{"id":35680,"date":"2024-12-29T16:00:15","date_gmt":"2024-12-29T08:00:15","guid":{"rendered":"https:\/\/17aitech.com\/?p=35680"},"modified":"2024-12-29T16:00:15","modified_gmt":"2024-12-29T08:00:15","slug":"%e4%bd%bf%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e6%9b%b4%e5%ae%b9%e6%98%93%e7%90%86%e8%a7%a3%ef%bc%8c%e4%bf%83%e8%bf%9b%e7%a7%91%e5%ad%a6%e5%8f%91%e7%8e%b0%ef%bc%8cmit%e5%88%98%e5%ad%90%e9%b8%a3","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=35680","title":{"rendered":"\u4f7f\u795e\u7ecf\u7f51\u7edc\u66f4\u5bb9\u6613\u7406\u89e3\uff0c\u4fc3\u8fdb\u79d1\u5b66\u53d1\u73b0\uff0cMIT\u5218\u5b50\u9e23\u56e2\u961f\u65b0\u67b6\u6784"},"content":{"rendered":"

\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:\u4f7f\u795e\u7ecf\u7f51\u7edc\u66f4\u5bb9\u6613\u7406\u89e3\uff0c\u4fc3\u8fdb\u79d1\u5b66\u53d1\u73b0\uff0cMIT\u5218\u5b50\u9e23\u56e2\u961f\u65b0\u67b6\u6784<\/a><\/p>\n

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\u7f16\u8bd1\u00a0| \u767d\u83dc\u53f6<\/p>\n

\u300c\u795e\u7ecf\u7f51\u7edc<\/mark>\u662f\u76ee\u524d\u4eba\u5de5\u667a\u80fd<\/mark>\u9886\u57df\u6700\u5f3a\u5927\u7684\u5de5\u5177\u3002\u300dPerimeter Institute for Theoretical Physics \u7684\u7814\u7a76\u5458 Sebastian Wetzel \u8868\u793a\uff0c\u300c\u5f53\u6211\u4eec\u5c06\u5b83\u4eec\u6269\u5c55\u5230\u66f4\u5927\u7684\u6570\u636e\u96c6\u65f6\uff0c\u6ca1\u6709\u4ec0\u4e48\u53ef\u4ee5\u4e0e\u4e4b\u7ade\u4e89\u3002\u300d<\/p>\n

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2024 \u5e74 4 \u6708\u7684\u4e00\u9879\u7814\u7a76\u63d0\u51fa\u4e86\u4e00\u79cd\u66ff\u4ee3\u795e\u7ecf\u7f51\u7edc<\/mark>\u8bbe\u8ba1\uff0c\u79f0\u4e3a Kolmogorov-Arnold \u7f51\u7edc\uff08KAN\uff09\uff0c\u5b83\u66f4\u52a0\u900f\u660e\uff0c\u4f46\u5bf9\u4e8e\u67d0\u4e00\u7c7b\u95ee\u9898\uff0c\u5b83\u51e0\u4e4e\u53ef\u4ee5\u5b8c\u6210\u5e38\u89c4\u795e\u7ecf\u7f51\u7edc<\/mark>\u53ef\u4ee5\u5b8c\u6210\u7684\u6240\u6709\u4e8b\u60c5\u3002\u5b83\u57fa\u4e8e 20 \u4e16\u7eaa\u4e2d\u53f6\u7684\u4e00\u4e2a\u6570\u5b66\u601d\u60f3\uff0c\u8be5\u601d\u60f3\u5728\u6df1\u5ea6\u5b66\u4e60<\/mark>\u65f6\u4ee3\u88ab\u7814\u7a76\u4eba\u5458\u91cd\u65b0\u8ba4\u8bc6\u3002<\/p>\n

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\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2404.19756<\/em><\/section>\n

\u867d\u7136\u8fd9\u4e00\u521b\u65b0\u4ec5\u6709\u51e0\u4e2a\u6708\u7684\u5386\u53f2\uff0c\u4f46\u65b0\u8bbe\u8ba1\u5df2\u7ecf\u5f15\u8d77\u4e86\u7814\u7a76\u548c\u7f16\u7801\u754c\u7684\u5e7f\u6cdb\u5174\u8da3\u3002\u7ea6\u7ff0\u970d\u666e\u91d1\u65af\u5927\u5b66\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6 Alan Yuille \u8868\u793a\uff1a\u300cKAN \u66f4\u6613\u4e8e\u89e3\u91ca\uff0c\u53ef\u80fd\u7279\u522b\u9002\u7528\u4e8e\u79d1\u5b66\u5e94\u7528\uff0c\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u4ece\u6570\u636e\u4e2d\u63d0\u53d6\u79d1\u5b66\u89c4\u5219\u3002[\u5b83\u4eec\u662f] \u65e0\u5904\u4e0d\u5728\u7684 MLP \u7684\u4e00\u79cd\u4ee4\u4eba\u5174\u594b\u7684\u65b0\u66ff\u4ee3\u54c1\u3002\u300d<\/p>\n

\u300c\u5b9e\u73b0\u4e0d\u53ef\u80fd\u300d<\/strong><\/p>\n

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\u795e\u7ecf\u7f51\u7edc<\/mark>\u7684\u4e00\u4e2a\u5e38\u89c1\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u6570\u5b66\u51fd\u6570\u6216\u66f2\u7ebf\uff0c\u4ee5\u6700\u4f73\u65b9\u5f0f\u8fde\u63a5\u67d0\u4e9b\u6570\u636e\u70b9\u3002\u7f51\u7edc\u8d8a\u63a5\u8fd1\u8be5\u51fd\u6570\uff0c\u5176\u9884\u6d4b\u5c31\u8d8a\u597d\uff0c\u7ed3\u679c\u5c31\u8d8a\u51c6\u786e\u3002\u5982\u679c\u60a8\u7684\u795e\u7ecf\u7f51\u7edc<\/mark>\u6a21\u62df\u67d0\u4e9b\u7269\u7406\u8fc7\u7a0b\uff0c\u5219\u8f93\u51fa\u51fd\u6570\u5c06\u7406\u60f3\u5730\u8868\u793a\u63cf\u8ff0\u7269\u7406\u5b66\u7684\u65b9\u7a0b – \u76f8\u5f53\u4e8e\u7269\u7406\u5b9a\u5f8b\u3002<\/p>\n

\u5bf9\u4e8e MLP\uff0c\u6709\u4e00\u4e2a\u6570\u5b66\u5b9a\u7406\u53ef\u4ee5\u544a\u8bc9\u4f60\u7f51\u7edc\u53ef\u4ee5\u591a\u63a5\u8fd1\u6700\u4f73\u51fd\u6570\u3002\u8fd9\u4e2a\u5b9a\u7406\u7684\u4e00\u4e2a\u7ed3\u679c\u662f MLP \u65e0\u6cd5\u5b8c\u7f8e\u5730\u8868\u793a\u8be5\u51fd\u6570\u3002<\/p>\n

\u4f46\u5728\u9002\u5f53\u7684\u60c5\u51b5\u4e0b\uff0cKAN \u53ef\u4ee5\u3002<\/p>\n

KAN \u8fdb\u884c\u51fd\u6570\u62df\u5408\uff08\u8fde\u63a5\u7f51\u7edc\u8f93\u51fa\u7684\u70b9\uff09\u7684\u65b9\u5f0f\u4e0e MLP \u5b8c\u5168\u4e0d\u540c\u3002KAN \u4e0d\u4f9d\u8d56\u5177\u6709\u6570\u503c\u6743\u91cd<\/mark>\u7684\u8fb9\uff0c\u800c\u662f\u4f7f\u7528\u51fd\u6570\u3002\u8fd9\u4e9b\u8fb9\u7f18\u51fd\u6570\u662f\u975e\u7ebf\u6027\u7684\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u53ef\u4ee5\u8868\u793a\u66f4\u590d\u6742\u7684\u66f2\u7ebf\u3002\u5b83\u4eec\u4e5f\u662f\u53ef\u5b66\u4e60\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u6bd4 MLP \u7684\u7b80\u5355\u6570\u503c\u6743\u91cd<\/mark>\u4ee5\u66f4\u9ad8\u7684\u7075\u654f\u5ea6\u8fdb\u884c\u8c03\u6574\u3002<\/p>\n

\u7136\u800c\u5728\u8fc7\u53bb\u7684 35 \u5e74\u91cc\uff0c\u4eba\u4eec\u8ba4\u4e3a KAN \u4ece\u6839\u672c\u4e0a\u6765\u8bf4\u4e0d\u5207\u5b9e\u9645\u3002\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7269\u7406\u5b66\u5bb6\u3001\u8ba1\u7b97\u795e\u7ecf\u5b66\u5bb6 Tomaso Poggio \u5728 1989 \u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d\u660e\u786e\u6307\u51fa\uff0cKAN \u6838\u5fc3\u7684\u6570\u5b66\u601d\u60f3\u300c\u4e0e\u5b66\u4e60\u7f51\u7edc\u65e0\u5173\u300d\u3002<\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttp:\/\/cbcl.mit.edu\/people\/poggio\/journals\/girosi-poggio-NeuralComputation-1989.pdf<\/em><\/p>\n

Poggio \u7684\u5173\u6ce8\u70b9\u4e4b\u4e00\u53ef\u4ee5\u8ffd\u6eaf\u5230 KAN \u6838\u5fc3\u7684\u6570\u5b66\u6982\u5ff5\u30021957 \u5e74\uff0c\u6570\u5b66\u5bb6 Andrey Kolmogorov \u548c Vladimir Arnold \u5728\u5404\u81ea\u4f46\u4e92\u8865\u7684\u8bba\u6587\u4e2d\u8868\u660e\uff0c\u5982\u679c\u4f60\u6709\u4e00\u4e2a\u4f7f\u7528\u591a\u4e2a\u53d8\u91cf\u7684\u5355\u4e00\u6570\u5b66\u51fd\u6570\uff0c\u4f60\u53ef\u4ee5\u5c06\u5176\u8f6c\u6362\u4e3a\u591a\u4e2a\u51fd\u6570\u7684\u7ec4\u5408\uff0c\u6bcf\u4e2a\u51fd\u6570\u90fd\u6709\u4e00\u4e2a\u53d8\u91cf\u3002<\/p>\n

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\u56e0\u6b64\uff0cKAN \u7684\u524d\u666f\u4f3c\u4e4e\u5e76\u4e0d\u4e50\u89c2\u2014\u2014\u76f4\u5230\u4eca\u5e74 1 \u6708\u7684\u4e00\u4e2a\u5bd2\u51b7\u7684\u65e5\u5b50\uff0c\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7269\u7406\u5b66\u7814\u7a76\u751f\u5218\u5b50\u9e23\uff08Ziming Liu\uff09\u51b3\u5b9a\u91cd\u65b0\u5ba1\u89c6\u8fd9\u4e2a\u8bfe\u9898\u3002\u4ed6\u548c\u4ed6\u7684\u5bfc\u5e08\u3001\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7269\u7406\u5b66\u5bb6\u00a0Max Tegmark\u00a0\u4e00\u76f4\u81f4\u529b\u4e8e\u8ba9\u795e\u7ecf\u7f51\u7edc<\/mark>\u66f4\u6613\u4e8e\u7406\u89e3\uff0c\u4ee5\u7528\u4e8e\u79d1\u5b66\u5e94\u7528\u2014\u2014\u5e0c\u671b\u80fd\u591f\u8ba9\u4eba\u4eec\u4e00\u7aa5\u9ed1\u5323\u5b50\u5185\u90e8\u2014\u2014\u4f46\u4e8b\u60c5\u5e76\u6ca1\u6709\u8fdb\u5c55\u3002<\/p>\n

\u65e0\u5948\u4e4b\u4e0b\uff0c\u5218\u5b50\u9e23\u51b3\u5b9a\u7814\u7a76\u4e00\u4e0b Kolmogorov-Arnold \u5b9a\u7406\u3002\u4ed6\u95ee\u9053\uff1a\u300c\u4e3a\u4ec0\u4e48\u4e0d\u8bd5\u4e00\u8bd5\uff0c\u770b\u770b\u5b83\u662f\u5982\u4f55\u8fd0\u4f5c\u7684\uff0c\u5373\u4f7f\u8fc7\u53bb\u4eba\u4eec\u5e76\u6ca1\u6709\u7ed9\u4e88\u5b83\u592a\u591a\u5173\u6ce8\uff1f\u300d<\/p>\n

Tegmark \u719f\u6089 Poggio \u7684\u8bba\u6587\uff0c\u5e76\u8ba4\u4e3a\u8fd9\u4e00\u52aa\u529b\u5c06\u518d\u6b21\u8d70\u5411\u6b7b\u80e1\u540c\u3002\u4f46\u5218\u5b50\u9e23\u6ca1\u6709\u6c14\u9981\uff0cTegmark \u5f88\u5feb\u5c31\u6539\u53d8\u4e86\u4e3b\u610f\u3002\u4ed6\u4eec\u8ba4\u8bc6\u5230\uff0c\u5373\u4f7f\u8be5\u5b9a\u7406\u751f\u6210\u7684\u5355\u503c\u51fd\u6570\u4e0d\u5e73\u6ed1\uff0c\u7f51\u7edc\u4ecd\u7136\u53ef\u4ee5\u7528\u5e73\u6ed1\u51fd\u6570\u6765\u8fd1\u4f3c\u5b83\u4eec\u3002<\/p>\n

\u4ed6\u4eec\u8fdb\u4e00\u6b65\u4e86\u89e3\u5230\uff0c\u6211\u4eec\u5728\u79d1\u5b66\u4e2d\u9047\u5230\u7684\u5927\u591a\u6570\u51fd\u6570\u90fd\u662f\u5e73\u6ed1\u7684\uff0c\u8fd9\u4f7f\u5f97\u5b8c\u7f8e\uff08\u800c\u975e\u8fd1\u4f3c\uff09\u7684\u8868\u793a\u6709\u53ef\u80fd\u5b9e\u73b0\u3002\u5218\u5b50\u9e23\u4e0d\u60f3\u5728\u6ca1\u6709\u5c1d\u8bd5\u7684\u60c5\u51b5\u4e0b\u5c31\u653e\u5f03\u8fd9\u4e2a\u60f3\u6cd5\uff0c\u56e0\u4e3a\u4ed6\u77e5\u9053\uff0c\u81ea 35 \u5e74\u524d Poggio \u7684\u8bba\u6587\u53d1\u8868\u4ee5\u6765\uff0c\u8f6f\u4ef6\u548c\u786c\u4ef6\u5df2\u7ecf\u53d6\u5f97\u4e86\u957f\u8db3\u7684\u8fdb\u6b65\u3002\u4ece\u8ba1\u7b97\u89d2\u5ea6\u6765\u8bf4\uff0c2024 \u5e74\u8bb8\u591a\u5728 1989 \u5e74\u751a\u81f3\u65e0\u6cd5\u60f3\u8c61\u7684\u4e8b\u60c5\u90fd\u5c06\u6210\u4e3a\u53ef\u80fd\u3002<\/p>\n

\u5218\u5b50\u9e23\u82b1\u4e86\u5927\u7ea6\u4e00\u5468\u7684\u65f6\u95f4\u7814\u7a76\u8fd9\u4e2a\u60f3\u6cd5\uff0c\u5728\u6b64\u671f\u95f4\uff0c\u4ed6\u5f00\u53d1\u4e86\u4e00\u4e9b\u539f\u578b KAN \u7cfb\u7edf\uff0c\u6240\u6709\u7cfb\u7edf\u90fd\u6709\u4e24\u5c42\u2014\u2014\u6700\u7b80\u5355\u7684\u7f51\u7edc\uff0c\u4ee5\u53ca\u7814\u7a76\u4eba\u5458\u51e0\u5341\u5e74\u6765\u4e00\u76f4\u5173\u6ce8\u7684\u7c7b\u578b\u3002\u53cc\u5c42 KAN \u4f3c\u4e4e\u662f\u663e\u800c\u6613\u89c1\u7684\u9009\u62e9\uff0c\u56e0\u4e3a Kolmogorov-Arnold \u5b9a\u7406\u672c\u8d28\u4e0a\u4e3a\u8fd9\u79cd\u7ed3\u6784\u63d0\u4f9b\u4e86\u84dd\u56fe\u3002<\/p>\n

\u8be5\u5b9a\u7406\u5177\u4f53\u5c06\u591a\u53d8\u91cf\u51fd\u6570\u5206\u89e3\u4e3a\u4e0d\u540c\u7684\u5185\u90e8\u51fd\u6570\u548c\u5916\u90e8\u51fd\u6570\u96c6\u3002\uff08\u5b83\u4eec\u4ee3\u8868\u4e86\u6cbf\u7740\u8fb9\u7684\u6fc0\u6d3b\u51fd\u6570<\/mark>\uff0c\u66ff\u4ee3\u4e86 MLP \u4e2d\u7684\u6743\u91cd<\/mark>\u3002\uff09\u8fd9\u79cd\u5b89\u6392\u81ea\u7136\u800c\u7136\u5730\u9002\u7528\u4e8e\u5177\u6709\u5185\u5c42\u548c\u5916\u5c42\u795e\u7ecf\u5143<\/mark>\u7684 KAN \u7ed3\u6784\u2014\u2014\u8fd9\u662f\u7b80\u5355\u795e\u7ecf\u7f51\u7edc<\/mark>\u7684\u5e38\u89c1\u5b89\u6392\u3002<\/p>\n

\u4f46\u4ee4\u5218\u5b50\u9e23\u5931\u671b\u7684\u662f\uff0c\u4ed6\u7684\u539f\u578b\u673a\u5728\u5b8c\u6210\u4ed6\u8bbe\u60f3\u7684\u79d1\u5b66\u76f8\u5173\u4efb\u52a1\u65f6\u8868\u73b0\u90fd\u4e0d\u4f73\u3002Tegmark \u968f\u540e\u63d0\u51fa\u4e86\u4e00\u4e2a\u5173\u952e\u5efa\u8bae\uff1a\u4e3a\u4ec0\u4e48\u4e0d\u5c1d\u8bd5\u4f7f\u7528\u4e24\u5c42\u4ee5\u4e0a\u7684 KAN\uff0c\u8fd9\u6837\u4e5f\u8bb8\u80fd\u591f\u5904\u7406\u66f4\u590d\u6742\u7684\u4efb\u52a1\uff1f<\/p>\n

\u8fd9\u79cd\u7a81\u7834\u6027\u7684\u60f3\u6cd5\u6b63\u662f\u4ed6\u4eec\u6240\u9700\u8981\u7684\u7a81\u7834\u3002\u5218\u5b50\u9e23\u521a\u8d77\u6b65\u7684\u7f51\u7edc\u5f00\u59cb\u5c55\u73b0\u51fa\u5e0c\u671b\uff0c\u56e0\u6b64\u4e24\u4eba\u5f88\u5feb\u8054\u7cfb\u4e86\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u3001\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u548c\u4e1c\u5317\u5927\u5b66\u7684\u540c\u4e8b\u3002\u4ed6\u4eec\u5e0c\u671b\u56e2\u961f\u4e2d\u65e2\u6709\u6570\u5b66\u5bb6\uff0c\u53c8\u6709\u4ed6\u4eec\u8ba1\u5212\u8ba9 KAN \u5206\u6790\u7684\u9886\u57df\u7684\u4e13\u5bb6\u3002<\/p>\n

\u5728\u4ed6\u4eec 4 \u6708\u4efd\u7684\u8bba\u6587\u4e2d\uff0c\u8be5\u56e2\u961f\u8868\u660e\u4e09\u5c42\u7684 KAN \u786e\u5b9e\u662f\u53ef\u80fd\u7684\uff0c\u5e76\u63d0\u4f9b\u4e86\u4e00\u4e2a\u53ef\u4ee5\u7cbe\u786e\u8868\u793a\u51fd\u6570\u7684\u4e09\u5c42 KAN \u7684\u793a\u4f8b\uff08\u800c\u4e24\u5c42 KAN \u5219\u4e0d\u80fd\uff09\u3002<\/p>\n

\u4ed6\u4eec\u5e76\u6ca1\u6709\u6b62\u6b65\u4e8e\u6b64\u3002\u6b64\u540e\uff0c\u8be5\u56e2\u961f\u5c1d\u8bd5\u4e86\u591a\u8fbe\u516d\u5c42\u7684\u795e\u7ecf\u7f51\u7edc<\/mark>\uff0c\u6bcf\u5c42\u795e\u7ecf\u7f51\u7edc<\/mark>\u90fd\u80fd\u591f\u4e0e\u66f4\u590d\u6742\u7684\u8f93\u51fa\u51fd\u6570\u76f8\u5339\u914d\u3002\u300c\u6211\u4eec\u53d1\u73b0\uff0c\u57fa\u672c\u4e0a\u53ef\u4ee5\u5806\u53e0<\/mark>\u4efb\u610f\u591a\u7684\u5c42\u3002\u300d\u8bba\u6587\u5408\u8457\u8005\u4e4b\u4e00\u738b\u9038\u8f69 (Yixuan Wang) \u8bf4\u9053\u3002<\/p>\n

\u7ecf\u8fc7\u9a8c\u8bc1\u7684\u6539\u8fdb<\/strong><\/p>\n

\u4f5c\u8005\u8fd8\u5c06\u4ed6\u4eec\u7684\u7f51\u7edc\u7528\u4e8e\u89e3\u51b3\u4e24\u4e2a\u73b0\u5b9e\u95ee\u9898\u3002\u7b2c\u4e00\u4e2a\u95ee\u9898\u4e0e\u6570\u5b66\u7684\u4e00\u4e2a\u5206\u652f\u6709\u5173\uff0c\u79f0\u4e3a\u7ed3\u7406\u8bba\u30022021 \u5e74\uff0cDeepMind<\/mark> \u7684\u4e00\u4e2a\u56e2\u961f\u5ba3\u5e03\u4ed6\u4eec\u5df2\u7ecf\u6784\u5efa\u4e86\u4e00\u4e2a MLP\uff0c\u5728\u8f93\u5165\u4e86\u8db3\u591f\u591a\u7684\u7ed3\u7684\u5176\u4ed6\u5c5e\u6027\u540e\uff0c\u5b83\u53ef\u4ee5\u9884\u6d4b\u7ed9\u5b9a\u7ed3\u7684\u67d0\u79cd\u62d3\u6251\u5c5e\u6027\u3002\u4e09\u5e74\u540e\uff0c\u65b0\u7684 KAN \u590d\u5236\u4e86\u8fd9\u4e00\u58ee\u4e3e\u3002\u7136\u540e\u5b83\u66f4\u8fdb\u4e00\u6b65\uff0c\u5c55\u793a\u4e86\u9884\u6d4b\u5c5e\u6027\u4e0e\u5176\u4ed6\u6240\u6709\u5c5e\u6027\u4e4b\u95f4\u7684\u5173\u7cfb\u2014\u2014\u5218\u5b50\u9e23\u8bf4\uff0c\u8fd9\u662f\u300cMLP \u6839\u672c\u505a\u4e0d\u5230\u7684\u300d\u3002<\/p>\n

\u7b2c\u4e8c\u4e2a\u95ee\u9898\u6d89\u53ca\u51dd\u805a\u6001\u7269\u7406\u5b66\u4e2d\u4e00\u79cd\u79f0\u4e3a Anderson \u5c40\u57df\u5316\u7684\u73b0\u8c61\u3002\u76ee\u6807\u662f\u9884\u6d4b\u7279\u5b9a\u76f8\u53d8\u53d1\u751f\u7684\u8fb9\u754c\uff0c\u7136\u540e\u786e\u5b9a\u63cf\u8ff0\u8be5\u8fc7\u7a0b\u7684\u6570\u5b66\u516c\u5f0f\u3002\u6ca1\u6709\u4efb\u4f55 MLP \u80fd\u591f\u505a\u5230\u8fd9\u4e00\u70b9\u3002\u4ed6\u4eec\u7684 KAN \u505a\u5230\u4e86\u3002<\/p>\n

\u4f46 Tegmark \u8868\u793a\uff0cKAN \u76f8\u5bf9\u4e8e\u5176\u4ed6\u5f62\u5f0f\u7684\u795e\u7ecf\u7f51\u7edc<\/mark>\u7684\u6700\u5927\u4f18\u52bf\uff0c\u4ee5\u53ca\u5176\u8fd1\u671f\u53d1\u5c55\u7684\u4e3b\u8981\u52a8\u673a\uff0c\u5728\u4e8e\u5176\u53ef\u89e3\u91ca\u6027\u3002\u5728\u8fd9\u4e24\u4e2a\u4f8b\u5b50\u4e2d\uff0cKAN \u4e0d\u53ea\u662f\u7ed9\u51fa\u7b54\u6848\uff0c\u5b83\u8fd8\u63d0\u4f9b\u4e86\u89e3\u91ca\u3002\u300c\u53ef\u89e3\u91ca\u662f\u4ec0\u4e48\u610f\u601d\uff1f\u300d\u4ed6\u95ee\u9053\uff0c\u300c\u5982\u679c\u4f60\u7ed9\u6211\u4e00\u4e9b\u6570\u636e\uff0c\u6211\u5c31\u4f1a\u7ed9\u4f60\u4e00\u4e2a\u53ef\u4ee5\u5199\u5728 T \u6064\u4e0a\u7684\u516c\u5f0f\u3002\u300d<\/p>\n

\u7ea6\u7ff0\u970d\u666e\u91d1\u65af\u5927\u5b66\u7814\u7a76\u673a\u5668\u5b66\u4e60<\/mark>\u7684\u7269\u7406\u5b66\u5bb6 Brice M\u00e9nard \u8868\u793a\uff0c\u5c3d\u7ba1 KAN \u5728\u8fd9\u65b9\u9762\u7684\u80fd\u529b\u76ee\u524d\u8fd8\u5f88\u6709\u9650\uff0c\u4f46\u4ece\u7406\u8bba\u4e0a\u8bb2\uff0c\u8fd9\u4e9b\u7f51\u7edc\u53ef\u4ee5\u6559\u4f1a\u6211\u4eec\u4e00\u4e9b\u5173\u4e8e\u4e16\u754c\u7684\u65b0\u77e5\u8bc6\u3002<\/p>\n

M\u00e9nard \u8bf4\uff1a\u300c\u5982\u679c\u95ee\u9898\u5b9e\u9645\u4e0a\u53ef\u4ee5\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u65b9\u7a0b\u6765\u63cf\u8ff0\uff0c\u90a3\u4e48 KAN \u7f51\u7edc\u5c31\u5f88\u64c5\u957f\u627e\u5230\u5b83\u3002\u300d\u4f46\u4ed6\u63d0\u9192\u9053\uff0cKAN \u6700\u9002\u7528\u7684\u9886\u57df\u53ef\u80fd\u4ec5\u9650\u4e8e\u95ee\u9898\u2014\u2014\u4f8b\u5982\u7269\u7406\u5b66\u4e2d\u7684\u95ee\u9898\u2014\u2014\u5176\u4e2d\u65b9\u7a0b\u5f80\u5f80\u53ea\u6709\u5f88\u5c11\u7684\u53d8\u91cf\u3002<\/p>\n

\u5218\u5b50\u9e23\u548c Tegmark \u5bf9\u6b64\u8868\u793a\u540c\u610f\uff0c\u4f46\u5e76\u4e0d\u8ba4\u4e3a\u8fd9\u662f\u4e00\u4e2a\u7f3a\u70b9\u3002\u300c\u51e0\u4e4e\u6240\u6709\u8457\u540d\u7684\u79d1\u5b66\u516c\u5f0f\u300d\u2014\u2014\u4f8b\u5982 E = mc^2\u2014\u2014\u300c\u90fd\u53ef\u4ee5\u7528\u4e00\u4e24\u4e2a\u53d8\u91cf\u7684\u51fd\u6570\u6765\u5199\u3002\u300dTegmark \u8bf4\uff0c\u300c\u6211\u4eec\u6240\u505a\u7684\u7edd\u5927\u591a\u6570\u8ba1\u7b97\u90fd\u4f9d\u8d56\u4e8e\u4e00\u4e24\u4e2a\u53d8\u91cf\u3002KAN \u5229\u7528\u8fd9\u4e00\u4e8b\u5b9e\u5e76\u5bfb\u627e\u8fd9\u79cd\u5f62\u5f0f\u7684\u89e3\u51b3\u65b9\u6848\u3002\u300d<\/p>\n

\u7ec8\u6781\u65b9\u7a0b<\/strong><\/p>\n

\u5218\u5b50\u9e23\u548c Tegmark \u7684 KAN \u8bba\u6587\u8fc5\u901f\u5f15\u8d77\u8f70\u52a8\uff0c\u5728\u5927\u7ea6\u4e09\u4e2a\u6708\u5185\u5c31\u83b7\u5f97\u4e86 75 \u6b21\u5f15\u7528\u3002\u5f88\u5feb\u5176\u4ed6\u56e2\u961f\u4e5f\u5f00\u59cb\u7814\u7a76\u81ea\u5df1\u7684 KAN\u3002<\/p>\n

<\/a><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2406.11045<\/em><\/p>\n

\u6e05\u534e\u5927\u5b66<\/mark> Wang Yizheng \u56e2\u961f\u4e8e 6 \u6708\u5728\u7ebf\u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587\u8868\u660e\uff0c\u4ed6\u4eec\u7684 Kolmogorov Arnold Infor<\/mark>med \u795e\u7ecf\u7f51\u7edc<\/mark> (KINN) \u5728\u89e3\u51b3\u504f\u5fae\u5206\u65b9\u7a0b (PDE) \u65b9\u9762\u300c\u660e\u663e\u4f18\u4e8e\u300d MLP\u3002Wang \u8bf4\uff0c\u8fd9\u4e0d\u662f\u5c0f\u4e8b\uff1a\u300cPDE \u5728\u79d1\u5b66\u4e2d\u65e0\u5904\u4e0d\u5728\u3002\u300d<\/p>\n

\u65b0\u52a0\u5761\u56fd\u7acb\u5927\u5b66\u7814\u7a76\u4eba\u5458\u5728 7 \u6708\u4efd\u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587\u5219\u66f4\u52a0\u559c\u5fe7\u53c2\u534a\u3002\u4ed6\u4eec\u5f97\u51fa\u7684\u7ed3\u8bba\u662f\uff0cKAN \u5728\u53ef\u89e3\u91ca\u6027\u76f8\u5173\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\u4f18\u4e8e MLP\uff0c\u4f46\u53d1\u73b0 MLP \u5728\u8ba1\u7b97\u673a\u89c6\u89c9<\/mark>\u548c\u97f3\u9891\u5904\u7406\u65b9\u9762\u8868\u73b0\u66f4\u4f73\u3002<\/p>\n

<\/a><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2407.16674<\/em><\/p>\n

\u8fd9\u4e24\u4e2a\u7f51\u7edc\u5728\u81ea\u7136\u8bed\u8a00\u5904\u7406<\/mark>\u548c\u5176\u4ed6\u673a\u5668\u5b66\u4e60<\/mark>\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\u5927\u81f4\u76f8\u5f53\u3002\u5bf9\u4e8e\u5218\u5b50\u9e23\u6765\u8bf4\uff0c\u8fd9\u4e9b\u7ed3\u679c\u5e76\u4e0d\u4ee4\u4eba\u610f\u5916\uff0c\u56e0\u4e3a\u6700\u521d\u7684 KAN \u56e2\u961f\u7684\u91cd\u70b9\u4e00\u76f4\u662f\u300c\u4e0e\u79d1\u5b66\u76f8\u5173\u7684\u4efb\u52a1\u300d\uff0c\u800c\u53ef\u89e3\u91ca\u6027\u662f\u5176\u4e2d\u7684\u91cd\u4e2d\u4e4b\u91cd\u3002<\/p>\n

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<\/a><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2408.10205<\/em><\/p>\n

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\u76f8\u5173\u5185\u5bb9\uff1ahttps:\/\/www.quantamagazine.org\/novel-architecture-makes-neural-networks-more-understandable-20240911\/<\/em><\/p>\n

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