{"id":38629,"date":"2025-02-19T22:00:52","date_gmt":"2025-02-19T14:00:52","guid":{"rendered":"https:\/\/17aitech.com\/?p=38629"},"modified":"2025-02-19T22:00:52","modified_gmt":"2025-02-19T14:00:52","slug":"%e5%a4%a7%e6%a8%a1%e5%9e%8b%e5%bc%ba%e5%8c%96%e5%ad%a6%e4%b9%a0%e6%96%b0%e5%8f%91%e7%8e%b0%ef%bc%9a%e5%88%a0%e5%87%8f84%e6%95%b0%e6%8d%ae%e5%8f%8d%e6%8f%90%e5%8d%87%e6%95%88%e6%9e%9c","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=38629","title":{"rendered":"\u5927\u6a21\u578b\u5f3a\u5316\u5b66\u4e60\u65b0\u53d1\u73b0\uff1a\u5220\u51cf84%\u6570\u636e\u53cd\u63d0\u5347\u6548\u679c"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-02-19-13\" target=\"_blank\">\u5927\u6a21\u578b\u5f3a\u5316\u5b66\u4e60\u65b0\u53d1\u73b0\uff1a\u5220\u51cf84%\u6570\u636e\u53cd\u63d0\u5347\u6548\u679c<\/a><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-996a0b8e77299af1f938b9c579f10a1d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-996a0b8e77299af1f938b9c579f10a1d.png\"><\/a><\/p>\n<blockquote data-author-name=\"\" data-content-utf8-length=\"166\" data-source-title=\"\" data-type=\"2\" data-url=\"\">\n<section>\n<p>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<\/p>\n<\/section>\n<\/blockquote>\n<section>\n<p>\u5728\u4eba\u5de5\u667a\u80fd\u9886\u57df\uff0c&#8221;\u66f4\u5927\u5373\u66f4\u5f3a&#8221; \u7684\u7406\u5ff5\u4e00\u76f4\u4e3b\u5bfc\u7740\u5927\u6a21\u578b\u5f3a\u5316\u5b66\u4e60\u7684\u53d1\u5c55\u65b9\u5411\u3002\u7279\u522b\u662f\u5728\u63d0\u5347\u5927\u8bed\u8a00\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u65b9\u9762\uff0c\u4e1a\u754c\u666e\u904d\u8ba4\u4e3a\u9700\u8981\u6d77\u91cf\u7684\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u6570\u636e\u624d\u80fd\u83b7\u5f97\u7a81\u7834\u3002\u7136\u800c\uff0c\u6700\u65b0\u7814\u7a76\u5374\u7ed9\u51fa\u4e86\u4e00\u4e2a\u4ee4\u4eba\u60ca\u559c\u7684\u53d1\u73b0\uff1a<strong>\u5728\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u4e2d\uff0c\u6570\u636e\u7684\u5b66\u4e60\u5f71\u54cd\u529b\u8fdc\u6bd4\u6570\u91cf\u91cd\u8981<\/strong>\u3002\u901a\u8fc7\u5206\u6790\u6a21\u578b\u7684\u5b66\u4e60\u8f68\u8ff9\uff0c\u7814\u7a76\u53d1\u73b0\u7cbe\u5fc3\u9009\u62e9\u7684 <strong>1,389 \u4e2a\u9ad8\u5f71\u54cd\u529b\u6837\u672c<\/strong>\uff0c\u5c31\u80fd<strong>\u8d85\u8d8a\u5b8c\u6574\u7684 8,523 \u4e2a\u6837\u672c<\/strong>\u6570\u636e\u96c6\u7684\u6548\u679c\u3002\u8fd9\u4e00\u53d1\u73b0\u4e0d\u4ec5\u6311\u6218\u4e86\u4f20\u7edf\u8ba4\u77e5\uff0c\u66f4\u63ed\u793a\u4e86\u4e00\u4e2a\u5173\u952e\u4e8b\u5b9e\uff1a<strong>\u63d0\u5347\u5f3a\u5316\u5b66\u4e60\u6548\u679c\u7684\u5173\u952e\uff0c\u5728\u4e8e\u627e\u5230\u4e0e\u6a21\u578b\u5b66\u4e60\u5386\u7a0b\u9ad8\u5ea6\u5339\u914d\u7684\u8bad\u7ec3\u6570\u636e\u3002<\/strong><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-f383d143e6b018a9ba44c5e9be62d83b.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-f383d143e6b018a9ba44c5e9be62d83b.png\"><\/a><\/p>\n<ul>\n<li>\n<p>\u8bba\u6587\u6807\u9898\uff1aLIMR: Less is More for RL Scaling<\/p>\n<\/li>\n<li>\n<p>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2502.11886<\/p>\n<\/li>\n<li>\n<p>\u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/GAIR-NLP\/LIMR<\/p>\n<\/li>\n<li>\n<p>\u6570\u636e\u96c6\u5730\u5740\uff1ahttps:\/\/huggingface.co\/datasets\/GAIR\/LIMR<\/p>\n<\/li>\n<li>\n<p>\u6a21\u578b\u5730\u5740\uff1ahttps:\/\/huggingface.co\/GAIR\/LIMR<\/p>\n<\/li>\n<\/ul>\n<p><strong>\u4e00\u3001\u6311\u6218\u4f20\u7edf\uff1a\u91cd\u65b0\u601d\u8003\u5f3a\u5316\u5b66\u4e60\u7684\u6570\u636e\u7b56\u7565<\/strong><\/p>\n<p>\u8fd1\u671f\uff0c\u5f3a\u5316\u5b66\u4e60\u5728\u63d0\u5347\u5927\u8bed\u8a00\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u65b9\u9762\u53d6\u5f97\u4e86\u663e\u8457\u6210\u6548\u3002\u4ece OpenAI \u7684 o1 \u5230 Deepseek R1\uff0c\u518d\u5230 Kimi1.5\uff0c\u8fd9\u4e9b\u6a21\u578b\u90fd\u5c55\u793a\u4e86\u5f3a\u5316\u5b66\u4e60\u5728\u57f9\u517b\u6a21\u578b\u7684\u81ea\u6211\u9a8c\u8bc1\u3001\u53cd\u601d\u548c\u6269\u5c55\u601d\u7ef4\u94fe\u7b49\u590d\u6742\u63a8\u7406\u884c\u4e3a\u65b9\u9762\u7684\u5de8\u5927\u6f5c\u529b\u3002\u8fd9\u4e9b\u6210\u529f\u6848\u4f8b\u4f3c\u4e4e\u5728\u6697\u793a\uff1a\u8981\u83b7\u5f97\u66f4\u5f3a\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5c31\u9700\u8981\u66f4\u591a\u7684\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u6570\u636e\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8fd9\u4e9b\u5f00\u521b\u6027\u5de5\u4f5c\u7559\u4e0b\u4e86\u4e00\u4e2a\u5173\u952e\u95ee\u9898\uff1a<strong>\u5230\u5e95\u9700\u8981\u591a\u5c11\u8bad\u7ec3\u6570\u636e\u624d\u80fd\u6709\u6548\u63d0\u5347\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\uff1f<\/strong>\u76ee\u524d\u7684\u7814\u7a76\u4ece 8000 \u5230 150000 \u6570\u636e\u91cf\u4e0d\u7b49\uff0c\u5374\u6ca1\u6709\u4e00\u4e2a\u660e\u786e\u7684\u7b54\u6848\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u79cd\u6570\u636e\u89c4\u6a21\u7684\u4e0d\u900f\u660e\u6027\u5e26\u6765\u4e86\u4e24\u4e2a\u6839\u672c\u6027\u6311\u6218\uff1a<\/p>\n<ul>\n<li>\n<p>\u7814\u7a76\u56e2\u961f\u53ea\u80fd\u4f9d\u9760\u53cd\u590d\u8bd5\u9519\u6765\u786e\u5b9a\u6570\u636e\u91cf\uff0c\u8fd9\u5bfc\u81f4\u4e86\u5927\u91cf\u8ba1\u7b97\u8d44\u6e90\u7684\u6d6a\u8d39<\/p>\n<\/li>\n<li>\n<p>\u9886\u57df\u5185\u7f3a\u4e4f\u5bf9\u6837\u672c\u6570\u91cf\u5982\u4f55\u5f71\u54cd\u6a21\u578b\u6027\u80fd\u7684\u7cfb\u7edf\u6027\u5206\u6790\uff0c\u4f7f\u5f97\u96be\u4ee5\u505a\u51fa\u5408\u7406\u7684\u8d44\u6e90\u5206\u914d\u51b3\u7b56<\/p>\n<\/li>\n<\/ul>\n<p>\u8fd9\u79cd\u60c5\u51b5\u4fc3\u4f7f\u7814\u7a76\u56e2\u961f\u63d0\u51fa\u4e00\u4e2a\u66f4\u672c\u8d28\u7684\u95ee\u9898\uff1a<strong>\u662f\u5426\u5b58\u5728\u4e00\u79cd\u65b9\u6cd5\uff0c\u80fd\u591f\u8bc6\u522b\u51fa\u771f\u6b63\u5bf9\u6a21\u578b\u5b66\u4e60\u6709\u5e2e\u52a9\u7684\u8bad\u7ec3\u6570\u636e\uff1f<\/strong>\u7814\u7a76\u4ece\u4e00\u4e2a\u57fa\u7840\u573a\u666f\u5f00\u59cb\u63a2\u7d22\uff1a\u76f4\u63a5\u4ece\u57fa\u5ea7\u6a21\u578b\u51fa\u53d1\uff0c\u4e0d\u501f\u52a9\u4efb\u4f55\u6570\u636e\u84b8\u998f\uff08\u7c7b\u4f3c Deepseek R1-zero \u7684\u8bbe\u7f6e\uff09\u3002\u901a\u8fc7\u6df1\u5165\u7814\u7a76\u6a21\u578b\u5728\u5f3a\u5316\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u7684\u5b66\u4e60\u8f68\u8ff9\uff0c\u7814\u7a76\u53d1\u73b0\uff1a<strong>\u5e76\u975e\u6240\u6709\u8bad\u7ec3\u6570\u636e\u90fd\u5bf9\u6a21\u578b\u7684\u8fdb\u6b65\u8d21\u732e\u76f8\u540c\u3002<\/strong>\u6709\u4e9b\u6570\u636e\u80fd\u591f\u663e\u8457\u63a8\u52a8\u6a21\u578b\u7684\u5b66\u4e60\uff0c\u800c\u6709\u4e9b\u5219\u51e0\u4e4e\u6ca1\u6709\u5f71\u54cd\u3002<\/p>\n<p>\u8fd9\u4e00\u53d1\u73b0\u4fc3\u4f7f\u7814\u7a76\u56e2\u961f\u5f00\u53d1\u4e86<strong>\u5b66\u4e60\u5f71\u54cd\u529b\u5ea6\u91cf<\/strong><strong>\uff08Learning Impact Measurement, LIM\uff09<\/strong>\u65b9\u6cd5\u3002\u901a\u8fc7\u5206\u6790\u6a21\u578b\u7684\u5b66\u4e60\u66f2\u7ebf\uff0cLIM \u53ef\u4ee5\u81ea\u52a8\u8bc6\u522b\u90a3\u4e9b\u4e0e\u6a21\u578b\u5b66\u4e60\u8fdb\u7a0b\u9ad8\u5ea6\u5339\u914d\u7684 &#8220;\u9ec4\u91d1\u6837\u672c&#8221;\u3002\u5b9e\u9a8c\u7ed3\u679c\u8bc1\u660e\u4e86\u8fd9\u4e00\u65b9\u6cd5\u7684\u6709\u6548\u6027\uff1a<\/p>\n<ul>\n<li>\n<p>\u7cbe\u9009\u7684 1,389 \u4e2a\u6837\u672c\u5c31\u80fd\u8fbe\u5230\u751a\u81f3\u8d85\u8d8a\u4f7f\u7528 8,523 \u4e2a\u6837\u672c\u7684\u6548\u679c\u3002<\/p>\n<\/li>\n<\/ul>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-e637d31bf40b0f1366249fcf1cd52b3b.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-e637d31bf40b0f1366249fcf1cd52b3b.png\"><\/a><\/p>\n<p><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u7cbe\u9009 1,389 \u4e2a\u6837\u672c\u5c31\u80fd\u8fbe\u5230\u5168\u91cf\u6570\u636e\u7684\u6548\u679c\uff0c\u5728\u5c0f\u6a21\u578b\u4e0a\u5f3a\u5316\u5b66\u4e60\u4f18\u4e8e\u76d1\u7763\u5fae\u8c03<\/sup><\/em><\/p>\n<p>\u8fd9\u4e9b\u53d1\u73b0\u66f4\u65b0\u4e86\u5b66\u672f\u754c\u5bf9\u5f3a\u5316\u5b66\u4e60\u6269\u5c55\u7684\u8ba4\u77e5\uff1a<strong>\u63d0\u5347\u6a21\u578b\u6027\u80fd\u7684\u5173\u952e\u4e0d\u5728\u4e8e\u7b80\u5355\u5730\u589e\u52a0\u6570\u636e\u91cf\uff0c\u800c\u5728\u4e8e\u5982\u4f55\u627e\u5230\u90a3\u4e9b\u771f\u6b63\u80fd\u4fc3\u8fdb\u6a21\u578b\u5b66\u4e60\u7684\u9ad8\u8d28\u91cf\u6837\u672c\u3002<\/strong>\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u9879\u7814\u7a76\u63d0\u4f9b\u4e86\u4e00\u79cd\u81ea\u52a8\u5316\u7684\u65b9\u6cd5\u6765\u8bc6\u522b\u8fd9\u4e9b\u6837\u672c\uff0c\u4f7f\u5f97\u9ad8\u6548\u7684\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u6210\u4e3a\u53ef\u80fd\u3002<\/p>\n<p><strong>\u4e8c\u3001\u5bfb\u627e &#8220;\u9ec4\u91d1&#8221; \u6837\u672c\uff1a\u6570\u636e\u7684\u5b66\u4e60\u5f71\u54cd\u529b\u6d4b\u91cf\uff08LIM\uff09<\/strong><\/p>\n<p>\u8981\u627e\u5230\u771f\u6b63\u6709\u4ef7\u503c\u7684\u8bad\u7ec3\u6837\u672c\uff0c\u7814\u7a76\u56e2\u961f\u6df1\u5165\u5206\u6790\u4e86\u6a21\u578b\u5728\u5f3a\u5316\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u7684\u5b66\u4e60\u52a8\u6001\u3002\u901a\u8fc7\u5bf9 MATH-FULL \u6570\u636e\u96c6\uff08\u5305\u542b 8,523 \u4e2a\u4e0d\u540c\u96be\u5ea6\u7ea7\u522b\u7684\u6570\u5b66\u95ee\u9898\uff09\u7684\u5206\u6790\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u4e86\u4e00\u4e2a\u6709\u8da3\u7684\u73b0\u8c61\uff1a\u4e0d\u540c\u7684\u8bad\u7ec3\u6837\u672c\u5bf9\u6a21\u578b\u5b66\u4e60\u7684\u8d21\u732e\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002<\/p>\n<p><strong>\u5b66\u4e60\u8f68\u8ff9\u7684\u5dee\u5f02\u6027<\/strong><\/p>\n<p>\u5728\u4ed4\u7ec6\u89c2\u5bdf\u6a21\u578b\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u8868\u73b0\u65f6\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u4e86\u4e09\u79cd\u5178\u578b\u7684\u5b66\u4e60\u6a21\u5f0f\uff1a<\/p>\n<ul>\n<li>\n<p>\u90e8\u5206\u6837\u672c\u7684\u5956\u52b1\u503c\u59cb\u7ec8\u63a5\u8fd1\u96f6\uff0c\u8868\u660e\u6a21\u578b\u5bf9\u8fd9\u4e9b\u95ee\u9898\u59cb\u7ec8\u96be\u4ee5\u638c\u63e1<\/p>\n<\/li>\n<li>\n<p>\u67d0\u4e9b\u6837\u672c\u80fd\u8fc5\u901f\u8fbe\u5230\u9ad8\u5956\u52b1\u503c\uff0c\u663e\u793a\u6a21\u578b\u5f88\u5feb\u5c31\u638c\u63e1\u4e86\u89e3\u51b3\u65b9\u6cd5<\/p>\n<\/li>\n<li>\n<p>\u6700\u6709\u8da3\u7684\u662f\u90a3\u4e9b\u5c55\u73b0\u51fa\u52a8\u6001\u5b66\u4e60\u8fdb\u5c55\u7684\u6837\u672c\uff0c\u5b83\u4eec\u7684\u5956\u52b1\u503c\u5448\u73b0\u4e0d\u540c\u7684\u63d0\u5347\u901f\u7387<\/p>\n<\/li>\n<\/ul>\n<p>\u8fd9\u4e00\u53d1\u73b0\u5f15\u53d1\u4e86\u4e00\u4e2a\u5173\u952e\u601d\u8003\uff1a<strong>\u5982\u679c\u80fd\u591f\u627e\u5230\u90a3\u4e9b\u6700\u5339\u914d\u6a21\u578b\u6574\u4f53\u5b66\u4e60\u8f68\u8ff9\u7684\u6837\u672c\uff0c\u662f\u5426\u5c31\u80fd\u5b9e\u73b0\u66f4\u9ad8\u6548\u7684\u8bad\u7ec3\uff1f<\/strong><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-4a3426672a694f7dc630ea7eec06e042.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-4a3426672a694f7dc630ea7eec06e042.png\"><\/a><\/p>\n<p><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (a) \u4e0d\u540c\u8bad\u7ec3\u6837\u672c\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5c55\u73b0\u51fa\u7684\u591a\u6837\u5316\u5b66\u4e60\u6a21\u5f0f\u3002(b) \u6837\u672c\u5b66\u4e60\u8f68\u8ff9\u4e0e\u5e73\u5747\u5956\u52b1\u66f2\u7ebf\uff08\u7ea2\u8272\uff09\u7684\u6bd4\u8f83\u3002<\/sup><\/em><\/p>\n<p><strong>LIM\uff1a\u4e00\u79cd\u81ea\u52a8\u5316\u7684\u6837\u672c\u8bc4\u4f30\u65b9\u6cd5<\/strong><\/p>\n<p>\u57fa\u4e8e\u4e0a\u8ff0\u89c2\u5bdf\uff0c\u7814\u7a76\u56e2\u961f\u5f00\u53d1\u4e86\u5b66\u4e60\u5f71\u54cd\u529b\u6d4b\u91cf\uff08Learning Impact Measurement, LIM\uff09\u65b9\u6cd5\u3002LIM \u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a\u597d\u7684\u8bad\u7ec3\u6837\u672c\u5e94\u8be5\u4e0e\u6a21\u578b\u7684\u6574\u4f53\u5b66\u4e60\u8fdb\u7a0b\u4fdd\u6301\u540c\u6b65\u3002\u5177\u4f53\u6765\u8bf4\uff1a<\/p>\n<p>1. \u8ba1\u7b97\u53c2\u8003\u66f2\u7ebf<\/p>\n<p>\u9996\u5148\uff0c\u8ba1\u7b97\u6a21\u578b\u5728\u6240\u6709\u6837\u672c\u4e0a\u7684\u5e73\u5747\u5956\u52b1\u66f2\u7ebf\u4f5c\u4e3a\u53c2\u8003\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a88e823f6a1efbfab785adda7382fc03.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-a88e823f6a1efbfab785adda7382fc03.png\"><\/a><\/p>\n<p>\u8fd9\u6761\u66f2\u7ebf\u53cd\u6620\u4e86\u6a21\u578b\u7684\u6574\u4f53\u5b66\u4e60\u8f68\u8ff9\u3002<\/p>\n<p>2. \u8bc4\u4f30\u6837\u672c\u5bf9\u9f50\u5ea6<\/p>\n<p>\u63a5\u7740\uff0c\u4e3a\u6bcf\u4e2a\u6837\u672c\u8ba1\u7b97\u4e00\u4e2a\u5f52\u4e00\u5316\u7684\u5bf9\u9f50\u5206\u6570\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-8ba0aea59ebb5a773d5ae7c901ff715e.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-8ba0aea59ebb5a773d5ae7c901ff715e.png\"><\/a><\/p>\n<p>\u8fd9\u4e2a\u5206\u6570\u8861\u91cf\u4e86\u6837\u672c\u7684\u5b66\u4e60\u6a21\u5f0f\u4e0e\u6574\u4f53\u5b66\u4e60\u8f68\u8ff9\u7684\u5339\u914d\u7a0b\u5ea6\u3002\u5206\u6570\u8d8a\u9ad8\uff0c\u8868\u793a\u8be5\u6837\u672c\u8d8a &#8220;\u6709\u4ef7\u503c&#8221;\u3002<\/p>\n<p>3. \u7b5b\u9009\u9ad8\u4ef7\u503c\u6837\u672c<\/p>\n<p>\u6700\u540e\uff0c\u8bbe\u5b9a\u4e00\u4e2a\u8d28\u91cf\u9608\u503c \u03b8\uff0c\u9009\u53d6\u90a3\u4e9b\u5bf9\u9f50\u5206\u6570\u8d85\u8fc7\u9608\u503c\u7684\u6837\u672c\u3002\u5728\u5b9e\u9a8c\u4e2d\uff0c\u8bbe\u7f6e \u03b8 = 0.6 \u7b5b\u9009\u51fa\u4e86 1,389 \u4e2a\u9ad8\u4ef7\u503c\u6837\u672c\uff0c\u6784\u6210\u4e86\u4f18\u5316\u540e\u7684 LIMR \u6570\u636e\u96c6\u3002<\/p>\n<p>\u5bf9\u6bd4\u4e0e\u9a8c\u8bc1<\/p>\n<p>\u4e3a\u4e86\u9a8c\u8bc1 LIM \u65b9\u6cd5\u7684\u6709\u6548\u6027\uff0c\u7814\u7a76\u56e2\u961f\u8bbe\u8ba1\u4e86\u4e24\u4e2a\u57fa\u7ebf\u65b9\u6cd5\uff1a<\/p>\n<p>1. \u968f\u673a\u91c7\u6837\uff08RAND\uff09\uff1a\u4ece\u539f\u59cb\u6570\u636e\u96c6\u4e2d\u968f\u673a\u9009\u62e9 1,389 \u4e2a\u6837\u672c<\/p>\n<p>2. \u7ebf\u6027\u8fdb\u5ea6\u5206\u6790\uff08LINEAR\uff09\uff1a\u4e13\u6ce8\u4e8e\u90a3\u4e9b\u663e\u793a\u7a33\u5b9a\u6539\u8fdb\u7684\u6837\u672c<\/p>\n<p>\u8fd9\u4e9b\u5bf9\u7167\u5b9e\u9a8c\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4e86 LIM \u7684\u4f18\u52bf\uff1a\u5b83\u4e0d\u4ec5\u80fd\u6355\u83b7\u7a33\u5b9a\u8fdb\u6b65\u7684\u6837\u672c\uff0c\u8fd8\u80fd\u8bc6\u522b\u90a3\u4e9b\u5728\u65e9\u671f\u5feb\u901f\u63d0\u5347\u540e\u8d8b\u4e8e\u7a33\u5b9a\u7684\u6709\u4ef7\u503c\u6837\u672c\u3002<\/p>\n<p>\u5956\u52b1\u8bbe\u8ba1<\/p>\n<p>\u5bf9\u4e8e\u5956\u52b1\u673a\u5236\u7684\u8bbe\u8ba1\uff0c\u7814\u7a76\u56e2\u961f\u501f\u9274\u4e86 Deepseek R1 \u7684\u7ecf\u9a8c\uff0c\u91c7\u7528\u4e86\u7b80\u5355\u800c\u6709\u6548\u7684\u89c4\u5219\u578b\u5956\u52b1\u51fd\u6570\uff1a<\/p>\n<ul>\n<li>\n<p>\u5f53\u7b54\u6848\u5b8c\u5168\u6b63\u786e\u65f6\uff0c\u7ed9\u4e88 + 1 \u7684\u6b63\u5411\u5956\u52b1<\/p>\n<\/li>\n<li>\n<p>\u5f53\u7b54\u6848\u9519\u8bef\u4f46\u683c\u5f0f\u6b63\u786e\u65f6\uff0c\u7ed9\u4e88 &#8211; 0.5 \u7684\u8d1f\u5411\u5956\u52b1<\/p>\n<\/li>\n<li>\n<p>\u5f53\u7b54\u6848\u5b58\u5728\u683c\u5f0f\u9519\u8bef\u65f6\uff0c\u7ed9\u4e88 &#8211; 1 \u7684\u8d1f\u5411\u5956\u52b1<\/p>\n<\/li>\n<\/ul>\n<p>\u8fd9\u79cd\u4e09\u7ea7\u5206\u660e\u7684\u5956\u52b1\u673a\u5236\u4e0d\u4ec5\u80fd\u51c6\u786e\u53cd\u6620\u6a21\u578b\u7684\u89e3\u9898\u80fd\u529b\uff0c\u8fd8\u80fd\u5f15\u5bfc\u6a21\u578b\u6ce8\u610f\u7b54\u6848\u7684\u89c4\u8303\u6027\u3002<\/p>\n<p><strong>\u4e09\u3001\u5b9e\u9a8c\u9a8c\u8bc1\uff1a\u5c11\u5373\u662f\u591a\u7684\u529b\u91cf<\/strong><\/p>\n<p><strong>\u5b9e\u9a8c\u8bbe\u7f6e\u4e0e\u57fa\u51c6<\/strong><\/p>\n<p>\u7814\u7a76\u56e2\u961f\u91c7\u7528 PPO \u7b97\u6cd5\u5728 Qwen2.5-Math-7B \u57fa\u5ea7\u6a21\u578b\u4e0a\u8fdb\u884c\u4e86\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\uff0c\u5e76\u5728\u591a\u4e2a\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u57fa\u51c6\u4e0a\u8fdb\u884c\u4e86\u8bc4\u4f30\uff0c\u5305\u62ec MATH500\u3001AIME2024 \u548c AMC2023 \u7b49\u7ade\u8d5b\u7ea7\u6570\u636e\u96c6\u3002<\/p>\n<p><strong>\u4e3b\u8981\u53d1\u73b0<\/strong><\/p>\n<p>\u5b9e\u9a8c\u7ed3\u679c\u4ee4\u4eba\u632f\u594b\u3002\u4f7f\u7528 LIMR \u7cbe\u9009\u7684 1,389 \u4e2a\u6837\u672c\uff0c\u6a21\u578b\u4e0d\u4ec5\u8fbe\u5230\u4e86\u4f7f\u7528\u5168\u91cf 8,523 \u4e2a\u6837\u672c\u8bad\u7ec3\u7684\u6027\u80fd\uff0c\u5728\u67d0\u4e9b\u6307\u6807\u4e0a\u751a\u81f3\u53d6\u5f97\u4e86\u66f4\u597d\u7684\u8868\u73b0\uff1a<\/p>\n<ul>\n<li>\n<p>\u5728 AIME2024 \u4e0a\u8fbe\u5230\u4e86 32.5% \u7684\u51c6\u786e\u7387<\/p>\n<\/li>\n<li>\n<p>\u5728 MATH500 \u4e0a\u8fbe\u5230\u4e86 78.0% \u7684\u51c6\u786e\u7387<\/p>\n<\/li>\n<li>\n<p>\u5728 AMC2023 \u4e0a\u8fbe\u5230\u4e86 63.8% \u7684\u51c6\u786e\u7387<\/p>\n<\/li>\n<\/ul>\n<p>\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u968f\u673a\u9009\u62e9\u76f8\u540c\u6570\u91cf\u6837\u672c\u7684\u57fa\u7ebf\u6a21\u578b\uff08RAND\uff09\u8868\u73b0\u663e\u8457\u8f83\u5dee\uff0c\u8fd9\u8bc1\u5b9e\u4e86 LIM \u9009\u62e9\u7b56\u7565\u7684\u6709\u6548\u6027\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-4b0f9c4cfaa362060961a57bcba6e401.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-4b0f9c4cfaa362060961a57bcba6e401.png\"><\/a><\/p>\n<p><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u4e09\u79cd\u6570\u636e\u9009\u62e9\u7b56\u7565\u7684\u6027\u80fd\u5bf9\u6bd4\uff1aLIMR \u4ee5\u66f4\u5c11\u7684\u6570\u636e\u8fbe\u5230\u66f4\u597d\u7684\u6548\u679c<\/sup><\/em><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-aae3103e3554f47e18035f4dedcd2005.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-aae3103e3554f47e18035f4dedcd2005.png\"><\/a><\/p>\n<p><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 LIMR \u5728\u4e09\u4e2a\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u4e0a\u7684\u8bad\u7ec3\u52a8\u6001\u8868\u73b0\u4e0e\u5168\u91cf\u6570\u636e\u76f8\u5f53\uff0c\u663e\u8457\u4f18\u4e8e\u968f\u673a\u91c7\u6837<\/sup><\/em><\/p>\n<p><strong>\u8bad\u7ec3\u52a8\u6001\u5206\u6790<\/strong><\/p>\n<p>\u66f4\u6709\u8da3\u7684\u662f\u6a21\u578b\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u8868\u73b0\u51fa\u7684\u52a8\u6001\u7279\u5f81\u3002LIMR \u4e0d\u4ec5\u5728\u51c6\u786e\u7387\u4e0a\u8868\u73b0\u51fa\u8272\uff0c\u5176\u8bad\u7ec3\u8fc7\u7a0b\u4e5f\u5c55\u73b0\u51fa\u4e86\u66f4\u7a33\u5b9a\u7684\u7279\u5f81\uff1a<\/p>\n<ul>\n<li>\n<p>\u51c6\u786e\u7387\u66f2\u7ebf\u4e0e\u4f7f\u7528\u5168\u91cf\u6570\u636e\u8bad\u7ec3\u7684\u6a21\u578b\u51e0\u4e4e\u91cd\u5408<\/p>\n<\/li>\n<li>\n<p>\u6a21\u578b\u751f\u6210\u7684\u5e8f\u5217\u957f\u5ea6\u53d8\u5316\u66f4\u52a0\u5408\u7406\uff0c\u5c55\u73b0\u51fa\u4e86\u66f4\u597d\u7684\u5b66\u4e60\u6a21\u5f0f<\/p>\n<\/li>\n<li>\n<p>\u8bad\u7ec3\u5956\u52b1\u589e\u957f\u66f4\u5feb\uff0c\u6700\u7ec8\u4e5f\u8fbe\u5230\u4e86\u66f4\u9ad8\u7684\u6c34\u5e73<\/p>\n<\/li>\n<\/ul>\n<p>\u8fd9\u4e9b\u7ed3\u679c\u4e0d\u4ec5\u9a8c\u8bc1\u4e86 LIM \u65b9\u6cd5\u7684\u6709\u6548\u6027\uff0c\u4e5f\u8868\u660e\u901a\u8fc7\u7cbe\u5fc3\u9009\u62e9\u7684\u8bad\u7ec3\u6837\u672c\uff0c\u786e\u5b9e\u53ef\u4ee5\u5b9e\u73b0 &#8220;\u5c11\u5373\u662f\u591a&#8221; \u7684\u6548\u679c\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-87a4169eec963f1f89ad076552e6328c.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-87a4169eec963f1f89ad076552e6328c.png\"><\/a><\/p>\n<p><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 LIMR \u7684\u8bad\u7ec3\u52a8\u6001\u5206\u6790\uff1a\u4ece\u7cbe\u9009\u6837\u672c\u4e2d\u83b7\u5f97\u66f4\u7a33\u5b9a\u7684\u5b66\u4e60\u6548\u679c<\/sup><\/em><\/p>\n<p><strong>\u56db\u3001\u6570\u636e\u7a00\u7f3a\u573a\u666f\u4e0b\u7684\u65b0\u53d1\u73b0\uff1aRL \u4f18\u4e8e 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