{"id":50312,"date":"2024-05-13T23:12:53","date_gmt":"2024-05-13T15:12:53","guid":{"rendered":"https:\/\/swarma.org\/?p=50312"},"modified":"2024-05-13T23:12:53","modified_gmt":"2024-05-13T15:12:53","slug":"kan%e4%b8%80%e4%bd%9c%e5%88%98%e5%ad%90%e9%b8%a3%e7%9b%b4%e6%92%ad%e6%80%bb%e7%bb%93%ef%bc%9akan%e7%9a%84%e8%83%bd%e5%8a%9b%e8%be%b9%e7%95%8c%e5%92%8c%e5%be%85%e8%a7%a3%e5%86%b3%e7%9a%84%e9%97%ae","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=50312","title":{"rendered":"KAN\u4e00\u4f5c\u5218\u5b50\u9e23\u76f4\u64ad\u603b\u7ed3\uff1aKAN\u7684\u80fd\u529b\u8fb9\u754c\u548c\u5f85\u89e3\u51b3\u7684\u95ee\u9898"},"content":{"rendered":"
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\u4e00\u79cd\u5d2d\u65b0\u7684\u6df1\u5ea6\u5b66\u4e60\u7f51\u7edc\u7ed3\u6784 KAN\uff0c\u4e00\u7ecf\u63a8\u51fa\u5c31\u5f15\u7206\u4e86AI\u793e\u533a\u3002\u5728\u81ea\u5a92\u4f53\u7684\u717d\u98ce\u70b9\u706b\u4e0b\uff0cKAN\u4e00\u591c\u5e72\u7ffbMLP\u7684\u723d\u6587\u5728\u793e\u4ea4\u5a92\u4f53\u4e0a\u75af\u4f20\u3002KAN \u5230\u5e95\u662f\u4ec0\u4e48\uff0c\u5b83\u662f\u4ec0\u4e48\u539f\u7406\uff0c\u8ddf MLP \u662f\u4ec0\u4e48\u5173\u7cfb\uff0c\u6027\u80fd\u7a76\u7adf\u6709\u6ca1\u6709\u5439\u7684\u90a3\u4e48\u597d\uff0c\u6709\u54ea\u4e9b\u5c40\u9650\uff0c\u4f5c\u8005\u662f\u600e\u4e48\u53d1\u73b0\u7684\u2014\u2014\u672c\u671f\u8bfb\u4e66\u4f1a\u7531 KAN \u7684\u7b2c\u4e00\u4f5c\u8005\u5218\u5b50\u9e23\u540c\u5b66\u73b0\u8eab\u8bf4\u6cd5\uff0c\u4e3a\u5927\u5bb6\u5e26\u6765\u7cbe\u5f69\u7684\u7b2c\u4e00\u89c6\u89d2\u3002<\/span><\/strong><\/section>\n

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 \u2022 KAN\u6709\u4f55\u7279\u522b\u4e4b\u5904\uff1f\u6709\u4f55\u521b\u65b0\uff1f<\/span><\/strong><\/p>\n

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 \u2022 KAN\u8bba\u6587\u8bad\u7ec3\u7ed3\u679c\u5c55\u793a\u4e86\u4e00\u4e9b\u8fb9\u7684\u6d88\u5931\uff0c\u5982\u4f55\u8868\u793a\u8fb9\u7684\u6d88\u5931\u7684\uff1f<\/span><\/strong><\/p>\n

 \u2022 \u5728\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u8bad\u7ec3B\u6837\u6761\uff08B-spline\uff09\u65f6\uff0c\u5f53\u6837\u6761\u51fd\u6570\u7ecf\u8fc7\u96f6\u70b9\u65f6\uff0c\u68af\u5ea6\u4f1a\u53d8\u4e3a\u96f6\u3002\u5982\u4f55\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\uff0c\u4f8b\u5982\uff0c\u5f53\u521d\u59cb\u5316\u6837\u6761\u51fd\u6570\u4e3a\u6b63\u503c\u4f46\u76ee\u6807\u5e94\u4e3a\u8d1f\u503c\u65f6\uff0c\u8be5\u5982\u4f55\u5904\u7406\uff1f<\/span><\/strong><\/p>\n

 \u2022 \u5728KAN\u6a21\u578b\u4e2d\u4f7f\u7528\u4e86\u4e00\u4e2a\u57fa\u4e8e\u6837\u6761\u51fd\u6570\u7684\u6fc0\u6d3b\u51fd\u6570\u3002\u5982\u679c\u5c06\u8fd9\u4e2a\u6837\u6761\u51fd\u6570\u66ff\u6362\u4e3a\u4e00\u4e2a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5e76\u8fdb\u884c\u8bad\u7ec3\uff0c\u662f\u5426\u80fd\u591f\u8fbe\u5230\u4e0e\u5f53\u524d\u6a21\u578b\u76f8\u4f3c\u7684\u6548\u679c\uff1f<\/span><\/strong><\/p>\n

 \u2022 AlphaFold\u7b49\u57fa\u4e8e Transformer \u548c\u6269\u6563\u6a21\u578b\u7684\u65b9\u6cd5\uff0c\u4f3c\u4e4e\u7ed3\u5408\u4e86\u7b26\u53f7\u8fde\u63a5\u4e3b\u4e49\u548c\u7edf\u8ba1\u65b9\u6cd5\u3002\u5728\u5904\u7406 AI for Science \u65f6\uff0c\u5b83\u4eec\u672c\u8d28\u4e0a\u662f\u5fae\u5206\u65b9\u7a0b\u5417\uff1f\u6216\u8005\u9664\u4e86\u5fae\u5206\u65b9\u7a0b\u4e4b\u5916\uff0c\u8fd8\u6709\u5176\u4ed6\u4e1c\u897f\u5728\u8d77\u4f5c\u7528\uff1f<\/span><\/strong><\/p>\n<\/section>\n

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\u57285\u670811\u65e5\u7684AI+Science\u8bfb\u4e66\u4f1a<\/a>\u4e2d\uff0c\u5218\u5b50\u9e23\u8be6\u7ec6\u4ecb\u7ecd\u4e86Max Tegmark\u56e2\u961f\u7684\u6700\u65b0\u5de5\u4f5c Kolmogorov-Arnold Network<\/span>\uff08\u7b80\u79f0KAN\uff09<\/span>\u3002\u81ea\u4ece4\u670830\u65e5\u9884\u5370\u672c\u53d1\u5e03\u4ee5\u6765\uff0c\u8fd9\u4e00\u4e3b\u9898\u5f15\u8d77\u4e86\u5e7f\u6cdb\u5173\u6ce8\uff0c\u4ee4\u4ed6\u4eec\u611f\u5230\u610f\u5916\u4e0e\u8363\u5e78\u3002\u5218\u5b50\u9e23\u6307\u51fa\uff0c\u539f\u672c\u4ee5\u4e3a\u7ed3\u5408\u4eba\u5de5\u667a\u80fd<\/span>\uff08AI\uff09<\/span>\u4e0e\u79d1\u5b66\u7684\u9886\u57df\u8f83\u4e3a\u5c0f\u4f17\uff0c\u4f46\u5b9e\u9645\u4e0a\u5374\u83b7\u5f97\u4e86\u4f17\u591a\u4eba\u58eb\u7684\u70ed\u60c5\u548c\u8ba4\u53ef\u3002<\/span><\/section>\n

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\u5728\u5206\u4eab\u7684\u5f00\u59cb\uff0c\u5218\u5b50\u9e23\u4ece\u6570\u5b66\u7684\u80cc\u666f\u8bb2\u8d77\uff0c\u63a5\u7740\u4ecb\u7ecd\u4e00\u4e9bKAN\u7684\u7b97\u6cd5\u5b9e\u73b0\uff0c\u5e0c\u671b\u63d0\u4f9b\u4e00\u4e2a\u5173\u4e8eKAN\u6240\u9700\u77e5\u8bc6\u7684\u603b\u4f53\u6982\u5ff5\u3002\u4ed6\u7279\u522b\u6307\u51fa\u4e86KAN\u5728\u5904\u7406\u4e00\u4e9b\u5c0f\u578b\u79d1\u5b66\u4efb\u52a1\u65f6\u7684\u4f18\u52bf\u2014\u2014\u5b83\u4e0d\u4ec5\u7cbe\u786e\uff0c\u5176\u89c4\u6a21\u5316\u5b9a\u5f8b\u76f8\u8f83\u4e8e\u591a\u5c42\u611f\u77e5\u673a<\/span>\uff08MLP\uff09<\/span>\u4e5f\u66f4\u4f18\uff0c\u66f4\u5177\u6709\u89e3\u91ca\u6027\u3002\u5bf9\u4e8e\u67d0\u4e9b\u95ee\u9898\uff0cKAN\u7684\u89e3\u91ca\u6027\u4f7f\u5f97\u4eba\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u8bad\u7ec3\u540e\u7684\u6a21\u578b\u8fdb\u884c\u89e3\u91ca\uff0c\u800cMLP\u53ef\u80fd\u9700\u8981\u590d\u6742\u7684\u540e\u5904\u7406\uff0c\u6709\u65f6\u5019\u751a\u81f3\u96be\u4ee5\u786e\u5b9a\u5982\u4f55\u8fdb\u884c\u8fd9\u4e9b\u5904\u7406\u3002\u56e0\u6b64\uff0c\u7531\u4e8e\u5176\u5929\u751f\u7684\u89e3\u91ca\u6027\uff0cKAN\u6210\u4e3a\u89e3\u51b3\u79d1\u5b66\u95ee\u9898\u7684\u7406\u60f3\u5de5\u5177\u3002\u5728\u8bb2\u5ea7\u7684\u6700\u540e\u90e8\u5206\uff0c\u5218\u5b50\u9e23\u8fd8\u8f7b\u677e\u5730\u8ba8\u8bba\u4e86\u4e00\u4e9b\u884c\u4e1a\u5185\u7684\u516b\u5366\uff0c\u589e\u6dfb\u4e86\u8bb2\u5ea7\u7684\u8da3\u5473\u6027\u3002\u6b64\u6b21\u8bb2\u5ea7\u4e0d\u4ec5\u5c55\u793a\u4e86KAN\u7684\u6f5c\u529b\u548c\u5c40\u9650\uff0c\u4e5f\u8ba8\u8bba\u4e86\u5b83\u5728\u77ed\u671f\u548c\u957f\u671f\u5185\u53ef\u80fd\u5bf9\u673a\u5668\u5b66\u4e60\u9886\u57df\u4ea7\u751f\u7684\u5f71\u54cd\u3002<\/span><\/span><\/section>\n
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KAN\u53d7\u5230Kolmogorov-Arnold Representation Theorem\u6216Kolmogorov-Arnold Superposition Theorem<\/span>\uff08\u4ee5\u4e0b\u7b80\u79f0KA\u8868\u793a\u5b9a\u7406\uff09<\/span>\u7684\u542f\u53d1\u3002\u8be5\u5b9a\u7406\u8868\u660e\uff0c\u5982\u679cf\u662f\u4e00\u4e2a\u8fde\u7eed\u7684\u591a\u5143\u51fd\u6570\uff0c\u90a3\u4e48f\u53ef\u4ee5\u8868\u793a\u4e3a\u6709\u9650\u4e2a\u5355\u5143\u51fd\u6570\u7684\u603b\u548c\u3002\u5c31\u50cf\u65b9\u7a0b\u6240\u5c55\u793a\u7684\u90a3\u6837\u3002\u8fd9\u4e2a\u5b9a\u7406\u7684\u5173\u952e\u5728\u4e8e\uff0c\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u771f\u6b63\u7684\u591a\u5143\u51fd\u6570\u5c31\u662f\u52a0\u6cd5\uff0c\u4e0d\u9700\u8981\u5176\u4ed6\u591a\u5143\u51fd\u6570\u3002<\/strong>\u53ea\u9700\u5355\u5143\u51fd\u6570\u548c\u52a0\u6cd5\uff0c\u5c31\u53ef\u4ee5\u6784\u9020\u51fa\u4e58\u6cd5\u3002<\/span><\/section>\n

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\u5982\u56fe\u6240\u793a\uff0cKolmogorov\u7f51\u7edc\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\uff0c\u6e90\u4e8eKolmogorov-Aronld\u8868\u793a\u5b9a\u7406\u3002\u5728MLP\u4e2d\uff0c\u795e\u7ecf\u5143\u7684\u6982\u5ff5\u662f\u6307\u5728\u8282\u70b9\u4e0a\u6709\u6fc0\u6d3b\uff0c\u4f46\u5728Kolmogorov Network\u4e2d\uff0c\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u4e0d\u5728\u8282\u70b9\u4e0a\uff0c\u800c\u5728\u8fb9\u4e0a\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u6211\u4eec\u4ecd\u628a\u8fd9\u4e9b\u56fe\u4e0a\u7684\u8282\u70b9\u79f0\u4e3a\u795e\u7ecf\u5143\u3002\u5f53\u6211\u4eec\u8c08\u8bba\u6743\u91cd\u65f6\uff0c\u5bf9\u5e94\u7684\u662f\u8ba1\u7b97\u56fe\u7684\u8fb9\u3002\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u4e24\u5c42\u7684Kolmogorov\u7f51\u7edc\uff0c\u5b83\u53ea\u6709\u4e24\u4e2a\u8f93\u5165\u53d8\u91cf\uff0c\u9690\u85cf\u5c42\u6709\u4e94\u4e2a\u795e\u7ecf\u5143\u3002\u5728\u8fd9\u4e2a\u7f51\u7edc\u4e2d\uff0c\u6bcf\u4e2a\u795e\u7ecf\u5143\u63a5\u6536\u4e24\u4e2a\u4fe1\u53f7\u3002\u7b2c\u4e00\u4e2a\u4fe1\u53f7x1<\/sub><\/span>\u7ecf\u8fc7\u4e00\u4e2a\u975e\u7ebf\u6027\u51fd\u6570\u03c6\u2081\u2081\u8fdb\u884c\u6fc0\u6d3b\uff0c\u7b2c\u4e8c\u4e2a\u4fe1\u53f7x2<\/sub><\/span>\u7ecf\u8fc7\u53e6\u4e00\u4e2a\u975e\u7ebf\u6027\u51fd\u6570\u03c6\u2081\u2082\u8fdb\u884c\u6fc0\u6d3b\uff0c\u7136\u540e\u5c06\u8fd9\u4e24\u4e2a\u7ed3\u679c\u52a0\u8d77\u6765\u3002\u5176\u4ed6\u9690\u85cf\u795e\u7ecf\u5143\u4e5f\u662f\u7c7b\u4f3c\u7684\u8fc7\u7a0b\u3002\u81f3\u4e8e\u7b2c\u4e8c\u5c42\uff0c\u4f8b\u5982\u6700\u540e\u7684\u8f93\u51fa\uff0c\u5b83\u662f\u7531\u7b2c\u4e00\u4e2a\u9690\u85cf\u795e\u7ecf\u5143\u7ecf\u8fc7\u4e00\u4e2a\u975e\u7ebf\u6027\u53d8\u6362\u03a6\u2081\uff0c\u52a0\u4e0a\u7b2c\u4e8c\u4e2a\u795e\u7ecf\u5143\u7ecf\u8fc7\u975e\u7ebf\u6027\u53d8\u6362\u03a6\u2082\u7b49\u7b49\uff0c\u5c06\u6240\u6709\u8fd9\u4e9b\u9690\u85cf\u795e\u7ecf\u5143\u7684\u7ecf\u8fc7\u975e\u7ebf\u6027\u53d8\u6362\u7684\u4fe1\u53f7\u52a0\u8d77\u6765\uff0c\u5f62\u6210\u6700\u7ec8\u7684\u8f93\u51fa\u3002<\/span><\/section>\n

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\u8fd9\u4e2a\u8fc7\u7a0b\u770b\u8d77\u6765\u6709\u4e9b\u62bd\u8c61\u3002\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u76f4\u89c2\u5730\u901a\u8fc7\u66f2\u7ebf\u6765\u8868\u793a\u8fd9\u4e9b\u51fd\u6570\uff0c\u56e0\u4e3a\u65e0<\/span>\u8bba\u662f\u03c6\u8fd8\u662f\u03a6\uff0c<\/span>\u5b83\u4eec\u90fd\u662f\u4e00\u5143\u51fd\u6570\u3002\u4e00\u5143\u51fd\u6570\u7684\u597d\u5904\u662f\u53ef\u4ee5\u7528\u66f2\u7ebf\u6765\u523b\u753b\uff0c\u8fd9\u6837\u5728\u76f4\u89c2\u4e0a\u66f4\u6709\u52a9\u4e8e\u7406\u89e3\u3002<\/span><\/section>\n

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<\/p>\n


<\/section>\n
\u4e00\u4e2a\u91cd\u8981\u7684\u89c2\u5bdf\u662f\uff0cKA\u65b9\u7a0b\u7684\u65b9\u5f0f\u53ef\u4ee5\u76f4\u63a5\u8f6c\u5316\u4e3a\u4e00\u4e2a\u7f51\u7edc\u3002\u8fd9\u4e0d\u662f\u6211\u4eec\u6700\u521d\u53d1\u73b0\u7684\u3002\u6700\u65e9\u7684Kolmogorov\u7f51\u7edc\u7279\u6307\u7684\u662f\u4e00\u4e2a\u4e24\u5c42\u4e14\u5bbd\u5ea6\u4e3a2n+1\u7684\u7f51\u7edc\u3002\u867d\u7136\u5728KA\u8868\u793a\u5b9a\u7406\u4e2d\uff0c\u5185\u90e8\u51fd\u6570\u548c\u5916\u90e8\u51fd\u6570\u662f\u5206\u5f00\u5904\u7406\u7684\uff0c\u4f46\u5982\u679c\u6211\u4eec\u4ece\u8ba1\u7b97\u4e0a\u8fdb\u884c\u7edf\u4e00\uff0c\u4f1a\u53d1\u73b0\u5185\u90e8\u51fd\u6570\u548c\u5916\u90e8\u51fd\u6570\u5b9e\u9645\u4e0a\u662f\u4e00\u6837\u7684\u3002\u5b83\u4eec\u90fd\u53ef\u4ee5\u88ab\u62bd\u8c61\u6210\u6211\u4eec\u73b0\u5728\u79f0\u4e3aKAN\u5c42\u7684\u7ed3\u6784\uff1a\u7b2c\u4e00\u5c42\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a5×2\u7684KAN \u5c42\uff0c\u7b2c\u4e8c\u5c42\u5219\u662f\u4e00\u4e2a1×5\u7684KAN \u5c42\uff0c\u4e0eMLP\u4e2d\u7684\u7ebf\u6027\u5c42\u76f8\u4f3c\u3002<\/span><\/section>\n

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<\/p>\n


<\/section>\n
\u4f46\u4f60\u53ef\u80fd\u4f1a\u95ee\uff0c\u5982\u679c\u539f\u59cb\u7684Kolmogorov\u8868\u793a\u5b9a\u7406\u8bf4\u4e00\u4e2a\u4e24\u5c42\u7684\u7f51\u7edc\u5c31\u53ef\u4ee5\u8868\u793a\u6240\u6709\u5149\u6ed1\u51fd\u6570\uff0c\u4e3a\u4ec0\u4e48\u8fd8\u8981\u6784\u5efa\u66f4\u6df1\u5c42\u7684\u7f51\u7edc\u5462\uff1f\u7b54\u6848\u662f\uff0c\u539f\u59cb\u7684\u4e24\u5c42\u7ed3\u6784\u5e76\u6ca1\u6709\u9650\u5236\u5176\u6fc0\u6d3b\u51fd\u6570\u662f\u5426\u5149\u6ed1\u3002\u6709\u65f6\uff0c\u8fd9\u4e9b\u6fc0\u6d3b\u51fd\u6570\u53ef\u80fd\u9700\u8981\u7528\u5230\u975e\u5e38\u975e\u5149\u6ed1\u751a\u81f3\u6709\u5206\u5f62\u884c\u4e3a\u7684\u201c\u75c5\u6001\u201d\u51fd\u6570\u6765\u8868\u8fbe\u3002\u8fd9\u5c31\u5931\u53bb\u4e86\u73b0\u5b9e\u610f\u4e49\u3002\u8fd9\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u610f\u4e49\u4e0d\u5927\u3002\u56e0\u6b64\uff0c\u52a0\u6df1\u7f51\u7edc\u7684\u76f4\u89c2\u7406\u7531\u662f\u5e0c\u671b\u90a3\u4e9b\u539f\u672c\u65e0\u6cd5\u88ab\u5149\u6ed1\u8868\u793a\u7684\u51fd\u6570\u80fd\u591f\u88ab\u5149\u6ed1\u5730\u8868\u793a\u3002<\/span><\/section>\n

<\/section>\n

<\/p>\n


<\/section>\n
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<\/section>\n
\u8fd9\u91cc\u5c55\u793a\u4e86MLP\u548cKAN\u7f51\u7edc\u5728\u7ed3\u6784\u4e0a\u6709\u4e00\u5b9a\u7684\u5bf9\u5e94\u5173\u7cfb\u3002MLP\u7684\u6570\u5b66\u57fa\u7840\u662f\u5168\u5c40\u903c\u8fd1\u5b9a\u7406<\/span>\uff08universal approximation theorem\uff09<\/span>\uff0c\u800cKAN\u7684\u57fa\u7840\u5219\u662fKA\u8868\u793a\u5b9a\u7406\u3002\u5c3d\u7ba1\u4e24\u8005\u90fd\u80fd\u5b9e\u73b0\u51fd\u6570\u903c\u8fd1\uff0c\u4f46\u5728\u5b83\u4eec\u7684\u5b9e\u73b0\u65b9\u5f0f\u548c\u7406\u8bba\u57fa\u7840\u4e0a\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002\u5168\u5c40\u903c\u8fd1\u5b9a\u7406\u6307\u51fa\uff0c\u4e00\u4e2a\u542b\u6709\u8db3\u591f\u591a\u795e\u7ecf\u5143\u7684\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u903c\u8fd1\u4efb\u4f55\u590d\u6742\u7684\u8fde\u7eed\u51fd\u6570\uff0c\u65e0\u8bba\u8fd9\u4e2a\u51fd\u6570\u6709\u591a\u5c11\u4e2a\u8f93\u5165\u53d8\u91cf\u3002\u5168\u5c40\u903c\u8fd1\u5b9a\u7406\u5f3a\u8c03\u4e86\u9700\u8981\u8db3\u591f\u5bbd<\/span>\uff08n\u8db3\u591f\u5927\uff09<\/span>\u7684\u7f51\u7edc\uff0c\u624d\u80fd\u5b9e\u73b0\u8f93\u51fa\u4e0e\u76ee\u6807\u51fd\u6570\u4e4b\u95f4\u8f83\u4f4e\u7684\u8bef\u5dee\uff0c\u7406\u8bba\u4e0a\u65e0\u7a77\u9ad8\u7684\u7cbe\u5ea6\u9700\u8981\u7528\u65e0\u7a77\u5bbd\u7684\u7f51\u7edc\u6765\u5b9e\u73b0\u3002\u800cKA\u8868\u793a\u5b9a\u7406\u5219\u8868\u660e\uff0c\u53ef\u4ee5\u7528\u6709\u9650\u5927\u5c0f\u7684\u7f51\u7edc\u5b9e\u73b0\u65e0\u9650\u7cbe\u5ea6\u7684\u903c\u8fd1\uff0c\u867d\u7136\u8fd9\u79cd\u903c\u8fd1\u53ef\u80fd\u4f9d\u8d56\u4e8e\u975e\u5149\u6ed1\u7684\u6fc0\u6d3b\u51fd\u6570\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd9\u4e0d\u610f\u5473\u7740Kolmogorov\u7f51\u7edc\u4e00\u5b9a\u4f18\u4e8eMLP\uff0c\u56e0\u4e3aKolmogorov\u7f51\u7edc\u7684\u6fc0\u6d3b\u51fd\u6570\u4e0d\u4e00\u5b9a\u662f\u5149\u6ed1\u7684\uff0c\u9700\u8981\u770b\u5177\u4f53\u60c5\u51b5\u3002\u4f8b\u5982\u5f53\u4e00\u4e2a\u51fd\u6570<\/span>\uff08\u5c24\u5176\u79d1\u5b66\u4e2d\u8bb8\u591a\u7b26\u53f7\u51fd\u6570\uff09<\/span>\u80fd\u88abKA\u8868\u793a\u5b9a\u7406\u4e25\u683c\u8868\u8fbe\uff0c\u90a3\u4e48KAN\u7f51\u7edc\u53ef\u80fd\u63d0\u4f9b\u6bd4MLP\u66f4\u7d27\u81f4\u548c\u66f4\u53ef\u89e3\u91ca\u7684\u8868\u8fbe\u65b9\u5f0f\u3002\u5982\u56fe(a)\u548c(b)\u6240\u793a\uff0c\u6211\u4eec\u6bd4\u8f83\u4e86\u4e24\u5c42MLP\u548c\u4e24\u5c42KAN\u7684\u7ed3\u6784\u3002\u5bf9\u4e8eMLP\uff0c\u6fc0\u6d3b\u51fd\u6570\u56fa\u5b9a\u5728\u8282\u70b9\u4e0a\uff0c\u4e00\u4e9bMLP\u67b6\u6784\u7684\u6fc0\u6d3b\u51fd\u6570\u662f\u53ef\u5b66\u7684\uff1b\u5bf9\u4e8eKAN\uff0c\u6fc0\u6d3b\u51fd\u6570\u8bbe\u7f6e\u5728\u8fb9\u4e0a\uff0c\u662f\u53ef\u5b66\u4e60\u7684\uff0c\u800c\u8282\u70b9\u4e0a\u7684\u64cd\u4f5c\u5219\u76f8\u5bf9\u7b80\u5355\uff0c\u5c31\u662f\u7ebf\u6027\u7ec4\u5408\uff0c\u628a\u6240\u6709\u8f93\u5165\u52a0\u8d77\u6765\u3002\u56fe(c)\u548c(d)\u5219\u5c55\u793a\u4e86\u66f4\u6df1\u5c42\u7684MLP\u548cKAN\u7684\u7ed3\u6784\u3002<\/span><\/section>\n

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KAN\u7b97\u6cd5\u7ec6\u8282\uff1a\u5b9e\u73b0\u6280\u5de7<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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


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<\/section>\n

<\/section>\n

\u6709\u4eba\u53ef\u80fd\u4f1a\u62c5\u5fc3KAN\u7684\u5b9e\u9645\u5e94\u7528\u6027\u2014\u2014\u5373\u54ea\u4e9b\u51fd\u6570\u662f\u53ef\u4ee5\u88abKAN\u8868\u793a\u7684\u3002\u524d\u9762\u5047\u8bbe\u51fd\u6570\u53ef\u4ee5\u88abKAN\u8868\u793a\uff0c\u5982\u679c\u4e0d\u80fd\uff0c\u90a3\u4e48\u5373\u4fbf\u5b58\u5728\u89c4\u6a21\u5b9a\u5f8b\uff0c\u5b83\u4e5f\u662f\u65e0\u610f\u4e49\u7684\u3002\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6211\u4eec\u8ba4\u4e3a\u867d\u7136\u6ca1\u6709\u4e25\u683c\u8bc1\u660e\uff0c\u4f46\u8bb8\u591a\u7b26\u53f7\u51fd\u6570\u5f88\u53ef\u80fd\u90fd\u53ef\u4ee5\u88abKAN\u8868\u793a\u3002\u8fd9\u662f\u56e0\u4e3a\u7b26\u53f7\u51fd\u6570\u672c\u8d28\u4e0a\u662f\u51fd\u6570\u7684\u590d\u5408\uff0c\u800cKAN\u7684\u6838\u5fc3\u80fd\u529b\u5c31\u662f\u6355\u6349\u8fd9\u79cd\u51fd\u6570\u7684\u590d\u5408\u7ed3\u6784\u3002\u8fd9\u91cc\u6709\u51e0\u4e2a\u4f8b\u5b50\u53ef\u4ee5\u8bf4\u660e\u8fd9\u4e00\u70b9\uff1a<\/span><\/p>\n

    \n
  1. \n

    \u4e58\u6cd5\u64cd\u4f5c<\/strong>\uff1a\u8003\u8651\u8f93\u5165 (x) \u548c (y)\uff0c\u5176\u76ee\u6807\u662f\u9884\u6d4b (x\u00d7y) \u7684\u7ed3\u679c\u3002\u5728\u7ecf\u8fc7\u8bad\u7ec3\u540e\uff0c\u6a21\u578b\u80fd\u591f\u8ba1\u7b97 ( (x+y)2<\/sup> ) \u4e0e ( x2<\/sup> + y2<\/sup> )\u3002\u8fdb\u4e00\u6b65\uff0c\u901a\u8fc7 ( (x+y)2<\/sup> – (x2<\/sup> + y2<\/sup>) ) \u7684\u8ba1\u7b97\uff0c\u53ef\u4ee5\u5f97\u5230 (2xy)\uff0c\u4ece\u800c\u5b9e\u73b0\u4e58\u6cd5\u64cd\u4f5c\u3002<\/span><\/p>\n<\/li>\n

  2. \n

    \u9664\u6cd5\u64cd\u4f5c<\/strong>\uff1a\u4e3a\u4e86\u7b80\u5316\uff0c\u5047\u8bbe x \u548c y \u90fd\u662f\u6b63\u6570\u3002\u8fd9\u65f6\uff0cKAN\u53ef\u80fd\u5b66\u4e60\u5230\u4e00\u79cd\u4f7f\u7528\u5bf9\u6570\u7684\u8868\u793a\u65b9\u6cd5\uff0c\u5373\u9996\u5148\u5bf9 x \u548c y \u53d6\u5bf9\u6570\uff0c\u7136\u540e\u5728\u5bf9\u6570\u7a7a\u95f4\u8fdb\u884c\u51cf\u6cd5\u64cd\u4f5c\uff0c\u6700\u540e\u901a\u8fc7\u6307\u6570\u5316\u8fd4\u56de\uff0c\u4ece\u800c\u5b9e\u73b0\u9664\u6cd5\u3002<\/span><\/p>\n<\/li>\n

  3. \n

    \u7279\u6b8a\u51fd\u6570<\/strong>\uff1a\u4f8b\u5982\uff0c\u8003\u8651\u662f\u5426\u53ef\u4ee5\u5b66\u4e60\u5230\u5982\u8d1d\u585e\u5c14\u51fd\u6570\u8fd9\u6837\u7684\u7279\u6b8a\u51fd\u6570\u3002\u8bad\u7ec3\u540e\uff0cKAN\u53ef\u80fd\u786e\u5b9e\u80fd\u591f\u5b66\u4e60\u5e76\u6a21\u62df\u51fa\u8d1d\u585e\u5c14\u51fd\u6570\u7684\u5f62\u72b6\u3002<\/span><\/p>\n<\/li>\n

  4. \n

    \u9636\u6bb5\u8f6c\u6362\u6a21\u62df<\/strong>\uff1a\u6a21\u62df\u4e00\u4e9b\u590d\u6742\u7684\u7269\u7406\u73b0\u8c61\uff0c\u5982\u56db\u6b21\u65b9\u548c\u53cc\u66f2\u6b63\u5207\uff0cKAN\u540c\u6837\u80fd\u591f\u5b66\u4e60\u5230\u5e76\u8868\u73b0\u51fa\u76f8\u5e94\u7684\u884c\u4e3a\u3002<\/span><\/p>\n<\/li>\n

  5. \n
    \u8ba1\u7b97\u8ddd\u79bb<\/strong>\uff1a\u5bf9\u4e8e\u9700\u8981\u8ba1\u7b97\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u4e24\u70b9\u8ddd\u79bb\u7684\u60c5\u5f62\uff0c\u53ef\u80fd\u9700\u8981\u81f3\u5c11\u4e09\u5c42\u7f51\u7edc\uff0c\u5305\u62ec\u7ebf\u6027\u5c42\u3001\u5e73\u65b9\u5c42\u548c\u5f00\u65b9\u5c42\u3002\u8fd9\u663e\u793a\u4e86KAN\u5728\u5904\u7406\u8fd9\u7c7b\u8ba1\u7b97\u65f6\u7684\u9002\u5e94\u6027\u548c\u6548\u7387\u3002<\/span><\/section>\n<\/li>\n<\/ol>\n

    <\/section>\n
    \u4ee5\u4e0a\u4f8b\u5b50\u8868\u660e\uff0cKAN\u4e0d\u4ec5\u80fd\u591f\u6355\u6349\u7b80\u5355\u7684\u7b97\u672f\u8fd0\u7b97\uff0c\u8fd8\u80fd\u6a21\u62df\u66f4\u590d\u6742\u7684\u6570\u5b66\u51fd\u6570\u548c\u7269\u7406\u73b0\u8c61\uff0c\u663e\u793a\u51fa\u5176\u5e7f\u6cdb\u7684\u5e94\u7528\u6f5c\u529b\u548c\u8868\u793a\u80fd\u529b\u3002<\/span><\/section>\n

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

    <\/section>\n

    \u4e0a\u9762\u63d0\u5230\u4e86\u7b26\u53f7\u51fd\u6570<\/span>\uff08symbolic formula\uff09<\/span>\u662f\u53ef\u4ee5\u901a\u8fc7KAN\u8fdb\u884c\u6709\u6548\u8868\u793a\u7684\u3002\u8fd9\u91cc\uff0c\u6211\u4eec\u901a\u8fc7\u4e00\u7cfb\u5217\u5b9e\u9a8c\u6765\u9a8c\u8bc1\u8fd9\u4e00\u70b9\uff0c\u5373\u6bd4\u8f83KAN\u548cMLP\u5728\u8868\u793a\u8fd9\u4e9b\u7b26\u53f7\u51fd\u6570\u4e0a\u7684\u6548\u80fd\u3002\u6211\u4eec\u9009\u53d6\u4e86\u4e94\u4e2a\u4f8b\u5b50\uff0c\u8fd9\u4e9b\u4f8b\u5b50\u90fd\u662f\u7ecf\u8fc7\u7cbe\u5fc3\u8bbe\u8ba1\u7684\uff0c\u4ee5\u786e\u4fdd\u5b83\u4eec\u80fd\u591f\u88ab\u7d27\u81f4\u5730\u7528KAN\u8868\u793a\u3002<\/span><\/p>\n

      \n
    1. \n

      \u8d1d\u585e\u5c14\u51fd\u6570<\/strong>\uff1a\u8fd9\u662f\u4e00\u4e2a\u4e00\u7ef4\u51fd\u6570\u7684\u4f8b\u5b50\uff0c\u867d\u7136\u76f8\u5bf9\u7b80\u5355\uff0c\u4f46\u6211\u4eec\u4e3a\u4e86\u5b8c\u6574\u6027\u4ecd\u7136\u5305\u62ec\u4e86\u5b83\u3002\u5728\u4e00\u7ef4\u60c5\u51b5\u4e0b\uff0c\u5176\u7f29\u653e\u662f N-4<\/sup>\uff0c\u8fd9\u662f\u6837\u6761\u51fd\u6570\u7684\u5178\u578b\u7f29\u653e\u884c\u4e3a\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cMLP\u5728 10-4<\/sup>\u540e\u5c31\u8d8b\u4e8e\u5e73\u7a33\uff0c\u8868\u660e\u5176\u5b66\u4e60\u80fd\u529b\u6709\u9650\u3002<\/span><\/p>\n<\/li>\n

    2. \n

      \u4e8c\u7ef4\u6848\u4f8b<\/strong>\uff1a\u8fd9\u4e2a\u4f8b\u5b50\u7684\u7f29\u653e\u57fa\u672c\u4e0a\u662f N-2<\/sup>\uff0cMLP\u5728\u521d\u671f\u4f3c\u4e4e\u9075\u5faa\u4e8c\u6b21\u7f29\u653e\u89c4\u5f8b\uff0c\u8fd9\u8868\u660e\u5b83\u53ef\u80fd\u53ea\u662f\u5728\u4e8c\u7ef4\u5e73\u9762\u4e0a\u7b80\u5355\u5730\u5212\u5206\u7f51\u683c\u5e76\u5c1d\u8bd5\u62df\u5408\uff0c\u800c\u4e0d\u662f\u771f\u6b63\u5b66\u4e60\u5230\u51fd\u6570\u7684\u7ed3\u6784\u3002<\/span><\/p>\n<\/li>\n

    3. \n

      \u4e58\u6cd5<\/strong>\uff1a\u8fd9\u662f\u4e00\u4e2a\u5f88\u6709\u8da3\u7684\u4f8b\u5b50\uff0c\u901a\u5e38\u4e58\u6cd5\u88ab\u8ba4\u4e3a\u662f\u4e8c\u5143\u8fd0\u7b97\u7b26\uff0c\u4f46\u6211\u4eec\u5c55\u793a\u4e86\u5b83\u5b9e\u9645\u4e0a\u53ef\u4ee5\u901a\u8fc7\u5c06\u5176\u5206\u89e3\u4e3a\u52a0\u6cd5\u548c\u4e00\u5143\u51fd\u6570\u7684\u7ec4\u5408\u6765\u8ba1\u7b97\u3002<\/span><\/p>\n<\/li>\n

    4. \n

      100\u7ef4\u7684\u4f8b\u5b50<\/strong>\uff1a\u8fd9\u662f\u4e00\u4e2a\u6784\u9020\u7684\u66f4\u590d\u6742\u7684\u4f8b\u5b50\uff0c\u5c06100\u7ef4\u7684\u6b63\u5f26\u5e73\u65b9\u503c\u76f8\u52a0\u540e\u518d\u5e94\u7528\u6307\u6570\u51fd\u6570\u3002\u7406\u8bba\u4e0a\uff0cMLP\u5728\u8fd9\u79cd\u9ad8\u7ef4\u60c5\u51b5\u4e0b\u7684\u8868\u73b0\u4f1a\u975e\u5e38\u5dee\uff0c\u5b9e\u9645\u4e0a\u4e5f\u786e\u5b9e\u5982\u6b64\u3002\u800cKAN\u867d\u7136\u6700\u7ec8\u4e5f\u8fbe\u5230\u4e86\u5e73\u7a33\u72b6\u6001\uff0c\u4f46\u5176\u635f\u5931\u660e\u663e\u4f4e\u4e8eMLP\uff0c\u663e\u793a\u51fa\u5176\u66f4\u5f3a\u7684\u5b66\u4e60\u80fd\u529b\u3002<\/span><\/p>\n<\/li>\n

    5. \n
      \u66f4\u6df1\u5c42\u6b21\u7684KAN\u9700\u6c42<\/strong>\uff1a\u6700\u540e\u4e00\u4e2a\u4f8b\u5b50\u662f\u4e3a\u4e86\u5c55\u793a\u5f53\u4efb\u52a1\u590d\u6742\u6027\u589e\u52a0\u65f6\uff0c\u66f4\u6df1\u5c42\u6b21\u7684KAN\u7684\u5fc5\u8981\u6027\u3002\u8fd9\u4e2a\u4f8b\u5b50\u9700\u8981\u81f3\u5c11\u4e09\u5c42\u7684KAN\u6765\u89e3\u51b3\uff0c\u800c\u5355\u5c42\u6216\u4e24\u5c42\u7684KAN\u65e0\u6cd5\u6709\u6548\u5b66\u4e60\u5230\u51fd\u6570\u7684\u7ed3\u6784\u3002<\/span><\/section>\n<\/li>\n<\/ol>\n

      <\/section>\n
      \u8fd9\u4e9b\u5b9e\u9a8c\u8868\u660e\uff0cKAN\u5728\u5904\u7406\u7b26\u53f7\u51fd\u6570\u65f6\u4e0d\u4ec5\u80fd\u66f4\u51c6\u786e\u5730\u6355\u6349\u51fd\u6570\u7684\u7ed3\u6784\uff0c\u800c\u4e14\u901a\u5e38\u6bd4MLP\u6709\u66f4\u597d\u7684\u6027\u80fd\uff0c\u5c24\u5176\u662f\u5728\u9ad8\u7ef4\u548c\u590d\u6742\u7684\u4efb\u52a1\u4e2d\u3002\u8fd9\u8bc1\u660e\u4e86KAN\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u6bd4\u4f20\u7edf\u7684MLP\u5177\u6709\u660e\u663e\u7684\u4f18\u52bf\u3002<\/span><\/section>\n

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

      <\/section>\n
      \u524d\u9762\u63d0\u5230\u7684\u4f8b\u5b50\u6d89\u53ca\u7b26\u53f7\u516c\u5f0f\uff0c\u6211\u4eec\u77e5\u9053\u8fd9\u4e9b\u516c\u5f0f\u901a\u5e38\u6709\u8f83\u4e3a\u7d27\u81f4\u7684KAN\u8868\u8fbe\u5f62\u5f0f\u3002\u4f46\u5982\u679c\u6211\u4eec\u4e0d\u77e5\u9053\u67d0\u4e2a\u4efb\u52a1\u662f\u5426\u62e5\u6709\u7d27\u81f4\u7684KAN\u8868\u793a\uff0c\u8be5\u600e\u4e48\u529e\u5462\uff1f<\/span><\/section>\n

      <\/span><\/section>\n
      \u8fd9\u5b9e\u9645\u4e0a\u662f\u7279\u6b8a\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u5982\u8d1d\u585e\u5c14\u51fd\u6570 J\u1d65(x) \u3002\u5f53\u5c06 \u03bd \u548c x \u540c\u65f6\u89c6\u4e3a\u8f93\u5165\u65f6\uff0c\u5b83\u662f\u4e00\u4e2a\u4e8c\u5143\u51fd\u6570\uff0c\u6211\u4eec\u4e0d\u77e5\u9053\u662f\u5426\u5b58\u5728\u7d27\u81f4\u7684KAN\u8868\u793a\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u867d\u7136KAN\u53ef\u80fd\u65e0\u6cd5\u627e\u5230\u4e00\u4e2a\u7cbe\u786e\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4f46\u5b83\u4ecd\u7136\u80fd\u591f\u627e\u5230\u975e\u5e38\u597d\u7684\u8fd1\u4f3c\u89e3\u3002\u6211\u4eec\u572815\u4e2a\u7279\u5b9a\u51fd\u6570\u7684\u4efb\u52a1\u4e0a\u9a8c\u8bc1\u4e86\u8fd9\u4e00\u7406\u8bba\uff0c\u5176\u4e2dKAN\u5728\u6240\u6709\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\u90fd\u4f18\u4e8eMLP\u3002\u6211\u4eec\u901a\u8fc7\u56fe\u8868\u5f62\u5f0f\u5c55\u793a\u4e86\u8fd9\u4e9b\u7ed3\u679c\uff0c\u6a2a\u8f74\u4ee3\u8868\u53c2\u6570\u6570\u91cf\uff0c\u800c\u7eb5\u8f74\u663e\u793a\u4e86\u635f\u5931\u8868\u73b0\u3002\u6211\u4eec\u5e76\u6ca1\u6709\u53ea\u8fd0\u884c\u4e00\u4e2a\u6a21\u578b\uff1b\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u5bf9\u6bcf\u4e2a\u6848\u4f8b\u90fd\u8fd0\u884c\u4e86\u6570\u767e\u4e2a\u6a21\u578b\uff0c\u5e76\u5728\u4e8c\u7ef4\u56fe\u4e0a\u5c55\u793a\u4e86\u90a3\u4e9b\u5904\u4e8ePareto\u524d\u6cbf\u7684\u6a21\u578b<\/span>\uff08\u5373\u6a21\u578b\u5728\u5904\u7406\u591a\u76ee\u6807\u4f18\u5316\u95ee\u9898\u4e2d\u8fbe\u5230\u6700\u4f18\u5e73\u8861\uff09<\/span>\u3002\u663e\u7136\uff0cKAN\u5728\u8fbe\u5230\u6700\u4f18\u5e73\u8861\u6027\u80fd\u4e0a\u4f18\u4e8eMLP\u3002\u4f46\u5728\u5904\u7406\u4f4e\u7ef4\u4efb\u52a1\u65f6\uff0cKAN\u7684\u8868\u73b0\u6709\u65f6\u751a\u81f3\u4e0d\u5982\u6837\u6761\u51fd\u6570\u3002\u8fd9\u610f\u5473\u7740KAN\u80cc\u540e\u4ecd\u7136\u5b58\u5728\u5404\u79cd\u5404\u6837\u7684\u4f18\u5316\u95ee\u9898\uff0c\u8fd9\u662f\u672a\u6765\u503c\u5f97\u7ee7\u7eed\u63a2\u7d22\u7684\u3002<\/span><\/section>\n

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

      <\/section>\n
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      KAN\u7528\u4e8e\u79d1\u5b66\u53d1\u73b0\u7684\u53ef\u89e3\u91ca\u6027<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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      \u5728\u8fd9\u4e00\u90e8\u5206\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8KAN\u7684\u53ef\u89e3\u91ca\u6027\u3002KAN\u80fd\u5728\u591a\u79cd\u8bbe\u7f6e\u4e0b\u8868\u73b0\u51fa\u8272\u5e76\u5177\u5907\u53ef\u89e3\u91ca\u6027\u3002<\/span><\/section>\n

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      \u79d1\u5b66\u7814\u7a76\u5927\u81f4\u53ef\u4ee5\u5206\u4e3a\u4e24\u7c7b\uff1a\u4e00\u7c7b\u662f\u5e94\u7528\u9a71\u52a8\u7684\uff0c\u5982AlphaFold\uff0c\u5176\u76ee\u6807\u660e\u786e\uff0c\u4e3b\u8981\u5173\u6ce8\u9884\u6d4b\u7684\u7269\u7406\u542b\u4e49\uff1b\u53e6\u4e00\u7c7b\u5219\u662f\u7531\u597d\u5947\u5fc3\u9a71\u52a8\uff0c\u4e0d\u4ec5\u5173\u6ce8\u6a21\u578b\u7684\u8f93\u51fa\uff0c\u8fd8\u8ffd\u6c42\u6df1\u5165\u7406\u89e3\u5176\u5185\u90e8\u673a\u5236\u3002AI\u5728\u597d\u5947\u5fc3\u9a71\u52a8\u7684\u79d1\u7814\u4e2d\u5c1a\u672a\u53d1\u6325\u91cd\u8981\u4f5c\u7528\u7684\u4e00\u4e2a\u539f\u56e0\u662f\uff0c\u5f53\u524d\u7684AI\u5927\u591a\u91c7\u7528\u8fde\u63a5\u4e3b\u4e49\u98ce\u683c\uff0c\u7f3a\u4e4f\u8db3\u591f\u7684\u53ef\u89e3\u91ca\u6027\u3002\u53e6\u4e00\u4e2a\u539f\u56e0\u662f\u79d1\u5b66\u5bb6\u4e0d\u592a\u613f\u610f\u4fe1\u4efb\u4e00\u4e2a\u4ed6\u4eec\u65e0\u6cd5\u53c2\u4e0e\u51b3\u7b56\u8fc7\u7a0b\u7684\u7cfb\u7edf\u3002\u6211\u4eec\u4e4b\u6240\u4ee5\u4fe1\u4efb\u5408\u4f5c\u4f19\u4f34\uff0c\u662f\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u4e0e\u4ed6\u4eec\u8fdb\u884c\u4ea4\u6d41\uff0c\u8fd9\u79cd\u53c2\u4e0e\u611f\u662f\u4fe1\u4efb\u7684\u57fa\u7840\u3002\u7136\u800c\uff0c\u73b0\u6709\u7684AI\u7cfb\u7edf\u5f80\u5f80\u7f3a\u4e4f\u8fd9\u79cd\u4e92\u52a8\u6027\uff0c\u8fd9\u4e5f\u662f\u79d1\u5b66\u5bb6\u96be\u4ee5\u4fe1\u4efbAI\u7ed3\u679c\u7684\u4e00\u4e2a\u539f\u56e0\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u56e0\u6b64\uff0c\u8981\u8ba9\u79d1\u5b66\u5bb6\u4fe1\u4efbAI\u7684\u7ed3\u679c\uff0c\u6211\u4eec\u9700\u8981\u5236\u4f5c\u4e0d\u4ec5\u53ef\u89e3\u91ca\u800c\u4e14\u4e92\u52a8\u7684AI\u7cfb\u7edf\u3002<\/span><\/section>\n


      <\/h4>\n

      \u7b26\u53f7\u56de\u5f52<\/strong><\/span><\/h4>\n

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      \u8fd9\u91cc\u6709\u4e00\u4e2a\u4f8b\u5b50\u53ef\u4ee5\u89e3\u91ca\u4ea4\u4e92\u6027\u7684\u542b\u4e49\u3002\u8003\u8651\u4e00\u4e2a\u76f8\u5bf9\u7b80\u5355\u7684\u7b26\u53f7\u56de\u5f52\u95ee\u9898\uff0c\u6211\u4eec\u6709\u53d8\u91cf(x)\u548c(y)\uff0c\u8f93\u51fa\u5219\u662f\u4e00\u4e2a\u516c\u5f0f\u3002\u5c3d\u7ba1\u5b9e\u9645\u7684\u8f93\u51fa\u662f\u6570\u503c\uff0c\u4f46\u5728\u8bad\u7ec3\u7f51\u7edc\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u65bd\u52a0\u4e00\u4e9b\u7279\u5b9a\u7684\u7ea6\u675f\u3002\u8fd9\u53ef\u80fd\u6700\u7ec8\u5bfc\u81f4\u6211\u4eec\u8bad\u7ec3\u51fa\u4e00\u4e2a\u76f8\u5bf9\u7a00\u758f\u7684\u7f51\u7edc\u3002\u8fd9\u65f6\u6211\u4eec\u53ef\u4ee5\u5c06\u7f51\u7edc\u526a\u679d\uff0c\u4f7f\u5176\u66f4\u5c0f\u3002<\/span><\/section>\n

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      \u6570\u5b66\uff1a\u7ebd\u7ed3\u7406\u8bba<\/strong><\/span><\/h4>\n

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      \u5728\u8fd9\u4e2a\u7814\u7a76\u8def\u7ebf\u4e0b\uff0c\u6211\u4eec\u5c1d\u8bd5\u4e86\u4e24\u4e2a\u6848\u4f8b\u3002\u5176\u4e2d\u4e00\u4e2a\u662fDeepMind\u5bf9\u62d3\u6251\u4e0d\u53d8\u91cf\u5173\u7cfb\u7684\u7814\u7a76\u3002\u5728\u4ed6\u4eec\u7684\u539f\u59cb\u8bba\u6587\u4e2d\uff0c\u8fd9\u7bc7\u8bba\u6587\u53d1\u8868\u4e8e\u4e24\u4e09\u5e74\u524d\uff0c\u4ed6\u4eec\u63cf\u8ff0\u4e86\u5982\u4f55\u901a\u8fc7AI\u4e0e\u4eba\u7c7b\u79d1\u5b66\u5bb6\u7684\u534f\u4f5c\u53d1\u73b0\u4e00\u4e2a\u65b0\u7684\u626d\u7ed3\u516c\u5f0f\u3002\u4ed6\u4eec\u7684AI\u91c7\u7528\u7684\u662f\u4e00\u79cd\u57fa\u7840\u65b9\u6cd5\uff0c\u901a\u8fc7\u7279\u5f81\u5f52\u56e0\u65b9\u6cd5\u8bad\u7ec3\u4e00\u4e2aMLP\uff0c\u4ee5\u8bc6\u522b\u54ea\u4e9b\u53d8\u91cf\u662f\u91cd\u8981\u7684\u3002\u5728\u786e\u5b9a\u4e86\u524d\u4e09\u4e2a\u91cd\u8981\u53d8\u91cf\u540e\uff0c\u4eba\u7c7b\u79d1\u5b66\u5bb6\u4e13\u6ce8\u4e8e\u7814\u7a76\u8fd9\u4e9b\u53d8\u91cf\uff0c\u5e76\u5b9a\u4e49\u4e86\u4e00\u4e2a\u65b0\u7684\u6982\u5ff5\u201cslope\u201d\uff0c\u7136\u540e\u7531\u6570\u5b66\u5bb6\u8fdb\u884c\u4e86\u8bc1\u660e\u3002<\/span><\/section>\n

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      \u540e\u6765\uff0cGeorgia Tech\u7684\u53f2\u5efa\u519b\u56e2\u961f\u53d1\u73b0\uff0c\u5bf9\u4e8e\u7279\u5b9a\u79d1\u5b66\u4efb\u52a1\uff0c\u4f7f\u7528\u5927\u89c4\u6a21\u7684MLP\u5e76\u975e\u603b\u662f\u5fc5\u8981\u7684\u3002\u4ed6\u4eec\u53d1\u73b0\uff0c\u4e00\u4e2a\u53ea\u6709\u4e24\u4e2a\u9690\u85cf\u5c42\u548c\u5927\u7ea660\u4e2a\u53c2\u6570\u7684\u7b80\u5355MLP\u6a21\u578b\uff0c\u5c31\u80fd\u8fbe\u5230\u4e0e\u5927\u578b\u6a21\u578b\u76f8\u4f3c\u7684\u6548\u679c\u3002\u8fd9\u4e2a\u7ed3\u679c\u51fa\u4e4e\u610f\u6599\uff0c\u56e0\u4e3a\u6211\u4eec\u5728KAN\u4e2d\u5e76\u6ca1\u6709\u8be6\u7ec6\u5730\u57fa\u51c6\u6d4b\u8bd5MLP\uff0c\u800c\u662f\u76f4\u63a5\u4f7f\u7528\u4e86DeepMind\u6587\u7ae0\u4e2d\u7684\u6570\u636e\u548c\u6a21\u578b\u3002\u56e0\u6b64\uff0c\u4e00\u4e2a\u5982\u6b64\u5c0f\u7684MLP\u4e5f\u80fd\u53d6\u5f97\u826f\u597d\u7684\u7ed3\u679c\uff0c\u8fd9\u662f\u4e00\u4e2a\u60ca\u4eba\u7684\u53d1\u73b0\u3002\u8fd9\u8bf4\u660e\uff0c\u5728\u79d1\u5b66\u7814\u7a76\u4e2d\uff0c\u6211\u4eec\u6709\u65f6\u5e76\u4e0d\u9700\u8981\u5e9e\u5927\u7684\u6a21\u578b\u3002\u8fd9\u4e0e\u673a\u5668\u5b66\u4e60\u9886\u57df\u666e\u904d\u7684\u601d\u7ef4\u6a21\u5f0f\u4e0d\u540c\uff0c\u540e\u8005\u901a\u5e38\u504f\u5411\u4e8e\u9ed8\u8ba4\u6784\u5efa\u5177\u6709\u591a\u4e2a\u5c42\u6b21\u548c\u6570\u767e\u4e2a\u8282\u70b9\u5bbd\u5ea6\u7684\u7f51\u7edc\u3002\u4f46\u5bf9\u4e8e\u79d1\u5b66\u4efb\u52a1\uff0c\u4e00\u4e2a\u8f83\u5c0f\u7684\u6a21\u578b\u5c31\u8db3\u4ee5\u5e94\u5bf9\uff0c\u800c\u4e14\u53ef\u4ee5\u5728\u672c\u5730\u673a\u5668\u4e0a\u8fd0\u884c\uff0c\u8fd9\u662f\u4e00\u4e2a\u663e\u8457\u7684\u4f18\u52bf\u3002\u6b64\u5916\uff0c\u8f83\u5c0f\u7684\u6a21\u578b\u901a\u5e38\u66f4\u6613\u4e8e\u89e3\u91ca\uff0c\u8fd9\u5bf9\u4e8e\u79d1\u5b66\u7814\u7a76\u5c24\u5176\u91cd\u8981\u3002<\/span><\/section>\n

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      \u51dd\u805a\u6001\u7269\u7406\uff1aAnderson \u5c40\u57df\u5316<\/strong><\/span><\/h4>\n

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      \u6211\u4eec\u8fd8\u6709\u4e00\u4e2a\u5173\u4e8e\u7269\u7406\u5b66\u4e2d\u51dd\u805a\u6001\u7269\u7406\u9886\u57df\u7684Anderson localization\u4f8b\u5b50\u3002\u8fd9\u4e2a\u4f8b\u5b50\u6d89\u53ca\u5230\u76f8\u53d8\uff0c\u7279\u522b\u662f\u5982\u4f55\u627e\u5230\u76f8\u53d8\u7684\u8fb9\u754c\u751a\u81f3\u5bfc\u51fa\u4e00\u4e2a\u89e3\u6790\u8868\u8fbe\u5f0f\u3002\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u4e86\u5047\u8bbe\u6d4b\u8bd5\u7684\u91cd\u8981\u6027\u3002\u5f53\u5b58\u5728\u4e24\u4e2a\u6216\u591a\u4e2a\u5047\u8bbe\u65f6\uff0c\u7528\u6237\u53ef\u4ee5\u5c1d\u8bd5\u8bbe\u7f6e\u4e0d\u540c\u7684\u5047\u8bbe\uff0c\u7ee7\u7eed\u8bad\u7ec3\u6a21\u578b\uff0c\u89c2\u5bdf\u51c6\u786e\u7387\u7684\u53d8\u5316\u3002\u6700\u540e\uff0c\u6839\u636e\u51c6\u786e\u7387\u6216\u7b80\u5355\u6027<\/span>\uff08\u5982\u679c\u4e24\u4e2a\u5047\u8bbe\u7684\u51c6\u786e\u7387\u76f8\u5f53\uff0c\u4f46\u4e00\u4e2a\u66f4\u4e3a\u7b80\u5355\uff09<\/span>\u6765\u9009\u62e9\u5047\u8bbe\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u4f53\u73b0\u4e86\u4eba\u5de5\u667a\u80fd\u7684\u5e94\u7528\uff0c\u8fd8\u5c55\u793a\u4e86\u4eba\u4e0eAI\u4e4b\u95f4\u7684\u4e92\u52a8\u662f\u5982\u4f55\u5728\u89e3\u51b3\u590d\u6742\u79d1\u5b66\u95ee\u9898\u4e2d\u53d1\u6325\u4f5c\u7528\u7684\u3002<\/span><\/section>\n

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      KAN\u7684\u7528\u9014\u3001\u4f18\u7f3a\u70b9\u3001\u5b9a\u4f4d\u548c\u82e5\u5e72\u4e89\u8bae\u6027\u95ee\u9898<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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      <\/section>\n

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


      <\/p>\n

      KAN\u6709\u4f55\u7279\u522b\u4e4b\u5904\uff1f<\/strong><\/span><\/h4>\n

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

      <\/section>\n
      \u9996\u5148\uff0c\u6211\u4eec\u6765\u63a2\u7d22KAN\u7684\u72ec\u7279\u6027\uff1aKAN\u7684\u7279\u522b\u4e4b\u5904\u5728\u54ea\u91cc\uff1f<\/span><\/section>\n

      <\/section>\n
      \u8bb8\u591a\u4eba\u8ba4\u4e3a\uff0cKAN\u7684\u521b\u65b0\u6027\u53ef\u80fd\u5e76\u4e0d\u5982\u9884\u671f\u90a3\u6837\u663e\u8457\u3002\u4f8b\u5982\uff0c\u53ef\u5b66\u4e60\u7684\u6fc0\u6d3b\u51fd\u6570\u8fd9\u4e00\u6982\u5ff5\uff0c\u5728\u6837\u6761\u7f51\u7edc\u6216\u662f\u6838\u673a\u5668\u4e2d\u5df2\u6709\u6240\u4f53\u73b0\uff0c\u8fd9\u5e76\u4e0d\u662f\u5168\u65b0\u7684\u6982\u5ff5\u3002\u540c\u6837\uff0c\u5c06\u6fc0\u6d3b\u51fd\u6570\u5e94\u7528\u4e8e\u8fb9\u800c\u975e\u8282\u70b9\u7684\u89c2\u5ff5\uff0c\u5728\u4e8c\u5c42\u7684Kolmogorov\u7f51\u7edc\u4e2d\u4e5f\u5df2\u7ecf\u5b58\u5728\u3002\u5982\u679c\u8bf4KAN\u662f\u4e00\u4e2a\u6df1\u5c42\u7f51\u7edc\uff0c\u90a3\u4e48\u8fd9\u540c\u6837\u4e0d\u662f\u4e00\u4e2a\u65b0\u9896\u7684\u6982\u5ff5\uff1b\u6df1\u5ea6\u5b66\u4e60\u672c\u8eab\u5c31\u5305\u542b\u4e86\u6784\u5efa\u591a\u5c42\u6df1\u5ea6\u7684\u7f51\u7edc\u7ed3\u6784\u3002\u7136\u800c\uff0c\u5c06\u8fd9\u4e09\u4e2a\u6982\u5ff5\u2014\u2014\u53ef\u5b66\u4e60\u7684\u6fc0\u6d3b\u51fd\u6570\u3001\u6fc0\u6d3b\u51fd\u6570\u5e94\u7528\u4e8e\u8fb9\u3001\u4ee5\u53ca\u6df1\u5c42\u7f51\u7edc\u7ed3\u6784\u7684\u7ed3\u5408\uff0c\u786e\u5b9e\u63d0\u4f9b\u4e86\u4e00\u79cd\u65b0\u7684\u89c6\u89d2\u3002\u6280\u672f\u4e0a\uff0cKAN\u7684\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u5728\u7f51\u7edc\u7684\u8fb9\u4e0a\u96c6\u6210\u4e86\u53ef\u8bad\u7ec3\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u5e76\u4e14\u53ef\u4ee5\u6784\u5efa\u4e3a\u975e\u5e38\u6df1\u7684\u7f51\u7edc\u3002\u7136\u800c\uff0c\u4ec5\u4ec5\u8ba8\u8bba\u8fd9\u4e9b\u6280\u672f\u7279\u6027\u7684\u521b\u65b0\u6027\u53ef\u80fd\u6ca1\u6709\u592a\u5927\u610f\u4e49\u3002\u66f4\u91cd\u8981\u7684\u662f\u8981\u8003\u8651\u8fd9\u4e9b\u65b0\u7279\u6027\u80fd\u4e3a\u6211\u4eec\u5e26\u6765\u4ec0\u4e48\u5b9e\u9645\u76ca\u5904\uff0c\u4ee5\u53caKAN\u80fd\u591f\u5b8c\u6210\u54ea\u4e9b\u4efb\u52a1\u3002\u8fd9\u662f\u6211\u4eec\u8bc4\u4f30\u4efb\u4f55\u65b0\u6280\u672f\u6216\u65b9\u6cd5\u65f6\u5e94\u5f53\u8003\u8651\u7684\u6838\u5fc3\u95ee\u9898\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u6b64\u6211\u4eec\u53ef\u4ee5\u56de\u987e\u7814\u7a76\u5386\u53f2\u3002\u6211\u4eec\u8ba4\u4e3a\uff0c\u6211\u4eec\u7684\u4e00\u4e2a\u91cd\u8981\u6280\u672f\u8d21\u732e\u662f\u5c06KAN\u4ece\u4e24\u5c42\u6269\u5c55\u5230\u4e09\u5c42\u53ca\u66f4\u6df1\u5c42\u6b21\u3002\u5c06\u4e24\u5c42\u611f\u77e5\u673a\u6269\u5c55\u4e3aMLP\u7684\u91cd\u8981\u91cc\u7a0b\u7891\u53ef\u4ee5\u8ffd\u6eaf\u52301974\u5e74\uff0c\u7531Paul Werbos\u5b9e\u73b0\u3002\u4ed6\u9996\u6b21\u5c06\u4e00\u4e2a\u5355\u9690\u85cf\u5c42\u7684\u611f\u77e5\u673a\u62d3\u5c55\u5230\u4e86\u591a\u5c42\uff0c\u8fd9\u4f7f\u5f97MLP\u80fd\u591f\u89e3\u51b3XOR\u95ee\u9898<\/span>\uff08\u5f02\u6216\u95ee\u9898\uff09<\/span>\u2014\u2014\u8fd9\u662f\u65e9\u671f\u5bf9\u611f\u77e5\u673a\u7684\u4e00\u5927\u6279\u8bc4\u3002\u4e0d\u8fc7\uff0cWerbos\u7684\u8fd9\u7bc7\u8bba\u6587\u4e3b\u8981\u805a\u7126\u4e8e\u653f\u6cbb\u5b66\u548c\u793e\u4f1a\u5b66\u9886\u57df\uff0c\u53ef\u80fd\u56e0\u6b64\u6ca1\u6709\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u754c\u5f15\u8d77\u8f83\u5927\u53cd\u54cd\uff0c\u518d\u52a0\u4e0a\u5f53\u65f6\u4fe1\u606f\u4f20\u64ad\u7684\u9650\u5236\uff0c\u5176\u5f71\u54cd\u5e76\u672a\u7acb\u5373\u663e\u73b0\u3002\u5728\u6211\u4eec\u7684\u5de5\u4f5c\u4e2d\uff0cKAN\u7684\u53d1\u5c55\u5b9e\u9645\u4e0a\u662f\u5728\u7c7b\u6bd4Werbos\u7684\u5de5\u4f5c\uff0c\u6211\u4eec\u5c06\u4e00\u4e2a\u4e24\u5c42\u7684Kolmogorov\u7f51\u7edc\u6269\u5c55\u4e3a\u591a\u5c42\u7ed3\u6784\u3002\u867d\u7136\u6211\u4eec\u79f0\u4e4b\u4e3aKAN\uff0c\u5b83\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u591a\u5c42\u7684Kolmogorov\u7f51\u7edc\uff0c\u540c\u65f6\u4e5f\u662f\u5411Arnold\u81f4\u656c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u56e0\u6b64\uff0c\u6211\u4eec\u5c55\u793a\u7684\u591a\u5c42Kolmogorov\u7f51\u7edc\uff0c\u5373KAN\uff0c\u80fd\u591f\u5728\u4e00\u4e9b\u5c0f\u578b\u79d1\u5b66\u95ee\u9898\u4e0a\u63d0\u4f9b\u6bd4MLP\u66f4\u9ad8\u7684\u51c6\u786e\u6027\u548c\u66f4\u597d\u7684\u53ef\u89e3\u91ca\u6027\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u6211\u4eec\u7684\u5e94\u7528\u9886\u57df\u5e76\u975e\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0c\u5982\u8ba1\u7b97\u673a\u89c6\u89c9\u6216\u81ea\u7136\u8bed\u8a00\u5904\u7406\uff0c\u800c\u662f\u79d1\u5b66\u7814\u7a76\u3002\u8fd9\u4e0ePaul Werbos\u5f53\u65f6\u7684\u7814\u7a76\u80cc\u666f\u76f8\u4f3c\uff0c\u5c3d\u7ba1\u4ed6\u662f\u5728\u653f\u6cbb\u5b66\u548c\u793e\u4f1a\u5b66\u9886\u57df\u5de5\u4f5c\u3002\u552f\u4e00\u7684\u4e0d\u540c\u53ef\u80fd\u5728\u4e8e\u4eca\u5929\u7684\u4fe1\u606f\u4f20\u64ad\u65b9\u5f0f\u8fdc\u6bd4\u8fc7\u53bb\u5feb\u901f\uff0c\u7279\u522b\u662f\u5a92\u4f53\u7684\u7092\u4f5c\u6548\u5e94\uff0c\u4f7f\u5f97\u8fd9\u4e9b\u6210\u5c31\u8fc5\u901f\u4e3a\u4eba\u6240\u77e5\u3002\u8fd9\u662f\u4e00\u4ef6\u597d\u4e8b\uff0c\u5c3d\u7ba1\u4eba\u4eec\u5bf9\u6b64\u6709\u4e0d\u540c\u7684\u770b\u6cd5\u3002<\/span><\/section>\n

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

      KAN\u7684\u80fd\u529b\u8fb9\u754c\u5728\u54ea\u91cc\uff1f<\/strong><\/span><\/h4>\n

      <\/strong><\/span><\/section>\n
      <\/section>\n
      \u7814\u7a76KAN\u7684\u8fb9\u754c\u662f\u4e00\u4e2a\u6211\u4eec\u4ecd\u9700\u6df1\u5165\u63a2\u7d22\u7684\u9886\u57df\u3002\u76ee\u524d\uff0c\u8fd9\u4e9b\u8fb9\u754c\u5c1a\u4e0d\u660e\u786e\uff0c\u7279\u522b\u662fKAN\u4e0eMLP\u4e4b\u95f4\u7684\u5177\u4f53\u5173\u7cfb\u3002\u6709\u89c2\u70b9\u8ba4\u4e3aKAN\u662fMLP\u7684\u4e00\u79cd\u7279\u4f8b\uff0c\u4f46\u4ece\u7406\u8bba\u89d2\u5ea6\u6765\u770b\uff0c\u4efb\u4f55\u88ab\u89c6\u4e3a\u901a\u7528\u903c\u8fd1\u5668\u7684\u7f51\u7edc\u5728\u7406\u8bba\u4e0a\u90fd\u662f\u7b49\u4ef7\u7684\u3002\u7136\u800c\uff0c\u4e3a\u4e86\u7406\u89e3\u8fd9\u4e9b\u6280\u672f\u4e4b\u95f4\u7684\u5177\u4f53\u5173\u7cfb\uff0c\u6211\u4eec\u9700\u8981\u4ece\u591a\u4e2a\u89d2\u5ea6\u5ba1\u89c6\u8fd9\u4e9b\u6280\u672f\uff0c\u4e0d\u4ec5\u8981\u4ece\u51fd\u6570\u903c\u8fd1\u7684\u89d2\u5ea6\uff0c\u8fd8\u8981\u8003\u8651\u5230\u4f18\u5316\u3001\u6cdb\u5316\u548c\u53ef\u89e3\u91ca\u6027\u7b49\u66f4\u5b9e\u7528\u7684\u56e0\u7d20\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u6211\u4eec\u8ba4\u4e3a\uff0c\u5c06KAN\u7b80\u5355\u5730\u89c6\u4e3a\u66ff\u4ee3MLP\u7684\u89c2\u70b9\u662f\u4e0d\u5408\u7406\u7684\u3002\u4f8b\u5982\uff0c\u901a\u8fc7\u4e00\u4e2a\u7b80\u5355\u7684\u201c\u6559\u5e08-\u5b66\u751f\u201d\u8bbe\u7f6e<\/span>\uff08teacher-student setup\uff09<\/span>\u53ef\u4ee5\u63ed\u793a\u8fd9\u4e00\u70b9\uff1a\u5982\u679c\u6559\u5e08\u7f51\u7edc\u662f\u4e00\u4e2aKAN\uff0c\u90a3\u4e48\u5b66\u751f\u7684KAN\u7f51\u7edc\u5e94\u8be5\u8868\u73b0\u5f97\u6bd4\u5b66\u751f\u7684MLP\u66f4\u597d\u3002\u76f8\u53cd\uff0c\u5982\u679c\u6559\u5e08\u7f51\u7edc\u662fMLP\uff0c\u90a3\u4e48\u5b66\u751f\u7684MLP\u5e94\u8be5\u8868\u73b0\u5f97\u6bd4\u5b66\u751f\u7684KAN\u66f4\u597d\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u8fd9\u79cd\u601d\u8003\u65b9\u5f0f\u5f15\u53d1\u4e86\u4e00\u4e9b\u54f2\u5b66\u6027\u7684\u95ee\u9898\uff0c\u4f8b\u5982\u81ea\u7136\u89c4\u5f8b\u662f\u901a\u8fc7\u4f55\u79cd\u7c7b\u578b\u7684\u201c\u7f51\u7edc\u201d\u6765\u6784\u5efa\u4e16\u754c\u7684\u3002\u5982\u679c\u5b58\u5728\u9020\u7269\u4e3b\uff0c\u4ed6\u53c8\u662f\u4f7f\u7528\u4f55\u79cd\u7c7b\u578b\u7684\u7f51\u7edc\u6765\u6784\u5efa\u8fd9\u4e2a\u4e16\u754c\u7684\u5462\uff1f\u5bf9\u4e8e\u4e0d\u540c\u7684\u9886\u57df\uff0c\u5982\u79d1\u5b66\u3001\u89c6\u89c9\u3001\u8bed\u8a00\u6216\u5176\u4ed6\u4f60\u5173\u6ce8\u7684\u6d4b\u8bd5\u9886\u57df\uff0c\u7531\u4e8e\u5b83\u4eec\u7684\u6570\u636e\u6765\u6e90\u548c\u751f\u6210\u65b9\u5f0f\u53ef\u80fd\u4e0d\u540c\uff0c\u56e0\u6b64\u6700\u9002\u5408\u7684\u7f51\u7edc\u7ed3\u6784\u4e5f\u53ef\u80fd\u4e0d\u540c\u3002\u4f8b\u5982\uff0c\u5728\u79d1\u5b66\u9886\u57df\uff0c\u7531\u4e8e\u51fd\u6570\u7684\u7ec4\u5408\u6027\u53ef\u80fd\u66f4\u4e3a\u91cd\u8981\uff0cKAN\u53ef\u80fd\u8868\u73b0\u5f97\u66f4\u597d\u3002\u800c\u5728\u5904\u7406\u56fe\u50cf\u7b49\u4efb\u52a1\u65f6\uff0c\u53ef\u80fd\u66f4\u9002\u5408\u4f7f\u7528\u7c7b\u4f3cMLP\u7684\u7ed3\u6784\uff0c\u56e0\u4e3a\u5b83\u4eec\u66f4\u4f9d\u8d56\u4e8e\u968f\u673a\u7279\u5f81\u6216\u5176\u4ed6\u7c7b\u4f3c\u7684\u7ed3\u6784\u3002\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u8da3\u7684\u8ba8\u8bba\u70b9\uff0c\u4f46\u76ee\u524d\u8fd9\u4e9b\u95ee\u9898\u8fd8\u96be\u4ee5\u91cf\u5316\u3002\u6211\u4eec\u9700\u8981\u66f4\u591a\u7684\u5b9e\u9a8c\u548c\u7406\u8bba\u5206\u6790\u6765\u6df1\u5165\u63a2\u7d22\u8fd9\u4e9b\u7f51\u7edc\u7684\u6f5c\u529b\u548c\u9650\u5236\u3002<\/span><\/section>\n

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

      \u7b26\u53f7\u4e3b\u4e49\u4e0e\u8fde\u63a5\u4e3b\u4e49<\/strong><\/span><\/h4>\n

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

      <\/span><\/section>\n
      \u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u7b26\u53f7\u4e3b\u4e49\u4e0e\u8fde\u63a5\u4e3b\u4e49\u4e4b\u95f4\u7684\u52a8\u6001\u53d8\u5316\uff0c\u4ee5\u53caKAN\u5e26\u6765\u7684\u65b0\u89c6\u89d2\uff0c\u6211\u4eec\u53ef\u4ee5\u56de\u987e\u4e00\u4e0b\u76f8\u5173\u7684\u5386\u53f2\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u65e9\u57281957\u5e74\uff0cFrank Rosenblatt\u53d1\u660e\u4e86\u611f\u77e5\u673a\uff0c\u5e76\u8bc1\u660e\u4e86\u5b83\u5728\u5904\u7406\u67d0\u4e9b\u7ebf\u6027\u53ef\u5206\u6570\u636e\u548c\u5fc3\u7406\u5b66\u5b9e\u9a8c\u4e2d\u7684\u6709\u6548\u6027\u3002\u7136\u800c\uff0c\u52301969\u5e74\uff0cMinsky\u548cPapert\u51fa\u7248\u4e86\u4e00\u672c\u6279\u8bc4\u611f\u77e5\u673a\u7684\u4e66\uff0c\u6307\u51fa\u611f\u77e5\u673a\u751a\u81f3\u65e0\u6cd5\u5904\u7406\u57fa\u672c\u7684XOR\u95ee\u9898\uff0c\u8fd9\u88ab\u89c6\u4e3a\u5176\u81f4\u547d\u7684\u5f31\u70b9\u3002\u8fd9\u672c\u4e66\u5bf9Rosenblatt\u7684\u7406\u8bba\u9020\u6210\u4e86\u91cd\u5927\u6253\u51fb\uff0c\u751a\u81f3\u6709\u4f20\u8a00\u79f0\u8fd9\u5bfc\u81f4\u4e86Rosenblatt\u7684\u81ea\u6740\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      1974\u5e74\uff0cPaul Werbos\u63d0\u51fa\uff0c\u901a\u8fc7\u5c06\u611f\u77e5\u673a\u6269\u5c55\u4e3a\u591a\u5c42\u7ed3\u6784\uff0c\u53ef\u4ee5\u89e3\u51b3\u5f02\u6216\u95ee\u9898\u3002\u4f46\u8fd9\u4e00\u53d1\u73b0\u5e76\u672a\u5f15\u8d77\u592a\u5927\u5173\u6ce8\uff0c\u56e0\u4e3a\u5b83\u662f\u5728\u653f\u6cbb\u5b66\u548c\u793e\u4f1a\u5b66\u7684\u7814\u7a76\u4e2d\u88ab\u63d0\u51fa\u7684\uff0c\u5f53\u65f6\u7684\u4fe1\u606f\u4f20\u64ad\u5e76\u4e0d\u7545\u901a\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      1975\u5e74\uff0cRobert Hecht-Nielsen\u63a2\u7d22\u4e86Kolmogorov\u8868\u793a\u7406\u8bba\uff0c\u8fd9\u662f\u4e00\u4e2a\u5173\u4e8e\u5982\u4f55\u6784\u9020\u4e00\u4e2a\u5bbd\u5ea6\u4e3a2n+1\u7684\u53cc\u5c42\u7f51\u7edc\u7684\u7406\u8bba\u30021988\u5e74\uff0cGeorge\u53d1\u73b0\u4e86\u4e24\u5c42\u7684Kolmogorov\u7f51\u7edc\u80fd\u591f\u5904\u7406\u5f02\u6216\u95ee\u9898\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u8fd9\u4e9b\u5e74\u7684\u53d1\u5c55\u63ed\u793a\u4e86\u611f\u77e5\u673a\u7406\u8bba\u7684\u5174\u8d77\u548c\u5bf9\u5176\u7684\u6279\u8bc4\uff0c\u5bfc\u81f4\u4e86\u8fde\u63a5\u4e3b\u4e49\u7684\u6682\u65f6\u8870\u9000\uff0c\u7b26\u53f7\u4e3b\u4e49\u6210\u4e3a\u4e86\u4e3b\u6d41\u3002\u968f\u7740Kolmogorov\u8868\u793a\u7406\u8bba\u7684\u53d1\u73b0\uff0c\u8fde\u63a5\u4e3b\u4e49\u53c8\u91cd\u65b0\u83b7\u5f97\u4e86\u5173\u6ce8\u3002\u7136\u800c\uff0c\u8fdb\u51651990\u5e74\u4ee3\uff0c\u8fde\u63a5\u4e3b\u4e49\u518d\u6b21\u906d\u9047\u51b7\u9047\uff0c\u5982MIT\u6559\u6388Thomas Poggio\u57281989\u5e74\u6307\u51fa\uff0cKolmogorov\u7684\u8868\u793a\u7406\u8bba\u5bf9\u795e\u7ecf\u7f51\u7edc\u662f\u65e0\u5173\u7684\uff0c\u4e3b\u8981\u662f\u56e0\u4e3a\u5728\u4ec5\u6709\u4e24\u5c42\u7684\u60c5\u51b5\u4e0b\uff0c\u7f51\u7edc\u7684\u6fc0\u6d3b\u51fd\u6570\u53ef\u4ee5\u975e\u5e38\u4e0d\u5149\u6ed1\uff0c\u8fd9\u4e0d\u4ec5\u7f3a\u4e4f\u53ef\u89e3\u91ca\u6027\uff0c\u800c\u4e14\u8868\u8fbe\u80fd\u529b\u4e5f\u5f88\u5dee\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4ece2012\u5e74\u5f00\u59cb\uff0c\u73b0\u4ee3\u6df1\u5ea6\u5b66\u4e60\u7684\u5174\u8d77\u6807\u5fd7\u7740\u8fde\u63a5\u4e3b\u4e49\u7684\u590d\u5174\uff0c\u8fd9\u662f\u4e00\u4e2a\u4ee5\u5927\u578b\u6a21\u578b\u548c\u5e7f\u6cdb\u8fde\u63a5\u4e3a\u7279\u5f81\u7684\u65f6\u4ee3\uff0c\u867d\u7136\u8fd9\u4e9b\u7cfb\u7edf\u901a\u5e38\u88ab\u89c6\u4e3a\u201c\u9ed1\u76d2\u201d\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u53ef\u89e3\u91ca\u6027\u8f83\u5dee\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u8fd9\u6bb5\u5386\u53f2\u6982\u8ff0\u4e0d\u4ec5\u5e2e\u52a9\u6211\u4eec\u7406\u89e3KAN\u7684\u6280\u672f\u80cc\u666f\uff0c\u8fd8\u63ed\u793a\u4e86\u79d1\u6280\u53d1\u5c55\u4e2d\u5468\u671f\u6027\u7684\u7406\u8bba\u5174\u8870\u548c\u79d1\u5b66\u793e\u533a\u7684\u89c2\u70b9\u53d8\u8fc1\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      KAN\u662f\u8fde\u63a5\u4e3b\u4e49\u4e0e\u7b26\u53f7\u4e3b\u4e49\u4e4b\u95f4\u7684\u4ea7\u7269\u3002\u5b83\u7684\u5168\u8fde\u63a5\u7ed3\u6784\u4e0eMLP\u975e\u5e38\u76f8\u4f3c\u3002\u7136\u800c\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06KAN\u7f29\u5c0f\u5e76\u8d4b\u4e88\u5176\u7b26\u53f7\u5316\u7684\u7279\u6027\uff0c\u8fd9\u53cd\u6620\u4e86KAN\u4e0e\u7b26\u53f7\u4e4b\u95f4\u7684\u8054\u7cfb\u3002\u56e0\u6b64\u6211\u4eec\u8ba4\u4e3a\uff0cKAN\u6784\u6210\u4e86\u8fde\u63a5\u4e3b\u4e49\u4e0e\u7b26\u53f7\u4e3b\u4e49\u4e4b\u95f4\u7684\u4e00\u5ea7\u6865\u6881\uff0c\u53ef\u80fd\u66f4\u6709\u6548\u5730\u8fde\u63a5\u8fd9\u4e24\u4e2a\u4e16\u754c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u5927\u8bed\u8a00\u6a21\u578b\u7684\u8ba8\u8bba\u4e2d\uff0c\u6211\u4eec\u7ecf\u5e38\u63a2\u8ba8\u5b83\u4eec\u662f\u5426\u771f\u6b63\u7406\u89e3\u4e86\u7269\u7406\u89c4\u5f8b\u3002\u8fd9\u9700\u8981\u4e00\u4e2a\u540c\u65f6\u5177\u5907\u7b26\u53f7\u4e3b\u4e49\u548c\u8fde\u63a5\u4e3b\u4e49\u7279\u6027\u7684\u6a21\u578b\u3002\u5982\u4f55\u8ba9\u8fde\u63a5\u4e3b\u4e49\u5b66\u4e60\uff0c\u5982\u4f55\u8ba9\u7b26\u53f7\u4e3b\u4e49\u7cbe\u901a\u5176\u9886\u57df\uff0c\u8fd9\u4e9b\u90fd\u662f\u6211\u4eec\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u3002\u6700\u7ec8\uff0c\u6211\u4eec\u63a2\u7d22\u7684\u662f\u7b26\u53f7\u4e3b\u4e49\u4e2d\u7684\u7269\u7406\u5b66\u89c4\u5f8b\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u6574\u4e2a\u7f51\u7edc\u53ef\u80fd\u5e26\u6765\u7684\u4e0d\u53ef\u89e3\u91ca\u6027\u3002<\/span><\/section>\n

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

      KAN vs. MLP \u662f\u8fd8\u539f\u8bba\u76f8\u5bf9\u4e8e\u6574\u4f53\u8bba\uff1f<\/strong><\/span><\/h4>\n

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

      <\/span><\/section>\n
      \u6211\u4eec\u4e5f\u521a\u521a\u610f\u8bc6\u5230\uff0cMLP\u4e0eKAN\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u5b83\u4eec\u5bf9\u5185\u90e8\u548c\u5916\u90e8\u81ea\u7531\u5ea6\u7684\u5904\u7406\u65b9\u5f0f\u3002\u4f8b\u5982\uff0c\u57fa\u672c\u7c92\u5b50\u5185\u90e8\u53ef\u80fd\u5177\u6709\u81ea\u65cb\u7b49\u81ea\u7531\u5ea6\uff0c\u8fd9\u662f\u5185\u90e8\u81ea\u7531\u5ea6\u3002\u5916\u90e8\u81ea\u7531\u5ea6\u5219\u6d89\u53ca\u5176\u4e0e\u5916\u754c\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u5728\u793e\u4f1a\u5b66\u4e2d\uff0c\u4eba\u53ef\u4ee5\u4ece\u5185\u5728\u54c1\u6027\u6216\u5916\u90e8\u793e\u4f1a\u5173\u7cfb\u6765\u5b9a\u4e49\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      KAN\u5728MLP\u7684\u57fa\u7840\u4e0a\u5f15\u5165\u4e86\u65b0\u6982\u5ff5\u548c\u66f4\u590d\u6742\u7684\u529f\u80fd\u3002\u5b83\u4e0d\u4ec5\u5173\u6ce8\u8fde\u63a5\uff0c\u8fd8\u5173\u6ce8\u90e8\u4ef6\u7684\u5185\u90e8\u590d\u6742\u6027\u3002MLP\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u51fa\u73b0\uff0c\u4e0d\u5173\u5fc3\u5185\u90e8\u53d1\u751f\u7684\u5177\u4f53\u8fc7\u7a0b\uff0c\u800c\u662f\u4f9d\u9760\u590d\u6742\u7684\u8fde\u63a5\u6765\u663e\u73b0\u80fd\u529b\u3002\u800cKAN\u5219\u9700\u8981\u7cbe\u7ec6\u5730\u8bbe\u8ba1\u6bcf\u4e00\u90e8\u5206\uff0c\u786e\u4fdd\u6bcf\u4e2a\u90e8\u5206\u7684\u91cd\u8981\u6027\uff0c\u4ece\u800c\u7b80\u5316\u90e8\u4ef6\u4e4b\u95f4\u7684\u8fde\u63a5\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4ece\u54f2\u5b66\u89d2\u5ea6\u770b\uff0c\u8fd9\u4f53\u73b0\u4e86\u8fd8\u539f\u8bba\u4e0e\u6574\u4f53\u8bba\u7684\u533a\u522b\u3002\u8fd8\u539f\u8bba\u8bd5\u56fe\u5c06\u590d\u6742\u4e16\u754c\u5206\u89e3\u4e3a\u7b80\u5355\u7684\u57fa\u672c\u90e8\u5206\uff0c\u800c\u6574\u4f53\u8bba\u5219\u8ba4\u4e3a\u67d0\u4e9b\u4e1c\u897f\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u6765\u5de5\u4f5c\uff0c\u4e0d\u80fd\u7b80\u5355\u5206\u89e3\u3002\u8fd9\u4e5f\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48KAN\u5728\u79d1\u5b66\u9886\u57df\u7279\u522b\u6709\u7528\uff0c\u56e0\u4e3a\u8bb8\u591a\u79d1\u5b66\u601d\u60f3\u57fa\u4e8e\u8fd8\u539f\u8bba\uff0c\u800c\u6574\u4f53\u8bba\u5219\u5728\u73b0\u4ee3\u79d1\u5b66\u4e2d\u9010\u6e10\u6d41\u884c\u3002<\/span><\/section>\n

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

      <\/section>\n
      \u6211\u4eec\u6240\u8ba8\u8bba\u7684KAN\u662f\u4e00\u4e2a\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff0c\u90a3\u4e48\u5b83\u5230\u5e95\u6709\u591a\u201c\u81ea\u7136\u201d\u5462\uff1f<\/span><\/section>\n

      <\/span><\/section>\n
      \u9996\u5148\uff0c\u8fd9\u662f\u4e00\u4e2a\u5f15\u4eba\u5165\u80dc\u7684\u95ee\u9898\uff1a\u5b83\u6709\u591a\u201c\u7269\u7406\u201d\uff1f\u8003\u8651\u5230\u8d39\u66fc\u56fe\uff0c\u5b83\u5b9e\u9645\u4e0a\u66f4\u50cf\u662fMLP\u3002\u5728\u8d39\u66fc\u56fe\u4e2d\uff0c\u7c92\u5b50\u5728\u8fb9\u7f18\u90e8\u5206\u81ea\u7531\u4f20\u64ad\uff0c\u800c\u5728\u8282\u70b9\u4e0a\u5219\u53d1\u751f\u590d\u6742\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u4e0eMLP\u7684\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u76f8\u4f3c\u3002\u6211\u4eec\u4e5f\u5728\u63a2\u8ba8\u662f\u5426\u5b58\u5728\u4e00\u4e9b\u7269\u7406\u8fc7\u7a0b\uff0c\u8fd9\u4e9b\u8fc7\u7a0b\u53ef\u80fd\u66f4\u63a5\u8fd1KAN\u800c\u4e0d\u662fMLP\uff0c\u5c3d\u7ba1\u8fd9\u79cd\u7c7b\u6bd4\u53ef\u80fd\u7c97\u7cd9\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5176\u6b21\uff0c\u662f\u5173\u4e8eKAN\u662f\u5426\u5177\u6709\u751f\u7269\u5b66\u7279\u6027\u3002\u6709\u4e00\u79cd\u89c2\u70b9\u8ba4\u4e3a\uff0c\u7c7b\u4f3cMLP\u7684\u7f51\u7edc\u53d7\u5230\u4eba\u8111\u7684\u542f\u53d1\uff0c\u800c\u89c6\u7f51\u819c\u4e0a\u7684\u795e\u7ecf\u5143\u5219\u66f4\u50cfKAN\u3002\u8fd9\u8868\u660e\uff0c\u81ea\u7136\u754c\u4e2d\u786e\u5b9e\u5b58\u5728\u7c7b\u4f3c\u7684\u673a\u5236\uff0c\u5c3d\u7ba1\u8fd9\u4e9b\u673a\u5236\u5e76\u4e0d\u662f\u5927\u8111\u4e2d\u7684\u4e3b\u5bfc\u673a\u5236\u3002<\/span><\/section>\n

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

      \u60f3\u6cd5\u6765\u6e90<\/strong><\/span><\/h4>\n

      <\/strong><\/span><\/section>\n
      \u8fd9\u9879\u7814\u7a76\u7684\u53d1\u73b0\u5176\u5b9e\u662f\u4e00\u4e2a\u8f83\u957f\u7684\u6545\u4e8b\u3002\u6700\u521d\u7684\u60f3\u6cd5\u4ea7\u751f\u5728\u5927\u7ea6\u4e24\u4e09\u5e74\u524d\uff0c\u76ee\u6807\u662f\u63d0\u9ad8\u79d1\u5b66\u7684\u53ef\u89e3\u91ca\u6027\uff0c\u5e76\u5c1d\u8bd5\u8fdb\u884c\u7b26\u53f7\u56de\u5f52\u3002\u90a3\u65f6\uff0c\u6211\u4eec\u5728\u81ea\u7136\u795e\u7ecf\u7f51\u7edc\u7684\u6846\u67b6\u4e0b\u8fdb\u884c\u601d\u8003\uff0c\u5e0c\u671b\u4f7f\u8282\u70b9\u4e0a\u7684\u6fc0\u6d3b\u51fd\u6570\u53d8\u5f97\u53ef\u5b66\u4e60\u3002\u521d\u6b65\u5b9e\u9a8c\u663e\u793a\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u4e8e\u6781\u5176\u7b80\u5355\u7684\u4f8b\u5b50\u662f\u6709\u6548\u7684\uff0c\u4f46\u5bf9\u4e8e\u7a0d\u5fae\u590d\u6742\u4e00\u70b9\u7684\u4f8b\u5b50\u5c31\u65e0\u6cd5\u5e94\u5bf9\u3002\u6709\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u67e5\u770b\u9644\u5f55\u4e2d\u540d\u4e3a\u201clearnable activation networks\u201d\u7684\u76f8\u5173\u5b9e\u9a8c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4eca\u5e74\u5e74\u521d\uff0c\u6211\u4eec\u91cd\u65b0\u5ba1\u89c6\u4e86\u8fd9\u4e2a\u672a\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u610f\u8bc6\u5230\u5c06\u51fd\u6570\u653e\u5728\u8fb9\u4e0a\u53ef\u80fd\u4f7f\u7ed3\u679c\u66f4\u5177\u89e3\u91ca\u6027\u3002\u5173\u4e8e\u8fd9\u4e00\u70b9\u7684\u542f\u793a\u6765\u81ea\u4e8e\u5bfc\u5e08Max\u548c\u5176\u4ed6\u8bb8\u591a\u4eba\u7684\u8ba8\u8bba\uff0c\u4ed6\u4eec\u66fe\u63d0\u5230Kolmogorov-Arnold\u8868\u793a\u8ddf\u673a\u5668\u5b66\u4e60\u6ca1\u6709\u5173\u8054\uff0c\u56e0\u4e3a\u5b83\u6d89\u53ca\u7684\u6fc0\u6d3b\u51fd\u6570\u662f\u975e\u5149\u6ed1\u7684\u3002\u8fd9\u6fc0\u53d1\u4e86\u4e00\u79cd\u53db\u9006\u60f3\u6cd5\uff1a\u5982\u679c\u4f60\u8bf4\u8fd9\u4e2a\u7406\u8bba\u65e0\u7528\uff0c\u90a3\u6211\u5c31\u8981\u521b\u9020\u4e00\u4e2a\u6709\u7528\u7684\u4e1c\u897f\u3002\u90a3\u4e48\u95ee\u9898\u5c31\u5728\u4e8e\u5982\u4f55\u5408\u7406\u5730\u8bbe\u8ba1Kolmogorov\u7f51\u7edc\uff0c\u4f7f\u5176\u5177\u6709\u5b9e\u9645\u5e94\u7528\u4ef7\u503c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u8fd9\u4e2a\u63a2\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u6700\u521d\u5728\u4e24\u5c42\u7f51\u7edc\u4e0a\u5c31\u9047\u5230\u4e86\u56f0\u96be\uff0c\u5c24\u5176\u662f\u5728\u5982\u4f55\u8bbe\u5b9a\u5bbd\u5ea6\u65b9\u9762\u3002\u5c3d\u7ba1\u7406\u8bba\u4e0a\u8bf4\u8f93\u5165\u7684\u9690\u85cf\u5c42\u5e94\u8be5\u662f2n+1\uff0c\u6211\u4eec\u82b1\u4e86\u5f88\u957f\u65f6\u95f4\u5728\u8fd9\u4e2a\u8bbe\u7f6e\u4e0a\u8c03\u6574\uff0c\u540e\u6765\u624d\u610f\u8bc6\u5230\u8fd9\u4e2a\u8bbe\u7f6e\u53ef\u4ee5\u66f4\u7075\u6d3b\u3002\u6700\u7ec8\uff0c\u6211\u4eec\u6ce8\u610f\u5230\u539f\u59cb\u7684Kolmogorov-Arnold\u8868\u793a\u6cd5\u662f\u57fa\u4e8e\u4e24\u5c42\u7684\u7f51\u7edc\uff0c\u6211\u4eec\u53ef\u4ee5\u81ea\u7136\u5730\u5c06\u8fd9\u4e9b\u5c42\u5806\u53e0\u8d77\u6765\uff0c\u5f62\u6210\u66f4\u6df1\u7684\u7f51\u7edc\u3002\u8fd9\u79cd\u5916\u63a8\u7684\u903b\u8f91\u4e0d\u662f\u4e00\u5f00\u59cb\u5c31\u660e\u663e\u7684\uff0c\u56e0\u4e3a\u5185\u5c42\u51fd\u6570\u548c\u5916\u5c42\u51fd\u6570\u7684\u6307\u6807\u4e0d\u540c\u3002\u4f46\u5f53\u6211\u4eec\u610f\u8bc6\u5230\u6240\u6709\u5c42\u90fd\u662f\u4e24\u4e2a\u6307\u6807\u540e\uff0c\u5c31\u50cf\u5806\u53e0\u7ebf\u6027\u5c42\u6216MLP\u90a3\u6837\u53d8\u5f97\u7b80\u5355\u3002<\/span><\/section>\n

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


      <\/strong><\/span><\/h4>\n

      KAN\u7684\u672a\u6765\u53d1\u5c55<\/strong><\/span><\/h4>\n

      <\/span><\/section>\n
      GitHub\u5f00\u53d1\u8005\u793e\u533a\u5bf9KAN\u7684\u53d1\u5c55\u975e\u5e38\u8fc5\u901f\u3002\u5728\u4e00\u5468\u65f6\u95f4\u5185\uff0c\u4e00\u4e9b\u539f\u672c\u8ba1\u5212\u7684\u540e\u7eed\u7814\u7a76\u51e0\u4e4e\u90fd\u88ab\u4ed6\u4eba\u5148\u884c\u4e00\u6b65\u5b8c\u6210\u4e86\u3002\u8fd9\u65e2\u4ee4\u4eba\u5174\u594b\u53c8\u663e\u793a\u51fa\u8fd9\u4e2a\u9886\u57df\u7684\u6d3b\u8dc3\u5ea6\u3002\u73b0\u5728\uff0c\u5982\u679c\u4f60\u5173\u5fc3\u53ef\u89e3\u91ca\u6027\uff0c\u6211\u4eec\u5efa\u8bae\u4f7f\u7528\u539f\u59cbKAN\u7248\u672c\uff1b\u5982\u679c\u4f60\u66f4\u5173\u5fc3\u6548\u7387\u6216\u51c6\u786e\u6027\uff0c\u90a3\u4e48\u53ef\u4ee5\u9009\u62e9\u5176\u4ed6\u66f4\u9ad8\u6548\u7684KAN\u53d8\u4f53\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u6211\u4eec\u5bf9KAN\u7684\u672a\u6765\u89d2\u8272\u8fd8\u4e0d\u592a\u6e05\u695a\u3002\u5b9e\u8df5\u662f\u68c0\u9a8c\u771f\u7406\u7684\u552f\u4e00\u6807\u51c6\u3002\u6211\u4eec\u9700\u8981\u66f4\u591a\u7684\u5b9e\u9a8c\u6765\u63a2\u7d22KAN\u7684\u754c\u9650\u3002\u76ee\u524d\u4e0d\u9700\u8981\u7279\u522b\u4f9d\u8d56\u4e8eKAN\uff0c\u56e0\u4e3a\u5b83\u5e94\u8be5\u662f\u4e00\u4e2a\u66f4\u5e7f\u9614\u6846\u67b6\u7684\u4e00\u90e8\u5206\uff0c\u53ef\u80fd\u9700\u8981\u5c06\u7b26\u53f7\u548c\u6570\u503c\u90e8\u5206\u5206\u79bb\u5f00\u6765\u3002\u4ece\u957f\u8fdc\u6765\u770b\uff0c\u6211\u4eec\u5e0c\u671b\u80fd\u7ee7\u7eed\u5c06KAN\u7528\u4e8eAI\u4e0e\u79d1\u5b66\u7684\u4ea4\u53c9\u7814\u7a76\uff0c\u8fd9\u53ef\u80fd\u662f\u4e00\u4e2a\u76f8\u5bf9\u8f83\u5c0f\u4f17\u7684\u65b9\u5411\u3002\u671f\u5f85\u4e0e\u5927\u5bb6\u8ba8\u8bba\uff0c\u63a2\u8ba8\u600e\u6837\u5c06KAN\u5e94\u7528\u5230\u5176\u4ed6\u66f4\u5e7f\u6cdb\u7684\u9886\u57df\u3002<\/span><\/section>\n

      <\/section>\n

      <\/section>\n
      \u6574\u7406\u8005\u7b80\u4ecb\uff1a<\/span><\/strong><\/span><\/section>\n
      \u674e\u9882\u5143(Shaun)\uff0c\u76ee\u524d\u662f\u4e2d\u5c71\u5927\u5b66\u7684\u5728\u7ad9\u535a\u58eb\u540e\uff0c\u76ee\u524d\u7684\u7814\u7a76\u5174\u8da3\u662f\u5177\u8eab\u667a\u80fd\u3002<\/span><\/section>\n

      <\/section>\n

      <\/section>\n
      \n
      \n
      \u4ee5\u4e0a\u662f\u62a5\u544a\u4e3b\u8981\u5185\u5bb9\u6574\u7406\uff0c\u6709\u5220\u51cf\u3002\u52a0\u5165<\/span>AI+Science\u8bfb\u4e66\u4f1a<\/span><\/a>\u53ef\u67e5\u770b\u5b8c\u6574\u62a5\u544a\u89c6\u9891\u3001PPT\u53ca1\u5c0f\u65f6\u95ee\u7b54\u73af\u8282\uff0c\u5e76\u53c2\u4e0e\u793e\u7fa4\u4ea4\u6d41\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n

      <\/p>\n


      <\/section>\n

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

      AI+Science \u8bfb\u4e66\u4f1a<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      \n


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

      AI+Science \u662f\u8fd1\u5e74\u5174\u8d77\u7684\u5c06\u4eba\u5de5\u667a\u80fd\u548c\u79d1\u5b66\u76f8\u7ed3\u5408\u7684\u4e00\u79cd\u8d8b\u52bf\u3002\u4e00\u65b9\u9762\u662f AI for Science\uff0c\u673a\u5668\u5b66\u4e60\u548c\u5176\u4ed6 AI \u6280\u672f\u53ef\u4ee5\u7528\u6765\u89e3\u51b3\u79d1\u5b66\u7814\u7a76\u4e2d\u7684\u95ee\u9898\uff0c\u4ece\u9884\u6d4b\u5929\u6c14\u548c\u86cb\u767d\u8d28\u7ed3\u6784\uff0c\u5230\u6a21\u62df\u661f\u7cfb\u78b0\u649e\u3001\u8bbe\u8ba1\u4f18\u5316\u6838\u805a\u53d8\u53cd\u5e94\u5806\uff0c\u751a\u81f3\u50cf\u79d1\u5b66\u5bb6\u4e00\u6837\u8fdb\u884c\u79d1\u5b66\u53d1\u73b0\uff0c\u88ab\u79f0\u4e3a\u79d1\u5b66\u53d1\u73b0\u7684\u201c\u7b2c\u4e94\u8303\u5f0f\u201d\u3002\u53e6\u4e00\u65b9\u9762\u662f Science for AI\uff0c\u79d1\u5b66\u5c24\u5176\u662f\u7269\u7406\u5b66\u4e2d\u7684\u89c4\u5f8b\u548c\u601d\u60f3\u542f\u53d1\u673a\u5668\u5b66\u4e60\u7406\u8bba\uff0c\u4e3a\u4eba\u5de5\u667a\u80fd\u7684\u53d1\u5c55\u63d0\u4f9b\u5168\u65b0\u7684\u89c6\u89d2\u548c\u65b9\u6cd5\u3002<\/span><\/section>\n

      <\/section>\n
      \u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u65af\u5766\u798f\u5927\u5b66\u8ba1\u7b97\u673a\u79d1\u5b66\u7cfb\u535a\u58eb\u540e\u7814\u7a76\u5458\u5434\u6cf0\u9716\uff08Jure Leskovec \u6559\u6388\u6307\u5bfc\uff09\u3001\u54c8\u4f5b\u91cf\u5b50\u8ba1\u5212\u7814\u7a76\u5458\u6248\u9e3f\u4e1a\u3001\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7269\u7406\u7cfb\u535a\u58eb\u751f\u5218\u5b50\u9e23\uff08Max Tegmark \u6559\u6388\u6307\u5bfc\uff09\uff0c\u5171\u540c\u53d1\u8d77\u4ee5\u201cAI+Science<\/a>\u201d\u4e3a\u4e3b\u9898\u7684\u8bfb\u4e66\u4f1a\uff0c\u63a2\u8ba8\u8be5\u9886\u57df\u7684\u91cd\u8981\u95ee\u9898\uff0c\u5171\u5b66\u5171\u7814\u76f8\u5173\u6587\u732e\u3002\u8bfb\u4e66\u4f1a\u5df2\u5b8c\u7ed3\uff0c\u73b0\u5728\u62a5\u540d\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u89e3\u9501\u56de\u653e\u89c6\u9891\u6743\u9650\u3002<\/span><\/span><\/section>\n

      <\/section>\n

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


      <\/p>\n

      \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n
      \u4eba\u5de5\u667a\u80fd\u548c\u79d1\u5b66\u53d1\u73b0\u76f8\u4e92\u8d4b\u80fd\u7684\u65b0\u8303\u5f0f\uff1aAI+Science \u8bfb\u4e66\u4f1a\u542f\u52a8<\/a><\/span><\/section>\n

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

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

      <\/h2>\n
      \n
      \n
      \n
      \n

      \u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a<\/strong>
      <\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


      <\/section>\n

      \u6570\u5341\u5e74\u6765\uff0c\u4eba\u5de5\u667a\u80fd\u7684\u7406\u8bba\u53d1\u5c55\u548c\u6280\u672f\u5b9e\u8df5\u4e00\u76f4\u4e0e\u79d1\u5b66\u63a2\u7d22\u76f8\u4f34\u800c\u751f\uff0c\u5c24\u5176\u5728\u4ee5\u5927\u6a21\u578b\u4e3a\u4ee3\u8868\u7684\u4eba\u5de5\u667a\u80fd\u6280\u672f\u5e94\u7528\u96c6\u4e2d\u7206\u53d1\u7684\u5f53\u4e0b\uff0c\u4eba\u5de5\u667a\u80fd\u6b63\u5728\u52a0\u901f\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7b49\u57fa\u7840\u79d1\u5b66\u7684\u9769\u65b0\uff0c\u800c\u8fd9\u4e9b\u5b66\u79d1\u4e5f\u5728\u53cd\u8fc7\u6765\u542f\u53d1\u4eba\u5de5\u667a\u80fd\u6280\u672f\u521b\u65b0\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u4f5c\u4e3a\u517c\u5177\u7406\u8bba\u5c5e\u6027\u4e0e\u5de5\u5177\u5c5e\u6027\u7684\u91cd\u8981\u57fa\u7840\u5b66\u79d1\uff0c\u4e0e\u4eba\u5de5\u667a\u80fd\u5173\u7cfb\u751a\u5bc6\uff0c\u76f8\u8f85\u76f8\u6210\u3002\u4e00\u65b9\u9762\uff0c\u4eba\u5de5\u667a\u80fd\u5728\u89e3\u51b3\u6570\u5b66\u9886\u57df\u7684\u8bf8\u591a\u5de5\u7a0b\u95ee\u9898\u3001\u7406\u8bba\u95ee\u9898\u4e43\u81f3\u5723\u676f\u96be\u9898\u4e0a\u5c61\u521b\u8bb0\u5f55\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6570\u5b66\u6301\u7eed\u4e3a\u4eba\u5de5\u667a\u80fd\u6784\u7b51\u7406\u8bba\u57fa\u77f3\u5e76\u62d3\u5c55\u5176\u672a\u6765\u7a7a\u95f4\u3002\u8fd9\u4e24\u4e2a\u5173\u952e\u9886\u57df\u7684\u4ea4\u53c9\u878d\u5408\uff0c\u6b63\u5728\u63ed\u5f00\u4e0b\u4e2a\u65f6\u4ee3\u7684\u79d1\u5b66\u4e4b\u5e55\u3002<\/span><\/p>\n


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

      \u4e3a\u4e86\u63a2\u7d22\u6570\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u6df1\u5ea6\u878d\u5408\u7684\u53ef\u80fd\u6027\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u540c\u6d4e\u5927\u5b66\u7279\u8058\u7814\u7a76\u5458\u9648\u5c0f\u6768\u3001\u6e05\u534e\u5927\u5b66\u4ea4\u53c9\u4fe1\u606f\u5b66\u9662\u52a9\u7406\u6559\u6388\u8881\u6d0b\u3001\u5357\u6d0b\u7406\u5de5\u5927\u5b66\u526f\u6559\u6388\u590f\u514b\u6797\u4e09\u4f4d\u8001\u5e08\uff0c\u5171\u540c\u53d1\u8d77\u201c\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u201d\u8bfb\u4e66\u4f1a\uff0c\u5e0c\u671b\u4ece AI\u3000for\u3000Math\uff0cMath\u3000for\u3000AI \u4e24\u4e2a\u65b9\u9762\u6df1\u5165\u63a2\u8ba8\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u7684\u5bc6\u5207\u8054\u7cfb\u3002\u8bfb\u4e66\u4f1a\u5df2\u5b8c\u7ed3\uff0c\u73b0\u5728\u62a5\u540d\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u89e3\u9501\u56de\u653e\u89c6\u9891\u6743\u9650\u3002<\/span><\/span><\/p>\n


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

      <\/section>\n

      \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/p>\n

      \u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1aAI for Math\uff0cMath for AI<\/a><\/span><\/p>\n

      \n


      <\/p>\n


      <\/p>\n

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

      1. <\/strong>\u6df1\u5ea6\u5b66\u4e60\u52a9\u529b\u7f51\u7edc\u79d1\u5b66\uff1a\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u793e\u533a\u53d1\u73b0\u6700\u65b0\u7efc\u8ff0<\/a><\/strong><\/span><\/strong><\/section>\n
      2. <\/strong>\u65e0\u5fc3\u63d2\u67f3\uff1a\u82cf\u8054\u6570\u5b66\u5bb6\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u4e0e\u795e\u7ecf\u7f51\u7edc\u7684\u65b0\u751f<\/a><\/strong><\/span><\/section>\n
      3. <\/strong>\u8bba\u6587\u89e3\u8bfb\uff1a\u7f51\u7edc\u79d1\u5b66\u5982\u4f55\u6253\u5f00\u6df1\u5ea6\u5b66\u4e60\u7684\u9ed1\u7bb1\uff1f<\/a><\/strong><\/span><\/strong><\/section>\n
      4. <\/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
      5.<\/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><\/section>\n
      6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


      <\/p>\n


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

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

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

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