{"id":1139186,"date":"2025-05-14T04:10:16","date_gmt":"2025-05-14T11:10:16","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-blog-post&#038;p=1139186"},"modified":"2025-06-05T03:53:25","modified_gmt":"2025-06-05T10:53:25","slug":"llms-reasoning-abilities","status":"publish","type":"msr-blog-post","link":"https:\/\/www.microsoft.com\/en-us\/research\/articles\/llms-reasoning-abilities\/","title":{"rendered":"\u4ece\u76f4\u89c9\u5230\u201c\u6df1\u5ea6\u601d\u8003\u201d\uff1a\u591a\u7ef4\u8fdb\u5316\u7684\u5927\u6a21\u578b\u63a8\u7406\u80fd\u529b"},"content":{"rendered":"\n<p>\u7f16\u8005\u6309\uff1a\u5c3d\u7ba1\u8fd1\u5e74\u6765\u4eba\u5de5\u667a\u80fd\u7684\u80fd\u529b\u8fc5\u901f\u589e\u5f3a\uff0c\u4f46\u5728\u590d\u6742\u7684\u63a8\u7406\u4efb\u52a1\u4e2d\u4ecd\u5b58\u5728\u4e0d\u8db3\u3002\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u4ece\u591a\u4e2a\u89d2\u5ea6\u5bf9\u6b64\u5c55\u5f00\u7814\u7a76\uff0c\u4e0d\u65ad\u63a2\u7d22\u63d0\u5347\u5927\u6a21\u578b\u63a8\u7406\u80fd\u529b\u7684\u65b0\u9014\u5f84\u3002\u4ece\u5229\u7528\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\u6a21\u62df\u4eba\u7c7b\u201c\u6df1\u5ea6\u601d\u8003\u201d\u8fc7\u7a0b\u7684 rStar-Math\uff0c\u5230\u57fa\u4e8e\u89c4\u5219\u7684\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5 Logic-RL\uff1b\u4ece\u878d\u5408\u5927\u8bed\u8a00\u6a21\u578b\u6570\u5b66\u76f4\u89c9\u4e0e\u7b26\u53f7\u65b9\u6cd5\u7684 LIPS\uff0c\u5230\u63d0\u5347\u81ea\u52a8\u5f62\u5f0f\u5316\u51c6\u786e\u6027\u7684\u65b0\u6846\u67b6\uff1b\u518d\u5230\u81ea\u52a8\u751f\u6210\u9ad8\u8d28\u91cf\u3001\u6709\u76d1\u7763\u6570\u5b66\u6570\u636e\u7684\u795e\u7ecf\u7b26\u53f7\u6846\u67b6\uff0c\u4ee5\u53ca\u7edf\u4e00\u63a8\u7406\u6846\u67b6 CoR \u548c\u5173\u952e\u8ba1\u5212\u6b65\u9aa4\u5b66\u4e60 CPL \u7684\u63d0\u51fa\uff0c\u6bcf\u4e00\u9879\u7814\u7a76\u90fd\u4e3a\u63d0\u5347\u5927\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u548c\u65b9\u6cd5\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4eba\u5de5\u667a\u80fd\u7684\u5feb\u901f\u53d1\u5c55\uff0c\u4f7f\u5176\u5728\u4f17\u591a\u9886\u57df\u5c55\u73b0\u51fa\u5f3a\u5927\u7684\u80fd\u529b\uff0c\u540c\u65f6\u4e5f\u4e0d\u65ad\u50ac\u751f\u51fa\u4eba\u4eec\u5bf9\u5176\u66f4\u9ad8\u7684\u671f\u5f85\uff0c\u5e0c\u671b\u4eba\u5de5\u667a\u80fd\u80fd\u591f\u5177\u5907\u6df1\u5ea6\u7684\u601d\u8003\u548c\u63a8\u7406\u80fd\u529b\uff0c\u5e2e\u52a9\u4eba\u7c7b\u89e3\u51b3\u5404\u79cd\u201c\u70e7\u8111\u201d\u7684\u73b0\u5b9e\u590d\u6742\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u63d0\u5347\u5927\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u4ece\u4e09\u4e2a\u65b9\u5411\u5f00\u5c55\u7814\u7a76\uff1a<strong>\u4e00\u662f\u901a\u8fc7\u6539\u8fdb\u6a21\u578b\u672c\u8eab\u6765\u589e\u5f3a\u5176\u63a8\u7406\u80fd\u529b\uff0c\u4f7f\u8f83\u5c0f\u89c4\u6a21\u7684\u6a21\u578b\u4e5f\u80fd\u5177\u6709\u5f3a\u5927\u7684\u63a8\u7406\u6027\u80fd\uff1b\u4e8c\u662f\u6df1\u5165\u5b66\u4e60\u6570\u5b66\u63a8\u7406\u7684\u89c4\u5219\uff0c\u4ee5\u63d0\u9ad8\u5927\u8bed\u8a00\u6a21\u578b\u7684\u53ef\u9760\u6027\uff1b\u4e09\u662f\u589e\u5f3a\u63a8\u7406\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u8ba9\u6a21\u578b\u80fd\u591f\u5728\u8de8\u9886\u57df\u7684\u4efb\u52a1\u4e2d\u7075\u6d3b\u5e94\u7528<\/strong>\uff0c\u4ece\u800c\u4fc3\u8fdb\u901a\u7528\u4eba\u5de5\u667a\u80fd\u7684\u8fdb\u6b65\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u91ca\u653e\u5927\u8bed\u8a00\u6a21\u578b\u6f5c\u529b-\u5c0f\u6a21\u578b\u63a8\u7406\u80fd\u529b\u66f4\u5f3a\u5927\">\u91ca\u653e\u5927\u8bed\u8a00\u6a21\u578b\u6f5c\u529b\u2014\u2014\u5c0f\u6a21\u578b\u63a8\u7406\u80fd\u529b\u66f4\u5f3a\u5927<\/h2>\n\n\n\n<p>\u201c\u57fa\u4e8e\u4e16\u754c\u77e5\u8bc6\u8bad\u7ec3\u7684\u5927\u6a21\u578b\u867d\u7136\u62e5\u6709\u6d77\u91cf\u7684\u77e5\u8bc6\u50a8\u5907\uff0c\u4f46\u662f\u73b0\u6709\u6a21\u578b\u5e76\u6ca1\u6709\u5145\u5206\u53d1\u6325\u5176\u6240\u8574\u542b\u7684\u5168\u90e8\u6f5c\u529b\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u73b0\u6709\u7684\u6a21\u578b\u8fd8\u7f3a\u4e4f\u6301\u7eed\u5b66\u4e60\u7684\u80fd\u529b\uff0c\u8fd9\u4e0e\u4eba\u7c7b\u4e0d\u65ad\u5b66\u4e60\u65b0\u77e5\u8bc6\u3001\u586b\u8865\u8ba4\u77e5\u7a7a\u767d\u7684\u80fd\u529b\u5f62\u6210\u9c9c\u660e\u5bf9\u6bd4\u3002\u201d\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u9996\u5e2d\u7814\u7a76\u5458\u5f20\u4e3d\u8bf4\u3002\u5353\u8d8a\u7684\u63a8\u7406\u80fd\u529b\u5f80\u5f80\u4f9d\u8d56\u4e8e\u5927\u89c4\u6a21\u6a21\u578b\u7684\u652f\u6301\uff0c\u56e0\u6b64\uff0c\u4e00\u4e9b\u79d1\u7814\u4eba\u5458\u4e5f\u5728\u63a2\u7d22\u5982\u4f55\u8ba9\u7c7b\u4f3c\u7684\u63a8\u7406\u80fd\u529b\u53ef\u4ee5\u5728\u89c4\u6a21\u8f83\u5c0f\u7684\u6a21\u578b\u4e2d\u5b9e\u73b0\u3002<\/p>\n\n\n\n<p>\u5728\u4f20\u7edf\u7684\u63a8\u7406\u6a21\u5f0f\u4e0b\uff0c\u5927\u6a21\u578b\u9762\u5bf9\u590d\u6742\u95ee\u9898\u65f6\u5e38\u5e38\u91c7\u7528\u7b80\u5355\u76f4\u63a5\u7684\u201c\u76f4\u89c9\u5f0f\u201d\u63a8\u7406\u6765\u751f\u6210\u7b54\u6848\u3002\u8fd9\u79cd\u65b9\u5f0f\u867d\u7136\u901f\u5ea6\u8f83\u5feb\uff0c\u4f46\u5f88\u5bb9\u6613\u51fa\u9519\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u4eba\u7c7b\u4f1a\u5bf9\u95ee\u9898\u8fdb\u884c\u9010\u6b65\u5206\u6790\uff0c\u5c1d\u8bd5\u591a\u79cd\u601d\u8def\uff0c\u6743\u8861\u5229\u5f0a\u540e\u518d\u7ed9\u51fa\u7b54\u6848\u3002\u9274\u4e8e\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86&nbsp;<a href=\"https:\/\/www.microsoft.com\/en-us\/research\/articles\/li-zhang-rstar-math\/\" target=\"_blank\" rel=\"noreferrer noopener\">rStar-Math<\/a>\uff0c\u5176\u6838\u5fc3\u5728\u4e8e\u5229\u7528\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\uff08MCTS\uff09\uff0c\u6a21\u62df\u4eba\u7c7b\u7684\u201c\u6df1\u5ea6\u601d\u8003\u201d\u8fc7\u7a0b\uff0c\u8ba9\u5c0f\u8bed\u8a00\u6a21\u578b\u5728\u63a8\u7406\u80fd\u529b\u65b9\u9762\u8fbe\u5230\u66f4\u9ad8\u7684\u6c34\u51c6\u3002<\/p>\n\n\n\n<p>rStar-Math \u901a\u8fc7\u4e09\u4e2a\u6b65\u9aa4\u5b9e\u73b0\u4e86\u81ea\u6211\u8fdb\u5316\uff1a\u9996\u5148\uff0c\u5c06\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u5206\u89e3\u4e3a\u591a\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u4f7f\u6a21\u578b\u80fd\u591f\u9010\u6b65\u63a2\u7d22\u5e76\u9a8c\u8bc1\u6bcf\u4e00\u6b65\u7684\u8d21\u732e\uff0c\u786e\u4fdd\u5c0f\u6a21\u578b\u751f\u6210\u7684\u63a8\u7406\u8f68\u8ff9\u7531\u6b63\u786e\u3001\u9ad8\u8d28\u91cf\u7684\u4e2d\u95f4\u6b65\u9aa4\u7ec4\u6210\uff1b\u5176\u6b21\uff0c\u8bad\u7ec3\u4e00\u4e2a\u4f5c\u4e3a\u8fc7\u7a0b\u504f\u597d\u6a21\u578b\uff08PPM\uff09\u7684\u5c0f\u6a21\u578b\uff0c\u7528\u4e8e\u53ef\u9760\u5730\u4e3a\u6bcf\u4e2a\u6570\u5b66\u63a8\u7406\u6b65\u9aa4\u9884\u6d4b\u5956\u52b1\u6807\u7b7e\uff0c\u4ece\u800c\u5b9e\u73b0\u6240\u9700\u7684\u8fc7\u7a0b\u5956\u52b1\u5efa\u6a21\u4ee5\u53ca\u53ef\u9760\u7684\u6807\u6ce8\uff1b\u6700\u540e\uff0c\u901a\u8fc7\u4e00\u4e2a\u56db\u8f6e\u81ea\u6211\u8fdb\u5316\u65b9\u6848\uff0c\u4ece\u96f6\u5f00\u59cb\u9010\u6b65\u6784\u5efa\u524d\u6cbf\u7684\u7b56\u7565\u6a21\u578b\u548c PPM\uff0c\u6bcf\u4e00\u8f6e\u90fd\u4f7f\u7528\u6700\u65b0\u7684\u7b56\u7565\u6a21\u578b\u548c PPM \u8fdb\u884c\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\uff0c\u8fdb\u800c\u9010\u6b65\u8fdb\u5316\uff0c\u8bad\u7ec3\u51fa\u66f4\u5f3a\u7684\u7b56\u7565\u6a21\u578b\u548c PPM\u3002<\/p>\n\n\n\n<p>\u5b9e\u9a8c\u663e\u793a\uff0crStar-Math \u5728\u56db\u4e2a\u5c0f\u8bed\u8a00\u6a21\u578b\uff0815\u4ebf &#8211; 70\u4ebf\u53c2\u6570\uff09\u4e0a\u9a8c\u8bc1\u4e86\u81ea\u8eab\u7684\u6709\u6548\u6027\u3002\u5728\u7f8e\u56fd\u6570\u5b66\u5965\u6797\u5339\u514b\u7ade\u8d5b\uff08AIME\uff09\u4e2d\uff0crStar-Math \u5e73\u5747\u80fd\u591f\u89e3\u51b353.3%\uff088\/15\uff09\u7684\u95ee\u9898\uff0c\u6392\u540d\u5728\u524d20%\u6700\u4f18\u79c0\u7684\u9ad8\u4e2d\u6570\u5b66\u5b66\u751f\u4e4b\u5217\u3002<\/p>\n\n\n\n<p><strong>rStar-Math: Small LLMs can master math reasoning with self-evolved deep thinking<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2501.04519\">https:\/\/arxiv.org\/pdf\/2501.04519<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"314\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-1-1024x314.png\" alt=\"chart, bubble chart\" class=\"wp-image-1139177\" srcset=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-1-1024x314.png 1024w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-1-300x92.png 300w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-1-768x236.png 768w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-1-240x74.png 240w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-1.png 1049w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe1\uff1arStar-Math \u793a\u610f\u56fe<\/figcaption><\/figure>\n\n\n\n<p>\u7814\u7a76\u5458\u4eec\u8fd8\u63d0\u51fa\u4e86<strong>\u57fa\u4e8e\u89c4\u5219\u7684\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5 Logic-RL<\/strong>\uff0c\u901a\u8fc7\u5408\u6210\u903b\u8f91\u8c1c\u9898\u4f5c\u4e3a\u8bad\u7ec3\u6570\u636e\u6765\u63d0\u9ad8\u6a21\u578b\u5728\u590d\u6742\u903b\u8f91\u95ee\u9898\u4e0a\u7684\u63a8\u7406\u80fd\u529b\u3002Logic-RL \u5f15\u5165\u4e86\u4e00\u79cd\u5b9e\u7528\u7cfb\u7edf\u63d0\u793a\u548c\u4e25\u683c\u7684\u683c\u5f0f\u5956\u52b1\u51fd\u6570\uff0c\u907f\u514d\u63a8\u7406\u6a21\u578b\u8d70\u6377\u5f84\u3002\u4f8b\u5982\uff0c\u6a21\u578b\u5728\u751f\u6210\u7b54\u6848\u65f6\uff0c\u5fc5\u987b\u6309\u7167\u7279\u5b9a\u683c\u5f0f\u7ec4\u7ec7\u63a8\u7406\u8fc7\u7a0b\u548c\u7b54\u6848\uff0c\u53ea\u6709\u5f53\u63a8\u7406\u8fc7\u7a0b\u548c\u7b54\u6848\u90fd\u7b26\u5408\u8981\u6c42\u65f6\uff0c\u624d\u80fd\u83b7\u5f97\u8f83\u9ad8\u5956\u52b1\uff0c\u4ee5\u6b64\u786e\u4fdd\u63a8\u7406\u8fc7\u7a0b\u7684\u5b8c\u6574\u6027\u548c\u51c6\u786e\u6027\u3002<\/p>\n\n\n\n<p>\u7ecf\u8fc7 Logic-RL \u8bad\u7ec3\u540e\u7684\u6a21\u578b\u4e0d\u4ec5\u5728\u903b\u8f91\u8c1c\u9898\u4e0a\u8868\u73b0\u51fa\u8272\uff0c\u572870\u4ebf\u53c2\u6570\u5c0f\u6a21\u578b\u7684\u6570\u5b66\u7ade\u8d5b\u57fa\u51c6\u6d4b\u8bd5\uff08\u5982 AIME\u548c AMC\uff09\u4e2d\u4e5f\u5c55\u73b0\u51fa\u4e86\u5f3a\u5927\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u51c6\u786e\u7387\u5206\u522b\u63d0\u9ad8\u4e86125%\u548c38%\u3002<\/p>\n\n\n\n<p><strong>Logic-RL: Unleashing LLM reasoning with rule-based reinforcement learning<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2502.14768\">https:\/\/arxiv.org\/pdf\/2502.14768<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u5f3a\u5316\u6570\u5b66\u63a8\u7406\u80fd\u529b-\u63a8\u7406\u66f4\u53ef\u9760\">\u5f3a\u5316\u6570\u5b66\u63a8\u7406\u80fd\u529b\u2014\u2014\u63a8\u7406\u66f4\u53ef\u9760<\/h2>\n\n\n\n<p>\u6570\u5b66\u4f5c\u4e3a\u79d1\u5b66\u7684\u57fa\u77f3\uff0c\u5177\u6709\u4e25\u5bc6\u7684\u903b\u8f91\u6027\u548c\u9ad8\u5ea6\u7684\u7cbe\u786e\u6027\u3002\u5bf9\u4e8e\u4eba\u5de5\u667a\u80fd\u800c\u8a00\uff0c\u89e3\u51b3\u6570\u5b66\u63a8\u7406\u96be\u9898\u5c06\u5927\u5e45\u63d0\u5347\u4eba\u5de5\u667a\u80fd\u7684\u63a8\u7406\u80fd\u529b\uff0c\u4e5f\u5c06\u4fc3\u8fdb\u6a21\u578b\u5728\u5404\u4e2a\u9886\u57df\u7684\u5e7f\u6cdb\u5e94\u7528\u3002\u7136\u800c\uff0c\u4ec5\u4ec5\u4f9d\u9760\u5927\u6a21\u578b\u7684\u81ea\u7136\u8bed\u8a00\u5904\u7406\u80fd\u529b\uff0c\u5f80\u5f80\u96be\u4ee5\u6ee1\u8db3\u6570\u5b66\u63a8\u7406\u6240\u9700\u7684\u4e25\u683c\u6807\u51c6\u3002\u4e3a\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u8fd0\u7528\u5f62\u5f0f\u5316\u548c\u7b26\u53f7\u5316\u7684\u7814\u7a76\u65b9\u6cd5\uff0c\u5e2e\u52a9\u6a21\u578b\u5b66\u4e60\u4eba\u7c7b\u5df2\u6709\u7684\u6570\u5b66\u65b9\u6cd5\u548c\u5de5\u5177\uff0c\u638c\u63e1\u6570\u5b66\u89c4\u5219\uff0c\u63d0\u5347\u63a8\u7406\u7684\u6548\u7387\u4e0e\u51c6\u786e\u6027\u3002<\/p>\n\n\n\n<p>\u201c\u81ea\u7136\u8bed\u8a00\u662f\u4eba\u7c7b\u7684\u8bed\u8a00\uff0c\u5e76\u4e0d\u662f\u8ba1\u7b97\u673a\u6216\u5927\u6a21\u578b\u7684\u539f\u751f\u8bed\u8a00\uff0c\u5b83\u4eec\u5e76\u4e0d\u80fd\u76f4\u63a5\u7406\u89e3\u81ea\u7136\u8bed\u8a00\u3002\u6211\u4eec\u5e0c\u671b\u5c06\u5927\u8bed\u8a00\u6a21\u578b\u7684\u8f93\u51fa\u8f6c\u6362\u4e3a\u4ee3\u7801\u5f62\u5f0f\uff0c\u5e76\u5c06\u5176\u6620\u5c04\u5230\u516c\u7406\u4e2d\uff0c\u4f8b\u5982\u20181+1=2\u2019\u8fd9\u6837\u4e0d\u8bc1\u81ea\u660e\u7684\u516c\u7406\uff0c\u4ece\u800c\u9a8c\u8bc1\u6a21\u578b\u8f93\u51fa\u7684\u6b63\u786e\u6027\u3002\u8fd9\u7c7b\u4f3c\u4e8e\u4eba\u7c7b\u5728\u4ea4\u6d41\u65f6\u5c06\u542c\u5230\u7684\u8bdd\u8bed\u8f6c\u6362\u4e3a\u81ea\u5df1\u7684\u7406\u89e3\uff0c\u800c\u6211\u4eec\u5219\u662f\u901a\u8fc7\u5f62\u5f0f\u5316\u6d41\u7a0b\u5c06\u5176\u8f6c\u6362\u4e3a\u8ba1\u7b97\u673a\u80fd\u591f\u7406\u89e3\u7684\u5de5\u5177\u3002\u201d\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u9ad8\u7ea7\u7814\u7a76\u5458\u5f20\u5baa\u8bf4\u3002<\/p>\n\n\n\n<p>\u6570\u5b66\u8bed\u8a00\u6db5\u76d6\u6570\u5b66\u5b9a\u7406\u3001\u4e0d\u7b49\u5f0f\u8bc1\u660e\u7b49\uff0c\u4e0e\u5927\u8bed\u8a00\u6a21\u578b\u7684\u8bed\u8a00\u4f53\u7cfb\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002\u8981\u8ba9\u5927\u6a21\u578b\u7406\u89e3\u6570\u5b66\u95ee\u9898\uff0c\u9996\u5148\u9700\u8981\u901a\u8fc7\u5f62\u5f0f\u5316\u548c\u7b26\u53f7\u5316\u7684\u65b9\u6cd5\u5c06\u6570\u5b66\u9898\u76ee\u8f6c\u5316\u4e3a\u4ee3\u7801\u5f62\u5f0f\uff0c\u518d\u6620\u5c04\u4e3a\u8ba1\u7b97\u673a\u53ef\u7406\u89e3\u7684\u516c\u7406\u3002\u57fa\u4e8e\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u8bbe\u8ba1\u4e86<strong>\u57fa\u4e8e\u5927\u6a21\u578b\u7684\u7b26\u53f7\u63a8\u7406\u4e0d\u7b49\u5f0f\u8bc1\u660e\u5668\uff08LLM-based inequality prover with symbolic reasoning\uff09LIPS<\/strong>\u3002\u5b83\u521b\u9020\u6027\u5730\u878d\u5408\u4e86\u5927\u6a21\u578b\u7684\u6570\u5b66\u76f4\u89c9\u4e0e\u7b26\u53f7\u65b9\u6cd5\u6240\u7f16\u7801\u7684\u9886\u57df\u7279\u5b9a\u89c1\u89e3\uff0c\u4ee5\u786e\u5b9a\u6570\u5b66\u63a8\u7406\u4e2d\u54ea\u4e9b\u90e8\u5206\u6700\u9002\u5408\u5927\u6a21\u578b\uff0c\u54ea\u4e9b\u90e8\u5206\u66f4\u9002\u5408\u91c7\u7528\u7b26\u53f7\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u5206\u6790\u4eba\u7c7b\u89e3\u51b3\u6b64\u7c7b\u95ee\u9898\u7684\u601d\u8def\uff0cLIPS \u63d0\u70bc\u51fa\u4e24\u79cd\u7b56\u7565\uff1a\u4e00\u662f\u7531\u7b26\u53f7\u65b9\u6cd5\u5904\u7406\u7684<strong>\u7f29\u653e\uff08scaling\uff09<\/strong>\uff1b\u4e8c\u662f\u7531\u5927\u6a21\u578b\u5904\u7406\u7684<strong>\u91cd\u5199\uff08rewriting\uff09<\/strong>\u3002\u5728\u4f7f\u7528\u6765\u81ea\u591a\u4e2a\u6570\u5b66\u7ade\u8d5b\u7684161\u4e2a\u6781\u5177\u6311\u6218\u6027\u7684\u4e0d\u7b49\u5f0f\u5bf9 LIPS \u8fdb\u884c\u8bc4\u4f30\u540e\uff0c\u7ed3\u679c\u663e\u793a LIPS \u5c55\u73b0\u51fa\u4e86\u76ee\u524d\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff0c\u5e76\u4e14\u5728\u65e0\u9700\u989d\u5916\u8bad\u7ec3\u6570\u636e\u7684\u60c5\u51b5\u4e0b\uff0c\u5927\u5927\u4f18\u4e8e\u73b0\u6709\u7684\u5927\u6a21\u578b\u548c\u7b26\u53f7\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p><strong>Proving Olympiad inequalities by synergizing LLMs and symbolic reasoning<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/openreview.net\/pdf?id=FiyS0ecSm0\">https:\/\/openreview.net\/pdf?id=FiyS0ecSm0<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"337\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-2-1024x337.png\" alt=\"diagram\" class=\"wp-image-1139178\" srcset=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-2-1024x337.png 1024w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-2-300x99.png 300w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-2-768x253.png 768w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-2-240x79.png 240w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-2.png 1295w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe2\uff1aLIPS \u7b26\u53f7\u63a8\u7406\u4e0d\u7b49\u5f0f\u8bc1\u660e\u5668<\/figcaption><\/figure>\n\n\n\n<p>\u5c3d\u7ba1\u5f62\u5f0f\u5316\u65b9\u6cd5\u4f7f\u5927\u6a21\u578b\u5728\u591a\u79cd\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e2d\u8868\u73b0\u51fa\u5de8\u5927\u6f5c\u529b\uff0c\u4f46\u5927\u6a21\u578b\u5728\u81ea\u52a8\u5f62\u5f0f\u5316\u6570\u636e\u9648\u8ff0\u4e0a\u7684\u6210\u529f\u7387\u4ecd\u7136\u8f83\u4f4e\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5728\u5927\u6a21\u578b\u7684\u81ea\u52a8\u5f62\u5f0f\u5316\u4e2d\uff0c\u4e00\u6b21\u901a\u8fc7\u7387\uff08\u6392\u540d\u7b2c\u4e00\u7684\u751f\u6210\u7ed3\u679c\u6b63\u786e\uff09\u548c k \u6b21\u901a\u8fc7\u7387\uff08\u6392\u540d\u524d k \u7684\u751f\u6210\u7ed3\u679c\u4e2d\u6709\u4e00\u4e2a\u6b63\u786e\uff09\u4e4b\u95f4\u6709\u660e\u663e\u7684\u5dee\u5f02\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u7f29\u5c0f\u8fd9\u4e00\u5dee\u8ddd\uff0c\u7814\u7a76\u5458\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u65b0\u6846\u67b6\uff0c\u4ece\u4e24\u4e2a\u521b\u65b0\u4e14\u4e92\u8865\u7684\u7ef4\u5ea6\u5efa\u7acb\u81ea\u52a8\u5f62\u5f0f\u5316\u7684\u81ea\u4e00\u81f4\u6027\u2014\u2014<strong>\u7b26\u53f7\u7b49\u4ef7\u6027\u548c\u8bed\u4e49\u4e00\u81f4\u6027<\/strong>\u3002\u7b26\u53f7\u7b49\u4ef7\u6027\u5c06\u4f20\u7edf\u7684\u6bd4\u8f83\uff08\u5982\u6700\u7ec8\u7b54\u6848\u548c\u6267\u884c\u884c\u4e3a\uff09\u8fdb\u884c\u6269\u5c55\uff0c\u4ee5\u9a8c\u8bc1\u81ea\u52a8\u5f62\u5f0f\u5316\u5019\u9009\u7ed3\u679c\u4e4b\u95f4\u7684\u903b\u8f91\u7b49\u4ef7\u6027\u3002\u8bed\u4e49\u4e00\u81f4\u6027\u5219\u901a\u8fc7\u6d4b\u91cf\u91cd\u65b0\u975e\u5f62\u5f0f\u5316\uff08\u53cd\u5411\u7ffb\u8bd1\uff09\u7ed3\u679c\u4e0e\u539f\u59cb\u81ea\u7136\u8bed\u8a00\u9648\u8ff0\u4e4b\u95f4\u7684\u5d4c\u5165\u76f8\u4f3c\u6027\uff0c\u7ea0\u6b63\u7b26\u53f7\u7b49\u4ef7\u6027\u53ef\u80fd\u5ffd\u7565\u7684\u610f\u5916\u63a8\u7406\u5dee\u5f02\u3002\u8fd9\u79cd\u65b9\u6cd5\u786e\u4fdd\u4e86\u81ea\u52a8\u5f62\u5f0f\u5316\u8fc7\u7a0b\u80fd\u591f\u4fdd\u7559\u539f\u59cb\u9648\u8ff0\u7684\u9884\u671f\u542b\u4e49\u548c\u8fde\u8d2f\u6027\u3002\u5728 MATH \u548c miniF2F \u6570\u636e\u96c6\u4e0a\u7684\u5b9e\u9a8c\u8868\u660e\uff0c\u8be5\u65b9\u6cd5\u6781\u5927\u5730\u63d0\u9ad8\u4e86\u81ea\u52a8\u5f62\u5f0f\u5316\u7684\u51c6\u786e\u6027\uff0c\u5728\u5404\u79cd\u5927\u8bed\u8a00\u6a21\u578b\u548c\u57fa\u7ebf\u65b9\u6cd5\u4e0a\u5b9e\u73b0\u4e86\u9ad8\u8fbe0.22-1.35\u500d\u7684\u76f8\u5bf9\u6539\u8fdb\u3002<\/p>\n\n\n\n<p><strong>Autoformalizing mathematical statements by symbolic equivalence and semantic consistency<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/openreview.net\/pdf?id=8ihVBYpMV4\">https:\/\/openreview.net\/pdf?id=8ihVBYpMV4<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"304\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-3-1024x304.png\" alt=\"diagram\" class=\"wp-image-1139179\" srcset=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-3-1024x304.png 1024w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-3-300x89.png 300w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-3-768x228.png 768w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-3-240x71.png 240w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-3.png 1271w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe3\uff1a\u81ea\u52a8\u5f62\u5f0f\u5316\u6846\u67b6<\/figcaption><\/figure>\n\n\n\n<p>\u6b64\u5916\uff0c\u7814\u7a76\u5458\u4eec\u8ba4\u4e3a\uff0c\u9ad8\u8d28\u91cf\u6570\u5b66\u6570\u636e\u96c6\u7684\u6781\u5ea6\u532e\u4e4f\u4e5f\u662f\u9650\u5236\u5927\u8bed\u8a00\u6a21\u578b\u6570\u5b66\u63a8\u7406\u80fd\u529b\u63d0\u5347\u7684\u5173\u952e\u56e0\u7d20\u4e4b\u4e00\u3002\u4e3a\u4e86\u7a81\u7834\u8fd9\u4e00\u56f0\u5883\uff0c\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd<strong>\u795e\u7ecf\u7b26\u53f7\u6846\u67b6\uff0c\u7528\u4e8e\u81ea\u52a8\u751f\u6210\u9ad8\u8d28\u91cf\u3001\u6709\u76d1\u7763\u7684\u6570\u5b66\u6570\u636e<\/strong>\u3002\u8fd9\u4e00\u8303\u5f0f\u7ed3\u5408\u4e86\u795e\u7ecf\u548c\u7b26\u53f7\u7684\u4f18\u52bf\uff0c\u4e00\u65b9\u9762\uff0c\u901a\u8fc7\u7cfb\u7edf\u91c7\u6837\u5728\u7b26\u53f7\u7a7a\u95f4\u4e2d\u751f\u6210\u591a\u6837\u5316\u7684\u6570\u5b66\u95ee\u9898\uff0c\u5e76\u5229\u7528\u7b26\u53f7\u6c42\u89e3\u5668\u4fdd\u8bc1\u95ee\u9898\u7684\u6709\u6548\u6027\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u5927\u6a21\u578b\u80fd\u591f\u6709\u6548\u5730\u652f\u6301\u4ece\u7b26\u53f7\u7a7a\u95f4\u5230\u81ea\u7136\u8bed\u8a00\u7a7a\u95f4\u7684\u8f6c\u6362\uff0c\u786e\u4fdd\u65b0\u751f\u6210\u7684\u5f62\u5f0f\u5316\u95ee\u9898\u4e0e\u5176\u76f8\u5e94\u7684\u81ea\u7136\u8bed\u8a00\u7248\u672c\u4fdd\u6301\u4e00\u81f4\u3002<\/p>\n\n\n\n<p><strong>Neuro-symbolic data generation for math reasoning<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/openreview.net\/pdf?id=CIcMZGLyZW\">https:\/\/openreview.net\/pdf?id=CIcMZGLyZW<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"330\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-4-1024x330.png\" alt=\"text\" class=\"wp-image-1139180\" srcset=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-4-1024x330.png 1024w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-4-300x97.png 300w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-4-768x247.png 768w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-4-240x77.png 240w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-4.png 1255w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe4\uff1a\u795e\u7ecf\u7b26\u53f7\u6846\u67b6<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u63d0\u5347\u5927\u8bed\u8a00\u6a21\u578b\u63a8\u7406\u6cdb\u5316\u80fd\u529b-\u63a8\u7406\u66f4\u53ef\u7528\">\u63d0\u5347\u5927\u8bed\u8a00\u6a21\u578b\u63a8\u7406\u6cdb\u5316\u80fd\u529b\u2014\u2014\u63a8\u7406\u66f4\u53ef\u7528<\/h2>\n\n\n\n<p>\u63a8\u7406\u6cdb\u5316\u80fd\u529b\u662f\u8861\u91cf\u4eba\u5de5\u667a\u80fd\u662f\u5426\u771f\u6b63\u5177\u5907\u901a\u7528\u6027\u7684\u91cd\u8981\u6307\u6807\u3002\u5177\u5907\u5f3a\u5927\u6cdb\u5316\u80fd\u529b\u7684\u6a21\u578b\uff0c\u80fd\u591f\u8de8\u8d8a\u4e0d\u540c\u9886\u57df\u7684\u77e5\u8bc6\u8fb9\u754c\uff0c\u505a\u5230\u201c\u4e3e\u4e00\u53cd\u4e09\u201d\uff0c\u8fdb\u800c\u62d3\u5c55\u4eba\u5de5\u667a\u80fd\u7684\u5e94\u7528\u8303\u56f4\u548c\u4ef7\u503c\u3002\u7814\u7a76\u5458\u4eec\u53d1\u73b0\uff0c<strong>\u6a21\u578b\u7ecf\u8fc7\u6570\u5b66\u6570\u636e\u8bad\u7ec3\u540e\uff0c\u5176\u63a8\u7406\u80fd\u529b\u5728\u79d1\u5b66\u3001\u4ee3\u7801\u7b49\u591a\u4e2a\u9886\u57df\u90fd\u6709\u663e\u8457\u63d0\u5347<\/strong>\u3002\u8fd9\u4e00\u53d1\u73b0\u4e3a\u63d0\u5347\u5927\u6a21\u578b\u7684\u63a8\u7406\u6cdb\u5316\u80fd\u529b\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\u548c\u65b9\u5411\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u5c06\u81ea\u7136\u8bed\u8a00\u3001\u4ee3\u7801\u548c\u7b26\u53f7\u8bed\u8a00\u4e09\u79cd\u63a8\u7406\u8303\u5f0f\u878d\u5165\u540c\u4e00\u6761\u63a8\u7406\u8f68\u8ff9\uff0c\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86<strong>\u7edf\u4e00\u63a8\u7406\u6846\u67b6 CoR\uff08Chain-of-Reasoning\uff09<\/strong>\u3002\u5176\u4e2d\uff0c\u81ea\u7136\u8bed\u8a00\u6709\u52a9\u4e8e\u7406\u89e3\u95ee\u9898\u7684\u80cc\u666f\u548c\u9700\u6c42\uff0c\u4ee3\u7801\u8bed\u8a00\u64c5\u957f\u7cbe\u786e\u7684\u8ba1\u7b97\u548c\u903b\u8f91\u5904\u7406\uff0c\u7b26\u53f7\u8bed\u8a00\u80fd\u4ee5\u7b80\u6d01\u3001\u4e25\u8c28\u7684\u65b9\u5f0f\u8868\u8fbe\u6570\u5b66\u548c\u903b\u8f91\u5173\u7cfb\u3002CoR \u5141\u8bb8\u6a21\u578b\u5148\u57fa\u4e8e\u67d0\u4e00\u8303\u5f0f\u63a8\u7406\uff0c\u518d\u6839\u636e\u95ee\u9898\u7684\u4e0d\u540c\u9636\u6bb5\u548c\u9700\u6c42\u7075\u6d3b\u5207\u6362\u8303\u5f0f\uff0c\u5728\u5148\u524d\u751f\u6210\u5185\u5bb9\u7684\u57fa\u7840\u4e0a\u7ee7\u7eed\u8fdb\u884c\u591a\u8303\u5f0f\u7684\u534f\u540c\u63a8\u7406\uff0c\u5b9e\u73b0\u901a\u7528\u6570\u5b66\u4efb\u52a1\u4e0a\u7684\u63a8\u7406\u6cdb\u5316\u3002<\/p>\n\n\n\n<p>\u53e6\u5916\uff0c\u5229\u7528\u8c03\u6574\u63d0\u793a\u8bcd\uff08prompt\uff09\uff0c\u6a21\u578b\u8fd8\u53ef\u4ee5\u6539\u53d8\u63a8\u7406\u6df1\u5ea6\u548c\u4f7f\u7528\u7684\u8303\u5f0f\u6570\u91cf\uff0c\u6781\u5927\u63d0\u9ad8\u4e86\u5176\u5bf9\u4e0d\u540c\u4efb\u52a1\u7684\u9002\u5e94\u6027\u3002\u57285\u4e2a\u6570\u5b66\u63a8\u7406\u6570\u636e\u96c6\u7684\u6d4b\u8bd5\u4e2d\uff0cCoR \u5747\u53d6\u5f97\u4e86\u5927\u5e45\u7684\u63d0\u5347\u6548\u679c\uff0c\u5c55\u73b0\u51fa\u4ee4\u4eba\u60ca\u559c\u7684\u901a\u7528\u6570\u5b66\u89e3\u9898\u80fd\u529b\u2014\u2014\u65e2\u80fd\u89e3\u51b3\u6570\u5b66\u8ba1\u7b97\u95ee\u9898\uff0c\u53c8\u80fd\u89e3\u51b3\u6570\u5b66\u8bc1\u660e\u95ee\u9898\u3002<\/p>\n\n\n\n<p><strong>Chain-of-Reasoning: Towards unified mathematical reasoning in LLMs via a multi-paradigm perspective<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2501.11110\">https:\/\/arxiv.org\/pdf\/2501.11110<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"427\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-5-1024x427.png\" alt=\"diagram\" class=\"wp-image-1139181\" srcset=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-5-1024x427.png 1024w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-5-300x125.png 300w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-5-768x320.png 768w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-5-240x100.png 240w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-5.png 1183w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe5\uff1a\u4e0d\u540c\u8303\u5f0f\u4e0b\u7684\u63a8\u7406\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p>\u6b64\u5916\uff0c\u73b0\u6709\u7684\u5927\u6a21\u578b\u4e3b\u8981\u4fa7\u91cd\u4e8e\u63d0\u5347\u7279\u5b9a\u4efb\u52a1\u6216\u7279\u5b9a\u9886\u57df\uff08\u5982\u6570\u5b66\u6216\u7f16\u7a0b\uff09\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5e76\u672a\u5145\u5206\u89e3\u51b3\u6a21\u578b\u5728\u5404\u79cd\u63a8\u7406\u4efb\u52a1\u4e2d\u7684\u6cdb\u5316\u80fd\u529b\u95ee\u9898\u3002\u4e3a\u4e86\u589e\u5f3a\u63a8\u7406\u4efb\u52a1\u4e2d\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u7814\u7a76\u5458\u4eec\u5efa\u8bae\u5728\u9ad8\u7ea7\u62bd\u8c61\u8ba1\u5212\u7684\u52a8\u4f5c\u7a7a\u95f4\u5185\u8fdb\u884c\u641c\u7d22\uff0c\u800c\u4e0d\u662f\u5c40\u9650\u4e8e\u901a\u5e38\u4f1a\u9650\u5236\u6cdb\u5316\u80fd\u529b\u7684\u7279\u5b9a\u4efb\u52a1\u52a8\u4f5c\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u5206\u6790\u6b64\u524d\u5229\u7528\u5927\u6a21\u578b\u751f\u6210\u63a8\u7406\u8ba1\u5212\u4ee5\u53ca\u7279\u5b9a\u4efb\u52a1\u89e3\u51b3\u65b9\u6848\uff0c\u6765\u63d0\u5347\u63a8\u7406\u80fd\u529b\u7684\u76f8\u5173\u7814\u7a76\uff0c\u7814\u7a76\u5458\u4eec\u53d1\u73b0\uff0c\u7279\u5b9a\u4efb\u52a1\u7684\u89e3\u51b3\u65b9\u6848\u4e0e\u7279\u5b9a\u4efb\u52a1\u7684\u6280\u80fd\u5bc6\u5207\u76f8\u5173\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u8ba1\u5212\u4ee3\u8868\u4e86\u4e00\u79cd\u89e3\u51b3\u95ee\u9898\u7684\u62bd\u8c61\u601d\u7ef4\uff0c\u5982\u51b3\u5b9a\u5e94\u7528\u54ea\u4e9b\u77e5\u8bc6\u6216\u5982\u4f55\u5206\u89e3\u95ee\u9898\uff0c\u8fd9\u6709\u52a9\u4e8e\u6a21\u578b\u57f9\u517b\u66f4\u5e7f\u6cdb\u7684\u3001\u4e0e\u4efb\u52a1\u65e0\u5173\u7684\u80fd\u529b\uff0c\u8fdb\u800c\u63d0\u5347\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n\n\n\n<p>\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u9996\u5e2d\u7814\u7a76\u5458\u97e9\u96ea\u5a77\u8868\u793a\uff0c\u201c\u4eba\u7c7b\u5728\u601d\u8003\u89e3\u51b3\u95ee\u9898\u65f6\uff0c\u5b58\u5728\u4e00\u4e9b\u5171\u6027\u7b56\u7565\u3002\u4f8b\u5982\uff0c\u5c06\u590d\u6742\u95ee\u9898\u62c6\u89e3\u4e3a\u5b50\u95ee\u9898\uff0c\u4ece\u4f17\u591a\u4fe1\u606f\u4e2d\u63d0\u53d6\u5173\u952e\u90e8\u5206\uff0c\u4ee5\u53ca\u6839\u636e\u7279\u5b9a\u4fe1\u606f\u56de\u5fc6\u3001\u8c03\u53d6\u5df2\u6709\u77e5\u8bc6\uff0c\u50cf\u662f\u6570\u5b66\u4e2d\u7684\u5b9a\u7406\u6216\u7f16\u7a0b\u4e2d\u7684\u7b97\u6cd5\u7b49\u3002\u901a\u8fc7\u5b66\u4e60\u8fd9\u4e9b\u89e3\u9898\u7b56\u7565\uff0c\u5f53\u9047\u5230\u65b0\u95ee\u9898\u65f6\uff0c\u5927\u6a21\u578b\u4e5f\u4f1a\u5f62\u6210\u4e00\u79cd\u7c7b\u4f3c\u4eba\u7c7b\u89e3\u9898\u7684\u601d\u8def\uff0c\u4ece\u800c\u66f4\u6709\u6548\u5730\u89e3\u51b3\u95ee\u9898\u3002\u201d<\/p>\n\n\n\n<p>\u57fa\u4e8e\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86<a href=\"https:\/\/www.microsoft.com\/en-us\/research\/articles\/cpl\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>\u5173\u952e\u8ba1\u5212\u6b65\u9aa4\u5b66\u4e60 CPL\uff08Critical Plan Step Learning\uff09<\/strong><\/a>\u65b9\u6cd5\uff0c\u5b83\u7531\u4e24\u4e2a\u5173\u952e\u90e8\u5206\u7ec4\u6210\uff1a\u57fa\u4e8e\u8ba1\u5212\u7684\u641c\u7d22\u548c\u901a\u8fc7\u6b65\u9aa4\u7ea7\u4f18\u52bf\u504f\u597d\u4f18\u5316\uff08Step-APO\uff09\uff0c\u6765\u5b66\u4e60\u5173\u952e\u8ba1\u5212\u6b65\u9aa4\u3002\u57fa\u4e8e\u8ba1\u5212\u7684\u641c\u7d22\u5229\u7528\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\u5728\u591a\u6b65\u63a8\u7406\u4efb\u52a1\u4e2d\u63a2\u7d22\u4e0d\u540c\u7684\u8ba1\u5212\u6b65\u9aa4\uff0c\u901a\u8fc7\u521b\u5efa\u8ba1\u5212\u6811\uff0c\u5e2e\u52a9\u6a21\u578b\u83b7\u5f97\u4e0e\u4efb\u52a1\u65e0\u5173\u7684\u6280\u80fd\uff0c\u63d0\u5347\u6a21\u578b\u5728\u4e0d\u540c\u4efb\u52a1\u4e2d\u7684\u6cdb\u5316\u80fd\u529b\u3002Step-APO \u5219\u6574\u5408\u4e86\u5229\u7528\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\u83b7\u5f97\u7684\u6b65\u9aa4\u7ea7\u504f\u597d\u5bf9\u7684\u4f18\u52bf\u4f30\u8ba1\uff0c\u4f7f\u6a21\u578b\u80fd\u591f\u5b66\u4e60\u6b65\u9aa4\u4e4b\u95f4\u7684\u7ec6\u7c92\u5ea6\u504f\u597d\uff0c\u8bc6\u522b\u5173\u952e\u8ba1\u5212\u6b65\u9aa4\uff0c\u5e76\u5f31\u5316\u9519\u8bef\u6b65\u9aa4\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u589e\u5f3a\u6a21\u578b\u7684\u6574\u4f53\u63a8\u7406\u80fd\u529b\uff0c\u63d0\u5347\u6a21\u578b\u5728\u4e0d\u540c\u4efb\u52a1\u4e2d\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n\n\n\n<p><strong>CPL: Critical plan step learning boosts LLM generalization in reasoning tasks<\/strong><\/p>\n\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2409.08642\">https:\/\/arxiv.org\/pdf\/2409.08642<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"484\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-6-1024x484.png\" alt=\"CPL \u793a\u610f\u56fe\" class=\"wp-image-1139182\" srcset=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-6-1024x484.png 1024w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-6-300x142.png 300w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-6-768x363.png 768w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-6-240x113.png 240w, https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2025\/05\/enhancing-llm-reasoning-abilities-6.png 1238w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe6\uff1aCPL \u793a\u610f\u56fe<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u6301\u7eed\u62d3\u5c55\u63a8\u7406\u80fd\u529b\u8fb9\u754c-\u5e94\u5bf9\u5927\u6a21\u578b\u56f0\u5883\">\u6301\u7eed\u62d3\u5c55\u63a8\u7406\u80fd\u529b\u8fb9\u754c\uff0c\u5e94\u5bf9\u5927\u6a21\u578b\u56f0\u5883<\/h2>\n\n\n\n<p>\u4ece\u6570\u5b66\u63a8\u7406\u5230\u63d0\u5347\u6a21\u578b\u63a8\u7406\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u4ece\u76f4\u89c9\u5f0f\u7684\u5feb\u901f\u56de\u7b54\u5230\u7ecf\u8fc7\u6df1\u5ea6\u601d\u8003\u7684\u56de\u7b54\uff0c\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u6301\u7eed\u63a2\u7d22\u5927\u6a21\u578b\u63a8\u7406\u6027\u80fd\u7684\u8fb9\u754c\u3002\u901a\u8fc7\u5f15\u5165\u65b0\u7684\u89c6\u89d2\u548c\u65b9\u6cd5\uff0c\u4ed6\u4eec\u4e0d\u4ec5\u63a8\u52a8\u4e86\u8be5\u9886\u57df\u7684\u524d\u6cbf\u53d1\u5c55\uff0c\u8fd8\u5e26\u52a8\u4e86\u66f4\u591a\u76f8\u5173\u7814\u7a76\u53d6\u5f97\u65b0\u8fdb\u5c55\u3002\u968f\u7740\u5927\u8bed\u8a00\u6a21\u578b\u6027\u80fd\u548c\u53ef\u9760\u6027\u7684\u63d0\u5347\uff0c\u4eba\u5de5\u667a\u80fd\u5728\u73b0\u5b9e\u573a\u666f\u4e2d\u7684\u5e94\u7528\u8303\u56f4\u4e5f\u5728\u4e0d\u65ad\u6269\u5927\uff0c\u4e3a\u667a\u80fd\u6559\u80b2\u3001\u667a\u80fd\u533b\u7597\u3001\u667a\u80fd\u79d1\u7814\u7b49\u9886\u57df\u63d0\u4f9b\u4e86\u5f3a\u6709\u529b\u7684\u6280\u672f\u652f\u6301\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u6211\u4eec\u4e5f\u5fc5\u987b\u8ba4\u8bc6\u5230\u5f53\u524d\u5927\u6a21\u578b\u4ecd\u9762\u4e34\u8bf8\u591a\u6311\u6218\uff0c\u5982\u751f\u6210\u5185\u5bb9\u65f6\u51fa\u73b0\u7684\u5e7b\u89c9\u95ee\u9898\u4ee5\u53ca\u63a8\u7406\u8fc7\u7a0b\u4e0d\u591f\u4e25\u8c28\u7b49\u3002\u8fd9\u4e9b\u95ee\u9898\u5728\u7279\u5b9a\u5e94\u7528\u573a\u666f\u4e2d\u53ef\u80fd\u4f1a\u5e26\u6765\u4e25\u91cd\u540e\u679c\u3002\u4f8b\u5982\uff0c\u5728\u79d1\u5b66\u7814\u7a76\u4e2d\uff0c\u6a21\u578b\u63a8\u7406\u7684\u504f\u5dee\u53ef\u80fd\u5bfc\u81f4\u9519\u8bef\u7684\u7814\u7a76\u65b9\u5411\uff0c\u9020\u6210\u8d44\u6e90\u7684\u5de8\u5927\u6d6a\u8d39\uff1b\u5728\u533b\u7597\u5065\u5eb7\u9886\u57df\uff0c\u4e0d\u51c6\u786e\u7684\u4fe1\u606f\u53ef\u80fd\u76f4\u63a5\u5371\u53ca\u60a3\u8005\u7684\u751f\u547d\u5b89\u5168\u3002<\/p>\n\n\n\n<p>\u9664\u4e86\u524d\u6587\u6240\u8ff0\u7684\u7814\u7a76\uff0c\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u4e5f\u5728\u5c1d\u8bd5\u4ece\u66f4\u591a\u4e0d\u540c\u7684\u89d2\u5ea6\u63d0\u5347\u4eba\u5de5\u667a\u80fd\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5305\u62ec\u4f7f\u7528 LLMs \u4e3a Rust \u4ee3\u7801\u81ea\u52a8\u751f\u6210\u6b63\u786e\u6027\u8bc1\u660e\uff0c\u8bbe\u8ba1\u4e0e Verus \u9a8c\u8bc1\u5de5\u5177\u72ec\u7279\u529f\u80fd\u76f8\u5339\u914d\u7684\u65b9\u6cd5\uff1b\u63d0\u51fa SAFE \u6846\u67b6\uff0c\u89e3\u51b3 Rust \u4ee3\u7801\u5f62\u5f0f\u5316\u8bc1\u660e\u4e2d\u6570\u636e\u7a00\u7f3a\u7684\u95ee\u9898\uff1b\u63a8\u51fa Alchemy \u6846\u67b6\uff0c\u901a\u8fc7\u53d8\u5316\u7b26\u53f7\u6784\u5efa\u5f62\u5f0f\u5316\u5b9a\u7406\uff0c\u7f13\u89e3\u795e\u7ecf\u5b9a\u7406\u8bc1\u660e\uff08NTP\uff09\u4e2d\u7684\u6570\u636e\u4e0d\u8db3\u95ee\u9898\uff0c\u7b49\u7b49\u3002\u8fd9\u4e9b\u6210\u679c\u4e3a\u5927\u8bed\u8a00\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u63d0\u5347\u63d0\u4f9b\u4e86\u66f4\u591a\u53ef\u80fd\u6027\uff0c\u4e5f\u4e3a\u672a\u6765\u7684\u7814\u7a76\u65b9\u5411\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u601d\u8def\u3002<\/p>\n\n\n\n<p>\u5176\u4ed6\u76f8\u5173\u7814\u7a76\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/abs\/2409.13082\">AutoVerus: Automated proof generation for rust code<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/li>\n\n\n\n<li><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2410.15756v1\">Automated proof generation for rust code via self-evolution<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/li>\n\n\n\n<li><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2410.15748\">Alchemy: Amplifying theorem-proving capability through symbolic mutation<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/li>\n\n\n\n<li><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/pdf\/2408.06195\">Mutual reasoning makes smaller LLMs stronger problem-solvers<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u7f16\u8005\u6309\uff1a\u5c3d\u7ba1\u8fd1\u5e74\u6765\u4eba\u5de5\u667a\u80fd\u7684\u80fd\u529b\u8fc5\u901f\u589e\u5f3a\uff0c\u4f46\u5728\u590d\u6742\u7684\u63a8\u7406\u4efb\u52a1\u4e2d\u4ecd\u5b58\u5728\u4e0d\u8db3\u3002\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u4ece\u591a\u4e2a\u89d2\u5ea6\u5bf9\u6b64\u5c55\u5f00\u7814\u7a76\uff0c\u4e0d\u65ad\u63a2\u7d22\u63d0\u5347\u5927\u6a21\u578b\u63a8\u7406\u80fd\u529b\u7684\u65b0\u9014\u5f84\u3002\u4ece\u5229\u7528\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\u6a21\u62df\u4eba\u7c7b\u201c\u6df1\u5ea6\u601d\u8003\u201d\u8fc7\u7a0b\u7684 rStar-Math\uff0c\u5230\u57fa\u4e8e\u89c4\u5219\u7684\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5 Logic-RL\uff1b\u4ece\u878d\u5408\u5927\u8bed\u8a00\u6a21\u578b\u6570\u5b66\u76f4\u89c9\u4e0e\u7b26\u53f7\u65b9\u6cd5\u7684 LIPS\uff0c\u5230\u63d0\u5347\u81ea\u52a8\u5f62\u5f0f\u5316\u51c6\u786e\u6027\u7684\u65b0\u6846\u67b6\uff1b\u518d\u5230\u81ea\u52a8\u751f\u6210\u9ad8\u8d28\u91cf\u3001\u6709\u76d1\u7763\u6570\u5b66\u6570\u636e\u7684\u795e\u7ecf\u7b26\u53f7\u6846\u67b6\uff0c\u4ee5\u53ca\u7edf\u4e00\u63a8\u7406\u6846\u67b6 CoR \u548c\u5173\u952e\u8ba1\u5212\u6b65\u9aa4\u5b66\u4e60 CPL \u7684\u63d0\u51fa\uff0c\u6bcf\u4e00\u9879\u7814\u7a76\u90fd\u4e3a\u63d0\u5347\u5927\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u548c\u65b9\u6cd5\u3002 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\u901a\u8fc7\u4e09\u4e2a\u6b65\u9aa4\u5b9e\u73b0\u4e86\u81ea\u6211\u8fdb\u5316\uff1a\u9996\u5148\uff0c\u5c06\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u5206\u89e3\u4e3a\u591a\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u4f7f\u6a21\u578b\u80fd\u591f\u9010\u6b65\u63a2\u7d22\u5e76\u9a8c\u8bc1\u6bcf\u4e00\u6b65\u7684\u8d21\u732e\uff0c\u786e\u4fdd\u5c0f\u6a21\u578b\u751f\u6210\u7684\u63a8\u7406\u8f68\u8ff9\u7531\u6b63\u786e\u3001\u9ad8\u8d28\u91cf\u7684\u4e2d\u95f4\u6b65\u9aa4\u7ec4\u6210\uff1b\u5176\u6b21\uff0c\u8bad\u7ec3\u4e00\u4e2a\u4f5c\u4e3a\u8fc7\u7a0b\u504f\u597d\u6a21\u578b\uff08PPM\uff09\u7684\u5c0f\u6a21\u578b\uff0c\u7528\u4e8e\u53ef\u9760\u5730\u4e3a\u6bcf\u4e2a\u6570\u5b66\u63a8\u7406\u6b65\u9aa4\u9884\u6d4b\u5956\u52b1\u6807\u7b7e\uff0c\u4ece\u800c\u5b9e\u73b0\u6240\u9700\u7684\u8fc7\u7a0b\u5956\u52b1\u5efa\u6a21\u4ee5\u53ca\u53ef\u9760\u7684\u6807\u6ce8\uff1b\u6700\u540e\uff0c\u901a\u8fc7\u4e00\u4e2a\u56db\u8f6e\u81ea\u6211\u8fdb\u5316\u65b9\u6848\uff0c\u4ece\u96f6\u5f00\u59cb\u9010\u6b65\u6784\u5efa\u524d\u6cbf\u7684\u7b56\u7565\u6a21\u578b\u548c 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