{"id":6883,"date":"2022-09-09T15:02:00","date_gmt":"2022-09-09T07:02:00","guid":{"rendered":"http:\/\/139.9.1.231\/?p=6883"},"modified":"2022-09-08T15:02:37","modified_gmt":"2022-09-08T07:02:37","slug":"model_compress","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/09\/09\/model_compress\/","title":{"rendered":"\u6a21\u578b\u538b\u7f29"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"960\" height=\"149\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-102.png\" alt=\"\" class=\"wp-image-7596\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-102.png 960w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-102-300x47.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-102-768x119.png 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n\n\n<p>      \u6700\u8fd1\u5728\u505a\u7684yolo\u7f51\u7edc\u786c\u4ef6\u52a0\u901f\u9879\u76ee\uff0c\u9700\u8981\u53bb\u5bf9\u539f\u59cb\u7f51\u7edc\u8fdb\u884c\u538b\u7f29\uff0c\u56e0\u6b64\u8bb0\u5f55\u4e0b\u76f8\u5173\u77e5\u8bc6\uff1a<\/p>\n\n\n\n<p>\u76f8\u5173\u7efc\u8ff0\uff1a<\/p>\n\n\n\n<p>\u300a<a href=\"https:\/\/arxiv.org\/abs\/1710.09282\" target=\"_blank\" rel=\"noreferrer noopener\">A Survey of Model Compression and Acceleration for Deep Neural Networks<\/a>\u300b<\/p>\n\n\n\n<p><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10462-020-09816-7\" data-type=\"URL\" data-id=\"https:\/\/link.springer.com\/article\/10.1007\/s10462-020-09816-7\" target=\"_blank\" rel=\"noreferrer noopener\">\u300aA Comprehensive Survey on Model Compression and Acceleration\u300b<\/a><\/p>\n\n\n\n<p>      \u76ee\u524d\uff0c\u5728\u6a21\u578b\u538b\u7f29\u548c\u52a0\u901f\u65b9\u9762\u5e38\u7528\u7684\u65b9\u6cd5\u5927\u81f4\u53ef\u4ee5\u5206\u4e3a\u56db\u7c7b\uff1a\u526a\u679d\u4e0e\u91cf\u5316\uff08parameter pruning and quantization\uff09\u3001\u4f4e\u79e9\u56e0\u5b50\u5206\u89e3\uff08low-rank factorization\uff09\u3001\u8fc1\u79fb\/\u538b\u7f29\u5377\u79ef\u6ee4\u6ce2\u5668\uff08transferred\/compact convolutional filters\uff09\u3001\u84b8\u998f\u5b66\u4e60\uff08knowledge distillation\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"241\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-103-1024x241.png\" alt=\"\" class=\"wp-image-7598\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-103-1024x241.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-103-300x71.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-103-768x181.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-103.png 1391w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"https:\/\/img-blog.csdnimg.cn\/20200528094115616.png?x-oss-process=image\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0Zhbm5pZV9QZW5n,size_16,color_FFFFFF,t_70\" alt=\"\" width=\"690\" height=\"305\"\/><figcaption>\u6a21\u578b\u538b\u7f29\u65b9\u6cd5<\/figcaption><\/figure>\n\n\n\n<h2>\u80cc\u666f     <\/h2>\n\n\n\n<p>     \u8fd1\u5e74\u6765\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff08deep neural networks\uff0cDNN\uff09\u9010\u6e10\u53d7\u5230\u5404\u884c\u5404\u4e1a\u7684\u5173\u6ce8\u3002\u5b83\u662f\u6307\u5177\u6709\u66f4\u6df1\u5c42\uff08\u4e0d\u6b62\u4e00\u4e2a\u9690\u85cf\u5c42\uff09\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u662f\u6df1\u5ea6\u5b66\u4e60\u7684\u57fa\u7840\u3002\u5f88\u591a\u5b9e\u9645\u7684\u5de5\u4f5c\u901a\u5e38\u4f9d\u8d56\u4e8e\u6570\u767e\u4e07\u751a\u81f3\u6570\u5341\u4ebf\u4e2a\u53c2\u6570\u7684\u6df1\u5ea6\u7f51\u7edc\uff0c\u8fd9\u6837\u590d\u6742\u7684\u5927\u89c4\u6a21\u6a21\u578b\u901a\u5e38\u5bf9\u8ba1\u7b97\u673a\u7684CPU\u548cGPU\u6709\u7740\u6781\u9ad8\u7684\u8981\u6c42\uff0c\u5e76\u4e14\u4f1a\u6d88\u8017\u5927\u91cf\u5185\u5b58\uff0c\u4ea7\u751f\u5de8\u5927\u7684\u8ba1\u7b97\u6210\u672c\u3002\u968f\u7740\u4e00\u4e9b\u4fbf\u643a\u5f0f\u8bbe\u5907\uff08\u5982\u79fb\u52a8\u7535\u8bdd\uff09\u7684\u5feb\u901f\u53d1\u5c55\uff0c\u5982\u4f55\u5c06\u8fd9\u4e9b\u590d\u6742\u7684\u8ba1\u7b97\u7cfb\u7edf\u90e8\u7f72\u5230\u8d44\u6e90\u6709\u9650\u7684\u8bbe\u5907\u4e0a\u5c31\u6210\u4e3a\u4e86\u9700\u8981\u5e94\u5bf9\u7684\u5168\u65b0\u6311\u6218\u3002\u8fd9\u4e9b\u8bbe\u5907\u901a\u5e38\u5185\u5b58\u6709\u9650\uff0c\u800c\u4e14\u8ba1\u7b97\u80fd\u529b\u8f83\u4f4e\uff0c\u4e0d\u652f\u6301\u5927\u6a21\u578b\u7684\u5728\u7ebf\u8ba1\u7b97\u3002\u56e0\u6b64\u9700\u8981\u5bf9\u6a21\u578b\u8fdb\u884c\u538b\u7f29\u548c\u52a0\u901f\uff0c\u4ee5\u6c42\u5728\u57fa\u672c\u4e0d\u635f\u5931\u6a21\u578b\u7cbe\u5ea6\u7684\u6761\u4ef6\u4e0b\uff0c\u8282\u7ea6\u53c2\u6570\u5e76\u964d\u4f4e\u5176\u8ba1\u7b97\u65f6\u95f4\u3002<\/p>\n\n\n\n<p>      <strong>\u526a\u679d\u4e0e\u91cf\u5316\u4e3b\u8981\u9488\u5bf9\u6a21\u578b\u4e2d\u7684\u5197\u4f59\u53c2\u6570\u8fdb\u884c\u5220\u51cf\uff1b\u4f4e\u79e9\u56e0\u5b50\u5206\u89e3\u4f7f\u7528\u5f20\u91cf\u5206\u89e3\u7684\u65b9\u6cd5\u6765\u4f30\u8ba1\u795e\u7ecf\u7f51\u7edc\u7684\u53c2\u6570\uff1b\u8fc1\u79fb\/\u538b\u7f29\u5377\u79ef\u6ee4\u6ce2\u5668\u5219\u662f\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u7279\u6b8a\u7ed3\u6784\u7684\u5377\u79ef\u6ee4\u6ce2\u5668\uff0c\u80fd\u591f\u51cf\u5c11\u53c2\u6570\u7a7a\u95f4\u5e76\u4e14\u8282\u7ea6\u5185\u5b58\uff1b\u84b8\u998f\u5b66\u4e60\u662f\u5148\u8bad\u7ec3\u4e00\u4e2a\u8f83\u5927\u7684\u6a21\u578b\uff0c\u518d\u8bad\u7ec3\u4e00\u4e2a\u8f83\u5c0f\u7684\u795e\u7ecf\u7f51\u7edc\u4ee5\u8fbe\u5230\u8ddf\u5927\u6a21\u578b\u540c\u6837\u7684\u6548\u679c\u3002\u5176\u4e2d\uff0c\u4f4e\u79e9\u56e0\u5b50\u5206\u89e3\u548c\u8fc1\u79fb\/\u538b\u7f29\u5377\u79ef\u6ee4\u6ce2\u5668\u4e24\u79cd\u65b9\u6cd5\u63d0\u4f9b\u4e86\u7aef\u5230\u7aef\u7684\u7ba1\u9053\uff0c\u53ef\u4ee5\u5728CPU\/GPU\u73af\u5883\u4e2d\u8f7b\u677e\u5b9e\u73b0\uff1b\u800c\u526a\u679d\u4e0e\u91cf\u5316\u4f7f\u7528\u4e8c\u8fdb\u5236\u53ca\u7a00\u758f\u7ea6\u675f\u7b49\u65b9\u6cd5\u6765\u5b9e\u73b0\u76ee\u6807\u3002\u6b64\u5916\uff0c\u526a\u679d\u4e0e\u91cf\u5316\u548c\u4f4e\u79e9\u56e0\u5b50\u5206\u89e3\u65b9\u6cd5\u53ef\u4ee5\u4ece\u9884\u8bad\u7ec3\u7684\u6a21\u578b\u4e2d\u63d0\u53d6\u6216\u8005\u662f\u4ece\u5934\u5f00\u59cb\u8bad\u7ec3\uff0c\u800c\u53e6\u5916\u4e24\u79cd\u65b9\u6cd5\u4ec5\u652f\u6301\u4ece\u5934\u5f00\u59cb\u7684\u8bad\u7ec3\u3002\u8fd9\u56db\u79cd\u65b9\u6cd5\u5927\u591a\u662f\u72ec\u7acb\u8bbe\u8ba1\u7684\uff0c\u4f46\u53c8\u76f8\u4e92\u8865\u5145\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5e38\u5e38\u53ef\u4ee5\u4e00\u8d77\u4f7f\u7528\uff0c\u5b9e\u73b0\u5bf9\u6a21\u578b\u8fdb\u4e00\u6b65\u7684\u538b\u7f29\u6216\u52a0\u901f\u3002\u63a5\u4e0b\u6765\u5c06\u5206\u522b\u5bf9\u8fd9\u56db\u79cd\u65b9\u6cd5\u8fdb\u884c\u4ecb\u7ecd\u3002<\/strong><\/p>\n\n\n\n<h2>\u526a\u679d\u4e0e\u91cf\u5316\uff08parameter pruning and quantization\uff09<\/h2>\n\n\n\n<p>    \u65e9\u671f\u7684\u7814\u7a76\u8868\u660e\uff0c\u5bf9\u6784\u5efa\u7684\u7f51\u7edc\u8fdb\u884c\u526a\u679d\u548c\u91cf\u5316\u5728\u964d\u4f4e\u7f51\u7edc\u590d\u6742\u6027\u4ee5\u53ca\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\u65b9\u9762\u662f\u6709\u6548\u7684\uff08Gong et al. 2014\uff09\u3002\u540c\u526a\u679d\u4e0e\u91cf\u5316\u6709\u5173\u7684\u65b9\u6cd5\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5206\u4e3a\u4e09\u4e2a\u5b50\u7c7b\uff1a\u91cf\u5316\u4e0e\u4e8c\u503c\u5316\uff08quantization and binarization\uff09\u3001\u7f51\u7edc\u526a\u679d\uff08network pruning\uff09\u3001\u7ed3\u6784\u77e9\u9635\uff08structural matrix\uff09\u3002<\/p>\n\n\n\n<h3>1.\u91cf\u5316\u4e0e\u4e8c\u503c\u5316\uff08quantization and binarization\uff09<\/h3>\n\n\n\n<p>   \u5728DNN\u4e2d\uff0c\u6743\u91cd\u901a\u5e38\u662f\u4ee532\u4f4d\u6d6e\u70b9\u6570\u7684\u5f62\u5f0f\uff08\u537332-bit\uff09\u8fdb\u884c\u5b58\u50a8\uff0c\u91cf\u5316\u6cd5\u5219\u662f\u901a\u8fc7\u51cf\u5c11\u8868\u793a\u6bcf\u4e2a\u6743\u91cd\u9700\u8981\u7684\u6bd4\u7279\u6570\uff08the number of bits\uff09\u6765\u538b\u7f29\u539f\u59cb\u7f51\u7edc\u3002\u6b64\u65f6\u6743\u91cd\u53ef\u4ee5\u91cf\u5316\u4e3a16-bit\u30018-bit\u30014-bit\u751a\u81f3\u662f1-bit\uff08\u8fd9\u662f\u91cf\u5316\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\uff0c\u6743\u91cd\u4ec5\u7528\u4e8c\u8fdb\u5236\u8868\u793a\uff0c\u79f0\u4e3a\u6743\u91cd\u4e8c\u503c\u5316\uff09\u30028-bit\u7684\u53c2\u6570\u91cf\u5316\u5df2\u7ecf\u53ef\u4ee5\u5728\u635f\u5931\u5c0f\u90e8\u5206\u51c6\u786e\u7387\u7684\u540c\u65f6\u5b9e\u73b0\u5927\u5e45\u5ea6\u52a0\u901f\uff08Vanhoucke et al. 2011\uff09\u3002\u56fe2\u5c55\u793a\u4e86\u57fa\u4e8e\u4fee\u526a\u3001\u91cf\u5316\u548c\u7f16\u7801\u4e09\u4e2a\u8fc7\u7a0b\u7684\u538b\u7f29\u6cd5\uff1a\u9996\u5148\u4fee\u526a\u5c0f\u6743\u91cd\u7684\u8fde\u63a5\uff0c\u7136\u540e\u4f7f\u7528\u6743\u91cd\u5171\u4eab\u6765\u91cf\u5316\u6743\u91cd\uff0c\u6700\u540e\u5c06\u54c8\u592b\u66fc\u7f16\u7801\u5e94\u7528\u4e8e\u91cf\u5316\u540e\u7684\u6743\u91cd\u548c\u7801\u672c\u4e0a\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"846\" height=\"375\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-104.png\" alt=\"\" class=\"wp-image-7604\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-104.png 846w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-104-300x133.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-104-768x340.png 768w\" sizes=\"(max-width: 846px) 100vw, 846px\" \/><\/figure>\n\n\n\n<p>\u6b64\u65b9\u6cd5\u7684\u7f3a\u70b9\u662f\uff0c\u5728\u5904\u7406\u5927\u578bCNN\uff08\u5982GoogleNet\uff09\u65f6\uff0c\u4e8c\u503c\u7f51\u7edc\u7684\u7cbe\u5ea6\u660e\u663e\u964d\u4f4e\u3002\u6b64\u5916\uff0c\u73b0\u6709\u7684\u4e8c\u503c\u5316\u65b9\u6cd5\u5927\u591a\u57fa\u4e8e\u7b80\u5355\u7684\u77e9\u9635\u8fd1\u4f3c\uff0c\u5ffd\u7565\u4e86\u4e8c\u503c\u5316\u5bf9\u7cbe\u5ea6\u635f\u5931\u4ea7\u751f\u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3>2.\u7f51\u7edc\u526a\u679d\uff08network pruning\uff09<\/h3>\n\n\n\n<p>\u526a\u679d\u662f\u6307\u901a\u8fc7\u4fee\u526a\u5f71\u54cd\u8f83\u5c0f\u7684\u8fde\u63a5\u6765\u663e\u8457\u51cf\u5c11DNN\u6a21\u578b\u7684\u5b58\u50a8\u548c\u8ba1\u7b97\u6210\u672c\uff0c\u76ee\u524d\u6bd4\u8f83\u4e3b\u6d41\u7684\u526a\u679d\u65b9\u6cd5\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u79cd\uff1a<\/p>\n\n\n\n<ul><li>\u6743\u91cd\u526a\u679d\uff08weight pruning\uff09\uff1a\u6b64\u65b9\u6cd5\u4e3b\u8981\u5e94\u7528\u4e8e\u5bf9\u4e0d\u91cd\u8981\u7684\u8fde\u63a5\u6743\u91cd\u8fdb\u884c\u4fee\u526a\u3002\u5982\u679c\u8fde\u63a5\u6743\u91cd\u4f4e\u4e8e\u9884\u5148\u8bbe\u5b9a\u7684\u67d0\u4e2a\u9608\u503c\uff0c\u5219\u8be5\u8fde\u63a5\u6743\u91cd\u5c06\u4f1a\u88ab\u4fee\u526a\uff08Han et al. 2015\uff09\u3002<\/li><li>\u795e\u7ecf\u5143\u526a\u679d\uff08neuron pruning\uff09\uff1a\u6b64\u65b9\u6cd5\u4e0e\u9010\u4e2a\u4fee\u526a\u6743\u91cd\u7684\u65b9\u6cd5\u4e0d\u540c\uff0c\u5b83\u76f4\u63a5\u79fb\u9664\u67d0\u4e2a\u5197\u4f59\u7684\u795e\u7ecf\u5143\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u8be5\u795e\u7ecf\u5143\u7684\u6240\u6709\u4f20\u5165\u548c\u4f20\u51fa\u8fde\u63a5\u4e5f\u5c06\u88ab\u79fb\u9664\uff08Srinivas and Babu 2015\uff09\u3002<\/li><li>\u5377\u79ef\u6838\u526a\u679d\uff08filter pruning\uff09\uff1a\u6b64\u65b9\u6cd5\u4f9d\u636e\u5377\u79ef\u6838\u7684\u91cd\u8981\u7a0b\u5ea6\u5c06\u5176\u8fdb\u884c\u6392\u5e8f\uff0c\u5e76\u4ece\u7f51\u7edc\u4e2d\u4fee\u526a\u6700\u4e0d\u91cd\u8981\/\u6392\u540d\u6700\u4f4e\u7684\u5377\u79ef\u6838\u3002\u5377\u79ef\u6838\u7684\u91cd\u8981\u7a0b\u5ea6\u53ef\u4ee5\u901a\u8fc7\u6216\u8303\u6570\u6216\u4e00\u4e9b\u5176\u4ed6\u65b9\u6cd5\u8ba1\u7b97\uff08Li et al. 2016\uff09\u3002<\/li><li>\u5c42\u526a\u679d\uff08layer pruning\uff09\uff1a\u6b64\u65b9\u6cd5\u4e3b\u8981\u5e94\u7528\u4e8e\u4e00\u4e9b\u975e\u5e38\u6df1\u5ea6\u7684\u7f51\u7edc\uff0c\u53ef\u4ee5\u76f4\u63a5\u4fee\u526a\u5176\u4e2d\u7684\u67d0\u4e9b\u5c42\uff08Chen and Zhao 2018\uff09\u3002<\/li><\/ul>\n\n\n\n<p>\u6309\u7167\u526a\u679d\u7684\u5bf9\u8c61\u5206\u7c7b\uff0c\u53ef\u4ee5\u5206\u4e3a\u5728\u5168\u8fde\u63a5\u5c42\u4e0a\u526a\u679d\u548c\u5728\u5377\u79ef\u5c42\u4e0a\u526a\u679d\u4e24\u79cd\u3002DNN\u4e2d\u7684\u5168\u8fde\u63a5\u5c42\u662f\u5b58\u50a8\u5bc6\u96c6\u7684\uff0c\u5bf9\u5168\u8fde\u63a5\u5c42\u4e2d\u7684\u53c2\u6570\u8fdb\u884c\u526a\u679d\u80fd\u591f\u663e\u8457\u964d\u4f4e\u5b58\u50a8\u6210\u672c\u3002\u5bf9\u4e8e\u5377\u79ef\u5c42\u800c\u8a00\uff0c\u6bcf\u4e2a\u5377\u79ef\u5c42\u4e2d\u90fd\u6709\u8bb8\u591a\u5377\u79ef\u6838\uff0c\u4ece\u5377\u79ef\u5c42\u4fee\u526a\u4e0d\u91cd\u8981\u7684\u5377\u79ef\u6838\u4e5f\u80fd\u591f\u51cf\u5c11\u8ba1\u7b97\u6210\u672c\u5e76\u52a0\u901f\u6a21\u578b\u3002<\/p>\n\n\n\n<p>\u5728\u5168\u8fde\u63a5\u5c42\u4e0a\u526a\u679d\uff1a\u8003\u8651\u4e00\u4e2a\u8f93\u5165\u5c42\u3001\u9690\u85cf\u5c42\u548c\u8f93\u51fa\u5c42\u5206\u522b\u5177\u67093\u30012\u548c1\u4e2a\u795e\u7ecf\u5143\u7684\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff0c\u5982\u56fe3\u6240\u793a\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"658\" height=\"277\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-105.png\" alt=\"\" class=\"wp-image-7607\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-105.png 658w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-105-300x126.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/figure>\n\n\n\n<p>\u5176\u4e2d,\u00a0<em>x<\/em>1\u200b\u3001<em>x<\/em>2\u200b\u3001<em>x<\/em>3\u200b\u00a0\u662f\u7f51\u7edc\u7684\u8f93\u5165,\u00a0<em>wijl<\/em>\u200b\u00a0\u662f\u4ece\u5f53\u524d\u5c42\u4e2d\u8282\u70b9\u00a0<em>i<\/em>\u00a0\u7684\u5c42\u00a0<em>l<\/em>\u00a0\u5230\u4e0b\u4e00\u5c42\u4e2d\u7684\u8282\u70b9\u00a0<em>j<\/em>\u00a0\u7684\u6743\u91cd\u3002\u4ece\u56fe3\uff08a\uff09\u53ef\u4ee5\u6e05\u695a\u5730\u770b\u51fa\uff0c\u76ee\u524d\u603b\u5171\u67098\u4e2a\u8fde\u63a5\u6743\u91cd\uff0c\u5982\u679c\u5220\u9664\u4e24\u4e2a\u6a59\u8272\uff08\u865a\u7ebf\uff09\u7684\u8fde\u63a5\uff0c\u90a3\u4e48\u603b\u8fde\u63a5\u6743\u91cd\u5c06\u51cf\u5c11\u52306\u4e2a\u3002\u7c7b\u4f3c\u5730\uff0c\u4ece\u56fe3\uff08b\uff09\u4e2d\uff0c\u5982\u679c\u79fb\u9664\u7ea2\u8272\u795e\u7ecf\u5143\uff0c\u90a3\u4e48\u5176\u6240\u6709\u76f8\u5173\u7684\u8fde\u63a5\u6743\u91cd\uff08\u865a\u7ebf\uff09\u4e5f\u5c06\u88ab\u79fb\u9664\uff0c\u5bfc\u81f4\u603b\u8fde\u63a5\u6743\u91cd\u51cf\u5c11\u52304\u4e2a\uff08\u53c2\u6570\u6570\u91cf\u51cf\u5c1150%\uff09\u3002<\/p>\n\n\n\n<ul><li>\u5728\u5377\u79ef\u5c42\u4e0a\u526a\u679d: \u5728\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u4e2d, \u5377\u79ef\u6838&nbsp;<em>W<\/em>\u2208<em>R<\/em><em>h<\/em>\u00d7<em>w<\/em>\u00d7<em>i<\/em><em>c<\/em>\u00d7<em>f<\/em>&nbsp;\u5e94\u7528\u4e8e\u6bcf\u4e2a\u8f93\u5165\u7684\u56fe\u50cf&nbsp;<em>I<\/em>,<em>I<\/em>\u2208<em>R<\/em><em>m<\/em>\u00d7<em>n<\/em>\u00d7<em>i<\/em><em>c<\/em>, \u5e76\u4e14\u7ecf\u8fc7\u5377\u79ef\u64cd\u4f5c\u540e\u8f93\u51fa\u7279\u5f81\u6620\u5c04&nbsp;<em>T<\/em>,<em>T<\/em>\u2208<em>R<\/em><em>p<\/em>\u00d7<em>q<\/em>\u00d7<em>f<\/em>&nbsp;\u3002\u5176\u4e2d,&nbsp;<em>h<\/em>&nbsp;\u548c&nbsp;<em>w<\/em>&nbsp;\u662f\u5377\u79ef\u6838\u7684\u5c3a\u5bf8,&nbsp;<em>i<\/em><em>c<\/em>&nbsp;\u662f\u8f93\u5165\u56fe\u50cf\u4e2d\u8f93\u5165\u901a\u9053\u7684\u6570\u91cf,&nbsp;<em>f<\/em>&nbsp;\u662f\u5e94\u7528\u7684\u5377\u79ef\u6838 \u7684\u6570\u91cf,&nbsp;<em>m<\/em>&nbsp;\u548c&nbsp;<em>n<\/em>&nbsp;\u662f\u8f93\u5165\u56fe\u50cf\u7684\u5c3a\u5bf8,&nbsp;<em>p<\/em>&nbsp;\u548c&nbsp;<em>q<\/em>&nbsp;\u662f\u7ed3\u679c\u7279\u5f81\u6620\u5c04\u7684\u8f93\u51fa\u5c3a\u5bf8\u3002\u8f93\u51fa\u7279\u5f81\u6620\u5c04\u7684\u5f62\u72b6\u8ba1\u7b97\u5982\u4e0b:<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"295\" height=\"74\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-106.png\" alt=\"\" class=\"wp-image-7609\"\/><\/figure><\/div>\n\n\n\n<p>\u5176\u4e2d,\u00a0<em>s<\/em>\u00a0\u4e3a\u6b65\u957f (stride)\uff0c\u00a0<em>p<\/em>\u00a0\u4e3a\u586b\u5145\uff08padding\uff09\u3002\u56fe4\u663e\u793a\u4e86\u6700\u7b80\u5355\u7684CNN\u5f62\u5f0f\uff0c\u5176 \u4e2d\u8f93\u5165\u56fe\u50cf\u7684\u5927\u5c0f\u4e3a\u00a04\u00d74\u00d73, \u5e94\u7528\u7684\u5377\u79ef\u6838\u5927\u5c0f\u4e3a\u00a03\u00d73\u00d73\u00d72\u00a0(2\u662f\u5377\u79ef\u6838\u7684\u6570 \u91cf)\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"540\" height=\"280\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-107.png\" alt=\"\" class=\"wp-image-7610\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-107.png 540w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-107-300x156.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/figure><\/div>\n\n\n\n<p>\u53d7\u5230\u65e9\u671f\u526a\u679d\u65b9\u6cd5\u548c\u795e\u7ecf\u7f51\u7edc\u8fc7\u5ea6\u53c2\u6570\u5316\u95ee\u9898\u7684\u542f\u53d1\uff0cHan et al.\uff082015\uff09\u63d0\u51fa\u4e86\u4e09\u6b65\u6cd5\u6765\u8fdb\u884c\u526a\u679d\u3002\u5176\u601d\u60f3\u662f\uff0c\u9996\u5148\u4fee\u526a\u6fc0\u6d3b\u5c0f\u4e8e\u67d0\u4e2a\u9884\u5b9a\u4e49\u9608\u503c\u7684\u6240\u6709\u8fde\u63a5\u6743\u91cd\uff08\u4e0d\u91cd\u8981\u7684\u8fde\u63a5\uff09\uff0c\u968f\u540e\u518d\u8bc6\u522b\u90a3\u4e9b\u91cd\u8981\u7684\u8fde\u63a5\u6743\u91cd\u3002\u6700\u540e\uff0c\u4e3a\u4e86\u8865\u507f\u7531\u4e8e\u4fee\u526a\u8fde\u63a5\u6743\u91cd\u800c\u5bfc\u81f4\u7684\u7cbe\u5ea6\u635f\u5931\uff0c\u518d\u6b21\u5fae\u8c03\/\u91cd\u65b0\u8bad\u7ec3\u526a\u679d\u6a21\u578b\u3002\u8fd9\u6837\u7684\u526a\u679d\u548c\u518d\u8bad\u7ec3\u8fc7\u7a0b\u5c06\u91cd\u590d\u6570\u6b21\uff0c\u4ee5\u51cf\u5c0f\u6a21\u578b\u7684\u5927\u5c0f\uff0c\u5c06\u5bc6\u96c6\u7f51\u7edc\u8f6c\u6362\u4e3a\u7a00\u758f\u7f51\u7edc\u3002\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u5bf9\u5168\u8fde\u63a5\u5c42\u548c\u5377\u79ef\u5c42\u8fdb\u884c\u4fee\u526a\uff0c\u800c\u4e14\u5377\u79ef\u5c42\u6bd4\u5168\u8fde\u63a5\u5c42\u5bf9\u4fee\u526a\u66f4\u52a0\u654f\u611f\u3002<\/p>\n\n\n\n<p>\u4ece\u5377\u79ef\u5c42\u4fee\u526a\u4e00\u4e9b\u4e0d\u91cd\u8981\u7684\u5377\u79ef\u6838\u80fd\u591f\u76f4\u63a5\u51cf\u5c11\u8ba1\u7b97\u6210\u672c\u5e76\u4e14\u52a0\u901f\u6a21\u578b\u3002\u4f46\u662f\uff0c\u4f7f\u7528\u7f51\u7edc\u526a\u679d\u65b9\u6cd5\u540c\u6837\u5b58\u5728\u7740\u4e00\u4e9b\u95ee\u9898\u3002\u9996\u5148\uff0c\u4f7f\u7528\u6216\u6b63\u5219\u5316\u8fdb\u884c\u526a\u679d\u6bd4\u5e38\u89c4\u65b9\u6cd5\u9700\u8981\u66f4\u591a\u7684\u8fed\u4ee3\u6b21\u6570\u624d\u80fd\u6536\u655b\u3002\u5176\u6b21\uff0c\u6240\u6709\u7684\u526a\u679d\u90fd\u9700\u8981\u624b\u52a8\u8bbe\u7f6e\u795e\u7ecf\u7f51\u7edc\u5c42\u7684\u7075\u654f\u5ea6\uff0c\u8fd9\u9700\u8981\u5bf9\u53c2\u6570\u8fdb\u884c\u5fae\u8c03\uff0c\u5728\u67d0\u4e9b\u5e94\u7528\u4e2d\u53ef\u80fd\u4f1a\u5341\u5206\u590d\u6742\u3002\u6700\u540e\uff0c\u7f51\u7edc\u526a\u679d\u867d\u7136\u901a\u5e38\u80fd\u591f\u4f7f\u5927\u6a21\u578b\u53d8\u5c0f\uff0c\u4f46\u662f\u5374\u4e0d\u80fd\u591f\u63d0\u9ad8\u8bad\u7ec3\u7684\u6548\u7387\u3002<\/p>\n\n\n\n<h3>3.\u7ed3\u6784\u77e9\u9635\uff08structural matrix\uff09<\/h3>\n\n\n\n<p>\u795e\u7ecf\u7f51\u7edc\u5404\u5c42\u4e4b\u95f4\u4f7f\u7528\u7684\u662f\u975e\u7ebf\u6027\u53d8\u6362\u00a0<em>f<\/em>(<em>x<\/em>,<em>N<\/em>)=<em>\u03c3<\/em>(<em>Mx<\/em>), \u8fd9\u91cc\u7684\u00a0<em>\u03c3<\/em>(\u22c5)\u00a0\u662f\u5bf9\u6bcf\u4e2a \u5143\u7d20\u7279\u5f02\u7684\u975e\u7ebf\u6027\u7b97\u5b50,\u00a0<em>x<\/em>\u00a0\u662f\u8f93\u5165\u5411\u91cf,\u00a0<em>M<\/em>\u00a0\u4ee3\u8868\u00a0<em>m<\/em>\u00d7<em>n<\/em>\u00a0\u7ef4\u7684\u53c2\u6570\u77e9\u9635, \u6b64\u65f6\u7684\u8fd0\u7b97\u590d \u6742\u5ea6\u4e3a\u00a0<em>O<\/em>(<em>mn<\/em>)\u00a0(V. Sindhwani et al. 2015) \u3002\u4e00\u4e2a\u76f4\u89c2\u7684\u526a\u679d\u65b9\u6cd5\u5c31\u662f\u4f7f\u7528\u53c2\u6570\u5316\u7684 \u7ed3\u6784\u77e9\u9635\u3002\u4e00\u4e2a\u5927\u5c0f\u4e3a\u00a0<em>m<\/em>\u00d7<em>n<\/em>, \u4f46\u662f\u53c2\u6570\u91cf\u5374\u5c0f\u4e8e\u00a0<em>mn<\/em>\u00a0\u7684\u77e9\u9635\u5c31\u53eb\u505a\u7ed3\u6784\u77e9\u9635\u3002Cheng et al. ( 2015 ) \u63d0 \u51fa\u4e86\u4e00\u79cd \u57fa\u4e8e\u5faa\u73af\u9884\u6d4b\u7684\u7b80\u5355\u65b9\u6cd5, \u5bf9\u4e8e\u4e00\u4e2a\u5411\u91cf\u00a0<em>r<\/em>=(<em>r<\/em>0\u200b,<em>r<\/em>1\u200b,\u22ef,<em>r<\/em>(<em>d<\/em>\u22121)\u200b), \u5176\u5bf9\u5e94\u7684\u00a0<em>d<\/em>\u00d7<em>d<\/em>\u00a0\u7ef4\u5faa\u73af\u77e9\u9635\u5b9a\u4e49\u5982\u4e0b:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"597\" height=\"180\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-108.png\" alt=\"\" class=\"wp-image-7611\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-108.png 597w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-108-300x90.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u6837\u4e00\u6765\u5b58\u50a8\u7684\u6210\u672c\u5c31\u4eceO&nbsp;(<em>d<\/em>2)&nbsp;\u53d8\u6210\u4e86O&nbsp;(<em>d<\/em>)&nbsp;\u3002\u7ed9\u5b9a&nbsp;<em>d<\/em>&nbsp;\u7ef4&nbsp;<em>r<\/em>&nbsp;\u5411\u91cf\u7684\u6761\u4ef6\u4e0b, \u4e0a\u5f0f\u4e2d\u7684 \u4e00\u5c42\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a&nbsp;<em>O<\/em>(<em>d<\/em>log<em>d<\/em>)&nbsp;\u3002<\/p>\n\n\n\n<p>\u7ed3\u6784\u77e9\u9635\u4e0d\u4ec5\u80fd\u591f\u964d\u4f4e\u5185\u5b58\u6210\u672c\uff0c\u800c\u4e14\u80fd\u591f\u901a\u8fc7\u77e9\u9635\u5411\u91cf\u548c\u68af\u5ea6\u8ba1\u7b97\u5927\u5e45\u5ea6\u52a0\u5feb\u8bad\u7ec3\u7684\u901f\u5ea6\u3002\u4f46\u662f\u8fd9\u79cd\u65b9\u6cd5\u7684\u7f3a\u70b9\u5728\u4e8e\uff0c\u7ed3\u6784\u7ea6\u675f\u901a\u5e38\u4f1a\u7ed9\u6a21\u578b\u5e26\u6765\u504f\u5dee\uff0c\u4ece\u800c\u635f\u5bb3\u6a21\u578b\u7684\u6027\u80fd\u3002\u518d\u8005\uff0c\u5982\u4f55\u627e\u5230\u5408\u9002\u7684\u7ed3\u6784\u77e9\u9635\u4e5f\u662f\u4e00\u4e2a\u96be\u9898\uff0c\u76ee\u524d\u8fd8\u6ca1\u6709\u7406\u8bba\u4e0a\u7684\u65b9\u6cd5\u80fd\u591f\u63a8\u5bfc\u51fa\u7ed3\u6784\u77e9\u9635\u3002<\/p>\n\n\n\n<h2>\u4f4e\u79e9\u56e0\u5b50\u5206\u89e3\uff08low-rank factorization\uff09<\/h2>\n\n\n\n<p>    \u4f4e\u79e9\u5206\u89e3\u7684\u601d\u60f3\u662f, \u5982\u679c\u539f\u59cb\u6743\u91cd\u77e9\u9635\u5177\u6709\u7ef4\u6570\u00a0<em>m<\/em>\u00d7<em>n<\/em>\u00a0\u548c\u79e9\u00a0<em>r<\/em>, \u5219\u6ee1\u79e9\u77e9\u9635\u53ef\u4ee5\u5206 \u89e3\u4e3a\u4e00\u4e2a\u00a0<em>m<\/em>\u00d7<em>r<\/em>\u00a0\u7684\u6743\u91cd\u77e9\u9635\u548c\u4e00\u4e2a\u00a0<em>r<\/em>\u00d7<em>n<\/em>\u00a0\u7684\u6743\u91cd\u77e9\u9635\u3002\u8be5\u65b9\u6cd5\u901a\u8fc7\u5c06\u5927\u77e9\u9635\u5206\u89e3\u4e3a\u5c0f\u77e9 \u9635, \u4ee5\u51cf\u5c0f\u6a21\u578b\u7684\u5c3a\u5bf8\u3002CNN\u901a\u5e38\u7531\u8bb8\u591a\u5c42\u7ec4\u6210, \u6bcf\u5c42\u90fd\u6709\u4e00\u7ec4\u6743\u91cd\u77e9\u9635, \u8fd9\u4e9b\u6743\u91cd\u53ef\u4ee5\u7528\u5f20\u91cf (Tensor) \u6765\u8868\u793a\u3002\u56fe5\u5c55\u793a\u4e86\u4e00\u4e2a\u7ef4\u6570\u4e3a\u00a0<em>X<\/em>\u00d7<em>Y<\/em>\u00d7<em>Z<\/em>\u00a0\u7684\u4e09\u7ef4\u5f20\u91cf\u3002<\/p>\n\n\n\n<p>   \u7ed9\u5b9a\u4e00\u4e2a\u7ef4\u6570\u4e3a\u00a0<em>N<\/em>\u00d7<em>N<\/em>\u00d7<em>D<\/em>, \u4e14\u6709\u00a0<em>K<\/em>\u00a0\u4e2a\u5377\u79ef\u6838\u7684\u5377\u79ef\u5c42, \u5176\u6743\u91cd\u77e9\u9635\u00a0<em>W<\/em>\u00a0\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u4e2a\u00a0<em>N<\/em>\u00d7<em>N<\/em>\u00d7<em>D<\/em>\u00d7<em>K<\/em>\u00a0\u7ef4\u7684\u5f20\u91cf (Gran\u00e9s and Santamaria 2017) \u3002\u5bf9\u4e8e\u5168\u8fde\u63a5\u5c42\u800c\u8a00,\u00a0<em>W<\/em>\u00a0\u53ef\u4ee5\u7528\u77e9\u9635 (2\u9636\u5f20\u91cf) \u6765\u8868\u793a\u3002\u56e0\u6b64\u5bf9\u6743\u91cd\u77e9\u9635\u8fdb\u884c\u5206\u89e3\u5c31\u662f\u5bf9\u5f20\u91cf\u8fdb\u884c\u5206\u89e3\u3002\u5f20\u91cf\u5206\u89e3\u6307\u7684\u662f, \u7528\u6807\u91cf (O\u9636\u5f20\u91cf) \u3001\u5411\u91cf (1\u9636\u5f20\u91cf) \u3001\u77e9\u9635 (2\u9636\u5f20\u91cf) \u548c\u4e00\u4e9b\u5176\u4ed6\u9ad8\u9636\u7684\u5f20\u91cf\u6765\u8868\u793a\u539f\u59cb\u5f20\u91cf\u7684\u65b9\u6cd5\u3002\u5bf9\u77e9\u9635\u53ef\u4ee5\u5e94\u7528\u6ee1\u79e9\u5206\u89e3 (full-rank decomposition) \u548c\u5947\u5f02\u503c\u5206\u89e3 (singular value decomposition, SVD), \u5bf9\u4e09\u7ef4\u53ca\u4e09\u7ef4\u4ee5\u4e0a\u5f20\u91cf\u53ef\u4ee5\u5e94\u7528 Tucker \u5206\u89e3\u548c CP\u5206\u89e3 (Canonical Polyadic) (Deng et al.2020) \u3002<\/p>\n\n\n\n<h3>1.\u5bf9\u77e9\u9635\u7684\u5206\u89e3<\/h3>\n\n\n\n<ul><li>\u6ee1\u79e9\u5206\u89e3\u3002\u5bf9\u4efb\u4f55\u7ed9\u5b9a\u7684\u77e9\u9635&nbsp;<em>A<\/em>\u2208<em>R<\/em>(<em>m<\/em>\u00d7<em>n<\/em>), \u5176\u79e9&nbsp;<em>r<\/em>\u2264<em>min<\/em>(<em>m<\/em>,<em>n<\/em>), \u5219&nbsp;<em>A<\/em>&nbsp;\u7684\u6ee1\u79e9\u5206\u89e3\u53ef\u4ee5\u8868\u793a\u4e3a&nbsp;<em>A<\/em>=<em>W<\/em><em>H<\/em>, \u5176\u4e2d&nbsp;<em>W<\/em>\u2208<em>R<\/em>(<em>m<\/em>\u00d7<em>r<\/em>),<em>H<\/em>\u2208<em>R<\/em>(<em>r<\/em>\u00d7<em>n<\/em>)&nbsp;\u3002\u5982\u679c&nbsp;<em>r<\/em>&nbsp;\u8fdc\u5c0f\u4e8e&nbsp;<em>m<\/em>&nbsp;\u6216&nbsp;<em>n<\/em>,\u6211\u4eec\u79f0&nbsp;<em>A<\/em>&nbsp;\u4e3a\u4f4e\u79e9\u77e9\u9635 (low-rank matrix) \u3002\u901a\u8fc7\u6ee1\u79e9\u5206\u89e3\u53ef\u4ee5\u5c06\u7a7a\u95f4\u590d\u6742\u5ea6\u4ece<em>O<\/em>(<em>mn<\/em>)&nbsp;\u663e\u8457\u51cf\u5c0f\u5230&nbsp;<em>O<\/em>(<em>r<\/em>(<em>m<\/em>+<em>n<\/em>))&nbsp;\u3002\u7279\u522b\u5730, \u5f53&nbsp;<em>m<\/em>&nbsp;\u548c&nbsp;<em>n<\/em>&nbsp;\u975e\u5e38\u63a5\u8fd1, \u5e76\u4e14\u539f\u59cb\u77e9\u9635\u662f\u884c(\u6216\u5217) \u6ee1\u79e9\u65f6, \u8fd9\u79cd\u51cf\u5c0f\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u4f5c\u7528\u4f1a\u5931\u6548\u3002\u6ee1\u79e9\u5206\u89e3\u65b9\u6cd5\u5bf9\u4e8e\u5168\u8fde\u63a5\u5c42\u5341\u5206\u6709\u6548, \u7279\u522b\u662f\u5f53\u4e24\u5c42\u4e4b\u95f4\u7684\u795e\u7ecf\u5143\u6570\u91cf\u76f8\u5dee\u5f88\u5927\u6216\u6743\u91cd\u77e9\u9635\u4f4e\u79e9\u7a00\u758f\u65f6\u3002\u7ed9\u5b9a\u4e00\u4e2a\u8f83\u5c0f\u7684\u6b63\u6574\u6570&nbsp;<em>k<\/em>&lt;<em>r<\/em>, \u53ef\u4ee5\u901a\u8fc7\u5982\u4e0b\u7684\u5f0f\u5b50\u6c42\u89e3\u6700\u4f18\u7684&nbsp;<em>W<\/em>\u2208<em>R<\/em>(<em>m<\/em>\u00d7<em>k<\/em>),<em>H<\/em>\u2208<em>R<\/em>(<em>k<\/em>\u00d7<em>n<\/em>), \u5176\u4e2d,&nbsp;<em>F<\/em>&nbsp;\u8868\u793aFrobenius\u8303\u6570\u3002<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"260\" height=\"79\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-109.png\" alt=\"\" class=\"wp-image-7612\"\/><\/figure><\/div>\n\n\n\n<ul><li>SVD\u3002SVD\u662f\u4e00\u79cd\u5c06\u539f\u59cb\u6743\u91cd\u77e9\u9635\u5206\u89e3\u4e3a\u4e09\u4e2a\u8f83\u5c0f\u7684\u77e9\u9635\u4ee5\u66ff\u6362\u539f\u59cb\u6743\u91cd\u77e9\u9635\u7684 \u65b9\u6cd5\u3002\u5bf9\u4e8e\u4efb\u610f\u7684\u77e9\u9635&nbsp;<em>A<\/em>\u2208<em>R<\/em>(<em>m<\/em>\u00d7<em>n<\/em>), \u5b58\u5728\u5206\u89e3&nbsp;<em>A<\/em>=<em>U<\/em><em>S<\/em><em>V<\/em><em>T<\/em>, \u5176\u4e2d,&nbsp;<em>U<\/em>\u2208<em>R<\/em>(<em>m<\/em>\u00d7<em>r<\/em>),&nbsp;<em>S<\/em>\u2208<em>R<\/em>(<em>r<\/em>\u00d7<em>r<\/em>),<em>V<\/em><em>T<\/em>\u2208<em>R<\/em>(<em>r<\/em>\u00d7<em>n<\/em>)&nbsp;\u3002&nbsp;<em>U<\/em>&nbsp;\u548c&nbsp;<em>V<\/em>&nbsp;\u662f\u6b63\u4ea4\u77e9\u9635\uff0c&nbsp;<em>S<\/em>&nbsp;\u662f\u5bf9\u89d2\u7ebf\u4e0a\u53ea\u6709\u5947\u5f02\u503c\u7684\u5bf9\u89d2\u77e9 \u9635, \u5176\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\u90fd\u6bd4\u5176\u4e0b\u4e00\u4e2a\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5927\u3002\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u4f7f\u7a7a\u95f4\u590d \u6742\u5ea6\u4ece&nbsp;<em>O<\/em>(<em>mn<\/em>)&nbsp;\u51cf\u5c0f\u5230&nbsp;<em>O<\/em>(<em>r<\/em>(<em>m<\/em>+<em>n<\/em>+1))&nbsp;\u3002\u5b9e\u9645\u5e94\u7528\u4e2d, \u53ef\u4ee5\u7528\u66f4\u5c0f\u7684&nbsp;<em>k<\/em>&nbsp;\u66ff\u6362&nbsp;<em>r<\/em>, \u8fd9 \u79cd\u65b9\u6cd5\u79f0\u4e3a\u622a\u65ad\u5947\u5f02\u503c\u5206\u89e3 (truncated SVD, TSVD) \u3002\u5728\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u548c\u5377\u79ef\u795e \u7ecf\u7f51\u7edc\u4e2d, SVD\u662f\u4e00\u79cd\u5e38\u7528\u7684\u5206\u89e3\u65b9\u6cd5, \u4e3b\u8981\u7528\u4e8e\u51cf\u5c11\u53c2\u6570\u7684\u4e2a\u6570\u3002<\/li><\/ul>\n\n\n\n<h3>2.\u5bf9\u4e09\u7ef4\u53ca\u4e09\u7ef4\u4ee5\u4e0a\u5f20\u91cf\u7684\u5206\u89e3<\/h3>\n\n\n\n<ul><li>Tucker\u5206\u89e3\u3002\u8be5\u65b9\u6cd5\u662f\u5c06TSVD\u65b9\u6cd5\u4e2d\u7684\u5bf9\u89d2\u77e9\u9635\u6269\u5c55\u4e3a\u5f20\u91cf\u7684\u4e00\u79cd\u65b9\u6cd5\u3002TSVD\u548cTucker\u5206\u89e3\u4e4b\u95f4\u7684\u5173\u7cfb\u53ef\u4ee5\u7528\u56fe\u6765\u8868\u793a\uff1a<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"498\" height=\"328\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-110.png\" alt=\"\" class=\"wp-image-7613\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-110.png 498w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-110-300x198.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/figure>\n\n\n\n<ul><li>CP\u5206\u89e3\u3002\u8be5\u5206\u89e3\u662fTucker\u5206\u89e3\u7684\u4e00\u79cd\u7279\u6b8a\u5f62\u5f0f\u3002\u5982\u679cTucker\u5206\u89e3\u4e2d\u7684\u6bcf\u4e2a&nbsp;<em>r<\/em><em>i<\/em>\u200b&nbsp;\u7b49\u4e8e\u6b63 \u6574\u6570&nbsp;<em>r<\/em><em>C<\/em>\u200b, \u5e76\u4e14\u6838\u5f20\u91cf&nbsp;<em>K<\/em>&nbsp;\u6ee1\u8db3, \u9664\u4e86&nbsp;<em>K<\/em>(<em>x<\/em>1\u200b,<em>x<\/em>2\u200b,\u2026,<em>x<\/em><em>d<\/em>\u200b),<em>x<\/em>1\u200b=<em>x<\/em>2\u200b=\u22ef=<em>x<\/em><em>d<\/em>\u200b&nbsp;\u4e4b\u5916 \u7684\u6240\u6709\u5143\u7d20\u90fd\u662f 0 , \u6b64\u65f6Tucker\u5206\u89e3\u5c31\u6210\u4e3a\u4e86CP\u5206\u89e3\u3002\u4e0eTucker\u5206\u89e3\u76f8\u6bd4, CP\u5206\u89e3 \u5e38\u7528\u4e8e\u89e3\u91ca\u6570\u636e\u7684\u7ec4\u6210\u6210\u5206, \u800c\u524d\u8005\u4e3b\u8981\u7528\u4e8e\u6570\u636e\u538b\u7f29\u3002\u56fe7\u5c55\u793a\u4e86\u4e09\u9636\u5f20\u91cf&nbsp;<em>x<\/em>\u2208<em>R<\/em>(<em>I<\/em>\u00d7<em>J<\/em>\u00d7<em>K<\/em>)&nbsp;\u88ab&nbsp;R&nbsp;\u4e2a\u7ec4\u6210\u90e8\u5206\u5206\u89e3\u7684\u8fc7\u7a0b, \u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u7528\u5982\u4e0b\u7684\u516c\u5f0f\u6765\u8868\u793a, \u5176\u4e2d,&nbsp;<em>a<\/em><em>r<\/em>\u200b\u2208<em>R<\/em><em>I<\/em>,<em>b<\/em><em>r<\/em>\u200b\u2208<em>R<\/em><em>J<\/em>,<em>c<\/em><em>r<\/em>\u200b\u2208<em>R<\/em><em>K<\/em>&nbsp;(Marcella Astrid and Seung- and Ik Lee 2018)\u3002<\/li><\/ul>\n\n\n\n<p>\u57fa\u4e8e\u4f4e\u79e9\u8fd1\u4f3c\u7684\u65b9\u6cd5\u867d\u7136\u662f\u6a21\u578b\u538b\u7f29\u548c\u52a0\u901f\u7684\u524d\u6cbf\uff0c\u7136\u800c\u5177\u4f53\u5b9e\u73b0\u5374\u5e76\u975e\u6613\u4e8b\u3002\u56e0\u4e3a\u8fd9\u6d89\u53ca\u5230\u5206\u89e3\u64cd\u4f5c\uff0c\u9700\u8981\u4ed8\u51fa\u9ad8\u6602\u7684\u8ba1\u7b97\u6210\u672c\u3002\u6b64\u5916\uff0c\u5f53\u524d\u7684\u65b9\u6cd5\u4ecd\u96c6\u4e2d\u4e8e\u9010\u5c42\u6267\u884c\u4f4e\u79e9\u8fd1\u4f3c\uff0c\u56e0\u6b64\u65e0\u6cd5\u6267\u884c\u5168\u5c40\u7684\u53c2\u6570\u538b\u7f29\u3002\u4f46\u5168\u5c40\u7684\u53c2\u6570\u538b\u7f29\u5341\u5206\u91cd\u8981\uff0c\u56e0\u4e3a\u4e0d\u540c\u7684\u5c42\u5305\u542b\u4e0d\u540c\u7684\u4fe1\u606f\u3002\u6700\u540e\uff0c\u4e0e\u539f\u59cb\u7684\u6a21\u578b\u76f8\u6bd4\uff0c\u56e0\u5b50\u5206\u89e3\u9700\u8981\u5bf9\u5927\u91cf\u7684\u6a21\u578b\u8fdb\u884c\u518d\u8bad\u7ec3\u4ee5\u5b9e\u73b0\u6536\u655b\u3002<\/p>\n\n\n\n<h2>\u8fc1\u79fb\/\u538b\u7f29\u5377\u79ef\u6ee4\u6ce2\u5668\uff08transferred\/compact convolutional filters\uff09<\/h2>\n\n\n\n<p>Cohen and Welling (2016) \u63d0\u51fa\u4e86\u4f7f\u7528\u5377\u79ef\u6ee4\u6ce2\u5668\u538b\u7f29CNN\u6a21\u578b\u7684\u60f3\u6cd5, \u5e76\u5728 \u7814\u7a76\u4e2d\u5f15\u5165\u4e86\u7b49\u53d8\u7fa4\u7406\u8bba (the equivariant group theory)\u3002\u8ba9&nbsp;<em>x<\/em>&nbsp;\u4f5c\u4e3a\u8f93\u5165,&nbsp;\u03a6(\u22c5)&nbsp;\u4f5c\u4e3a \u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u6216\u8005\u7f51\u7edc\u5c42,&nbsp;\u0393(\u22c5)&nbsp;\u4f5c\u4e3a\u8fc1\u79fb\u77e9\u9635, \u5219\u7b49\u4ef7\u7684\u6982\u5ff5\u5b9a\u4e49\u5982\u4e0b:\u0393\u2032(\u03a6(<em>x<\/em>))=\u03a6(\u0393(<em>x<\/em>))<\/p>\n\n\n\n<p>\u8fd9\u6837\u7684\u5b9a\u4e49\u6307\u7684\u662f, \u8fc1\u79fb\u77e9\u9635&nbsp;\u0393(\u22c5)&nbsp;\u5148\u5bf9\u8f93\u5165x\u8fdb\u884c\u53d8\u6362, \u518d\u5c06\u5176\u4f20\u8f93\u5230&nbsp;\u03a6(\u22c5)&nbsp;\u6240\u5f97\u5230 \u7684\u7ed3\u679c\u5e94\u8be5\u8ddf\u5148\u5c06\u8f93\u5165&nbsp;<em>x<\/em>&nbsp;\u6620\u5c04\u5230\u795e\u7ecf\u7f51\u7edc&nbsp;\u03a6(\u22c5)&nbsp;\u4e0a\u518d\u505a\u53d8\u6362&nbsp;\u0393(\u22c5)&nbsp;\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u540c\u3002\u503c\u5f97\u6ce8 \u610f\u7684\u662f,&nbsp;\u0393(\u22c5)&nbsp;\u548c&nbsp;\u0393\u2032(\u22c5)&nbsp;\u4e0d\u4e00\u5b9a\u76f8\u540c, \u56e0\u4e3a\u5b83\u4eec\u4f5c\u7528\u5728\u4e0d\u540c\u7684\u5bf9\u8c61\u4e0a\u3002\u6839\u636e\u8fd9\u6837\u7684\u7406\u8bba, \u901a\u8fc7\u5c06\u53d8\u6362\u5e94\u7528\u4e8e\u5c42\u6216\u8005\u6ee4\u6ce2\u5668&nbsp;\u03a6(\u22c5)&nbsp;\u6765\u538b\u7f29\u6574\u4e2a\u7f51\u7edc\u6a21\u578b\u5c31\u5341\u5206\u5408\u7406\u3002\u4ece\u7ecf\u9a8c\u6765\u770b, \u4f7f\u7528\u4e00\u7ec4\u5927\u7684\u5377\u79ef\u6ee4\u6ce2\u5668\u4e5f\u5bf9\u6df1\u5c42CNN\u6709\u76ca, \u5177\u4f53\u65b9\u6cd5\u662f\u5c06\u4e00\u4e9b\u53d8\u6362&nbsp;\u0393(\u22c5)&nbsp;\u5e94\u7528\u4e8e\u4e00\u7ec4 \u5145\u5f53\u6a21\u578b\u6b63\u5219\u5316\u5668\u7684\u5c0f\u578b\u57fa\u6ee4\u6ce2\u5668\u4e0a\u3002<\/p>\n\n\n\n<p>\u6cbf\u7740\u8fd9\u4e00\u7814\u7a76\u65b9\u5411, \u8fd1\u671f\u7684\u8bb8\u591a\u7814\u7a76\u63d0\u51fa\u4e86\u4ece\u4e00\u7ec4\u57fa\u6ee4\u6ce2\u5668\u51fa\u53d1\u6784\u5efa\u5377\u79ef\u5c42\u7684\u601d \u60f3\u3002\u5b83\u4eec\u7684\u5171\u540c\u70b9\u662f, \u8fc1\u79fb\u77e9\u9635&nbsp;\u0393(\u22c5)&nbsp;\u662f\u53ea\u5728\u5377\u79ef\u6ee4\u6ce2\u5668\u7684\u7a7a\u95f4\u57df\u4e2d\u64cd\u4f5c\u7684\u4e00\u7c7b\u51fd\u6570\u3002 \u4f8b\u5982, Shang et al. (2016) \u53d1\u73b0, CNN\u7684\u8f83\u4f4e\u5377\u79ef\u5c42\u901a\u8fc7\u5b66\u4e60\u340c\u4f59\u7684\u6ee4\u6ce2\u5668\u6765\u63d0\u53d6 \u8f93\u5165\u4fe1\u53f7\u7684\u6b63\u8d1f\u76f8\u4f4d\u4fe1\u606f, \u5e76\u5c06&nbsp;\u0393(\u22c5)&nbsp;\u5b9a\u4e49\u4e3a\u7b80\u5355\u7684\u5426\u5b9a\u51fd\u6570:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"227\" height=\"48\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/09\/image-111.png\" alt=\"\" class=\"wp-image-7615\"\/><\/figure><\/div>\n\n\n\n<p>\u5176\u4e2d,&nbsp;<em>W<\/em><em>x<\/em>\u200b&nbsp;\u662f\u57fa\u7840\u7684\u5377\u79ef\u6ee4\u6ce2\u5668,&nbsp;<em>W<\/em><em>x<\/em>\u2212\u200b\u662f\u7531\u6fc0\u6d3b\u4e0e&nbsp;<em>W<\/em><em>x<\/em>\u200b&nbsp;\u76f8\u53cd\u7684\u79fb\u4f4d (shift) \u6784\u6210\u7684\u6ee4\u6ce2 \u5668, \u5e76\u4e14\u8fd9\u4e9b\u79fb\u4f4d\u662f\u5728\u6700\u5927\u6c60 (max-pooling) \u64cd\u4f5c\u540e\u9009\u62e9\u7684\u3002\u901a\u8fc7\u8fd9\u6837\u64cd\u4f5c, \u5c31\u53ef\u4ee5 \u5f88\u5bb9\u6613\u7684\u5b9e\u73b0\u5728\u6240\u6709\u5377\u79ef\u5c42\u4e0a\u7684\u4e8c\u500d\u538b\u7f29\u7387\u3002\u5b83\u8fd8\u8868\u660e, \u5426\u5b9a\u53d8\u6362\u4f5c\u4e3a\u4e00\u4e2a\u5f3a\u5927\u7684\u6b63 \u5219\u5316\u65b9\u6cd5, \u80fd\u591f\u7528\u4ee5\u63d0\u9ad8\u5206\u7c7b\u7cbe\u5ea6\u3002\u4e00\u79cd\u76f4\u89c2\u7684\u7406\u89e3\u662f, \u5177\u6709\u6210\u5bf9\u6b63\u8d1f\u7ea6\u675f\u7684\u5b66\u4e60\u7b97 \u6cd5\u53ef\u4ee5\u4ea7\u751f\u5b9e\u7528\u800c\u4e0d\u662f\u5197\u4f59\u7684\u7684\u5377\u79ef\u6ee4\u6ce2\u5668\u3002\u6b64\u5916, Zhai et al. (2016) \u5c06&nbsp;\u0393(\u22c5)&nbsp;\u5b9a\u4e49\u4e3a \u5e94\u7528\u4e8e 2 \u7ef4\u6ee4\u6ce2\u5668\u7684\u5e73\u79fb\u51fd\u6570\u96c6:\u0393\u2032\u03a6(<em>x<\/em>)=T(\u22c5,<em>x<\/em>,<em>y<\/em>)<em>x<\/em>,<em>y<\/em>\u2208{\u2212<em>k<\/em>,\u2026,<em>k<\/em>},(<em>x<\/em>,<em>y<\/em>)\ue020=(0,0)<\/p>\n\n\n\n<p>\u5176\u4e2d,&nbsp;T(\u22c5,<em>x<\/em>,<em>y<\/em>)&nbsp;\u8868\u793a\u7b2c\u4e00\u4e2a\u64cd\u4f5c\u6570\u6cbf\u5176\u7a7a\u95f4\u7ef4\u5ea6\u5e73\u79fb&nbsp;(<em>x<\/em>,<em>y<\/em>), \u5e76\u5728\u8fb9\u754c\u5904\u8fdb\u884c\u9002\u5f53\u7684\u96f6 \u586b\u5145\u4ee5\u4fdd\u6301\u5f62\u72b6\u3002\u63d0\u51fa\u7684\u6846\u67b6\u53ef\u7528\u4e8e\u516c\u5f0f (1) \u6539\u5584\u5206\u7c7b\u7cbe\u5ea6\u7684\u95ee\u9898, \u8fdb\u800c\u4f5c\u4e3a maxout\u7f51\u7edc\u7684\u6b63\u5219\u5316\u7248\u672c\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u5c06\u53d8\u6362\u7ea6\u675f\u5e94\u7528\u4e8e\u5377\u79ef\u6ee4\u6ce2\u5668\u7684\u65b9\u6cd5\uff0c\u8fd8\u6709\u51e0\u4e2a\u95ee\u9898\u9700\u8981\u89e3\u51b3\u3002\u9996\u5148\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u53ef\u4ee5\u5728\u5bbd\/\u5e73\u7684\u67b6\u6784\uff08\u5982VGGNet\uff0cAlexNet\uff09\u4e0a\u5b9e\u73b0\u6709\u7ade\u4e89\u529b\u7684\u6027\u80fd\uff0c\u4f46\u662f\u5728\u7a84\/\u6df1\u7684\u67b6\u6784\uff08\u5982ResNet\uff09\u4e0a\u5219\u4e0d\u884c\u3002\u5176\u6b21\uff0c\u8fc1\u79fb\u5047\u8bbe\u6709\u65f6\u592a\u5f3a\uff0c\u65e0\u6cd5\u6307\u5bfc\u5b66\u4e60\u8fc7\u7a0b\uff0c\u5bfc\u81f4\u5f97\u5230\u7684\u7ed3\u679c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u4e0d\u7a33\u5b9a\u3002\u6b64\u5916\uff0c\u4f7f\u7528\u7d27\u51d1\u7684\u5377\u79ef\u6ee4\u6ce2\u5668\u867d\u7136\u53ef\u4ee5\u76f4\u63a5\u964d\u4f4e\u8ba1\u7b97\u6210\u672c\uff0c\u4f46\u5173\u952e\u601d\u60f3\u662f\u8981\u7528\u7d27\u51d1\u7684\u5757\u66ff\u6362\u677e\u6563\u7684\u548c\u8fc7\u5ea6\u53c2\u6570\u5316\u7684\u6ee4\u6ce2\u5668\u4ee5\u63d0\u9ad8\u8ba1\u7b97\u901f\u5ea6\u3002<\/p>\n\n\n\n<h2>\u84b8\u998f\u5b66\u4e60\uff08knowledge distillation\uff09<\/h2>\n\n\n\n<p>\u84b8\u998f\u5b66\u4e60\uff08knowledge distillation\uff0cKD\uff09\u662f\u6307\u901a\u8fc7\u6784\u5efa\u4e00\u4e2a\u8f7b\u91cf\u5316\u7684\u5c0f\u6a21\u578b\uff0c\u5229\u7528\u6027\u80fd\u66f4\u597d\u7684\u5927\u6a21\u578b\u7684\u76d1\u7763\u4fe1\u606f\uff0c\u6765\u8bad\u7ec3\u8fd9\u4e2a\u5c0f\u6a21\u578b\uff0c\u4ee5\u671f\u8fbe\u5230\u66f4\u597d\u7684\u6027\u80fd\u548c\u7cbe\u5ea6\u3002KD\u4e0e\u8fc1\u79fb\u5b66\u4e60\uff08transfer learning\uff09\u4e0d\u540c\uff0c\u5728\u8fc1\u79fb\u5b66\u4e60\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u76f8\u540c\u7684\u6a21\u578b\u4f53\u7cfb\u7ed3\u6784\u548c\u5b66\u4e60\u7684\u6743\u91cd\uff0c\u4ec5\u6839\u636e\u5e94\u7528\u7684\u8981\u6c42\u4f7f\u7528\u65b0\u5c42\u6765\u66ff\u6362\u90e8\u5206\u5168\u8fde\u63a5\u5c42\u3002\u800c\u5728KD\u4e2d\uff0c\u901a\u8fc7\u5728\u5927\u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u7684\u66f4\u5927\u7684\u590d\u6742\u7f51\u7edc\uff08\u4e5f\u79f0\u4e4b\u4e3a\u6559\u5e08\u6a21\u578b\uff08teacher model\uff09\uff09\u5b66\u4e60\u5230\u7684\u77e5\u8bc6\u53ef\u4ee5\u8fc1\u79fb\u5230\u4e00\u4e2a\u66f4\u5c0f\u3001\u66f4\u8f7b\u7684\u7f51\u7edc\u4e0a\uff08\u4e5f\u79f0\u4e4b\u4e3a\u5b66\u751f\u6a21\u578b\uff08student model\uff09\uff09\u3002\u524d\u4e00\u4e2a\u5927\u6a21\u578b\u53ef\u4ee5\u662f\u5355\u4e2a\u7684\u5927\u6a21\u578b\uff0c\u4e5f\u53ef\u4ee5\u662f\u72ec\u7acb\u8bad\u7ec3\u6a21\u578b\u7684\u96c6\u5408\u3002KD\u65b9\u6cd5\u7684\u4e3b\u8981\u601d\u60f3\u662f\u901a\u8fc7softmax\u51fd\u6570\u5b66\u4e60\u8bfe\u5802\u5206\u5e03\u8f93\u51fa\uff0c\u5c06\u77e5\u8bc6\u4ece\u5927\u578b\u6559\u5e08\u6a21\u578b\u8f6c\u6362\u4e3a\u4e00\u4e2a\u66f4\u5c0f\u7684\u5b66\u751f\u6a21\u578b\u3002\u4ece\u6559\u5e08\u6a21\u578b\u8bad\u7ec3\u5b66\u751f\u6a21\u578b\u7684\u4e3b\u8981\u76ee\u7684\u662f\u5b66\u4e60\u6559\u5e08\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n\n\n\n<p>\u5728\u73b0\u6709\u7684KD\u65b9\u6cd5\u4e2d\uff0c\u5b66\u751f\u6a21\u578b\u7684\u5b66\u4e60\u4f9d\u8d56\u4e8e\u6559\u5e08\u6a21\u578b\uff0c\u662f\u4e00\u4e2a\u4e24\u9636\u6bb5\u7684\u8fc7\u7a0b\u3002Lan et al.\uff082018\uff09\u63d0\u51fa\u4e86\u5b9e\u65f6\u672c\u5730\u96c6\u6210\uff08On-the-fly Native Ensemble\uff0cONE\uff09\uff0c\u8fd9\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u5355\u9636\u6bb5\u5728\u7ebf\u84b8\u998f\u5b66\u4e60\u65b9\u6cd5\u3002\u5728\u8bad\u7ec3\u671f\u95f4\uff0cONE\u6dfb\u52a0\u8f85\u52a9\u5206\u652f\u4ee5\u521b\u5efa\u76ee\u6807\u7f51\u7edc\u7684\u591a\u5206\u652f\u53d8\u4f53\uff0c\u7136\u540e\u4ece\u6240\u6709\u5206\u652f\u4e2d\u521b\u5efa\u672c\u5730\u96c6\u6210\u6559\u5e08\u6a21\u578b\u3002\u5bf9\u4e8e\u76f8\u540c\u7684\u76ee\u6807\u6807\u7b7e\u7ea6\u675f\uff0c\u53ef\u4ee5\u540c\u65f6\u5b66\u4e60\u5b66\u751f\u548c\u6bcf\u4e2a\u5206\u652f\u3002\u6bcf\u4e2a\u5206\u652f\u4f7f\u7528\u4e24\u4e2a\u635f\u5931\u9879\u8fdb\u884c\u8bad\u7ec3\uff0c\u5176\u4e2d\u6700\u5e38\u7528\u7684\u5c31\u662f\u6700\u5927\u4ea4\u53c9\u71b5\u635f\u5931\uff08softmax cross-entropy loss\uff09\u548c\u84b8\u998f\u635f\u5931\uff08distillation loss\uff09\u3002<\/p>\n\n\n\n<p>\u5728\u7f51\u7edc\u538b\u7f29\u8fd9\u4e00\u6b65\uff0c\u53ef\u4ee5\u4f7f\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002Romero et al.\uff082015\uff09\u63d0\u51fa\u4e86\u4e00\u79cd\u8bad\u7ec3\u8584\u800c\u6df1\u7684\u7f51\u7edc\u7684\u65b9\u6cd5\uff0c\u79f0\u4e3aFitNets\uff0c\u7528\u4ee5\u538b\u7f29\u5bbd\u4e14\u76f8\u5bf9\u8f83\u6d45\uff08\u4f46\u5b9e\u9645\u4e0a\u4ecd\u7136\u5f88\u6df1\uff09\u7684\u7f51\u7edc\u3002\u8be5\u65b9\u6cd5\u6269\u5c55\u4e86\u539f\u6765\u7684\u601d\u60f3\uff0c\u5141\u8bb8\u5f97\u5230\u66f4\u8584\u3001\u66f4\u6df1\u7684\u5b66\u751f\u6a21\u578b\u3002\u4e3a\u4e86\u5b66\u4e60\u6559\u5e08\u7f51\u7edc\u7684\u4e2d\u95f4\u8868\u793a\uff0cFitNet\u8ba9\u5b66\u751f\u6a21\u4eff\u8001\u5e08\u7684\u5b8c\u5168\u7279\u5f81\u56fe\u3002\u7136\u800c\uff0c\u8fd9\u6837\u7684\u5047\u8bbe\u592a\u8fc7\u4e8e\u4e25\u683c\uff0c\u56e0\u4e3a\u6559\u5e08\u548c\u5b66\u751f\u7684\u80fd\u529b\u53ef\u80fd\u4f1a\u6709\u5f88\u5927\u7684\u5dee\u522b\u3002<\/p>\n\n\n\n<p>\u57fa\u4e8e\u84b8\u998f\u5b66\u4e60\u7684\u65b9\u6cd5\u53ef\u4ee5\u4f7f\u6a21\u578b\u7684\u6df1\u5ea6\u53d8\u6d45\uff0c\u5e76\u4e14\u80fd\u591f\u663e\u8457\u964d\u4f4e\u8ba1\u7b97\u6210\u672c\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u4e5f\u5b58\u5728\u4e00\u4e9b\u5f0a\u7aef\u3002\u5176\u4e2d\u4e4b\u4e00\u662fKD\u65b9\u6cd5\u53ea\u80fd\u5e94\u7528\u4e8e\u5177\u6709softmax\u635f\u5931\u51fd\u6570\u7684\u4efb\u52a1\u4e2d\u3002\u518d\u8005\u5c31\u662f\uff0c\u4e0e\u5176\u4ed6\u7c7b\u578b\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u57fa\u4e8e\u84b8\u998f\u5b66\u4e60\u7684\u65b9\u6cd5\u5f80\u5f80\u5177\u6709\u8f83\u5dee\u7684\u7ade\u4e89\u6027\u80fd\u3002<\/p>\n\n\n\n<h2>\u9762\u4e34\u7684\u95ee\u9898<\/h2>\n\n\n\n<p>\u5728\u6587\u7ae0\u7684\u6700\u540e\u4e00\u90e8\u5206\uff0c\u4f5c\u8005\u603b\u7ed3\u4e86\u73b0\u6709\u7684\u8fd9\u4e9b\u6a21\u578b\u538b\u7f29\u548c\u52a0\u901f\u7684\u65b9\u6cd5\u4ecd\u7136\u9762\u4e34\u7684\u4e00\u4e9b\u95ee\u9898\u4e0e\u6311\u6218\uff0c\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u9762\uff1a<\/p>\n\n\n\n<ol><li>\u5f53\u524d\u7684\u5927\u591a\u6570\u5148\u8fdb\u65b9\u6cd5\u5efa\u7acb\u5728\u7cbe\u5fc3\u8bbe\u8ba1\u7684CNN\u6a21\u578b\u4e4b\u4e0a\uff0c\u8fd9\u4e9b\u6a21\u578b\u9650\u5236\u4e86\u66f4\u6539\u914d\u7f6e\u7684\u81ea\u7531\u5ea6\uff08\u4f8b\u5982\uff0c\u7f51\u7edc\u67b6\u6784\u3001\u8d85\u53c2\u6570\u7b49\uff09\u3002\u4e3a\u4e86\u5904\u7406\u66f4\u590d\u6742\u7684\u4efb\u52a1\uff0c\u672a\u6765\u5e94\u8be5\u63d0\u4f9b\u66f4\u52a0\u5408\u7406\u7684\u65b9\u6cd5\u6765\u914d\u7f6e\u538b\u7f29\u6a21\u578b\u3002<\/li><li>\u5404\u79cd\u5c0f\u578b\u5e73\u53f0\uff08\u4f8b\u5982\u79fb\u52a8\u8bbe\u5907\u3001\u673a\u5668\u4eba\u3001\u81ea\u52a8\u9a7e\u9a76\u6c7d\u8f66\u7b49\uff09\u7684\u786c\u4ef6\u9650\u5236\u4ecd\u7136\u662f\u963b\u788d\u6df1\u5c42CNN\u6269\u5c55\u7684\u4e3b\u8981\u95ee\u9898\u3002\u5982\u4f55\u5145\u5206\u5229\u7528\u6709\u9650\u7684\u8ba1\u7b97\u8d44\u6e90\u4ee5\u53ca\u5982\u4f55\u4e3a\u8fd9\u4e9b\u5e73\u53f0\u8bbe\u8ba1\u7279\u6b8a\u7684\u538b\u7f29\u65b9\u6cd5\u4ecd\u7136\u662f\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u3002<\/li><li>\u526a\u679d\u662f\u538b\u7f29\u548c\u52a0\u901fCNN\u7684\u6709\u6548\u65b9\u6cd5\u3002\u76ee\u524d\u7684\u526a\u679d\u6280\u672f\u5927\u591a\u662f\u4e3a\u4e86\u4fee\u526a\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8fde\u63a5\u800c\u8bbe\u8ba1\u7684\u3002\u6b64\u5916\uff0c\u5bf9\u901a\u9053\u8fdb\u884c\u526a\u679d\u80fd\u591f\u76f4\u63a5\u51cf\u5c11\u7279\u5f81\u6620\u5c04\u7684\u5bbd\u5ea6\u5e76\u538b\u7f29\u6a21\u578b\u3002\u8fd9\u79cd\u65b9\u6cd5\u867d\u7136\u5f88\u6709\u6548\uff0c\u4f46\u662f\u4fee\u526a\u901a\u9053\u53ef\u80fd\u4f1a\u663e\u8457\u5730\u6539\u53d8\u4e0b\u4e00\u5c42\u7684\u8f93\u5165\uff0c\u56e0\u6b64\u4e5f\u5b58\u5728\u6311\u6218\u6027\u3002<\/li><li>\u5982\u524d\u6240\u8ff0\uff0c\u7ed3\u6784\u77e9\u9635\u548c\u8fc1\u79fb\u5377\u79ef\u6ee4\u6ce2\u5668\u7684\u65b9\u6cd5\u5fc5\u987b\u4f7f\u6a21\u578b\u5177\u6709\u4eba\u7c7b\u7684\u5148\u9a8c\u77e5\u8bc6\uff0c\u8fd9\u5c06\u4f1a\u663e\u8457\u5f71\u54cd\u6a21\u578b\u7684\u6027\u80fd\u548c\u7a33\u5b9a\u6027\u3002\u7814\u7a76\u5982\u4f55\u63a7\u5236\u5f3a\u52a0\u8fd9\u4e9b\u5148\u9a8c\u77e5\u8bc6\u5e26\u6765\u7684\u5f71\u54cd\u81f3\u5173\u91cd\u8981\u3002<\/li><li>\u84b8\u998f\u5b66\u4e60\u7684\u65b9\u6cd5\u5177\u6709\u5f88\u591a\u7684\u4f18\u70b9\uff0c\u6bd4\u5982\u65e0\u9700\u7279\u5b9a\u7684\u786c\u4ef6\u5c31\u80fd\u591f\u76f4\u63a5\u52a0\u901f\u6a21\u578b\u3002\u5f00\u53d1\u57fa\u4e8eKD\u7684\u66f4\u591a\u65b9\u6cd5\u5e76\u4e14\u63a2\u7d22\u5982\u4f55\u63d0\u9ad8\u5176\u6027\u80fd\u662f\u672a\u6765\u4e3b\u8981\u7684\u53d1\u5c55\u65b9\u5411\u3002<\/li><li>\u5c3d\u7ba1\u8fd9\u4e9b\u538b\u7f29\u65b9\u6cd5\u53d6\u5f97\u4e86\u5de8\u5927\u7684\u6210\u5c31\uff0c\u4f46\u662f\u9ed1\u7bb1\u673a\u5236\uff08black box mechanism\uff09\u4ecd\u7136\u662f\u5176\u5e94\u7528\u7684\u5173\u952e\u969c\u788d\u3002\u6bd4\u5982\uff0c\u67d0\u4e9b\u795e\u7ecf\u5143\/\u8fde\u63a5\u88ab\u4fee\u526a\u7684\u539f\u56e0\u5c1a\u4e0d\u6e05\u695a\u3002\u63a2\u7d22\u8fd9\u4e9b\u65b9\u6cd5\u7684\u89e3\u91ca\u80fd\u529b\u4ecd\u7136\u662f\u4e00\u4e2a\u91cd\u5927\u6311\u6218\u3002<\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6700\u8fd1\u5728\u505a\u7684yolo\u7f51\u7edc\u786c\u4ef6\u52a0\u901f\u9879\u76ee\uff0c\u9700\u8981\u53bb\u5bf9\u539f\u59cb\u7f51\u7edc\u8fdb\u884c\u538b\u7f29\uff0c\u56e0\u6b64\u8bb0\u5f55\u4e0b\u76f8\u5173\u77e5\u8bc6\uff1a \u76f8\u5173\u7efc\u8ff0\uff1a \u300aA Surv &hellip; <a href=\"http:\/\/139.9.1.231\/index.php\/2022\/09\/09\/model_compress\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u6a21\u578b\u538b\u7f29<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12,26],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/6883"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=6883"}],"version-history":[{"count":19,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/6883\/revisions"}],"predecessor-version":[{"id":7616,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/6883\/revisions\/7616"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=6883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=6883"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=6883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}