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pruning\uff09\uff0c\u5b83\u4ecb\u4e8e\u7ed3\u6784\u5316\u526a\u679d\u548c\u975e\u7ed3\u6784\u5316\u526a\u679d\u4e4b\u95f4\u3002\u5728\u6761\u5e26\u526a\u679d\u4e2d\uff0c\u6211\u4eec\u526a\u6389\u795e\u7ecf\u7f51\u7edc\u4e2d\u8fde\u7eed\u7684\u4e00\u7ec4\u6743\u91cd\uff0c\u5f62\u6210\u4e00\u4e2a\u201c\u6761\u5e26\u201d\u3002\u8fd9\u79cd\u526a\u679d\u65b9\u6cd5\u8bd5\u56fe\u5728\u4fdd\u6301\u4e00\u5b9a\u7a0b\u5ea6\u7684\u89c4\u6574\u6027\uff08\u4ee5\u5b9e\u73b0\u8f83\u597d\u7684\u786c\u4ef6\u53cb\u597d\u6027\uff09\u548c\u7075\u6d3b\u6027\uff08\u4ee5\u5b9e\u73b0\u66f4\u7cbe\u786e\u7684\u526a\u679d\u7b56\u7565\uff09\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff0c\u5728\u4e00\u4e2a\u5377\u79ef\u5c42\u4e2d\uff0c\u53ef\u4ee5\u6cbf\u7740\u5bbd\u5ea6\u3001\u9ad8\u5ea6\u6216\u901a\u9053\u65b9\u5411\u526a\u6389\u4e00\u6574\u6761\u6743\u91cd\u3002\u8fd9\u6837\u505a\u53ef\u4ee5\u51cf\u5c11\u53c2\u6570\u6570\u91cf\uff0c\u540c\u65f6\u4fdd\u6301\u4e00\u5b9a\u7a0b\u5ea6\u7684\u89c4\u6574\u6027\uff0c\u4ece\u800c\u5728\u4e0d\u663e\u8457\u964d\u4f4e\u6027\u80fd\u7684\u60c5\u51b5\u4e0b\u964d\u4f4e\u8ba1\u7b97\u548c\u5b58\u50a8\u9700\u6c42\u3002<\/p>\n\n\n\n<p>\u76f8\u6bd4\u4e8e\u4f20\u7edf\u7684\u6ee4\u6ce2\u5668\u7ea7\u522b\u526a\u679d\u65b9\u6cd5\uff0c\u6761\u5e26\u526a\u679d\u65b9\u6cd5\u53ef\u4ee5\u66f4\u7ec6\u7c92\u5ea6\u5730\u63a7\u5236\u526a\u679d\u7a0b\u5ea6\uff0c\u5e76\u4e14\u53ef\u4ee5\u51cf\u5c11\u5bf9\u6a21\u578b\u6027\u80fd\u7684\u5f71\u54cd\uff0c\u540c\u65f6\u8fd8\u53ef\u4ee5\u63d0\u9ad8\u526a\u679d\u540e\u6a21\u578b\u7684\u7a00\u758f\u6027\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u6761\u5e26\u526a\u679d\u76f8\u5bf9\u4e8e\u7ed3\u6784\u5316\u526a\u679d\u548c\u975e\u7ed3\u6784\u5316\u526a\u679d\u6765\u8bf4\uff0c\u53ef\u80fd\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u8f83\u5c11\u88ab\u4f7f\u7528\u3002\u7ed3\u6784\u5316\u526a\u679d\u548c\u975e\u7ed3\u6784\u5316\u526a\u679d\u5df2\u7ecf\u5728\u8bb8\u591a\u573a\u666f\u4e2d\u53d6\u5f97\u4e86\u826f\u597d\u7684\u6027\u80fd\u548c\u538b\u7f29\u6548\u679c\u3002\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u5c06\u6761\u5e26\u526a\u679d\u4e0e\u5176\u4ed6\u526a\u679d\u65b9\u6cd5\u7ed3\u5408\u4f7f\u7528\uff0c\u4ee5\u8fdb\u4e00\u6b65\u4f18\u5316\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n\n\n\n<h3>2.2 \u4f4e\u79e9\u5206\u89e3<\/h3>\n\n\n\n<p>\u4f20\u7edf\u7684\u4f4e\u79e9\u5206\u89e3\u662f\u6307\u5c06\u4e00\u4e2a\u77e9\u9635\u5206\u89e3\u4e3a\u4e24\u4e2a\u4f4e\u79e9\u77e9\u9635\u7684\u4e58\u79ef\uff0c\u5176\u4e2d\u8fd9\u4e24\u4e2a\u4f4e\u79e9\u77e9\u9635\u7684\u79e9\u8fdc\u8fdc\u5c0f\u4e8e\u539f\u59cb\u77e9\u9635\u7684\u79e9\u3002\u8fd9\u79cd\u5206\u89e3\u53ef\u4ee5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u538b\u7f29\u6570\u636e\uff0c\u964d\u4f4e\u5b58\u50a8\u548c\u8ba1\u7b97\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n<p>\u8fd9\u79cd\u65b9\u6cd5\u5c06\u4e00\u4e2a\u5927\u578b\u7684\u77e9\u9635\u6216\u8005\u5f20\u91cf\u5206\u89e3\u6210\u591a\u4e2a\u5c0f\u578b\u7684\u4f4e\u79e9\u77e9\u9635\u7684\u4e58\u79ef\uff0c\u4ece\u800c\u53ef\u4ee5\u964d\u4f4e\u6570\u636e\u7684\u590d\u6742\u6027\u548c\u5b58\u50a8\u7a7a\u95f4\u9700\u6c42\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5047\u8bbe\u6709\u4e00\u4e2a\u6570\u636e\u77e9\u9635X\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5206\u89e3\u6210\u4e24\u4e2a\u5c0f\u578b\u7684\u77e9\u9635U\u548cV\u7684\u4e58\u79ef\uff0c\u5373X=UV\uff0c\u6765\u8868\u793aX\u3002\u5176\u4e2dU\u4e3am*k\u7684\u77e9\u9635\uff0cV\u4e3ak*n\u7684\u77e9\u9635\uff0ck\u901a\u5e38\u6bd4m\u548cn\u8981\u5c0f\u5f88\u591a\u3002\u7531\u4e8eU\u548cV\u7684\u79e9\u90fd\u6bd4X\u7684\u79e9\u8981\u4f4e\uff0c\u56e0\u6b64\u53ef\u4ee5\u7528\u66f4\u5c11\u7684\u7a7a\u95f4\u5b58\u50a8\u5b83\u4eec\uff0c\u5e76\u4e14\u4f7f\u7528\u5b83\u4eec\u8fdb\u884c\u8ba1\u7b97\u7684\u901f\u5ea6\u4e5f\u66f4\u5feb\u3002\u53e6\u5916\uff0c\u77e9\u9635\u5206\u89e3\u4e5f\u53ef\u4ee5\u7528\u4e8e\u7279\u5f81\u63d0\u53d6\u3001\u6570\u636e\u964d\u7ef4\u7b49\u4efb\u52a1\u4e2d\u3002<\/p>\n\n\n\n<h3>2.3 \u91cf\u5316<\/h3>\n\n\n\n<p>\u91cf\u5316\u6280\u672f\u662f\u6307\u5c06\u8fde\u7eed\u7684\u6570\u503c\u6216\u4fe1\u53f7\u8f6c\u6362\u4e3a\u79bb\u6563\u7684\u6570\u503c\u6216\u4fe1\u53f7\u7684\u8fc7\u7a0b\u3002\u5728\u673a\u5668\u5b66\u4e60\u548c\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u4e2d\uff0c\u91cf\u5316\u901a\u5e38\u7528\u4e8e\u51cf\u5c11\u795e\u7ecf\u7f51\u7edc\u4e2d\u53c2\u6570\u7684\u4f4d\u6570\u548c\u7cbe\u5ea6\uff0c\u4ee5\u964d\u4f4e\u6a21\u578b\u7684\u5b58\u50a8\u548c\u8ba1\u7b97\u5f00\u9500\u3002\u901a\u8fc7\u5c06\u53c2\u6570\u91cf\u5316\u4e3a\u8f83\u4f4e\u4f4d\u6570\u7684\u6574\u6570\u6216\u6d6e\u70b9\u6570\uff0c\u53ef\u4ee5\u5927\u5e45\u51cf\u5c0f\u6a21\u578b\u7684\u5927\u5c0f\u5e76\u63d0\u9ad8\u6a21\u578b\u5728\u79fb\u52a8\u8bbe\u5907\u7b49\u8d44\u6e90\u6709\u9650\u7684\u73af\u5883\u4e0b\u7684\u6027\u80fd\u3002\u540c\u65f6\uff0c\u91cf\u5316\u6280\u672f\u4e5f\u53ef\u4ee5\u7528\u4e8e\u964d\u4f4e\u795e\u7ecf\u7f51\u7edc\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u7684\u529f\u8017\u548c\u5ef6\u8fdf\uff0c\u4ece\u800c\u63d0\u9ad8\u6a21\u578b\u7684\u8fd0\u884c\u901f\u5ea6\u3002\u91cf\u5316\u6280\u672f\u662f\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u6280\u672f\uff0c\u5728\u5f88\u591a\u5b9e\u9645\u5e94\u7528\u4e2d\u5177\u6709\u5f88\u9ad8\u7684\u5b9e\u7528\u4ef7\u503c\u3002<\/p>\n\n\n\n<p>\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u91cf\u5316\u6307\u7684\u662f\u5c06\u6a21\u578b\u4e2d\u7684\u6d6e\u70b9\u6570\u53c2\u6570\u8f6c\u6362\u4e3a\u66f4\u5c0f\u7684\u6574\u6570\u6216\u56fa\u5b9a\u4f4d\u5bbd\u7684\u6570\u5b57\uff0c\u4ee5\u4fbf\u4e8e\u5b58\u50a8\u548c\u8ba1\u7b97\u3002\u8fd9\u901a\u5e38\u53ef\u4ee5\u901a\u8fc7\u51cf\u5c11\u6a21\u578b\u4e2d\u53c2\u6570\u7684\u4f4d\u6570\u6765\u5b9e\u73b0\uff0c\u4ece\u800c\u964d\u4f4e\u5185\u5b58\u548c\u8ba1\u7b97\u5f00\u9500\uff0c\u5e76\u63d0\u9ad8\u63a8\u7406\u901f\u5ea6\u3002\u91cf\u5316\u6280\u672f\u53ef\u80fd\u4f1a\u5bf9\u6a21\u578b\u7684\u7cbe\u5ea6\u9020\u6210\u4e00\u5b9a\u7684\u5f71\u54cd\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u53c2\u6570\u7684\u7cbe\u5ea6\u3002<\/p>\n\n\n\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6a21\u578b\u7684\u53c2\u6570\u901a\u5e38\u662fFP32\u5355\u7cbe\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6574\u6570\u3001FP16\u3001TF32\u3001MPT\u7b49\u4ee3\u66ff\u3002<\/p>\n\n\n\n<h4>2.3.1 INT<\/h4>\n\n\n\n<p>PyTorch\u4e2d\u7684Quantized Tensor\u53ef\u4ee5\u5b58\u50a8 int8\/uint8\u7b49\u7c7b\u578b\u7684\u6570\u636e\u3002<\/p>\n\n\n\n<p>\u6570\u636e\u7c7b\u578b\uff1a<\/p>\n\n\n\n<ul>\n<li>weight\u76848 bit\u91cf\u5316 \uff1adata_type = qint8\uff0c\u6570\u636e\u8303\u56f4\u4e3a[-128, 127]<\/li>\n\n\n\n<li>activation\u76848 bit\u91cf\u5316\uff1adata_type = quint8\uff0c\u6570\u636e\u8303\u56f4\u4e3a[0, 255]<\/li>\n<\/ul>\n\n\n\n<p>\u540c\u65f6\uff0c\u4e5f\u6709\u8bb8\u591a\u4e13\u7528\u4e8e\u6574\u6570\u7cbe\u5ea6\u8ba1\u7b97\u7684\u786c\u4ef6\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"990\" height=\"147\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/image-20230327171302383.png\" alt=\"\" class=\"wp-image-647\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171302383.png 990w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171302383-300x45.png 300w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171302383-768x114.png 768w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171302383-769x114.png 769w\" sizes=\"(max-width: 990px) 100vw, 990px\" \/><\/figure>\n\n\n\n<p>\u4e0d\u8fc7\uff0c\u5728\u8bad\u7ec3\u7684\u524d\u671f\uff0c\u901a\u5e38\u4e0d\u4f7f\u7528INT8\/UINT8\u7cbe\u5ea6\uff0c\u56e0\u4e3a\u8fd9\u53ef\u80fd\u4f1a\u635f\u5bb3\u6a21\u578b\u7684\u8d28\u91cf\u548c\u8868\u73b0\u3002\u4f46\u662f\uff0c\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u5f53\u6a21\u578b\u8fbe\u5230\u4e00\u5b9a\u7684\u51c6\u786e\u5ea6\u548c\u7a33\u5b9a\u6027\u65f6\uff0c\u53ef\u4ee5\u8003\u8651\u901a\u8fc7\u91cf\u5316\u6280\u672f\u5c06FP32\u6743\u91cd\u538b\u7f29\u4e3aINT8\/UINT8\u683c\u5f0f\uff0c\u4f7f\u7528\u4f4e\u7cbe\u5ea6\u7684\u6574\u6570\u8fd0\u7b97\u6765\u52a0\u901f\u6a21\u578b\u7684\u63a8\u65ad\u548c\u90e8\u7f72\u3002<\/p>\n\n\n\n<h4>2.3.2 FP16<\/h4>\n\n\n\n<p>\u534a\u7cbe\u5ea6\u6d6e\u70b9\uff08FP16\uff09\u8bad\u7ec3\uff1a\u8fd9\u79cd\u65b9\u6cd5\u901a\u8fc7\u5c06\u6743\u91cd\u548c\u6fc0\u6d3b\u503c\u4ece32\u4f4d\u6d6e\u70b9\u6570\uff08FP32\uff09\u964d\u4f4e\u523016\u4f4d\u6d6e\u70b9\u6570\uff08FP16\uff09\u6765\u51cf\u5c11\u5b58\u50a8\u548c\u8ba1\u7b97\u9700\u6c42\u3002\u534a\u7cbe\u5ea6\u6d6e\u70b9\u8bad\u7ec3\u53ef\u4ee5\u5728\u652f\u6301FP16\u8ba1\u7b97\u7684\u786c\u4ef6\u4e0a\u63d0\u9ad8\u8bad\u7ec3\u901f\u5ea6\uff0c\u5e76\u964d\u4f4e\u5185\u5b58\u6d88\u8017\u3002<\/p>\n\n\n\n<p>NVIDIA 20\u7cfbTuring\u67b6\u6784\u4e4b\u524d\uff0cGPU\u7684\u5355\u7cbe\u5ea6\u3001\u534a\u7cbe\u5ea6\u8ba1\u7b97\u901f\u5ea6\u4e00\u6837\uff0c\u5355Turing\u67b6\u6784\u53ca\u4e4b\u540e\uff0c\u534a\u7cbe\u5ea6\u8ba1\u7b97\u901f\u5ea6\u4e00\u822c\u90fd\u662f\u5355\u7cbe\u5ea6\u8ba1\u7b97\u7684\u6570\u500d\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"80\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/image-20230327171912276-1024x80.png\" alt=\"\" class=\"wp-image-648\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171912276-1024x80.png 1024w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171912276-300x23.png 300w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171912276-768x60.png 768w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171912276-1536x119.png 1536w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171912276-769x60.png 769w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327171912276.png 1659w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u4f7f\u7528FP16\u76f8\u5bf9\u4e8eFP32\u53ef\u80fd\u5e26\u6765\u4ee5\u4e0b\u5f71\u54cd\uff1a<\/p>\n\n\n\n<ol>\n<li>\u51cf\u5c11\u663e\u5b58\u5360\u7528\uff1a\u7531\u4e8eFP16\u6570\u636e\u7c7b\u578b\u7684\u5c3a\u5bf8\u6bd4FP32\u5c0f\u4e00\u534a\uff0c\u56e0\u6b64\u4f7f\u7528FP16\u53ef\u4ee5\u51cf\u5c11\u6a21\u578b\u548c\u68af\u5ea6\u5f20\u91cf\u7684\u663e\u5b58\u5360\u7528\u3002\u8fd9\u53ef\u4ee5\u4f7f\u5f97\u66f4\u5927\u7684\u6a21\u578b\u80fd\u591f\u5728\u76f8\u540c\u7684\u8bbe\u5907\u4e0a\u8fdb\u884c\u8bad\u7ec3\uff0c\u5e76\u4e14\u53ef\u4ee5\u63d0\u9ad8GPU\u5e76\u884c\u8ba1\u7b97\u7684\u6548\u7387\u3002<\/li>\n\n\n\n<li>\u52a0\u901f\u8bad\u7ec3\uff1a\u7531\u4e8eFP16\u7684\u8ba1\u7b97\u901f\u5ea6\u66f4\u5feb\uff0c\u56e0\u6b64\u4f7f\u7528FP16\u53ef\u4ee5\u52a0\u901f\u6a21\u578b\u7684\u8bad\u7ec3\u3002\u8fd9\u662f\u56e0\u4e3a\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u5927\u91cf\u7684\u8ba1\u7b97\u90fd\u662f\u77e9\u9635\u4e58\u6cd5\u8fd0\u7b97\uff0c\u800cGPU\u5bf9FP16\u7684\u77e9\u9635\u4e58\u6cd5\u8fd0\u7b97\u652f\u6301\u5f97\u66f4\u597d\uff0c\u53ef\u4ee5\u5b9e\u73b0\u66f4\u9ad8\u7684\u5e76\u884c\u5ea6\uff0c\u4ece\u800c\u63d0\u9ad8\u8bad\u7ec3\u901f\u5ea6\u3002<\/li>\n\n\n\n<li>\u53ef\u80fd\u5bfc\u81f4\u6570\u503c\u4e0d\u7a33\u5b9a\uff1aFP16\u5bf9\u4e8e\u975e\u5e38\u5c0f\u6216\u975e\u5e38\u5927\u7684\u6570\u503c\uff0c\u7cbe\u5ea6\u53ef\u80fd\u4f1a\u53d7\u5230\u5f71\u54cd\uff0c\u4ece\u800c\u5bfc\u81f4\u6570\u503c\u4e0d\u7a33\u5b9a\u7684\u95ee\u9898\u3002\u8fd9\u53ef\u80fd\u4f1a\u5bf9\u4f18\u5316\u5668\u7684\u6027\u80fd\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\uff0c\u5e76\u4e14\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u53ef\u80fd\u4f1a\u51fa\u73b0NaN\u6216Inf\u7b49\u5f02\u5e38\u60c5\u51b5\u3002<\/li>\n\n\n\n<li>\u53ef\u80fd\u964d\u4f4e\u6a21\u578b\u7684\u7cbe\u5ea6\uff1a\u7531\u4e8eFP16\u7684\u7cbe\u5ea6\u8f83\u4f4e\uff0c\u5f53\u6a21\u578b\u7684\u53c2\u6570\u6216\u68af\u5ea6\u5177\u6709\u8f83\u5927\u7684\u8303\u56f4\u65f6\uff0c\u4f7f\u7528FP16\u53ef\u80fd\u4f1a\u5bfc\u81f4\u7cbe\u5ea6\u635f\u5931\uff0c\u5e76\u4e14\u53ef\u80fd\u4f1a\u964d\u4f4e\u6a21\u578b\u7684\u51c6\u786e\u6027\u3002<\/li>\n<\/ol>\n\n\n\n<h4>2.3.3 TF32<\/h4>\n\n\n\n<p>Tensor Float 32\uff08TF32\uff09\u662f\u4e00\u79cd\u65b0\u7684\u6d6e\u70b9\u6570\u683c\u5f0f\uff0c\u7531NVIDIA\u5728\u5176\u6700\u65b0\u7684Ampere\u67b6\u6784\u4e2d\u5f15\u5165\u3002TF32 \u662f\u4e00\u79cd\u622a\u77ed\u7684 Float32 \u6570\u636e\u683c\u5f0f\uff0c\u5c06 FP32 \u4e2d 23 \u4e2a\u5c3e\u6570\u4f4d\u622a\u77ed\u4e3a 10 bits\uff0c\u800c\u6307\u6570\u4f4d\u4ecd\u4e3a 8 bits\uff0c\u603b\u957f\u5ea6\u4e3a 19 (=1 + 8 + 10) bits\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/developer.nvidia.com\/blog\/wp-content\/uploads\/2020\/07\/numerical-formats-supported-by-ampere-gpus-1.png\" alt=\"Numerical formats supported by Ampere GPUs include FP32, TF32, FP16, and BF16.\"\/><\/figure>\n\n\n\n<p>TF32 \u53ef\u4ee5\u5b9e\u73b0\u4e0e FP16 \u76f8\u540c\u7684\u8ba1\u7b97\u901f\u5ea6\uff0c\u540c\u65f6\u5bf9\u8ba1\u7b97\u7ed3\u679c\u7684\u5f71\u54cd\u4e0e FP32 \u51e0\u4e4e\u6ca1\u6709\u53d8\u5316\u3002<\/p>\n\n\n\n<h4>2.3.4 MPT<\/h4>\n\n\n\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u7ecf\u5e38\u9762\u4e34FP32\u8ba1\u7b97\u901f\u5ea6\u8fc7\u6162\uff0c\u800cFP16\u53c8\u53ef\u80fd\u56e0\u4e3a\u7cbe\u5ea6\u4e0d\u8db3\u5e26\u6765\u6570\u636e\u6ea2\u51fa\u95ee\u9898\u548c\u820d\u5165\u8bef\u5dee\u7b49\u95ee\u9898\u3002\u6df7\u5408\u7cbe\u5ea6\u8bad\u7ec3MPT\uff08Mixed Precision Training\uff09\u662f\u4e00\u79cd\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u65b9\u6cd5\uff0c\u5229\u7528\u534a\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff0816\u4f4d\uff09\u52a0\u901f\u6a21\u578b\u8bad\u7ec3\u8fc7\u7a0b\u3002\u5728\u6df7\u5408\u7cbe\u5ea6\u8bad\u7ec3\u4e2d\uff0c\u7f51\u7edc\u6743\u91cd\u548c\u68af\u5ea6\u4f7f\u7528\u534a\u7cbe\u5ea6\u6d6e\u70b9\u6570\u6765\u8ba1\u7b97\uff0c\u800c\u6240\u6709\u7684\u7d2f\u79ef\u64cd\u4f5c\u548c\u53c2\u6570\u66f4\u65b0\u5219\u4f7f\u7528\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff0832\u4f4d\uff09\u8fdb\u884c\u8ba1\u7b97\u3002<\/p>\n\n\n\n<h3>2.4 \u77e5\u8bc6\u84b8\u998f<\/h3>\n\n\n\n<p>\u77e5\u8bc6\u84b8\u998f\u662f\u4e00\u79cd\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u8f7b\u91cf\u5316\u65b9\u6cd5\uff0c\u65e8\u5728\u901a\u8fc7\u5c06\u4e00\u4e2a\u5927\u578b\u6559\u5e08\u6a21\u578b\u7684\u77e5\u8bc6\u8fc1\u79fb\u5230\u4e00\u4e2a\u8f83\u5c0f\u7684\u5b66\u751f\u6a21\u578b\uff0c\u4ece\u800c\u5b9e\u73b0\u5728\u4fdd\u6301\u8f83\u9ad8\u6027\u80fd\u7684\u540c\u65f6\u51cf\u5c0f\u6a21\u578b\u5927\u5c0f\u548c\u8ba1\u7b97\u590d\u6742\u5ea6\u3002\u77e5\u8bc6\u84b8\u998f\u7684\u57fa\u672c\u539f\u7406\u662f\u8ba9\u5b66\u751f\u6a21\u578b\u5b66\u4e60\u6559\u5e08\u6a21\u578b\u7684\u8f93\u51fa\u5206\u5e03\uff0c\u4ece\u800c\u5438\u6536\u6559\u5e08\u6a21\u578b\u7684\u77e5\u8bc6\u3002<\/p>\n\n\n\n<p>\u77e5\u8bc6\u84b8\u998f\u7684\u8fc7\u7a0b\u4e3b\u8981\u5305\u62ec\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"567\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/image-20230327174112347-1024x567.png\" alt=\"\" class=\"wp-image-649\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327174112347-1024x567.png 1024w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327174112347-300x166.png 300w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327174112347-768x425.png 768w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327174112347-769x426.png 769w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/image-20230327174112347.png 1273w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h3>2.5 \u7d27\u51d1\u7f51\u7edc\u67b6\u6784<\/h3>\n\n\n\n<p>\u7d27\u51d1\u7f51\u7edc\u67b6\u6784\u662f\u4e00\u79cd\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u8f7b\u91cf\u5316\u65b9\u6cd5\uff0c\u65e8\u5728\u901a\u8fc7\u8bbe\u8ba1\u66f4\u9ad8\u6548\u7684\u7f51\u7edc\u7ed3\u6784\u6765\u964d\u4f4e\u6a21\u578b\u590d\u6742\u5ea6\uff0c\u4ece\u800c\u5b9e\u73b0\u5728\u4fdd\u6301\u8f83\u9ad8\u6027\u80fd\u7684\u540c\u65f6\u51cf\u5c0f\u6a21\u578b\u5927\u5c0f\u548c\u8ba1\u7b97\u590d\u6742\u5ea6\u3002\u7d27\u51d1\u7f51\u7edc\u67b6\u6784\u7684\u57fa\u672c\u539f\u7406\u662f\u5229\u7528\u66f4\u5c11\u7684\u53c2\u6570\u548c\u8ba1\u7b97\u91cf\u6765\u5b9e\u73b0\u540c\u7b49\u751a\u81f3\u66f4\u9ad8\u7684\u6027\u80fd\u3002<\/p>\n\n\n\n<p>\u5728\u7d27\u51d1\u7f51\u7edc\u67b6\u6784\u4e2d\uff0c\u6211\u9996\u5148\u60f3\u5230\u5728\u7ade\u8d5b\u4e2d\u6700\u7ecf\u5e38\u7528\u5230\u7684CNN\u6a21\u578b\u2014\u2014EfficientNet\u3002EfficientNet\u662f\u4e00\u79cd\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u56fe\u50cf\u5206\u7c7b\u6a21\u578b\uff0c\u7531\u8c37\u6b4c\u7684\u7814\u7a76\u56e2\u961f\u57282019\u5e74\u63d0\u51fa\u3002EfficientNet\u662f\u901a\u8fc7\u5728\u6a21\u578b\u7684\u5bbd\u5ea6\u3001\u6df1\u5ea6\u548c\u5206\u8fa8\u7387\u65b9\u9762\u8fdb\u884c\u4e86\u4e00\u79cd\u79f0\u4e3aCompound Scaling\uff08\u590d\u5408\u7f29\u653e\uff09\u7684\u4f18\u5316\u800c\u8bbe\u8ba1\u51fa\u6765\u7684\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic2.zhimg.com\/v2-cd04fea5dd2039d7ed31f1b60af54132_b.jpg\" alt=\"EfficientNet-\u53ef\u80fd\u662f\u8fc4\u4eca\u4e3a\u6b62\u6700\u597d\u7684CNN\u7f51\u7edc - \u77e5\u4e4e\"\/><\/figure>\n\n\n\n<p>\u5177\u4f53\u6765\u8bf4\uff0cCompound Scaling\uff08\u590d\u5408\u7f29\u653e\uff09\u5305\u62ec\u4ee5\u4e0b\u4e09\u4e2a\u65b9\u9762\uff1a<\/p>\n\n\n\n<ol>\n<li>\u7f51\u7edc\u6df1\u5ea6\uff1a\u5373\u7f51\u7edc\u5c42\u6570\uff0c\u6df1\u5ea6\u8d8a\u5927\uff0c\u7f51\u7edc\u7684\u8868\u793a\u80fd\u529b\u8d8a\u5f3a\u3002\u901a\u5e38\uff0c\u589e\u52a0\u7f51\u7edc\u7684\u6df1\u5ea6\u53ef\u4ee5\u5e2e\u52a9\u6a21\u578b\u6355\u6349\u66f4\u591a\u7684\u62bd\u8c61\u5c42\u6b21\u7279\u5f81\uff0c\u4ece\u800c\u63d0\u9ad8\u6027\u80fd\u3002\u7136\u800c\uff0c\u8fc7\u6df1\u7684\u7f51\u7edc\u53ef\u80fd\u5bfc\u81f4\u68af\u5ea6\u6d88\u5931\u6216\u7206\u70b8\u95ee\u9898\uff0c\u4ee5\u53ca\u8fc7\u62df\u5408\u73b0\u8c61\u3002<\/li>\n\n\n\n<li>\u7f51\u7edc\u5bbd\u5ea6\uff1a\u5373\u6bcf\u5c42\u7f51\u7edc\u4e2d\u7684\u901a\u9053\u6570\u6216\u795e\u7ecf\u5143\u6570\u91cf\u3002\u589e\u52a0\u7f51\u7edc\u7684\u5bbd\u5ea6\u53ef\u4ee5\u63d0\u9ad8\u6a21\u578b\u7684\u5bb9\u91cf\uff0c\u6709\u52a9\u4e8e\u5b66\u4e60\u66f4\u591a\u7684\u7279\u5f81\u8868\u793a\u3002\u4f46\u8fc7\u5bbd\u7684\u7f51\u7edc\u53ef\u80fd\u5bfc\u81f4\u8ba1\u7b97\u8d44\u6e90\u7684\u6d6a\u8d39\uff0c\u4ee5\u53ca\u8bad\u7ec3\u548c\u63a8\u7406\u901f\u5ea6\u7684\u964d\u4f4e\u3002<\/li>\n\n\n\n<li>\u8f93\u5165\u5206\u8fa8\u7387\uff1a\u5373\u8f93\u5165\u56fe\u50cf\u7684\u5c3a\u5bf8\uff0c\u5206\u8fa8\u7387\u8d8a\u9ad8\uff0c\u56fe\u50cf\u4e2d\u7684\u4fe1\u606f\u8d8a\u4e30\u5bcc\u3002\u901a\u5e38\uff0c\u589e\u52a0\u8f93\u5165\u5206\u8fa8\u7387\u53ef\u4ee5\u5e2e\u52a9\u6a21\u578b\u6355\u6349\u66f4\u591a\u7684\u7ec6\u8282\u4fe1\u606f\u3002\u7136\u800c\uff0c\u8fc7\u9ad8\u7684\u5206\u8fa8\u7387\u4f1a\u589e\u52a0\u8ba1\u7b97\u590d\u6742\u5ea6\u548c\u5185\u5b58\u6d88\u8017\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u590d\u5408\u7f29\u653e\u901a\u8fc7\u5728\u8fd9\u4e09\u4e2a\u7ef4\u5ea6\u4e0a\u540c\u65f6\u8fdb\u884c\u5e73\u8861\u7684\u7f29\u653e\uff0c\u4f7f\u5f97\u7f51\u7edc\u5728\u4fdd\u6301\u8f83\u4f4e\u8ba1\u7b97\u590d\u6742\u5ea6\u548c\u53c2\u6570\u6570\u91cf\u7684\u540c\u65f6\uff0c\u5b9e\u73b0\u4e86\u9ad8\u6548\u7684\u6027\u80fd\u8868\u73b0\u3002\u5728EfficientNet\u7684\u8bbe\u8ba1\u8fc7\u7a0b\u4e2d\uff0c\u7814\u7a76\u8005\u4eec\u901a\u8fc7\u7cfb\u7edf\u5730\u7814\u7a76\u4e0d\u540c\u7f29\u653e\u6bd4\u4f8b\u5bf9\u6027\u80fd\u7684\u5f71\u54cd\uff0c\u627e\u5230\u4e86\u4e00\u79cd\u6700\u4f73\u7684\u590d\u5408\u7f29\u653e\u7b56\u7565\u3002\u8fd9\u4f7f\u5f97EfficientNet\u5728\u5404\u79cd\u56fe\u50cf\u5206\u7c7b\u4efb\u52a1\u4e2d\u8868\u73b0\u51fa\u8272\uff0c\u540c\u65f6\u5177\u5907\u8f83\u9ad8\u7684\u53c2\u6570\u548c\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n\n\n\n<h3>2.6 \u7a00\u758f\u6027<\/h3>\n\n\n\n<p>\u7a00\u758f\u6027\u662f\u6307\u5728\u6a21\u578b\u4e2d\u5b58\u5728\u5927\u91cf\u7684\u96f6\u503c\u6216\u63a5\u8fd1\u96f6\u503c\u7684\u53c2\u6570\uff0c\u901a\u8fc7\u5229\u7528\u8fd9\u4e9b\u7a00\u758f\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u51cf\u5c11\u6a21\u578b\u7684\u53c2\u6570\u6570\u91cf\uff0c\u4ece\u800c\u8fbe\u5230\u8f7b\u91cf\u5316\u7684\u76ee\u7684\u3002\u7a00\u758f\u6027\u53ef\u4ee5\u4ece\u539f\u59cb\u57df\u6216\u53d8\u6362\u57df\u4e2d\u8ba1\u7b97\u5f97\u51fa\uff0c\u8fdb\u4e00\u6b65\u5e2e\u52a9\u6211\u4eec\u8bc6\u522b\u5e76\u53bb\u9664\u5197\u4f59\u6216\u65e0\u5173\u7684\u53c2\u6570\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"720\" height=\"511\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/475ea1fdfe5ed07868b1e5781526de87_b.png\" alt=\"\" class=\"wp-image-650\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/475ea1fdfe5ed07868b1e5781526de87_b.png 720w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/475ea1fdfe5ed07868b1e5781526de87_b-300x213.png 300w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<h4>2.6.1 \u539f\u59cb\u57df\u7a00\u758f\u6027<\/h4>\n\n\n\n<p>\u539f\u59cb\u57df\u7a00\u758f\u6027\u662f\u6307\u5728\u6a21\u578b\u53c2\u6570\u7684\u539f\u59cb\u8868\u793a\u4e2d\u5b58\u5728\u7a00\u758f\u6027\u3002\u4f8b\u5982\uff0c\u6743\u91cd\u77e9\u9635\u4e2d\u53ef\u80fd\u5b58\u5728\u5927\u91cf\u7684\u96f6\u503c\u6216\u63a5\u8fd1\u96f6\u503c\u7684\u5143\u7d20\u3002\u901a\u8fc7\u8bc6\u522b\u5e76\u5254\u9664\u8fd9\u4e9b\u65e0\u5173\u7d27\u8981\u7684\u53c2\u6570\uff0c\u53ef\u4ee5\u51cf\u5c11\u6a21\u578b\u7684\u5b58\u50a8\u548c\u8ba1\u7b97\u8d1f\u62c5\u3002\u539f\u59cb\u57df\u7a00\u758f\u6027\u7684\u5b9e\u73b0\u65b9\u6cd5\u5305\u62ec\u6743\u91cd\u526a\u679d\u3001\u6b63\u5219\u5316\u65b9\u6cd5\u7b49\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u5229\u7528\u539f\u59cb\u57df\u7a00\u758f\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u8bad\u7ec3\u671f\u95f4\u5c06\u6743\u91cd\u77e9\u9635\u8fdb\u884c\u7a00\u758f\u5316\u3002<\/p>\n\n\n\n<ol>\n<li>\u9996\u5148\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7a00\u758f\u77e9\u9635\u8868\u793a\u6743\u91cd\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ea\u5b58\u50a8\u975e\u96f6\u6743\u91cd\u503c\uff0c\u800c\u4e0d\u662f\u5b58\u50a8\u6574\u4e2a\u6743\u91cd\u77e9\u9635\u3002\u8fd9\u53ef\u4ee5\u5927\u5927\u51cf\u5c11\u6a21\u578b\u7684\u5927\u5c0f\u3002<\/li>\n\n\n\n<li>\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5f15\u5165L1\u6b63\u5219\u5316\u6216\u8005\u5176\u4ed6\u7a00\u758f\u6027\u60e9\u7f5a\u9879\u6765\u9f13\u52b1\u6a21\u578b\u5b66\u4e60\u7a00\u758f\u7684\u6743\u91cd\u3002\u901a\u8fc7\u5bf9\u6743\u91cd\u65bd\u52a0\u7a00\u758f\u6027\u7ea6\u675f\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u8bad\u7ec3\u671f\u95f4\u9010\u6b65\u6d88\u9664\u4e0d\u91cd\u8981\u7684\u8fde\u63a5\uff0c\u4ece\u800c\u51cf\u5c11\u6a21\u578b\u7684\u8ba1\u7b97\u590d\u6742\u6027\u3002<\/li>\n\n\n\n<li>\u4e3a\u4e86\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e13\u95e8\u9488\u5bf9\u7a00\u758f\u77e9\u9635\u64cd\u4f5c\u7684\u7b97\u6cd5\u548c\u5e93\uff0c\u4f8b\u5982SparseConvNet\u6216Intel MKL\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<h4>2.6.2 \u53d8\u6362\u57df\u7a00\u758f\u6027<\/h4>\n\n\n\n<p>\u53d8\u6362\u57df\u7a00\u758f\u6027\u662f\u6307\u5c06\u6a21\u578b\u53c2\u6570\u4ece\u539f\u59cb\u57df\u8f6c\u6362\u5230\u53e6\u4e00\u4e2a\u57df\uff0c\u4ee5\u4fbf\u5728\u8be5\u57df\u4e2d\u66f4\u5bb9\u6613\u5730\u8bc6\u522b\u7a00\u758f\u6027\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u5c06\u6743\u91cd\u77e9\u9635\u8f6c\u6362\u4e3a\u9891\u7387\u57df\uff08\u5982\u5085\u91cc\u53f6\u53d8\u6362\u6216\u5c0f\u6ce2\u53d8\u6362\uff09\uff0c\u5728\u9891\u7387\u57df\u4e2d\u66f4\u5bb9\u6613\u53d1\u73b0\u7a00\u758f\u6027\u3002\u7136\u540e\u53ef\u4ee5\u901a\u8fc7\u9608\u503c\u65b9\u6cd5\u6216\u5176\u4ed6\u6280\u672f\u53bb\u9664\u4e0d\u91cd\u8981\u7684\u53c2\u6570\uff0c\u518d\u5c06\u5269\u4f59\u53c2\u6570\u8f6c\u6362\u56de\u539f\u59cb\u57df\u3002\u8fd9\u6837\u53ef\u4ee5\u5728\u4e0d\u635f\u5931\u6a21\u578b\u6027\u80fd\u7684\u60c5\u51b5\u4e0b\uff0c\u5b9e\u73b0\u6a21\u578b\u53c2\u6570\u7684\u538b\u7f29\u3002<\/p>\n\n\n\n<h5>\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362DFT<\/h5>\n\n\n\n<p>DFT (\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362) \u516c\u5f0f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>X[k]=\\sum_{n=0}^{N-1} x[n] \\cdot e^{-j \\frac{2 \\pi n k}{N}}<\/pre><\/div>\n\n\n\n<p>IDFT (\u9006\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362) \u516c\u5f0f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x[n]=\\frac{1}{N} \\sum_{k=0}^{N-1} X[k] \\cdot e^{j \\frac{2 \\pi n k}{N}}<\/pre><\/div>\n\n\n\n<p>\u4f18\u70b9\uff1a\u65f6\u57df\u4fe1\u606f-&gt;\u9891\u57df\u4fe1\u606f<\/p>\n\n\n\n<p>\u7f3a\u70b9\uff1a\u53ea\u80fd\u83b7\u53d6<strong>\u4e00<\/strong>\u6bb5\u4fe1\u53f7\u603b\u4f53\u4e0a\u5305\u542b\u54ea\u4e9b\u9891\u7387\u7684\u6210\u5206\uff0c\u4f46\u662f\u5bf9\u5404<strong>\u6210\u5206\u51fa\u73b0\u7684\u65f6\u523b\u5e76\u65e0\u6240\u77e5<\/strong>\u3002\u56e0\u6b64\u65f6\u57df\u76f8\u5dee\u5f88\u5927\u7684\u4e24\u4e2a\u4fe1\u53f7\uff0c\u53ef\u80fd\u9891\u8c31\u56fe\u4e00\u6837\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"690\" height=\"612\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/def600cea95fa10e3872e88dc8059d6c_720w.webp\" alt=\"\" class=\"wp-image-652\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/def600cea95fa10e3872e88dc8059d6c_720w.webp 690w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/def600cea95fa10e3872e88dc8059d6c_720w-300x266.webp 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/figure>\n\n\n\n<h5>\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362STFT<\/h5>\n\n\n\n<p>STFT\u4e3a\u4e86\u5728\u9891\u57df\u4e2d\u8868\u73b0\u51fa\u6210\u5206\u51fa\u73b0\u7684\u65f6\u523b\uff0c\u5728\u5bf9\u539f\u59cb\u4fe1\u53f7\u8fdb\u884cDFT\u4e4b\u524d\u5148\u8fdb\u884c\u56fa\u5b9a\u65f6\u95f4\u95f4\u9694\u7684\u65f6\u57df\u5206\u5272\u3002\u7a84\u7a97\u53e3\u65f6\u95f4\u5206\u8fa8\u7387\u9ad8\u3001\u9891\u7387\u5206\u8fa8\u7387\u4f4e\uff0c\u5bbd\u7a97\u53e3\u65f6\u95f4\u5206\u8fa8\u7387\u4f4e\u3001\u9891\u7387\u5206\u8fa8\u7387\u9ad8\u3002\u5bf9\u4e8e\u65f6\u53d8\u7684\u975e\u7a33\u6001\u4fe1\u53f7\uff0c\u9ad8\u9891\u9002\u5408\u5c0f\u7a97\u53e3\uff0c\u4f4e\u9891\u9002\u5408\u5927\u7a97\u53e3\u3002\u7136\u800cSTFT\u7684\u7a97\u53e3\u662f\u56fa\u5b9a\u7684\uff0c\u5728\u4e00\u6b21STFT\u4e2d\u5bbd\u5ea6\u4e0d\u4f1a\u53d8\u5316\uff0c\u6240\u4ee5STFT\u8fd8\u662f\u65e0\u6cd5\u6ee1\u8db3\u975e\u7a33\u6001\u4fe1\u53f7\u53d8\u5316\u7684\u9891\u7387\u7684\u9700\u6c42\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/565a3c57d43c8f2f78a5b1dc0de66e34_720w.webp\" alt=\"\" class=\"wp-image-653\" width=\"456\" height=\"219\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/565a3c57d43c8f2f78a5b1dc0de66e34_720w.webp 608w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/565a3c57d43c8f2f78a5b1dc0de66e34_720w-300x144.webp 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/c7d2d230a8c4766569c5a77fac901eea_720w.webp\" alt=\"\" class=\"wp-image-654\" width=\"453\" height=\"221\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/c7d2d230a8c4766569c5a77fac901eea_720w.webp 604w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/c7d2d230a8c4766569c5a77fac901eea_720w-300x147.webp 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/39822d6589c4486a0a91a148e0a3e571_720w.webp\" alt=\"\" class=\"wp-image-655\" width=\"461\" height=\"211\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/39822d6589c4486a0a91a148e0a3e571_720w.webp 614w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/39822d6589c4486a0a91a148e0a3e571_720w-300x137.webp 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/figure>\n\n\n\n<h5>\u5c0f\u6ce2\u53d8\u6362<\/h5>\n\n\n\n<p>\u76f8\u8f83\u4e8eDFT\u7528\u5468\u671f\u6027\u7684\u91c7\u6837\u4fe1\u53f7\u53bb\u91c7\u6837\uff0c\u5c0f\u6ce2\u505a\u7684\u6539\u53d8\u5c31\u5728\u4e8e\uff0c\u5c06\u65e0\u9650\u957f\u7684\u4e09\u89d2\u51fd\u6570\u57fa\u6362\u6210\u4e86\u6709\u9650\u957f\u7684\u4f1a\u8870\u51cf\u7684\u5c0f\u6ce2\u57fa\u3002\u901a\u8fc7\u5bf9\u5c0f\u6ce2\u8fdb\u884c\u5e73\u79fb\u6765\u8fbe\u5230\u5bf9\u4e0d\u540c\u65f6\u671f\u7684\u91c7\u6837\uff0c\u5bf9\u5c0f\u6ce2\u8fdb\u884c\u62c9\u4f38\uff08\u6539\u53d8\u9891\u7387\uff09\u6765\u5bf9\u4e0d\u540c\u9891\u7387\u7684\u4fe1\u53f7\u91c7\u6837\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"675\" height=\"477\" src=\"https:\/\/x2.mday.top\/wp-content\/uploads\/2023\/04\/94b5f53d29d655e0a4d90fa867027eda_720w.png\" alt=\"\" class=\"wp-image-656\" srcset=\"https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/94b5f53d29d655e0a4d90fa867027eda_720w.png 675w, https:\/\/scutvk.cn\/wp-content\/uploads\/2023\/04\/94b5f53d29d655e0a4d90fa867027eda_720w-300x212.png 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/figure>\n\n\n\n<p>\u5c0f\u6ce2\u53d8\u6362\u516c\u5f0f\uff1a<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>W T(a, \\tau)=\\frac{1}{\\sqrt{a}} \\int_{-\\infty}^{\\infty} f(t) * \\psi\\left(\\frac{t-\\tau}{a}\\right) d t<\/pre><\/div>\n\n\n\n<h5>\u79bb\u6563\u4f59\u5f26\u53d8\u6362DCT<\/h5>\n\n\n\n<p>DCT\uff08Discrete Cosine Transform\uff0c\u79bb\u6563\u4f59\u5f26\u53d8\u6362\uff09\u662f\u4e00\u79cd\u5c06\u79bb\u6563\u4fe1\u53f7\u4ece\u65f6\u57df\u8f6c\u6362\u5230\u9891\u57df\u7684\u65b9\u6cd5\uff0c\u4e0eDFT\uff08Discrete Fourier Transform\uff0c\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\uff09\u7c7b\u4f3c\u3002DCT\u7684\u4e3b\u8981\u4f18\u52bf\u5728\u4e8e\u5b83\u7684\u57fa\u51fd\u6570\u662f\u5b9e\u6570\uff0c\u56e0\u6b64\u5728\u67d0\u4e9b\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u56fe\u50cf\u548c\u89c6\u9891\u538b\u7f29\uff0cDCT\u901a\u5e38\u5177\u6709\u66f4\u597d\u7684\u80fd\u91cf\u96c6\u4e2d\u548c\u66f4\u5c11\u7684\u8fb9\u754c\u6548\u5e94\u3002<\/p>\n\n\n\n<p>DCT\u548cDFT\u4e4b\u95f4\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u5b83\u4eec\u4f7f\u7528\u7684\u57fa\u51fd\u6570\u4e0d\u540c\u3002DCT\u4f7f\u7528\u4f59\u5f26\u51fd\u6570\u4f5c\u4e3a\u57fa\u51fd\u6570\uff0c\u800cDFT\u4f7f\u7528\u590d\u6307\u6570\u51fd\u6570\uff08\u5305\u62ec\u6b63\u5f26\u548c\u4f59\u5f26\u51fd\u6570\uff09\u4f5c\u4e3a\u57fa\u51fd\u6570\u3002<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>F(u, v)=\\frac{1}{\\sqrt{2 N}} C(u) C(v) \\sum_{x=0}^{N-1} \\sum_{y=0}^{N-1} f(x, y) \\cos \\left[\\frac{(2 x+1) u \\pi}{2 N}\\right] \\cos \\left[\\frac{(2 y+1) v \\pi}{2 N}\\right]<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>C(u)=\\left\\{\\begin{array}{ll} \\frac{1}{\\sqrt{2}}, &amp; u=0 \\\\ 1, &amp; u>0 \\end{array}\\right.<\/pre><\/div>\n\n\n\n<p>\u53c2\u8003\uff1a<\/p>\n\n\n\n<ol>\n<li><a href=\"https:\/\/zhuanlan.zhihu.com\/p\/22450818\" target=\"_blank\" rel=\"noopener\">\u5f62\u8c61\u6613\u61c2\u8bb2\u89e3\u7b97\u6cd5I\u2014\u2014\u5c0f\u6ce2\u53d8\u6362 &#8211; \u77e5\u4e4e (zhihu.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/zhuanlan.zhihu.com\/p\/85299446\" target=\"_blank\" rel=\"noopener\">\u8be6\u89e3\u79bb\u6563\u4f59\u5f26\u53d8\u6362\uff08DCT\uff09 &#8211; \u77e5\u4e4e (zhihu.com)<\/a><\/li>\n<\/ol>\n\n\n\n<h3>2.7 \u5176\u4ed6\u7684\u8f7b\u91cf\u5316\u65b9\u6cd5<\/h3>\n\n\n\n<h4>2.7.1 \u795e\u7ecf\u7ed3\u6784\u641c\u7d22NAS<\/h4>\n\n\n\n<p>\u795e\u7ecf\u7ed3\u6784\u641c\u7d22\uff08Neural Architecture Search\uff0c\u7b80\u79f0 NAS\uff09\u662f\u4e00\u79cd\u81ea\u52a8\u5316\u6280\u672f\uff0c\u65e8\u5728\u641c\u7d22\u548c\u4f18\u5316\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u6784\u3002\u4f20\u7edf\u4e0a\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u8bbe\u8ba1\u662f\u4e00\u4e2a\u590d\u6742\u4e14\u8017\u65f6\u7684\u8fc7\u7a0b\uff0c\u9700\u8981\u9886\u57df\u4e13\u5bb6\u624b\u52a8\u8bbe\u8ba1\u548c\u8c03\u6574\u7f51\u7edc\u7ed3\u6784\u3002NAS \u901a\u8fc7\u81ea\u52a8\u641c\u7d22\u8fc7\u7a0b\u7b80\u5316\u4e86\u8fd9\u4e2a\u4efb\u52a1\uff0c\u4f7f\u5f97\u673a\u5668\u5b66\u4e60\u7cfb\u7edf\u80fd\u591f\u81ea\u4e3b\u627e\u5230\u6700\u4f73\u7684\u7f51\u7edc\u7ed3\u6784\u4ee5\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u3002<\/p>\n\n\n\n<p>NAS \u7684\u5de5\u4f5c\u539f\u7406\u662f\u5728\u4e00\u4e2a\u9884\u5b9a\u4e49\u7684\u641c\u7d22\u7a7a\u95f4\u5185\u8fdb\u884c\u63a2\u7d22\uff0c\u5c1d\u8bd5\u4e0d\u540c\u7684\u7f51\u7edc\u7ed3\u6784\u548c\u8d85\u53c2\u6570\u914d\u7f6e\u3002\u641c\u7d22\u7a7a\u95f4\u5b9a\u4e49\u4e86\u53ef\u7528\u7684\u7f51\u7edc\u5c42\u3001\u8fde\u63a5\u65b9\u5f0f\u548c\u5176\u4ed6\u6f5c\u5728\u914d\u7f6e\u3002\u7136\u540e\uff0cNAS \u4f7f\u7528\u4f18\u5316\u7b97\u6cd5\uff08\u5982\u5f3a\u5316\u5b66\u4e60\u3001\u8fdb\u5316\u7b97\u6cd5\u3001\u8d1d\u53f6\u65af\u4f18\u5316\u7b49\uff09\u6765\u63a2\u7d22\u8fd9\u4e9b\u53ef\u80fd\u7684\u7ec4\u5408\uff0c\u5e76\u8bc4\u4f30\u5b83\u4eec\u7684\u6027\u80fd\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u4f18\u5316\u7b97\u6cd5\u6839\u636e\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u7684\u8868\u73b0\u6765\u8c03\u6574\u641c\u7d22\u65b9\u5411\uff0c\u4ece\u800c\u9010\u6e10\u627e\u5230\u66f4\u597d\u7684\u7f51\u7edc\u7ed3\u6784\u3002<\/p>\n\n\n\n<p>\u7ecf\u8fc7\u8db3\u591f\u957f\u65f6\u95f4\u7684\u641c\u7d22\u548c\u8bc4\u4f30\uff0cNAS \u6700\u7ec8\u4f1a\u627e\u5230\u4e00\u79cd\u7f51\u7edc\u7ed3\u6784\uff0c\u8be5\u7ed3\u6784\u5728\u6240\u7ed9\u5b9a\u7684\u4efb\u52a1\u4e0a\u5177\u6709\u8f83\u597d\u7684\u6027\u80fd\u8868\u73b0\u3002\u8fd9\u6837\u7684\u81ea\u52a8\u5316\u65b9\u6cd5\u53ef\u4ee5\u8282\u7701\u5927\u91cf\u7684\u65f6\u95f4\u548c\u8d44\u6e90\uff0c\u540c\u65f6\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u751a\u81f3\u53ef\u4ee5\u627e\u5230\u8d85\u8d8a\u4eba\u7c7b\u4e13\u5bb6\u8bbe\u8ba1\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0cNAS \u4e5f\u6709\u4e00\u5b9a\u7684\u5c40\u9650\u6027\u3002\u5176\u641c\u7d22\u8fc7\u7a0b\u53ef\u80fd\u9700\u8981\u5927\u91cf\u7684\u8ba1\u7b97\u8d44\u6e90\u548c\u65f6\u95f4\uff0c\u7279\u522b\u662f\u5728\u5927\u578b\u641c\u7d22\u7a7a\u95f4\u4e2d\u3002\u6b64\u5916\uff0cNAS 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exiting\uff09\u662f\u4e00\u79cd\u5728\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff0c\u5c24\u5176\u662f\u795e\u7ecf\u7f51\u7edc\u4e2d\u4f7f\u7528\u7684\u6280\u5de7\u3002\u5b83\u7684\u4e3b\u8981\u76ee\u7684\u662f\u5728\u4e0d\u635f\u5931\u8fc7\u591a\u6027\u80fd\u7684\u60c5\u51b5\u4e0b\uff0c\u51cf\u5c11\u8ba1\u7b97\u91cf\u548c\u63d0\u9ad8\u6a21\u578b\u7684\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n\n\n\n<p>\u5728\u795e\u7ecf\u7f51\u7edc\uff08\u5c24\u5176\u662f\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff09\u4e2d\uff0c\u6a21\u578b\u901a\u5e38\u5305\u62ec\u591a\u5c42\u795e\u7ecf\u5143\u3002\u5728\u4f20\u7edf\u7684\u524d\u5411\u4f20\u64ad\u8fc7\u7a0b\u4e2d\uff0c\u8f93\u5165\u6570\u636e\u4f1a\u7ecf\u8fc7\u6240\u6709\u5c42\u7684\u8ba1\u7b97\uff0c\u6700\u540e\u5f97\u5230\u9884\u6d4b\u7ed3\u679c\u3002\u7136\u800c\uff0c\u6709\u65f6\u5019\u6a21\u578b\u5728\u7ecf\u8fc7\u51e0\u5c42\u8ba1\u7b97\u540e\uff0c\u5c31\u5df2\u7ecf\u53ef\u4ee5\u5f97\u5230\u8db3\u591f\u597d\u7684\u9884\u6d4b\u7ed3\u679c\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7ee7\u7eed\u8fdb\u884c\u66f4\u591a\u5c42\u7684\u8ba1\u7b97\u53ef\u80fd\u4f1a\u6d6a\u8d39\u8ba1\u7b97\u8d44\u6e90\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u63d0\u524d\u9000\u51fa\u7b56\u7565\u88ab\u5f15\u5165\u5230\u795e\u7ecf\u7f51\u7edc\u4e2d\u3002\u5728\u8fd9\u79cd\u7b56\u7565\u4e0b\uff0c\u7f51\u7edc\u7684\u67d0\u4e9b\u4e2d\u95f4\u5c42\u4f1a\u88ab\u8bbe\u7f6e\u4e3a\u6f5c\u5728\u7684\u8f93\u51fa\u5c42\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5f53\u8f93\u5165\u6570\u636e\u7ecf\u8fc7\u8fd9\u4e9b\u4e2d\u95f4\u5c42\u65f6\uff0c\u53ef\u4ee5\u6839\u636e\u67d0\u79cd\u6807\u51c6\uff08\u5982\u7f6e\u4fe1\u5ea6\u6216\u635f\u5931\u51fd\u6570\u9608\u503c\uff09\u6765\u5224\u65ad\u9884\u6d4b\u7ed3\u679c\u662f\u5426\u8db3\u591f\u597d\u3002\u5982\u679c\u6ee1\u8db3\u8fd9\u4e2a\u6807\u51c6\uff0c\u6a21\u578b\u53ef\u4ee5\u63d0\u524d\u7ec8\u6b62\u8ba1\u7b97\uff0c\u5e76\u8f93\u51fa\u5f53\u524d\u5c42\u7684\u9884\u6d4b\u7ed3\u679c\u3002\u8fd9\u6837\uff0c\u6a21\u578b\u53ef\u4ee5\u5728\u4e0d\u5f71\u54cd\u8f93\u51fa\u8d28\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u8282\u7701\u8ba1\u7b97\u91cf\u548c\u63d0\u9ad8\u6548\u7387\u3002<\/p>\n\n\n\n<p>\u603b\u7684\u6765\u8bf4\uff0c\u63d0\u524d\u9000\u51fa\uff08Early 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