{"id":37682,"date":"2025-02-02T12:00:59","date_gmt":"2025-02-02T04:00:59","guid":{"rendered":"https:\/\/17aitech.com\/?p=37682"},"modified":"2025-02-02T12:00:59","modified_gmt":"2025-02-02T04:00:59","slug":"%e8%ae%a97b%e5%8d%83%e9%97%ae%e6%a8%a1%e5%9e%8b%e8%b6%85%e8%b6%8ao1%ef%bc%8c%e5%be%ae%e8%bd%afrstar-math%e6%83%8a%e8%89%b3%e7%99%bb%e5%9c%ba%ef%bc%8c%e7%bd%91%e5%8f%8b%e7%9b%9b%e8%b5%9e","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=37682","title":{"rendered":"\u8ba97B\u5343\u95ee\u6a21\u578b\u8d85\u8d8ao1\uff0c\u5fae\u8f6frStar-Math\u60ca\u8273\u767b\u573a\uff0c\u7f51\u53cb\u76db\u8d5e"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-01-10-6\" target=\"_blank\">\u8ba97B\u5343\u95ee\u6a21\u578b\u8d85\u8d8ao1\uff0c\u5fae\u8f6frStar-Math\u60ca\u8273\u767b\u573a\uff0c\u7f51\u53cb\u76db\u8d5e<\/a><\/p>\n<p>OpenAI o1 \u7ed9\u5927\u6a21\u578b\u89c4\u6a21\u6269\u5c55 vs \u6027\u80fd\u7684\u66f2\u7ebf\u5e26\u6765\u4e86\u4e00\u6b21\u4e0a\u7fd8\u3002\u5b83\u5728\u5927\u6a21\u578b\u9886\u57df\u91cd\u73b0\u4e86\u5f53\u5e74 AlphaGo \u5f3a\u5316\u5b66\u4e60\u7684\u6210\u529f \u2014\u2014 \u7ed9\u8d8a\u591a\u7b97\u529b\uff0c\u5c31\u8f93\u51fa\u8d8a\u591a\u667a\u80fd\uff0c\u4e00\u76f4\u5230\u8d85\u8d8a\u4eba\u7c7b\u6c34\u5e73\u3002<\/p>\n<p>\u4f46\u8fd9\u79cd\u7a81\u7834\u80cc\u540e\u662f\u5e9e\u5927\u7684\u7b97\u529b\u652f\u6301\u4e0e\u63a8\u7406\u5f00\u9500\uff1aAPI \u7684\u4ef7\u683c\u4e0a\uff0co1-preview \u6bcf\u767e\u4e07\u8f93\u5165 15 \u7f8e\u5143\uff0c\u6bcf\u767e\u4e07\u8f93\u51fa 60 \u7f8e\u5143\uff0c\u800c\u6700\u65b0\u7248\u7684 o3 \u5728\u5904\u7406\u590d\u6742\u63a8\u7406\u4efb\u52a1\u65f6\uff0c\u5355\u6b21\u6210\u672c\u66f4\u662f\u9ad8\u8fbe\u6570\u5343\u7f8e\u5143\u3002<\/p>\n<p>\u4e1a\u754c\u4e00\u76f4\u5728\u5bfb\u627e\u4e00\u4e2a\u66f4\u7ecf\u6d4e\u3001\u66f4\u9ad8\u6548\u7684\u89e3\u51b3\u65b9\u6848\u3002\u800c\u8fd9\u4e2a\u7b54\u6848\u53ef\u80fd\u6bd4\u9884\u671f\u6765\u5f97\u66f4\u5feb\u4e00\u4e9b\u3002<\/p>\n<p>\u4eca\u5929\u767b\u9876 Hugging Face \u70ed\u95e8\u699c\u4e00\u7684\u8bba\u6587\u5c55\u793a\u4e86\u5c0f\u6a21\u578b\u7684\u6f5c\u529b\u3002\u6765\u81ea\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u56e2\u961f\u63d0\u51fa\u4e86 <strong>rStar-Math<\/strong>\u3002rStar-Math \u5411\u6211\u4eec\u8bc1\u660e\uff0c1.5B \u5230 7B \u89c4\u6a21\u7684\u5c0f\u578b\u8bed\u8a00\u6a21\u578b\uff08SLM\uff09\u65e0\u9700\u4ece\u66f4\u5927\u6a21\u578b\u84b8\u998f\uff0c\u5c31\u80fd\u5728\u6570\u5b66\u63a8\u7406\u80fd\u529b\u4e0a\u5ab2\u7f8e\u751a\u81f3\u8d85\u8d8a OpenAI o1\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-14230a2be63409aa0df796b45a8d09f3.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-14230a2be63409aa0df796b45a8d09f3.png\"><\/a><\/section>\n<ul>\n<li>\n<section>\u8bba\u6587\u6807\u9898\uff1arStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking<\/section>\n<\/li>\n<li>\n<section>\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/pdf\/2501.04519<\/section>\n<\/li>\n<li>\n<section>Github \u94fe\u63a5\uff1ahttps:\/\/github.com\/microsoft\/rStar\uff08\u5373\u5c06\u5f00\u6e90\uff09<\/section>\n<\/li>\n<\/ul>\n<section><\/section>\n<section>\u7ecf\u8fc7 4 \u8f6e\u81ea\u6211\u8fdb\u5316\uff0c\u5438\u7eb3\u4e86 747k \u6570\u5b66\u95ee\u9898\u5408\u6210\u7684\u6570\u767e\u4e07\u6570\u636e\uff0crStar-Math \u5c06 SLM \u7684\u6570\u5b66\u63a8\u7406\u80fd\u529b\u63d0\u5347\u5230\u4e86\u6700\u5148\u8fdb\u6c34\u5e73\u3002<\/section>\n<section><\/section>\n<section>\u4f8b\u5982\uff0c\u5728 MATH \u57fa\u51c6\u6d4b\u8bd5\u4e0a\uff0c\u5b83\u5c06 Qwen2.5-Math-7B \u7684\u6210\u7ee9\u4ece 58.8% \u63d0\u5347\u5230\u4e86 90.0%\uff0c\u5c06 Phi3-mini-3.8B \u7684\u6b63\u786e\u7387\u4ece 41.4% \u63d0\u5347\u5230\u4e86 86.4%\uff0c\u5206\u522b\u8d85\u8fc7\u4e86 o1-preview 4.5% \u548c 0.9%\u3002<\/section>\n<section><\/section>\n<section>\u62c9\u5230\u7f8e\u56fd\u6570\u5b66\u5965\u6797\u5339\u514b\uff08AIME\uff09\u7684\u8003\u573a\u4e0a\uff0c15 \u9053\u9898\uff0crStar-Math \u80fd\u591f\u505a\u5bf9 8 \u9053\uff0c\u5728\u6700\u4f18\u79c0\u7684\u9ad8\u4e2d\u6570\u5b66\u7ade\u8d5b\u751f\u4e2d\u4e5f\u80fd\u6392\u5230\u524d 20%\u3002<\/section>\n<section><\/section>\n<section>\u66f4\u91cd\u8981\u7684\u662f\uff0c\u4ed6\u4eec<strong>\u53ea\u82b1\u4e86 60 \u5757 A100 \u5c31\u8fbe\u5230\u4e86\u5982\u6b64\u6548\u679c<\/strong>\uff0c\u9879\u76ee\u548c\u4ee3\u7801\u5373\u5c06\u5f00\u6e90\u3002<\/section>\n<section><\/section>\n<section>AI \u6295\u8d44\u4eba Chetan Puttagunta \u9510\u8bc4\uff1a\u300c\u5bf9\u521b\u4e1a\u516c\u53f8\u6765\u8bf4\uff0c\u8fd9\u5c06\u662f\u4e00\u4e2a\u7edd\u4f73\u7684\u673a\u4f1a\uff01\u300d<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-5222b13c1b5bb4c68e4b6bf74fd7adad.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-5222b13c1b5bb4c68e4b6bf74fd7adad.png\"><\/a><\/section>\n<section>\u5f53\u5982\u6b64\u5f3a\u5927\u7684\u63a8\u7406\u80fd\u529b\u53ef\u4ee5\u7528\u66f4\u4f4e\u7684\u6210\u672c\u5b9e\u73b0\u65f6\uff0cKeras \u521b\u59cb\u4eba Fran\u00e7ois Chollet \u4e5f\u611f\u53f9\u9053\uff1a\u300c2025 \u5e74\u5c06\u662f\u5f00\u6e90 o3 \u590d\u523b\u4e4b\u5e74\u3002\u300d<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-a9a208981dfb9ac1302dd34d38e8a10b.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-a9a208981dfb9ac1302dd34d38e8a10b.png\"><\/a><\/section>\n<section>\u5b66\u672f\u5708\u7684\u4eba\u5bf9 rStar-Math \u7684\u6b23\u8d4f\uff0c\u8868\u8fbe\u8d77\u6765\u5c31\u76f4\u767d\u591a\u4e86\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-b6793868dd61a5c30946d172baea8ce3.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-b6793868dd61a5c30946d172baea8ce3.png\"><\/a><\/section>\n<section>\u53d1\u5e03\u4e0d\u5230 20 \u4e2a\u5c0f\u65f6\uff0c\u751a\u81f3\u5c31\u5df2\u7ecf\u6709\u4eba\u4e13\u95e8\u505a\u4e86\u4e00\u671f\u89c6\u9891\u6765\u6df1\u5ea6\u89e3\u8bfb\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-24180dd635fb45e0cbf0f13af86fa30d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-24180dd635fb45e0cbf0f13af86fa30d.png\"><\/a><\/section>\n<ul>\n<li>\n<section>\u89c6\u9891\u94fe\u63a5\uff1ahttps:\/\/www.youtube.com\/watch?v=cHgHS6Y3QP0<\/section>\n<\/li>\n<\/ul>\n<section><\/section>\n<section>\u4ece\u6280\u672f\u5c42\u9762\u6765\u8bf4\uff0crStar-Math \u5f15\u5165\u4e86\u4e00\u79cd<strong>\u53ef\u4ee5\u81ea\u5df1\u8fdb\u5316\u7684 System 2 \u63a8\u7406\u65b9\u6cd5<\/strong>\uff0c\u901a\u8fc7\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\uff08MCTS\uff09\u6765\u5b9e\u73b0\u300c\u6df1\u5ea6\u601d\u8003\u300d\u80fd\u529b\u3002\u5728\u6d4b\u8bd5\u9636\u6bb5\uff0c\u5b83\u4f1a\u5728\u5956\u52b1\u6a21\u578b\u7684\u6307\u5bfc\u4e0b\uff0c\u8ba9\u6570\u5b66\u7b56\u7565\u6a21\u578b\u8fdb\u884c\u641c\u7d22\u63a8\u7406\u3002<\/section>\n<section><\/section>\n<section>\u5177\u4f53\u6765\u770b\uff0c\u5728 MCTS \u4e2d\uff0c\u6570\u5b66\u95ee\u9898\u6c42\u89e3\u88ab\u5206\u89e3\u4e3a\u591a\u6b65\u751f\u6210\u3002\u6bcf\u4e00\u6b65\u90fd\u5c06\u4f5c\u4e3a\u7b56\u7565\u6a21\u578b\u7684 SLM \u91c7\u6837\u5019\u9009\u8282\u70b9\u3002\u6bcf\u4e2a\u8282\u70b9\u751f\u6210\u4e00\u6b65 CoT \u548c\u76f8\u5e94\u7684 Python \u4ee3\u7801\u3002\u4e3a\u9a8c\u8bc1\u751f\u6210\u8d28\u91cf\uff0c\u53ea\u4fdd\u7559 Python \u4ee3\u7801\u6267\u884c\u6210\u529f\u7684\u8282\u70b9\uff0c\u4ece\u800c\u51cf\u5c11\u4e2d\u95f4\u6b65\u9aa4\u7684\u9519\u8bef\u3002<\/section>\n<section><\/section>\n<section>\u6b64\u5916\uff0c\u5927\u91cf MCTS rollout \u57fa\u4e8e\u6bcf\u4e2a\u4e2d\u95f4\u6b65\u9aa4\u7684\u8d21\u732e\u81ea\u52a8\u5206\u914d Q \u503c\uff1a\u5bf9\u6b63\u786e\u7b54\u6848\u8d21\u732e\u66f4\u591a\u7684\u6b65\u9aa4\u83b7\u5f97\u66f4\u9ad8 Q \u503c\uff0c\u88ab\u8ba4\u4e3a\u8d28\u91cf\u66f4\u9ad8\u3002\u8fd9\u786e\u4fdd\u4e86 SLM \u751f\u6210\u7684\u662f\u6b63\u786e\u3001\u9ad8\u8d28\u91cf\u7684\u63a8\u7406\u8f68\u8ff9\u3002<\/section>\n<section><\/section>\n<section>\u7531\u4e8e rStar-Math \u7684\u603b\u4f53\u67b6\u6784\u6d89\u53ca\u4e24\u4e2a SLM\uff0c\u4e00\u4e2a\u662f\u6570\u5b66\u7b56\u7565\u6a21\u578b\uff0c\u4e00\u4e2a\u662f\u5956\u52b1\u6a21\u578b\uff0c\u8be5\u56e2\u961f\u5f15\u5165\u4e86\u4e09\u4e2a\u5173\u952e\u521b\u65b0\uff1a<\/section>\n<ol>\n<li>\n<p>\u521b\u65b0\u7684\u4ee3\u7801\u589e\u5f3a CoT \u6570\u636e\u5408\u6210\u65b9\u6cd5\uff0c\u901a\u8fc7\u5927\u91cf MCTS rollout \u751f\u6210\u7ecf\u8fc7\u9a8c\u8bc1\u7684\u9010\u6b65\u63a8\u7406\u8f68\u8ff9\uff0c\u7528\u4e8e\u8bad\u7ec3\u7b56\u7565 SLM\uff1b<\/p>\n<\/li>\n<li>\n<p>\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u8bad\u7ec3\u65b9\u6cd5\u4e5f\u6709\u6240\u6539\u8fdb\uff0c\u907f\u514d\u4e86\u7b80\u5355\u7684\u6b65\u7ea7\u5206\u6570\u6807\u6ce8\uff0c\u63d0\u5347\u4e86\u8fc7\u7a0b\u504f\u597d\u6a21\u578b\uff08PPM\uff09\u7684\u8bc4\u4f30\u6548\u679c\uff1b<\/p>\n<\/li>\n<li>\n<p>\u6a21\u578b\u4f1a\u81ea\u6211\u8fdb\u5316\uff0c\u91c7\u7528\u5b8c\u5168\u81ea\u4e3b\u8bad\u7ec3\u65b9\u6848\uff0c\u4ece\u96f6\u5f00\u59cb\u6784\u5efa\u5e76\u8bad\u7ec3\u6a21\u578b\uff0c\u901a\u8fc7\u6301\u7eed\u7684\u8fed\u4ee3\u4f18\u5316\u6765\u4e0d\u65ad\u63d0\u5347\u63a8\u7406\u80fd\u529b\u3002<\/p>\n<\/li>\n<\/ol>\n<section><strong>\u65b9\u6cd5<\/strong><\/section>\n<section><\/section>\n<section>\u8be5\u7814\u7a76\u7684\u76ee\u6807\u662f\u8bad\u7ec3\u6570\u5b66\u7b56\u7565 SLM \u548c\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b (PRM)\uff0c\u5e76\u5c06\u4e24\u8005\u96c6\u6210\u5230\u8499\u7279\u5361\u7f57\u6811\u641c\u7d22 (MCTS) \u4e2d\u4ee5\u5b9e\u73b0 System 2 \u6df1\u5ea6\u601d\u8003\u3002<\/section>\n<section><\/section>\n<section>\u9009\u62e9 MCTS \u6709\u4e24\u4e2a\u4e3b\u8981\u539f\u56e0\u3002<\/section>\n<section><\/section>\n<section>\u9996\u5148\uff0c\u5b83\u5c06\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u5206\u89e3\u4e3a\u66f4\u7b80\u5355\u7684\u5355\u6b65\u751f\u6210\u4efb\u52a1\uff0c\u4e0e Best-of-N \u6216 self-consistency \u7b49\u5176\u4ed6 System 2 \u65b9\u6cd5\u76f8\u6bd4\uff0cMCTS \u964d\u4f4e\u4e86\u7b56\u7565 SLM \u7684\u96be\u5ea6\u3002<\/section>\n<section><\/section>\n<section>\u5176\u6b21\uff0cMCTS \u4e2d\u7684\u9010\u6b65\u751f\u6210\u4f1a\u81ea\u7136\u4ea7\u751f\u4e24\u4e2a\u6a21\u578b\u7684 step-level \u8bad\u7ec3\u6570\u636e\u3002\u6807\u51c6 MCTS rollout \u4f1a\u6839\u636e\u6bcf\u4e2a\u6b65\u9aa4\u5bf9\u6700\u7ec8\u6b63\u786e\u7b54\u6848\u7684\u8d21\u732e\u81ea\u52a8\u4e3a\u6bcf\u4e2a\u6b65\u9aa4\u5206\u914d Q \u503c\uff0c\u4ece\u800c\u65e0\u9700\u4eba\u5de5\u751f\u6210\u6b65\u9aa4\u7ea7\u6ce8\u91ca\u6765\u8fdb\u884c\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u8bad\u7ec3\u3002<\/section>\n<section><\/section>\n<section>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0cGPT-4 \u7b49\u9ad8\u7ea7 LLM \u53ef\u4ee5\u96c6\u6210\u5230 MCTS \u4e2d\u4ee5\u751f\u6210\u8bad\u7ec3\u6570\u636e\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u65b9\u6cd5\u9762\u4e34\u4e24\u4e2a\u5173\u952e\u6311\u6218\u3002\u9996\u5148\uff0c\u5373\u4f7f\u662f\u5f3a\u5927\u7684\u6a21\u578b\u4e5f\u96be\u4ee5\u6301\u7eed\u89e3\u51b3\u96be\u9898\uff0c\u4f8b\u5982\u5965\u6797\u5339\u514b\u7ea7\u522b\u7684\u6570\u5b66\u95ee\u9898\u3002<\/section>\n<section><\/section>\n<section>\u56e0\u6b64\uff0c\u751f\u6210\u7684\u8bad\u7ec3\u6570\u636e\u5c06\u4e3b\u8981\u7531\u66f4\u7b80\u5355\u7684\u53ef\u89e3\u51b3\u95ee\u9898\u7ec4\u6210\uff0c\u9650\u5236\u4e86\u5176\u591a\u6837\u6027\u548c\u8d28\u91cf\u3002<\/section>\n<section><\/section>\n<section>\u5176\u6b21\uff0c\u6ce8\u91ca\u6bcf\u6b65 Q \u503c\u9700\u8981\u5e7f\u6cdb\u7684 MCTS \u90e8\u7f72\uff1b\u6811\u63a2\u7d22\uff08tree exploration\uff09\u4e0d\u8db3\u53ef\u80fd\u4f1a\u5bfc\u81f4\u865a\u5047\u7684 Q \u503c\u5206\u914d\uff0c\u4f8b\u5982\u9ad8\u4f30\u6b21\u4f18\u6b65\u9aa4\u3002\u9274\u4e8e\u6bcf\u6b21 rollout \u90fd\u6d89\u53ca\u591a\u4e2a\u5355\u6b65\u751f\u6210\uff0c\u5e76\u4e14\u8fd9\u4e9b\u6a21\u578b\u7684\u8ba1\u7b97\u6210\u672c\u5f88\u9ad8\uff0c\u56e0\u6b64\u589e\u52a0 rollout \u4f1a\u663e\u8457\u63d0\u9ad8\u63a8\u7406\u6210\u672c\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u6b64\uff0c\u8be5\u7814\u7a76\u63a2\u7d22\u4f7f\u7528\u4e24\u4e2a 7B SLM\uff08\u7b56\u7565 SLM \u548c PRM\uff09\u6765\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e\uff0c\u5176\u8f83\u5c0f\u7684\u6a21\u578b\u5927\u5c0f\u5141\u8bb8\u5728\u53ef\u8bbf\u95ee\u7684\u786c\u4ef6\uff08\u4f8b\u5982 4\u00d740GB A100 GPU\uff09\u4e0a\u5e7f\u6cdb\u90e8\u7f72 MCTS\u3002<\/section>\n<section><\/section>\n<section>\u7136\u800c\uff0c\u7531\u4e8e\u81ea\u751f\u6210\u6570\u636e\u7684\u80fd\u529b\u8f83\u5f31\uff0cSLM \u7ecf\u5e38\u65e0\u6cd5\u751f\u6210\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u5373\u4f7f\u6700\u7ec8\u7b54\u6848\u6b63\u786e\uff0c\u4e2d\u95f4\u6b65\u9aa4\u4e5f\u5e38\u5e38\u5b58\u5728\u7f3a\u9677\u6216\u8d28\u91cf\u8f83\u5dee\u3002\u6b64\u5916\uff0c\u4e0e GPT-4 \u7b49\u9ad8\u7ea7\u6a21\u578b\u76f8\u6bd4\uff0cSLM \u89e3\u51b3\u7684\u6311\u6218\u6027\u95ee\u9898\u8f83\u5c11\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-0d2188932672ffef1d1dcdb5598efd65.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-0d2188932672ffef1d1dcdb5598efd65.png\"><\/a><\/section>\n<section>\u5982\u56fe 1 \u6240\u793a\uff0c\u4e3a\u4e86\u51cf\u5c11\u9519\u8bef\u548c\u4f4e\u8d28\u91cf\u7684\u4e2d\u95f4\u6b65\u9aa4\uff0c\u8be5\u7814\u7a76\u63d0\u51fa\u4e86\u4e00\u79cd\u4ee3\u7801\u589e\u5f3a\u7684 CoT \u5408\u6210\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u6267\u884c\u5e7f\u6cdb\u7684 MCTS \u90e8\u7f72\u4ee5\u751f\u6210\u9010\u6b65\u9a8c\u8bc1\u7684\u63a8\u7406\u8f68\u8ff9\uff0c\u7528 Q \u503c\u6ce8\u91ca\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63d0\u9ad8 SLM \u5728\u6311\u6218\u6027\u95ee\u9898\u4e0a\u7684\u6027\u80fd\uff0c\u8be5\u7814\u7a76\u63d0\u51fa\u4e86\u56db\u8f6e\u81ea\u8fdb\u5316\u65b9\u6848\u3002\u5728\u6bcf\u4e00\u8f6e\u4e2d\uff0c\u7b56\u7565 SLM \u548c\u5956\u52b1\u6a21\u578b\u90fd\u4f1a\u66f4\u65b0\u4e3a\u66f4\u5f3a\u7684\u7248\u672c\uff0c\u9010\u6b65\u89e3\u51b3\u66f4\u56f0\u96be\u7684\u95ee\u9898\u5e76\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-f8528a042cec0747c5c3dca32604cb3d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-f8528a042cec0747c5c3dca32604cb3d.png\"><\/a><\/section>\n<section>\u6700\u540e\uff0c\u8be5\u7814\u7a76\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u9896\u7684\u6d41\u7a0b\u5956\u52b1\u6a21\u578b\u8bad\u7ec3\u65b9\u6cd5\uff0c\u65e0\u9700\u7cbe\u786e\u7684\u6bcf\u6b65\u5956\u52b1\u6ce8\u91ca\uff0c\u4ece\u800c\u4ea7\u751f\u66f4\u6709\u6548\u7684\u6d41\u7a0b\u504f\u597d\u6a21\u578b\uff08PPM\uff09\u3002<\/section>\n<section><\/section>\n<section><strong>\u5b9e\u9a8c\u8bc4\u4f30<\/strong><\/section>\n<section><\/section>\n<section>\u8be5\u56e2\u961f\u5728\u591a\u4e2a\u6570\u5b66\u6570\u636e\u96c6\u4e0a\u5bf9 rStar-Math \u8fdb\u884c\u4e86\u8bc4\u4f30\uff0c\u5e76\u4e0e\u591a\u4e2a\u6a21\u578b\u8fdb\u884c\u4e86\u5bf9\u6bd4\u3002\u5177\u4f53\u8bbe\u7f6e\u8bf7\u53c2\u9605\u539f\u8bba\u6587\uff0c\u8fd9\u91cc\u6211\u4eec\u4e3b\u8981\u6765\u770b\u7814\u7a76\u7ed3\u679c\u3002<\/section>\n<section><\/section>\n<section><strong>\u4e3b\u8981\u7ed3\u679c<\/strong><\/section>\n<section><\/section>\n<section>\u8868 5 \u5c55\u793a\u4e86 rStar-Math \u4e0e\u5176\u5b83 SOTA \u63a8\u7406\u6a21\u578b\u5728\u4e0d\u540c\u7684\u6570\u5b66\u57fa\u51c6\u4e0a\u7684\u7ed3\u679c\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-96d4b58f91fbd07e0cadf0fffdfe3966.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-96d4b58f91fbd07e0cadf0fffdfe3966.png\"><\/a><\/section>\n<section>\u57fa\u4e8e\u8fd9\u4e9b\u7ed3\u679c\uff0c\u8be5\u56e2\u961f\u5f97\u51fa\u4e86\u4e09\u70b9\u89c2\u5bdf\uff1a<\/section>\n<ol>\n<li>\n<p>rStar-Math \u663e\u8457\u63d0\u9ad8\u4e86\u5c0f\u8bed\u8a00\u6a21\u578b\uff08SLM\uff09\u7684\u6570\u5b66\u63a8\u7406\u80fd\u529b\uff0c\u5728\u6a21\u578b\u89c4\u6a21\u663e\u8457\u7f29\u5c0f\uff081.5B-7B\uff09\u7684\u60c5\u51b5\u4e0b\uff0c\u5176\u6027\u80fd\u53ef\u5ab2\u7f8e\u751a\u81f3\u8d85\u8d8a OpenAI o1\u3002<\/p>\n<\/li>\n<li>\n<p>\u5c3d\u7ba1\u4f7f\u7528\u4e86\u8f83\u5c0f\u7684\u7b56\u7565\u6a21\u578b\uff081.5B-7B\uff09\u548c\u5956\u52b1\u6a21\u578b\uff087B\uff09\uff0crStar-Math \u7684\u8868\u73b0\u4ecd\u660e\u663e\u4f18\u4e8e\u6700\u5148\u8fdb\u7684 System 2 \u57fa\u7ebf\u3002<\/p>\n<\/li>\n<li>\n<p>\u9664\u4e86 MATH\u3001GSM8K \u548c AIME \u7b49\u53ef\u80fd\u5b58\u5728\u8fc7\u5ea6\u4f18\u5316\u98ce\u9669\u7684\u77e5\u540d\u57fa\u51c6\u4e4b\u5916\uff0crStar-Math \u5728\u5176\u4ed6\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u57fa\u51c6\u4e0a\u8868\u73b0\u51fa\u5f88\u5f3a\u7684\u901a\u7528\u6027\uff0c\u5305\u62ec Olympiad Bench\u3001College Math \u548c Chinese College Entrance Math Exam\uff08Gaokao\uff09\uff0c\u521b\u4e0b\u4e86\u65b0\u7684\u6700\u9ad8\u5206\u3002<\/p>\n<\/li>\n<\/ol>\n<section>\u6269\u5c55\u6d4b\u8bd5\u65f6\u95f4\u8ba1\u7b97\u3002rStar-Math \u4f7f\u7528\u4e86 MCTS \u6765\u589e\u5f3a\u7b56\u7565\u6a21\u578b\uff0c\u5728 PPM \u7684\u5f15\u5bfc\u4e0b\u641c\u7d22\u95ee\u9898\u7684\u89e3\u3002\u901a\u8fc7\u589e\u52a0\u6d4b\u8bd5\u65f6\u95f4\u8ba1\u7b97\uff0c\u5b83\u53ef\u4ee5\u63a2\u7d22\u66f4\u591a\u8f68\u8ff9\uff0c\u4ece\u800c\u53ef\u80fd\u5b9e\u73b0\u6027\u80fd\u63d0\u5347\u3002<\/section>\n<section><\/section>\n<section>\u5728\u56fe 3 \u4e2d\uff0c\u8be5\u56e2\u961f\u901a\u8fc7\u6bd4\u8f83\u5b98\u65b9 Qwen Best-of-N \u5728\u56db\u4e2a\u9ad8\u96be\u5ea6\u6570\u5b66\u57fa\u51c6\u4e0a\u4e0d\u540c\u6570\u91cf\u7684\u91c7\u6837\u8f68\u8ff9\u7684\u51c6\u786e\u5ea6\uff0c\u5c55\u793a\u4e86\u6d4b\u8bd5\u65f6\u95f4\u8ba1\u7b97\u6269\u5c55\u7684\u5f71\u54cd\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-92ecddbc6a770a56ef80b0476bc4a315.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-92ecddbc6a770a56ef80b0476bc4a315.png\"><\/a><\/section>\n<section><strong>\u6d88\u878d\u7814\u7a76\u548c\u5206\u6790<\/strong><\/section>\n<section><\/section>\n<section>\u8be5\u56e2\u961f\u4e5f\u8fdb\u884c\u4e86\u6d88\u878d\u7814\u7a76\uff0c\u8bc1\u660e\u4e86\u4e09\u9879\u521b\u65b0\u7684\u6709\u6548\u6027\u3002<\/section>\n<section><\/section>\n<section>\u81ea\u6211\u8fdb\u5316\u7684\u6709\u6548\u6027\u3002\u8868 5 \u5c55\u793a\u4e86\u7ecf\u8fc7 4 \u8f6e rStar-Math \u81ea\u6211\u8fdb\u5316\u6df1\u5ea6\u601d\u8003\u540e\u5f97\u5230\u7684\u7ed3\u679c\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u8868\u73b0\u5f88\u4e0d\u9519\u3002<\/section>\n<section><\/section>\n<section>\u8868 6 \u7ed9\u51fa\u4e86\u6bcf\u4e00\u8f6e\u7684\u6570\u5b66\u63a8\u7406\u6027\u80fd\uff0c\u53ef\u4ee5\u660e\u663e\u770b\u5230\u5176\u51c6\u786e\u5ea6\u5728\u4e0d\u65ad\u63d0\u9ad8\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-91eac43e1e7983a99c0403f4793ef609.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-91eac43e1e7983a99c0403f4793ef609.png\"><\/a><\/section>\n<section>\u8868 7 \u5219\u5c55\u793a\u4e86\u5728\u4e0d\u540c\u6570\u636e\u96c6\u4e0a\u5fae\u8c03\u7684 Qwen2.5-Math-7B \u7684\u6570\u5b66\u63a8\u7406\u51c6\u786e\u5ea6\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-757d54ca398eb3602e51f4db658732ba.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-757d54ca398eb3602e51f4db658732ba.png\"><\/a><\/section>\n<section>\u8be5\u56e2\u961f\u7ed9\u51fa\u4e86\u4e24\u9879\u91cd\u8981\u89c2\u5bdf\uff1a<\/section>\n<section><\/section>\n<ul>\n<li>\n<section>\u4f7f\u7528\u65b0\u63d0\u51fa\u7684\u9010\u6b65\u9a8c\u8bc1\u7684\u8f68\u8ff9\u8fdb\u884c\u5fae\u8c03\u660e\u663e\u4f18\u4e8e\u6240\u6709\u5176\u4ed6\u57fa\u7ebf\u3002\u8fd9\u4e3b\u8981\u5f52\u529f\u4e8e\u7528\u4e8e\u4ee3\u7801\u589e\u5f3a\u578b CoT \u5408\u6210\u7684 PPM \u589e\u5f3a\u578b MCTS\uff0c\u5b83\u80fd\u5728\u6570\u5b66\u89e3\u7b54\u751f\u6210\u671f\u95f4\u63d0\u4f9b\u66f4\u5bc6\u96c6\u7684\u9a8c\u8bc1\u3002<\/section>\n<\/li>\n<li>\n<section>\u4f7f\u7528\u8be5\u56e2\u961f\u7684\u5c0f\u8bed\u8a00\u6a21\u578b\uff0c\u5373\u4f7f\u968f\u673a\u91c7\u6837\u4ee3\u7801\u589e\u5f3a\u578b CoT \u89e3\u7b54\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u4e5f\u53ef\u5ab2\u7f8e\u6216\u4f18\u4e8e GPT-4 \u5408\u6210\u7684 NuminaMath \u548c MetaMath \u6570\u636e\u96c6\u3002\u8fd9\u8868\u660e\uff0c\u7ecf\u8fc7\u51e0\u8f6e\u81ea\u6211\u8fdb\u5316\u540e\uff0c\u65b0\u7684\u7b56\u7565 SLM \u53ef\u4ee5\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u6570\u5b66\u89e3\u7b54\u3002\u8fd9\u4e9b\u7ed3\u679c\u8bc1\u660e\u65b0\u65b9\u6cd5\u5728\u4e0d\u4f9d\u8d56\u9ad8\u7ea7 LLM \u84b8\u998f\u7684\u60c5\u51b5\u4e0b\uff0c\u5c31\u5177\u5907\u81ea\u6211\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u63a8\u7406\u6570\u636e\u7684\u5de8\u5927\u6f5c\u529b\u3002<\/section>\n<\/li>\n<\/ul>\n<section><\/section>\n<section>\u53e6\u5916\uff0c\u5728\u6700\u540e\u4e00\u8f6e\u7b56\u7565\u6a21\u578b\u7684\u57fa\u7840\u4e0a\uff0c\u8be5\u56e2\u961f\u6bd4\u8f83\u4e86 ORM\u3001PQM \u548c PPM \u5728 System 2 \u63a8\u7406\u4e0a\u7684\u6027\u80fd\u3002\u7ed3\u679c\u89c1\u8868 8\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-d3862a5ba3e18ec6a6985c6e719bf185.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-d3862a5ba3e18ec6a6985c6e719bf185.png\"><\/a><\/section>\n<section>\u53ef\u4ee5\u770b\u5230\uff0cPQM \u548c PPM \u90fd\u4f18\u4e8e ORM\uff0c\u56e0\u4e3a\u5b83\u4eec\u53ef\u63d0\u4f9b\u66f4\u5bc6\u96c6\u7684\u6b65\u9aa4\u7ea7\u5956\u52b1\u4fe1\u53f7\uff0c\u4ece\u800c\u5728\u590d\u6742\u7684\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e0a\u83b7\u5f97\u66f4\u9ad8\u7684\u51c6\u786e\u5ea6\u3002\u7136\u800c\uff0c\u7531\u4e8e Q \u503c\u56fa\u6709\u7684\u4e0d\u7cbe\u786e\u6027\uff0cPQM \u5728\u66f4\u96be\u7684\u57fa\u51c6\u6d4b\u8bd5\uff08\u4f8b\u5982 MATH \u548c Olympiad Bench\uff09\u4e0a\u8868\u73b0\u4e0d\u4f73\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cPPM \u6784\u5efa\u4e86\u6b65\u9aa4\u7ea7\u504f\u597d\u6570\u636e\u8fdb\u884c\u8bad\u7ec3\uff0c\u4f7f\u8be5\u56e2\u961f\u7684 7B \u7b56\u7565\u6a21\u578b\u5728\u6240\u6709\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u90fd\u80fd\u591f\u5b9e\u73b0\u4e0e o1-mini \u76f8\u5f53\u6216\u66f4\u4f18\u7684\u6027\u80fd\u3002<\/section>\n<section><\/section>\n<section><strong>\u53d1\u73b0\u4e0e\u8ba8\u8bba<\/strong><\/section>\n<section><\/section>\n<section><strong>\u6a21\u578b\u51fa\u73b0\u81ea\u6211\u53cd\u601d\u80fd\u529b<\/strong><\/section>\n<section><\/section>\n<section>OpenAI o1 \u7684\u4e00\u4e2a\u91cd\u8981\u7a81\u7834\u662f\u5b83\u80fd\u81ea\u7701\u3002\u5f53\u5b83\u51fa\u9519\u65f6\uff0co1 \u80fd\u8bc6\u522b\u9519\u8bef\u5e76\u81ea\u6211\u7ea0\u6b63\u3002\u8fd9\u5728\u5f00\u6e90 LLM \u4e2d\u4e00\u76f4\u96be\u4ee5\u5b9e\u73b0\u3002\u5728\u5b9e\u9a8c\u4e2d\uff0c\u8be5\u56e2\u961f\u610f\u5916\u53d1\u73b0 MCTS \u9a71\u52a8\u7684\u6df1\u5ea6\u601d\u8003\u5c55\u73b0\u51fa\u4e86\u53cd\u601d\u80fd\u529b\u3002\u5982\u56fe 4 \u6240\u793a\uff0c\u6a21\u578b\u6700\u521d\u5728\u524d\u4e09\u6b65\u4f7f\u7528 SymPy \u5f62\u5f0f\u5316\u65b9\u7a0b\u4f1a\u5199\u51fa\u9519\u8bef\u7b54\u6848\uff08\u5de6\u5206\u652f\uff09\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-f4bf1fe75151198242dafa00c3bf4326.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-f4bf1fe75151198242dafa00c3bf4326.png\"><\/a><\/section>\n<section>\u5728\u6211\u4eec\u7684\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u610f\u5916\u5730\u89c2\u5bdf\u5230\u6211\u4eec\u7684 MCTS \u9a71\u52a8\u7684\u6df1\u5ea6\u601d\u8003\u5728\u89e3\u51b3\u95ee\u9898\u8fc7\u7a0b\u4e2d\u8868\u73b0\u51fa\u81ea\u53cd\u601d\u3002\u5982\u56fe 4 \u6240\u793a\uff0c\u6a21\u578b\u6700\u521d\u5728\u524d\u4e09\u6b65\u4f7f\u7528 SymPy \u5f62\u5f0f\u5316\u65b9\u7a0b\uff0c\u8fd9\u5c06\u5bfc\u81f4\u7b54\u6848\u9519\u8bef (\u5de6\u5206\u652f)\u3002<\/section>\n<section><\/section>\n<section>\u4f46\u5728\u7b2c\u56db\u6b65\uff0c\u6a21\u578b\u5c31\u8bc6\u522b\u51fa\u4e86\u524d\u51e0\u6b65\u7684\u95ee\u9898\uff08\u53f3\u5206\u652f\uff09\uff0c\u5e76\u4e3b\u52a8\u56de\u6eaf\u91c7\u7528\u66f4\u7b80\u5355\u7684\u65b9\u6cd5\u91cd\u65b0\u6c42\u89e3\uff0c\u6700\u7ec8\u5f97\u5230\u6b63\u786e\u7b54\u6848\u3002<\/section>\n<section><\/section>\n<section>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u79cd\u81ea\u53cd\u601d\u80fd\u529b\u662f\u5728\u6ca1\u6709\u4e13\u95e8\u8bad\u7ec3\u548c\u63d0\u793a\u7684\u60c5\u51b5\u4e0b\u81ea\u53d1\u4ea7\u751f\u7684\uff0c\u8868\u660e\u9ad8\u7ea7 System 2 \u63a8\u7406\u53ef\u4ee5\u81ea\u7136\u57f9\u517b\u51fa\u5185\u5728\u7684\u81ea\u7701\u80fd\u529b\u3002<\/section>\n<section><\/section>\n<section><strong>PPM \u5851\u9020 System 2 \u6df1\u5ea6\u601d\u8003\u7684\u63a8\u7406\u8fb9\u754c<\/strong><\/section>\n<section><\/section>\n<section>\u7b56\u7565\u6a21\u578b\u548c\u5956\u52b1\u6a21\u578b\u5bf9 System 2 \u6df1\u5ea6\u63a8\u7406\u90fd\u81f3\u5173\u91cd\u8981\u3002\u5b9e\u9a8c\u8868\u660e\uff0c\u4e00\u65e6\u7b56\u7565\u6a21\u578b\u8fbe\u5230\u76f8\u5f53\u5f3a\u7684\u80fd\u529b\u6c34\u5e73\uff0cPPM \u5c31\u6210\u4e3a\u51b3\u5b9a\u6027\u80fd\u4e0a\u9650\u7684\u5173\u952e\u3002<\/section>\n<section><\/section>\n<section>\u5982\u4e0b\u56fe 5 \u6240\u793a\uff0c\u901a\u8fc7\u52a0\u5165 System 2 \u63a8\u7406\u673a\u5236\uff0c\u5373\u4f7f\u662f Phi3.8B \u8fd9\u6837\u7684\u5c0f\u6a21\u578b\u4e5f\u80fd\u83b7\u5f97\u663e\u8457\u6027\u80fd\u63d0\u5347\uff0c\u5728\u591a\u4e2a\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u7684\u51c6\u786e\u7387\u63d0\u9ad8\u4e86\u7ea6 20-30 \u4e2a\u767e\u5206\u70b9\u3002\u8fd9\u8868\u660e\uff0c\u5956\u52b1\u6a21\u578b\uff08\u800c\u4e0d\u662f\u57fa\u7840\u6a21\u578b\u7684\u5927\u5c0f\uff09\u624d\u662f\u51b3\u5b9a\u6700\u7ec8\u6027\u80fd\u7684\u5173\u952e\u56e0\u7d20\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-c027fa9b10cf9679e720088324b99efb.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/01\/frc-c027fa9b10cf9679e720088324b99efb.png\"><\/a><\/section>\n<section>\u66f4\u591a\u7814\u7a76\u7ec6\u8282\uff0c\u8bf7\u53c2\u9605\u8bba\u6587\u539f\u6587\u3002<\/section>\n<section><\/section>\n<section><em><sup>\u53c2\u8003\u94fe\u63a5\uff1a<\/sup><\/em><\/section>\n<section><sup><em>https:\/\/arxiv.org\/pdf\/2501.04519<\/em><\/sup><\/section>\n<section><em><sup>https:\/\/www.reddit.com\/r\/MachineLearning\/comments\/1hxk2ab\/r_rstarmath_small_llms_can_master_math_reasoning\/<\/sup><\/em><\/section>\n<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-01-10-6\" target=\"_blank\">\u8ba97B\u5343\u95ee\u6a21\u578b\u8d85\u8d8ao1\uff0c\u5fae\u8f6frStar-Math\u60ca\u8273\u767b\u573a\uff0c\u7f51\u53cb\u76db\u8d5e<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:\u8ba97B\u5343\u95ee\u6a21\u578b\u8d85\u8d8ao1 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[27],"tags":[68,81],"class_list":["post-37682","post","type-post","status-publish","format-standard","hentry","category-news","tag-68","tag-81"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u8ba97B\u5343\u95ee\u6a21\u578b\u8d85\u8d8ao1\uff0c\u5fae\u8f6frStar-Math\u60ca\u8273\u767b\u573a\uff0c\u7f51\u53cb\u76db\u8d5e - \u4e00\u8d77AI\u6280\u672f<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/17aitech.com\/?p=37682\" \/>\n<script type=\"application\/ld+json\" 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