai.com\/index\/learning-to-reason-with-llms\/. Accessed: September 12, 2024.\u00a0<\/em><\/sup><\/section>\n<section><sup><em>[5] DeepSeek-AI. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning, 2025. URL https:\/\/arxiv.org\/abs\/2501.12948.<\/em><\/sup><\/section>\n<section><sup><em>[6] Team, Q. Qwq: Reflect deeply on the boundaries of the unknown, November 2024b. URL https:\/\/qwenlm. github.io\/blog\/qwq-32b-preview\/.<\/em><\/sup><\/section>\n<section><sup><em>[7] Lightman, H., Kosaraju, V., Burda, Y., Edwards, H., Baker, B., Lee, T., &#8230; &amp; Cobbe, K. (2023). Let&#8217;s verify step by step. arXiv preprint arXiv:2305.20050.\u00a0<\/em><\/sup><\/section>\n<section><sup><em>[8] Brown, B., Juravsky, J., Ehrlich, R., Clark, R., Le, Q. V., R\u00e9, C., &amp; Mirhoseini, A. (2024). Large language monkeys: Scaling inference compute with repeated sampling. arXiv preprint arXiv:2407.21787.<\/em><\/sup><\/section>\n<section><sup><em>[9] \u00a0Cobbe, K., Kosaraju, V., Bavarian, M., Chen, M., Jun, H., Kaiser, L., &#8230; &amp; Schulman, J. (2021). Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168.<\/em><\/sup><\/section>\n<section><sup><em>[10] Wei, J., Wang, X., Schuurmans, D., Bosma, M., Xia, F., Chi, E., &#8230; &amp; Zhou, D. (2022). Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35, 24824-24837.<\/em><\/sup><\/section>\n<section><sup><em>[11] Yao, S., Yu, D., Zhao, J., Shafran, I., Griffiths, T., Cao, Y., &amp; Narasimhan, K. (2024). Tree of thoughts: Deliberate problem solving with large language models. Advances in Neural Information Processing Systems, 36.\u00a0<\/em><\/sup><\/section>\n<section><sup><em>[12] Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., Van Den Driessche, G., &#8230; &amp; Hassabis, D. (2016). Mastering the game of Go with deep neural networks and tree search. nature, 529 (7587), 484-489.<\/em><\/sup><\/section>\n<section><sup><em>[13] Zhang, D., Zhoubian, S., Yue, Y., Dong, Y., &amp; Tang, J. (2024). ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search. arXiv preprint arXiv:2406.03816.<\/em><\/sup><\/section>\n<section><sup><em>[14] Feng, X., Wan, Z., Wen, M., Wen, Y., Zhang, W., &amp; Wang, J. (2023). Alphazero-like tree-search can guide large language model decoding and training. arXiv preprint arXiv:2309.17179.<\/em><\/sup><\/section>\n<section><sup><em>[15] Bachmann, G., &amp; Nagarajan, V. (2024). The pitfalls of next-token prediction. arXiv preprint arXiv:2403.06963.<\/em><\/sup><\/section>\n<section><em><sup>[16] Ton, J. F., Taufiq, M. F., &amp; Liu, Y. (2024). Understanding Chain-of-Thought in LLMs through Information Theory. arXiv preprint arXiv:2411.11984.<\/sup><\/em><\/section>\n<section><\/section>\n<section><strong>\u4f5c\u8005\u4ecb\u7ecd<\/strong><\/section>\n<section><\/section>\n<section>\u5218\u52c7\uff0c\u4e2d\u56fd\u4eba\u6c11\u5927\u5b66\uff0c\u957f\u8058\u526f\u6559\u6388\uff0c\u535a\u58eb\u751f\u5bfc\u5e08\uff0c\u56fd\u5bb6\u7ea7\u9ad8\u5c42\u6b21\u9752\u5e74\u4eba\u624d\u3002\u957f\u671f\u4ece\u4e8b\u673a\u5668\u5b66\u4e60\u57fa\u7840\u7406\u8bba\u7814\u7a76\uff0c\u5171\u53d1\u8868\u8bba\u6587 100 \u4f59\u7bc7\uff0c\u5176\u4e2d\u4ee5\u7b2c\u4e00\u4f5c\u8005 \/ \u901a\u8baf\u4f5c\u8005\u53d1\u8868\u9876\u7ea7\u671f\u520a\u548c\u4f1a\u8bae\u8bba\u6587\u8fd1 50 \u7bc7\uff0c\u6db5\u76d6\u673a\u5668\u5b66\u4e60\u9886\u57df\u9876\u7ea7\u671f\u520a JMLR\u3001IEEE TPAMI\u3001Artificial Intelligence \u548c\u9876\u7ea7\u4f1a\u8bae ICML\u3001NeurIPS \u7b49\u3002\u83b7\u4e2d\u56fd\u4eba\u6c11\u5927\u5b66\u300c\u6770\u51fa\u5b66\u8005\u300d\u3001\u4e2d\u56fd\u79d1\u5b66\u9662\u300c\u9752\u5e74\u521b\u65b0\u4fc3\u8fdb\u4f1a\u300d\u6210\u5458\u3001\u4e2d\u56fd\u79d1\u5b66\u9662\u4fe1\u606f\u5de5\u7a0b\u7814\u7a76\u6240\u300c\u5f15\u8fdb\u4f18\u9752\u300d\u7b49\u79f0\u53f7\u3002\u4e3b\u6301\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u9762\u4e0a \/ \u57fa\u91d1\u9752\u5e74\u3001\u5317\u4eac\u5e02\u9762\u4e0a\u9879\u76ee\u3001\u4e2d\u79d1\u9662\u57fa\u7840\u524d\u6cbf\u79d1\u5b66\u7814\u7a76\u8ba1\u5212\u3001\u817e\u8baf\u7280\u725b\u9e1f\u57fa\u91d1\u3001CCF &#8211; 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