{"data":{"id":14722,"name":"\u82f1\u4f1f\u8fbe\u5f00\u6e90AIMO\u5965\u8d5b\u51a0\u519b\u6a21\u578b\uff0c\u4ec5\u75281.4B\u53c2\u6570\u91cf\u8d85\u8d8a14B DeeSeek-R1","name_en":null,"summary":"\u8fd9\u51e0\u6b3e\u6a21\u578b\u8868\u73b0\u51fa\u8272\uff0c\u5728 AIME \u548c HMMT \u7ade\u8d5b\u4e2d\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u51c6\u786e\u7387\u5168\u9762\u8d85\u8d8a\u4e86 14B \u7684 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\u5c0f\u65f6\u5185\u89e3\u51b3 50 \u9053\u56fd\u5bb6\u5965\u6797\u5339\u514b\u7ea7\u522b\u7684\u590d\u6742\u6570\u5b66\u95ee\u9898\u3002\u82f1\u4f1f\u8fbe\u7684 7 \u4eba\u56e2\u961f\u201cNemoSkills\u201d\u6700\u7ec8\u6b63\u786e\u89e3\u7b54\u4e86 34 \u9053\u9898\u76ee\uff08\u76f8\u6bd4 2024 \u5e74\u7684\u51a0\u519b\u63d0\u9ad8\u4e86 5 \u9053\uff09\uff0c\u593a\u5f97\u4e86\u51a0\u519b\u3002\u56fe\u4e28\u6b64\u6b21\u6bd4\u8d5b\u7684\u6392\u884c\u699c\uff08\u6765\u6e90\uff1aKaggle\uff09\u73b0\u5728\uff0c\u82f1\u4f1f\u8fbe\u5411\u5168\u7403\u5f00\u653e\u4e86\u5e2e\u52a9\u4ed6\u4eec\u83b7\u80dc\u7684\u6838\u5fc3\u6280\u672f\uff0c\u5305\u62ec\u5c0f\u53c2\u6570\u7684 OpenMath-Nemotron-1.5B\u3001OpenMath-Nemotron-7B \u548c\u76f4\u63a5\u7528\u4e8e\u7ade\u8d5b\u5e76\u4f18\u5316\u7684 OpenMath-Nemotron-14B-Kaggle \u6a21\u578b\u3001\u6027\u80fd\u66f4\u4e3a\u5f3a\u5927\u7684\u65d7\u8230\u6a21\u578b OpenMath-Nemotron-32B\uff0c\u4ee5\u53ca\u8bad\u7ec3\u5b83\u4eec\u6240\u4f9d\u8d56\u7684 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\u6570\u636e\u96c6\u3002\u4ed6\u4eec\u5148\u4ece\u201cArt of Problem Solving\uff08AoPS\uff09\u201d\u7b49\u5728\u7ebf\u6570\u5b66\u793e\u533a\u6536\u96c6\u4e86\u5927\u91cf\u7684\u539f\u59cb\u6570\u5b66\u95ee\u9898\u548c\u8ba8\u8bba\u3002\u968f\u540e\uff0c\u56e2\u961f\u5229\u7528 Qwen2.5-32B-Instruct \u5f00\u53d1\u4e86\u4e00\u5957\u81ea\u52a8\u5316\u6d41\u7a0b\uff0c\u5bf9\u8fd9\u4e9b\u539f\u59cb\u6570\u636e\u8fdb\u884c\u7ec6\u81f4\u5904\u7406\u3002\u8fd9\u5305\u62ec\u4ece\u5e16\u5b50\u4e2d\u63d0\u53d6\u5b8c\u6574\u7684\u6570\u5b66\u95ee\u9898\uff0c\u5bf9\u95ee\u9898\u8fdb\u884c\u5206\u7c7b\uff08\u4f8b\u5982\uff0c\u5254\u9664\u9009\u62e9\u9898\u548c\u662f\u975e\u9898\uff09\uff0c\u5e76\u5c06\u4e00\u4e9b\u9700\u8981\u8bc1\u660e\u8fc7\u7a0b\u7684\u95ee\u9898\u5de7\u5999\u5730\u8f6c\u5316\u4e3a\u9700\u8981\u5177\u4f53\u7b54\u6848\u7684\u5f62\u5f0f\uff0c\u4ee5\u4fbf\u4e8e\u6a21\u578b\u8bad\u7ec3\u548c\u81ea\u52a8\u8bc4\u4f30\u3002\u540c\u65f6\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u4ed6\u4eec\u8fd8\u8fdb\u884c\u4e86\u57fa\u51c6\u53bb\u6c61\u67d3\u5904\u7406\uff0c\u79fb\u9664\u4e86\u4e0e\u73b0\u6709\u5e38\u89c1\u6570\u5b66\u6d4b\u8bd5\u96c6\uff08\u5982 MATH\u3001GSM8K\uff09\u4e2d\u9898\u76ee\u8fc7\u4e8e\u76f8\u4f3c\u7684\u95ee\u9898\u3002\u6700\u7ec8\u5b8c\u6210\u7684 OpenMathReasoning \u6570\u636e\u96c6\uff0c\u5305\u542b\u4e86 54 \u4e07\u4e2a\u9ad8\u8d28\u91cf\u6570\u5b66\u95ee\u9898\uff0c\u5176\u4e2d\u6db5\u76d6\u4e86\u4ece\u4e2d\u5b66\u5230\u5965\u6797\u5339\u514b\u7ade\u8d5b\u7b49\u4e0d\u540c\u96be\u5ea6\u7ea7\u522b\u3002\u4e3a\u4e86\u8ba9\u6a21\u578b\u5b66\u4f1a\u201c\u601d\u8003\u8fc7\u7a0b\u201d\uff0c\u56e2\u961f\u66f4\u8fdb\u4e00\u6b65\u5730\u5229\u7528 DeepSeek-R1 \u548c QwQ-32B \u7b49\u5f3a\u5927\u7684\u73b0\u6709\u6a21\u578b\uff0c\u4e3a\u8fd9\u4e9b\u95ee\u9898\u751f\u6210\u4e86 320 \u4e07\u6761\u5305\u542b\u8be6\u7ec6\u89e3\u9898\u6b65\u9aa4\u7684\u201c\u601d\u7ef4\u94fe\u201d\uff08CoT\uff0cChain-of-Thought\uff09\u89e3\u51b3\u65b9\u6848\u3002\u56fe\u4e28\u6570\u636e\u96c6\u7ec4\u6210\uff08\u6765\u6e90\uff1aarXiv\uff09\u7b2c\u4e8c\u4e2a\u6838\u5fc3\u90e8\u5206\u662f\u5de5\u5177\u96c6\u6210\u63a8\u7406\u3002\u73b0\u4ee3 AI \u7814\u7a76\u7684\u4e00\u4e2a\u91cd\u8981\u8d8b\u52bf\u662f\u8ba9\u8bed\u8a00\u6a21\u578b\u5b66\u4f1a\u4f7f\u7528\u5916\u90e8\u5de5\u5177\uff0c\u4f8b\u5982\u8c03\u7528\u8ba1\u7b97\u5668\u6216\u6267\u884c\u4ee3\u7801\u7247\u6bb5\uff0c\u6765\u8f85\u52a9\u89e3\u51b3\u95ee\u9898\uff0c\u5c24\u5176\u662f\u5728\u9700\u8981\u7cbe\u786e\u8ba1\u7b97\u6216\u6a21\u62df\u7684\u573a\u666f\u4e0b\u3002\u7136\u800c\uff0c\u56e2\u961f\u5728\u5b9e\u8df5\u4e2d\u53d1\u73b0\uff0c\u5373\u4fbf\u662f\u5f53\u65f6\u6700\u5f3a\u7684\u5f00\u6e90\u6570\u5b66\u6a21\u578b\uff0c\u4e5f\u96be\u4ee5\u901a\u8fc7\u7b80\u5355\u7684\u63d0\u793a\u5de5\u7a0b\u6765\u5f15\u5bfc\u5b83\u4eec\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u3001\u5c06\u4ee3\u7801\u6267\u884c\u4e0e\u81ea\u7136\u8bed\u8a00\u63a8\u7406\u6df1\u5ea6\u878d\u5408\u7684\u89e3\u51b3\u65b9\u6848\uff08\u5373 TIR\uff09\u3002\u8fd9\u4e9b\u6a21\u578b\u4f3c\u4e4e\u5bf9\u5176\u81ea\u8eab\u56fa\u6709\u7684\u7eaf\u6587\u672c\u63a8\u7406\u6a21\u5f0f\u4ea7\u751f\u4e86\u67d0\u79cd\u201c\u8def\u5f84\u4f9d\u8d56\u201d\u3002\u4e3a\u4e86\u514b\u670d\u8fd9\u4e00\u969c\u788d\uff0cNemoSkills \u56e2\u961f\u8bbe\u8ba1\u5e76\u5b9e\u65bd\u4e86\u4e00\u5957\u8fed\u4ee3\u5f0f\u5f00\u53d1\u6d41\u7a0b\u3002\u4ed6\u4eec\u9996\u5148\u9009\u62e9\u4e86\u4e00\u4e2a\u6307\u4ee4\u9075\u5faa\u80fd\u529b\u8f83\u597d\u7684\u57fa\u7840\u6a21\u578b\uff08LIMO-Qwen-32B\uff09\uff0c\u7528\u5c11\u91cf\u63a8\u7406\u6570\u636e\u5bf9\u5176\u8fdb\u884c\u521d\u6b65\u5fae\u8c03\u3002\u7136\u540e\uff0c\u5f15\u5bfc\u8fd9\u4e2a\u6a21\u578b\u751f\u6210\u7b2c\u4e00\u6279\u5305\u542b Python \u4ee3\u7801\u7684 TIR \u89e3\u51b3\u65b9\u6848\u3002\u5173\u952e\u7684\u4e0b\u4e00\u6b65\u662f\u8fdb\u884c\u4e25\u683c\u7684\u8d28\u91cf\u8fc7\u6ee4\uff1a\u5229\u7528\u53e6\u4e00\u4e2a\u5f3a\u5927\u7684\u5927\u6a21\u578b\uff08 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\u7684\u80fd\u529b\u3002\u968f\u540e\uff0c\u5229\u7528\u8fd9\u4e2a\u5fae\u8c03\u540e\u7684\u6a21\u578b\u751f\u6210\u66f4\u591a\u3001\u66f4\u9ad8\u8d28\u91cf\u7684 TIR \u6570\u636e\uff0c\u5e76\u518d\u6b21\u8fd0\u7528\u4e0a\u8ff0\u8fc7\u6ee4\u6807\u51c6\u8fdb\u884c\u7b5b\u9009\u3002\u8fd9\u4e2a\u201c\u751f\u6210-\u8fc7\u6ee4-\u8bad\u7ec3\u201d\u7684\u95ed\u73af\u88ab\u91cd\u590d\u6267\u884c\uff0c\u6bcf\u4e00\u8f6e\u90fd\u63d0\u5347\u4e86 TIR \u6570\u636e\u7684\u89c4\u6a21\u548c\u8d28\u91cf\u3002\u6700\u7ec8\uff0c\u56e2\u961f\u6784\u5efa\u8d77\u4e86\u4e00\u4e2a\u5305\u542b 170 \u4e07\u6761\u9ad8\u8d28\u91cf TIR \u89e3\u51b3\u65b9\u6848\u7684\u6570\u636e\u96c6\u3002\u57fa\u4e8e\u6b64\u8bad\u7ec3\u51fa\u7684 OpenMath-Nemotron \u6a21\u578b\uff0c\u80fd\u591f\u719f\u7ec3\u5730\u5728\u81ea\u7136\u8bed\u8a00\u63a8\u7406\u4e2d\u5d4c\u5165 Python \u4ee3\u7801\u6267\u884c\uff0c\u4ece\u800c\u653b\u514b\u90a3\u4e9b\u7eaf\u6587\u672c\u63a8\u7406\u96be\u4ee5\u89e3\u51b3\u7684\u590d\u6742\u8ba1\u7b97\u95ee\u9898\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u8bbe\u8ba1\u4e86\u4e00\u79cd\u673a\u5236\uff0c\u4f7f\u5f97\u6a21\u578b\u5728\u751f\u6210\u7b54\u6848\u65f6\u80fd\u591f\u9075\u5faa\u5bf9\u4ee3\u7801\u5757\u4f7f\u7528\u6b21\u6570\u7684\u9650\u5236\uff0c\u8fd9\u5bf9\u4e8e\u8d44\u6e90\u53d7\u9650\u7684\u63a8\u7406\u573a\u666f\u81f3\u5173\u91cd\u8981\u3002\u7b2c\u4e09\u4e2a\u6838\u5fc3\u90e8\u5206\u5219\u662f\u56e2\u961f\u63d0\u51fa\u7684\u751f\u6210\u5f0f\u89e3\u51b3\u65b9\u6848\u9009\u62e9\u3002\u5728\u89e3\u51b3\u56f0\u96be\u95ee\u9898\u65f6\uff0c\u8ba9\u6a21\u578b\u751f\u6210\u591a\u4e2a\u5019\u9009\u7b54\u6848\u5e76\u4ece\u4e2d\u62e9\u4f18\uff0c\u662f\u63d0\u5347\u6700\u7ec8\u51c6\u786e\u7387\u7684\u5e38\u7528\u6280\u5de7\u3002\u4f20\u7edf\u7684\u201c\u591a\u6570\u6295\u7968\u201d\u65b9\u6cd5\u867d\u7136\u76f4\u89c2\uff0c\u4f46\u5f80\u5f80\u65e0\u6cd5\u5145\u5206\u53d1\u6398\u6a21\u578b\u751f\u6210\u7684\u6240\u6709\u7b54\u6848\u4e2d\u7684\u6f5c\u5728\u6b63\u786e\u4fe1\u606f\uff0c\u5176\u6027\u80fd\u901a\u5e38\u8fdc\u4f4e\u4e8e\u7406\u8bba\u4e0a\u7684\u201cpass@k\u201d\uff08\u5373 k \u4e2a\u7b54\u6848\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u6b63\u786e\u7684\u6982\u7387\uff09\u4e0a\u9650\u3002\u4e3a\u4e86\u5f25\u8865\u8fd9\u4e00\u5dee\u8ddd\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u5f00\u53d1\u4e86 GenSelect \u6280\u672f\u3002\u5176\u6838\u5fc3\u601d\u60f3\u4e0d\u518d\u662f\u7b80\u5355\u5730\u5bf9\u6700\u7ec8\u7b54\u6848\u8fdb\u884c\u6295\u7968\uff0c\u800c\u662f\u8bad\u7ec3\u4e00\u4e2a\u6a21\u578b\uff0c\u8ba9\u5b83\u626e\u6f14\u201c\u8bc4\u5ba1\u5458\u201d\u7684\u89d2\u8272\uff0c\u80fd\u591f\u201c\u9605\u8bfb\u201d\u5e76\u201c\u7406\u89e3\u201d\u591a\u4e2a\u5019\u9009\u89e3\u51b3\u65b9\u6848\u7684\u5b8c\u6574\u6458\u8981\uff0c\u7136\u540e\u57fa\u4e8e\u5bf9\u89e3\u9898\u903b\u8f91\u3001\u6b65\u9aa4\u5408\u7406\u6027\u7b49\u7684\u5224\u65ad\uff0c\u9009\u51fa\u6700\u53ef\u4fe1\u3001\u6700\u6709\u53ef\u80fd\u6b63\u786e\u7684\u90a3\u4e00\u4e2a\u3002\u56fe\u4e28 GenSelect \u7684\u6570\u636e\u6784\u5efa\u6d41\u7a0b\uff08\u6765\u6e90\uff1aarXiv\uff09\u5177\u4f53\u6765\u8bf4\uff0c\u56e2\u961f\u9996\u5148\u5229\u7528 Qwen2.5-32B-Instruct \u6a21\u578b\u4e3a OpenMathReasoning \u6570\u636e\u96c6\u4e2d\u6240\u6709\u5df2\u751f\u6210\u7684 CoT \u548c TIR \u89e3\u51b3\u65b9\u6848\u91cd\u65b0\u751f\u6210\u4e86\u7ed3\u6784\u5316\u7684\u3001\u4fe1\u606f\u66f4\u4e30\u5bcc\u7684\u6458\u8981\u3002\u7136\u540e\uff0c\u4ed6\u4eec\u6784\u5efa\u4e86 GenSelect \u7684\u8bad\u7ec3\u6570\u636e\uff1a\u4e3a\u6bcf\u4e2a\u539f\u59cb\u95ee\u9898\uff0c\u968f\u673a\u62bd\u53d6 2 \u5230 16 \u4e2a\u5019\u9009\u65b9\u6848\u7684\u6458\u8981\uff08\u7279\u522b\u8bbe\u8ba1\u4ee5\u786e\u4fdd\u6837\u672c\u7ec4\u4e2d\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u6b63\u786e\u548c\u4e00\u4e2a\u9519\u8bef\u7684\u89e3\uff09\uff0c\u5c06\u8fd9\u4e9b\u6458\u8981\u8fde\u540c\u539f\u95ee\u9898\u4e00\u8d77\u8f93\u5165\u7ed9 QwQ-32B \u6a21\u578b\uff0c\u5e76\u8981\u6c42\u5b83\u751f\u6210\u4e00\u6bb5\u8be6\u7ec6\u7684\u6bd4\u8f83\u5206\u6790\u6587\u672c\uff0c\u6700\u7ec8\u660e\u786e\u6307\u51fa\u54ea\u4e2a\u7d22\u5f15\u53f7\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6700\u4f73\u7684\u3002\u901a\u8fc7\u7b5b\u9009\u6389\u90a3\u4e9b\u6a21\u578b\u5224\u65ad\u9519\u8bef\uff08\u5373\u9009\u62e9\u4e86\u9519\u8bef\u7b54\u6848\uff09\u7684\u6848\u4f8b\uff0c\u4ed6\u4eec\u6784\u5efa\u4e86\u4e00\u4e2a\u5305\u542b 56.6 \u4e07\u4e2a\u6837\u672c\u7684 GenSelect \u8bad\u7ec3\u6570\u636e\u96c6\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u7ecf\u8fc7 GenSelect \u52a0\u6301\u7684\u6a21\u578b\uff0c\u5176\u6700\u7ec8\u51c6\u786e\u7387\u76f8\u6bd4\u7b80\u5355\u7684\u591a\u6570\u6295\u7968\u6709\u4e86\u663e\u8457\u63d0\u5347\uff0c\u5c24\u5176\u662f\u5728\u5019\u9009\u65b9\u6848\u6570\u91cf\u4e0d\u591a\u65f6\u6548\u679c\u66f4\u4e3a\u660e\u663e\u3002\u867d\u7136\u7531\u4e8e AIMO \u7ade\u8d5b\u4e25\u683c\u7684\u65f6\u95f4\u548c\u8ba1\u7b97\u9650\u5236\uff0cGenSelect \u672a\u80fd\u88ab\u7eb3\u5165\u6700\u7ec8\u7684\u83b7\u80dc\u63d0\u4ea4\u65b9\u6848\u4e2d\uff0c\u4f46\u8fd9\u9879\u6280\u672f\u5df2\u88ab\u5b8c\u5168\u6574\u5408\u5230\u6b64\u6b21\u53d1\u5e03\u7684 OpenMath-Nemotron-32B \u6a21\u578b\u4e2d\uff0c\u6784\u6210\u4e86\u5176\u652f\u6301\u7684\u4e09\u5927\u63a8\u7406\u6a21\u5f0f\u4e4b\u4e00\u3002\u57fa\u4e8e\u4e0a\u8ff0\u4e09\u5927\u652f\u67f1\u548c\u6d77\u91cf\u6570\u636e\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u8bad\u7ec3\u4e86\u4e00\u7cfb\u5217\u540d\u4e3a OpenMath-Nemotron \u7684\u6a21\u578b\uff0c\u53c2\u6570\u89c4\u6a21\u6db5\u76d6 1.5B\u30017B\u300114B \u548c 32B\u3002\u8fd9\u4e9b\u6a21\u578b\u5747\u57fa\u4e8e\u5f3a\u5927\u7684 Qwen2.5 \u57fa\u5ea7\u6a21\u578b\u8fdb\u884c\u5fae\u8c03\u3002\u5bf9\u4e8e 1.5B \u548c 7B \u7248\u672c\uff0c\u4ed6\u4eec\u751a\u81f3\u4f7f\u7528\u4e86\u4e13\u95e8\u4e3a\u6570\u5b66\u4efb\u52a1\u4f18\u5316\u7684 Qwen2.5-Math \u7248\u672c\u4f5c\u4e3a\u8d77\u70b9\u3002\u8bad\u7ec3\u8fc7\u7a0b\u91c7\u7528\u4e86\u76d1\u7763\u5fae\u8c03\uff0c\u6df7\u5408\u4f7f\u7528\u4e86 CoT\u3001TIR \u548c GenSelect \u4e09\u79cd\u4efb\u52a1\u7684\u6570\u636e\uff0c\u603b\u8ba1\u8fbe 550 \u4e07\u4e2a\u6837\u672c\u3002\u8fd9\u610f\u5473\u7740\u540c\u4e00\u4e2a\u6a21\u578b\u53ef\u4ee5\u901a\u8fc7\u4e0d\u540c\u7684\u63d0\u793a\uff08prompt\uff09\u5728 CoT\uff08\u7eaf\u6587\u672c\u63a8\u7406\uff09\u3001TIR\uff08\u5de5\u5177\u96c6\u6210\u63a8\u7406\uff09\u548c GenSelect\uff08\u591a\u65b9\u6848\u9009\u62e9\uff09\u6a21\u5f0f\u4e0b\u5de5\u4f5c\u3002\u56fe\u4e28\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u51c6\u786e\u7387\u7684\u63d0\u5347\uff08\u6765\u6e90\uff1aarXiv\uff09\u4e3a\u4e86\u5904\u7406\u957f\u8fbe\u6570\u5343\u751a\u81f3\u4e0a\u4e07\u4e2a token \u7684\u957f\u5e8f\u5217\u63a8\u7406\uff0c\u56e2\u961f\u5e94\u7528\u4e86\u65cb\u8f6c\u4f4d\u7f6e\u7f16\u7801\uff08RoPE\uff0cRotary Position Embedding\uff09\u6269\u5c55\u6280\u672f\uff0c\u5e76\u5c06\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u4e0a\u4e0b\u6587\u7a97\u53e3\u6269\u5c55\u5230\u652f\u6301\u957f\u5e8f\u5217\u3002\u8bad\u7ec3\u4f7f\u7528\u4e86\u82f1\u4f1f\u8fbe\u81ea\u5bb6\u7684 NeMo-Aligner \u5de5\u5177\u5305\uff0c\u5e76\u7ed3\u5408\u4e86\u5e8f\u5217\u6253\u5305\u3001\u4e0a\u4e0b\u6587\u5e76\u884c\u7b49\u6280\u672f\u6765\u52a0\u901f\u957f\u5e8f\u5217\u8bad\u7ec3\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u91c7\u7528\u4e86\u68c0\u67e5\u70b9\u5e73\u5747\uff08checkpoint averaging\uff09\u548c\u5728\u66f4\u96be\u95ee\u9898\u5b50\u96c6\u4e0a\u8fdb\u884c\u7b2c\u4e8c\u8f6e\u5fae\u8c03\u7b49\u7b56\u7565\uff0c\u8fdb\u4e00\u6b65\u63d0\u5347\u6a21\u578b\u6027\u80fd\u3002\u591a\u9879\u4f18\u5316\u63a8\u7406\u63aa\u65bd\u8d62\u5f97 AIMO-2 \u7ade\u8d5b\u4e0d\u4ec5\u9700\u8981\u6a21\u578b\u672c\u8eab\u5f3a\u5927\uff0c\u8fd8\u9700\u8981\u5728\u6781\u5176\u82db\u523b\u7684 5 \u5c0f\u65f6\u30014x L4 GPU \u9650\u5236\u4e0b\u9ad8\u6548\u5b8c\u6210\u63a8\u7406\u3002\u8fd9\u8981\u6c42\u56e2\u961f\u5728\u6a21\u578b\u9009\u62e9\u548c\u63a8\u7406\u4f18\u5316\u4e0a\u505a\u51fa\u6781\u81f4\u6743\u8861\u3002\u4ed6\u4eec\u7684\u6700\u7ec8\u63d0\u4ea4\u65b9\u6848\u57fa\u4e8e OpenMath-Nemotron-14B \u6a21\u578b\u7684\u4e00\u4e2a\u65e9\u671f\u7248\u672c\uff0c\u8be5\u7248\u672c\u5728\u4e00\u4e2a\u7a0d\u5c0f\u7684 CoT \u6570\u636e\u96c6\uff08\u4ec5 DeepSeek-R1 \u751f\u6210\uff09\u4e0a\u8bad\u7ec3\uff0c\u5e76\u8fdb\u884c\u4e86\u8f7b\u91cf\u7ea7\u7684 TIR \u5fae\u8c03\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4ed6\u4eec\u91c7\u7528\u4e86\u6a21\u578b\u5408\u5e76\u6280\u672f\uff0c\u5c06\u7eaf CoT \u8bad\u7ec3\u7684\u68c0\u67e5\u70b9\u548c\u7ecf\u8fc7 TIR \u5fae\u8c03\u7684\u68c0\u67e5\u70b9\u8fdb\u884c\u7ebf\u6027\u7ec4\u5408\u3002\u8fd9\u79cd\u7b80\u5355\u800c\u6709\u6548\u7684\u65b9\u6cd5\uff0c\u8ba9\u4ed6\u4eec\u80fd\u591f\u5728\u4fdd\u6301 TIR \u80fd\u529b\u7684\u540c\u65f6\uff0c\u90e8\u5206\u6062\u590d CoT \u6a21\u578b\u7684\u751f\u6210\u6d41\u7545\u6027\u548c\u901f\u5ea6\u4f18\u52bf\uff0c\u5e76\u51cf\u5c11\u4ee3\u7801\u8c03\u7528\u6b21\u6570\uff0c\u4ece\u800c\u66f4\u597d\u5730\u9002\u5e94\u7ade\u8d5b\u73af\u5883\u3002\u4e3a\u4e86\u5728\u6709\u9650\u7684\u65f6\u95f4\u5185\u6700\u5927\u5316\u89e3\u9898\u6570\u91cf\u548c\u51c6\u786e\u7387\uff0c\u56e2\u961f\u5b9e\u65bd\u4e86\u591a\u9879\u63a8\u7406\u4f18\u5316\u63aa\u65bd\uff1a\u9996\u5148\uff0c\u4ed6\u4eec\u4f7f\u7528 TensorRT-LLM \u5c06\u9884\u8bad\u7ec3\u6a21\u578b\u8f6c\u6362\u4e3a TensorRT \u5f15\u64ce\u3002\u8fd9\u4e00\u5de5\u5177\u7684\u52a8\u6001\u6279\u5904\u7406\u529f\u80fd\u901a\u8fc7\u52a8\u6001\u5206\u7ec4\u63a8\u7406\u8bf7\u6c42\u63d0\u9ad8\u4e86\u541e\u5410\u91cf\uff0c\u5728\u6837\u672c\u5b8c\u6210\u540e\u5373\u523b\u91ca\u653e\uff0c\u51cf\u5c11\u5ef6\u8fdf\u5e76\u4f18\u5316 GPU \u5229\u7528\u7387\u3002\u7531\u4e8e\u6837\u672c\u662f\u72ec\u7acb\u5904\u7406\u7684\uff0c\u6279\u5904\u7406\u53ef\u4ee5\u65e0\u7f1d\u6df7\u5408\u4e0d\u540c\u7684\u63d0\u793a\u6216\u63a8\u7406\u53c2\u6570\u3002TensorRT-LLM \u8fd8\u5305\u62ec\u81ea\u5b9a\u4e49\u6ce8\u610f\u529b\u5185\u6838\u548c\u5206\u9875 KV \u7f13\u5b58\u7b49\u591a\u79cd\u4f18\u5316\u3002\u5728\u91cf\u5316\u65b9\u9762\uff0c\u56e2\u961f\u4f18\u5148\u91c7\u7528 int8 \u6743\u91cd\u91cf\u5316\uff08W8A16\uff09\u548c FP8 \u91cf\u5316\uff0c\u76f8\u6bd4 BF16 \u683c\u5f0f\u901f\u5ea6\u63d0\u5347\u4e86 1.5 \u500d\uff0c\u540c\u65f6\u5bf9\u51c6\u786e\u7387\u7684\u5f71\u54cd\u6700\u5c0f\u3002\u51cf\u5c0f\u7684\u6743\u91cd\u5927\u5c0f\u8fd8\u4e3a\u66f4\u5927\u7684\u952e\u503c\u7f13\u5b58\u91ca\u653e\u4e86\u5185\u5b58\uff0c\u5141\u8bb8\u5904\u7406\u66f4\u957f\u7684\u5e8f\u5217\u3002\u56e2\u961f\u8fd8\u4f7f\u7528\u4e86\u82f9\u679c\u5f00\u53d1\u7684 ReDrafter \u6280\u672f\uff0c\u8fd9\u662f\u4e00\u79cd\u5faa\u73af\u63a8\u6d4b\u89e3\u7801\u65b9\u6cd5\uff0c\u4f7f\u7528\u57fa\u4e8e RNN \u7684\u8d77\u8349\u5668\u5728\u6bcf\u4e2a\u89e3\u7801\u6b65\u9aa4\u63d0\u51fa\u5e76\u9a8c\u8bc1\u591a\u4e2a token\u3002\u4ed6\u4eec\u8bad\u7ec3\u4e86\u4e00\u4e2a\u80fd\u591f\u5728\u6bcf\u4e00\u6b65\u63d0\u51fa\u6700\u591a\u4e09\u4e2a token \u7684\u8d77\u8349\u5668\uff0c\u5728\u5927\u7ea6 65% \u7684\u6b65\u9aa4\u4e2d\u6210\u529f\u63a5\u53d7\u6240\u6709\u4e09\u4e2a token\uff0c\u663e\u8457\u52a0\u901f\u4e86\u751f\u6210\u8fc7\u7a0b\u3002\u56fe\u4e28\u5728 4 \u4e2a L4 GPU \u4e0a\u5bf9\u5177\u6709\u4e0d\u540c\u4f18\u5316\u65b9\u6cd5\u7684\u63d0\u4ea4\u7ba1\u9053\u8fdb\u884c\u57fa\u51c6\u6d4b\u8bd5\uff08\u6765\u6e90\uff1aarXiv\uff09\u6b64\u5916\uff0c\u56e2\u961f\u901a\u8fc7\u5c06 CoT \u548c TIR \u68c0\u67e5\u70b9\u7ebf\u6027\u7ec4\u5408\u521b\u5efa\u4e86\u6700\u7ec8\u6a21\u578b\uff0c\u8fd9\u79cd\u7b56\u7565\u5141\u8bb8\u4ed6\u4eec\u63a7\u5236\u6bcf\u4e2a\u5fae\u8c03\u9636\u6bb5\u5bf9\u6700\u7ec8\u6a21\u578b\u884c\u4e3a\u7684\u5f71\u54cd\u7a0b\u5ea6\u3002\u6700\u4f73\u6a21\u578b\u662f\u4f7f\u7528 CoT0.3+TIR0.7 \u7684\u7ec4\u5408\u521b\u5efa\u7684\uff0c\u8fd9\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u51c6\u786e\u7387\uff0c\u8fd8\u901a\u8fc7\u51cf\u5c11\u89e3\u51b3\u65b9\u6848\u957f\u5ea6\u548c\u4ee3\u7801\u6267\u884c\u6b21\u6570\u52a0\u901f\u4e86\u751f\u6210\u3002\u56e2\u961f\u5b9e\u73b0\u4e86\u4e00\u79cd\u7f13\u51b2\u7b56\u7565\uff0c\u4e3a\u6bcf\u4e2a\u95ee\u9898\u5206\u914d 350 \u79d2\u7684\u57fa\u672c\u65f6\u95f4\u9650\u5236\uff0c\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u63d0\u524d\u5b8c\u6210\uff0c\u672a\u4f7f\u7528\u7684\u65f6\u95f4\u4f1a\u88ab\u6dfb\u52a0\u5230\u5171\u4eab\u7f13\u51b2\u533a\uff0c\u4f9b\u540e\u7eed\u95ee\u9898\u4f7f\u7528\u3002\u56e2\u961f\u8fd8\u5229\u7528\u4e86 NeMo-Skills \u7684\u5f02\u6b65\u751f\u6210\u529f\u80fd\u5b9e\u73b0\u6279\u91cf\u5904\u7406\u548c\u65e9\u505c\u3002\u4f8b\u5982\uff0c\u5728 16 \u4e2a\u6837\u672c\u7684\u6279\u5904\u7406\u4e2d\uff0c\u5982\u679c\u524d 4-5 \u4e2a\u5b8c\u6210\u7684\u6837\u672c\u5c31\u5df2\u7ecf\u5bf9\u6700\u7ec8\u7b54\u6848\u8fbe\u6210\u4e00\u81f4\uff0c\u5219\u53d6\u6d88\u5269\u4f59\u7684\u751f\u6210\u5e76\u7ee7\u7eed\u4e0b\u4e00\u4e2a\u95ee\u9898\u3002\u8fd9\u79cd\u673a\u5236\u6781\u5927\u5730\u8282\u7ea6\u4e86\u5728\u7b80\u5355\u6216\u4e2d\u7b49\u96be\u5ea6\u95ee\u9898\u4e0a\u53ef\u80fd\u6d6a\u8d39\u7684\u65f6\u95f4\uff0c\u4e3a\u653b\u514b\u96be\u9898\u4e89\u53d6\u4e86\u5b9d\u8d35\u7684\u65f6\u95f4\u7a97\u53e3\u3002\u65e9\u505c\u7b56\u7565\u589e\u52a0\u4e86\u54cd\u5e94\u76f8\u5173\u6027\uff0c\u56e0\u4e3a\u8f83\u77ed\u7684\u7b54\u6848\u5f80\u5f80\u8d28\u91cf\u66f4\u9ad8\u3002\u56fe\u4e28\u5f02\u6b65\u6279\u5904\u7406\u6d41\u7a0b\uff08\u6765\u6e90\uff1aKaggle\uff09\u5b9e\u9a8c\u7ed3\u679c\u663e\u793a\uff0c\u5728 Comp-Math-24-25 \u6d4b\u8bd5\u96c6\uff08\u5305\u542b\u6765\u81ea AIME \u548c HMMT \u7ade\u8d5b\u7684\u95ee\u9898\uff09\u4e0a\uff0c\u56e2\u961f\u7684\u6a21\u578b\u8868\u73b0\u51fa\u8272\u30021.5B \u6a21\u578b\u5728 CoT \u6a21\u5f0f\u4e0b\u5355\u6b21\u901a\u8fc7\u51c6\u786e\u7387\u4e3a 58.2%\uff0c\u591a\u6570\u6295\u7968\u51c6\u786e\u7387\u8fbe 80.0%\uff1b\u5728 TIR \u6a21\u5f0f\u4e0b\uff0c\u8fd9\u4e9b\u6570\u5b57\u5206\u522b\u63d0\u9ad8\u5230 64.5% \u548c 83.3%\uff1b\u4f7f\u7528 GenSelect \u6280\u672f\u540e\uff0c\u51c6\u786e\u7387\u8fdb\u4e00\u6b65\u63d0\u5347\u81f3 83.3%\u300214B \u6a21\u578b\u7684\u8868\u73b0\u66f4\u4e3a\u51fa\u8272\uff0c\u5728 TIR \u6a21\u5f0f\u7ed3\u5408 GenSelect \u4f7f\u7528\u65f6\uff0c\u51c6\u786e\u7387\u9ad8\u8fbe 90.0%\u3002\u6700\u5927\u7684 32B \u6a21\u578b\u5728\u76f8\u540c\u6761\u4ef6\u4e0b\u751a\u81f3\u8fbe\u5230\u4e86 93.3% \u7684\u51c6\u786e\u7387\u3002\u8fd9\u4e9b\u7ed3\u679c\u4e5f\u8868\u660e\uff0c\u65e0\u8bba\u6a21\u578b\u5927\u5c0f\u5982\u4f55\uff0cTIR \u6a21\u5f0f\u59cb\u7ec8\u4f18\u4e8e\u7eaf CoT \u6a21\u5f0f\uff0c\u800c GenSelect \u6280\u672f\u80fd\u8fdb\u4e00\u6b65\u63d0\u9ad8\u51c6\u786e\u7387\u3002\u56fe\uff5c\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u7684\u8bc4\u4f30\u7ed3\u679c\uff08\u6765\u6e90\uff1aarXiv\uff09\u76ee\u524d\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u5df2\u5c06\u5b8c\u6574\u7684 OpenMathReasoning \u6570\u636e\u96c6\u3001\u8bad\u7ec3\u597d\u7684 OpenMath-Nemotron \u6a21\u578b\u7cfb\u5217\u4ee5\u53ca\u6240\u6709\u76f8\u5173\u4ee3\u7801\u4ee5\u5546\u4e1a\u8bb8\u53ef\u65b9\u5f0f\u53d1\u5e03\u5230 Hugging Face \u548c GitHub \u4e0a\uff08\u9879\u76ee\u5730\u5740\uff1ahttps:\/\/huggingface.co\/collections\/nvidia\/openmathreasoning-68072c0154a5099573d2e730\uff09\u3002\u53c2\u8003\u8d44\u6599\uff1a1.https:\/\/arxiv.org\/abs\/2504.168912.https:\/\/www.kaggle.com\/competitions\/ai-mathematical-olympiad-progress-prize-2\/discussion\/574765\u8fd0\u8425\/\u6392\u7248\uff1a\u4f55\u6668\u9f99","content":"

\u82f1\u4f1f\u8fbe\u6b63\u5f0f\u5f00\u6e90\u4e86\u5176\u4e0d\u4e45\u524d\u5728 AI \u6570\u5b66\u5965\u6797\u5339\u514b\u7ade\u8d5b\uff08AIMO\uff0cAI Mathematical Olympiad\uff09\u4e2d\u65a9\u83b7\u51a0\u519b\u7684\u6838\u5fc3\u6a21\u578b\u7cfb\u5217\u3002<\/span><\/span><\/p>

\u5728\u672c\u5c4a AIMO-2 Kaggle \u7ade\u8d5b\u4e2d\uff0c\u8d85\u8fc7 2,200 \u652f\u53c2\u8d5b\u961f\u4f0d\u63d0\u4ea4\u4e86 AI \u6a21\u578b\uff0c\u6311\u6218\u5728 5 \u5c0f\u65f6\u5185\u89e3\u51b3 50 \u9053\u56fd\u5bb6\u5965\u6797\u5339\u514b\u7ea7\u522b\u7684\u590d\u6742\u6570\u5b66\u95ee\u9898\u3002\u82f1\u4f1f\u8fbe\u7684 7 \u4eba\u56e2\u961f\u201cNemoSkills\u201d\u6700\u7ec8\u6b63\u786e\u89e3\u7b54\u4e86 34 \u9053\u9898\u76ee\uff08\u76f8\u6bd4 2024 \u5e74\u7684\u51a0\u519b\u63d0\u9ad8\u4e86 5 \u9053\uff09\uff0c\u593a\u5f97\u4e86\u51a0\u519b\u3002<\/span><\/span><\/p>

\u56fe\u4e28\u6b64\u6b21\u6bd4\u8d5b\u7684\u6392\u884c\u699c\uff08\u6765\u6e90\uff1aKaggle\uff09<\/div>
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\u73b0\u5728\uff0c\u82f1\u4f1f\u8fbe\u5411\u5168\u7403\u5f00\u653e\u4e86\u5e2e\u52a9\u4ed6\u4eec\u83b7\u80dc\u7684\u6838\u5fc3\u6280\u672f\uff0c\u5305\u62ec\u5c0f\u53c2\u6570\u7684 OpenMath-Nemotron-1.5B\u3001OpenMath-Nemotron-7B \u548c\u76f4\u63a5\u7528\u4e8e\u7ade\u8d5b\u5e76\u4f18\u5316\u7684 OpenMath-Nemotron-14B-Kaggle \u6a21\u578b\u3001\u6027\u80fd\u66f4\u4e3a\u5f3a\u5927\u7684\u65d7\u8230\u6a21\u578b OpenMath-Nemotron-32B\uff0c\u4ee5\u53ca\u8bad\u7ec3\u5b83\u4eec\u6240\u4f9d\u8d56\u7684 OpenMathReasoning \u6570\u636e\u96c6\u3002<\/span><\/span><\/p>

\u57fa\u51c6\u6d4b\u8bd5\u7684\u7ed3\u679c\u663e\u793a\uff0c<\/span>\u8fd9\u51e0\u6b3e\u6a21\u578b\u8868\u73b0\u51fa\u8272\uff0c\u5728 AIME \u548c HMMT \u7ade\u8d5b\u4e2d\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u51c6\u786e\u7387\u5168\u9762\u8d85\u8d8a\u4e86 14B \u7684 DeepSeek-R1\u3002<\/span><\/strong><\/span><\/p>

\u56fe\u4e28 AIME \u548c HMMT \u7ade\u8d5b\u4e2d\u6570\u5b66\u95ee\u9898\u7684\u51c6\u786e\u7387\uff08\u6765\u6e90\uff1aarXiv\uff09<\/div>
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\u82f1\u4f1f\u8fbe\u662f\u5982\u4f55\u6784\u5efa OpenMath-Nemotron \u7684\uff1f<\/span><\/strong><\/span><\/p>

\u90a3\u4e48\uff0c\u82f1\u4f1f\u8fbe\u662f\u5982\u4f55\u6784\u5efa OpenMath-Nemotron \u6a21\u578b\u7684\uff1f<\/span><\/span><\/p>

\u8fd9\u9996\u5148\u5728\u4e8e\u4e00\u4e2a\u5927\u89c4\u6a21\u4e14\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e\u96c6\u3002\u8ba4\u8bc6\u5230\u73b0\u6709\u8d44\u6e90\u7684\u4e0d\u8db3\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u9996\u5148\u6295\u5165\u4e86\u5927\u91cf\u7684\u5de5\u4f5c\u6765\u521b\u5efa OpenMathReasoning \u6570\u636e\u96c6\u3002<\/span><\/span><\/p>

\u4ed6\u4eec\u5148\u4ece\u201cArt of Problem Solving\uff08AoPS\uff09\u201d\u7b49\u5728\u7ebf\u6570\u5b66\u793e\u533a\u6536\u96c6\u4e86\u5927\u91cf\u7684\u539f\u59cb\u6570\u5b66\u95ee\u9898\u548c\u8ba8\u8bba\u3002<\/span><\/span><\/p>

\u968f\u540e\uff0c\u56e2\u961f\u5229\u7528 Qwen2.5-32B-Instruct \u5f00\u53d1\u4e86\u4e00\u5957\u81ea\u52a8\u5316\u6d41\u7a0b\uff0c\u5bf9\u8fd9\u4e9b\u539f\u59cb\u6570\u636e\u8fdb\u884c\u7ec6\u81f4\u5904\u7406\u3002\u8fd9\u5305\u62ec\u4ece\u5e16\u5b50\u4e2d\u63d0\u53d6\u5b8c\u6574\u7684\u6570\u5b66\u95ee\u9898\uff0c\u5bf9\u95ee\u9898\u8fdb\u884c\u5206\u7c7b\uff08\u4f8b\u5982\uff0c\u5254\u9664\u9009\u62e9\u9898\u548c\u662f\u975e\u9898\uff09\uff0c\u5e76\u5c06\u4e00\u4e9b\u9700\u8981\u8bc1\u660e\u8fc7\u7a0b\u7684\u95ee\u9898\u5de7\u5999\u5730\u8f6c\u5316\u4e3a\u9700\u8981\u5177\u4f53\u7b54\u6848\u7684\u5f62\u5f0f\uff0c\u4ee5\u4fbf\u4e8e\u6a21\u578b\u8bad\u7ec3\u548c\u81ea\u52a8\u8bc4\u4f30\u3002\u540c\u65f6\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u4ed6\u4eec\u8fd8\u8fdb\u884c\u4e86\u57fa\u51c6\u53bb\u6c61\u67d3\u5904\u7406\uff0c\u79fb\u9664\u4e86\u4e0e\u73b0\u6709\u5e38\u89c1\u6570\u5b66\u6d4b\u8bd5\u96c6\uff08\u5982 MATH\u3001GSM8K\uff09\u4e2d\u9898\u76ee\u8fc7\u4e8e\u76f8\u4f3c\u7684\u95ee\u9898\u3002<\/span><\/span><\/p>

\u6700\u7ec8\u5b8c\u6210\u7684 OpenMathReasoning \u6570\u636e\u96c6\uff0c\u5305\u542b\u4e86 54 \u4e07\u4e2a\u9ad8\u8d28\u91cf\u6570\u5b66\u95ee\u9898\uff0c\u5176\u4e2d\u6db5\u76d6\u4e86\u4ece\u4e2d\u5b66\u5230\u5965\u6797\u5339\u514b\u7ade\u8d5b\u7b49\u4e0d\u540c\u96be\u5ea6\u7ea7\u522b\u3002\u4e3a\u4e86\u8ba9\u6a21\u578b\u5b66\u4f1a\u201c\u601d\u8003\u8fc7\u7a0b\u201d\uff0c\u56e2\u961f\u66f4\u8fdb\u4e00\u6b65\u5730\u5229\u7528 DeepSeek-R1 \u548c QwQ-32B \u7b49\u5f3a\u5927\u7684\u73b0\u6709\u6a21\u578b\uff0c\u4e3a\u8fd9\u4e9b\u95ee\u9898\u751f\u6210\u4e86 320 \u4e07\u6761\u5305\u542b\u8be6\u7ec6\u89e3\u9898\u6b65\u9aa4\u7684\u201c\u601d\u7ef4\u94fe\u201d\uff08CoT\uff0cChain-of-Thought\uff09\u89e3\u51b3\u65b9\u6848\u3002<\/span><\/span><\/p>

\u56fe\u4e28\u6570\u636e\u96c6\u7ec4\u6210\uff08\u6765\u6e90\uff1aarXiv\uff09<\/div>
<\/a>

\u7b2c\u4e8c\u4e2a\u6838\u5fc3\u90e8\u5206\u662f\u5de5\u5177\u96c6\u6210\u63a8\u7406\u3002<\/span><\/span><\/p>

\u73b0\u4ee3 AI \u7814\u7a76\u7684\u4e00\u4e2a\u91cd\u8981\u8d8b\u52bf\u662f\u8ba9\u8bed\u8a00\u6a21\u578b\u5b66\u4f1a\u4f7f\u7528\u5916\u90e8\u5de5\u5177\uff0c\u4f8b\u5982\u8c03\u7528\u8ba1\u7b97\u5668\u6216\u6267\u884c\u4ee3\u7801\u7247\u6bb5\uff0c\u6765\u8f85\u52a9\u89e3\u51b3\u95ee\u9898\uff0c\u5c24\u5176\u662f\u5728\u9700\u8981\u7cbe\u786e\u8ba1\u7b97\u6216\u6a21\u62df\u7684\u573a\u666f\u4e0b\u3002\u7136\u800c\uff0c\u56e2\u961f\u5728\u5b9e\u8df5\u4e2d\u53d1\u73b0\uff0c\u5373\u4fbf\u662f\u5f53\u65f6\u6700\u5f3a\u7684\u5f00\u6e90\u6570\u5b66\u6a21\u578b\uff0c\u4e5f\u96be\u4ee5\u901a\u8fc7\u7b80\u5355\u7684\u63d0\u793a\u5de5\u7a0b\u6765\u5f15\u5bfc\u5b83\u4eec\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u3001\u5c06\u4ee3\u7801\u6267\u884c\u4e0e\u81ea\u7136\u8bed\u8a00\u63a8\u7406\u6df1\u5ea6\u878d\u5408\u7684\u89e3\u51b3\u65b9\u6848\uff08\u5373 TIR\uff09\u3002\u8fd9\u4e9b\u6a21\u578b\u4f3c\u4e4e\u5bf9\u5176\u81ea\u8eab\u56fa\u6709\u7684\u7eaf\u6587\u672c\u63a8\u7406\u6a21\u5f0f\u4ea7\u751f\u4e86\u67d0\u79cd\u201c\u8def\u5f84\u4f9d\u8d56\u201d\u3002<\/span><\/span><\/p>

\u4e3a\u4e86\u514b\u670d\u8fd9\u4e00\u969c\u788d\uff0cNemoSkills \u56e2\u961f\u8bbe\u8ba1\u5e76\u5b9e\u65bd\u4e86\u4e00\u5957\u8fed\u4ee3\u5f0f\u5f00\u53d1\u6d41\u7a0b\u3002\u4ed6\u4eec\u9996\u5148\u9009\u62e9\u4e86\u4e00\u4e2a\u6307\u4ee4\u9075\u5faa\u80fd\u529b\u8f83\u597d\u7684\u57fa\u7840\u6a21\u578b\uff08LIMO-Qwen-32B\uff09\uff0c\u7528\u5c11\u91cf\u63a8\u7406\u6570\u636e\u5bf9\u5176\u8fdb\u884c\u521d\u6b65\u5fae\u8c03\u3002\u7136\u540e\uff0c\u5f15\u5bfc\u8fd9\u4e2a\u6a21\u578b\u751f\u6210\u7b2c\u4e00\u6279\u5305\u542b Python \u4ee3\u7801\u7684 TIR \u89e3\u51b3\u65b9\u6848\u3002\u5173\u952e\u7684\u4e0b\u4e00\u6b65\u662f\u8fdb\u884c\u4e25\u683c\u7684\u8d28\u91cf\u8fc7\u6ee4\uff1a\u5229\u7528\u53e6\u4e00\u4e2a\u5f3a\u5927\u7684\u5927\u6a21\u578b\uff08 Qwen2.5-32B-Instruct\uff09\uff0c\u6765\u5224\u65ad\u6bcf\u4e2a\u4ee3\u7801\u5757\u7684\u201c\u65b0\u9896\u6027\u201d\uff08\u662f\u4ea7\u751f\u4e86\u65b0\u7ed3\u679c\u8fd8\u662f\u4ec5\u4ec5\u9a8c\u8bc1\u5df2\u77e5\u6b65\u9aa4\uff09\u548c\u201c\u91cd\u8981\u6027\u201d\uff08\u662f\u89e3\u51b3\u95ee\u9898\u7684\u5173\u952e\u73af\u8282\u8fd8\u662f\u53ef\u4ee5\u88ab\u51e0\u6b65\u7b80\u5355 CoT \u53d6\u4ee3\uff09\u3002\u53ea\u6709\u90a3\u4e9b\u4ee3\u7801\u6267\u884c\u63d0\u4f9b\u4e86\u663e\u8457\u63a8\u7406\u4ef7\u503c\uff08\u800c\u975e\u5197\u4f59\u8ba1\u7b97\uff09\u7684\u6837\u672c\u624d\u88ab\u4fdd\u7559\u4e0b\u6765\uff0c\u5f62\u6210\u4e86\u7ea6 1.5 \u4e07\u4e2a\u6837\u672c\u7684\u521d\u59cb TIR \u8bad\u7ec3\u96c6\u3002<\/span><\/span><\/p>

\u63a5\u4e0b\u6765\uff0c\u4ed6\u4eec\u7528\u8fd9\u4e2a\u9ad8\u8d28\u91cf\u7684\u521d\u59cb\u96c6\u53bb\u5fae\u8c03\u66f4\u5f3a\u5927\u7684\u6a21\u578b\uff08\u5982 QwQ-32B\uff09\uff0c\u4f7f\u5176\u521d\u6b65\u5177\u5907\u751f\u6210 TIR \u7684\u80fd\u529b\u3002\u968f\u540e\uff0c\u5229\u7528\u8fd9\u4e2a\u5fae\u8c03\u540e\u7684\u6a21\u578b\u751f\u6210\u66f4\u591a\u3001\u66f4\u9ad8\u8d28\u91cf\u7684 TIR \u6570\u636e\uff0c\u5e76\u518d\u6b21\u8fd0\u7528\u4e0a\u8ff0\u8fc7\u6ee4\u6807\u51c6\u8fdb\u884c\u7b5b\u9009\u3002\u8fd9\u4e2a\u201c\u751f\u6210-\u8fc7\u6ee4-\u8bad\u7ec3\u201d\u7684\u95ed\u73af\u88ab\u91cd\u590d\u6267\u884c\uff0c\u6bcf\u4e00\u8f6e\u90fd\u63d0\u5347\u4e86 TIR \u6570\u636e\u7684\u89c4\u6a21\u548c\u8d28\u91cf\u3002\u6700\u7ec8\uff0c\u56e2\u961f\u6784\u5efa\u8d77\u4e86\u4e00\u4e2a\u5305\u542b 170 \u4e07\u6761\u9ad8\u8d28\u91cf TIR \u89e3\u51b3\u65b9\u6848\u7684\u6570\u636e\u96c6\u3002\u57fa\u4e8e\u6b64\u8bad\u7ec3\u51fa\u7684 OpenMath-Nemotron \u6a21\u578b\uff0c\u80fd\u591f\u719f\u7ec3\u5730\u5728\u81ea\u7136\u8bed\u8a00\u63a8\u7406\u4e2d\u5d4c\u5165 Python \u4ee3\u7801\u6267\u884c\uff0c\u4ece\u800c\u653b\u514b\u90a3\u4e9b\u7eaf\u6587\u672c\u63a8\u7406\u96be\u4ee5\u89e3\u51b3\u7684\u590d\u6742\u8ba1\u7b97\u95ee\u9898\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u8bbe\u8ba1\u4e86\u4e00\u79cd\u673a\u5236\uff0c\u4f7f\u5f97\u6a21\u578b\u5728\u751f\u6210\u7b54\u6848\u65f6\u80fd\u591f\u9075\u5faa\u5bf9\u4ee3\u7801\u5757\u4f7f\u7528\u6b21\u6570\u7684\u9650\u5236\uff0c\u8fd9\u5bf9\u4e8e\u8d44\u6e90\u53d7\u9650\u7684\u63a8\u7406\u573a\u666f\u81f3\u5173\u91cd\u8981\u3002<\/span><\/span><\/p>

\u7b2c\u4e09\u4e2a\u6838\u5fc3\u90e8\u5206\u5219\u662f\u56e2\u961f\u63d0\u51fa\u7684\u751f\u6210\u5f0f\u89e3\u51b3\u65b9\u6848\u9009\u62e9\u3002<\/span><\/span><\/p>

\u5728\u89e3\u51b3\u56f0\u96be\u95ee\u9898\u65f6\uff0c\u8ba9\u6a21\u578b\u751f\u6210\u591a\u4e2a\u5019\u9009\u7b54\u6848\u5e76\u4ece\u4e2d\u62e9\u4f18\uff0c\u662f\u63d0\u5347\u6700\u7ec8\u51c6\u786e\u7387\u7684\u5e38\u7528\u6280\u5de7\u3002\u4f20\u7edf\u7684\u201c\u591a\u6570\u6295\u7968\u201d\u65b9\u6cd5\u867d\u7136\u76f4\u89c2\uff0c\u4f46\u5f80\u5f80\u65e0\u6cd5\u5145\u5206\u53d1\u6398\u6a21\u578b\u751f\u6210\u7684\u6240\u6709\u7b54\u6848\u4e2d\u7684\u6f5c\u5728\u6b63\u786e\u4fe1\u606f\uff0c\u5176\u6027\u80fd\u901a\u5e38\u8fdc\u4f4e\u4e8e\u7406\u8bba\u4e0a\u7684\u201cpass@k\u201d\uff08\u5373 k \u4e2a\u7b54\u6848\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u6b63\u786e\u7684\u6982\u7387\uff09\u4e0a\u9650\u3002<\/span><\/span><\/p>

\u4e3a\u4e86\u5f25\u8865\u8fd9\u4e00\u5dee\u8ddd\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u5f00\u53d1\u4e86 GenSelect \u6280\u672f\u3002<\/span>\u5176\u6838\u5fc3\u601d\u60f3\u4e0d\u518d\u662f\u7b80\u5355\u5730\u5bf9\u6700\u7ec8\u7b54\u6848\u8fdb\u884c\u6295\u7968\uff0c\u800c\u662f\u8bad\u7ec3\u4e00\u4e2a\u6a21\u578b\uff0c\u8ba9\u5b83\u626e\u6f14\u201c\u8bc4\u5ba1\u5458\u201d\u7684\u89d2\u8272\uff0c\u80fd\u591f\u201c\u9605\u8bfb\u201d\u5e76\u201c\u7406\u89e3\u201d\u591a\u4e2a\u5019\u9009\u89e3\u51b3\u65b9\u6848\u7684\u5b8c\u6574\u6458\u8981\uff0c\u7136\u540e\u57fa\u4e8e\u5bf9\u89e3\u9898\u903b\u8f91\u3001\u6b65\u9aa4\u5408\u7406\u6027\u7b49\u7684\u5224\u65ad\uff0c\u9009\u51fa\u6700\u53ef\u4fe1\u3001\u6700\u6709\u53ef\u80fd\u6b63\u786e\u7684\u90a3\u4e00\u4e2a\u3002<\/span><\/strong><\/span><\/p>

<\/div>
\u56fe\u4e28 GenSelect \u7684\u6570\u636e\u6784\u5efa\u6d41\u7a0b\uff08\u6765\u6e90\uff1aarXiv\uff09<\/div>
<\/a>

\u5177\u4f53\u6765\u8bf4\uff0c\u56e2\u961f\u9996\u5148\u5229\u7528 Qwen2.5-32B-Instruct \u6a21\u578b\u4e3a OpenMathReasoning \u6570\u636e\u96c6\u4e2d\u6240\u6709\u5df2\u751f\u6210\u7684 CoT \u548c TIR \u89e3\u51b3\u65b9\u6848\u91cd\u65b0\u751f\u6210\u4e86\u7ed3\u6784\u5316\u7684\u3001\u4fe1\u606f\u66f4\u4e30\u5bcc\u7684\u6458\u8981\u3002\u7136\u540e\uff0c\u4ed6\u4eec\u6784\u5efa\u4e86 GenSelect \u7684\u8bad\u7ec3\u6570\u636e\uff1a\u4e3a\u6bcf\u4e2a\u539f\u59cb\u95ee\u9898\uff0c\u968f\u673a\u62bd\u53d6 2 \u5230 16 \u4e2a\u5019\u9009\u65b9\u6848\u7684\u6458\u8981\uff08\u7279\u522b\u8bbe\u8ba1\u4ee5\u786e\u4fdd\u6837\u672c\u7ec4\u4e2d\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u6b63\u786e\u548c\u4e00\u4e2a\u9519\u8bef\u7684\u89e3\uff09\uff0c\u5c06\u8fd9\u4e9b\u6458\u8981\u8fde\u540c\u539f\u95ee\u9898\u4e00\u8d77\u8f93\u5165\u7ed9 QwQ-32B \u6a21\u578b\uff0c\u5e76\u8981\u6c42\u5b83\u751f\u6210\u4e00\u6bb5\u8be6\u7ec6\u7684\u6bd4\u8f83\u5206\u6790\u6587\u672c\uff0c\u6700\u7ec8\u660e\u786e\u6307\u51fa\u54ea\u4e2a\u7d22\u5f15\u53f7\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6700\u4f73\u7684\u3002\u901a\u8fc7\u7b5b\u9009\u6389\u90a3\u4e9b\u6a21\u578b\u5224\u65ad\u9519\u8bef\uff08\u5373\u9009\u62e9\u4e86\u9519\u8bef\u7b54\u6848\uff09\u7684\u6848\u4f8b\uff0c\u4ed6\u4eec\u6784\u5efa\u4e86\u4e00\u4e2a\u5305\u542b 56.6 \u4e07\u4e2a\u6837\u672c\u7684 GenSelect \u8bad\u7ec3\u6570\u636e\u96c6\u3002<\/span><\/span><\/p>

\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u7ecf\u8fc7 GenSelect \u52a0\u6301\u7684\u6a21\u578b\uff0c\u5176\u6700\u7ec8\u51c6\u786e\u7387\u76f8\u6bd4\u7b80\u5355\u7684\u591a\u6570\u6295\u7968\u6709\u4e86\u663e\u8457\u63d0\u5347\uff0c\u5c24\u5176\u662f\u5728\u5019\u9009\u65b9\u6848\u6570\u91cf\u4e0d\u591a\u65f6\u6548\u679c\u66f4\u4e3a\u660e\u663e\u3002\u867d\u7136\u7531\u4e8e AIMO \u7ade\u8d5b\u4e25\u683c\u7684\u65f6\u95f4\u548c\u8ba1\u7b97\u9650\u5236\uff0cGenSelect \u672a\u80fd\u88ab\u7eb3\u5165\u6700\u7ec8\u7684\u83b7\u80dc\u63d0\u4ea4\u65b9\u6848\u4e2d\uff0c\u4f46\u8fd9\u9879\u6280\u672f\u5df2\u88ab\u5b8c\u5168\u6574\u5408\u5230\u6b64\u6b21\u53d1\u5e03\u7684 OpenMath-Nemotron-32B \u6a21\u578b\u4e2d\uff0c\u6784\u6210\u4e86\u5176\u652f\u6301\u7684\u4e09\u5927\u63a8\u7406\u6a21\u5f0f\u4e4b\u4e00\u3002<\/span><\/span><\/p>

\u57fa\u4e8e\u4e0a\u8ff0\u4e09\u5927\u652f\u67f1\u548c\u6d77\u91cf\u6570\u636e\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u8bad\u7ec3\u4e86\u4e00\u7cfb\u5217\u540d\u4e3a <\/span>OpenMath-Nemotron <\/span><\/strong>\u7684\u6a21\u578b\uff0c\u53c2\u6570\u89c4\u6a21\u6db5\u76d6 1.5B\u30017B\u300114B \u548c 32B\u3002\u8fd9\u4e9b\u6a21\u578b\u5747\u57fa\u4e8e\u5f3a\u5927\u7684 Qwen2.5 \u57fa\u5ea7\u6a21\u578b\u8fdb\u884c\u5fae\u8c03\u3002\u5bf9\u4e8e 1.5B \u548c 7B \u7248\u672c\uff0c\u4ed6\u4eec\u751a\u81f3\u4f7f\u7528\u4e86\u4e13\u95e8\u4e3a\u6570\u5b66\u4efb\u52a1\u4f18\u5316\u7684 Qwen2.5-Math \u7248\u672c\u4f5c\u4e3a\u8d77\u70b9\u3002<\/span><\/p>

\u8bad\u7ec3\u8fc7\u7a0b\u91c7\u7528\u4e86\u76d1\u7763\u5fae\u8c03\uff0c\u6df7\u5408\u4f7f\u7528\u4e86 CoT\u3001TIR \u548c GenSelect \u4e09\u79cd\u4efb\u52a1\u7684\u6570\u636e\uff0c\u603b\u8ba1\u8fbe 550 \u4e07\u4e2a\u6837\u672c\u3002\u8fd9\u610f\u5473\u7740\u540c\u4e00\u4e2a\u6a21\u578b\u53ef\u4ee5\u901a\u8fc7\u4e0d\u540c\u7684\u63d0\u793a\uff08prompt\uff09\u5728 CoT\uff08\u7eaf\u6587\u672c\u63a8\u7406\uff09\u3001TIR\uff08\u5de5\u5177\u96c6\u6210\u63a8\u7406\uff09\u548c GenSelect\uff08\u591a\u65b9\u6848\u9009\u62e9\uff09\u6a21\u5f0f\u4e0b\u5de5\u4f5c\u3002<\/span><\/span><\/p>

\u56fe\u4e28\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u51c6\u786e\u7387\u7684\u63d0\u5347\uff08\u6765\u6e90\uff1aarXiv\uff09<\/div>
<\/a>

\u4e3a\u4e86\u5904\u7406\u957f\u8fbe\u6570\u5343\u751a\u81f3\u4e0a\u4e07\u4e2a token \u7684\u957f\u5e8f\u5217\u63a8\u7406\uff0c\u56e2\u961f\u5e94\u7528\u4e86\u65cb\u8f6c\u4f4d\u7f6e\u7f16\u7801\uff08RoPE\uff0cRotary Position Embedding\uff09\u6269\u5c55\u6280\u672f\uff0c\u5e76\u5c06\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u4e0a\u4e0b\u6587\u7a97\u53e3\u6269\u5c55\u5230\u652f\u6301\u957f\u5e8f\u5217\u3002\u8bad\u7ec3\u4f7f\u7528\u4e86\u82f1\u4f1f\u8fbe\u81ea\u5bb6\u7684 NeMo-Aligner \u5de5\u5177\u5305\uff0c\u5e76\u7ed3\u5408\u4e86\u5e8f\u5217\u6253\u5305\u3001\u4e0a\u4e0b\u6587\u5e76\u884c\u7b49\u6280\u672f\u6765\u52a0\u901f\u957f\u5e8f\u5217\u8bad\u7ec3\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u91c7\u7528\u4e86\u68c0\u67e5\u70b9\u5e73\u5747\uff08checkpoint averaging\uff09\u548c\u5728\u66f4\u96be\u95ee\u9898\u5b50\u96c6\u4e0a\u8fdb\u884c\u7b2c\u4e8c\u8f6e\u5fae\u8c03\u7b49\u7b56\u7565\uff0c\u8fdb\u4e00\u6b65\u63d0\u5347\u6a21\u578b\u6027\u80fd\u3002<\/span><\/span><\/p>

<\/a>

\u591a\u9879\u4f18\u5316\u63a8\u7406\u63aa\u65bd<\/span><\/strong><\/span><\/p>

\u8d62\u5f97 AIMO-2 \u7ade\u8d5b\u4e0d\u4ec5\u9700\u8981\u6a21\u578b\u672c\u8eab\u5f3a\u5927\uff0c\u8fd8\u9700\u8981\u5728\u6781\u5176\u82db\u523b\u7684 5 \u5c0f\u65f6\u30014x L4 GPU \u9650\u5236\u4e0b\u9ad8\u6548\u5b8c\u6210\u63a8\u7406\u3002\u8fd9\u8981\u6c42\u56e2\u961f\u5728\u6a21\u578b\u9009\u62e9\u548c\u63a8\u7406\u4f18\u5316\u4e0a\u505a\u51fa\u6781\u81f4\u6743\u8861\u3002<\/span><\/span><\/p>

\u4ed6\u4eec\u7684\u6700\u7ec8\u63d0\u4ea4\u65b9\u6848\u57fa\u4e8e OpenMath-Nemotron-14B \u6a21\u578b\u7684\u4e00\u4e2a\u65e9\u671f\u7248\u672c\uff0c\u8be5\u7248\u672c\u5728\u4e00\u4e2a\u7a0d\u5c0f\u7684 CoT \u6570\u636e\u96c6\uff08\u4ec5 DeepSeek-R1 \u751f\u6210\uff09\u4e0a\u8bad\u7ec3\uff0c\u5e76\u8fdb\u884c\u4e86\u8f7b\u91cf\u7ea7\u7684 TIR \u5fae\u8c03\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4ed6\u4eec\u91c7\u7528\u4e86\u6a21\u578b\u5408\u5e76\u6280\u672f\uff0c\u5c06\u7eaf CoT \u8bad\u7ec3\u7684\u68c0\u67e5\u70b9\u548c\u7ecf\u8fc7 TIR \u5fae\u8c03\u7684\u68c0\u67e5\u70b9\u8fdb\u884c\u7ebf\u6027\u7ec4\u5408\u3002\u8fd9\u79cd\u7b80\u5355\u800c\u6709\u6548\u7684\u65b9\u6cd5\uff0c\u8ba9\u4ed6\u4eec\u80fd\u591f\u5728\u4fdd\u6301 TIR \u80fd\u529b\u7684\u540c\u65f6\uff0c\u90e8\u5206\u6062\u590d CoT \u6a21\u578b\u7684\u751f\u6210\u6d41\u7545\u6027\u548c\u901f\u5ea6\u4f18\u52bf\uff0c\u5e76\u51cf\u5c11\u4ee3\u7801\u8c03\u7528\u6b21\u6570\uff0c\u4ece\u800c\u66f4\u597d\u5730\u9002\u5e94\u7ade\u8d5b\u73af\u5883\u3002<\/span><\/span><\/p>

\u4e3a\u4e86\u5728\u6709\u9650\u7684\u65f6\u95f4\u5185\u6700\u5927\u5316\u89e3\u9898\u6570\u91cf\u548c\u51c6\u786e\u7387\uff0c\u56e2\u961f\u5b9e\u65bd\u4e86\u591a\u9879\u63a8\u7406\u4f18\u5316\u63aa\u65bd\uff1a<\/span><\/span><\/p>

\u9996\u5148\uff0c\u4ed6\u4eec\u4f7f\u7528 TensorRT-LLM \u5c06\u9884\u8bad\u7ec3\u6a21\u578b\u8f6c\u6362\u4e3a TensorRT \u5f15\u64ce\u3002\u8fd9\u4e00\u5de5\u5177\u7684\u52a8\u6001\u6279\u5904\u7406\u529f\u80fd\u901a\u8fc7\u52a8\u6001\u5206\u7ec4\u63a8\u7406\u8bf7\u6c42\u63d0\u9ad8\u4e86\u541e\u5410\u91cf\uff0c\u5728\u6837\u672c\u5b8c\u6210\u540e\u5373\u523b\u91ca\u653e\uff0c\u51cf\u5c11\u5ef6\u8fdf\u5e76\u4f18\u5316 GPU \u5229\u7528\u7387\u3002\u7531\u4e8e\u6837\u672c\u662f\u72ec\u7acb\u5904\u7406\u7684\uff0c\u6279\u5904\u7406\u53ef\u4ee5\u65e0\u7f1d\u6df7\u5408\u4e0d\u540c\u7684\u63d0\u793a\u6216\u63a8\u7406\u53c2\u6570\u3002TensorRT-LLM \u8fd8\u5305\u62ec\u81ea\u5b9a\u4e49\u6ce8\u610f\u529b\u5185\u6838\u548c\u5206\u9875 KV \u7f13\u5b58\u7b49\u591a\u79cd\u4f18\u5316\u3002<\/span><\/span><\/p>

\u5728\u91cf\u5316\u65b9\u9762\uff0c\u56e2\u961f\u4f18\u5148\u91c7\u7528 int8 \u6743\u91cd\u91cf\u5316\uff08W8A16\uff09\u548c FP8 \u91cf\u5316\uff0c\u76f8\u6bd4 BF16 \u683c\u5f0f\u901f\u5ea6\u63d0\u5347\u4e86 1.5 \u500d\uff0c\u540c\u65f6\u5bf9\u51c6\u786e\u7387\u7684\u5f71\u54cd\u6700\u5c0f\u3002\u51cf\u5c0f\u7684\u6743\u91cd\u5927\u5c0f\u8fd8\u4e3a\u66f4\u5927\u7684\u952e\u503c\u7f13\u5b58\u91ca\u653e\u4e86\u5185\u5b58\uff0c\u5141\u8bb8\u5904\u7406\u66f4\u957f\u7684\u5e8f\u5217\u3002\u56e2\u961f\u8fd8\u4f7f\u7528\u4e86\u82f9\u679c\u5f00\u53d1\u7684 ReDrafter \u6280\u672f\uff0c\u8fd9\u662f\u4e00\u79cd\u5faa\u73af\u63a8\u6d4b\u89e3\u7801\u65b9\u6cd5\uff0c\u4f7f\u7528\u57fa\u4e8e RNN \u7684\u8d77\u8349\u5668\u5728\u6bcf\u4e2a\u89e3\u7801\u6b65\u9aa4\u63d0\u51fa\u5e76\u9a8c\u8bc1\u591a\u4e2a token\u3002\u4ed6\u4eec\u8bad\u7ec3\u4e86\u4e00\u4e2a\u80fd\u591f\u5728\u6bcf\u4e00\u6b65\u63d0\u51fa\u6700\u591a\u4e09\u4e2a token \u7684\u8d77\u8349\u5668\uff0c\u5728\u5927\u7ea6 65% \u7684\u6b65\u9aa4\u4e2d\u6210\u529f\u63a5\u53d7\u6240\u6709\u4e09\u4e2a token\uff0c\u663e\u8457\u52a0\u901f\u4e86\u751f\u6210\u8fc7\u7a0b\u3002<\/span><\/span><\/p>

<\/div>
\u56fe\u4e28\u5728 4 \u4e2a L4 GPU \u4e0a\u5bf9\u5177\u6709\u4e0d\u540c\u4f18\u5316\u65b9\u6cd5\u7684\u63d0\u4ea4\u7ba1\u9053\u8fdb\u884c\u57fa\u51c6\u6d4b\u8bd5\uff08\u6765\u6e90\uff1aarXiv\uff09<\/div>
<\/a>

\u6b64\u5916\uff0c\u56e2\u961f\u901a\u8fc7\u5c06 CoT \u548c TIR \u68c0\u67e5\u70b9\u7ebf\u6027\u7ec4\u5408\u521b\u5efa\u4e86\u6700\u7ec8\u6a21\u578b\uff0c\u8fd9\u79cd\u7b56\u7565\u5141\u8bb8\u4ed6\u4eec\u63a7\u5236\u6bcf\u4e2a\u5fae\u8c03\u9636\u6bb5\u5bf9\u6700\u7ec8\u6a21\u578b\u884c\u4e3a\u7684\u5f71\u54cd\u7a0b\u5ea6\u3002\u6700\u4f73\u6a21\u578b\u662f\u4f7f\u7528 CoT0.3+TIR0.7 \u7684\u7ec4\u5408\u521b\u5efa\u7684\uff0c\u8fd9\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u51c6\u786e\u7387\uff0c\u8fd8\u901a\u8fc7\u51cf\u5c11\u89e3\u51b3\u65b9\u6848\u957f\u5ea6\u548c\u4ee3\u7801\u6267\u884c\u6b21\u6570\u52a0\u901f\u4e86\u751f\u6210\u3002\u56e2\u961f\u5b9e\u73b0\u4e86\u4e00\u79cd\u7f13\u51b2\u7b56\u7565\uff0c\u4e3a\u6bcf\u4e2a\u95ee\u9898\u5206\u914d 350 \u79d2\u7684\u57fa\u672c\u65f6\u95f4\u9650\u5236\uff0c\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u63d0\u524d\u5b8c\u6210\uff0c\u672a\u4f7f\u7528\u7684\u65f6\u95f4\u4f1a\u88ab\u6dfb\u52a0\u5230\u5171\u4eab\u7f13\u51b2\u533a\uff0c\u4f9b\u540e\u7eed\u95ee\u9898\u4f7f\u7528\u3002<\/span><\/span><\/p>

\u56e2\u961f\u8fd8\u5229\u7528\u4e86 NeMo-Skills \u7684\u5f02\u6b65\u751f\u6210\u529f\u80fd\u5b9e\u73b0\u6279\u91cf\u5904\u7406\u548c\u65e9\u505c\u3002\u4f8b\u5982\uff0c\u5728 16 \u4e2a\u6837\u672c\u7684\u6279\u5904\u7406\u4e2d\uff0c\u5982\u679c\u524d 4-5 \u4e2a\u5b8c\u6210\u7684\u6837\u672c\u5c31\u5df2\u7ecf\u5bf9\u6700\u7ec8\u7b54\u6848\u8fbe\u6210\u4e00\u81f4\uff0c\u5219\u53d6\u6d88\u5269\u4f59\u7684\u751f\u6210\u5e76\u7ee7\u7eed\u4e0b\u4e00\u4e2a\u95ee\u9898\u3002\u8fd9\u79cd\u673a\u5236\u6781\u5927\u5730\u8282\u7ea6\u4e86\u5728\u7b80\u5355\u6216\u4e2d\u7b49\u96be\u5ea6\u95ee\u9898\u4e0a\u53ef\u80fd\u6d6a\u8d39\u7684\u65f6\u95f4\uff0c\u4e3a\u653b\u514b\u96be\u9898\u4e89\u53d6\u4e86\u5b9d\u8d35\u7684\u65f6\u95f4\u7a97\u53e3\u3002\u65e9\u505c\u7b56\u7565\u589e\u52a0\u4e86\u54cd\u5e94\u76f8\u5173\u6027\uff0c\u56e0\u4e3a\u8f83\u77ed\u7684\u7b54\u6848\u5f80\u5f80\u8d28\u91cf\u66f4\u9ad8\u3002<\/span><\/span><\/p>

\u56fe\u4e28\u5f02\u6b65\u6279\u5904\u7406\u6d41\u7a0b\uff08\u6765\u6e90\uff1aKaggle\uff09<\/div>
<\/a>

\u5b9e\u9a8c\u7ed3\u679c\u663e\u793a\uff0c\u5728 Comp-Math-24-25 \u6d4b\u8bd5\u96c6\uff08\u5305\u542b\u6765\u81ea AIME \u548c HMMT \u7ade\u8d5b\u7684\u95ee\u9898\uff09\u4e0a\uff0c\u56e2\u961f\u7684\u6a21\u578b\u8868\u73b0\u51fa\u8272\u3002<\/span>1.5B \u6a21\u578b\u5728 CoT \u6a21\u5f0f\u4e0b\u5355\u6b21\u901a\u8fc7\u51c6\u786e\u7387\u4e3a 58.2%\uff0c\u591a\u6570\u6295\u7968\u51c6\u786e\u7387\u8fbe 80.0%\uff1b\u5728 TIR \u6a21\u5f0f\u4e0b\uff0c\u8fd9\u4e9b\u6570\u5b57\u5206\u522b\u63d0\u9ad8\u5230 64.5% \u548c 83.3%\uff1b\u4f7f\u7528 GenSelect \u6280\u672f\u540e\uff0c\u51c6\u786e\u7387\u8fdb\u4e00\u6b65\u63d0\u5347\u81f3 83.3%\u300214B \u6a21\u578b\u7684\u8868\u73b0\u66f4\u4e3a\u51fa\u8272\uff0c\u5728 TIR \u6a21\u5f0f\u7ed3\u5408 GenSelect \u4f7f\u7528\u65f6\uff0c\u51c6\u786e\u7387\u9ad8\u8fbe 90.0%\u3002\u6700\u5927\u7684 32B \u6a21\u578b\u5728\u76f8\u540c\u6761\u4ef6\u4e0b\u751a\u81f3\u8fbe\u5230\u4e86 93.3% \u7684\u51c6\u786e\u7387\u3002<\/span><\/strong>\u8fd9\u4e9b\u7ed3\u679c\u4e5f\u8868\u660e\uff0c\u65e0\u8bba\u6a21\u578b\u5927\u5c0f\u5982\u4f55\uff0cTIR \u6a21\u5f0f\u59cb\u7ec8\u4f18\u4e8e\u7eaf CoT \u6a21\u5f0f\uff0c\u800c GenSelect \u6280\u672f\u80fd\u8fdb\u4e00\u6b65\u63d0\u9ad8\u51c6\u786e\u7387\u3002<\/span><\/p>

\u56fe\uff5c\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u7684\u8bc4\u4f30\u7ed3\u679c\uff08\u6765\u6e90\uff1aarXiv\uff09<\/div>
<\/a>

\u76ee\u524d\uff0c\u82f1\u4f1f\u8fbe\u56e2\u961f\u5df2\u5c06\u5b8c\u6574\u7684 OpenMathReasoning \u6570\u636e\u96c6\u3001\u8bad\u7ec3\u597d\u7684 OpenMath-Nemotron \u6a21\u578b\u7cfb\u5217\u4ee5\u53ca\u6240\u6709\u76f8\u5173\u4ee3\u7801\u4ee5\u5546\u4e1a\u8bb8\u53ef\u65b9\u5f0f\u53d1\u5e03\u5230 Hugging Face \u548c GitHub \u4e0a\uff08\u9879\u76ee\u5730\u5740\uff1ahttps:\/\/huggingface.co\/collections\/nvidia\/openmathreasoning-68072c0154a5099573d2e730\uff09\u3002<\/span><\/span><\/p>

\u53c2\u8003\u8d44\u6599\uff1a<\/span><\/span><\/p>

1.https:\/\/arxiv.org\/abs\/2504.16891<\/span><\/span><\/p>

2.https:\/\/www.kaggle.com\/competitions\/ai-mathematical-olympiad-progress-prize-2\/discussion\/574765<\/span><\/span><\/p>

<\/p>

\u8fd0\u8425\/\u6392\u7248\uff1a\u4f55\u6668\u9f99<\/span><\/span><\/p><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>","content_en":null,"content_all":null,"article_url":"http:\/\/www.sciphi.cn\/article\/view\/14722","typeName":"AI"},"code":10000,"message":"\u6210\u529f"}