{"id":39824,"date":"2025-04-01T21:02:23","date_gmt":"2025-04-01T13:02:23","guid":{"rendered":"https:\/\/17aitech.com\/?p=39824"},"modified":"2025-04-01T21:02:23","modified_gmt":"2025-04-01T13:02:23","slug":"%e8%87%aa%e5%8a%a8%e5%ad%a6%e4%bc%9a%e5%b7%a5%e5%85%b7%e8%a7%a3%e9%a2%98%ef%bc%8crl%e6%89%a9%e5%b1%95%e5%82%ac%e5%8c%96%e5%a5%a5%e6%95%b0%e8%83%bd%e5%8a%9b%e6%bf%80%e5%a2%9e17","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=39824","title":{"rendered":"\u81ea\u52a8\u5b66\u4f1a\u5de5\u5177\u89e3\u9898\uff0cRL\u6269\u5c55\u50ac\u5316\u5965\u6570\u80fd\u529b\u6fc0\u589e17%"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-04-01-13\" target=\"_blank\">\u81ea\u52a8\u5b66\u4f1a\u5de5\u5177\u89e3\u9898\uff0cRL\u6269\u5c55\u50ac\u5316\u5965\u6570\u80fd\u529b\u6fc0\u589e17%<\/a><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-770f79c00e36194de6b8562af5460bb7.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-770f79c00e36194de6b8562af5460bb7.png\"><\/a><\/section>\n<p>\u5728\u5927\u6a21\u578b\u63a8\u7406\u80fd\u529b\u63d0\u5347\u7684\u63a2\u7d22\u4e2d\uff0c\u5de5\u5177\u4f7f\u7528\u4e00\u76f4\u662f\u514b\u670d\u8bed\u8a00\u6a21\u578b\u8ba1\u7b97\u5c40\u9650\u6027\u7684\u5173\u952e\u8def\u5f84\u3002\u4e0d\u8fc7\uff0c\u5f53\u4eca\u7684\u5927\u6a21\u578b\u5728\u4f7f\u7528\u5de5\u5177\u65b9\u9762\u8fd8\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\uff0c\u6bd4\u5982\u9884\u5148\u786e\u5b9a\u4e86\u5de5\u5177\u7684\u4f7f\u7528\u6a21\u5f0f\u3001\u9650\u5236\u4e86\u5bf9\u6700\u4f18\u7b56\u7565\u7684\u63a2\u7d22\u3001\u5b9e\u73b0\u900f\u660e\u5ea6\u4e0d\u8db3\u7b49\u3002<\/p>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e9b\u96be\u9898\uff0c\u6765\u81ea<strong>\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u3001SII \u548c GAIR <\/strong>\u7684\u7814\u7a76\u56e2\u961f\u63d0\u51fa\u4e86\u4e00\u79cd\u5168\u65b0\u6846\u67b6<strong>\u00a0ToRL\uff08Tool-Integrated Reinforcement Learning\uff09<\/strong>\uff0c\u8be5\u65b9\u6cd5\u5141\u8bb8\u6a21\u578b<strong>\u76f4\u63a5\u4ece\u57fa\u5ea7\u6a21\u578b\u5f00\u59cb<\/strong>\uff0c\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u81ea\u4e3b\u63a2\u7d22\u6700\u4f18\u5de5\u5177\u4f7f\u7528\u7b56\u7565\uff0c\u800c\u975e\u53d7\u9650\u4e8e\u9884\u5b9a\u4e49\u7684\u5de5\u5177\u4f7f\u7528\u6a21\u5f0f\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-16e47acb7173dd12c9d296f76019cc8c.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-16e47acb7173dd12c9d296f76019cc8c.png\"><\/a><\/section>\n<ul>\n<li>\n<p>\u8bba\u6587\u6807\u9898\uff1aToRL: Scaling Tool-Integrated RL<\/p>\n<\/li>\n<li>\n<p>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2503.23383<\/p>\n<\/li>\n<li>\n<p>\u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/GAIR-NLP\/ToRL<\/p>\n<\/li>\n<li>\n<p>\u6570\u636e\u96c6\u5730\u5740\uff1ahttps:\/\/github.com\/GAIR-NLP\/ToRL\/tree\/main\/data\/torl_data<\/p>\n<\/li>\n<li>\n<p>\u6a21\u578b\u5730\u5740\uff1ahttps:\/\/huggingface.co\/GAIR\/ToRL-7B<\/p>\n<\/li>\n<\/ul>\n<p>\u5b9e\u9a8c\u8868\u660e\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5728\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86\u663e\u8457\u7a81\u7834\uff1a<strong>ToRL-7B \u5728 AIME24 \u4e0a\u8fbe\u5230\u4e86 43.3% \u7684\u51c6\u786e\u7387<\/strong>\uff0c\u6bd4\u4e0d\u4f7f\u7528\u5de5\u5177\u7684\u57fa\u7ebf RL \u6a21\u578b\u63d0\u9ad8\u4e86 14%\uff0c\u6bd4\u73b0\u6709\u7684\u5de5\u5177\u96c6\u6210\u5927\u6a21\u578b\u63d0\u9ad8\u4e86 17%\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-6979293b984f7eab5a72f07c14dd2573.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-6979293b984f7eab5a72f07c14dd2573.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 1: ToRL \u5728 AIME24 \u7b49\u57fa\u51c6\u4e2d\u7684\u6027\u80fd\u5bf9\u6bd4\uff0c\u4f18\u4e8e\u57fa\u7ebf\u548c\u73b0\u6709 TIR \u7cfb\u7edf<\/sup><\/p>\n<p><strong>\u4e00\u3001\u4e3a\u4ec0\u4e48\u8981\u76f4\u63a5\u4ece\u57fa\u5ea7\u6a21\u578b\u6269\u5c55\u5de5\u5177\u96c6\u6210\u5f3a\u5316\u5b66\u4e60\uff1f<\/strong><\/p>\n<p>\u5728\u4f20\u7edf\u5de5\u5177\u96c6\u6210\u63a8\u7406\uff08TIR\uff09\u9886\u57df\uff0c\u7814\u7a76\u8005\u4eec\u957f\u671f\u9075\u5faa\u7740\u4e00\u6761\u770b\u4f3c\u4e0d\u53ef\u64bc\u52a8\u7684\u94c1\u5f8b\uff1a\u5fc5\u987b\u5148\u901a\u8fc7\u76d1\u7763\u5fae\u8c03\uff08SFT\uff09\u6559\u4f1a\u6a21\u578b\u4f7f\u7528\u5de5\u5177\uff0c\u624d\u80fd\u8fdb\u884c\u5f3a\u5316\u5b66\u4e60\u4f18\u5316\u3002\u8fd9\u79cd &#8220;\u5148 SFT \u518d RL&#8221; \u7684\u8303\u5f0f\uff0c\u5c31\u50cf\u7ed9 AI \u5957\u4e0a\u9884\u8bbe\u7684\u601d\u7ef4\u67b7\u9501\uff0c\u867d\u7136\u80fd\u83b7\u5f97\u7a33\u5b9a\u7684\u6027\u80fd\u63d0\u5347\uff0c\u5374\u53ef\u80fd\u6c38\u8fdc\u65e0\u6cd5\u53d1\u73b0\u6700\u4f18\u7684\u5de5\u5177\u4f7f\u7528\u7b56\u7565\u3002<\/p>\n<p>\u6b63\u5f53\u5927\u5bb6\u6cbf\u7740\u8fd9\u6761\u65e2\u5b9a\u8def\u7ebf\u5806\u780c\u6570\u636e\u548c\u7b97\u529b\u65f6\uff0c\u8be5\u7814\u7a76\u56e2\u961f\u5374\u5927\u80c6\u63d0\u51fa\u4e86\u4e00\u4e2a\u5047\u8bbe\uff1a\u5982\u679c\u8ba9\u6a21\u578b\u5b8c\u5168\u81ea\u4e3b\u63a2\u7d22\u5de5\u5177\u4f7f\u7528\u65b9\u5f0f\uff0c\u4f1a\u600e\u6837\uff1f\u4ed6\u4eec\u5f00\u53d1\u7684 ToRL \u6846\u67b6\u5c31\u50cf\u6253\u5f00\u4e86\u4e00\u6247\u5168\u65b0\u7684\u5927\u95e8 \u2014\u2014 \u76f4\u63a5\u4ece\u57fa\u5ea7\u6a21\u578b\u51fa\u53d1\uff0c<strong>\u5355\u7eaf\u901a\u8fc7\u6269\u5c55\u5f3a\u5316\u5b66\u4e60<\/strong>\u8ba9 AI \u81ea\u4e3b\u638c\u63e1\u5de5\u5177\u4f7f\u7528\u7684\u7cbe\u9ad3\u3002<\/p>\n<p>\u5b9e\u9a8c\u7ed3\u679c\u4ee4\u4eba\u60ca\u559c\uff1aToRL \u4e0d\u4ec5\u6253\u7834\u4e86\u4f20\u7edf TIR \u65b9\u6cd5\u7684\u6027\u80fd\u5929\u82b1\u677f\uff0c\u66f4\u8ba9\u6a21\u578b\u81ea\u53d1\u6d8c\u73b0\u51fa\u4e09\u5927\u91cd\u8981\u80fd\u529b\uff1a<\/p>\n<ol>\n<li>\n<p>\u50cf\u4eba\u7c7b\u4e13\u5bb6\u822c\u7684\u5de5\u5177\u9009\u62e9\u76f4\u89c9<\/p>\n<\/li>\n<li>\n<p>\u81ea\u6211\u4fee\u6b63\u65e0\u6548\u4ee3\u7801\u7684\u5143\u80fd\u529b<\/p>\n<\/li>\n<li>\n<p>\u52a8\u6001\u5207\u6362\u8ba1\u7b97\u4e0e\u63a8\u7406\u7684\u89e3\u9898\u667a\u6167<\/p>\n<\/li>\n<\/ol>\n<p>\u8fd9\u4e9b\u80fd\u529b\u5b8c\u5168\u7531\u5956\u52b1\u4fe1\u53f7\u9a71\u52a8\u81ea\u7136\u5f62\u6210\uff0c\u6ca1\u6709\u4efb\u4f55\u4eba\u4e3a\u9884\u8bbe\u7684\u75d5\u8ff9\u3002<\/p>\n<p>\u8fd9\u4e0d\u7981\u8ba9\u4eba\u601d\u8003\uff1aToRL \u8bc1\u660e\u4e86\u5927\u6a21\u578b\u53ef\u80fd\u65e9\u5df2\u5177\u5907\u5f3a\u5927\u7684\u5de5\u5177\u4f7f\u7528\u80fd\u529b\uff0c\u53ea\u662f\u9700\u8981\u66f4\u5f00\u653e\u7684\u5b66\u4e60\u65b9\u5f0f\u53bb\u91ca\u653e\u3002\u5f53\u4e3b\u6d41\u7814\u7a76\u8fd8\u5728\u4e3a\u6570\u636e\u89c4\u6a21\u548c\u7b97\u6cd5\u590d\u6742\u5ea6\u8f83\u52b2\u65f6\uff0cToRL \u7528\u4e8b\u5b9e\u544a\u8bc9\u6211\u4eec\uff1a<strong>\u6709\u65f6\u5019\uff0c\u5c11\u4e00\u4e9b\u4eba\u4e3a\u5e72\u9884\uff0c\u53cd\u800c\u80fd\u6536\u83b7\u66f4\u591a\u610f\u5916\u4e4b\u559c\u3002<\/strong><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-2d97053d226417867a06e686ac51868d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-2d97053d226417867a06e686ac51868d.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 2: ToRL \u4f7f\u7528\u81ea\u7136\u8bed\u8a00\u548c\u4ee3\u7801\u5de5\u5177\u4ea4\u53c9\u9a8c\u8bc1\uff0c\u5e76\u5728\u53d1\u73b0\u4e0d\u4e00\u81f4\u540e\u8fdb\u4e00\u6b65\u4f7f\u7528\u4f7f\u7528\u5de5\u5177\u9a8c\u8bc1<\/sup><\/p>\n<p><strong>\u4e8c\u3001\u6280\u672f\u89e3\u6790\uff1aToRL \u5982\u4f55\u8d4b\u4e88\u6a21\u578b\u81ea\u4e3b\u5de5\u5177\u80fd\u529b<\/strong><\/p>\n<p><strong>\u5de5\u5177\u96c6\u6210\u63a8\u7406 (TIR) \u7684\u57fa\u672c\u6846\u67b6<\/strong><\/p>\n<p>\u5de5\u5177\u96c6\u6210\u63a8\u7406 (TIR) \u4f7f\u5927\u8bed\u8a00\u6a21\u578b\u80fd\u591f\u901a\u8fc7\u7f16\u5199\u4ee3\u7801\uff0c\u5229\u7528\u5916\u90e8\u5de5\u5177\u6267\u884c\u8ba1\u7b97\uff0c\u5e76\u57fa\u4e8e\u6267\u884c\u7ed3\u679c\u8fed\u4ee3\u751f\u6210\u63a8\u7406\u8fc7\u7a0b\u3002\u8fd9\u4e00\u8fc7\u7a0b\u53ef\u4ee5\u7528\u7b80\u5355\u7684\u8bed\u8a00\u63cf\u8ff0\u4e3a\uff1a<\/p>\n<p>\u5f53\u8bed\u8a00\u6a21\u578b\u9762\u5bf9\u4e00\u4e2a\u95ee\u9898\u65f6\uff0cTIR \u5141\u8bb8\u6a21\u578b\u6784\u5efa\u4e00\u4e2a\u5305\u542b\u591a\u4e2a\u6b65\u9aa4\u7684\u63a8\u7406\u8f68\u8ff9\u3002\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u6a21\u578b\u9996\u5148\u7528\u81ea\u7136\u8bed\u8a00\u8fdb\u884c\u63a8\u7406\uff0c\u7136\u540e\u751f\u6210\u76f8\u5173\u4ee3\u7801\uff0c\u63a5\u7740\u83b7\u53d6\u4ee3\u7801\u7684\u6267\u884c\u7ed3\u679c\uff0c\u5e76\u5c06\u8fd9\u4e09\u90e8\u5206\u5185\u5bb9\u7ec4\u5408\u8d77\u6765\u5f62\u6210\u5b8c\u6574\u7684\u63a8\u7406\u8fc7\u7a0b\u3002\u968f\u7740\u63a8\u7406\u7684\u6df1\u5165\uff0c\u6a21\u578b\u4f1a\u4e0d\u65ad\u53c2\u8003\u4e4b\u524d\u7684\u63a8\u7406\u5185\u5bb9\u3001\u4ee3\u7801\u53ca\u5176\u6267\u884c\u7ed3\u679c\uff0c\u8fdb\u4e00\u6b65\u8c03\u6574\u81ea\u5df1\u7684\u601d\u8def\u3002<\/p>\n<p><strong>ToRL: \u76f4\u63a5\u4ece\u57fa\u5ea7\u6a21\u578b\u7684\u5f3a\u5316\u5b66\u4e60<\/strong><\/p>\n<p>ToRL \u6846\u67b6\u5c06 TIR \u4e0e\u76f4\u63a5\u4ece\u57fa\u5ea7\u8bed\u8a00\u6a21\u578b\u5f00\u59cb\u7684\u5f3a\u5316\u5b66\u4e60\u76f8\u7ed3\u5408\uff0c\u800c\u4e0d\u9700\u8981\u5148\u8fdb\u884c\u76d1\u7763\u5fae\u8c03\u3002\u8fd9\u4f7f\u5f97\u6a21\u578b\u80fd\u591f\u81ea\u4e3b\u53d1\u73b0\u6709\u6548\u7684\u5de5\u5177\u4f7f\u7528\u7b56\u7565\u3002<\/p>\n<p>\u5728\u6a21\u578b\u7684\u63a8\u7406\u8fc7\u7a0b\u4e2d\uff0c\u5f53\u68c0\u6d4b\u5230\u4ee3\u7801\u7ec8\u6b62\u6807\u8bc6\u7b26 (&#8220;`output) \u65f6\uff0c\u7cfb\u7edf\u4f1a\u6682\u505c\u6587\u672c\u751f\u6210\uff0c\u63d0\u53d6\u6700\u65b0\u7684\u4ee3\u7801\u5757\u6267\u884c\uff0c\u5e76\u5c06\u7ed3\u6784\u5316\u6267\u884c\u7ed3\u679c\u63d2\u5165\u4e0a\u4e0b\u6587\u4e2d\u3002\u7cfb\u7edf\u4f1a\u7ee7\u7eed\u751f\u6210\u540e\u7eed\u7684\u81ea\u7136\u8bed\u8a00\u63a8\u7406\uff0c\u76f4\u5230\u6a21\u578b\u63d0\u4f9b\u6700\u7ec8\u7b54\u6848\u6216\u751f\u6210\u65b0\u7684\u4ee3\u7801\u5757\u3002<\/p>\n<p><strong>\u8bbe\u8ba1\u9009\u62e9\u4e0e\u8003\u91cf\uff1a<\/strong><\/p>\n<ul>\n<li>\n<p><strong>\u5de5\u5177\u8c03\u7528\u9891\u7387\u63a7\u5236<\/strong>\uff1a\u4e3a\u4e86\u5e73\u8861\u8bad\u7ec3\u6548\u7387\uff0c\u5f15\u5165\u8d85\u53c2\u6570 C\uff0c\u8868\u793a\u6bcf\u6b21\u54cd\u5e94\u751f\u6210\u5141\u8bb8\u7684\u6700\u5927\u5de5\u5177\u8c03\u7528\u6b21\u6570\uff1b<\/p>\n<\/li>\n<li>\n<p><strong>\u6267\u884c\u73af\u5883\u9009\u62e9<\/strong>\uff1a\u9009\u62e9\u7a33\u5b9a\u3001\u51c6\u786e\u548c\u54cd\u5e94\u8fc5\u901f\u7684\u4ee3\u7801\u89e3\u91ca\u5668\u5b9e\u73b0\uff1b<\/p>\n<\/li>\n<li>\n<p><strong>\u9519\u8bef\u6d88\u606f\u5904\u7406<\/strong>\uff1a\u63d0\u53d6\u5173\u952e\u9519\u8bef\u4fe1\u606f\uff0c\u51cf\u5c11\u4e0a\u4e0b\u6587\u957f\u5ea6\uff1b<\/p>\n<\/li>\n<li>\n<p><strong>\u6c99\u76d2\u8f93\u51fa\u63a9\u7801<\/strong>\uff1a\u5728\u635f\u5931\u8ba1\u7b97\u4e2d\u63a9\u76d6\u6c99\u76d2\u73af\u5883\u7684\u8f93\u51fa\uff0c\u63d0\u9ad8\u8bad\u7ec3\u7a33\u5b9a\u6027\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>\u5956\u52b1\u8bbe\u8ba1<\/strong>\uff1a\u5b9e\u73b0\u4e86\u57fa\u4e8e\u89c4\u5219\u7684\u5956\u52b1\u51fd\u6570\uff0c\u6b63\u786e\u7b54\u6848\u83b7\u5f97 + 1 \u5956\u52b1\uff0c\u9519\u8bef\u7b54\u6848\u83b7\u5f97 &#8211; 1 \u5956\u52b1\u3002\u6b64\u5916\uff0c\u7814\u7a76\u8fd8\u5c1d\u8bd5\u63a2\u7a76\u4e86\u57fa\u4e8e\u6267\u884c\u7684\u60e9\u7f5a\uff1a\u542b\u6709\u4e0d\u53ef\u6267\u884c\u4ee3\u7801\u7684\u54cd\u5e94\u4f1a\u5bfc\u81f4 &#8211; 0.5 \u7684\u5956\u52b1\u51cf\u5c11\u3002\u5728\u9ed8\u8ba4\u5b9e\u9a8c\u8bbe\u7f6e\u4e2d\uff0c\u4ec5\u4f7f\u7528\u4e86\u7b54\u6848\u6b63\u786e\u6027\u7684 reward\u3002<\/p>\n<p><strong>\u4e09\u3001\u5b9e\u9a8c\u9a8c\u8bc1\uff1aToRL \u7684\u6027\u80fd\u4f18\u52bf<\/strong><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-a64bf4dfb3598c107e464d3ae2cae55d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-a64bf4dfb3598c107e464d3ae2cae55d.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u56fe 3: ToRL \u5728\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u4e0a\u7684\u51c6\u786e\u7387\u6bd4\u8f83<\/sup><\/p>\n<p>\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0cToRL \u5728\u6240\u6709\u6d4b\u8bd5\u57fa\u51c6\u4e0a\u7684\u8868\u73b0\u59cb\u7ec8\u4f18\u4e8e\u57fa\u7ebf\u6a21\u578b\u3002\u5bf9\u4e8e 1.5B \u53c2\u6570\u6a21\u578b\uff0cToRL-1.5B \u7684\u5e73\u5747\u51c6\u786e\u7387\u8fbe\u5230\u4e86 48.5%\uff0c\u8d85\u8fc7\u4e86 Qwen2.5-Math-1.5B-Instruct (35.9%) \u548c Qwen2.5-Math-1.5B-Instruct-TIR (41.3%)\u3002\u5728 7B \u53c2\u6570\u6a21\u578b\u4e2d\uff0c\u6027\u80fd\u63d0\u5347\u66f4\u52a0\u663e\u8457\uff0cToRL-7B \u8fbe\u5230\u4e86 62.1% \u7684\u5e73\u5747\u51c6\u786e\u7387\uff0c\u6bd4\u5177\u6709\u76f8\u540c\u57fa\u7840\u6a21\u578b\u7684\u5176\u4ed6\u5f00\u6e90\u6a21\u578b\u9ad8\u51fa 14.7%\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-542d9d447e868a05a218f1213deb52ad.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-542d9d447e868a05a218f1213deb52ad.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 4: ToRL \u5728\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u4e0a\u7684\u8bad\u7ec3\u52a8\u6001<\/sup><\/p>\n<p>\u56fe 4 \u5c55\u793a\u4e86\u5728\u4e94\u4e2a\u4e0d\u540c\u6570\u5b66\u57fa\u51c6\u4e0a\u7684\u8bad\u7ec3\u52a8\u6001\u3002ToRL-7B \u5728\u8bad\u7ec3\u6b65\u9aa4\u4e2d\u663e\u793a\u51fa\u6301\u7eed\u6539\u8fdb\uff0c\u5e76\u4fdd\u6301\u660e\u663e\u4f18\u52bf\u3002\u8fd9\u79cd\u6027\u80fd\u5dee\u8ddd\u5728\u5177\u6709\u6311\u6218\u6027\u7684\u57fa\u51c6\u4e0a\u5c24\u4e3a\u663e\u8457\uff0c\u5982 AIME24 (43.3%)\u3001AIME25 (30.0%) \u548c OlympiadBench (49.9%)\u3002<\/p>\n<p><strong>\u56db\u3001\u884c\u4e3a\u63a2\u7d22\uff1a\u6a21\u578b\u4f7f\u7528\u5de5\u5177\u7684\u8ba4\u77e5\u6a21\u5f0f<\/strong><\/p>\n<p><strong>\u8bad\u7ec3\u4e2d\u7684\u5de5\u5177\u4f7f\u7528\u8fdb\u5316<\/strong><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-aa479989a045deb6a91ea184af401622.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-aa479989a045deb6a91ea184af401622.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 5: \u8bad\u7ec3\u6b65\u6570\u589e\u52a0\u65f6\uff0cToRL \u7684\u4ee3\u7801\u4f7f\u7528\u7387\u4e0e\u6709\u6548\u6027\u53d8\u5316<\/sup><\/p>\n<p>\u56fe 5 \u63d0\u4f9b\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5de5\u5177\u4f7f\u7528\u6a21\u5f0f\u7684\u6df1\u5165\u6d1e\u5bdf\uff1a<\/p>\n<ul>\n<li>\n<p><strong>\u4ee3\u7801\u6bd4\u7387<\/strong>\uff1a\u6a21\u578b\u751f\u6210\u7684\u5305\u542b\u4ee3\u7801\u7684\u54cd\u5e94\u6bd4\u4f8b\u5728\u524d 100 \u6b65\u5185\u4ece 40% \u589e\u52a0\u5230 80%\uff0c\u5c55\u793a\u4e86\u6574\u4e2a\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u7a33\u5b9a\u63d0\u5347<\/p>\n<\/li>\n<li>\n<p><strong>\u901a\u8fc7\u7387<\/strong>\uff1a\u6210\u529f\u6267\u884c\u7684\u4ee3\u7801\u6bd4\u4f8b\u5448\u73b0\u6301\u7eed\u4e0a\u5347\u8d8b\u52bf\uff0c\u53cd\u6620\u4e86\u6a21\u578b\u589e\u5f3a\u7684\u7f16\u7801\u80fd\u529b<\/p>\n<\/li>\n<li>\n<p><strong>\u6b63\u786e \/ \u9519\u8bef\u54cd\u5e94\u7684\u901a\u8fc7\u7387<\/strong>\uff1a\u63ed\u793a\u4e86\u4ee3\u7801\u6267\u884c\u9519\u8bef\u4e0e\u6700\u7ec8\u7b54\u6848\u51c6\u786e\u6027\u4e4b\u95f4\u7684\u76f8\u5173\u6027\uff0c\u6b63\u786e\u54cd\u5e94\u8868\u73b0\u51fa\u66f4\u9ad8\u7684\u4ee3\u7801\u901a\u8fc7\u7387<\/p>\n<\/li>\n<li>\n<p><strong>\u6709\u6548\u4ee3\u7801\u6bd4\u7387<\/strong>\uff1a\u68c0\u67e5\u6709\u6548\u4ee3\u7801\u6bd4\u4f8b\u7684\u53d8\u5316\uff0c\u5305\u62ec\u6210\u529f\u6267\u884c\u7684\u4ee3\u7801\u548c\u5728\u6a21\u578b\u63d0\u4f9b\u6700\u7ec8\u7b54\u6848\u524d\u751f\u6210\u7684\u4ee3\u7801\uff0c\u4e24\u8005\u90fd\u968f\u7740\u8bad\u7ec3\u65f6\u95f4\u589e\u52a0\u800c\u63d0\u9ad8<\/p>\n<\/li>\n<\/ul>\n<p><strong>\u5173\u952e\u53d1\u73b0<\/strong>\uff1a\u968f\u7740\u8bad\u7ec3\u6b65\u9aa4\u7684\u589e\u52a0\uff0c\u6a21\u578b\u89e3\u51b3\u95ee\u9898\u4f7f\u7528\u4ee3\u7801\u7684\u6bd4\u4f8b\u4ee5\u53ca\u53ef\u4ee5\u6b63\u786e\u6267\u884c\u7684\u4ee3\u7801\u6bd4\u4f8b\u6301\u7eed\u589e\u957f\u3002\u540c\u65f6\uff0c\u6a21\u578b\u80fd\u591f\u8bc6\u522b\u5e76\u51cf\u5c11\u65e0\u6548\u4ee3\u7801\u7684\u751f\u6210\u3002<\/p>\n<p><strong>\u5173\u952e\u53c2\u6570\u8bbe\u7f6e\u7684\u5f71\u54cd<\/strong><\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-75cfe6fd53ef692fbbf5fadc9d568a54.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-75cfe6fd53ef692fbbf5fadc9d568a54.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 6: \u63a2\u7d22\u76f8\u5e94\u6700\u5927\u6b21\u6570\uff08\u5de6 2 \u56fe\uff09\u548c\u53ef\u6267\u884c\uff08\u53f3 2 \u56fe\uff09\u5bf9\u6a21\u578b\u6027\u80fd\u7684\u5f71\u54cd<\/sup><\/p>\n<p>\u7814\u7a76\u56e2\u961f\u63a2\u7d22\u4e86\u5173\u952e ToRL \u8bbe\u7f6e\u5bf9\u6700\u7ec8\u6027\u80fd\u548c\u884c\u4e3a\u7684\u5f71\u54cd\uff1a<\/p>\n<p>\u9996\u5148\uff0c\u5b9e\u9a8c\u63a2\u7a76\u4e86\u589e\u52a0 C\uff08\u5355\u6b21\u54cd\u5e94\u751f\u6210\u4e2d\u53ef\u8c03\u7528\u7684\u6700\u5927\u5de5\u5177\u6570\uff09\u7684\u5f71\u54cd\u3002\u5c06 C \u4ece 1 \u589e\u52a0\u5230 2 \u663e\u8457\u63d0\u9ad8\u4e86\u6027\u80fd\uff0c\u5e73\u5747\u51c6\u786e\u7387\u63d0\u9ad8\u7ea6 2%\u3002\u7136\u800c\uff0c\u589e\u52a0 C \u4f1a\u5927\u5e45\u964d\u4f4e\u8bad\u7ec3\u901f\u5ea6\uff0c\u9700\u8981\u5728\u6027\u80fd\u548c\u6548\u7387\u4e4b\u95f4\u8fdb\u884c\u6743\u8861\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u5206\u6790\u4e86\u5c06\u4ee3\u7801\u53ef\u6267\u884c\u6027\u5956\u52b1\u7eb3\u5165\u5956\u52b1\u5851\u9020\u7684\u5f71\u54cd\u3002\u7ed3\u679c\u8868\u660e\uff0c\u8fd9\u79cd\u5956\u52b1\u8bbe\u8ba1\u5e76\u672a\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u3002\u7814\u7a76\u56e2\u961f\u63a8\u6d4b\uff0c\u5bf9\u6267\u884c\u9519\u8bef\u8fdb\u884c\u60e9\u7f5a\u53ef\u80fd\u4f1a\u6fc0\u52b1\u6a21\u578b\u751f\u6210\u8fc7\u4e8e\u7b80\u5355\u7684\u4ee3\u7801\u4ee5\u6700\u5c0f\u5316\u9519\u8bef\uff0c\u4ece\u800c\u53ef\u80fd\u963b\u788d\u5176\u6b63\u786e\u89e3\u51b3\u95ee\u9898\u7684\u80fd\u529b\u3002<\/p>\n<p><strong>\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u6269\u5c55\u6d8c\u73b0\u7684\u8ba4\u77e5\u884c\u4e3a<\/strong><\/p>\n<p>\u6a21\u578b\u8bad\u7ec3\u540e\u671f\u51fa\u73b0\u4e86\u4e00\u4e9b\u6709\u8da3\u7684\u73b0\u8c61\uff0c\u8fd9\u4e9b\u73b0\u8c61\u5e2e\u52a9\u6211\u4eec\u6df1\u5165\u7406\u89e3\u6a21\u578b\u4f7f\u7528\u5de5\u5177\u89e3\u51b3\u95ee\u9898\u7684\u8ba4\u77e5\u884c\u4e3a\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u6a21\u578b\u80fd\u591f\u6839\u636e\u4ee3\u7801\u89e3\u91ca\u5668\u7684\u6267\u884c\u53cd\u9988\u8c03\u6574\u5176\u63a8\u7406\u3002\u5728\u4e00\u4e2a\u6848\u4f8b\u4e2d\uff0c\u6a21\u578b\u9996\u5148\u7f16\u5199\u4e86\u4ee3\u7801\uff0c\u4f46\u7531\u4e8e\u4e0d\u5f53\u5904\u7406\u5bfc\u81f4\u7d22\u5f15\u9519\u8bef\u3002\u5728\u6536\u5230 &#8220;TypeError: &#8216;int&#8217; object is not subscriptable&#8221; \u7684\u53cd\u9988\u540e\uff0c\u5b83\u8fc5\u901f\u8c03\u6574\u5e76\u751f\u6210\u4e86\u53ef\u6267\u884c\u4ee3\u7801\uff0c\u6700\u7ec8\u63a8\u65ad\u51fa\u6b63\u786e\u7b54\u6848\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-b603974f892b4dc7f805eaa86709ecb3.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-b603974f892b4dc7f805eaa86709ecb3.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u56fe 7: \u6848\u4f8b 1-ToRL \u901a\u8fc7\u6267\u884c\u5668\u62a5\u9519\u53cd\u9988\u91cd\u65b0\u6784\u5efa\u63a8\u7406\u4ee3\u7801<\/sup><\/p>\n<p>\u53e6\u4e00\u4e2a\u6848\u4f8b\u5c55\u793a\u4e86\u6a21\u578b\u7684\u53cd\u601d\u8ba4\u77e5\u884c\u4e3a\u3002\u6a21\u578b\u6700\u521d\u901a\u8fc7\u81ea\u7136\u8bed\u8a00\u63a8\u7406\u89e3\u51b3\u95ee\u9898\uff0c\u7136\u540e\u901a\u8fc7\u5de5\u5177\u8fdb\u884c\u9a8c\u8bc1\uff0c\u4f46\u53d1\u73b0\u4e0d\u4e00\u81f4\u3002\u56e0\u6b64\uff0c\u6a21\u578b\u8fdb\u4e00\u6b65\u8fdb\u884c\u4fee\u6b63\uff0c\u6700\u7ec8\u751f\u6210\u6b63\u786e\u7b54\u6848\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-6e9b2dda015ea76746d4289954c7c582.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-6e9b2dda015ea76746d4289954c7c582.png\"><\/a><\/section>\n<p><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 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