{"id":34770,"date":"2024-12-12T17:57:40","date_gmt":"2024-12-12T09:57:40","guid":{"rendered":"https:\/\/17aitech.com\/?p=34770"},"modified":"2024-12-12T17:57:40","modified_gmt":"2024-12-12T09:57:40","slug":"%e5%8f%8d%e8%bd%ac%e4%ba%86%ef%bc%9f%e5%9c%a8%e4%b8%80%e5%9c%ba%e6%96%b0%e8%be%83%e9%87%8f%e4%b8%ad%ef%bc%8c%e5%8f%b7%e7%a7%b0%e6%9b%bf%e4%bb%a3mlp%e7%9a%84kan%e5%8f%aa%e8%b5%a2%e4%b8%80%e5%b1%80","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=34770","title":{"rendered":"\u53cd\u8f6c\u4e86\uff1f\u5728\u4e00\u573a\u65b0\u8f83\u91cf\u4e2d\uff0c\u53f7\u79f0\u66ff\u4ee3MLP\u7684KAN\u53ea\u8d62\u4e00\u5c40"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2024-07-27-4\" target=\"_blank\">\u53cd\u8f6c\u4e86\uff1f\u5728\u4e00\u573a\u65b0\u8f83\u91cf\u4e2d\uff0c\u53f7\u79f0\u66ff\u4ee3MLP\u7684KAN\u53ea\u8d62\u4e00\u5c40<\/a><\/p>\n<blockquote data-author-name=\"\" data-content-utf8-length=\"1\" data-source-title=\"\" data-type=\"2\" data-url=\"\">\n<p>KAN \u5728\u7b26\u53f7\u8868\u793a\u4e2d\u9886\u5148\uff0c\u4f46 MLP \u4ecd\u662f\u591a\u9762\u624b\u3002<\/p>\n<\/blockquote>\n<section><\/section>\n<section>\u591a\u5c42\u611f\u77e5\u5668 (Multi-Layer Perceptrons\uff0cMLP) \uff0c\u4e5f\u88ab\u79f0\u4e3a\u5168\u8fde\u63a5\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff0c\u662f\u5f53\u4eca\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\u3002MLP \u7684\u91cd\u8981\u6027\u65e0\u8bba\u600e\u6837\u5f3a\u8c03\u90fd\u4e0d\u4e3a\u8fc7\uff0c\u56e0\u4e3a\u5b83\u662f\u673a\u5668\u5b66\u4e60\u4e2d\u7528\u4e8e\u903c\u8fd1\u975e\u7ebf\u6027\u51fd\u6570\u7684\u9ed8\u8ba4\u65b9\u6cd5\u3002<\/section>\n<section><\/section>\n<section>\u7136\u800c\uff0cMLP \u4e5f\u5b58\u5728\u67d0\u4e9b\u5c40\u9650\u6027\uff0c\u4f8b\u5982\u96be\u4ee5\u89e3\u91ca\u5b66\u4e60\u5230\u7684\u8868\u793a\uff0c\u4ee5\u53ca\u96be\u4ee5\u7075\u6d3b\u5730\u6269\u5c55\u7f51\u7edc\u89c4\u6a21\u3002<\/section>\n<section><\/section>\n<section>KAN\uff08Kolmogorov\u2013Arnold Networks\uff09\u7684\u51fa\u73b0\uff0c\u4e3a\u4f20\u7edf MLP \u63d0\u4f9b\u4e86\u4e00\u79cd\u521b\u65b0\u7684\u66ff\u4ee3\u65b9\u6848\u3002\u8be5\u65b9\u6cd5\u5728\u51c6\u786e\u6027\u548c\u53ef\u89e3\u91ca\u6027\u65b9\u9762\u4f18\u4e8e MLP\uff0c\u800c\u4e14\uff0c\u5b83\u80fd\u4ee5\u975e\u5e38\u5c11\u7684\u53c2\u6570\u91cf\u80dc\u8fc7\u4ee5\u66f4\u5927\u53c2\u6570\u91cf\u8fd0\u884c\u7684 MLP\u3002<\/section>\n<section><\/section>\n<section>\u90a3\u4e48\uff0c\u95ee\u9898\u6765\u4e86\uff0cKAN \u3001MLP \u5230\u5e95\u8be5\u9009\u54ea\u4e00\u79cd\uff1f\u6709\u4eba\u652f\u6301 MLP\uff0c\u56e0\u4e3a KAN \u53ea\u662f\u4e00\u4e2a\u666e\u901a\u7684 MLP\uff0c\u6839\u672c\u66ff\u4ee3\u4e0d\u4e86\uff0c\u4f46\u4e5f\u6709\u4eba\u5219\u8ba4\u4e3a KAN \u66f4\u80dc\u4e00\u7b79\uff0c\u800c\u5f53\u524d\u5bf9\u4e24\u8005\u7684\u6bd4\u8f83\u4e5f\u662f\u5c40\u9650\u5728\u4e0d\u540c\u53c2\u6570\u6216 FLOP \u4e0b\u8fdb\u884c\u7684\uff0c\u5b9e\u9a8c\u7ed3\u679c\u5e76\u4e0d\u516c\u5e73\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u63a2\u7a76 KAN \u7684\u6f5c\u529b\uff0c\u6709\u5fc5\u8981\u5728\u516c\u5e73\u7684\u8bbe\u7f6e\u4e0b\u5168\u9762\u6bd4\u8f83 KAN \u548c MLP \u4e86\u3002<\/section>\n<section><\/section>\n<section>\u4e3a\u6b64\uff0c\u6765\u81ea\u65b0\u52a0\u5761\u56fd\u7acb\u5927\u5b66\u7684\u7814\u7a76\u8005\u5728\u63a7\u5236\u4e86 KAN \u548c MLP \u7684\u53c2\u6570\u6216 FLOP \u7684\u60c5\u51b5\u4e0b\uff0c\u5728\u4e0d\u540c\u9886\u57df\u7684\u4efb\u52a1\u4e2d\u5bf9\u5b83\u4eec\u8fdb\u884c\u8bad\u7ec3\u548c\u8bc4\u4f30\uff0c\u5305\u62ec\u7b26\u53f7\u516c\u5f0f\u8868\u793a\u3001\u673a\u5668\u5b66\u4e60\u3001\u8ba1\u7b97\u673a\u89c6\u89c9\u3001NLP \u548c\u97f3\u9891\u5904\u7406\u3002\u5728\u8fd9\u4e9b\u516c\u5e73\u7684\u8bbe\u7f6e\u4e0b\uff0c\u4ed6\u4eec\u53d1\u73b0<strong>\u00a0KAN \u4ec5\u5728\u7b26\u53f7\u516c\u5f0f\u8868\u793a\u4efb\u52a1\u4e2d\u4f18\u4e8e MLP\uff0c\u800c MLP \u901a\u5e38\u5728\u5176\u4ed6\u4efb\u52a1\u4e2d\u4f18\u4e8e KAN<\/strong>\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-5a61b9c5c99cc799453773ab67d0ce33.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-5a61b9c5c99cc799453773ab67d0ce33.png\"><\/a><\/section>\n<ul>\n<li>\n<section>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2407.16674<\/section>\n<\/li>\n<li>\n<section>\u9879\u76ee\u94fe\u63a5\uff1ahttps:\/\/github.com\/yu-rp\/KANbeFair<\/section>\n<\/li>\n<li>\n<section>\u8bba\u6587\u6807\u9898\uff1aKAN or MLP: A Fairer Comparison<\/section>\n<\/li>\n<\/ul>\n<section><\/section>\n<section>\u4f5c\u8005\u8fdb\u4e00\u6b65\u53d1\u73b0\uff0c<strong>KAN \u5728\u7b26\u53f7\u516c\u5f0f\u8868\u793a\u65b9\u9762\u7684\u4f18\u52bf\u6e90\u4e8e\u5176\u4f7f\u7528\u7684 B &#8211; \u6837\u6761\u6fc0\u6d3b\u51fd\u6570<\/strong>\u3002\u6700\u521d\uff0cMLP \u7684\u6574\u4f53\u6027\u80fd\u843d\u540e\u4e8e KAN\uff0c\u4f46\u5728\u7528 B &#8211; \u6837\u6761\u4ee3\u66ff MLP \u7684\u6fc0\u6d3b\u51fd\u6570\u540e\uff0c\u5176\u6027\u80fd\u8fbe\u5230\u751a\u81f3\u8d85\u8fc7\u4e86 KAN\u3002\u4f46\u662f\uff0cB &#8211; \u6837\u6761\u65e0\u6cd5\u8fdb\u4e00\u6b65\u63d0\u9ad8 MLP \u5728\u5176\u4ed6\u4efb\u52a1\uff08\u5982\u8ba1\u7b97\u673a\u89c6\u89c9\uff09\u4e0a\u7684\u6027\u80fd\u3002<\/section>\n<section><\/section>\n<section>\u4f5c\u8005\u8fd8\u53d1\u73b0\uff0c<strong>KAN \u5728\u8fde\u7eed\u5b66\u4e60\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\u5b9e\u9645\u4e0a\u5e76\u4e0d\u6bd4 MLP \u597d<\/strong>\u3002\u6700\u521d\u7684 KAN \u8bba\u6587\u4f7f\u7528\u4e00\u7cfb\u5217\u4e00\u7ef4\u51fd\u6570\u6bd4\u8f83\u4e86 KAN \u548c MLP \u5728\u8fde\u7eed\u5b66\u4e60\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\uff0c\u5176\u4e2d\u6bcf\u4e2a\u540e\u7eed\u51fd\u6570\u90fd\u662f\u524d\u4e00\u4e2a\u51fd\u6570\u6cbf\u6570\u8f74\u7684\u5e73\u79fb\u3002\u800c\u672c\u6587\u6bd4\u8f83\u4e86 KAN \u548c MLP \u5728\u66f4\u6807\u51c6\u7684\u7c7b\u9012\u589e\u6301\u7eed\u5b66\u4e60\u8bbe\u7f6e\u4e2d\u7684\u8868\u73b0\u3002\u5728\u56fa\u5b9a\u7684\u8bad\u7ec3\u8fed\u4ee3\u6761\u4ef6\u4e0b\uff0c\u4ed6\u4eec\u53d1\u73b0 <strong>KAN \u7684\u9057\u5fd8\u95ee\u9898\u6bd4 MLP \u66f4\u4e25\u91cd<\/strong>\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-d2cba336dd409501bbfa57e924f06940.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-d2cba336dd409501bbfa57e924f06940.png\"><\/a><\/section>\n<section><strong>KAN\u3001MLP \u7b80\u5355\u4ecb\u7ecd<\/strong><\/section>\n<section><\/section>\n<section>KAN \u6709\u4e24\u4e2a\u5206\u652f\uff0c\u7b2c\u4e00\u4e2a\u5206\u652f\u662f B \u6837\u6761\u5206\u652f\uff0c\u53e6\u4e00\u4e2a\u5206\u652f\u662f shortcut \u5206\u652f\uff0c\u5373\u975e\u7ebf\u6027\u6fc0\u6d3b\u4e0e\u7ebf\u6027\u53d8\u6362\u8fde\u63a5\u5728\u4e00\u8d77\u3002\u5728\u5b98\u65b9\u5b9e\u73b0\u4e2d\uff0cshortcut \u5206\u652f\u662f\u4e00\u4e2a SiLU \u51fd\u6570\uff0c\u540e\u9762\u8ddf\u7740\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u3002\u4ee4 x \u8868\u793a\u4e00\u4e2a\u6837\u672c\u7684\u7279\u5f81\u5411\u91cf\u3002\u90a3\u4e48\uff0cKAN \u6837\u6761\u5206\u652f\u7684\u524d\u5411\u65b9\u7a0b\u53ef\u4ee5\u5199\u6210\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-2c100ecd226c9f673fbbf728f1f96479.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-2c100ecd226c9f673fbbf728f1f96479.png\"><\/a><\/section>\n<section>\u5728\u539f\u59cb KAN \u67b6\u6784\u4e2d\uff0c\u6837\u6761\u51fd\u6570\u88ab\u9009\u62e9\u4e3a B \u6837\u6761\u51fd\u6570\u3002\u6bcf\u4e2a B \u6837\u6761\u51fd\u6570\u7684\u53c2\u6570\u4e0e\u5176\u4ed6\u7f51\u7edc\u53c2\u6570\u4e00\u8d77\u5b66\u4e60\u3002<\/section>\n<section><\/section>\n<section>\u76f8\u5e94\u7684\uff0c\u5355\u5c42 MLP \u7684\u524d\u5411\u65b9\u7a0b\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-8ab7c7427994c7b24fffeb36a17791b4.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-8ab7c7427994c7b24fffeb36a17791b4.png\"><\/a><\/section>\n<section>\u8be5\u516c\u5f0f\u4e0e KAN \u4e2d\u7684 B \u6837\u6761\u5206\u652f\u516c\u5f0f\u5177\u6709\u76f8\u540c\u7684\u5f62\u5f0f\uff0c\u53ea\u662f\u5728\u975e\u7ebf\u6027\u51fd\u6570\u4e2d\u6709\u6240\u4e0d\u540c\u3002\u56e0\u6b64\uff0c\u629b\u5f00\u539f\u8bba\u6587\u5bf9 KAN \u7ed3\u6784\u7684\u89e3\u8bfb\uff0cKAN \u4e5f\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u79cd\u5168\u8fde\u63a5\u5c42\u3002<\/section>\n<section><\/section>\n<section>\u56e0\u800c\uff0cKAN \u548c\u666e\u901a MLP \u7684\u533a\u522b\u4e3b\u8981\u6709\u4e24\u70b9\uff1a<\/section>\n<section><\/section>\n<ol>\n<li>\n<section>\u6fc0\u6d3b\u51fd\u6570\u4e0d\u540c\u3002\u901a\u5e38 MLP \u4e2d\u7684\u6fc0\u6d3b\u51fd\u6570\u5305\u62ec ReLU\u3001GELU \u7b49\uff0c\u6ca1\u6709\u53ef\u5b66\u4e60\u7684\u53c2\u6570\uff0c\u5bf9\u6240\u6709\u8f93\u5165\u5143\u7d20\u90fd\u662f\u7edf\u4e00\u7684\uff0c\u800c\u5728 KAN \u4e2d\uff0c\u6fc0\u6d3b\u51fd\u6570\u662f\u6837\u6761\u51fd\u6570\uff0c\u6709\u53ef\u5b66\u4e60\u7684\u53c2\u6570\uff0c\u5e76\u4e14\u5bf9\u4e8e\u6bcf\u4e2a\u8f93\u5165\u5143\u7d20\u90fd\u662f\u4e0d\u4e00\u6837\u7684\u3002<\/section>\n<\/li>\n<li>\n<section>\u7ebf\u6027\u548c\u975e\u7ebf\u6027\u8fd0\u7b97\u7684\u987a\u5e8f\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u7814\u7a76\u8005\u4f1a\u628a MLP \u6982\u5ff5\u5316\u4e3a\u5148\u8fdb\u884c\u7ebf\u6027\u53d8\u6362\uff0c\u518d\u8fdb\u884c\u975e\u7ebf\u6027\u53d8\u6362\uff0c\u800c KAN \u5176\u5b9e\u662f\u5148\u8fdb\u884c\u975e\u7ebf\u6027\u53d8\u6362\uff0c\u518d\u8fdb\u884c\u7ebf\u6027\u53d8\u6362\u3002\u4f46\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\uff0c\u5c06 MLP \u4e2d\u7684\u5168\u8fde\u63a5\u5c42\u63cf\u8ff0\u4e3a\u5148\u975e\u7ebf\u6027\uff0c\u540e\u7ebf\u6027\u4e5f\u662f\u53ef\u884c\u7684\u3002<\/section>\n<\/li>\n<\/ol>\n<section><\/section>\n<section>\u901a\u8fc7\u6bd4\u8f83 KAN \u548c MLP\uff0c\u8be5\u7814\u7a76\u8ba4\u4e3a<strong>\u4e24\u8005\u4e4b\u95f4\u7684\u5dee\u5f02\u4e3b\u8981\u662f\u6fc0\u6d3b\u51fd\u6570<\/strong>\u3002\u56e0\u800c\uff0c\u4ed6\u4eec\u5047\u8bbe\u6fc0\u6d3b\u51fd\u6570\u7684\u5dee\u5f02\u4f7f\u5f97 KAN \u548c MLP \u9002\u7528\u4e8e\u4e0d\u540c\u7684\u4efb\u52a1\uff0c\u4ece\u800c\u5bfc\u81f4\u4e24\u4e2a\u6a21\u578b\u5728\u529f\u80fd\u4e0a\u5b58\u5728\u5dee\u5f02\u3002\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e00\u5047\u8bbe\uff0c\u7814\u7a76\u8005\u6bd4\u8f83\u4e86 KAN \u548c MLP \u5728\u4e0d\u540c\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\uff0c\u5e76\u63cf\u8ff0\u4e86\u6bcf\u4e2a\u6a21\u578b\u9002\u5408\u7684\u4efb\u52a1\u3002\u4e3a\u4e86\u786e\u4fdd\u516c\u5e73\u6bd4\u8f83\uff0c\u8be5\u7814\u7a76\u9996\u5148\u63a8\u5bfc\u51fa\u4e86\u8ba1\u7b97 KAN \u548c MLP \u53c2\u6570\u6570\u91cf\u548c FLOP \u7684\u516c\u5f0f\u3002\u5b9e\u9a8c\u8fc7\u7a0b\u63a7\u5236\u76f8\u540c\u6570\u91cf\u7684\u53c2\u6570\u6216 FLOP \u6765\u6bd4\u8f83 KAN \u548c MLP \u7684\u6027\u80fd\u3002<\/section>\n<section><\/section>\n<section><strong>KAN \u548c MLP \u7684\u53c2\u6570\u6570\u91cf\u53caFLOP\u00a0<\/strong><\/section>\n<section><\/section>\n<section><strong>\u63a7\u5236\u53c2\u6570\u6570\u91cf<\/strong><\/section>\n<section><\/section>\n<section>KAN \u4e2d\u53ef\u5b66\u4e60\u7684\u53c2\u6570\u5305\u62ec B \u6837\u6761\u63a7\u5236\u70b9\u3001shortcut \u6743\u91cd\u3001B \u6837\u6761\u6743\u91cd\u548c\u504f\u7f6e\u9879\u3002\u603b\u7684\u53ef\u5b66\u4e60\u53c2\u6570\u6570\u91cf\u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-ada1bfaa7e94947c8db862db6bebe836.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-ada1bfaa7e94947c8db862db6bebe836.png\"><\/a><\/section>\n<section>\u5176\u4e2d\uff0c d_in \u548c d_out \u8868\u793a\u795e\u7ecf\u7f51\u7edc\u5c42\u7684\u8f93\u5165\u548c\u8f93\u51fa\u7ef4\u5ea6\uff0cK \u8868\u793a\u6837\u6761\u7684\u9636\u6570\uff0c\u5b83\u4e0e\u5b98\u65b9 nn.Module KANLayer \u7684\u53c2\u6570 k \u76f8\u5bf9\u5e94\uff0c\u5b83\u662f\u6837\u6761\u51fd\u6570\u4e2d\u591a\u9879\u5f0f\u57fa\u7840\u7684\u9636\u6570\u3002G \u8868\u793a\u6837\u6761\u95f4\u9694\u6570\uff0c\u5b83\u5bf9\u5e94\u4e8e\u5b98\u65b9 nn.Module KANLayer \u7684 num \u53c2\u6570\u3002\u5b83\u662f\u586b\u5145\u524d B \u6837\u6761\u66f2\u7ebf\u7684\u95f4\u9694\u6570\u3002\u5728\u586b\u5145\u4e4b\u524d\uff0c\u5b83\u7b49\u4e8e\u63a7\u5236\u70b9\u7684\u6570\u91cf &#8211; 1\u3002\u5728\u586b\u5145\u540e\uff0c\u5e94\u8be5\u6709 (K +G) \u4e2a\u6709\u6548\u63a7\u5236\u70b9\u3002<\/section>\n<section><\/section>\n<section>\u76f8\u5e94\u7684\uff0c\u4e00\u4e2a MLP \u5c42\u7684\u53ef\u5b66\u4e60\u53c2\u6570\u662f\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-2e68f7d1257d1cb9f7760af2a0707797.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-2e68f7d1257d1cb9f7760af2a0707797.png\"><\/a><\/section>\n<section><strong>KAN \u548c MLP \u7684 FLOP<\/strong><\/section>\n<section><\/section>\n<section>\u5728\u4f5c\u8005\u7684\u8bc4\u4f30\u4e2d\uff0c\u4efb\u4f55\u7b97\u672f\u64cd\u4f5c\u7684 FLOP \u88ab\u8003\u8651\u4e3a 1\uff0c\u800c\u5e03\u5c14\u64cd\u4f5c\u7684 FLOP \u88ab\u8003\u8651\u4e3a 0\u3002De Boor-Cox \u7b97\u6cd5\u4e2d\u7684 0 \u9636\u64cd\u4f5c\u53ef\u4ee5\u8f6c\u6362\u4e3a\u4e00\u7cfb\u5217\u5e03\u5c14\u64cd\u4f5c\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u4e0d\u9700\u8981\u8fdb\u884c\u6d6e\u70b9\u8fd0\u7b97\u3002\u56e0\u6b64\uff0c\u4ece\u7406\u8bba\u4e0a\u8bb2\uff0c\u5176 FLOP \u4e3a 0\u3002\u8fd9\u4e0e\u5b98\u65b9 KAN \u5b9e\u73b0\u4e0d\u540c\uff0c\u5728\u5b98\u65b9\u5b9e\u73b0\u4e2d\uff0c\u5b83\u5c06\u5e03\u5c14\u6570\u636e\u8f6c\u6362\u56de\u6d6e\u70b9\u6570\u636e\u6765\u8fdb\u884c\u64cd\u4f5c\u3002<\/section>\n<section><\/section>\n<section>\u5728\u4f5c\u8005\u7684\u8bc4\u4f30\u4e2d\uff0cFLOP \u662f\u9488\u5bf9\u4e00\u4e2a\u6837\u672c\u8ba1\u7b97\u7684\u3002\u5b98\u65b9 KAN \u4ee3\u7801\u4e2d\u4f7f\u7528 De Boor-Cox \u8fed\u4ee3\u516c\u5f0f\u5b9e\u73b0\u7684 B \u6837\u6761 FLOP \u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-148d4fe8c895f4a810ea3f838df3a9af.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-148d4fe8c895f4a810ea3f838df3a9af.png\"><\/a><\/section>\n<section>\u8fde\u540c shortcut \u8def\u5f84\u7684 FLOP \u4ee5\u53ca\u5408\u5e76\u4e24\u4e2a\u5206\u652f\u7684 FLOP\uff0c\u4e00\u4e2a KAN \u5c42\u7684\u603b FLOP \u662f\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-5eb56a23c85b3a82a9e9220f0254d3f4.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-5eb56a23c85b3a82a9e9220f0254d3f4.png\"><\/a><\/section>\n<section>\u76f8\u5e94\u7684\uff0c\u4e00\u4e2a MLP \u5c42\u7684 FLOP \u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-9dfb008b2b56bff8e876e52a36ce03bc.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-9dfb008b2b56bff8e876e52a36ce03bc.png\"><\/a><\/section>\n<section>\u5177\u6709\u76f8\u540c\u8f93\u5165\u7ef4\u5ea6\u548c\u8f93\u51fa\u7ef4\u5ea6\u7684 KAN \u5c42\u4e0e MLP \u5c42\u4e4b\u95f4\u7684 FLOP \u5dee\u5f02\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-286972eceb14d66e08551bf3a043ef6c.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-286972eceb14d66e08551bf3a043ef6c.png\"><\/a><\/section>\n<section>\u5982\u679c MLP \u4e5f\u9996\u5148\u8fdb\u884c\u975e\u7ebf\u6027\u64cd\u4f5c\uff0c\u90a3\u4e48\u9996\u9879\u5c06\u4e3a\u96f6\u3002<\/section>\n<section><\/section>\n<section><strong>\u00a0\u5b9e\u9a8c<\/strong><\/section>\n<section><\/section>\n<section>\u4f5c\u8005\u7684\u76ee\u6807\u662f\uff0c\u5728\u53c2\u6570\u6570\u91cf\u6216 FLOP \u76f8\u7b49\u7684\u524d\u63d0\u4e0b\uff0c\u5bf9\u6bd4 KAN \u548c MLP \u7684\u6027\u80fd\u5dee\u5f02\u3002\u8be5\u5b9e\u9a8c\u6db5\u76d6\u591a\u4e2a\u9886\u57df\uff0c\u5305\u62ec\u673a\u5668\u5b66\u4e60\u3001\u8ba1\u7b97\u673a\u89c6\u89c9\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3001\u97f3\u9891\u5904\u7406\u4ee5\u53ca\u7b26\u53f7\u516c\u5f0f\u8868\u793a\u3002\u6240\u6709\u5b9e\u9a8c\u90fd\u91c7\u7528\u4e86 Adam \u4f18\u5316\u5668\uff0c\u8fd9\u4e9b\u5b9e\u9a8c\u5168\u90e8\u5728\u4e00\u5757 RTX3090 GPU \u4e0a\u8fdb\u884c\u3002<\/section>\n<section><\/section>\n<section><strong>\u6027\u80fd\u6bd4\u8f83<\/strong><\/section>\n<section><\/section>\n<section>\u673a\u5668\u5b66\u4e60\u3002\u4f5c\u8005\u5728 8 \u4e2a\u673a\u5668\u5b66\u4e60\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u4e86\u5b9e\u9a8c\uff0c\u4f7f\u7528\u4e86\u5177\u6709\u4e00\u5230\u4e24\u4e2a\u9690\u85cf\u5c42\u7684 KAN \u548c MLP\uff0c\u6839\u636e\u5404\u4e2a\u6570\u636e\u96c6\u7684\u7279\u70b9\uff0c\u4ed6\u4eec\u8c03\u6574\u4e86\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u548c\u8f93\u51fa\u7ef4\u5ea6\u3002<\/section>\n<section><\/section>\n<section>\u5bf9\u4e8e MLP\uff0c\u9690\u85cf\u5c42\u5bbd\u5ea6\u8bbe\u7f6e\u4e3a 32\u300164\u3001128\u3001256\u3001512 \u6216 1024\uff0c\u5e76\u91c7\u7528 GELU \u6216 ReLU \u4f5c\u4e3a\u6fc0\u6d3b\u51fd\u6570\uff0c\u540c\u65f6\u5728 MLP \u4e2d\u4f7f\u7528\u4e86\u5f52\u4e00\u5316\u5c42\u3002\u5bf9\u4e8e KAN\uff0c\u9690\u85cf\u5c42\u5bbd\u5ea6\u5219\u4e3a 2\u30014\u30018 \u6216 16\uff0cB \u6837\u6761\u7f51\u683c\u6570\u4e3a 3\u30015\u300110 \u6216 20\uff0cB \u6837\u6761\u7684\u5ea6\u6570\uff08degree\uff09\u4e3a 2\u30013 \u6216 5\u3002<\/section>\n<section><\/section>\n<section>\u7531\u4e8e\u539f\u59cb KAN \u67b6\u6784\u4e0d\u5305\u62ec\u5f52\u4e00\u5316\u5c42\uff0c\u4e3a\u4e86\u5e73\u8861 MLP \u4e2d\u5f52\u4e00\u5316\u5c42\u53ef\u80fd\u5e26\u6765\u7684\u4f18\u52bf\uff0c\u4f5c\u8005\u6269\u5927\u4e86 KAN \u6837\u6761\u51fd\u6570\u7684\u53d6\u503c\u8303\u56f4\u3002\u6240\u6709\u5b9e\u9a8c\u90fd\u8fdb\u884c\u4e86 20 \u8f6e\u8bad\u7ec3\uff0c\u5b9e\u9a8c\u8bb0\u5f55\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5728\u6d4b\u8bd5\u96c6\u4e0a\u53d6\u5f97\u7684\u6700\u4f73\u51c6\u786e\u7387\uff0c\u5982\u56fe 2 \u548c\u56fe 3 \u6240\u793a\u3002<\/section>\n<section><\/section>\n<section>\u5728\u673a\u5668\u5b66\u4e60\u6570\u636e\u96c6\u4e0a\uff0cMLP \u901a\u5e38\u4fdd\u6301\u4f18\u52bf\u3002\u5728\u4ed6\u4eec\u5bf9\u516b\u4e2a\u6570\u636e\u96c6\u7684\u5b9e\u9a8c\u4e2d\uff0cMLP \u5728\u5176\u4e2d\u7684\u516d\u4e2a\u4e0a\u8868\u73b0\u4f18\u4e8e KAN\u3002\u7136\u800c\uff0c\u4ed6\u4eec\u4e5f\u89c2\u5bdf\u5230\u5728\u4e00\u4e2a\u6570\u636e\u96c6\u4e0a\uff0cMLP \u548c KAN \u7684\u6027\u80fd\u51e0\u4e4e\u76f8\u5f53\uff0c\u800c\u5728\u53e6\u4e00\u4e2a\u6570\u636e\u96c6\u4e0a\uff0cKAN \u8868\u73b0\u5219\u4f18\u4e8e MLP\u3002<\/section>\n<section><\/section>\n<section>\u603b\u4f53\u800c\u8a00\uff0c<strong>MLP \u5728\u673a\u5668\u5b66\u4e60\u6570\u636e\u96c6\u4e0a\u4ecd\u7136\u5177\u6709\u666e\u904d\u4f18\u52bf<\/strong>\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-143b6f8e557556147992773de2bb9ffe.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-143b6f8e557556147992773de2bb9ffe.png\"><\/a><\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-6f3008a021fc4ab58f9b8b390a81b5f7.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-6f3008a021fc4ab58f9b8b390a81b5f7.png\"><\/a><\/section>\n<section>\u8ba1\u7b97\u673a\u89c6\u89c9\u3002\u4f5c\u8005\u5bf9 8 \u4e2a\u8ba1\u7b97\u673a\u89c6\u89c9\u6570\u636e\u96c6\u8fdb\u884c\u4e86\u5b9e\u9a8c\u3002\u4ed6\u4eec\u4f7f\u7528\u4e86\u5177\u6709\u4e00\u5230\u4e24\u4e2a\u9690\u85cf\u5c42\u7684 KAN \u548c MLP\uff0c\u6839\u636e\u6570\u636e\u96c6\u7684\u4e0d\u540c\uff0c\u8c03\u6574\u4e86\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u548c\u8f93\u51fa\u7ef4\u5ea6\u3002<\/section>\n<section><\/section>\n<section>\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u6570\u636e\u96c6\u4e2d\uff0c<strong>KAN\u00a0<\/strong>\u7684\u6837\u6761\u51fd\u6570\u5f15\u5165\u7684\u5904\u7406\u504f\u5dee\u5e76\u6ca1\u6709\u8d77\u5230\u6548\u679c\uff0c\u5176<strong>\u6027\u80fd\u59cb\u7ec8\u4e0d\u5982\u5177\u6709\u76f8\u540c\u53c2\u6570\u6570\u91cf\u6216 FLOP \u7684 MLP\u3002<\/strong><\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-095472667c1743a5351f3330dce849d6.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-095472667c1743a5351f3330dce849d6.png\"><\/a><\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-3762816d76da3e743805fab9c4131cea.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/07\/frc-3762816d76da3e743805fab9c4131cea.png\"><\/a><\/section>\n<section>\u97f3\u9891\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3002\u4f5c\u8005\u5728 2 \u4e2a\u97f3\u9891\u5206\u7c7b\u548c 2 \u4e2a\u6587\u672c\u5206\u7c7b\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u4e86\u5b9e\u9a8c\u3002\u4ed6\u4eec\u4f7f\u7528\u4e86\u4e00\u5230\u4e24\u4e2a\u9690\u85cf\u5c42\u7684 KAN \u548c MLP\uff0c\u5e76\u6839\u636e\u6570\u636e\u96c6\u7684\u7279\u6027\uff0c\u8c03\u6574\u4e86\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u548c\u8f93\u51fa\u7ef4\u5ea6\u3002<\/section>\n<section><\/section>\n<section><strong>\u5728\u4e24\u4e2a\u97f3\u9891\u6570\u636e\u96c6\u4e0a\uff0cMLP \u7684\u8868\u73b0\u4f18\u4e8e KAN\u3002<\/strong><\/section>\n<section><\/section>\n<section>\u5728\u6587\u672c\u5206\u7c7b\u4efb\u52a1\u4e2d\uff0cMLP \u5728 AG \u65b0\u95fb\u6570\u636e\u96c6\u4e0a\u4fdd\u6301\u4e86\u4f18\u52bf\u3002\u7136\u800c\uff0c\u5728\u00a0CoLA \u6570\u636e\u96c6\u4e0a\uff0cMLP \u548c KAN \u4e4b\u95f4\u7684\u6027\u80fd\u6ca1\u6709\u663e\u8457\u5dee\u5f02\u3002\u5f53\u63a7\u5236\u53c2\u6570\u6570\u91cf\u76f8\u540c\u65f6\uff0cKAN \u5728 CoLA \u6570\u636e\u96c6\u4e0a\u4f3c\u4e4e\u6709\u4f18\u52bf\u3002\u7136\u800c\uff0c\u7531\u4e8e KAN \u7684\u6837\u6761\u51fd\u6570\u9700\u8981\u8f83\u9ad8\u7684 FLOP\uff0c\u8fd9\u4e00\u4f18\u52bf\u5728\u63a7\u5236 FLOP 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