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\u901a\u8fc7\u8fd9\u6837\u7684\u94fe\u5f0f\u8fc7\u7a0b\u6765\u751f\u6210\u65b0\u53c2\u6570\uff1a\u968f\u673a\u566a\u58f0 \u2192 \u53cd\u5411\u8fc7\u7a0b \u2192 \u5df2\u8bad\u7ec3\u7684\u89e3\u7801\u5668 \u2192 \u751f\u6210\u7684\u53c2\u6570\u3002<\/p>\n<h4>\u5b9e\u9a8c<\/h4>\n<p>\u8be5\u56e2\u961f\u5728\u8bba\u6587\u4e2d\u7ed9\u51fa\u4e86\u8be6\u7ec6\u7684\u5b9e\u9a8c\u8bbe\u7f6e\uff0c\u53ef\u5e2e\u52a9\u5176\u4ed6\u7814\u7a76\u8005\u590d\u73b0\u5176\u7ed3\u679c\uff0c\u8be6\u89c1\u539f\u8bba\u6587\uff0c\u6211\u4eec\u8fd9\u91cc\u66f4\u5173\u6ce8\u5176\u7ed3\u679c\u548c\u6d88\u878d\u7814\u7a76\u3002<\/p>\n<p><strong>\u7ed3\u679c<\/strong><\/p>\n<p>\u8868 1 \u662f\u5728 8 \u4e2a\u6570\u636e\u96c6\u548c 6 \u79cd\u67b6\u6784\u4e0a\u4e0e\u4e24\u79cd\u57fa\u51c6\u65b9\u6cd5\u7684\u7ed3\u679c\u6bd4\u8f83\u3002<\/p>\n<p>\u57fa\u4e8e\u8fd9\u4e9b\u7ed3\u679c\uff0c\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u89c2\u5bdf\uff1a1\uff09\u5728\u5927\u591a\u6570\u5b9e\u9a8c\u6848\u4f8b\u4e2d\uff0c\u65b0\u65b9\u6cd5\u80fd\u53d6\u5f97\u4e0e\u4e24\u79cd\u57fa\u51c6\u65b9\u6cd5\u5ab2\u7f8e\u6216\u66f4\u4f18\u7684\u7ed3\u679c\u3002\u8fd9\u8868\u660e\u65b0\u63d0\u51fa\u7684\u65b9\u6cd5\u53ef\u4ee5\u9ad8\u6548\u5730\u5b66\u4e60\u9ad8\u6027\u80fd\u53c2\u6570\u7684\u5206\u5e03\uff0c\u5e76\u80fd\u57fa\u4e8e\u968f\u673a\u566a\u58f0\u751f\u6210\u66f4\u4f18\u7684\u6a21\u578b\u30022\uff09\u65b0\u65b9\u6cd5\u5728\u591a\u4e2a\u4e0d\u540c\u6570\u636e\u96c6\u4e0a\u7684\u8868\u73b0\u90fd\u5f88\u597d\uff0c\u8fd9\u8bf4\u660e\u8fd9\u79cd\u65b9\u6cd5\u5177\u6709\u5f88\u597d\u7684\u6cdb\u5316\u6027\u80fd\u3002<\/p>\n<p><strong>\u6d88\u878d\u7814\u7a76\u548c\u5206\u6790<\/strong><\/p>\n<p>\u8868 2(a) \u5c55\u793a\u4e86\u4e0d\u540c\u8bad\u7ec3\u6570\u636e\u89c4\u6a21\uff08\u5373\u539f\u59cb\u6a21\u578b\u7684\u6570\u91cf\uff09\u7684\u5f71\u54cd\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u4e0d\u540c\u6570\u91cf\u7684\u539f\u59cb\u6a21\u578b\u7684\u6700\u4f73\u7ed3\u679c\u4e4b\u95f4\u7684\u6027\u80fd\u5dee\u5f02\u5176\u5b9e\u4e0d\u5927\u3002<\/p>\n<p>\u4e3a\u4e86\u7814\u7a76 p-diff \u5728\u5176\u5b83\u5f52\u4e00\u5316\u5c42\u6df1\u5ea6\u4e0a\u7684\u6709\u6548\u6027\uff0c\u8be5\u56e2\u961f\u8fd8\u63a2\u7d22\u4e86\u65b0\u65b9\u6cd5\u5408\u6210\u5176\u5b83\u6d45\u5c42\u53c2\u6570\u7684\u6027\u80fd\u3002\u4e3a\u4e86\u4fdd\u8bc1 BN \u53c2\u6570\u7684\u6570\u91cf\u76f8\u7b49\uff0c\u8be5\u56e2\u961f\u4e3a\u4e09\u7ec4 BN \u5c42\uff08\u5b83\u4eec\u4f4d\u4e8e\u4e0d\u540c\u6df1\u5ea6\u7684\u5c42\u4e4b\u95f4\uff09\u5b9e\u73b0\u4e86\u65b0\u63d0\u51fa\u7684\u65b9\u6cd5\u3002\u5b9e\u9a8c\u7ed3\u679c\u89c1\u8868 2(b)\uff0c\u53ef\u4ee5\u770b\u5230\u5728\u6240\u6709\u6df1\u5ea6\u7684 BN \u5c42\u8bbe\u7f6e\u4e0a\uff0c\u65b0\u65b9\u6cd5\u7684\u8868\u73b0\uff08\u6700\u4f73\u51c6\u786e\u5ea6\uff09\u90fd\u4f18\u4e8e\u539f\u59cb\u6a21\u578b\u3002<\/p>\n<p>\u566a\u58f0\u589e\u5f3a\u7684\u76ee\u7684\u662f\u63d0\u5347\u8bad\u7ec3\u81ea\u52a8\u7f16\u7801\u5668\u7684\u7a33\u5065\u6027\u548c\u6cdb\u5316\u80fd\u529b\u3002\u8be5\u56e2\u961f\u5bf9\u566a\u58f0\u589e\u5f3a\u5728\u8f93\u5165\u53c2\u6570\u548c\u9690\u542b\u8868\u5f81\u65b9\u9762\u7684\u5e94\u7528\u8fdb\u884c\u4e86\u6d88\u878d\u7814\u7a76\u3002\u7ed3\u679c\u89c1\u8868 2(c)\u3002<\/p>\n<p>\u6b64\u524d\uff0c\u5b9e\u9a8c\u8bc4\u4f30\u7684\u90fd\u662f\u65b0\u65b9\u6cd5\u5728\u5408\u6210\u6a21\u578b\u53c2\u6570\u5b50\u96c6\uff08\u5373\u6279\u5f52\u4e00\u5316\u53c2\u6570\uff09\u65b9\u9762\u7684\u6548\u679c\u3002\u90a3\u4e48\u6211\u4eec\u4e0d\u7981\u8981\u95ee\uff1a\u80fd\u5426\u4f7f\u7528\u6b64\u65b9\u6cd5\u5408\u6210\u6a21\u578b\u7684\u6574\u4f53\u53c2\u6570\uff1f<\/p>\n<p>\u4e3a\u4e86\u89e3\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u8be5\u56e2\u961f\u4f7f\u7528\u4e24\u4e2a\u5c0f\u578b\u67b6\u6784\u8fdb\u884c\u4e86\u5b9e\u9a8c\uff1aMLP-3 \u548c ConvNet-3\u3002\u5176\u4e2d MLP-3 \u5305\u542b\u4e09\u4e2a\u7ebf\u6027\u5c42\u548c ReLU \u6fc0\u6d3b\u51fd\u6570\uff0cConvNet-3 \u5219\u5305\u542b\u4e09\u4e2a\u5377\u79ef\u5c42\u548c\u4e00\u4e2a\u7ebf\u6027\u5c42\u3002\u4e0d\u540c\u4e8e\u4e4b\u524d\u63d0\u5230\u7684\u8bad\u7ec3\u6570\u636e\u6536\u96c6\u7b56\u7565\uff0c\u8be5\u56e2\u961f\u57fa\u4e8e 200 \u4e2a\u4e0d\u540c\u7684\u968f\u673a\u79cd\u5b50\u4ece\u5934\u5f00\u59cb\u8bad\u7ec3\u4e86\u8fd9\u4e9b\u67b6\u6784\u3002<\/p>\n<p>\u8868 3 \u7ed9\u51fa\u4e86\u5b9e\u9a8c\u7ed3\u679c\uff0c\u5176\u4e2d\u5c06\u65b0\u65b9\u6cd5\u4e0e\u4e24\u79cd\u57fa\u51c6\u65b9\u6cd5\uff08\u539f\u59cb\u65b9\u6cd5\u548c\u96c6\u6210\u65b9\u6cd5\uff09\u8fdb\u884c\u4e86\u6bd4\u8f83\u3002\u5176\u4e2d\u62a5\u544a\u4e86 ConvNet-3 \u5728 CIFAR-10\/100 \u4ee5\u53ca MLP-3 \u5728 CIFAR-10 \u548c MNIST \u4e0a\u7684\u7ed3\u679c\u6bd4\u8f83\u548c\u53c2\u6570\u6570\u91cf\u3002<\/p>\n<p>\u8fd9\u4e9b\u5b9e\u9a8c\u8868\u660e\u65b0\u65b9\u6cd5\u5728\u5408\u6210\u6574\u4f53\u6a21\u578b\u53c2\u6570\u65b9\u9762\u7684\u6709\u6548\u6027\u548c\u6cdb\u5316\u80fd\u529b\uff0c\u4e5f\u5c31\u662f\u8bf4\u65b0\u65b9\u6cd5\u5b9e\u73b0\u4e86\u4e0e\u57fa\u51c6\u65b9\u6cd5\u76f8\u5f53\u6216\u66f4\u4f18\u7684\u6027\u80fd\u3002\u8fd9\u4e9b\u7ed3\u679c\u4e5f\u80fd\u4f53\u73b0\u65b0\u65b9\u6cd5\u7684\u5b9e\u9645\u5e94\u7528\u6f5c\u529b\u3002<\/p>\n<p>\u4f46\u8be5\u56e2\u961f\u4e5f\u5728\u8bba\u6587\u4e2d\u8868\u660e\u76ee\u524d\u8fd8\u65e0\u6cd5\u5408\u6210 ResNet\u3001ViT \u548c ConvNeXt \u7b49\u5927\u578b\u67b6\u6784\u7684\u6574\u4f53\u53c2\u6570\u3002\u8fd9\u4e3b\u8981\u662f\u53d7\u9650\u4e8e GPU \u5185\u5b58\u7684\u6781\u9650\u3002<\/p>\n<p>\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u8fd9\u79cd\u65b0\u65b9\u6cd5\u80fd\u591f\u6709\u6548\u5730\u751f\u6210\u795e\u7ecf\u7f51\u7edc\u53c2\u6570\uff0c\u8be5\u56e2\u961f\u4e5f\u5c1d\u8bd5\u63a2\u7d22\u5206\u6790\u4e86\u539f\u56e0\u3002\u4ed6\u4eec\u4f7f\u7528 3 \u4e2a\u968f\u673a\u79cd\u5b50\u4ece\u5934\u5f00\u59cb\u8bad\u7ec3\u4e86 ResNet-18 \u5e76\u5bf9\u5176\u53c2\u6570\u8fdb\u884c\u4e86\u53ef\u89c6\u5316\uff0c\u5982\u56fe 3 \u6240\u793a\u3002<\/p>\n<p>\u4ed6\u4eec\u901a\u8fc7 min-max \u5f52\u4e00\u5316\u65b9\u6cd5\uff0c\u5206\u522b\u5f97\u5230\u4e86\u4e0d\u540c\u5c42\u7684\u53c2\u6570\u5206\u5e03\u7684\u70ed\u529b\u56fe\u3002\u57fa\u4e8e\u5377\u79ef\u5c42\uff08Conv.-layer2\uff09\u548c\u5168\u8fde\u63a5\u5c42\uff08FC-layer18\uff09\u7684\u53ef\u89c6\u5316\u7ed3\u679c\uff0c\u53ef\u4ee5\u770b\u5230\u8fd9\u4e9b\u5c42\u4e2d\u786e\u5b9e\u5b58\u5728\u4e00\u5b9a\u7684\u53c2\u6570\u6a21\u5f0f\u3002\u901a\u8fc7\u5b66\u4e60\u8fd9\u4e9b\u6a21\u5f0f\uff0c\u65b0\u65b9\u6cd5\u5c31\u80fd\u751f\u6210\u9ad8\u6027\u80fd\u7684\u795e\u7ecf\u7f51\u7edc\u53c2\u6570\u3002<\/p>\n<h4>p-diff \u662f\u5355\u7eaf\u9760\u8bb0\u5fc6\u5417\uff1f<\/h4>\n<p>p-diff 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