{"id":1859,"date":"2022-01-12T15:39:19","date_gmt":"2022-01-12T07:39:19","guid":{"rendered":"http:\/\/139.9.1.231\/?p=1859"},"modified":"2022-01-12T15:39:21","modified_gmt":"2022-01-12T07:39:21","slug":"convolution","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/01\/12\/convolution\/","title":{"rendered":"\u8f6c\u7f6e\u5377\u79ef\u3001\u5fae\u6b65\u5377\u79ef\u3001\u7a7a\u6d1e\u5377\u79ef"},"content":{"rendered":"\n<p class=\"has-light-pink-background-color has-background\">1\u3001\u8f6c\u7f6e\u5377\u79ef \u53c8\u53ef\u4ee5\u79f0\u4e3a \u53cd\u5377\u79ef\uff08\u6570\u636e\u4ece\u4f4e\u7ef4\u5230\u9ad8\u7ef4\uff09<\/p>\n\n\n\n<p>\u8f6c\u7f6e\u5377\u79ef\u662f\u4e00\u4e2a\u5c06\u4f4e\u7ef4\u7279\u5f81\u8f6c\u6362\u5230\u9ad8\u7ef4\u7279\u5f81\u3002\u4e3a\u4ec0\u4e48\u53eb\u505a\u8f6c\u7f6e\u5377\u79ef\u5462\uff1f\u5176\u5b9e\u5c31\u662f\u5f15\u5165\u4e86\u8f6c\u7f6e\u7684\u601d\u60f3\u3002<\/p>\n\n\n\n<ul><li>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u4e00\u4e2ap\u7ef4\u7684\u5411\u91cfZ\uff0c\u7136\u540e\u6709\u4e2ad\u7ef4\u7684\u5411\u91cfX\uff0cp&lt;d.<\/li><li>\u8fd9\u6837\u5c31\u4f1a\u51fa\u73b0 Z = W\u00b7X\uff0c\u5176\u4e2dW\u7684\u7ef4\u5ea6\u4e3a(p,d)\uff0c\u53eb\u505a\u8f6c\u6362\u77e9\u9635.<\/li><li>\u73b0\u5728\uff0c\u6211\u4eec\u8981\u4eceZ\u901a\u8fc7\u76f8\u4f3c\u7684\u65b9\u6cd5\u6765\u5f97\u5230X\uff0c\u8fd9\u6837\u6211\u4eec\u4e0d\u96be\u60f3\u5230\uff1a<code>X= W.T \u00b7 X<\/code>&nbsp;\u5176\u4e2dW.T\u7684\u7ef4\u5ea6\u662f(d,p)\uff0c\u4f46\u662f\u8fd9\u4e24\u4e2aW\u5e76\u4e0d\u662f\u540c\u4e00\u4e2a\u503c\uff0c\u800c\u662f\u5177\u6709\u8f6c\u7f6e\u7684\u5f62\u5f0f\u800c\u5df2\u3002<\/li><\/ul>\n\n\n\n<p>\u4e0a\u9762\u7684\u4f8b\u5b50\u662f\u4e00\u7ef4\u5411\u91cf\u7684\u60c5\u51b5\uff0c\u5728\u5377\u79ef\u64cd\u4f5c\u4e2d\uff0c\u4e5f\u53ef\u4ee5\u501f\u7528\u8fd9\u4e2a\u601d\u60f3\uff0c\u4ece\u4f4e\u7ef4\u5230\u9ad8\u7ef4\u7684\u8f6c\u53d8\u53ef\u4ee5\u5728\u5f62\u5f0f\u4e0a\u770b\u6210\u662f\u8f6c\u7f6e\u64cd\u4f5c\u3002<\/p>\n\n\n\n<ul><li>\u6bd4\u5982\u6211\u4eec\u73b0\u5728\u5bf9\u4e00\u4e2a4 * 4\u7684\u8f93\u5165\u505a3 * 3\u7684\u5377\u79ef\u64cd\u4f5c\uff08m=3\u6838\u7684\u5927\u5c0f\uff0cstride=1\uff0cpadding=0\uff09\uff0c\u5f97\u5230\u4e00\u4e2a2 * 2\u7684\u7279\u5f81\u6620\u5c04<\/li><li>\u5982\u679c\u6211\u4eec\u60f3\u5bf9\u8fd9\u4e2a2 * 2\u7279\u5f81\u6620\u5c04\u8fdb\u884c3 * 3\u5377\u79ef\uff0c\u5e76\u53cd\u8fc7\u6765\u5f97\u52304 * 4\u7684\u8f93\u51fa\uff0c\u5c31\u53ef\u4ee5\u7528\u5230\u8f6c\u7f6e\u5377\u79ef\uff1a<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/v2-286ac2cfb69abf4d8aa06b8eeb39ced3_b.gif\" alt=\"\" class=\"wp-image-1863\" width=\"171\" height=\"192\"\/><\/figure><\/div>\n\n\n\n<p>\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u5bf92 * 2\u7684\u7279\u5f81\u6620\u5c04\u5148\u505a<code>\uff08m-1\uff09<\/code> <code>padding<\/code>\u5f97\u52306 * 6\u7684\u8f93\u5165\uff0c\u7136\u540e\u5bf9\u5176\u8fdb\u884c3*3\u7684\u5377\u79ef\u64cd\u4f5c\uff0c\u4ece\u800c\u5f97\u52304 * 4\u7684\u7279\u5f81\u6620\u5c04\u3002 \u540c\u6837\uff0c\u8fd9\u4e2a\u4e24\u4e2a3 * 3\u7684\u5377\u79ef\u53c2\u6570\u4e0d\u662f\u4e00\u81f4\u7684\uff0c\u90fd\u662f\u53ef\u5b66\u4e60\u7684\u3002<\/p>\n\n\n\n<p class=\"has-light-pink-background-color has-background\">2\u3001\u5fae\u6b65\u5377\u79ef\uff08\u6b65\u957f\u4e0d\u4e3a1\u7684\u8f6c\u7f6e\u5377\u79ef\uff08\u53cd\u5377\u79ef\uff09\uff09<\/p>\n\n\n\n<p>\u5fae\u6b65\u5377\u79ef\u5176\u5b9e\u662f\u4e00\u4e2a\u8f6c\u7f6e\u5377\u79ef\u7684\u4e00\u4e2a\u7279\u6b8a\u60c5\u51b5\uff0c\u5c31\u662f\u5377\u79ef\u64cd\u4f5c\u7684<code>stride \u2260 1<\/code>\u3002\u56e0\u4e3a\u5728\u73b0\u5b9e\u4e2d\uff0c\u4e3a\u4e86\u5927\u5e45\u5ea6\u964d\u4f4e\u7279\u5f81\u7ef4\u6570\uff0c\u5377\u79ef\u7684\u6b65\u957f\u4f1a\u5927\u4e8e1\u3002\u540c\u6837\uff0c\u4e3a\u4e86\u5927\u5e45\u5ea6\u63d0\u9ad8\u7279\u5f81\u7ef4\u5ea6\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528\u901a\u8fc7\u5377\u79ef\u6765\u5b9e\u73b0\uff0c\u8fd9\u79cd\u5377\u79ef<code>stride &lt; 1<\/code>&nbsp;\uff0c\u6240\u4ee5\u53eb\u505a\u5fae\u6b65\u5377\u79ef\u3002<\/p>\n\n\n\n<ul><li>\u5982\u679c\u5377\u79ef\u64cd\u4f5cstride&gt;1\uff0c\u5176\u5bf9\u5e94\u7684\u8f6c\u7f6e\u5377\u79ef\u6b65\u957f\u4e3a1\/s \uff1a\u5c31\u662f\u5728\u8f93\u5165\u7279\u5f81\u4e4b\u95f4\u63d2\u5165s &#8211; 1\u4e2a0\uff0c\u6765\u4f7f\u5f97\u6b65\u957f\u53d8\u2019\u5c0f\u2019\u3002<\/li><li>\u4f8b\u5982\uff0c\u6211\u5bf9\u4e00\u4e2a5 * 5\u7684\u8f93\u5165\u505a3 * 3\u7684\u5377\u79ef\u64cd\u4f5c(m=3, padding=0,\u4f46\u662f<code>stride=2<\/code>)\uff0c\u4ece\u800c\u6211\u5f97\u5230\u7684\u7279\u5f81\u8f93\u51fa\u4e3a2 * 2.<\/li><li>\u73b0\u5728\u5bf9\u5176\u8fdb\u884c\u5fae\u6b65\u5377\u79ef\uff1a<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-191.png\" alt=\"\" class=\"wp-image-1866\" width=\"312\" height=\"247\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-191.png 520w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-191-300x237.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/figure><\/div>\n\n\n\n<p>\u8ddf\u8f6c\u7f6e\u5377\u79ef\u4e00\u6837\uff0c\u5148\u5bf92 * 2\u7684\u8f93\u5165\u505a<code>\uff08m-1\uff09padding<\/code>\u00a0\uff0c\u7136\u540e\u518d\u5728\u7279\u5f81\u4e4b\u95f4\u63d2\u5165<code>stride -1<\/code>\u4e2a0\uff0c\u4ece\u800c\u5f97\u5230\u4e00\u4e2a7 * 7\u7684\u7279\u5f81\u8f93\u5165\uff0c\u7136\u540e\u5bf9\u5176\u505a3 * 3 \u7684\u5377\u79ef\u64cd\u4f5c\uff0c\u5f97\u52305 * 5\u7684\u7279\u5f81\u8f93\u51fa\u3002<\/p>\n\n\n\n<p class=\"has-bright-blue-background-color has-background\"><strong>\u5982\u4f55\u8ba1\u7b97\u53cd\u5377\u79ef\uff1a<\/strong><\/p>\n\n\n\n<p>\u5f53\u8f93\u5165\u7684\u77e9\u9635\u9ad8\u5bbd\u4e3an\uff0c\u6838\u5927\u5c0f\u4e3ak\uff0cpadding\u4e3ap\uff0cstride\u4e3as<\/p>\n\n\n\n<ul><li>\u5f53\u8f93\u5165\u7684\u77e9\u9635\u9ad8\u5bbd\u4e3a n \uff0c\u6838\u5927\u5c0f\u4e3a k \uff0cpadding\u4e3a p \uff0c stride\u4e3a s \u3002<\/li><li>\u8f6c\u7f6e\u5377\u79ef\u4f5c\u7528\u540e\u7684\u5c3a\u5bf8\u53d8\u5316: \\(n^{1}=s n+k-2 p-s\\) \u3002\u5982\u679c\u60f3\u8ba9\u9ad8\u5bbd\u6210\u500d\u589e\u52a0\uff0c\u90a3\u4e48 \\(k=2 p+s\\) \u3002<\/li><li>\u5377\u79ef\u4f5c\u7528\u540e\u7684\u5c3a\u5bf8\u53d8\u5316: \\(n^{1}=\\left\\lfloor\\frac{n-k+2 p+s}{s}\\right\\rfloor\\) \u3002\u5982\u679c\u60f3\u8ba9\u9ad8\u5bbd\u6210\u500d\u51cf\u5c11\uff0c\u90a3\u4e48 \\(k=2 p+1\\)\u3002<\/li><\/ul>\n\n\n\n<p>1\u3001\u5f53\u586b\u5145\u4e3a0\u6b65\u957f\u4e3a1\u65f6<\/p>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">\u5c06\u8f93\u5165\u586b\u5145 k \u2212 1 \u3002\uff08k\u662f \u5377\u79ef\u6838\u5927\u5c0f\uff09<br>\u5c06\u6838\u77e9\u9635\u4e0a\u4e0b\uff0c\u5de6\u53f3\u7ffb\u8f6c\u3002<br>\u4e4b\u540e\u6b63\u5e38\u505a\u586b\u5145\u4e3a0\uff08\u65e0\u586b\u5145\uff09\uff0c\u6b65\u5e45\u4e3a1\u7684\u5377\u79ef\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" width=\"1024\" height=\"206\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-193-1024x206.png\" alt=\"\" class=\"wp-image-1884\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-193-1024x206.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-193-300x60.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-193-768x154.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-193.png 1462w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>2 \u5f53\u586b\u5145\u4e3a p \u6b65\u5e45\u4e3a1\u65f6<\/p>\n\n\n\n<p>\u5c06\u8f93\u5165\u586b\u5145 k \u2212 p \u2212 1 \u3002<br>\u5c06\u6838\u77e9\u9635\u4e0a\u4e0b\uff0c\u5de6\u53f3\u7ffb\u8f6c\u3002<br>\u4e4b\u540e\u6b63\u5e38\u505a\u586b\u5145\u4e3a0\uff0c\u6b65\u5e45\u4e3a1\u7684\u5377\u79ef\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" width=\"1024\" height=\"190\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-194-1024x190.png\" alt=\"\" class=\"wp-image-1887\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-194-1024x190.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-194-300x56.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-194-768x142.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-194.png 1426w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>3 \u5f53\u586b\u5145\u4e3a p pp \u6b65\u5e45\u4e3as ss\u65f6<\/p>\n\n\n\n<p>\u5728\u884c\u548c\u5217\u4e4b\u95f4\u63d2\u5165s \u2212 1 \u884c\u548c\u5217\u3002<br>\u5c06\u8f93\u5165\u586b\u5145 k \u2212 p \u2212 1\u3002<br>\u5c06\u6838\u77e9\u9635\u4e0a\u4e0b\uff0c\u5de6\u53f3\u7ffb\u8f6c\u3002<br>\u4e4b\u540e\u6b63\u5e38\u505a\u586b\u5145\u4e3a0\uff0c\u6b65\u5e45\u4e3a1\u7684\u5377\u79ef\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" width=\"1024\" height=\"232\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-195-1024x232.png\" alt=\"\" class=\"wp-image-1890\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-195-1024x232.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-195-300x68.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-195-768x174.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-195.png 1486w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-light-pink-background-color has-background\">3\u3001\u7a7a\u6d1e\u5377\u79ef\uff08\u81a8\u80c0\u5377\u79ef\uff09<\/p>\n\n\n\n<p>\u901a\u5e38\u6765\u8bf4\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u5377\u79ef\u5c42\uff0c\u5982\u679c\u5e0c\u671b\u589e\u52a0\u8f93\u51fa\u5355\u5143\u7684\u611f\u53d7\u91ce\uff0c\u4e00\u822c\u7531\u4e09\u4e2a\u65b9\u5f0f\uff1a<\/p>\n\n\n\n<ol><li>\u589e\u52a0\u5377\u79ef\u6838\u5927\u5c0f<\/li><li>\u589e\u52a0\u5c42\u6570<\/li><li>\u8fdb\u884cpooling\u64cd\u4f5c<\/li><\/ol>\n\n\n\n<p class=\"has-bright-blue-background-color has-background\">\u5176\u4e2d1\u548c2\u90fd\u4f1a\u589e\u52a0\u53c2\u6570\u91cf\uff0c\u800c3\u4f1a\u4e22\u5931\u7279\u5f81\u4fe1\u606f\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u5f15\u5165\u2018\u7a7a\u6d1e\u5377\u79ef\u2019\u7684\u6982\u5ff5\uff0c\u5b83\u4e0d\u589e\u52a0\u53c2\u6570\u91cf\uff0c\u540c\u65f6\u5b83\u4e5f\u53ef\u4ee5\u589e\u52a0\u8f93\u51fa\u7684\u611f\u53d7\u91ce\u3002<br><strong>\u5b83\u4e3b\u8981\u662f\u901a\u8fc7\u7ed9\u5377\u79ef\u6838\u63d2\u5165\u7a7a\u6d1e\u6765\u589e\u52a0\u5176\u611f\u53d7\u91ce\u5927\u5c0f\uff0c\u5982\u679c\u5377\u79ef\u6838\u6bcf\u4e24\u4e2a\u5143\u7d20\u4e4b\u95f4\u63d2\u5165d-1\u4e2a\u7a7a\u6d1e\uff0c\u90a3\u4e48\u5377\u79ef\u6838\u7684\u6709\u6548\u5927\u5c0f\u4e3a\uff1a<code>M = m + (m-1)*(d-1)<\/code><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" width=\"1024\" height=\"420\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-192-1024x420.png\" alt=\"\" class=\"wp-image-1872\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-192-1024x420.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-192-300x123.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-192-768x315.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/01\/image-192.png 1147w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img src=\"https:\/\/w.wallhaven.cc\/full\/l3\/wallhaven-l3r32p.jpg\" alt=\"\"\/><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>1\u3001\u8f6c\u7f6e\u5377\u79ef \u53c8\u53ef\u4ee5\u79f0\u4e3a \u53cd\u5377\u79ef\uff08\u6570\u636e\u4ece\u4f4e\u7ef4\u5230\u9ad8\u7ef4\uff09 \u8f6c\u7f6e\u5377\u79ef\u662f\u4e00\u4e2a\u5c06\u4f4e\u7ef4\u7279\u5f81\u8f6c\u6362\u5230\u9ad8\u7ef4\u7279\u5f81\u3002\u4e3a\u4ec0\u4e48\u53eb\u505a\u8f6c\u7f6e\u5377 &hellip; <a href=\"http:\/\/139.9.1.231\/index.php\/2022\/01\/12\/convolution\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span 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