{"id":54350,"date":"2024-12-14T17:09:00","date_gmt":"2024-12-14T09:09:00","guid":{"rendered":"https:\/\/swarma.org\/?p=54350"},"modified":"2024-12-14T17:09:00","modified_gmt":"2024-12-14T09:09:00","slug":"2024%e5%b9%b4%e8%af%ba%e5%a5%96%e8%a7%a3%e8%af%bb%ef%bc%9a%e7%bb%9f%e8%ae%a1%e7%89%a9%e7%90%86%e3%80%81%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e4%b8%8e%e5%a4%8d%e6%9d%82%e7%a7%91%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=54350","title":{"rendered":"2024\u5e74\u8bfa\u5956\u89e3\u8bfb\uff1a\u7edf\u8ba1\u7269\u7406\u3001\u4eba\u5de5\u667a\u80fd\u4e0e\u590d\u6742\u79d1\u5b66"},"content":{"rendered":"
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\u5c24\u4ea6\u5e84\u3001\u5f20\u6c5f\u3001\u5510\u4e7e\u5143<\/span> <\/span>| \u8bb2\u8005<\/span><\/p>\n

\u6731\u6b23\u6021<\/span> <\/span>| \u6574\u7406<\/span><\/span><\/p>\n

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    John Hopfield \u548c Geoffrey Hinton \u7684\u4e3b\u8981\u8d21\u732e\u662f\u4ec0\u4e48\uff1f<\/section>\n<\/li>\n
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    AI \u4f1a\u8d85\u8d8a\u4eba\u7c7b\u7684\u7406\u89e3\u529b\u53d1\u73b0\u65b0\u7269\u7406\u5417\uff1f<\/section>\n<\/li>\n
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    \u56e0\u6b64\uff0c\u5c3d\u7ba1\u4ece\u83b7\u5956\u5185\u5bb9\u6765\u770b\uff0c\u5982\u5f20\u6c5f\u8001\u5e08\u6240\u8a00\uff0c\u76f8\u5bf9\u4e8e\u5f53\u524d\u7684\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\uff0c\u8fd9\u4e9b\u6210\u679c\u4f3c\u4e4e\u6709\u4e9b\u6ede\u540e\uff0c\u4f46\u4ece\u7269\u7406\u5b66\u8303\u5f0f\u7684\u53d1\u5c55\u548c\u6574\u4e2a\u5b66\u79d1\u7684\u521b\u65b0\u6765\u770b\uff0c\u8fd9\u4e2a\u5956\u9879\u7684\u9881\u53d1\u662f\u975e\u5e38\u53ca\u65f6\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5510\u4e7e\u5143<\/strong>\uff1a\u6211\u8fd8\u60f3\u8865\u5145\u4e00\u70b9\uff0c\u5c3d\u7ba1\u4eca\u5e74\u7684\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7ed3\u679c\u51fa\u4eba\u610f\u6599\uff0c\u4f46\u4e0d\u4e45\u524d\u7f51\u7edc\u4e0a\u6d41\u4f20\u7684\u4e00\u4e2a\u70ed\u95e8\u5e16\u5b50\u63ed\u793a\u4e86\u4e00\u4e2a\u6709\u8da3\u7684\u73b0\u8c61\u3002\u6709\u4eba\u53d1\u73b0\u4e00\u672c\u6559\u6750\u5728\u4ecb\u7ecd\u65f6\uff0c\u5df2\u7ecf\u5c06 Hopfield \u6807\u6ce8\u4e3a\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u5f97\u4e3b\u4e86\uff0c\u8fd9\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u9884\u8a00\uff0c\u56e0\u4e3a\u5f53\u65f6\u4ed6\u8fd8\u672a\u83b7\u5f97\u8be5\u5956\u9879\u3002\u8fd9\u8868\u660e\uff0c\u5c3d\u7ba1\u5b58\u5728\u8bef\u89e3\uff0c\u4f46\u8bb8\u591a\u4eba\u5df2\u7ecf\u8ba4\u4e3a\u4ed6\u7684\u6210\u5c31\u8db3\u4ee5\u83b7\u5f97\u8bfa\u8d1d\u5c14\u5956\u7684\u8ba4\u53ef\u3002\u8fd9\u4e2a\u9519\u8bef\u53ef\u80fd\u662f\u4f5c\u8005\u5728\u7f16\u5199\u65f6\u8bef\u4ee5\u4e3a\u4ed6\u5df2\u7ecf\u662f\u8bfa\u8d1d\u5c14\u5956\u5f97\u4e3b\u4e86\u3002\u56e0\u6b64\uff0c\u5b9e\u9645\u4e0a\u7269\u7406\u5b66\u754c\u5bf9 Hopfield \u7684\u8d21\u732e\u662f\u975e\u5e38\u8ba4\u53ef\u7684\uff0c\u4ed6\u751a\u81f3\u57282022\u5e74\u7edf\u8ba1\u7269\u7406\u5927\u4f1a\u4e0a\u83b7\u5f97\u4e86\u73bb\u5c14\u5179\u66fc\u5956\uff0c\u73bb\u5c14\u5179\u66fc\u5956\u662f\u7edf\u8ba1\u7269\u7406\u9886\u57df\u7684\u6700\u9ad8\u8363\u8a89\uff0c\u8fd9\u8868\u660e\u7269\u7406\u5b66\u754c\u5bf9 Hopfield \u7684\u8d21\u732e\u7ed9\u4e88\u4e86\u6781\u9ad8\u7684\u8bc4\u4ef7\u3002Hinton \u7684\u83b7\u5956\u5219\u76f8\u5bf9\u4ee4\u4eba\u610f\u5916\u3002<\/span><\/section>\n

    <\/section>\n

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

    <\/section>\n

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

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

    John Hopfield \u548c Geoffrey Hinton<\/strong><\/p>\n

    \u7684\u4e3b\u8981\u8d21\u732e\u662f\u4ec0\u4e48\uff1f<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


    <\/strong><\/span><\/section>\n
    \u5510\u4e7e\u5143<\/strong>\uff1a\u6211\u4eec\u5148\u4ece Hopfield \u8bb2\u8d77\uff0c\u6211\u53ef\u4ee5\u4ecb\u7ecd\u4e00\u4e9b\u4ed6\u5728 Hopfield \u7f51\u7edc\u4e4b\u5916\u7684\u5de5\u4f5c\u3002\u5b9e\u9645\u4e0a\uff0c\u4ed6\u7684\u7236\u4eb2\u4e5f\u662f\u4e00\u4f4d\u7269\u7406\u5b66\u5bb6\uff0c\u4ed6\u81ea\u5df1\u4e5f\u4e00\u76f4\u5728\u5b66\u7269\u7406\uff0c\u65e9\u671f\u5728\u51dd\u805a\u6001\u9886\u57df\u505a\u8fc7\u4e00\u4e9b\u5de5\u4f5c\u3002\u540e\u6765\u4ece\u4e0a\u4e16\u7eaa 70 \u5e74\u4ee3\u8d77\uff0c\u4ed6\u5f00\u59cb\u8f6c\u5411\u751f\u7269\u7269\u7406\u65b9\u9762\u7684\u7814\u7a76\u3002\u6700\u521d\uff0c\u4ed6\u7814\u7a76\u4e86\u751f\u7269\u5316\u5b66\u53cd\u5e94\u91cc\u7684\u4e00\u79cd\u6821\u5bf9\u673a\u5236\uff0c\u56e0\u4e3a\u5f88\u591a\u751f\u7269\u5316\u5b66\u53cd\u5e94\u5b58\u5728\u968f\u673a\u6027\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e9b\u975e\u5e73\u8861\u673a\u5236\u6765\u5b9e\u73b0\u9519\u8bef\u6821\u5bf9\u3002\u5728\u975e\u5e73\u8861\u7269\u7406\u4f53\u7cfb\u5efa\u7acb\u4e4b\u524d\uff0cHopfield \u5df2\u7ecf\u63d0\u51fa\u4e86\u8fd9\u79cd\u673a\u5236\u3002\u4e4b\u540e\u4ed6\u5f00\u59cb\u7814\u7a76\u795e\u7ecf\u7f51\u7edc\uff0c\u4e5f\u5c31\u662f Hopfield \u7f51\u7edc\u3002\u5728\u8fd9\u9879\u7814\u7a76\u4e4b\u540e\uff0c\u4ed6\u53c8\u505a\u4e86\u5f88\u591a\u5de5\u4f5c\uff0c\u6bd4\u5982\u5173\u4e8e\u55c5\u89c9\u95ee\u9898\u7684\u7f16\u7801\u673a\u5236\uff0c\u4ee5\u53ca\u66f4\u591a\u6709\u5173\u795e\u7ecf\u7f51\u7edc\u7684\u7406\u8bba\u7814\u7a76\u3002\u8fd1\u4e9b\u5e74\u4ed6\u4ecd\u5728\u505a\u4e00\u4e9b\u76f8\u5173\u7814\u7a76\uff0c\u4f9d\u7136\u662f\u4e00\u4f4d\u6d3b\u8dc3\u7684\u5b66\u8005\u3002\u5173\u4e8e Hopfield \u7f51\u7edc\uff0c\u6211\u60f3\u542c\u5f20\u6c5f\u8001\u5e08\u4ece\u6700\u65e9\u671f\u7684\u57fa\u4e8e\u80fd\u91cf\u7684\u6a21\u578b\u6765\u7ed9\u5927\u5bb6\u7b80\u5355\u7684\u4ecb\u7ecd\u4e00\u4e0b\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5f20\u6c5f<\/strong>\uff1a\u5927\u7ea6 20 \u5e74\u524d\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u521a\u5efa\u7acb\u90a3\u4f1a\u513f\uff0c\u6211\u53c2\u52a0\u4e86\u5723\u5854\u83f2\u7814\u7a76\u6240\u548c\u4e2d\u79d1\u9662\u7406\u8bba\u7269\u7406\u7814\u7a76\u6240\u8054\u5408\u4e3e\u529e\u7684\u6691\u671f\u5b66\u6821\uff0c\u5728\u91cc\u9762\u542c\u4e86\u5f88\u591a\u5173\u4e8e\u7edf\u8ba1\u7269\u7406\u7684\u77e5\u8bc6\u540e\u5f00\u59cb\u8fdb\u5165\u76f8\u5173\u9886\u57df\u3002\u6211\u5370\u8c61\u7279\u522b\u6df1\u523b\u7684\u662f\u4f0a\u8f9b\u6a21\u578b\uff0c\u5728\u767e\u79d1\u4e0a\u4e5f\u6709\u5173\u4e8e\u5b83\u7684\u79d1\u666e\u4ecb\u7ecd\uff0c\u6211\u4eec\u5b8c\u5168\u53ef\u4ee5\u628a\u5b83\u7406\u89e3\u6210\u662f\u6751\u6c11\u6295\u7968\u7684\u60c5\u666f\uff0c\u6bcf\u4e2a\u6751\u6c11\u53ef\u80fd\u4f1a\u53d7\u5468\u56f4\u90bb\u5c45\u7684\u5f71\u54cd\uff0c\u8fd9\u6837\u5c31\u6784\u6210\u4e86\u4e00\u4e2a\u76f8\u4e92\u5f71\u54cd\u7684\u4e92\u52a8\u7cfb\u7edf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \n
    \u201c\u4f0a\u8f9b\u6a21\u578b\u201d\u96c6\u667a\u767e\u79d1\uff1a<\/span>\u4ec0\u4e48\u662f\u4f0a\u8f9b\u6a21\u578b Ising Model | \u96c6\u667a\u767e\u79d1<\/a><\/span><\/section>\n
    https:\/\/wiki.swarma.org\/index.php\/\u4f0a\u8f9b\u6a21\u578b<\/span><\/section>\n<\/blockquote>\n

    <\/span><\/section>\n
    \u5728\u8fd9\u4e2a\u7cfb\u7edf\u91cc\uff0c\u6700\u6709\u610f\u601d\u7684\u662f\u6709\u5e8f\u548c\u65e0\u5e8f\u4e4b\u95f4\u7684\u7ade\u4e89\u3002\u6240\u8c13\u6709\u5e8f<\/strong>\uff0c\u5c31\u662f\u6bcf\u4e2a\u6751\u6c11\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u8981\u670d\u4ece\u7edd\u5927\u591a\u6570\uff0c\u4f1a\u770b\u5468\u56f4\u90bb\u5c45\u5bf9\u81ea\u5df1\u7684\u5f71\u54cd\uff1b\u800c\u65e0\u5e8f<\/strong>\u5219\u662f\u6bcf\u4e2a\u6751\u6c11\u5728\u6295\u7968\u9009\u62e9\u65f6\u5b58\u5728\u4e00\u5b9a\u968f\u673a\u6027\u3002\u5728\u8fd9\u4e2a\u7269\u7406\u7cfb\u7edf\u91cc\uff0c\u6700\u65e9\u4f0a\u8f9b\u6a21\u578b\u662f\u7528\u4e8e\u5bf9\u94c1\u78c1\u987a\u78c1<\/span>\uff08\u4e5f\u5c31\u662f\u78c1\u94c1\uff09<\/span>\u7684\u76f8\u53d8\u884c\u4e3a\u8fdb\u884c\u5efa\u6a21\uff1a\u5f53\u6e29\u5ea6\u5347\u9ad8\u5230\u4e00\u5b9a\u7a0b\u5ea6\uff0c\u4f1a\u53d8\u5f97\u975e\u5e38\u65e0\u5e8f\uff1b\u6e29\u5ea6\u5f88\u4f4e\u65f6\uff0c\u5c31\u4f1a\u4ea7\u751f\u76f8\u5e94\u78c1\u6027\uff0c\u6240\u6709\u81ea\u65cb\u7684\u884c\u4e3a\u53d8\u5f97\u4e00\u81f4\u3002\u6bd4\u8f83\u6709\u610f\u601d\u7684\u662f\uff0c\u4e2d\u95f4\u5b58\u5728\u4e00\u4e2a\u4e34\u754c\u70b9\uff0c\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u65f6\uff0c\u6574\u4e2a\u7cfb\u7edf\u4f1a\u53d8\u5f97\u975e\u5e38\u590d\u6742\uff0c\u51fa\u73b0\u5206\u5f62\u3001\u81ea\u76f8\u4f3c\u7ed3\u6784\u7b49\u6709\u8da3\u73b0\u8c61\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u90a3\u5b83\u548c Hopfield \u7f51\u7edc\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u5b9e\u9645\u4e0a\uff0cHopfield <\/strong>\u7f51\u7edc\u662f\u4f0a\u8f9b\u6a21\u578b\u7684\u6269\u5c55<\/strong>\u3002\u4f0a\u8f9b\u6a21\u578b\u662f\u6676\u683c\u5316\u7cfb\u7edf\uff0c\u5c06\u5176\u53d8\u6210\u5168\u8fde\u901a\u7f51\u7edc\uff0c\u5e76\u4e14\u5f7c\u6b64\u4e4b\u95f4\u8054\u7cfb\u7684\u5f3a\u5ea6\u53ef\u4ee5\u968f\u673a\u53d6\u503c\uff0c\u8fd9\u6837\u5c31\u53d8\u6210\u4e86\u4e00\u4e2a\u5f88\u590d\u6742\u7684\u7f51\u7edc\u3002\u540c\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e00\u79cd\u5b66\u4e60\u673a\u5236\u8ba9\u7f51\u7edc\u7684\u6743\u91cd\u6709\u4e00\u5b9a\u53d8\u5316\uff0c\u4f7f\u5f97\u80fd\u91cf\u7684\u6700\u5c0f\u70b9\u521a\u597d\u5bf9\u5e94\u6211\u4eec\u9700\u8981\u8bb0\u5fc6\u7684\u4e00\u4e9b\u6a21\u5f0f\u3002\u6240\u4ee5 Hopfield \u7f51\u7edc\u521a\u9020\u51fa\u6765\u65f6\uff0c\u6700\u65e9\u662f\u7528\u4e8e\u8054\u60f3\u8bb0\u5fc6\u7684\u3002\u6bd4\u5982\u7ed9\u5b83\u4e00\u4e9b\u6570\u636e\uff0c\u91cc\u9762\u6709\u50cf 1234 \u8fd9\u6837\u7684\u624b\u5199\u4f53\u6570\u5b57\u7b49\u6a21\u5f0f\uff0c\u5b83\u4f1a\u6162\u6162\u6536\u655b\uff0c\u5176\u80fd\u91cf\u6700\u5c0f\u503c\u5c31\u4f1a\u5bf9\u5e94\u5230\u8fd9\u4e9b\u6a21\u5f0f\u4e0a\u3002\u53cd\u8fc7\u6765\uff0c\u5728\u8fd0\u884c\u65f6\uff0c\u7ed9\u5b83\u4e00\u5b9a\u523a\u6fc0\uff0c\u8981\u662f\u548c\u67d0\u4e2a\u624b\u5199\u4f53\u6570\u5b57\u5f88\u50cf\uff0c\u5b83\u5c31\u4f1a\u6162\u6162\u6536\u655b\u5230\u90a3\u4e2a\u5438\u5f15\u5b50\uff0c\u4ece\u800c\u628a\u8bb0\u5fc6\u4e2d\u7684\u6a21\u5f0f\u6062\u590d\u51fa\u6765\uff0c\u8fd9\u5c31\u662f\u6700\u65e9\u7684 Hopfield \u6a21\u578b\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n
    \u56fe1. Hopfield \u7f51\u7edc\u53ef\u4ee5\u5b58\u50a8\u548c\u91cd\u5efa\u6570\u636e\u4e2d\u7684\u6a21\u5f0f\u3002<\/span><\/section>\n

    <\/strong><\/span><\/section>\n
    \u5c24\u4ea6\u5e84<\/strong>\uff1a\u6211\u89c9\u5f97\u4eca\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7684\u8fd9\u4e24\u4e2a\u5de5\u4f5c\u90fd\u8ddf\u7edf\u8ba1\u7269\u7406\u6709\u5bc6\u5207\u7684\u5173\u7cfb\u3002Hopfield \u63d0\u51fa\u6765\u7684 Hopfield model \u662f\u6700\u65e9\u7684\u4e00\u7c7b\u57fa\u4e8e\u80fd\u91cf\u7684\u751f\u6210\u5f0f\u6a21\u578b\uff0c\u5b83\u5176\u5b9e\u662f\u5229\u7528\u4e86\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u539f\u7406\u2014\u2014\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u3002\u4e8b\u5b9e\u4e0a\uff0c\u73b0\u5728\u6211\u4eec\u6240\u8c13\u7684\u57fa\u4e8e\u80fd\u91cf\u7684\u751f\u6210\u5f0f\u6a21\u578b\uff0c\u5c31\u662f\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u7684\u6700\u57fa\u672c\u65b9\u5f0f\u3002\u65e9\u671f\uff0c\u7269\u7406\u5b66\u5bb6\u4eec\u60f3\u8981\u7406\u89e3\u5927\u91cf\u4e2a\u4f53\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u4ed6\u4eec\u6f14\u751f\u51fa\u6765\u7684\u96c6\u4f53\u884c\u4e3a\u662f\u600e\u6837\u7684\uff0c\u8fd9\u662f\u7edf\u8ba1\u7269\u7406\u6240\u60f3\u8981\u7406\u89e3\u7684\u4e3b\u8981\u76ee\u6807\u3002\u7edf\u8ba1\u7269\u7406\u4e2d\u201c\u7edf\u8ba1\u201d\u8fd9\u4e2a\u8bcd\u5c31\u662f\u5728\u7edf\u8ba1\u4e2a\u4f53\u7684\u884c\u4e3a\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6bd4\u5982\u8bf4\u50cf\u6211\u81ea\u5df1\u5427\uff0c\u5c0f\u65f6\u5019\u6211\u5c31\u5bf9\u6a21\u62df\u591a\u4e2a\u7c92\u5b50\u4e4b\u95f4\u76f8\u4e92\u4f5c\u7528\u8fd9\u4ef6\u4e8b\u60c5\u5f88\u611f\u5174\u8da3\uff0c\u4f1a\u81ea\u5df1\u5199\u8ba1\u7b97\u673a\u6a21\u578b\u6765\u6a21\u62df\u3002\u6211\u5f53\u65f6\u6709\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\u4e5f\u8bb8\u6211\u7406\u89e3\u6240\u6709\u7c92\u5b50\u7684\u8fd0\u52a8\u4e4b\u540e\uff0c\u5c31\u53ef\u4ee5\u4e86\u89e3\u5b8f\u89c2\u7684\u884c\u4e3a\u3002\u4f46\u540e\u6765\u6211\u53d1\u73b0\u6211\u9519\u4e86\uff0c\u5176\u5b9e\u7406\u89e3\u5355\u4e2a\u7c92\u5b50\u7684\u8fd0\u52a8\uff0c\u5e76\u4e0d\u80fd\u5e2e\u52a9\u4f60\u7406\u89e3\u5b8f\u89c2\u884c\u4e3a\u3002\u76f8\u53cd\uff0c\u5b8f\u89c2\u884c\u4e3a\u5b9e\u9645\u4e0a\u5f80\u5f80\u53ea\u53d6\u51b3\u4e8e\u5f88\u5c11\u7684\u4e00\u4e9b\u91cf\uff0c\u6bd4\u5982\u8bf4\u8fd9\u4e2a\u7cfb\u7edf\u7684\u603b\u80fd\u91cf\u3002<\/strong>\u90a3\u4e48\u7edf\u8ba1\u7269\u7406\u5b66\u5bb6\u540e\u6765\u53d1\u73b0\uff0c\u4e00\u4e2a\u591a\u4f53\u7cfb\u7edf\u4e2d\u7684\u6982\u7387\u5206\u5e03\uff0c\u53ea\u8ddf\u8fd9\u4e2a\u591a\u4f53\u7cfb\u7edf\u7684\u80fd\u91cf\u51fd\u6570\u6709\u5173<\/strong>\uff0c\u4eba\u4eec\u53ef\u4ee5\u5199\u4e0b\u6982\u7387\u5206\u5e03\u548c\u80fd\u91cf\u51fd\u6570\u76f8\u5bf9\u5e94\u7684\u8868\u8fbe\u5f0f\uff0c\u57fa\u672c\u4e0a\u80fd\u91cf\u51fd\u6570\u5c31\u6b63\u6bd4\u4e8e\u6982\u7387\u5206\u5e03\u7684\u5bf9\u6570\u3002\u57fa\u4e8e\u8fd9\u4e2a\u539f\u7406\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u7528\u80fd\u91cf\u51fd\u6570\u6765\u6a21\u62df\u5f88\u591a\u4e0d\u540c\u7684\u591a\u4f53\u7cfb\u7edf\u7684\u5206\u5e03\u3002\u8fd9\u91cc\u9762\u7684\u591a\u4f53\u7cfb\u7edf\uff0c\u5f53\u7136\u4e5f\u5305\u62ec\u78c1\u6027\u7cfb\u7edf\u3002\u5728\u7814\u7a76\u78c1\u6027\u7cfb\u7edf\u65f6\uff0c\u7269\u7406\u5b66\u5bb6\u4eec\u53d1\u73b0\uff0c\u78c1\u6027\u7cfb\u7edf\u5728\u4f4e\u6e29\u4e0b\u4f1a\u5c55\u73b0\u51fa\u5f88\u591a\u4e0d\u540c\u7684\u6a21\u5f0f\uff0c\u6bd4\u5982\u8bf4\u6709\u94c1\u78c1\u6001\u548c\u53cd\u94c1\u78c1\u6001\u3002\u8fd9\u4f1a\u51fa\u73b0\u5f88\u591a\u5f88\u5947\u602a\u7684\u81ea\u65cb\u73bb\u7483\u7684\u72b6\u6001\u3002\u4eba\u4eec\u7ecf\u8fc7\u4e00\u756a\u7814\u7a76\u4e86\u89e3\u5230\uff0c\u539f\u6765\u8fd9\u4e9b\u72b6\u6001\u90fd\u662f\u8ddf\u81ea\u65cb\u548c\u81ea\u65cb\u4e4b\u95f4\u76f8\u4e92\u4f5c\u7528\u3001\u80fd\u91cf\u662f\u600e\u4e48\u5206\u914d\u7684\u6709\u5173\u3002\u8fd9\u5c31\u5f62\u6210\u4e86\u6211\u4eec\u770b\u5230\u7684\u5b8f\u89c2\u73b0\u8c61\u2014\u2014\u67d0\u4e00\u79cd pattern \u7684\u5f62\u6210\u90fd\u5b58\u5728\u4e00\u4e2a\u80cc\u540e\u7684\u80fd\u91cf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4f46\u662f\u6211\u89c9\u5f97 Hopfield \u7684\u5de5\u4f5c\u5728\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u7684\u57fa\u7840\u4e0a\u9762\u6709\u4e00\u4e2a\u8303\u5f0f\u7a81\u7834\u3002\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u8bf4\u5462\uff1f\u4ee5\u524d\u7684\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u90fd\u662f\u5728\u95ee\uff1a\u7ed9\u4e00\u4e2a\u80fd\u91cf\u51fd\u6570\uff0c\u7ed9\u5b9a\u7cfb\u7edf\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u5b83\u5728\u9ad8\u6e29\u548c\u4f4e\u6e29\u4e0b\u90fd\u6709\u4ec0\u4e48\u6837\u7684\u884c\u4e3a\uff1f\u4eba\u4eec\u662f\u60f3\u8981\u53bb\u6c42\u89e3\u8fd9\u4e2a\u7cfb\u7edf\u7684\u884c\u4e3a\u3002\u4f46\u662f Hopfield \u8bf4\uff1a\u4e0d\uff0c\u4f60\u53ef\u4ee5\u6539\u53d8\uff0c\u4f60\u53ef\u4ee5\u4fee\u6539\u4f60\u7684\u95ee\u9898\uff0c\u4f60\u53ef\u4ee5\u4fee\u6539\u4f60\u7684\u80fd\u91cf\u51fd\u6570\uff0c\u4f60\u53ef\u4ee5\u4fee\u6539\u8fd9\u4e9b\u81ea\u65cb\u4e4b\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u6a21\u5f0f\u3002<\/strong>\u901a\u8fc7\u4fee\u6539\u76f8\u4e92\u4f5c\u7528\u7684\u6a21\u5f0f\uff0c\u4ee5\u671f\u5f85\u80fd\u591f\u5f62\u6210\u67d0\u4e2a\u4f60\u60f3\u8981\u8ba9\u5b83\u5f62\u6210\u7684\u7279\u5b9a\u6a21\u5f0f\u3002\u8fd9\u5b9e\u9645\u4e0a\u5c31\u662f\u4ece\u7ed9\u5b9a\u751f\u6210\u673a\u5236\uff0c\u88ab\u52a8\u5730\u53bb\u751f\u6210\u7ed3\u679c\uff08\u751f\u6210\u673a\u5236-\u7ed3\u679c\uff09\uff0c\u5230\u60f3\u8981\u83b7\u5f97\u67d0\u4e2a\u7ed3\u679c\uff0c\u4ece\u800c\u53bb\u5bfb\u6c42\u5b83\u7684\u751f\u6210\u673a\u5236\uff08\u7ed3\u679c-\u751f\u6210\u673a\u5236\uff09\uff0c\u53d8\u6210\u4e00\u4e2a\u5b66\u4e60\u8fc7\u7a0b<\/strong>\u3002\u6240\u4ee5\u4ed6\u5c31\u628a\u7edf\u8ba1\u529b\u5b66\uff0c\u4ece\u4e00\u95e8\u56de\u7b54\u95ee\u9898\u7684\u5b66\u95ee\uff0c\u53d8\u6210\u4e86\u4e00\u95e8\u53bb\u5b66\u4e60\uff0c\u4ece\u5b66\u4e60\u4e2d\u95f4\u627e\u5230\u67d0\u4e2a\u6a21\u5f0f\u80cc\u540e\u751f\u6210\u673a\u5236\u7684\u5b66\u4e60\u7b97\u6cd5\u3002<\/strong>\u4ed6\u60f3\u5230\u8981\u53cd\u8fc7\u6765\u95ee\u8fd9\u4e2a\u95ee\u9898\uff0c\u80fd\u591f\u901a\u8fc7\u5bf9\u81ea\u65cb\u6a21\u5f0f\u7684\u89c2\u5bdf\uff0c\u7136\u540e\u53bb\u4fee\u6539\u51fa\u6700\u9002\u5408\u7a33\u5b9a\u81ea\u65cb\u6a21\u5f0f\u7684\u76f8\u4e92\u4f5c\u7528\u7684\u6a21\u578b\u3002\u8fd9\u4e2a\u6a21\u578b\u5728\u5e94\u7528\u7684\u65f6\u5019\u81ea\u7136\u800c\u7136\u5730\u80fd\u591f\u5229\u7528\u7edf\u8ba1\u7269\u7406\u7684\u529b\u91cf\uff0c\u5728\u4f4e\u6e29\u65f6\u91cd\u73b0\u76f8\u5e94\u7684\u7ed3\u6784\u3002\u800c\u4e14\u5f53\u76f8\u5e94\u7684\u7ed3\u6784\u4e00\u65e6\u53d1\u751f\u7834\u574f\u65f6\uff0c\u91cd\u65b0\u964d\u4f4e\u6e29\u5ea6\uff0c\u8fd9\u4e2a\u7834\u574f\u6216\u8005\u8fd9\u4e2a\u9519\u8bef\u4e5f\u53ef\u4ee5\u88ab\u7ea0\u6b63\u56de\u6765\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u4e9b\u5de5\u4f5c\u5176\u5b9e\u5728\u73b0\u4ee3\u7684\u4fe1\u606f\u5904\u7406\u4e2d\u6709\u76f8\u5f53\u91cd\u8981\u7684\u5e94\u7528\u3002\u6211\u4eec\u90fd\u77e5\u9053\uff0c\u901a\u8baf\u8fc7\u7a0b\u4e2d\u53ef\u80fd\u4f1a\u51fa\u73b0\u5f88\u591a\u9519\u8bef\uff0c\u73b0\u4ee3\u91cf\u5b50\u8ba1\u7b97\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u540c\u6837\u4e5f\u4f1a\u4ea7\u751f\u9519\u8bef\uff0c\u800c\u8fd9\u4e9b\u9519\u8bef\u90fd\u9700\u8981\u8fdb\u884c\u7ea0\u9519\u5904\u7406\u3002\u5b9e\u9645\u4e0a\uff0c\u50cf Hopfield \u8fd9\u79cd\u501f\u52a9\u80fd\u91cf\u6a21\u578b\u6765\u5efa\u7acb\u67d0\u79cd\u80cc\u540e\u673a\u5236\uff0c\u7136\u540e\u901a\u8fc7\u964d\u6e29\u7684\u65b9\u5f0f\u6765\u7ea0\u9519\u7684\u505a\u6cd5\uff0c\u662f\u4e00\u79cd\u6700\u4e3a\u81ea\u7136\u7684\u7ea0\u9519\u673a\u5236<\/strong>\u3002\u6211\u8fd8\u8bb0\u5f97\u65e9\u671f\u7684\u8ba1\u7b97\u673a\u7528\u7684\u662f\u78c1\u76d8\u5b58\u50a8\u3002\u78c1\u76d8\u4e4b\u6240\u4ee5\u80fd\u591f\u957f\u671f\u4fdd\u5b58\u4fe1\u606f\uff0c\u5c31\u662f\u56e0\u4e3a\u78c1\u76d8\u91cc\u9762\u5b58\u5728\u7740\u8fd9\u79cd\u94c1\u78c1\u6027\u7684\u7ea0\u9519\u673a\u5236\u3002\u867d\u7136\u78c1\u76d8\u5904\u4e8e\u590d\u6742\u7684\u73af\u5883\u4e2d\uff0c\u65f6\u4e0d\u65f6\u5c31\u4f1a\u6709\u4e00\u4e9b\u81ea\u65cb\u7ffb\u8f6c\uff0c\u4f46\u5b83\u4f9d\u7136\u80fd\u591f\u51ed\u501f\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u5c06\u8fd9\u4e9b\u9519\u8bef\u7ea0\u6b63\u56de\u6765\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6240\u4ee5\u6211\u89c9\u5f97\u8fd9\u9879\u5de5\u4f5c\u975e\u5e38\u5389\u5bb3\u7684\u5730\u65b9\u4f53\u73b0\u5728\u4e24\u4e2a\u65b9\u9762\u3002\u7b2c\u4e00\uff0c\u5b83\u6539\u53d8\u4e86\u6211\u4eec\u5bf9\u4e8e\u7edf\u8ba1\u7269\u7406\u7684\u770b\u6cd5\uff0c\u4e0d\u518d\u662f\u5355\u7eaf\u5730\uff0c\u4e00\u7fa4\u7269\u7406\u5b66\u5bb6\u4ec5\u4ec5\u60f3\u7740\u53bb\u6c42\u89e3\u67d0\u4e2a\u6570\u5b66\u6a21\u578b\u5728\u4f4e\u6e29\u73af\u5883\u4e0b\u7684\u72b6\u51b5\uff0c\u800c\u662f\u8981\u601d\u8003\u5982\u4f55\u4ece\u73b0\u5b9e\u7684\u6570\u636e\u5f53\u4e2d\u53bb\u6784\u5efa\u4e00\u4e2a\u65b0\u7684\u6a21\u578b\u3002\u5176\u4e8c\uff0c\u5b83\u4e5f\u544a\u8bc9\u6211\u4eec\u53ef\u4ee5\u5982\u4f55\u7528\u7269\u7406\u6765\u5e2e\u52a9\u6211\u4eec\u7ea0\u9519\uff0c\u7269\u7406\u662f\u5982\u4f55\u548c\u4fe1\u606f\u8054\u7cfb\u8d77\u6765\uff0c\u5982\u4f55\u548c\u7f16\u7801\u8054\u7cfb\u8d77\u6765\u7684<\/strong>\u3002\u8fd9\u662f\u6211\u89c9\u5f97\u5b83\u975e\u5e38\u503c\u5f97\u83b7\u5f97\u8fd9\u6b21\u8bfa\u8d1d\u5c14\u5956\uff0c\u800c\u4e14\u8fd9\u4e2a\u8bfa\u8d1d\u5c14\u5956\u4e5f\u786e\u5b9e\u548c\u7269\u7406\u6709\u5f88\u6709\u5173\u7cfb\u7684\u4e00\u4e2a\u539f\u56e0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5f20\u6c5f<\/strong>\uff1a<\/strong>\u6211\u60f3\u8865\u5145 Hinton \u7684\u5de5\u4f5c\u5bf9\u4e8e\u795e\u7ecf\u7f51\u7edc\u7814\u7a76\u7684\u4ef7\u503c\u548c\u610f\u4e49\uff0c\u4ee5\u53ca\u5b83\u4e0e Hopfield \u7f51\u7edc\u7684\u5173\u7cfb\u3002\u5b9e\u9645\u4e0a\u6700\u521d\u63a5\u89e6\u795e\u7ecf\u7f51\u7edc\u65f6\uff0c\u6211\u5b8c\u5168\u6ca1\u6709\u610f\u8bc6\u5230\u5b83\u4e0e\u7edf\u8ba1\u7269\u7406\u7684\u8054\u7cfb\u3002\u795e\u7ecf\u7f51\u7edc\u770b\u8d77\u6765\u5c31\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u8f93\u5165\u63a5\u6536\u5668\uff0c\u6bcf\u4e2a\u795e\u7ecf\u5143\u63a5\u6536\u8f93\u5165\u4fe1\u53f7\uff0c\u5f53\u8f93\u5165\u8db3\u591f\u591a\u65f6\uff0c\u795e\u7ecf\u5143\u53ef\u80fd\u4f1a\u88ab\u6fc0\u6d3b\uff0c\u5e76\u7ee7\u7eed\u5411\u4e0b\u4f20\u64ad\u4fe1\u53f7\u3002\u901a\u8fc7\u68af\u5ea6\u53cd\u5411\u4f20\u64ad\u7684\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u8bad\u7ec3\u7f51\u7edc\u8fdb\u884c\u5b66\u4e60\u3002\u672c\u79d1\u671f\u95f4\uff0c\u6211\u4eec\u5f53\u65f6\u505a\u8fc7\u4e00\u4e2a\u9879\u76ee\uff0c\u4f7f\u7528\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u6570\u636e\u4e2d\u7684\u6a21\u5f0f\u5e76\u8fdb\u884c\u9884\u6d4b\u3002\u4f46\u76f4\u5230\u540e\u6765\u6211\u53c2\u52a0\u4e86\u6691\u671f\u5b66\u6821\uff0c\u63a5\u89e6\u5230\u4f0a\u8f9b\u6a21\u578b\uff0c\u624d\u8c41\u7136\u5f00\u6717\uff0c\u610f\u8bc6\u5230\u795e\u7ecf\u7f51\u7edc\u4e0e\u4f0a\u8f9b\u6a21\u578b\u3001\u81ea\u65cb\u4e4b\u95f4\u53ef\u4ee5\u5b8c\u5168\u5bf9\u5e94\u8d77\u6765\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6211\u4eec\u53ef\u4ee5\u5c06\u6bcf\u4e2a\u795e\u7ecf\u5143\u89c6\u4e3a\u4f0a\u8f9b\u6a21\u578b\u4e2d\u7684\u4e00\u4e2a\u81ea\u65cb<\/span>\uff08spin\uff09<\/span>\uff0c\u6bcf\u4e2a\u81ea\u65cb\u6709\u4e24\u79cd\u72b6\u6001\uff1a\u671d\u4e0a\u6216\u671d\u4e0b\uff0c\u8fd9\u6b63\u597d\u5bf9\u5e94\u4e8e\u795e\u7ecf\u5143\u7684\u6fc0\u6d3b\u548c\u975e\u6fc0\u6d3b\u72b6\u6001\u3002\u5728\u4f0a\u8f9b\u6a21\u578b\u4e2d\uff0c\u6bcf\u4e2a\u81ea\u65cb\u7684\u72b6\u6001\u53d7\u5230\u5468\u56f4\u90bb\u5c45\u4ee5\u53ca\u81ea\u8eab\u968f\u673a\u6027\u7684\u5f71\u54cd\u3002\u5bf9\u4e8e\u795e\u7ecf\u7f51\u7edc\u6765\u8bf4\uff0c\u5176\u4ed6\u795e\u7ecf\u5143\u5bf9\u5b83\u7684\u72b6\u6001\u4e5f\u6709\u4e00\u5b9a\u7684\u5f71\u54cd\uff0c\u56e0\u6b64\uff0c\u5b83\u4eec\u4e5f\u662f\u901a\u8fc7\u76f8\u4e92\u4f5c\u7528\u6765\u51b3\u5b9a\u662f\u5426\u6fc0\u6d3b\u3002\u6b64\u5916\uff0c\u6fc0\u6d3b\u51fd\u6570\u672c\u8eab\u5c06\u968f\u673a\u6027\u5bf9\u5e94\u5230 S \u578b\u6fc0\u6d3b\u51fd\u6570\u66f2\u7ebf\u4e2d\uff0c\u4ece\u800c\u5efa\u7acb\u4e86\u4e24\u8005\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u6211\u8ba4\u4e3a\uff0c\u6700\u65e9\u660e\u786e\u5efa\u7acb\u8fd9\u79cd\u5173\u7cfb\uff0c\u5e76\u4f7f\u795e\u7ecf\u7f51\u7edc\u80fd\u591f\u4ee5\u7edf\u8ba1\u7269\u7406\u7684\u65b9\u5f0f\u8fd0\u4f5c\uff0c\u4e0e Hinton \u7684\u7814\u7a76\u5de5\u4f5c\u5bc6\u4e0d\u53ef\u5206\u3002\u4ed6\u5bf9\u795e\u7ecf\u7f51\u7edc\u7684\u4e00\u4e2a\u91cd\u5927\u6539\u8fdb\u662f\u5c06\u7f51\u7edc\u5206\u4e3a\u4e24\u5c42\uff1a\u4e00\u4e2a\u662f\u663e\u5c42\uff0c\u76f8\u5f53\u4e8e\u8f93\u5165\u5c42\uff0c\u7528\u4e8e\u63a5\u6536\u6570\u636e\uff1b\u53e6\u4e00\u4e2a\u662f\u9690\u5c42\uff0c\u8d77\u5230\u6570\u636e\u538b\u7f29\u548c\u8868\u5f81\u7684\u4f5c\u7528\u3002\u5728\u4eca\u5929\u7684\u6df1\u5ea6\u5b66\u4e60\u4e2d\uff0c\u8fd9\u79cd\u8868\u793a\u5b66\u4e60\u2014\u2014\u83b7\u5f97\u6570\u636e\u7684\u538b\u7f29\u8868\u793a\u2014\u2014\u662f\u975e\u5e38\u91cd\u8981\u7684\uff0c\u4e5f\u662f\u6211\u4eec\u4eba\u8111\u5904\u7406\u590d\u6742\u4fe1\u606f\u7684\u57fa\u7840<\/strong>\u3002\u56e0\u6b64\uff0c\u6211\u8ba4\u4e3a Hinton \u7684\u7814\u7a76\u5de5\u4f5c\u662f\u975e\u5e38\u4e86\u4e0d\u8d77\u7684\uff0c\u4ed6\u5c06\u7edf\u8ba1\u7269\u7406\u7684\u6982\u5ff5\u5b8c\u5168\u878d\u5165\u4e86\u795e\u7ecf\u7f51\u7edc\u8fd9\u4e00\u5b66\u79d1\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5510\u4e7e\u5143<\/strong>\uff1a<\/strong>Hopfield \u7684\u8d21\u732e\u5176\u5b9e\u8fd8\u4f53\u73b0\u4e86\u201cmore is different\u201d\u8fd9\u4e00\u975e\u5e38\u57fa\u7840\u7684\u6982\u5ff5\u3002\u5b89\u5fb7\u68ee\u5728\u4f20\u8bb0\u4e2d\u5c06 Hopfield \u89c6\u4e3a\u672a\u5171\u540c\u53d1\u8868\u8fc7\u6587\u7ae0\u7684\u9690\u85cf\u5408\u4f5c\u4f19\u4f34\u3002\u5728\u4f20\u7edf\u795e\u7ecf\u79d1\u5b66\u4e2d\uff0c\u4eba\u4eec\u8ba4\u4e3a\u5927\u8111\u4e2d\u7684\u8bb0\u5fc6\u5b58\u50a8\u5728\u7279\u5b9a\u533a\u57df\uff0c\u4f46<\/strong> <\/strong>Hopfield<\/strong> <\/strong>\u63d0\u51fa\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u89c2\u70b9\uff1a\u8bb0\u5fc6\u6ca1\u6709\u50a8\u5b58\u5728\u5927\u8111\u7684\u4efb\u4f55\u4e00\u4e2a\u5730\u65b9\uff0c<\/strong>\u800c\u662f<\/strong>\u50a8\u5b58\u5728\u5927\u8111\u7684\u6240\u6709\u5730\u65b9\u3002<\/strong>\u6240\u6709\u795e\u7ecf\u5143\u5171\u540c\u4f5c\u7528\uff0c\u5f62\u6210\u4e86\u8bb0\u5fc6\uff0c\u8fd9\u53ef\u80fd\u662f\u5927\u8111\u6267\u884c\u8bb0\u5fc6\u53ca\u5176\u4ed6\u529f\u80fd\u7684\u5de5\u4f5c\u65b9\u5f0f\u3002\u800c\u4e14\u8fd9\u4e2a\u673a\u5236\u4e5f\u6709\u5b83\u76f8\u5e94\u7684\u795e\u7ecf\u79d1\u5b66\u80cc\u666f\uff0c\u5373\u6240\u8c13\u7684\u201cHebbian \u5b66\u4e60\u89c4\u5219\u201d\uff0c\u7b80\u800c\u8a00\u4e4b\u5c31\u662f\u201c\u5728\u5b66\u4e60\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u4e24\u4e2a\u795e\u7ecf\u5143\u7ecf\u5e38\u4e00\u8d77\u653e\u7535\uff0c\u90a3\u4e48\u5b83\u4eec\u5c31\u66f4\u6709\u53ef\u80fd\u4ea7\u751f\u8fde\u63a5\u201d\uff0c\u5373\u201cFire together wire together\u201d\uff0c\u8fd9\u4e2a\u673a\u5236\u5c31\u662f\u521a\u624d\u5c24\u4ea6\u5e84\u8001\u5e08\u6240\u8bb2\u7684\uff0c\u600e\u4e48\u6837\u628a\u4e00\u4e2a\u8981\u8bb0\u5fc6\u7684\u6a21\u5f0f\u7f16\u7801\u5230\u795e\u7ecf\u4e0a\u3002Hopfield \u901a\u8fc7\u7269\u7406\u6a21\u578b\u5c06\u8fd9\u4e00\u6982\u5ff5\u5177\u4f53\u5316\uff0c\u8fd9\u662f\u4ed6\u7684\u4e00\u4e2a\u91cd\u8981\u8d21\u732e\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6b64\u5916\uff0cHopfield \u8fd8\u6709\u53e6\u4e00\u4e2a\u4e0d\u592a\u4e3a\u4eba\u6240\u77e5\u7684\u8d21\u732e\u3002\u521a\u521a\u5f20\u6c5f\u8001\u5e08\u4e5f\u6709\u63d0\u5230\uff0c\u5728\u78c1\u6027\u7cfb\u7edf\u4e2d\uff0c\u4e34\u754c\u6027\u662f\u4e00\u4e2a\u975e\u5e38\u5173\u952e\u7684\u7279\u5f81\u3002\u5728\u6c64\u8d85\u8001\u5e08\u4ed6\u4eec\u63d0\u51fa\u81ea\u7ec4\u7ec7\u4e34\u754c\u73b0\u8c61\u4e4b\u540e\uff0cHopfield \u4e5f\u5f88\u65e9\u5bf9\u5927\u8111\u4e2d\u7684\u4e34\u754c\u73b0\u8c61\u4ea7\u751f\u4e86\u5174\u8da3\uff0c\u5e76\u64b0\u5199\u8bba\u6587\u4f7f\u7528\u5730\u9707\u6a21\u578b\u6765\u8bf4\u660e\u5927\u8111\u4e2d\u53ef\u80fd\u5b58\u5728\u7684\u4e34\u754c\u673a\u5236\uff0c\u56e0\u6b64 Hopfield \u4e5f\u53ef\u4ee5\u8bf4\u662f\u5927\u8111\u4e34\u754c\u6027\u5047\u8bf4\u7684\u5148\u9a71\u4e4b\u4e00\u3002<\/span>\uff08\u53c2\u770b\uff1a\u300a\u300a\u5927\u81ea\u7136\u5982\u4f55\u8fd0\u4f5c\u300b\uff1a\u5173\u4e8e\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u7684\u79d1\u5b66\uff5c\u6c64\u8d85\u9662\u58eb\u4f5c\u5e8f\u63a8\u8350<\/a>\u300b\uff09<\/span><\/section>\n

    <\/span><\/section>\n
    \u5173\u4e8e Hinton \u7684\u8d21\u732e\uff0cHinton \u6700\u65e9\u63d0\u51fa\u7684\u73bb\u5c14\u5179\u66fc\u673a\u53ef\u4ee5\u770b\u4f5c\u662f Hopfield \u6a21\u578b\u7684\u4e00\u4e2a\u63a8\u5e7f\u3002\u73bb\u5c14\u5179\u66fc\u673a\u672c\u8eab\u662f\u5168\u8fde\u63a5\u7684\uff0c\u4f46\u7531\u4e8e\u9700\u8981\u5904\u7406\u7684\u8fde\u63a5\u6570\u592a\u591a\uff0c\u4e0d\u592a\u5b9e\u7528\uff0c\u540e\u6765\u88ab\u6539\u9020\u6210\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a\uff0c\u533a\u5206\u4e86\u9690\u5c42\u548c\u8f93\u5165\u5c42\u3002\u867d\u7136 Hinton \u5e76\u975e\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a\u7684\u6700\u521d\u53d1\u660e\u8005\uff0c\u4f46\u4ed6\u7684\u8d21\u732e\u4e0d\u80fd\u5ffd\u89c6\uff0c\u4e8b\u5b9e\u4e0a\u4ed6\u91cd\u65b0\u6316\u6398\u4e86\u8fd9\u4e00\u6a21\u578b\uff0c\u5e76\u63d0\u51fa\u4e86\u5bf9\u6bd4\u6563\u5ea6<\/span>\uff08Contrast Divergence\uff09<\/span>\u7684\u8bad\u7ec3\u65b9\u6cd5\uff0c\u4f7f\u5f97\u73bb\u5c14\u5179\u66fc\u673a\u53d8\u5f97\u771f\u6b63\u53ef\u7528\u3002\u5bf9\u6bd4\u6563\u5ea6\u662f\u4e00\u4e2a\u590d\u6742\u7684\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u4f46 Hinton \u7684\u4e00\u4e9b\u5de5\u4f5c\u4f7f\u5176\u53d8\u5f97\u53ef\u884c\u3002\u6240\u4ee5\u6211\u671f\u5f85\u5c24\u4ea6\u5e84\u8001\u5e08\u80fd\u8fdb\u4e00\u6b65\u8bb2\u8ff0 Hinton \u5728\u5bf9\u6bd4\u6563\u5ea6\u4ee5\u53ca\u91c7\u6837\u65b9\u9762\u7684\u4e00\u4e9b\u8d21\u732e\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5c24\u4ea6\u5e84<\/strong>\uff1a<\/strong>Hinton \u7684\u5de5\u4f5c\u5b9e\u9645\u4e0a\u662f\u5bf9 Hopfield \u6a21\u578b\u7684\u63a8\u5e7f\uff0c\u4ed6\u5c06 Hopfield \u6a21\u578b\u63a8\u5411\u4e86\u65b0\u7684\u9ad8\u5ea6\u3002\u8fd9\u79cd\u751f\u6210\u5f0f\u6a21\u578b\u7684\u6838\u5fc3\u76ee\u6807\u662f\u5b66\u4e60\u4e00\u4e2a\u80fd\u91cf\u51fd\u6570\uff0c\u4ee5\u6b64\u6765\u4ee3\u8868\u6837\u672c\u7684\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u3002\u6240\u6709\u7684\u751f\u6210\u5f0f\u6a21\u578b\u90fd\u9700\u8981\u57fa\u4e8e\u6837\u672c\u8fdb\u884c\u8bad\u7ec3\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4f46\u600e\u6837\u8bad\u7ec3\u73bb\u5c14\u5179\u66fc\u673a\u5c31\u6210\u4e3a\u4e00\u4e2a\u95ee\u9898\u3002Hinton \u60f3\u4e86\u4e00\u4e9b\u975e\u5e38\u5de7\u5999\u7684\u65b9\u6cd5\u6765\u8fdb\u884c\u8bad\u7ec3\uff0c\u4ed6\u7684\u57fa\u672c\u601d\u8def\u662f\u8fd9\u6837\u7684\uff1a\u5982\u679c\u6211\u4eec\u7528\u67d0\u4e2a\u80fd\u91cf\u51fd\u6570\u4f5c\u4e3a\u6a21\u578b\uff0c\u751f\u6210\u4e00\u4e2a\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\uff0c\u800c\u6837\u672c\u672c\u8eab\u4e5f\u6709\u5176\u81ea\u8eab\u7684\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u3002\u539f\u5219\u4e0a\uff0c\u6211\u4eec\u5e0c\u671b\u8fd9\u4e24\u4e2a\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u5c3d\u53ef\u80fd\u63a5\u8fd1\uff0c\u4e5f\u5c31\u662f\u8ba9\u6a21\u578b\u7684\u5206\u5e03\u5c3d\u53ef\u80fd\u63a5\u8fd1\u6837\u672c\u7684\u5206\u5e03\u3002\u6211\u4eec\u9700\u8981\u6700\u5c0f\u5316\u4e00\u4e2a\u540d\u4e3a KL \u6563\u5ea6\u7684\u91cf\u2014\u2014\u4e5f\u5c31\u662f\u4e24\u4e2a\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u5bf9\u5dee\u5f02\u3002\u7ecf\u8fc7\u4e00\u756a\u7814\u7a76\uff0c\u4ed6\u53d1\u73b0\u76f8\u5bf9\u71b5\u57fa\u672c\u4e0a\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a\u4e24\u79cd\u81ea\u7531\u80fd\u4e4b\u95f4\u7684\u5dee\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u5176\u5b9e\u662f\u975e\u5e38\u6709\u8da3\u7684\u4e00\u70b9\u3002\u60f3\u8c61\u4e00\u4e0b\uff0c\u5982\u679c\u6211\u4eec\u8ba9\u6a21\u578b\u95ed\u7740\u773c\u775b\uff0c\u6309\u7167\u81ea\u5df1\u7684\u65b9\u5f0f\u53bb\u8fd0\u884c\uff0c\u5b83\u4f1a\u4ea7\u751f\u4e00\u4e2a\u7edf\u8ba1\u529b\u5b66\u7cfb\u7edf\u7684\u81ea\u7531\u80fd\uff0c\u8fd9\u4e2a\u81ea\u7531\u80fd\u4ee3\u8868\u4e86\u7cfb\u7edf\u5728\u67d0\u79cd\u5e73\u5747\u610f\u4e49\u4e0a\u7684\u80fd\u91cf\u3002\u800c\u5f53\u6a21\u578b\u7684\u663e\u5c42<\/span>\uff08visible layer\uff09<\/span>\u4e2d\u6709\u6837\u672c\u6570\u636e\u65f6\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u201cclaimed free energy\u201d\uff0c\u5f53\u6570\u636e\u88ab\u5f3a\u8feb\u52a0\u8f7d\u5230\u663e\u5c42\u65f6\uff0c\u6a21\u578b\u540c\u6837\u4f1a\u6709\u4e00\u4e2a\u81ea\u7531\u80fd\u3002\u8fd9\u4e24\u4e2a\u81ea\u7531\u80fd\u4e4b\u95f4\u7684\u5dee\uff0c\u6b63\u597d\u5c31\u662f KL \u6563\u5ea6\u6240\u4ee3\u8868\u7684\u635f\u5931\u51fd\u6570<\/span>\uff08loss function\uff09<\/span>\u3002\u8fd9\u4e3a\u6211\u4eec\u6307\u660e\u4e86\u4e00\u4e2a\u8bad\u7ec3\u7684\u65b9\u5411\uff0c\u5c31\u597d\u50cf\u7741\u773c\u548c\u95ed\u773c\u7684\u5173\u7cfb\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u4f60\u53ef\u4ee5\u5148\u8ba9\u6a21\u578b\u95ed\u7740\u773c\u775b\uff0c\u81ea\u5df1\u60f3\u8c61\u4e00\u4e0b\u3002\u5047\u8bbe\u6211\u73b0\u5728\u624b\u4e0a\u6709\u4e00\u5806\u81ea\u65cb\uff0c\u4e00\u90e8\u5206\u81ea\u65cb\u5c5e\u4e8e\u663e\u5c42\uff0c\u5b83\u4eec\u9700\u8981\u4e0e\u6570\u636e\u4fdd\u6301\u4e00\u81f4\uff1b\u53e6\u4e00\u90e8\u5206\u81ea\u65cb\u5c5e\u4e8e\u9690\u5c42\uff0c\u6570\u636e\u5bf9\u5b83\u4eec\u6765\u8bf4\u5e76\u4e0d\u91cd\u8981\u3002\u5728\u95ed\u773c\u7684\u65f6\u5019\uff0c\u6211\u4eec\u89c2\u5bdf\u663e\u5c42\u81ea\u65cb\u4e4b\u95f4\u7684\u5173\u8054\u6709\u591a\u5f3a\uff0c\u8fd9\u662f\u6a21\u578b\u5728\u60f3\u8c61\u6216\u201c\u505a\u68a6\u201d\u8fc7\u7a0b\u4e2d\u6784\u60f3\u51fa\u6765\u7684\u663e\u5c42\u4e4b\u95f4\u7684\u5173\u8054\u3002\u7136\u540e\u5728\u6709\u6570\u636e\u4e4b\u540e\uff0c\u6a21\u578b\u4f1a\u518d\u6b21\u89c2\u5bdf\u663e\u5c42\u7684\u6570\u636e\uff0c\u8fdb\u800c\u7814\u7a76\u5728\u663e\u5c42\u6570\u636e\u56fa\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u70ed\u529b\u5b66\u7cfb\u7edf\u8fbe\u5230\u5e73\u8861\u65f6\uff0c\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u7684\u5173\u8054\u6709\u591a\u5f3a\u3002\u4f8b\u5982\uff0c\u5728\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a\u4e2d\uff0c\u6211\u4eec\u552f\u4e00\u9700\u8981\u5173\u5fc3\u7684\u5173\u8054\u662f\u4ecb\u4e8e\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u7684\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ea\u9700\u8981\u6bd4\u8f83\u6709\u6570\u636e\u548c\u6ca1\u6709\u6570\u636e\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\u7684\u5173\u8054\u5f3a\u5ea6\uff0c\u5c31\u53ef\u4ee5\u5224\u65ad\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u7684\u8fde\u63a5\u662f\u5e94\u8be5\u589e\u5f3a\u8fd8\u662f\u51cf\u5f31\u3002\u5982\u679c\u6570\u636e\u5230\u6765\u540e\uff0c\u7ecf\u8fc7\u70ed\u5e73\u8861\uff0c\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u7684\u5173\u8054\u8f83\u5f31\uff0c\u800c\u6ca1\u6709\u6570\u636e\u65f6\uff0c\u7cfb\u7edf\u7684\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u7684\u5173\u8054\u8f83\u5f3a\uff0c\u8fd9\u8868\u660e\u7cfb\u7edf\u7684\u60f3\u8c61\u4e0e\u5b9e\u9645\u60c5\u51b5\u4e0d\u7b26\uff0c\u56e0\u6b64\u5e94\u8be5\u51cf\u5c11\u663e\u5c42\u548c\u9690\u5c42\u4e4b\u95f4\u7684\u5173\u8054\u5f3a\u5ea6\u3002\u76f8\u5e94\u5730\uff0c\u5c31\u5e94\u8be5\u51cf\u5c11\u5b83\u4eec\u4e4b\u95f4\u7684\u8026\u5408\u5f3a\u5ea6\u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\u3002\u8fd9\u5c31\u662f\u5bf9\u6bd4\u6563\u5ea6\u7684\u57fa\u672c\u601d\u60f3\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u5c31\u50cf\u6211\u4eec\u5e73\u65f6\u5b66\u4e60\u65f6\u6709\u7ffb\u4e66\u5b66\u4e60\u548c\u95ed\u5377\u601d\u8003\u7684\u8fc7\u7a0b\uff0c\u4e5f\u5982\u540c\u5b54\u5b50\u6240\u8bf4\u201c\u5b66\u800c\u4e0d\u601d\u5219\u7f54\uff0c\u601d\u800c\u4e0d\u5b66\u5219\u6b86\u201d\uff0c\u610f\u5473\u7740\u5b66\u4e60\u548c\u601d\u8003\u5e94\u8be5\u76f8\u7ed3\u5408\u3002\u6211\u8ba4\u4e3a\uff0c\u5bf9\u6bd4\u6563\u5ea6\u7684\u601d\u60f3\u975e\u5e38\u597d\u5730\u4f53\u73b0\u4e86\u5b66\u4e60\u548c\u601d\u8003\u4e24\u4e2a\u8fc7\u7a0b\u7684\u7ed3\u5408\u3002\u5f53\u6709\u6570\u636e\u6765\u65f6\uff0c\u4f60\u9700\u8981\u5b66\u4e60\u4ee5\u8fbe\u5230\u67d0\u79cd\u5e73\u8861\uff0c\u4f60\u8fd8\u9700\u8981\u6709\u601d\u8003\uff0c\u7136\u540e\u5bf9\u6bd4\u7741\u7740\u773c\u775b\u5b66\u4e60\u548c\u95ed\u7740\u773c\u775b\u601d\u8003\u7684\u5370\u8c61\u5dee\u5f02\uff0c\u4ece\u800c\u5bf9\u81ea\u5df1\u7684\u795e\u7ecf\u7f51\u7edc\u6743\u91cd\u8fdb\u884c\u8c03\u6574<\/strong>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5f53\u7136\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u6d89\u53ca\u5230\u70ed\u5e73\u8861\u7684\u6b65\u9aa4\u3002\u5f53\u6570\u636e\u8f93\u5165\u65f6\uff0c\u6211\u4eec\u9700\u8981\u6839\u636e\u6570\u636e\u8ba9\u6574\u4e2a\u7cfb\u7edf\u8fbe\u5230\u70ed\u5e73\u8861\uff0c\u8fd9\u610f\u5473\u7740\u8981\u7ecf\u8fc7\u53cd\u590d\u591a\u6b21\u7684\u91c7\u6837\u8fed\u4ee3\uff0c\u624d\u80fd\u4f7f\u81ea\u65cb\u7cfb\u7edf\u8fbe\u5230\u5e73\u8861\u3002\u5728\u95ed\u773c\u601d\u8003\u7684\u65f6\u5019\uff0c\u4e5f\u9700\u8981\u8fdb\u884c\u591a\u6b21\u91c7\u6837\u8fed\u4ee3\u3002\u8fd9\u65f6\u5c31\u6d89\u53ca\u5230\u4e86\u4e00\u4e9b\u8ba1\u7b97\u590d\u6742\u5ea6\u7684\u8003\u91cf\u3002\u65e9\u671f\u7684\u7b97\u6cd5\u5e76\u4e0d\u5341\u5206\u6210\u529f\uff0c\u90e8\u5206\u539f\u56e0\u662f\u5728\u81ea\u65cb\u6a21\u578b\u4e0a\u4f7f\u7528\u8499\u7279\u5361\u7f57\u91c7\u6837\u65b9\u6cd5\u6c42\u89e3\u9700\u8981\u6d88\u8017\u5927\u91cf\u7684\u8ba1\u7b97\u8d44\u6e90\u3002Hinton \u6709\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u89c2\u5bdf\uff1a\u5b9e\u9645\u4e0a\uff0c\u4f60\u5e76\u4e0d\u9700\u8981\u8ba9\u4e24\u4e2a\u7cfb\u7edf\u8fbe\u5230\u70ed\u5e73\u8861\u3002\u867d\u7136\u4ece\u6570\u5b66\u539f\u5219\u4e0a\u8bb2\uff0c\u4f60\u5e94\u8be5\u6bd4\u8f83\u5e73\u8861\u6001\u4e4b\u95f4\u7684\u5173\u8054\u5f3a\u5ea6\uff0c\u4f46\u6211\u4eec\u5b9e\u9645\u4e0a\u5df2\u7ecf\u80fd\u591f\u770b\u51fa\u95ed\u773c\u548c\u7741\u773c\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\u2014\u2014\u4e5f\u5c31\u662f\u6709\u6570\u636e\u548c\u6ca1\u6709\u6570\u636e\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\u2014\u2014\u5173\u8054\u7684\u5dee\u522b\uff0c\u8fd9\u5df2\u7ecf\u53ef\u4ee5\u63d0\u4f9b\u67d0\u79cd\u5b66\u4e60\u4fe1\u53f7\u3002Hinton \u8fd8\u8bc1\u660e\uff0c\u5373\u4f7f\u4f60\u6309\u7167\u8fd9\u6837\u4e00\u4e2a\u4e0d\u5b8c\u5168\u6b63\u786e\u7684\u4fe1\u53f7\uff0c\u6700\u7ec8\uff0c\u635f\u5931\u51fd\u6570\uff08loss function\uff09\u7684\u6700\u5c0f\u70b9\u548c\u539f\u6765\u7684\u6700\u5c0f\u70b9\u4e5f\u662f\u4e00\u6837\u7684\u3002\u8fd9\u5c31\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u7528\u66f4\u9ad8\u7684\u6548\u7387\u8fdb\u884c\u91c7\u6837\u548c\u5b66\u4e60\u3002<\/strong>\u8fd9\u4e9b\u601d\u60f3\u4ece\u5e73\u8861\u6001\u7269\u7406\u8d70\u5411\u975e\u5e73\u8861\u6001\u7269\u7406\uff0c\u90fd\u662f\u7edf\u8ba1\u529b\u5b66\u4e2d\u975e\u5e38\u6709\u8da3\u7684\u601d\u8def\u3002\u6211\u8ba4\u4e3a\uff0c\u8fd9\u4e9b\u90fd\u662f\u975e\u5e38\u503c\u5f97\u6211\u4eec\u601d\u8003\u548c\u501f\u9274\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5f20\u6c5f<\/strong>\uff1a<\/strong>Hinton \u5728\u795e\u7ecf\u7f51\u7edc\u5b66\u6d3e\u7684\u5386\u53f2\u4e2d\u626e\u6f14\u4e86\u4e24\u6b21\u5173\u952e\u6027\u7684\u62ef\u6551\u8005\u89d2\u8272\u3002\u7b2c\u4e00\u6b21\u5927\u7ea6\u5728\u4e0a\u4e16\u7eaa80\u5e74\u4ee3\u3002\u5728\u6b64\u4e4b\u524d\uff0c\u4eba\u5de5\u667a\u80fd\u81ea1956\u5e74\u8d77\u6b65\u4ee5\u6765\uff0c\u4e3b\u8981\u662f\u4ee5\u641c\u7d22\u3001\u63a8\u7406\u903b\u8f91\u7b49\u4e3a\u4e3b\u7684\u4f20\u7edf AI \u5360\u636e\u4e3b\u6d41\u3002\u5c3d\u7ba1\u795e\u7ecf\u7f51\u7edc\u7684\u6982\u5ff5\u6700\u65e9\u53ef\u4ee5\u8ffd\u6eaf\u52301943\u5e74\u7531 Warren McCullough \u548c Walter Pitts \u63d0\u51fa\u7684\u795e\u7ecf\u7f51\u7edc\u6570\u5b66\u6a21\u578b\uff0c\u4f46\u7531\u4e8e Minsky \u548c Papert \u5728\u4ed6\u4eec\u7684\u8457\u4f5c\u300aPerceptrons\u300b\u4e2d\u8bc1\u660e\u4e86\u5355\u5c42\u611f\u77e5\u673a\u6a21\u578b\u65e0\u6cd5\u89e3\u51b3\u7b80\u5355\u7684\u5f02\u6216XOR\u7b49\u7ebf\u6027\u4e0d\u53ef\u5206\u95ee\u9898\uff0c\u8fd9\u5bfc\u81f4\u795e\u7ecf\u7f51\u7edc\u5b66\u6d3e\u51e0\u4e4e\u88ab\u627c\u6740\u3002\u5728\u90a3\u4e2a\u65f6\u671f\uff0c\u7814\u7a76\u8005\u4eec\u62c5\u5fc3\u81ea\u5df1\u7684\u8bba\u6587\u65e0\u6cd5\u53d1\u8868\uff0c\u795e\u7ecf\u7f51\u7edc\u5b66\u79d1\u5dee\u70b9\u56e0\u6b64\u6d88\u4ea1\u3002\u7136\u800c\uff0c\u6b63\u662f Hinton \u575a\u6301\u795e\u7ecf\u7f51\u7edc\u7684\u7814\u7a76\uff0c\u5e76\u6210\u529f\u5c06\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u5e94\u7528\u4e8e\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\uff0c\u8fd9\u6807\u5fd7\u7740\u4ed6\u7b2c\u4e00\u6b21\u62ef\u6551\u4e86\u795e\u7ecf\u7f51\u7edc\u5b66\u6d3e\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7b2c\u4e8c\u6b21\u62ef\u6551\u53d1\u751f\u5728\u6df1\u5ea6\u5b66\u4e60\u7684\u840c\u82bd\u65f6\u671f\u3002\u5f53\u65f6\uff0c\u5c3d\u7ba1\u4eba\u4eec\u770b\u5230\u795e\u7ecf\u7f51\u7edc\u5728\u5f88\u591a\u5b66\u4e60\u4efb\u52a1\u4e2d\u8868\u73b0\u5f97\u5f88\u597d\uff0c\u4f46\u7531\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u6709\u9650\uff0c\u80fd\u89e3\u51b3\u7684\u95ee\u9898\u975e\u5e38\u53d7\u9650\u3002\u56e0\u6b64\uff0c\u5f53\u65f6\u5927\u5bb6\u5bf9\u795e\u7ecf\u7f51\u7edc\u5e76\u4e0d\u770b\u597d\uff0c\u800c\u4e14\u6709\u5f88\u591a\u5176\u4ed6\u7684\u7ade\u4e89\u7b97\u6cd5\u3002Hinton \u901a\u8fc7\u5c06\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a\u505a\u5f97\u5f88\u6df1\uff0c\u8bc1\u660e\u4e86\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6f5c\u529b\u3002\u6839\u636e\u6211\u7684\u5370\u8c61\uff0c\u4ed6\u53ef\u80fd\u662f\u57282006\u5e74\u53d1\u8868\u7684\u6587\u7ae0\u4e2d\u7b2c\u4e00\u6b21\u4f7f\u7528\u4e86\u201cdeep neural network\u201d\u8fd9\u4e2a\u8bcd\u3002\u8fd9\u4f7f\u5f97\u4eba\u4eec\u610f\u8bc6\u5230\uff0c\u4e0d\u662f\u795e\u7ecf\u7f51\u7edc\u4e0d\u884c\uff0c\u800c\u662f\u6211\u4eec\u505a\u5f97\u4e0d\u591f\u6df1\u3002\u5f53\u6211\u4eec\u628a\u5b83\u505a\u6df1\u4e86\u4ee5\u540e\uff0c\u5b83\u771f\u7684\u5c31\u80fd\u5de5\u4f5c\uff0c\u800c\u4e14\u6548\u679c\u5f88\u597d\u3002\u6700\u65e9\u7684\u65f6\u5019\uff0c\u4ed6\u4eec\u5728\u8bed\u97f3\u8bc6\u522b\u548c\u56fe\u50cf\u8bc6\u522b\u4e0a\u53d6\u5f97\u4e86\u5de8\u5927\u7684\u7a81\u7834\uff0c\u8fd9\u8ba9\u66f4\u591a\u4eba\u770b\u5230\uff0c\u539f\u6765\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6df1\u5ea6\u5b66\u4e60\u7684\u65b9\u5f0f\u8ba9\u4eba\u5de5\u667a\u80fd\u5b8c\u5168\u901a\u8fc7\u6df1\u5ea6\u7684\u65b9\u5f0f\u8fdb\u884c\u5b66\u4e60\uff0c\u5e76\u4e14\u53d6\u5f97\u4e86\u975e\u5e38\u597d\u7684\u6548\u679c\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \n
    Hinton \u5728\u795e\u7ecf\u7f51\u7edc\u7814\u7a76\u5386\u53f2\u4e0a\u7684\u7b2c\u4e00\u6b21\u5173\u952e\u7a81\u7834\uff1a\u5c06\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u5e94\u7528\u4e8e\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3<\/span><\/section>\n
    Rumelhart, D., Hinton, G. & Williams, R. Learning representations by back-propagating errors. Nature<\/em> 323<\/strong>, 533\u2013536 (1986). https:\/\/doi.org\/10.1038\/323533a0<\/span><\/section>\n<\/blockquote>\n
    \n
    Hinton \u5728\u795e\u7ecf\u7f51\u7edc\u7814\u7a76\u5386\u53f2\u4e0a\u7684\u7b2c\u4e8c\u6b21\u5173\u952e\u7a81\u7834\uff1a\u63d0\u51fa\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc<\/span><\/section>\n
    Hinton, Geoffrey E., Simon Osindero, and Yee-Whye Teh. A fast learning algorithm for deep belief nets. Neural computation 18.7 (2006): 1527-1554. https:\/\/direct.mit.edu\/neco\/article-abstract\/18\/7\/1527\/7065\/A-Fast-Learning-Algorithm-for-Deep-Belief-Nets<\/span><\/section>\n
    Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504-507.<\/span><\/section>\n<\/blockquote>\n


    <\/p>\n


    <\/strong><\/span><\/section>\n
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    – 3 –<\/span><\/strong><\/span><\/p>\n

    \u673a\u5668\u5b66\u4e60\u4e0e\u7edf\u8ba1\u7269\u7406\u6709\u7740\u600e\u6837\u7684\u8054\u7cfb\uff1f<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


    <\/p>\n

    \u5c24\u4ea6\u5e84<\/strong>\uff1a\u6211\u8ba4\u4e3a\uff0c\u7269\u7406\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u4e4b\u6240\u4ee5\u80fd\u591f\u7d27\u5bc6\u7ed3\u5408\uff0c\u5f88\u5927\u7a0b\u5ea6\u4e0a\u662f\u56e0\u4e3a\u7269\u7406\u5b66\u672c\u8d28\u4e0a\u8bd5\u56fe\u5bf9\u73b0\u5b9e\u8fdb\u884c\u5efa\u6a21\uff0c\u800c<\/strong> <\/strong>AI<\/strong> <\/strong>\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4e5f\u662f\u8981\u5bf9\u73b0\u5b9e\u8fdb\u884c\u5efa\u6a21<\/strong>\u3002\u4ec0\u4e48\u662f\u73b0\u5b9e\uff1f\u73b0\u5b9e\u5c31\u662f\u6211\u4eec\u60f3\u8981\u5b66\u4e60\u7684\u6570\u636e\u3002\u5efa\u6a21\u53c8\u662f\u4ec0\u4e48\u5462\uff1f\u5c31\u662f\u6211\u4eec\u8981\u8bad\u7ec3\u7684<\/strong> <\/strong>AI<\/strong> <\/strong>\u7684\u6a21\u578b<\/strong>\u3002\u6240\u4ee5\u5b83\u4eec\u7684\u76ee\u6807\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\u662f\u4e00\u81f4\u7684\u3002\u6b63\u56e0\u5982\u6b64\uff0c\u7269\u7406\u5b66\u5bb6\u5728\u957f\u671f\u4e3a\u4e16\u754c\u5efa\u6a21\u7684\u8fc7\u7a0b\u4e2d\u53d1\u5c55\u51fa\u7684\u8bb8\u591a\u6570\u5b66\u6a21\u578b\uff0c\u662f\u503c\u5f97 AI \u9886\u57df\u501f\u9274\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u5f53\u524d\u8bb8\u591a\u751f\u6210\u5f0f\u6a21\u578b\u90fd\u501f\u9274\u4e86\u7269\u7406\u5b66\u601d\u60f3\u3002\u6bd4\u5982\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u4eca\u5e74\u83b7\u5f97\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7684\u57fa\u4e8e\u80fd\u91cf\u7684\u751f\u6210\u5f0f\u6a21\u578b\uff0c\u4ee5\u53ca\u57fa\u4e8e\u6d41\u7684\u751f\u6210\u5f0f\u6a21\u578b\uff0c\u8fd9\u4e9b\u6a21\u578b\u4e0e\u6982\u7387\u6d41\u3001\u4e0d\u53ef\u538b\u7f29\u6d41\u4f53\u7b49\u7269\u7406\u6982\u5ff5\u6709\u5173\u3002\u8fd8\u6709\u57fa\u4e8e\u6269\u6563\u7684\u751f\u6210\u5f0f\u6a21\u578b\uff0c\u5b83\u4eec\u4e0e\u7269\u7406\u5b66\u4e2d\u7684\u6269\u6563\u8fc7\u7a0b\u76f8\u5173\u3002\u751a\u81f3\u5728\u91cf\u5b50\u7269\u7406\u9886\u57df\uff0c\u4eba\u4eec\u63d0\u51fa\u4e86\u57fa\u4e8e\u91cf\u5b50\u529b\u5b66\u7684\u6a21\u578b\uff0c\u6bd4\u5982\u50cf\u5f20\u91cf\u7f51\u7edc\uff0c\u738b\u78ca\u8001\u5e08\u5728\u8fd9\u65b9\u9762\u6709\u5f00\u521b\u6027\u7684\u5de5\u4f5c\u3002\u7279\u522b\u662f\u5728\u6df1\u5ea6\u6a21\u578b\u9886\u57df\uff0c\u6211\u4eec\u7684\u4e3b\u8981\u4efb\u52a1\u662f\u5bf9\u4e16\u754c\u8fdb\u884c\u5efa\u6a21\uff0c\u4f46\u9057\u61be\u7684\u662f\uff0c\u4e16\u754c\u662f\u968f\u673a\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u5bf9\u6982\u7387\u5bc6\u5ea6\u548c\u6982\u7387\u5206\u5e03\u8fdb\u884c\u5efa\u6a21\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u5bf9\u6982\u7387\u5206\u5e03\u8fdb\u884c\u5efa\u6a21\u65f6\uff0c\u6d89\u53ca\u5230\u7269\u7406\u5b66\u4e2d\u4e0e\u6982\u7387\u5206\u5e03\u76f8\u5173\u7684\u4e24\u5927\u5b66\u79d1\uff1a\u7edf\u8ba1\u529b\u5b66\u548c\u91cf\u5b50\u529b\u5b66<\/strong>\u3002\u8fd9\u4e24\u4e2a\u9886\u57df\u5404\u81ea\u6709\u4e00\u5957\u5efa\u6a21\u6982\u7387\u5206\u5e03\u7684\u65b9\u6cd5\u3002\u56e0\u4e3a\u6982\u7387\u5206\u5e03\u5fc5\u987b\u662f\u4e00\u4e2a\u6b63\u5b9a\u7684\u6570\uff0c\u6211\u4eec\u4e0d\u80fd\u968f\u610f\u8bbe\u8ba1\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\uff0c\u7136\u540e\u58f0\u79f0\u8fd9\u4e2a\u7f51\u7edc\u7684\u8f93\u51fa\u5c31\u662f\u6982\u7387\u5206\u5e03\u3002\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u51fa\u6ca1\u6709\u6b63\u5b9a\u6027\u7684\u4fdd\u8bc1\uff0c\u6240\u4ee5\u7edf\u8ba1\u529b\u5b66\u91c7\u7528\u4e86\u4e00\u79cd\u65b9\u6cd5\uff1a\u4f7f\u7528\u73bb<\/strong>\u5c14\u5179\u66fc\u5206\u5e03<\/strong>\u3002\u8fd9\u79cd\u65b9\u6cd5\u9996\u5148\u6784\u9020\u4e00\u4e2a\u80fd\u91cf\u51fd\u6570\uff0c\u7136\u540e\u5bf9\u5176\u8fdb\u884c\u6307\u6570\u5316\uff0c\u901a\u8fc7\u6307\u6570\u6620\u5c04\u5c06\u4efb\u4f55\u5b9e\u6570\u6620\u5c04\u5230\u6b63\u7684\u6982\u7387\u4e0a\u3002\u800c\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\uff0c\u5219\u662f\u6784\u9020\u6ce2\u51fd\u6570<\/strong>\u3002\u6ce2\u51fd\u6570\u672c\u8eab\u4e0d\u9700\u8981\u6b63\u5b9a\u6027\u7684\u8981\u6c42\uff0c\u4f46\u901a\u8fc7\u53d6\u5176\u6a21\u7684\u5e73\u65b9\uff0c\u6211\u4eec\u540c\u6837\u80fd\u5f97\u5230\u4e00\u4e2a\u6b63\u5b9a\u7684\u6982\u7387\u5206\u5e03\u3002\u8fd9\u4e9b\u5efa\u6a21\u7684\u601d\u8def\u542c\u8d77\u6765\u53ef\u80fd\u662f\u7b80\u5355\u7684\u6280\u5de7\uff0c\u4f46\u5b9e\u9645\u4e0a\u5b83\u4eec\u90fd\u53ef\u4ee5\u88ab\u5e94\u7528\u5230\u673a\u5668\u5b66\u4e60\u4e2d\u3002\u7269\u7406\u5b66\u7684\u6587\u732e\u6216\u8bfe\u672c\u4e2d\u6563\u5e03\u7740\u5404\u79cd\u5404\u6837\u7684\u5c0f\u6280\u5de7\uff0c\u6211\u8ba4\u4e3a\u4ece\u8fd9\u91cc\u9762\u6c72\u53d6\u7ecf\u9a8c\u5bf9\u4e8e\u6211\u4eec\u8fdb\u5165\u673a\u5668\u5b66\u4e60\u9886\u57df\u662f\u975e\u5e38\u6709\u5e2e\u52a9\u7684<\/strong>\u3002<\/span><\/section>\n

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    \n
    \u5199\u7ed9\u7269\u7406\u5b66\u5bb6\u7684\u751f\u6210\u6a21\u578b<\/a><\/span>. \u738b\u78ca\uff0c\u5f20\u6f58\uff0c\u300a\u7269\u7406\u300b2024\u5e74\u7b2c6\u671f<\/span><\/section>\n<\/blockquote>\n

    <\/strong><\/span><\/section>\n
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    <\/span><\/section>\n
    \u5c24\u4ea6\u5e84<\/strong>\uff1a<\/strong>\u521a\u624d\u63d0\u5230\u91cd\u6574\u5316\u7fa4\uff0c\u6211\u975e\u5e38\u613f\u610f\u6df1\u5165\u8fd9\u4e2a\u8bdd\u9898\uff0c\u56e0\u4e3a\u8fd9\u4e5f\u6b63\u662f\u6211\u4e2a\u4eba\u7814\u7a76\u7684\u4e3b\u8981\u65b9\u5411\u4e4b\u4e00\u3002\u6211\u60f3\u5728\u8fd9\u4e00\u70b9\u4e0a\u7a0d\u5fae\u5c55\u5f00\u4e00\u4e0b\uff0c\u4f20\u7edf\u4e0a\uff0c\u91cd\u6574\u5316\u7fa4\u662f\u6211\u4eec\u7406\u89e3\u590d\u6742\u7cfb\u7edf\u7684\u4e00\u4e2a\u975e\u5e38\u6709\u6548\u7684\u5de5\u5177\u3002\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5148\u5c06\u4e00\u4e2a\u590d\u6742\u7cfb\u7edf\u5728\u5c40\u90e8\u8fdb\u884c\u7c97\u7c92\u5316\u5904\u7406\uff0c\u7136\u540e\u63d0\u53d6\u51fa\u6700\u91cd\u8981\u7684\u7279\u5f81\uff0c\u5e76\u601d\u8003\u8fd9\u4e9b\u7279\u5f81\u5728\u66f4\u5927\u5c3a\u5ea6\u4e0a\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u4ece\u800c\u63d0\u53d6\u51fa\u6709\u6548\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u6784\u5efa\u4e86\u4e00\u4e2a\u6709\u6548\u6a21\u578b\uff0c\u53ef\u4ee5\u5728\u6709\u6548\u6a21\u578b\u7684\u57fa\u7840\u4e0a\u8fdb\u4e00\u6b65\u7b80\u5316\uff0c\u63d0\u53d6\u51fa\u66f4\u6709\u6548\u7684\u6a21\u578b\uff0c\u4f7f\u5f97\u7cfb\u7edf\u5f97\u4ee5\u9010\u6b65\u89e3\u6790\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u5982\u4f55\u63d0\u53d6\u6709\u6548\u7684\u7279\u5f81\u4e00\u76f4\u662f\u4e00\u4e2a\u95ee\u9898\uff0c\u957f\u671f\u4ee5\u6765\u5e76\u6ca1\u6709\u975e\u5e38\u660e\u786e\u6216\u7edf\u4e00\u7684\u505a\u6cd5\u3002\u5f88\u591a\u65f6\u5019\uff0c\u8fd9\u4f9d\u8d56\u4e8e\u50cf Leo Kadanoff \u8fd9\u6837\u6770\u51fa\u7684\u7269\u7406\u5b66\u5bb6\u6765\u63d0\u51fa\u91cd\u6574\u5316\u65b9\u6848\u3002\u6211\u4eec\u56e2\u961f\u7684\u4e00\u4e9b\u7814\u7a76\u5c31\u662f\u60f3\u5229\u7528\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\uff0c\u5c24\u5176\u662f\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a\u7684\u4e00\u4e2a\u91cd\u8981\u529f\u80fd\u5c31\u662f\u80fd\u591f\u63d0\u53d6\u7279\u5f81\uff0c\u5b83\u80fd\u591f\u901a\u8fc7\u8868\u793a\u5b66\u4e60\uff0c\u5728\u89c2\u5bdf\u5230\u7684\u8f83\u4e3a\u7ec6\u8282\u5316\u7684\u6837\u672c\u4e2d\u63d0\u53d6\u51fa\u5173\u952e\u7279\u5f81\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    <\/span><\/section>\n
    \u53cd\u8fc7\u6765\uff0c\u7269\u7406\u5b66\u5bf9<\/strong> <\/strong>AI<\/strong> <\/strong>\u5176\u5b9e\u4e5f\u6709\u5e2e\u52a9<\/strong>\uff0c<\/strong>\u7edf\u8ba1\u7269\u7406\u672c\u8eab\u5bf9\u4e8e\u7406\u89e3\u6df1\u5ea6\u5b66\u4e60\u7684\u539f\u7406\u5c31\u6709\u5f88\u5927\u7684\u8d21\u732e<\/strong>\u3002\u50cf Dan Roberts \u7b49\u79d1\u5b66\u5bb6\u4eec\u7814\u7a76\u4e86\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e3a\u4f55\u80fd\u5b66\u4e60\uff0c\u5e76\u8fd0\u7528\u4e00\u4e9b\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u91cf\uff0c\u7279\u522b\u662f\u91cf\u5b50\u573a\u8bba\u4e2d\u7684\u6280\u5de7\uff0c\u4ed6\u4eec\u8bd5\u56fe\u7406\u89e3\uff0c\u5728\u795e\u7ecf\u7f51\u7edc\u795e\u7ecf\u5143\u6570\u91cf\u8d8b\u4e8e\u65e0\u9650\u7684\u60c5\u51b5\u4e0b\uff0c\u7f51\u7edc\u4f1a\u5c55\u73b0\u51fa\u600e\u6837\u7684\u884c\u4e3a\u3002\u8fd9\u4e9b\u884c\u4e3a\u662f\u53ef\u4ee5\u7528\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u53bb\u7406\u89e3\u7684\uff0c\u56e0\u4e3a\u7edf\u8ba1\u7269\u7406\u60f3\u8981\u7406\u89e3\u7684\u6070\u6070\u662f\u591a\u4f53\u7cfb\u7edf\u4e2d\u7c92\u5b50\u8d8b\u4e8e\u65e0\u9650\u7684\u6781\u9650\u60c5\u51b5\u3002\u6240\u4ee5\uff0c\u5f53\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u795e\u7ecf\u5143\u6570\u91cf\u8d8b\u4e8e\u65e0\u9650\u65f6\uff0c\u5b83\u4e5f\u4f1a\u5c55\u73b0\u51fa\u4e00\u4e9b\u7edf\u8ba1\u7269\u7406\u53ef\u4ee5\u5904\u7406\u7684\u884c\u4e3a\uff0c\u7edf\u8ba1\u7269\u7406\u5c31\u80fd\u4e3a\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u5982\u4f55\u5de5\u4f5c\u63d0\u4f9b\u4e00\u4e9b\u7406\u8bba\u652f\u6301\u3002\u6bd4\u5982\uff0c\u5728\u8fd9\u4e9b\u7814\u7a76\u4e2d\u53d1\u73b0\u4e86\u795e\u7ecf\u7f51\u7edc\u7684\u6807\u5ea6\u5f8b<\/span>\uff08neural scaling law\uff09<\/span>\uff0c\u53d1\u73b0\u4e86\u5982\u4f55\u521d\u59cb\u5316\u795e\u7ecf\u7f51\u7edc\u53c2\u6570\uff0c\u6bcf\u4e00\u5c42\u5e94\u8be5\u521d\u59cb\u5316\u7684\u9ad8\u65af\u5bbd\u5ea6\u5e94\u8be5\u662f\u591a\u5c11\uff0c\u624d\u80fd\u4f7f\u795e\u7ecf\u7f51\u7edc\u6070\u597d\u5904\u4e8e\u7406\u8bba\u8981\u6c42\u7684\u6700\u4f73\u72b6\u6001\uff0c\u4f7f\u5176\u5b66\u4e60\u548c\u8bad\u7ec3\u6548\u679c\u6700\u4f73\u3002\u6211\u8ba4\u4e3a\uff0c\u65e0\u8bba\u662f AI for Physics \u8fd8\u662f Physics for AI\uff0c\u8fd9\u4e24\u65b9\u9762\u90fd\u662f\u76f8\u4e92\u4fc3\u8fdb\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \n
    Roberts, Daniel A., Sho Yaida, and Boris Hanin. The principles of deep learning theory<\/em>. Vol. 46. Cambridge, MA, USA: Cambridge University Press, 2022.<\/span><\/section>\n<\/blockquote>\n

    <\/section>\n
    \u76f8\u5173\u6587\u7ae0\uff1a<\/span><\/section>\n