{"id":55238,"date":"2025-01-24T17:18:26","date_gmt":"2025-01-24T09:18:26","guid":{"rendered":"https:\/\/swarma.org\/?p=55238"},"modified":"2025-01-24T17:18:26","modified_gmt":"2025-01-24T09:18:26","slug":"%e5%a4%a7%e8%87%aa%e7%84%b6%e7%9a%84%e8%ae%a1%e7%ae%97%ef%bc%9a%e4%bb%8e%e4%bc%8a%e8%be%9b%e6%a8%a1%e5%9e%8b%e5%88%b0%e7%94%9f%e6%88%90%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=55238","title":{"rendered":"\u5927\u81ea\u7136\u7684\u8ba1\u7b97\uff1a\u4ece\u4f0a\u8f9b\u6a21\u578b\u5230\u751f\u6210\u5b66\u4e60"},"content":{"rendered":"
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2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7\u548c\u6770\u5f17\u91cc\u00b7\u8f9b\u987f\uff0c\u8fd9\u5bf9\u5f88\u591a\u4eba\u6765\u8bf4\u662f\u51fa\u4e4e\u610f\u6599\u7684\u3002\u6587\u7ae0\u5c06\u4ece\u7edf\u8ba1\u7269\u7406\u7684\u89c6\u89d2\uff0c\u4ece\u4f0a\u8f9b\u6a21\u578b\u51fa\u53d1\uff0c\u9010\u6b65\u4ecb\u7ecd\u970d\u666e\u83f2\u5c14\u5fb7\u548c\u8f9b\u987f\u7684\u4e3b\u8981\u8d21\u732e\uff0c\u5176\u4e2d\u5305\u62ecHopfield\u6a21\u578b\u3001\u73bb\u5c14\u5179\u66fc\u673a\u3001\u975e\u76d1\u7763\u5b66\u4e60\uff0c\u4ee5\u53ca\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u3002\u8fd8\u5c06\u56de\u987e\u7edf\u8ba1\u7269\u7406\u548c\u673a\u5668\u5b66\u4e60\u572820\u4e16\u7eaa\u672b\u671f\u7684\u7cbe\u5f69\u5408\u4f5c\u5386\u7a0b\uff0c\u5e76\u5bf9\u672a\u6765\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u4ea4\u4e92\u9886\u57df\u7684\u53d1\u5c55\u65b9\u5411\u8fdb\u884c\u7b80\u5355\u5c55\u671b\u3002<\/span><\/span><\/span><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n

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\u5173\u952e\u8bcd\uff1a\u73bb\u5c14\u5179\u66fc\u673a\uff0cHopfield\u6a21\u578b\uff0c\u4f0a\u8f9b\u6a21\u578b\uff0c\u673a\u5668\u5b66\u4e60\uff0c\u7edf\u8ba1\u7269\u7406\uff0c\u751f\u6210\u6a21\u578b<\/strong><\/span><\/strong><\/strong><\/strong><\/section>\n
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\u4e2d\u56fd\u7269\u7406\u5b66\u4f1a\u671f\u520a\u7f51\uff0c\u9009\u81ea\u300a\u7269\u7406\u300b2025\u5e74\u7b2c1\u671f<\/span> <\/span>| \u6765\u6e90<\/span><\/span><\/p>\n


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2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7684\u9881\u5956\u8bcd\u662f\u201cfor foundational discoveries and inventions that enable machine learning with artificial neural networks\u201d<\/span> (\u56e0\u5960\u5b9a\u4e86\u4f7f\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u673a\u5668\u5b66\u4e60\u7684\u57fa\u7840\u6027\u53d1\u73b0\u548c\u53d1\u660e)<\/span>\uff0c\u201cthey trained artificial neural networks using physics\u201d<\/span> (\u4ed6\u4eec\u4f7f\u7528\u7269\u7406\u5b66\u8bad\u7ec3\u4e86\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc)<\/span> [1]\u3002\u8a00\u4e0b\u4e4b\u610f\u662f\u9881\u53d1\u7ed9\u201cScience for AI\u201d\uff0c\u8fd9\u6b63\u597d\u548c\u8bfa\u8d1d\u5c14\u5316\u5b66<\/span>\u5956[2]\u7684\u201cAI f<\/span>or Science\u201d\u5f62\u6210\u547c\u5e94\u3002<\/span><\/p>\n


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\u8bfa\u5956\u9881\u5956\u8bcd\u8fd8\u5f3a\u8c03\u4e86\u4e24\u4e2a\u540d\u8bcd\uff0c\u970d\u666e\u83f2\u5c14\u5fb7\u7f51\u7edc<\/span> (Hopfield network) <\/span>\u548c\u73bb\u5c14\u5179\u66fc\u673a<\/span>(Boltzmann machine)<\/span>\uff0c\u8fd9\u4e24\u4e2a\u6a21\u578b\u53ef\u4ee5\u88ab\u89c6\u4e3a\u751f\u6210\u5b66\u4e60\u7684\u5f00\u7aef\u3002\u751f\u6210\u5b66\u4e60\u7684\u4efb\u52a1\u662f\u4ece\u6ca1\u6709\u6807\u7b7e\u7684\u6570\u636e\u4e2d\u5b66\u4e60\u5230\u6570\u636e\u53d8\u91cf\u7684\u8054\u5408\u5206\u5e03\u6982\u7387\uff0c\u5e76\u5bf9\u5b66\u4e60\u5230\u7684\u6982\u7387\u5206\u5e03\u8fdb\u884c\u91c7\u6837\u4ece\u800c\u751f\u6210\u65b0\u7684\u5b66\u4e60\u6837\u672c\u3002\u4ece\u7269\u7406\u7684\u89d2\u5ea6\u4e0a\u770b\uff0c\u8fd9\u5c31\u662f\u8d39\u66fc\u8bf4\u8fc7\u7684\u201cWhat I cannot create\uff0cI do not understand\u201d\uff0c\u5176\u4e2dcreate\u610f\u5473\u7740\u751f\u6210\uff0cunderstand\u610f\u5473\u7740\u5b66\u4e60\u548c\u7406\u89e3\u3002<\/span><\/p>\n


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\u751f\u6210\u5b66\u4e60\u7684\u6570\u636e\u662f\u591a\u79cd\u591a\u6837\u7684\uff0c\u5bf9\u5e94\u7684\u751f\u6210\u6a21\u578b\u53ef\u4ee5\u521b\u9020\u51fa\u5404\u79cd\u5404\u6837\u7684\u4fe1\u606f\u3002\u6570\u636e\u662f\u56fe\u50cf\u65f6\uff0cMidjourney[3]\u53ef\u4ee5\u753b\u51fa\u65b0\u7684\u753b\u5377\uff1b\u6570\u636e\u662f\u97f3\u7b26\u65f6\uff0cWavenet[4]\u53ef\u4ee5\u751f\u6210\u65b0\u7684\u4e50\u7ae0\uff1b\u5f53\u6570\u636e\u662f\u81ea\u7136\u8bed\u8a00\u65f6\uff0cChatGPT[5]\u53ef<\/span>\u4ee5\u5199\u51fa\u534e\u4e3d\u7684\u6587\u7ae0\u3002\u751f\u6210\u6a21\u578b\u9762\u5bf9\u7684\u6700\u5927\u6311\u6218\u662f\u5982\u4f55\u5b66\u4e60\u5230\u5728\u4e00\u4e2a\u5de8\u5927\u7a7a\u95f4\u4e2d\u7684\u6982\u7387\u5206\u5e03\u3002\u4ee528\u00d728\u50cf\u7d20\u7684\u9ed1\u767d\u56fe\u7247\u4e3a\u4f8b\uff0c\u5168\u90e8\u53ef\u80fd\u7684\u56fe\u7247\u6570\u76ee\u662f2<\/span>784<\/sup>\uff1b\u5bf9\u4e8e\u4e00\u9996\u957f\u5ea6\u4e3a20\u4e2a\u6c49\u5b57\u7684\u8bd7\uff0c\u5373\u4f7f\u6bcf\u4e2a\u6c49\u5b57\u53ea\u67093000\u79cd\u53ef\u80fd\u6027\uff0c\u6240\u6709\u53ef\u80fd\u51fa\u73b0\u7684\u8bd7\u53e5\u6570\u76ee\u4e3a3000<\/span>20<\/sup>\u3002\u8fd9\u90fd\u662f\u4e2a\u5929\u6587\u6570\u5b57\uff0c\u4e0d\u53ef\u80fd\u7b80\u5355\u5730\u901a\u8fc7\u7a77\u4e3e\u6bcf\u4e2a\u53ef\u80fd\u7684\u56fe\u7247\u6216\u8005\u8bd7\u53e5\u8fd9\u79cd\u65b9\u5f0f\u6765\u63cf\u8ff0\u50cf\u7d20\u6216\u8005\u6c49\u5b57\u7684\u8054\u5408\u5206\u5e03\u6982\u7387\u3002\u572820\u4e16\u7eaa\uff0c\u7531\u4e8e\u7f3a\u4e4f\u6570\u636e\u3001\u8ba1\u7b97\u80fd\u529b\uff0c\u4ee5\u53ca\u5177\u4f53\u7684\u5e94\u7528\uff0c\u8fd9\u79cd\u7c7b\u578b\u7684\u9ad8\u7ef4\u6982\u7387\u5206\u5e03\u7684\u5efa\u6a21\u95ee\u9898\u5728\u5404\u4e2a\u9886\u57df\u8fd8\u4e0d\u662f\u5f88\u666e\u904d\uff0c\u4f46\u7edf\u8ba1\u7269\u7406\u5728\u5176\u5efa\u7acb\u4e4b\u521d\u5df2\u7ecf\u4e60\u60ef\u4e8e\u7814\u7a76\u7c7b\u4f3c\u7684\u9ad8\u7ef4\u6982\u7387\u5206\u5e03\u95ee\u9898\u4e86\u3002\u719f\u6089\u7edf\u8ba1\u7269\u7406\u7684\u8bfb\u8005\u53ef\u80fd\u4f1a\u7acb\u523b\u610f\u8bc6\u5230\uff0c\u63cf\u8ff0\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u6982\u7387\u5206\u5e03\u7684\u6027\u8d28\u662f\u7edf\u8ba1\u7269\u7406\u7684\u4e3b\u8981\u7814\u7a76\u5bf9\u8c61\u3002\u4f8b\u5982\uff0c\u5728\u7edf\u8ba1\u7269\u7406\u4e2d\u6700\u5e38\u89c1\u7684\u6982\u7387\u5206\u5e03\u4e4b\u4e00\u662f\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff1a<\/span><\/span><\/p>\n


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\u5176\u4e2dE<\/em>(s<\/em>)\u662f\u80fd\u91cf\u51fd\u6570\uff0c<\/span>\u662f\u914d\u5206\u51fd\u6570\uff0c\u5373\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u5f52\u4e00\u5316\u56e0\u5b50\u3002\u5982\u679c\u8981\u95ee\u6bcf\u4e2a\u6784\u578bs<\/em>\u4e25\u683c\u7684\u6982\u7387\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u914d\u5206\u51fd\u6570\u7684\u6570\u503c\u3002\u76f4\u63a5\u7684\u914d\u5206\u51fd\u6570\u8ba1\u7b97\u9700\u8981\u5bf92n<\/sup><\/em>\u4e2a\u6784\u578b\u7684\u73bb\u5c14\u5179\u66fc\u6743\u91cd\u6c42\u548c\uff0c\u8fd9\u5728\u5927\u7684\u7cfb\u7edf\u4e2d\u4e5f\u662f\u4e2a\u5929\u6587\u6570\u5b57\uff0c\u65e0\u6cd5\u76f4\u63a5\u8ba1\u7b97\u3002\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u5728\u673a\u5668\u5b66\u4e60\u548c\u7edf\u8ba1\u7269\u7406\u4e2d\u90fd\u9762\u5bf9\u7740\u975e\u5e38\u76f8\u4f3c\u7684\u8ba1\u7b97\u56f0\u96be\uff0c\u4e5f\u90fd\u9700\u8981\u6709\u6548\u7684\u7b97\u6cd5\uff0c\u4ee5\u53ca\u5f3a\u5927\u7684\u8ba1\u7b97\u80fd\u529b\u3002\u76f8\u6bd4\u4e8e\u7edf\u8ba1\u7269\u7406\u4e2d\u90a3\u4e9b\u81ea\u7136\u754c\u7ed9\u5b9a\u7684\u54c8\u5bc6\u987f\u91cf\u548c\u5206\u5e03\uff0c\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u63cf\u8ff0\u6982\u7387\u5206\u5e03\u662f\u66f4\u52a0\u56f0\u96be\u7684\u95ee\u9898\uff0c\u56e0\u4e3a\u4eba\u4eec\u751a\u81f3\u6ca1\u6709\u4e00\u4e2a\u201c\u7ed9\u5b9a\u201d\u7684\u6a21\u578b\u6765\u63cf\u8ff0\u6570\u636e\u5206\u5e03\u3002\u6b63\u5982\u672c\u6587\u5c06\u8981\u5411\u5927\u5bb6\u4ecb\u7ecd\u7684\uff0c\u5728\u751f\u6210\u5b66\u4e60\u7684\u5f00\u7aef\uff0c\u53d7\u5230\u7edf\u8ba1\u7269\u7406\u7684\u542f\u53d1\uff0c\u6770\u5f17\u91cc\u00b7\u8f9b\u987f<\/span> (Geoffrey Hinton) <\/span>\u786e\u5b9e\u662f\u7528\u81ea\u7136\u754c\u7684\u5206\u5e03\u2014\u2014\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff0c\u6765\u53c2\u6570\u5316\u6570\u636e\u7684\u6982\u7387\u5206\u5e03\u7684\u3002<\/span><\/p>\n


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\u5728\u81ea\u7136\u754c\u4e2d\uff0c\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u662f\u53f8\u7a7a\u89c1\u60ef\u7684\u3002\u4f8b\u5982\u6211\u4eec\u90fd\u5f88\u719f\u6089\u7684\u51b0\u548c\u6db2\u6001\u6c34\uff0c\u5b83\u4eec\u7531\u540c\u6837\u7684\u6c34\u5206\u5b50\u6784\u6210\uff0c\u4f46\u6c34\u5206\u5b50\u7684\u6784\u578b\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u9075\u4ece\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4e0d\u540c\u3002\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u5bf9\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u8fdb\u884c\u91c7\u6837\uff0c\u6240\u89c2\u5bdf\u5230\u7684\u6c34\u5206\u5b50\u7684\u6784\u578b\u5c31\u4e0d\u76f8\u540c\u4e86\u3002\u8fd9\u9020\u5c31\u4e86\u5728\u4f4e\u6e29\u4e0b\u5e38\u5e38\u770b\u5230\u51b0\u8fd9\u79cd\u5f62\u6001\uff0c\u800c\u5728\u9ad8\u6e29\u4e0b\u4e00\u822c\u770b\u5230\u7684\u662f\u6c34\u8fd9\u79cd\u5f62\u6001\u3002\u800c\u8fd9\u4e9b\u6837\u672c\u662f\u5927\u81ea\u7136\u4ece\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4e2d\u91c7\u6837\u6240\u751f\u6210\u7684\uff0c\u91c7\u6837\u7684\u80fd\u529b\u6765\u81ea\u4e8e\u81ea\u7136\u754c\u3002<\/span><\/section>\n

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\u56fe1 \u540c\u6837\u7684\u6c34\u5206\u5b50\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u662f\u4e0d\u540c\u7684\uff0c\u5bf9\u5b83\u4eec\u8fdb\u884c\u91c7\u6837\u4f1a\u5f97\u5230\u4e0d\u540c\u7684\u6837\u672c\u4ee5\u53ca\u7269\u8d28\u5f62\u6001<\/span><\/p>\n


<\/span><\/section>\n
\u5728\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u52a0\u4ee5\u7c7b\u6bd4\uff0c\u628a\u56fe1\u5de6\u8fb9\u7684\u51b0\u5f53\u4f5c\u4e00\u5f20\u6570\u636e\uff0c\u53f3\u8fb9\u7684\u6c34\u4e5f\u5f53\u4f5c\u4e00\u5f20\u6570\u636e\u3002\u8fd9\u6837\u4f4e\u6e29\u65f6\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7f16\u7801\u4e86\u51b0\u8fd9\u4e2a\u6570\u636e\uff0c\u800c\u9ad8\u6e29\u65f6\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7f16\u7801\u4e86\u6c34\u8fd9\u4e2a\u6570\u636e\u2014\u2014\u8fd9\u662f\u5927\u81ea\u7136\u7684\u751f\u6210\u6a21\u578b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53e6\u5916\u4e00\u4e2a\u4f8b\u5b50\u662f\u7edf\u8ba1\u7269\u7406\u4e2d\u8457\u540d\u7684\u4f0a\u8f9b\u6a21<\/span>\u578b[6]\u3002\u4f0a\u8f9b<\/span>\u6a21\u578b\u7684\u53d8\u91cf\u88ab\u79f0\u4e3a\u81ea\u65cb\u53d8\u91cf\uff0c\u6bcf\u4e2a\u53d8\u91cf\u53ea\u80fd\u53d6+1\u548c-1\u4e24\u79cd\u72b6\u6001\u3002n<\/em>\u4e2a\u81ea\u65cb\u53d8\u91cf\u72b6\u6001\u7684\u7ec4\u5408\u88ab\u79f0\u4e3a\u4e00\u4e2a\u6784\u578bs<\/em>={1,-1}n<\/sup><\/em>\u3002\u6700\u7b80\u5355\u7684\u94c1\u78c1\u4f0a\u8f9b\u6a21\u578b\u7684\u80fd\u91cf\u51fd\u6570<\/span>\uff0c\u5373\u81ea\u65cb\u4e4b\u95f4\u7684\u8026\u5408\u53c2\u6570Jij<\/sub><\/em>=1\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u80fd\u91cf\u662f\u7531\u6bcf\u4e00\u7ec4(ij<\/em>)\u5bf9\u6240\u8d21\u732e\u7684\uff0c\u76f8\u5f53\u4e8e\u7b2ci <\/em>\u4e2a\u81ea\u65cb\u548c\u7b2cj <\/em>\u4e2a\u81ea\u65cb\u90fd\u6709\u76f8\u4e92\u4f5c\u7528\u3002\u5b83\u4eec\u53d6\u76f8\u540c\u7684\u503c\u4f1a\u4f7f\u8fd9\u4e2a\u81ea\u65cb\u5bf9\u7684\u80fd\u91cf\u6700\u5c0f\u3002\u6240\u6709\u53ef\u80fd\u7684\u6784\u578b\u51712n<\/sup><\/em>\u4e2a\uff0c\u6bcf\u4e2a\u6784\u578bs<\/em>\u7684\u6982\u7387\u53d6\u51b3\u4e8e\u80fd\u91cf\uff0c\u4e5f\u53d6\u51b3\u4e8e\u6e29\u5ea6P<\/em>(s<\/em>)=<\/span>\u3002\u5728\u975e\u5e38\u9ad8\u6e29\u7684\u65f6\u5019\u03b2<\/em>\u51e0\u4e4e\u4e3a0\uff0c\u6240\u6709\u6784\u578b\u7684\u6982\u7387\u90fd\u4e00\u6837\u3002\u5728\u975e\u5e38\u4f4e\u6e29\u03b2<\/em>\u2192\u221e\u4e0b\uff0c\u53ea\u6709\u90a3\u4e9b\u80fd\u91cf\u6700\u4f4e\u7684\u6784\u578b\uff0c\u5373\u6240\u6709\u81ea\u65cb\u90fd\u53d6+1\uff0c\u6216\u8005\u90fd\u53d6-1\u7684\u90a3\u4e9b\u6784\u578b\u624d\u6709\u8db3\u591f\u9ad8\u7684\u6982\u7387\uff0c\u5176\u4ed6\u6784\u578b\u7684\u6982\u7387\u51e0\u4e4e\u662f0\u3002\u5982\u679c\u4ece\u4f4e\u6e29\u7684\u4f0a\u8f9b\u6a21\u578b\u4e2d\u8fdb\u884c\u91c7\u6837\uff0c\u6240\u5f97\u5230<\/span> (\u6216\u8005\u8bf4\u751f\u6210) <\/span>\u7684\u6784\u578b\u5c31\u53ea\u6709\u4e24\u79cd\u3002\u57fa\u4e8e\u524d\u9762\u6240\u4ecb\u7ecd\u7684\u4ece\u56fe\u7247\u5230\u4f0a\u8f9b\u6784\u578b\u7684\u7c7b\u6bd4\uff0c\u4e0d\u540c\u7684\u6e29\u5ea6\u5bf9\u5e94\u4e0d\u540c\u7684\u751f\u6210\u6a21\u578b\uff0c\u800c\u4f4e\u6e29\u4e0b\u7684\u94c1\u78c1\u4f0a\u8f9b\u6a21\u578b\u53ef\u4ee5\u8ba4\u4e3a\u662f\u5b66\u4e60\u4e86\u5168\u90e8\u90fd\u662f\u9ed1\u8272\u548c\u5168\u90e8\u90fd\u662f\u767d\u8272\u50cf\u7d20\u7684\u4e24\u5e45\u56fe\u7247\u3002\u8fd9\u51e0\u4e4e\u662f\u6700\u7b80\u5355\u7684\u56fe\u7247\u751f\u6210\u6a21\u578b\u4e86\uff0c\u5b66\u4e60\u5230\u7684\u6982\u7387\u5206\u5e03\u53ea\u6709\u4e24\u5f20\u56fe\u7247\u7684\u6982\u7387\u503c\u975e\u96f6\uff0c\u5176\u4ed6\u6784\u578b\u6982\u7387\u5747\u4e3a\u96f6\uff0c\u56e0\u6b64\u53ea\u80fd\u8bb0\u4f4f\u4e24\u5f20\u56fe\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\n
Hopfield\u6a21\u578b[7]\u53ef\u4ee5\u8ba4\u4e3a\u662f\u94c1\u78c1\u4f0a\u8f9b\u6a21\u578b\u7684\u63a8\u5e7f\uff0c\u5b83\u662f\u4e2a\u4f0a\u8f9b<\/span>\u6a21\u578b\uff0c\u4ecd\u7136\u7528\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u6765\u8868\u8fbe\u6570\u636e\u53d8\u91cf\u7684\u5206\u5e03\u3002\u4f46\u53d7\u5230\u795e\u7ecf\u751f\u7269\u5b66\u7684Hebb\u89c4\u5219[8]\u6240<\/span>\u542f\u53d1\uff0c\u8026\u5408\u53c2\u6570\u662f\u4ece\u6570\u636e\u7684\u5173\u8054\u5f97\u5230\u7684Jij<\/sub><\/em>=<\/span>\u3002\u5176\u4e2d\u4e00\u5171\u5b58\u50a8\u4e86\u03b1n<\/em>\u4e2a\u6570\u636e\uff0c\u00b5<\/em>\u662f\u6570\u636e\u7684\u7d22\u5f15\uff0ci<\/em>\u548cj<\/em>\u662f\u81ea\u65cb\u6307\u6807\u3002\u5982\u679c\u53ea\u5b58\u50a8\u4e86\u4e00\u4e2a\u6570\u636e\uff0c\u5373\u03b1n<\/em>=1\uff0c\u53ef\u4ee5\u770b\u5230Jij<\/sub><\/em>=\u03bei<\/sub>\u03bej<\/sub><\/em>\uff0c\u4ecd\u7136\u662f\u4e00\u4e2a\u81ea\u65cb\u53d8\u91cf\u3002\u8fd9\u4e2a\u6a21\u578b\u4e5f\u88ab\u79f0\u4e3aMattis\u73bb\u7483\uff0c\u5176\u5b9e\u548c\u94c1\u78c1\u4f0a\u8f9b\u6a21\u578b\u53ea\u76f8\u5dee\u4e00\u4e2a\u5c06+1\u6620\u5c04\u5230\u968f\u673a\u00b11\u7684\u53d8\u6362\uff0c\u672c\u8d28\u4e0a\u662f\u4e00\u6837\u7684\uff0c\u53ea\u5b58\u50a8\u4e86\u4e24\u4e2a\u6570\u636e{\u03bei<\/sub>\u03bc<\/sup><\/em><\/em>}\u548c\u5b83\u7684\u955c\u50cf\u3002\u5f53\u6211\u4eec\u8fd0\u884c\u4e00\u79cd\u52a8\u529b\u5b66\uff0c\u4f8b\u5982\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u7f57\u6cd5\u5bf9\u7cfb\u7edf\u8fdb\u884c\u91c7\u6837\u65f6\uff0c\u5728\u96f6\u6e29\u4e0b\u53ea\u80fd\u91c7\u6837\u5230\u5b58\u50a8\u7684\u6570\u636e\uff0c\u5728\u4f4e\u6e29\u4e0b\u53ef\u4ee5\u91c7\u6837\u5230\u548c\u5b58\u50a8\u7684\u6570\u636e\u76f8\u4f3c\u7684\u6784\u578b\u3002\u5f53\u03b1n<\/em>>1\u65f6\uff0c\u60c5\u51b5\u5c31\u4e0d\u540c\u4e86\u3002\u4e3a\u4e86\u65b9\u4fbf\u7406\u89e3\uff0c\u6211\u4eec\u8003\u8651\u4f7f\u7528\u5e76\u884c\u7684Glauber\u52a8\u529b\u5b66\u5bf9\u7cfb\u7edf\u8fdb\u884c\u91c7\u6837\uff0c\u7ed9\u5b9a\u7cfb\u7edf\u7684\u72b6\u6001st<\/sup><\/em>\uff0c\u5bf9\u6bcf\u4e2a\u81ea\u65cbi <\/em>\u6765\u8bf4\uff0c\u4e0b\u4e00\u4e2a\u65f6\u523b\u53d6si<\/sub>t<\/sup><\/em>+1<\/sup>\u7684\u6982\u7387\u4e3a<\/span>\u3002\u5728\u5b58\u50a8\u7684\u6570\u636e\u6bd4\u8f83\u5c11\u65f6\uff0c\u8fd9\u4e9b\u6570\u636e\u90fd\u4f1a\u8868\u73b0\u4e3a\u52a8\u529b\u5b66\u7684\u5438\u5f15\u5b50\u3002\u5f53\u7f51\u7edc\u72b6\u6001\u5df2\u7ecf\u5728\u5b58\u50a8\u7684\u4e00\u4e2a\u6570\u636e\u65f6\uff0c\u4e0b\u4e00\u4e2a\u65f6\u523b\u53d6\u503c\u6982\u7387\u4e3a<\/span><\/section>\n

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

<\/span><\/section>\n
\u53ef\u4ee5\u770b\u5230\uff0c\u8fd9\u4e2a\u6982\u7387\u6709\u4e24\u90e8\u5206\u6784\u6210\uff0c\u7b2c\u4e00\u90e8\u5206\u662f\u4fe1\u53f7\u9879\uff0c\u7b2c\u4e8c\u90e8\u5206\u662f\u7531\u5f88\u591a\u9879\u6570\u636e\u53d8\u91cf\u4e58\u5728\u4e00\u8d77\u7684\u566a\u97f3\u9879\u3002\u4fe1\u53f7\u9879\u503e\u5411\u4e8e\u5f85\u5728\u7b2c\u4e00\u4e2a\u6570\u636e\uff0c\u800c\u566a\u97f3\u9879\u9a71\u4f7f\u52a8\u529b\u5b66\u79bb\u5f00\u7b2c\u4e00\u4e2a\u6570\u636e\u3002\u5f53\u5b58\u50a8\u7684\u6570\u636e\u5f88\u591a\u65f6\uff0c\u566a\u97f3\u4f1a\u5f88\u5927\uff0c\u4f7f\u5f97\u6bcf\u4e00\u4e2a\u6570\u636e\u90fd\u4e0d\u80fd\u518d\u6210\u4e3a\u52a8\u529b\u5b66\u7684\u5438\u5f15\u5b50\uff0c\u4ece\u800c\u65e0\u6cd5\u8bb0\u4f4f\u4efb\u4f55\u4e00\u4e2a\u6570\u636e\u3002Hopfield\u6a21\u578b\u7684\u5e73\u8861\u6001\u5206\u6790\u572820\u4e16\u7eaa80\u5e74\u4ee3\u662f\u975e\u5e38\u91cd\u8981\u7684\u95ee\u9898\uff0c\u57281985\u5e74\u65f6\uff0c\u4e09\u4f4d\u4ee5\u8272\u5217\u79d1\u5b66\u5bb6\u5229\u7528\u7edf\u8ba1\u7269\u7406\u7684\u590d\u672c\u65b9\u6cd5<\/span> (replica method) <\/span>\u6c42\u89e3Hopfield\u6a21\u578b\u7684\u76f8\u56fe<\/span> (\u56fe2) <\/span>[9]\u3002\u76f8\u56fe\u5206\u4e3a\u4e09\u4e2a\u533a\u57df\uff1a\u5728\u9ad8\u6e29\u65f6\u7cfb\u7edf\u4e3a\u987a\u78c1\u6001\uff1b\u5728\u4f4e\u6e29\u4e14\u03b1<\/em>\u5c0f\u65f6\uff0c\u7cfb\u7edf\u53ef\u4ee5\u8bb0\u4f4f\u8bad\u7ec3\u7684\u6570\u636e\uff0c\u6210\u4e3a\u8bb0\u5fc6\u6001\uff1b\u5728\u4f4e\u6e29\u4e14\u03b1<\/em>\u5927\u65f6\uff0c\u7cfb\u7edf\u5fd8\u8bb0\u4e86\u6240\u6709\u8bad\u7ec3\u6570\u636e\u7684\u6001\uff0c\u79f0\u4e3a\u81ea\u65cb\u73bb\u7483\u6001\u3002\u5728\u96f6\u6e29\u65f6Hopfield\u6a21\u578b\u6700\u591a\u53ef\u4ee5\u5b58\u50a80.138n<\/em>\u7684\u6570\u636e\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u56fe2 (a)\u6570\u636e\u4f5c\u4e3a\u52a8\u529b\u5b66\u7684\u5438\u5f15\u5b50\uff1b(b)Hopfield\u6a21\u578b\u7684\u76f8<\/span><\/span>\u56fe[9]<\/span><\/section>\n

<\/span><\/section>\n
\u572820\u4e16\u7eaa70\u523090\u5e74\u4ee3\uff0c\u5bf9Hopfield \u7b49\u6a21\u578b\u7684\u5e73\u5747\u573a\u7406\u8bba\u7814\u7a76\u662f\u7edf\u8ba1\u7269\u7406\u7684\u4e00\u4e2a\u91cd\u8981\u7814\u7a76\u65b9\u5411\u3002\u5f53\u65f6\u7684\u4e00\u4e9b\u7edf\u8ba1\u7269\u7406\u5b66\u5bb6\u8ba4\u4e3a\u795e\u7ecf\u7f51\u7edc\u7684\u5206\u6790\u53ef\u4ee5\u88ab\u5f53\u6210\u7edf\u8ba1\u529b\u5b66\u7684\u53cd\u95ee\u9898<\/span> (inverse problem) <\/span>\u6765\u5904\u7406[10]\u3002\u6b63\u95ee\u9898\u662f\u7ed9\u5b9a\u7cfb\u7edf\u7684\u80fd\u91cf\u51fd\u6570\uff0c\u6c42\u89e3\u73bb\u5c14\u5179\u66fc\u51fd\u6570\u7684\u6027\u8d28\uff0c\u4ee5\u53ca\u83b7\u5f97\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u65e0\u504f\u7684\u6837\u672c\u3002\u800c\u53cd\u95ee\u9898<\/span> (\u4e5f\u79f0\u53cd\u4f0a\u8f9b\u6a21\u578b) <\/span>\u5219\u8ba4\u4e3a\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u6837\u672c\u5df2\u7ecf\u83b7\u53d6\u4e86\uff0c\u5c31\u662f\u7528\u6765\u8bad\u7ec3\u7684\u6570\u636e\uff0c\u8981\u4ece\u8fd9\u4e9b\u6837\u672c\u63a8\u65ad <\/span>(\u6216\u8005\u5b66\u4e60) <\/span>\u51fa\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u53c2\u6570\uff0c\u5373\u80fd\u91cf\u51fd\u6570\u4e2d\u7684\u53c2\u6570\u3002<\/span><\/section>\n

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\n
\n
\u4ece\u5386\u53f2\u7684\u89d2\u5ea6\u770b\uff0c\u7edf\u8ba1\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u572820\u4e16\u7eaa\u786e\u5b9e\u6709\u7740\u5f88\u957f\u4e00\u6bb5\u65f6\u95f4\u7684\u4ea4\u4e92\u548c\u4e92\u76f8\u53d1\u5c55\u9636\u6bb5\u3002\u57fa\u4e8e\u4e2a\u4eba\u89c2\u70b9\uff0c\u6211\u4eec\u603b\u7ed3\u4e86\u4e00\u4e2a\u5bf9\u7167\u56fe\uff0c\u5982\u56fe3\u6240\u793a\uff0c\u5927\u81f4\u5206\u4e3a4\u4e2a\u9636\u6bb5\u3002\u572819\u4e16\u7eaa\u65f6\uff0c\u56fe3\u7edf\u8ba1\u7269\u7406\u8fd9\u8fb9\u53ef\u4ee5\u770b\u5230\u4e00\u4e9b\u8457\u540d\u7684\u7edf\u8ba1\u7269\u7406\u5b66\u5bb6\u7684\u540d\u5b57\uff0c\u800c\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3001\u8d1d\u53f6\u65af\u5b9a\u7406\u88ab\u5efa\u7acb\u548c\u4f7f\u7528\u3002\u57281900\u5e74\u52301950\u5e74\u5de6\u53f3\u7684\u7b2c\u4e8c\u9636\u6bb5\uff0c\u7edf\u8ba1\u7269\u7406\u5728\u4f0a\u8f9b\u6a21\u578b\u65b9\u9762\u3001\u91c7\u6837\u7b49\u65b9\u5411\u9010\u6e10\u53d1\u5c55\u8d77\u6765\uff0c\u7279\u522b\u662f\u57281957\u5e74Jaynes\u63d0\u51fa\u4e86\u6700\u5927\u71b5\u539f\u7406\uff0c\u5efa\u7acb\u4e86\u7edf\u8ba1\u7269\u7406\u4e0e\u7edf\u8ba1\u63a8\u65ad\u7684\u8054\u7cfb\u3002\u5728\u673a\u5668\u5b66\u4e60\u65b9\u9762\uff0c\u4fe1\u606f\u4e0e\u8ba1\u7b97\u7684\u57fa\u7840\u7406\u8bba\u9010\u6b65\u5efa\u7acb\u8d77\u6765\uff0c\u611f\u77e5\u5668<\/span> (perceptron)<\/span> [11]\u4e5f\u572820\u4e16\u7eaa50\u5e74\u4ee3\u88ab\u53d1\u660e\u5e76\u5f15\u53d1\u4e86\u4eba\u5de5\u667a\u80fd\u7684\u7b2c\u4e00\u6ce2\u7814\u7a76\u70ed\u6f6e\u3002\u7136\u800c\u5230\u4e861969\u5e74\uff0cMinsky\u548cPapert[12]\u6307\u51fa\u611f\u77e5\u5668\u751a\u81f3\u90fd\u89e3\u51b3\u4e0d\u4e86XOR\u5206\u7c7b\u95ee\u9898\uff0c\u56e0\u6b64\u5927\u5bb6\u5f00\u59cb\u91cd\u65b0\u5ba1\u89c6\u4eba\u5de5\u667a\u80fd\uff0c\u4eba\u5de5\u667a\u80fd\u4e5f\u9677\u5165\u4e86\u7b2c\u4e00\u4e2a\u5bd2\u51ac\u3002\u5728\u56fe3\u4e2d\u7684\u7b2c\u4e09\u4e2a\u9636\u6bb5\uff0c\u7edf\u8ba1\u7269\u7406\u5728\u81ea\u65cb\u73bb\u7483\u9886\u57df\u83b7\u5f97\u4e86\u8fdb\u5c55\u3002\u81ea\u65cb\u73bb\u7483\u662f\u5177\u6709\u968f\u673a\u8026\u5408\u53c2\u6570\u7684\u4f0a\u8f9b\u6a21\u578b\uff0c\u80fd\u91cf\u56fe\u666f\u975e\u5e38\u4e30\u5bcc\u30022021\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u5f97\u4e3bParisi\u6559\u6388\u4e3aSherrington\u2014Kirkpatrick\u81ea\u65cb\u73bb\u7483[13]\u5efa\u7acb\u4e86\u5168\u9636\u526f\u672c\u7834\u7f3a\u7684\u6e10\u8fdb\u4e25\u683c\u89e3[14]\uff0c\u5c55\u793a\u4e86\u5176\u80fd\u91cf\u56fe\u666f\u5177\u6709\u81ea\u76f8\u4f3c\u7684\u5c42\u7ea7\u7ed3\u6784\u3002\u7814\u7a76\u81ea\u65cb\u73bb\u7483\u4f7f\u7528\u7684\u65b9\u6cd5\uff0c\u4f8b\u5982\u526f\u672c\u65b9\u6cd5\uff0c\u4e5f\u53ef\u4ee5\u7528\u6765\u7814\u7a76\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\uff0c\u8fd9\u5176\u4e2d\u7684\u8457\u540d\u5de5\u4f5c\u5305\u62ecGardner\u548cDerrida\u5173\u4e8e\u611f\u77e5\u5668\u7684\u5bb9\u91cf[15]\uff0cKrauth\u548cMezard\u5173\u4e8e\u4e8c\u5143\u611f\u77e5\u5668\u5bb9\u91cf[16]\u7684\u7edf\u8ba1\u7269\u7406\u7814\u7a76\u3002\u5728\u795e\u7ecf\u7f51\u7edc\u9886\u57df\uff0c\u8fd9\u4e2a\u9636\u6bb5\u5efa\u7acb\u4e86\u57fa\u7840\u7684\u76d1\u7763\u4e0e\u975e\u76d1\u7763\u6a21\u578b\uff0c\u4f8b\u5982\u5377\u79ef\u7f51\u7edc\u7684\u524d\u8eabNecognitron\u3001\u73bb\u5c14\u5179\u66fc\u673a\u3001\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\uff0c\u4ee5\u53ca\u5f3a\u5316\u5b66\u4e60\u7684\u5f00\u7aef\u3002\u7136\u800c\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7edf\u8ba1\u7269\u7406\u7684\u65b9\u6cd5\u5728\u5f53\u65f6\u5e76\u4e0d\u80fd\u6210\u529f\u7406\u89e3\u66f4\u590d\u6742\u7684\u5377\u79ef\u7f51\u7edc\u3001\u73bb\u5c14\u5179\u66fc\u673a\u7b49\u795e\u7ecf\u7f51\u7edc\u7684\u8fd0\u884c\u673a\u7406\uff0c\u56e0\u4e3a\u65e0\u6cd5\u5206\u6790\u591a\u5c42\u7684\u7f51\u7edc\uff0c\u4e5f\u5f88\u96be\u4e3a\u5b9e\u9645\u7684\u6570\u636e\u5efa\u7acb\u6a21\u578b\u3002\u7136\u800c\u57281995\u5e74\u65f6\uff0c\u652f\u6301\u5411\u91cf\u673a<\/span>(support vector machine) <\/span>[17]\u7684\u51fa\u73b0\u4f7f\u5f97\u4eba\u5de5\u667a\u80fd\u9886\u57df\u7684\u6ce8\u610f\u529b\u4ece\u795e\u7ecf\u7f51\u7edc\u8f6c\u79fb\u4e86\u51fa\u6765\uff0c\u56e0\u4e3a\u652f\u6301\u5411\u91cf\u673a\u5f53\u65f6\u6bd4\u591a\u5c42\u795e\u7ecf\u7f51\u7edc<\/span> (MLP) <\/span>\u7684\u7ed3\u679c\u66f4\u597d\uff0c\u800c\u4e14\u66f4\u5bb9\u6613\u89e3\u91ca\u3002\u8fd9\u53c8\u4f7f\u5f97\u795e\u7ecf\u7f51\u7edc\u7684\u7814\u7a76\u8fdb\u5165\u4e86\u7b2c\u4e8c\u4e2a\u5bd2\u51ac\u3002\u57282000\u5e74\u4e4b\u540e\u7684\u53d1\u5c55\u4e2d\uff0c\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u88ab\u5e94\u7528\u4e8e\u66f4\u52a0\u5e7f\u6cdb\u7684\u9886\u57df\u4e2d\uff0c\u8fd9\u5305\u542b\u7ec4\u5408\u4f18\u5316\u3001\u7edf\u8ba1\u63a8\u65ad\u95ee\u9898\u7b49\uff0c\u4f46\u7531\u4e8e\u4ecd\u7136\u5f88\u96be\u5206\u6790\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u7684\u6027\u8d28\uff0c\u7edf\u8ba1\u7269\u7406\u4e0e\u795e\u7ecf\u7f51\u7edc\u9886\u57df\u7684\u53d1\u5c55\u9010\u6e10\u5206\u9053\u626c\u9573\uff0c\u5e76\u6700\u7ec8\u9519\u8fc7\u4e86\u673a\u5668\u5b66\u4e60\u57282012\u5e74\u4e4b\u540e\u4ea7\u751f\u7684\u6df1\u5ea6\u5b66\u4e60\u65f6\u4ee3\u7684\u5e8f\u5e55\u3002<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n
\u56fe3 \u4e0e\u673a\u5668\u5b66\u4e60\u76f8\u5173\u7684\u7edf\u8ba1\u7269\u7406\u548c\u795e\u7ecf\u7f51\u7edc\u53d1\u5c55\u7684\u5bf9\u7167\u8868\u683c<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u673a\u5668\u5b66\u4e60\u65b9\u9762\uff0c\u751f\u6210\u5b66\u4e60\u7684\u786e\u662f\u572820\u4e16\u7eaa80\u5e74\u4ee3\u65f6\u6cbf\u7740\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u5c55\u5f00\u7684\u3002Hopfield\u6a21\u578b\u867d\u7136\u5728\u7406\u8bba\u795e\u7ecf\u79d1\u5b66\u3001\u8054\u60f3\u8bb0\u5fc6\u3001\u673a\u5668\u5b66\u4e60\u9886\u57df\u90fd\u5177\u6709\u91cc\u7a0b\u7891\u4f3c\u7684\u610f\u4e49\uff0c\u4f46\u5b83\u6700\u591a\u80fd\u5b58\u50a80.138n<\/em>\u4e2a\u6570\u636e[9]\uff0c\u4e14\u8981\u6c42\u6570\u636e\u4e4b\u95f4\u4e0d\u80fd\u5b58\u5728\u5173\u8054\uff0c\u8fd9\u7ed9Hopfield\u6a21\u578b\u7684\u5b9e\u9645\u5e94\u7528\u5e26\u6765\u4e86\u5f88\u591a\u56f0\u96be\u3002\u5bf9Hopfield\u6a21\u578b\u7684\u6539\u8fdb\u662f\u975e\u5e38\u81ea\u7136\u7684\uff1a\u53ef\u4ee5\u4e0d\u7528\u901a\u8fc7Hebb\u89c4\u5219\u6784\u9020\u4f0a\u8f9b\u6a21\u578b\u7684\u8026\u5408\u53c2\u91cfJij<\/sub><\/em>\uff0c\u9010\u6b65\u5b66\u4e60\u8fd9\u4e9b\u8026\u5408\u53c2\u91cf\u3002\u5728\u7edf\u8ba1\u7269\u7406\u4e2d\u8fd9\u79cd\u505a\u6cd5\u88ab\u79f0\u4e3a\u53cd\u4f0a\u8f9b\u95ee\u9898 <\/span>(inverse Ising problem)<\/span>\u3002\u5728\u53cd\u4f0a\u8f9b\u95ee\u9898\u4e2d\uff0c\u635f\u5931\u51fd\u6570<\/span>\u662f\u8d1f\u5bf9\u6570\u4f3c\u7136\u5ea6<\/span> (negative log-likelihood)<\/span>\u3002\u5bf9\u5b83\u4f18\u5316\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u7ec4Jij<\/sub><\/em>\uff0c\u4f7f\u5f97\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u5728\u751f\u6210\u6240\u6709\u8bad\u7ec3\u6570\u636e<\/span>\u65f6\u7684\u6982\u7387\u6700\u5927\u5316\uff0c\u4e5f\u7b49\u4ef7\u4e8e\u6700\u5c0f\u5316\u8bad\u7ec3\u6570\u636e\u7684\u7ecf\u9a8c\u5206\u5e03\u4e0e\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4e4b\u95f4\u7684Kullback\u2014Leibler(KL)\u6563\u5ea6\u3002\u901a\u5e38\u7684\u4f18\u5316\u65b9\u6cd5\u662f\u8ba1\u7b97\u51fa\u635f\u5931\u51fd\u6570\u76f8\u5bf9\u4e8e\u53c2\u6570\u7684\u68af\u5ea6\uff0c\u7136\u540e\u5229\u7528\u68af\u5ea6\u4fe1\u606f\u4f18\u5316\u635f\u5931\u51fd\u6570\u3002\u5bf9\u4e8e\u53cd\u4f0a\u8f9b\u95ee<\/span>\u9898[18]\uff0c<\/span>\u5b83\u7684\u68af\u5ea6\u4e3a<\/span><\/section>\n

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

<\/span><\/section>\n
\u5176\u4e2d<\/span>\u662f\u6570\u636e\u4e2d\u7b2ci<\/em>\u4e2a\u53d8\u91cf\u4e0e\u7b2cj<\/em>\u4e2a\u53d8\u91cf\u7684\u5173\u8054\uff0c\u800c<\/span>\u662f\u5728\u6a21\u578b\u4e2d\u7684\u5173\u8054\u3002\u8fd9\u4e2a\u68af\u5ea6\u7684\u8868\u8fbe\u5f0f\u4ece\u4fa7\u9762\u8bf4\u660e\u4e86\uff0c\u4f0a\u8f9b\u6a21\u578b\u662f\u7ed9\u5b9a\u6570\u636e\u4e00\u9636\u77e9\u548c\u4e8c\u9636\u77e9\u7684\u6700\u5927\u71b5\u6a21\u578b\uff0c\u4f5c\u4e3a\u6307\u6570\u65cf\u51fd\u6570\uff0c\u5b83\u7684\u5145\u5206\u7edf\u8ba1\u91cf<\/span> (sufficient statistics) <\/span>\u662f\u4e00\u9636\u77e9\u548c\u4e8c\u9636\u77e9\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u5b83\u5f88\u96be\u523b\u753b\u6570\u636e\u4e2d\u7684\u9ad8\u9636\u5173\u8054\u3002\u53e6\u5916\uff0c\u867d\u7136\u6570\u636e\u5173\u8054\u662f\u5bb9\u6613\u8ba1\u7b97\u7684\uff0c\u4f46\u6a21\u578b\u5173\u8054\u7684\u8ba1\u7b97\u4e0e\u914d\u5206\u51fd\u6570\u7684\u8ba1\u7b97\u540c\u5c5e\u4e8e#P\u96be\u95ee\u9898\uff0c\u4e0d\u5b58\u5728\u591a\u9879\u5f0f\u7684\u4e25\u683c\u7b97\u6cd5\u3002\u9664\u4e86\u68af\u5ea6\u8ba1\u7b97\u7684\u56f0\u96be\u4e4b\u5916\uff0c\u53cd\u4f0a\u8f9b\u6a21\u578b\u7684\u8868\u8fbe\u80fd\u529b\u4e5f\u4e0d\u8db3\uff0c\u56e0\u4e3a\u6240\u6709\u53c2\u6570\u4e00\u5171\u53ea\u6709n<\/em>2<\/sup>\/2\u4e2a\uff0c\u5f88\u96be\u6269\u5c55\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8f9b\u987f\u4e0e\u5408\u4f5c\u8005\u53d1\u660e\u7684\u73bb\u5c14\u5179\u66fc\u673a<\/span> (Boltzmann machine\uff0cB<\/span>M)<\/span><\/span> [19]\u53ef\u4ee5<\/span>\u89e3\u51b3\u53cd\u4f0a\u8f9b\u6a21\u578b\u4e2d\u5bf9\u5173\u8054\u7684\u8868\u8ff0\uff0c\u4ee5\u53ca\u6a21\u578b\u7684\u6574\u4f53\u8868\u8fbe\u80fd\u529b\u95ee\u9898\u3002\u5728\u73bb\u5c14\u5179\u66fc\u673a\u4e2d\uff0cn<\/em>\u4e2a\u663e\u53d8\u91cf\u7684\u6784\u578bv<\/em><\/strong>={v<\/em>1<\/sub>, v<\/em>2 <\/sub>\u22ef, vn<\/sub><\/em>}\u4ee5\u53cam<\/em>\u4e2a\u9690\u53d8\u91cf\u7684\u6784\u578bh<\/em><\/strong>={h<\/em>1<\/sub>, h<\/em>2<\/sub> \u22ef, hm<\/sub><\/em>}\u7684\u8054\u5408\u5206\u5e03\u6982\u7387\u6ee1\u8db3\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff1a<\/span><\/section>\n

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\u800c\u663e\u53d8\u91cf(\u6570\u636e\u53d8\u91cf)\u7684\u8054\u5408\u5206\u5e03\u6982\u7387\u901a\u8fc7\u5bf9\u9690\u53d8\u91cf\u7684\u6c42\u548c\u6765\u5f97\u5230\uff1a<\/span><\/section>\n

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<\/section>\n
\u901a\u8fc7\u5f15\u5165\u591a\u4e2a\u9690\u53d8\u91cf\uff0c\u4f7f\u5f97\u6240\u6709\u53d8\u91cf\u90fd\u8fde\u63a5\u5728\u4e00\u8d77\u3002\u8fd9\u6837\u4e00\u65b9\u9762\u589e\u52a0\u4e86\u7cfb\u7edf\u7684\u53c2\u6570\u6570\u76ee\uff0c\u56e0\u4e3a\u9690\u53d8\u91cf\u548c\u663e\u53d8\u91cf\u4e4b\u95f4\u7684\u8026\u5408\u53c2\u91cf\u7684\u6570\u76ee\u968f\u7740\u9690\u53d8\u91cf\u7684\u589e\u52a0\u800c\u589e\u52a0\uff1b\u53e6\u4e00\u65b9\u9762\u4e5f\u901a\u8fc7\u4e0e\u6240\u6709\u663e\u53d8\u91cf\u8fde\u63a5\u7684\u9690\u53d8\u91cf\u8bf1\u5bfc\u4e86\u663e\u53d8\u91cf\u4e4b\u95f4\u7684\u9ad8\u9636\u5173\u8054\u3002\u867d\u7136\u89e3\u51b3\u4e86\u8868\u8ff0\u80fd\u529b\u7684\u95ee\u9898\uff0c\u4f46\u73bb\u5c14\u5179\u66fc\u673a\u6ca1\u6709\u89e3\u51b3\u53cd\u4f0a\u8f9b\u6a21\u578b\u7684\u68af\u5ea6\u8ba1\u7b97\u95ee\u9898\uff0c\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u95ee\u9898\u53d8\u5f97\u66f4\u4e25\u91cd\u4e86\u3002\u4f8b\u5982\uff0c\u5bf9\u6570\u4f3c\u7136\u5ea6\u76f8\u5bf9\u4e8e\u663e\u53d8\u91cfi\u548c\u9690\u53d8\u91cfa<\/em>\u4e4b\u95f4\u7684\u8026\u5408\u53c2\u91cfWia<\/sub><\/em>\u7684\u68af\u5ea6\u53ef\u4ee5\u5199\u6210\uff1a<\/span><\/section>\n

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\u4e0d\u4ec5\u7b2c\u4e8c\u9879\u7684\u68af\u5ea6\u8ba1\u7b97\u6ca1\u6709\u53d8\u5f97\u7b80\u5355\uff0c\u8fde\u7b2c\u4e00\u9879\u7684\u8ba1\u7b97\u4e5f\u53d8\u5f97\u66f4\u4e3a\u590d\u6742\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u8f9b\u987f\u4e0e\u5408\u4f5c\u8005\u63d0\u51fa\u4e86\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a<\/span> (restricted Boltzmann machine\uff0cRBM) <\/span>[20]\u3002\u76f8\u6bd4\u4e8e\u73bb\u5c14\u5179\u66fc\u673a\uff0cRBM\u53bb\u9664\u4e86\u663e\u53d8\u91cf\u4e4b\u95f4\u7684\u8fde\u63a5\u4ee5\u53ca\u9690\u53d8\u91cf\u4e4b\u95f4\u7684\u8fde\u63a5\u3002\u56e0\u6b64\u5b83\u662f\u4e00\u4e2a\u5b9a\u4e49\u5728\u53ea\u6709\u663e\u53d8\u91cf\u548c\u9690\u53d8\u91cf\u4e4b\u95f4\u6709\u8fde\u63a5\u7684\u4e8c\u5206\u56fe\u4e0a\u3002\u867d\u7136\u635f\u5931\u4e86\u4e00\u4e9b\u53c2\u6570\u548c\u8868\u8fbe\u80fd\u529b\uff0cRBM\u7684\u4f18\u70b9\u662f\u53ef\u4ee5\u5feb\u901f\u5730\u8fdb\u884c\u91c7\u6837\uff0c\u7136\u540e\u5229\u7528\u6837\u672c\u8ba1\u7b97<\/span>\u4ee5\u53ca<\/span>\u3002\u8fd9\u4e2a\u6027\u8d28\u5b8c\u5168\u6765\u81ea\u4e8e\u4e8c\u5206\u56fe\uff0c\u8fd9\u4f7f\u5f97\u7ed9\u5b9a\u9690\u53d8\u91cf\u4e4b\u540e\uff0c\u663e\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u4e25\u683c\u5730\u5206\u89e3\u4e3a\u8fde\u4e58\u7684\u5f62\u5f0f\uff1a<\/span><\/section>\n

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\u5f53\u7ed9\u5b9a\u9690\u53d8\u91cf\u7684\u6784\u578b\u4ee5\u540e\uff0c\u663e\u53d8\u91cf\u53ef\u4ee5\u975e\u5e38\u6709\u6548\u5730\u8fdb\u884c\u91c7\u6837\u3002\u6839\u636e\u540c\u6837\u7684\u9053\u7406\uff0c\u7ed9\u5b9a\u663e\u53d8\u91cf\u6784\u578b<\/span> (\u5373\u6570\u636e\u6784\u578b)<\/span>\uff0c\u9690\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\u4e5f\u5177\u6709\u8fde\u4e58\u7684\u5f62\u5f0f\uff0c\u56e0\u6b64\u9690\u53d8\u91cf\u4e5f\u53ef\u4ee5\u8fc5\u901f\u91c7\u6837\u3002\u901a\u8fc7\u8fd9\u4e2a\u6027\u8d28\u6765\u8ba1\u7b97RBM\u68af\u5ea6\u5e76\u8fdb\u884c\u5b66\u4e60\u7684\u65b9\u6cd5\u88ab\u79f0\u4e3a\u5bf9\u6bd4\u6563\u5ea6\u7b97\u6cd5\uff0c\u5982\u56fe4\u6240\u793a\u3002\u8bad\u7ec3\u7528\u7684\u6570\u636e\u662f\u4e00\u7ec4\u4e8c\u503c\u7684\u624b\u5199\u5b57\u7b26\u56fe\u7247\uff0c\u6bcf\u4e2a\u56fe\u7247\u88ab\u89c6\u4e3a\u4e00\u7ec4\u81ea\u65cb\u6784\u578b\u3002\u901a\u8fc7\u6700\u5927\u5316\u5bf9\u6570\u4f3c\u7136\u7684\u65b9\u6cd5\uff0c\u5b9a\u4e49\u5728\u4e8c\u5206\u56fe\u4e0a\u7684RBM\u53c2\u6570Wia<\/sub><\/em>\u53ef\u4ee5\u88ab\u5b66\u4e60\u5230\u3002\u5728\u5b66\u4e60\u7ed3\u675f\u4e4b\u540e\uff0cRBM\u7684\u80fd\u91cf\u56fe\u666f\u5177\u6709\u56fe\u4e2d\u7684\u5f62\u5f0f\uff0c\u5373\u8bad\u7ec3\u56fe\u7247\u4ee5\u53ca\u548c\u5b83\u4eec\u76f8\u8fd1\u7684\u56fe\u7247\u7684\u80fd\u91cf\u6bd4\u8f83\u4f4e\uff0c\u800c\u5176\u4ed6\u90a3\u4e9b\u968f\u673a\u6784\u578b\u56fe\u7247\u7684\u80fd\u91cf\u90fd\u6bd4\u8f83\u9ad8\u3002\u8fd9\u6837\u5982\u679c\u4ece\u80fd\u91cf\u9ad8\u7684\u6784\u578b\u51fa\u53d1\u505a\u91c7\u6837\uff0c\u5c31\u53ef\u4ee5\u751f\u6210\u548c\u8bad\u7ec3\u56fe\u7247\u76f8\u4f3c\u7684\u56fe\u7247\u3002<\/span><\/section>\n

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\u56fe4 \u4ece\u8bad\u7ec3\u6570\u636e\u4e2d\u5b66\u4e60\u5230RBM\u7684\u53c2\u6570<\/span>Wia<\/sub><\/em>\uff0c\u4f7f\u5f97\u5728RBM\u7684\u80fd\u91cf\u56fe\u666f\u4e2d\uff0c\u6570\u636e\u6784\u578b\u80fd\u91cf\u4f4e\u800c\u968f\u673a\u6784\u578b\u80fd\u91cf\u9ad8\u3002\u4eceRBM\u7684\u5206\u5e03\u4e2d\u91c7\u6837\u53ef\u4ee5\u751f\u6210\u65b0\u7684\u6570\u636e<\/span><\/span><\/p>\n


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RBM\u4e2d\u7684\u9690\u53d8\u91cf\u4e0d\u4ec5\u53ef\u4ee5\u4e3a\u663e\u53d8\u91cf\u63d0\u4f9b\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\uff0c\u4e5f\u53ef\u4ee5\u4f5c\u4e3a\u6570\u636e\u53d8\u91cf\u7684\u8868\u793a\uff1a\u5982\u679c\u6211\u4eec\u628a<\/span>P<\/em>(<\/span>v<\/em><\/strong>,<\/span> h<\/em><\/strong>)\u5bf9\u663e\u53d8\u91cf\u6c42\u548c\uff0c\u5c31\u80fd\u5f97\u5230\u9690\u53d8\u91cf\u7684\u8fb9\u9645\u5206\u5e03\u3002\u5982\u679c\u9690\u53d8\u91cf\u6bd4\u8f83\u5c11\uff0c\u8fd9\u4e2a\u5206\u5e03\u53ef\u4ee5\u8ba4\u4e3a\u662f\u6570\u636e\u5206\u5e03\u7684\u4f4e\u7ef4\u8868\u793a\u3002\u8fd9\u548c\u7269\u7406\u4e2d\u7684\u91cd\u6b63\u5316\u7fa4\u6709\u76f8\u4f3c\u4e4b\u5904\u3002\u53ef\u4ee5\u60f3\u8c61\u4e00\u4e2a\u4e8c\u7ef4\u4f0a\u8f9b\u6a21\u578b\uff0c\u5982\u679c\u6bcf\u4e2a\u9690\u53d8\u91cf\u8fde\u63a5\u5230\u4e8c\u7ef4\u683c\u70b9\u4e0a\u76f8\u90bb\u76844\u4e2a\u81ea\u65cb\u4e0a\uff0c\u90a3\u4e48\u628a\u81ea\u65cb\u53d8\u91cf\u6c42\u548c\u5c31\u7c7b\u4f3c\u505a\u4e86\u4e00\u6b21\u91cd\u6b63\u5316\u7fa4\uff0c\u63d0\u53d6\u4e86\u7cfb\u7edf\u7c97\u7c92\u5316\u7684\u4fe1\u606f\u3002\u8f9b\u987f\u4e0e\u4ed6\u7684\u5b66\u751fRuslan Salakhutinov\u57282006\u5e74\u53d1\u8868\u4e86\u4e00\u7bc7<\/span><\/span>Science<\/span><\/em>\u8bba<\/span>\u6587[21]<\/span>\uff0c\u63d0\u51fa\u53ef\u4ee5\u5c06\u591a\u4e2aRBM\u5806\u53e0\u8d77\u6765\uff0c\u5c06\u4e0b\u4e00\u5c42\u7684RBM\u7684\u9690\u53d8\u91cf\u5f53\u4f5c\u4e0a\u4e00\u5c42\u7684\u663e\u53d8\u91cf\uff0c\u9690\u53d8\u91cf\u6570\u76ee\u9010\u5c42\u51cf\u5c11\uff0c\u6700\u7ec8\u5806\u6210\u4e00\u4e2a\u91d1\u5b57\u5854\u5f62\u72b6\u7684\u6df1\u5ea6\u73bb\u5c14\u5179\u66fc\u673a\u3002\u5c06\u8fd9\u4e2a\u91d1\u5b57\u5854\u5012\u7740\u6263\u8fc7\u6765\uff0c\u548c\u4e4b\u524d\u7684\u73bb\u5c14\u5179\u66fc\u673a\u5f62\u6210\u4e00\u4e2a\u6c99\u6f0f\u5f62\u72b6\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u8f9b\u987f\u5c06\u5b83\u79f0\u4e3a\u81ea\u7f16\u7801\u5668\u3002\u81ea\u7f16\u7801\u5668\u8f93\u5165\u548c\u8f93\u51fa\u7684\u7ef4\u5ea6\u662f\u4e00\u6837\u7684\uff0c\u5982\u679c\u53ef\u4ee5\u8bad\u7ec3\u5b83\u4f7f\u5f97\u8f93\u5165\u548c\u8f93\u51fa\u7684\u7ed3\u679c\u51e0\u4e4e\u4e00\u81f4\uff0c\u5c31\u610f\u5473\u7740\u5728\u6700\u4e2d\u95f4\u90a3\u4e2a\u7ef4\u5ea6\u6700\u4f4e\u7684\u9690\u5c42\u4e2d\u627e\u5230\u4e86\u4e00\u4e2a\u7531\u9690\u53d8\u91cf\u6240\u627f\u8f7d\u7684\u4f4e\u7ef4\u8868\u793a\u3002\u8fd9\u4e2a\u8bad\u7ec3\u7684\u65b9\u5f0f\u88ab\u79f0\u4e3a\u975e\u76d1\u7763\u9884\u8bad\u7ec3\uff0c\u5982\u4eca\u5df2\u7ecf\u5728\u4ee5GPT<\/span>[5]<\/sup>\u4e3a\u4ee3\u8868\u7684\u5927\u8bed\u8a00\u6a21\u578b\u4e2d\u5e7f\u6cdb\u91c7\u7528\u3002\u5176\u4e2dGPT\u7684\u542b\u4e49\u662fgenerative pretrained transformer\uff0c\u5373\u751f\u6210\u5f0f\u9884\u8bad\u7ec3Transformer\u3002\u5bf9\u4e8e\u6df1\u5ea6\u73bb\u5c14\u5179\u66fc\u673a\u548c\u81ea\u7f16\u7801\u5668\u6765\u8bf4\uff0c\u9884\u8bad\u7ec3\u4e4b\u540e\u7684\u6a21\u578b\u53ef\u4ee5\u505a\u597d\u5f88\u591a\u4e8b\u60c5\uff0c\u4f8b\u5982\u5728\u56fe\u50cf\u5206\u7c7b\u4efb\u52a1\u4e2d\u53ef\u4ee5\u5de5\u4f5c\u5f97\u6bd4\u652f\u6301\u5411\u91cf\u673a\u66f4\u597d\u3002\u81f3\u6b64\uff0c\u4e5f\u62c9\u5f00\u4e86\u65b0\u4e00\u8f6e\u795e\u7ecf\u7f51\u7edc\u7814\u7a76\u70ed\u6f6e\u7684\u5e8f\u5e55\u3002<\/span><\/span><\/section>\n

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3. \u5f53\u4e0b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u56fe5 \u751f\u6210\u5f0f\u673a\u5668\u5b66\u4e60\u7684\u65f6\u95f4\u8f74<\/span><\/section>\n

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\u7ed9\u8fd9\u4e2a\u9886\u57df\u5e26\u6765\u771f\u6b63\u7a81\u7834\u6027\u8fdb\u5c55\u7684\u4e8b\u4ef6\u6765\u81ea\u4e8e2009\u5e74\u548c2012\u5e74<\/span> (\u56fe5)<\/span>\u3002\u57282009\u5e74\uff0c\u5e26\u7740\u201cData will redefine how we think about models\u201d\u7684\u7406\u5ff5\uff0c\u534e\u4eba\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u674e\u98de\u98de\u5728WordNet\u7684\u57fa\u7840\u4e0a\uff0c\u5229\u7528Amazon\u7684\u4f17\u5305\u670d\u52a1\u4e3a\u4e00\u4e2a\u5177\u67091200\u4e07\u5f20\u56fe\u7247\u7684\u6570\u636e\u96c6\u6253\u4e0a\u4e86\u4eba\u5de5\u7684\u6807\u7b7e\uff0c\u5e76\u7ec4\u7ec7\u4e86\u6bcf\u5e74\u4e00\u5ea6\u7684ImageNet[23]\u6311\u6218\u8d5b\u3002\u57282012\u5e74\u65f6\uff0c\u8f9b\u987f\u5e26\u9886\u5b66\u751fAlex Krizhevsky\u548cIlya Sutskever\u7528Alexnet[24]\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4ee5\u6781\u5927\u7684\u4f18\u52bf\u6218\u80dc\u4e86\u5f53\u65f6\u6240\u6709\u7684\u7ade\u4e89\u5bf9\u624b\u3002Alexnet\u7684\u6a2a\u7a7a\u51fa\u4e16\u53ef\u8c13\u662f\u5929\u65f6\u5730\u5229\u4eba\u548c\uff0c\u5c06\u6df1\u5ea6\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u8fd9\u4e2a\u6a21\u578b\uff0c\u5229\u7528\u5f53\u65f6\u5148\u8fdb\u7684GPU\u8ba1\u7b97\u80fd\u529b\uff0c\u5e94\u7528\u5230\u5927\u91cf\u6570\u636eImagenet\u4e0a\uff0c\u624d\u83b7\u5f97\u4e86\u6210\u529f\u3002\u8fd9\u4f7f\u5f97\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e00\u6218\u6210\u540d\uff0c\u6b63\u5f0f\u5ba3\u5e03\u6df1\u5ea6\u5b66\u4e60\u65f6\u4ee3\u7684\u5230\u6765\u30022012\u5e74\u4e4b\u540e\uff0c\u5728\u751f\u6210\u5b66\u4e60\u9886\u57df\u4e5f\u51fa\u73b0\u4e86\u5feb\u901f\u7684\u53d1\u5c55\uff0c2014\u5e74\u7684Generative Adversarial Network[25]\uff0cVariational Autoencoder[26]\uff0c2015\u5e74\u7684Flow Models\uff0cDiffusion Models\uff0c2017\u5e74\u7684Self-Attention\u673a\u5236\u548cTransformer[27]\u63a5\u8e35\u51fa\u73b0\uff0c\u6700\u7ec8\u50ac\u751f\u4e862022\u5e74\u7684ChatGPT[5]\u3002<\/span><\/section>\n
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\u53ef\u4ee5\u770b\u5230\u5728\u8fd9\u573a\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u7684\u6d6a\u6f6e\u4e2d\uff0c\u73bb\u5c14\u5179\u66fc\u673a\u7684\u8eab\u5f71\u9010\u6e10\u6d88\u5931\u4e86\u3002\u5177\u4f53\u7684\u539f\u56e0\u662f\u73b0\u4ee3\u7684\u751f\u6210\u6a21\u578b\u4ece\u6a21\u578b\u7684\u89d2\u5ea6\u4e0a\u89e3\u51b3\u4e86\u73bb\u5c14\u5179\u66fc\u673a\u7684\u914d\u5206\u51fd\u6570\u8ba1\u7b97\u4ee5\u53ca\u91c7\u6837\u8fd9\u4e24\u4e2a\u96be\u9898\u3002\u8fd9\u91cc\u6211\u4eec\u4ee5\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u4e4b\u4e00\u7684\u81ea\u56de\u5f52\u795e\u7ecf\u7f51\u7edc\u6a21\u578b<\/span> (\u53ef\u53c2\u9605\u4f5c\u80052024\u5e74\u7b2c6\u671f\u5728\u672c\u520a\u53d1\u8868\u7684\u79d1\u666e\u6587\u7ae0\u300a<\/span>\u5199\u7ed9\u7269\u7406\u5b66\u5bb6\u7684\u751f\u6210\u6a21\u578b<\/a><\/span>\u300b)<\/span> \u4e3a\u4f8b\u5177\u4f53\u89e3\u91ca\u662f\u5982\u4f55\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u3002\u5728\u81ea\u56de\u5f52\u6a21\u578b\u4e2d\uff0c\u8054\u5408\u6982\u7387\u5206\u5e03\u5177\u6709\u6761\u4ef6\u6982\u7387\u8fde\u4e58\u7684\u5f62\u5f0f<\/span>\u3002\u9996\u5148\uff0c\u53d8\u91cf\u88ab\u4e8b\u5148\u5236\u5b9a\u4e86\u4e00\u4e2a\u987a\u5e8f\uff0cj<\/em><i<\/em>\u4ee3\u8868\u5728\u53d8\u91cfi<\/em>\u4e4b\u524d\u7684\u53d8\u91cf\uff0c\u5728\u8fd9\u91cc\u79f0\u4e3a\u5386\u53f2\u53d8\u91cf\uff0cs<\/em>j<\/sub><\/em><i<\/em><\/sub>\u4ee3\u8868\u5b83\u4eec\u7684\u6784\u578b\u3002q <\/em>(si<\/sub><\/em>|s<\/em>j<\/sub><\/em><i<\/em><\/sub>)\u7684\u610f\u4e49\u662f\u7ed9\u5b9ai<\/em>\u4e4b\u524d\u53d8\u91cf\u7684\u6784\u578b\uff0c\u53d8\u91cfi<\/em>\u53d6si<\/sub><\/em>\u7684\u6761\u4ef6\u6982\u7387\u3002\u56fe6\u7ed9\u51fa\u7684\u4f8b\u5b50\u4e2dsi<\/sub><\/em>\u4e3a\u4e8c\u503c\u53d8\u91cf\uff0c\u56e0\u6b64\u5728\u7ed9\u5b9a\u5386\u53f2\u53d8\u91cf\u6784\u578b\u4e4b\u540e\u7684\u6761\u4ef6\u6982\u7387\u53ef\u4ee5\u7528Sigmoid\u51fd\u6570\u6765\u53c2\u6570\u5316\u3002\u4ee54\u4e2a\u53d8\u91cf\u7684\u81ea\u56de\u5f52\u6a21\u578b\u4e3a\u4f8b\uff0c\u4e25\u683c\u7684\u6982\u7387\u5206\u5e03\u4e3aq<\/em>(s<\/em>1<\/sub>, s<\/em>2<\/sub>, <\/span>s<\/em>3<\/sub>, <\/span>s<\/em>4<\/sub>)\u3002\u4f7f\u7528\u8d1d\u53f6\u65af\u516c\u5f0f\uff0c\u53ef\u4ee5\u5148\u5c06\u5b83\u9010\u6b65\u5199\u6210\u6761\u4ef6\u6982\u7387\u7684\u4e58\u79ef\uff1a<\/span><\/section>\n

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\u6bcf\u4e2a\u6761\u4ef6\u6982\u7387\u901a\u8fc7\u795e\u7ecf\u7f51\u7edc\u6765\u53c2\u6570\u5316\uff0c\u5982\u56fe6\u6240\u793a\u3002<\/span><\/section>\n

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\u56fe6 \u67094\u4e2a\u53d8\u91cf\u7684\u81ea\u56de\u5f52\u6a21\u578b\u7684\u4e00\u4e2a\u7b80\u5355\u5b9e\u73b0<\/span><\/section>\n

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\u6ce8\u610f\uff0c\u5bf9\u4e8e\u4e0d\u540c\u5386\u53f2\u6784\u578b\u7684\u6761\u4ef6\u6982\u7387\u7684\u53c2\u6570\u662f\u5171\u4eab\u7684\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4e0d\u540c\u53d8\u91cf\u6761\u4ef6\u6982\u7387\u7684\u53c2\u6570\u4e5f\u53ef\u4ee5\u5171\u4eab\u3002\u5728\u56fe6\u6240\u5c55\u793a\u7684\u53c2\u6570\u5316\u4e0b\uff0c\u53ef\u4ee5\u770b\u5230\uff0c\u7ed9\u5b9a\u4efb\u4f55\u4e00\u4e2a\u7f51\u7edc\u6784\u578bs<\/em>1<\/sub>, <\/span>s<\/em>2<\/sub>, <\/span>s<\/em>3<\/sub>, <\/span>s<\/em>4<\/sub>\u4f5c\u4e3a\u8f93\u5165\uff0c\u7f51\u7edc\u8f93\u51fa\u7684\u8fde\u4e58<\/span>\u5373\u4e3a\u8fd9\u4e2a\u6784\u578b\u7684\u8054\u5408\u5206\u5e03\u6982\u7387\uff0c\u800c\u4e14\u5176\u5f52\u4e00\u5316\u56e0\u5b50\u4e3a1\u3002\u53e6\u5916\uff0c\u65e2\u7136\u5df2\u7ecf\u5b58\u50a8\u4e86\u6240\u6709\u7684\u6761\u4ef6\u6982\u7387\uff0c\u5bf9\u8054\u5408\u6982\u7387\u7684\u65e0\u504f\u6837\u672c\u53ef\u4ee5\u901a\u8fc7\u5bf9\u6bcf\u4e2a\u6761\u4ef6\u6982\u7387\u5355\u72ec\u91c7\u6837\u6765\u5f97\u5230\u3002\u5728\u56fe6\u4e2d\u6211\u4eec\u53ef\u4ee5\u53d6q<\/em>(s<\/em>1<\/sub>=1)\u91c7\u6837\u51fas<\/em>1<\/sub>\uff0c\u7136\u540e\u5e26\u5165\u5230q<\/em>(s<\/em>2<\/sub>=1|s<\/em>1<\/sub>)\u6765\u91c7\u6837\u51fas<\/em>2<\/sub>\uff0c\u7136\u540e\u5c06s<\/em>1<\/sub>, s<\/em>2<\/sub>\u4ee3\u5165\u5230q<\/em>(s<\/em>3<\/sub>=1|s<\/em>2<\/sub>,s<\/em>1<\/sub>)\u6765\u91c7\u6837s<\/em>3<\/sub>\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002\u800c\u4e14\u591a\u4e2a\u6837\u672c\u53ef\u4ee5\u88ab\u5e76\u884c\u5730\u91c7\u6837\uff0c\u4ece\u800c\u9ad8\u6548\u5730\u5229\u7528GPU\u7684\u8ba1\u7b97\u80fd\u529b\u3002\u56e0\u6b64\u81ea\u56de\u5f52\u6a21\u578b\u7528\u6761\u4ef6\u6982\u7387\u4e58\u79ef\u7684\u5f62\u5f0f\u89e3\u51b3\u4e86\u73bb\u5c14\u5179\u66fc\u673a\u7684\u914d\u5206\u51fd\u6570\u8ba1\u7b97\u4ee5\u53ca\u65e0\u504f\u91c7\u6837\u95ee\u9898\u3002<\/span><\/section>\n

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\u4eba\u4eec\u5229\u7528ChatGPT\u548c\u7c7b\u4f3c\u7684\u6a21\u578b\u6839\u636e\u63d0\u793a\u8bcd\u751f\u6210\u65b0\u7684\u6587\u672c\uff0c\u8fd9\u4e2a\u751f\u6210\u8fc7\u7a0b\u7684\u672c\u8d28\u662f\u5229\u7528\u4e86\u81ea\u56de\u5f52\u6a21\u578b\u7684\u91c7\u6837\uff0c\u56e0\u4e3a\u63cf\u8ff0\u4e00\u53e5\u8bdd\u4e2d\u5b57\u7b26<\/span> (token) <\/span>\u7684\u8054\u5408\u5206\u5e03\u6982\u7387\u7684Transformer\u52a0\u4e0a\u4e86\u56e0\u679c\u63a9\u7801<\/span> (Causal mask) <\/span>\u4e4b\u540e\uff0c\u5c31\u53ef\u4ee5\u4ece\u5b66\u4e60\u5230\u7684\u8054\u5408\u5206\u5e03\u4e2d\u4e00\u4e2a\u8bcd\u4e00\u4e2a\u8bcd\u7684\u91c7\u6837\uff0c\u5c31\u50cf\u56fe6\u4e2d\u6240\u5c55\u793a\u7684\uff0c\u4e00\u4e2a\u81ea\u65cb\u4e00\u4e2a\u81ea\u65cb\u5730\u751f\u62104\u4e2a\u53d8\u91cf\u7684\u81ea\u65cb\u6784\u578b\u4e00\u6837\u3002\u8fd9\u79cd\u65b9\u5f0f\u4e5f\u9020\u5c31\u4e86\u8fd1\u5e74\u6765\u5927\u8bed\u8a00\u6a21\u578b\u7684\u8f89\u714c\u3002<\/span><\/section>\n

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\u5728\u8fde\u7eed\u53d8\u91cf\u7684\u8054\u5408\u5206\u5e03\u523b\u753b\u95ee\u9898\u4e2d\uff0c\u66f4\u6709\u6548\u7684\u6a21\u578b\u662f\u6d41\u6a21\u578b<\/span> (flow model)<\/span>\u3001\u6269\u6563\u6a21\u578b <\/span>(diffusion model)<\/span>\uff0c\u4ee5\u53ca\u6d41\u5339\u914d\u65b9\u6cd5<\/span> (flow matching)<\/span>\uff0c\u5b83\u4eec\u5229\u7528\u4e0d\u540c\u7684\u65b9\u5f0f\u6765\u89e3\u51b3\u91c7\u6837\u95ee\u9898\uff0c\u8fdb\u800c\u63d0\u4f9b\u4e86\u56fe\u7247\u3001\u89c6\u9891\u4ee5\u53ca\u97f3\u4e50\u751f\u6210\u7684\u7cbe\u5f69\u5e94\u7528\u3002\u5177\u4f53\u7684\u4ecb\u7ecd\u53ef\u4ee5\u53c2\u8003\u4f5c\u8005\u7684\u79d1\u666e\u6587\u7ae0\u300a\u5199\u7ed9\u7269\u7406\u5b66\u5bb6\u7684\u751f\u6210\u6a21\u578b<\/a>\u300b\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
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4. \u672a\u6765<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u6700\u540e\u56de\u5230\u5927\u81ea\u7136\u7684\u91c7\u6837\u4e0e\u751f\u6210\u5b66\u4e60\u3002\u6211\u4eec\u8ba8\u8bba\u8fc7\u5229\u7528\u81ea\u7136\u754c\u7684\u5206\u5e03\u2014\u2014\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u8fdb\u884c\u91c7\u6837\u542f\u53d1\u4e86\u73bb\u5c14\u5179\u66fc\u673a\u7b49\u57fa\u7840\u6027\u7684\u751f\u6210\u6a21\u578b\uff0c\u4e5f\u83b7\u5f97\u4e86\u8bfa\u8d1d\u5c14\u5956\u3002\u4f46\u4e5f\u5e94\u8be5\u6307\u51fa\uff0c\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u5177\u6709\u8ba1\u7b97\u5f52\u4e00\u5316\u7684\u6982\u7387\u503c\u4ee5\u53ca\u65e0\u504f\u91c7\u6837\u7684\u96be\u9898\u3002\u8fd9\u4e24\u4e2a\u96be\u9898\u5373\u4f7f\u662f\u5927\u81ea\u7136\u672c\u8eab\u4e5f\u662f\u5f88\u96be\u89e3\u51b3\u7684\uff0c\u56e0\u4e3a\u81ea\u7136\u754c\u7684\u91c7\u6837\u4e5f\u4f1a\u9677\u5165\u4e9a\u7a33\u6001\uff0c\u4ece\u800c\u4ea7\u751f\u8fc7\u51b7\u6db2\u4f53\u3001\u73bb\u7483\u6001\u7b49\u6ca1\u6709\u5e73\u8861\u7684\u7269\u8d28\uff0c\u56e0\u6b64\u5229\u7528\u4e86\u5927\u81ea\u7136\u8ba1\u7b97\u80fd\u529b\u7684\u7ecf\u5178\u8ba1\u7b97\u673a\u5f88\u96be\u5f7b\u5e95\u89e3\u51b3\u73bb\u5c14\u5179\u66fc\u7684\u91c7\u6837\u95ee\u9898\u3002\u9664\u4e86\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4ee5\u5916\uff0c\u7269\u7406\u5b66\u8fd8\u6709\u53e6\u5916\u4e00\u4e2a\u91cd\u8981\u7684\u6982\u7387\u5206\u5e03\uff0c\u5373\u73bb\u6069\u6cd5\u5219<\/span> (Born\u2019s rule)<\/span>\u3002\u73bb\u6069\u6cd5\u5219\u4e2d\u6ce2\u51fd\u6570\u7684\u6a21\u5e73\u65b9\u6240\u8868\u8fbe\u7684\u6982\u7387\u7ed9\u51fa\u4e86\u5fae\u89c2\u4e16\u754c\u5728\u91cf\u5b50\u529b\u5b66\u63a7\u5236\u8303\u56f4\u5185\u7684\u89c2\u6d4b\u6982\u7387\u3002\u4ece\u8fd9\u4e2a\u6982\u7387\u5206\u5e03\u4e2d\u4ea7\u751f\u6837\u672c\u662f\u81ea\u7136\u754c\u91cf\u5b50\u4f18\u52bf\u7684\u4e00\u79cd\u4f53\u73b0\uff0c\u5982\u679c\u4eba\u4eec\u53ef\u4ee5\u5229\u7528\u8fd9\u79cd\u4f18\u52bf\uff0c\u4e5f\u8bb8\u53ef\u4ee5\u5728\u4e0d\u8fdc\u7684\u5c06\u6765\u6781\u5927\u5730\u63a8\u8fdb\u751f\u6210\u6a21\u578b\u7684\u53d1\u5c55\u3002<\/span><\/section>\n<\/section>\n<\/section>\n

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\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u8bfb\u4e66\u4f1a\u542f\u52a8\uff01<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n

2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff0c\u8fd9\u662f\u4e00\u573a\u7edf\u8ba1\u7269\u7406\u5f15\u53d1\u7684\u673a\u5668\u5b66\u4e60\u9769\u547d\u3002\u7edf\u8ba1\u7269\u7406\u5b66\u4e0d\u4ec5\u80fd\u89e3\u91ca\u70ed\u5b66\u73b0\u8c61\uff0c\u8fd8\u80fd\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4ece\u5fae\u89c2\u7c92\u5b50\u5230\u5b8f\u89c2\u5b87\u5b99\u7684\u5404\u4e2a\u5c42\u7ea7\u5982\u4f55\u8054\u7cfb\u8d77\u6765\uff0c\u590d\u6742\u73b0\u8c61\u5982\u4f55\u6d8c\u73b0\u3002\u5b83\u901a\u8fc7\u7814\u7a76\u5927\u91cf\u7c92\u5b50\u7684\u96c6\u4f53\u884c\u4e3a\uff0c\u6210\u529f\u5730\u5c06\u5fae\u89c2\u4e16\u754c\u7684\u968f\u673a\u6027\u4e0e\u5b8f\u89c2\u4e16\u754c\u7684\u786e\u5b9a\u6027\u8054\u7cfb\u8d77\u6765\uff0c\u4e3a\u6211\u4eec\u7406\u89e3\u81ea\u7136\u754c\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u4e5f\u4e3a\u673a\u5668\u5b66\u4e60\u548c\u4eba\u5de5\u667a\u80fd\u9886\u57df\u7684\u53d1\u5c55\u63d0\u4f9b\u4e86\u91cd\u8981\u63a8\u52a8\u529b\u3002<\/span><\/p>\n


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\u4e3a\u4e86\u6df1\u5165\u63a2\u7d22\u7edf\u8ba1\u7269\u7406\u524d\u6cbf\u8fdb\u5c55\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u897f\u6e56\u5927\u5b66\u7406\u5b66\u9662\u53ca\u4ea4\u53c9\u79d1\u5b66\u4e2d\u5fc3\u8bb2\u5e2d\u6559\u6388\u6c64\u96f7\u7ff0\u3001\u7ebd\u7ea6\u5dde\u7acb\u5927\u5b66\u77f3\u6eaa\u5206\u6821\u5316\u5b66\u548c\u7269\u7406\u5b66\u7cfb\u6559\u6388\u6c6a\u52b2\u3001\u5fb7\u7d2f\u65af\u987f\u7cfb\u7edf\u751f\u7269\u5b66\u4e2d\u5fc3\u535a\u58eb\u540e\u7814\u7a76\u5458\u6881\u5e08\u7fce\u3001\u9999\u6e2f\u6d78\u4f1a\u5927\u5b66\u7269\u7406\u7cfb\u52a9\u7406\u6559\u6388\u5510\u4e7e\u5143\uff0c\u4ee5\u53ca\u591a\u4f4d\u56fd\u5185\u5916\u77e5\u540d\u5b66\u8005\u5171\u540c\u53d1\u8d77\u300c\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u300d\u8bfb\u4e66\u4f1a<\/a>\u3002\u8bfb\u4e66\u4f1a\u65e8\u5728\u63a2\u8ba8\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u6700\u65b0\u7406\u8bba\u7a81\u7834\uff0c\u7edf\u8ba1\u7269\u7406\u5728\u590d\u6742\u7cfb\u7edf\u548c\u751f\u547d\u79d1\u5b66\u4e2d\u7684\u5e94\u7528\uff0c\u4ee5\u53ca\u4e0e\u673a\u5668\u5b66\u4e60\u7b49\u524d\u6cbf\u9886\u57df\u7684\u4ea4\u53c9\u7814\u7a76\u3002\u8bfb\u4e66\u4f1a\u4ece12\u670812\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u56db\u665a20:00-22:00\u8fdb\u884c\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba112\u5468\u3002\u6211\u4eec\u8bda\u631a\u9080\u8bf7\u5404\u4f4d\u670b\u53cb\u53c2\u4e0e\u8ba8\u8bba\u4ea4\u6d41\uff0c\u4e00\u8d77\u63a2\u7d22\u7231\u56e0\u65af\u5766\u773c\u4e2d\u7684\u666e\u9002\u7406\u8bba\uff01<\/span><\/span><\/p>\n


<\/section>\n
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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>\u4ece\u70ed\u529b\u5b66\u3001\u751f\u547d\u5230\u4eba\u5de5\u667a\u80fd\u7684\u7edf\u8ba1\u7269\u7406\u4e4b\u8def\uff1a\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u8bfb\u4e66\u4f1a\u542f\u52a8\uff01<\/a><\/span><\/p>\n<\/section>\n


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

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

<\/strong><\/section>\n
1. <\/strong>2024\u5e74\u8bfa\u5956\u89e3\u8bfb\uff1a\u7edf\u8ba1\u7269\u7406\u3001\u4eba\u5de5\u667a\u80fd\u4e0e\u590d\u6742\u79d1\u5b66<\/a><\/strong><\/span><\/section>\n
2. <\/strong>2024\u5e74\u7269\u7406\u8bfa\u5956\u6388\u4e88\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff1a\u7edf\u8ba1\u7269\u7406\u5f15\u53d1\u7684\u673a\u5668\u5b66\u4e60\u9769\u547d<\/a><\/strong><\/span><\/section>\n
3. <\/strong>\u7269\u7406\u5b66\u9047\u89c1\u673a\u5668\u5b66\u4e60\uff1a\u6df1\u5ea6\u5b66\u4e60\u7684\u4e0b\u4e00\u4e2a\u7a81\u7834\u53ef\u80fd\u6765\u81ea\u7edf\u8ba1\u7269\u7406\u5b66<\/a><\/strong><\/span><\/section>\n
<\/strong><\/strong><\/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
<\/strong>5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n


<\/p>\n


<\/p>\n

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

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

\u5bfc\u8bed 2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7\u548c\u6770\u5f17\u91cc\u00b7\u8f9b\u987f\uff0c\u8fd9\u5bf9\u5f88\u591a\u4eba\u6765\u8bf4\u662f\u51fa\u4e4e\u610f\u6599\u7684\u3002\u6587\u7ae0\u5c06\u4ece\u7edf\u8ba1\u7269\u7406\u7684\u89c6\u89d2\uff0c\u4ece\u4f0a\u8f9b\u6a21\u578b\u51fa\u53d1\uff0c\u9010\u6b65\u4ecb\u7ecd\u970d\u666e\u83f2\u5c14\u5fb7\u548c\u8f9b\u987f\u7684\u4e3b\u8981\u8d21\u732e\uff0c\u5176\u4e2d\u5305\u62ecHopfield\u6a21\u578b\u3001\u73bb\u5c14\u5179\u66fc\u673a\u3001\u975e\u76d1\u7763\u5b66\u4e60\uff0c\u4ee5\u53ca\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u3002\u8fd8\u5c06\u56de\u987e\u7edf\u8ba1\u7269\u7406\u548c\u673a\u5668\u5b66\u4e60\u572820\u4e16\u7eaa\u672b\u671f\u7684\u7cbe\u5f69\u5408\u4f5c\u5386\u7a0b\uff0c\u5e76…<\/p>\n","protected":false},"author":0,"featured_media":55209,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/55238"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=55238"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/55238\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/55209"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=55238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=55238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=55238"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=55238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}