{"id":47815,"date":"2024-01-17T18:06:58","date_gmt":"2024-01-17T10:06:58","guid":{"rendered":"https:\/\/swarma.org\/?p=47815"},"modified":"2024-01-17T18:06:58","modified_gmt":"2024-01-17T10:06:58","slug":"%e6%95%b0%e5%ad%a6%e6%8e%a8%e7%90%86%e4%b8%8eai%ef%bc%9a%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e7%b3%bb%e7%bb%9f%e8%83%bd%e5%9c%a8%e5%a4%9a%e5%a4%a7%e7%a8%8b%e5%ba%a6%e4%b8%8a%e7%90%86%e8%a7%a3%e6%95%b0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=47815","title":{"rendered":"\u6570\u5b66\u63a8\u7406\u4e0eAI\uff1a\u673a\u5668\u5b66\u4e60\u7cfb\u7edf\u80fd\u5728\u591a\u5927\u7a0b\u5ea6\u4e0a\u7406\u89e3\u6570\u5b66\uff1f"},"content":{"rendered":"
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2023\u5e7412\u6708\u7684 NeurIPS \u4f1a\u8bae\u4e0a\u4e3e\u529e\u4e86\u8bb8\u591a\u4e3b\u9898\u7814\u8ba8\u4f1a\uff0c\u5176\u4e2d MATH AI \u7814\u8ba8\u4f1a\u4e3a\u7b2c\u4e09\u5c4a\uff0c\u4e3b\u9898\u4e3a\u201c\u6570\u5b66\u63a8\u7406\u4e0eAI\u201d\u3002\u6570\u5b66\u63a8\u7406\u662f\u4eba\u7c7b\u8ba4\u77e5\u7684\u57fa\u672c\u65b9\u9762\uff0c\u6d89\u53ca\u5206\u6790\u590d\u6742\u4fe1\u606f\u3001\u8bc6\u522b\u6a21\u5f0f\u548c\u5173\u7cfb\u4ee5\u53ca\u4ece\u8bc1\u636e\u4e2d\u5f97\u51fa\u903b\u8f91\u7ed3\u8bba\uff0c\u5728\u79d1\u5b66\u3001\u5de5\u7a0b\u3001\u91d1\u878d\u548c\u65e5\u5e38\u73af\u5883\u4e2d\u6709\u7740\u91cd\u8981\u5e94\u7528\u3002\u6700\u8fd1\u5927\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u7684\u8fdb\u5c55\u5728\u4eba\u5de5\u667a\u80fd\u548c\u6570\u5b66\u63a8\u7406\u7684\u4ea4\u53c9\u9886\u57df\u5f00\u8f9f\u4e86\u65b0\u673a\u9047\uff0c\u4ece\u89e3\u51b3\u590d\u6742\u95ee\u9898\u6216\u8bc1\u660e\u5b9a\u7406\u7684\u65b0\u65b9\u6cd5\uff0c\u5230\u6570\u5b66\u53ca\u5176\u4ed6\u9886\u57df\u4e2d\u4eba\u673a\u534f\u4f5c\u7684\u65b0\u5f62\u5f0f\u3002<\/span><\/strong><\/p>\n


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NeurIPS \u8fd1\u4e09\u5e74\u90fd\u6709\u9488\u5bf9 MATH AI \u7684\u7814\u8ba8\u4f1a\uff0c\u5176\u4e2d 2023\u5e74\u5171\u5305\u542b <\/span><\/strong>41 \u7bc7\u6587\u7ae0<\/span><\/strong>\uff0c\u672c\u6587\u6309\u4ee5\u4e0b\u516b\u4e2a\u4e3b\u9898\u5206\u7c7b\u6574\u7406\uff08\u7c7b\u522b\u95f4\u53ef\u80fd\u5b58\u5728\u4ea4\u53c9\uff09\uff1a\uff081\uff09\u5f62\u5f0f\u5316\uff082\uff09\u7814\u7a76\u5bfc\u5411\uff083\uff09\u6570\u636e\u96c6\uff084\uff09\u5de5\u5177 & \u667a\u80fd\u4f53\uff085\uff09\u6570\u5b66\u63a8\u7406 & \u5e94\u7528\u9898\uff086\uff09\u5c0f\u6a21\u578b\u5b9e\u9a8c & \u8bad\u7ec3\u5fae\u8c03\uff087\uff09\u591a\u6a21\u6001\uff088\uff09\u8ba4\u77e5\u79d1\u5b66\u3002<\/span><\/strong><\/p>\n<\/section>\n

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    2021 \u5e74\uff1aMathAi4ED \u7814\u8ba8\u4f1a\uff08Math AI for Education: Bridging the Gap Between Research and Smart Education\uff0chttps:\/\/mathai4ed.github.io\/\uff09<\/span><\/section>\n<\/li>\n
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    2022 \u5e74\uff1aMathAI \u7814\u8ba8\u4f1a\uff08Toward Human-Level Mathematical Reasoning\uff0chttps:\/\/mathai2022.github.io\/\uff09<\/span><\/section>\n<\/li>\n
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    2023 \u5e74\uff1aMathAI \u7814\u8ba8\u4f1a\uff08Mathematical Reasoning and AI\uff0chttps:\/\/mathai2023.github.io\/\uff09<\/span><\/section>\n<\/li>\n<\/ul>\n
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      ICLR\u201921 MathAI \u7814\u8ba8\u4f1a\uff08The Role of Mathematical Reasoning in General Artificial Intelligence\uff0chttps:\/\/mathai-iclr.github.io\/\uff09<\/span><\/p>\n<\/li>\n<\/ul>\n


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      1. \u5f62\u5f0f\u5316<\/span><\/strong><\/p>\n

      2. \u7814\u7a76\u5bfc\u5411<\/span><\/strong><\/p>\n

      3. \u6570\u636e\u96c6<\/span><\/strong><\/p>\n

      4. \u5de5\u5177 & \u667a\u80fd\u4f53<\/span><\/strong><\/p>\n

      5. \u6570\u5b66\u63a8\u7406 & \u5e94\u7528\u9898<\/span><\/strong><\/p>\n

      6. \u591a\u6a21\u6001<\/span><\/strong><\/p>\n

      7. \u5c0f\u6a21\u578b\u5b9e\u9a8c & \u8bad\u7ec3\u5fae\u8c03<\/span><\/strong><\/p>\n

      8. \u8ba4\u77e5\u79d1\u5b66<\/span><\/strong><\/p>\n

      <\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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      \u5f62\u5f0f\u5316\u76f8\u5173\u7684\u6587\u7ae0\u6709 8 \u7bc7\uff0c\u9664\u53bb\u7a0b\u5e8f\u9a8c\u8bc1\u7684\u4e00\u7bc7\uff0c\u5176\u4f59\u5747\u4e0e\u5b9a\u7406\u8bc1\u660e\u6709\u5173\uff0c\u4e14\u4e0d\u5c11\u5728 LEAN \u793e\u533a\u91cc\u6709\u5355\u72ec\u7684\u5e16\u5b50\u5728\u8ba8\u8bba\u3002\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\u6307\u5728\u903b\u8f91\u548c\u6570\u5b66\u4e2d\uff0c\u7528\u5f62\u5f0f\u5316\u65b9\u6cd5\u6839\u636e\u4e00\u5957\u65e2\u5b9a\u89c4\u5219\u53bb\u8bc1\u660e\u5b9a\u7406\u3002\u8fd9\u79cd\u8bc1\u660e\u8fc7\u7a0b\u4e0d\u4f9d\u8d56\u4e8e\u76f4\u89c2\u6216\u5176\u4ed6\u975e\u5f62\u5f0f\u5316\u7684\u63a8\u7406\uff0c\u800c\u662f\u5b8c\u5168\u4f9d\u9760\u4e25\u683c\u5b9a\u4e49\u7684\u7b26\u53f7\u548c\u64cd\u4f5c\u89c4\u5219\u3002\u5728\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\u7cfb\u7edf\u4e2d\uff0c\u5b9a\u7406\u662f\u4ece\u516c\u7406\uff08\u4e0d\u8bc1\u81ea\u660e\u7684\u57fa\u7840\u9648\u8ff0\uff09\u548c\u5148\u524d\u5df2\u8bc1\u5b9a\u7406\u51fa\u53d1\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u5141\u8bb8\u7684\u63a8\u7406\u6b65\u9aa4\u5f97\u5230\u7684\u7ed3\u8bba<\/strong>\u3002\u8fd9\u4e9b\u63a8\u7406\u6b65\u9aa4\u9075\u5faa\u7279\u5b9a\u7684\u3001\u88ab\u8be5\u7cfb\u7edf\u8ba4\u53ef\u7684\u63a8\u7406\u89c4\u5219\u6216\u8f6c\u6362\u89c4\u5219\u3002\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\u7684\u76ee\u7684\u662f\u63d0\u4f9b\u4e00\u4e2a\u5b8c\u5168\u5ba2\u89c2\u548c\u53ef\u9a8c\u8bc1\u7684\u8bc1\u660e\u8fc7\u7a0b\uff0c\u4f7f\u5f97\u4efb\u4f55\u4e86\u89e3\u8be5\u5f62\u5f0f\u4f53\u7cfb\u7684\u4eba\u90fd\u80fd\u591f\u68c0\u67e5\u8bc1\u660e\u7684\u6b63\u786e\u6027\uff0c\u800c\u4e0d\u9700\u8981\u5bf9\u8bc1\u660e\u672c\u8eab\u8fdb\u884c\u4e3b\u89c2\u5224\u65ad\u3002\u8fd9\u5728\u6570\u5b66\u57fa\u7840\u7814\u7a76\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u7a0b\u5e8f\u9a8c\u8bc1\u7b49\u9886\u57df\u6709\u7740\u91cd\u8981\u5e94\u7528\u3002<\/span><\/p>\n


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      1.1 LLEMMA\uff1a\u4e00\u4e2a\u5f00\u653e\u7684\u6570\u5b66\u8bed\u8a00\u6a21\u578b<\/span><\/strong><\/h3>\n


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      \u8bba\u6587\u5730\u5740\uff1ahttps:\/\/mathai2023.github.io\/papers\/45.pdf<\/span><\/p>\n

      \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/EleutherAI\/math-lm<\/span><\/p>\n

      \u9884\u8bad\u7ec3\u6570\u636e\u96c6\uff1ahttps:\/\/huggingface.co\/datasets\/EleutherAI\/proof-pile-2<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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      \u6587\u7ae0\u63d0\u51fa\u4e86 LLEMMA\uff0c\u4e00\u4e2a\u4e13\u6ce8\u4e8e\u6570\u5b66\u9886\u57df\u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b\u3002\u901a\u8fc7\u5728 Proof-Pile-2 \u4e0a\u5bf9 Code Llama \u7ee7\u7eed\u8fdb\u884c\u9884\u8bad\u7ec3\uff0c\u4ece\u800c\u5f97\u5230 LLEMMA\u3002\u5176\u4e2d Proof-Pile-2 \u662f\u7531\u79d1\u5b66\u8bba\u6587\u3001\u5305\u542b\u6570\u5b66\u5185\u5bb9\u7684\u7f51\u7edc\u6570\u636e\u548c\u6570\u5b66\u4ee3\u7801\u6df7\u5408\u7684\u6570\u636e\u96c6\u3002\u6b64\u5916\uff0cLlemma \u80fd\u591f\u4f7f\u7528\u5de5\u5177\u548c\u8fdb\u884c\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\uff0c\u800c\u65e0\u9700\u4efb\u4f55\u5fae\u8c03<\/strong>\u3002\u5728 MATH \u57fa\u51c6\u6d4b\u8bd5\u4e2d\uff0cLLEMMA \u8d85\u8d8a\u4e86\u6240\u6709\u5df2\u77e5\u7684\u516c\u5f00\u53d1\u5e03\u7684\u6a21\u578b\uff0c\u751a\u81f3\u5728\u53c2\u6570\u76f8\u540c\u7684\u60c5\u51b5\u4e0b\u4e5f\u8d85\u8fc7\u4e86\u672a\u516c\u5f00\u53d1\u5e03\u7684 Minerva \u6a21\u578b\u7cfb\u5217\u3002\u4ed6\u4eec\u516c\u5f00\u53d1\u5e03\u4e86\u6240\u6709\u5de5\u4ef6\uff0c\u5305\u62ec 7B \u548c 34B \u53c2\u6570\u6a21\u578b\u3001Proof-Pile-2\uff0c\u4ee5\u53ca\u5b9e\u9a8c\u7684\u590d\u73b0\u4ee3\u7801\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      Llemma \u5728\u81ea\u7136\u8bed\u8a00\u95ee\u9898\u548c\u5f62\u5f0f\u5316\u8bed\u8a00\u95ee\u9898\u4e0a\u90fd\u8868\u73b0\u51fa\u4e86\u975e\u51e1\u7684\u80fd\u529b\uff1a<\/span><\/p>\n


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      \u81ea\u7136\u8bed\u8a00\u80fd\u529b<\/span><\/p>\n


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      \u5f62\u5f0f\u5316\u8bed\u8a00\u80fd\u529b\u3002\u5de6\u4fa7\uff1a\u7ed9\u5b9a\u5f62\u5f0f\u547d\u9898\u3001\u81ea\u7136\u8bed\u8a00\u547d\u9898\u548c\u81ea\u7136\u8bed\u8a00 LaTeX \u8bc1\u660e\uff0c\u751f\u6210 Isabelle \u5f62\u5f0f\u8bc1\u660e\uff1b\u53f3\u4fa7\uff1a\u7ed9\u5b9a\u5f62\u5f0f\u547d\u9898\uff0c\u751f\u6210 Lean \u5f62\u5f0f\u8bc1\u660e<\/span><\/section>\n


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      \u8fd9\u4e2a\u5de5\u4f5c\u5bf9\u6807\u8c37\u6b4c\u7684 Minerva \u6a21\u578b\uff0c\u6a21\u578b\u5f00\u6e90\u4e14\u8bad\u7ec3\u6570\u636e\u548c\u4ee3\u7801\u5b8c\u5168\u516c\u5f00\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u540e\u7eed\u5f00\u5c55\u5176\u4ed6\u6570\u5b66\u5b9e\u9a8c\u7684\u57fa\u7840\u6a21\u578b<\/span><\/p>\n


      <\/span><\/p>\n

      1.2 llmstep\uff1a\u57fa\u4e8e LLM \u7684 Lean \u8bc1\u660e\u6b65\u9aa4\u5efa\u8bae<\/span><\/strong>
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      \u8bba\u6587\u5730\u5740\uff1a<\/span>https:\/\/mathai2023.github.io\/papers\/40.pdf<\/span><\/span><\/p>\n

      \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/wellecks\/llmstep<\/span><\/p>\n

      \u57fa\u7840\u6a21\u578b\uff1ahttps:\/\/github.com\/EleutherAI\/pythia<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


      <\/section>\n

      \u8fd9\u662f\u4e00\u4e2a\u57fa\u4e8e LeanDojo \u7684\u975e\u5e38\u5177\u6709\u5b9e\u7528\u6027\u7684\u5de5\u4f5c\uff0c\u8bba\u6587\u4f5c\u8005 Sean Welleck \u516b\u6708\u4efd\u5c31\u5728\u793e\u533a\u5f00\u4e86\u5e16\u5b50 llmstep <\/span>\uff08https:\/\/leanprover.zulipchat.com\/#narrow\/stream\/219941-Machine-Learning-for-Theorem-Proving\/topic\/llmstep\uff09<\/span>\u5e76\u5f00\u653e\u4ee3\u7801\u3002\u9644\u5e26\u5730\uff0c\u5176\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5b9e\u7528\u7684\u63d2\u4ef6\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/span><\/p>\n


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      llmstep \u793a\u4f8b-vscode<\/span><\/p>\n


      <\/p>\n

      LLMSTEP \u662f\u4e00\u4e2a\u96c6\u6210\u8bed\u8a00\u6a21\u578b\u81f3 Lean \u8bc1\u660e\u52a9\u624b\u7684\u5de5\u5177\u3002\u5b83\u901a\u8fc7 Lean4 \u7b56\u7565<\/span>(tactic) <\/span>\u5c06\u7528\u6237\u7684\u8bc1\u660e\u72b6\u6001\u53d1\u9001\u7ed9\u6258\u7ba1\u6709\u8bed\u8a00\u6a21\u578b\u7684\u670d\u52a1\u5668<\/span>\uff08\u4e0b\u56fe\u5de6\u4fa7\uff09<\/span>\uff0c\u7136\u540e\u8c03\u7528\u6a21\u578b\u4f1a\u751f\u6210\u5efa\u8bae\uff0c\u8fd9\u4e9b\u5efa\u8bae\u968f\u540e\u5728 Lean \u4e2d\u8fdb\u884c\u68c0\u67e5\uff0c\u5e76\u5728\u7528\u6237\u7684\u5f00\u53d1\u73af\u5883\u5185\u663e\u793a<\/span>\uff08\u4e0b\u56fe\u53f3\u4fa7\uff09<\/span>\u3002\u7814\u7a76\u56e2\u961f\u63d0\u4f9b\u4e86\u4e00\u4e2a\u8bed\u8a00\u6a21\u578b\u57fa\u51c6\uff0c\u5e76\u4e14\u63d0\u4f9b\u4e86\u7528\u4e8e\u5fae\u8c03\u548c\u8bc4\u4f30\u7684\u4ee3\u7801\uff0c\u4ee5\u652f\u6491\u672a\u6765\u7684\u53d1\u5c55\u3002\u4ed6\u4eec\u8fd8\u5b9e\u73b0\u4e86\u51e0\u79cd\u670d\u52a1\u5668\u9009\u9879\uff0c\u5305\u62ec\u5728 CPU\u3001CUDA GPU \u6216 Google Colab \u7b14\u8bb0\u672c\u4e0a\u8fd0\u884c\u7684\u670d\u52a1\uff0c\u65e8\u5728\u4e3a\u4e00\u822c\u7528\u6237<\/strong>\u63d0\u4f9b\u5feb\u901f\u4e14\u6709\u6548\u7684\u8bed\u8a00\u6a21\u578b\u5efa\u8bae\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      <\/p>\n

      \u539f\u7406\u56fe\uff1a\u5de6\u4fa7\u5bf9\u63a5\u673a\u5668\uff0c\u53f3\u4fa7\u5bf9\u63a5\u4eba\u7c7b<\/span><\/p>\n


      <\/span><\/p>\n

      \u9ed8\u8ba4\u5730\uff0cllmstep \u57fa\u4e8e\u5f00\u6e90\u6a21\u578b Pythia 2.8b \u4f7f\u7528 LeanDojo \u6570\u636e\u96c6\u8fdb\u884c\u5fae\u8c03\uff0c\u4f46\u5177\u4f53\u5b9e\u73b0\u4e0e\u6a21\u578b\u65e0\u5173\uff0c\u56e0\u6b64\u652f\u6301\u4f7f\u7528\u4efb\u4f55\u8bed\u8a00\u6a21\u578b\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      1.3 \u57fa\u4e8e\u8bed\u8a00\u4ee3\u7406\u7684\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\u65b9\u6cd5<\/span><\/strong>
      <\/p>\n


      <\/span><\/p>\n

      <\/p>\n

      \n
      \n
      \n

      \u8bba\u6587\u5730\u5740\uff1a<\/span>https:\/\/mathai2023.github.io\/papers\/29.pdf<\/span><\/p>\n

      \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/trishullab\/copra<\/span><\/p>\n

      \u793e\u533a\u5e16\u5b50\uff1ahttps:\/\/leanprover.zulipchat.com\/#narrow\/stream\/219941-Machine-Learning-for-Theorem-Proving\/topic\/COPRA<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


      <\/section>\n

      \u8be5\u7814\u7a76\u56e2\u961f\u63d0\u51fa\u4e86\u4e00\u79cd\u4f7f\u7528\u8bed\u8a00\u4ee3\u7406\u7684\u65b9\u6cd5\uff0cCOPRA<\/span> (In-Co<\/strong>ntext Pr<\/strong>over A<\/strong>gent)<\/span>\uff0c\u5e76\u5728\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\u4efb\u52a1\u4e2d\u5c55\u73b0\u51fa\u4e86\u6700\u65b0\u7684\u6027\u80fd\u3002\u8be5\u65b9\u6cd5\u5c06\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08GPT-4\uff09<\/span>\u4f5c\u4e3a\u6267\u884c\u72b6\u6001\u56de\u6eaf\u641c\u7d22\u7684\u7b56\u7565\u7ec4\u6210\u90e8\u5206\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u8be5\u7b56\u7565\u80fd\u591f\u9009\u62e9\u9002\u5f53\u7684\u8bc1\u660e\u6280\u5de7\uff0c\u5e76\u4ece\u5916\u90e8\u6570\u636e\u5e93\u4e2d\u68c0\u7d22\u5f15\u7406\u548c\u5b9a\u4e49\u3002\u6240\u9009\u7684\u6bcf\u4e2a\u7b56\u7565\u90fd\u5728\u5e95\u5c42\u8bc1\u660e\u6846\u67b6\u5185\u6267\u884c\uff0c\u4e14\u6267\u884c\u53cd\u9988\u88ab\u7528\u6765\u6784\u5efa\u4e0b\u4e00\u6b21\u7b56\u7565\u8c03\u7528\u7684\u63d0\u793a\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u8be5\u641c\u7d22\u8fc7\u7a0b\u4f1a\u8ffd\u8e2a\u5176\u5386\u53f2\u4fe1\u606f\uff0c\u5229\u7528\u8fd9\u4e9b\u4fe1\u606f\u51cf\u5c11\u5e7b\u89c9\u73b0\u8c61\u548c\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684LLM\u67e5\u8be2\u3002\u7814\u7a76\u56e2\u961f\u5728 Lean \u7684 miniF2F \u57fa\u51c6\u6d4b\u8bd5\u4ee5\u53ca Compcert \u9879\u76ee\u7684 Coq \u4efb\u52a1\u96c6\u4e0a\u5bf9 COPRA \u8fdb\u884c\u4e86\u8bc4\u4f30\u3002\u7ed3\u679c\u663e\u793a\uff0c\u5728\u8fd9\u4e9b\u57fa\u51c6\u6d4b\u8bd5\u4e2d\uff0cCOPRA \u7684\u6027\u80fd\u663e\u8457\u4f18\u4e8e\u5355\u6b21\u8c03\u7528 GPT-4 \u4ee5\u53ca\u5176\u4ed6\u5728\u8bc1\u660e\u6570\u636e\u4e0a\u8fdb\u884c\u5fae\u8c03\u7684\u6700\u5148\u8fdb\u6a21\u578b\uff0c\u5c24\u5176\u662f\u5728\u5feb\u901f\u627e\u5230\u6b63\u786e\u8bc1\u660e\u7684\u80fd\u529b\u65b9\u9762\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      <\/p>\n

      \u7b56\u7565\u751f\u6210\u6d41\u7a0b\u793a\u610f\u56fe<\/span><\/p>\n


      <\/span><\/p>\n

      \n
      \n
      \u5c06\u6267\u884c\u8bc1\u660e\u7684\u53cd\u9988\u72b6\u6001\u5b58\u50a8\u4e0b\u6765\uff0c\u7528\u4e8e\u6307\u5bfc\u4e0b\u4e00\u6b21\u51b3\u7b56\u3002\u8fd9\u7bc7\u5de5\u4f5c\u540c\u65f6\u4e5f\u662f ICLR2024 \u7684\u5728\u6295\u6587\u7ae0\uff08https:\/\/openreview.net\/forum?id=XCMbagV0No\uff09<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      1.4 Lemur\uff1a\u5c06\u5927\u8bed\u8a00\u6a21\u578b\u96c6\u6210\u5230\u81ea\u52a8\u7a0b\u5e8f\u9a8c\u8bc1<\/span>
      <\/strong><\/p>\n


      <\/span><\/p>\n

      <\/p>\n

      \n
      \n
      \u8bba\u6587\u5730\u5740\uff1a<\/span>https:\/\/mathai2023.github.io\/papers\/28.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      \u5927\u578b\u8bed\u8a00\u6a21\u578b\u5c55\u793a\u7684\u4ee3\u7801\u7406\u89e3\u80fd\u529b\u5f15\u53d1\u4e86\u4e00\u4e2a\u95ee\u9898\uff1a\u5b83\u4eec\u662f\u5426\u53ef\u4ee5\u7528\u4e8e\u81ea\u52a8\u7a0b\u5e8f\u9a8c\u8bc1\uff0c\u8fd9\u7c7b\u4efb\u52a1\u901a\u5e38\u9700\u8981\u5bf9\u7a0b\u5e8f\u5c5e\u6027\u8fdb\u884c\u9ad8\u6c34\u5e73\u7684\u62bd\u8c61\u63a8\u7406\uff0c\u800c\u8fd9\u5bf9\u9a8c\u8bc1\u5de5\u5177\u6765\u8bf4\u662f\u6781\u5177\u6311\u6218\u6027\u7684\u3002\u7814\u7a76\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u5c06 LLMs \u548c\u81ea\u52a8\u63a8\u7406\u5668\u7684\u80fd\u529b\u7ed3\u5408\u8d77\u6765\u7528\u4e8e\u81ea\u52a8\u7a0b\u5e8f\u9a8c\u8bc1\u7684\u901a\u7528\u65b9\u6cd5\u3002\u4ed6\u4eec\u5f62\u5f0f\u5730<\/em>\u63cf\u8ff0\u4e86\u8fd9\u79cd\u65b9\u6cd5\uff0c\u5e76\u5c06\u5176\u5f62\u5f0f\u5316\u4e3a\u4e00\u7cfb\u5217\u63a8\u5bfc\u89c4\u5219\uff0c\u5e76\u8bc1\u660e\u4e86\u5176\u6b63\u786e\u6027\u3002\u7814\u7a76\u8005\u5c06\u8fd9\u4e2a\u6f14\u7b97\u4f53\u7cfb\u5b9e\u4f8b\u5316\u4e3a\u4e00\u4e2a\u53ef\u9760\u7684\u81ea\u52a8\u9a8c\u8bc1\u8fc7\u7a0b\uff0c\u5728\u5408\u6210\u7a0b\u5e8f\u4ee5\u53ca\u7ade\u8d5b\u6570\u636e\u96c6\u4e0a\u90fd\u53d6\u5f97\u4e86\u5b9e\u9645\u7684\u6539\u8fdb\u6548\u679c\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \n
      \n
      \u8fd9\u4e2a\u5de5\u4f5c\u4e3b\u8981\u662f\u9762\u5411\u7a0b\u5e8f\u9a8c\u8bc1<\/span><\/section>\n<\/section>\n<\/blockquote>\n

      <\/section>\n

      1.5 \u57fa\u4e8e\u5927\u8bed\u8a00\u6a21\u578b\u6e29\u5ea6\u7f29\u653e\u7684 Lean \u8bc1\u660e\u6b65\u9aa4\u9884\u6d4b<\/span><\/strong>
      <\/p>\n


      <\/span><\/strong><\/p>\n

      <\/p>\n

      \n
      \n
      \u8bba\u6587\u5730\u5740\uff1ahttps:\/\/mathai2023.github.io\/papers\/25.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/p>\n

      \u5229\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u7684\u63a8\u7406\u80fd\u529b\u6765\u8fdb\u884c\u5b9a\u7406\u8bc1\u660e\u662f\u4e2a\u5145\u6ee1\u5e0c\u671b\u4f46\u53c8\u5bcc\u6709\u6311\u6218\u6027\u7684\u4efb\u52a1\u3002\u8fd9\u9879\u4efb\u52a1\u9700\u8981\u5728\u7279\u5b9a\u9886\u57df\u5185\u8fdb\u884c\u5fae\u8c03\uff0c\u4f46\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5bb9\u6613\u8fc7\u62df\u5408\u3002\u8fd9\u4e2a\u95ee\u9898\u56e0\u4e3a\u4e24\u4e2a\u539f\u56e0\u800c\u53d8\u5f97\u66f4\u52a0\u4e25\u91cd\uff1a\u4e00\u662f\u50cf Lean \u6216 Isabelle \u8fd9\u6837\u7684\u5f62\u5f0f\u5316\u73af\u5883\u4e2d\u8bad\u7ec3\u6570\u636e\u7684\u7a00\u7f3a\u6027\uff1b\u4e8c\u662f\u4f7f\u7528\u8bc4\u4f30\u57fa\u51c6\u8fdb\u884c\u8d85\u53c2\u6570\u641c\u7d22\u548c\u6a21\u578b\u9009\u62e9\u7684\u6210\u672c\u8fc7\u9ad8\u3002\u5728\u672c\u7814\u7a76\u4e2d\uff0c\u4ed6\u4eec\u63d0\u51fa\u4e86\u6e29\u5ea6\u7f29\u653e\u4f5c\u4e3a\u5c0f\u6570\u636e\u96c6\u4e0a\u591a\u8f6e\u8bad\u7ec3\u7684\u6b63\u5219\u5316\u65b9\u6cd5\uff0c\u5e76\u901a\u8fc7\u5b9e\u9a8c\u8bc1\u660e\u4e86\u5176\u6709\u6548\u6027<\/strong>\uff0c\u5728 Lean3 \u4e0a\u5f97\u5230\u4e86 1.5B\u30017B \u548c 13B \u53c2\u6570\u7684\u76d1\u7763\u5f0f\u7b56\u7565\u7684 SOTA \u751f\u6210\u6a21\u578b\u3002\u6b64\u5916\uff0c\u4f5c\u8005\u4eec\u5bf9\u8bc1\u660e\u641c\u7d22\u7684\u8d85\u53c2\u6570\u505a\u4e86\u8be6\u7ec6\u7684\u6d88\u878d\u5b9e\u9a8c\uff0c\u5206\u6790\u6240\u5f97\u6a21\u578b\u7684\u8bc1\u660e\u641c\u7d22\u884c\u4e3a\uff0c\u5e76\u5c55\u793a\u4e86\u57fa\u4e8e\u7b56\u7565\u7684\u8bc1\u660e\u641c\u7d22\u4e0e\u65f6\u95f4\u9884\u7b97\u7ea6\u4e3a\u5bf9\u6570\u589e\u957f\u89c4\u6a21\u3002<\/span><\/p>\n


      <\/p>\n

      1.6 Magnushammer\uff1a\u57fa\u4e8e Transformer \u7684\u524d\u63d0\u9009\u62e9\u65b9\u6cd5<\/span><\/strong>
      <\/p>\n


      <\/span><\/p>\n

      <\/p>\n

      \n
      \n

      \u8bba\u6587\u5730\u5740\uff1ahttps:\/\/mathai2023.github.io\/papers\/23.pdf<\/span><\/p>\n

      \u793e\u533a\u5e16\u5b50\uff1ahttps:\/\/leanprover.zulipchat.com\/#narrow\/stream\/219941-Machine-Learning-for-Theorem-Proving\/topic\/New.20paper.3A.20Magnushammer<\/span><\/p>\n

      \u6570\u636e\u96c6\uff1ahttps:\/\/huggingface.co\/datasets\/Simontwice\/premise_selection_in_isabelle<\/span><\/p>\n<\/blockquote>\n<\/section>\n

      \u524d\u63d0\u9009\u62e9\u662f\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u4e2d\u7684\u5173\u952e\u4efb\u52a1\uff0c\u672c\u6587\u4ecb\u7ecd\u4e86 Magnushammer\uff0c\u4e00\u79cd\u65b0\u9896\u7684\u524d\u63d0\u9009\u62e9\u65b9\u6cd5\u3002\u4f20\u7edf\u4e0a\uff0c\u8fd9\u4e00\u4efb\u52a1\u4f9d\u8d56\u4e8e\u9886\u57df\u77e5\u8bc6\u548c\u5de5\u7a0b\u52aa\u529b\u7684\u7b26\u53f7\u65b9\u6cd5\u3002\u4e0e\u4e4b\u76f8\u53cd\uff0c\u6b64\u9879\u5de5\u4f5c\u5c55\u793a\u4e86\u4f7f\u7528 Transformer \u67b6\u6784\u8fdb\u884c\u5bf9\u6bd4\u8bad\u7ec3\u53ef\u4ee5\u5b9e\u73b0\u66f4\u9ad8\u8d28\u91cf\u7684\u76f8\u5173\u524d\u63d0\u68c0\u7d22\uff0c\u800c\u4e0d\u9700\u8981\u9886\u57df\u77e5\u8bc6\u6216\u7279\u5f81\u5de5\u7a0b\u5f00\u9500<\/strong>\u3002Magnushammer \u5728\u6027\u80fd\u4e0a\u8d85\u8d8a\u4e86\u4ea4\u4e92\u5f0f\u5b9a\u7406\u8bc1\u660e\u4e2d\u6700\u5148\u8fdb\u4e14\u5e7f\u6cdb\u4f7f\u7528\u7684\u81ea\u52a8\u5316\u5de5\u5177\uff1aSledgehammer\u3002\u5728 PISA \u548c miniF2F \u57fa\u51c6\u6d4b\u8bd5\u4e2d Magnushammer \u5206\u522b\u5b9e\u73b0\u4e86 59.5%\uff08\u5bf9\u6bd4 38.3%\uff09\u548c 34.0%\uff08\u5bf9\u6bd4 20.9%\uff09\u7684\u6210\u529f\u7387\u3002\u901a\u8fc7\u5c06 Magnushammer \u4e0e\u57fa\u4e8e\u8bed\u8a00\u6a21\u578b\u7684\u5b9a\u7406\u8bc1\u660e\u5668\u7ed3\u5408\uff0c\u8fdb\u4e00\u6b65\u5c06 PISA \u57fa\u51c6\u6d4b\u8bd5\u7684\u6700\u4f73\u8bc1\u660e\u6210\u529f\u7387\u4ece 57.0% \u63d0\u9ad8\u5230 71.0%\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u5f00\u53d1\u5e76\u5f00\u6e90\u4e86\u4e00\u4e2a\u7528\u4e8e\u524d\u63d0\u9009\u62e9\u7684\u65b0\u9896\u7684\u5927\u578b\u6570\u636e\u96c6\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      1.7 \u5927\u8bed\u8a00\u6a21\u578b\u4f5c\u4e3a Lean \u5b9a\u7406\u8bc1\u660e\u7684\u201c\u526f\u9a7e\u9a76\u201d<\/span><\/strong><\/p>\n


      <\/span><\/strong><\/p>\n

      <\/p>\n

      \n
      \n
      \u8bba\u6587\u5730\u5740\uff1aTowards Large Language Models as Copilots for Theorem Proving in Lean\uff0chttps:\/\/mathai2023.github.io\/papers\/4.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      \u5f62\u5f0f\u5316\u8bc1\u660e\u53ef\u4ee5\u901a\u8fc7\u5982 Lean \u8fd9\u6837\u7684\u8bc1\u660e\u52a9\u624b\u4e25\u683c\u68c0\u67e5\uff0c\u4e0d\u7ed9\u6a21\u578b\u7559\u4e0b\u4efb\u4f55\u5e7b\u89c9\u7684\u53ef\u80fd<\/strong> \u3002\u73b0\u6709\u57fa\u4e8e LLM \u7684\u8bc1\u660e\u5668\u5c1d\u8bd5\u5728\u6ca1\u6709\u4eba\u5de5\u5e72\u9884\u7684\u60c5\u51b5\u4e0b\u5b8c\u5168\u81ea\u52a8\u5730\u8bc1\u660e\u5b9a\u7406\u3002\u5728\u8fd9\u79cd\u6a21\u5f0f\u4e0b\uff0c\u4ed6\u4eec\u5728\u5904\u7406\u5168\u65b0\u4e14\u5177\u6709\u6311\u6218\u6027\u7684\u5b9a\u7406\u65f6\u4f1a\u9047\u5230\u56f0\u96be\uff0c\u5bf9\u4e8e\u8fd9\u4e9b\u5b9a\u7406\uff0c\u4eba\u7c7b\u7684\u6d1e\u5bdf\u53ef\u80fd\u81f3\u5173\u91cd\u8981<\/strong>\u3002\u8fd9\u7bc7\u5de5\u4f5c\u63a2\u7d22\u4e86\u4f5c\u4e3a\u534f\u52a9\u4eba\u7c7b\u8bc1\u660e\u5b9a\u7406 Copilot \u7684 LLMs\uff0cLean Copilot\uff0c\u4e00\u4e2a\u5728 Lean \u4e2d\u8fd0\u884c\u795e\u7ecf\u7f51\u7edc\u63a8\u65ad\u7684\u6846\u67b6\u3002\u5b83\u4f7f\u7a0b\u5e8f\u5458\u80fd\u591f\u6784\u5efa\u5404\u79cd\u57fa\u4e8e LLM \u7684\u8bc1\u660e\u81ea\u52a8\u5316\u5de5\u5177\uff0c\u8fd9\u4e9b\u5de5\u5177\u53ef\u4ee5\u65e0\u7f1d\u96c6\u6210\u5230 Lean \u7528\u6237\u7684\u5de5\u4f5c\u6d41\u7a0b\u4e2d\u3002Lean Copilot \u5de5\u5177\u5229\u7528 LLMs \u63d0\u51fa\u8bc1\u660e\u6b65\u9aa4\u548c\u5b8c\u6210\u4e2d\u95f4\u8bc1\u660e\u76ee\u6807\uff0c\u5b9e\u9a8c\u7ed3\u679c\u8bc1\u660e\u4e86\u8be5\u65b9\u6cd5\u5728\u534f\u52a9\u4eba\u7c7b\u65b9\u9762\u76f8\u6bd4\u4e8e Lean \u4e2d\u73b0\u6709\u7684\u57fa\u4e8e\u89c4\u5219\u7684\u8bc1\u660e\u81ea\u52a8\u5316\u66f4\u4e3a\u6709\u6548\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \n
      \n
      \u8fd9\u7bc7\u5de5\u4f5c\u548c llmstep \u7c7b\u4f3c\uff0c\u4f46\u662f\u4ee3\u7801\u4f3c\u4e4e\u8fd8\u6ca1\u6709\u5f00\u653e\uff1f<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      1.8 LLM \u5bf9\u6bd4 ITP<\/span><\/strong><\/p>\n


      <\/span><\/strong><\/p>\n

      <\/p>\n

      \n

      \u8bba\u6587\u5730\u5740\uff1ahttps:\/\/mathai2023.github.io\/papers\/19.pdf<\/span><\/p>\n

      \u901a\u8baf\u4f5c\u8005\u4e3b\u9875\uff1aSimon Frieder\uff0chttps:\/\/www.snfrieder.org\/<\/span><\/p>\n

      \u793e\u533a\u5173\u8054\u7684\u5e16\u5b50\uff1ahttps:\/\/leanprover.zulipchat.com\/#narrow\/stream\/219941-Machine-Learning-for-Theorem-Proving\/topic\/Bangalore.20talk.20on.20LLM.2BITP<\/span><\/p>\n

      \u5f62\u5f0f\u5316\u7684100\u4e2a\u5b9a\u7406\uff1ahttps:\/\/www.cs.ru.nl\/~freek\/100\/<\/span><\/p>\n

      GHOSTS\u6570\u636e\u96c6\uff1ahttps:\/\/github.com\/friederrr\/GHOSTS<\/span><\/p>\n

      GHOSTS\u5173\u8054\u6587\u7ae0\uff1ahttps:\/\/arxiv.org\/pdf\/2301.13867.pdf<\/span><\/p>\n

      \u6570\u636e\u96c6\uff1ahttps:\/\/llmknow.friederrr.org\/ \uff08\u94fe\u63a5\u672a\u5f00\u653e\uff09<\/span><\/p>\n<\/blockquote>\n


      <\/p>\n

      Wiedijk \u7684 100 \u4e2a\u5b9a\u7406\u5217\u8868\u4e3a\u6bd4\u8f83\u4ea4\u4e92\u5f0f\u5b9a\u7406\u8bc1\u660e\u5668<\/span>\uff08ITP\uff09<\/span>\u53ca\u5176\u6570\u5b66\u5e93\u63d0\u4f9b\u4e86\u4e00\u4e2a\u57fa\u51c6\u3002\u800c\u6b63\u5982 GHOSTS \u6570\u636e\u96c6\u6240\u5c55\u793a\u7684\uff0c\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLM\uff09<\/span>\u4e5f\u53ef\u4ee5\u4f5c\u4e3a\u53ef\u641c\u7d22\u7684\u6570\u5b66\u5e93\uff0c\u56e0\u4e3a\u5b83\u4eec\u5728\u9884\u8bad\u7ec3\u6216\u5fae\u8c03\u9636\u6bb5\u80fd\u591f\u5438\u6536\u5927\u91cf\u7684\u6570\u5b66\u6587\u732e\u3002ITP \u5e93\u662f\u552f\u4e00\u53ef\u4e0e\u5176\u5ab2\u7f8e\u7684\u3001\u5728\u89c4\u6a21\u548c\u6570\u5b66\u590d\u6742\u6027\u8303\u56f4\u4e0a\u76f8\u5f53\u7684\u8d44\u6e90\u5e93\u3002\u672c\u6587\u4ee5 Wiedijk \u7684\u5217\u8868\u4e3a\u4e2d\u5fc3\uff0c\u63d0\u51fa\u4e86\u9996\u6b21\u5c06\u8fd9\u4e24\u79cd\u72ec\u7279\u7684\u6570\u5b66\u8d44\u6e90\u8fdb\u884c\u6bd4\u8f83\u7684\u7814\u7a76\u3002\u9664\u4e86\u5bf9\u6b64\u7c7b\u6bd4\u8f83\u672c\u8eab\u7684\u5174\u8da3\u5916\uff0c\u6587\u7ae0\u4ee5 GPT-4 \u548c Claude 2 \u4e3a\u4ee3\u8868\uff0c\u8ba8\u8bba\u4e86\u201cLLM \u4e2d\u5305\u542b\u7684\u77e5\u8bc6\u662f\u5426\u4e0e ITPs \u4e2d\u7f16\u7801\u7684\u77e5\u8bc6\u76f8\u5339\u914d\u201d\u8fd9\u4e00\u95ee\u9898\u7684\u91cd\u8981\u6027<\/strong>\u3002\u8fd9\u79cd\u5206\u6790\u8fdb\u4e00\u6b65\u63a8\u8fdb\u4e86 LLM \u548c ITP \u6280\u672f\u4e4b\u95f4\u7684\u4ea4\u96c6<\/span>\uff08\u4f8b\u5982\u81ea\u52a8\u5f62\u5f0f\u5316\u3001\u7531 LLM \u5f15\u5bfc\u7684\u8bc1\u660e\u751f\u6210\u6216\u8bc1\u660e\u5b8c\u6210\u7b49\u4efb\u52a1\uff09<\/span>\uff0c\u786e\u4fdd LLM \u9664\u4e86\u5177\u5907 ITP \u4ee3\u7801\u751f\u6210\u80fd\u529b\u5916\uff0c\u8fd8\u62e5\u6709\u6267\u884c\u6240\u9700\u5f62\u5f0f\u5316\u7684\u5145\u8db3\u6570\u5b66\u77e5\u8bc6\u3002\u8fd9\u4e00\u8c03\u67e5\u7ed3\u679c\u7684\u6570\u636e\u96c6\u79f0\u4e3a\u201cLLMKNOW\u201d\uff0c\u5df2\u5411\u516c\u4f17\u5f00\u653e\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \n
      \n
      \u8fd9\u7bc7\u5de5\u4f5c\u5f88\u6709\u610f\u601d\uff0c\u76f8\u5f53\u4e8e\u5728\u89e3\u91ca\u4e3a\u4ec0\u4e48 \u201c\u5927\u8bed\u8a00\u6a21\u578b\u80fd\u7528\u4e8e\u5f62\u5f0f\u5b9a\u7406\u8bc1\u660e\u201d\uff0c\u4ee5\u53ca\u5224\u65ad\u67d0\u4e2a\u6a21\u578b\u662f\u5426\u6709\u8fd9\u65b9\u9762\u7684\u80fd\u529b\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/p>\n


      <\/p>\n

      \n
      \n
      \n
      \n
      \n

      <\/section>\n

      <\/section>\n
      \n
      <\/svg><\/section>\n<\/section>\n<\/section>\n
      \n

      2. \u7814\u7a76\u5bfc\u5411<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

      <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


      <\/p>\n

      \u8fd9\u4e2a\u7c7b\u522b\u6307\u9762\u5411\u79d1\u5b66\u7814\u7a76\u9886\u57df<\/strong>\u7684\u5de5\u4f5c\uff0c\u533a\u522b\u4e8e\u9488\u5bf9\u4e2d\u5c0f\u5b66\u7684\u5e94\u7528\u9898\u7ade\u8d5b\u9898\u6216\u5e38\u89c4\u7684\u63a8\u7406\u9898\uff0c\u8fd9\u4e9b\u5de5\u4f5c\u63a2\u7d22 AI \u5728\u6570\u5b66\u7814\u7a76\u65b9\u9762\u7684\u5e94\u7528\u6f5c\u529b\u3002\u7b2c\u4e00\u7bc7\u662f\u8bc4\u4f30\u7efc\u5408\u80fd\u529b\u7684\u57fa\u51c6\uff0c\u540e\u8fb9\u51e0\u7bc7\u6d89\u53ca\uff1a\u4ee3\u6570\u7ec4\u5408\uff0c\u6781\u503c\u56fe\u8bba\uff0c\u91cf\u5b50\u8ba1\u7b97\uff0c\u52a8\u529b\u7cfb\u7edf\uff0c\u63a7\u5236\u8bba\uff0c\u6750\u6599\u79d1\u5b66\u7b49\u9886\u57df\u7684\u95ee\u9898\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      2.1 SCIBENCH\uff1a\u8bc4\u4f30\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5728\u5927\u5b66\u6c34\u5e73\u79d1\u5b66\u95ee\u9898\u7684\u89e3\u51b3\u80fd\u529b<\/span>
      <\/strong><\/p>\n


      <\/span><\/strong><\/p>\n

      <\/p>\n

      \n
      \n
      \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/44.pdf<\/span><\/section>\n
      \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/mandyyyyii\/scibench<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      \u968f\u7740\u5927\u578b\u8bed\u8a00\u6a21\u578b\u7684\u53d1\u5c55\u8fdb\u6b65\uff0c\u5176\u5728\u8bb8\u591a\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u53d6\u5f97\u4e86\u663e\u8457\u8fdb\u5c55\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u57fa\u51c6\u6d4b\u8bd5\u5927\u591a\u53ea\u5305\u542b\u521d\u9ad8\u4e2d\u79d1\u76ee\u7684\u95ee\u9898\u3001\u4ec5\u8bbe\u6709\u9009\u62e9\u9898\uff0c\u5e76\u4e14\u9650\u5236\u5728\u57fa\u672c\u7b97\u672f\u8fd0\u7b97\u7684\u72ed\u7a84\u8303\u56f4\u5185\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\uff0c\u8fd9\u7bc7 \u8bba\u6587\u4ecb\u7ecd\u4e86\u4e00\u4e2a\u5168\u9762\u7684\u57fa\u51c6\u6d4b\u8bd5\u5957\u4ef6 SCIBENCH\uff0c\u65e8\u5728\u7cfb\u7edf\u5730\u68c0\u9a8c\u89e3\u51b3\u590d\u6742\u79d1\u5b66\u95ee\u9898\u6240\u9700\u7684\u63a8\u7406\u80fd\u529b\u3002<\/strong> SCIBENCH \u5305\u542b\u4e24\u4e2a\u6570\u636e\u96c6\uff1a\u4e00\u4e2a\u5f00\u6e90\u96c6\uff0c\u5305\u62ec\u4e00\u7cfb\u5217\u5927\u5b66\u7ea7\u522b\u7684\u79d1\u5b66\u95ee\u9898\uff1b\u53e6\u4e00\u4e2a\u95ed\u6e90\u96c6\uff0c\u5305\u62ec\u672c\u79d1\u6c34\u5e73\u8003\u8bd5\u4e2d\u7684\u95ee\u9898\u3002\u57fa\u4e8e\u8fd9\u4e24\u4e2a\u6570\u636e\u96c6\uff0c\u7814\u7a76\u8005\u5bf9\u4e94\u4e2a\u5177\u6709\u4ee3\u8868\u6027\u7684 LLMs \u8fdb\u884c\u4e86\u6df1\u5165\u7684\u57fa\u51c6\u6d4b\u8bd5\u7814\u7a76\uff0c\u5e76\u91c7\u7528\u4e86\u4e0d\u540c\u7684\u63d0\u793a\u7b56\u7565\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u8be6\u7ec6\u7684\u7528\u6237\u7814\u7a76\uff0c\u7814\u7a76\u8005\u5f97\u5230\uff1a\u6ca1\u6709\u4efb\u4f55\u5355\u4e00\u63d0\u793a\u7b56\u7565\u80fd\u663e\u8457\u4f18\u4e8e\u5176\u4ed6\u7b56\u7565\uff0c\u4e00\u4e9b\u5728\u7279\u5b9a\u95ee\u9898\u89e3\u51b3\u6280\u80fd\u4e0a\u663e\u793a\u51fa\u8fdb\u6b65\u7684\u7b56\u7565\uff0c\u53ef\u80fd\u4f1a\u9020\u6210\u5176\u4ed6\u6280\u80fd\u7684\u4e0b\u964d\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \u4e0e\u5176\u4ed6\u57fa\u51c6\u7684\u5bf9\u6bd4<\/strong>\uff1aSCIBENCH \u4e2d\u7684\u6240\u6709\u95ee\u9898\u90fd\u662f\u5f00\u653e\u5f0f\u7684\u3001\u81ea\u7531\u56de\u7b54\u7684\u95ee\u9898\u3002\u5b83\u4eec\u9700\u8981\u591a\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u5176\u4e2d\u7684\u8ba1\u7b97\u6d89\u53ca\u590d\u6742\u7684\u7b97\u672f\u8fd0\u7b97\uff0c\u5982\u5fae\u5206\u548c\u79ef\u5206\u3002\u8bb8\u591a\u73b0\u6709\u57fa\u51c6\uff0c\u5982 ScienceQA \u548c GSM8K\uff0c\u53ea\u5305\u542b\u57fa\u4e8e\u5e74\u7ea7\u6c34\u5e73\u79d1\u76ee\u7684\u95ee\u9898\uff0c\u7f3a\u4e4f\u8db3\u591f\u7684\u590d\u6742\u6027\uff1b\u5c3d\u7ba1\u50cf MATH \u8fd9\u6837\u7684\u5176\u4ed6\u57fa\u51c6\u5f15\u5165\u4e86\u9ad8\u4e2d\u6c34\u5e73\u7684\u95ee\u9898\uff0c\u4f46\u5b83\u4eec\u53ea\u6d89\u53ca\u6709\u9650\u7684\u8fd0\u7b97\u8303\u56f4<\/span>\uff08\u56db\u5219\u8fd0\u7b97\u548c\u6c42\u5e42\uff09<\/span>\uff0c\u4e0d\u80fd\u5145\u5206\u8bc4\u4f30 LLM \u7684\u63a8\u7406\u80fd\u529b\u7684\u6df1\u5ea6\uff1b\u5176\u6b21\uff0c\u6700\u8fd1\u7684\u5de5\u4f5c\uff0c\u5305\u62ec MMLU\u3001AGIEval \u548c CEval\uff0c\u5c3d\u7ba1\u5f15\u5165\u4e86\u8de8\u8d8a\u5e7f\u6cdb\u5b66\u79d1\u7684\u5177\u6709\u6311\u6218\u6027\u7684\u95ee\u9898\uff0c\u4f46\u4e3b\u8981\u96c6\u4e2d\u5728\u591a\u9879\u9009\u62e9\u9898\u4e0a\uff0c\u800c\u6ca1\u6709\u63d0\u4f9b\u8be6\u7ec6\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u800c\u65e0\u6cd5\u7406\u89e3 LLM \u7684\u5c40\u9650\u6027\uff0c\u4e5f\u65e0\u6cd5\u8fa8\u522b\u5b83\u4eec\u4e3a\u4ec0\u4e48\u4f1a\u72af\u67d0\u4e9b\u9519\u8bef\uff1b\u8fd9\u4e9b\u57fa\u51c6\u901a\u5e38\u6765\u81ea\u5728\u7ebf\u6750\u6599\uff0c\u95ee\u9898\u540e\u5f80\u5f80\u7d27\u8ddf\u7740\u7b54\u6848\uff0c\u6a21\u578b\u53ef\u80fd\u5728\u4e0d\u771f\u6b63\u7406\u89e3\u95ee\u9898\u7684\u60c5\u51b5\u4e0b\u76f4\u63a5\u9884\u6d4b\u7b54\u6848\u3002\u8fd9\u4e9b\u6f5c\u5728\u7684\u6570\u636e\u6cc4\u9732\u4e3a LLM \u8bc4\u4f30\u63d0\u4f9b\u4e86\u4e00\u6761\u6377\u5f84\uff0c\u8fdb\u4e00\u6b65\u635f\u5bb3\u4e86\u5176\u6709\u6548\u6027\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \n
      \n
      \u8fd9\u4e2a\u5de5\u4f5c\u63d0\u51fa\u4e86\u6570\u5b66\u7269\u7406\u5316\u5b66\u4e09\u95e8\u5b66\u79d1\u7684\u6570\u636e\u96c6\uff0c\u5e76\u7ed9\u51fa Baseline<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      <\/p>\n

      \u6570\u5b66\u7269\u7406\u5316\u5b66-\u8bc4\u6d4b\u7ed3\u679c<\/span><\/p>\n


      <\/span><\/p>\n

      2.2 \u6211\u4eec\u80fd\u4f9d\u8d56\u6df1\u5ea6\u5b66\u4e60\u5417\uff1a\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u63a2\u7d22\u548c\u8868\u5f81\u7ec4\u5408\u7ed3\u6784<\/span><\/strong>
      <\/p>\n

      <\/p>\n

      \n
      \n
      \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/10.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


      <\/span><\/p>\n

      \u6df1\u5ea6\u5b66\u4e60\u56e0\u5176\u51fa\u8272\u7684\u6a21\u5f0f\u5339\u914d\u80fd\u529b\uff0c\u5728\u591a\u4e2a\u79d1\u5b66\u9886\u57df\u4e2d\u5c55\u73b0\u4e86\u5f3a\u5927\u7684\u5b9e\u7528\u6027\uff0c\u7279\u522b\u662f\u6570\u5b66\u7814\u7a76\u9886\u57df\u3002\u8fd1\u671f\u7814\u7a76\u663e\u793a\u6df1\u5ea6\u5b66\u4e60\u53ef\u4ee5\u53d1\u73b0\u6570\u5b66\u5bf9\u8c61\u95f4\u7ec6\u5fae\u5173\u8054\uff0c\u8fd9\u4e9b\u5173\u8054\u53ef\u80fd\u88ab\u4eba\u7c7b\u4e13\u5bb6\u6240\u5ffd\u7565\u3002\u672c\u7814\u7a76\u63d0\u51fa\u4e00\u79cd\u7b80\u5355\u65b9\u6cd5\uff0c\u5e2e\u52a9\u9886\u57df\u4e13\u5bb6\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u5bf9\u6570\u5b66\u5bf9\u8c61\u8fdb\u884c\u8868\u5f81\u3002\u5f53\u67d0\u7c7b\u51fd\u6570\u3001\u7a7a\u95f4\u6216\u7ebf\u6027\u8868\u793a\u7b49\u5728\u8ba1\u7b97\u4e2d\u81ea\u7136\u51fa\u73b0\u4f46\u96be\u4ee5\u7b80\u660e\u63cf\u8ff0\u65f6\uff0c\u5c31\u4f1a\u9762\u4e34\u6b64\u7c7b\u8868\u5f81\u95ee\u9898\u3002\u603b\u7684\u76ee\u6807\u662f\u627e\u5230\u7b80\u5355\u7684\u89c4\u5219\uff0c\u5e76\u63ed\u793a\u5176\u4e2d\u7684\u6570\u5b66\u539f\u7406\u3002\u4f5c\u8005\u5f00\u53d1\u4e86\u4e00\u79cd\u540d\u4e3a\u7279\u5f81\u5f52\u56e0\u805a\u7c7b\u63a2\u7d22<\/span>\uff08Feature Attribution Clustering for Exploration, FACE\uff09<\/span>\u7684\u65b9\u6cd5\uff0c\u901a\u8fc7\u805a\u7c7b\u5206\u6790\u8bad\u7ec3\u6a21\u578b\u4e2d\u7684\u7279\u5f81\u5f52\u56e0\uff0c\u5f97\u5230\u51e0\u79cd\u539f\u578b\u5f52\u56e0\uff0c\u4e13\u5bb6\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5c06\u8fd9\u4e9b\u539f\u578b\u8f6c\u6362\u4e3a\u6b63\u5f0f\u4e14\u4e25\u683c\u7684\u89c4\u5219<\/strong>\u3002\u5728\u6848\u4f8b\u7814\u7a76\u4e2d\uff0c\u4f5c\u8005\u5e94\u7528\u8be5\u65b9\u6cd5\u5728\u7ec4\u5408\u6570\u5b66\u4e2d\u53d6\u5f97\u65b0\u6210\u679c\uff0c\u8868\u8bc1\u4e86\u4e00\u7c7b\u5bf9\u5e94\u4e8e\u67d0\u4e9b\u7f6e\u6362\u8868\u793a\u76840-1\u77e9\u9635\u7684\u5b50\u96c6\uff0c\u8fd9\u4e9b\u7f6e\u6362\u8868\u793a\u88ab\u79f0\u4e3a\u53cc\u8fb9\u6709\u5e8f\u8bcd\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \u8fd9\u7bc7\u5de5\u4f5c\u8ba8\u8bba\u5b50\u96c6\u523b\u753b\u95ee\u9898<\/strong><\/span>\uff08Characterization problem\uff09<\/span>\uff1a\u7ed9\u5b9a\u96c6\u5408 B \u4e2d\u7684\u4e00\u4e2a\u5143\u7d20\u5b50\u96c6 A\uff0c\u627e\u5230\u4e00\u79cd\u7b80\u5355\u7684\u5224\u522b\u65b9\u6cd5\u4ee5\u786e\u5b9a\u4efb\u610f\u5143\u7d20 b \u2208 B \u662f\u5426\u5c5e\u4e8e A\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \u8fd9\u7c7b\u95ee\u9898\u5728\u6570\u5b66\u4e2d\u65e0\u5904\u4e0d\u5728\uff0c\u7ecf\u5178\u4f8b\u5b50\u5305\u62ec\uff1a<\/span><\/section>\n
        \n
      • \n
        \u4e00\u4e2a\u77e9\u9635\u662f\u975e\u5947\u5f02\u7684\u5f53\u4e14\u4ec5\u5f53\u5b83\u7684\u884c\u5217\u5f0f\u975e\u96f6<\/strong>\u3002<\/span><\/section>\n<\/li>\n
      • \n
        \u5b9e\u6570\u7a7a\u95f4 Rn<\/sup> \u4e2d\u7684\u4e00\u4e2a\u5b50\u96c6\u662f\u7d27\u51d1\u7684\u5f53\u4e14\u4ec5\u5f53\u5b83\u662f\u95ed\u5408\u4e14\u6709\u754c\u7684<\/strong>\u3002<\/span><\/section>\n<\/li>\n
      • \n
        \u4e00\u4e2a\u56fe\u662f\u53ef\u5c55\u5e73\u7684(planar)\u5f53\u4e14\u4ec5\u5f53\u5b83\u4e0d\u5305\u542b K5<\/sub> \u6216 K3,3<\/sub> \u4f5c\u4e3a\u5176\u5b50\u56fe\u3002<\/span><\/section>\n<\/li>\n
      • \n

        \u672c\u539f\u6bd5\u8fbe\u54e5\u62c9\u65af\u4e09\u5143\u7ec4 (x, y, z) \u603b\u662f\u5f62<\/span>\u5982 x = r2<\/sup> \u2212 s2<\/sup>\u3001y = 2r\u00b7s\u548c z = r2<\/sup> + s2<\/sup>\u7684\uff0c\u5176\u4e2d r \u548c s \u662f\u6b63\u7684\u4e92\u8d28\u6574\u6570<\/span>\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


        <\/span><\/h3>\n

        2.3 \u4f7f\u7528 AlphaZero \u548c\u7981\u5fcc\u641c\u7d22\u5bfb\u627e\u975e\u5e38\u5927\u7684\u6781\u503c\u56fe<\/span><\/strong><\/h3>\n

        <\/span><\/strong><\/section>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u5730\u5740\uff1ahttps:\/\/mathai2023.github.io\/papers\/21.pdf<\/span><\/section>\n

        \u65b0\u7684\u6781\u503c\u56fe\uff1ahttps:\/\/storage.googleapis.com\/gdm_girth5_graphs\/girth5_graphs.zip<\/p>\n

        \u524d 11 \u9636\u7b80\u5355\u56fe\u7684\u540c\u6784\u7c7b\uff1ahttps:\/\/users.cecs.anu.edu.au\/~bdm\/data\/graphs.html<\/p>\n

        Mathematica \u56fe\u8bba\u5de5\u5177\uff1ahttps:\/\/github.com\/szhorvat\/IGraphM<\/p>\n

        <\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u672c\u7814\u7a76\u63a2\u8ba8\u4e86\u7531 Erdos \u5728 1975 \u5e74\u63d0\u51fa\u7684\u6781\u503c\u56fe\u8bba\u7684\u4e00\u4e2a\u4e2d\u5fc3\u95ee\u9898\uff0c\u8be5\u95ee\u9898\u65e8\u5728\u627e\u5230\u5177\u6709<\/span>\u7ed9\u5b9a\u8282\u70b9\u6570\u76ee\u7684\uff0c\u6700\u5927\u5316\u8fb9\u6570\u7684\uff0c\u4e0d\u542b\u67093-\u73af\u62164-\u73af\u7684\u56fe<\/span><\/strong> \u3002\u6587\u7ae0\u5c06\u8fd9\u4e00\u95ee\u9898\u5f62\u5f0f\u5316\u4e3a\u5e8f\u5217\u51b3\u7b56\u95ee\u9898\uff0c\u5e76\u6bd4\u8f83\u4e86 AlphaZero<\/span>\uff08\u4e00\u79cd\u4ee5\u795e\u7ecf\u7f51\u7edc\u6307\u5bfc\u7684\u6811\u641c\u7d22\u65b9\u6cd5\uff09<\/span>\u548c\u7981\u5fcc\u641c\u7d22<\/span>\uff08\u4e00\u79cd\u542f\u53d1\u5f0f\u5c40\u90e8\u641c\u7d22\u65b9\u6cd5\uff09<\/span>\u4e24\u79cd\u65b9\u6cd5\u3002\u5bf9\u4efb\u4e00\u65b9\u6cd5\uff0c\u901a\u8fc7\u5f15\u5165\u8bfe\u7a0b\u5b66\u4e60\u2014\u2014\u5229\u7528\u5728\u8f83\u5c0f\u89c4\u6a21\u65f6\u627e\u5230\u7684\u597d\u56fe\u6765\u52a0\u901f\u641c\u7d22\u66f4\u5927\u56fe\u7684\u8fc7\u7a0b\u2014\u2014\u6587\u7ae0\u63d0\u9ad8\u4e86\u82e5\u5e72\u56fe\u89c4\u6a21\u7684\u73b0\u884c\u6700\u4f4e\u8fb9\u754c\u8bb0\u5f55\uff0c\u6210\u4e3a\u65b0\u7684 SOTA\u3002\u6587\u7ae0\u8fd8\u63d0\u51fa\u4e86\u4e00\u4e2a\u7075\u6d3b\u7684\u56fe\u751f\u6210\u73af\u5883\u4ee5\u53ca\u4e00\u4e2a\u6392\u5217\u4e0d\u53d8\u7684\u7f51\u7edc\u67b6\u6784\uff0c\u7528\u4e8e\u5b66\u4e60\u5728\u56fe\u7a7a\u95f4\u4e2d\u8fdb\u884c\u641c\u7d22\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u6781\u503c\u56fe<\/span>\uff08Extremal Graphs\uff09<\/span>\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u6982\u5ff5\uff0c\u5176\u7814\u7a76\u76ee\u6807\u662f\u5728\u6ee1\u8db3\u67d0\u4e9b\u7ea6\u675f\u6761\u4ef6\u4e0b\uff0c\u56fe\u7684\u67d0\u4e2a\u53c2\u6570\u8fbe\u5230\u6781\u503c\u7684\u60c5\u51b5\u3002\u975e\u5e38\u7ecf\u5178\u7684\u4f8b\u5b50\u662fTur\u00e1n\u56fe<\/span>\uff08Tur\u00e1n Graph\uff09<\/span>\u3002\u901a\u5e38\uff0c\u4f4e\u9636\u6781\u503c\u56fe\u662f\u53ef\u4ee5\u76f4\u63a5\u66b4\u529b\u641c\u7d22\u3002\u5229\u7528 Mathematica \u7684 IGraphM \u66b4\u529b\u6c42\u89e3\uff0c\u7528\u666e\u901a\u7b14\u8bb0\u672c\u7684CPU\u8ba1\u7b97\u80fd\u904d\u5386\u524d 10 \u9636\u3002\u4f46\u56fe\u8bba\u95ee\u9898\u6709\u4e2a\u5171\u540c\u7279\u70b9\uff0c\u968f\u9636\u6570\u589e\u957f\u8ba1\u7b97\u590d\u6742\u6027\u901a\u5e38\u5448\u6307\u6570\u589e\u957f\uff0c\u4e0b\u8868\u4e3a\u6bcf\u4e00\u9636\u7b80\u5355\u56fe\u7684\u6570\u636e\uff1a<\/span><\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        1-11\u9636\u7b80\u5355\u56fe\u7684\u6570\u76ee<\/span><\/p>\n


        <\/span><\/p>\n

        \u5e38\u89c4\u505a\u6cd5\u662f\u89c2\u5bdf\u4f4e\u9636\u7684\u89c4\u5f8b\uff0c\u7136\u540e\u8fdb\u884c\u5f52\u7eb3\u8bc1\u660e\u3002\u4f46\u5982\u679c\u5e0c\u671b\u8ba1\u7b97\u66f4\u9ad8\u9636\u7684\u4f8b\u5b50\uff0c\u5c31\u5fc5\u987b\u91c7\u7528\u7ed3\u5408\u6df1\u5ea6\u5b66\u4e60\u7684\u7b56\u7565\uff0c\u6bd4\u5982\u8fd9\u7bc7\u5de5\u4f5c\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \u4e0b\u8fb9\u51e0\u7bc7\u7b80\u5355\u5e26\u8fc7\uff0c\u5206\u522b\u6d89\u53ca\u91cf\u5b50\u8ba1\u7b97\uff0c\u63a7\u5236\u8bba\u4e0e\u52a8\u529b\u7cfb\u7edf\uff0c\u957f\u5ea6\u6cdb\u5316\u95ee\u9898\uff0c\u6750\u6599\u79d1\u5b66\u95ee\u9898\u7684\u7814\u7a76\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        2.4 \u6559\u5c0f\u578b Transformer \u6539\u5199 ZX \u91cf\u5b50\u7ebf\u8def\u56fe<\/span><\/strong><\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/34.pdf<\/span><\/section>\n
        \u76f8\u5173\u6982\u5ff5\uff1ahttps:\/\/zxcalculus.com\/<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        ZX \u6f14\u7b97<\/span>\uff08ZX calculus) <\/span>\u662f\u4e00\u4e2a\u7528\u4e8e\u63a8\u7406\u7ebf\u6027\u6620\u5c04\u7684\u56fe\u5f62\u8bed\u8a00\u3002\u6620\u5c04\u901a\u8fc7\u56fe\u8868\u793a\uff0c\u800c\u63a8\u7406\u5219\u6d89\u53ca\u56fe\u7684\u6539\u5199\u3002ZX \u6f14\u7b97\u4e3b\u8981\u5e94\u7528\u5728\u91cf\u5b50\u8ba1\u7b97\u9886\u57df\u3002\u7814\u7a76\u4eba\u5458\u8bad\u7ec3\u4e86\u5c0f\u578b Transformer \u6a21\u578b\u6765\u7b80\u5316 ZX \u56fe\uff0c\u5373\u6267\u884c\u91cf\u5b50\u7535\u8def\u7684\u8d44\u6e90\u4f18\u5316\u3002\u521d\u6b65\u5b9e\u9a8c\u8868\u660e\uff0c\u8fd9\u4e9b\u6a21\u578b\u53ef\u4ee5\u88ab\u8bad\u7ec3\u4ee5\u9ad8\u7cbe\u5ea6\u7b80\u5316 CNOT \u548c Clifford \u7535\u8def\u3002\u8fd9\u4e9b\u662f\u6700\u7b80\u5355\u7c7b\u578b\u7684 ZX \u56fe\uff0c\u56e0\u4e3a\u5b83\u4eec\u5b58\u5728\u6709\u6548\u7684\u6539\u5199\u7b56\u7565\u3002\u6b64\u5916\uff0c\u8fd8\u6709\u8bc1\u636e\u663e\u793a\uff0c\u8fd9\u4e9b Transformer \u6a21\u578b\u5b66\u4f1a\u4e86\u7b80\u5316\u66f4\u4e3a\u590d\u6742\u7684 Clifford + T \u56fe\uff0c\u800c\u8fd9\u7c7b\u56fe\u901a\u5e38\u4e0d\u5b58\u5728\u9ad8\u6548\u7684\u7b80\u5316\u7b97\u6cd5\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        2.5 \u5f3a\u5316\u5b66\u4e60\u5728\u63a7\u5236\u8bba\u4e2d\u7684\u5e94\u7528\uff1a\u6570\u5b66\u95ee\u9898\u89e3\u51b3\u7684\u65b0\u65b9\u6cd5<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/section>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1a<\/span>https:\/\/mathai2023.github.io\/papers\/35.pdf<\/span>\u200d<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u672c\u6587\u4ecb\u7ecd\u4e86\u4e00\u79cd\u7ed3\u5408\u5f3a\u5316\u5b66\u4e60<\/span>\uff08RL\uff09<\/span>\u4e0e\u6570\u5b66\u5206\u6790\u7684\u65b0\u65b9\u6cd5\uff0c\u65e8\u5728\u89e3\u51b3\u63a7\u5236\u7406\u8bba\u7684\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\uff1a\u5982\u4f55\u901a\u8fc7\u53cd\u9988\u63a7\u5236\u5b9e\u73b0\u7a33\u5b9a\u6027\u3002\u8fd9\u9879\u7814\u7a76\u7279\u522b\u5173\u6ce8\u4e0d\u80b2\u6606\u866b\u6280\u672f<\/span>\uff08SIT\uff09<\/span>\u7cfb\u7edf\uff0c\u5e76\u81f4\u529b\u4e8e\u627e\u5230\u4e00\u4e2a\u80fd\u591f\u7a33\u5b9a\u868a\u5b50\u79cd\u7fa4\u6a21\u578b\u7684\u53cd\u9988\u63a7\u5236\u65b9\u5f0f\u3002\u5c3d\u7ba1\u5b58\u5728\u6570\u5b66\u590d\u6742\u6027\u4e14\u8be5\u7279\u5b9a\u95ee\u9898\u6ca1\u6709\u5df2\u77e5\u89e3\u51b3\u65b9\u6848\uff0c\u4f46\u7814\u7a76\u8005\u4eec\u7684 RL \u65b9\u6cd5\u8bc6\u522b\u51fa\u4e86\u4e00\u4e2a\u663e\u5f0f\u7a33\u5b9a\u63a7\u5236\u7684\u5019\u9009\u89e3\u3002\u8be5\u7814\u7a76\u5f3a\u8c03\u4e86\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u4e4b\u95f4\u7684\u534f\u540c\u4f5c\u7528\uff0c\u4e3a\u89e3\u51b3\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u5f00\u8f9f\u4e86\u65b0\u9014\u5f84\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        2.6 \u4f7f\u7528 Transformer \u63a2\u7d22 Lyapunov \u51fd\u6570<\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/13.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/p>\n

        \u672c\u6587\u8003\u8651\u4e86\u6570\u5b66\u4e2d\u4e00\u4e2a\u957f\u671f\u5b58\u5728\u7684\u5f00\u653e\u95ee\u9898\uff1a\u63a2\u7d22\u63a7\u5236\u52a8\u529b\u7cfb\u7edf\u5168\u5c40\u7a33\u5b9a\u6027\u7684 Lyapunov \u51fd\u6570\u3002\u4f5c\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u751f\u6210\u8bad\u7ec3\u6570\u636e\u7684\u65b9\u6cd5\uff0c\u5e76\u8bad\u7ec3\u4e86\u5e8f\u5217\u5230\u5e8f\u5217\u7684 Transformer \u6a21\u578b\uff0c\u4ee5\u9ad8\u7cbe\u5ea6\u9884\u6d4b\u591a\u9879\u5f0f\u548c\u975e\u591a\u9879\u5f0f\u7cfb\u7edf\u7684 Lyapunov \u51fd\u6570\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u5f15\u5165\u4e86\u8fd9\u4e2a\u95ee\u9898\u7684\u65b0\u57fa\u51c6\uff0c\u5e76\u5c55\u793a\u4e86\u4ed6\u4eec\u7684\u6a21\u578b\u8fbe\u5230\u4e86\u65b0\u7684 SOTA\uff0c\u8d85\u8fc7\u4e86\u57fa\u4e8e\u8fd1\u4f3c\u7684\u6280\u672f\u548c\u5e73\u65b9\u548c\u7b97\u6cd5\u5e38\u89c4\u7a0b\u5e8f\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        2.7 Transformer \u53ef\u4ee5\u5b66\u54ea\u4e9b\u7b97\u6cd5\uff1f\u4e00\u9879\u957f\u5ea6\u6cdb\u5316\u7684\u7814\u7a76<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/47.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5927\u8bed\u8a00\u6a21\u578b\u8868\u73b0\u51fa\u4ee4\u4eba\u60ca\u8bb6\u7684\u6d8c\u73b0\u6cdb\u5316\u7279\u6027\uff0c\u4f46\u5728\u8bb8\u591a\u7b80\u5355\u7684\u63a8\u7406\u4efb\u52a1\u4e0a\uff0c\u4f8b\u5982\u7b97\u672f\u548c\u5947\u5076\u6027\u5224\u65ad\uff0c\u5b83\u4eec\u5374\u5e38\u5e38\u9047\u5230\u56f0\u96be\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u7814\u7a76\u8005\u4eec\u96c6\u4e2d\u63a2\u8ba8\u4e86\u957f\u5ea6\u6cdb\u5316\u95ee\u9898\uff0c\u5e76\u63d0\u51fa\u4e86\u4e00\u4e2a\u7edf\u4e00\u6846\u67b6\u6765\u7406\u89e3 Transformers \u5728\u7ed9\u5b9a\u4efb\u52a1\u4e0a \u4f55\u65f6\u4ee5\u53ca\u5982\u4f55\u5b9e\u73b0\u957f\u5ea6\u6cdb\u5316<\/strong> \u3002\u9996\u5148\uff0c\u4ed6\u4eec\u5c55\u793a\u5b58\u5728\u67d0\u4e9b\u7b97\u6cd5\u4efb\u52a1\uff0c\u6807\u51c6\u7684 Decoder Only \u6a21\u578b\u7ecf\u8fc7\u4ece\u5934\u5f00\u59cb\u7684\u8bad\u7ec3\u540e\u81ea\u7136\u800c\u7136\u80fd\u8868\u73b0\u51fa\u5f3a\u5927\u7684\u957f\u5ea6\u6cdb\u5316\u80fd\u529b\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u4efb\u52a1\uff0c\u7814\u7a76\u8005\u4eec\u5229\u7528 RASP \u7f16\u7a0b\u8bed\u8a00\u8bc1\u660e\u6b63\u786e\u7684\u7b97\u6cd5\u89e3\u51b3\u65b9\u6848\u53ef\u4ee5\u88ab\u4e00\u4e2a\u7b80\u5355\u7684 Transformer \u6240\u8868\u793a\u3002\u57fa\u4e8e\u6b64\uff0c\u4ed6\u4eec\u63d0\u51fa\u5e76\u652f\u6301\u4e86 RASP-\u6cdb\u5316\u731c\u60f3\uff1a\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u7b80\u6d01\u7684\u3001\u5bf9\u6240\u6709\u8f93\u5165\u957f\u5ea6\u90fd\u6709\u6548\u7684 RASP-L \u7a0b\u5e8f\uff0c\u90a3\u4e48 Transformers \u503e\u5411\u4e8e\u5b66\u4e60\u4e00\u4e2a\u80fd\u591f\u8fdb\u884c\u957f\u5ea6\u6cdb\u5316\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/strong> \u968f\u540e\uff0c\u4ed6\u4eec\u5229\u7528\u8fd9\u4e9b\u6d1e\u89c1\u4e3a\u4f20\u7edf\u4e0a\u96be\u4ee5\u5904\u7406\u7684\u4efb\u52a1<\/span>\uff08\u5982\u5947\u5076\u6027\u5224\u65ad\u548c\u52a0\u6cd5\uff09<\/span>\u5f00\u53d1\u4e86\u65b0\u7684\u4fbf\u7b7e<\/span>\uff08scratchpad\uff09<\/span>\u683c\u5f0f\uff0c\u8fd9\u4e9b\u683c\u5f0f\u5728\u957f\u5ea6\u6cdb\u5316\u65b9\u9762\u8868\u73b0\u51fa\u8272\u3002\u603b\u4f53\u800c\u8a00\uff0c\u8fd9\u4e9b\u5de5\u4f5c\u4e3a\u7406\u89e3\u957f\u5ea6\u6cdb\u5316\u673a\u5236\u4ee5\u53ca Transformers \u7684\u7b97\u6cd5\u80fd\u529b\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u89c6\u89d2\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        2.8 \u5782\u76f4\u9886\u57df\u7684\u4eba\u5de5\u667a\u80fd\u9a71\u52a8\u7684\u79d1\u5b66\u53d1\u73b0<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/15.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n

        <\/section>\n

        \u5c06\u79d1\u5b66\u53d1\u73b0\u7684\u8fc7\u7a0b\u81ea\u52a8\u5316\u4e00\u76f4\u662f\u4eba\u5de5\u667a\u80fd\u7684\u5b8f\u4f1f\u76ee\u6807\uff0c\u5982\u679c\u6210\u529f\uff0c\u5b83\u5c06\u4f1a\u5e26\u6765\u5de8\u5927\u7684\u793e\u4f1a\u5f71\u54cd\u3002\u5c3d\u7ba1\u76ee\u524d\u53d6\u5f97\u4e86\u4ee4\u4eba\u5174\u594b\u7684\u8fdb\u5c55\uff0c\u4f46\u5927\u591a\u6570\u4ece\u5b9e\u9a8c\u6570\u636e\u4e2d\u5b66\u4e60\u79d1\u5b66\u65b9\u7a0b\u5f0f\u7684\u52aa\u529b\u90fd\u96c6\u4e2d\u5728\u6c34\u5e73\u53d1\u73b0\u8def\u5f84\u4e0a\uff0c\u5373\u76f4\u63a5\u5728\u5b8c\u6574\u5047\u8bbe\u7a7a\u95f4\u4e2d\u641c\u7d22\u6700\u4f73\u65b9\u7a0b\u3002\u6c34\u5e73\u8def\u5f84\u5177\u6709\u6311\u6218\u6027\uff0c\u56e0\u4e3a\u76f8\u5173\u7684\u641c\u7d22\u7a7a\u95f4\u5448\u6307\u6570\u7ea7\u589e\u957f\u3002\u8fd9\u7bc7\u5de5\u4f5c\u63a2\u7d22\u4e86\u53e6\u4e00\u79cd\u65b9\u5f0f\uff0c\u5782\u76f4\u8def\u5f84\uff0c\u8be5\u8def\u5f84\u4ee5\u589e\u91cf\u65b9\u5f0f\u6784\u5efa\u79d1\u5b66\u65b9\u7a0b\uff0c\u4ece\u57fa\u7840\u6a21\u578b\u5f00\u59cb\uff0c\u8be5\u6a21\u578b\u901a\u8fc7\u63a7\u5236\u53d8\u91cf\u5b9e\u9a8c\u5bf9\u6570\u636e\u8fdb\u884c\u5efa\u6a21\uff0c\u5728\u6b64\u5b9e\u9a8c\u4e2d\uff0c\u5927\u90e8\u5206\u53d8\u91cf\u88ab\u89c6\u4e3a\u5e38\u6570\u3002\u7136\u540e\u901a\u8fc7\u6dfb\u52a0\u65b0\u7684\u72ec\u7acb\u53d8\u91cf\uff0c\u4f7f\u7528\u5141\u8bb8\u8fd9\u4e9b\u53d8\u91cf\u53d8\u5316\u7684\u65b0\u7684\u63a7\u5236\u53d8\u91cf\u5b9e\u9a8c\uff0c\u6765\u6269\u5c55\u5148\u524d\u4e16\u4ee3\u4e2d\u5b66\u5230\u7684\u8868\u8fbe\u5f0f\u3002\u8fd9\u79cd\u5782\u76f4\u8def\u5f84\u662f\u7531\u4eba\u7c7b\u79d1\u5b66\u53d1\u73b0\u8fc7\u7a0b\u6240\u542f\u53d1\u7684\u3002\u5b9e\u9a8c\u8bc1\u660e\uff0c\u8fd9\u6837\u7684\u5782\u76f4\u53d1\u73b0\u8def\u5f84\u52a0\u5feb\u4e86\u7b26\u53f7\u56de\u5f52\uff0c\u5e76\u4e14\u5728\u8ba1\u7b97\u6750\u6599\u79d1\u5b66\u4e2d\u63cf\u8ff0\u7eb3\u7c73\u7ed3\u6784\u6f14\u53d8\u7684\u7269\u7406\u6a21\u578b\u7684\u5b66\u4e60\u65b9\u9762\u53d6\u5f97\u4e86\u6539\u8fdb\u3002<\/span><\/p>\n


        <\/span><\/section>\n

        <\/span><\/section>\n

        \n
        \n
        \n
        \n
        \n

        <\/section>\n

        <\/section>\n
        \n
        <\/svg><\/section>\n<\/section>\n<\/section>\n
        \n

        3. \u6570\u636e\u96c6<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        \u90e8\u5206\u5de5\u4f5c\u6bd4\u5982\uff1aSCIBENCH\uff0c\u5728\u524d\u8fb9\u5df2\u7ecf\u51fa\u73b0\uff0c\u5c31\u4e0d\u91cd\u590d\u8ba8\u8bba\u4e86\u3002\u968f\u7740\u5927\u6a21\u578b\u80fd\u529b\u7684\u4e0d\u65ad\u63d0\u5347\uff0c\u5f88\u591a\u57fa\u51c6\u6d4b\u8bd5\u6b63\u5728\u5931\u53bb\u5176\u4f5c\u4e3a\u8bc4\u4f30\u5de5\u5177\u7684\u4f5c\u7528\u3002\u4e0e\u4e4b\u5bf9\u5e94\uff0c\u4e00\u4e9b\u96be\u5ea6\u66f4\u5927\uff0c\u9762\u5411\u66f4\u52a0\u7ec6\u5206\u9886\u57df\u7684\u6570\u636e\u96c6\u88ab\u63d0\u4e86\u51fa\u6765\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        3.1 SIRD\uff1a\u7b26\u53f7\u79ef\u5206\u89c4\u5219\u6570\u636e\u96c6<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \n

        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/39.pdf<\/span><\/p>\n

        \u6570\u636e\u96c6\uff1ahttps:\/\/github.com\/mfbalin\/SIRD-Symbolic-Integration-Rules-Dataset<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u968f\u7740\u795e\u7ecf\u7f51\u7edc\u548c\u8ba1\u7b97\u673a\u786c\u4ef6\u7684\u4e0d\u65ad\u8fdb\u6b65\uff0c\u6df1\u5ea6\u5b66\u4e60\u5728\u81ea\u7136\u79d1\u5b66\u9886\u57df\u7684\u65b0\u5e94\u7528\u573a\u666f\u6b63\u65e5\u76ca\u589e\u591a\u3002\u5c3d\u7ba1\u7b26\u53f7\u6570\u5b66\u4efb\u52a1\u5df2\u5f97\u5230\u4e00\u5b9a\u7684\u63a2\u7d22\uff0c\u4f46\u5173\u4e8e\u7b26\u53f7\u79ef\u5206\u7684\u7814\u7a76\u5374\u4ecd\u7136\u8f83\u5c11\uff0c\u7279\u522b\u662f\u90a3\u4e9b\u4f7f\u7528\u9ed1\u7bb1\u6a21\u578b\u7684\u7814\u7a76\uff0c\u5e76\u4e14\u8fd9\u4e9b\u7814\u7a76\u901a\u5e38\u7f3a\u4e4f\u53ef\u89e3\u91ca\u6027\u3002\u7b26\u53f7\u79ef\u5206\u672c\u8eab\u662f\u4e00\u4e2a\u5145\u6ee1\u6311\u6218\u7684\u641c\u7d22\u95ee\u9898\uff0c\u5176\u6700\u7ec8\u7ed3\u679c\u9700\u8981\u5728\u6bcf\u4e00\u6b65\u9aa4\u4e2d\u5e94\u7528\u4e0d\u540c\u7684\u79ef\u5206\u89c4\u5219\u6765\u83b7\u53d6\u3002\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u9896\u4e14\u53ef\u89e3\u91ca\u7684\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u901a\u8fc7\u9884\u6d4b\u79ef\u5206\u89c4\u5219\u6765\u5229\u7528\u6df1\u5ea6\u5b66\u4e60\u8fdb\u884c\u7b26\u53f7\u79ef\u5206<\/strong>\uff0c\u4ee5\u52a0\u5feb\u641c\u7d22\u8fc7\u7a0b\u3002\u4f5c\u8005\u4eec\u63d0\u51fa\u4e86\u7b2c\u4e00\u4e2a\u6b64\u7c7b\u7684\u7b26\u53f7\u79ef\u5206\u89c4\u5219\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u4e24\u767e\u4e07\u4e2a\u72ec\u7279\u7684\u51fd\u6570\u4e0e\u79ef\u5206\u89c4\u5219\u914d\u5bf9\u3002\u8be5\u6570\u636e\u96c6\u8fd8\u5305\u62ec\u4e86\u5e94\u7528\u8bf8\u5982 u-\u66ff\u6362\u548c\u5206\u90e8\u79ef\u5206\u6cd5\u7b49\u590d\u6742\u89c4\u5219\u6240\u9700\u7684\u8868\u8fbe\u5f0f\u3002\u6b64\u5916\uff0c\u6587\u7ae0\u5728\u8fd9\u4e00\u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u4e86\u4e00\u4e2a Transformer \u6a21\u578b\uff0c\u5e76\u5c06\u5176\u878d\u5408\u8fdb SymPy \u7684 integral_steps \u51fd\u6570\uff0c\u4ece\u800c\u521b\u9020\u4e86 guided_integral_steps\u3002\u8fd9\u4e2a\u65b9\u6cd5\u901a\u8fc7\u5141\u8bb8\u8be5\u6a21\u578b\u6307\u5bfc\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u7a0b\u5e8f\uff0c\u4f7f\u5f97\u63a2\u7d22\u7684\u5206\u652f\u6570\u91cf\u51cf\u5c11\u4e866\u500d\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \u5bf9 Sympy \u7684\u6539\u8fdb\uff0c\u4f46\u6587\u7ae0\u4f3c\u4e4e\u6ca1\u548c Mathematica \u8fdb\u884c\u6bd4\u8f83\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        3.2 ARB\uff1a\u9762\u5411\u5927\u578b\u8bed\u8a00\u6a21\u578b\u7684\u9ad8\u7ea7\u63a8\u7406\u57fa\u51c6<\/span><\/strong><\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/7.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u5728\u5404\u79cd\u6570\u91cf\u63a8\u7406\u548c\u77e5\u8bc6\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u8868\u73b0\u51fa\u4e86\u60ca\u4eba\u7684\u6027\u80fd\u3002\u7136\u800c\uff0c\u968f\u7740 LLMs \u8d8a\u6765\u8d8a\u9ad8\u7684\u5f97\u5206\uff0c\u8bb8\u591a\u8fd9\u6837\u7684\u57fa\u51c6\u6d4b\u8bd5\u6b63\u5728\u5931\u53bb\u5176\u4f5c\u4e3a\u8bc4\u4f30\u5de5\u5177\u7684\u6548\u7528\uff0c\u5c3d\u7ba1\u5b83\u4eec\u8fd8\u6ca1\u6709\u5728\u8fd9\u4e9b\u9886\u57df\u8fbe\u5230\u4e13\u5bb6\u7ea7\u522b\u7684\u8868\u73b0\u3002\u7814\u7a76\u8005\u4eec\u4ecb\u7ecd\u4e86ARB\uff0c\u8fd9\u662f\u4e00\u4e2a\u7531\u9ad8\u7ea7\u63a8\u7406\u95ee\u9898\u6784\u6210\u7684\u65b0\u9896\u7684\u57fa\u51c6\uff0c\u5176\u6db5\u76d6\u4e86\u6570\u5b66\u3001\u7269\u7406\u3001\u751f\u7269\u3001\u5316\u5b66\u548c\u6cd5\u5f8b\u7b49\u591a\u4e2a\u9886\u57df\uff0c\u6bd4\u4ee5\u5f80\u7684\u57fa\u51c6\u6d4b\u8bd5\u63d0\u51fa\u4e86\u66f4\u9ad8\u7684\u6311\u6218\u6807\u51c6\u3002\u4f5c\u4e3a ARB \u7684\u4e00\u90e8\u5206\uff0c\u7814\u7a76\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u7cfb\u5217\u9700\u8981\u8fdb\u884c\u9ad8\u7ea7\u7b26\u53f7\u63a8\u7406\u548c\u5177\u5907\u6df1\u5c42\u9886\u57df\u77e5\u8bc6\u7684\u6570\u5b66\u4e0e\u7269\u7406\u9898\u76ee\u3002\u4ed6\u4eec\u5bf9\u6700\u8fd1\u7684\u6a21\u578b\u5982 GPT-4 \u548c Claude \u5728 ARB \u4e0a\u7684\u8868\u73b0\u8fdb\u884c\u4e86\u8bc4\u4f30\uff0c\u7ed3\u679c\u663e\u793a\u5f53\u524d\u6a21\u578b\u5728\u66f4\u5177\u6311\u6218\u6027\u7684\u4efb\u52a1\u4e0a\u7684\u5f97\u5206\u8fdc\u8fdc\u4f4e\u4e8e50%<\/strong>\u3002\u4e3a\u4e86\u6539\u5584\u81ea\u52a8\u548c\u8f85\u52a9\u8bc4\u4f30\u80fd\u529b\uff0c\u7814\u7a76\u8005\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u57fa\u4e8e\u8bc4\u5206\u6807\u51c6\u7684\u8bc4\u4f30\u65b9\u6cd5\uff0c\u5141\u8bb8 GPT-4 \u5bf9\u5176\u81ea\u8eab\u7684\u4e2d\u95f4\u63a8\u7406\u6b65\u9aa4\u6253\u5206\u3002\u4ed6\u4eec\u53d1\u73b0\uff0c\u8bc4\u6ce8\u5458\u4e0eGPT-4\u4f9d\u636e\u8bc4\u5206\u6807\u51c6\u6240\u505a\u7684\u8bc4\u4f30\u5f97\u5206\u4e4b\u95f4\u6709\u826f\u597d\u7684\u4e00\u81f4\u6027\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u6570\u636e\u96c6\u6784\u6210\uff1a<\/span><\/p>\n

        <\/p>\n

        ARB \u6570\u636e\u96c6\u7ec4\u6210\u6210\u5206<\/span><\/p>\n


        <\/span><\/p>\n

        \u8bc4\u6d4b\u6548\u679c\uff1a<\/span><\/p>\n

        <\/p>\n

        \u4e0d\u540c\u6a21\u578b\u5728 ARB \u6570\u636e\u96c6\u4e0a\u7684\u6548\u679c<\/span><\/p>\n


        <\/span><\/p>\n

        3.3 CHAMP\uff1a\u7528\u4e8e\u7ec6\u81f4\u5206\u6790\u5927\u8bed\u8a00\u6a21\u578b\u6570\u5b66\u63a8\u7406\u80fd\u529b\u7684\u7ade\u8d5b\u7ea7\u6570\u636e\u96c6<\/span><\/strong>
        <\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/14.pdf<\/span><\/section>\n
        \u4ee3\u7801\uff1ahttps:\/\/yujunmao1.github.io\/CHAMP<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u9488\u5bf9\u6311\u6218\u6027\u6570\u5b66\u95ee\u9898\uff0c\u76ee\u524d\u5c1a\u4e0d\u6e05\u695a\u54ea\u4e9b\u5173\u4e8e\u95ee\u9898\u7684\u4fe1\u606f\u662f\u6709\u76ca\u7684<\/span>\uff08\u6216\u8005\u662f\u6709\u5bb3\u7684\uff09<\/span>\u3002\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u4e2a\u7528\u4e8e\u6b64\u7c7b\u5206\u6790\u7684\u5177\u6709\u6311\u6218\u6027\u7684\u57fa\u51c6\u6570\u636e\u96c6\u3002\u547d\u540d\u4e3a\u201c\u6982\u5ff5\u548c\u63d0\u793a\u6ce8\u91ca\u6570\u5b66\u95ee\u9898\u201d<\/span>\uff08The Concept and Hint-Annotated Math Problems\uff0cCHAMP\uff09<\/span>\uff0c\u8be5\u6570\u636e\u96c6\u7531\u5177\u6709\u7ade\u8d5b\u6c34\u5e73\u7684\u6570\u5b66\u95ee\u9898\u7ec4\u6210\uff0c\u5e76\u9644\u52a0\u4e86\u201c\u6982\u5ff5\u201d\uff0c\u5373\u4e00\u822c\u6570\u5b66\u4e8b\u5b9e\uff0c\u201c\u63d0\u793a\u201d\uff0c\u5373\u9488\u5bf9\u7279\u5b9a\u95ee\u9898\u7684\u7b56\u7565\u3002\u8fd9\u4e9b\u5b9e\u4f53\u53ca\u5176\u76f8\u4e92\u8054\u7cfb\u4f7f\u5f97\u7814\u7a76\u8005\u80fd\u591f\u63a2\u7d22\u989d\u5916\u4fe1\u606f\u7684\u5f71\u54cd\uff0c\u5982\u76f8\u5173\u63d0\u793a\u3001\u8bef\u5bfc\u6027\u6982\u5ff5\u6216\u76f8\u5173\u95ee\u9898\u3002\u4f5c\u8005\u4f7f\u75284\u79cd\u6a21\u578b\u8fdb\u884c\u4e8612\u9879\u521d\u6b65\u7814\u7a76\uff0c\u603b\u7ed3\u4e86\u4ed6\u4eec\u7684\u53d1\u73b0\uff0c\u5e76\u8ba8\u8bba\u4e86 CHAMP \u662f\u5982\u4f55\u652f\u6301\u56f4\u7ed5\u5927\u578b\u8bed\u8a00\u6a21\u578b\u7406\u89e3\u4e0e\u5229\u7528\u4e0a\u4e0b\u6587\u7684\u4e00\u822c\u8ba8\u8bba\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        3.4 OpenWebMath\uff1a\u4e00\u4e2a\u9ad8\u8d28\u91cf\u6570\u5b66\u7f51\u9875\u6587\u672c\u7684\u5f00\u653e\u6570\u636e\u96c6<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \n

        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/31.pdf<\/span><\/p>\n

        \u6570\u636e\u96c6\uff1ahttps:\/\/huggingface.co\/datasets\/open-web-math\/open-web-math<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u8d8a\u6765\u8d8a\u591a\u7684\u8bc1\u636e\u8868\u660e\uff0c\u9884\u8bad\u7ec3\u5927\u8bed\u8a00\u6a21\u578b\u5728\u9ad8\u8d28\u91cf\u3001\u7ecf\u8fc7\u6df1\u601d\u719f\u8651\u7684\u8bcd\u5143\u4e0a\uff0c\u5982\u4ee3\u7801\u6216\u6570\u5b66\u5185\u5bb9\uff0c\u5bf9\u4e8e\u63d0\u5347\u5176\u63a8\u7406\u80fd\u529b\u8d77\u7740\u5173\u952e\u4f5c\u7528\u3002\u4f8b\u5982\uff0cMinerva \u8fd9\u4e00\u7ecf\u8fc7\u5728 arXiv \u548c\u7f51\u7edc\u4e0a\u6570\u5341\u4ebf\u6570\u5b66\u6587\u6863\u5fae\u8c03\u7684 PaLM \u6a21\u578b\uff0c\u5728\u9700\u8981\u6570\u91cf\u63a8\u7406\u7684\u95ee\u9898\u4e0a\u53d6\u5f97\u4e86\u663e\u8457\u8fdb\u6b65\u3002\u7136\u800c\uff0c\u76ee\u524d\u5df2\u77e5\u7684\u516c\u5f00\u53d1\u5e03\u7684\u7f51\u7edc\u6570\u636e\u96c6\u5728\u9884\u5904\u7406\u65f6\u90fd\u6ca1\u6709\u5fe0\u5b9e\u5730\u4fdd\u7559\u6570\u5b66\u7b26\u53f7\uff0c\u56e0\u6b64\u65e0\u6cd5\u5229\u7528\u5927\u89c4\u6a21\u8bad\u7ec3\u7f51\u9875\u6587\u6863\u7684\u4f18\u52bf\u670d\u52a1\u4e8e\u7814\u7a76\u793e\u533a\u3002\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u6765 OpenWebMath\uff0c\u4e00\u4e2a\u53d7\u5230\u8fd9\u4e9b\u5de5\u4f5c\u542f\u53d1\u7684\u5f00\u653e\u6570\u636e\u96c6\uff0c\u5305\u542b\u6765\u81ea Common Crawl \u7684 14.7B token \u7684\u6570\u5b66\u7f51\u9875\u3002\u6587\u7ae0\u8be6\u7ec6\u63cf\u8ff0\u4e86\u4ece HTML \u6587\u6863\u4e2d\u63d0\u53d6\u6587\u672c\u548c LaTeX \u5185\u5bb9\u4ee5\u53ca\u79fb\u9664\u6837\u677f\u6587\u4ef6\u7684\u65b9\u6cd5\uff0c\u5e76\u4e14\u4ecb\u7ecd\u4e86\u7528\u4e8e\u8d28\u91cf\u7b5b\u9009\u548c\u53bb\u91cd\u7684\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u5728 1.4B \u53c2\u6570\u7684\u8bed\u8a00\u6a21\u578b\u4e0a\u4f7f\u7528 OpenWebMath \u8fdb\u884c\u4e86\u5c0f\u89c4\u6a21\u5b9e\u9a8c\uff0c\u5b9e\u9a8c\u7ed3\u679c\u663e\u793a\uff0c\u57fa\u4e8e\u8fd9\u4e9b\u6570\u636e\u96c6\u4e2d\u7684 14.7B \u8bcd\u5143\u8bad\u7ec3\u51fa\u7684\u6a21\u578b\uff0c\u5728\u6027\u80fd\u4e0a\u8d85\u8fc7\u4e86\u90a3\u4e9b\u5728\u8d85\u8fc7 20 \u500d\u8bed\u8a00\u6570\u636e\u91cf\u4e0a\u8fdb\u884c\u8bad\u7ec3\u7684\u6a21\u578b<\/strong>\u3002\u4f5c\u8005\u4eec\u5e0c\u671b\u8fd9\u4e00\u516c\u5f00\u53d1\u5e03\u7684\u6570\u636e\u96c6\u80fd\u6709\u52a9\u4e8e\u63a8\u52a8\u5927\u578b\u8bed\u8a00\u6a21\u578b\u63a8\u7406\u80fd\u529b\u7684\u8fdb\u4e00\u6b65\u53d1\u5c55\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u6570\u636e\u8fc7\u6ee4\u8fc7\u7a0b\uff1a<\/span><\/p>\n

        <\/p>\n

        \u6570\u636e\u6e05\u6d17 Pipeline<\/span><\/p>\n


        <\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \n
        \n
        \n

        <\/section>\n

        <\/section>\n
        \n
        <\/svg><\/section>\n<\/section>\n<\/section>\n
        \n

        4. \u5de5\u5177 & \u667a\u80fd\u4f53<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        \u5de5\u5177\u662f\u667a\u80fd\u4f53\u6784\u5efa\u4e2d\u6700\u4e3a\u91cd\u8981\u7684\u4e00\u73af\uff0c\u5176\u4f7f\u5f97\u667a\u80fd\u4f53\u80fd\u591f\u5b8c\u6210\u8bb8\u591a\u5355\u9760 LLM \u96be\u4ee5\u5b8c\u6210\u7684\u4efb\u52a1\u3002\u4e0b\u8fb9\u51e0\u7bc7\u5de5\u4f5c\u5bf9\u6570\u5b66\u667a\u80fd\u4f53\u6784\u5efa\u662f\u975e\u5e38\u597d\u7684\u53c2\u8003\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        4.1 Chameleon\uff1a\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5373\u63d2\u5373\u7528\u7684\u7ec4\u5408\u5f0f\u63a8\u7406<\/span><\/strong>
        <\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        \n
        \n
        \n

        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/51.pdf<\/span><\/p>\n

        \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/lupantech\/chameleon-llm.git<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u56e0\u5176\u6d8c\u73b0\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5728\u89e3\u51b3\u5404\u79cd\u81ea\u7136\u8bed\u8a00\u5904\u7406\u4efb\u52a1\u65b9\u9762\u53d6\u5f97\u4e86\u663e\u8457\u8fdb\u5c55\u3002\u7136\u800c\uff0cLLMs \u5b58\u5728\u56fa\u6709\u7684\u5c40\u9650\u6027\uff0c\u5b83\u4eec\u65e0\u6cd5\u8bbf\u95ee\u6700\u65b0\u4fe1\u606f<\/span>\uff08\u5b58\u50a8\u5728\u7f51\u7edc\u6216\u7279\u5b9a\u4efb\u52a1\u77e5\u8bc6\u5e93\u4e2d\uff09<\/span>\u3001\u4f7f\u7528\u5916\u90e8\u5de5\u5177\u4ee5\u53ca\u8fdb\u884c\u7cbe\u786e\u7684\u6570\u5b66\u548c\u903b\u8f91\u63a8\u7406\u3002\u4e3a\u4e86\u51cf\u8f7b\u8fd9\u4e9b\u9650\u5236\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u4e2a\u540d\u4e3a Chameleon<\/span>\uff08\u53d8\u8272\u9f99\uff09<\/span>\u7684\u4eba\u5de5\u667a\u80fd\u7cfb\u7edf\u3002\u8be5\u7cfb\u7edf\u901a\u8fc7\u589e\u52a0\u5373\u63d2\u5373\u7528\u7684\u6a21\u5757\u589e\u5f3a LLMs \u7684\u7ec4\u5408\u63a8\u7406\u80fd\u529b\u3002Chameleon \u901a\u8fc7\u7ec4\u5408\u5404\u79cd\u5de5\u5177<\/span>\uff08\u4f8b\u5982\uff0cLLMs\u3001\u73b0\u6210\u7684\u89c6\u89c9\u6a21\u578b\u3001\u7f51\u7edc\u641c\u7d22\u5f15\u64ce\u3001Python \u51fd\u6570\u548c\u57fa\u4e8e\u542f\u53d1\u5f0f\u7684\u6a21\u5757\uff09<\/span>\u6765\u5408\u6210\u7a0b\u5e8f\uff0c\u5b8c\u6210\u590d\u6742\u7684\u63a8\u7406\u4efb\u52a1\u3002Chameleon \u7684\u6838\u5fc3\u662f\u4e00\u4e2a\u57fa\u4e8e LLM \u7684\u89c4\u5212\u5668\uff0c\u8d1f\u8d23\u7ec4\u88c5\u4e00\u7cfb\u5217\u5de5\u5177\u4ee5\u6267\u884c\u751f\u6210\u6700\u7ec8\u54cd\u5e94\u3002\u5728\u4e24\u4e2a\u591a\u6a21\u6001\u77e5\u8bc6\u5bc6\u96c6\u578b\u63a8\u7406\u4efb\u52a1 ScienceQA \u548c TabMWP \u4e0a\uff0cChameleon \u8bc1\u660e\u4e86\u5176\u6709\u6548\u6027\u3002\u7531 GPT-4 \u9a71\u52a8\u7684 Chameleon \u5728 ScienceQA \u4e0a\u8fbe\u5230\u4e86 86.54% \u7684\u603b\u4f53\u51c6\u786e\u7387\uff0c\u6bd4\u6700\u4f73\u53d1\u5e03\u7684 few-shot \u7ed3\u679c\u63d0\u9ad8\u4e86 11.37%\u3002\u5728 TabMWP \u4e0a\uff0cGPT-4 \u9a71\u52a8\u7684 Chameleon \u5c06\u51c6\u786e\u7387\u63d0\u9ad8\u4e86 17.0%\uff0c\u5c06\u6700\u65b0\u6280\u672f\u6c34\u5e73\u63d0\u5347\u5230 98.78%\u3002\u5206\u6790\u8fd8\u8868\u660e\uff0c\u5728\u63a8\u65ad\u6307\u4ee4\u4e2d\u6f5c\u5728\u7ea6\u675f\u65f6\uff0c\u4e0e ChatGPT \u9a71\u52a8\u7684\u89c4\u5212\u5668\u76f8\u6bd4\uff0cGPT-4 \u9a71\u52a8\u7684\u89c4\u5212\u5668\u5c55\u793a\u4e86\u66f4\u4e3a\u4e00\u81f4\u548c\u7406\u6027\u7684\u5de5\u5177\u9009\u62e9\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u4e24\u4e2a\u7b80\u5355\u793a\u4f8b\uff0c\u53d6\u81ea\u5728 TabMWP \u6570\u636e\u96c6\uff1a<\/span><\/p>\n

        <\/p>\n

        \u8ba1\u7b97\u8def\u7a0b\u4e2d\u4f4d\u6570\uff08\u4e0a\uff09\u83b7\u53d6\u53d1\u8f66\u65f6\u95f4\uff08\u4e0b\uff09<\/span><\/p>\n


        <\/span><\/p>\n

        \u8fd9\u4e2a\u5de5\u4f5c\u6784\u5efa\u4e86\u4e00\u4e2a\u667a\u80fd\u4f53\uff0c\u901a\u8fc7\u7ec4\u5408\u5404\u79cd\u5de5\u5177\u6765\u83b7\u53d6\u7b54\u6848\uff0c\u4e14\u652f\u6301\u4e00\u822c\u7684 QA \u95ee\u7b54\uff0c\u800c\u4e0d\u5c40\u9650\u4e8e\u6570\u5b66\u95ee\u9898\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        QA + \u7b80\u5355\u63a8\u7406<\/span><\/p>\n


        <\/span><\/p>\n

        4.2 ToolDec\uff1a\u901a\u8fc7\u6709\u9650\u72b6\u6001\u89e3\u7801\u5b9e\u73b0 LLM \u7684\u65e0\u8bed\u6cd5\u9519\u8bef\u548c\u6cdb\u5316\u6027\u5de5\u5177\u4f7f\u7528<\/span><\/strong>
        <\/section>\n

        <\/span><\/strong><\/section>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/49.pdf<\/span><\/section>\n
        \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/chenhongqiao\/tooldec<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5927\u578b\u8bed\u8a00\u6a21\u578b\u5df2\u7ecf\u5c55\u793a\u4e86\u5728\u4f7f\u7528\u5916\u90e8\u5de5\u5177\u65b9\u9762\u7684\u4ee4\u4eba\u77a9\u76ee\u7684\u80fd\u529b\u3002\u7136\u800c\uff0c\u73b0\u6709\u65b9\u6cd5\u4f9d\u8d56\u4e8e\u5fae\u8c03\u6216\u4e0a\u4e0b\u6587\u5b66\u4e60\u6765\u4f7f\u7528\u5de5\u5177\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u4f1a\u4ea7\u751f\u8bed\u6cd5\u9519\u8bef\u4e14\u96be\u4ee5\u6cdb\u5316\u3002\u672c\u6587\u63d0\u51fa\u4e86 ToolDec\uff0c\u4e00\u79cd\u57fa\u4e8e\u6709\u9650\u72b6\u6001\u673a\u5f15\u5bfc\u7684\u89e3\u7801\u7b97\u6cd5\uff0c\u7528\u4e8e\u5de5\u5177\u589e\u5f3a\u578b LLM\u3002ToolDec \u901a\u8fc7\u786e\u4fdd\u5de5\u5177\u540d\u79f0\u7684\u6709\u6548\u6027\u548c\u53c2\u6570\u7c7b\u578b\u7684\u4e00\u81f4\u6027\uff0c\u6d88\u9664\u4e86\u4e0e\u5de5\u5177\u76f8\u5173\u7684\u9519\u8bef\u3002\u6b64\u5916\uff0cToolDec \u4f7f\u5f97 LLM \u80fd\u591f\u4ec5\u4ec5\u6839\u636e\u5de5\u5177\u7684\u540d\u79f0\u6765\u6709\u6548\u5730\u9009\u62e9\u5de5\u5177\uff0c\u65e0\u9700\u8fdb\u884c\u9488\u5bf9\u7279\u5b9a\u5de5\u5177\u7684\u5fae\u8c03\u3002\u4f5c\u8005\u4eec\u5728\u591a\u4e2a\u5e94\u7528\u9898\u95ee\u9898\u6570\u636e\u96c6\u4e0a\u7684\u5b9e\u9a8c\u8868\u660e\uff0cToolDec \u5c06\u8bed\u6cd5\u9519\u8bef\u964d\u81f3\u96f6\uff0c\u4ece\u800c\u663e\u8457\u63d0\u5347\u4e86\u6027\u80fd\uff0c\u5e76\u4e14\u901f\u5ea6\u63d0\u9ad8\u4e86\u6700\u591a2\u500d\u3002\u7814\u7a76\u8fd8\u663e\u793a\uff0c\u5728\u4ece\u672a\u89c1\u8fc7\u7684\u5de5\u5177\u4e0a\uff0cTookDec \u7684\u6cdb\u5316\u6027\u80fd\u6bd4\u57fa\u7ebf\u9ad8\u8fbe8\u500d\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u901a\u8fc7\u6709\u9650\u72b6\u6001\u673a<\/span>\uff08FSM\uff09<\/span>\u8fdb\u884c\u5f15\u5bfc<\/span>\uff08\u7ed3\u5408\u7b26\u53f7\u4e0e\u7edf\u8ba1\uff09<\/span><\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        \u7528\u6709\u9650\u72b6\u6001\u673a\uff08FSM\uff09\u8fdb\u884c\u5f15\u5bfc\u5927\u6a21\u578b<\/span><\/p>\n


        <\/span><\/p>\n

        4.3 \u7ed3\u5408\u8bed\u8a00\u6a21\u578b\u4e0e\u7b26\u53f7\u6c42\u89e3\u5668\u89e3\u51b3\u6570\u5b66\u5e94\u7528\u9898<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/16.pdf<\/span><\/section>\n
        \u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/github.com\/joyheyueya\/declarative-math-word-problem<\/span><\/section>\n<\/section>\n<\/blockquote>\n

        <\/section>\n

        \u5728\u6559\u80b2\u9886\u57df\uff0c\u81ea\u52a8\u4ea7\u751f\u9ad8\u8d28\u91cf\u7684\u6570\u5b66\u5e94\u7528\u9898\u9010\u6b65\u89e3\u7b54\u5177\u6709\u5e7f\u6cdb\u5e94\u7528\u3002\u8fd1\u6765\uff0c\u5c06\u5927\u578b\u8bed\u8a00\u6a21\u578b\u4e0e\u5916\u90e8\u5de5\u5177\u7ed3\u5408\u8d77\u6765\u6267\u884c\u590d\u6742\u63a8\u7406\u548c\u8ba1\u7b97\uff0c\u5df2\u6210\u4e3a\u89e3\u51b3\u6570\u5b66\u5e94\u7528\u9898\u7684\u4e00\u4e2a\u6709\u524d\u666f\u7684\u7814\u7a76\u65b9\u5411\uff0c\u4f46\u662f\u4e4b\u524d\u7684\u65b9\u6cd5\u5982\u7a0b\u5e8f\u8f85\u52a9\u8bed\u8a00\u6a21\u578b<\/span>\uff08Program-Aided\uff0cPAL\uff09<\/span>\u503e\u5411\u4e8e\u89e3\u51b3\u7b80\u5355\u7684\u7a0b\u5e8f\u6027\u95ee\u9898\uff0c\u5728\u9700\u8981\u58f0\u660e\u5f0f\u63a8\u7406\u7684\u95ee\u9898\u4e0a\u6548\u679c\u4e0d\u4f73\u3002\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u7ed3\u5408\u4e86\u4e00\u4e2a\u80fd\u591f\u9010\u6b65\u5c06\u5e94\u7528\u9898\u5f62\u5f0f\u5316\u4e3a\u4e00\u7ec4\u53d8\u91cf\u548c\u65b9\u7a0b\u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff0c\u4ee5\u53ca\u4e00\u4e2a\u80fd\u591f\u89e3\u8fd9\u4e9b\u65b9\u7a0b\u7684\u5916\u90e8\u7b26\u53f7\u6c42\u89e3\u5668\u3002\u5728 GSM8K \u6570\u5b66\u5e94\u7528\u9898\u57fa\u51c6\u6d4b\u8bd5\u4e2d\uff0c\u8fd9\u4e00\u65b0\u65b9\u6cd5\u6240\u8fbe\u5230\u7684\u51c6\u786e\u7387\u4e0e\u539f\u59cb\u7684 PAL \u76f8\u5f53\u3002\u800c\u5728 ALGEBRA \u6570\u636e\u96c6\u4e0a\uff0c\u5b83\u76f8\u6bd4 PAL \u8fbe\u5230\u4e86 20% \u7684\u7edd\u5bf9\u63d0\u5347\u3002\u8fd9\u91cc ALGEBRA \u662f\u4e00\u4e2a\u4ece\u4ee3\u6570\u6559\u79d1\u4e66\u4e2d\u63d0\u53d6\u7684\u66f4\u5177\u6311\u6218\u6027\u95ee\u9898\u7684\u65b0\u6570\u636e\u96c6\u3002\u8fd9\u9879\u7814\u7a76\u5f3a\u8c03\u4e86\u5728\u4e0e\u5916\u90e8\u5de5\u5177\u4ea4\u4e92\u89e3\u51b3\u590d\u6742\u6570\u5b66\u5e94\u7528\u9898\u65f6\uff0c\u4f7f\u7528\u58f0\u660e\u5f0f\u548c\u589e\u91cf\u5f0f\u8868\u793a\u7684\u4f18\u52bf\u3002\u6570\u636e\u548c\u63d0\u793a\u4fe1\u606f\u5747\u5df2\u5f00\u6e90\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u58f0\u660e\u5f0f\u65b9\u6cd5\u7684\u7b80\u5355\u793a\u4f8b\uff1a<\/span><\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        \u58f0\u660e\u5f0f\u65b9\u6cd5\uff08\u5de6\u56fe\uff09<\/span><\/p>\n


        <\/span><\/section>\n

        <\/span><\/section>\n

        \n
        \n
        \n
        \n
        \n

        <\/section>\n

        <\/section>\n
        \n
        <\/svg><\/section>\n<\/section>\n<\/section>\n
        \n

        5. \u6570\u5b66\u63a8\u7406 & \u5e94\u7528\u9898<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        \u4f5c\u4e3a\u533a\u5206\uff0c\u8fd9\u4e00\u4e13\u9898\u9488\u5bf9\u5e94\u7528\u9898\u6216\u7b80\u5355\u4efb\u52a1\u7684\u6570\u5b66\u63a8\u7406\uff0c\u8fd9\u6b21\u8bba\u575b\u4e3b\u9898\u5c31\u662f\u63a8<\/span>\u7406\uff0cWorkshop on Mathematical Reasoning and AI\uff0c\u5927\u90e8\u5206\u8bba\u6587\u53ef\u4ee5\u5f52\u5230\u6b64\u7c7b\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        5.1 TinyGSM\uff1a\u901a\u8fc7 1B \u53c2\u6570\u5728 GSM8K \u4e0a\u5b9e\u73b080%\u51c6\u786e\u7387<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/pdf\/2312.09241.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5c0f\u578b\u6a21\u578b\u63d0\u4f9b\u4e86\u8bf8\u591a\u8ba1\u7b97\u4e0a\u7684\u4f18\u52bf\uff0c\u4f46\u6a21\u578b\u53c2\u6570\u91cf\u5bf9\u4e8e\u89e3\u51b3\u95ee\u9898\u80fd\u529b\u7684\u5f71\u54cd\u7a0b\u5ea6\u4ecd\u7136\u662f\u4e2a\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\u3002\u8fd9\u9879\u5de5\u4f5c\u7814\u7a76\u4e86\u5c0f\u578b\u6a21\u578b\u5728\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\uff0c\u4e00\u4e2a\u5177\u6709 1.3B \u53c2\u6570\u7684\u6a21\u578b\u5728\u89e3\u51b3\u6570\u5b66\u5e94\u7528\u9898\u4e0a\u80fd\u591f\u8fbe\u5230 80.1% \u7684\u51c6\u786e\u7387\uff0c\u8fd9\u4e2a\u8868\u73b0\u8d85\u8d8a\u4e86\u5927\u5f97\u591a\u7684\u73b0\u6709\u6a21\u578b\uff0c\u5e76\u4e14\u751a\u81f3\u53ef\u4ee5\u4e0e\u5176\u751f\u6210\u8bad\u7ec3\u6570\u636e\u7684 GPT-3.5-turbo \u6559\u5e08\u6a21\u578b\u7684\u6027\u80fd\u76f8\u5ab2\u7f8e\u3002\u8bba\u6587\u7684\u65b9\u6cd5\u5f88\u7b80\u5355\uff0c\u4e3b\u8981\u5305\u542b\u4e24\u4e2a\u5173\u952e\u90e8\u5206\uff1a\u7b2c\u4e00\u90e8\u5206\u662f\u4f7f\u7528\u4e00\u4e2a\u7531 GPT-3.5-turbo \u751f\u6210\u7684\u3001\u5305\u542b\u89e3\u7b54\u7684\u6570\u5b66\u5e94\u7528\u9898\u5408\u6210\u6570\u636e\u96c6\uff0c\u8be5\u6570\u636e\u96c6\u5c06\u5b8c\u5168\u516c\u5f00\u3002\u7b2c\u4e8c\u90e8\u5206\u662f\u4f7f\u7528\u4e00\u4e2a\u9a8c\u8bc1\u5668\uff0c\u4ece\u591a\u4e2a\u5019\u9009\u7b54\u6848\u4e2d\u9009\u62e9\u6700\u7ec8\u8f93\u51fa\u3002<\/strong><\/span><\/p>\n


        <\/span><\/p>\n

        5.2 MinT\uff1a\u901a\u8fc7\u591a\u89c6\u56fe\u5fae\u8c03\u63d0\u9ad8\u6570\u5b66\u63a8\u7406\u7684\u6cdb\u5316\u80fd\u529b<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/55.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u6570\u5b66\u9886\u57df\u7684\u63a8\u7406\u5bf9\u4e8e\u76f8\u5bf9\u8f83\u5c0f\u7684\u8bed\u8a00\u6a21\u578b<\/span>\uff08LMs\uff09<\/span>\u4f9d\u7136\u662f\u4e00\u4e2a\u91cd\u5927\u6311\u6218\u3002\u8bb8\u591a\u73b0\u884c\u65b9\u6cd5\u4e13\u6ce8\u4e8e\u4f7f LMs \u4e13\u957f\u4e8e\u6570\u5b66\u63a8\u7406\uff0c\u5e76\u4e14\u4e25\u91cd\u4f9d\u8d56\u4ece\u5f3a\u5927\u4f46\u6548\u7387\u4e0d\u9ad8\u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u4e2d\u63d0\u53d6\u77e5\u8bc6\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u63a2\u7d22\u4e86\u4e00\u79cd\u65b0\u65b9\u5411\uff0c\u907f\u514d\u8fc7\u5ea6\u4f9d\u8d56 LLM \u6559\u5e08\uff0c\u5f15\u5165\u4e86\u4e00\u79cd\u591a\u89c6\u56fe\u5fae\u8c03\u65b9\u6cd5<\/strong>\uff0c\u8be5\u65b9\u6cd5\u6709\u6548\u5229\u7528\u4e86\u5177\u6709\u591a\u6837\u5316\u6ce8\u91ca\u98ce\u683c\u7684\u73b0\u6709\u6570\u5b66\u95ee\u9898\u6570\u636e\u96c6\u3002\u8be5\u65b9\u6cd5\u72ec\u7279\u5730\u8003\u8651\u5230\u5404\u79cd\u6ce8\u91ca\u683c\u5f0f\u4f5c\u4e3a\u53ef\u80fd\u4e92\u76f8\u5e2e\u52a9\u7684\u4e0d\u540c\u201c\u89c6\u56fe\u201d\uff0c\u5e76\u5728\u8bad\u7ec3\u6a21\u578b\u65f6\u5229\u7528\u5b83\u4eec<\/strong>\u3002\u901a\u8fc7\u5728\u8f93\u5165\u95ee\u9898\u540e\u9644\u52a0\u4e0d\u540c\u7684\u6307\u4ee4\uff0c\u6a21\u578b\u53ef\u4ee5\u7075\u6d3b\u5730\u5b66\u4f1a\u4ee5\u591a\u79cd\u683c\u5f0f\u751f\u6210\u89e3\u51b3\u65b9\u6848\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u8be5\u7b56\u7565\u4f7f\u76f8\u5bf9\u8f83\u5c0f\u7684 LMs \u7684\u8868\u73b0\u8d85\u8d8a\u4e86\u5148\u524d\u4e25\u91cd\u4f9d\u8d56\u77e5\u8bc6\u84b8\u998f\u7684\u65b9\u6cd5\uff0c\u4ee5\u53ca\u7cbe\u5fc3\u5efa\u7acb\u7684\u57fa\u7ebf\u3002\u6b64\u5916\uff0c\u6240\u63d0\u51fa\u7684\u65b9\u6cd5\u8d4b\u4e88\u6a21\u578b\u5728\u4e0d\u540c\u89c6\u56fe\u548c\u6570\u636e\u96c6\u4e0a\u7684\u6f5c\u5728\u6cdb\u5316\u80fd\u529b\uff0c\u4ee5\u53ca\u4ece\u4e0d\u51c6\u786e\u6216\u4e0d\u5b8c\u6574\u7684\u566a\u58f0\u6570\u636e\u4e2d\u5b66\u4e60\u7684\u80fd\u529b\u3002\u4f5c\u8005\u4eec\u5e0c\u671b\u901a\u8fc7\u591a\u89c6\u56fe\u8bad\u7ec3\u8303\u5f0f\u80fd\u6fc0\u53d1\u5176\u4ed6\u673a\u5668\u63a8\u7406\u9886\u57df\u672a\u6765\u7684\u7814\u7a76\u3002<\/span><\/p>\n


        <\/p>\n

        <\/p>\n

        \u591a\u89c6\u56fe\u5fae\u8c03\u6570\u636e<\/span><\/p>\n


        <\/span><\/p>\n

        5.3 \u57fa\u4e8e\u7b26\u53f7\u89c4\u5219\u5b66\u4e60\u7684\u5927\u8bed\u8a00\u6a21\u578b\uff0c\u7528\u4ee5\u589e\u5f3a\u6570\u503c\u63a8\u7406\u9c81\u68d2\u6027<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/46.pdf<\/span><\/section>\n

        ILASP \u7b80\u4ecb\uff1aInductive Logic Programming Answer Set Programming,<\/span><\/p>\n

        https:\/\/www.doc.ic.ac.uk\/~ml1909\/ILASP_ALP_2020.pdf<\/span><\/p>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u867d\u7136\u4eba\u4eec\u5df2\u7ecf\u63d0\u51fa\u4e86\u4e00\u4e9b\u63d0\u793a\u7b56\u7565\u6765\u5f15\u5bfc\u5927\u578b\u8bed\u8a00\u6a21\u578b\u8fdb\u884c\u63a8\u7406\uff0c\u4f46\u5bf9\u4e8e\u673a\u5668\u9605\u8bfb\u7406\u89e3\u4efb\u52a1\uff0c\u6570\u503c\u63a8\u7406\u4f9d\u7136\u662f\u4e00\u4e2a\u6311\u6218\u3002\u7814\u7a76\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u795e\u7ecf\u7b26\u53f7\u65b9\u6cd5\uff0c\u5229\u7528 LLM \u7684\u4e0a\u4e0b\u6587\u5b66\u4e60\u80fd\u529b\u5c06\u590d\u6742\u95ee\u9898\u5206\u89e3\u6210\u66f4\u7b80\u5355\u7684\u5b50\u95ee\u9898\uff0c\u5e76\u91c7\u7528\u7b26\u53f7\u5b66\u4e60\u65b9\u6cd5\u5b66\u4e60\u91cd\u7ec4\u90e8\u5206\u7b54\u6848\u7684\u89c4\u5219<\/strong>\u3002\u8be5\u65b9\u6cd5\u5728 DROP \u57fa\u51c6\u7684\u4e0d\u540c\u6570\u5b57\u5b50\u96c6\u4e0a\u8fdb\u884c\u4e86\u8bc4\u4f30\uff1b\u7ed3\u679c\u8868\u660e\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4e0e\u4e3a DROP \u4e13\u95e8\u8bbe\u8ba1\u7684 SOTA \u6a21\u578b\u7ade\u4e89\u529b\u76f8\u5f53\uff0c\u5e76\u4e14\u663e\u8457\u4f18\u4e8e\u7eaf\u7cb9\u4f9d\u9760 LLM \u63d0\u793a\u7684\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u8be5\u65b9\u6cd5\u5177\u6709\u6570\u636e\u6548\u7387\u9ad8\u7684\u7279\u70b9\uff0c\u56e0\u4e3a\u5b83\u65e0\u9700\u8fdb\u884c\u4efb\u4f55\u989d\u5916\u7684\u8bad\u7ec3\u6216\u5fae\u8c03\u3002\u795e\u7ecf\u7b26\u53f7\u65b9\u6cd5\u8fd8\u4fc3\u8fdb\u4e86\u9c81\u68d2\u7684\u6570\u503c\u63a8\u7406\u80fd\u529b\uff0c\u786e\u4fdd\u6a21\u578b\u5fe0\u5b9e\u4e8e\u5176\u6240\u5448\u73b0\u7684\u6587\u672c\uff0c\u5e76\u63d0\u4f9b\u53ef\u89e3\u91ca\u548c\u53ef\u9a8c\u8bc1\u7684\u63a8\u7406\u8fc7\u7a0b\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        <\/span><\/p>\n

        \u795e\u7ecf\u7b26\u53f7\u7b97\u6cd5<\/span><\/p>\n


        <\/span><\/p>\n

        5.4 \u8ba1\u5212\u3001\u9a8c\u8bc1\u548c\u8f6c\u6362\uff1a\u591a\u6837\u5316\u601d\u7ef4\u65b9\u5f0f\u7684\u96c6\u6210\u63a8\u7406<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/section>\n
        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/pdf\/2310.14628.pdf<\/span><\/section>\n
        \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/tengxiaoliu\/XoT<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u968f\u7740\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5c55\u73b0\u51fa\u5728\u4e0d\u540c\u63d0\u793a\u65b9\u6cd5\u4e0b\u7684\u6709\u6548\u6027\uff0c\u4f8b\u5982\u201c\u601d\u7ef4\u94fe\u201d\u548c\u201c\u601d\u7ef4\u7a0b\u5e8f\u201d<\/span>\uff08Program of Thought\uff09<\/span>\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u5728\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e0a\u5df2\u7ecf\u663e\u793a\u51fa\u4e86\u76f8\u4e92\u4e4b\u95f4\u7684\u6781\u4f73\u4e92\u8865\u6027\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u4e86 XoT\uff0c\u4e00\u4e2a\u901a\u8fc7\u7528\u591a\u6837\u5316\u63a8\u7406\u601d\u8def\u542f\u53d1 LLM \u7684\u96c6\u6210\u95ee\u9898\u89e3\u51b3\u6846\u67b6\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u95ee\u9898\uff0cXoT \u603b\u662f\u5148\u9009\u62e9\u6700\u5408\u9002\u7684\u65b9\u6cd5\uff0c\u7136\u540e\u8fed\u4ee3\u6267\u884c\u6bcf\u79cd\u65b9\u6cd5\u3002\u5728\u6bcf\u6b21\u8fed\u4ee3\u8fc7\u7a0b\u4e2d\uff0cXoT \u4f1a\u4e3b\u52a8\u68c0\u67e5\u751f\u6210\u7b54\u6848\u7684\u6709\u6548\u6027\uff0c\u5e76\u7eb3\u5165\u5916\u90e8\u6267\u884c\u5668\u7684\u53cd\u9988\uff0c\u4ece\u800c\u80fd\u591f\u5728\u4e0d\u540c\u7684\u63d0\u793a\u65b9\u6cd5\u4e4b\u95f4\u52a8\u6001\u5207\u6362\u3002\u901a\u8fc7\u5728 10 \u4e2a\u4e3b\u6d41\u7684\u6570\u5b66\u63a8\u7406\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u5e7f\u6cdb\u5b9e\u9a8c\uff0c\u7814\u7a76\u8005\u8bc1\u660e\u4e86\u4ed6\u4eec\u6240\u63d0\u51fa\u7684\u65b9\u6cd5\u7684\u6709\u6548\u6027\uff0c\u5e76\u5f7b\u5e95\u5206\u6790\u4e86\u6bcf\u4e2a\u6a21\u5757\u7684\u5f3a\u9879\u3002\u6b64\u5916\uff0c\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u8be5\u6846\u67b6\u4e0e\u8fd1\u671f\u5728\u5355\u4e00\u63a8\u7406\u65b9\u6cd5\u4e0a\u53d6\u5f97\u6539\u8fdb\u7684\u5de5\u4f5c\u76f8\u6b63\u4ea4\uff0c\u5e76\u4e14\u80fd\u591f\u8fdb\u4e00\u6b65\u6cdb\u5316\u5230\u903b\u8f91\u63a8\u7406\u9886\u57df\u3002\u901a\u8fc7\u5141\u8bb8\u65b9\u6cd5\u95f4\u7684\u5207\u6362\uff0cXoT \u4e3a\u5728\u7edf\u4e00\u6846\u67b6\u5185\u534f\u540c\u96c6\u6210\u591a\u6837\u5316\u63a8\u7406\u601d\u7ef4\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        5.5 EchoPrompt\uff1a\u901a\u8fc7\u91cd\u8ff0\u95ee\u9898\u63d0\u9ad8\u4e0a\u4e0b\u6587\u5b66\u4e60\u80fd\u529b<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \n

        \u8bba\u6587\u94fe\u63a5\uff1a <\/span>https:\/\/mathai2023.github.io\/papers\/22.pdf<\/span><\/p>\n

        \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/rajasekharmekala\/echoprompt<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


        <\/section>\n

        \u8be5\u6587\u7ae0\u63d0\u51fa\u4e86 EchoPrompt\uff0c\u4e00\u79cd\u901a\u8fc7\u8ba9\u6a21\u578b\u5728\u56de\u7b54\u95ee\u9898\u4e4b\u524d\u91cd\u65b0\u8868\u8ff0\u67e5\u8be2\u6765\u63d0\u5347\u6027\u80fd\u7684\u7b80\u5355\u800c\u6709\u6548\u7684\u6280\u672f<\/strong>\u3002\u8be5\u6280\u672f\u9002\u7528\u4e8e\u96f6\u6b21\u63d0\u793a\u548c\u5c11\u6570\u793a\u4f8b\u63d0\u793a\u7684\u573a\u666f\uff0c\u5e76\u4e14\u80fd\u591f\u4e0e\u6807\u51c6\u63d0\u793a\u4ee5\u53ca\u601d\u8def\u94fe\u63d0\u793a\u7ed3\u5408\u4f7f\u7528\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0cEchoPrompt \u5728\u591a\u4e2a\u56e0\u679c\u8bed\u8a00\u6a21\u578b\u65cf\u7684\u5404\u79cd\u8bbe\u7f6e\u4e2d\u5927\u5e45\u63d0\u5347\u4e86\u6027\u80fd\uff0c\u5305\u62ec\u6570\u503c\u63a8\u7406<\/span>\uff08\u4f8b\u5982\uff0cGSM8K, SVAMP\uff09<\/span>\u3001\u9605\u8bfb\u7406\u89e3<\/span>\uff08\u4f8b\u5982\uff0cDROP\uff09<\/span>\u548c\u903b\u8f91\u63a8\u7406<\/span>\uff08\u4f8b\u5982\uff0c\u7ffb\u786c\u5e01\uff09<\/span>\u7b49\u4efb\u52a1\u3002\u7279\u522b\u662f\uff0c\u5b83\u4f7f\u5f97 code-davinci-002 \u6a21\u578b\u5728\u96f6\u6b21\u63d0\u793a\u7684\u601d\u8def\u94fe\u73af\u5883\u4e0b\uff0c\u5728\u6570\u503c\u4efb\u52a1\u4e0a\u7684\u6027\u80fd\u63d0\u5347\u4e86 5%\uff0c\u5728\u9605\u8bfb\u7406\u89e3\u4efb\u52a1\u4e0a\u63d0\u5347\u4e86 13%\u3002\u8fd9\u4e9b\u7ed3\u679c\u663e\u793a\uff0cEchoPrompt \u53ef\u4ee5\u6709\u6548\u5730\u52a0\u5f3a\u5728\u4e0a\u4e0b\u6587\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u7684\u8868\u73b0\uff0c\u5efa\u8bae\u5c06\u5176\u878d\u5165\u5230\u5404\u7c7b\u57fa\u7ebf\u63d0\u793a\u7b56\u7565\u4e2d\uff0c\u4ee5\u63d0\u9ad8\u6574\u4f53\u6548\u80fd\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u8fd9\u7c7b\u5de5\u4f5c\u7684\u60f3\u6cd5\u90fd\u5f88\u7b80\u5355\uff0c\u8ba9\u6a21\u578b\u5728\u56de\u7b54\u524d\u91cd\u65b0\u8868\u8ff0\u95ee\u9898\uff0c\u52a0\u5f3a\u5bf9\u95ee\u9898\u7684\u7406\u89e3\uff0c\u4f8b\u5b50\u5982\u4e0b\uff1a<\/span><\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        \u56de\u7b54\u524d\u91cd\u65b0\u8868\u8ff0\u95ee\u9898\uff08\u53f3\u56fe\uff09<\/span><\/p>\n


        <\/span><\/p>\n

        5.6 \u901a\u8fc7\u7b97\u672f\u4efb\u52a1\u5b66\u4e60\u591a\u6b65\u63a8\u7406<\/span>
        <\/strong><\/p>\n


        <\/span><\/strong><\/p>\n

        <\/strong><\/p>\n

        \n
        \n
        \n

        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/1.pdf<\/span><\/p>\n

        \u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/github.com\/TianduoWang\/MsAT<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u6570\u5b66\u63a8\u7406\u88ab\u89c6\u4e3a\u8bed\u8a00\u6a21\u578b\u6240\u5fc5\u9700\u7684\u80fd\u529b\u3002\u6700\u8fd1\u7684\u7814\u7a76\u8868\u660e\uff0c\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5728\u89e3\u51b3\u6570\u5b66\u95ee\u9898\u65b9\u9762\u6709\u7740\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\u7684\u8868\u73b0\u3002\u8fd9\u79cd\u6210\u529f\u88ab\u5f52\u56e0\u4e8e\u5b83\u4eec\u7684\u201c\u94fe\u5f0f\u601d\u8003\u201d<\/span>\uff08COT\uff09<\/span>\u63a8\u7406\u80fd\u529b\uff0c\u5373\u5206\u89e3\u590d\u6742\u95ee\u9898\u6210\u4e3a\u9010\u6b65\u63a8\u7406\u94fe\u7684\u80fd\u529b\uff0c\u4f46\u8fd9\u6837\u7684\u80fd\u529b\u4f3c\u4e4e\u53ea\u51fa\u73b0\u5728\u53c2\u6570\u975e\u5e38\u591a\u7684\u6a21\u578b\u4e2d\u3002\u8fd9\u9879\u5de5\u4f5c\u63a2\u8ba8\u4e86\u5982\u4f55\u5c06\u591a\u6b65\u63a8\u7406\u80fd\u529b\u6574\u5408\u8fdb\u76f8\u5bf9\u5c0f\u578b\u7684\u8bed\u8a00\u6a21\u578b\u4e2d\u3002<\/strong>\u4f5c\u8005\u63d0\u51fa\u901a\u8fc7\u5728\u4e00\u4e2a\u7531\u591a\u6b65\u7b97\u672f\u4efb\u52a1<\/span>\uff08MSAT\uff09<\/span>\u7ec4\u6210\u7684\u5408\u6210\u6570\u636e\u96c6\u4e0a\u7ee7\u7eed\u9884\u8bad\u7ec3\u8bed\u8a00\u6a21\u578b\u6765\u5f15\u5165\u8fd9\u79cd\u80fd\u529b\u3002\u5728\u6570\u5b66\u5e94\u7528\u9898\u4efb\u52a1\u4e0a\u7684\u5b9e\u9a8c\u5c55\u793a\u4e86\u8fd9\u4e00\u65b9\u6cd5\u5728\u63d0\u5347\u8bed\u8a00\u6a21\u578b\u6570\u5b66\u63a8\u7406\u80fd\u529b\u65b9\u9762\u7684\u6709\u6548\u6027\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        5.7 \u901a\u8fc7\u91cd\u65b0\u68c0\u9a8c\u89e3\u51b3\u6570\u5b66\u5e94\u7528\u9898<\/span><\/strong><\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/18.pdf<\/span><\/section>\n
        \u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/github.com\/steven640pixel\/PsedualMWP<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u89e3\u51b3\u6570\u5b66\u5e94\u7528\u9898<\/span>\uff08MWP\uff09<\/span>\u7684\u76ee\u6807\u662f\u7406\u89e3\u63cf\u8ff0\u6027\u6570\u5b66\u95ee\u9898\u5e76\u8ba1\u7b97\u7ed3\u679c\uff0c\u4e4b\u524d\u7684\u52aa\u529b\u5927\u591a\u81f4\u529b\u4e8e\u63d0\u5347\u4e0d\u540c\u6280\u672f\u6a21\u5757\u3002\u672c\u6587\u5e26\u6765\u4e86\u4e00\u4e2a\u4e0d\u540c\u4e14\u65b0\u9896\u7684\u89c6\u89d2\u2014\u2014\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u8fdb\u884c\u91cd\u65b0\u68c0\u9a8c\uff0c\u5e76\u5f15\u5165\u4e86\u4e00\u4e2a\u4f2a\u53cc\u4efb\u52a1\u4ee5\u589e\u5f3a MWP \u89e3\u51b3\u80fd\u529b\u3002\u7814\u7a76\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u6a21\u578b\u65e0\u5173\u7684\u4f2a\u53cc\u91cd<\/span>\uff08PseDual\uff09<\/span>\u5b66\u4e60\u65b9\u6848\uff0c\u53ef\u4ee5\u9002\u914d\u4efb\u4f55\u73b0\u6709\u7684 MWP \u89e3\u51b3\u5668\u3002\u8fd9\u4e2a\u7279\u5b9a\u5b9a\u4e49\u7684\u4f2a\u53cc\u4efb\u52a1\u662f\u5c06\u6570\u5b66\u8868\u8fbe\u5f0f\u4e2d\u7684\u6570\u5b57\u91cd\u65b0\u586b\u5145\u56de\u539f\u59cb\u7684\u5e94\u7528\u9898\u4e2d\uff0c\u5e76\u4f7f\u6570\u5b57\u5904\u4e8e\u5c4f\u853d\u72b6\u6001\u3002\u4e3a\u4e86\u6709\u6548\u5730\u8054\u5408\u4e24\u4e2a\u4efb\u52a1\u7684\u5b66\u4e60\uff0c\u7814\u7a76\u8005\u8fd8\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u9884\u5b9a\u878d\u5408\u7b56\u7565\uff0c\u7528\u4e8e\u6570\u5b57\u586b\u5145\u4efb\u52a1\uff0c\u8be5\u7b56\u7565\u5e73\u6ed1\u5730\u5c06\u8f93\u5165\u4ece\u771f\u5b9e\u6570\u5b66\u8868\u8fbe\u5f0f\u8f6c\u6362\u4e3a\u9884\u6d4b\u7684\u8868\u8fbe\u5f0f\u3002\u901a\u8fc7\u5b9e\u8bc1\u7814\u7a76\uff0c\u4f2a\u53cc\u91cd\u5b66\u4e60\u65b9\u6848\u5df2\u88ab\u9a8c\u8bc1\u5728\u591a\u4e2a\u4ee3\u8868\u6027MWP\u89e3\u51b3\u5668\u4e2d\u6709\u6548\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        5.8 SATLM: \u4f7f\u7528\u58f0\u660e\u5f0f\u63d0\u793a\u7684\u53ef\u6ee1\u8db3\u6027\u8f85\u52a9\u8bed\u8a00\u6a21\u578b<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/32.pdf<\/span><\/section>\n
        \u4ee3\u7801\u5730\u5740\uff1ahttps:\/\/github.com\/xiye17\/sat-lm<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5148\u524d\u7684\u5de5\u4f5c\u5c06\u601d\u7ef4\u94fe\u6280\u672f\u4e0e\u7a0b\u5e8f\u5316\u8868\u8fbe\u7ed3\u5408\u5728\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u4e2d\uff0c\u7528\u4ee5\u8fdb\u884c\u63a8\u7406\u3002\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u4e8e\u53ea\u9700\u5355\u5411\u63a8\u7406\u7684\u4efb\u52a1<\/span>\uff08\u4f8b\u5982\uff0c\u7b80\u5355\u7684\u7b97\u672f\u95ee\u9898\uff09<\/span>\u6548\u679c\u826f\u597d\uff0c\u4f46\u5bf9\u4e8e\u9700\u8981\u66f4\u590d\u6742\u89c4\u5212\u548c\u641c\u7d22\u7684\u95ee\u9898\uff0c\u5219\u6548\u679c\u4e0d\u4f73\u3002\u5728\u672c\u6587\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u79cd\u540d\u4e3a\u53ef\u6ee1\u8db3\u6027\u8f85\u52a9\u8bed\u8a00\u5efa\u6a21<\/span>\uff08SATLM\uff09<\/span>\u7684\u65b0\u65b9\u6cd5\u6765\u589e\u5f3a LLMs \u7684\u63a8\u7406\u80fd\u529b\uff1a\u5229\u7528 LLM \u751f\u6210\u4e00\u4e2a\u58f0\u660e\u5f0f\u4efb\u52a1\u8bf4\u660e\u800c\u975e\u547d\u4ee4\u5f0f\u7a0b\u5e8f\uff0c\u5e76\u4e14\u501f\u52a9\u73b0\u6210\u7684\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u5668\u6765\u5f97\u51fa\u6700\u7ec8\u7b54\u6848\u3002\u901a\u8fc7\u5c06\u5b9e\u9645\u63a8\u7406\u4efb\u52a1\u5916\u5305\u7ed9\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u5668\uff0c\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u4fdd\u8bc1\u76f8\u5bf9\u4e8e\u89e3\u6790\u51fa\u7684\u89c4\u683c\u7684\u7b54\u6848\u7684\u6b63\u786e\u6027\uff0c\u5e76\u907f\u514d\u5728\u89e3\u9898\u8fc7\u7a0b\u4e2d\u53d1\u751f\u89c4\u5212\u9519\u8bef\u3002\u8be5\u7814\u7a76\u5728 6 \u4e2a\u6570\u636e\u96c6\u4e0a\u8bc4\u4f30\u4e86 SATLM \u7684\u8868\u73b0\uff0c\u5e76\u6307\u51fa\u5b83\u5728\u547d\u4ee4\u5f0f\u8303\u4f8b\u4e2d\u6301\u7eed\u8d85\u8d8a\u4e86\u7a0b\u5e8f\u8f85\u52a9 LLMs \u7684\u6027\u80fd\u3002\u7279\u522b\u5730\uff0c\u5728 GSM \u7b97\u672f\u63a8\u7406\u6570\u636e\u96c6\u7684\u4e00\u4e2a\u5177\u6709\u6311\u6218\u6027\u7684\u5b50\u96c6\u4e0a\uff0cSATLM \u6bd4\u7a0b\u5e8f\u8f85\u52a9 LLMs \u7684\u6027\u80fd\u9ad8\u51fa 20% \u4ee5\u4e0a\uff1b\u540c\u65f6\uff0c\u5728\u6cd5\u5b66\u9662\u5165\u5b66\u8003\u8bd5<\/span>\uff08LSAT\uff09<\/span>\u548c BOARDGAMEQA \u4e0a\uff0cSATLM \u4e5f\u8fbe\u5230\u4e86\u65b0\u7684 SoTA\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        <\/p>\n

        \u4e09\u79cd\u6a21\u5f0f\u5bf9\u6bd4\u56fe<\/span><\/p>\n


        <\/span><\/p>\n

        5.9 \u8bed\u8a00\u6a21\u578b\u63d0\u793a\u7a7a\u95f4\u4e2d\u57fa\u7840\u7b97\u672f\u6027\u8d28\u7684\u7814\u7a76<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/24.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u6700\u8fd1\uff0c\u80fd\u591f\u6709\u6548\u5229\u7528\u5927\u91cf\u672a\u6807\u6ce8\u6587\u672c\u6570\u636e\u7684\u5927\u578b\u9884\u8bad\u7ec3\u795e\u7ecf\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u5f7b\u5e95\u6539\u53d8\u4e86\u81ea\u7136\u8bed\u8a00\u5904\u7406\u9886\u57df\u3002\u901a\u8fc7\u5229\u7528\u8fd9\u4e9b\u6a21\u578b\u56fa\u6709\u7684\u4e0a\u4e0b\u6587\u5b66\u4e60\u80fd\u529b\u652f\u6301\u7684\u63d0\u793a\u6280\u672f\uff0c\u5df2\u7ecf\u8bc1\u660e LLMs \u80fd\u591f\u4e0e\u4e3a\u4e0b\u6e38\u4efb\u52a1\u4e13\u95e8\u8bad\u7ec3\u7684\u6a21\u578b\u76f8\u5ab2\u7f8e\u3002\u5176\u4e2d\u4e00\u4e2a\u4efb\u52a1\u662f\u6570\u503c\u63a8\u7406\uff0c\u7279\u522b\u662f\u8fdb\u884c\u57fa\u672c\u7b97\u672f\u8fd0\u7b97\u7684\u80fd\u529b\u3002\u7814\u7a76\u8005\u4eec\u63a2\u8ba8\u4e86\u7b97\u672f\u8fd0\u7b97\u7684\u57fa\u672c\u6027\u8d28\uff0c\u4f8b\u5982\u4ea4\u6362\u5f8b\uff0c\u5728LLM\u63d0\u793a\u7684\u73af\u5883\u4e0b\u662f\u5426\u4f9d\u65e7\u9002\u7528\u2014\u2014\u5373\u8981\u6c42LLM\u8ba1\u7b9713 + 37\u4e0e37 + 13\u662f\u5426\u901a\u5e38\u4f1a\u5bfc\u81f4\u76f8\u540c\u7684\u7ed3\u679c\u3002\u4e0e\u4e4b\u524d\u5927\u591a\u6570\u53ea\u62a5\u544a\u51c6\u786e\u5ea6\u7684\u5de5\u4f5c\u4e0d\u540c\uff0c\u4ed6\u4eec\u901a\u8fc7\u66f4\u4ed4\u7ec6\u5730\u89c2\u5bdf\u9519\u8bef\u5206\u5e03<\/span>\uff08\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee\u3001\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570R\uff09<\/span>\uff0c\u6765\u66f4\u597d\u5730\u7406\u89e3\u5728\u63d0\u793a\u6270\u52a8\u548c\u89c4\u6a21\u6cd5\u5219\u4e0b\u7684\u6027\u80fd\u8868\u73b0\u3002<\/span><\/p>\n


        <\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \n
        \n
        \n

        <\/section>\n

        <\/section>\n
        \n
        <\/svg><\/section>\n<\/section>\n<\/section>\n
        \n

        6. \u591a\u6a21\u6001<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        6.1 MathVista\uff1a\u5728\u89c6\u89c9\u4e0a\u4e0b\u6587\u4e2d\u8bc4\u4f30\u57fa\u7840\u6a21\u578b\u7684\u6570\u5b66\u63a8\u7406\u80fd\u529b<\/span><\/strong>
        <\/section>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/52.pdf<\/span><\/section>\n
        \u8bba\u6587\u7f51\u7ad9\uff1ahttps:\/\/mathvista.github.io\/<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5c3d\u7ba1\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u548c\u5927\u578b\u591a\u6a21\u6001\u6a21\u578b<\/span>\uff08LMMs\uff09<\/span>\u5728\u4e0d\u540c\u9886\u57df\u5c55\u73b0\u4e86\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\u7684\u6280\u80fd\uff0c\u4f46\u5b83\u4eec\u5728\u89c6\u89c9\u80cc\u666f\u4e0b\u8fdb\u884c\u6570\u5b66\u63a8\u7406\u7684\u80fd\u529b\u5c1a\u672a\u6b63\u5f0f\u8bc4\u4f30\u3002\u4e3aLLMs\u548cLMMs\u88c5\u5907\u8fd9\u79cd\u80fd\u529b\u5bf9\u4e8e\u901a\u7528\u76ee\u7684AI\u52a9\u624b\u81f3\u5173\u91cd\u8981\uff0c\u5e76\u4e14\u5728\u6559\u80b2\u3001\u6570\u636e\u5206\u6790\u548c\u79d1\u5b66\u53d1\u73b0\u7b49\u65b9\u9762\u5c55\u73b0\u51fa\u5de8\u5927\u6f5c\u529b\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u4e3a\u586b\u8865\u8fd9\u4e00\u7a7a\u767d\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86 MATHVISTA \u57fa\u51c6\u6d4b\u8bd5\uff0c\u8be5\u6d4b\u8bd5\u65e8\u5728\u7ed3\u5408\u6765\u81ea\u6587\u732e\u4e2d\u8bc6\u522b\u51fa\u7684\u591a\u6837\u5316\u7684\u6570\u5b66\u548c\u89c6\u89c9\u4efb\u52a1\u6311\u6218\u3002\u7814\u7a76\u8005\u9996\u5148\u4ece28\u4e2a\u73b0\u6709\u7684\u4ee5\u6570\u5b66\u4e3a\u7126\u70b9\u548c\u89c6\u89c9\u95ee\u7b54\u6570\u636e\u96c6\u4e2d\uff0c\u5f52\u7c7b\u5e76\u786e\u5b9a\u4e86\u5173\u952e\u7684\u4efb\u52a1\u7c7b\u578b\u3001\u63a8\u7406\u6280\u80fd\u548c\u89c6\u89c9\u80cc\u666f\u3002\u7136\u540e\u6784\u5efa\u4e86\u4e09\u4e2a\u65b0\u7684\u6570\u636e\u96c6\uff0c\u5373IQTest\u3001FunctionQA\u548cPaperQA\uff0c\u4ee5\u8986\u76d6\u7f3a\u5931\u7684\u89c6\u89c9\u80cc\u666f\u7c7b\u578b<\/strong><\/span>\u3002\u6240\u5448\u73b0\u7684\u95ee\u9898\u901a\u5e38\u9700\u8981\u8d85\u8d8a\u5149\u5b66\u5b57\u7b26\u8bc6\u522b<\/span>\uff08OCR\uff09<\/span>\u6216\u56fe\u50cf\u5b57\u5e55\u7684\u6df1\u5165\u89c6\u89c9\u7406\u89e3\uff0c\u5e76\u4e14\u8981\u6c42\u4f7f\u7528\u4e30\u5bcc\u7684\u9886\u57df\u7279\u5b9a\u5de5\u5177\u8fdb\u884c\u7ec4\u5408\u63a8\u7406\uff0c\u8fd9\u5bf9\u73b0\u6709\u6a21\u578b\u6765\u8bf4\u662f\u4e00\u4e2a\u663e\u8457\u7684\u6311\u6218\u3002\u7814\u7a76\u8005\u5bf911\u4e2a\u77e5\u540d\u7684\u5f00\u6e90\u548c\u4e13\u6709\u57fa\u7840\u6a21\u578b<\/span>\uff08\u5305\u62ecLLMs\u3001\u589e\u5f3a\u5de5\u5177LLMs\u548cLMMs\uff09<\/span>\u8fdb\u884c\u4e86\u5168\u9762\u8bc4\u4f30\u3002\u8868\u73b0\u6700\u4f73\u7684\u6a21\u578b\u2014\u2014\u591a\u6a21\u6001\u5df4\u5fb7<\/span>\uff08Multimodal Bard\uff09<\/span>\uff0c\u4ec5\u8fbe\u5230\u4e86\u4eba\u7c7b\u6027\u80fd\u768458%<\/span>\uff0834.8%\u76f8\u6bd460.3%\uff09<\/span>\uff0c\u8868\u660e\u6539\u8fdb\u7684\u7a7a\u95f4\u4ecd\u7136\u5f88\u5927\u3002\u9274\u4e8e\u8fd9\u4e00\u663e\u8457\u7684\u5dee\u8ddd\uff0cMATHVISTA\u6fc0\u52b1\u4e86\u672a\u6765\u7684\u7814\u7a76\uff0c\u63a8\u52a8\u901a\u7528AI\u4ee3\u7406\u7684\u53d1\u5c55\uff0c\u4f7f\u5176\u80fd\u591f\u5904\u7406\u6570\u5b66\u5bc6\u96c6\u578b\u548c\u89c6\u89c9\u4e30\u5bcc\u7684\u73b0\u5b9e\u4e16\u754c\u4efb\u52a1\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        6.2 \u7528\u4e8e\u5bb6\u5ead\u6570\u5b66\u5b66\u4e60\u7684\u53e3\u8bed\u7406\u89e3\u8bc4\u4f30<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/41.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u968f\u7740\u6700\u8fd1\u5728\u4f1a\u8bdd\u5f0f\u4eba\u5de5\u667a\u80fd\u6280\u672f\u65b9\u9762\u7684\u8fdb\u6b65\uff0c\u501f\u52a9\u4e92\u52a8\u5f0f\u6570\u5b66\u5b66\u4e60\u5bb6\u5ead\u7cfb\u7edf\u63d0\u5347\u65e9\u671f\u513f\u7ae5\u6559\u80b2\u8d28\u91cf\u6b63\u9010\u6b65\u53d8\u6210\u73b0\u5b9e\u3002\u672c\u7814\u7a76\u901a\u8fc7\u5b9e\u65bd\u4e00\u79cd\u591a\u6a21\u6001\u5bf9\u8bdd\u7cfb\u7edf\uff0c\u5728\u5bb6\u4e2d\u652f\u6301\u57fa\u4e8e\u6e38\u620f\u7684\u5b66\u4e60\u4f53\u9a8c\uff0c\u5f15\u5bfc\u513f\u7ae5\u638c\u63e1\u57fa\u7840\u6570\u5b66\u6982\u5ff5\u3002\u7814\u7a76\u56e2\u961f\u63a2\u7d22\u4e86\u4efb\u52a1\u5bfc\u5411\u578b\u5bf9\u8bdd\u7cfb\u7edf\u5185\u90e8\u7684\u53e3\u8bed\u7406\u89e3<\/span>\uff08SLU\uff09<\/span>\u6d41\u7a0b\uff0c\u8be5\u6d41\u7a0b\u91c7\u7528\u4e86\u7ea7\u8054\u81ea\u52a8\u8bed\u97f3\u8bc6\u522b<\/span>\uff08ASR\uff09<\/span>\u548c\u81ea\u7136\u8bed\u8a00\u7406\u89e3<\/span>\uff08NLU\uff09<\/span>\u7ec4\u4ef6\uff0c\u5e76\u5728\u5b69\u5b50\u4eec\u53c2\u4e0e\u7684\u201c\u513f\u7ae5\u7a7a\u95f4\u201d\u5bb6\u5ead\u90e8\u7f72\u6570\u636e\u4e0a\u8fdb\u884c\u4e86\u8bc4\u4f30\u3002\u8fd9\u4e9b\u6570\u636e\u6765\u81ea\u4e8e\u5b69\u5b50\u4eec\u53c2\u4e0e\u7684\u6e38\u620f\u5316\u6570\u5b66\u5b66\u4e60\u6d3b\u52a8\u3002\u7814\u7a76\u9a8c\u8bc1\u4e86NLU\u591a\u4efb\u52a1\u67b6\u6784\u7684\u4f18\u52bf\uff0c\u5e76\u4e14\u8bd5\u9a8c\u4e86\u591a\u79cd\u9884\u8bad\u7ec3\u8bed\u8a00\u8868\u793a\uff0c\u7528\u4e8e\u6570\u5b66\u5b66\u4e60\u9886\u57df\u7684\u610f\u56fe\u8bc6\u522b\u548c\u5b9e\u4f53\u62bd\u53d6\u3002\u4e3a\u4e86\u5728\u771f\u5b9e\u5bb6\u5ead\u73af\u5883\u4e2d\u8bc6\u522b\u513f\u7ae5\u7684\u8bed\u97f3\uff0c\u7814\u7a76\u8c03\u67e5\u4e86\u82e5\u5e72ASR\u7cfb\u7edf\uff0c\u5305\u62ec\u8c37\u6b4c\u4e91\u670d\u52a1\u548c\u6700\u65b0\u7684\u5f00\u6e90Whisper\u89e3\u51b3\u65b9\u6848\uff0c\u6d89\u53ca\u4e0d\u540c\u5927\u5c0f\u7684\u6a21\u578b\u3002\u901a\u8fc7\u5728\u5e26\u566a\u58f0\u7684ASR\u8f93\u51fa\u4e0a\u6d4b\u8bd5\u8868\u73b0\u6700\u4f73\u7684NLU\u6a21\u578b\uff0c\u7814\u7a76\u8bc4\u4f30\u4e86SLU\u6d41\u7a0b\uff0c\u4ee5\u5ba1\u89c6\u5728\u771f\u5b9e\u5bb6\u5ead\u73af\u5883\u4e2d\u7406\u89e3\u513f\u7ae5\u6570\u5b66\u5b66\u4e60\u8bed\u97f3\u7684\u6311\u6218\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        6.3 \u901a\u8fc7\u5728\u5411\u91cf\u7b26\u53f7\u67b6\u6784\u4e2d\u5b66\u4e60\u89c4\u5219\u8fdb\u884c\u89c6\u89c9\u62bd\u8c61\u63a8\u7406\u7684\u6982\u7387\u5f52\u7eb3<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/20.pdf<\/span><\/section>\n
        \u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/github.com\/IBM\/learn-vector-symbolic-architectures-rule-formulations<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/p>\n

        \u62bd\u8c61\u63a8\u7406\u662f\u4eba\u7c7b\u667a\u80fd\u7684\u57fa\u77f3\uff0c\u7528\u4eba\u5de5\u667a\u80fd<\/span>\uff08AI\uff09<\/span>\u590d\u5236\u8fd9\u4e00\u80fd\u529b\u662f\u4e00\u4e2a\u6301\u7eed\u7684\u6311\u6218\u3002\u8be5\u7814\u7a76\u4e13\u6ce8\u4e8e\u901a\u8fc7\u5229\u7528\u5206\u5e03\u5f0f\u8ba1\u7b97\u548c\u5411\u91cf\u7b26\u53f7\u67b6\u6784<\/span>\uff08VSA\uff09<\/span>\u63d0\u4f9b\u7684\u8fd0\u7b97\u7b26\uff0c\u9ad8\u6548\u5730\u89e3\u51b3\u96f7\u6587\u9012\u8fdb\u77e9\u9635<\/span>\uff08RPM\uff09<\/span>\uff0c\u4e00\u79cd\u7528\u4e8e\u8bc4\u4f30\u62bd\u8c61\u63a8\u7406\u80fd\u529b\u7684\u89c6\u89c9\u6d4b\u8bd5\u3002\u8be5\u65b9\u6cd5\u65e0\u9700\u786c\u7f16\u7801RPM\u76f8\u5173\u7684\u89c4\u5219\u516c\u5f0f\uff0c\u800c\u662f\u80fd\u591f\u5728\u5bf9\u8bad\u7ec3\u6570\u636e\u4ec5\u8fdb\u884c\u4e00\u6b21\u904d\u5386\u7684\u60c5\u51b5\u4e0b\u5b66\u4e60VSA\u89c4\u5219\u516c\u5f0f<\/span>\uff08\u56e0\u6b64\u5f97\u540dLearn-VRF\uff09<\/span>\u3002\u5c3d\u7ba1\u53c2\u6570\u7d27\u51d1\uff0c\u8be5\u65b9\u6cd5\u4fdd\u6301\u4e86\u900f\u660e\u5ea6\u548c\u53ef\u89e3\u91ca\u6027\u3002Learn-VRF\u5728I-RAVEN\u7684\u5206\u5e03\u5185\u6570\u636e\u4e0a\u63d0\u4f9b\u4e86\u51c6\u786e\u7684\u9884\u6d4b\uff0c\u5e76\u5728\u5904\u7406\u672a\u89c1\u8fc7\u7684\u5c5e\u6027-\u89c4\u5219\u7ec4\u5408\u65f6\u8868\u73b0\u51fa\u5f3a\u5927\u7684\u5206\u5e03\u5916\u80fd\u529b\uff0c\u663e\u8457\u8d85\u8d8a\u4e86\u5305\u62ec\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5728\u5185\u7684\u7eaf\u8fde\u63a5\u4e3b\u4e49\u57fa\u7ebf\u3002<\/span><\/p>\n


        <\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \n
        \n
        \n

        <\/section>\n

        <\/section>\n
        \n
        <\/svg><\/section>\n<\/section>\n<\/section>\n
        \n

        7. \u5c0f\u6a21\u578b\u5b9e\u9a8c & \u8bad\u7ec3\u5fae\u8c03<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        7.1 \u5411\u5c0f\u578b Transformer \u6559\u6388\u7b97\u672f<\/span><\/strong>
        <\/section>\n

        <\/span><\/strong><\/section>\n

        <\/p>\n

        \n
        \n
        \n

        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/36.pdf<\/span><\/p>\n

        \u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/anonymous.4open.science\/r\/nanoGPT-25D2<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u5373\u4f7f\u662f\u5c0f\u578b Transformer\uff0c\u5728\u63a5\u53d7\u5927\u91cf\u6587\u672c\u6570\u636e\u8bad\u7ec3\u540e\uff0c\u4e5f\u80fd\u591f\u5c55\u73b0\u51fa\u5728\u57fa\u672c\u7b97\u672f\u7b49\u901a\u7528\u4efb\u52a1\u4e0a\u7684\u6d8c\u73b0\u80fd\u529b\uff0c\u5c3d\u7ba1\u8fd9\u4e9b\u4efb\u52a1\u5e76\u6ca1\u6709\u901a\u8fc7\u65e0\u76d1\u7763\u7684\u4e0b\u4e00\u4e2a\u8bcd\u9884\u6d4b\u76ee\u6807\u660e\u786e\u7f16\u7801\u3002\u672c\u7814\u7a76\u8c03\u67e5\u4e86\u4ece\u968f\u673a\u521d\u59cb\u5316\u5f00\u59cb\u8bad\u7ec3\u7684\u5c0f\u578b Transformer\uff0c\u5982\u4f55\u9ad8\u6548\u5b66\u4e60\u7b97\u672f\u8fd0\u7b97<\/span>\uff08\u6bd4\u5982\u52a0\u6cd5\u3001\u4e58\u6cd5\u548c\u6c42\u5e73\u65b9\u6839\u7b49\u521d\u7ea7\u51fd\u6570\uff09<\/span>\uff0c\u4f7f\u7528\u4e0b\u4e00\u4e2a\u8bcd\u9884\u6d4b\u76ee\u6807\u3002\u7814\u7a76\u8bc1\u5b9e\uff0c\u4f20\u7edf\u8bad\u7ec3\u6570\u636e\u5e76\u4e0d\u662f\u6700\u6709\u6548\u5730\u8fdb\u884c\u7b97\u672f\u5b66\u4e60\uff0c\u5e76\u4e14\u7b80\u5355\u7684\u683c\u5f0f\u66f4\u6539<\/strong>\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\u3002\u8fd9\u5bfc\u81f4\u4e86\u8bad\u7ec3\u6570\u636e\u89c4\u6a21\u51fd\u6570\u7684\u5267\u70c8\u76f8\u53d8\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e0e\u4f4e\u79e9\u77e9\u9635\u8865\u5168\u7684\u8054\u7cfb\u6765\u89e3\u91ca\u3002\u57fa\u4e8e\u5df2\u6709\u7684\u5de5\u4f5c\uff0c\u7814\u7a76\u8005\u5728\u5305\u542b\u4e2d\u95f4\u6b65\u9aa4\u7ed3\u679c\u7684\u94fe\u5f0f\u601d\u7ef4\u98ce\u683c\u6570\u636e\u4e0a\u8fdb\u884c\u8bad\u7ec3\u3002\u5373\u4f7f\u5728\u5b8c\u5168\u6ca1\u6709\u9884\u8bad\u7ec3\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4e5f\u663e\u8457\u5730\u540c\u65f6\u63d0\u9ad8\u4e86\u51c6\u786e\u6027\u3001\u6837\u672c\u590d\u6742\u6027\u548c\u6536\u655b\u901f\u5ea6\u3002\u7814\u7a76\u4e5f\u8003\u5bdf\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7b97\u672f\u4e0e\u6587\u672c\u6570\u636e\u4e4b\u95f4\u7684\u4e92\u52a8\uff0c\u5e76\u68c0\u9a8c\u4e86\u5c11\u91cf\u63d0\u793a\u3001\u9884\u8bad\u7ec3\u548c\u53c2\u6570\u7f29\u653e\u7684\u6548\u5e94\u3002\u6b64\u5916\uff0c\u6587\u7ae0\u8fd8\u8ba8\u8bba\u4e86\u4e0e\u957f\u5ea6\u6cdb\u5316\u76f8\u5173\u7684\u6311\u6218\u3002\u8be5\u5de5\u4f5c\u5f3a\u8c03\u4e86\u9ad8\u8d28\u91cf\u3001\u5177\u6709\u6307\u5bfc\u6027\u7684\u6570\u636e\u7684\u91cd\u8981\u6027<\/strong>\uff0c\u8fd9\u4e9b\u6570\u636e\u8003\u8651\u5230\u4e86\u4e0b\u4e00\u8bcd\u9884\u6d4b\u635f\u5931\u7684\u7279\u5b9a\u7279\u5f81\uff0c\u4ee5\u4fbf\u8fc5\u901f\u6fc0\u53d1\u51fa\u7b97\u672f\u80fd\u529b\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        7.2 \u5b66\u4e60\u6700\u5927\u516c\u7ea6\u6570\u2014\u2014Transformer \u4e2d\u7684\u53ef\u89e3\u91ca\u9884\u6d4b<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/8.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/p>\n

        \u4f5c\u8005\u8bad\u7ec3\u4e86\u5c0f\u578bTransformer\u6a21\u578b\u6765\u8ba1\u7b97\u4e24\u4e2a\u6b63\u6574\u6570\u7684\u6700\u5927\u516c\u7ea6\u6570<\/span>\uff08GCD\uff09<\/span>\uff0c\u5e76\u8bc1\u660e\u8fd9\u4e9b\u6a21\u578b\u7684\u9884\u6d4b\u662f\u5b8c\u5168\u53ef\u89e3\u91ca\u7684\u3002\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u6a21\u578b\u5b66\u4f1a\u4e86\u8bc6\u522b\u4e00\u4e2a\u9664\u6570\u5217\u8868D\uff0c\u5e76\u4e14\u80fd\u591f\u9884\u6d4b\u51fa\u8be5\u5217\u8868\u4e2d\u80fd\u540c\u65f6\u6574\u9664\u4e24\u4e2a\u8f93\u5165\u6574\u6570\u7684\u6700\u5927\u5143\u7d20\u3002\u7814\u7a76\u8fd8\u8868\u660e\uff0c\u8bad\u7ec3\u5206\u5e03\u5bf9\u6a21\u578b\u6027\u80fd\u6709\u663e\u8457\u5f71\u54cd\u3002\u4ec5\u4ece\u5747\u5300\u5206\u5e03\u7684\u64cd\u4f5c\u6570\u8fdb\u884c\u8bad\u7ec3\u7684\u6a21\u578b\u53ea\u638c\u63e1\u4e86\u5c11\u91cf\u7684GCD\uff0838\/100\uff09\u3002\u5f53\u4f7f\u7528\u5bf9\u6570\u5747\u5300\u5206\u5e03\u7684\u64cd\u4f5c\u6570\u8fdb\u884c\u8bad\u7ec3\u65f6\uff0c\u6a21\u578b\u6027\u80fd\u63d0\u9ad8\u5230\u6b63\u786e\u9884\u6d4b73\u4e2aGCD\uff0c\u800c\u57fa\u4e8e\u5bf9\u6570\u5747\u5300\u5206\u5e03\u7684GCD\u8fdb\u884c\u8bad\u7ec3\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u5347\u6027\u80fd\uff0c\u8fbe\u523091\u4e2a\u6b63\u786e\u7684GCD\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        7.3 \u7cfb\u7edf\u63a8\u7406\u4efb\u52a1\u4e2d\u7684\u6301\u7eed\u5b66\u4e60\u4e0e\u5206\u5e03\u5916\u6cdb\u5316<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/54.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u4eba\u7c7b\u7ecf\u5e38\u80fd\u591f\u4ece\u4e00\u7cfb\u5217\u72ed\u7a84\u7684\u4f8b\u5b50\u4e2d\u5b66\u4e60\u65b0\u7684\u89e3\u51b3\u95ee\u9898\u7b56\u7565\uff0c\u5e76\u5c06\u8fd9\u4e9b\u7b56\u7565\u6cdb\u5316\u5230\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u672a\u66fe\u6d89\u53ca\u7684\u5b9e\u4f8b\uff0c\u4f46\u795e\u7ecf\u7f51\u7edc\u5728\u6b64\u65b9\u9762\u7684\u6cdb\u5316\u80fd\u529b\u4ecd\u7136\u9762\u4e34\u6311\u6218\u3002\u8fd9\u79cd\u9650\u5236\u5f71\u54cd\u4e86\u6570\u5b66\u6280\u5de7\u7684\u5b66\u4e60\uff0c\u8fd9\u4e9b\u6280\u5de7\u9002\u7528\u4e8e\u65e0\u754c\u7684\u95ee\u9898\u7a7a\u95f4<\/span>\uff08\u4f8b\u5982\uff0c\u6240\u6709\u5b9e\u6570\uff09<\/span>\u3002\u7814\u7a76\u8005\u5229\u7528\u795e\u7ecf\u7f51\u7edc\u63a2\u7d22\u4e86\u8fd9\u4e00\u5c40\u9650\u6027\uff0c\u5b83\u4eec\u5728\u8bad\u7ec3\u89e3\u51b36\u00d76\u6570\u72ec\u8c1c\u9898\u7684\u7279\u5b9a\u5355\u5143\u683c\u7684\u7b56\u7565\u65f6\u4f7f\u7528\u4e86\u4e00\u79cd\u65b0\u9896\u7684\u8bfe\u7a0b\u2014\u2014\u6a21\u578b\u9996\u5148\u5b66\u4e60\u4e24\u4e2a\u521d\u7ea7\u4efb\u52a1\uff0c\u968f\u540e\u7814\u7a76\u8005\u5728\u8bad\u7ec3\u66f4\u590d\u6742\u89e3\u51b3\u7b56\u7565\u53ef\u80fd\u4f1a\u9047\u5230\u7684\u8bad\u7ec3\u6837\u4f8b\u5b50\u96c6\u671f\u95f4\u8bc4\u4f30\u5176\u5206\u5e03\u5916\u6cdb\u5316\u80fd\u529b\u3002\u57fa\u7ebf\u6a21\u578b\u80fd\u591f\u638c\u63e1\u8bad\u7ec3\u5206\u5e03\uff0c\u4f46\u672a\u80fd\u5728\u5206\u5e03\u5916\u8fdb\u884c\u6cdb\u5316\u3002\u7136\u800c\uff0c\u7814\u7a76\u8005\u4ecb\u7ecd\u4e86\u4e00\u7ec4\u8db3\u4ee5\u652f\u6301\u9ad8\u51c6\u786e\u5ea6\u548c\u53ef\u9760\u7684\u5206\u5e03\u5916\u6cdb\u5316\u7684\u6269\u5c55\u7ec4\u5408\u3002\u8fd9\u4e9b\u7ed3\u679c\u4e3a\u589e\u5f3a\u5728\u81ea\u7136\u6570\u636e\u96c6\u4e2d\u7531\u4e8e\u6570\u636e\u5206\u5e03\u9ad8\u5ea6\u4e0d\u5e73\u8861\u800c\u8bad\u7ec3\u51fa\u7684\u6a21\u578b\u7684\u5065\u58ee\u6027\u63d0\u4f9b\u4e86\u65b0\u7684\u65b9\u5411\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        7.4 \u591a\u6837\u5316\u76d1\u7763\u7684\u539f\u5219\u63a2\u7d22<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/17.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u901a\u8fc7\u4e0b\u4e00\u4e2a\u8bcd\u9884\u6d4b\u6765\u8bad\u7ec3\u5927\u578b Transformer \u6a21\u578b\uff0c\u63a8\u52a8\u4e86AI\u9886\u57df\u7684\u91cd\u5927\u8fdb\u6b65\u3002\u5c3d\u7ba1\u8fd9\u79cd\u751f\u6210\u5f0f AI \u7684\u65b9\u6cd5\u53d6\u5f97\u4e86\u663e\u8457\u6210\u679c\uff0c\u4f46\u5b83\u6781\u5ea6\u4f9d\u8d56\u4e8e\u4eba\u7c7b\u76d1\u7763\u3002\u5373\u4fbf\u662f\u50cfChatGPT\u8fd9\u6837\u7684\u6700\u5148\u8fdbAI\u6a21\u578b\uff0c\u4e5f\u9700\u8981\u901a\u8fc7\u4eba\u7c7b\u6f14\u793a\u8fdb\u884c\u5fae\u8c03\uff0c\u8fd9\u8981\u6c42\u5927\u91cf\u7684\u4eba\u5de5\u8f93\u5165\u548c\u9886\u57df\u4e13\u4e1a\u77e5\u8bc6\u3002\u8fd9\u79cd\u5bf9\u4eba\u7c7b\u76d1\u7763\u7684\u9ad8\u5ea6\u4f9d\u8d56\u6210\u4e3aAI\u521b\u65b0\u53d1\u5c55\u7684\u4e00\u4e2a\u91cd\u8981\u969c\u788d\u3002\u4e3a\u4e86\u5e94\u5bf9\u8fd9\u4e00\u6311\u6218\uff0c\u7814\u7a76\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u88ab\u79f0\u4e3a\u63a2\u7d22\u6027AI<\/span>\uff08EAI\uff09<\/span>\u7684\u65b0\u8303\u5f0f\uff0c\u5176\u76ee\u6807\u662f\u81ea\u4e3b\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e<\/strong>\u3002EAI\u4ece\u65e0\u76d1\u7763\u5f3a\u5316\u5b66\u4e60<\/span>\uff08RL\uff09<\/span>\u7684\u9884\u8bad\u7ec3\u4e2d\u6c72\u53d6\u7075\u611f\uff0c\u5728\u81ea\u7136\u8bed\u8a00\u7a7a\u95f4\u5b9e\u73b0\u63a2\u7d22\u3002\u8be5\u65b9\u6cd5\u5229\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u6765\u8bc4\u4f30\u751f\u6210\u5185\u5bb9\u7684\u65b0\u9896\u6027\uff0c\u5e76\u5305\u542b\u4e24\u4e2a\u5173\u952e\u7ec4\u6210\u90e8\u5206\uff1a\u4e00\u4e2a\u6309\u7167\u63a2\u7d22\u539f\u5219\u751f\u6210\u65b0\u9896\u5185\u5bb9\u7684\u201c\u884c\u52a8\u8005\u201d\u548c\u4e00\u4e2a\u8bc4\u4f30\u5e76\u63d0\u4f9b\u6307\u5bfc\u6027\u6279\u8bc4\u4ee5\u5f15\u5bfc\u884c\u52a8\u8005\u7684\u201c\u8bc4\u4ef7\u8005\u201d\u3002\u5b9e\u8bc1\u8bc4\u4f30\u663e\u793a\uff0cEAI\u5728\u590d\u6742\u63a8\u7406\u4efb\u52a1\u4e0a\u663e\u8457\u63d0\u5347\u4e86\u6a21\u578b\u6027\u80fd\uff0c\u514b\u670d\u4e86\u5bf9\u4eba\u529b\u5bc6\u96c6\u578b\u76d1\u7763\u7684\u4f9d\u8d56\u9650\u5236\u3002<\/span><\/p>\n


        <\/span><\/p>\n


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        <\/svg><\/section>\n<\/section>\n<\/section>\n
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        8. \u8ba4\u77e5\u79d1\u5b66<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        8.1 AI for Mathematics: \u8ba4\u77e5\u79d1\u5b66\u89c6\u89d2<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/38.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u6570\u5b66\u662f\u4eba\u7c7b\u79cd\u65cf\u5f00\u53d1\u548c\u4f7f\u7528\u7684\u6700\u5f3a\u5927\u7684\u6982\u5ff5\u7cfb\u7edf\u4e4b\u4e00\u3002\u81ea\u52a8\u5316\u6570\u5b66\u5bb6\u7684\u68a6\u60f3\u5728\u4eba\u5de5\u667a\u80fd<\/span>\uff08AI\uff09<\/span>\u7684\u5386\u53f2\u4e2d\u5360\u6709\u4e00\u5e2d\u4e4b\u5730\u3002\u7279\u522b\u662f\u5927\u578b\u8bed\u8a00\u6a21\u578b<\/span>\uff08LLMs\uff09<\/span>\u7684\u98de\u901f\u8fdb\u6b65\u91cd\u65b0\u70b9\u71c3\u4e86\u5e7f\u6cdb\u5174\u8da3\uff0c\u4fc3\u4f7f\u4eba\u4eec\u5efa\u7acb\u6b64\u7c7b\u7cfb\u7edf\u3002\u672c\u6587\u4ece\u8ba4\u77e5\u79d1\u5b66\u7684\u89c6\u89d2\u53cd\u601d\u8fd9\u4e9b\u76ee\u6807\u3002\u4f5c\u8005\u6307\u51fa\u4e86\u51e0\u4e2a\u8ba4\u77e5\u79d1\u5b66\u9886\u57df\u4e2d\u65e2\u7ecf\u5178\u53c8\u6301\u7eed\u7684\u7814\u7a76\u65b9\u5411\uff0c\u8ba4\u4e3a\u8fd9\u4e9b\u65b9\u5411\u5bf9\u4e8e\u90a3\u4e9b\u5bfb\u6c42\u6784\u5efa\u771f\u6b63\u8fbe\u5230\u6216\u8d85\u8d8a\u4eba\u7c7b\u6c34\u5e73\u7684\u6570\u5b66\u7cfb\u7edf\u7684AI\u5b9e\u8df5\u8005\u6781\u4e3a\u91cd\u8981\u3002\u6587\u7ae0\u6700\u540e\u63d0\u51fa\u4e86\u4e00\u4e9b\u5f00\u653e\u6027\u95ee\u9898\uff0c\u8ba4\u4e3a\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u9700\u8981\u591a\u5b66\u79d1\u5408\u4f5c\uff1a\u8ba4\u77e5\u79d1\u5b66\u5bb6\u3001AI\u7814\u7a76\u5458\u4ee5\u53ca\u6570\u5b66\u5bb6\u5171\u540c\u52aa\u529b\uff0c\u4ee5\u671f\u6784\u5efa\u66f4\u597d\u7684\u6570\u5b66AI\u7cfb\u7edf\uff0c\u8fd9\u4e0d\u4ec5\u53ef\u4ee5\u63a8\u8fdb\u6570\u5b66\u7684\u8fb9\u754c\uff0c\u8fd8\u80fd\u63ed\u793a\u4eba\u7c7b\u5982\u4f55\u5177\u5907\u5b8c\u6210\u8fd9\u6837\u4f1f\u5927\u8ba4\u77e5\u4efb\u52a1\u7684\u80fd\u529b\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        8.2 \u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5bf9\u6570\u91cf\u6982\u5ff5\u7684\u654f\u611f\u6027<\/span><\/strong>
        <\/p>\n


        <\/span><\/strong><\/p>\n

        <\/p>\n

        \n
        \n
        \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/mathai2023.github.io\/papers\/37.pdf<\/span><\/section>\n<\/section>\n<\/blockquote>\n


        <\/span><\/p>\n

        \u6570\u7684\u672c\u8d28\u662f\u6570\u5b66\u54f2\u5b66\u4e2d\u7684\u4e00\u4e2a\u7ecf\u5178\u8bae\u9898\u3002\u8ba4\u77e5\u79d1\u5b66\u5bb6\u5df2\u8bc1\u5b9e\uff0c\u4eba\u7c7b\u5fc3\u7406\u4e0a\u5c06\u6570\u5b57\u8868\u793a\u4e3a\u7ec4\u7ec7\u6210\u5fc3\u7406\u6570\u7ebf<\/span>\uff08MNL\uff09<\/span>\u7684\u91cf\u7ea7\u3002\u672c\u7814\u7a76\u63a2\u8ba8\u4e86\u5728\u5b66\u4e60\u5206\u7c7b\u56fe\u50cf\u65f6\uff0c\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u662f\u5426\u4f1a\u65e0\u610f\u4e2d\u5b66\u5230\u5173\u4e8e\u6570\u5b57\u548c\u6570\u91cf\u7684\u6982\u5ff5<\/strong>\u3002\u4e8b\u5b9e\u786e\u5b9e\u5982\u6b64\u3002\u4e00\u4e2a\u4ee3\u8868\u6027\u7684\u6a21\u578b\u663e\u793a\u51fa\u8ddd\u79bb\u6548\u5e94\u3001\u5927\u5c0f\u6548\u5e94\u548c\u6bd4\u4f8b\u6548\u5e94\uff0c\u8fd9\u4e9b\u90fd\u662f\u4eba\u7c7b\u6570\u91cf\u8868\u793a\u4e2d\u7684\u6807\u5fd7\u6027\u7279\u5f81\u3002\u901a\u8fc7\u5bf9\u5176\u6f5c\u5728\u8868\u793a\u8fdb\u884c\u591a\u7ef4\u5c3a\u5ea6\u5206\u6790<\/span>\uff08MDS\uff09<\/span>\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u8fd9\u4e9b\u8868\u793a\u4e0e\u4eba\u7c7b\u6240\u8bb0\u5f55\u7684\u5fc3\u7406\u6570\u7ebf\u6709\u7740\u5bc6\u5207\u7684\u76f8\u4f3c\u6027\u3002\u8fd9\u4e9b\u53d1\u73b0\u6311\u6218\u4e86\u53d1\u5c55\u79d1\u5b66\u4e2d\u7684\u89c2\u70b9\uff0c\u8be5\u89c2\u70b9\u8ba4\u4e3a\u6570\u5b57\u662f\u6240\u6709\u4eba\u7c7b\u5a74\u513f\u56fa\u6709\u7684\u201c\u6838\u5fc3\u77e5\u8bc6\u201d<\/strong>\uff0c\u5e76\u4e14\u63d0\u4f9b\u4e86\u6570\u5b57\u6982\u5ff5\u53ef\u5b66\u4e60\u6027\u7684\u5b58\u5728\u8bc1\u660e\u3002<\/span><\/p>\n


        <\/p>\n


        <\/section>\n
        \n
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        \u4f5c\u8005\u7b80\u4ecb<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

        \n
        <\/section>\n<\/section>\n
        \u738b\u81f3\u5b8f<\/strong>\uff0c\u534e\u4e1c\u5e08\u8303\u5927\u5b66\u8ba1\u7b97\u673a\u5b66\u9662\u5728\u8bfb\u535a\u58eb\uff0c\u672c\u7855\u57fa\u7840\u6570\u5b66\u4e13\u4e1a\u3002\u672c\u79d1\u83b7\u5168\u56fd\u5927\u5b66\u751f\u6570\u5b66\u7ade\u8d5b\u51b3\u8d5b\u4e00\u7b49\u5956\uff0c\u5168\u56fd\u9ad8\u6821\u6570\u5b66\u5bc6\u7801\u6311\u6218\u8d5b\u4e2d\u5357\u8d5b\u533a\u4e8c\u7b49\u5956\u7b49\u7ade\u8d5b\u5956\u9879\uff0c\u7855\u58eb\u81ea\u5b66 GAP\uff0cSageMath \u7b49\u4ee3\u6570\u7f16\u7a0b\u8bed\u8a00\uff0c\u63a2\u7d22 Programming For Math\uff0c\u5f53\u524d\u65b9\u5411\u4e3a\u5927\u8bed\u8a00\u6a21\u578b\u4e0e\u57fa\u7840\u6570\u5b66\u7684\u878d\u5408\u7814\u7a76\u3002<\/span><\/section>\n
        \u5b66\u8005\u4e3b\u9875\uff1ahttps:\/\/pattern.swarma.org\/master\/878<\/span><\/section>\n

        <\/section>\n

        <\/section>\n
        \u5728\u96c6\u667a\u4ff1\u4e50\u90e8\u300c\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u300d\u8bfb\u4e66\u4f1a<\/a>\u4e2d\uff0c\u738b\u81f3\u5b8f\u505a\u4e86\u4e3b\u9898\u4e3a\u201c\u667a\u80fd\u4f53\u4e0e\u6570\u5b66\u7684\u4ea4\u6c47\u201d\u7684\u5206\u4eab\uff0c\u4ecb\u7ecd\u667a\u80fd\u4f53\u5728\u6570\u5b66\u9886\u57df\u7684\u5e94\u7528\uff0c\u8bfb\u4e66\u4f1a\u56de\u653e\u89c6\u9891\u5df2\u7ecf\u4e0a\u7ebf\uff0c\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u6df1\u5165\u4e86\u89e3\u3002<\/span><\/section>\n
        <\/section>\n
        https:\/\/pattern.swarma.org\/study_group_issue\/570<\/span><\/section>\n

        <\/section>\n

        <\/section>\n
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        \u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a<\/strong>
        <\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


        <\/section>\n

        \u6570\u5341\u5e74\u6765\uff0c\u4eba\u5de5\u667a\u80fd\u7684\u7406\u8bba\u53d1\u5c55\u548c\u6280\u672f\u5b9e\u8df5\u4e00\u76f4\u4e0e\u79d1\u5b66\u63a2\u7d22\u76f8\u4f34\u800c\u751f\uff0c\u5c24\u5176\u5728\u4ee5\u5927\u6a21\u578b\u4e3a\u4ee3\u8868\u7684\u4eba\u5de5\u667a\u80fd\u6280\u672f\u5e94\u7528\u96c6\u4e2d\u7206\u53d1\u7684\u5f53\u4e0b\uff0c\u4eba\u5de5\u667a\u80fd\u6b63\u5728\u52a0\u901f\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7b49\u57fa\u7840\u79d1\u5b66\u7684\u9769\u65b0\uff0c\u800c\u8fd9\u4e9b\u5b66\u79d1\u4e5f\u5728\u53cd\u8fc7\u6765\u542f\u53d1\u4eba\u5de5\u667a\u80fd\u6280\u672f\u521b\u65b0\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u4f5c\u4e3a\u517c\u5177\u7406\u8bba\u5c5e\u6027\u4e0e\u5de5\u5177\u5c5e\u6027\u7684\u91cd\u8981\u57fa\u7840\u5b66\u79d1\uff0c\u4e0e\u4eba\u5de5\u667a\u80fd\u5173\u7cfb\u751a\u5bc6\uff0c\u76f8\u8f85\u76f8\u6210\u3002\u4e00\u65b9\u9762\uff0c\u4eba\u5de5\u667a\u80fd\u5728\u89e3\u51b3\u6570\u5b66\u9886\u57df\u7684\u8bf8\u591a\u5de5\u7a0b\u95ee\u9898\u3001\u7406\u8bba\u95ee\u9898\u4e43\u81f3\u5723\u676f\u96be\u9898\u4e0a\u5c61\u521b\u8bb0\u5f55\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6570\u5b66\u6301\u7eed\u4e3a\u4eba\u5de5\u667a\u80fd\u6784\u7b51\u7406\u8bba\u57fa\u77f3\u5e76\u62d3\u5c55\u5176\u672a\u6765\u7a7a\u95f4\u3002\u8fd9\u4e24\u4e2a\u5173\u952e\u9886\u57df\u7684\u4ea4\u53c9\u878d\u5408\uff0c\u6b63\u5728\u63ed\u5f00\u4e0b\u4e2a\u65f6\u4ee3\u7684\u79d1\u5b66\u4e4b\u5e55\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u4e3a\u4e86\u63a2\u7d22\u6570\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u6df1\u5ea6\u878d\u5408\u7684\u53ef\u80fd\u6027\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u540c\u6d4e\u5927\u5b66\u7279\u8058\u7814\u7a76\u5458\u9648\u5c0f\u6768\u3001\u6e05\u534e\u5927\u5b66\u4ea4\u53c9\u4fe1\u606f\u5b66\u9662\u52a9\u7406\u6559\u6388\u8881\u6d0b\u3001\u5357\u6d0b\u7406\u5de5\u5927\u5b66\u526f\u6559\u6388\u590f\u514b\u6797\u4e09\u4f4d\u8001\u5e08\uff0c\u5171\u540c\u53d1\u8d77\u201c\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u201d\u8bfb\u4e66\u4f1a\uff0c\u5e0c\u671b\u4ece AI\u3000for\u3000Math\uff0cMath\u3000for\u3000AI \u4e24\u4e2a\u65b9\u9762\u6df1\u5165\u63a2\u8ba8\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u7684\u5bc6\u5207\u8054\u7cfb\u3002<\/span><\/p>\n


        <\/section>\n
        <\/span><\/a><\/section>\n

        <\/section>\n

        \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/p>\n

        \u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1aAI for Math\uff0cMath for AI<\/a><\/span><\/p>\n


        <\/span><\/section>\n

        <\/span><\/section>\n
        \n
        \n

        \u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

        1.  <\/strong>\u6570\u5b66\u63a2\u7d22\u7684\u672a\u6765\uff1a\u4eceAI\u5f15\u5bfc\u4eba\u7c7b\u76f4\u89c9\u5230\u6570\u5b66\u5927\u8bed\u8a00\u6a21\u578b<\/a><\/strong><\/span><\/section>\n
        2. <\/strong>\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u524d\u6cbf\u7efc\u8ff0\uff1a\u5982\u4f55\u501f\u52a9 AI \u53d1\u73b0\u6570\u5b66\u89c4\u5f8b\uff1f<\/a><\/strong><\/span><\/section>\n
        3. <\/strong>\u5f53\u673a\u5668\u5b66\u4e60\u9047\u89c1\u62d3\u6251\uff1a\u62d3\u6251\u6570\u636e\u5206\u6790\u4e0e\u62d3\u6251\u6df1\u5ea6\u5b66\u4e60<\/a><\/strong><\/span><\/section>\n
        4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
        5. <\/strong>\u52a0\u5165\u96c6\u667a\u5b66\u56edVIP\uff0c\u4e00\u6b21\u6027\u83b7\u53d6\u96c6\u667a\u5e73\u53f0\u6240\u6709\u5185\u5bb9\u8d44\u6e90<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
        6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n<\/section>\n


        <\/p>\n<\/section>\n


        <\/p>\n

        \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/section>\n

        \u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200b<\/p>\n

        <\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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