{"id":4444,"date":"2017-08-05T01:00:00","date_gmt":"2017-08-04T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%swarma-paper%\/"},"modified":"2018-12-11T14:47:30","modified_gmt":"2018-12-11T06:47:30","slug":"%e9%87%8f%e5%ad%90%e7%ba%a0%e7%bc%a0%ef%bc%9a%e4%bb%8e%e9%87%8f%e5%ad%90%e7%89%a9%e8%b4%a8%e6%80%81%e5%88%b0%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=4444","title":{"rendered":"\u91cf\u5b50\u7ea0\u7f20\uff1a\u4ece\u91cf\u5b50\u7269\u8d28\u6001\u5230\u6df1\u5ea6\u5b66\u4e60"},"content":{"rendered":"
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\u8f6c\u8f7d\u58f0\u660e\uff1a\u672c\u6587\u8f6c\u8f7d\u81ea\u300c\u4e2d\u56fd\u7269\u7406\u5b66\u4f1a\u671f\u520a\u7f51\u300d\uff0c\u641c\u7d22\u300ccpsjournals\u300d\u5373\u53ef\u5173\u6ce8\u3002<\/span><\/strong><\/span><\/p>\n<\/blockquote>\n

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

\u5f15\u8a00<\/strong><\/span><\/p>\n<\/section>\n

\u7ecf\u5178\u7269\u7406\u5b66\u7684\u4e3b\u89d2\u662f\u7269\u8d28\u548c\u80fd\u91cf\u300220 \u4e16\u7eaa\u521d\uff0c\u7231\u56e0\u65af\u5766\u5199\u4e0bE =mc2 \uff0c\u5c06\u8d28\u91cf\u548c\u80fd\u91cf\u7edf\u4e00\u5728\u4e86\u4e00\u8d77\u3002\u800c\u4ece\u90a3\u4e4b\u540e\uff0c\u4e00\u4e2a\u65b0\u89d2\u8272\u2014\u2014\u4fe1\u606f(Information)\u2014\u2014\u9010\u6e10\u8d70\u5411\u4e86\u7269\u7406\u5b66\u821e\u53f0\u7684\u4e2d\u592e\u3002\u4fe1\u606f\u662f\u5173\u4e8e\u4e0d\u786e\u5b9a\u7a0b\u5ea6\u7684\u5ea6\u91cf\u3002Shannon \u521b\u7acb\u4fe1\u606f\u8bba\u7684\u521d\u8877\u662f\u4e3a\u4e86\u5b9a\u91cf\u5316\u5730\u63cf\u8ff0\u4fe1\u606f\u7684\u5b58\u50a8\u548c\u4f20\u8f93\u3002Jaynes \u4ece\u4fe1\u606f\u8bba\u7684\u89d2\u5ea6\u7814\u7a76\u591a\u7c92\u5b50\u4f53\u7cfb\uff0c\u91cd\u65b0\u9610\u91ca\u4e86\u7edf\u8ba1\u529b\u5b66\u3002\u539f\u6765\uff0c\u7269\u7406\u5b66\u5bb6\u6240\u719f\u77e5\u7684\u70ed\u529b\u5b66\u71b5\u4e0eShannon \u7528\u6765\u8861\u91cf\u4fe1\u606f\u91cf\u7684\u4fe1\u606f\u71b5(Information Entropy)\u7cfb\u51fa\u540c\u6e90\u3002Landauer \u6307\u51fa\u64e6\u9664\u4fe1\u606f\u4f1a\u589e\u52a0\u70ed\u529b\u5b66\u71b5\uff0c\u4ece\u800c\u4ea7\u751f\u70ed\u91cf\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u4fe1\u606f\u7684\u4e00\u5207\u5904\u7406(\u6bd4\u5982\u8ba1\u7b97)\u90fd\u53d7\u5230\u70ed\u529b\u5b66\u57fa\u672c\u5b9a\u5f8b\u7684\u7ea6\u675f\u3002\u8fd9\u4e9b\u5de5\u4f5c\u4f7f\u4eba\u4eec\u9010\u6e10\u610f\u8bc6\u5230\uff0c\u4fe1\u606f\u4e0d\u662f\u4e00\u4e2a\u5355\u7eaf\u7684\u6570\u5b66\u6982\u5ff5\uff0c\u800c\u662f\u4e0e\u7269\u8d28\u548c\u80fd\u91cf\u4e00\u6837\u57fa\u672c\u7684\u7269\u7406\u6982\u5ff5\u3002<\/span><\/p>\n

\u91cf\u5b50\u529b\u5b66\u7ed9\u7269\u7406\u4e16\u754c\u5e26\u6765\u4e86\u56fa\u6709\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u4ece\u800c\u4fc3\u751f\u4e86\u91cf\u5b50\u4fe1\u606f\u7406\u8bba\u3002\u91cf\u5b50\u4fe1\u606f\u8bba\u4e2d\u6700\u6838\u5fc3\u7684\u6982\u5ff5\u662f\u91cf\u5b50\u7ea0\u7f20\u3002\u5982\u679c\u4e24\u4e2a\u5fae\u89c2\u7c92\u5b50\u7684\u6574\u4f53\u6ce2\u51fd\u6570\u4e0d\u80fd\u591f\u88ab\u5199\u6210\u5404\u90e8\u5206\u7684\u76f4\u79ef\uff0c\u90a3\u4e48\u5b83\u4eec\u4e4b\u95f4\u5c31\u5b58\u5728\u7ea0\u7f20\u3002\u5bf9\u4e8e\u5b58\u5728\u91cf\u5b50\u7ea0\u7f20\u7684\u4f53\u7cfb\uff0c\u89c2\u5bdf\u5176\u4e2d\u7684\u4e00\u90e8\u5206\u80fd\u591f\u544a\u8bc9\u6211\u4eec\u5173\u4e8e\u53e6\u5916\u4e00\u90e8\u5206\u7684\u4fe1\u606f\u3002\u7c7b\u6bd4\u4e8e\u7ecf\u5178\u4fe1\u606f\u71b5\uff0c \u6211\u4eec\u4f7f\u7528\u7ea0\u7f20\u71b5(Entanglement Entropy)\u6765\u5ea6\u91cf\u91cf\u5b50\u7ea0\u7f20\u7684\u5927\u5c0f\u3002\u91cf\u5b50\u4fe1\u606f\u8bba\u7684\u89c6\u89d2\uff0c\u7279\u522b\u662f\u91cf\u5b50\u7ea0\u7f20\u7684\u6982\u5ff5\u5728\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u7814\u7a76\u4e2d\u626e\u6f14\u7740\u65e5\u8d8b\u91cd\u8981\u7684\u89d2\u8272\u3002<\/span>\"\u96c6\u667a\"<\/p>\n

\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6\u7528\u91cf\u5b50\u7ea0\u7f20\u6765\u523b\u753b\u91cf\u5b50\u7269\u8d28\u6001\u3002\u4f20\u7edf\u4e0a\uff0c\u4ed6\u4eec\u4f7f\u7528\u5bf9\u79f0\u6027\u548c\u5b8f\u89c2\u5e8f\u53c2\u91cf\u6765\u533a\u5206\u4e0d\u540c\u7684\u7269\u8d28\u72b6\u6001\u3002\u8fd9\u6210\u529f\u5730\u89e3\u91ca\u4e86\u8d85\u6d41\u4f53\u3001\u8d85\u5bfc\u4f53\u3001\u78c1\u6027\u7b49\u4e30\u5bcc\u591a\u5f69\u7684\u81ea\u7136\u73b0\u8c61\u3002\u7136\u800c\uff0c\u8fd1\u4e9b\u5e74\u6765\u4eba\u4eec\u53d1\u73b0\u4e86\u8d8a\u6765\u8d8a\u591a\u4ec5\u7528\u5bf9\u79f0\u6027\u96be\u4ee5\u533a\u5206\u7684\u7269\u8d28\u6001\uff0c\u6bd4\u5982\u4e0d\u540c\u79cd\u7c7b\u7684\u81ea\u65cb\u6db2\u4f53\u6001\u3001\u5206\u6570\u91cf\u5b50\u970d\u5c14\u6001\u7b49\u7b49\u3002\u91cf\u5b50\u7ea0\u7f20\u53ef\u4ee5\u7ed9\u8fd9\u4e9b\u65b0\u7684\u7269\u8d28\u6001\u4e00\u4e2a\u6070\u5f53\u7684\u6807\u8bb0\u3002\u6bd4\u5982\uff0c\u7ea0\u7f20\u71b5\u968f\u7740\u4f53\u7cfb\u5c3a\u5bf8\u7684\u6807\u5ea6\u884c\u4e3a\u53cd\u6620\u4e86\u91cf\u5b50\u7269\u8d28\u6001\u7684\u57fa\u672c\u7279\u6027\u3002\u800c\u5bf9\u4e8e\u6807\u5ea6\u884c\u4e3a\u7684\u4fee\u6b63\u4e5f\u53ef\u80fd\u5305\u542b\u7740\u5173\u4e8e\u7269\u8d28\u6001\u7684\u666e\u9002\u4fe1\u606f\u3002\u7814\u7a76\u91cf\u5b50\u7269\u8d28\u6001\u4e2d\u7ea0\u7f20\u7684\u5927\u5c0f\u548c\u6a21\u5f0f\u6210\u4e3a\u73b0\u4ee3\u51dd\u805a\u6001\u7269\u7406\u7684\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\u3002\u6b64\u5916\uff0c\u91cf\u5b50\u7ea0\u7f20\u8fd8\u6307\u5f15\u8ba1\u7b97\u7269\u7406\u5b66\u5bb6\u53d1\u5c55\u9ad8\u6548\u7684\u6570\u503c\u7b97\u6cd5\u7cbe\u786e\u5730\u6a21\u62df\u91cf\u5b50\u591a\u4f53\u73b0\u8c61\u3002\u672c\u6b21\u4e13\u9898\u7684\u53e6\u5916\u51e0\u7bc7\u6587\u7ae0\u4ecb\u7ecd\u4e86\u4f7f\u7528\u5f20\u91cf\u7f51\u7edc\u6001(Tensor Network State)\u65b9\u6cd5\u7814\u7a76\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u7684\u8fdb\u5c55\u3002\u5f20\u91cf\u7f51\u7edc\u7b97\u6cd5\u7684\u6210\u529f\u5f88\u5927\u7a0b\u5ea6\u4e0a\u6765\u6e90\u4e8e\u91cf\u5b50\u7269\u8d28\u6001\u5178\u578b\u7684\u7ea0\u7f20\u7ed3\u6784\uff1a\u9762\u79ef\u5b9a\u5f8b\u3002\u5f88\u591a\u4eba\u4eec\u5173\u5fc3\u7684\u91cf\u5b50\u4f53\u7cfb\u7684\u4e24\u90e8\u5206\u4e4b\u95f4\u7684\u7ea0\u7f20\u71b5\u4ec5\u4ec5\u6b63\u6bd4\u4e8e\u5176\u8fb9\u754c\u7684\u5927\u5c0f\uff0c\u8fd9\u4f7f\u5f97\u5229\u7528\u7ecf\u5178\u8ba1\u7b97\u673a\u9ad8\u6548\u800c\u7cbe\u786e\u5730\u7814\u7a76\u8fd9\u4e9b\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u6210\u4e3a\u53ef\u80fd\u3002\u6709\u610f\u601d\u7684\u662f\uff0c\u91cf\u5b50\u6001\u6240\u9075\u5faa\u7684\u9762\u79ef\u5b9a\u5f8b\u8fd8\u548c\u9ed1\u6d1e\u7684\u71b5\u6709\u7740\u6df1\u523b\u7684\u8054\u7cfb\u3002\u4ece\u91cf\u5b50\u4fe1\u606f\u7684\u89c6\u89d2\u5ba1\u89c6\u5f15\u529b\u3001\u866b\u6d1e\u4ee5\u53ca\u91cf\u5b50\u6df7\u6c8c\u7b49\u73b0\u8c61\uff0c\u751a\u81f3\u6709\u53ef\u80fd\u52a0\u6df1\u6211\u4eec\u5173\u4e8e\u65f6\u7a7a\u7684\u672c\u6e90\u7684\u7406\u89e3\u3002\u56fd\u9645\u4e0a\u5173\u4e8e\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u5f00\u5c55\u5f97\u5982\u706b\u5982\u837c\u3002\u7f8e\u56fd\u7684Simons \u57fa\u91d1\u4f1a\u652f\u6301\u4e86\u4e00\u9879\u4e13\u6ce8\u4e8e\u6b64\u7684\u5408\u4f5c\u7814\u7a76\u9879\u76ee\u3002<\/span>
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\u91cf\u5b50\u7ea0\u7f20\u7684\u6df1\u8fdc\u5f71\u54cd\u5e76\u6ca1\u6709\u5c31\u6b64\u6b62\u6b65\uff0c\u4e00\u4e9b\u6700\u65b0\u7684\u7814\u7a76\u8fdb\u5c55\u8868\u660e\uff0c\u5b83\u5bf9\u673a\u5668\u5b66\u4e60(Machine Learning)\u4e2d\u7684\u4e00\u4e9b\u95ee\u9898\u4e5f\u53ef\u80fd\u6709\u542f\u53d1\u548c\u6307\u5bfc\u610f\u4e49\u3002\u673a\u5668\u5b66\u4e60\u7684\u7814\u7a76\u76ee\u6807\u662f\u8ba9\u8ba1\u7b97\u673a\u83b7\u5f97\u4e00\u5b9a\u7a0b\u5ea6\u7684\u667a\u80fd\uff0c\u4e0d\u9700\u8981\u8fc7\u591a\u7684\u4eba\u4e3a\u5e72\u9884\u5c31\u53ef\u4ee5\u9ad8\u6548\u5730\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u3002\u901a\u5e38\uff0c\u8fd9\u79cd\u770b\u4f3c\u795e\u5947\u7684\u80fd\u529b\u662f\u4ece\u5927\u91cf\u6837\u672c\u7684\u5b66\u4e60\u4e2d\u83b7\u5f97\u7684\u3002\u7531\u4e8e\u8fd1\u5e74\u6765\u7b97\u6cd5\u548c\u786c\u4ef6\u7684\u5feb\u901f\u53d1\u5c55\u4ee5\u53ca\u5927\u91cf\u7684\u6570\u636e\u79ef\u7d2f\uff0c\u673a\u5668\u5b66\u4e60\u53d6\u5f97\u4e86\u4e00\u7cfb\u5217\u4ee4\u4eba\u632f\u594b\u7684\u6210\u679c\u3002\u7279\u522b\u662f2016 \u5e743 \u6708Google DeepMind \u6240\u5236\u9020\u7684AlphaGo \u7a0b\u5e8f\u6218\u80dc\u4e86\u4e16\u754c\u56f4\u68cb\u51a0\u519b\u674e\u4e16\u4e6d\uff0c\u4f7f\u5f97\u4ee5\u6df1\u5ea6\u5b66\u4e60(Deep Learning)\u4e3a\u4ee3\u8868\u7684\u65b0\u4e00\u4ee3\u673a\u5668\u5b66\u4e60\u6280\u672f\u8d70\u8fdb\u4e86\u5927\u4f17\u7684\u89c6\u91ce\u3002\u5982\u4eca\uff0c\u673a\u5668\u5b66\u4e60\u5728\u56fe\u50cf\u548c\u8bed\u97f3\u8bc6\u522b\u3001\u673a\u5668\u7ffb\u8bd1\u3001\u8ba1\u7b97\u5e7f\u544a\u3001\u63a8\u8350\u7cfb\u7edf\u7b49\u4eba\u7c7b\u751f\u6d3b\u7684\u65b9\u65b9\u9762\u9762\u90fd\u626e\u6f14\u7740\u65e5\u8d8b\u91cd\u8981\u7684\u89d2\u8272\u3002\u800c\u5b83\u7684\u5e94\u7528\u4e5f\u5728\u9010\u6e10\u5411\u5929\u6587\u3001\u7269\u7406\u3001\u5316\u5b66\u3001\u6750\u6599\u3001\u751f\u7269\u3001\u533b\u836f\u7b49\u4f17\u591a\u79d1\u5b66\u7814\u7a76\u9886\u57df\u6e17\u900f\u3002\u5177\u4f53\u5230\u672c\u6587\u4f5c\u8005\u6240\u5de5\u4f5c\u7684\u9886\u57df\uff1a\u5c06\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u5e94\u7528\u4e8e\u91cf\u5b50\u591a\u4f53\u95ee\u9898\uff0c\u53ef\u4ee5\u4ece\u9ad8\u7ef4\u7a7a\u95f4\u7eb7\u6742\u7684\u5fae\u89c2\u6784\u578b\u6570\u636e\u4e2d\u63d0\u53d6\u51fa\u5173\u952e\u7684\u7269\u7406\u4fe1\u606f\u3002\u800c\u5c06\u673a\u5668\u5b66\u4e60\u7684\u601d\u60f3\u4e0e\u4f20\u7edf\u8ba1\u7b97\u9014\u5f84\u76f8\u7ed3\u5408\uff0c\u4e3a\u89e3\u51b3\u51dd\u805a\u6001\u548c\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u7591\u96be\u95ee\u9898\u63d0\u4f9b\u4e86\u65b0\u601d\u8def\u3002\u6700\u8fd1\u7684\u4e00\u4e9b\u5c1d\u8bd5\u5305\u62ec\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u63a2\u6d4b\u76f8\u53d8\u548c\u5206\u7c7b\u7269\u8d28\u76f8\uff0c\u63a2\u7d22\u4f7f\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4f5c\u4e3a\u91cf\u5b50\u4f53\u7cfb\u7684\u8bd5\u63a2\u6ce2\u51fd\u6570\u7b49\u7b49\u3002\u8fd9\u4e9b\u5c1d\u8bd5\u8ba9\u7269\u7406\u5b66\u5bb6\u4eec\u6709\u673a\u4f1a\u4ed4\u7ec6\u5ba1\u89c6\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u6838\u5fc3\u601d\u60f3\u548c\u6280\u672f\u3002\u672c\u6587\u4ecb\u7ecd\u7684\u5c31\u662f\u8fd9\u4e00\u65b9\u5411\u4e0a\u65b0\u6d8c\u73b0\u51fa\u7684\u4e00\u4e2a\u7814\u7a76\u601d\u8def\uff1a\u4ece\u91cf\u5b50\u7ea0\u7f20\u7684\u89c6\u89d2\u5ba1\u89c6\u6df1\u5ea6\u5b66\u4e60\uff0c\u4ece\u800c\u53cd\u9988\u673a\u5668\u5b66\u4e60\u7684\u53d1\u5c55\u3002<\/span><\/p>\n


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\u6df1\u5ea6\u5b66\u4e60\u548c\u91cf\u5b50\u591a\u4f53\u7269\u7406\u4e2d\u7684\u51fd\u6570\u8fd1\u4f3c<\/span><\/strong><\/span><\/p>\n<\/section>\n

\u6df1\u5ea6\u5b66\u4e60\u7a76\u7adf\u5728\u505a\u4ec0\u4e48\uff1f\u7528\u6700\u7b80\u77ed\u7684\u8bdd\u6982\u62ec\uff0c\u5c31\u662f\u51fd\u6570\u8fd1\u4f3c(Function Approximation)\u3002\u51fd\u6570\u8fd1\u4f3c\u7684\u76ee\u7684\u662f\u7528\u9ad8\u6548\u7ecf\u6d4e\u7684\u65b9\u5f0f\u5c3d\u53ef\u80fd\u7cbe\u786e\u5730\u63cf\u8ff0\u590d\u6742\u7684\u51fd\u6570\u6620\u5c04\u3002\u5b9e\u9645\u95ee\u9898\u4e2d\u7684\u76ee\u6807\u51fd\u6570\u53ef\u80fd\u662f\u56fe\u50cf\u8bc6\u522b\u5e94\u7528\u4e2d\u4ece\u5fae\u89c2\u50cf\u7d20\u5230\u56fe\u7247\u7c7b\u522b\u7684\u6620\u5c04\uff0c\u53ef\u80fd\u662fAlphaGo \u4e2d\u56f4\u68cb\u7684\u5c40\u9762\u5230\u6700\u7ec8\u80dc\u7387\u7684\u4f30\u8ba1\uff0c\u4e5f\u53ef\u80fd\u662fAtari \u89c6\u9891\u6e38\u620f\u4e2d\u7684\u753b\u9762\u5230\u6700\u4f18\u63a7\u5236\u7b56\u7565\u7684\u6620\u5c04\u7b49\u7b49\u3002\u8bfb\u8005\u4e5f\u8bb8\u5df2\u7ecf\u770b\u51fa\u6765\u4e86\uff0c\u4ee5\u4e0a\u8fd9\u51e0\u4e2a\u51fd\u6570\u6050\u6015\u90fd\u5f88\u96be\u7528\u4e00\u4e2a\u7b80\u6d01\u7684\u65b9\u5f0f\u8868\u8fbe\u3002\u5373\u4f7f\u8003\u8651\u4e00\u4e2a\u6781\u7aef\u7b80\u5316\u7684\u60c5\u5f62\uff1a\u600e\u6837\u63cf\u8ff0\u6709N \u4e2a\u4e8c\u8fdb\u5236\u81ea\u53d8\u91cf\u7684\u591a\u5143\u51fd\u6570\uff1f\u539f\u5219\u4e0a\uff0c\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u5b58\u50a8\u4e00\u4e2a2N \u884c\u7684\u8868\u683c\u6765\u7cbe\u786e\u8868\u8fbe\u8fd9\u6837\u4e00\u4e2a\u51fd\u6570\u3002\u8fd9\u4e2a\u8868\u683c\u7684\u6bcf\u4e00\u884c\u5bf9\u5e94\u4e86\u4e00\u79cd\u53ef\u80fd\u7684\u8f93\u5165\u548c\u8f93\u51fa\uff0c\u51fd\u6570\u7684\u8ba1\u7b97\u4e5f\u5c31\u7b49\u4ef7\u4e8e\u67e5\u8868\u3002\u53ef\u662f\u53ea\u8981N \u2273 70 \uff0c\u5373\u4f7f\u7528\u4e0a\u5168\u4e16\u754c\u6240\u6709\u7684\u5b58\u50a8\u4ecb\u8d28\uff0c\u6211\u4eec\u4e5f\u6ca1\u6709\u80fd\u529b\u5b58\u4e0b\u8fd9\u5f20\u8868\u683c\uff0c\u66f4\u4e0d\u8981\u8bf4\u5bf9\u5b83\u8fdb\u884c\u9ad8\u6548\u7684\u67e5\u627e\u4e86\u3002<\/span><\/p>\n

\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u8fde\u63a5\u4e3b\u4e49\u5b66\u6d3e(Connectionism)\u63d0\u5021\u4f7f\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc(Artifical Neural Network)\u6765\u89e3\u51b3\u8fd9\u7c7b\u51fd\u6570\u8fd1\u4f3c\u95ee\u9898\u3002\u8fde\u63a5\u4e3b\u4e49\u5f3a\u8c03\u590d\u6742\u7684\u73b0\u8c61(\u6bd4\u5982\u667a\u80fd)\u4e0d\u6765\u81ea\u4e8e\u76f8\u5bf9\u7b80\u5355\u7684\u7ec4\u6210\u5355\u5143\uff0c\u800c\u6765\u81ea\u4e8e\u8fd9\u4e9b\u5355\u5143\u4e4b\u95f4\u7684\u8fde\u63a5\u3002\u56fe1(a)\uff0c(b)\u5c55\u793a\u4e86\u4e24\u79cd\u5e38\u89c1\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u3002\u56fe1(a)\u662f\u524d\u9988\u795e\u7ecf\u7f51\u7edc(Feedforward Neural Network)\u3002\u56fe\u4e2d\u7684\u6bcf\u4e00\u4e2a\u84dd\u8272\u5706\u5708\u4ee3\u8868\u4e00\u4e2a\u4eba\u5de5\u795e\u7ecf\u5143\uff0c\u5b83\u63a5\u53d7\u4e0a\u4e00\u5c42\u7ed3\u679c\u4f5c\u4e3a\u8f93\u5165\uff0c\u52a0\u6743\u6c42\u548c\u4e4b\u540e\u901a\u8fc7\u4e00\u4e2a\u975e\u7ebf\u6027\u7684\u6fc0\u6d3b\u51fd\u6570\u4f20\u9012\u7ed9\u4e0b\u4e00\u5c42\u3002\u53ef\u89c1\uff0c\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u662f\u901a\u8fc7\u591a\u5c42\u975e\u7ebf\u6027\u51fd\u6570\u7684\u5d4c\u5957\u6765\u8868\u8fbe\u590d\u6742\u7684\u591a\u5143\u51fd\u6570\u7684\u3002\u800c\u56fe1(b)\u663e\u793a\u4e86\u53e6\u5916\u4e00\u79cd\u51fd\u6570\u53c2\u6570\u5316\u65b9\u5f0f\uff1a\u9650\u5236\u73bb\u5c14\u5179\u66fc\u673a(Restricted Boltzmann Machine)\u3002\u4ece\u540d\u5b57\u5c31\u53ef\u4ee5\u770b\u51fa\uff0c\u73bb\u5c14\u5179\u66fc\u673a\u548c\u7edf\u8ba1\u7269\u7406\u6709\u7740\u5341\u5206\u5bc6\u5207\u7684\u5173\u8054\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u7406\u89e3\u6210\u4e00\u4e2a\u7edf\u8ba1\u529b\u5b66\u7cfb\u7edf\uff0c\u5176\u4e2d\u5305\u542b\u4e86\u4e24\u7ec4\u76f8\u4e92\u4f5c\u7528\u7684\u968f\u673a\u53d8\u91cf\uff1a\u663e\u53d8\u91cf(\u7ea2\u8272)\u548c\u9690\u53d8\u91cf(\u84dd\u8272)\u3002\u201c\u73bb\u5c14\u5179\u66fc\u673a\u201d\u7684\u540d\u5b57\u6765\u6e90\u4e8e\u8fd9\u4e9b\u968f\u673a\u53d8\u91cf\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u9075\u5faa\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u3002\u800c\u201c\u9650\u5236\u201d\u8fd9\u4e2a\u8bcd\u6765\u6e90\u4e8e\u56fe1(b)\u4e2d\u6240\u793a\u7684\u7279\u6b8a\u7f51\u7edc\u7ed3\u6784\uff1a\u6240\u6709\u8fde\u63a5\u90fd\u4ec5\u5728\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u3002\u548c\u5168\u8fde\u63a5\u7684\u73bb\u5c14\u5179\u66fc\u673a\u76f8\u6bd4\uff0c\u8fd9\u6837\u7684\u7ed3\u6784\u53ef\u4ee5\u6781\u5927\u5730\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002\u800c\u5bf9\u4e8e\u4e00\u4e2a\u53ea\u5173\u5fc3\u663e\u53d8\u91cf\u7684\u89c2\u5bdf\u8005\u6765\u8bf4\uff0c\u5373\u4fbf\u663e\u5c42\u5185\u90e8\u6ca1\u6709\u76f4\u63a5\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u9690\u5c42\u795e\u7ecf\u5143\u6240\u8bf1\u5bfc\u7684\u6709\u6548\u76f8\u4e92\u4f5c\u7528\u8fd8\u662f\u53ef\u4ee5\u5c06\u5b83\u4eec\u5173\u8054\u8d77\u6765\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe1 \u51e0\u79cd\u53c2\u6570\u5316\u591a\u5143\u51fd\u6570\u7684\u65b9\u5f0f(a)\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff1b(b)\u9650\u5236\u73bb\u5c14\u5179\u66fc\u673a\uff1b(c)\u77e9\u9635\u4e58\u79ef\u6001<\/span><\/strong><\/span><\/p>\n

\u4e0e\u4f7f\u7528\u4e00\u4e2a2N \u884c\u7684\u8868\u683c\u76f8\u6bd4\uff0c\u56fe1(a)\uff0c(b)\u4e2d\u6240\u793a\u7684\u4e24\u7c7b\u7f51\u7edc\u7ed3\u6784\u90fd\u53ef\u4ee5\u7528\u5c11\u5f97\u591a\u7684\u53c2\u6570\u8fd1\u4f3c\u8868\u8fbe\u590d\u6742\u7684\u591a\u5143\u51fd\u6570\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8c03\u8282\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u6743\u91cd\u53c2\u6570\uff0c\u4f7f\u5f97\u5b83\u5b66\u4f1a\u4ece\u56fe\u7247\u50cf\u7d20\u4fe1\u606f\u4e2d\u5206\u8fa8\u5176\u4e2d\u7269\u4f53\u7684\u79cd\u7c7b\u3002\u6216\u8005\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u8c03\u8282\u9650\u5236\u73bb\u5c14\u5179\u66fc\u673a\u4e2d\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5f3a\u5ea6\uff0c\u4f7f\u5f97\u663e\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\u5c3d\u53ef\u80fd\u91cd\u73b0\u76ee\u6807\u6570\u636e\u96c6\u7684\u5206\u5e03\u3002\u8bad\u7ec3\u597d\u7684\u73bb\u5c14\u5179\u66fc\u673a\u53ef\u4ee5\u751f\u6210\u66f4\u591a\u9075\u5faa\u76ee\u6807\u6982\u7387\u5206\u5e03\u7684\u65b0\u6837\u672c\u3002\u4ee5\u4e0a\u4e24\u7c7b\u4efb\u52a1\u5206\u522b\u5bf9\u5e94\u4e86\u5224\u522b\u578b\u5b66\u4e60(Discriminative Learning) \u548c\u751f\u6210\u578b\u5b66\u4e60(Generative Learning)\u3002\u6253\u4e2a\u6bd4\u65b9\uff0c\u5224\u522b\u578b\u5b66\u4e60\u76f8\u5f53\u4e8e\u5b66\u4f1a\u8ba4\u5b57\uff0c\u800c\u751f\u6210\u578b\u5b66\u4e60\u7684\u76ee\u6807\u662f\u5b66\u4f1a\u5199\u5b57\u3002\u6b63\u5982\u8d39\u66fc\u5728\u4ed6\u7684\u9ed1\u677f\u4e0a\u7559\u4e0b\u7684\u90a3\u53e5\u540d\u8a00\u201cWhat I can not create,I do not understand\u201d\uff0c\u5b66\u4f1a\u5199\u53ef\u6bd4\u5b66\u4f1a\u8bfb\u56f0\u96be\u5f97\u591a\uff0c\u4e5f\u8981\u6c42\u66f4\u6df1\u5c42\u6b21\u7684\u7406\u89e3\u3002\u5224\u522b\u578b\u5b66\u4e60\u652f\u6491\u7740\u5927\u91cf\u5f53\u4e0b\u6210\u529f\u7684\u5546\u4e1a\u5e94\u7528\uff0c\u800c\u63a2\u7d22\u751f\u6210\u578b\u5b66\u4e60\u7684\u6a21\u578b\u548c\u7b97\u6cd5\u5219\u4ee3\u8868\u4e86\u6df1\u5ea6\u5b66\u4e60\u7814\u7a76\u7684\u524d\u6cbf\u548c\u672a\u6765\u3002<\/span><\/p>\n

\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4eba\u4eec\u5e0c\u671b\u4f7f\u7528\u901a\u7528\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u8868\u8fbe\u5c3d\u53ef\u80fd\u590d\u6742\u591a\u53d8\u7684\u51fd\u6570\u5f62\u5f0f\u3002\u8fd9\u81ea\u7136\u5f15\u51fa\u4e00\u4e2a\u95ee\u9898\uff1a\u56fe1(a)\uff0c(b)\u6240\u793a\u7684\u7f51\u7edc\u90fd\u80fd\u591f\u8868\u8fbe\u4ec0\u4e48\u6837\u7684\u51fd\u6570\u5f62\u5f0f\uff1f\u4e3a\u6b64\uff0c\u4eba\u4eec\u8bc1\u660e\u4e86\u6240\u8c13\u7684\u201c\u666e\u9002\u8868\u793a\u5b9a\u7406\u201d\uff1a\u968f\u7740\u7f51\u7edc\u4e2d\u9690\u5c42\u795e\u7ecf\u5143\u4e2a\u6570\u7684\u589e\u52a0\uff0c\u56fe1(a)\u4e2d\u6240\u793a\u7684\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784(\u5373\u4f7f\u53ea\u6709\u5355\u4e2a\u9690\u5c42)\u53ef\u4ee5\u4efb\u610f\u903c\u8fd1\u4efb\u4f55\u7684\u8fde\u7eed\u51fd\u6570\u3002\u7c7b\u4f3c\u5730\uff0c\u901a\u8fc7\u589e\u52a0\u56fe1(b)\u4e2d\u9650\u5236\u73bb\u5c14\u5179\u66fc\u673a\u7684\u9690\u5c42\u795e\u7ecf\u5143\u6570\u76ee\uff0c\u5b83\u4e5f\u53ef\u4ee5\u8868\u8fbe\u5173\u4e8e\u663e\u53d8\u91cf\u4efb\u610f\u590d\u6742\u7684\u6982\u7387\u5206\u5e03\u51fd\u6570\u3002\u7136\u800c\u9057\u61be\u7684\u662f\uff0c\u9488\u5bf9\u4e00\u4e2a\u5177\u4f53\u7684\u51fd\u6570\u8fd1\u4f3c\u95ee\u9898\uff0c\u4ee5\u4e0a\u8fd9\u4e9b\u666e\u9002\u8868\u793a\u5b9a\u7406\u6ca1\u529e\u6cd5\u544a\u8bc9\u6211\u4eec\u81f3\u5c11\u9700\u8981\u591a\u5c11\u9690\u5c42\u795e\u7ecf\u5143\uff0c\u4e5f\u6ca1\u529e\u6cd5\u544a\u8bc9\u6211\u4eec\u7a76\u7adf\u5982\u4f55\u786e\u5b9a\u8fd9\u4e9b\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8fde\u63a5\u6743\u91cd\u3002\u800c\u73b0\u5b9e\u4e2d\u6211\u4eec\u5173\u5fc3\u7684\u9996\u8981\u95ee\u9898\u5c31\u662f\uff1a\u7ed9\u5b9a\u6709\u9650\u7684\u8ba1\u7b97\u65f6\u95f4\u548c\u5b58\u50a8\u8d44\u6e90\uff0c\u5e94\u8be5\u5982\u4f55\u6700\u4f18\u5730\u5206\u914d\u5b83\u4eec\u5462\uff1f<\/span><\/p>\n

\u7ecf\u8fc7\u591a\u5e74\u7684\u6478\u7d22\u5b9e\u8df5\uff0c\u4eba\u4eec\u6709\u4e00\u4e2a\u5173\u952e\u7684\u53d1\u73b0\uff1a\u5728\u53c2\u6570\u4e2a\u6570\u4e00\u6837\u7684\u60c5\u51b5\u4e0b\uff0c\u6df1\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\u6bd4\u6d45\u5c42\u7684\u7f51\u7edc\u5177\u6709\u66f4\u5f3a\u7684\u8868\u8fbe\u80fd\u529b\u3002\u8bad\u7ec3\u8d8a\u6765\u8d8a\u6df1\u7684\u795e\u7ecf\u7f51\u7edc\u6765\u8fd1\u4f3c\u8868\u8fbe\u590d\u6742\u7684\u51fd\u6570\u5f62\u5f0f\uff0c\u662f\u6df1\u5ea6\u5b66\u4e60\u8fd9\u4e2a\u540d\u8bcd\u4e2d\u201c\u6df1\u5ea6\u201d\u7684\u6765\u6e90\u3002\u5f53\u7136\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u8868\u8fbe\u80fd\u529b\u4e5f\u5e76\u4e0d\u662f\u8d8a\u5f3a\u8d8a\u597d\u3002\u8fc7\u4e8e\u590d\u6742\u7684\u7f51\u7edc\u7ed3\u6784\u4e0d\u4ec5\u589e\u52a0\u4e86\u8ba1\u7b97\u91cf\uff0c\u8fd8\u53ef\u80fd\u9020\u6210\u795e\u7ecf\u7f51\u7edc\u8fc7\u62df\u5408(Over-fitting)\uff0c\u8fd9\u5c31\u662f\u5178\u578b\u7684\u201c\u8fc7\u72b9\u4e0d\u53ca\u201d\u3002\u795e\u7ecf\u7f51\u7edc\u7684\u8868\u8fbe\u80fd\u529b\u6700\u597d\u662f\u4e0e\u9700\u8981\u63cf\u8ff0\u7684\u51fd\u6570\u7684\u590d\u6742\u7a0b\u5ea6\u76f8\u5339\u914d\u3002\u4e3a\u6b64\uff0c\u4eba\u4eec\u8bbe\u8ba1\u51fa\u4e86\u79cd\u7c7b\u7e41\u591a\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u3002\u5f88\u591a\u8fd9\u4e9b\u7ed3\u6784\u8bbe\u8ba1\u4e3b\u8981\u7531\u5de5\u7a0b\u5b9e\u8df5\u7ecf\u9a8c\u9a71\u52a8\uff0c\u8fd9\u4f7f\u5f97\u6df1\u5ea6\u5b66\u4e60\u5f97\u5230\u4e86\u201c\u7ecf\u9a8c\u4e3b\u4e49\u201d\u7684\u540d\u58f0\u3002\u5229\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4f5c\u51fd\u6570\u8fd1\u4f3c\u7684\u521d\u8877\u662f\u5229\u7528\u5b83\u4eec\u7684\u901a\u7528\u6027\uff0c\u4e0d\u9700\u8981\u592a\u591a\u7684\u4eba\u4e3a\u4ecb\u5165\u5c31\u53ef\u4ee5\u81ea\u52a8\u5bfb\u627e\u5230\u6570\u636e\u4e2d\u7684\u5173\u952e\u7279\u5f81(Feature)\u3002\u53ef\u5f53\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u53d8\u5f97\u8d8a\u6765\u8d8a\u591a\u6837\u4e4b\u540e\uff0c\u9762\u4e34\u7f51\u7edc\u7684\u4eba\u4e3a\u9009\u62e9\u95ee\u9898\uff0c\u6211\u4eec\u53c8\u56de\u5230\u4e86\u8d77\u70b9\u3002\"\u96c6\u667a\"<\/span><\/p>\n

\u56e0\u6b64\uff0c\u4eba\u4eec\u8feb\u5207\u9700\u8981\u4e00\u4e9b\u66f4\u5177\u6307\u5bfc\u610f\u4e49\u7684\u5224\u522b\u6807\u51c6\uff0c\u6765\u5e2e\u52a9\u6211\u4eec\u5b9a\u91cf\u5316\u5730\u754c\u5b9a\u795e\u7ecf\u7f51\u7edc\u7684\u8868\u8fbe\u80fd\u529b\u548c\u6570\u636e\u96c6\u7684\u590d\u6742\u7a0b\u5ea6\uff0c\u4ee5\u4fbf\u5728\u4e0d\u540c\u7ed3\u6784\u7684\u795e\u7ecf\u7f51\u7edc\u4e4b\u95f4\u4f5c\u51fa\u6bd4\u8f83\u548c\u53d6\u820d\u3002\u4e3a\u6b64\u6211\u4eec\u9700\u8981\u5bf9\u4e8e\u795e\u7ecf\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u5bf9\u8c61\u2014\u2014\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u591a\u5143\u51fd\u6570\u2014\u2014\u6709\u66f4\u6df1\u523b\u7684\u7406\u89e3\u3002\u5728\u6211\u4eec\u524d\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u867d\u7136\u6240\u6709\u53ef\u80fd\u7684\u8f93\u5165\u539f\u5219\u4e0a\u67092N \u79cd\uff0c\u4f46\u5178\u578b\u7684\u8f93\u5165\u5176\u5b9e\u901a\u5e38\u9075\u5faa\u67d0\u4e00\u7279\u5b9a\u5206\u5e03\u3002\u5173\u4e8e\u76ee\u6807\u6570\u636e\u5206\u5e03\u548c\u51fd\u6570\u6027\u8d28\u7684\u5148\u9a8c\u77e5\u8bc6(Prior Knowledge)\u6709\u52a9\u4e8e\u6307\u5bfc\u6211\u4eec\u8bbe\u8ba1\u5408\u9002\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u3002\u4e00\u4e2a\u6700\u660e\u663e\u7684\u5148\u9a8c\u77e5\u8bc6\u5c31\u662f\u51fd\u6570\u7684\u5bf9\u79f0\u6027\u3002\u6bd4\u5982\uff0c\u5728\u56fe\u50cf\u8bc6\u522b\u7684\u4f8b\u5b50\u4e2d\uff0c\u56fe\u7247\u7684\u79cd\u7c7b\u4e0e\u5176\u4e2d\u7269\u4f53\u7684\u5177\u4f53\u4f4d\u7f6e\u65e0\u5173\u3002\u7c7b\u4f3c\u5730\uff0c\u5bf9\u4e8e\u56f4\u68cb\u5c40\u9762\u7684\u4f30\u503c\u5bf9\u76d8\u9762\u6784\u578b\u4e5f\u5e94\u8be5\u5177\u6709\u53cd\u6f14\u548c\u65cb\u8f6c\u4e0d\u53d8\u6027\u3002\u5728\u56fe1(a)\u7684\u7f51\u7edc\u4e2d\u5b9e\u73b0\u8fd9\u4e9b\u9650\u5236\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u5377\u79ef\u795e\u7ecf\u7f51\u7edc(Convolutional Neural Network)\u3002\u5b83\u4f7f\u7528\u5c40\u57df\u611f\u77e5\u533a(Local Receptive Fields)\u626b\u63cf\u6574\u5f20\u56fe\u7247\u5bfb\u627e\u7279\u5f81\uff0c\u901a\u8fc7\u4e0d\u540c\u611f\u77e5\u533a\u5171\u4eab\u6743\u91cd\u6765\u4fdd\u8bc1\u51fd\u6570\u7684\u4e0d\u53d8\u6027\u3002\u5982\u4f55\u53d1\u6398\u548c\u5229\u7528\u66f4\u591a\u7c7b\u4f3c\u7684\u201c\u5148\u9a8c\u77e5\u8bc6\u201d\u662f\u6df1\u5ea6\u5b66\u4e60\u6210\u529f\u7684\u5173\u952e\u3002<\/span><\/p>\n

\u4e0e\u4e0a\u8ff0\u4f8b\u5b50\u7c7b\u4f3c\uff0c\u91cf\u5b50\u7269\u7406\u7684\u7814\u7a76\u4e2d\u4e5f\u5e38\u5e38\u4f7f\u7528\u5230\u51fd\u6570\u8fd1\u4f3c\u3002\u6bd4\u5982\uff0c\u4e00\u4e2a\u91cf\u5b50\u81ea\u65cb\u4f53\u7cfb\u7684\u6ce2\u51fd\u6570\u65e0\u975e\u662f\u4e00\u4e2a\u5173\u4e8e\u81ea\u65cb\u6784\u578b\u7684\u591a\u5143\u51fd\u6570\u3002\u548c\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u76ee\u6807\u4e00\u6837\uff0c\u6211\u4eec\u4e5f\u5e0c\u671b\u4f7f\u7528\u5c3d\u91cf\u7b80\u5355\u7684\u53c2\u6570\u5316\u65b9\u5f0f\u548c\u5c3d\u91cf\u5c11\u7684\u53c2\u6570\u63cf\u8ff0\u5c3d\u53ef\u80fd\u590d\u6742\u7684\u6ce2\u51fd\u6570\u3002\u603b\u7ed3\u4e00\u53e5\u8bdd\uff0c\u90a3\u5c31\u662f\u201c\u5929\u7f51\u6062\u6062\uff0c\u758f\u800c\u4e0d\u6f0f\u201d\u3002\u56fe1(c)\u663e\u793a\u91cf\u5b50\u591a\u4f53\u7269\u7406\u7814\u7a76\u4e2d\u5e38\u7528\u7684\u4e00\u79cd\u53c2\u6570\u5316\u6ce2\u51fd\u6570\u7684\u65b9\u6cd5\uff1a\u77e9\u9635\u4e58\u79ef\u6001(Matrix Product State)\u3002\u5b83\u7684\u57fa\u672c\u7ec4\u6210\u5355\u5143\u662f\u7ea2\u8272\u65b9\u5757\u6240\u793a\u7684\u4e09\u9636\u5f20\u91cf\u3002\u7ad6\u7ebf\u4ee3\u8868\u7269\u7406\u6307\u6807\uff0c\u800c\u65b9\u5757\u4e4b\u95f4\u7684\u6a2a\u7ebf\u5219\u79f0\u4e3a\u201c\u865a\u62df\u952e\u201d(Vitual Bond)\u3002\u6a2a\u7ebf\u4e4b\u95f4\u7684\u8fde\u63a5\u4ee3\u8868\u5bf9\u4e8e\u865a\u62df\u952e\u6307\u6807\u7684\u6c42\u548c\u3002\u4e0d\u96be\u731c\u6d4b\uff0c\u968f\u7740\u865a\u62df\u952e\u7ef4\u6570(Vitual Bond Dimension)\u7684\u589e\u5927\uff0c\u77e9\u9635\u4e58\u79ef\u6001\u53ef\u4ee5\u8868\u8fbe\u5173\u4e8e\u7269\u7406\u6307\u6807\u6108\u52a0\u590d\u6742\u7684\u51fd\u6570\u3002\u9664\u4e86\u589e\u52a0\u865a\u62df\u952e\u7ef4\u6570\uff0c\u53e6\u4e00\u79cd\u589e\u52a0\u77e9\u9635\u4e58\u79ef\u6001\u8868\u8fbe\u80fd\u529b\u7684\u65b9\u6cd5\u662f\u5c06\u56fe1(c)\u4e2d\u6240\u793a\u7684\u65b9\u5757\u63a8\u5e7f\u6210\u4e3a\u66f4\u9ad8\u9636\u7684\u5f20\u91cf\uff0c\u4e5f\u5c31\u662f\u589e\u52a0\u865a\u62df\u952e\u7684\u4e2a\u6570\u3002\u5c06\u6240\u6709\u865a\u62df\u952e\u8fde\u63a5\u8d77\u6765\uff0c\u6c42\u548c\u5b8c\u6240\u6709\u7684\u5185\u90e8\u5f20\u91cf\u6307\u6807\uff0c\u5c31\u5f97\u5230\u4e86\u524d\u6587\u63d0\u5230\u7684\u5f20\u91cf\u7f51\u7edc\u6001\u3002\u548c\u6df1\u5ea6\u5b66\u4e60\u4e2d\u79cd\u7c7b\u7e41\u591a\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u4e00\u6837\uff0c\u7269\u7406\u5b66\u5bb6\u4e5f\u53d1\u660e\u4e86\u5f88\u591a\u4e0d\u540c\u7ed3\u6784\u7684\u5f20\u91cf\u7f51\u7edc\u6001\u4ee5\u53ca\u76f8\u5bf9\u5e94\u7684\u7b97\u6cd5\u3002\u7136\u800c\uff0c\u548c\u6df1\u5ea6\u5b66\u4e60\u4e0d\u540c\u7684\u662f\uff0c\u7269\u7406\u5b66\u5bb6\u4eec\u5bf9\u4e8e\u5f20\u91cf\u7f51\u7edc\u7684\u8868\u8fbe\u80fd\u529b\u6709\u7740\u66f4\u4e3a\u5b9a\u91cf\u5316\u7684\u7406\u89e3\uff1a\u5173\u952e\u5728\u4e8e\u91cf\u5b50\u7ea0\u7f20\uff01\u5207\u5272\u4e00\u4e2a\u5f20\u91cf\u7f51\u7edc\u6001\u6240\u65ad\u5f00\u7684\u865a\u62df\u952e\u7684\u4e2a\u6570\u548c\u7ef4\u6570\u4e0e\u8fd9\u4e2a\u7f51\u7edc\u80fd\u591f\u63cf\u8ff0\u7684\u7ea0\u7f20\u71b5\u76f4\u63a5\u76f8\u5173\u3002\u800c\u53e6\u4e00\u65b9\u9762\uff0c\u867d\u7136\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u7684\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\u975e\u5e38\u5927\uff0c\u4f46\u5e78\u8fd0\u7684\u662f\u5927\u591a\u6570\u4eba\u4eec\u611f\u5174\u8da3\u7684\u91cf\u5b50\u6001\u53ea\u662f\u5176\u4e2d\u7684\u4e00\u4e2a\u5f88\u5c0f\u7684\u5b50\u96c6\u3002\u8fd9\u4e9b\u6001\u7684\u91cf\u5b50\u7ea0\u7f20\u71b5\u5e76\u4e0d\u662f\u4efb\u610f\u7684\uff0c\u800c\u662f\u9075\u5faa\u524d\u6587\u63d0\u5230\u7684\u9762\u79ef\u5b9a\u5f8b\u3002\u5f20\u91cf\u7f51\u7edc\u6001\u6070\u597d\u6293\u4f4f\u4e86\u7269\u7406\u95ee\u9898\u7684\u8fd9\u4e2a\u91cd\u8981\u7279\u6027\uff0c\u56e0\u800c\u83b7\u5f97\u6210\u529f\u3002\u5728\u5b9e\u9645\u7814\u7a76\u4e2d\uff0c\u7269\u7406\u5b66\u5bb6\u4eec\u901a\u5e38\u9488\u5bf9\u5177\u4f53\u7269\u7406\u95ee\u9898\u7684\u7ea0\u7f20\u5927\u5c0f\u548c\u6a21\u5f0f\u6765\u7075\u6d3b\u9009\u62e9\u8bbe\u8ba1\u5f20\u91cf\u7f51\u7edc\u6001\u7ed3\u6784\u3002\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0b\uff0c\u91cf\u5b50\u7ea0\u7f20\u5176\u5b9e\u5c31\u662f\u6307\u5f15\u7269\u7406\u5b66\u5bb6\u4eec\u5e94\u7528\u5f20\u91cf\u7f51\u7edc\u7814\u7a76\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u7684\u201c\u5148\u9a8c\u77e5\u8bc6\u201d\u3002<\/span><\/p>\n


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3<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
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\u6df1\u5ea6\u5b66\u4e60\u52a9\u529b\u91cf\u5b50\u7269\u7406<\/span><\/strong><\/span><\/p>\n<\/section>\n

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\"\u96c6\u667a\"<\/p>\n

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<\/p>\n

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4<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
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\u91cf\u5b50\u7ea0\u7f20\u6307\u5f15\u6df1\u5ea6\u5b66\u4e60<\/span><\/strong><\/span><\/p>\n<\/section>\n

\u4e0a\u8ff0\u8fd9\u4e9b\u5de5\u4f5c\u7684\u7814\u7a76\u601d\u8def\u662f\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u8fd1\u4f3c\u91cf\u5b50\u591a\u4f53\u6ce2\u51fd\u6570\u3002\u6709\u8da3\u7684\u662f\uff0c\u4f7f\u7528\u9006\u5411\u601d\u7ef4\uff0c\u91cf\u5b50\u591a\u4f53\u7269\u7406\u4e5f\u80fd\u591f\u5e2e\u52a9\u56de\u7b54\u4e00\u4e9b\u5173\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u95ee\u9898\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u91cf\u5b50\u7ea0\u7f20\u7684\u89c6\u89d2\u6765\u8bf4\u660e\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u6df1\u5ea6\u4e3a\u4ec0\u4e48\u91cd\u8981\u3002\u8003\u8651\u56fe2 \u4e2d\u6240\u793a\u7684\u4e24\u4e2a\u73bb\u5c14\u5179\u66fc\u673a\uff0c\u5b83\u4eec\u7684\u9690\u5c42\u795e\u7ecf\u5143\u4e2a\u6570\u548c\u6743\u91cd\u53c2\u6570\u4e2a\u6570\u90fd\u5b8c\u5168\u76f8\u7b49\u3002\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u56fe2(a)\u7684\u9690\u5c42\u795e\u7ecf\u5143\u5448\u6d45\u5c42\u6241\u5e73\u5316\u6392\u5217\uff0c\u800c\u5728\u56fe2(b)\u4e2d\u9690\u5c42\u795e\u7ecf\u5143\u6cbf\u7eb5\u6df1\u65b9\u5411\u6392\u5217\u6210\u4e86\u5c42\u7ea7\u7ed3\u6784\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

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\"\u96c6\u667a\"<\/p>\n

\u56fe3 MNIST\u6570\u636e\u96c6\u4e2d\u7684\u4e00\u4e9b\u6837\u672c<\/span><\/strong><\/p>\n

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\u4ee5\u4e0a\u7684\u8ba8\u8bba\u90fd\u662f\u9488\u5bf9\u751f\u6210\u578b\u5b66\u4e60\u800c\u8a00\u7684\uff0c\u90a3\u4e48\uff0c\u91cf\u5b50\u7ea0\u7f20\u5bf9\u4e8e\u7406\u89e3\u5224\u522b\u578b\u7684\u5b66\u4e60\u662f\u5426\u4e5f\u6709\u7c7b\u4f3c\u7684\u5e2e\u52a9\u5462\uff1f\u8003\u8651\u5230\u6df1\u5c42\u7684\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u5e7f\u6cdb\u5e94\u7528\uff0c\u8fd9\u662f\u76ee\u524d\u6df1\u5ea6\u5b66\u4e60\u7814\u7a76\u7684\u4e00\u4e2a\u70ed\u70b9\u95ee\u9898\u3002\u8fd9\u65b9\u9762\u4e00\u4e2a\u5f88\u6709\u542f\u53d1\u7684\u5de5\u4f5c\u6765\u81ea\u8ba1\u7b97\u7269\u7406\u5b66\u5bb6Stoudenmire\u548c\u751f\u7269\u7269\u7406\u5b66\u5bb6Schwab\uff0c\u4ed6\u4eec\u6210\u529f\u8bad\u7ec3\u4e86\u4e00\u4e2a\u77e9\u9635\u4e58\u79ef\u6001\u6765\u8bc6\u522bMNIST \u6570\u636e\u96c6\u4e2d\u7684\u6570\u5b57\u3002\u4ed6\u4eec\u7684\u6210\u529f\u8bf4\u660e\uff0c\u4eceMNIST\u7684\u50cf\u7d20\u5230\u6570\u5b57\u6807\u8bb0\u7684\u51fd\u6570\u6620\u5c04\u7684\u7ea0\u7f20\u71b5\u770b\u8d77\u6765\u5e76\u4e0d\u5927\uff0c\u5b8c\u5168\u53ef\u4ee5\u88ab\u77e9\u9635\u4e58\u79ef\u6001\u6709\u6548\u63cf\u8ff0\u3002\u65e0\u72ec\u6709\u5076\uff0c\u8036\u8def\u6492\u51b7\u5e0c\u4f2f\u6765\u5927\u5b66\u7684\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6Amnon Shashua \u6240\u9886\u5bfc\u7684\u56e2\u961f\u4e00\u76f4\u81f4\u529b\u4e8e\u4f7f\u7528\u5f20\u91cf\u5206\u6790\u7684\u624b\u6bb5\u7814\u7a76\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u3002\u7ecf\u8fc7\u4e00\u7cfb\u5217\u524d\u671f\u5de5\u4f5c\u7684\u94fa\u57ab\uff0c\u4ed6\u4eec\u7684\u6ce8\u610f\u529b\u6700\u8fd1\u4e5f\u88ab\u5438\u5f15\u5230\u91cf\u5b50\u7ea0\u7f20\u8fd9\u4e2a\u6982\u5ff5\u4e0a\u30022017 \u5e744 \u6708\u521d\uff0cShashua \u7b49\u4eba\u5728arXiv \u4e0a\u8d34\u51fa\u4e00\u7bc7\u9898\u4e3a\u201cDeep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Design\u201d\u7684\u957f\u6587\u3002\u8fd9\u7bc7\u8bba\u6587\u7684\u7b2c\u4e00\u4f5c\u8005Yoav Levine \u7855\u58eb\u671f\u95f4\u5728\u4ee5\u8272\u5217\u7684\u9b4f\u8328\u66fc\u79d1\u5b66\u9662(Weizmann Institute of Science)\u5b66\u4e60\u7406\u8bba\u51dd\u805a\u6001\u7269\u7406\uff0c\u73b0\u5728\u5219\u662fShashua\u7684\u535a\u58eb\u751f\u3002\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0cLevine \u7b49\u4eba\u91c7\u7528\u4e0e\u6587\u732e\u7c7b\u4f3c\u7684\u7b56\u7565\uff0c\u5c06\u4e00\u7c7b\u7279\u6b8a\u7684\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u8f6c\u5316\u4e3a\u5f20\u91cf\u7f51\u7edc\u6001\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u901a\u8fc7\u5bf9\u4e8e\u5f20\u91cf\u7f51\u7edc\u7684\u6700\u5c0f\u5207\u5272(Min-Cut)\u5206\u6790\u6765\u786e\u5b9a\u539f\u6765\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u7ea0\u7f20\u8868\u8fbe\u80fd\u529b\u4e86\u3002\u4f5c\u4e3a\u4e00\u4e2a\u5177\u4f53\u7684\u4f8b\u5b50\uff0c\u4ed6\u4eec\u8003\u8651\u4e86\u201c\u4e0a\u5bbd\u4e0b\u7a84\u201d\u548c\u201c\u4e0a\u7a84\u4e0b\u5bbd\u201d\u4e24\u79cd\u7ed3\u6784\u7684\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff0c\u5e76\u4ece\u7406\u8bba\u4e0a\u8bc1\u660e\u5176\u6027\u80fd\u7684\u4f18\u52a3\u53d6\u51b3\u4e8e\u76ee\u6807\u6570\u636e\u96c6\u7684\u7ea0\u7f20\u7279\u6027\u3002\u4ed6\u4eec\u5728MNIST\u6570\u636e\u96c6\u4e0a\u8bbe\u8ba1\u6570\u503c\u5b9e\u9a8c\uff0c\u4e5f\u7684\u786e\u9a8c\u8bc1\u4e86\u8fd9\u4e9b\u7406\u8bba\u9884\u8a00\u3002<\/span><\/p>\n

\u53ef\u89c1\uff0c\u5728\u6df1\u5ea6\u5b66\u4e60\u4e0e\u91cf\u5b50\u591a\u4f53\u7269\u7406\u7684\u4ea4\u754c\u5904\u6b63\u5728\u5f62\u6210\u4e00\u4e2a\u65b0\u5174\u7814\u7a76\u65b9\u5411\uff0c\u91cf\u5b50\u7ea0\u7f20\u6b63\u662f\u8fde\u63a5\u5b83\u4eec\u7684\u6865\u6881\u3002\u4e00\u4e9b\u55c5\u89c9\u654f\u9510\u7684\u7814\u7a76\u8005\u5df2\u7ecf\u610f\u8bc6\u5230\u4e86\u5bf9\u65b9\u7684\u601d\u60f3\u3001\u65b9\u6cd5\u548c\u6280\u672f\u5bf9\u4e8e\u672c\u9886\u57df\u7684\u5e2e\u52a9\uff0c\u6b63\u5728\u79ef\u6781\u5730\u76f8\u4e92\u5b66\u4e60\u3002\u9884\u8ba1\u968f\u7740\u66f4\u591a\u601d\u7ef4\u6d3b\u8dc3\u7684\u7814\u7a76\u8005\u7684\u52a0\u5165\uff0c\u6df1\u5ea6\u5b66\u4e60\u548c\u91cf\u5b50\u591a\u4f53\u7269\u7406\u7684\u7814\u7a76\u4f1a\u78b0\u649e\u51fa\u66f4\u52a0\u707f\u70c2\u7684\u706b\u82b1\u3002<\/span><\/p>\n


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\u7ed3\u8bed<\/span><\/strong><\/span><\/p>\n<\/section>\n

\u91cf\u5b50\u591a\u4f53\u7269\u7406\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u76f8\u9047\u4e5f\u8bb8\u672c\u4e0d\u5e94\u4f7f\u4eba\u60ca\u8bb6\uff0c\u6bd5\u7adf\uff0c\u8fd9\u4e24\u4e2a\u9886\u57df\u90fd\u5173\u5fc3\u5927\u91cf\u5fae\u89c2\u81ea\u7531\u5ea6\u7ec4\u6210\u7684\u590d\u6742\u4f53\u7cfb\u4e2d\u6d8c\u73b0\u51fa\u6765\u7684\u5b8f\u89c2\u73b0\u8c61\u3002\u4eba\u4eec\u4e3a\u4e86\u8ba4\u8bc6\u81ea\u7136\u754c\u4e30\u5bcc\u591a\u5f69\u7684\u91cf\u5b50\u7269\u6001\u6240\u5f62\u6210\u7684\u5de5\u5177\uff0c\u4e5f\u8bb8\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u8bbe\u8ba1\u51fa\u66f4\u667a\u80fd\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u548c\u5b66\u4e60\u7b97\u6cd5\u3002\u201c\u91cf\u5b50\u673a\u5668\u5b66\u4e60\u201d(Quantum Machine Learning)\u662f\u4e00\u4e2a\u6b63\u5728\u84ec\u52c3\u53d1\u5c55\u7684\u9886\u57df\uff0c\u672c\u6587\u4ec5\u4ecb\u7ecd\u4e86\u5176\u4e2d\u7684\u51b0\u5c71\u4e00\u89d2\u3002\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u53c2\u9605\u300a\u7269\u7406\u300b\u6742\u5fd7\u4e0a\u7684\u4ecb\u7ecd\u6587\u7ae0\u548c\u6700\u8fd1\u7684\u7efc\u8ff0\u3002<\/span><\/p>\n

\u7231\u56e0\u65af\u5766\u6709\u4e00\u53e5\u540d\u8a00\uff1a\u201c\u81ea\u7136\u662f\u5fae\u5999\u7684\uff0c\u53ef\u5979\u6ca1\u6709\u6076\u610f\u201d\u3002\u9690\u85cf\u5728\u8fd9\u4e2a\u7eb7\u7e41\u590d\u6742\u7684\u4e16\u754c\u80cc\u540e\u7684\u7ed3\u6784\u7b97\u5f97\u4e0a\u662f\u5fae\u5999\u5427\u3002\u53ef\u4e00\u65e6\u6293\u4f4f\u8bc0\u7a8d\uff0c\u5c45\u7136\u53ef\u4ee5\u7528\u51e0\u884c\u7b80\u6d01\u7f8e\u5999\u7684\u516c\u5f0f\u7406\u89e3\u3002\u6df1\u5ea6\u5b66\u4e60\u662f\u4e0d\u662f\u80fd\u5e2e\u6211\u4eec\u6355\u6349\u81ea\u7136\u7684\u5584\u610f\u5462\uff1f\u6211\u4eec\u628a\u8fd9\u4e2a\u95ee\u9898\u653e\u5728\u8fd9\u91cc\uff0c\u671f\u5f85\u91cf\u5b50\u7269\u7406\u548c\u673a\u5668\u5b66\u4e60\u7684\u9082\u9005\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u53d1\u73b0\u66f4\u591a\u81ea\u7136\u7684\u5fae\u5999\uff01<\/span><\/p>\n


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\u81f4\u8c22<\/span><\/strong><\/span> \u611f\u8c22\u4e0e\u8c22\u6d77\u4e1c\u3001\u5411\u6d9b\u7684\u5408\u4f5c\uff1b\u611f\u8c22\u4e0e\u9093\u4e1c\u7075\u3001\u674e\u6653\u9e4f\u3001\u90dc\u52cb\u3001\u6d82\u9e3f\u6d69\u3001\u6768\u4e49\u5cf0\u3001\u5f20\u6f58\u3001\u8521\u5b50\u3001\u674e\u4f1f\u4ee5\u53caE. Miles Stoudenmire \u7684\u8ba8\u8bba\uff1b\u611f\u8c22\u8bb8\u9704\u7430\u3001\u7f57\u79c0\u54f2\u3001\u5f20\u8d8a\u6c34\u3001\u5218\u51b6\u534e\u548c\u5f20\u94f6\u5bf9\u4e8e\u672c\u6587\u5199\u4f5c\u7684\u5efa\u8bae\u3002<\/span><\/p>\n

\u672c\u6587\u9009\u81ea\u300a\u7269\u7406\u300b2017\u5e74\u7b2c7\u671f<\/span><\/p>\n<\/section>\n


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

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

\u91cd\u78c5\u7cfb\u5217\u8bfe\uff1a\u706b\u70ac\u4e0a\u7684\u6df1\u5ea6\u5b66\u4e60(\u4e0a)<\/span><\/a>
<\/p>\n

\u5bf9\u673a\u5668\u5b66\u4e60\u3001\u5f20\u91cf\u7f51\u7edc\u548c\u7269\u7406\u7684\u4e00\u4e9b\u770b\u6cd5 | \u7a0b\u5d69<\/a><\/span>
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\u7edf\u4e00\u4e4b\u8def\uff1a\u91cf\u5b50\u7ea0\u7f20\u3001\u65f6\u7a7a\u51e0\u4f55\u4e0e\u673a\u5668\u5b66\u4e60<\/span><\/a>
<\/p>\n

\u4e00\u79cd\u9762\u5411\u5173\u7cfb\u7684\u7269\u7406\u5b66\uff1a\u4ece\u793e\u4ea4\u7f51\u7edc\u5230\u91cf\u5b50\u7ea0\u7f20 <\/span><\/a>
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\"\u96c6\u667a\"<\/div>\n


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\"\u96c6\u667a\"
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\u96c6\u667aQQ\u7fa4\uff5c292641157
\u5546\u52a1\u5408\u4f5c\uff5czhangqian@swarma.org
\u6295\u7a3f\u8f6c\u8f7d\uff5cwangting@swarma.org<\/span><\/strong><\/p>\n

\n

\u25c6 <\/span>\u25c6 <\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n


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\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

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\"\u96c6\u667a\"<\/p>\n<\/section>\n

\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff1a \u96c6\u667a\u4ff1\u4e50\u90e8 <\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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