{"id":1985,"date":"2025-10-28T11:30:34","date_gmt":"2025-10-28T03:30:34","guid":{"rendered":"http:\/\/www.applicationsofllm.com\/?p=1985"},"modified":"2025-10-28T11:30:34","modified_gmt":"2025-10-28T03:30:34","slug":"delta-%e6%a1%86%e6%9e%b6%e9%aa%8c%e8%af%81%ef%bc%9arl-%e5%8f%af%e7%aa%81%e7%a0%b4%e5%9f%ba%e7%a1%80%e6%a8%a1%e5%9e%8b%e6%8e%a8%e7%90%86%e4%b8%8a%e9%99%90%ef%bc%8cuc-berkeley-%e5%9b%a2%e9%98%9f","status":"publish","type":"post","link":"http:\/\/www.applicationsofllm.com\/index.php\/2025\/10\/28\/delta-%e6%a1%86%e6%9e%b6%e9%aa%8c%e8%af%81%ef%bc%9arl-%e5%8f%af%e7%aa%81%e7%a0%b4%e5%9f%ba%e7%a1%80%e6%a8%a1%e5%9e%8b%e6%8e%a8%e7%90%86%e4%b8%8a%e9%99%90%ef%bc%8cuc-berkeley-%e5%9b%a2%e9%98%9f\/","title":{"rendered":"DELTA \u6846\u67b6\u9a8c\u8bc1\uff1aRL \u53ef\u7a81\u7834\u57fa\u7840\u6a21\u578b\u63a8\u7406\u4e0a\u9650\uff0cUC Berkeley \u56e2\u961f\u8be6\u89e3 \u201c\u987f\u609f\u5f0f\u5b66\u4e60\u201d \u673a\u5236"},"content":{"rendered":"\n<p>UC Berkeley\u3001UW\u3001AI2 \u7b49\u673a\u6784\u8054\u5408\u56e2\u961f\u6700\u65b0\u5de5\u4f5c\u63d0\u51fa\uff1a\u5728\u6070\u5f53\u7684\u8bad\u7ec3\u8303\u5f0f\u4e0b\uff0c\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\u4e0d\u4ec5\u80fd\u300c\u6253\u78e8\u300d\u5df2\u6709\u80fd\u529b\uff0c\u66f4\u80fd\u903c\u51fa\u300c\u5168\u65b0\u7b97\u6cd5\u300d\u7ea7\u7684\u63a8\u7406\u6a21\u5f0f\u3002\u4ed6\u4eec\u6784\u5efa\u4e86\u4e00\u4e2a\u4e13\u95e8\u9a8c\u8bc1\u8fd9\u4e00\u547d\u9898\u7684\u6d4b\u8bd5\u6846\u67b6 DELTA\uff0c\u5e76\u89c2\u5bdf\u5230\u4ece\u300c\u96f6\u5956\u52b1\u300d\u5230\u63a5\u8fd1100%\u7a81\u7834\u5f0f\u8dc3\u8fc1\u7684\u300cRL grokking\u300d\u73b0\u8c61\u3002<\/p>\n\n\n\n<p>\u5728AI\u7814\u7a76\u5708\uff0c\u4e00\u4e2a\u6838\u5fc3\u4e89\u8bba\u662f\uff1a\u5f3a\u5316\u5b66\u4e60\uff08<strong>RL<\/strong>\uff09\u662f\u5426\u80fd\u591f\u8d4b\u4e88\u6a21\u578b\u8d85\u8d8a\u5176\u57fa\u7840\u6a21\u578b\uff08<strong>base model<\/strong>\uff09\u7684\u63a8\u7406\u80fd\u529b\u3002<\/p>\n\n\n\n<p>\u6000\u7591\u6d3e\u89c2\u70b9\uff1a\u65e9\u5728\u56db\u6708\u4efd\uff0c\u6e05\u534e\u7684\u9ec4\u9ad8\u56e2\u961f[arXiv:2504.13837]\u6307\u51fa\uff0c\u5c3d\u7ba1\u7ecf\u8fc7 RLVR \u8bad\u7ec3\u7684\u6a21\u578b\u5728\u8f83\u5c0f\u7684\u91c7\u6837\u503c (k)\uff08\u4f8b\u5982 (k=1)\uff09\u65f6\u80fd\u4f18\u4e8e\u5176\u57fa\u7840\u6a21\u578b\uff0c\u4f46\u5f53\u91c7\u6837\u6570\u8f83\u5927\u65f6\uff0c\u57fa\u7840\u6a21\u578b\u5f80\u5f80\u80fd\u53d6\u5f97\u76f8\u540c\u6216\u66f4\u597d\u7684 pass@k \u8868\u73b0\u3002<\/p>\n\n\n\n<p>\u4ed6\u4eec\u901a\u8fc7\u8986\u76d6\u7387\uff08coverage\uff09\u548c\u56f0\u60d1\u5ea6\uff08perplexity\uff09\u5206\u6790\u63a8\u65ad\uff0c\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u6700\u7ec8\u53d7\u9650\u4e8e\u57fa\u7840\u6a21\u578b\u7684\u652f\u6301\u8303\u56f4\u3002<\/p>\n\n\n\n<p>\u7c7b\u4f3c\u5730\uff0c\u65af\u5766\u798f\u5d14\u827a\u73cd\u56e2\u961f [arXiv:2507.14843] \u4ece\u7406\u8bba\u4e0a\u8bba\u8bc1\u4e86 RLVR \u65e0\u6cd5\u7a81\u7834\u57fa\u7840\u6a21\u578b\u7684\u8868\u5f81\u6781\u9650\u3002<\/p>\n\n\n\n<p>\u8fd9\u79cd\u6000\u7591\u7684\u76f4\u89c9\u5728\u4e8e\uff1a<\/p>\n\n\n\n<p>\u5927\u591a\u6570\u9762\u5411\u63a8\u7406\u7684\u5f3a\u5316\u5b66\u4e60\uff08\u5982 GRPO\u3001PPO \u7b49\u53d8\u4f53\uff09\u901a\u8fc7\u6bd4\u8f83\u540c\u4e00\u63d0\u793a\u8bcd\uff08prompt\uff09\u4e0b\u591a\u4e2a\u91c7\u6837\u7684\u5956\u52b1\u6765\u66f4\u65b0\u6a21\u578b\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u8fd9\u4e9b\u91c7\u6837\u4e2d\u6ca1\u6709\u4e00\u4e2a\u6210\u529f\u89e3\u51b3\u4efb\u52a1\uff08\u5373 pass@K = 0\uff09\uff0c\u90a3\u4e48\u6240\u6709\u6837\u672c\u7684\u5956\u52b1\u90fd\u662f\u4e00\u6837\u5dee\u7684\uff0c\u6b64\u65f6\u68af\u5ea6\u5c06\u4f1a\u6d88\u5931\u3002<\/p>\n\n\n\n<p><strong>\u6240\u4ee5\u5173\u952e\u7684\u95ee\u9898\u5728\u4e8e<\/strong>\uff0c\u5f53\u57fa\u7840\u6a21\u578b\uff08base model\uff09\u5728\u67d0\u7c7b\u4efb\u52a1\u4e0a\u5b8c\u5168\u65e0\u6cd5\u89e3\u7b54\uff08pass@K=0\uff09\u65f6\uff1a<\/p>\n\n\n\n<p><strong>RL\u662f\u5426\u8fd8\u80fd\u7a81\u7834\u96f6\u68af\u5ea6\u74f6\u9888\uff0c\u771f\u6b63\u5b66\u5230\u65b0\u7b56\u7565\uff1f<\/strong><\/p>\n\n\n\n<p>\u6765\u81ea\u52a0\u5dde\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\uff08UC Berkeley\uff09\u4e0eAI2\u3001\u534e\u76db\u987f\u5927\u5b66\u7b49\u673a\u6784\u7684\u7814\u7a76\u56e2\u961f\uff0c\u8fd1\u65e5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u4ee4\u4eba\u632f\u594b\u7684<strong>\u7b54\u6848<\/strong>\uff1a<\/p>\n\n\n\n<p><strong>RL\u786e\u5b9e\u80fd\u8ba9\u6a21\u578b\u53d1\u73b0\u5168\u65b0\u7684\u63a8\u7406\u6a21\u5f0f\u2014\u2014\u4f46\u524d\u63d0\u662f\uff0c\u9700\u8981\u4e0d\u4e00\u6837\u7684\u8bad\u7ec3\u65b9\u5f0f\u3002<\/strong><\/p>\n\n\n\n<p>\u4ed6\u4eec\u7684\u6700\u65b0\u5de5\u4f5c\u300a<strong>RL Grokking Receipe: How Does RL Unlock and Transfer New Algorithms in LLMs?<\/strong>\u300b\u63d0\u51fa\u4e86\u4e00\u4e2a\u5d2d\u65b0\u7684\u6d4b\u8bd5\u6846\u67b6&nbsp;<strong>DELTA<\/strong>\uff0c\u4e13\u95e8\u7528\u6765\u9a8c\u8bc1\u8be5\u89c2\u70b9\u3002<\/p>\n\n\n\n<p>\u8fd9\u9879\u7814\u7a76\u4e3a<strong>\u300cRL<\/strong>\u662f\u5426\u80fd\u7a81\u7834\u6a21\u578b\u8fb9\u754c<strong>\u300d<\/strong>\u8fd9\u4e00\u4e89\u8bba\uff0c\u5e26\u6765\u4e86\u65b0\u7684\u5b9e\u9a8c\u4f9d\u636e\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"831\" height=\"261\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-91.jpeg\" alt=\"\" class=\"wp-image-1986\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-91.jpeg 831w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-91-300x94.jpeg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-91-768x241.jpeg 768w\" sizes=\"auto, (max-width: 831px) 100vw, 831px\" \/><\/figure>\n\n\n\n<p>\u8bba\u6587\uff1ahttps:\/\/www.arxiv.org\/abs\/2509.21016<\/p>\n\n\n\n<p>\u535a\u5ba2\uff1ahttps:\/\/rdi.berkeley.edu\/blog\/rl-grokking-recipe<\/p>\n\n\n\n<p><strong>\u4ece\u300c\u6253\u78e8\u300d\u5230\u300c\u987f\u609f\u300d<\/strong><\/p>\n\n\n\n<p><strong>RL\u771f\u5b66\u5230\u65b0\u7b97\u6cd5\u4e86\uff1f<\/strong><\/p>\n\n\n\n<p>\u5728\u4e3b\u6d41\u89c2\u70b9\u4e2d\uff0cRL\u4f3c\u4e4e\u88ab\u56f0\u5728\u300c\u9690\u5f62\u7684\u7ef3\u5b50\u300d\u4e0a \u2014\u2014<\/p>\n\n\n\n<p>\u6a21\u578b\u7684pass@1\u867d\u7136\u63d0\u9ad8\uff0c\u4f46\u5728\u5927\u89c4\u6a21\u91c7\u6837\u4e0b\uff08\u5982pass@128\uff09\u6027\u80fd\u5e76\u672a\u6269\u5c55\u3002<\/p>\n\n\n\n<p>\u8fd9\u610f\u5473\u7740\u5b83\u53ef\u80fd\u53ea\u662f\u91cd\u65b0\u5206\u914d\u5df2\u6709\u7b56\u7565\u7684\u6982\u7387\uff0c\u800c\u4e0d\u662f\u521b\u9020\u65b0\u7684\u7b56\u7565\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u4f2f\u514b\u5229\u56e2\u961f\u5728<strong>&nbsp;DELTA&nbsp;<\/strong>\u6d4b\u8bd5\u4e2d\u53d1\u73b0\u4e86<strong>\u300c<\/strong>\u987f\u609f\u5f0f\u8dc3\u8fc1<strong>\u300d<\/strong>\uff1a&nbsp;<strong>\u5728\u591a\u4e2a\u57fa\u7840\u6a21\u578b\u5b8c\u5168\u5931\u8d25\u7684\u4efb\u52a1\u65cf\u4e2d\uff0cRL\u8bad\u7ec3\u7ecf\u5386\u4e86\u4e00\u4e2a\u957f\u65f6\u95f4\u7684\u300c\u96f6\u5956\u52b1\u5e73\u53f0\u671f\u300d\uff0c\u968f\u540e\u7a81\u7136\u51fa\u73b0\u4e86\u51c6\u786e\u7387\u63a5\u8fd1100%\u7684\u8dc3\u8fc1 (phase transition) \u3002<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u5c06\u6b64\u63cf\u8ff0\u4e3a \u300cRL grokking\u300d\uff1a\u90a3\u4e0d\u662f\u5fae\u8c03\u7684\u5ef6\u5c55\uff0c\u800c\u662f\u300c\u60f3\u901a\u4e86\u300d\u7684\u77ac\u95f4\u3002<\/p>\n\n\n\n<p><strong>\u4e00\u4e2a\u300c\u5206\u5e03\u5916\u4efb\u52a1\u5b66\u4e60\u6027\u300d\u8bd5\u70bc\u573a<\/strong><\/p>\n\n\n\n<p>\u5f88\u591a\u5de5\u4f5c\u58f0\u79f0\u300c\u65b0\u4efb\u52a1\u300d\uff0c\u4f46\u5176\u5b9e\u4ecd\u843d\u5728\u6a21\u578b\u7684\u77e5\u8bc6\u8303\u56f4\u5185\u3002<\/p>\n\n\n\n<p>\u4f2f\u514b\u5229\u56e2\u961f\u8fd9\u6b21\u523b\u610f\u8bbe\u8ba1\u7684\u4efb\u52a1\uff0c\u5374\u771f\u6b63\u505a\u5230\u4e86\u8131\u79bb\u6a21\u578b\u7ecf\u9a8c\u7684\u5916\u90e8\u5206\u5e03 (Out-of-Distribution):<\/p>\n\n\n\n<p><strong>1. \u5168\u65b0\u7684\u8bed\u8a00\u2014\u2014\u4e92\u8054\u7f51\u4e0a\u4ece\u672a\u51fa\u73b0\u8fc7\u3002<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u56e2\u961f\u4ee5\u7ecf\u51782010 flash\u6e38\u620fManufactoria\u4e3a\u7075\u611f\uff0c\u6784\u5efa\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u5408\u6210\u7f16\u7a0b\u4e16\u754c\u3002<\/p>\n\n\n\n<p>\u8be5\u6e38\u620f\u7684\u89e3\u6cd5\u4ec5\u4ee5\u56fe\u7247\u7684\u5f62\u5f0f\u5b58\u5728\uff0c\u4e3a\u4e86\u9002\u914d\u8bed\u8a00\u6a21\u578b\uff0c\u4f5c\u8005\u5f15\u5165\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u7a0b\u5e8f\u63cf\u8ff0\u8bed\u8a00\uff0c\u4ec5\u7531\u4e24\u79cd\u539f\u59cb\u6307\u4ee4\u7ec4\u6210\uff1a<\/p>\n\n\n\n<p>Puller\uff1a\u4ece\u5de6\u4fa7\u8bfb\u53d6\u5e76\u79fb\u52a8\u7b26\u53f7\uff1b<\/p>\n\n\n\n<p>Painter\uff1a\u5728\u53f3\u4fa7\u5199\u5165\u6216\u6807\u8bb0\u7b26\u53f7\uff0c\u4ee5\u6b64\u6765\u5b8c\u6210\u8f93\u5165\u8f93\u51fa\u5339\u914d\u4efb\u52a1\u3002<\/p>\n\n\n\n<p><strong>2. \u5168\u65b0\u7684\u4efb\u52a1\u5bb6\u65cf\u2014\u2014\u4e0d\u662f\u91cd\u6df7\u5173\u5361\uff0c\u800c\u662f\u5168\u65b0\u6253\u9020\u3002<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u4e0d\u662f\u7b80\u5355\u590d\u523b\u539f\u59cb\u7684\u8c1c\u9898\uff0c\u800c\u662f\u5408\u6210\u4e86\u4e00\u6279\u5168\u65b0\u95ee\u9898\u65cf\u3002\u8fd9\u4e9b\u95ee\u9898\u65cf\u7684\u96be\u5ea6\u6709\u7b80\u5355\u6709\u56f0\u96be\uff0c\u6700\u96be\u7684\u95ee\u9898\u4f7f\u5f97GPT-5\u90fd\u53ea\u67090\u7684\u6b63\u786e\u7387\u3002<\/p>\n\n\n\n<p><strong>3. \u5168\u65b0\u7684\u63a8\u7406\u65b9\u5f0f\u2014\u2014\u4e0e\u5e38\u89c4\u4ee3\u7801\u63a8\u7406\u5b8c\u5168\u4e0d\u540c\u3002<\/strong><\/p>\n\n\n\n<p>\u4f20\u7edf\u4ee3\u7801\u5b66\u4e60\u4f9d\u8d56\u63a7\u5236\u6d41\uff08if\/for\/while\uff09\u548c\u6570\u636e\u7ed3\u6784\uff08stack\/list\/map\uff09\u3002<\/p>\n\n\n\n<p>\u800c\u5728\u8fd9\u4e2a\u6781\u7b80\u4e16\u754c\u91cc\uff0c\u6a21\u578b\u5fc5\u987b\u53d1\u660e\u4e00\u79cd\u6709\u9650\u72b6\u6001\u673a\u5f0f\u7684\u63a8\u7406\u65b9\u5f0f\uff1a\u901a\u8fc7\u5728\u5e26\u5b50\u4e24\u7aef\u4e0d\u65ad\u642c\u8fd0\u548c\u6807\u8bb0\u989c\u8272\uff0c\u5b8c\u6210\u8def\u7531\u3001\u7f13\u5b58\u3001\u6bd4\u8f83\u7b49\u64cd\u4f5c\u3002<\/p>\n\n\n\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u6a21\u578b\u5f97\u5728\u6ca1\u6709\u53d8\u91cf\u7684\u73af\u5883\u4e2d\u300c\u81ea\u9020\u7b97\u6cd5\u300d\u3002\u8fd9\u662f\u4e00\u79cd\u4eba\u7c7b\u90fd\u8981\u91cd\u65b0\u601d\u8003\u7684\u63a8\u7406\u65b9\u5f0f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"830\" height=\"310\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-25.png\" alt=\"\" class=\"wp-image-1989\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-25.png 830w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-25-300x112.png 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-25-768x287.png 768w\" sizes=\"auto, (max-width: 830px) 100vw, 830px\" \/><\/figure>\n\n\n\n<p>\u5982\u679c\u4e00\u4e2aRL\u6a21\u578b\u5728\u8fd9\u91cc\u80fd\u5b66\u4f1a\u901a\u7528\u7b56\u7565\uff0c\u90a3\u51e0\u4e4e\u53ef\u4ee5\u6392\u9664\u6389\u300c\u8bb0\u5fc6\u5df2\u6709\u4ee3\u7801\u6a21\u5f0f\u300d\u7684\u53ef\u80fd\uff0c\u5b83\u786e\u5b9e\u5728\u5b66\u4e60\u65b0\u7684\u7b97\u6cd5\u7ed3\u6784\u3002<\/p>\n\n\n\n<p><strong>\u7834\u89e3\u96f6\u68af\u5ea6\u8bc5\u5492\u7684\u5173\u952e<\/strong><\/p>\n\n\n\n<p><strong>\u4e24\u9636\u6bb5\u5956\u52b1\u8c03\u5ea6<\/strong><\/p>\n\n\n\n<p>\u4f2f\u514b\u5229\u56e2\u961f\u7684\u7a81\u7834\u5728\u4e8e\uff0c\u4ed6\u4eec\u91cd\u65b0\u8bbe\u8ba1\u4e86\u5956\u52b1\u51fd\u6570\u7684\u7ed3\u6784\u3002<\/p>\n\n\n\n<p><strong>\u9636\u6bb5\u4e00\uff1a\u5bc6\u96c6\u5956\u52b1\uff08dense reward\uff09<\/strong><\/p>\n\n\n\n<p>\u5728\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u4e0a\u7ed9\u90e8\u5206\u5206\u6570\uff0c\u800c\u975e\u975e\u9ed1\u5373\u767d\u76840\/1\u3002\u5373\u4f7f\u7a0b\u5e8f\u53ea\u901a\u8fc7\u4e86\u4e00\u534a\u6d4b\u8bd5\uff0c\u4e5f\u80fd\u83b7\u5f97\u90e8\u5206\u5956\u52b1\u3002\u8fd9\u8ba9\u6a21\u578b\u4ece\u300c\u5168\u96f6\u300d\u4e2d\u83b7\u5f97\u4e00\u4e1d\u68af\u5ea6\u4fe1\u53f7\uff0c\u5f00\u59cb\u6478\u7d22\u3002<\/p>\n\n\n\n<p>\u95ee\u9898\u662f\uff1a \u5bc6\u96c6\u5956\u52b1\u867d\u7136\u8ba9\u6a21\u578b\u300c\u6d3b\u4e86\u300d\uff0c\u4f46\u5b83\u5b66\u4f1a\u7684\u5f80\u5f80\u662f\u300c\u6295\u673a\u89e3\u300d\u2014\u2014\u901a\u8fc7\u7b80\u5355\u6a21\u5f0f\u9a97\u8fc7\u90e8\u5206\u6d4b\u8bd5\u3002<\/p>\n\n\n\n<p>\u7ed3\u679c\u662f\uff1a\u5e73\u5747\u5206\u9ad8\u4e86\uff0c\u5b8c\u5168\u901a\u8fc7\u7387\u4ecd\u63a5\u8fd1<strong>0<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"831\" height=\"309\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-24.png\" alt=\"\" class=\"wp-image-1988\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-24.png 831w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-24-300x112.png 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-24-768x286.png 768w\" sizes=\"auto, (max-width: 831px) 100vw, 831px\" \/><\/figure>\n\n\n\n<p><strong>\u9636\u6bb5\u4e8c\uff1a\u5207\u6362\u56de\u4e8c\u503c\u5956\u52b1\uff08binary reward\uff09<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u53d1\u73b0\uff0c\u5173\u952e\u5728\u4e8e\u65f6\u673a\u7684\u5207\u6362\u3002\u5f53\u6a21\u578b\u901a\u8fc7\u5bc6\u96c6\u5956\u52b1\u9636\u6bb5\u83b7\u5f97\u300c\u534a\u6b63\u786e\u300d\u7b56\u7565\u540e\uff0c\u518d\u5207\u6362\u5230\u300c\u5168\u5bf9\u624d\u7b97\u8d62\u300d\u7684\u4e8c\u503c\u5956\u52b1\uff0c\u6a21\u578b\u7a81\u7136\u8fce\u6765\u90a3\u4e00\u523b\u2014\u2014Grokking Phase Transition\uff1a\u4ece\u6a21\u7cca\u5230\u7cbe\u786e\u7684\u98de\u8dc3\u3002<\/p>\n\n\n\n<p>\u5728\u7ea6450\u6b65\u540e\uff0c\u6a21\u578b\u7a81\u7136\u5b66\u4f1a\u4e86\u4efb\u52a1\u7684\u6838\u5fc3\u7b97\u6cd5\uff0c\u4ece\u6b64\u8bad\u7ec3\u8fdb\u5165\u300c\u5f3a\u5316\u6536\u655b\u300d\u9636\u6bb5\uff0c\u6210\u529f\u7387\u7a33\u5b9a\u5728\u8fd1100%\u3002\u90a3\u4e00\u77ac\u95f4\uff0c\u4f60\u51e0\u4e4e\u80fd\u770b\u5230\u6a21\u578b\u2018\u9886\u609f\u2019\u4e86\u89c4\u5f8b\u3002<\/p>\n\n\n\n<p>\u5728DELTA\u7684\u591a\u79cd\u4efb\u52a1\u65cf\u4e2d\uff0c\u7814\u7a76\u8005\u89c2\u6d4b\u5230\u9ad8\u5ea6\u4e00\u81f4\u7684\u5b66\u4e60\u66f2\u7ebf\uff1a\u524d\u51e0\u767e\u6b65\u5185\uff0c\u5956\u52b1\u51e0\u4e4e\u4e3a\u96f6\uff1b\u63a5\u7740\u51fa\u73b0\u4e00\u6b21\u9661\u5ced\u7684\u63d0\u5347\uff1b\u6a21\u578b\u5b66\u4f1a\u4e86\u4efb\u52a1\u6838\u5fc3\u903b\u8f91\uff0c\u6027\u80fd\u7a33\u5b9a\u5728\u8fd1\u4e4e100%\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"830\" height=\"367\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-27.png\" alt=\"\" class=\"wp-image-1991\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-27.png 830w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-27-300x133.png 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-27-768x340.png 768w\" sizes=\"auto, (max-width: 830px) 100vw, 830px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u6761\u66f2\u7ebf\u5982\u540c\u4eba\u7c7b\u7684\u5b66\u4e60\u5386\u7a0b\u2014\u2014\u5148\u662f\u6f2b\u957f\u6478\u7d22\uff0c\u7136\u540e\u7075\u5149\u4e4d\u73b0\u3002<\/p>\n\n\n\n<p><strong>\u987f\u609f\u540e\u7684\u6280\u80fd\u80fd\u5426\u8fc1\u79fb\uff1f<\/strong><\/p>\n\n\n\n<p>\u56e2\u961f\u8fdb\u4e00\u6b65\u8bbe\u8ba1\u4e86&nbsp;<strong>BouncingSim<\/strong>&nbsp;\u6d4b\u8bd5\u573a\u666f\uff0c\u8ba9\u6a21\u578b\u9884\u6d4b\u5c0f\u7403\u7684\u5f39\u8df3\u8f68\u8ff9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"830\" height=\"309\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-26.png\" alt=\"\" class=\"wp-image-1990\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-26.png 830w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-26-300x112.png 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/10\/image-26-768x286.png 768w\" sizes=\"auto, (max-width: 830px) 100vw, 830px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u6d89\u53ca\u7269\u7406\u89c4\u5f8b\u4e0e\u7ec4\u5408\u63a8\u7406\u7684\u4efb\u52a1\uff0c\u662f\u4e00\u4e2a\u6781\u5177\u6311\u6218\u6027\u7684\u7f16\u7a0b\u4efb\u52a1\u3002<\/p>\n\n\n\n<p>\u7ed3\u679c\u663e\u793a\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6a21\u578b\u80fd\u5728\u8bad\u7ec3\u540e\u671f\u51fa\u73b0\u76f8\u4f3c\u7684\u300c\u987f\u609f\u66f2\u7ebf\u300d\uff1b<\/li>\n\n\n\n<li>\u5bf9\u4e8e\u53ef\u7ec4\u5408\uff08Compositional\uff09\u4efb\u52a1\uff0c\u5b83\u80fd\u590d\u7528\u5b66\u5230\u7684\u5b50\u6280\u80fd\uff1b<\/li>\n\n\n\n<li>\u4f46\u9762\u5bf9\u7279\u6b8a\u7684\u52a8\u529b\u5b66\u89c4\u5f8b\uff0c\u6a21\u578b\u4ecd\u4f1a\u5931\u6548\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u8868\u660e\uff0cRL 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\/><\/figure>\n\n\n\n<p><strong>\u6df1\u5c42\u542f\u793a1\uff1aRL\u7684\u4e24\u79cd\u6a21\u5f0f<\/strong><\/p>\n\n\n\n<p>\u8be5\u7814\u7a76\u603b\u7ed3\u51faRLVR\u5728LLM\u4e2d\u7684\u4e24\u79cd\u6a21\u5f0f\uff1a<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u538b\u7f29\u6a21\u5f0f\uff08Sharpening\uff09<\/strong>\uff1a\u91cd\u65b0\u5206\u914d\u6982\u7387\uff0c\u51cf\u5c11\u8f93\u51fa\u65b9\u5dee\uff0c\u63d0\u5347\u5355\u6b21\u91c7\u6837\u7684\u6027\u80fd\u3002<\/li>\n\n\n\n<li><strong>\u53d1\u73b0\u6a21\u5f0f\uff08Discovery\uff09<\/strong>\uff1a\u4ece\u5b8c\u5168\u4e0d\u4f1a\uff08pass@K=0\uff09\u5230\u7a33\u5b9a\u89e3\u9898\uff0c\u5b9e\u73b0\u7ed3\u6784\u6027\u7a81\u7834\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u800c\u8fdb\u5165\u53d1\u73b0\u6a21\u5f0f\u7684\u5173\u952e\u5728\u4e8e\uff1a\u5956\u52b1\u51fd\u6570\u8bbe\u8ba1\uff1b\u63a2\u7d22\u6301\u7eed\u65f6\u95f4\uff1b\u6570\u636e\u6df7\u5408\u7b56\u7565\uff1b\u4ee5\u53ca\u4efb\u52a1\u7684\u590d\u6742\u5ea6\u8fb9\u754c\u7b49\u7b49\u3002<\/strong><\/p>\n\n\n\n<p><strong>\u6df1\u5c42\u542f\u793a2\uff1a\u63d0\u5347\u300c\u786c\u6838\u4efb\u52a1\u300d\u7684\u800c\u975e\u5e73\u5747\u5206<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u56e2\u961f\u6307\u51fa\uff0c\u76ee\u524dRLVR\u7684\u8bc4\u6d4b\u5f80\u5f80\u5728\u300c\u6df7\u5408\u4efb\u52a1\u6c60\u300d\u4e0a\u53d6\u5e73\u5747\uff0c\u8fd9\u63a9\u76d6\u4e86\u6700\u5173\u952e\u7684\u300c\u786c\u6838\u4efb\u52a1\u300d\u7a81\u7834\u3002<\/p>\n\n\n\n<p>\u5728\u90a3\u4e9b\u57fa\u7840\u6a21\u578b\u5b8c\u5168\u4e0d\u4f1a\uff08pass@K=0\uff09\u7684\u4efb\u52a1\u4e0a\uff0c\u624d\u6700\u6709\u673a\u4f1a\u89c2\u5bdf\u5230RL\u7684\u300c\u521b\u9020\u6027\u7a81\u7834\u300d\u3002\u4ed6\u4eec\u5efa\u8bae\u672a\u6765\u8bc4\u4f30\u6307\u6807\u5e94\u663e\u5f0f\u62a5\u544a\u8be5\u5b50\u96c6\u7684\u8868\u73b0\uff0c\u56e0\u4e3a\u90a3\u624d\u662f\u8861\u91cf\u300c\u6a21\u578b\u662f\u5426\u80fd\u53d1\u73b0\u65b0\u7b56\u7565\u300d\u7684\u771f\u5b9e\u4fe1\u53f7\u3002<\/p>\n\n\n\n<p>\u4e3a\u6b64\uff0c\u4f2f\u514b\u5229\u56e2\u961f\u641c\u96c6\u5e76\u7ef4\u62a4\u4e86\u4e00\u4e2a\u5728\u6b64\u65b9\u5411\u4e0a\u7684\u4ee3\u8868\u6027\u5de5\u4f5c\uff1a<\/p>\n\n\n\n<p>\u6309\u300c\u7acb\u573a\u2014\u65b9\u6cd5\u2014\u8bc4\u6d4b\u2014\u6570\u636e\/\u57fa\u51c6\u2014\u8ba8\u8bba\u300d\u5206\u95e8\u522b\u7c7b\u7684\u5217\u8868\uff0c\u4fbf\u4e8e\u7814\u7a76\u8005\u76f4\u63a5\u5b9a\u4f4d\u5230<strong>&nbsp;pass@k=0&nbsp;<\/strong>\u7b49\u786c\u6838\u5b50\u96c6\u4e0a\u7684\u6700\u65b0\u8bc1\u636e\u4e0e\u65b9\u6cd5\u8def\u5f84\u3002<\/p>\n\n\n\n<p>\u9879\u76ee\u5730\u5740: https:\/\/github.com\/sunblaze-ucb\/awesome-RLVR-boundary<\/p>\n\n\n\n<p><strong>\u6df1\u5c42\u542f\u793a3\uff1a\u4ece\u7f16\u7a0b\u8fc8\u5411\u6570\u5b66\u4e0e\u79d1\u5b66\uff1aRL\u7684\u65b0\u8fb9\u7586<\/strong><\/p>\n\n\n\n<p>\u4e3a\u4f55\u8be5\u5de5\u4f5c\u9009\u62e9\u7f16\u7a0b\u4f5c\u4e3a\u7a81\u7834\u53e3\uff1f<\/p>\n\n\n\n<p>\u56e0\u4e3a\u4ee3\u7801\u4efb\u52a1\u5929\u7136\u5177\u5907\uff1a\u53ef\u9a8c\u8bc1\u7684\u5355\u5143\u6d4b\u8bd5\uff1b\u7ec6\u7c92\u5ea6\u3001\u53ef\u7ec4\u5408\u7684\u53cd\u9988\u4fe1\u53f7\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e9b\u7279\u6027\u8ba9RL\u80fd\u591f\u7cbe\u786e\u8c03\u8282\u5956\u52b1\uff0c\u5f62\u6210\u63a2\u7d22\u8def\u5f84\u3002<\/p>\n\n\n\n<p><strong>\u7814\u7a76\u8005\u8ba4\u4e3a\uff0c\u8fd9\u4e00\u601d\u8def\u5b8c\u5168\u53ef\u6269\u5c55\u5230\u6570\u5b66\u4e0e\u79d1\u5b66\u63a8\u7406\u9886\u57df\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u901a\u8fc7\u81ea\u52a8\u8bc4\u5206\uff08rubric scoring\uff09\u3001\u9010\u6b65\u68c0\u9a8c\uff08step checker\uff09\u6216\u7269\u7406\u4eff\u771f\u5668\uff08simulator feedback\uff09<\/li>\n\n\n\n<li>\u6784\u5efa\u7ec6\u7c92\u5ea6\u7684\u5956\u52b1\u7cfb\u7edf\uff0c\u4ece\u800c\u8ba9RL\u5f15\u5bfc\u6a21\u578b\u7a7f\u8d8a\u300c\u65e0\u68af\u5ea6\u300d\u5730\u5e26<\/li>\n<\/ul>\n\n\n\n<p><strong>\u7ed3\u8bed<\/strong><\/p>\n\n\n\n<p><strong>\u6a21\u578b\u300c\u771f\u6b63\u601d\u8003\u300d\u90a3\u4e00\u523b<\/strong><\/p>\n\n\n\n<p>\u8fd9\u9879\u7814\u7a76\u7684\u610f\u4e49\u4e0d\u4ec5\u5728\u4e8e\u6027\u80fd\u63d0\u5347\uff0c\u800c\u5728\u4e8e\u5b83\u5c55\u793a\u4e86<strong>LLM<\/strong>\u771f\u6b63\u7684\u5b66\u4e60\u6f5c\u80fd\uff1a<\/p>\n\n\n\n<p>\u5f3a\u5316\u5b66\u4e60\u4e0d\u53ea\u662f\u6253\u78e8\uff0c\u800c\u662f\u8ba9\u6a21\u578b\u5b66\u4f1a\u300c\u5982\u4f55\u601d\u8003\u300d\u3002<\/p>\n\n\n\n<p>\u5728AGI\u524d\u591c\u7684\u8bf8\u591a\u6280\u672f\u8def\u5f84\u4e2d\uff0cRLVR 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\u5e74\u4e8e\u5a01\u65af\u5eb7\u661f\u5927\u5b66\u9ea6\u8fea\u900a\u5206\u6821\u83b7\u535a\u58eb\u5b66\u4f4d\uff08\u5bfc\u5e08\u674e\u4e00\u7487<strong>Sharon Li<\/strong>\uff09\uff0c\u4e3b\u8981\u7814\u7a76<strong>Out-of-Distribution<\/strong>\uff08<strong>OOD<\/strong>\uff09 \u5206\u5e03\u5916\u6570\u636e\u7684\u76f8\u5173\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u53e6\u5916\u5728\u4eca\u5e745\u6708\uff0cYiyou Sun\u4e0e\u5b8b\u6653\u4e1c\uff08Dawn Song\uff09\u7b49\u4eba\u8fd8\u5728NeurIPS\u4e0a\u53d1\u8868\u4e86\u8bba\u6587\u300aOMEGA: Can LLMs Reason Outside the Box in Math?\u300b\u3002<\/p>\n\n\n\n<p>\u8be5\u7814\u7a76\u9996\u6b21\u7cfb\u7edf\u6027\u5730\u8bc4\u4f30\u4e86\u5927\u6a21\u578b\u5728\u300c\u8df3\u51fa\u76d2\u5b50\u300d\u5f0f\u6570\u5b66\u63a8\u7406\u4e2d\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u57fa\u51c6\u2014\u2014OMEGA\u3002<\/p>\n\n\n\n<p>\u9879\u76ee\u5730\u5740: https:\/\/github.com\/sunblaze-ucb\/omega<\/p>\n\n\n\n<p>\u8bba\u6587\u5730\u5740: https:\/\/arxiv.org\/abs\/2506.18880<\/p>\n\n\n\n<p>OMEGA\u805a\u7126\u4e8e\u4e09\u79cd\u5173\u952e\u7684\u300c\u8d85\u5206\u5e03\u300d\u6cdb\u5316\u80fd\u529b\uff1a<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Exploratory\uff08\u63a2\u7d22\u5f0f\uff09<\/strong>\uff1a\u8981\u6c42\u6a21\u578b\u5c06\u5df2\u638c\u63e1\u7684\u89e3\u9898\u6280\u80fd\u5e94\u7528\u5230\u540c\u9886\u57df\u4e2d\u66f4\u590d\u6742\u7684\u5b9e\u4f8b\uff1b<\/li>\n\n\n\n<li><strong>Compositional\uff08\u7ec4\u5408\u5f0f<\/strong>\uff09\uff1a\u6d4b\u8bd5\u6a21\u578b\u80fd\u5426\u6574\u5408\u4e0d\u540c\u63a8\u7406\u6280\u80fd\u89e3\u51b3\u65b0\u7684\u7efc\u5408\u6027\u95ee\u9898\uff1b<\/li>\n\n\n\n<li><strong>Transformative\uff08\u53d8\u9769\u5f0f\uff09<\/strong>\uff1a\u8003\u5bdf\u6a21\u578b\u662f\u5426\u80fd\u91c7\u7528\u521b\u65b0\u6027\u3001\u975e\u4f20\u7edf\u7684\u7b56\u7565\u8de8\u8d8a\u719f\u6089\u8303\u5f0f\uff0c\u771f\u6b63\u5b9e\u73b0\u300c\u7c7b\u4eba\u521b\u9020\u6027\u300d\u7684\u8fc1\u79fb\u63a8\u7406\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u7814\u7a76\u56e2\u961f\u57fa\u4e8e\u51e0\u4f55\u3001\u6570\u8bba\u3001\u4ee3\u6570\u3001\u7ec4\u5408\u3001\u903b\u8f91\u4e0e\u8c1c\u9898\u7b49\u591a\u9886\u57df\u6a21\u677f\u6784\u5efa\u4e86\u591a\u5c42\u7ea7\u6d4b\u8bd5\u96c6\uff0c\u5bf9\u591a\u6b3e\u9876\u7ea7\u5927\u6a21\u578b\uff08\u5305\u62ecQwen\u7cfb\u5217\uff09\u8fdb\u884c\u7cfb\u7edf\u8bc4\u4f30\u3002<\/p>\n\n\n\n<p>\u7ed3\u679c\u663e\u793a\uff0c\u5f53\u524dLLMs\u5728\u4e09\u7c7b\u6cdb\u5316\u4efb\u52a1\u4e2d\u4ecd\u5b58\u5728\u663e\u8457\u5dee\u8ddd\uff0c\u5c24\u5176\u5728\u53d8\u9769\u5f0f\u6cdb\u5316\u4e0a\u51e0\u4e4e\u6ca1\u6709\u63d0\u5347\u3002<\/p>\n\n\n\n<p><strong>\u8fd9\u4e00\u53d1\u73b0\u63ed\u793a\u51fa\u5f53\u4e0b\u6a21\u578b\u867d\u7136\u80fd\u300c\u6a21\u4eff\u601d\u8003\u300d\uff0c\u4f46\u5728\u521b\u9020\u6027\u548c\u7ed3\u6784\u6027\u8fc1\u79fb\u63a8\u7406\u4e0a\u4ecd\u53d7\u9650\u4e8e\u57fa\u7840\u6a21\u578b\u7684\u8fb9\u754c\u3002<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u4f5c\u8005\u6307\u51fa\uff0cOMEGA\u4e0d\u4ec5\u63d0\u4f9b\u4e86\u4e00\u4e2a\u8861\u91cf\u6a21\u578b\u300c\u6570\u5b66\u521b\u9020\u529b\u300d\u7684\u65b0\u89c6\u89d2\uff0c\u66f4\u4e3a\u672a\u6765RL-for-Reasoning\uff08\u63a8\u7406\u5f3a\u5316\u5b66\u4e60\uff09\u7814\u7a76\u63d0\u4f9b\u4e86\u5b9e\u9a8c\u57fa\u7840\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>UC Berkeley\u3001UW\u3001AI2 \u7b49\u673a\u6784\u8054\u5408\u56e2\u961f\u6700\u65b0\u5de5\u4f5c\u63d0\u51fa\uff1a\u5728\u6070\u5f53\u7684\u8bad\u7ec3\u8303\u5f0f\u4e0b\uff0c\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\u4e0d\u4ec5\u80fd\u300c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1987,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-1985","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10"],"_links":{"self":[{"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/posts\/1985","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/comments?post=1985"}],"version-history":[{"count":1,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/posts\/1985\/revisions"}],"predecessor-version":[{"id":1993,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/posts\/1985\/revisions\/1993"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/media\/1987"}],"wp:attachment":[{"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/media?parent=1985"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/categories?post=1985"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.applicationsofllm.com\/index.php\/wp-json\/wp\/v2\/tags?post=1985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}