{"id":54626,"date":"2024-12-23T20:20:26","date_gmt":"2024-12-23T12:20:26","guid":{"rendered":"https:\/\/swarma.org\/?p=54626"},"modified":"2024-12-23T20:20:26","modified_gmt":"2024-12-23T12:20:26","slug":"%e7%89%a9%e7%90%86%e5%ad%a6%e4%b8%8e%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e7%9a%84%e8%bf%9e%e6%8e%a5%ef%bc%9a2024%e5%b9%b4%e8%af%ba%e8%b4%9d%e5%b0%94%e7%89%a9%e7%90%86%e5%ad%a6%e5%a5%96%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=54626","title":{"rendered":"\u7269\u7406\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u7684\u8fde\u63a5\uff1a2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u89e3\u6790"},"content":{"rendered":"
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2024<\/span>\u5e74<\/span>10<\/span>\u6708<\/span>8<\/span>\u65e5\uff0c\u745e\u5178\u7687\u5bb6\u79d1\u5b66\u9662\u5ba3\u5e03\u5c06<\/span>\u8be5\u5e74\u5ea6\u7684\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88<\/span>John Hopfield <\/span>\u548c <\/span>Geoffrey Hinton<\/span>\uff0c\u4ee5\u8868\u5f70\u4ed6\u4eec\u5728\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u5f00\u521b\u6027\u8d21\u732e\u3002<\/span>\u8fd9\u4e00\u51b3\u5b9a\u5728\u79d1\u5b66\u754c\u5185\u90e8\u5f15\u8d77\u4e86\u5e7f\u6cdb\u70ed\u8bae\u4e0e\u597d\u5947\u3002<\/span>\u6765\u81ea\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u7269\u7406\u5b66\u4ee5\u53ca\u76f8\u5173\u9886\u57df\u7684\u7814\u7a76\u4eba\u5458\u7eb7\u7eb7\u5bf9\u6b64\u8868\u793a\u7591\u60d1\uff1a\u4e3a\u4f55\u4f20\u7edf\u4e0a\u88ab\u89c6\u4e3a\u4eba\u5de5\u667a\u80fd\u4e0e\u795e\u7ecf\u7f51\u7edc\u9886\u57df\u5185\u7684\u7814\u7a76\u8005\u80fd\u591f\u83b7\u5f97\u7269\u7406\u5b66\u9886\u57df\u7684\u6700\u9ad8\u8363\u8a89\uff1f<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u5b9e\u9645\u4e0a\uff0cJohn Hopfield\u548cGeoffrey Hinton\u7684\u5de5\u4f5c\u6070\u6070\u5c55\u793a\u4e86\u7269\u7406\u5b66\u3001\u673a\u5668\u5b66\u4e60\u53ca\u795e\u7ecf\u8ba1\u7b97\u539f\u7406\u4e4b\u95f4\u7684\u6df1\u523b\u8054\u7cfb\u3002\u8fd9\u4e9b\u5f00\u521b\u6027\u7684\u5de5\u4f5c\u5728\u7edf\u8ba1\u7269\u7406\u5b66\u3001\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u4e4b\u95f4\u5efa\u7acb\u4e86\u5173\u952e\u6865\u6881\uff0c\u4e0d\u4ec5\u5bf9\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\u610f\u4e49\u91cd\u5927\uff0c\u4e5f\u4f53\u73b0\u4e86\u7269\u7406\u5b66\u5728\u4eba\u5de5\u667a\u80fd\u53d1\u5c55\u4e2d\u7684\u5173\u952e\u4f5c\u7528\uff0c\u6545\u800c\u80fd\u591f\u5f97\u5230\u8bfa\u8d1d\u5c14\u5956\u59d4\u5458\u4f1a\u7684\u8ba4\u53ef\u3002\u672c\u6587\u65e8\u5728\u4ecb\u7ecd\u7269\u7406\u5b66\u539f\u7406\u5728\u795e\u7ecf\u7f51\u7edc\u53d1\u5c55\u4e2d\u8d77\u5230\u7684\u5173\u952e\u4f5c\u7528\uff0c\u63a2\u8ba8\u7269\u7406\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u8fd9\u4e24\u4e2a\u9886\u57df\u4e4b\u95f4\u7684\u6df1\u523b\u8054\u7cfb\uff0c\u91cd\u70b9\u9610\u8ff0Hopfield\u548cHinton\u5982\u4f55\u5c06\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u6982\u5ff5\u4e0e\u6a21\u578b\u5e94\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0c\u5efa\u7acb\u795e\u7ecf\u8ba1\u7b97\u7684\u7406\u8bba\u6846\u67b6\uff0c\u4e3a\u73b0\u4ee3\u4eba\u5de5\u667a\u80fd\u7684\u53d1\u5c55\u5960\u5b9a\u7406\u8bba\u57fa\u7840\u3002<\/span><\/section>\n

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1.1 \u5b66\u672f\u5386\u7a0b<\/span><\/strong><\/span><\/section>\n

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John J. Hopfield\u4e8e1933\u5e74\u51fa\u751f\u4e8e\u7f8e\u56fd\u829d\u52a0\u54e5\uff0c1958\u5e74\u83b7\u5f97\u5eb7\u5948\u5c14\u5927\u5b66\u7269\u7406\u5b66\u535a\u58eb\u5b66\u4f4d\uff0c\u968f\u540e\u5728\u52a0\u5dde\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\u3001\u666e\u6797\u65af\u987f\u5927\u5b66\u548c\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u7b49\u77e5\u540d\u5b66\u5e9c\u4efb\u6559\u3002Hopfield\u65e9\u671f\u7684\u7814\u7a76\u805a\u7126\u4e8e\u51dd\u805a\u6001\u7269\u7406\uff0c\u5e76\u5728\u6fc0\u5b50\u548c\u534a\u5bfc\u4f53\u7406\u8bba\u65b9\u9762\u505a\u51fa\u4e86\u91cd\u8981\u8d21\u732e[1,2]\u3002\u8fd9\u4e9b\u5bf9\u51dd\u805a\u6001\u7cfb\u7edf\u4e2d\u96c6\u4f53\u884c\u4e3a\u4e0e\u6d8c\u73b0\u73b0\u8c61[3]\u7684\u65e9\u671f\u7814\u7a76\u7ecf\u5386\u4e3aHopfield\u540e\u6765\u5728\u7406\u8bba\u795e\u7ecf\u79d1\u5b66\u548c\u751f\u7269\u8ba1\u7b97\u65b9\u9762\u53d6\u5f97\u7684\u7a81\u7834\u6027\u6210\u679c\u63d0\u4f9b\u4e86\u5173\u952e\u76f4\u89c9[4]\u300220\u4e16\u7eaa70\u5e74\u4ee3\uff0cHopfield\u5f00\u59cb\u63a2\u7d22\u751f\u547d\u79d1\u5b66\u4e2d\u7684\u7269\u7406\u95ee\u9898\uff0c\u4ed6\u4e0eJacques Ninio\u5404\u81ea\u72ec\u7acb\u63d0\u51fa\u4e86\u751f\u5316\u53cd\u5e94\u4e2d\u7684\u52a8\u529b\u5b66\u6821\u6b63<\/span>\uff08kinetic proofreading\uff09<\/span>\u673a\u5236[5,6]\uff0c\u5efa\u7acb\u4e86\u80fd\u91cf\u6d88\u8017\u4e0e\u751f\u7269\u7cfb\u7edf\u4fe1\u606f\u5904\u7406\u51c6\u786e\u6027\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u4e3a\u7406\u89e3\u751f\u7269\u7cfb\u7edf\u5982\u4f55\u901a\u8fc7\u975e\u5e73\u8861\u8fc7\u7a0b\u5b9e\u73b0\u9ad8\u7279\u5f02\u6027\u63d0\u4f9b\u4e86\u6df1\u523b\u7684\u89c1\u89e3\uff0c\u4fc3\u8fdb\u4e86\u975e\u5e73\u8861\u70ed\u529b\u5b66\u7684\u53d1\u5c55\u3002\u968f\u540e\uff0cHopfield\u5f00\u59cb\u5c06\u7814\u7a76\u7684\u91cd\u70b9\u8f6c\u5411\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e0e\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\uff0c\u5176\u6700\u8457\u540d\u7684\u6210\u5c31\u662f\u57281982\u5e74\u63d0\u51fa\u7684Hopfield\u6a21\u578b[7]\u3002<\/span><\/o:p><\/section>\n

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\u56fe1  Hopfield\u6a21\u578b\u53ca\u5176\u5de5\u4f5c\u539f\u7406\u793a\u610f\u56fe\u3002(a) \u4e00\u4e2a\u5305\u542b6\u4e2a\u795e\u7ecf\u5143\u7684Hopfield\u7f51\u7edc\u793a\u610f\u56fe\uff0c\u6bcf\u4e2a\u5706\u5708\u4ee3\u8868\u4e00\u4e2a\u795e\u7ecf\u5143\uff0c\u5176\u72b6\u6001si<\/sub>\u53ef\u53d6+1\u6216-1\uff1b\u8fde\u63a5\u7ebf\u8868\u793a\u795e\u7ecf\u5143\u95f4\u7684\u7a81\u89e6\u8fde\u63a5\uff0c\u6743\u91cd\u4e3awij<\/sub>\u3002(b) \u5229\u752811\u00d711\u4e2a\u50cf\u7d20\u70b9\u7684\u4e8c\u503c\u56fe\u50cf\uff08\u6bcf\u4e2a\u50cf\u7d20\u503c\u5bf9\u5e94\u4e00\u4e2a\u795e\u7ecf\u5143\u72b6\u6001\uff0c\u53d6\u503c\u4e3a+1\u6216-1\uff09\u5c55\u793aHopfield\u7f51\u7edc\u7684\u6a21\u5f0f\u5b58\u50a8\u548c\u6062\u590d\u8fc7\u7a0b\u3002\u7f51\u7edc\u5c06\u201c\u5341\u201d\u5b57\u5f62\u56fe\u6848\u7f16\u7801\u4e3a\u80fd\u91cf\u6700\u5c0f\u503c\u72b6\u6001\uff0c\u5f53\u4ee5\u968f\u673a\u566a\u58f0\u4f5c\u4e3a\u521d\u59cb\u795e\u7ecf\u5143\u72b6\u6001\u65f6\uff0c\u7ecf\u8fc7\u591a\u8f6e\u8fed\u4ee3\u66f4\u65b0\uff0c\u7cfb\u7edf\u72b6\u6001\u9010\u6e10\u6f14\u5316\u4e3a\u5176\u6240\u8bb0\u5fc6\u7684\u6a21\u5f0f\u3002(c) \u7cfb\u7edf\u80fd\u91cf\u51fd\u6570\u968f\u7740\u795e\u7ecf\u5143\u72b6\u6001\u7684\u8fed\u4ee3\u66f4\u65b0\u800c\u5355\u8c03\u4e0b\u964d\uff0c\u6700\u7ec8\u5728\u5230\u8fbe\u80fd\u91cf\u6781\u5c0f\u503c\u65f6\u5b8c\u5168\u6062\u590d\u51fa\u5b58\u50a8\u7684\u56fe\u50cf\u6a21\u5f0f<\/span><\/o:p><\/p>\n


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1.2 Hopfield\u6a21\u578b\uff1a\u57fa\u7840\u4e0e\u7269\u7406\u89e3\u91ca<\/span><\/strong><\/o:p><\/section>\n

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Hopfield\u6a21\u578b[7]\u4e3a\u673a\u5668\u8bbe\u8ba1\u4e86\u4e00\u79cd\u201c\u8054\u60f3\u8bb0\u5fc6\u201d\u7684\u80fd\u529b\u3002\u5c31\u50cf\u4eba\u4eec\u80fd\u591f\u901a\u8fc7\u8bb0\u5fc6\u5c06\u4e00\u5f20\u6a21\u7cca\u7834\u635f\u7684\u8001\u7167\u7247\u62fc\u51d1\u5b8c\u6574\u4e00\u6837\uff0cHopfield\u6a21\u578b\u53ef\u4ee5\u901a\u8fc7\u4e0d\u65ad\u8c03\u6574\u81ea\u8eab\u72b6\u6001\u63d0\u53d6\u6240\u8bb0\u5fc6\u7684\u4fe1\u606f\u3002\u5982\u56fe1(a)\u6240\u793a\uff0cHopfield\u7f51\u7edc\u7531N\u4e2a\u5168\u8fde\u63a5\u795e\u7ecf\u5143\u7ec4\u6210\uff0c\u5176\u4e2d\u795e\u7ecf\u5143i\u7684\u72b6\u6001\u7528si<\/sub>\u8868\u793a\uff0c\u53ef\u4ee5\u5c06\u5176\u8bbe\u5b9a\u4e3a\u00b11\u4e24\u79cd\u72b6\u6001\uff0c\u4e5f\u53ef\u4ee5\u53d6\u5404\u79cd\u8fde\u7eed\u6570\u503c\u4ee5\u63d0\u9ad8\u7f51\u7edc\u5904\u7406\u6a21\u62df\u6a21\u5f0f\u7684\u5b58\u50a8\u548c\u5904\u7406\u80fd\u529b[8]\u3002\u795e\u7ecf\u5143\u4e4b\u95f4\u7531\u7a81\u89e6\u8fde\u63a5\uff0c\u795e\u7ecf\u5143i\u4e0ej\u4e4b\u95f4\u7684\u7a81\u89e6\u8fde\u63a5\u6743\u91cd\u4e3awij<\/sub>\u3002\u8be5\u7f51\u7edc\u6784\u6210\u4e86\u4e00\u4e2a\u5faa\u73af\u795e\u7ecf\u7f51\u7edc<\/span>\uff08recurrent neural network, RNN\uff09<\/span>\uff0c\u5176\u72b6\u6001\u6f14\u5316\u9075\u5faa\u4e00\u4e2a\u7b80\u5355\u7684\u52a8\u529b\u5b66\u89c4\u5219, \u5373\u5bf9\u4e8e\u4efb\u610f\u795e\u7ecf\u5143i\uff0c\u5176t+1\u65f6\u523b\u7684\u72b6\u6001\u7531t\u65f6\u523b\u7684\u72b6\u6001\u51b3\u5b9a\uff1a<\/span><\/o:p><\/section>\n

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\u5176\u4e2d\uff0c\u8fde\u63a5\u6743\u91cdwij<\/sub>\u7531Hebbian\u5b66\u4e60\u89c4\u5219[9]\u786e\u5b9a\u3002\u8be5\u89c4\u5219\u53ef\u4ee5\u7b80\u5355\u8868\u8ff0\u6210\u201c\u4e00\u8d77\u6fc0\u53d1\u7684\u795e\u7ecf\u5143\u8fde\u5728\u4e00\u8d77<\/span>\uff08Neurons that fire together wire together\uff09<\/span>\u201d\uff1a<\/span><\/section>\n

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\u5176\u4e2d\uff0c\u03be\u4ee3\u8868\u7684\u662f\u7f51\u7edc\u6240\u8bb0\u5fc6\u7684\u7b2c\u03bc\u4e2a\u6a21\u5f0f\u7684\u7b2ci\u5206\u91cf\u3002\u7531\u4e0a\u8ff0\u89c4\u5219\u63cf\u8ff0\u7684Hopfield\u7f51\u7edc\u7684\u52a8\u529b\u5b66\u53ef\u4ee5\u63cf\u8ff0\u4e3a\u5982\u4e0b\u7684\u80fd\u91cf\u51fd\u6570\uff1a<\/span><\/section>\n

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\u8be5\u80fd\u91cf\u51fd\u6570\u4e0e\u81ea\u65cb\u73bb\u7483\u7cfb\u7edf\u7684\u80fd\u91cf\u51fd\u6570\u5728\u5f62\u5f0f\u4e0a\u5b8c\u5168\u76f8\u540c[10,11]\uff1a\u795e\u7ecf\u5143\u72b6\u6001\u5bf9\u5e94\u4e8e\u7c92\u5b50\u7684\u81ea\u65cb\u72b6\u6001\uff0c\u7a81\u89e6\u8fde\u63a5\u5bf9\u5e94\u4e8e\u7c92\u5b50\u81ea\u65cb\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u5982\u56fe1(b)\u548c(c)\u6240\u793a\uff0c\u7f51\u7edc\u4e2d\u5b58\u50a8\u7684\u8bb0\u5fc6\u6a21\u5f0f\u5bf9\u5e94\u4e8e\u7cfb\u7edf\u7684\u57fa\u6001\uff0c\u800c\u8bb0\u5fc6\u63d0\u53d6\u8fc7\u7a0b\u5219\u7c7b\u4f3c\u4e8e\u7cfb\u7edf\u5411\u5c40\u90e8\u80fd\u91cf\u6781\u5c0f\u503c\u7684\u5f1b\u8c6b\u8fc7\u7a0b\u3002Hopfield\u6a21\u578b\u4e0e\u81ea\u65cb\u73bb\u7483\u7406\u8bba\u90fd\u5173\u6ce8\u7cfb\u7edf\u7684\u57fa\u6001\u4e0e\u80fd\u91cf\u6700\u5c0f\u5316\u7684\u8fc7\u7a0b\u3002\u5728Hopfield\u6a21\u578b\u4e2d\uff0c\u901a\u8fc7Hebbian\u5b66\u4e60\u89c4\u5219\u786e\u5b9a\u7684\u7a81\u89e6\u6743\u91cd\uff0c\u4f7f\u5f97\u671f\u671b\u8bb0\u5fc6\u7684\u6a21\u5f0f\u5bf9\u5e94\u4e8e\u80fd\u91cf\u51fd\u6570\u7684\u5c40\u90e8\u6700\u5c0f\u503c\uff0c\u8fd9\u4e9b\u5c40\u90e8\u6700\u5c0f\u503c\u6784\u6210\u4e86\u7f51\u7edc\u7684\u5438\u5f15\u5b50<\/strong>\u3002\u8be5\u6a21\u578b\u4e3a\u7406\u89e3\u795e\u7ecf\u7cfb\u7edf\u7684\u4fe1\u606f\u5b58\u50a8\u4e0e\u68c0\u7d22\u673a\u5236\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u7406\u8bba\u6846\u67b6\u3002<\/span><\/o:p><\/section>\n

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Hopfield\u6a21\u578b\u8bc1\u660e\u5206\u5e03\u5f0f\u7684\u8868\u5f81\u53ef\u4ee5\u5b9e\u73b0\u7a33\u5065\u7684\u4fe1\u606f\u5b58\u50a8\uff0c\u8fd9\u4e0d\u4ec5\u542f\u53d1\u4e86\u751f\u7269\u795e\u7ecf\u7cfb\u7edf\u5438\u5f15\u5b50\u52a8\u529b\u5b66\u7684\u5e7f\u6cdb\u7814\u7a76[12]\uff0c\u4e5f\u4e3a\u540e\u6765\u51fa\u73b0\u7684\u5404\u79cd\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u3001\u7c7b\u8111\u8ba1\u7b97\u7b49\u63d0\u4f9b\u4e86\u7406\u8bba\u4f9d\u636e\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8be5\u6a21\u578b\u5f15\u5165\u4e86\u80fd\u91cf\u666f\u89c2<\/strong><\/span>\uff08energy landscape\uff09<\/span>\u4f5c\u4e3a\u7406\u89e3\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u6709\u529b\u5de5\u5177\u3002\u5229\u7528\u81ea\u65cb\u73bb\u7483\u4e2d\u7684\u526f\u672c\u65b9\u6cd5\uff0c\u53ef\u4ee5\u4e25\u683c\u89e3\u6790Hopfield\u7f51\u7edc\u7684\u5b58\u50a8\u5bb9\u91cf\uff0c\u5bf9\u4e8e\u968f\u673a\u6a21\u5f0f\uff0c\u7f51\u7edc\u53ef\u4ee5\u53ef\u9760\u5730\u5b58\u50a8\u548c\u68c0\u7d22\u7684\u6a21\u5f0f\u6570\u4e0e\u7f51\u7edc\u7684\u8282\u70b9\u6570N\u6210\u6b63\u6bd4\uff0c\u5927\u7ea6\u4e3a0.138N [13]\u3002<\/span><\/o:p><\/section>\n

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Hopfield\u7f51\u7edc\u5728\u88ab\u63d0\u51fa\u540e\uff0c\u7ecf\u5386\u4e86\u8bb8\u591a\u62d3\u5c55\u4e0e\u521b\u65b0\uff0c\u663e\u8457\u6269\u5c55\u4e86\u5176\u80fd\u529b\u548c\u5e94\u7528\u8303\u56f4[14~16]\u3002\u8fd9\u4e9b\u589e\u5f3a\u578b\u67b6\u6784\u901a\u8fc7\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff0c\u6216\u4f7f\u5f97\u6a21\u578b\u7684\u5b58\u50a8\u5bb9\u91cf\u5448\u6307\u6570\u7ea7\u589e\u957f\uff0c\u6216\u4f7f\u5f97\u6a21\u578b\u5728\u566a\u58f0\u73af\u5883\u4e0b\u7684\u80fd\u529b\u663e\u8457\u6539\u5584\uff0c\u5bf9\u5b58\u50a8\u6a21\u5f0f\u4e4b\u95f4\u7684\u5e72\u6270\u8868\u73b0\u51fa\u66f4\u5f3a\u7684\u9c81\u68d2\u6027\u3002\u4e5f\u6709\u5b66\u8005\u5c06\u7ecf\u5178\u7684Hopfield\u7f51\u7edc\u4e0e\u73b0\u4ee3\u7684\u6df1\u5ea6\u5b66\u4e60\u67b6\u6784\u201c\u6ce8\u610f\u529b\u673a\u5236\u201d\u7ed3\u5408\u8d77\u6765\uff0c\u5728\u6a21\u5f0f\u8bc6\u522b\u4efb\u52a1\u4e2d\u53d6\u5f97\u4e86\u6210\u529f[17]\u3002\u8fd9\u4e9b\u540e\u7eed\u5de5\u4f5c\u663e\u793a\u4e86Hopfield\u7f51\u7edc\u5e76\u672a\u8fc7\u65f6\uff0c\u5176\u57fa\u7840\u539f\u7406\u4ecd\u5728\u6301\u7eed\u5f71\u54cd\u4eba\u5de5\u667a\u80fd\u7684\u53d1\u5c55\u3002<\/span><\/o:p><\/section>\n

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1.3 \u5176\u4ed6\u4ee3\u8868\u6027\u5de5\u4f5c<\/span><\/strong><\/o:p><\/section>\n

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20\u4e16\u7eaa90\u5e74\u4ee3\uff0cHopfield\u5c06\u6ce8\u610f\u529b\u8f6c\u5411\u795e\u7ecf\u7cfb\u7edf\u4e2d\u7684\u65f6\u95f4\u7f16\u7801\uff0c\u5c24\u5176\u662f\u55c5\u89c9\u4fe1\u53f7\u7684\u5904\u7406[18]\u3002\u4ed6\u7684\u5de5\u4f5c\u6307\u51fa\uff0c\u7c7b\u4f3c\u4e8e\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u76f8\u4f4d\u9501\u5b9a\u7684\u540c\u6b65\u73b0\u8c61\u4e5f\u80fd\u591f\u5728\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u4e2d\u5b9e\u73b0\u7a33\u5065\u7684\u6a21\u5f0f\u8bc6\u522b[19]\u3002\u8fd9\u4e00\u6a21\u578b\u5c55\u793a\u4e86\u65f6\u95f4\u52a8\u529b\u5b66\u5982\u4f55\u663e\u8457\u589e\u5f3a\u795e\u7ecf\u7f51\u7edc\u7684\u8ba1\u7b97\u80fd\u529b\uff0c\u4e3a\u751f\u7269\u7cfb\u7edf\u4e2d\u7684\u4fe1\u606f\u5904\u7406\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u3002<\/span><\/o:p><\/section>\n

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\u6b64\u5916\uff0c\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0cHopfield\u8fd8\u662f\u201c\u4e34\u754c\u8111\u5047\u8bf4\u201d\u7684\u5148\u9a71\u4e4b\u4e00\u30021994\u5e74\uff0c\u4ed6\u5c06\u795e\u7ecf\u7f51\u7edc\u4e0ePer Bak\u3001\u6c64\u8d85\u3001Kurt Wiesenfeld\u63d0\u51fa\u7684\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027<\/span>\uff08\u5373\u5f00\u653e\u7cfb\u7edf\u81ea\u53d1\u6f14\u5316\u5230\u4e34\u754c\u72b6\u6001\u7684\u73b0\u8c61\uff09<\/span>[20]\u8054\u7cfb\u8d77\u6765\uff0c\u5e76\u5c06\u5176\u4e0e\u63cf\u8ff0\u5730\u9707\u7684\u7269\u7406\u6a21\u578b\u8fdb\u884c\u4e86\u7c7b\u6bd4[21]\u30021995\u5e74\uff0cHopfield\u4e0e\u5408\u4f5c\u8005\u89c2\u5bdf\u5230\u4e86\u795e\u7ecf\u7cfb\u7edf\u4e2d\u7684\u96c6\u4f53\u6d3b\u52a8\u51fa\u73b0\u7684\u7a81\u53d1\u6027\u534f\u540c\u884c\u4e3a\uff0c\u8fd9\u79cd\u534f\u540c\u653e\u7535\u6d3b\u52a8\u9075\u5faa\u4e0e\u5730\u9707\u7cfb\u7edf\u76f8\u4f3c\u7684\u5e42\u5f8b\u5206\u5e03\uff0c\u8868\u660e\u795e\u7ecf\u7cfb\u7edf\u53ef\u80fd\u5728\u4e34\u754c\u72b6\u6001\u9644\u8fd1\u8fd0\u884c[22]\u3002\u8fd9\u4e00\u53d1\u73b0\u4e3a\u7406\u89e3\u5927\u8111\u4fe1\u606f\u5904\u7406\u7684\u52a8\u529b\u5b66\u673a\u5236\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u3002<\/span><\/section>\n

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2. Geoffrey Hinton\u7684\u8d21\u732e\uff1a<\/strong><\/span><\/strong><\/strong><\/p>\n

\u4ece\u7edf\u8ba1\u7269\u7406\u5230\u6df1\u5ea6\u5b66\u4e60<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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2.1 \u5b66\u672f\u80cc\u666f<\/span><\/strong><\/span><\/section>\n

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Geoffrey Hinton\u4e8e1947\u5e74\u51fa\u751f\u4e8e\u82f1\u56fd\u6e29\u5e03\u5c14\u767b\uff0c1970\u5e74\u5728\u5251\u6865\u5927\u5b66\u83b7\u5f97\u5b9e\u9a8c\u5fc3\u7406\u5b66\u5b66\u58eb\u5b66\u4f4d\uff0c1978\u5e74\u83b7\u7231\u4e01\u5821\u5927\u5b66\u4eba\u5de5\u667a\u80fd\u535a\u58eb\u5b66\u4f4d\u3002Hinton\u4e00\u76f4\u6d3b\u8dc3\u4e8e\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5b66\u672f\u7814\u7a76\u4e0e\u5de5\u4e1a\u5e94\u7528\u7684\u7b2c\u4e00\u7ebf\u3002\u81ea20\u4e16\u7eaa80\u5e74\u4ee3\u4ee5\u6765\uff0cHinton\u5728\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u8bbe\u8ba1\u548c\u8bad\u7ec3\u65b9\u6cd5\u4e0a\u505a\u51fa\u4e86\u4e00\u7cfb\u5217\u91cd\u8981\u8d21\u732e\u3002\u4ed6\u5728\u7f8e\u56fd\u5361\u5185\u57fa\u6885\u9686\u5927\u5b66\u3001\u52a0\u62ff\u5927\u591a\u4f26\u591a\u5927\u5b66\u548cGoogle\u516c\u53f8\u7684\u76f8\u5173\u5de5\u4f5c\u5f88\u5927\u7a0b\u5ea6\u4e0a\u63a8\u52a8\u4e86\u6df1\u5ea6\u5b66\u4e60\u7684\u8bde\u751f<\/span>\uff08\u6216\u8005\u8bf4\uff0c\u6df1\u5c42\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u590d\u5174\uff09<\/span>\u3002Hinton\u7684\u5de5\u4f5c\u8fd8\u4f7f\u5f97\u6df1\u5ea6\u5b66\u4e60\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406\u7b49\u9886\u57df\u53d6\u5f97\u4e86\u7a81\u7834\u6027\u8fdb\u5c55\uff0c\u4e3a\u4eca\u5929\u5e7f\u6cdb\u5e94\u7528\u7684\u4eba\u5de5\u667a\u80fd\u5960\u5b9a\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u548c\u5b9e\u8df5\u57fa\u7840\u30022019\u5e74\uff0cHinton\u4e0e\u53e6\u5916\u4e24\u4f4d\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u7684\u5148\u9a71\u8005Yoshua Bengio\u548cYann LeCun\u4e00\u540c\u83b7\u5f97\u4e86\u5f53\u5e74\u7684\u56fe\u7075\u5956\u3002<\/span><\/o:p><\/section>\n

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2.2 \u4eceBoltzmann\u673a\u5230\u6df1\u5ea6\u4fe1\u5ff5\u7f51\u7edc<\/span><\/strong><\/span><\/o:p><\/section>\n

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Hinton\u4e0eSejnowski\u3001Ackley\u5408\u4f5c\u63d0\u51fa\u7684Boltzmann\u673a[23,24]\u662f\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u6982\u7387\u6a21\u578b\u7684\u4e00\u79cd\u57fa\u7840\u67b6\u6784\uff0c\u4f53\u73b0\u51fa\u7edf\u8ba1\u7269\u7406\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u6df1\u523b\u5e94\u7528\u3002\u5728\u6807\u51c6\u7684Boltzmann\u673a\u4e2d\uff0c\u7f51\u7edc\u7684\u6240\u6709\u795e\u7ecf\u5143\u4e4b\u95f4\u90fd\u5141\u8bb8\u53cc\u5411\u8fde\u63a5<\/span>\uff08\u5982\u56fe2(a)\u6240\u793a\uff09<\/span>\uff0c\u5176\u80fd\u91cf\u51fd\u6570\u5b9a\u4e49\u4e3a<\/span><\/section>\n

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\u5176\u4e2d\uff0cwij<\/sub>\u8868\u793a\u8fde\u63a5\u6743\u91cd\uff0csi<\/sub>\u548csj<\/sub>\u8868\u793a\u795e\u7ecf\u5143\u72b6\u6001<\/span>\uff08\u81ea\u65cb\uff09<\/span>\uff0cbi<\/sub>\u8868\u793a\u504f\u7f6e\u9879<\/span>\uff08\u5916\u573a\uff09<\/span>\u3002\u57fa\u4e8e\u8be5\u80fd\u91cf\u51fd\u6570\uff0c\u7cfb\u7edf\u72b6\u6001\u7684\u6982\u7387\u5206\u5e03\u6ee1\u8db3\u73bb\u5c14\u5179\u66fc\u5206\u5e03<\/span>\uff0c\u5176\u4e2dZ\u4e3a\u914d\u5206\u51fd\u6570\uff0c\u03b2\u4e3a\u9006\u6e29\u5ea6\u3002\u5176\u5b66\u4e60\u8fc7\u7a0b\u57fa\u4e8e\u6781\u5927\u4f3c\u7136\u539f\u7406\uff0c\u68af\u5ea6\u53ef\u8868\u793a\u4e3a<\/span><\/section>\n

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\u5176\u4e2d\uff0c<\/span>\u548c<\/span>\u5206\u522b\u8868\u793a\u7ecf\u9a8c\u5206\u5e03\u548c\u6a21\u578b\u5206\u5e03\u4e0b\u7684\u671f\u671b\u3002Hopfield\u7f51\u7edc\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u89c6\u4e3a\u786e\u5b9a\u6027\u7684Boltzmann\u673a\uff0c\u800cBoltzmann\u673a\u53ef\u4ee5\u89c6\u4e3a\u968f\u673a\u6027\u7684Hopfield\u7f51\u7edc\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u8be5\u6a21\u578b\u5728\u7406\u8bba\u4e0a\u7b80\u6d01\u4f18\u96c5\uff0c\u4f46\u7531\u4e8e\u5176\u5168\u8fde\u901a\u7279\u6027\uff0c\u5bfc\u81f4\u8bad\u7ec3\u96be\u5ea6\u8f83\u5927\uff0c\u5176\u5e7f\u6cdb\u5e94\u7528\u53d7\u5230\u4e86\u9650\u5236\u3002\u5728\u8be5\u6a21\u578b\u7684\u57fa\u7840\u4e0a\uff0c\u540e\u7eed\u53d1\u5c55\u51fa\u7684\u6700\u8457\u540d\u7684\u4e00\u79cd\u6a21\u578b\u662f\u53d7\u9650Boltzmann\u673a<\/strong><\/span>\uff08restricted Boltzmann machine, RBM\uff09<\/span>\u3002RBM\u7684\u60f3\u6cd5\u6700\u65e9\u7531Paul Smolensky[25]\u63d0\u51fa\uff0c\u968f\u540e\uff0cFreund\u548cHaussler[26]\u8bc1\u660e\u4e86\u4e0eRBM\u7ed3\u6784\u4e00\u81f4\u7684\u4e8c\u503c\u4e24\u5c42\u968f\u673a\u7f51\u7edc\u80fd\u591f\u903c\u8fd1\u4efb\u610f\u4e8c\u503c\u5411\u91cf\u5206\u5e03\uff0c\u4e3aRBM\u7684\u7406\u8bba\u53d1\u5c55\u5960\u5b9a\u4e86\u7406\u8bba\u57fa\u7840\u30022000\u5e74\u4ee3\u521d\u671f\uff0cHinton[27]\u63d0\u51fa\u4e86\u9ad8\u6548\u7684\u5bf9\u6bd4\u6563\u5ea6\u8bad\u7ec3\u7b97\u6cd5\uff0c\u5e76\u5c06RBM\u6210\u529f\u5e94\u7528\u4e8e\u6df1\u5ea6\u5b66\u4e60\u9884\u8bad\u7ec3\u3002\u5982\u56fe2(b)\u6240\u793a\uff0c\u8be5\u67b6\u6784\u5f15\u5165\u4e86\u4e00\u4e2a\u5173\u952e\u7684\u67b6\u6784\u7ea6\u675f\uff1a\u8fde\u63a5\u4ec5\u5141\u8bb8\u5728\u53ef\u89c1\u5c42\u548c\u9690\u85cf\u5c42\u4e4b\u95f4\u5efa\u7acb\uff0c\u6d88\u9664\u4e86\u5c42\u5185\u8fde\u63a5\u3002\u8fd9\u79cd\u9650\u5236\u663e\u8457\u7b80\u5316\u4e86\u8bad\u7ec3\u8fc7\u7a0b\uff0c\u540c\u65f6\u4fdd\u6301\u4e86\u5f3a\u5927\u7684\u8868\u793a\u80fd\u529b\u3002RBM\u7684\u80fd\u91cf\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u4e3a<\/span><\/section>\n

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<\/section>\n

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\u5176\u4e2d\uff0cv\u8868\u793a\u53ef\u89c1\u5355\u5143\uff0ch\u8868\u793a\u9690\u85cf\u5355\u5143\u3002\u8be5\u80fd\u91cf\u51fd\u6570\u6240\u5bf9\u5e94\u7684\u6982\u7387\u5206\u5e03\u670d\u4eceBoltzmann\u5206\u5e03\uff1a<\/span>, \u5176\u4e2dZ\u4e3a\u914d\u5206\u51fd\u6570\u3002<\/span><\/section>\n

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RBM\u7684\u8bad\u7ec3\u6700\u5e38\u7528\u7684\u662fHinton\u7b49\u4eba[27]\u63d0\u51fa\u7684\u5bf9\u6bd4\u6563\u5ea6<\/strong><\/span>\uff08contrastive divergence\uff0cCD\uff09<\/span>\u7b97\u6cd5\uff0c\u5176\u901a\u8fc7\u6700\u5c0f\u5316\u6a21\u578b\u5e73\u8861\u5206\u5e03\u4e0e\u6570\u636e\u5206\u5e03\u4e4b\u95f4\u7684KL\u6563\u5ea6<\/strong><\/span>\uff08Kullback-Leibler divergence\uff09<\/span>\u6765\u5b9e\u73b0<\/span><\/strong>\u3002\u4ece\u7edf\u8ba1\u7269\u7406\u7684\u89c6\u89d2\u6765\u770b\uff0c\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u4e4b\u95f4\u7684KL\u6563\u5ea6\u53ef\u4ee5\u89e3\u91ca\u4e3a\u6570\u636e\u5206\u5e03 pdata<\/sub>(v) \u4e0e\u6a21\u578b\u5206\u5e03 pmodel<\/sub>(v) \u4e4b\u95f4\u81ea\u7531\u80fd\u7684\u5dee\u5f02\uff0c\u7cfb\u7edf\u7684\u5b66\u4e60\u8fc7\u7a0b\u53ef\u4ee5\u8868\u793a\u4e3a\u6700\u5c0f\u5316\u4e24\u4e2a\u5206\u5e03\u4e4b\u95f4\u7684\u81ea\u7531\u80fd\u5dee\u3002\u5728\u5b9e\u8df5\u4e2d\uff0cCD\u7b97\u6cd5\u901a\u8fc7\u622a\u65adGibbs\u91c7\u6837\u6b65\u6570\u6765\u8fd1\u4f3c\u8ba1\u7b97\u68af\u5ea6\uff0c\u663e\u8457\u63d0\u9ad8\u4e86\u8bad\u7ec3\u6548\u7387\u3002\u7531\u4e8e\u8be5\u7b97\u6cd5\u5728k\u6b65\u91c7\u6837\u540e\u5373\u505c\u6b62\uff0c\u56e0\u800c\u8be5\u65b9\u6cd5\u5f97\u540d\u201cCD-k\u7b97\u6cd5\u201d[27~29]\uff0c\u5176\u4e2d\u7684k\u901a\u5e38\u53d6\u4e00\u4e2a\u8f83\u5c0f\u503c\uff08k=1\uff09\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u7c7b\u4f3c\u4e8e\u201c\u53d7\u9650\u9000\u706b\u201d\uff0c\u6bcf\u6b21\u8fdb\u884ck\u6b65\u91c7\u6837\u76f8\u5f53\u4e8e\u8ba9\u7cfb\u7edf\u8fdb\u884c\u4e00\u6b21\u77ed\u6682\u7684\u9000\u706b\uff0c\u7136\u540e\u6839\u636e\u9000\u706b\u7ed3\u679c\u6765\u8c03\u6574\u7cfb\u7edf\u53c2\u6570\u3002\u7406\u8bba\u4e0e\u5b9e\u8df5\u90fd\u8bc1\u660e\uff0c\u867d\u7136\u8fd9\u79cd\u8fd1\u4f3c\u53ef\u80fd\u5bfc\u81f4\u4f30\u8ba1\u504f\u5dee\uff0c\u4f46\u5728\u5927\u591a\u6570\u5e94\u7528\u573a\u666f\u4e2d\u90fd\u80fd\u53d6\u5f97\u4ee4\u4eba\u6ee1\u610f\u7684\u6548\u679c\u3002<\/span><\/o:p><\/section>\n

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\u6df1\u5ea6\u4fe1\u5ff5\u7f51\u7edc<\/span><\/strong>\uff08deep belief network, DBN\uff09<\/span>\u7531Hinton\u7b49\u4eba[30,31]\u57282006\u5e74\u9996\u6b21\u63d0\u51fa\uff0c\u5b83\u7531\u591a\u4e2aRBM\u5806\u53e0\u800c\u6210<\/span>\uff08\u5982\u56fe2(c)\u6240\u793a\uff09<\/span>\u3002DBN\u7684\u8bad\u7ec3\u91c7\u7528\u8d2a\u5a6a\u9010\u5c42\u8bad\u7ec3\u7b56\u7565, \u8be5\u8bad\u7ec3\u65b9\u6cd5\u663e\u8457\u63d0\u9ad8\u4e86\u6df1\u5ea6\u7f51\u7edc\u7684\u8bad\u7ec3\u6548\u679c\uff0c\u88ab\u8ba4\u4e3a\u662f\u6df1\u5ea6\u5b66\u4e60\u5f97\u4ee5\u5e7f\u6cdb\u5e94\u7528\u7684\u5173\u952e\u521b\u65b0\u3002\u5b9e\u8df5\u8868\u660e\uff0cDBN\u5728\u56fe\u50cf\u8bc6\u522b\u7b49\u4efb\u52a1\u4e2d\u5c55\u73b0\u51fa\u826f\u597d\u7684\u6027\u80fd\u3002\u4e0e\u5355\u5c42RBM\u76f8\u6bd4\uff0cDBN\u80fd\u591f\u5b66\u4e60\u5230\u66f4\u52a0\u62bd\u8c61\u7684\u7279\u5f81\u8868\u793a\uff0c\u5e76\u4e14\u5728\u9762\u5bf9\u5305\u542b\u566a\u58f0\u7684\u6570\u636e\u65f6\u4ecd\u80fd\u4fdd\u6301\u826f\u597d\u6027\u80fd\u3002\u4ee5\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u7684\u89c6\u89d2\u6765\u770b[32]\uff0cDBN\u65b9\u6cd5\u4e4b\u6240\u4ee5\u80fd\u4ea7\u751f\u4e0a\u8ff0\u4f18\u70b9\uff0c\u5c31\u5728\u4e8e\u5176\u63d0\u53d6\u7684\u7279\u5f81\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u5448\u73b0\u4e86\u5c42\u7ea7\u5316\u7684\u7ec4\u7ec7\u3002<\/span><\/o:p><\/section>\n

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\u4ee5Hopfield\u7f51\u7edc\u3001RBM\u3001DBN\u7b49\u4e3a\u4ee3\u8868\u7684\u57fa\u4e8e\u80fd\u91cf\u7684\u6a21\u578b<\/span>\uff08energy-based models, EBMs\uff09<\/span>\u4e3a\u6982\u7387\u5bc6\u5ea6\u4f30\u8ba1\u548c\u8868\u793a\u5b66\u4e60\u63d0\u4f9b\u4e86\u4e00\u79cd\u7edf\u4e00\u7684\u6846\u67b6[33]\uff0c\u8fd9\u7c7b\u6a21\u578b\u7684\u7406\u8bba\u57fa\u7840\u53ef\u4ee5\u90fd\u8ffd\u6eaf\u5230\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u81ea\u65cb\u73bb\u7483\u6a21\u578b[34]\u3002EBM\u901a\u8fc7\u5b9a\u4e49\u80fd\u91cf\u51fd\u6570\u6765\u8868\u793a\u6240\u5e0c\u671b\u5b66\u4e60\u7684\u6982\u7387\u5206\u5e03\uff0c\u56e0\u800c\u4e5f\u53ef\u4f5c\u4e3a\u751f\u6210\u6a21\u578b<\/span>\uff08generative model\uff09<\/span>\u5b66\u4e60\u6570\u636e\u5206\u5e03\u5e76\u751f\u6210\u4e0e\u8bad\u7ec3\u6570\u636e\u7c7b\u4f3c\u7684\u65b0\u6837\u672c\u3002\u4e0e\u663e\u5f0f\u5b9a\u4e49\u6982\u7387\u5206\u5e03\u7684\u6a21\u578b\u76f8\u6bd4\uff0cEBM\u5177\u6709\u66f4\u5927\u7684\u7075\u6d3b\u6027\uff0c\u80fd\u591f\u5efa\u6a21\u66f4\u52a0\u590d\u6742\u7684\u4f9d\u8d56\u5173\u7cfb\u3002\u8fd1\u5e74\u6765\uff0c\u57fa\u4e8e\u80fd\u91cf\u7684\u6a21\u578b\u7684\u7406\u8bba\u4ecd\u5728\u4e0d\u65ad\u53d1\u5c55[35,36]\uff0c\u540c\u65f6\u4e5f\u9762\u4e34\u4e0d\u5c11\u6311\u6218\uff1a\u5176\u4e2d\uff0c\u914d\u5206\u51fd\u6570\u7684\u8ba1\u7b97\u548c\u91c7\u6837\u6548\u7387\u95ee\u9898\u4ecd\u662f\u5236\u7ea6\u6a21\u578b\u5e94\u7528\u7684\u4e3b\u8981\u74f6\u9888\u3002\u5176\u6b21\uff0c\u80fd\u91cf\u51fd\u6570\u7684\u8bbe\u8ba1\u7f3a\u4e4f\u7cfb\u7edf\u7684\u6307\u5bfc\u539f\u5219\uff0c\u5f80\u5f80\u9700\u8981\u4f9d\u8d56\u7ecf\u9a8c\u548c\u542f\u53d1\u5f0f\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u6a21\u578b\u7684\u7406\u8bba\u6027\u8d28<\/span>\uff08\u5982\u8868\u8fbe\u80fd\u529b\u3001\u6cdb\u5316\u6027\u80fd\u7b49\uff09<\/span>\u4ea6\u7f3a\u4e4f\u66f4\u6df1\u5165\u7684\u7814\u7a76\u3002<\/span><\/o:p><\/section>\n

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\u56fe2  \u4eceBoltzmann\u673a\u5230\u6df1\u5ea6\u4fe1\u5ff5\u7f51\u7edc\u3002(a) \u4e00\u4e2a\u5305\u542b8\u4e2a\u795e\u7ecf\u5143\u7684\u5168\u8fde\u63a5Boltzmann\u673a\u793a\u610f\u56fe\u3002(b) \u4e00\u4e2a\u53d7\u9650Boltzmann\u673a\u793a\u610f\u56fe\uff0c\u5176\u4e2d\u5305\u542b4\u4e2a\u9690\u85cf\u5c42\u8282\u70b9(H1<\/sub>, H2<\/sub>, H3<\/sub>, H4<\/sub>)\u4e0e6\u4e2a\u53ef\u89c1\u5c42\u8282\u70b9(V1<\/sub>, V2<\/sub>, \u2026, V6<\/sub>)\u3002(c) \u4e00\u4e2a\u7531\u591a\u5c42\u53d7\u9650Boltzmann\u673a\u5806\u53e0\u7684\u795e\u7ecf\u7f51\u7edc\u793a\u610f\u56fe\u3002\u8be5\u7f51\u7edc\u5305\u542b4\u5c42: \u4e00\u4e2a\u8f93\u5165\u5c42(I)\uff0c\u4e24\u4e2a\u9690\u85cf\u5c42(H1<\/sup>,H2<\/sup>)\uff0c\u4e00\u4e2a\u8f93\u51fa\u5c42(O)\u3002\u8fd94\u5c42\u5206\u522b\u5305\u542b8, 6, 6, 4\u4e2a\u795e\u7ecf\u5143\u3002\u8fd9\u79cd\u591a\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u4e0d\u65ad\u5806\u53e0\uff0c\u6784\u6210\u4e86\u6df1\u5ea6\u4fe1\u5ff5\u7f51\u7edc<\/span><\/o:p><\/p>\n


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2.3 Hinton\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u7684\u5176\u4ed6\u5b9e\u8df5\u521b\u65b0<\/span><\/strong><\/span><\/o:p><\/section>\n

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\u9664\u4e86DBN\u4ee5\u5916\uff0cHinton\u8fd8\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u505a\u51fa\u4e86\u5176\u4ed6\u5f00\u521b\u6027\u8d21\u732e\uff0c\u4ece\u5404\u79cd\u7406\u8bba\u65b9\u6cd5\u7684\u521b\u65b0\uff0c\u518d\u5230\u5404\u79cd\u521b\u65b0\u6027\u7684\u6a21\u578b\u67b6\u6784\u548c\u8bad\u7ec3\u6280\u672f\uff0c\u8fd9\u4e9b\u5de5\u4f5c\u6781\u5927\u63a8\u52a8\u4e86\u6df1\u5ea6\u5b66\u4e60\u7684\u7406\u8bba\u53d1\u5c55\u548c\u5b9e\u8df5\u5e94\u7528\u3002\u9996\u5148\uff0cHinton\u7b49\u4eba[37,38]\u5173\u4e8e\u53cd\u5411\u4f20\u64ad\u7684\u5de5\u4f5c\u4e3a\u8bad\u7ec3\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u63d0\u4f9b\u4e86\u57fa\u7840\u7b97\u6cd5\uff0c\u901a\u8fc7\u5bf9\u94fe\u5f0f\u6c42\u5bfc\u6cd5\u5219\u7684\u5de7\u5999\u5e94\u7528\uff0c\u5927\u5927\u964d\u4f4e\u4e86\u6a21\u578b\u8bad\u7ec3\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u4f7f\u5f97\u6df1\u5ea6\u7f51\u7edc\u7684\u8bad\u7ec3\u5728\u8ba1\u7b97\u4e0a\u53d8\u5f97\u53ef\u884c\u3002\u5176\u6b21\uff0c2006\u5e74\uff0cHinton\u548cSalakhutdinov[39]\u63d0\u51fa\u4e86\u4f7f\u7528\u6df1\u5ea6\u81ea\u7f16\u7801\u5668<\/span>\uff08autoencoder\uff09<\/span>\u8fdb\u884c\u964d\u7ef4\u7684\u65b9\u6cd5\u3002\u8be5\u5de5\u4f5c\u7684\u5173\u952e\u521b\u65b0\u5728\u4e8e\u63d0\u51fa\u4e86\u4e00\u4e2a\u4e24\u9636\u6bb5\u7684\u8bad\u7ec3\u7b56\u7565\uff1a(1) \u5bf9\u7f51\u7edc\u8fdb\u884c\u9010\u5c42\u9884\u8bad\u7ec3\uff0c\u5373\u9996\u5148\u5c06\u8f93\u5165\u5c42\u548c\u7b2c\u4e00\u4e2a\u9690\u85cf\u5c42\u6784\u6210\u4e00\u4e2aRBM\uff0c\u4f7f\u7528CD\u7b97\u6cd5\u8bad\u7ec3\u8fd9\u4e2aRBM\uff0c\u7136\u540e\u7528\u8fd9\u4e2aRBM\u7684\u9690\u85cf\u5c42\u6fc0\u6d3b\u503c\u4f5c\u4e3a\u7b2c\u4e8c\u4e2aRBM\u7684\u8f93\u5165\u5c42\uff0c\u9010\u5c42\u5806\u53e0\u5e76\u8bad\u7ec3RBM\uff0c\u76f4\u5230\u5b8c\u6210\u6240\u6709\u7f16\u7801\u5c42\u7684\u9884\u8bad\u7ec3; (2) \u4f7f\u7528\u53cd\u5411\u4f20\u64ad\u5bf9\u6574\u4e2a\u7f51\u7edc\u8fdb\u884c\u5fae\u8c03\u3002\u5b9e\u9a8c\u8868\u660e\uff0c\u91c7\u7528RBM\u9884\u8bad\u7ec3\u53ef\u4ee5\u663e\u8457\u6539\u5584\u6df1\u5ea6\u81ea\u7f16\u7801\u5668\u7684\u6027\u80fd\uff0c\u8fd9\u8bf4\u660e\u65e0\u76d1\u7763\u9884\u8bad\u7ec3\u4e3a\u7f51\u7edc\u63d0\u4f9b\u4e86\u4e00\u4e2a\u597d\u7684\u53c2\u6570\u521d\u59cb\u5316\uff0c\u5e2e\u52a9\u7f51\u7edc\u907f\u514d\u9677\u5165\u4e0d\u826f\u5c40\u90e8\u6781\u5c0f\u503c\uff0c\u4ece\u800c\u514b\u670d\u4e86\u6df1\u5ea6\u7f51\u7edc\u8bad\u7ec3\u4e2d\u7684\u68af\u5ea6\u6d88\u5931\u95ee\u9898[40]\u3002<\/span><\/o:p><\/section>\n

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\u5728\u6df1\u5ea6\u5b66\u4e60\u7684\u5b9e\u8df5\u5e94\u7528\u65b9\u9762\uff0cHinton\u53ca\u5176\u5408\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u7cfb\u5217\u521b\u65b0\u6280\u672f\u30022012\u5e74\uff0c\u4ed6\u4e0e\u5b66\u751fKrizhevsky\u7b49\u4eba[41]\u63d0\u51fa\u7684AlexNet\u5728ImageNet\u7ade\u8d5b\u4e2d\u53d6\u5f97\u4e86\u4f18\u5f02\u7684\u6210\u7ee9\uff0c\u5c55\u793a\u4e86\u6df1\u5ea6\u5377\u79ef\u7f51\u7edc\u5728\u56fe\u50cf\u8bc6\u522b\u9886\u57df\u7684\u5f3a\u5927\u6027\u80fd\uff0c\u88ab\u8ba4\u4e3a\u662f\u6df1\u5ea6\u5b66\u4e60\u590d\u5174\u7684\u6807\u5fd7\u6027\u5de5\u4f5c\u3002\u540c\u5e74\u63d0\u51fa\u7684Dropout[42]\u662f\u4e00\u79cd\u7b80\u5355\u6709\u6548\u7684\u9632\u6b62\u8fc7\u62df\u5408\u7684\u6280\u672f\uff0c\u901a\u8fc7\u5728\u8bad\u7ec3\u65f6\u968f\u673a\u4e22\u5f03\u795e\u7ecf\u5143\u6765\u63d0\u9ad8\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002\u5728\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u65b9\u9762\uff0cHinton\u63d0\u51fa\u7684\u52a8\u91cf<\/span>\uff08momentum\uff09<\/span>\u6cd5[43]\u6210\u4e3a\u6df1\u5ea6\u5b66\u4e60\u8bad\u7ec3\u4e2d\u5e7f\u6cdb\u4f7f\u7528\u7684\u6280\u672f\u30022015\u5e74\u63d0\u51fa\u7684\u77e5\u8bc6\u84b8\u998f\u65b9\u6cd5[44]\u5219\u4e3a\u6a21\u578b\u538b\u7f29\u548c\u77e5\u8bc6\u8fc1\u79fb\u63d0\u4f9b\u4e86\u65b0\u8303\u5f0f\uff0c\u901a\u8fc7\u4f7f\u7528\u5927\u6a21\u578b\u6307\u5bfc\u5c0f\u6a21\u578b\u7684\u8bad\u7ec3\u6765\u5b9e\u73b0\u77e5\u8bc6\u8fc1\u79fb\u3002\u6b64\u5916\uff0ct-SNE\u7b97\u6cd5[45]\u80fd\u591f\u5728\u4f4e\u7ef4\u7a7a\u95f4\u4e2d\u4fdd\u6301\u6570\u636e\u7684\u5c40\u90e8\u7ed3\u6784\u7279\u5f81\uff0c\u6210\u4e3a\u9ad8\u7ef4\u6570\u636e\u53ef\u89c6\u5316\u7684\u91cd\u8981\u65b9\u6cd5\u3002\u8fd1\u5e74\u6765\uff0cHinton\u63d0\u51fa\u4e86\u80f6\u56ca\u7f51\u7edc[46]\u6765\u89e3\u51b3CNN\u5728\u5904\u7406\u7a7a\u95f4\u5173\u7cfb\u65f6\u7684\u5c40\u9650\u6027\uff1b\u4ed6\u63d0\u51fa\u7684GLOM\u7406\u8bba[47]\u548c\u524d\u5411-\u524d\u5411\u7f51\u7edc[48]\u5206\u522b\u63a2\u7d22\u4e86\u795e\u7ecf\u8868\u793a\u7684\u7ec4\u7ec7\u539f\u7406\u548c\u65b0\u578b\u5b66\u4e60\u8303\u5f0f\u3002<\/span><\/o:p><\/section>\n

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\u7eb5\u89c2Hinton\u7684\u7814\u7a76\u8f68\u8ff9\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u4e00\u6761\u575a\u5b88\u4e0e\u521b\u65b0\u4e4b\u8def\uff1a\u4ed6\u59cb\u7ec8\u575a\u6301\u63a2\u7d22\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u673a\u5236\u8fd9\u4e00\u6838\u5fc3\u4e3b\u9898\uff0c\u5728\u6a21\u578b\u67b6\u6784\u4e0e\u4f18\u5316\u65b9\u6cd5\u7b49\u65b9\u9762\u63d0\u51fa\u521b\u65b0\u6027\u89e3\u51b3\u65b9\u6848\u3002\u4ed6\u7684\u5de5\u4f5c\u5bf9\u4eba\u5de5\u667a\u80fd\u9886\u57df\u4ea7\u751f\u4e86\u6df1\u8fdc\u5f71\u54cd\uff0c\u4f7f\u4ed6\u5f53\u4e4b\u65e0\u6127\u5730\u88ab\u79f0\u4e3a\u201c\u6df1\u5ea6\u5b66\u4e60\u4e4b\u7236\u201d\u3002<\/span><\/section>\n

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3. \u603b\u7ed3\u4e0e\u5c55\u671b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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3.1 \u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4f5c\u4e3a\u7269\u7406\u7cfb\u7edf\uff1aPhysics of AI<\/span><\/strong><\/span><\/section>\n

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Hopfield\u4e0eHinton\u4e24\u4f4d\u79d1\u5b66\u5bb6\u7684\u5de5\u4f5c\u5728\u7269\u7406\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u4e4b\u95f4\u5efa\u7acb\u8d77\u4e86\u201c\u8fde\u63a5\u201d\uff0c\u8fd9\u79cd\u201c\u8fde\u63a5\u201d\u4e0d\u4ec5\u4f53\u73b0\u5728\u5b66\u79d1\u7684\u8054\u7cfb\u4e0a\uff0c\u66f4\u6df1\u523b\u5730\u4f53\u73b0\u5728\u4ed6\u4eec\u5bf9\u8ba4\u77e5\u7684\u7406\u89e3\u65b9\u5f0f\u2014\u2014\u201c\u8054\u7ed3\u4e3b\u4e49\u201d<\/span>\uff08Connectionism\uff09<\/span>\u4e0a\u3002\u8054\u7ed3\u4e3b\u4e49\u662f\u8ba4\u77e5\u79d1\u5b66\u7684\u91cd\u8981\u7406\u8bba\u8303\u5f0f\uff0c\u5176\u6838\u5fc3\u4e3b\u5f20\u5982\u4e0b\uff1a\u8ba4\u77e5\u7cfb\u7edf\u662f\u7531\u5927\u91cf\u7b80\u5355\u5904\u7406\u5355\u5143\u6784\u6210\u7684\u7f51\u7edc[49,50]\uff1b\u8fd9\u4e9b\u5904\u7406\u5355\u5143\u901a\u8fc7\u6743\u91cd\u53ef\u8c03\u7684\u8fde\u63a5\u76f8\u4e92\u4f5c\u7528\uff0c\u5f62\u6210\u5206\u5e03\u5f0f\u7684\u4fe1\u606f\u5904\u7406\u7cfb\u7edf\uff1b\u6240\u6709\u8ba4\u77e5\u529f\u80fd\uff0c\u5305\u62ec\u611f\u77e5\u3001\u8bb0\u5fc6\u3001\u63a8\u7406\u7b49\u590d\u6742\u7684\u5fc3\u7406\u8fc7\u7a0b\uff0c\u90fd\u53ef\u4ee5\u901a\u8fc7\u7f51\u7edc\u7ed3\u6784\u6765\u5b9e\u73b0\u548c\u89e3\u91ca\u3002\u4f5c\u4e3a\u8054\u7ed3\u4e3b\u4e49\u7684\u4ee3\u8868\u4eba\u7269\uff0cHopfield\u4e0eHinton\u7684\u6838\u5fc3\u89c2\u70b9\u4e0e\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6P. W. Anderson \u201cMore is different\u201d\u7684\u6d8c\u73b0\u8bba\u89c2\u70b9[51]\u4e0d\u8c0b\u800c\u5408\uff1a\u590d\u6742\u7684\u8ba4\u77e5\u529f\u80fd\u662f\u5927\u91cf\u7b80\u5355\u795e\u7ecf\u5143\u901a\u8fc7\u52a8\u6001\u8fde\u63a5\u76f8\u4e92\u4f5c\u7528\u540e\u7684\u6d8c\u73b0\u5c5e\u6027\uff0c\u800c\u4e0d\u80fd\u4ec5\u4ece\u5355\u4e2a\u795e\u7ecf\u5143\u7684\u884c\u4e3a\u6765\u89e3\u91ca<\/strong>\u3002\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u5f3a\u5927\u80fd\u529b\u6b63\u662f\u6e90\u4e8e\u5176\u5177\u5907\u8db3\u591f\u7684\u89c4\u6a21\u548c\u590d\u6742\u6027\uff0c\u4f7f\u5f97\u9ad8\u5c42\u6b21\u7684\u590d\u6742\u529f\u80fd\u80fd\u591f\u6d8c\u73b0[52,53]\u3002<\/span><\/o:p><\/section>\n

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\u7edf\u8ba1\u7269\u7406\u4e0e\u590d\u6742\u7cfb\u7edf\u8fd8\u4e3a\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u6df1\u5ea6\u5b66\u4e60\u63d0\u4f9b\u4e86\u7cfb\u7edf\u6027\u5de5\u5177[54]\uff1a\u80fd\u91cf\u666f\u89c2\u7684\u6982\u5ff5\u63ed\u793a\u4e86\u795e\u7ecf\u7f51\u7edc\u72b6\u6001\u7684\u6f14\u5316\u89c4\u5f8b[55]\u3001\u81ea\u65cb\u73bb\u7483\u7406\u8bba\u89e3\u91ca\u4e86\u795e\u7ecf\u5143\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5982\u4f55\u5bfc\u81f4\u7f51\u7edc\u5f62\u6210\u7a33\u5b9a\u7684\u4fe1\u606f\u8868\u5f81\u6a21\u5f0f\u4e0e\u5b66\u4e60\u6570\u636e\u7684\u5c42\u6b21\u7ed3\u6784[56]\u3002Huang\u548cToyoizumi[57]\u53d1\u5c55\u7684\u9ad8\u9636\u5e73\u5747\u573a\u7406\u8bba\u7cbe\u786e\u63cf\u8ff0\u4e86RBM\u7684\u76f8\u6001\u7279\u5f81\u3002Decelle\u7b49\u4eba[58]\u4ece\u70ed\u529b\u5b66\u89d2\u5ea6\u7814\u7a76\u4e86RBM\u7684\u5b66\u4e60\u52a8\u529b\u5b66\uff0c\u53d1\u73b0\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u5173\u952e\u76f8\u53d8\u70b9\u3002\u6b64\u5916\uff0c\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u4e3a\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u7684\u975e\u7ebf\u6027\u7279\u6027\u63d0\u4f9b\u4e86\u5173\u952e\u5de5\u5177[59~63]\u3002\u8fd9\u79cd\u52a8\u529b\u7cfb\u7edf\u89c6\u89d2\u4e0d\u4ec5\u63ed\u793a\u4e86\u795e\u7ecf\u7f51\u7edc\u8ba1\u7b97\u80fd\u529b\u7684\u672c\u8d28\uff0c\u8fd8\u4e3a\u8bbe\u8ba1\u66f4\u7a33\u5065\u6216\u66f4\u6613\u4e8e\u8bad\u7ec3\u7684\u7f51\u7edc\u67b6\u6784\u63d0\u4f9b\u4e86\u7406\u8bba\u6307\u5bfc\u3002\u5728\u7406\u89e3\u673a\u5668\u5b66\u4e60\u7684\u5de5\u4f5c\u539f\u7406\u65b9\u9762\uff0c\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u53ef\u80fd\u6709\u52a9\u4e8e\u89e3\u91ca\u6df1\u5ea6\u7f51\u7edc\u7684\u7279\u5f81\u63d0\u53d6\u673a\u5236[64~66]\uff0c\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u53ef\u7528\u4e8e\u5206\u6790\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u6536\u655b\u7279\u6027\u548c\u6cdb\u5316\u884c\u4e3a[67~70]\u3002\u6b64\u5916\uff0c\u5728\u6269\u6563\u6a21\u578b\u7b49\u751f\u6210\u6a21\u578b\u4e2d\uff0c\u968f\u673a\u8fc7\u7a0b\u7406\u8bba\u4e5f\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u7406\u8bba\u652f\u6491[71,72]\u3002\u6b64\u5916\uff0c\u7531\u4e8e\u91cf\u5b50\u6001\u7684Hilbert\u7a7a\u95f4\u5177\u6709\u6307\u6570\u7ea7\u7684\u7ef4\u5ea6\uff0c\u800c\u91cf\u5b50\u53e0\u52a0\u548c\u7ea0\u7f20\u7b49\u7279\u6027\u5219\u4e3a\u4fe1\u606f\u5904\u7406\u63d0\u4f9b\u4e86\u72ec\u7279\u4f18\u52bf[73~75]\uff0c\u8fd9\u79cd\u6269\u5c55\u7684\u8ba1\u7b97\u80fd\u529b\u5f00\u8f9f\u4e86\u7ecf\u5178\u8ba1\u7b97\u65e0\u6cd5\u4f01\u53ca\u7684\u91cf\u5b50\u673a\u5668\u5b66\u4e60\u65b0\u8303\u5f0f[76]\u3002\u672a\u6765\uff0c\u968f\u7740\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\u7684\u4e0d\u65ad\u53d1\u5c55\uff0c\u7269\u7406\u5b66\u4e0e\u6df1\u5ea6\u5b66\u4e60\u7684\u7ed3\u5408\u53ef\u80fd\u5728\u8bb8\u591a\u9886\u57df\u91cd\u65b0\u7115\u53d1\u6d3b\u529b\uff0c\u63a8\u52a8\u8de8\u5b66\u79d1\u7684\u7a81\u7834\u6027\u8fdb\u5c55\u3002<\/span><\/o:p><\/section>\n

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3.2 \u8de8\u5b66\u79d1\u7684\u878d\u5408\u63a8\u52a8\u672a\u6765\u521b\u65b0\uff1aAI for Sciences<\/span><\/strong><\/o:p><\/section>\n

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Hopfield\u4e0eHinton\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u5c55\u793a\u4e86\u7269\u7406\u5b66\u539f\u7406\u5728\u8ba1\u7b97\u95ee\u9898\u4e2d\u7684\u6df1\u8fdc\u5f71\u54cd\u3002\u901a\u8fc7\u5c06\u6df1\u5ea6\u5b66\u4e60\u89c6\u4e3a\u590d\u6742\u52a8\u529b\u5b66\u548c\u6d8c\u73b0\u884c\u4e3a\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u7269\u7406\u5b66\u65b9\u6cd5\u4e3a\u7406\u89e3\u6df1\u5ea6\u5b66\u4e60\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\u4ee5\u53ca\u4e0e\u201cScience of AI\u201d\u76f8\u5173\u7684\u65b0\u7814\u7a76\u8bfe\u9898\u3002\u4e0e\u6b64\u540c\u65f6\uff0c\u4eba\u5de5\u667a\u80fd\u4e5f\u6b63\u5728\u9769\u65b0\u4f20\u7edf\u79d1\u5b66\u7814\u7a76\u65b9\u6cd5\uff0c\u5f62\u6210\u4e86\u201cAI for Science\u201d\u7684\u5b66\u672f\u7814\u7a76\u65b0\u8303\u5f0f[77]\u3002\u6700\u5177\u4ee3\u8868\u6027\u7684\u662fAlphaFold 2\u5728\u86cb\u767d\u8d28\u7ed3\u6784\u9884\u6d4b\u9886\u57df\u7684\u7a81\u7834\u6027\u8fdb\u5c55[78]\uff1a\u5b83\u5c06\u539f\u672c\u9700\u8981\u6570\u6708\u4e43\u81f3\u6570\u5e74\u7684\u7ed3\u6784\u89e3\u6790\u65f6\u95f4\u7f29\u77ed\u5230\u5c0f\u65f6\u7ea7\u522b\uff0c\u6781\u5927\u63a8\u52a8\u4e86\u751f\u7269\u5316\u5b66\u548c\u533b\u836f\u7814\u7a76\u7684\u53d1\u5c55\u3002\u8fd9\u4e00\u6210\u5c31\u4f7f\u5f97\u5176\u4e3b\u8981\u5f00\u53d1\u8005Demis Hassabis\u3001John M. Jumper\u4e0e\u8ba1\u7b97\u86cb\u767d\u8d28\u8bbe\u8ba1\u4e13\u5bb6David Baker\u5171\u540c\u83b7\u5f972024\u5e74\u8bfa\u8d1d\u5c14\u5316\u5b66\u5956\u3002\u6b64\u5916\uff0c\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u8fd8\u5728\u6c14\u8c61\u9884\u6d4b[79]\u3001\u6750\u6599\u7279\u6027\u5206\u6790[80]\u548c\u91cf\u5b50\u7cfb\u7edf\u7814\u7a76[81]\u7b49\u9886\u57df\u5c55\u73b0\u51fa\u5f3a\u5927\u6f5c\u529b\u3002<\/span><\/o:p><\/section>\n

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\u201cScience of AI\u201d\u4e0e\u201cAI for Science\u201d\u7684\u8fd9\u79cd\u53cc\u5411\u4e92\u52a8\u6b63\u5728\u52a0\u901f\u8de8\u5b66\u79d1\u878d\u5408\uff0c\u5f00\u521b\u4e86\u79d1\u5b66\u7814\u7a76\u7684\u65b0\u8303\u5f0f\u3002\u8fd9\u79cd\u878d\u5408\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u79d1\u5b66\u7814\u7a76\u6548\u7387\uff0c\u66f4\u4e3a\u7406\u89e3\u81ea\u7136\u754c\u63d0\u4f9b\u4e86\u65b0\u7684\u65b9\u6cd5\u8bba\uff0c\u8fd9\u5fc5\u5c06\u4e0d\u65ad\u6253\u7834\u4f20\u7edf\u7684\u5b66\u79d1\u58c1\u5792\uff0c\u5e26\u6765\u5f71\u54cd\u66f4\u5e7f\u6cdb\u9886\u57df\u7684\u79d1\u6280\u7a81\u7834\u3002<\/span><\/o:p><\/section>\n

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\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\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


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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>2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u4e3a\u4f55\u6388\u4e88\u673a\u5668\u5b66\u4e60\u9886\u57df\uff1f<\/a><\/strong><\/span><\/section>\n
4. <\/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
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5. <\/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
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7. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n


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