{"id":53975,"date":"2024-12-04T18:38:01","date_gmt":"2024-12-04T10:38:01","guid":{"rendered":"https:\/\/swarma.org\/?p=53975"},"modified":"2024-12-04T18:38:01","modified_gmt":"2024-12-04T10:38:01","slug":"%e7%89%a9%e7%90%86%e5%ad%a6%e9%81%87%e8%a7%81%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%ef%bc%9a%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%e7%9a%84%e4%b8%8b%e4%b8%80%e4%b8%aa%e7%aa%81%e7%a0%b4%e5%8f%af%e8%83%bd","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=53975","title":{"rendered":"\u7269\u7406\u5b66\u9047\u89c1\u673a\u5668\u5b66\u4e60\uff1a\u6df1\u5ea6\u5b66\u4e60\u7684\u4e0b\u4e00\u4e2a\u7a81\u7834\u53ef\u80fd\u6765\u81ea\u7edf\u8ba1\u7269\u7406\u5b66"},"content":{"rendered":"
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2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u201c\u901a\u8fc7\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u673a\u5668\u5b66\u4e60\u7684\u57fa\u7840\u6027\u53d1\u73b0\u548c\u53d1\u660e\u201d\uff0c\u5f15\u53d1\u4eba\u4eec\u5bf9\u7edf\u8ba1\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u4e4b\u95f4\u6df1\u523b\u8054\u7cfb\u7684\u5173\u6ce8\u548c\u5e7f\u6cdb\u8ba8\u8bba\u3002\u673a\u5668\u5b66\u4e60\u80fd\u4e3a\u7269\u7406\u5b66\u505a\u4e9b\u4ec0\u4e48\uff1f\u7269\u7406\u5b66\u53c8\u80fd\u4e3a\u673a\u5668\u5b66\u4e60\u505a\u4e9b\u4ec0\u4e48\uff1f\u8fd1\u671f PNAS<\/em> \u6742\u5fd7\u53d1\u8868\u300c\u7269\u7406\u5b66\u9047\u89c1\u673a\u5668\u5b66\u4e60\u300d\uff08Physics Meets Machine Learning\uff09\u4e3b\u9898\u7279\u520a\uff0c\u5c55\u73b0\u4e86\u7269\u7406\u5b66\u4e0e\u673a\u5668\u5b66\u4e60\u4e24\u4e2a\u9886\u57df\u4e4b\u95f4\u7684\u6d3b\u8dc3\u5bf9\u8bdd\uff0c\u8bba\u6587\u4e3b\u9898\u6db5\u76d6\u751f\u7269\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u3001\u52a8\u6001\u5b66\u4e60\u7cfb\u7edf\u3001\u751f\u6210\u6a21\u578b\u3001\u8868\u5f81\u4e0e\u6cdb\u5316\u3001\u795e\u7ecf\u6807\u5ea6\u5f8b\u7b49\u5404\u4e2a\u65b9\u5411\u3002\u672c\u6587\u7ffb\u8bd1\u81ea\u7f8e\u56fd\u4e1c\u5317\u5927\u5b66\u7269\u7406\u7cfb\u4e0e\u751f\u7269\u5de5\u7a0b\u7cfb\u6770\u51fa\u6559\u6388 Herbert Levine \u4e0e IBM \u6c83\u68ee\u7814\u7a76\u4e2d\u5fc3\u7814\u7a76\u5458\u6d82\u8c6b\u6d77<\/span><\/strong><\/span><\/strong>\u64b0\u5199\u7684\u7279\u520a\u5f15\u8a00\uff0c\u6587\u7ae0\u8ba4\u4e3a\uff0c\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u53d7\u76ca\u4e8e\u7edf\u8ba1\u7269\u7406\u5b66\u548c\u795e\u7ecf\u79d1\u5b66\u8fd9\u4e24\u4e2a\u81ea\u7136\u79d1\u5b66\u5b66\u79d1\uff0c\u6df1\u5ea6\u5b66\u4e60\u7684\u4e0b\u4e00\u4e2a\u7a81\u7834\u53ef\u80fd\u6765\u81ea\u57fa\u4e8e\u7edf\u8ba1\u7269\u7406\u5b66\u6982\u5ff5\u548c\u65b9\u6cd5\u5efa\u7acb\u7684\u575a\u5b9e\u7406\u8bba\u57fa\u7840\uff0c\u800c\u63a2\u7d22\u771f\u5b9e\u5927\u8111\u8ba1\u7b97\u4e0e\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u53ef\u80fd\u4f1a\u4ea7\u751f\u65b0\u7684\u8111\u542f\u53d1\u7b97\u6cd5\u3002<\/span><\/span><\/strong><\/span><\/strong><\/p>\n


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Herbert Levine\uff0cYuhai Tu\uff08\u6d82\u8c6b\u6d77\uff09<\/span> <\/span>| \u4f5c\u8005<\/span><\/p>\n

\u5434\u6668\u9633<\/span> <\/span>| \u8bd1\u8005<\/span><\/span><\/p>\n

\u6881\u91d1<\/span> <\/span>| \u5ba1\u6821<\/span><\/span><\/p>\n


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Machine learning meets physics: A two-way street<\/span><\/section>\n
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https:\/\/www.pnas.org\/doi\/10.1073\/pnas.2403580121<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

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1. \u673a\u5668\u5b66\u4e60\u4e0e\u86cb\u767d\u8d28\u6298\u53e0\u95ee\u9898<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u4ece\u86cb\u767d\u8d28\u6298\u53e0\u5e94\u7528\u7684\u5386\u53f2\u4e2d\u53ef\u4ee5\u83b7\u5f97\u4e00\u4e9b\u6709\u8da3\u7684\u542f\u793a\u3002\u6211\u548c Terry Sejnowski \u4e24\u4eba\u572820\u4e16\u7eaa80\u5e74\u4ee3\u672b\u90fd\u5728\u52a0\u5dde\u5927\u5b66\u5723\u5730\u4e9a\u54e5\u5206\u6821<\/span>\uff08UCSD\uff09<\/span>\uff0c\u5f53\u65f6\u4ed6\u505a\u4e86\u4e00\u4e2a\u8bba\u6587\u62a5\u544a\uff0c\u662f\u5173\u4e8e\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u7814\u7a76\u7403\u72b6\u86cb\u767d\u7684\u4e8c\u7ea7\u7ed3\u6784[7]\u3002\u4ed6\u7684\u7b97\u6cd5\u6027\u80fd\u76f8\u5f53\u5e73\u5eb8\uff0c\u6211\u4eec\u4e2d\u7684\u8bb8\u591a\u4eba\u5728\u79bb\u5f00\u90a3\u6b21\u8bb2\u5ea7\u65f6\u90fd\u5728\u60f3\uff0c\u4e3a\u4ec0\u4e48\u6709\u4eba\u4f1a\u653e\u5f03\u4f20\u7edf\u7684\u751f\u7269\u5316\u5b66\u65b9\u6cd5\uff0c\u800c\u9752\u7750\u6211\u4eec\u73b0\u5728\u79f0\u4e4b\u4e3a\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\u3002\u90a3\u4e48\uff0c\u4ece\u90a3\u65f6\u52302018\u5e74\u8fd930\u5e74\u95f4\u53d1\u751f\u4e86\u4ec0\u4e48\uff1f\u4f3c\u4e4e\u6709\u56db\u4e2a\u56e0\u7d20\u5728\u8d77\u4f5c\u7528\u3002<\/span><\/section>\n

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\u9996\u5148\uff0c\u7528\u4e8e\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u8ba1\u7b97\u80fd\u529b\u4ee5\u51e0\u4e4e\u96be\u4ee5\u60f3\u8c61\u7684\u901f\u5ea6\u589e\u957f<\/strong>\u3002\u4f8b\u5982\uff0c1985\u5e74\u5de6\u53f3\u7684 Cray 2 \u8d85\u7ea7\u8ba1\u7b97\u673a\u4f5c\u4e3a\u90a3\u4e2a\u65f6\u4ee3\u6700\u5feb\u7684\u8ba1\u7b97\u673a\uff0c\u8fd0\u7b97\u901f\u5ea6\u8fbe\u52301.9\u5343\u5146\u6d6e\u70b9\u8fd0\u7b97\u6bcf\u79d2<\/span>\uff08gigaflops\uff09<\/span>\uff1b\u800c\u73b0\u5728\u8fd9\u5927\u7ea6\u76f8\u5f53\u4e8e iPhone 4 \u7684\u8ba1\u7b97\u80fd\u529b\u3002\u5f53\u4e0b\u6700\u5148\u8fdb\u7684\u8d85\u7ea7\u8ba1\u7b97\u673a\u8fd0\u7b97\u80fd\u529b\u5df2\u8fbe\u5230109<\/sup>\u5343\u5146\u6d6e\u70b9\u8fd0\u7b97\u6bcf\u79d2\u3002\u5728\u5f53\u65f6\u5b8c\u5168\u65e0\u6cd5\u5b9e\u73b0\u7684\u8ba1\u7b97\uff0c\u73b0\u5728\u5df2\u53d8\u5f97\u8f7b\u800c\u6613\u4e3e\u3002\u5173\u4e8e\u5185\u5b58\u5bb9\u91cf\u4e5f\u53ef\u4ee5\u4e3e\u51fa\u7c7b\u4f3c\u7684\u6570\u636e\u3002\u53ef\u4ee5\u8bf4\uff0c\u5982\u679c\u76f8\u5173\u7814\u7a76\u4eba\u5458\u672a\u80fd\u83b7\u5f97\u8fd9\u4e9b\u8ba1\u7b97\u80fd\u529b\uff0c\u90a3\u4e48\u7814\u7a76\u8fdb\u5c55\u5c06\u4f1a\u53d7\u5230\u6781\u5927\u963b\u788d\u3002<\/span><\/section>\n

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\u786c\u4ef6\u6539\u8fdb\u662f\u5fc5\u8981\u7684\uff0c\u4f46\u8fd8\u4e0d\u591f\u3002\u7b2c\u4e8c\u4e2a\u56e0\u7d20\u662f\u5404\u79cd\u673a\u5668\u5b66\u4e60\u6280\u672f\u7684\u53d1\u660e<\/strong>\uff0c\u4ece\u800c<\/strong>\u80fd\u591f\u4ece\u73b0\u6709\u6570\u636e\u4e2d\u5b66\u4e60\u9884\u6d4b\u6a21\u578b<\/strong>\u3002\u7531\u4e8e\u672a\u80fd\u8ba4\u8bc6\u5230 Minsky \u548c Papert \u5728\u611f\u77e5\u673a\u7814\u7a76\u4e2d\u63d0\u51fa\u7684\u8457\u540d\u7684\u201c\u5426\u5b9a\u6027\u201d<\/span>\uff08no-go\uff09<\/span>\u7ed3\u8bba[8]\u7684\u4e25\u91cd\u5c40\u9650\u6027\uff0c\u795e\u7ecf\u7f51\u7edc\u9886\u57df\u572820\u4e16\u7eaa80\u5e74\u4ee3\u4ecd\u5904\u4e8e\u4f4e\u8ff7\u671f\u3002\u90a3\u65f6\uff0c\u4eba\u4eec\u624d\u521a\u521a\u610f\u8bc6\u5230\u5e26\u6709\u9690\u85cf\u5c42\u7684\u201c\u6df1\u5ea6\u7f51\u7edc\u201d\u53ef\u80fd\u5f00\u521b\u65b0\u5c40\u9762\uff0c\u8fd9\u4e00\u8fdb\u5c55\u59cb\u4e8e\u73bb\u5c14\u5179\u66fc\u673a<\/span>\uff08Boltzmann machine\uff09<\/span>[9]\u7b49\u7ed3\u6784\u7684\u51fa\u73b0\uff0c\u5e76\u5728\u968f\u540e\u53d1\u5c55\u51fa\u4e86\u53cd\u5411\u4f20\u64ad\u8bad\u7ec3\u7b97\u6cd5[10]\u3002\u5982\u4eca\uff0ctransformer \u67b6\u6784[11]\u3001\u81ea\u7f16\u7801\u5668[12]\u548c\u5bf9\u6297\u7f51\u7edc[13]\u7b49\u7406\u5ff5\u5df2\u7ecf\u5f7b\u5e95\u6539\u53d8\u4e86\u4eba\u4eec\u5bf9\u673a\u5668\u5b66\u4e60\u8fc7\u7a0b\u7684\u7406\u89e3\u3002\u5c31 AlphaFold \u7684\u4f8b\u5b50\u800c\u8a00\uff0ctransformer \u7406\u5ff5\u4f3c\u4e4e\u662f\u7edd\u5bf9\u5fc5\u8981\u7684\u3002Martin \u7b49\u4eba[15]\u7684\u8bba\u6587\u8ba8\u8bba\u4e86 transformer \u5982\u4f55\u4e0e\u66f4\u4e00\u822c\u7684\u673a\u5668\u5b66\u4e60\u6982\u5ff5\u76f8\u7ed3\u5408\uff0c\u8fd9\u4e9b\u6982\u5ff5\u53ef\u4ee5\u8ffd\u6eaf\u5230 Hopfield \u8054\u60f3\u8bb0\u5fc6\u6a21\u578b[14]\u3002<\/span><\/section>\n

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\u4e0b\u4e00\u4e2a\u56e0\u7d20\u662f\u8bad\u7ec3\u6240\u9700\u7684\u6570\u636e\u53ef\u7528\u6027<\/strong>\u3002\u86cb\u767d\u8d28\u6570\u636e\u5e93<\/span>\uff08PDB\uff09<\/span>\u6210\u7acb\u4e8e1971\u5e74\uff0c\u7528\u4e8e\u5b58\u50a8\u86cb\u767d\u8d28\u7ed3\u6784\u4fe1\u606f [16]\u3002\u540c\u6837\uff0c\u53ef\u4f9b\u6240\u6709\u7814\u7a76\u4eba\u5458\u4f7f\u7528\u7684\u7ed3\u6784\u6570\u636e\u91cf\u51fa\u73b0\u4e86\u7206\u70b8\u6027\u589e\u957f\u3002\u7ed3\u6784\u6570\u91cf\u5927\u7ea6\u6bcf6\u52308\u5e74\u7ffb\u4e00\u756a\uff1b\u52302024\u5e74\u521d\uff0cPDB \u6570\u636e\u5e93\u5df2\u8d85\u8fc720\u4e07\u4e2a\u7ed3\u6784\uff0c\u76f8\u6bd4\u4e4b\u4e0b1990\u5e74\u4ec5\u6709\u7ea61000\u4e2a\u7ed3\u6784\uff1b\u53c2\u89c1\u56fe1\u3002\u4f46\u8fd9\u5e76\u4e0d\u662f\u552f\u4e00\u91cd\u8981\u7684\u6570\u636e\u6765\u6e90\u3002\u6b63\u5982 Martin \u7b49\u4eba [15] \u7684\u6587\u7ae0\u6240\u8ff0\uff0c\u86cb\u767d\u8d28\u6298\u53e0\u9886\u57df\u7684\u8bb8\u591a\u8fdb\u5c55\u6e90\u4e8e\u8fd9\u6837\u4e00\u4e2a\u8ba4\u8bc6\uff1a\u901a\u8fc7\u6bd4\u8f83\u4e0d\u540c\u751f\u7269\u4f53\u4e2d\u540c\u4e00\u86cb\u767d\u8d28\u7684\u5e8f\u5217\uff0c\u53ef\u4ee5\u83b7\u5f97\u6709\u5173\u63a5\u89e6\u56fe\u8c31<\/span>\uff08contact map\uff09<\/span>\u7684\u91cd\u8981\u4fe1\u606f\u3002\u63a5\u89e6\u56fe\u8c31\u662f\u4e00\u79cd\u77e9\u9635\u8868\u793a\uff0c\u663e\u793a\u4e86\u6cbf\u4e3b\u94fe\u76f8\u8ddd\u8f83\u8fdc\u7684\u6b8b\u57fa\u5728\u6298\u53e0\u7ed3\u6784\u4e2d\u53ef\u80fd\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u9760\u8fd1\u7684\u6982\u7387\u3002\u8fd9\u91cc\u7684\u6838\u5fc3\u601d\u60f3\u6e90\u4e8e\u76f4\u63a5\u8026\u5408\u5206\u6790<\/span>\uff08direct coupling analysis\uff0cDCA\uff09<\/span>[17, 18] \u7b49\u7b97\u6cd5\u7684\u7814\u7a76\uff0c\u5373\uff0c\u4ece\u4e00\u4e2a\u7269\u79cd\u5230\u53e6\u4e00\u4e2a\u7269\u79cd\u7684\u6f14\u5316\u8fc7\u7a0b\u4e2d\uff0c\u4e00\u5bf9\u63a5\u89e6\u7684\u6b8b\u57fa\u5fc5\u987b\u5171\u540c\u8fdb\u5316\u4ee5\u7ef4\u6301\u8fd9\u79cd\u63a5\u89e6\u3002\u56e0\u6b64\uff0c\u5bf9\u76f8\u5173\u8fdb\u5316\u7684\u89c2\u5bdf\u53ef\u4ee5\u5e2e\u52a9\u8bc6\u522b\u8fd9\u4e9b\u63a5\u89e6\u3002\u5f97\u76ca\u4e8e\u6d4b\u5e8f\u9886\u57df\u4ee4\u4eba\u60ca\u53f9\u7684\u6280\u672f\u8fdb\u6b65\uff0c\u8fc7\u53bb\u5341\u5e74\u4e2d\u6bd4\u8f83\u57fa\u56e0\u7ec4\u5b66\u6570\u636e\u5448\u73b0\u51fa\u6d77\u5578\u822c\u7684\u589e\u957f\u3002<\/span><\/section>\n

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\u56fe1. 2019\u5e74\u86cb\u767d\u8d28\u6570\u636e\u5e93\uff08PDB\uff09\u6838\u5fc3\u6863\u6848\u5e93\u589e\u957f\u62a5\u544a\u3002\u6bcf\u4e2a\u67f1\u72b6\u56fe\u7684\u603b\u9ad8\u5ea6\u8868\u793a\u7d2f\u8ba1\u53d1\u5e03\u7684\u7ed3\u6784\u603b\u6570\uff0c\u67f1\u72b6\u56fe\u4e2d\u4e0d\u540c\u989c\u8272\u4ee3\u8868\u4e0d\u540c\u7684\u5b9e\u9a8c\u6280\u672f\uff08MX\uff08\u5927\u5206\u5b50\u6676\u4f53\u5b66\uff09-\u7eff\u8272\u30013DEM\uff08\u4e09\u7ef4\u7535\u5b50\u663e\u5fae\u955c\uff09-\u9ec4\u8272\u3001NMR\uff08\u6838\u78c1\u5171\u632f\uff09-\u84dd\u8272\uff09\u3002\u5f15\u81ea\u53c2\u8003\u6587\u732e[16]\u3002<\/span><\/p>\n


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\u6700\u540e\u4e00\u4e2a\uff0c\u53ef\u80fd\u4e5f\u662f\u6700\u6709\u8da3\u7684\u56e0\u7d20\uff0c\u8fd9\u4e2a\u95ee\u9898\u5bf9\u673a\u5668\u5b66\u4e60\u7814\u7a76\u7684\u672a\u6765\u53d1\u5c55\u6709\u7740\u91cd\u8981\u5f71\u54cd\u3002\u95ee\u9898\u662f\uff1a\u8fc7\u53bb\u4e09\u5341\u5e74\u4f7f\u7528\u4f20\u7edf\u6280\u672f\u5bf9\u86cb\u767d\u8d28\u6298\u53e0\u8fdb\u884c\u7684\u5927\u91cf\u7406\u8bba\u7814\u7a76\uff0c\u5230\u5e95\u6709\u591a\u91cd\u8981\uff1f\u66f4\u7b80\u5355\u5730\u8bf4\uff0c\u5982\u679c\u5728\u4e00\u4e2a\u5e73\u884c\u5b87\u5b99\u4e2d\uff0c\u5728 AlphaFold \u65f6\u4ee3\u4e4b\u524d\u6ca1\u6709\u4eba\u5173\u6ce8\u86cb\u767d\u8d28\u6298\u53e0\u8ba1\u7b97\uff0c\u6211\u4eec\u73b0\u5728\u7684\u7814\u7a76\u8fdb\u5c55\u4f1a\u843d\u540e\u591a\u5c11\uff1f\u5f53\u7136\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e0d\u53ef\u80fd\u6709\u786e\u5207\u7b54\u6848\uff0c\u4f46\u6211\u4eec\u8ba4\u4e3a\u7406\u8bba\u7814\u7a76\u786e\u5b9e\u662f\u5f53\u524d\u8fdb\u5c55\u5f97\u4ee5\u5b9e\u73b0\u7684\u91cd\u8981\u63a8\u624b<\/strong>\u3002\u6211\u4eec\u5df2\u7ecf\u63d0\u5230\uff0c\u4f7f\u7528\u6bd4\u8f83\u57fa\u56e0\u7ec4\u5b66\u6570\u636e\u7684\u60f3\u6cd5\u5c31\u6e90\u4e8e\u7406\u8bba\u7814\u7a76\u7fa4\u4f53\u3002\u4e00\u4e2a\u540c\u6837\u91cd\u8981\u7684\u60f3\u6cd5\u662f\u5c06\u7ed3\u6784\u6570\u636e\u7f16\u7801\u5230\u6807\u51c6\u751f\u7269\u7269\u7406\u6a21\u578b\u4e2d[19]\uff0c\u8fd9\u79cd\u65b9\u6cd5\u65e2\u5229\u7528\u4e86\u7269\u7406\u6d1e\u89c1\u53c8\u8fd0\u7528\u4e86\u6d4b\u91cf\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u7531\u6c28\u57fa\u9178\u5e8f\u5217\u9884\u6d4b\u86cb\u767d\u8d28\u7ed3\u6784\u4f5c\u4e3a\u86cb\u767d\u8d28\u6298\u53e0\u5728\u5de5\u7a0b\u5e94\u7528\u65b9\u9762\u7684\u8fdb\u6b65\uff0c\u4e0d\u5e94\u4e0e\u6700\u5c0f\u963b\u632b<\/span>\uff08minimal frustration\uff09<\/span> [20]\u3001\u6298\u53e0\u6f0f\u6597<\/span>\uff08folding funnel\uff09<\/span>[21] \u7b49\u6982\u5ff5\u6240\u5e26\u6765\u7684\u86cb\u767d\u8d28\u6298\u53e0\u7406\u8bba\u8fdb\u6b65\u6df7\u4e3a\u4e00\u8c08\u3002\u8fd9\u4e9b\u6982\u5ff5\u7684\u91cd\u8981\u6027\u662f\u5168\u5c40\u7684\uff0c\u5728\u5176\u4ed6\u7684\u80cc\u666f\u4e0b\u4e5f\u6709\u5e94\u7528\uff0c\u5305\u62ec\u5206\u5b50\u6c34\u5e73 [22, 23] \u548c\u7ec6\u80de\u6c34\u5e73 [24]\u3002\u800c\u4e14\uff0c\u5373\u4f7f\u4ece\u7eaf\u5b9e\u7528\u7684\u89d2\u5ea6\u6765\u770b\u5e76\u975e\u5fc5\u9700\uff0c\u62e5\u6709\u201c\u4eba\u7c7b\u53ef\u7406\u89e3\u7684\u201d\u65b9\u6cd5\u6709\u65f6\u4e5f\u662f\u5f88\u597d\u7684\u3002<\/span><\/section>\n

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\u8fd9\u4e00\u7814\u7a76\u65b9\u5411\u5f53\u524d\u9762\u4e34\u54ea\u4e9b\u6311\u6218\uff1f\u9996\u5148\u662f\u90a3\u4e9b\u4e0d\u5b58\u5728\u552f\u4e00\u7ed3\u6784\u7684\u7cfb\u7edf\uff0c\u5728\u8fd9\u4e9b\u7cfb\u7edf\u4e2d\uff0c\u6298\u53e0\u95ee\u9898\u8f6c\u5316\u4e3a\u5bfb\u627e\u4e00\u4e2a\u7ed3\u6784\u96c6\u5408\u4ee5\u53ca\u4e0e\u4e4b\u76f8\u4f34\u968f\u7684\u7ed3\u6784\u4e4b\u95f4\u8f6c\u6362\u7684\u52a8\u529b\u5b66\u3002\u8fd9\u7c7b\u7cfb\u7edf\u5305\u62ec\u5185\u5728\u65e0\u5e8f\u86cb\u767d\u8d28<\/span>\uff08intrinsically disordered proteins\uff09<\/span> [25] \u4ee5\u53ca\u57fa\u56e0\u7ec4\u6298\u53e0 [26, 27]\u3002\u53e6\u4e00\u4e2a\u65b9\u5411\u6d89\u53ca\u751f\u7269\u5206\u5b50\u76f8\u4e92\u4f5c\u7528\u7684\u7814\u7a76\uff0c\u5176\u4e2d Alpha-Multimer \u7684\u7eaf\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u5728\u8bb8\u591a\u5e94\u7528\u4e2d\u5c1a\u672a\u88ab\u8bc1\u660e\u8db3\u591f\u53ef\u9760\u3002Lupo \u7b49\u4eba\u7684\u8bba\u6587 [28] \u8bd5\u56fe\u901a\u8fc7\u5e94\u7528\u8bed\u8a00\u6a21\u578b\u6765\u66f4\u597d\u5730\u5bf9\u9f50\u86cb\u767d\u8d28-\u86cb\u767d\u8d28\u754c\u9762\u5904\u76f8\u5173\u7684\u76f8\u4e92\u4f5c\u7528\u5e8f\u5217\uff0c\u4ee5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u6b64\u5916\u8fd8\u5e94\u5f53\u6ce8\u610f\u5230T\u7ec6\u80de\u53d7\u4f53\u5bf9\u6297\u539f\u7684\u8bc6\u522b\u95ee\u9898\uff0c\u8fd9\u79cd\u6297\u539f\u8bc6\u522b\u662f\u9002\u5e94\u6027\u514d\u75ab\u7cfb\u7edf\u7684\u5173\u952e\u7ec4\u6210\u90e8\u5206\u3002\u5728\u8fd9\u65b9\u9762\uff0c\u6700\u8fd1\u7684\u7814\u7a76[29, 30]\u5219\u901a\u8fc7\u4f7f\u7528\u8bed\u8a00\u6a21\u578b\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4e0e\u4e4b\u7ade\u4e89\u7684\u8fd8\u6709\u6df7\u5408\u65b9\u6cd5[31]\uff0c\u8fd9\u7c7b\u65b9\u6cd5\u6574\u5408\u4e86\u7ed3\u6784\u6570\u636e\u4f46\u4e5f\u56e0\u6b64\u4f1a\u53d7\u5230\u7ed3\u6784\u6570\u636e\u7f3a\u4e4f\u7684\u9650\u5236\u3002<\/span><\/section>\n

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2. \u673a\u5668\u5b66\u4e60\u7684\u6269\u5c55<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u751f\u7269\u7269\u7406\u5b66<\/strong>\u662f\u63a2\u7d22\u673a\u5668\u5b66\u4e60\u5e94\u7528\u7684\u4e00\u4e2a\u81ea\u7136\u9014\u5f84\u3002\u4e0e\u7269\u7406\u5b66\u7684\u5176\u4ed6\u8bb8\u591a\u9886\u57df\u4e0d\u540c\uff0c\u5927\u591a\u6570\u4e0e\u751f\u547d\u4e16\u754c\u76f8\u5173\u7684\u5b9e\u9a8c\u7cfb\u7edf\u90fd\u6781\u5176\u590d\u6742\uff0c\u56e0\u6b64\u4ece\u7b2c\u4e00\u6027\u539f\u7406\u5efa\u7acb\u6a21\u578b\u7684\u80fd\u529b\u76f8\u5f53\u6709\u9650\u3002\u4ee5\u5206\u5b50\u5c3a\u5ea6\u4e4b\u4e0a\u7684\u4e00\u4e2a\u4f8b\u5b50\u6765\u8bf4\uff0c\u4e0d\u53ef\u80fd\u6709\u4efb\u4f55\u7b2c\u4e00\u6027\u539f\u7406\u6a21\u578b\u80fd\u591f\u6070\u5982\u5176\u5206\u5730\u5904\u7406\u7ec6\u80de\u96c6\u4f53\u8fd0\u52a8 [32] \u6240\u6d89\u7ec6\u80de\u673a\u5236\u7684\u5168\u90e8\u590d\u6742\u6027\u3002\u8fd9\u91cc\u6ca1\u6709\u7eb3\u7ef4-\u65af\u6258\u514b\u65af<\/span>\uff08Navier\u2013Stokes\uff09<\/span>\u65b9\u7a0b\u53ef\u4ee5\u6765\u6551\u573a\uff0c\u56e0\u6b64\u4eba\u4eec\u81ea\u7136\u4f1a\u601d\u8003\uff0c\u662f\u5426\u53ef\u4ee5\u7528\u7eaf\u6570\u636e\u9a71\u52a8\u7684\u6a21\u578b\u6765\u6709\u6548\u66ff\u4ee3\u624b\u5de5\u6784\u5efa\u7684\u6a21\u578b[33, 34]\u3002\u7814\u7a76\u8005\u4eec\u6b63\u5728\u591a\u4e2a\u7ec6\u80de\u8fd0\u52a8\u5b9e\u9a8c\u7cfb\u7edf [35, 36] \u4e2d\u79ef\u6781\u7814\u7a76\u8be5\u95ee\u9898\uff0c\u5f53\u7136\uff0c\u8bb8\u591a\u751f\u7269\u533b\u836f\u9886\u57df\u7684\u5de5\u4f5c\u4e5f\u5728\u6df1\u5165\u7814\u7a76\u8be5\u95ee\u9898\uff0c\u4f8b\u5982\u6570\u5b57\u75c5\u7406\u5b66\u65b9\u9762\u7684\u5de5\u4f5c [37]\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c1d\u8bd5\u901a\u8fc7\u673a\u5668\u5b66\u4e60\u6765\u63a8\u5bfc\u51fa\u66f4\u597d\u7684\u624b\u5de5\u6a21\u578b<\/span>\uff08\u53c2\u89c1\u6587\u732e38\uff09<\/span>\uff1b\u4f46\u76ee\u524d\u5c1a\u4e0d\u6e05\u695a\u4e3a\u4ec0\u4e48\u8fd9\u6837\u505a\u4f1a\u6bd4\u76f4\u63a5\u4f7f\u7528\u5b66\u4e60\u5230\u7684\u795e\u7ecf\u7f51\u7edc\u9884\u6d4b\u7ed3\u679c\u66f4\u597d\u3002<\/span><\/section>\n

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\u6bd4\u8d77\u4e0a\u8ff0\u60c5\u51b5\uff0c\u6216\u8bb8\u66f4\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u6b63\u5728\u6e17\u900f\u5230\u90a3\u4e9b\u540d\u4e49\u4e0a\u5177\u6709\u53ef\u9760\u8ba1\u7b97\u6846\u67b6\u7684\u7269\u7406\u7cfb\u7edf\u7814\u7a76\u4e2d<\/strong>\u3002Yu \u548c Wang \u7684\u8bba\u6587 [39] \u5f88\u597d\u5730\u603b\u7ed3\u4e86\u8fd9\u4e9b\u7cfb\u7edf\u3002\u4e00\u79cd\u89c2\u70b9\u8ba4\u4e3a\uff0c\u5373\u4f7f\u5728\u6709\u7b2c\u4e00\u6027\u539f\u7406\u6a21\u578b\u53ef\u7528\u7684\u60c5\u51b5\u4e0b\uff0c\u673a\u5668\u5b66\u4e60\u4e5f\u53ef\u4ee5\u52a0\u901f\u8ba1\u7b97\u3002Kochkov \u7b49\u4eba [40] \u5c31\u6301\u6709\u8fd9\u79cd\u89c2\u70b9\uff0c\u4ed6\u4eec\u660e\u786e\u5173\u6ce8\u524d\u9762\u63d0\u5230\u7684\u7528\u4e8e\u6d41\u4f53\u52a8\u529b\u5b66\u7684\u7eb3\u7ef4-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u3002\u4e5f\u8bb8\u5728\u90a3\u4e9b\u539f\u5219\u4e0a\u53ef\u77e5\u4f46\u53ef\u80fd\u8fc7\u4e8e\u590d\u6742\u800c\u96be\u4ee5\u5b9e\u73b0\u7684\u7269\u7406\u95ee\u9898\u4e2d\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4f1a\u66f4\u6709\u8bf4\u670d\u529b\uff1b\u6c14\u5019\u6a21\u62df\u5668\u4e2d\u7684\u4e91\u6a21\u578b\u53ef\u80fd\u5c31\u662f\u8fd9\u6837\u4e00\u4e2a\u4f8b\u5b50\u3002\u603b\u4f53\u4e0a\u770b\uff0c\u5728\u7ed3\u5408\u4f20\u7edf\u5efa\u6a21\u7684\u53ef\u89e3\u91ca\u6027\u4e0e\u673a\u5668\u5b66\u4e60\u7684\u6cdb\u5316\u80fd\u529b\u65b9\u9762\uff0c\u4f3c\u4e4e\u8fd8\u6709\u5f88\u5927\u7684\u8fdb\u6b65\u7a7a\u95f4\u3002<\/span><\/section>\n

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\u5982\u679c\u6211\u4eec\u5173\u6ce8\u4e8e\u67d0\u4e2a\u975e\u5e38\u5177\u4f53\u7684\u7269\u7406\u7cfb\u7edf\u7684\u6a21\u578b\uff0c\u4e3a\u83b7\u5f97\u6709\u610f\u4e49\u7684\u7ed3\u679c\uff0c\u901a\u5e38\u5fc5\u8981\u7684\u5927\u89c4\u6a21\u8ba1\u7b97\u662f\u53ef\u4ee5\u627f\u53d7\u7684\uff1b\u5e76\u4e14\uff0c\u968f\u7740\u8ba1\u7b97\u80fd\u529b\u6301\u7eed\u6307\u6570\u589e\u957f\uff0c\u8fd9\u53d8\u5f97\u8d8a\u6765\u8d8a\u5bb9\u6613\u3002\u7136\u800c\uff0c\u6b63\u5982 King \u7b49\u4eba [41] \u5728\u672c\u671f\u5173\u4e8e\u6750\u6599\u7ec4\u88c5\u7684\u8bba\u6587\u4e2d\u6240\u5f3a\u8c03\u7684\u90a3\u6837\uff0c\u5f53\u4efb\u52a1\u662f\u8bbe\u8ba1\u65b0\u4e8b\u7269\u65f6\uff0c\u8fd9\u4f1a\u53d8\u5f97\u56f0\u96be\u5f97\u591a\u3002\u8fd9\u4e2a\u6311\u6218\u9700\u8981\u4e00\u4e2a\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u5373\u5728\u5fae\u89c2\u5c3a\u5ea6\u4e0a\u9009\u62e9\u76f8\u4e92\u4f5c\u7528\uff0c\u5e76\u6700\u7ec8\u5728\u66f4\u5927\u5c3a\u5ea6\u4e0a\u4ea7\u751f\u67d0\u79cd\u529f\u80fd\u6027\u884c\u4e3a\u3002\u8fd9\u4e2a\u8fed\u4ee3\u8fc7\u7a0b\u901a\u5e38\u6d89\u53ca\u67d0\u79cd\u529f\u80fd\u6027\u5ea6\u91cf<\/span>\uff08measure\uff09<\/span>\u7684\u68af\u5ea6\u4e0b\u964d\uff0c\u4f46\u4f5c\u4e3a\u6536\u655b\u8fc7\u7a0b\u7684\u4e00\u90e8\u5206\uff0c\u201c\u6b63\u5411\u201d\u95ee\u9898\u5fc5\u987b\u88ab\u8ba1\u7b97\u591a\u6b21\u3002\u6b63\u5982\u8be5\u8bba\u6587\u6240\u8ba8\u8bba\u7684\uff0c\u8fd9\u4e2a\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u673a\u5668\u5b66\u4e60\u7684\u601d\u60f3\u5f97\u5230\u6781\u5927\u6539\u5584\uff0c\u5305\u62ec\u81ea\u52a8\u5fae\u5206[42]\u7684\u6982\u5ff5\uff0c\u5b83\u80fd\u591f\u5c06\u5927\u5c3a\u5ea6\u8bef\u5dee\u201c\u53cd\u5411\u4f20\u64ad\u201d\u5230\u5fae\u89c2\u81ea\u7531\u5ea6\u7684\u5fc5\u8981\u6539\u53d8\u4e2d\u3002\u5f53\u7136\uff0c\u8fd9\u4e2a\u601d\u60f3\u539f\u672c\u662f\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u4e2d\u8bad\u7ec3\u9690\u85cf\u5c42\u7684\u7b97\u6cd5\u6838\u5fc3\uff0c\u4f46\u73b0\u5728\uff0c\u8fd9\u4e2a\u7406\u5ff5\u53ef\u4ee5\u81ea\u52a8\u5e94\u7528\u4e8e\u4efb\u4f55\u5927\u89c4\u6a21\u8ba1\u7b97\u3002<\/span><\/section>\n

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\u5f53\u4eba\u4eec\u601d\u8003\u673a\u5668\u5b66\u4e60\u53ca\u5176\u5728\u7269\u7406\u5b66\u4e2d\u7684\u5e94\u7528\u65f6\uff0c\u5f26\u8bba<\/strong>\u53ef\u80fd\u4e0d\u4f1a\u7acb\u5373\u6d6e\u73b0\u5728\u8111\u6d77\u4e2d\u3002\u7136\u800c\uff0c\u5f26\u8bba\u7814\u7a76\u8005\u4eec\u6b63\u5728\u79ef\u6781\u63a2\u7d22\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u662f\u5426\u6709\u7528[43]\u3002\u5f53\u7136\uff0c\u5f26\u8bba\u8bd5\u56fe\u6784\u5efa\u4e00\u4e2a\u201c\u4e07\u7269\u7406\u8bba\u201d\uff0c\u901a\u8fc7\u5b58\u5728\u4e8e11\u7ef4\u7a7a\u95f4\u4e2d\u7684\u201c\u5f26\u201d<\/span>\uff08\u4e00\u7ef4\u5ef6\u5c55\u7684\u91cf\u5b50\u5bf9\u8c61\uff09<\/span>\u6765\u89e3\u91ca\u6240\u6709\u57fa\u672c\u7c92\u5b50\u53ca\u5176\u76f8\u4e92\u4f5c\u7528\u3002\u673a\u5668\u5b66\u4e60\u88ab\u7528\u6765\u5bfb\u627e\u65b9\u6cd5\u5c06\u8fd9\u4e2a11\u7ef4\u7a7a\u95f4\u538b\u7f29\u5230\u6211\u4eec\u4f53\u9a8c\u76844\u7ef4\u4e16\u754c\u3002\u5bfb\u627e\u5408\u7406\u7684\u7d27\u81f4\u5316\u662f\u4e00\u4e2a\u975e\u5e38\u56f0\u96be\u7684\u8ba1\u7b97\u95ee\u9898\uff0c\u800c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u673a\u5668\u5b66\u4e60\u7684\u7406\u5ff5\u5f97\u5230\u6539\u5584\u3002\u8c01\u77e5\u9053\u5462\uff1f<\/span><\/section>\n

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\u5728\u673a\u5668\u5b66\u4e60\u4e0e\u7269\u7406\u5b66<\/span>\uff08ML-Physics\uff09<\/span>\u4ea4\u53c9\u9886\u57df\uff0c\u8fd8\u6709\u6700\u540e\u4e00\u4e2a\u6b63\u5728\u7814\u7a76\u7684\u65b9\u5411\u3002\u4e00\u4e9b\u7814\u7a76\u7ec4\u6b63\u5728\u5c1d\u8bd5\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u4ece\u6570\u636e\u4e2d\u81ea\u52a8\u53d1\u73b0\u65b0\u65b9\u7a0b<\/strong>\uff1b\u60f3\u8c61\u4e00\u4e0b\uff0c\u5229\u7528\u884c\u661f\u6570\u636e\u6765\u5c1d\u8bd5\u540c\u65f6\u5b66\u4e60\u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b\u548c\u5f15\u529b\u7684\u5e73\u65b9\u53cd\u6bd4\u5b9a\u5f8b\u3002\u8fd9\u4e2a\u60f3\u6cd5\u5728Yu[39]\u7684\u8bba\u6587\u4e2d\u6709\u7b80\u8981\u6982\u8ff0\uff0c\u5e76\u63d0\u4f9b\u4e86\u76f8\u5173\u53c2\u8003\u6587\u732e\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u9879\u52aa\u529b\u89c6\u4e3a\u8bd5\u56fe\u6700\u7ec8\u5c06\u7406\u8bba\u7269\u7406\u5b66\u5bb6\u7528\u5176\u4eba\u5de5\u667a\u80fd\u7248\u672c\u53d6\u4ee3\u3002\u4e0d\u8fc7\u5728\u673a\u5668\u80fd\u591f\u89c2\u5bdf\u5929\u4f53\u7269\u7406\u6570\u636e\u5e76\u53d1\u73b0\u6b63\u786e\u7684\u7406\u89e3\u6846\u67b6\u662f\u56db\u7ef4\u65f6\u7a7a\u4e2d\u7684\u9ece\u66fc\u51e0\u4f55\u4e4b\u524d\uff0c\u6211\u4eec\u5bf9\u81ea\u5df1\u7684\u5de5\u4f5c\u8fd8\u4e0d\u7528\u62c5\u5fc3\u3002<\/span><\/section>\n

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3. \u7269\u7406\u80fd\u4e3a\u673a\u5668\u5b66\u4e60\u505a\u4ec0\u4e48\uff1f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5f53\u7136\uff0c\u673a\u5668\u5b66\u4e60\u7684\u5f71\u54cd\u8fdc\u4e0d\u6b62\u4e8e\u63a8\u8fdb\u7269\u7406\u79d1\u5b66\u3002\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Deep learning neural network\uff0c DLNN\uff09<\/span>\u6a21\u578b [44, 45] \u5728\u56fe\u50cf\u8bc6\u522b[46]\u3001\u673a\u5668\u7ffb\u8bd1[47]\u3001\u6e38\u620f[48]\u7b49\u9886\u57df\u53d6\u5f97\u4e86\u4e00\u8fde\u4e32\u5feb\u901f\u800c\u5de8\u5927\u7684\u6210\u529f\uff0c\u800c\u4e14\u6b63\u5982\u6211\u4eec\u5df2\u7ecf\u8ba8\u8bba\u8fc7\u7684\uff0c\u751a\u81f3\u89e3\u51b3\u4e86\u86cb\u767d\u8d28\u6298\u53e0[1]\u8fd9\u6837\u957f\u671f\u5b58\u5728\u7684\u91cd\u5927\u79d1\u5b66\u6311\u6218\u3002\u65e0\u8bba\u597d\u574f\uff0c\u50cfChatGPT\u8fd9\u6837\u7684\u6700\u65b0\u751f\u6210\u6a21\u578b\u6b63\u4ece\u6839\u672c\u4e0a\u6539\u53d8\u7740\u6211\u4eec\u8fd9\u4e2a\u65f6\u4ee3\u7684\u793e\u4f1a\u3001\u7ecf\u6d4e\u548c\u653f\u6cbb\u683c\u5c40\u3002<\/span><\/section>\n

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\u7136\u800c\uff0c\u6700\u8fd1\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4ee4\u4eba\u96be\u4ee5\u7f6e\u4fe1\u7684\u6210\u529f\u4ea7\u751f\u4e86\u4e00\u4e2a\u526f\u4f5c\u7528<\/strong>\uff0c<\/strong>\u5373\u4eba\u4eec\u4e3a\u4e86\u8ffd\u6c42\u5feb\u901f\u3001\u72ed\u9698\u7684\u5e94\u7528\u9a71\u52a8\u578b\u53d1\u5c55\uff0c\u800c\u5ffd\u89c6\u4e86\u5176\u7406\u8bba\u52a8\u673a\u548c\u57fa\u7840<\/strong>\u3002\u8fd9\u6b63\u5728\u9010\u6e10\u5bfc\u81f4\u8d8a\u6765\u8d8a\u591a\u7684\u6b21\u4f18\u5b9e\u8df5\uff0c\u5305\u62ec\u5728\u7f3a\u4e4f\u7406\u8bba\u6307\u5bfc\u7684\u4f18\u5316\u548c\u6b63\u5219\u5316\u6b65\u9aa4<\/span>\uff08optimization and regularization procedure\uff09<\/span>\u6240\u6d89\u53ca\u7684\u5927\u91cf\u8d85\u53c2\u6570\u4e0a\u8017\u8d39\u5927\u91cf\u8ba1\u7b97\u548c\u65f6\u95f4\u8fdb\u884c\u8c03\u4f18\uff0c\u5bf9\u9ad8\u7cbe\u5ea6\u7f16\u7801\u53c2\u6570\u7684\u4f4e\u6548\u5229\u7528\uff0c\u5bf9\u6602\u8d35\u6807\u8bb0\u6570\u636e\u7684\u4f4e\u6548\u5229\u7528\uff0c\u6700\u7ec8\u7ed3\u679c\u7f3a\u4e4f\u53ef\u91cd\u590d\u6027\uff0c\u4ee5\u53ca\u6ee5\u7528\u8fd9\u9879\u5f3a\u5927\u6280\u672f\u7684\u53ef\u80fd\u6027\u3002\u53d1\u5c55\u8fc7\u53c2\u6570\u5316\u8fde\u63a5\u4e3b\u4e49\u673a\u5668\u5b66\u4e60\u6a21\u578b<\/span>\uff08\u5982\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\uff09<\/span>\u7684\u7406\u8bba\u57fa\u7840\uff0c\u5c06\u6709\u52a9\u4e8e\u907f\u514d\u6b64\u7c7b\u95ee\u9898\uff0c\u4ece\u800c\u7b80\u5316\u5176\u4f18\u5316\u8fc7\u7a0b\uff0c\u5e76\u5b9e\u73b0\u7528\u66f4\u5c11\u6570\u636e\u8bad\u7ec3\u51fa\u7a33\u5065\u6a21\u578b\u3002\u540c\u65f6\uff0c\u89c4\u8303\u6027\u7406\u8bba\u63d0\u4f9b\u7684\u9884\u6d4b\u53ef\u4ee5\u6307\u5bfc\u6539\u8fdb\u672a\u6765\u7684\u67b6\u6784\u548c\u8bad\u7ec3\u8303\u5f0f\u3002<\/span><\/section>\n

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\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Artificial neural network\uff0cANN\uff09<\/span>\u6a21\u578b\u6e90\u4e8e\u7edf\u8ba1\u7269\u7406\u5b66\u548c\u795e\u7ecf\u79d1\u5b66\u8fd9\u4e24\u4e2a\u81ea\u7136\u79d1\u5b66\u5b66\u79d1\u7684\u7ed3\u5408\u3002\u4ece\u672c\u8d28\u4e0a\u8bb2\uff0c\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u63cf\u8ff0\u4e86\u4e00\u7ec4\u9ad8\u5ea6\u62bd\u8c61\u7684\u201c\u795e\u7ecf\u5143\u201d\u5728\u7f51\u7edc\u4e2d\u901a\u8fc7\u81ea\u9002\u5e94\u65b9\u5f0f\u76f8\u4e92\u4f5c\u7528\u800c\u4ea7\u751f\u7684\u6d8c\u73b0<\/span>\uff08\u96c6\u4f53\uff09<\/span>\u884c\u4e3a\uff0c\u8fd9\u79cd\u7f51\u7edc\u4e0e\u5927\u8111\u4e2d\u7684\u771f\u5b9e\u795e\u7ecf\u7f51\u7edc\u6709\u67d0\u4e9b\u76f8\u4f3c\u4e4b\u5904\u3002\u6a21\u578b\u52a8\u529b\u5b66\u4f7f\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u80fd\u591f\u8fdb\u884c\u5173\u8054\u548c\u5b66\u4e60\u3002\u4ece\u5386\u53f2\u4e0a\u770b\uff0c\u7edf\u8ba1\u7269\u7406\u5b66\u548c\u795e\u7ecf\u79d1\u5b66\u5728\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u521b\u7acb\u548c\u65e9\u671f\u53d1\u5c55\u4e2d\u90fd\u53d1\u6325\u4e86\u5f00\u521b\u6027\u4f5c\u7528\u3002McCulloch \u548c Pitts \u57281943\u5e74\u4e3a\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u5efa\u6a21\u9996\u6b21\u5f15\u5165\u7ebf\u6027-\u975e\u7ebf\u6027\u4eba\u5de5\u795e\u7ecf\u5143\u4ee5\u53ca\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u7a81\u89e6\u6743\u91cd[49]\uff0c\u8fd9\u81f3\u4eca\u4ecd\u662f\u73b0\u4ee3\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7684\u57fa\u672c\u6784\u5efa\u5757\u3002\u7edf\u8ba1\u7269\u7406\u5b66\u572880\u5e74\u4ee3\u672b\u548c90\u5e74\u4ee3\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u521d\u671f\u53d1\u5c55\u548c\u7406\u8bba\u7406\u89e3\u4e2d\u4e5f\u53d1\u6325\u4e86\u91cd\u8981\u4f5c\u7528\uff0c\u63a8\u52a8\u4e86\u8bf8\u591a\u5173\u952e\u53d1\u5c55\uff0c\u5305\u62ec Hopfield \u6a21\u578b [14]\u3001\u73bb\u5c14\u5179\u66fc\u673a [9] \u4ee5\u53ca\u81ea\u65cb\u73bb\u7483<\/span>\uff08spin-glass\uff09<\/span>\u7406\u8bba\u7684\u795e\u7ecf\u7f51\u7edc\u5e94\u7528[50]\u7b49\u3002<\/span><\/section>\n

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\u73b0\u5728\u6709\u4ec0\u4e48\u4e0d\u540c\uff1f\u5728\u57fa\u672c\u5c42\u9762\u4e0a\uff0c\u6ca1\u6709\u592a\u5927\u53d8\u5316\uff0cMcCulloch\u2013Pitts \u795e\u7ecf\u5143\u4ecd\u7136\u662f\u6240\u6709\u6df1\u5ea6\u5b66\u4e60\u7b97\u6cd5\u7684\u57fa\u672c\u6784\u5efa\u5757\uff0c\u7ebf\u6027\u6c42\u548c\u4e0e\u975e\u7ebf\u6027\u6fc0\u6d3b\u4ecd\u7136\u662f\u5355\u4e2a\u795e\u7ecf\u5143\u5c42\u9762\u7684\u57fa\u672c\u8ba1\u7b97\u8fc7\u7a0b\u3002\u7136\u800c\uff0c\u89c4\u6a21\u5374\u6709\u7740\u5de8\u5927\u7684\u5dee\u5f02\u3002\u6b63\u5982\u5728\u524d\u9762\u86cb\u767d\u8d28\u6298\u53e0\u80cc\u666f\u4e2d\u6240\u8ba8\u8bba\u7684\uff0c\u6211\u4eec\u73b0\u5728\u62e5\u6709\u6d77\u91cf\u6570\u636e\u6765\u8bad\u7ec3\u5927\u578b\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\uff1b\u53cd\u8fc7\u6765\uff0c\u8fd9\u4e9b\u6a21\u578b\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u5927\u91cf\u53c2\u6570\u6765\u5438\u6536\u5927\u578b\u6570\u636e\u96c6\u4e2d\u7684\u4fe1\u606f\u3002\u8fd9\u4e9b\u5927\u6a21\u578b\u7684\u67b6\u6784\u6bd4 Rosenblatt \u7684\u539f\u59cb\u611f\u77e5\u5668\u6a21\u578b[51]\u590d\u6742\u5f97\u591a\uff0c\u4f8b\u5982\uff0c\u5bf9\u73b0\u4ee3\u5927\u8bed\u8a00\u6a21\u578b<\/span>\uff08large language model\uff0c LLM\uff09<\/span>\u6765\u8bf4 transformer \u67b6\u6784\u81f3\u5173\u91cd\u8981\u3002\u5f53\u7136\uff0c\u8fd9\u4e9b\u5927\u578b\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u6027\u80fd\u8fdc\u8fdc\u8d85\u51fa\u4e86\u6211\u4eec\u57fa\u4e8e\u89c2\u5bdf\u5355\u4e2a\u795e\u7ecf\u5143\u6240\u5f62\u6210\u7684\u9884\u671f\u3002<\/span><\/section>\n

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\u8fd9\u8ba9\u6211\u4eec\u60f3\u8d77 P. W. \u5b89\u5fb7\u68ee<\/span>\uff08Anderson\uff09<\/span>\u7684\u8457\u540d\u8bba\u65ad\uff1a\u201c\u591a\u8005\u5f02\u4e5f\u201d<\/span>\uff08More is different\uff09<\/span>[52]\uff0c\u4ed6\u63d0\u51fa\u6574\u4e2a\u7cfb\u7edf\u4e0d\u4ec5\u4ec5\u662f\u5176\u5404\u4e2a\u90e8\u5206\u7684\u603b\u548c\uff0c\u7cfb\u7edf\u4e2d\u5404\u4e2a\u90e8\u5206\u7684\u76f8\u4e92\u4f5c\u7528\u53ef\u4ee5\u4ea7\u751f\u6d8c\u73b0<\/span>\uff08\u4e0d\u540c\u7684\uff09<\/span>\u884c\u4e3a\u3002\u5b89\u5fb7\u68ee\u8fd9\u53e5\u540d\u8a00\u6fc0\u52b1\u4e86\u51e0\u4ee3\u7269\u7406\u5b66\u5bb6\u7814\u7a76\u590d\u6742\u591a\u4f53\u7cfb\u7edf\u7684\u6d8c\u73b0\u884c\u4e3a\uff0c\u6211\u4eec\u4e5f\u60f3\u7528\u5b83\u4f5c\u4e3a\u53e3\u53f7\uff0c\u53f7\u53ec\u7269\u7406\u5b66\u5bb6\u4eec\u6765\u7814\u7a76\u51fa\u73b0\u5728<\/span>\uff08\u6709\u65f6\uff09<\/span>\u5e9e\u5927\u4f46\u59cb\u7ec8\u5177\u6709\u826f\u597d\u7ed3\u6784\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u8ff7\u4eba\u6d8c\u73b0\u884c\u4e3a\u2014\u2014\u5b66\u4e60<\/strong><\/span>\uff08learning\uff09<\/span>\u3002\u8fd9\u4e9b\u7814\u7a76\u9700\u8981\u56de\u7b54\u4e00\u4e9b\u666e\u904d\u6027\u95ee\u9898\uff1a\u5b66\u4e60\u5982\u4f55\u4ece\u795e\u7ecf\u5143\u76f8\u4e92\u4f5c\u7528\u4e2d\u4ea7\u751f\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7a76\u7adf\u5b66\u5230\u4e86\u4ec0\u4e48\uff0c\u4ee5\u53ca\u5b83\u4eec\u662f\u5426\u80fd\u591f\u6cdb\u5316\u6240\u5b66\u5230\u7684\u77e5\u8bc6<\/strong>\u3002<\/span><\/section>\n

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\u786e\u5b9e\uff0c\u6211\u4eec\u8ba4\u4e3a\u6df1\u5ea6\u5b66\u4e60\u7684\u4e0b\u4e00\u4e2a\u7a81\u7834\u53ef\u80fd\u6765\u81ea\u4e8e\u57fa\u4e8e\u7edf\u8ba1\u7269\u7406\u5b66\u6982\u5ff5\u548c\u65b9\u6cd5\u5efa\u7acb\u7684\u575a\u5b9e\u7406\u8bba\u57fa\u7840<\/strong>\u3002\u8fd9\u5c06\u4e0e\u4e0d\u65ad\u63a8\u51fa\u7684\u66f4\u5148\u8fdb\u7684\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7b97\u6cd5\u76f8\u8f85\u76f8\u6210\uff0c\u8fd9\u4e9b\u7b97\u6cd5\u5c06\u52a0\u5feb\u7269\u7406\u548c\u751f\u7269\u4e16\u754c\u7684\u79d1\u5b66\u53d1\u73b0\u6b65\u4f10\u3002\u8fd9\u4e24\u4e2a\u76f8\u4e92\u5173\u8054\u7684\u65b0\u5174\u7814\u7a76\u4e3b\u9898\u2014\u2014\u57fa\u7840\u7406\u8bba\u548c\u590d\u6742\u5e94\u7528\u2014\u2014\u5c06\u6781\u5927\u5730\u63a8\u8fdb\u79d1\u5b66\u548c\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u53d1\u5c55\u3002\u5728\u4e0b\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u5728\u6df1\u5165\u63a2\u8ba8\u51e0\u4e2a\u53ef\u80fd\u53d6\u5f97\u8fdb\u5c55\u7684\u6709\u524d\u666f\u7684\u65b9\u5411\u4e4b\u524d\uff0c\u5148\u4ecb\u7ecd\u63cf\u8ff0\u673a\u5668\u5b66\u4e60\u8fc7\u7a0b\u7684\u4e00\u822c\u6846\u67b6\u3002\u6211\u4eec\u7684\u8ba8\u8bba\u5c06\u7b80\u8981\u6982\u8ff0\u672c\u7279\u520a\u4e2d\u4e0e\u8fd9\u4e9b\u65b9\u5411\u76f8\u5173\u7684\u5df2\u53d1\u8868\u8bba\u6587\u3002<\/span><\/section>\n

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3.1 \u673a\u5668\u5b66\u4e60\u7684\u4e2d\u5fc3\u6cd5\u5219<\/span><\/strong><\/span><\/h2>\n

<\/span><\/section>\n
\u5728 Ambrose \u7b49\u4eba[53]\u6240\u8457\u7684\u300a\u5b66\u4e60\u5982\u4f55\u8fd0\u4f5c\uff1f\u300b<\/span>\uff08How learning works?<\/em>\uff09<\/span>\u4e00\u4e66\u4e2d\uff0c\u5b66\u4e60\u88ab\u5b9a\u4e49\u4e3a\u201c\u4e00\u4e2a\u5bfc\u81f4\u53d8\u5316\u7684\u8fc7\u7a0b\uff0c\u8fd9\u79cd\u53d8\u5316\u6e90\u4e8e\u7ecf\u9a8c\uff0c\u5e76\u589e\u52a0\u4e86\u63d0\u9ad8\u672a\u6765\u8868\u73b0\u548c\u5b66\u4e60\u80fd\u529b\u7684\u6f5c\u529b\u201d\u3002\u867d\u7136\u8fd9\u672c\u4e66\u662f\u5728\u4eba\u7c7b<\/span>\uff08\u5b66\u751f\uff09<\/span>\u5b66\u4e60\u7684\u80cc\u666f\u4e0b\u5199\u6210\u7684\uff0c\u4f46\u8fd9\u4e2a\u7b80\u660e\u7684\u5b66\u4e60\u5b9a\u4e49\u540c\u6837\u53ef\u4ee5\u7528\u6765\u63cf\u8ff0\u673a\u5668\u5b66\u4e60\u3002\u5728\u56fe2\u4e2d\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u673a\u5668\u5b66\u4e60<\/span>\uff08\u5982\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\uff09<\/span>\u7684\u5173\u952e\u7ec4\u6210\u90e8\u5206\u548c\u5de5\u4f5c\u6d41\u7a0b\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u673a\u5668\u5b66\u4e60\u7684\u201c\u4e2d\u5fc3\u6cd5\u5219\u201d\u3002\u673a\u5668\u5b66\u4e60\u8fc7\u7a0b\u7684\u76ee\u6807\u662f\u5b66\u4e60\u4e00\u4e2a\u80fd\u591f\u6355\u6349\u89c2\u6d4b\u6570\u636e\u6240\u4ee3\u8868\u7684\u5916\u90e8\u4e16\u754c\u5185\u5728\u5c5e\u6027\u7684\u6a21\u578b\u3002\u8be5\u6a21\u578b\u5177\u6709\u7279\u5b9a\u7684\u7ed3\u6784\uff0c\u5373\u51fd\u6570\u5f62\u5f0f\uff0c\u5e76\u7531\u5176\u53c2\u6570<\/span>\uff08\u5728\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u4e2d\u79f0\u4e3a\u6743\u91cd\uff09<\/span>\u6765\u53c2\u6570\u5316\u3002\u9075\u5faa Ambrose \u7b49\u4eba\u7ed9\u51fa\u7684\u5b9a\u4e49\uff0c\u5728\u5b66\u4e60\u8fc7\u7a0b\u7684\u8bad\u7ec3\u9636\u6bb5\uff0c\u6a21\u578b\u4e2d\u7684\u53c2\u6570\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u8fd9\u79cd\u53d8\u5316\u6e90\u4e8e\u5bf9\u7ecf\u9a8c<\/span>\uff08\u6216\u8005\u673a\u5668\u5b66\u4e60\u6240\u8bf4\u7684\u8bad\u7ec3\u6570\u636e\uff09<\/span>\u7684\u8bad\u7ec3\u3002\u4e00\u65e6\u7ecf\u8fc7\u8bad\u7ec3\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8bad\u7ec3\u540e\u6a21\u578b\u5728\u672a\u89c1\u8fc7\u7684\u6d4b\u8bd5\u6570\u636e\u4e0a\u7684\u8868\u73b0\uff0c\u4ee5\u53ca\u8bad\u7ec3\u540e\u6a21\u578b\u662f\u5426\u4e3a\u672a\u6765\u5b66\u4e60\u5f62\u6210\u4e86\u826f\u597d\u7684\u57fa\u7840<\/span>\uff08\u8d77\u70b9\uff09<\/span>\u6765\u8bc4\u4f30\u5176\u5b66\u4e60\u8d28\u91cf\u3002<\/span><\/section>\n

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\u56fe2. \u673a\u5668\u5b66\u4e60\u4e2d\u4e3b\u8981\u6b65\u9aa4\u548c\u5de5\u4f5c\u6d41\u7a0b\u7684\u8bf4\u660e\u3002\u7528\u7ea2\u8272\u7a81\u51fa\u663e\u793a\u7684\u662f\u53ef\u80fd\u901a\u8fc7\u57fa\u4e8e\u7269\u7406\u7684\u65b9\u6cd5\u89e3\u51b3\u7684\u4e09\u4e2a\u65b9\u5411\u3002<\/span><\/p>\n


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\u56fe2\u6240\u793a\u7684\u673a\u5668\u5b66\u4e60\u5de5\u4f5c\u6d41\u7a0b\u7acb\u5373\u63d0\u793a\u4e86\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u4e24\u4e2a\u91cd\u8981\u95ee\u9898\u3002\u7b2c\u4e00\u4e2a\u95ee\u9898\u5173\u6ce8\u5b66\u4e60\u52a8\u529b\u5b66<\/strong><\/span>\uff08learning dynamics\uff09<\/span>\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u7ed9\u5b9a\u8bad\u7ec3\u6570\u636e\u65f6\uff0c\u6a21\u578b\u7684\u53c2\u6570\u5982\u4f55\u53d8\u5316\uff1f\u901a\u5e38\u7684\u5b66\u4e60\u8fc7\u7a0b\u662f\u901a\u8fc7\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u6765\u8fdb\u884c\u7684\uff0c\u635f\u5931\u51fd\u6570\u523b\u753b\u4e86\u6a21\u578b\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u62df\u5408\u7a0b\u5ea6\u3002\u4ece\u4e00\u7ec4\u521d\u59cb\u53c2\u6570\u503c\u5f00\u59cb\uff0c\u53c2\u6570\u5728\u635f\u5931\u51fd\u6570\u7684\u6307\u5bfc\u4e0b\u5728\u9ad8\u7ef4\u53c2\u6570\u7a7a\u95f4\u4e2d\u8fed\u4ee3\u66f4\u65b0\uff0c\u76f4\u5230\u8fbe\u5230\u6700\u5c0f\u503c\u3002\u6a21\u578b\u5728\u8fd9\u6837\u7684\u6700\u5c0f\u503c\u5904\u7684\u53c2\u6570\u6784\u6210\u4e86\u95ee\u9898\u7684\u4e00\u4e2a\u89e3\u3002\u4f18\u5316\u8fc7\u7a0b\uff0c\u5373\u53c2\u6570\u66f4\u65b0\u5e8f\u5217\uff0c\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4ee5\u66f4\u65b0\u6b65\u4e3a\u65f6\u95f4\u7684\u5b66\u4e60\u52a8\u529b\u5b66\u3002\u7b2c\u4e8c\u4e2a\u95ee\u9898\u5904\u7406\u6cdb\u5316\u95ee\u9898<\/strong>\u3002\u901a\u5e38\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u662f\u8fc7\u53c2\u6570\u5316\u7684\u3002\u56e0\u6b64\uff0c\u62df\u5408\u8bad\u7ec3\u6570\u636e\u8fd9\u4e00\u95ee\u9898\u6709\u8bb8\u591a\u53ef\u80fd\u7684\u89e3<\/span>\uff08\u6700\u5c0f\u503c\uff09<\/span>\u3002\u95ee\u9898\u5728\u4e8e\u54ea\u4e2a\u89e3\u5177\u6709\u66f4\u597d\u7684\u6cdb\u5316\u6027\uff0c\u5373\u5728\u8bad\u7ec3\u8fc7\u7a0b\u672a\u4f7f\u7528\u7684\u6d4b\u8bd5\u6570\u636e\u4e0a\u8868\u73b0\u66f4\u597d\u3002\u5982\u679c\u6211\u4eec\u77e5\u9053\u4ec0\u4e48\u7c7b\u578b\u7684\u89e3\u5177\u6709\u66f4\u597d\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u4e00\u4e2a\u76f8\u5173\u7684\u95ee\u9898\u662f\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ec0\u4e48\u6b63\u5219\u5316\u9879<\/span>\uff08\u9664\u4e86\u635f\u5931\u51fd\u6570\u4e4b\u5916\uff09<\/span>\u6765\u63a8\u52a8\u7cfb\u7edf\u671d\u7740\u90a3\u4e9b\u66f4\u5177\u53ef\u6cdb\u5316\u6027\u7684\u89e3\u53d1\u5c55\u3002\u5728\u63a5\u4e0b\u6765\u7684\u4e24\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u66f4\u8be6\u7ec6\u5730\u6df1\u5165\u63a2\u8ba8\u8fd9\u4e24\u4e2a\u4e00\u822c\u6027\u95ee\u9898\uff0c\u5e76\u5f3a\u8c03\u8fd9\u4e9b\u65b9\u5411\u4e0a\u7684\u4e00\u4e9b\u6700\u65b0\u53d1\u5c55\u3002<\/span><\/section>\n

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3.2 \u968f\u673a\u5b66\u4e60\u52a8\u529b\u5b66\uff1a\u4ece\u6da8\u843d\u7684\u635f\u5931\u666f\u89c2\u4e0a\u6eda\u843d<\/span><\/strong><\/span><\/h2>\n


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\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u4e00\u822c\u4f18\u5316\u7b56\u7565\u5305\u62ec\u901a\u8fc7\u8ddf\u968f\u635f\u5931\u51fd\u6570\u7684\u68af\u5ea6\u6765\u66f4\u65b0\u6743\u91cd\uff0c\u8fd9\u79cd\u65b9\u6cd5\u79f0\u4e3a\u68af\u5ea6\u4e0b\u964d<\/span>\uff08gradient descent\uff0cGD\uff09<\/span>\u3002\u9274\u4e8e\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7684\u524d\u9988\u67b6\u6784\uff0c\u68af\u5ea6\u4e0b\u964d\u53ef\u4ee5\u901a\u8fc7\u53cd\u5411\u4f20\u64ad<\/span>\uff08backpropagation\uff09<\/span>\u9ad8\u6548\u5b9e\u73b0\u3002\u7136\u800c\uff0c\u5982\u679c\u4f7f\u7528\u5728\u6240\u6709\u8bad\u7ec3\u6570\u636e\u4e0a\u53d6\u5e73\u5747\u7684\u635f\u5931\u51fd\u6570\uff0c\u68af\u5ea6\u4e0b\u964d\u5bf9\u5927\u578b\u6570\u636e\u96c6\u6765\u8bf4\u5728\u8ba1\u7b97\u4e0a\u5c06\u662f\u4e0d\u53ef\u884c\u7684\u3002\u4e3a\u4e86\u89c4\u907f\u5927\u6570\u636e\u96c6\u95ee\u9898\uff0c\u53ef\u5229\u7528\u968f\u673a\u68af\u5ea6\u4e0b\u964d<\/strong><\/span>\uff08stochastic gradient descent\uff0cSGD\uff09<\/span>\u65b9\u6cd5\u4ee3\u66ff\u68af\u5ea6\u4e0b\u964d\uff0c\u8be5\u65b9\u6cd5\u5728\u6bcf\u6b21\u8fed\u4ee3\u65f6\u4f1a\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u6837\u672c\u5b50\u96c6<\/span>\uff08\u5c0f\u6279\u91cf\uff09<\/span>\uff0c\u5e76\u7528\u5176\u66f4\u65b0\u6743\u91cd [54, 55]\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u968f\u540e\u4eba\u4eec\u53d1\u73b0\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5bf9\u4e8e\u5728\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\u627e\u5230\u66f4\u5177\u6cdb\u5316\u80fd\u529b\u7684\u89e3\u540c\u6837\u81f3\u5173\u91cd\u8981\u3002<\/span><\/section>\n

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\u7136\u800c\uff0c\u5c3d\u7ba1\u6df1\u5ea6\u5b66\u4e60\u53d6\u5f97\u4e86\u5de8\u5927\u6210\u529f\uff0c\u4f46\u6211\u4eec\u4ecd\u672a\u5145\u5206\u7406\u89e3\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u4e3a\u4ec0\u4e48\u80fd\u5728\u9ad8\u7ef4\u975e\u51f8\u635f\u5931\u51fd\u6570<\/span>\uff08\u80fd\u91cf\uff09<\/span>\u666f\u89c2\u4e2d\u6709\u6548\u5730\u5b66\u5230\u597d\u7684\u89e3\u51b3\u65b9\u6848\u3002\u968f\u673a\u6027\u4f3c\u4e4e\u662f\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u5173\u952e\uff0c\u4f46\u8fd9\u4e5f\u4f7f\u5176\u66f4\u96be\u7406\u89e3\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u8bb8\u591a\u7269\u7406\u548c\u751f\u7269\u7cfb\u7edf\u90fd\u5305\u542b\u8fd9\u6837\u7684\u968f\u673a\u5143\u7d20\uff0c\u4f8b\u5982\u5e03\u6717\u8fd0\u52a8\u548c\u968f\u673a\u751f\u5316\u53cd\u5e94\u3002\u5e76\u4e14\u6211\u4eec\u5df2\u7ecf\u5f00\u53d1\u51fa\u4e86\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u6765\u7406\u89e3\u5177\u6709\u591a\u4e2a\u81ea\u7531\u5ea6\u7684\u968f\u673a\u7cfb\u7edf\u4e2d\u7684\u96c6\u4f53\u884c\u4e3a\u3002\u4e8b\u5b9e\u4e0a\uff0c\u7edf\u8ba1\u7269\u7406\u5b66\u548c\u968f\u673a\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u4e2d\u7684\u6982\u5ff5\u548c\u65b9\u6cd5\u6700\u8fd1\u5df2\u88ab\u7528\u4e8e\u7814\u7a76\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u52a8\u529b\u5b66\u3001\u635f\u5931\u51fd\u6570\u666f\u89c2\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/span><\/section>\n

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\u4e3a\u4e86\u5c55\u793a\u8fd9\u79cd\u57fa\u4e8e\u7269\u7406\u5b66\u7684\u65b9\u6cd5\u5728\u7406\u89e3\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u65b9\u9762\u7684\u5b9e\u7528\u6027\uff0c\u6211\u4eec\u7b80\u8981\u63cf\u8ff0\u4e00\u4e2a\u7814\u7a76\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5b66\u4e60\u52a8\u529b\u5b66\u7684\u7406\u8bba\u6846\u67b6\uff0c\u53ca\u4ece\u4e2d\u83b7\u5f97\u7684\u4e00\u4e9b\u6709\u8da3\u89c1\u89e3\u3002\u6211\u4eec\u9996\u5148\u5c06\u57fa\u4e8e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u5b66\u4e60\u8fc7\u7a0b\u89c6\u4e3a\u4e00\u4e2a\u968f\u673a\u52a8\u529b\u7cfb\u7edf\u3002\u50cf\u795e\u7ecf\u7f51\u7edc<\/span>\uff08neural network\uff0cNN\uff09<\/span>\u7279\u522b\u662f\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc<\/span>\uff08deep neural network\uff0cDNN\uff09<\/span>\u8fd9\u6837\u7684\u5b66\u4e60\u7cfb\u7edf\u5177\u6709\u5927\u91cf\uff08N\uff09\u7684\u6743\u91cd\u53c2\u6570wi<\/sub>\uff081, 2, \u2026, N\uff09\u3002\u5bf9\u4e8e\u76d1\u7763\u5b66\u4e60<\/span>\uff08supervised learning\uff09<\/span>\uff0c\u6211\u4eec\u6709M\u4e2a\u8bad\u7ec3\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c\u90fd\u6709\u4e00\u4e2a\u8f93\u5165<\/sub><\/span>\u548c\u4e00\u4e2a\u6b63\u786e\u8f93\u51fa<\/sub><\/span>\uff0c\u5176\u4e2dk = 1, 2, …, M\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u8f93\u5165<\/span><\/sub><\/span>\uff0c\u5b66\u4e60\u7cfb\u7edf\u4f1a\u9884\u6d4b\u4e00\u4e2a\u8f93\u51fa<\/sub><\/span>\uff0c\u5176\u4e2d\u8f93\u51fa\u51fd\u6570G\u53d6\u51b3\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u67b6\u6784\u548c\u5176\u6743\u91cd<\/sub><\/span>\u3002\u5b66\u4e60\u7684\u76ee\u6807\u662f\u627e\u5230\u6743\u91cd\u53c2\u6570\u4ee5\u6700\u5c0f\u5316\u9884\u6d4b\u8f93\u51fa\u548c\u6b63\u786e\u8f93\u51fa\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u8fd9\u79cd\u5dee\u5f02\u7531\u6574\u4f53\u635f\u5931\u51fd\u6570<\/span>\uff08\u6216\u80fd\u91cf\u51fd\u6570\uff09<\/span>\u523b\u753b\uff1a<\/span><\/section>\n

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\u5176\u4e2dd(<\/sub><\/span>, <\/sub><\/span>)\u662f<\/sub><\/span>\u548c<\/sub><\/span>\u4e4b\u95f4\u7684\u8ddd\u79bb\u5ea6\u91cf\u3002\u8fd9\u91cc\uff0c\u4e00\u4e2a\u5178\u578b\u7684\u8ddd\u79bb\u5ea6\u91cf\u662f\u4ea4\u53c9\u71b5\u3002<\/span><\/section>\n

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\u5177\u4f53\u6765\u8bf4\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u4e2d\u7b2ct\u6b21\u8fed\u4ee3\u7684\u6743\u91cdwi<\/sub>\uff081, 2, …<\/span>, N\uff09\u7684\u53d8\u5316\u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a<\/span><\/section>\n

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\u5176\u4e2d<\/span>\u03b1<\/span>\u662f\u5b66\u4e60\u7387\uff0c\u03bc<\/span>(t)\u8868\u793a\u7b2ct\u6b21\u8fed\u4ee3\u4f7f\u7528\u7684\u968f\u673a\u5c0f\u6279\u91cf\u3002\u5927\u5c0f\u4e3aB\u7684\u5c0f\u6279\u91cf\u03bc<\/span>\u7684\u5c0f\u6279\u91cf\u635f\u5931\u51fd\u6570<\/span>\uff08minibatch loss function\uff0c MLF\uff09<\/span>\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

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\u5176\u4e2d\u03bcl<\/sub><\/span>\u6807\u8bb0\u968f\u673a\u9009\u62e9\u7684B\u4e2a\u6837\u672c\u3002<\/span><\/section>\n

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\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u5f15\u5165\u5c0f\u6279\u91cf\u635f\u5931\u51fd\u6570\u7cfb\u7efc<\/span>\uff08ensemble\uff09<\/sub><\/span><\/span>\u8fd9\u4e2a\u5173\u952e\u6982\u5ff5\uff0c\u5373\u4e00\u4e2a\u80fd\u91cf\u666f\u89c2\u7684\u7cfb\u7efc\uff0c\u6bcf\u4e2a\u666f\u89c2\u6765\u81ea\u4e8e\u4e00\u4e2a\u968f\u673a\u5c0f\u6279\u91cf\u3002\u6574\u4f53\u635f\u5931\u51fd\u6570<\/sub><\/span>\u53ea\u662f\u5c0f\u6279\u91cf\u635f\u5931\u51fd\u6570\u7684\u7cfb\u7efc\u5e73\u5747\uff1a<\/sub><\/span>\u3002\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u566a\u58f0\u6765\u81ea\u5c0f\u6279\u91cf\u635f\u5931\u51fd\u6570\u4e0e\u5176\u7cfb\u7efc\u5e73\u5747\u4e4b\u95f4\u7684\u53d8\u5316\uff1a<\/sub><\/span>\u3002\u901a\u8fc7\u91c7\u7528\u8fde\u7eed\u65f6\u95f4\u8fd1\u4f3c\u5e76\u4fdd\u7559\u65b9\u7a0b\uff082\uff09\u4e2d\u7684\u4e00\u9636\u65f6\u95f4\u5bfc\u6570\u9879\uff0c\u6211\u4eec\u5f97\u5230\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u968f\u673a\u504f\u5fae\u5206\u65b9\u7a0b<\/strong>\u5982\u4e0b\uff1a<\/span><\/section>\n

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\u5176\u4e2d\u65f6\u95f4t\u548c\u672c\u7814\u7a76\u4e2d\u7684\u6240\u6709\u65f6\u95f4\u5c3a\u5ea6\u90fd\u4ee5\u5c0f\u6279\u91cf\u8fed\u4ee3\u65f6\u95f4\u0394<\/span>t=1\u4e3a\u5355\u4f4d\u6765\u5ea6\u91cf\u3002\u8fde\u7eed\u65f6\u95f4\u6781\u9650\u76f8\u5f53\u4e8e\u8003\u8651\u8fdc\u5927\u4e8e\u0394\u7684\u65f6\u95f4\u5c3a\u5ea6\uff0c\u4f8b\u5982\uff0c\u4e00\u8f6e<\/span>\uff08epoch\uff09<\/span>\u7684\u65f6\u95f4\u662fM\/B(>>1)\u3002\u65b9\u7a0b\uff084\uff09\u7c7b\u4f3c\u4e8e\u7edf\u8ba1\u7269\u7406\u5b66\u4e2d\u7684\u6717\u4e4b\u4e07\u65b9\u7a0b<\/span>\uff08Langevin equation\uff09<\/span>\u3002\u7b2c\u4e00\u9879<\/sub><\/span>\u662f\u7531\u6574\u4f53\u635f\u5931\u51fd\u6570<\/strong> <\/strong>L<\/strong> <\/strong>\u652f\u914d\u7684\u786e\u5b9a\u6027\u68af\u5ea6\u4e0b\u964d<\/strong>\uff0c\u7c7b\u4f3c\u4e8e\u7269\u7406\u5b66\u4e2d\u7684\u80fd\u91cf\u51fd\u6570\u3002\u7b2c\u4e8c\u9879\u662f\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u566a\u58f0\u9879<\/strong><\/sub><\/span>\uff0c\u5176\u5747\u503c\u4e3a\u96f6<\/sub><\/span>\uff0c\u7b49\u65f6\u534f\u65b9\u5dee\u77e9\u9635\u4e3a<\/span><\/section>\n

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<\/p>\n


<\/span><\/section>\n
\u8be5\u77e9\u9635\u660e\u786e\u4f9d\u8d56\u4e8e<\/sub><\/span>\uff0c\u5176\u7ed9\u51fa\u4e86\u4e00\u79cd\u590d\u6742\u5f62\u5f0f\u7684\u4e58\u6027\u566a\u58f0\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u7f51\u7edc\u67b6\u6784\uff0c\u5b66\u4e60\u52a8\u529b\u5b66\u56e0\u6b64\u53ef\u4ee5\u6620\u5c04\u4e3a\u4e00\u4e2a\u201c\u5b66\u4e60\u7c92\u5b50\u201d\u7684\u968f\u673a\u8fd0\u52a8\uff0c\u8be5\u7c92\u5b50\u7684\u5750\u6807\u662f\u7f51\u7edc\u7684\u6743\u91cd\u3002\u7279\u522b\u5730\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5b66\u4e60\u7b97\u6cd5\u5bf9\u5e94\u4e8e\u5b66\u4e60\u7c92\u5b50\u5728\u6da8\u843d\u7684\u80fd\u91cf\u666f\u89c2\u4e2d\u7684\u4e0b\u964d\u8fc7\u7a0b\uff0c\u5176\u7531\u6717\u4e4b\u4e07\u65b9\u7a0b<\/span>\uff08\u65b9\u7a0b2\uff09<\/span>\u652f\u914d\uff0c\u5305\u542b\u4e00\u4e2a\u786e\u5b9a\u6027\u68af\u5ea6\u4e0b\u964d\u9879\u548c\u4e00\u4e2a\u566a\u58f0\u9879\uff0c\u5176\u4e2d\u566a\u58f0\u9879\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7531\u65b9\u7a0b5\u7ed9\u51fa\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5b66\u4e60\u52a8\u529b\u5b66\u4e2d\u6700\u4e0d\u5bfb\u5e38\u548c\u6700\u6709\u8da3\u7684\u90e8\u5206\u6765\u81ea\u566a\u58f0\u9879\u3002\u6b63\u5982 Chaudhauri \u548c Soatto [56]\u9996\u6b21\u6307\u51fa\u7684\uff0c\u4e0e\u5e73\u8861\u7269\u7406\u7cfb\u7edf\u4e2d\u566a\u58f0\u5f3a\u5ea6\u7531\u70ed\u6e29\u5ea6\u7ed9\u5b9a\u7684\u60c5\u51b5\u4e0d\u540c\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u52a8\u529b\u5b66\u662f\u9ad8\u5ea6\u975e\u5e73\u8861\u7684\uff0c\u56e0\u4e3a\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u566a\u58f0\u65e2\u4e0d\u662f\u5404\u5411\u540c\u6027\u7684\u4e5f\u4e0d\u662f\u5747\u5300\u7684\u3002\u4ece\u5176\u5b9a\u4e49\u6765\u770b\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u566a\u58f0\u4f9d\u8d56\u4e8e\u635f\u5931\u666f\u89c2\u672c\u8eab\u3002\u5176\u4e2d\u6700\u6709\u8da3\u7684\u4e00\u4e2a\u53d1\u73b0\u662f\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u566a\u58f0\u7684\u534f\u65b9\u5dee\u77e9\u9635\u4e0e\u635f\u5931\u51fd\u6570\u7684 Hessian \u77e9\u9635\u9ad8\u5ea6\u76f8\u5173\uff1a\u5b83\u4eec\u7684\u7279\u5f81\u65b9\u5411\u9ad8\u5ea6\u5bf9\u9f50\uff0c\u4e14\u76f8\u5e94\u7684\u7279\u5f81\u503c\u9ad8\u5ea6\u76f8\u5173 [57, 58]\u3002\u7279\u522b\u662f\uff0c\u5728\u635f\u5931\u666f\u89c2\u4e2d\u8f83\u9661\u5ced\u7684\u65b9\u5411\u4e0a<\/span>\uff08Hessian \u77e9\u9635\u4e2d\u8f83\u5927\u7684\u7279\u5f81\u503c\uff09<\/span>\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u566a\u58f0\u4e5f\u66f4\u5927\u3002\u8fd9\u5bfc\u81f4\u5728\u6240\u6709\u65b9\u5411\u4e0a\u6743\u91cd\u65b9\u5dee\u4e0e\u635f\u5931\u666f\u89c2\u5e73\u5766\u5ea6\u4e4b\u95f4\u5b58\u5728\u7a33\u5065\u7684\u53cd\u6bd4\u5173\u7cfb\uff0c\u8fd9\u4e0e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u5b66\u4e2d\u7684\u6da8\u843d-\u54cd\u5e94\u5173\u7cfb<\/span>\uff08fluctuation\u2013response relation\uff0c\u53c8\u79f0\u7231\u56e0\u65af\u5766\u5173\u7cfb\uff09<\/span>\u76f8\u53cd\u3002<\/span><\/section>\n

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\u8d8a\u6765\u8d8a\u591a\u7684\u7ecf\u9a8c\u8bc1\u636e\u652f\u6301\u8fd9\u6837\u4e00\u4e2a\u89c2\u70b9\uff1a\u201c\u597d\u7684\u201d<\/span>\uff08\u53ef\u6cdb\u5316\u7684\uff09<\/span>\u89e3\u5b58\u5728\u4e8e\u635f\u5931\u51fd\u6570\u7684\u5e73\u5766<\/span>\uff08\u6d45\uff09<\/span>\u6781\u5c0f\u503c\u5904 [59-65]\uff1b\u7136\u800c\uff0c\u5bf9\u4e8e\u57fa\u4e8e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u7b97\u6cd5\u5982\u4f55\u5728\u9ad8\u7ef4\u6743\u91cd\u7a7a\u95f4\u4e2d\u627e\u5230\u8fd9\u4e9b\u5e73\u5766\u6781\u5c0f\u503c\uff0c\u6211\u4eec\u4ecd\u7136\u77e5\u4e4b\u751a\u5c11\u3002\u5728\u968f\u673a\u5b66\u4e60\u52a8\u529b\u5b66\u6846\u67b6\u5185\u83b7\u5f97\u7684\u201c\u53cd\u7231\u56e0\u65af\u5766\u5173\u7cfb\u201d[57]\u8868\u660e\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5145\u5f53\u4e86\u4e00\u4e2a\u4f9d\u8d56\u4e8e\u666f\u89c2\u7684\u9000\u706b\u7b97\u6cd5\u3002\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u6709\u6548\u6e29\u5ea6\u968f\u7740\u666f\u89c2\u5e73\u5766\u5ea6\u800c\u964d\u4f4e\uff0c\u56e0\u6b64\u7cfb\u7edf\u503e\u5411\u4e8e\u5bfb\u627e\u5e73\u5766\u7684\u6781\u5c0f\u503c\u800c\u975e\u5c16\u9510\u7684\u6781\u5c0f\u503c\u3002\u6b63\u5982\u6700\u8fd1\u4e00\u7bc7\u4f7f\u7528\u798f\u514b-\u666e\u6717\u514b\u65b9\u7a0b<\/span>\uff08Fokker-Planck equation\uff09<\/span>\u7814\u7a76\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5b66\u4e60\u52a8\u529b\u5b66\u6743\u91cd\u5206\u5e03\u7684\u8bba\u6587[58]\u6240\u793a\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u5728\u6709\u6548\u635f\u5931\u51fd\u6570\u4e2d\u5f15\u5165\u4e86\u4e00\u4e2a\u4f9d\u8d56\u4e8e\u5e73\u5766\u5ea6\u7684\u9879\uff0c\u8be5\u9879\u4f7f\u7cfb\u7edf\u503e\u5411\u4e8e\u66f4\u5e73\u5766\u7684\u6781\u5c0f\u503c\u3002<\/span><\/section>\n

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\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u7c7b\u522b\u662f\u751f\u6210\u6a21\u578b\uff0c\u5b83\u4eec\u80fd\u591f\u901a\u8fc7\u5bf9\u73b0\u6709\u6837\u672c\u7684\u8bad\u7ec3\u6765\u751f\u6210\u65b0\u7684\u6837\u672c\u3002\u4e00\u4e2a\u8457\u540d\u7684\u65e9\u671f\u4f8b\u5b50\u662f\u751f\u6210\u5bf9\u6297\u7f51\u7edc<\/span>\uff08generative adversarial network\uff0cGAN\uff09<\/span>\u6a21\u578b [66]\uff0c\u5df2\u7ecf\u6709\u5de5\u4f5c\u4f7f\u7528\u968f\u673a\u52a8\u529b\u7cfb\u7edf\u65b9\u6cd5\u5bf9\u5176\u5b66\u4e60\u52a8\u529b\u5b66\u8fdb\u884c\u4e86\u7814\u7a76 [67]\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e00\u4e9b\u6700\u6210\u529f\u7684\u751f\u6210\u6a21\u578b\uff0c\u5982\u57fa\u4e8e\u6269\u6563\u7684\u6a21\u578b[68]\uff0c\u90fd\u8d77\u6e90\u4e8e\u7269\u7406\u5b66\uff0c\u5e76\u56e0\u6b64\u4e3a\u57fa\u4e8e\u7269\u7406\u5b66\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u5e7f\u9614\u7a7a\u95f4\u3002\u5728\u672c\u7279\u520a\u4e2d\uff0cZdeborova \u7b49\u4eba[69]\u4ece\u81ea\u65cb\u73bb\u7483\u7684\u89c6\u89d2\u5bf9\u4e0d\u540c\u751f\u6210\u6a21\u578b\u8fdb\u884c\u4e86\u5168\u9762\u6bd4\u8f83\uff0c\u8fd9\u4e3a\u7406\u89e3\u8fd9\u4e9b\u5f3a\u5927\u751f\u6210\u6a21\u578b\u7684\u80fd\u529b\u548c\u5c40\u9650\u6027\u63d0\u4f9b\u4e86\u7406\u8bba\u89c1\u89e3\u3002<\/span><\/section>\n

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3.3 \u6cdb\u5316\uff1a\u9ad8\u7ef4\u7684\u795d\u798f\u4e0e\u8bc5\u5492<\/span><\/strong><\/span><\/h2>\n

<\/strong><\/span><\/section>\n
\u7269\u7406\u5b66\u4e2d\u7684\u5927\u591a\u6570\u95ee\u9898\u90fd\u662f\u8fc7\u5ea6\u7ea6\u675f\u7684\uff08\u6216\u6b20\u53c2\u6570\u5316\u7684\uff09<\/strong>\u3002\u4f8b\u5982\uff0c\u5728\u4e00\u4e2a\u5177\u6709N\u4e2a\u6c28\u57fa\u9178\u7684\u86cb\u767d\u8d28\u6298\u53e0\u95ee\u9898\u4e2d\uff0c\u5373\u4f7f\u6211\u4eec\u53ea\u8003\u8651\u6210\u5bf9\u7684\u76f8\u4e92\u4f5c\u7528\u80fd\u91cf\uff0c\u4e5f\u6709~N2<\/sup>\u4e2a\u7ea6\u675f\uff0c\u8fdc\u9ad8\u4e8e~2N\u4e2a\u81ea\u7531\u5ea6<\/span>\uff08\u5373\u4e00\u7ef4\u94fe\u4e0a\u6c28\u57fa\u9178\u7684\u72ec\u7acb\u5750\u6807\uff09<\/span>\u3002\u901a\u5e38\uff0c\u4e00\u4e2a\u8fc7\u5ea6\u7ea6\u675f\u7684\u95ee\u9898\u5177\u6709\u552f\u4e00\u89e3\u3002\u8fd9\u79cd\u60c5\u51b5\u5982\u56fe3A\u6240\u793a\uff0c\u5176\u4e2d\u80fd\u91cf\u666f\u89c2\u5177\u6709\u552f\u4e00\u7684\u6700\u5c0f\u503c\uff0c\u5bf9\u5e94\u4e8e\u6298\u53e0\u86cb\u767d\u8d28\u7684\u5929\u7136\u7ed3\u6784\u3002\u901a\u8fc7\u6700\u5c0f\u5316\u6574\u4f53\u80fd\u91cf\u51fd\u6570\u6765\u89e3\u51b3\u8fc7\u5ea6\u7ea6\u675f\u7684\u95ee\u9898\uff0c\u4f8b\u5982\u4ece\u5934\u7b97\u8d77\u7684\u86cb\u767d\u8d28\u6298\u53e0\u95ee\u9898\u662f\u4e00\u4e2a\u4f17\u6240\u5468\u77e5\u7684\u96be\u9898\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u662f\u8fc7\u53c2\u6570\u5316\u7684<\/strong>\u3002\u53c2\u6570<\/span>\uff08\u6743\u91cd\uff09<\/span>\u7684\u6570\u91cf\u8fdc\u5927\u4e8e\u6570\u636e\u4e2d\u7684\u5185\u90e8\u81ea\u7531\u5ea6\u3002\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\u62e5\u6709\u5927\u91cf\u53c2\u6570\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u4f7f\u627e\u5230\u89e3<\/span>\uff08\u635f\u5931\u666f\u89c2\u4e2d\u7684\u6700\u5c0f\u503c\uff09<\/span>\u76f8\u5bf9\u5bb9\u6613\u3002\u7136\u800c\uff0c\u53c2\u6570\u7a7a\u95f4\u9ad8\u7ef4\u6027\u7684\u8bc5\u5492\u5728\u4e8e\u5b58\u5728\u8bb8\u591a\u89e3<\/span>\uff08\u635f\u5931\u51fd\u6570\u7684\u6700\u5c0f\u503c\uff09<\/span>\uff0c\u5982\u56fe3B\u6240\u793a\u3002\u56e0\u6b64\uff0c\u91cd\u8981\u7684\u95ee\u9898\u53d8\u6210\u4e86\u54ea\u4e00\u4e2a\u89e3\u5bf9\u6d4b\u8bd5\u6570\u636e\u8868\u73b0\u66f4\u597d\uff0c\u5373\u54ea\u4e2a\u89e3\u5177\u6709\u66f4\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/section>\n

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<\/section>\n

\u56fe3. \u8fc7\u5ea6\u7ea6\u675f\u548c\u7ea6\u675f\u4e0d\u8db3\u95ee\u9898\u4e2d\u666f\u89c2\u548c\u89e3\u7684\u5dee\u5f02\u3002\uff08A\uff09\u86cb\u767d\u8d28\u6298\u53e0\uff08\u4e00\u4e2a\u8fc7\u5ea6\u7ea6\u675f\u7684\u95ee\u9898\uff09\u4e2d\u7684\u81ea\u7531\u80fd\u666f\u89c2\uff0c\u5176\u4e2d\u5b58\u5728\u4e00\u4e2a\u552f\u4e00\u7684\u5168\u5c40\u6700\u5c0f\u503c\uff0c\u8fd9\u901a\u5e38\u5f88\u96be\u627e\u5230\u3002\u8be5\u56fe\u7247\u91c7\u7528\u81ea Dill \u548c Maccallum [70]\u3002\uff08B\uff09\u8fc7\u53c2\u6570\u5316\uff08\u7ea6\u675f\u4e0d\u8db3\uff09\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u4e2d\u7684\u635f\u5931\u666f\u89c2\uff0c\u5176\u53ef\u4ee5\u5177\u6709\u591a\u4e2a\u5168\u5c40\u6700\u5c0f\u503c\u3002\u6311\u6218\u5728\u4e8e\u627e\u51fa\u54ea\u4e2a\u89e3\u5177\u6709\u66f4\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/p>\n


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\u786e\u5b9e\uff0c\u6cdb\u5316\u662f\u673a\u5668\u5b66\u4e60\u4e2d\u6700\u91cd\u8981\u7684\u95ee\u9898\u4e4b\u4e00\u3002\u8003\u8651\u5230\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\u4f7f\u7528\u7684\u5e9e\u5927\u53c2\u6570<\/span>\uff08\u6743\u91cd\uff09<\/span>\u6570\u91cf\uff0c\u8fd9\u4e2a\u95ee\u9898\u53d8\u5f97\u66f4\u52a0\u7d27\u8feb\u3002\u5df2\u7ecf\u6709\u5f88\u591a\u5de5\u4f5c\u57fa\u4e8e\u5404\u79cd\u7406\u8bba\u548c\u5b9e\u8bc1\u9a71\u52a8\u7684\u590d\u6742\u5ea6\u5ea6\u91cf<\/span>\uff08VC\u7ef4\u3001\u53c2\u6570\u8303\u6570\u3001\u9510\u5ea6\uff08sharpness\uff09\u3001\u8def\u5f84\u8303\u6570\u7b49\uff09<\/span>\u5bf9\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7684\u6cdb\u5316\u6027\u8fdb\u884c\u4e86\u7814\u7a76\u3002\u6b63\u5982 Jiang \u7b49 [71] \u5728\u6700\u8fd1\u7684\u7efc\u8ff0\u4e2d\u603b\u7ed3\u7684\u90a3\u6837\uff0c\u7ecf\u9a8c\u8bc1\u636e\u8868\u660e\u57fa\u4e8e\u9510\u5ea6\u7684\u5ea6\u91cf\u4e0e\u6cdb\u5316\u4e4b\u95f4\u5b58\u5728\u5f3a\u76f8\u5173\u6027 [72]\uff0c\u800c\u8bb8\u591a\u5176\u4ed6<\/span>\uff08\u7406\u8bba\u9a71\u52a8\u7684\uff09<\/span>\u5ea6\u91cf\uff0c\u5982\u57fa\u4e8e\u8303\u6570\u7684\u5ea6\u91cf\uff0c\u5e76\u4e0d\u80fd\u4f5c\u4e3a\u6cdb\u5316\u7684\u53ef\u9760\u6307\u6807 [71]\u3002\u5373\u4f7f\u5bf9\u4e8e\u57fa\u4e8e\u9510\u5ea6\u7684\u5ea6\u91cf\uff0c\u6211\u4eec\u4e5f\u4e0d\u7406\u89e3\u5b83\u4eec\u4e3a\u4ec0\u4e48\u4ee5\u53ca\u5982\u4f55\u5728\u9884\u6d4b\u6cdb\u5316\u65b9\u9762\u6709\u6548\u3002\u6b64\u5916\uff0c\u57fa\u4e8e Dinh \u7b49\u4eba [73] \u6307\u51fa\u7684\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u4e00\u822c\u6807\u5ea6\u4e0d\u53d8\u6027\uff0c\u6700\u8fd1\u6709\u7814\u7a76\u5de5\u4f5c\u5bf9\u4ec5\u4f7f\u7528\u635f\u5931\u666f\u89c2\u9510\u5ea6\u6765\u786e\u5b9a\u6cdb\u5316\u7684\u6709\u6548\u6027\u63d0\u51fa\u4e86\u8d28\u7591\u3002\u786e\u5b9e\uff0c\u5bf9\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\u6cdb\u5316\u7684\u5168\u9762\u7406\u89e3\u4ecd\u7136\u96be\u4ee5\u6349\u6478\u3002<\/span><\/section>\n

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\u6cdb\u5316\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u95ee\u9898\u662f\u786e\u5b9a\u89e3\u7684\u54ea\u4e9b\u6027\u8d28\u51b3\u5b9a\u4e86\u5176\u6cdb\u5316\u80fd\u529b<\/strong>\u3002\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u7684\u56f0\u96be\u5728\u4e8e\uff0c\u867d\u7136\u5b66\u4e60\u662f\u7531\u8bad\u7ec3\u635f\u5931\u5f15\u5bfc\u7684\uff0c\u4f46\u6cdb\u5316\u6027\u80fd\u662f\u7531\u6d4b\u8bd5\u635f\u5931\u8bc4\u4f30\u7684\uff0c\u800c\u5728\u65e0\u6cd5\u83b7\u53d6\u6d4b\u8bd5\u635f\u5931\u666f\u89c2\u7684\u60c5\u51b5\u4e0b\u5f88\u96be\u53d6\u5f97\u7406\u8bba\u8fdb\u5c55\u3002\u6700\u8fd1\uff0c\u6709\u5de5\u4f5c\u901a\u8fc7\u4f7f\u7528\u6570\u636e\u53d8\u5316\u548c\u6743\u91cd\u53c2\u6570\u53d8\u5316\u4e4b\u95f4\u7684\u7b49\u4ef7\u6027<\/span>\uff08\u5bf9\u5076\u6027\uff09<\/span>\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898 [74]\u3002\u4e00\u822c\u601d\u8def\u662f\uff0c\u5982\u679c\u8bad\u7ec3\u6570\u636e\uff08x\uff09\u548c\u6d4b\u8bd5\u6570\u636e\uff08x’\uff09\u4e4b\u95f4\u7684\u8f93\u5165\u53d8\u5316\u7b49\u4ef7\u4e8e\u4ece\u89e3\u7684\u6743\u91cd\uff08W\uff09\u5230\u65b0\u6743\u91cd\uff08W’\uff09\u7684\u53d8\u5316\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u8fd9\u79cd\u5bf9\u5076\u5173\u7cfb\u5c06\u8f93\u5165\u7a7a\u95f4\u4e2d\u7684\u5206\u5e03\u6620\u5c04\u5230\u6743\u91cd\u7a7a\u95f4\u4e2d\uff0c\u5728\u90a3\u91cc\u6211\u4eec\u53ef\u4ee5\u8bc4\u4f30\u6cdb\u5316\u635f\u5931\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u4efb\u610f\u5bc6\u96c6\u8fde\u63a5\u5c42<\/span>\uff08densely connected layer\uff09<\/span>\u4e2d\u90fd\u80fd\u627e\u5230\u8fd9\u79cd\u7cbe\u786e\u5bf9\u5076\u5173\u7cfb\u7684\u65e0\u9650\u65cf\u3002\u901a\u8fc7\u4f7f\u7528\u5177\u6709\u6700\u5c0f\u6743\u91cd\u53d8\u5316\u7684\u201c\u6700\u5c0f\u201d\u5bf9\u5076\u5173\u7cfb\uff0c\u6cdb\u5316\u635f\u5931\u53ef\u4ee5\u88ab\u5206\u89e3\u4e3a\u6743\u91cd\u7a7a\u95f4\u4e2d\u89e3\u7684\u635f\u5931\u51fd\u6570 Hessian \u77e9\u9635\u7684\u4e0d\u540c\u7279\u5f81\u65b9\u5411\u4e0a\u7684\u8d21\u732e\u3002\u8fd9\u4e9b\u8d21\u732e\u7684\u5f62\u5f0f\u63ed\u793a\u4e86\u6cdb\u5316\u7684\u4e24\u4e2a\u4e0d\u540c\u51b3\u5b9a\u56e0\u7d20\u2014\u2014\u4e00\u4e2a\u7531\u635f\u5931\u666f\u89c2\u7684\u9510\u5ea6\u652f\u914d\uff0c\u53e6\u4e00\u4e2a\u5bf9\u5e94\u4e8e\u7531\u8bad\u7ec3\u6570\u636e\u548c\u6d4b\u8bd5\u6570\u636e\u4e4b\u95f4\u76f8\u5bf9\u5dee\u5f02\u7684\u534f\u65b9\u5dee\u52a0\u6743\u7684\u89e3\u8303\u6570\u3002\u4ece\u8fd9\u9879\u7814\u7a76\u83b7\u5f97\u7684\u4e3b\u8981\u89c1\u89e3\u4e4b\u4e00\u662f\uff0c\u6cdb\u5316\u7531\u8fd9\u4e24\u4e2a\u51b3\u5b9a\u56e0\u7d20\u7684\u4e58\u79ef\u51b3\u5b9a<\/strong>\uff0c\u8fd9\u89e3\u51b3\u4e86 Dinh \u7b49\u4eba[73]\u63d0\u51fa\u7684\u5173\u4e8e\u5e73\u5766\u5ea6\u7684\u56f0\u60d1\u3002<\/span><\/section>\n

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\u5728\u7ea6\u675f\u4e0d\u8db3<\/span>\uff08\u6216\u8fc7\u53c2\u6570\u5316\uff09<\/span>\u7684\u5b66\u4e60\u7cfb\u7edf<\/span>\uff08\u5982\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\uff09<\/span>\u4e2d\uff0c\u6b63\u5219\u5316<\/strong><\/span>\uff08regularization\uff09<\/span>\u662f\u6dfb\u52a0\u5230\u635f\u5931\u51fd\u6570\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u7ec4\u6210\u90e8\u5206\uff0c\u76ee\u7684\u662f\u5c06\u7cfb\u7edf\u63a8\u5411\u5177\u6709\u66f4\u9ad8\u6cdb\u5316\u80fd\u529b\u7684\u89e3\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u6b63\u5219\u5316\u5f88\u91cd\u8981\uff0c\u4f46\u5b83\u4eec\u901a\u5e38\u662f\u57fa\u4e8e\u5bf9\u66f4\u5177\u6cdb\u5316\u80fd\u529b\u7684\u89e3\u5e94\u5177\u6709\u4ec0\u4e48\u7279\u6027\u7684\u4e00\u4e9b\u76f4\u89c9\u3002\u4ece\u5f71\u54cd\u6cdb\u5316\u635f\u5931\u7684\u4e24\u4e2a\u8d21\u732e\u56e0\u7d20<\/span>\uff08\u9510\u5ea6\u548c\u5927\u5c0f\uff09<\/span>\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u548c\u6743\u91cd\u8870\u51cf\u4f5c\u4e3a\u4e24\u79cd\u6709\u6548\u6b63\u5219\u5316\u65b9\u6848\u7684\u80fd\u529b\u80cc\u540e\u7684\u673a\u5236\u53d8\u5f97\u6e05\u6670\u3002\u663e\u7136\uff0c\u57fa\u4e8e\u5e95\u5c42\u7cfb\u7edf\u7684\u7279\u6027<\/span>\uff08\u4f8b\u5982\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u5bf9\u79f0\u6027\u548c\u5b88\u6052\u5b9a\u5f8b\uff09<\/span>\u548c\/\u6216\u5f71\u54cd\u89e3\u7684\u6cdb\u5316\u80fd\u529b\u7684\u67d0\u4e9b\u4e00\u822c\u56e0\u7d20\u6765\u8bbe\u8ba1\u6b63\u5219\u5316\u65b9\u6848\uff0c\u5c06\u6210\u4e3a\u4e00\u4e2a\u6709\u8da3\u7684\u672a\u6765\u7814\u7a76\u65b9\u5411\u3002<\/span><\/section>\n

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\u4f5c\u4e3a\u8fc7\u62df\u5408\u7684\u6781\u7aef\u60c5\u51b5\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u751a\u81f3\u53ef\u4ee5\u201c\u8bb0\u5fc6\u201d\u6240\u6709\u8bad\u7ec3\u6837\u672c\uff0c\u5373\u4f7f\u5b83\u4eec\u7684\u6807\u7b7e\u88ab\u66ff\u6362\u4e3a\u7eaf\u566a\u58f0[75]\u3002\u8fd9\u79cd\u8fc7\u62df\u5408<\/span>\uff08\u8bb0\u5fc6\u5316\uff09<\/span>\u89e3\u6ca1\u6709\u6cdb\u5316\u80fd\u529b\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u907f\u514d\u4e86\u8fc7\u62df\u5408\uff0c\u5176\u6d4b\u8bd5\u8bef\u5dee\u9075\u5faa\u6240\u8c13\u7684\u201c\u53cc\u4e0b\u964d\u201d<\/span>\uff08double descent\uff09<\/span>\u66f2\u7ebf[76]\u3002\u968f\u7740\u6a21\u578b\u5bb9\u91cf<\/span>\uff08\u590d\u6742\u5ea6\uff09<\/span>\u7684\u589e\u52a0\uff0c\u6d4b\u8bd5\u8bef\u5dee\u5728\u5f00\u59cb\u65f6\u9075\u5faa\u5e38\u89c4\u7684 U \u5f62\u66f2\u7ebf\uff0c\u5148\u4e0b\u964d\uff0c\u7136\u540e\u5728\u6a21\u578b\u8fbe\u5230\u96f6\u8bad\u7ec3\u8bef\u5dee\u65f6\u7684\u63d2\u503c\u9608\u503c\u9644\u8fd1\u8fbe\u5230\u5cf0\u503c\u3002\u7136\u800c\uff0c\u5f53\u6a21\u578b\u5bb9\u91cf\u8d85\u8fc7\u8fd9\u4e2a\u63d2\u503c\u9608\u503c\u65f6\uff0c\u5b83\u518d\u6b21\u4e0b\u964d\uff0c\u6d4b\u8bd5\u8bef\u5dee\u5728\u8fc7\u53c2\u6570\u5316\u533a\u57df<\/span>\uff08\u53c2\u6570\u6570\u91cf\u8fdc\u5927\u4e8e\u6837\u672c\u6570\u91cf\uff09<\/span>\u8fbe\u5230\u5176<\/span>\uff08\u5168\u5c40\uff09<\/span>\u6700\u5c0f\u503c\u3002\u901a\u8fc7\u4f7f\u7528\u7b80\u5355\u6a21\u578b\uff0c\u4eba\u4eec\u5728\u7406\u89e3\u8fd9\u79cd\u53cc\u4e0b\u964d\u884c\u4e3a\u65b9\u9762\u53d6\u5f97\u4e86\u5feb\u901f\u8fdb\u5c55\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u8fc7\u53c2\u6570\u5316\u7684\u7b80\u5355\u4e24\u5c42\u7f51\u7edc\uff0c\u5728\u7ebf\u6027\u53ef\u5206\u6570\u636e\u4e0a\u4f7f\u7528\u5e26\u6cc4\u6f0f\u7684 ReLU \u6fc0\u6d3b\u51fd\u6570\u65f6\uff0c\u5df2\u6709\u5de5\u4f5c\u8bc1\u660e\u4e86\u4f18\u5316\u548c\u6cdb\u5316\u6027\u5f97\u4ee5\u786e\u4fdd [77]\u3002\u8fd9\u4e00\u7ed3\u679c\u968f\u540e\u88ab\u6269\u5c55\u5230\u4f7f\u7528 ReLU \u6fc0\u6d3b\u51fd\u6570\u76842\u5c42\u7f51\u7edc [78] \u548c\u4f7f\u7528\u5e73\u6ed1\u6fc0\u6d3b\u51fd\u6570\u76842&3\u5c42\u7f51\u7edc[79]\u3002\u795e\u7ecf\u6b63\u5207\u6838<\/span>\uff08Neural Tangent Kernel\uff0cNTK\uff09<\/span>[80] \u5c06\u5927\u578b<\/span>\uff08\u5bbd\uff09<\/span>\u795e\u7ecf\u7f51\u7edc\u4e0e\u6838\u65b9\u6cd5\u8054\u7cfb\u4e86\u8d77\u6765\uff0c\u4f7f\u7528 NTK \u7684\u65b9\u6cd5\u8868\u660e\uff0c\u5728\u8fc7\u53c2\u6570\u5316\u533a\u57df\uff0c\u6cdb\u5316\u8bef\u5dee\u4ee5\u5e42\u5f8b\u65b9\u5f0f<\/sub><\/span><\/span>\uff08\u5176\u4e2dNp<\/sub>\u4e3a\u53c2\u6570\u6570\u91cf\uff09<\/span>\u5411\u5e73\u53f0\u503c\u4e0b\u964d [81]\u3002\u5728\u7b80\u5355\u7684\u5408\u6210\u5b66\u4e60\u6a21\u578b<\/span>\uff08synthetic learning models\uff09<\/span>\u4e2d\uff0c\u5982\u5177\u6709\u5cad\u56de\u5f52<\/span>\uff08ridge regression\uff09<\/span>\u635f\u5931\u51fd\u6570\u7684\u968f\u673a\u7279\u5f81\u6a21\u578b\uff0c\u53cc\u4e0b\u964d\u884c\u4e3a\u5df2\u7ecf\u5f97\u5230\u89e3\u6790\u8bc1\u660e [82]\u3002\u8fd9\u4e00\u89e3\u6790\u7ed3\u679c\u5df2\u7ecf\u901a\u8fc7\u4f7f\u7528\u526f\u672c\u65b9\u6cd5<\/span>\uff08replica method\uff09<\/span>\u6269\u5c55\u5230\u5176\u4ed6\u5408\u6210\u5b66\u4e60\u6a21\u578b<\/span>\uff08\u4f8b\u5982\u968f\u673a\u6d41\u5f62\u6a21\u578b\uff09<\/span>\u548c\u66f4\u4e00\u822c\u7684\u635f\u5931\u51fd\u6570 [83]\u3002<\/span><\/section>\n

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\u4e8b\u5b9e\u4e0a\uff0c\u5728\u5927\u8bed\u8a00\u6a21\u578b\u7b49\u5927\u6a21\u578b\u4e2d\uff0c\u6700\u4ee4\u4eba\u5174\u594b\u7684\u5b9e\u8bc1\u53d1\u73b0\u4e4b\u4e00\u662f\uff0c\u5f53\u6a21\u578b\u89c4\u6a21\u548c\u6570\u636e\u89c4\u6a21\u6309\u6bd4\u4f8b\u4e00\u8d77\u589e\u52a0\u65f6\uff0c\u6cdb\u5316\u635f\u5931\u4f1a\u968f\u7740\u5b83\u4eec\u7684\u589e\u52a0\u800c\u6301\u7eed\u4e0b\u964d\uff0c\u5448\u73b0\u51fa\u660e\u663e\u7684\u5e42\u5f8b\u4f9d\u8d56\u5173\u7cfb\u3002\u7269\u7406\u5b66\u5bb6\u5f88\u81ea\u7136\u5730\u88ab\u5e42\u5f8b\u6240\u63cf\u8ff0\u7684\u884c\u4e3a\u5438\u5f15\uff0c\u5e76\u5f00\u53d1\u51fa\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u7b49\u5f3a\u5927\u5de5\u5177\u6765\u89e3\u91ca\u4e34\u754c\u73b0\u8c61\u4e2d\u7684\u6807\u5ea6\u5f8b<\/span>\uff08scaling law\uff09<\/span>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8ba4\u4e3a\u7406\u89e3\u5927\u578b\u590d\u6742\u5b66\u4e60\u7cfb\u7edf\u4e2d\u6cdb\u5316\u5bf9\u6570\u636e\u89c4\u6a21\u548c\u6a21\u578b\u89c4\u6a21\u7684\u201c\u5e42\u5f8b\u201d\u4f9d\u8d56\u5173\u7cfb\uff0c\u662f\u5bf9\u7269\u7406\u5b66\u5bb6\u6700\u5177\u5438\u5f15\u529b\u4e14\u6781\u5176\u91cd\u8981\u7684\u7814\u7a76\u65b9\u5411\u4e4b\u4e00\u3002\u5728\u672c\u7279\u520a\u4e2d\uff0cBahri \u7b49\u4eba [84] \u7814\u7a76\u4e86\u8fd9\u79cd\u201c\u6807\u5ea6\u5f8b\u201d\u80cc\u540e\u53ef\u80fd\u7684\u8d77\u6e90\uff0c\u5e76\u4e3a\u4e0d\u540c\u7684\u6807\u5ea6\u533a\u57df\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5206\u7c7b\u6cd5\u3002<\/span><\/section>\n

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3.4 \u771f\u5b9e\u795e\u7ecf\u7f51\u7edc\u548c\u771f\u5b9e\u795e\u7ecf\u5143\u7684\u542f\u53d1<\/span><\/strong><\/span><\/h2>\n

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\u5982\u6211\u4eec\u4e0a\u8ff0\u6240\u8a00\uff0c\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u53d7\u76ca\u4e8e\u4e24\u4e2a\u81ea\u7136\u79d1\u5b66\u5b66\u79d1\uff0c\u5373\u795e\u7ecf\u79d1\u5b66\u548c\u7edf\u8ba1\u7269\u7406\u5b66\u3002\u7136\u800c\uff0c\u9664\u4e86\u4f53\u73b0\u5728 McCulloch\u2013Pitts \u795e\u7ecf\u5143\u548c\u5206\u5c42\u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span>\uff08\u611f\u77e5\u5668\uff09<\/span>\u67b6\u6784\u4e2d\u7684\u6700\u521d\u795e\u7ecf\u79d1\u5b66\u542f\u53d1\u4e4b\u5916\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u5e76\u6ca1\u6709\u5305\u542b\u592a\u591a\u795e\u7ecf\u79d1\u5b66\u7684\u89c1\u89e3\u3002\u5c3d\u7ba1\u672c\u7279\u520a\u4e3b\u8981\u5173\u6ce8\u7269\u7406\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e4b\u95f4\u7684\u4ea4\u53c9\u5bf9\u8bdd\uff0c\u4f46\u6211\u4eec\u5bf9\u795e\u7ecf\u79d1\u5b66\u4ea7\u751f\u7684\u65b0\u6982\u5ff5\u7684\u9700\u6c42\u6bd4\u4ee5\u5f80\u4efb\u4f55\u65f6\u5019\u90fd\u66f4\u5927<\/strong>\u3002\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7684\u51e0\u4e2a\u5177\u4f53\u67b6\u6784\u9650\u5236\u65b9\u9762\u53ef\u80fd\u4f1a\u4ece\u66f4\u6df1\u5165\u7684\u795e\u7ecf\u79d1\u5b66\u539f\u7406\u4e2d\u53d7\u76ca\u3002\u4f8b\u5982\uff0c\u6df1\u5ea6\u5b66\u4e60\u7684\u6210\u529f\u4e3b\u8981\u5c40\u9650\u4e8e\u5177\u6709\u9759\u6001\u6570\u636e\u96c6\u7684\u9759\u6001\u4efb\u52a1\uff0c\u800c\u4e14\u8fd8\u9700\u8981\u5927\u91cf\u660e\u786e\u6807\u8bb0\u7684\u6570\u636e\u3002\u7531\u4e8e\u8bb8\u591a\u7814\u7a76\u4eba\u5458\u5df2\u7ecf\u6ce8\u610f\u5230\u751f\u7269\u5927\u8111\u6781\u5176\u9002\u5e94\u52a8\u6001\u73af\u5883\u4e2d\u7684\u52a8\u6001\u4efb\u52a1\uff0c\u6211\u4eec\u8ba4\u4e3a\u66f4\u597d\u5730\u7406\u89e3\u5927\u8111\u5982\u4f55\u6267\u884c\u52a8\u6001\u4efb\u52a1\u5c06\u5e26\u6765\u65b0\u7684\u6982\u5ff5\uff0c\u4ece\u800c\u63a8\u52a8\u673a\u5668\u5b66\u4e60\u5728\u6b64\u7c7b\u4efb\u52a1\u4e0a\u6027\u80fd\u7684\u63d0\u9ad8\u3002\u901a\u8fc7\u63a2\u7d22\u771f\u5b9e\u5927\u8111\u8ba1\u7b97\u4e0e\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7b97\u6cd5\u548c\u67b6\u6784\u4e4b\u95f4\u7684\u4e3b\u8981\u5dee\u5f02\uff0c\u53ef\u80fd\u4f1a\u4ea7\u751f\u65b0\u7684\u8111\u542f\u53d1\u7684\u7b97\u6cd5<\/strong>\u3002\u5728\u672c\u7279\u520a\u4e2d\uff0c Haim Sompolinksy \u7b49\u4eba[85] \u4ece\u8868\u5f81\u548c\u6cdb\u5316\u7684\u89d2\u5ea6\u5bf9\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u548c\u5927\u8111\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u4e86\u65b0\u9896\u7684\u89c2\u70b9\u9610\u8ff0\u548c\u6df1\u5165\u6bd4\u8f83\u3002<\/span><\/section>\n

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\u9664\u4e86\u8868\u5f81\u548c\u6cdb\u5316\u4e4b\u5916\uff0c\u6211\u4eec\u5217\u51fa\u4eba\u5de5\u7f51\u7edc\u548c\u5927\u8111\u7f51\u7edc\u7684\u53e6\u5916\u4e24\u4e2a\u5dee\u5f02\uff0c\u5e0c\u671b\u80fd\u591f\u6fc0\u53d1\u672a\u6765\u7684\u5de5\u4f5c\uff0c\u56e0\u4e3a\u5b83\u4eec\u90fd\u53ef\u4ee5\u7528\u524d\u9762\u7ae0\u8282\u6982\u8ff0\u7684\u57fa\u4e8e\u7269\u7406\u5b66\u7684\u65b9\u6cd5\u8fdb\u884c\u7814\u7a76\uff1a<\/span><\/p>\n

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  • \n

    \u5927\u8111\u4f7f\u7528\u5c40\u90e8\u5b66\u4e60\u89c4\u5219\u5e76\u4e14\u5f88\u5c11\u53d7\u76d1\u7763<\/strong>\u3002\u9996\u5148\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e3b\u8981\u5173\u6ce8\u76d1\u7763\u5b66\u4e60\uff0c\u5373\u5bf9\u7ed9\u5b9a\u8f93\u5165\u6a21\u5f0f\u6709\u660e\u786e\u6807\u6ce8\u6b63\u786e\u8f93\u51fa\u7684\u60c5\u51b5\uff0c\u800c\u5927\u8111\u4f3c\u4e4e\u5f88\u5c11\u8fdb\u884c\u76d1\u7763\u5b66\u4e60\u3002\u76f8\u53cd\uff0c\u7406\u8bba\u548c\u5b9e\u9a8c\u6570\u636e\u8868\u660e\uff0c\u795e\u7ecf\u5b66\u4e60\u4e3b\u8981\u91c7\u7528\u65e0\u76d1\u7763\u5b66\u4e60<\/span>\uff08unsupervised learning\uff09<\/span>\u3001\u65f6\u95f4\u9884\u6d4b\u6027\u5b66\u4e60<\/span>\uff08temporal-predictive learning\uff09<\/span>\u548c\u5f3a\u5316\u5b66\u4e60<\/span>\uff08reinforcement learning\uff0cRL\uff09<\/span>\u6280\u672f\u3002\u5728\u7b97\u6cd5\u5c42\u9762\uff0c\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u901a\u8fc7\u53cd\u5411\u4f20\u64ad\u5b9e\u73b0\uff0c\u8fd9\u662f\u4e00\u4e2a\u5168\u5c40\u5b66\u4e60\u89c4\u5219\uff0c\u800c\u5927\u8111\u4e2d\u7684\u5b66\u4e60\u662f\u901a\u8fc7\u8d6b\u5e03\u89c4\u5219<\/span>\uff08Hebbian rule\uff09<\/span>\u7b49\u5c40\u90e8\u5b66\u4e60\u89c4\u5219\u5b9e\u73b0\u7684\u3002<\/span><\/p>\n<\/li>\n

  • \n
    \u5927\u8111\u5177\u6709\u9ad8\u5ea6\u52a8\u6001\u6027\u5e76\u6301\u7eed\u4e0e\u73af\u5883\u4e92\u52a8<\/strong>\u3002\u5927\u591a\u6570\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4f7f\u7528\u9759\u6001\u524d\u9988\u67b6\u6784\uff0c\u6216\u8005\u5177\u6709\u5bfc\u5411\u7a33\u6001\u7684\u5f1b\u8c6b\u7279\u6027\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u5927\u8111\u8868\u73b0\u51fa\u590d\u6742\u7684\u52a8\u6001\u884c\u4e3a<\/span>\uff08\u4f8b\u5982\uff0c\u4e0d\u540c\u7684\u5927\u8111\u8282\u5f8b\/\u632f\u8361\uff09<\/span>\uff0c\u8fd9\u662f\u7531\u5927\u91cf\u5faa\u73af\u8fde\u63a5\u5b9e\u73b0\u7684\u3002\u6b64\u5916\uff0c\u5f53\u524d\u7684\u6df1\u5ea6\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u51e0\u4e4e\u5b8c\u5168\u81f4\u529b\u4e8e\u9759\u6001\u7684\u7eaf\u611f\u77e5\u4efb\u52a1\uff0c\u800c\u5927\u8111\u7684\u9996\u8981\u76ee\u7684\u662f\u5728\u4e0e\u73af\u5883\u7684\u6301\u7eed\u611f\u77e5-\u884c\u52a8\u5faa\u73af\u4e2d\u4ea7\u751f\u884c\u4e3a\u3002<\/span><\/section>\n<\/li>\n<\/ul>\n

    <\/span><\/section>\n
    \u5982\u672c\u7279\u520a\u4e2d Chklovskii \u7b49\u4eba[86]\u6240\u8ff0\uff0c\u4ece\u795e\u7ecf\u79d1\u5b66\u83b7\u5f97\u7684\u65b0\u542f\u53d1\u4e5f\u53ef\u4ee5\u6765\u81ea\u5355\u4e2a\u795e\u7ecf\u5143\u5c42\u9762\u3002\u4f5c\u8005\u4eec\u5f15\u5165\u6982\u5ff5\u5c06\u795e\u7ecf\u5143\u4f5c\u4e3a\u5176\u73af\u5883\u53cd\u9988\u7684\u63a7\u5236\u5668\uff0c\u8fd9\u662f\u8fdc\u8d85\u4f20\u7edf McCulloch\u2013Pitts \u795e\u7ecf\u5143\u7684\u529f\u80fd\u3002\u8fd9\u79cd\u521b\u65b0\u65b9\u6cd5\u4e0d\u4ec5\u89e3\u91ca\u4e86\u6b64\u524d\u770b\u4f3c\u65e0\u5173\u7684\u5404\u79cd\u5b9e\u9a8c\u53d1\u73b0\uff0c\u8fd8\u53ef\u80fd\u4e3a\u521b\u5efa\u66f4\u590d\u6742\u7684\u3001\u53d7\u751f\u7269\u542f\u53d1\u7684\u4eba\u5de5\u667a\u80fd\u7cfb\u7edf\u6307\u660e\u65b9\u5411\u3002<\/span><\/section>\n

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      \u4f5c\u8005\u7b80\u4ecb<\/span><\/strong><\/span><\/p>\n

      <\/p>\n

      \u6d82\u8c6b\u6d77<\/span><\/strong>\uff0cIBM\u6c83\u68ee\u7814\u7a76\u4e2d\u5fc3\u7814\u7a76\u5458\uff0c\u5e76\u4e8e2003-2015\u5e74\u62c5\u4efb\u7406\u8bba\u7ec4\u7ec4\u957f\u30021987\u5e74\u6bd5\u4e1a\u4e8e\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\uff0c1991\u5e74\u5728\u52a0\u5dde\u5927\u5b66\u5723\u5730\u4e9a\u54e5\u5206\u6821\u83b7\u5f97\u7269\u7406\u5b66\u535a\u58eb\u5b66\u4f4d\u3002<\/span>\u7531\u4e8e\u5728\u7406\u8bba\u7edf\u8ba1\u7269\u7406\u65b9\u9762\u7684\u5de5\u4f5c\uff0c\u4ed6\u4e0eJohn Toner\u548cTamas Vicsek\u4e00\u8d77\u88ab\u7f8e\u56fd\u7269\u7406\u5b66\u4f1a\u6388\u4e882020\u5e74Lars Onsager\u5956\uff1a\u201c\u56e0\u4e3a\u4ed6\u5728\u96c6\u7fa4\u7406\u8bba\u65b9\u9762\u7684\u5f00\u521b\u6027\u5de5\u4f5c\uff0c\u8fd9\u6807\u5fd7\u7740\u6d3b\u6027\u7269\u8d28\u9886\u57df\u7684\u8bde\u751f\uff0c\u5e76\u5bf9\u5176\u53d1\u5c55\u505a\u51fa\u4e86\u5de8\u5927\u8d21\u732e\u3002\u201d <\/span><\/section>\n

      <\/span><\/section>\n
      \u4ed6\u5728\u591a\u4e2a\u9886\u57df\u505a\u51fa\u4e86\u5f00\u521b\u6027\u8d21\u732e\uff0c\u5305\u62ec\u6d3b\u6027\u7cfb\u7edf\uff08\u96c6\u7fa4\u52a8\u529b\u5b66\uff09\uff0c\u9ad8\u901a\u91cf\u8f6c\u5f55\u7ec4\u6570\u636e\uff08\u5fae\u9635\u5217\u5206\u6790\uff09\u7684\u7b97\u6cd5\u5f00\u53d1\u548c\u7edf\u8ba1\u5206\u6790\uff0c\u7ec6\u83cc\u8d8b\u5316\u6027\u4e2d\u4fe1\u53f7\u8f6c\u5bfc\u548c\u8fd0\u52a8\u7684\u5b9a\u91cf\u5efa\u6a21\uff0c\u4ee5\u53ca\u975e\u5e73\u8861\u751f\u5316\u7f51\u7edc\u7684\u70ed\u529b\u5b66\u3002\u6700\u8fd1\u7684\u5de5\u4f5c\u96c6\u4e2d\u5728\u4e09\u4e2a\u65b9\u5411\uff1a\uff081\uff09\u751f\u7269\u7f51\u7edc\u7684\u52a8\u529b\u5b66\uff0c\u7528\u4e8e\u4fe1\u53f7\u8f6c\u5bfc\u7684\u751f\u5316\u7f51\u7edc\u548c\u7528\u4e8e\u7f16\u7801\u4e0e\u8ba1\u7b97\u7684\u795e\u7ecf\u7f51\u7edc\uff1b\uff082\uff09\u751f\u7269\u7cfb\u7edf\u4fe1\u606f\u5904\u7406\u7684\u70ed\u529b\u5b66\uff1b\uff083\uff09\u5927\u8111\u548c\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e2d\u5b66\u4e60\u7684\u7edf\u8ba1\u7269\u7406\u3002<\/span><\/section>\n
      \u5b66\u8005\u4e3b\u9875\uff1ahttps:\/\/research.ibm.com\/people\/yuhai-tu<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      <\/section>\n


      <\/p>\n

      \n
      \n
      \n
      \n

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


      <\/section>\n

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


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

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


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

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

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


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

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

      <\/strong><\/section>\n
      1. <\/strong>2024\u5e74\u7269\u7406\u8bfa\u5956\u6388\u4e88\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff1a\u7edf\u8ba1\u7269\u7406\u5f15\u53d1\u7684\u673a\u5668\u5b66\u4e60\u9769\u547d<\/a><\/strong><\/span><\/section>\n
      2. <\/strong>2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u4e3a\u4f55\u6388\u4e88\u673a\u5668\u5b66\u4e60\u9886\u57df\uff1f<\/a><\/strong><\/span><\/section>\n
      3. <\/strong>\u795e\u7ecf\u7f51\u7edc\u7406\u8bba\u7814\u7a76\u7684\u6311\u6218\u6027\u8bfe\u9898\uff1a\u7edf\u8ba1\u7269\u7406\u80fd\u5426\u7ed9\u667a\u80fd\u79d1\u5b66\u5e26\u6765\u7b2c\u4e00\u6027\u539f\u7406\uff1f<\/a><\/strong><\/span><\/section>\n
      4. <\/strong>Nature Physics\u8bc4\u8bba\uff1a\u91cd\u6574\u5316\u7fa450\u5e74\uff0c\u5e94\u7528\u4e8e\u975e\u5e73\u8861\u7cfb\u7edf\u524d\u666f\u5e7f\u9614<\/a><\/strong><\/span><\/section>\n
      5. <\/strong><\/strong>\u6c6a\u52b2\uff1a\u63cf\u8ff0\u751f\u7269\u7cfb\u7edf\u6d8c\u73b0\u884c\u4e3a\u7684\u666f\u89c2\u548c\u6d41\u7406\u8bba\u89c6\u89d2<\/a><\/strong><\/strong><\/span><\/section>\n
      6. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
      <\/strong>7.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

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


      <\/p>\n


      <\/p>\n

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

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

      \u5bfc\u8bed 2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u201c\u901a\u8fc7\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u673a\u5668\u5b66\u4e60\u7684\u57fa\u7840\u6027\u53d1\u73b0\u548c\u53d1\u660e\u201d\uff0c\u5f15\u53d1\u4eba\u4eec\u5bf9\u7edf\u8ba1\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u4e4b\u95f4\u6df1\u523b\u8054\u7cfb\u7684\u5173\u6ce8\u548c\u5e7f\u6cdb\u8ba8\u8bba\u3002\u673a\u5668\u5b66\u4e60\u80fd\u4e3a\u7269\u7406\u5b66\u505a\u4e9b\u4ec0\u4e48\uff1f\u7269\u7406\u5b66\u53c8\u80fd\u4e3a\u673a\u5668\u5b66\u4e60\u505a\u4e9b\u4ec0\u4e48\uff1f\u8fd1\u671f PNAS \u6742\u5fd7\u53d1\u8868\u300c\u7269\u7406\u5b66\u9047\u89c1\u673a\u5668\u5b66\u4e60\u300d\uff08Physics Meets Machine Lea…<\/p>\n","protected":false},"author":0,"featured_media":53947,"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\/53975"}],"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=53975"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/53975\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/53947"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=53975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=53975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=53975"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=53975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}