{"id":6951,"date":"2026-05-02T12:24:30","date_gmt":"2026-05-02T04:24:30","guid":{"rendered":"https:\/\/nullthought.net\/?p=6951"},"modified":"2026-05-02T12:24:32","modified_gmt":"2026-05-02T04:24:32","slug":"%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%e7%90%86%e8%ae%ba%e7%a0%94%e7%a9%b6%e7%9a%84%e4%b8%80%e4%ba%9b%e8%bf%9b%e5%b1%95","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=6951","title":{"rendered":"\u6df1\u5ea6\u5b66\u4e60\u7406\u8bba\u7814\u7a76\u7684\u4e00\u4e9b\u8fdb\u5c55"},"content":{"rendered":"\n<p>\u6df1\u5ea6\u5b66\u4e60\u7684\u7406\u8bba\u7814\u7a76\u6b63\u5728\u4ece\u65e9\u671f\u7684\u7ecf\u9a8c\u4e3b\u4e49\uff0c\u9010\u6e10\u53d1\u5c55\u4e3a\u4e00\u5957\u4e25\u5bc6\u7684\u201c\u5b66\u4e60\u529b\u5b66\u201d\uff08<a href=\"https:\/\/arxiv.org\/abs\/2604.21691\" target=\"_blank\" rel=\"noreferrer noopener\">Learning Mechanics<\/a>\uff09\u79d1\u5b66\u4f53\u7cfb\uff0c\u5176\u7814\u7a76\u8303\u5f0f\u8d8a\u6765\u8d8a\u63a5\u8fd1\u7edf\u8ba1\u529b\u5b66\u3001\u91cf\u5b50\u529b\u5b66\u7b49\u7269\u7406\u5b66\u5206\u652f\u3002\u57fa\u4e8e\u73b0\u6709\u6587\u732e\uff0c\u6df1\u5ea6\u5b66\u4e60\u7684\u6838\u5fc3\u7406\u8bba\u53ef\u5f52\u7eb3\u4e3a\u4ee5\u4e0b\u56db\u4e2a\u4e3b\u8981\u7ef4\u5ea6\uff1a<\/p>\n\n\n\n<p><strong>1. \u4f18\u5316\u52a8\u529b\u5b66\u4e0e\u635f\u5931\u5730\u5f62\uff08Optimization and Loss Landscape\uff09<\/strong> \u6df1\u5ea6\u7f51\u7edc\u7531\u4e8e\u9ad8\u5ea6\u8fc7\u53c2\u6570\u5316\uff0c\u5176\u635f\u5931\u51fd\u6570\u5448\u73b0\u51fa\u6781\u5ea6\u975e\u51f8\u7684\u9ad8\u7ef4\u590d\u6742\u7279\u5f81\uff0c\u4f46\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08SGD\uff09\u5374\u80fd\u7a33\u5b9a\u5730\u627e\u5230\u5168\u5c40\u6781\u5c0f\u503c\u3002\u4ece\u7edf\u8ba1\u529b\u5b66\u7684\u89c6\u89d2\u770b\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u635f\u5931\u5730\u5f62\u7c7b\u4f3c\u4e8e\u81ea\u65cb\u73bb\u7483\uff08Spin Glasses\uff09\u7684\u80fd\u91cf\u66f2\u9762\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5e73\u5766\u6781\u5c0f\u503c\u4e0e\u4f53\u79ef\u5047\u8bf4\uff08Flat Minima and Volume Hypothesis\uff09<\/strong>\uff1a\u7406\u8bba\u8ba4\u4e3a\uff0cSGD\u503e\u5411\u4e8e\u6536\u655b\u5230\u5177\u6709\u8f83\u5927\u4f53\u79ef\u7684\u201c\u5e73\u5766\u6781\u5c0f\u503c\u201d\uff08Flat Minima\uff09\uff0c\u5728\u8fd9\u4e9b\u5e73\u5766\u533a\u57df\u5fae\u8c03\u53c2\u6570\u4e0d\u4f1a\u663e\u8457\u589e\u52a0\u8bad\u7ec3\u635f\u5931\uff0c\u4ece\u800c\u5e26\u6765\u66f4\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002\u5927\u504f\u5dee\u7406\u8bba\uff08LDT\uff09\u4e5f\u8868\u660e\uff0cSGD\u5b58\u5728\u4e00\u79cd\u9690\u5f0f\u504f\u7f6e\uff0c\u5f15\u5bfc\u6a21\u578b\u907f\u5f00\u5f02\u5e38\u504f\u5dee\uff0c\u6536\u655b\u81f3\u6cdb\u5316\u6027\u66f4\u5f3a\u7684\u89e3\u3002<\/li>\n\n\n\n<li><strong>\u6570\u636e\u91cf\u5bf9\u5730\u5f62\u7684\u91cd\u5851<\/strong>\uff1a\u6700\u65b0\u7684\u7814\u7a76\u5bf9\u7edd\u5bf9\u7684\u5e73\u5766\u6027\u63d0\u51fa\u4e86\u8865\u5145\uff0c\u53d1\u73b0\u540c\u6837\u5b58\u5728\u80fd\u591f\u826f\u597d\u6cdb\u5316\u7684\u201c\u5c16\u9510\u6781\u5c0f\u503c\u201d\uff08Sharp Minima\uff09\u3002\u968f\u7740\u8bad\u7ec3\u6570\u636e\u91cf\u7684\u589e\u52a0\uff0c\u635f\u5931\u5730\u5f62\u4f1a\u88ab\u91cd\u5851\uff0c\u539f\u672c\u96be\u4ee5\u53d1\u73b0\u7684\u5c16\u9510\u6781\u5c0f\u503c\u4f1a\u76f8\u5bf9\u6269\u5927\uff0c\u4ece\u800c\u88ab\u68af\u5ea6\u4e0b\u964d\u6355\u83b7\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>2. \u65e0\u9650\u5bbd\u5ea6\u6781\u9650\u4e0e\u7279\u5f81\u5b66\u4e60\uff08Infinite-Width Limits and Feature Learning\uff09<\/strong> \u4e3a\u4e86\u5728\u6570\u5b66\u4e0a\u4f7f\u795e\u7ecf\u7f51\u7edc\u53d8\u5f97\u53ef\u89e3\uff0c\u7406\u8bba\u754c\u5e38\u7814\u7a76\u7f51\u7edc\u5bbd\u5ea6\u8d8b\u4e8e\u65e0\u7a77\u5927\u7684\u6781\u9650\u72b6\u6001\u3002\u5728\u8fd9\u4e2a\u65b9\u5411\u4e0a\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u79cd\u7406\u8bba\u6a21\u578b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u795e\u7ecf\u6b63\u5207\u6838\uff08NTK\uff09\u4e0e\u201c\u61d2\u60f0\u8bad\u7ec3\u201d<\/strong>\uff1a\u5728\u6807\u51c6\u7684 1\/sqrt(n) \u53c2\u6570\u7f29\u653e\u4e0b\uff0c\u65e0\u9650\u5bbd\u7f51\u7edc\u7684\u8bad\u7ec3\u7b49\u4ef7\u4e8e\u4f7f\u7528\u56fa\u5b9a\u6838\uff08\u5373NTK\uff09\u7684\u6838\u5cad\u56de\u5f52\u3002\u5728\u6b64\u201c\u61d2\u60f0\u8bad\u7ec3\u201d\uff08Lazy Training\uff09\u673a\u5236\u4e0b\uff0c\u7f51\u7edc\u53c2\u6570\u5728\u8bad\u7ec3\u671f\u95f4\u51e0\u4e4e\u4e0d\u79fb\u52a8\uff0c\u6a21\u578b\u6839\u672c\u4e0d\u53d1\u751f\u672c\u8d28\u7684\u201c\u7279\u5f81\u5b66\u4e60\u201d\u3002\u6b64\u5916\uff0cNTK\u5bf9\u4e8e\u67d0\u4e9b\u7b80\u5355\u975e\u5e73\u6ed1\u51fd\u6570\uff08\u5982\u5355\u4e2aReLU\uff09\u7684\u6837\u672c\u590d\u6742\u5ea6\u6781\u5dee\uff0c\u65e0\u6cd5\u5b8c\u5168\u89e3\u91ca\u771f\u5b9e\u6709\u9650\u5bbd\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6210\u529f\u3002<\/li>\n\n\n\n<li><strong>\u5e73\u5747\u573a\u7406\u8bba\uff08MFT\uff09<\/strong>\uff1a\u91c7\u7528 1\/n \u7684\u7f29\u653e\u6bd4\u4f8b\u65f6\uff0c\u53c2\u6570\u80fd\u591f\u5728\u8bad\u7ec3\u4e2d\u53d1\u751f O(1) \u5c3a\u5ea6\u7684\u79fb\u52a8\uff0c\u6b64\u65f6\u6838\u51fd\u6570\u4f1a\u52a8\u6001\u6f14\u5316\uff0c\u7f51\u7edc\u5f97\u4ee5\u771f\u6b63\u5b66\u4e60\u7279\u5f81\u3002<\/li>\n\n\n\n<li><strong>\u6700\u5927\u66f4\u65b0\u53c2\u6570\u5316\uff08<em>\u03bc<\/em>P\uff09<\/strong>\uff1a\u4e3a\u4e86\u7edf\u4e00\u4e0a\u8ff0\u7406\u8bba\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86 <em>\u03bc<\/em>P \u67b6\u6784\u3002\u5b83\u5728\u65e0\u9650\u5bbd\u6781\u9650\u4e0b\u4fdd\u8bc1\u4e86\u5404\u5c42\u53c2\u6570\u90fd\u80fd\u53d1\u751f\u6700\u5927\u7a0b\u5ea6\u7684\u6709\u6548\u66f4\u65b0\uff0c\u4ece\u800c\u5b9e\u73b0\u4e86\u201c\u7279\u5f81\u5b66\u4e60\u201d\u3002\u8fd9\u4e00\u7406\u8bba\u6781\u5176\u91cd\u8981\u7684\u4e00\u9879\u5b9e\u9645\u5e94\u7528\u662f<strong>\u96f6\u6837\u672c\u8d85\u53c2\u6570\u8fc1\u79fb\uff08Zero-Shot Hyperparameter Transfer\uff09<\/strong>\uff1a\u5728\u5c0f\u89c4\u6a21\u4ee3\u7406\u6a21\u578b\u4e0a\u8c03\u4f18\u7684\u5b66\u4e60\u7387\u7b49\u8d85\u53c2\u6570\uff0c\u53ef\u4ee5\u76f4\u63a5\u65e0\u7f1d\u8fc1\u79fb\u5230\u5177\u6709\u6570\u5341\u4ebf\u53c2\u6570\u7684\u5927\u6a21\u578b\u4e0a\u3002\u4e3a\u4e86\u8fdb\u4e00\u6b65\u89e3\u91caNTK\u5931\u6548\u7684\u533a\u57df\uff0c\u6700\u8fd1\u7684\u7406\u8bba\u8fd8\u5f15\u5165\u4e86\u4e8c\u9636\u6cf0\u52d2\u5c55\u5f00\uff0c\u8bd5\u56fe\u901a\u8fc7\u523b\u753b\u4e8c\u6b21\u9879\u6765\u89e3\u91ca\u8d85\u8d8aNTK\u7684\u975e\u7ebf\u6027\u7279\u5f81\u5b66\u4e60\u673a\u5236\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>3. \u6cdb\u5316\u8c1c\u9898\uff1a\u53cc\u91cd\u4e0b\u964d\u4e0e\u4fe1\u606f\u74f6\u9888\uff08Generalization: Double Descent and Information Bottleneck\uff09<\/strong> \u8fc7\u53c2\u6570\u5316\u6a21\u578b\u4e3a\u4f55\u4e0d\u4f1a\u906d\u9047\u4e25\u91cd\u7684\u8fc7\u62df\u5408\uff1f<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u53cc\u91cd\u4e0b\u964d\uff08Double Descent\uff09<\/strong>\uff1a\u8fd9\u662f\u5bf9\u7ecf\u5178\u504f\u5dee-\u65b9\u5dee\u6743\u8861\uff08Bias-Variance Trade-off\uff09\u7684\u98a0\u8986\u3002\u968f\u7740\u6a21\u578b\u590d\u6742\u5ea6\u3001\u8bad\u7ec3\u5468\u671f\uff08Epochs\uff09\u6216\u6570\u636e\u91cf\u7684\u589e\u52a0\uff0c\u6d4b\u8bd5\u8bef\u5dee\u5728\u7ecf\u5386\u7ecf\u5178\u7684\u201cU\u578b\u201d\u4e0a\u5347\uff08\u8fc7\u62df\u5408\uff09\u540e\uff0c\u4e00\u65e6\u8d8a\u8fc7\u63d2\u503c\u9608\u503c\uff08Interpolation Threshold\uff09\uff0c\u8bef\u5dee\u7adf\u7136\u4f1a\u518d\u6b21\u4e0b\u964d\u3002\u8fd9\u79cd\u73b0\u8c61\u8bf4\u660e\u6781\u5ea6\u8fc7\u53c2\u6570\u5316\u7684\u6a21\u578b\u5728\u4f18\u5316\u7b97\u6cd5\uff08\u5982SGD\uff09\u7684\u9690\u5f0f\u6b63\u5219\u5316\u4e0b\uff0c\u4f1a\u81ea\u52a8\u5bfb\u627e\u80fd\u591f\u66f4\u597d\u6cdb\u5316\u7684\u201c\u66f4\u7b80\u5355\u201d\u6216\u201c\u66f4\u5e73\u5766\u201d\u7684\u89e3\u3002<\/li>\n\n\n\n<li><strong>\u4fe1\u606f\u74f6\u9888\uff08Information Bottleneck, IB\uff09\u7406\u8bba\u4e0e\u4e89\u8bae<\/strong>\uff1aIB\u7406\u8bba\u63d0\u51fa\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u5206\u4e3a\u62df\u5408\uff08Fitting\uff09\u548c\u538b\u7f29\uff08Compression\uff09\u4e24\u4e2a\u9636\u6bb5\u3002\u9690\u85cf\u5c42\u9996\u5148\u5c3d\u53ef\u80fd\u591a\u5730\u63d0\u53d6\u8f93\u5165\u7279\u5f81\uff0c\u968f\u540e\u201c\u538b\u7f29\u201d\u5e76\u4e22\u5f03\u4e0e\u76ee\u6807\u8f93\u51fa\u65e0\u5173\u7684\u5197\u4f59\u4fe1\u606f\uff0c\u8fd9\u79cd\u538b\u7f29\u88ab\u8ba4\u4e3a\u662f\u6cdb\u5316\u80fd\u529b\u7684\u5173\u952e\u3002\u7136\u800c\uff0c\u8fd9\u4e00\u5047\u8bbe\u906d\u5230\u4e86\u5f3a\u70c8\u7684\u6311\u6218\uff1aSaxe\u7b49\u4eba\u7684\u7814\u7a76\u8bc1\u660e\uff0c\u538b\u7f29\u73b0\u8c61\u4e3b\u8981\u662f\u7531\u4e8e\u4f7f\u7528\u4e86\u53cc\u4fa7\u9971\u548c\u6fc0\u6d3b\u51fd\u6570\uff08\u5982tanh\uff09\u4ee5\u53ca\u4e92\u4fe1\u606f\u7684\u79bb\u6563\u5206\u7bb1\u4f30\u7b97\u5bfc\u81f4\u7684\uff1b\u5728\u5b9e\u9645\u5e38\u7528\u7684ReLU\u7f51\u7edc\u548c\u7ebf\u6027\u7f51\u7edc\u4e2d\uff0c\u5e76\u6ca1\u6709\u89c2\u5bdf\u5230\u660e\u663e\u7684\u538b\u7f29\u9636\u6bb5\uff0c\u4e14\u6ca1\u6709\u538b\u7f29\u6a21\u578b\u4f9d\u7136\u80fd\u5f88\u597d\u5730\u6cdb\u5316\u3002\u4e3a\u4e86\u4fee\u6b63\u8fd9\u4e00\u95ee\u9898\uff0c\u540e\u7eed\u63d0\u51fa\u4e86<strong>\u5e7f\u4e49\u4fe1\u606f\u74f6\u9888\uff08GIB\uff09<\/strong>\uff0c\u901a\u8fc7\u5f15\u5165\u7279\u5f81\u95f4\u7684\u201c\u534f\u540c\u4f5c\u7528\u201d\uff08Synergy\uff09\uff0c\u6210\u529f\u5728\u5305\u62ecReLU\u548cTransformer\u5728\u5185\u7684\u67b6\u6784\u4e2d\u518d\u6b21\u89c2\u5bdf\u5230\u4e86\u538b\u7f29\u9636\u6bb5\uff0c\u5e76\u5c06\u5176\u4e0e\u5bf9\u6297\u9c81\u68d2\u6027\u8054\u7cfb\u8d77\u6765\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>4. \u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u4e0e\u6d41\u5f62\u5047\u8bf4\uff08Geometric Deep Learning and Manifold Hypothesis\uff09<\/strong> \u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u62df\u5408\u51fd\u6570\u9762\u4e34\u7ef4\u5ea6\u707e\u96be\uff0c\u6df1\u5ea6\u5b66\u4e60\u4e4b\u6240\u4ee5\u6210\u529f\uff0c\u662f\u56e0\u4e3a\u73b0\u5b9e\u4e16\u754c\u7684\u6570\u636e\u5b58\u5728\u5e95\u5c42\u7684\u4f4e\u7ef4\u51e0\u4f55\u7ed3\u6784\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6d41\u5f62\u5047\u8bf4\uff08Manifold Hypothesis\uff09<\/strong>\uff1a\u9ad8\u7ef4\u6570\u636e\u901a\u5e38\u5206\u5e03\u5728\u4f4e\u7ef4\u5ea6\u6d41\u5f62\uff08Manifold\uff09\u4e0a\u3002\u6df1\u5c42\u795e\u7ecf\u7f51\u7edc\u7684\u672c\u8d28\u53ef\u88ab\u89c6\u4e3a\u4e00\u79cd\u975e\u7ebf\u6027\u964d\u7ef4\u673a\u5236\uff0c\u5b83\u4e0d\u4ec5\u5c06\u6570\u636e\u6620\u5c04\u5230\u4f4e\u7ef4\u7684\u9690\u7a7a\u95f4\u4e2d\uff0c\u800c\u4e14\u5f53\u8fd9\u4e9b\u8868\u793a\u6d41\u5f62\u53d8\u5f97\u66f4\u52a0\u201c\u5e73\u5766\u201d\u65f6\uff0c\u5206\u7c7b\u7684\u7ebf\u6027\u53ef\u5206\u6027\u548c\u6cdb\u5316\u80fd\u529b\u90fd\u4f1a\u5f97\u5230\u663e\u8457\u63d0\u5347\u3002<\/li>\n\n\n\n<li><strong>\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff08GDL\uff09<\/strong>\uff1a\u8fd9\u662f\u4e00\u4e2a\u901a\u8fc7\u5bf9\u79f0\u6027\uff08Symmetry\uff09\u548c\u4e0d\u53d8\u6027\uff08Invariance\uff09\u6765\u7edf\u4e00\u5404\u79cd\u7f51\u7edc\u67b6\u6784\u7684\u7406\u8bba\u84dd\u56fe\u3002GDL\u5229\u7528\u7fa4\u8bba\uff08Group 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Mechanics [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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