{"id":45098,"date":"2023-09-13T18:51:19","date_gmt":"2023-09-13T10:51:19","guid":{"rendered":"https:\/\/swarma.org\/?p=45098"},"modified":"2023-09-13T18:51:19","modified_gmt":"2023-09-13T10:51:19","slug":"%e5%a4%a7%e6%a8%a1%e5%9e%8b%e7%9a%84%e8%83%bd%e5%8a%9b%e8%be%b9%e7%95%8c%e5%9c%a8%e5%93%aa%e9%87%8c%ef%bc%9f%e6%9d%a5%e8%87%aa%e8%8c%83%e7%95%b4%e8%ae%ba%e8%a7%86%e8%a7%92%e7%9a%84%e7%ad%94%e6%a1%88","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=45098","title":{"rendered":"\u5927\u6a21\u578b\u7684\u80fd\u529b\u8fb9\u754c\u5728\u54ea\u91cc\uff1f\u6765\u81ea\u8303\u7574\u8bba\u89c6\u89d2\u7684\u7b54\u6848"},"content":{"rendered":"
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\u7814\u7a76\u9886\u57df\uff1a\u8303\u7574\u8bba\uff0c<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong>\u4eba\u5de5\u667a\u80fd\uff0c\u673a\u5668\u5b66\u4e60\uff0c\u5927\u8bed\u8a00\u6a21\u578b\uff0cAI + Math<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/section>\n<\/section>\n
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1. \u8303\u7574\u8bba\u662f\u4ec0\u4e48\uff1f<\/span><\/strong>
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2. \u76d1\u7763\u5b66\u4e60\u7684\u8303\u7574\u8bba\u89c6\u89d2<\/span><\/strong><\/p>\n

3. \u81ea\u76d1\u7763\u5b66\u4e60\u7684\u8303\u7574\u8bba\u89c6\u89d2<\/span><\/strong><\/p>\n

4. \u63d0\u793a\u8c03\u4f18\uff08Prompt tuning\uff09: \u89c1\u591a\u624d\u80fd\u8bc6\u5e7f<\/span><\/strong><\/p>\n

5. \u5fae\u8c03\uff08Fine tuning\uff09: \u8868\u5f81\u4e0d\u4e22\u4fe1\u606f<\/span><\/strong><\/p>\n

6. \u8ba8\u8bba\u4e0e\u603b\u7ed3<\/span><\/strong><\/p>\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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\u4eca\u5929\uff0c\u6211\u7ed9\u5927\u5bb6\u4ecb\u7ecd\u4e00\u4e0b\u6211\u5728ICML’2023\u53d1\u8868\u7684\u8bba\u6587On the Power of Foundation Models\uff0c\u4ece\u8303\u7574\u8bba\u7684\u89d2\u5ea6\u7ed9\u51fa\u4e00\u4e2a\u7b54\u6848\u3002<\/span><\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1aOn the Power of Foundation Models<\/span><\/span><\/section>\n
\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/proceedings.mlr.press\/v202\/yuan23b.html<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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

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

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

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<\/p>\n

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<\/p>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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\u81ea\u76d1\u7763\u5b66\u4e60\u7684\u8303\u7574\u8bba\u89c6\u89d2<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

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\u9884\u8bad\u7ec3\u4efb\u52a1\u4e0e\u8303\u7574<\/span><\/strong><\/span><\/h3>\n


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

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

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\u5177\u4f53\u6765\u8bf4\uff1a<\/span><\/section>\n
    \n
  • \n
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  • \n
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  • \n

    \u8bed\u8a00\u6a21\u578b<\/strong>\u3002\u5bf9\u8c61 X \u662f\u4e00\u4e2a\u53e5\u5b50\uff0c\u5bf9\u8c61 Y \u5219\u662f\u5b83\u7684\u7eed\u5199\uff0c\u53ea\u6709\u6700\u540e\u4e00\u4e2a\u8bcd\u4e0d\u540c\u3002\u4f8b\u5982\uff0c \u6211\u4eca\u5929\u5f88\u5f00X=\u2018\u2018\u6211\u4eca\u5929\u5f88\u5f00\u201d\uff0c \u6211\u4eca\u5929\u5f88\u5f00\u5fc3Y=\u2018\u2018\u6211\u4eca\u5929\u5f88\u5f00\u5fc3\u201d\u3002\u8bed\u8a00\u6a21\u578b\u5173\u5fc3\u7684\u662f Pr(Y|X) \uff0c\u6211\u4eec\u628a\u5b83\u5b9a\u4e49\u4e3aHomC<\/sub><\/span>(X,Y) \u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


    <\/p>\n

    \u6362\u53e5\u8bdd\u8bf4\uff0c\u5f53\u6211\u4eec\u5728\u4e00\u4e2a\u6570\u636e\u96c6\u4e0a\u5b9a\u4e49\u4e86\u9884\u8bad\u7ec3\u4efb\u52a1\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u5b9a\u4e49\u4e86\u4e00\u4e2a\u5305\u542b\u5bf9\u5e94\u5173\u7cfb\u7ed3\u6784\u7684\u8303\u7574\u3002\u9884\u8bad\u7ec3\u4efb\u52a1\u7684\u5b66\u4e60\u76ee\u6807\uff0c\u5c31\u662f\u8ba9\u6a21\u578b\u628a\u8fd9\u4e2a\u8303\u7574\u5b66\u597d\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u770b\u4e00\u4e0b\u7406\u60f3\u6a21\u578b\u7684\u6982\u5ff5\u3002<\/span><\/p>\n


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

    \u7406\u60f3\u6a21\u578b<\/span><\/strong><\/span><\/h3>\n


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

    \u7ed9\u5b9a\u4e00\u4e2a\u9884\u8bad\u7ec3\u6a21\u578b <\/sub><\/span>\uff0c\u5b83\u4ec0\u4e48\u65f6\u5019\u662f\u6bd4\u8f83\u7406\u60f3\u7684\u5462\uff1f\u5f88\u7b80\u5355\uff0c\u5f53\u5b83\u8ba1\u7b97\u51fa\u7684\u7279\u5f81\u53ef\u4ee5\u7528\u6765\u5f88\u65b9\u4fbf\u5730\u523b\u753b\u8303\u7574 <\/sub><\/span> \u5185\u90e8\u5173\u7cfb\u7684\u65f6\u5019\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u6982\u5ff5\u4e0d\u592a\u660e\u767d\u7684\u670b\u53cb\uff0c\u53ef\u4ee5\u53c2\u89c1\u4e0a\u4e00\u7bc7\u300a\u5bf9\u6bd4\u5b66\u4e60\u5728\u5b66\u5565\uff1f\u300b<\/span>\uff08https:\/\/zhuanlan.zhihu.com\/p\/634466306\uff09<\/span>\uff0c\u91cc\u9762\u6709\u4e00\u4e9b\u76f4\u89c2\u7684\u4f8b\u5b50\u3002<\/span><\/p>\n


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

    \u4e25\u683c\u6765\u8bf4\uff0c\u7ed9\u5b9a\u7531\u9884\u8bad\u7ec3\u4efb\u52a1\u5b9a\u4e49\u7684\u8303\u7574 <\/sub><\/span> \uff0c\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u9884\u5b9a\u4e49\u7684\u51fd\u6570 <\/sub><\/span>\uff0c\u4f7f\u5f97\u5bf9\u4efb\u610f\u7684 <\/sub><\/span>\uff0c\u90a3\u4e48\u6a21\u578b <\/sub><\/span> \u5c31\u662f\u7406\u60f3\u7684\u3002<\/span><\/p>\n


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

    \u5728\u8fd9\u91cc\uff0c\u201c\u6570\u636e\u65e0\u5173\u201d\u610f\u5473\u7740 k<\/span>f<\/sub><\/span> \u662f\u5728\u770b\u5230\u6570\u636e\u4e4b\u524d\u5c31\u9884\u5148\u5b9a\u4e49\u7684\uff1b\u4f46\u4e0b\u6807 f \u5219\u8868\u793ak<\/span>f<\/sub><\/span>\u53ef\u4ee5\u901a\u8fc7\u9ed1\u76d2\u8c03\u7528\u7684\u65b9\u5f0f\u4f7f\u7528 f \u548c f-1<\/span><\/sup> \u8fd9\u4e24\u4e2a\u51fd\u6570\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c k<\/span>f<\/sub><\/span> \u662f\u4e00\u4e2a\u201c\u7b80\u5355\u201d\u7684\u51fd\u6570\uff0c\u4f46\u53ef\u4ee5\u501f\u52a9\u6a21\u578b f \u7684\u80fd\u529b\u6765\u8868\u793a\u66f4\u590d\u6742\u7684\u5173\u7cfb\u3002\u8fd9\u4e00\u70b9\u53ef\u80fd\u4e0d\u592a\u597d\u7406\u89e3\uff0c\u6211\u4eec\u7528\u538b\u7f29\u7b97\u6cd5\u6765\u6253\u4e2a\u6bd4\u65b9\u3002\u538b\u7f29\u7b97\u6cd5\u672c\u8eab\u53ef\u80fd\u662f\u6570\u636e\u76f8\u5173\u7684\uff0c\u6bd4\u5982\u5b83\u53ef\u80fd\u662f\u9488\u5bf9\u6570\u636e\u5206\u5e03\u8fdb\u884c\u4e86\u7279\u6b8a\u4f18\u5316\u3002\u7136\u800c\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u6570\u636e\u65e0\u5173\u7684\u51fd\u6570 k<\/span>f<\/sub><\/span> \uff0c\u5b83\u65e0\u6cd5\u8bbf\u95ee\u6570\u636e\u5206\u5e03\uff0c\u4f46\u53ef\u4ee5\u8c03\u7528\u538b\u7f29\u7b97\u6cd5\u6765\u89e3\u538b\u6570\u636e\uff0c\u56e0\u4e3a\u201c\u8c03\u7528\u538b\u7f29\u7b97\u6cd5\u201d\u8fd9\u4e00\u64cd\u4f5c\u662f\u6570\u636e\u65e0\u5173\u7684\u3002<\/span><\/p>\n


    <\/p>\n

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      \n
    • \n
      \u5bf9\u6bd4\u5b66\u4e60<\/strong>\u3002\u5728\u5bf9\u6bd4\u5b66\u4e60\u4e2d\uff0c\u4efb\u4f55\u4e24\u4e2a\u5bf9\u8c61\u4e4b\u95f4\u7684\u5173\u7cfb\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u5b9e\u6570\u8868\u793a\uff0c\u56e0\u6b64 <\/span><\/sub><\/span> \u53ef\u4ee5\u88ab\u770b\u4f5c\u4ee5 kf<\/sub><\/span> \u4e3a\u6838\u51fd\u6570\u7684\u7a7a\u95f4\u3002\u4f8b\u5982\uff0c\u5728SimCLR[1]\u548cMoCo[2]\u4e2d\uff0c k<\/span>f<\/sub><\/span> \u662f\u4e00\u4e2a\u7b80\u5355\u7684\u9ad8\u65af\u6838\u51fd\u6570\u3002<\/span><\/section>\n<\/li>\n
    • \n
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    • \n

      \u8bed\u8a00\u6a21\u578b<\/strong>\u3002\u6211\u4eec\u60f3\u8981\u8ba1\u7b97 Pr(Y|X) \uff0c\u5176\u4e2d Y \u662f X \u7684\u7eed\u5199\uff0c\u53ea\u6709\u6700\u540e\u4e00\u4e2a\u8bcd\u4e0d\u540c\u3002k<\/span>f<\/sub><\/span> \u8fd0\u884c\u4e00\u4e2a\u7ebf\u6027\u51fd\u6570<\/span>\uff08\u53ef\u4ee5\u9884\u5148\u5b9a\u4e49\u597d\uff0c\u4e0d\u53c2\u4e0e\u4f18\u5316\uff09<\/span>\u548c\u4e00\u4e2aSoftmax\u51fd\u6570\u6765\u8ba1\u7b97\u4e0b\u4e00\u4e2a\u8bcd\u7684\u6982\u7387\u5206\u5e03\u3002\u57fa\u4e8e\u8fd9\u4e2a\u5206\u5e03\uff0ck<\/span>f<\/sub><\/span> \u8fd0\u884cf<\/span>-1<\/span><\/sup>(f(Y)) \u6765\u63d0\u53d6 Y\uff0c\u5e76\u8ba1\u7b97 Pr(Y|X) \u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


      <\/p>\n

      \u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u8fd9\u4e48\u8bf4\uff1a\u9884\u8bad\u7ec3\u5b66\u4e60\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u5728\u5bfb\u627e\u7406\u60f3\u6a21\u578b f \u7684\u8fc7\u7a0b\u3002<\/strong><\/span><\/p>\n


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

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      <\/p>\n

      \u7ed9\u5b9a\u7531\u9884\u8bad\u7ec3\u4efb\u52a1\u5b9a\u4e49\u7684\u8303\u7574 <\/span><\/sub><\/span> \uff0c\u5bf9\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7406\u60f3\u7684 f \uff0c\u5b83\u80fd\u89e3\u51b3\u54ea\u4e9b\u4efb\u52a1\uff1f<\/span><\/strong><\/p>\n


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

      \u8fd9\u662f\u6211\u4eec\u5728\u672c\u6587\u4e00\u5f00\u59cb\u5c31\u60f3\u56de\u7b54\u7684\u6838\u5fc3\u95ee\u9898\u3002\u6211\u4eec\u5148\u4ecb\u7ecd\u4e00\u4e2a\u91cd\u8981\u6982\u5ff5\u3002<\/span><\/p>\n


      <\/h3>\n

      \u7c73\u7530\u5d4c\u5165<\/span><\/strong><\/span><\/h3>\n


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

      \u6211\u4eec\u5b9a\u4e49\u7c73\u7530\u5d4c\u5165\u51fd\u5b50\u4e3a <\/sub>\u3002\u9488\u5bf9\u4efb\u4f55<\/sub>\uff0c\u5373\u53ef\u4ee5\u63a5\u53d7\u8f93\u5165<\/sub> \u5e76\u8f93\u51fa HomC<\/sub><\/span>(Y,X)\u3002<\/span><\/p>\n


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

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

      \u5f88\u5bb9\u6613\u8bc1\u660e\uff0c <\/span><\/sub> \u662f\u80fd\u529b\u6700\u5f31\u7684\u7406\u60f3\u6a21\u578b\uff0c\u56e0\u4e3a\u7ed9\u5b9a\u5176\u4ed6\u7406\u60f3\u6a21\u578b f \uff0c <\/sub> \u4e2d\u7684\u6240\u6709\u5173\u7cfb\u4e5f\u5305\u542b\u5728 f \u4e2d\u3002\u540c\u65f6\uff0c\u5b83\u4e5f\u662f\u6ca1\u6709\u5176\u4ed6\u989d\u5916\u5047\u8bbe\u524d\u63d0\u4e4b\u4e0b\uff0c\u9884\u8bad\u7ec3\u6a21\u578b\u5b66\u4e60\u7684\u6700\u7ec8\u76ee\u6807\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u56de\u7b54\u6211\u4eec\u7684\u6838\u5fc3\u95ee\u9898\uff0c\u6211\u4eec\u4e0b\u9762\u4e13\u95e8\u8003\u8651 <\/span><\/sub>\u3002<\/span><\/p>\n


      <\/h2>\n


      <\/p>\n

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

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

      \u63d0\u793a\u8c03\u4f18\uff08Prompt tuning\uff09: \u89c1\u591a\u624d\u80fd\u8bc6\u5e7f<\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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


      <\/p>\n

      \u4e3a\u4e86\u7406\u89e3\u6a21\u578b\u80fd\u591f\u89e3\u51b3\u54ea\u4e9b\u4efb\u52a1\uff0c\u6211\u4eec\u9700\u8981\u5148\u660e\u786e\u4ec0\u4e48\u662f\u4efb\u52a1\u3002\u4e00\u4e2a\u4efb\u52a1 T \u53ef\u4ee5\u770b\u4f5c\u662f <\/span><\/sub> <\/span>\u4e2d\u7684\u51fd\u5b50\u3002\u6211\u4eec\u8bf4\u6a21\u578b\u89e3\u51b3\u4e86\u4e00\u4e2a\u4efb\u52a1 T\u2208<\/sub> <\/span>\uff0c\u5982\u679c\u5bf9\u4e8e\u4efb\u4f55\u8f93\u5165  <\/span><\/sub> <\/span> \uff0c\u6a21\u578b\u8f93\u51fa\u7684\u7b54\u6848\u4e0e T(X) \u662f\u540c\u6784\u7684\u3002\u5728\u8303\u7574\u8bba\u4e2d\uff0c\u5f53\u4e24\u4e2a\u5bf9\u8c61<\/span>\uff08\u6216\u51fd\u5b50\uff09<\/span>\u662f\u540c\u6784\u7684\uff0c\u6211\u4eec\u5c31\u5c06\u5b83\u4eec\u89c6\u4e3a\u76f8\u7b49\u7684\u3002\u6211\u4eec\u4e0d\u53bb\u8003\u8651\u5982\u4f55\u8ba9\u4e24\u4e2a\u540c\u6784\u7684\u5bf9\u8c61\u53d8\u5f97\u5b8c\u5168\u4e00\u81f4\uff0c\u56e0\u4e3a\u8fd9\u5728\u73b0\u4ee3\u795e\u7ecf\u7f51\u7edc\u4e2d\u5e76\u4e0d\u662f\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e24\u4e2a\u5bf9\u8c61 X \u548c Y \u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u540c\u6784\u6620\u5c04\uff0c\u4f7f\u5f97 \u03d5(X)=Y\uff0c\u90a3\u4e48\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u8f7b\u677e\u5730\u627e\u5230\u8fd9\u4e2a \u03d5 \u3002<\/span><\/p>\n


      <\/p>\n

       <\/span><\/sub> \u80fd\u5426\u89e3\u51b3\u67d0\u4e2a\u4efb\u52a1 T \uff1f\u8981\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5148\u4ecb\u7ecd\u8303\u7574\u8bba\u4e2d\u6700\u91cd\u8981\u7684\u4e00\u4e2a\u5b9a\u7406\u3002<\/span><\/p>\n


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

      \u7c73\u7530\u5f15\u7406<\/span><\/strong><\/span><\/h3>\n


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

      \u7c73\u7530\u5f15\u7406\uff1a<\/span><\/strong>\u5bf9\u4e8e T\u2208<\/span><\/sub> <\/span>\u548c <\/span><\/sub> <\/span> \uff0c\u6709 <\/sub> \u3002<\/span><\/p>\n


      <\/p>\n

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

      <\/p>\n


      <\/p>\n


      <\/p>\n

      \u5373\uff0ck<\/span>f<\/sub><\/span> \u53ef\u4ee5\u7528\u8fd9\u4e24\u79cd\u8868\u5f81\u8ba1\u7b97\u51fa T(X) \u3002\u7136\u800c\uff0c\u6ce8\u610f\u5230\u4efb\u52a1\u63d0\u793a P \u5fc5\u987b\u901a\u8fc7 <\/span><\/sub> \u800c\u975e k<\/span>f <\/sub><\/span>\u53d1\u9001\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u4f1a\u5f97\u5230 <\/span><\/sub>(P) \u800c\u975e T \u4f5c\u4e3a k<\/span>f<\/sub><\/span> \u7684\u8f93\u5165\u3002\u8fd9\u5f15\u51fa\u4e86\u8303\u7574\u8bba\u4e2d\u53e6\u4e00\u4e2a\u91cd\u8981\u7684\u5b9a\u4e49\u3002<\/span><\/p>\n


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

      \u53ef\u8868\u51fd\u5b50\uff1a\u5bf9\u4e8e T\u2208 <\/span><\/sub> \uff0c\u5982\u679c\u5b58\u5728\u67d0\u4e2a <\/sub> \u4f7f\u5f97 <\/span><\/sub>(X)\u2243T \uff0c\u5219\u79f0 T \u662f\u53ef\u8868\u7684\u3002X \u88ab\u79f0\u4e3a T \u7684\u4ee3\u8868\u3002<\/span><\/p>\n


      <\/p>\n

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

      \u5b9a\u74061\u4e0e\u63a8\u8bba<\/span><\/strong><\/h3>\n


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

      \u5b9a\u74061.  <\/span><\/sub> \u53ef\u4ee5\u901a\u8fc7\u63d0\u793a\u8c03\u4f18\u89e3\u51b3\u4efb\u52a1 T \uff0c\u5f53\u4e14\u4ec5\u5f53\u4efb\u52a1 T\u2208 <\/span><\/sub> <\/span> \u662f\u53ef\u8868\u7684\u3002\u5f53 T \u53ef\u8868\u65f6\uff0c\u6700\u4f18\u7684\u63d0\u793a\u662f T \u7684\u4ee3\u8868\u3002<\/span><\/p>\n


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

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

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

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      <\/p>\n

      \u8bc1\u660e\uff1a\u9884\u6d4b\u56fe\u50cf\u65cb\u8f6c\u89d2\u5ea6\u7684\u9884\u8bad\u7ec3\u4efb\u52a1\u4f1a\u5c06\u7ed9\u5b9a\u56fe\u50cf\u65cb\u8f6c\u56db\u4e2a\u4e0d\u540c\u7684\u89d2\u5ea6\uff1a0\u00b0, 90\u00b0, 180\u00b0, \u548c 270\u00b0\uff0c\u5e76\u8ba9\u6a21\u578b\u8fdb\u884c\u9884\u6d4b\u3002\u56e0\u6b64\uff0c\u8fd9\u4e2a\u9884\u8bad\u7ec3\u4efb\u52a1\u5b9a\u4e49\u7684\u8303\u7574\u5c06\u6bcf\u4e2a\u5bf9\u8c61\u90fd\u653e\u5165\u4e00\u4e2a\u5305\u542b4\u4e2a\u5143\u7d20\u7684\u7fa4\u4e2d\u3002\u663e\u7136\uff0c\u50cf\u5206\u5272\u6216\u5206\u7c7b\u8fd9\u6837\u7684\u4efb\u52a1\u4e0d\u80fd\u7531\u8fd9\u6837\u7b80\u5355\u7684\u5bf9\u8c61\u8868\u51fa\u3002<\/span><\/p>\n


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

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


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

      \n
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      \n
      \n

      <\/section>\n

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

      \u5fae\u8c03\uff08Fine tuning\uff09: \u8868\u5f81\u4e0d\u4e22\u4fe1\u606f<\/span><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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


      <\/p>\n

      \u63d0\u793a\u8c03\u4f18\u7684\u80fd\u529b\u6709\u9650\uff0c\u90a3\u4e48\u5fae\u8c03\u7b97\u6cd5\u5462\uff1f\u57fa\u4e8e\u7c73\u7530\u51fd\u5b50\u6269\u5c55\u5b9a\u7406<\/span>\uff08\u53c2\u89c1[5]\u4e2d\u7684\u547d\u98982.7.1\uff09<\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u5b9a\u7406\u3002<\/span><\/p>\n


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

      \u5b9a\u74062. \u7ed9\u5b9a\u8db3\u591f\u7684\u8d44\u6e90\uff0c\u9488\u5bf9\u4efb\u4f55\u4efb\u52a1F:<\/sub>\u2192Set\uff0c<\/sub>\u7684\u8868\u5f81\u53ef\u4ee5\u7528\u4e8e\u5b66\u4e60 G:<\/sub>\u2192Set \uff0c\u4f7f\u5f97 <\/sub>\u3002<\/span><\/p>\n


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

      \u5b9a\u74062\u8003\u8651\u7684\u4e0b\u6e38\u4efb\u52a1\u662f\u57fa\u4e8e<\/sub> \u7684\u7ed3\u6784\uff0c\u800c\u4e0d\u662f\u6570\u636e\u96c6\u4e2d\u7684\u6570\u636e\u5185\u5bb9\u3002\u56e0\u6b64\uff0c\u4e4b\u524d\u63d0\u5230\u7684\u9884\u6d4b\u65cb\u8f6c\u56fe\u7247\u89d2\u5ea6\u7684\u9884\u8bad\u7ec3\u4efb\u52a1\u5b9a\u4e49\u7684\u8303\u7574\u4ecd\u7136\u5177\u6709\u975e\u5e38\u7b80\u5355\u7684\u7fa4\u7ed3\u6784\u3002\u4f46\u662f\u6839\u636e\u5b9a\u74062\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u89e3\u51b3\u66f4\u591a\u6837\u5316\u7684\u4efb\u52a1\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6240\u6709\u5bf9\u8c61\u6620\u5c04\u5230\u540c\u4e00\u4e2a\u8f93\u51fa\uff0c\u8fd9\u662f\u65e0\u6cd5\u901a\u8fc7\u63d0\u793a\u8c03\u4f18\u6765\u5b9e\u73b0\u7684\u3002\u5b9a\u74062\u660e\u786e\u4e86\u9884\u8bad\u7ec3\u4efb\u52a1\u7684\u91cd\u8981\u6027\uff0c\u56e0\u4e3a\u66f4\u597d\u7684\u9884\u8bad\u7ec3\u4efb\u52a1\u5c06\u521b\u5efa\u66f4\u5f3a\u5927\u7684\u8303\u7574<\/sub> \uff0c\u4ece\u800c\u8fdb\u4e00\u6b65\u63d0\u9ad8\u4e86\u6a21\u578b\u7684\u5fae\u8c03\u6f5c\u529b\u3002<\/span><\/p>\n


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

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


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

      \n
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      <\/section>\n

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

      \u8ba8\u8bba\u4e0e\u603b\u7ed3<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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


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

      \u76d1\u7763\u5b66\u4e60\u4e0e\u81ea\u76d1\u7763\u5b66\u4e60<\/span><\/strong>\u3002\u4ece\u673a\u5668\u5b66\u4e60\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u81ea\u76d1\u7763\u5b66\u4e60\u4ecd\u7136\u662f\u4e00\u79cd\u76d1\u7763\u5b66\u4e60\uff0c\u53ea\u662f\u83b7\u53d6\u6807\u7b7e\u7684\u65b9\u5f0f\u66f4\u5de7\u5999\u4e00\u4e9b\u800c\u5df2\u3002\u4f46\u662f\u4ece\u8303\u7574\u8bba\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u81ea\u76d1\u7763\u5b66\u4e60\u5b9a\u4e49\u4e86\u8303\u7574\u5185\u90e8\u7684\u7ed3\u6784\uff0c\u800c\u76d1\u7763\u5b66\u4e60\u5b9a\u4e49\u4e86\u8303\u7574\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u5904\u4e8e\u4eba\u5de5\u667a\u80fd\u5730\u56fe\u7684\u4e0d\u540c\u677f\u5757\uff0c\u5728\u505a\u5b8c\u5168\u4e0d\u4e00\u6837\u7684\u4e8b\u60c5\u3002<\/span><\/p>\n


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

      \u4e0eChatGPT\u7684\u5173\u7cfb<\/span><\/strong>\u3002\u5f88\u591a\u670b\u53cb\u53ef\u80fd\u4f1a\u5173\u5fc3\u672c\u6587\u7684\u7ed3\u8bba\u5e94\u8be5\u5982\u4f55\u5e94\u7528\u5230ChatGPT\u7b49\u804a\u5929\u6a21\u578b\u4e0a\u53bb\uff1f\u7b80\u5355\u6765\u8bf4\uff0cChatGPT\u7b49\u6a21\u578b\u4e0d\u5149\u6709\u9884\u8bad\u7ec3\u7684\u8fc7\u7a0b\uff0c\u8fd8\u6709RLHF\u7b49\u8fdb\u4e00\u6b65\u5fae\u8c03\u90e8\u5206\uff0c\u6240\u4ee5\u5b9a\u74061\u7684\u7ed3\u8bba\u6ca1\u6cd5\u76f4\u63a5\u5e94\u7528\u3002\u4e0d\u8fc7\uff0c\u5b83\u4e5f\u53ef\u4ee5\u770b\u4f5c\u662f\u5bf9 <\/sub> \u8fdb\u884c\u5fae\u8c03\u7684\u4e00\u79cd\u53d8\u4f53\uff0c\u83b7\u5f97\u4e86\u5f3a\u5927\u7684\u80fd\u529b\u3002\u8fd9\u4e5f\u7b26\u5408\u6570\u5b66\u5bb6\u4eec\u4f7f\u7528 <\/sub> \u7684\u611f\u53d7\uff1a\u5f88\u591a\u95ee\u9898\u5728\u539f\u6765\u7684\u8303\u7574<\/sub> \u4e2d\u5f88\u56f0\u96be\uff0c\u4f46\u662f\u5f80\u5f80\u5728 <\/sub>\u4e2d\u5c31\u8fce\u5203\u800c\u89e3\u3002<\/span><\/p>\n


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

      \u9002\u7528\u573a\u666f<\/span><\/strong>\u3002\u7531\u4e8e\u672c\u6587\u5f00\u5934\u8003\u8651\u4e86\u65e0\u9650\u8d44\u6e90\u7684\u5047\u8bbe\uff0c\u5bfc\u81f4\u5f88\u591a\u670b\u53cb\u53ef\u80fd\u4f1a\u8ba4\u4e3a\uff0c\u8fd9\u4e9b\u7406\u8bba\u53ea\u6709\u5728\u865a\u7a7a\u4e4b\u4e2d\u624d\u4f1a\u771f\u6b63\u6210\u7acb\u3002\u5176\u5b9e\u5e76\u975e\u5982\u6b64\u3002\u5728\u6211\u4eec\u771f\u6b63\u7684\u63a8\u5bfc\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u53ea\u662f\u8003\u8651\u4e86\u7406\u60f3\u6a21\u578b\u4e0e k<\/span>f<\/sub><\/span> <\/span>\u8fd9\u4e00\u9884\u5b9a\u4e49\u7684\u51fd\u6570\u3002\u5b9e\u9645\u4e0a\uff0c\u53ea\u8981 k<\/span>f<\/sub><\/span> \u786e\u5b9a\u4e86\u4e4b\u540e\uff0c\u4efb\u4f55\u4e00\u4e2a\u9884\u8bad\u7ec3\u6a21\u578b f <\/span>\uff08\u54ea\u6015\u662f\u5728\u968f\u673a\u521d\u59cb\u5316\u9636\u6bb5\uff09<\/span>\u90fd\u53ef\u4ee5\u9488\u5bf9\u8f93\u5165 X\u2208<\/sub> \u8ba1\u7b97\u51fa f(X) \uff0c\u4ece\u800c\u4f7f\u7528 k<\/span>f<\/sub><\/span> \u8ba1\u7b97\u51fa\u4e24\u4e2a\u5bf9\u8c61\u7684\u5173\u7cfb\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u53ea\u8981\u5f53 k<\/span>f<\/sub><\/span> \u786e\u5b9a\u4e4b\u540e\uff0c\u6bcf\u4e2a\u9884\u8bad\u7ec3\u6a21\u578b\u90fd\u5bf9\u5e94\u4e8e\u4e00\u4e2a\u8303\u7574\uff0c\u800c\u9884\u8bad\u7ec3\u7684\u76ee\u6807\u4e0d\u8fc7\u662f\u5c06\u8fd9\u4e2a\u8303\u7574\u4e0d\u65ad\u4e0e\u7531\u9884\u8bad\u7ec3\u4efb\u52a1\u5b9a\u4e49\u7684\u8303\u7574\u5bf9\u9f50\u800c\u5df2\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7684\u7406\u8bba\u9488\u5bf9\u6bcf\u4e00\u4e2a\u9884\u8bad\u7ec3\u6a21\u578b\u90fd\u6210\u7acb\u3002<\/span><\/p>\n


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

      \u6838\u5fc3\u516c\u5f0f<\/span><\/strong>\u3002\u5f88\u591a\u4eba\u8bf4\uff0c\u5982\u679cAI\u771f\u6709\u4e00\u5957\u7406\u8bba\u652f\u6491\uff0c\u90a3\u4e48\u5b83\u80cc\u540e\u5e94\u8be5\u6709\u4e00\u4e2a\u6216\u8005\u51e0\u4e2a\u7b80\u6d01\u4f18\u7f8e\u7684\u516c\u5f0f\u3002\u6211\u60f3\uff0c\u5982\u679c\u9700\u8981\u7528\u4e00\u4e2a\u8303\u7574\u8bba\u7684\u516c\u5f0f\u6765\u63cf\u7ed8\u5927\u6a21\u578b\u80fd\u529b\u7684\u8bdd\uff0c\u5b83\u5e94\u8be5\u5c31\u662f\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\uff1a<\/span><\/p>\n


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

      <\/p>\n


      <\/p>\n


      <\/p>\n

      \u5bf9\u4e8e\u5927\u6a21\u578b\u6bd4\u8f83\u719f\u6089\u7684\u670b\u53cb\uff0c\u5728\u6df1\u5165\u7406\u89e3\u8fd9\u4e2a\u516c\u5f0f\u7684\u542b\u4e49\u4e4b\u540e\uff0c\u53ef\u80fd\u4f1a\u89c9\u5f97\u8fd9\u4e2a\u5f0f\u5b50\u5728\u8bf4\u5e9f\u8bdd\uff0c\u4e0d\u8fc7\u662f\u628a\u73b0\u5728\u5927\u6a21\u578b\u7684\u5de5\u4f5c\u6a21\u5f0f\u7528\u6bd4\u8f83\u590d\u6742\u7684\u6570\u5b66\u5f0f\u5b50\u5199\u51fa\u6765\u4e86\u800c\u5df2\u3002<\/span><\/p>\n


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

      \u4f46\u4e8b\u5b9e\u5e76\u975e\u5982\u6b64\u3002\u73b0\u4ee3\u79d1\u5b66\u57fa\u4e8e\u6570\u5b66\uff0c\u73b0\u4ee3\u6570\u5b66\u57fa\u4e8e\u8303\u7574\u8bba\uff0c\u800c\u8303\u7574\u8bba\u4e2d\u6700\u91cd\u8981\u7684\u5b9a\u7406\u5c31\u662f\u7c73\u7530\u5f15\u7406\u3002\u6211\u5199\u7684\u8fd9\u4e2a\u5f0f\u5b50\u5c06\u7c73\u7530\u5f15\u7406\u7684\u540c\u6784\u5f0f\u62c6\u5f00\u53d8\u6210\u4e86\u4e0d\u5bf9\u79f0\u7684\u7248\u672c\uff0c\u5374\u6b63\u597d\u548c\u5927\u6a21\u578b\u7684\u6253\u5f00\u65b9\u5f0f\u5b8c\u5168\u4e00\u81f4\u3002<\/span><\/p>\n


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

      \u6211\u8ba4\u4e3a\u8fd9\u4e00\u5b9a\u4e0d\u662f\u5de7\u5408\u3002\u5982\u679c\u8303\u7574\u8bba\u53ef\u4ee5\u7167\u8000\u73b0\u4ee3\u6570\u5b66\u7684\u5404\u4e2a\u5206\u652f\uff0c\u5b83\u4e5f\u4e00\u5b9a\u53ef\u4ee5\u7167\u4eae\u901a\u7528\u4eba\u5de5\u667a\u80fd\u7684\u524d\u8fdb\u4e4b\u8def\u3002<\/strong><\/span><\/p>\n


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

      \u672c\u6587\u7075\u611f\u6e90\u4e8e\u4e0e\u5317\u4eac\u667a\u6e90\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u9662\u5343\u65b9\u56e2\u961f\u7684\u957f\u671f\u7d27\u5bc6\u5408\u4f5c\u3002<\/span><\/p>\n

      <\/h2>\n


      <\/span><\/h2>\n

      \u53c2\u8003\u6587\u732e<\/span><\/strong><\/h2>\n

      [1] https:\/\/arxiv.org\/abs\/2002.05709<\/span><\/p>\n

      [2] <\/span>https:\/\/arxiv.org\/abs\/1911.05722<\/span><\/p>\n

      [3] <\/span>https:\/\/arxiv.org\/abs\/2111.06377<\/span><\/p>\n

      [4] <\/span>abhttps:\/\/arxiv.org\/abs\/1803.07728<\/span><\/p>\n

      [5] <\/span>Masaki Kashiwara, P. S. Categories and Sheaves. Springer, 2006. https:\/\/link.springer.com\/book\/10.1007\/3-540-27950-4<\/span><\/p>\n


      <\/section>\n
      \u672c\u6587\u9996\u53d1\u4e8e\u4f5c\u8005\u77e5\u4e4e\uff1a<\/span><\/section>\n
      https:\/\/zhuanlan.zhihu.com\/p\/634467074<\/span><\/section>\n

      <\/section>\n

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

      <\/span><\/strong><\/span><\/section>\n
      <\/section>\n
      \u8881\u6d0b<\/span><\/strong>\uff0c\u6e05\u534e\u5927\u5b66\u4ea4\u53c9\u4fe1\u606f\u5b66\u9662\u52a9\u7406\u6559\u6388\u30022012\u5e74\u6bd5\u4e1a\u4e8e\u5317\u4eac\u5927\u5b66\u8ba1\u7b97\u673a\u7cfb\uff0c2018\u5e74\u83b7\u5f97\u7f8e\u56fd\u5eb7\u5948\u5c14\u5927\u5b66\u8ba1\u7b97\u673a\u535a\u58eb\u5b66\u4f4d\uff0c\u5e08\u4eceRobert Kleinberg\u6559\u6388\u3002\u5728\u535a\u58eb\u671f\u95f4\uff0c\u4e8e2014\u5e74-2015\u5e74\u524d\u5f80\u5fae\u8f6f\u65b0\u82f1\u683c\u5170\u7814\u7a76\u9662\u505a\u8bbf\u95ee\u5b66\u751f\uff0c\u5e76\u4e8e2016\u5e74\u79cb\u5b63\u524d\u5f80\u7f8e\u56fd\u666e\u6797\u65af\u987f\u5927\u5b66\u505a\u8bbf\u95ee\u5b66\u751f\u30022018-2019\u5e74\u524d\u5f80\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u5927\u6570\u636e\u79d1\u5b66\u5b66\u9662\uff08MIFODS\uff09\u505a\u535a\u58eb\u540e\u3002\u8881\u6d0b\u7684\u4e3b\u8981\u7814\u7a76\u65b9\u5411\u662f\u667a\u80fd\u533b\u7597\u3001AI\u57fa\u7840\u7406\u8bba\u3001\u5e94\u7528\u8303\u7574\u8bba\u3002<\/span><\/section>\n

      <\/section>\n

      <\/section>\n

      <\/p>\n

      \n
      \n
      \n
      \n


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

      \u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8<\/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\u672c\u8bfb\u4e66\u4f1a\u662f\u201cAI+Science\u201d\u4e3b\u9898\u8bfb\u4e66\u4f1a\u7684\u7b2c\u4e09\u5b63\u3002\u8bfb\u4e66\u4f1a\u81ea9\u670815\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e94\u665a20:00-22:00\uff0c\u9884\u8ba1\u6301\u7eed\u65f6\u95f48\uff5e10\u5468\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n


      <\/span><\/section>\n
      <\/span><\/a><\/span><\/section>\n
      \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>
      <\/section>\n

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


      <\/p>\n


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

      \n

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

      1.  <\/strong><\/strong><\/a>\u63a2\u7d22\u201cAI \u5927\u7edf\u4e00\u7406\u8bba\u201d\uff1a\u79d1\u5b66\u542f\u53d1\u7684\u673a\u5668\u5b66\u4e60\u7406\u8bba<\/a><\/strong><\/strong><\/span><\/strong><\/section>\n
      2.<\/strong> \u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff1a\u8ba9\u7269\u7406\u4e16\u754c\u62e5\u6709AI | \u9ec4\u6587\u70b3\u5206\u4eab\u6574\u7406<\/a><\/strong><\/strong><\/span><\/section>\n
      3. <\/strong><\/strong> AI \u8fd8\u9700\u8981\u7406\u8bba\u4e48\uff1f<\/a><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n
      4. <\/strong><\/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
      <\/a><\/strong><\/strong><\/span><\/section>\n
      5. <\/strong><\/strong>\u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/a><\/span><\/strong><\/section>\n
      <\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
      6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


      <\/p>\n


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

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

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