{"id":59960,"date":"2025-05-22T20:44:40","date_gmt":"2025-05-22T12:44:40","guid":{"rendered":"https:\/\/swarma.org\/?p=59960"},"modified":"2025-05-22T20:44:40","modified_gmt":"2025-05-22T12:44:40","slug":"quanta%ef%bc%9ahopfield%e7%bd%91%e7%bb%9c%ef%bc%9a%e5%82%ac%e7%94%9fai%e7%9a%84%e6%b6%8c%e7%8e%b0%e7%89%a9%e7%90%86%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=59960","title":{"rendered":"Quanta\uff1aHopfield\u7f51\u7edc\uff1a\u50ac\u751fAI\u7684\u6d8c\u73b0\u7269\u7406\u5b66"},"content":{"rendered":"
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\u4eba\u5de5\u667a\u80fd\u6b63\u4ee5\u524d\u6240\u672a\u6709\u7684\u901f\u5ea6\u6539\u53d8\u4e16\u754c\uff0c\u4f46\u5176\u80cc\u540e\u7684\u6838\u5fc3\u673a\u5236\uff0c\u8fdc\u4e0d\u6b62\u4e8e\u590d\u6742\u7684\u7b97\u6cd5\u548c\u7b97\u529b\u5806\u53e0\u3002\u672c\u6587\u4ece\u795e\u7ecf\u79d1\u5b66\u5148\u9a71\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7\uff08John Hopfield\uff09\u7684\u7814\u7a76\u51fa\u53d1\uff0c\u8ffd\u6eaf\u6df1\u5ea6\u5b66\u4e60\u7684\u53d1\u5c55\u8109\u7edc\uff0c\u63ed\u793a\u4e00\u4e2a\u4ee4\u4eba\u610f\u60f3\u4e0d\u5230\u7684\u4e8b\u5b9e\uff1a\u8bb8\u591a\u73b0\u4ee3AI\u6a21\u578b\u7684\u7406\u8bba\u57fa\u7840\uff0c\u6e90\u81ea\u4e0a\u4e16\u7eaa\u7269\u7406\u5b66\u5bb6\u7814\u7a76\u78c1\u6027\u6750\u6599\u65f6\u63d0\u51fa\u7684\u201c\u81ea\u65cb\u73bb\u7483\u201d\u6a21\u578b\u3002\u8fd9\u4e9b\u6e90\u4e8e\u7edf\u8ba1\u7269\u7406\u7684\u6982\u5ff5\uff0c\u4e0d\u4ec5\u89e3\u91ca\u4e86\u795e\u7ecf\u7f51\u7edc\u5982\u4f55\u201c\u8bb0\u5fc6\u201d\uff0c\u4e5f\u9884\u793a\u4e86\u5b83\u4eec\u5728\u9762\u5bf9\u6d77\u91cf\u6570\u636e\u65f6\u5982\u4f55\u201c\u521b\u9020\u201d\u3002\u5f53AI\u8868\u73b0\u51fa\u8d85\u51fa\u8bbe\u8ba1\u9884\u671f\u7684\u884c\u4e3a\uff0c\u6211\u4eec\u6216\u8bb8\u6b63\u5728\u89c1\u8bc1\u201c\u6d8c\u73b0\u201d\u73b0\u8c61\u7684\u53d1\u751f\u3002\u7406\u89e3\u8fd9\u4e00\u5207\uff0c\u6216\u8bb8\u6b63\u662f\u901a\u5411\u53ef\u89e3\u91caAI\u7684\u91cd\u8981\u4e00\u6b65\u3002<\/span><\/span><\/strong><\/p>\n


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\u5173\u952e\u8bcd\uff1aHopfield\u7f51\u7edc\u3001\u6269\u6563\u6a21\u578b\u3001\u81ea\u65cb\u73bb\u7483\u3001\u80fd\u91cf\u666f\u89c2\u3001\u6d8c\u73b0\u3001\u7edf\u8ba1\u7269\u7406\u3001\u6df1\u5ea6\u5b66\u4e60\u3001AI<\/span>
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\u6587\u7ae0\u9898\u76ee\uff1aThe Strange Physics That Gave Birth to AI<\/span><\/span><\/p>\n

\u6587\u7ae0\u5730\u5740\uff1ahttps:\/\/www.quantamagazine.org\/the-strange-physics-that-gave-birth-to-ai-20250430\/<\/span><\/span><\/p>\n

\u6765\u6e90\uff1aQuantamagazine<\/span><\/span><\/p>\n<\/blockquote>\n

\u81ea\u65cb\u73bb\u7483\u6216\u8bb8\u662f\u53f2\u4e0a\u6700\u6709\u7528\u7684\u201c\u65e0\u7528\u4e4b\u7269\u201d\u3002\u8fd9\u79cd\u6750\u6599\u867d\u7136\u53eb\u201c\u73bb\u7483\u201d\uff0c\u5176\u5b9e\u591a\u4e3a\u91d1\u5c5e\u6750\u8d28\u3002\u572820\u4e16\u7eaa\u4e2d\u53f6\uff0c\u56e0\u5176\u4ee4\u4eba\u8d39\u89e3\u7684\u884c\u4e3a\u5438\u5f15\u4e86\u4e00\u5c0f\u7fa4\u7269\u7406\u5b66\u5bb6\u7684\u5173\u6ce8\u3002\u81ea\u65cb\u73bb\u7483\u4f5c\u4e3a\u6750\u6599\uff0c\u672c\u8eab\u5e76\u6ca1\u6709\u4efb\u4f55\u5b9e\u9645\u5e94\u7528\u3002\u4f46\u4e3a\u4e86\u89e3\u91ca\u5176\u5947\u5f02\u6027\u800c\u53d1\u5c55\u51fa\u7684\u7406\u8bba\uff0c\u6700\u7ec8\u5f15\u53d1\u4e86\u5f53\u4eca\u7684\u4eba\u5de5\u667a\u80fd\u9769\u547d\u3002<\/span><\/span><\/p>\n

1982\u5e74\uff0c\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7<\/span>\uff08John Hopfield\uff09<\/span>\u501f\u9274\u81ea\u65cb\u73bb\u7483\u7684\u7269\u7406\u539f\u7406\uff0c\u6784\u5efa\u51fa\u53ef\u4ee5\u5b66\u4e60\u548c\u8bb0\u5fc6\u7684\u7b80\u5355\u7f51\u7edc\u3002\u8fd9\u9879\u5de5\u4f5c\u4e5f\u91cd\u65b0\u5524\u8d77\u4e86\u4eba\u4eec\u5bf9\u795e\u7ecf\u7f51\u7edc\u7684\u7814\u7a76\u5174\u8da3\u2014\u2014\u8fd9\u4e9b\u7f51\u72b6\u7684\u201c\u4eba\u5de5\u795e\u7ecf\u5143\u201d\u5728\u5f53\u65f6\u51e0\u4e4e\u5df2\u88ab\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u8005\u653e\u5f03\u2014\u2014\u5e76\u628a\u7269\u7406\u5b66\u5f15\u5165\u4e86\u4e00\u4e2a\u65b0\u9886\u57df\uff1a\u5bf9\u5fc3\u667a\u7684\u7814\u7a76\uff0c\u65e0\u8bba\u662f\u751f\u7269\u7684\uff0c\u8fd8\u662f\u673a\u68b0\u7684\u3002<\/span><\/span><\/p>\n

\u970d\u666e\u83f2\u5c14\u5fb7\u5c06\u201c\u8bb0\u5fc6\u201d\u770b\u4f5c\u7edf\u8ba1\u529b\u5b66\u4e2d\u7ecf\u5178\u7684\u96c6\u4f53\u7269\u7406\u5b66\u95ee\u9898\uff1a\u4e00\u4e2a\u7531\u591a\u4e2a\u90e8\u5206\u7ec4\u6210\u7684\u7cfb\u7edf\u5982\u4f55\u6f14\u5316\uff1f\u5bf9\u4e8e\u4efb\u4f55\u7b80\u5355\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u5305\u62ec\u81ea\u65cb\u73bb\u7483\uff0c\u70ed\u529b\u5b66\u544a\u8bc9\u6211\u4eec\u7684\u7b54\u6848\u90fd\u662f\uff1a\u201c\u8d8b\u5411\u4e8e\u66f4\u4f4e\u7684\u80fd\u91cf\u72b6\u6001\u201d\u3002\u970d\u666e\u83f2\u5c14\u5fb7\u5229\u7528\u8fd9\u4e00\u96c6\u4f53\u73b0\u8c61\u7684\u7b80\u5355\u5c5e\u6027\uff0c\u627e\u5230\u4e86\u5229\u7528\u201c\u4eba\u5de5\u795e\u7ecf\u5143\u201c\u7f51\u7edc\u6765\u50a8\u5b58\u548c\u8bb0\u5fc6\u6570\u636e\u7684\u65b9\u6cd5\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u4ed6\u627e\u5230\u4e86\u4e00\u4e2a\u5c06\u8bb0\u5fc6\u201c\u5b89\u7f6e\u201d\u5728\u80fd\u91cf\u8c37\u5e95\u7684\u65b9\u6cd5\u3002\u56e0\u6b64\u5f97\u540d\u7684<\/span><\/span>Hopfield\u7f51\u7edc<\/span><\/span><\/strong>\uff0c\u65e0\u9700\u67e5\u627e\u4fe1\u606f\uff0c\u53ea\u9700\u201c\u987a\u5761\u800c\u4e0b\u201d\u5373\u53ef\u5b8c\u6210\u8bb0\u5fc6\u3002<\/span><\/span><\/p>\n

\u201cHopfield\u7f51\u7edc\u662f\u4e00\u4e2a\u2018\u6982\u5ff5\u6027\u7684\u7a81\u7834\u2019\u201d\uff0c\u610f\u5927\u5229\u7c73\u5170\u535a\u79d1\u5c3c\u5927\u5b66\u7684\u7406\u8bba\u7269\u7406\u5b66\u5bb6\u9a6c\u514b\u00b7\u6885\u624e\u5c14<\/span>\uff08Marc M\u00e9zard\uff09<\/span>\u8bf4\u3002\u501f\u52a9\u81ea\u65cb\u73bb\u7483\u7684\u7269\u7406\u5b66\uff0c\u540e\u6765\u4ece\u4e8b\u4eba\u5de5\u667a\u80fd\u7684\u7814\u7a76\u8005\u53ef\u4ee5\u201c\u4f7f\u7528\u4e3a\u8fd9\u4e9b\u53e4\u8001\u7269\u7406\u7cfb\u7edf\u53d1\u5c55\u51fa\u6765\u7684\u4e00\u6574\u5957\u5de5\u5177\u201d\u3002<\/span><\/span><\/p>\n

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\u56fe1 Marc M\u00e9zard\uff0c\u610f\u5927\u5229\u7c73\u5170\u535a\u79d1\u5c3c\u5927\u5b66\u7684\u7406\u8bba\u7269\u7406\u5b66\u5bb6\uff0c\u65e0\u5e8f\u7cfb\u7edf\u7edf\u8ba1\u7269\u7406\u9886\u57df\u4e13\u5bb6\u3002\u4ed6\u6700\u521d\u4e3a\u63cf\u8ff0\u65e0\u5e8f\u78c1\u6027\u7cfb\u7edf\u2014\u2014\u81ea\u65cb\u73bb\u7483\u7684\u884c\u4e3a\u800c\u53d1\u5c55\u51fa\u7684\u5de5\u4f5c\uff0c\u6784\u5efa\u4e86\u4e00\u4e2a\u6982\u5ff5\u6846\u67b6\u548c\u4e00\u7cfb\u5217\u65b9\u6cd5\uff08\u5305\u62ec\u7a7a\u8154\u6cd5\uff09\u3002\u8fd9\u4e9b\u65b9\u6cd5\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u63cf\u8ff0\u548c\u7406\u89e3\u7ecf\u6d4e\u5b66\u3001\u751f\u7269\u5b66\u3001\u4fe1\u606f\u8bba\u548c\u8111\u79d1\u5b66\u4e2d\u7684\u6d8c\u73b0\u73b0\u8c61\u3002<\/span><\/span><\/p>\n

2024\u5e74\uff0c\u970d\u666e\u83f2\u5c14\u5fb7\u548c\u4eba\u5de5\u667a\u80fd\u5148\u950b\u6770\u5f17\u91cc\u00b7\u8f9b\u987f<\/span>\uff08Geoffrey Hinton\uff09<\/span>\u56e0\u4ed6\u4eec\u5728\u795e\u7ecf\u7f51\u7edc\u7edf\u8ba1\u7269\u7406\u65b9\u9762\u7684\u5de5\u4f5c\u83b7\u5f97\u4e86\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u3002\u8fd9\u4e00\u5956\u9879\u4ee4\u8bb8\u591a\u4eba\u611f\u5230\u60ca\u8bb6\uff0c\u4e5f\u6709\u4eba\u62b1\u6028\u8fd9\u66f4\u50cf\u662f\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u7684\u80dc\u5229\uff0c\u800c\u4e0d\u662f\u7269\u7406\u5b66\u7684\u8363\u8a89\u3002\u4f46\u5f53\u81ea\u65cb\u73bb\u7483\u7684\u7269\u7406\u5b66\u88ab\u7528\u6765\u5efa\u6a21\u8bb0\u5fc6\u3001\u6784\u5efa\u80fd\u601d\u8003\u7684\u673a\u5668\u65f6\uff0c\u5b83\u5e76\u672a\u56e0\u6b64\u5931\u53bb\u5176\u7269\u7406\u5b66\u672c\u8d28\u3002\u5982\u4eca\uff0c\u4e00\u4e9b\u7814\u7a76\u8005\u76f8\u4fe1\uff0c\u970d\u666e\u83f2\u5c14\u5fb7\u5f53\u521d\u7528\u6765\u8ba9\u673a\u5668\u201c\u8bb0\u4f4f\u201d\u7684\u540c\u4e00\u5957\u7269\u7406\u539f\u7406\uff0c\u4e5f\u53ef\u4ee5\u7528\u6765\u5e2e\u52a9\u673a\u5668\u201c\u60f3\u8c61\u201d\uff0c\u5e76\u8bbe\u8ba1\u51fa\u6211\u4eec\u771f\u6b63\u80fd\u591f\u7406\u89e3\u7684\u795e\u7ecf\u7f51\u7edc\u3002<\/span><\/span><\/p>\n


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\u56fe2\uff1a\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7\uff08John Hopfield\uff09\uff0c\u7f8e\u56fd\u7269\u7406\u5b66\u5bb6\u3002\u4ed6\u5f00\u53d1\u4e86\u4e00\u79cd\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\uff0c\u4e3a\u73b0\u4ee3\u4eba\u5de5\u667a\u80fd\u5960\u5b9a\u4e86\u57fa\u7840\u3002\uff08\u62cd\u6444\u4e8e1988\u5e74\uff0c\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u6863\u6848\u4e0e\u7279\u85cf\u9986\uff09<\/span><\/span><\/p>\n

\u970d\u666e\u83f2\u5c14\u5fb7\u57281960\u5e74\u4ee3\u5f00\u59cb\u4ed6\u7684\u804c\u4e1a\u751f\u6daf\uff0c\u7814\u7a76\u534a\u5bfc\u4f53\u7684\u7269\u7406\u5b66\u3002\u4f46\u5230\u4e8660\u5e74\u4ee3\u672b\u671f\uff0c\u4ed6\u5199\u9053\uff1a<\/span><\/span><\/p>\n

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\u201c\u5728\u51dd\u805a\u6001\u7269\u7406\u4e2d\uff0c\u6211\u5df2\u627e\u4e0d\u5230\u9002\u5408\u6211\u7279\u957f\u7684\u95ee\u9898\u3002\u201d\uff08\u5f15\u81ea\u4ed62018\u5e74\u7684\u4e00\u7bc7\u968f\u7b14[1]\uff09<\/span><\/span><\/p>\n<\/blockquote>\n

\u4e8e\u662f\u4ed6\u5f00\u59cb\u5bfb\u627e\u65b0\u7684\u65b9\u5411\u3002\u4e00\u6b21\u77ed\u6682\u6d89\u8db3\u751f\u7269\u5316\u5b66\u7684\u7ecf\u5386\u8ba9\u4ed6\u63d0\u51fa\u4e86\u4e00\u4e2a\u5173\u4e8e\u751f\u7269\u4f53\u5982\u4f55\u201c\u6821\u5bf9\u201d\u751f\u5316\u53cd\u5e94\u7684\u7406\u8bba[2]\uff0c\u968f\u540e\u4ed6\u5c06\u76ee\u5149\u6295\u5411\u4e86\u795e\u7ecf\u79d1\u5b66\u3002<\/span><\/span><\/p>\n

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\u201c\u6211\u5728\u5bfb\u627e\u4e00\u4e2a<\/span><\/span>problem<\/span><\/span><\/em>\uff08\u5927\u95ee\u9898\uff09\uff0c\u800c\u4e0d\u662f\u4e00\u4e2a\u666e\u901a\u7684\u2018\u95ee\u9898\u2019\uff0c\u201d\u4ed6\u5728\u968f\u7b14\u4e2d\u56de\u5fc6\u9053\uff0c\u7279\u522b\u5f3a\u8c03\u4e86\u627e\u5230\u771f\u6b63\u91cd\u8981\u8bae\u9898\u7684\u5fc5\u8981\u6027\u3002\u201c\u5bf9\u6211\u800c\u8a00\uff0c\u2018\u5fc3\u667a\u5982\u4f55\u4ece\u5927\u8111\u4e2d\u6d8c\u73b0\u2019\u662f\u6211\u4eec\u4eba\u7c7b\u63d0\u51fa\u7684\u6700\u6df1\u523b\u7684\u95ee\u9898\u3002\u8fd9\u65e0\u7591\u662f\u4e00\u4e2a<\/span><\/span>problem<\/span><\/span><\/em>\u3002\u201d<\/span><\/span><\/p>\n<\/blockquote>\n

\u970d\u666e\u83f2\u5c14\u5fb7\u610f\u8bc6\u5230\uff0c<\/span><\/span>\u8054\u60f3\u8bb0\u5fc6<\/span><\/span><\/strong>\u662f\u8fd9\u4e2a\u5927\u95ee\u9898\u7684\u4e00\u90e8\u5206\u2014\u2014\u800c\u4ed6\u4ece\u51dd\u805a\u6001\u7269\u7406\u4e2d\u79ef\u7d2f\u7684\u5de5\u5177\u6b63\u53ef\u4ee5\u7528\u6765\u89e3\u51b3\u5b83\u3002<\/span><\/span><\/p>\n

\u5728\u666e\u901a\u8ba1\u7b97\u673a\u4e2d\uff0c\u6570\u636e\u662f\u9759\u6001\u5b58\u50a8\u7684\uff0c\u901a\u8fc7\u5730\u5740\u8bbf\u95ee\u3002\u8fd9\u4e2a\u5730\u5740\u4e0e\u5b58\u50a8\u7684\u4fe1\u606f\u672c\u8eab\u65e0\u5173\uff0c\u5b83\u53ea\u662f\u4e00\u4e2a\u8bbf\u95ee\u4ee3\u7801\u3002\u56e0\u6b64\uff0c\u4e00\u65e6\u5730\u5740\u51fa\u9519\u54ea\u6015\u4e00\u70b9\u70b9\uff0c\u4f60\u5c31\u4f1a\u8bfb\u5230\u9519\u8bef\u7684\u6570\u636e\u3002\u4f46\u4eba\u7c7b\u8bb0\u5fc6\u4f3c\u4e4e\u5e76\u4e0d\u662f\u8fd9\u6837\u7684\u3002\u6211\u4eec\u5e38\u5e38\u901a\u8fc7\u8054\u60f3\u6765\u8bb0\u4f4f\u4e8b\u60c5\u3002\u4e00\u4e2a\u7ebf\u7d22\u3001\u4e00\u6bb5\u6a21\u7cca\u7684\u8bb0\u5fc6\u5c31\u53ef\u80fd\u5524\u8d77\u6574\u4e2a\u8bb0\u5fc6\u3002\u6bd4\u5982\u4f60\u95fb\u5230\u7d2b\u4e01\u9999\u7684\u9999\u6c14\uff0c\u7a81\u7136\u56de\u60f3\u8d77\u7237\u7237\u82b1\u56ed\u91cc\u7ae5\u5e74\u7684\u4e00\u5e55\uff1b\u53c8\u6216\u662f\u542c\u5230\u4e00\u9996\u6b4c\u7684\u524d\u51e0\u53e5\uff0c\u7a81\u7136\u53d1\u73b0\u81ea\u5df1\u80fd\u5531\u51fa\u6574\u9996\u4f60\u4ee5\u4e3a\u65e9\u5df2\u5fd8\u8bb0\u7684\u60c5\u6b4c\u3002\u970d\u666e\u83f2\u5c14\u5fb7\u82b1\u8d39\u6570\u5e74\u65f6\u95f4\u7814\u7a76\u8054\u60f3\u8bb0\u5fc6\uff0c\u5e76\u5c06\u5176\u8f6c\u5316\u4e3a\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u3002\u4ed6\u5c1d\u8bd5\u4e86\u5404\u79cd\u968f\u673a\u8fde\u63a5\u7684\u795e\u7ecf\u7f51\u7edc\u548c\u5176\u4ed6\u53ef\u80fd\u7684\u8bb0\u5fc6\u6a21\u578b\u3002\u4e00\u5f00\u59cb\u5e76\u4e0d\u987a\u5229\uff0c\u76f4\u5230\u6700\u7ec8\uff0c\u4ed6\u53d1\u73b0\u4e86\u89e3\u51b3\u8fd9\u4e2a<\/span><\/span>problem<\/span><\/span><\/em>\u7684\u4e00\u4e2a\u51fa\u4eba\u610f\u6599\u7684\u5173\u952e\u3002<\/span><\/span><\/p>\n

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\u56fe3\uff1a\u6770\u5f17\u91cc\u00b7\u8f9b\u987f\uff08\u5de6\uff09\u548c\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7\uff08\u53f3\uff09\u57282024\u5e7412\u6708\u4e8e\u65af\u5fb7\u54e5\u5c14\u6469\u4e3e\u884c\u7684\u4eea\u5f0f\u4e0a\u63a5\u53d7\u4e86\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u3002\u8be5\u5956\u9879\u8868\u5f70\u4e86\u4ed6\u4eec\u57fa\u4e8e\u81ea\u65cb\u73bb\u7483\u7269\u7406\u7684\u6700\u65e9\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u3002<\/span><\/span><\/p>\n


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\u81ea\u65cb\u73bb\u7483<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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20\u4e16\u7eaa50\u5e74\u4ee3\uff0c\u79d1\u5b66\u5bb6\u5728\u7814\u7a76\u67d0\u4e9b\u7a00\u91ca\u5408\u91d1<\/span>\uff08\u5982\u91d1\u4e2d\u7684\u94c1\uff09<\/span>\u65f6\u53d1\u73b0\u4e86\u8fd9\u4e9b\u6750\u6599\u8868\u73b0\u51fa\u4e00\u4e9b\u5947\u602a\u7684\u73b0\u8c61\u3002\u5728\u67d0\u4e2a\u6e29\u5ea6\u4ee5\u4e0a\uff0c\u8fd9\u4e9b\u5408\u91d1<\/span>\uff08\u5982\u94dd\uff09<\/span>\u7684\u884c\u4e3a\u7c7b\u4f3c\u4e8e\u666e\u901a\u6750\u6599\u3002\u5b83\u4eec\u672c\u8eab\u4e0d\u5e26\u78c1\u6027\uff0c\u4f46\u4f1a\u5bf9\u5916\u90e8\u78c1\u573a\u6709\u5fae\u5f31\u54cd\u5e94\u3002\u6bd4\u5982\uff0c\u4f7f\u7528\u975e\u5e38\u5f3a\u7684\u78c1\u94c1\u53ef\u4ee5\u79fb\u52a8\u4e00\u4e2a\u94dd\u7f50\uff0c\u4f46\u94dd\u672c\u8eab\u5e76\u4e0d\u80fd\u5f53\u4f5c\u78c1\u94c1\u4f7f\u7528\u3002\u901a\u5e38\uff0c\u50cf\u94dd\u8fd9\u6837\u7684\u6750\u6599\u5728\u5916\u90e8\u78c1\u573a\u64a4\u53bb\u540e\u7acb\u5373\u5931\u53bb\u78c1\u6027\u3002\u4f46\u5f53\u6e29\u5ea6\u4f4e\u4e8e\u67d0\u4e00\u4e34\u754c\u503c\u65f6\uff0c\u81ea\u65cb\u73bb\u7483\u7684\u884c\u4e3a\u5c31\u4e0d\u540c\u4e86\u2014\u2014\u5b83\u4eec\u7684\u77ac\u65f6\u78c1\u5316\u72b6\u6001\u4f1a\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u4fdd\u7559\u4e0b\u6765<\/span>\uff08\u5c3d\u7ba1\u503c\u8f83\u4f4e\uff09<\/span>\u3002\u8fd9\u53ea\u662f\u81ea\u65cb\u73bb\u7483\u7684\u602a\u5f02\u884c\u4e3a\u4e4b\u4e00\uff0c\u5b83\u4eec\u7684\u70ed\u5b66\u6027\u8d28\u4e5f\u540c\u6837\u4ee4\u4eba\u56f0\u60d1\u3002<\/span><\/span><\/p>\n

\u5927\u7ea6\u57281970\u5e74\u524d\u540e\uff0c\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6\u5f00\u59cb\u901a\u8fc7\u8c03\u6574\u7269\u7406\u5b66\u4e2d\u7814\u7a76\u96c6\u4f53\u78c1\u6027\u884c\u4e3a\u7684\u7ecf\u5178\u6a21\u578b\u2014\u2014<\/span><\/span>\u4f0a\u8f9b\u6a21\u578b\uff08Ising model\uff09<\/span><\/span><\/strong>\u2014\u2014\u6765\u5efa\u7acb\u5bf9\u8fd9\u4e9b\u6750\u6599\u7684\u7406\u8bba\u7406\u89e3\u3002\u4f0a\u8f9b\u6a21\u578b\u770b\u8d77\u6765\u5c31\u50cf\u4e00\u4e2a\u7531\u7bad\u5934\u7ec4\u6210\u7684\u7b80\u5355\u7f51\u683c\uff0c\u6bcf\u4e2a\u7bad\u5934\u53ef\u4ee5\u6307\u5411\u4e0a\u6216\u4e0b\u3002\u6bcf\u4e2a\u7bad\u5934\u4ee3\u8868\u4e00\u4e2a\u539f\u5b50\u7684\u5185\u5728\u78c1\u77e9\uff0c\u6216\u79f0\u201c\u81ea\u65cb\u201d\u3002\u8fd9\u662f\u4e00\u79cd\u5bf9\u771f\u5b9e\u539f\u5b50\u7cfb\u7edf\u7684\u7b80\u5316\u63cf\u8ff0\uff0c\u4f46\u901a\u8fc7\u8c03\u6574\u90bb\u8fd1\u81ea\u65cb\u4e4b\u95f4\u76f8\u4e92\u5f71\u54cd\u7684\u89c4\u5219\uff0c\u8fd9\u4e2a\u6a21\u578b\u5374\u80fd\u4ea7\u751f\u51fa\u4ee4\u4eba\u60ca\u8bb6\u7684\u590d\u6742\u884c\u4e3a\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u56fe4\uff1a\u5728\u4f0a\u8f9b\u6a21\u578b\u4e2d\uff0c\u70ed\u91cf\u4f1a\u4f7f\u7bad\u5934\uff08\u81ea\u65cb\uff09\u968f\u673a\u7ffb\u8f6c\uff0c\u800c\u78c1\u6027\u5438\u5f15\u529b\u5219\u4f7f\u76f8\u90bb\u7684\u7bad\u5934\u8d8b\u4e8e\u5bf9\u9f50\u3002\u8fd9\u79cd\u201c\u7ade\u4e89\u201d\u63cf\u8ff0\u4e86\u5927\u91cf\u771f\u5b9e\u4e16\u754c\u7cfb\u7edf\u7684\u7279\u6027\uff08\u5f15\u7528\u81ea\u300aThe Cartoon Picture of Magnets That Has Transformed Science\u300b\uff09\u3002<\/span><\/span><\/p>\n

\u4e00\u822c\u6765\u8bf4\uff0c\u76f8\u90bb\u7bad\u5934\u671d\u540c\u4e00\u65b9\u5411\u65f6\u80fd\u91cf\u8f83\u4f4e\uff0c\u800c\u65b9\u5411\u76f8\u53cd\u5219\u80fd\u91cf\u8f83\u9ad8\u3002\u5982\u679c\u81ea\u65cb\u53ef\u4ee5\u7ffb\u8f6c\uff0c\u4f0a\u8f9b\u6a21\u578b\u4e2d\u7684\u7cfb\u7edf\u72b6\u6001\u5c31\u4f1a\u5411\u80fd\u91cf\u66f4\u4f4e\u7684\u5bf9\u9f50\u72b6\u6001\u6f14\u5316\uff0c\u5c31\u50cf\u5c0f\u7403\u5f80\u4f4e\u5904\u6eda\u4e00\u6837\u3002\u78c1\u6027\u6750\u6599\u5982\u94c1\uff0c\u6700\u7ec8\u4f1a\u5b9a\u683c\u5728\u4e00\u4e2a\u7b80\u5355\u7684\u72b6\u6001\u4e2d\uff0c\u5373\u6240\u6709\u81ea\u65cb\u5168\u90e8\u671d\u4e0a\u6216\u5168\u90e8\u671d\u4e0b\u3002<\/span><\/span><\/p>\n

1975\u5e74\uff0c\u7269\u7406\u5b66\u5bb6\u5927\u536b\u00b7\u820d\u6797\u987f<\/span>\uff08David Sherrington\uff09<\/span>\u4e0e\u65af\u79d1\u7279\u00b7\u67ef\u514b\u5e15\u7279\u91cc\u514b<\/span>\uff08Scott Kirkpatrick\uff09<\/span>\u901a\u8fc7\u4fee\u6539\u81ea\u65cb\u4e4b\u95f4\u7684\u4ea4\u4e92\u89c4\u5219\uff0c\u6784\u5efa\u4e86\u4e00\u4e2a\u53ef\u4ee5\u6355\u6349\u81ea\u65cb\u73bb\u7483\u590d\u6742\u884c\u4e3a\u7684\u6a21\u578b\u3002\u4ed6\u4eec\u8ba9\u81ea\u65cb\u5bf9\u4e4b\u95f4\u7684\u4ea4\u4e92\u5f3a\u5ea6\u968f\u673a\u53d8\u5316\uff0c\u5e76\u5141\u8bb8\u6bcf\u4e2a\u81ea\u65cb\u4e0e\u7cfb\u7edf\u4e2d\u6240\u6709\u5176\u4ed6\u81ea\u65cb\u53d1\u751f\u4f5c\u7528\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u4e0e\u6700\u8fd1\u90bb\u53d1\u751f\u4f5c\u7528\u3002\u8fd9\u4e00\u53d8\u5316\u5bfc\u81f4\u4e86\u4e00\u4e2a\u201c\u5d0e\u5c96\u201d\u7684<\/span><\/span>\u80fd\u91cf\u72b6\u6001\u666f\u89c2<\/span><\/span><\/strong>\uff0c\u5b58\u5728\u7740\u591a\u4e2a\u80fd\u91cf\u9ad8\u4f4e\u8d77\u4f0f\u7684\u201c\u5c71\u5cf0\u201d\u4e0e\u201c\u5c71\u8c37\u201d\uff1b\u53d6\u51b3\u4e8e\u81ea\u65cb\u73bb\u7483\u6700\u521d\u5904\u5728\u54ea\u4e2a\u4f4d\u7f6e\uff0c\u5b83\u6700\u7ec8\u4f1a\u201c\u51bb\u7ed3\u201d\u5728\u67d0\u4e2a\u72ec\u7279\u7684\u80fd\u91cf\u8c37\u5e95<\/span>\uff08\u5373\u5e73\u8861\u6001\uff09<\/span>\u3002\u8fd9\u4e0e\u94c1\u78c1\u4f53\u7cfb\u7edf<\/span>\uff08\u5982\u94c1\uff09<\/span>\u5927\u4e0d\u76f8\u540c\uff0c\u94c1\u78c1\u4f53\u6700\u7ec8\u4f1a\u51bb\u7ed3\u5728\u4ec5\u6709\u7684\u4e24\u79cd\u6709\u5e8f\u72b6\u6001\u4e2d<\/span>\uff08\u5168\u4e0a\u6216\u5168\u4e0b\uff09<\/span>\uff0c\u800c\u975e\u94c1\u78c1\u4f53\u7cfb\u7edf\u7684\u81ea\u65cb\u5219\u59cb\u7ec8\u968f\u673a\u6ce2\u52a8\uff0c\u4e0d\u4f1a\u7a33\u5b9a\u4e0b\u6765\u3002\u5728\u81ea\u65cb\u73bb\u7483\u4e2d\uff0c<\/span><\/span>\u968f\u673a\u6027\u88ab\u51bb\u7ed3\u4e86<\/span><\/span><\/strong>\u3002<\/span><\/span><\/p>\n

\u4f0a\u8f9b\u6a21\u578b<\/span><\/span><\/strong>\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u201c\u73a9\u5177\u6a21\u578b\u201d\uff0c\u7528\u5b83\u6765\u9884\u6d4b\u771f\u5b9e\u6750\u6599\u7684\u884c\u4e3a\u6709\u70b9\u50cf\u7528\u706b\u67f4\u4eba\u56fe\u6765\u89c4\u5212\u4e00\u573a\u624b\u672f\u3002\u4f46\u795e\u5947\u7684\u662f\uff0c\u5b83\u5f80\u5f80\u786e\u5b9e\u594f\u6548\u3002\u5982\u4eca\uff0c<\/span><\/span>\u4f0a\u8f9b\u6a21\u578b<\/span><\/span><\/strong>\u5df2\u6210\u4e3a\u7edf\u8ba1\u529b\u5b66\u4e2d\u7684\u4e3b\u529b\u5de5\u5177\u3002\u5b83\u7684\u5404\u79cd\u53d8\u4f53\u51e0\u4e4e\u51fa\u73b0\u5728\u6240\u6709\u590d\u6742\u96c6\u4f53\u73b0\u8c61\u7814\u7a76\u7684\u89d2\u843d\u2014\u2014\u5305\u62ec\u56e0\u970d\u666e\u83f2\u5c14\u5fb7\u7684\u5de5\u4f5c\u800c\u5ef6\u4f38\u51fa\u7684\u8bb0\u5fc6\u7814\u7a76\u3002<\/span><\/span><\/p>\n


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\u81ea\u65cb\u8bb0\u5fc6<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u4ece\u7b80\u5355\u89d2\u5ea6\u770b\uff0c\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u4e0e<\/span><\/span>\u4f0a\u8f9b\u6a21\u578b<\/span><\/span><\/strong>\u4e2d\u7684\u78c1\u81ea\u65cb\u4e4b\u95f4\u7684\u884c\u4e3a\u6709\u8bb8\u591a\u76f8\u4f3c\u4e4b\u5904\u3002\u9996\u5148\uff0c\u795e\u7ecf\u5143\u5e38\u88ab\u5efa\u6a21\u4e3a\u4e8c\u5143\u7684\u5f00-\u5173\u5f00\u5173\uff1a\u8981\u4e48\u53d1\u653e\u4fe1\u53f7\uff0c\u8981\u4e48\u4e0d\u53d1\u653e\u3002\u800c\u81ea\u65cb\u4e5f\u6709\u4e24\u4e2a\u72b6\u6001\uff1a\u5411\u4e0a\u6216\u5411\u4e0b\u3002\u6b64\u5916\uff0c\u4e00\u4e2a\u795e\u7ecf\u5143\u7684\u53d1\u653e\u53ef\u4ee5\u4fc3\u4f7f\u6216\u6291\u5236\u90bb\u5c45\u795e\u7ecf\u5143\u7684\u53d1\u653e\u3002\u795e\u7ecf\u5143\u4e4b\u95f4\u8fd9\u4e9b\u53ef\u53d8\u7684\u76f8\u4e92\u5f71\u54cd\uff0c\u5c31\u50cf\u81ea\u65cb\u73bb\u7483\u4e2d\u53ef\u53d8\u7684\u81ea\u65cb\u95f4\u76f8\u4e92\u4f5c\u7528\u3002\u745e\u58eb\u6d1b\u6851\u8054\u90a6\u7406\u5de5\u5b66\u9662\u7684\u7269\u7406\u5b66\u5bb6\u517c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6Lenka Zdeborov\u00e1\u8bf4\u9053\uff1a<\/span><\/span><\/p>\n

\n

\u201c\u5728\u6570\u5b66\u4e0a\uff0c\u4eba\u4eec\u53ef\u4ee5\u628a\u539f\u672c\u4ee3\u8868\u81ea\u65cb\u6216\u539f\u5b50\u7684\u90a3\u4e9b\u4e1c\u897f\u66ff\u6362\u6389\uff0c\u5176\u4ed6\u7cfb\u7edf\u4e5f\u53ef\u4ee5\u7528\u8fd9\u5957\u5de5\u5177\u7bb1\u6765\u63cf\u8ff0\u3002\u201d<\/span><\/span><\/p>\n<\/blockquote>\n

<\/section>\n

\u56fe5\uff1aLenka Zdeborov\u00e1\uff0c\u662f\u745e\u58eb\u6d1b\u6851\u8054\u90a6\u7406\u5de5\u5b66\u9662\uff08\u7684\u4e00\u540d\u7269\u7406\u5b66\u5bb6\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\uff0c\u5979\u7814\u7a76\u7269\u8d28\u7269\u7406\u5b66\u5982\u4f55\u5e2e\u52a9\u5efa\u6a21\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u7684\u884c\u4e3a\u3002<\/span><\/span><\/p>\n

\u4e3a\u4e86\u6784\u5efa\u7f51\u7edc\uff0c\u970d\u666e\u83f2\u5c14\u5fb7\u4ece\u4e00\u4e2a\u7531\u4eba\u5de5\u795e\u7ecf\u5143\u6784\u6210\u7684\u7f51\u7edc\u5f00\u59cb\uff0c\u8fd9\u4e9b\u795e\u7ecf\u5143\u53ef\u4ee5\u662f\u201c\u5f00\u201d<\/span>\uff08\u53d1\u653e\uff09<\/span>\u6216\u201c\u5173\u201d<\/span>\uff08\u9759\u606f\uff09<\/span>\u72b6\u6001\u3002\u6bcf\u4e2a\u795e\u7ecf\u5143\u90fd\u5f71\u54cd\u5176\u4ed6\u6240\u6709\u795e\u7ecf\u5143\u7684\u72b6\u6001\uff0c\u5e76\u4e14\u8fd9\u79cd\u5f71\u54cd\u662f\u53ef\u4ee5\u8c03\u8282\u7684\u3002\u67d0\u4e00\u65f6\u523b\uff0c\u7f51\u7edc\u7684\u72b6\u6001\u7531\u54ea\u4e9b\u795e\u7ecf\u5143\u5904\u4e8e\u53d1\u653e\u72b6\u6001\u3001\u54ea\u4e9b\u5904\u4e8e\u9759\u606f\u72b6\u6001\u6765\u5b9a\u4e49\u3002\u4f60\u53ef\u4ee5\u7528\u4e8c\u8fdb\u5236\u65b9\u5f0f\u6765\u7f16\u7801\u8fd9\u79cd\u72b6\u6001\uff1a\u53d1\u653e\u7684\u795e\u7ecf\u5143\u75281\u8868\u793a\uff0c\u9759\u606f\u7684\u795e\u7ecf\u5143\u75280\u8868\u793a\u3002\u628a\u6574\u4e2a\u7f51\u7edc\u5f53\u524d\u7684\u72b6\u6001\u5199\u51fa\u6765\uff0c\u5c31\u662f\u4e00\u4e32\u6bd4\u7279\u3002\u8fd9\u79cd\u7f51\u7edc\u5e76\u4e0d\u662f\u5728\u201c\u5b58\u50a8\u201d\u4fe1\u606f\uff0c\u5b83\u672c\u8eab\u5c31\u662f\u4fe1\u606f\u3002<\/span><\/span><\/p>\n

\u4e3a\u4e86\u201c\u6559\u4f1a\u201d\u7f51\u7edc\u4e00\u4e2a\u7279\u5b9a\u7684\u6a21\u5f0f\uff0c\u970d\u666e\u83f2\u5c14\u5fb7\u901a\u8fc7\u8c03\u6574\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5f3a\u5ea6\u6765\u201c\u96d5\u523b\u201d\u5176<\/span><\/span>\u80fd\u91cf\u666f\u89c2<\/span><\/span><\/strong>\uff0c\u4ece\u800c\u8ba9\u76ee\u6807\u6a21\u5f0f\u5904\u4e8e\u4e00\u4e2a\u4f4e\u80fd\u91cf\u7684\u7a33\u6001\u4e2d\u3002\u5728\u8fd9\u79cd\u7a33\u6001\u4e0b\uff0c\u7f51\u7edc\u505c\u6b62\u6f14\u5316\uff0c\u7a33\u5b9a\u5730\u8868\u73b0\u4e3a\u4e00\u4e2a\u6a21\u5f0f\u3002\u4ed6\u627e\u5230\u4e86\u4e00\u4e2a\u53d7\u795e\u7ecf\u79d1\u5b66\u7ecf\u5178\u6cd5\u5219\u201c\u540c\u6b65\u53d1\u653e\u7684\u795e\u7ecf\u5143\u66f4\u5bb9\u6613\u5efa\u7acb\u8fde\u63a5\u201d\u542f\u53d1\u7684\u89c4\u5219\uff1a\u5982\u679c\u4e24\u4e2a\u795e\u7ecf\u5143\u5728\u76ee\u6807\u6a21\u5f0f\u4e2d\u90fd\u662f\u53d1\u653e\u72b6\u6001<\/span>\uff08\u6216\u90fd\u9759\u606f\uff09<\/span>\uff0c\u5c31\u589e\u5f3a\u5b83\u4eec\u4e4b\u95f4\u7684\u8fde\u63a5\uff1b\u800c\u5982\u679c\u72b6\u6001\u4e0d\u4e00\u81f4\uff0c\u5219\u51cf\u5f31\u8fde\u63a5\u3002\u7ecf\u8fc7\u8fd9\u6837\u7684\u8bad\u7ec3\uff0c\u7f51\u7edc\u4fbf\u80fd\u518d\u6b21\u201c\u56de\u5fc6\u201d\u8d77\u8fd9\u4e2a\u6a21\u5f0f\uff0c\u53ea\u9700\u5728\u5176<\/span><\/span>\u80fd\u91cf\u666f\u89c2<\/span><\/span><\/strong>\u4e2d\u201c\u987a\u5761\u6ed1\u884c\u201d\u5230\u80fd\u91cf\u8c37\u5e95\u5373\u53ef\uff1b\u5b83\u4f1a\u81ea\u7136\u6f14\u5316\u81f3\u8fd9\u4e2a\u6a21\u5f0f\u6240\u5bf9\u5e94\u7684\u5e73\u8861\u6001\u3002<\/span><\/span><\/p>\n

\u6b63\u5982\u7406\u8bba\u7269\u7406\u5b66\u5bb6M\u00e9zard\u6240\u8bf4\uff1a<\/span><\/span><\/p>\n

\n

\u201c\u970d\u666e\u83f2\u5c14\u5fb7\u5efa\u7acb\u4e86\u8fd9\u4e2a\u8054\u7cfb\uff0c\u4ed6\u8bf4\uff1a\u2018\u770b\uff0c\u5982\u679c\u6211\u4eec\u80fd\u50cf\u8c03\u8282\u81ea\u65cb\u73bb\u7483\u90a3\u6837\u8c03\u8282\u8fd9\u4e9b\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8fde\u63a5\u5f3a\u5ea6\uff0c\u4e5f\u8bb8\u6211\u4eec\u5c31\u80fd\u628a\u5e73\u8861\u70b9\u53d8\u6210\u8bb0\u5fc6\u3002\u2019\u201d<\/span><\/span><\/p>\n<\/blockquote>\n

Hopfield\u7f51\u7edc\u53ef\u4ee5\u8bb0\u4f4f\u591a\u4e2a\u6a21\u5f0f\uff0c\u6bcf\u4e00\u4e2a\u6a21\u5f0f\u5bf9\u5e94\u4e00\u4e2a\u80fd\u91cf\u8c37\u3002\u7f51\u7edc\u4f1a\u843d\u5165\u54ea\u4e2a\u8c37\uff0c\u53d6\u51b3\u4e8e\u5b83\u4ece\u54ea\u4e00\u70b9\u5f00\u59cb\u6f14\u5316\u3002\u4f8b\u5982\uff0c\u5728\u4e00\u4e2a\u540c\u65f6\u8bb0\u6709\u201c\u732b\u201d\u548c\u201c\u98de\u8239\u201d\u56fe\u50cf\u7684\u7f51\u7edc\u4e2d\uff0c\u5982\u679c\u521d\u59cb\u72b6\u6001\u5927\u81f4\u50cf\u4e00\u53ea\u732b\uff0c\u90a3\u4e48\u5b83\u66f4\u53ef\u80fd\u6ed1\u5165\u201c\u732b\u8c37\u201d\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u521d\u59cb\u72b6\u6001\u542b\u6709\u98de\u8239\u7684\u51e0\u4f55\u7279\u5f81\uff0c\u7f51\u7edc\u4f1a\u503e\u5411\u4e8e\u8d70\u5411\u201c\u98de\u8239\u8c37\u201d\u3002\u8fd9\u4f7f\u5f97Hopfield\u7f51\u7edc\u6210\u4e3a<\/span><\/span>\u8054\u60f3\u8bb0\u5fc6<\/span><\/span><\/strong>\u7684\u4e00\u79cd\u6a21\u578b\uff1a\u7ed9\u51fa\u4e00\u4e2a\u4e0d\u5b8c\u6574\u6216\u88ab\u5e72\u6270\u7684\u8bb0\u5fc6\uff0c\u5b83\u4f1a\u52a8\u6001\u5730\u6062\u590d\u51fa\u5b8c\u6574\u6a21\u5f0f\u3002<\/span><\/span><\/p>\n

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\u8457\u540d\u79d1\u666e\u6742\u5fd7 <\/span><\/span>Physics Today <\/span><\/span><\/em>\u53d1\u8868\u6587\u7ae0\u68b3\u7406\u4e86\u8bfa\u5956\u5f97\u4e3b John Hopfield \u548c Geoffrey Hinton \u7684\u4e3b\u8981\u8d21\u732e\uff0c\u8ba4\u4e3a\u4ece\u795e\u7ecf\u7f51\u7edc\u7684\u5e95\u5c42\u539f\u7406\uff0c\u5230\u5927\u6a21\u578b\u7684\u6d8c\u73b0\u80fd\u529b\uff0c\u7269\u7406\u5b66\u5bf9\u4e8e\u7406\u89e3\u4eba\u5de5\u667a\u80fd\u7684\u5e95\u5c42\u673a\u5236\u5177\u6709\u91cd\u8981\u610f\u4e49\uff0c\u5c06\u7269\u7406\u5b66\u601d\u7ef4\u5e94\u7528\u5230\u73b0\u5b9e\u4e16\u754c\u7cfb\u7edf\u4e2d\uff0c\u6709\u671b\u4e3a\u4eba\u5de5\u667a\u80fd\u7684\u7a81\u7834\u63d0\u4f9b\u6d1e\u5bdf\u3002<\/span><\/span><\/p>\n

\u795e\u7ecf\u7f51\u7edc\u7684\u7269\u7406\u6839\u6e90\uff1a\u4ece\u81ea\u65cb\u73bb\u7483\u5230\u80fd\u91cf\u666f\u89c2\uff5c2024\u5e74\u8bfa\u8d1d\u5c14\u5956<\/a><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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


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1983\u81f31985\u5e74\u95f4\uff0c\u6770\u5f17\u91cc\u00b7\u8f9b\u987f\u548c\u540c\u4e8b\u5728\u970d\u666e\u83f2\u5c14\u5fb7\u7f51\u7edc\u7684\u57fa\u7840\u4e0a\u505a\u4e86\u8fdb\u4e00\u6b65\u62d3\u5c55\u3002\u4ed6\u4eec\u5f15\u5165\u4e86\u968f\u673a\u6027\uff0c\u6784\u5efa\u51fa\u4e00\u79cd\u65b0\u578b\u795e\u7ecf\u7f51\u7edc\u2014\u2014<\/span><\/span>\u73bb\u5c14\u5179\u66fc\u673a<\/span><\/span><\/strong>\uff08Boltzmann machine\uff09<\/span>\u3002\u8fd9\u79cd\u7f51\u7edc\u4e0d\u518d\u662f\u201c\u8bb0\u4f4f\u201d\u5177\u4f53\u6a21\u5f0f\uff0c\u800c\u662f\u5b66\u4e60\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u7edf\u8ba1\u89c4\u5f8b\uff0c\u5e76\u80fd\u751f\u6210\u7b26\u5408\u8fd9\u4e9b\u89c4\u5f8b\u7684\u65b0\u6570\u636e\u2014\u2014\u8fd9\u662f\u4e00\u79cd\u65e9\u671f\u7684\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u6a21\u578b\u3002\u5230\u4e8621\u4e16\u7eaa\u521d\uff0c\u8f9b\u987f\u4f7f\u7528\u7b80\u5316\u7248\u73bb\u5c14\u5179\u66fc\u673a\u89e3\u51b3\u4e86\u56f0\u6270\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u7684\u96be\u9898\uff0c\u4ece\u800c\u63a8\u52a8\u4e86<\/span><\/span>\u6df1\u5ea6\u5b66\u4e60<\/span><\/span><\/strong>\u7684\u53d1\u5c55\u3002<\/span><\/span><\/p>\n

\u52302012\u5e74\uff0c\u8f9b\u987f\u548c\u5176\u4ed6\u5148\u9a71\u5f00\u53d1\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5f00\u59cb\u5728\u5404\u9886\u57df\u53d6\u5f97\u7a81\u7834\u6027\u6210\u679c\uff0c\u4ee4\u4eba\u65e0\u6cd5\u5ffd\u89c6\u3002\u201c\u5f53\u65f6\u5927\u5bb6\u90fd\u610f\u8bc6\u5230\uff1a\u8fd9\u771f\u7684\u6548\u679c\u60ca\u4eba\uff0c\u6b63\u5728\u5f7b\u5e95\u6539\u53d8\u6574\u4e2a\u79d1\u6280\u884c\u4e1a\uff0c\u201dZdeborov\u00e1\u8bf4\u3002\u5982\u4eca\uff0c\u6211\u4eec\u6bcf\u5929\u4f7f\u7528\u7684\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u6a21\u578b\u2014\u2014\u5982\u5927\u578b\u8bed\u8a00\u6a21\u578b ChatGPT \u548c\u56fe\u50cf\u751f\u6210\u6a21\u578b Midjourney \u2014\u2014\u672c\u8d28\u4e0a\u90fd\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff0c\u5b83\u4eec\u7684\u6210\u529f\u53ef\u4ee5\u8ffd\u6eaf\u52301970\u5e74\u4ee3\u90a3\u4e9b\u4e0d\u7518\u5fc3\u8ba9\u201c\u81ea\u65cb\u73bb\u7483\u7684\u602a\u5f02\u884c\u4e3a\u201d\u88ab\u5ffd\u7565\u7684\u7269\u7406\u5b66\u5bb6\u3002<\/span><\/span><\/p>\n

\u7136\u800c\uff0cHopfield\u7f51\u7edc\u5e76\u4e0d\u4ec5\u4ec5\u662fAI\u53d1\u5c55\u7684\u201c\u65e7\u6865\u6881\u201d\u3002\u968f\u7740\u65b0\u7684\u60f3\u6cd5\u51fa\u73b0\uff0c\u8fd9\u79cd\u8001\u6a21\u578b\u6b63\u5728\u83b7\u5f97\u65b0\u751f\u3002<\/span><\/span><\/p>\n

2016\u5e74\uff0c\u970d\u666e\u83f2\u5c14\u5fb7\u4e0eIBM\u7814\u7a76\u9662\u7684\u5fb7\u7c73\u7279\u91cc\u00b7\u514b\u7f57\u6258\u592b<\/span>\uff08Dmitry Krotov\uff09<\/span>\u53d1\u73b0\uff0cHopfield\u7f51\u7edc\u4e0d\u662f\u4e00\u4e2a\u6a21\u578b\uff0c\u800c\u662f\u4e00\u5927\u7c7b\u6a21\u578b\u7684\u7edf\u79f0\uff0c\u5b83\u4eec\u5177\u6709\u4e0d\u540c\u7684\u8bb0\u5fc6\u5b58\u50a8\u80fd\u529b[3]\u30022020\u5e74\uff0c\u80e1\u8d1d\u7279\u00b7\u62c9\u59c6\u7ecd\u5c14<\/span>\uff08Hubert Ramsauer\uff09<\/span>\u7684\u7814\u7a76\u56e2\u961f\u8fdb\u4e00\u6b65\u6307\u51fa\uff0c\u5927\u591a\u6570\u73b0\u4ee3AI\u6a21\u578b\u91c7\u7528\u7684<\/span><\/span>Transformer<\/span><\/span><\/strong>\u67b6\u6784\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u90e8\u5206[4]\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u8fd9\u4e2aHopfield\u7f51\u7edc\u5bb6\u65cf\u7684\u4e00\u5458\u3002<\/span><\/span><\/p>\n

\u57fa\u4e8e\u8fd9\u4e00\u53d1\u73b0\uff0c\u514b\u7f57\u6258\u592b\u548c\u56e2\u961f\u8fd1\u671f\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u578b<\/span><\/span>\u6df1\u5ea6\u5b66\u4e60<\/span><\/span><\/strong>\u67b6\u6784\uff0c\u79f0\u4e3a<\/span><\/span>\u80fd\u91cf<\/span><\/span><\/strong>\u8f6c\u6362<\/span><\/span><\/strong>\u5668<\/span><\/span><\/strong>\uff08Energy Transformer\uff09<\/span>[5]\u3002\u4f20\u7edfAI\u67b6\u6784\u901a\u5e38\u4f9d\u8d56\u5927\u91cf\u8bd5\u9519\u624d\u80fd\u8bbe\u8ba1\u51fa\u6765\uff0c\u800c\u514b\u7f57\u6258\u592b\u8ba4\u4e3a\uff0c<\/span><\/span>\u80fd\u91cf<\/span><\/span><\/strong>\u8f6c\u6362<\/span><\/span><\/strong>\u5668<\/span><\/span><\/strong>\u53ef\u4ee5\u901a\u8fc7\u5bf9\u5176<\/span><\/span>\u80fd\u91cf\u666f\u89c2<\/span><\/span><\/strong>\u8fdb\u884c\u6709\u76ee\u7684\u7684\u8bbe\u8ba1\uff0c\u4ece\u800c\u66f4\u7cfb\u7edf\u6027\u5730\u6784\u5efaAI\u6a21\u578b\uff0c\u5c31\u50cf\u5728\u5efa\u6784\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u970d\u666e\u83f2\u5c14\u5fb7\u7f51\u7edc\u3002<\/span><\/span><\/p>\n

\u867d\u7136Hopfield\u7f51\u7edc\u6700\u521d\u662f\u4e3a\u201c\u8bb0\u5fc6\u201d\u800c\u8bbe\u8ba1\uff0c\u4f46\u5982\u4eca\u7814\u7a76\u8005\u6b63\u5728\u63a2\u7d22\u5176\u201c\u521b\u9020\u201d\u7684\u6f5c\u529b\u3002\u6bd4\u5982\uff0c\u56fe\u50cf\u751f\u6210\u5668 Midjourney \u80cc\u540e\u7684<\/span><\/span>\u6269\u6563\u6a21\u578b\uff08diffusion model\uff09<\/span><\/span><\/strong>\u7075\u611f\u5c31\u6765\u6e90\u4e8e\u7269\u7406\u4e2d\u7684\u6269\u6563\u8fc7\u7a0b\u3002\u5728\u8bad\u7ec3\u65f6\uff0c\u7814\u7a76\u4eba\u5458\u4f1a\u5411\u56fe\u50cf\u6570\u636e<\/span>\uff08\u6bd4\u5982\u732b\u7684\u56fe\u7247\uff09<\/span>\u4e2d\u6dfb\u52a0\u566a\u58f0\uff0c\u518d\u8bad\u7ec3\u6a21\u578b\u628a\u566a\u58f0\u53bb\u9664\u3002\u8fd9\u548cHopfield\u7f51\u7edc\u7684\u529f\u80fd\u975e\u5e38\u76f8\u4f3c\u2014\u2014\u4e0d\u540c\u7684\u662f\uff0c<\/span><\/span>\u6269\u6563\u6a21\u578b<\/span><\/span><\/strong>\u4e0d\u662f\u56de\u5230\u540c\u4e00\u5f20\u732b\u56fe\uff0c\u800c\u662f\u4ece\u4e00\u4e2a\u5e26\u566a\u7684\u968f\u673a\u521d\u59cb\u72b6\u6001\u4e2d\u6d88\u9664\u201c\u975e\u732b\u201d\u7279\u5f81\uff0c\u4ece\u800c\u751f\u6210\u4e00\u53ea\u65b0\u732b\u3002<\/span><\/span><\/p>\n

Krotov \u53ca\u5176\u540c\u4e8b<\/span>\uff08\u5305\u62ec Benjamin Hoover\u3001Yuchen Liang \u548c Bao Pham\uff09<\/span>\u6307\u51fa\uff0c<\/span><\/span>\u6269\u6563\u6a21\u578b\u5b9e\u9645\u4e0a\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u4e00\u79cd\u7279\u6b8a\u7c7b\u578b\u7684\u73b0\u4ee3Hopfield\u7f51\u7edc<\/span><\/span><\/strong>[6]\u3002\u8fd9\u79cd\u7406\u89e3\u65b9\u5f0f\u8fd8\u80fd\u7528\u4e8e<\/span><\/span>\u9884\u6d4b\u8fd9\u7c7b\u7f51\u7edc\u7684\u67d0\u4e9b\u884c\u4e3a\u7279\u5f81<\/span><\/span><\/strong>\u3002\u4ed6\u4eec\u7684\u7814\u7a76\u8868\u660e\uff0c\u5411\u4e00\u4e2a\u73b0\u4ee3\u970d\u666e\u83f2\u5c14\u5fb7\u7f51\u7edc\u8f93\u5165\u8d8a\u6765\u8d8a\u591a\u7684\u6570\u636e\uff0c\u5e76\u4e0d\u4ec5\u4ec5\u662f\u8ba9\u5176\u8bb0\u5fc6\u80fd\u529b\u8fbe\u5230\u9971\u548c\u3002\u76f8\u53cd\uff0c\u6a21\u578b\u7684<\/span><\/span>\u80fd\u91cf\u666f\u89c2<\/span><\/span><\/strong>\u4f1a\u53d8\u5f97\u6781\u5176\u5d0e\u5c96\uff0c<\/span><\/span>\u6700\u7ec8\u66f4\u53ef\u80fd\u201c\u8bb0\u4f4f\u201d\u4e00\u4e2a\u865a\u6784\u7684\u8bb0\u5fc6\uff0c\u800c\u4e0d\u662f\u4e00\u4e2a\u771f\u5b9e\u7684\u8bb0\u5fc6<\/span><\/span><\/strong>\u2014\u2014\u6b64\u65f6\uff0c\u5b83\u5c31\u201c\u53d8\u6210\u201d\u4e86\u4e00\u4e2a<\/span><\/span>\u6269\u6563\u6a21\u578b<\/span><\/span><\/strong>[7]\u3002<\/span><\/span><\/p>\n

<\/section>\n

\u56fe6\uff1aDmitry Krotov\u662fIBM\u7814\u7a76\u9662\u7684\u4e00\u540d\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\uff0c\u4ed6\u8868\u660e\uff0c\u5f53\u524d\u4f7f\u7528\u7684\u4e00\u4e9b\u6700\u5148\u8fdb\u7684\u4eba\u5de5\u667a\u80fd\u6a21\u578b\u9075\u5faa\u7740\u4ece\u4e00\u5f00\u59cb\u5c31\u5e94\u7528\u4e8eHopfield\u7f51\u7edc\u7684\u76f8\u540c\u57fa\u672c\u539f\u7406\u3002<\/span><\/span><\/p>\n

\u5bf9\u4e8e\u7269\u7406\u5b66\u5bb6\u6765\u8bf4\uff0c\u8fd9\u79cd\u7531\u6570\u91cf\u7684\u7b80\u5355\u53d8\u5316<\/span>\uff08\u4f8b\u5982\u8bad\u7ec3\u6570\u636e\u7684\u589e\u52a0\uff09<\/span>\u5f15\u53d1\u8d28\u53d8\u7684\u73b0\u8c61\u5e76\u4e0d\u7a00\u5947\u3002\u6b63\u5982\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6\u83f2\u5229\u666e\u00b7\u5b89\u5fb7\u68ee\u5728 1972 \u5e74\u6240\u8bf4\u7684\u90a3\u6837\uff1a\u201c\u591a\u8005\u5f02\u4e5f<\/span>\uff08more is different\uff09<\/span>\u3002\u201d[8]\u5728\u96c6\u4f53\u7cfb\u7edf\u4e2d\uff0c\u4ec5\u4ec5\u662f\u6269\u5927\u7ec4\u6210\u90e8\u5206\u4e4b\u95f4\u7684\u7f51\u7edc\u89c4\u6a21\uff0c\u4e5f\u53ef\u80fd\u5e26\u6765\u51fa\u4eba\u610f\u6599\u7684\u65b0\u884c\u4e3a\u3002\u201c\u795e\u7ecf\u7f51\u7edc\u4e4b\u6240\u4ee5\u80fd\u8fd0\u4f5c\uff0c\u672c\u8eab\u5c31\u662f\u4e00\u79cd<\/span><\/span>\u6d8c\u73b0<\/span><\/span><\/strong>\u7279\u6027\u3002\u201dM\u00e9zard \u8bf4\u9053\u3002<\/span><\/span><\/p>\n

\u65e0\u8bba\u662f\u6df1\u5ea6\u5b66\u4e60\u67b6\u6784\uff0c\u8fd8\u662f\u4eba\u8111\u672c\u8eab\uff0c\u5176\u2018<\/span><\/span>\u6d8c\u73b0\u6027<\/span><\/span><\/strong>\u2019\u65e2\u4ee4\u4eba\u7740\u8ff7\uff0c\u4e5f\u5145\u6ee1\u8c1c\u56e2\u2014\u2014\u6211\u4eec\u5c1a\u672a\u62e5\u6709\u666e\u9002\u7684<\/span><\/span>\u6d8c\u73b0\u7406\u8bba<\/span><\/span><\/strong>\u3002\u4e5f\u8bb8\uff0c\u6b63\u662f\u7edf\u8ba1\u7269\u7406\u5b66\u2014\u2014\u8fd9\u4e00\u6700\u65e9\u7528\u4e8e\u7406\u89e3\u96c6\u4f53\u73b0\u8c61\u7684\u5de5\u5177\u2014\u2014\u4e0d\u4ec5\u80fd\u5e2e\u52a9\u6211\u4eec\u4f7f\u7528\u8fd9\u4e9b\u590d\u6742\u7684\u4eba\u5de5\u667a\u80fd\u7cfb\u7edf\uff0c\u4e5f\u5c06\u662f\u6211\u4eec\u7406\u89e3\u5b83\u4eec\u672c\u8d28\u7684\u5173\u952e\u3002<\/span><\/span><\/p>\n

\u53c2\u8003\u6587\u732e\uff1a<\/span><\/span><\/section>\n

[1] Hopfield, John. <\/span><\/span>Now What?<\/span><\/span><\/em> 2018.<\/span><\/span><\/p>\n

[2] Hopfield JJ. Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity. Proc Natl Acad Sci U S A. 1974 Oct;71(10):4135-9. doi: 10.1073\/pnas.71.10.4135. PMID: 4530290; PMCID: PMC434344.<\/span><\/span><\/p>\n

[3] Krotov, Dmitry, and John J. Hopfield. \u201cDense Associative Memory for Pattern Recognition.\u201d <\/span><\/span>ArXiv:1606.01164 [Cond-Mat, Q-Bio, Stat]<\/span><\/span><\/em>, 27 Sept. 2016, arxiv.org\/abs\/1606.01164.<\/span><\/span><\/p>\n

[4] Ramsauer, Hubert, et al. \u201cHopfield Networks Is All You Need.\u201d <\/span><\/span>ArXiv:2008.02217 [Cs, Stat]<\/span><\/span><\/em>, 28 Apr. 2021, arxiv.org\/abs\/2008.02217.<\/span><\/span><\/p>\n

[5] Hoover, Benjamin, et al. \u201cEnergy Transformer.\u201d <\/span><\/span>ArXiv.org<\/span><\/span><\/em>, 2023, arxiv.org\/abs\/2302.07253.<\/span><\/span><\/p>\n

[6]Hoover, Benjamin, et al.\u201cMemory in Plain Sight: Surveying the Uncanny Resemblances of Associative Memories and Diffusion Models.\u201d <\/span><\/span>ArXiv.org<\/span><\/span><\/em>, 2023, arxiv.org\/abs\/2309.16750. Accessed 20 May 2025.<\/span><\/span><\/p>\n

[7] Pham, Bao, et al. \u201cMemorization to Generalization: The Emergence of Diffusion Models from Associative Memory.\u201d <\/span><\/span>OpenReview<\/span><\/span><\/em>, 2024, openreview.net\/forum?id=zVMMaVy2BY. Accessed 20 May 2025.<\/span><\/span><\/p>\n

[8] Anderson, P. W. \u201cMore Is Different.\u201d <\/span><\/span>Science<\/span><\/span><\/em>, vol. 177, no. 4047, 4 Aug. 1972, pp. 393\u2013396, https:\/\/doi.org\/10.1126\/science.177.4047.393.<\/span><\/span><\/p>\n


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\u4e3a\u4ec0\u4e48\u795e\u7ecf\u7f51\u7edc\u80fd\u591f\u5b66\u4e60\uff1f\u4e3a\u4ec0\u4e48\u751f\u547d\u7cfb\u7edf\u80fd\u591f\u5b9e\u73b0\u81ea\u7ec4\u7ec7\u548c\u8fdb\u5316\uff1f\u4fe1\u606f\u5982\u4f55\u6210\u4e3a\u751f\u547d\u8fc7\u7a0b\u7684\u91cd\u8981\u7ec4\u6210\u90e8\u5206\uff1f\u4fe1\u606f\u548c\u80fd\u91cf\u4e4b\u95f4\u6709\u600e\u6837\u7684\u6df1\u523b\u5173\u7cfb\uff1f\u4ece\u5b8f\u89c2\u8fdb\u5165\u5fae\u89c2\uff0c\u70ed\u529b\u5b66\u5b9a\u5f8b\u4ecd\u7136\u4fdd\u6301\u4e0d\u53d8\u5417\uff1f\u4ece\u76f8\u53d8\u9884\u6d4b\u5230\u91cf\u5b50\u591a\u4f53\u7cfb\u7edf\u6a21\u62df\uff0c\u673a\u5668\u5b66\u4e60\u5982\u4f55\u6539\u53d8\u7edf\u8ba1\u7269\u7406\u7814\u7a76\uff1f\u4ece\u795e\u7ecf\u7f51\u7edc\u7684\u80fd\u91cf\u666f\u89c2\u5230\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u76f8\u53d8\u73b0\u8c61\uff0c\u7edf\u8ba1\u7269\u7406\u5b66\u4e3a\u7406\u89e3\u548c\u6539\u8fdb\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u63d0\u4f9b\u600e\u6837\u7684\u542f\u53d1\uff1f<\/span>\u300c\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u300d\u8bfb\u4e66\u4f1a<\/span><\/a>\u5c06\u5e26\u9886\u5927\u5bb6\u4e00\u8d77\u63a2\u7d22\u8fd9\u4e9b\u6709\u8da3\u800c\u6df1\u523b\u7684\u95ee\u9898\u3002<\/span><\/span><\/p>\n

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<\/span><\/h1>\n
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1. \u751f\u6210\u6269\u6563\u6a21\u578b\u7684\u7edf\u8ba1\u70ed\u529b\u5b66\uff1a\u76f8\u53d8\u3001\u5bf9\u79f0\u6027\u7834\u7f3a\u4e0e\u4e34\u754c\u4e0d\u7a33\u5b9a\u6027<\/span><\/a><\/span><\/strong>
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2. \u5f53\u6269\u6563\u6a21\u578b\u9047\u89c1\u7269\u7406\u95ed\u73af\uff1aCL-DiffPhyCon\u7a81\u7834\u751f\u6210\u6548\u7387\u74f6\u9888<\/span><\/a><\/span>
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3. \u8bfa\u5956\u5f97\u4e3b Parisi \u6700\u65b0 Nature \u901f\u9012\uff1a\u4e8c\u7ef4\u4f0a\u8f9b\u81ea\u65cb\u73bb\u7483\u7684\u91cf\u5b50\u76f8\u53d8<\/span><\/a><\/span>
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4. <\/span><\/strong><\/span>\u6e38\u620f\u5316\u79d1\u7814\u2014\u2014\u8ba9\u6211\u4eec\u7a81\u7834\u5185\u5377\u3001\u5171\u7814\u6d8c\u73b0<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
<\/strong>5. <\/span><\/strong>\u63a2\u7d22\u8005\u8ba1\u5212 | \u96c6\u667a\u4ff1\u4e50\u90e82025\u5185\u5bb9\u56e2\u961f\u62db\u52df\uff08\u5168\u804c&\u517c\u804c\uff09<\/a><\/span><\/strong><\/span><\/section>\n

6. \u52a0\u5165\u96c6\u667a\uff0c\u73a9\u8f6c\u590d\u6742\uff0c\u5171\u521b\u6591\u56fe\uff01\u96c6\u667a\u4ff1\u4e50\u90e8\u7ebf\u4e0b\u5fd7\u613f\u8005\u62db\u52df<\/span><\/a><\/span><\/strong>
<\/span><\/strong><\/span><\/p>\n


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u4eba\u5de5\u667a\u80fd\u6b63\u4ee5\u524d\u6240\u672a\u6709\u7684\u901f\u5ea6\u6539\u53d8\u4e16\u754c\uff0c\u4f46\u5176\u80cc\u540e\u7684\u6838\u5fc3\u673a\u5236\uff0c\u8fdc\u4e0d\u6b62\u4e8e\u590d\u6742\u7684\u7b97\u6cd5\u548c\u7b97\u529b\u5806\u53e0\u3002\u672c\u6587\u4ece\u795e\u7ecf\u79d1\u5b66\u5148\u9a71\u7ea6\u7ff0\u00b7\u970d\u666e\u83f2\u5c14\u5fb7\uff08John Hopfield\uff09\u7684\u7814\u7a76\u51fa\u53d1\uff0c\u8ffd\u6eaf\u6df1\u5ea6\u5b66\u4e60\u7684\u53d1\u5c55\u8109\u7edc\uff0c\u63ed\u793a\u4e00\u4e2a\u4ee4\u4eba\u610f\u60f3\u4e0d\u5230\u7684\u4e8b\u5b9e\uff1a\u8bb8\u591a\u73b0\u4ee3AI\u6a21\u578b\u7684\u7406\u8bba\u57fa\u7840\uff0c\u6e90\u81ea\u4e0a\u4e16\u7eaa\u7269\u7406\u5b66\u5bb6\u7814\u7a76\u78c1\u6027\u6750\u6599\u65f6\u63d0\u51fa\u7684\u201c\u81ea\u65cb\u73bb\u7483\u201d\u6a21…<\/p>\n","protected":false},"author":0,"featured_media":59948,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/59960"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=59960"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/59960\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/59948"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=59960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=59960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=59960"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=59960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}