{"id":25626,"date":"2025-04-27T12:19:57","date_gmt":"2025-04-27T04:19:57","guid":{"rendered":"https:\/\/aif.amtbbs.org\/?p=25626"},"modified":"2025-04-27T12:19:57","modified_gmt":"2025-04-27T04:19:57","slug":"%e4%b8%80%e6%96%87%e8%af%a6%e8%a7%a3%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%e4%b8%ad%e7%9a%84%e6%a0%87%e9%87%8f%e3%80%81%e5%90%91%e9%87%8f%e3%80%81%e7%9f%a9%e9%98%b5%e3%80%81%e5%bc%a0%e9%87%8f","status":"publish","type":"post","link":"https:\/\/aif.amtbbs.org\/index.php\/2025\/04\/27\/25626\/","title":{"rendered":"\u4e00\u6587\u8be6\u89e3\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u6807\u91cf\u3001\u5411\u91cf\u3001\u77e9\u9635\u3001\u5f20\u91cf"},"content":{"rendered":"<div><img data-dominant-color=\"7e9eb9\" data-has-transparency=\"false\" style=\"--dominant-color: #7e9eb9;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-25628\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-300x167-1.jpg\" width=\"300\" height=\"167\" alt=\"\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-300x167-1.jpg 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-300x167-1-150x84.jpg 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<div><\/div>\n<div class=\"article-desc\">\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\uff0c\u6807\u91cf\u3001\u5411\u91cf\u3001\u77e9\u9635\u548c\u5f20\u91cf\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u57fa\u672c\u6982\u5ff5\u3002\u672c\u6587\u5c06\u7b80\u8981\u4ecb\u7ecd\u8fd9\u4e9b\u6570\u5b66\u57fa\u7840\uff0c\u5e2e\u52a9\u8bfb\u8005\u66f4\u597d\u5730\u7406\u89e3\u5b83\u4eec\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u4f5c\u7528\u548c\u5e94\u7528\u3002<\/div>\n<div id=\"postspictures\" class=\"article-content\">\n<div id=\"container\" class=\"container am-engine\" data-v-1d7a5742=\"\" data-element=\"root\">\n<p><img data-dominant-color=\"7e9eb9\" data-has-transparency=\"false\" style=\"--dominant-color: #7e9eb9;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-25629\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-1.jpg\" width=\"1248\" height=\"696\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-1.jpg 1248w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-1-300x167.jpg 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-1-1024x571.jpg 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-1-150x84.jpg 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e1f6a1f3347cc0de9a05211ff4bd15e402b013-1-768x428.jpg 768w\" sizes=\"auto, (max-width: 1248px) 100vw, 1248px\" \/><\/p>\n<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\uff0c\u6807\u91cf\u3001\u5411\u91cf\u3001\u77e9\u9635\u548c\u5f20\u91cf\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u57fa\u672c\u6982\u5ff5\u3002\u5b83\u4eec\u4e0d\u4ec5\u662f\u6570\u5b66\u5de5\u5177\uff0c\u66f4\u662f\u7406\u89e3\u548c\u6784\u5efa\u795e\u7ecf\u7f51\u7edc\u7684\u5173\u952e\u3002\u4ece\u7b80\u5355\u7684\u6807\u91cf\u8fd0\u7b97\u5230\u590d\u6742\u7684\u5f20\u91cf\u5904\u7406\uff0c\u8fd9\u4e9b\u6982\u5ff5\u8d2f\u7a7f\u4e8e\u6570\u636e\u8868\u793a\u3001\u6a21\u578b\u6784\u5efa\u548c\u7b97\u6cd5\u4f18\u5316\u7684\u5168\u8fc7\u7a0b\u3002\u672c\u6587\u5c06\u7b80\u8981\u4ecb\u7ecd\u8fd9\u4e9b\u6570\u5b66\u57fa\u7840\uff0c\u5e2e\u52a9\u8bfb\u8005\u66f4\u597d\u5730\u7406\u89e3\u5b83\u4eec\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u4f5c\u7528\u548c\u5e94\u7528\u3002<\/p>\n<h3>1\u3001\u6807\u91cf<\/h3>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a<strong>\u4ec5\u5305\u542b\u4e00\u4e2a\u6570\u503c\u7684\u91cf<\/strong>\uff0c\u50cf\u5317\u4eac\u6e29\u5ea6 52\u00b0F\uff0c\u5176\u4e2d 52 \u5c31\u662f\u6807\u91cf\u3002\u5728\u6570\u5b66\u91cc\uff0c\u6807\u91cf\u53d8\u91cf\u5e38\u7528\u666e\u901a\u5c0f\u5199\u5b57\u6bcd\uff08\u5982 x\u3001y\u3001z\uff09\u8868\u793a \uff0c\u6240\u6709\uff08\u8fde\u7eed\uff09\u5b9e\u6570\u6807\u91cf\u7684\u7a7a\u95f4\u7528 R \u8868\u793a\uff0cx \u2208 R \u8868\u793a x \u662f\u5b9e\u503c\u6807\u91cf\u3002<\/p>\n<p><strong>\u8868\u793a\u4e0e\u8fd0\u7b97<\/strong>\uff1a\u7531\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u7684\u5f20\u91cf\u8868\u793a\u3002\u901a\u8fc7\u4ee3\u7801\u80fd\u5bf9\u5176\u8fdb\u884c\u52a0\u3001\u4e58\u3001\u9664\u3001\u6307\u6570\u7b49\u7b97\u672f\u8fd0\u7b97\u3002<\/p>\n<p><strong>\u793a\u4f8b\uff1a<\/strong><\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_0\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">import torch\r\nx = torch.tensor(3.0)\r\ny = torch.tensor(2.0)\r\nx + y, x * y, x \/ y, x**y<\/code><\/pre>\n<ul id=\"code_id_0\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u7ed3\u679c\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s5.51cto.com\/oss\/202504\/27\/193244b155f94f01093458cf0d4c133f8f6dfe.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<h3>2\u3001\u5411\u91cf<\/h3>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u53ef\u770b\u4f5c<strong>\u6807\u91cf\u503c\u7ec4\u6210\u7684\u5217\u8868<\/strong>\uff0c\u5176\u5143\u7d20\u6216\u5206\u91cf\u5177\u6709\u5b9e\u9645\u610f\u4e49\u3002\u5728\u6570\u5b66\u8868\u793a\u6cd5\u4e2d\uff0c\u5411\u91cf\u901a\u5e38\u8bb0\u4e3a<strong>\u7c97\u4f53<\/strong>\u3001\u5c0f\u5199\u7b26\u53f7\uff08\u5982<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/f1f47f30502a8c26910202ebdf47c0fe14c6c8.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff09\uff0c\u901a\u8fc7\u4e00\u7ef4\u5f20\u91cf\u8868\u793a\u3002<\/p>\n<p><strong>\u8868\u793a\u4e0e\u8fd0\u7b97<\/strong>\uff1a\u7528\u4e0b\u6807\u5f15\u7528\u5143\u7d20\uff0c\u5982<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202504\/27\/85382e16324b63e1f6546016b0e561cce8549f.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<strong>\u5411\u91cf\u9ed8\u8ba4\u65b9\u5411\u662f\u5217\u5411\u91cf<\/strong>\u3002<\/p>\n<p><strong>\u793a\u4f8b\uff1a<\/strong><\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_1\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">x = torch.arange(4)\r\nx<\/code><\/pre>\n<ul id=\"code_id_1\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u7ed3\u679c\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/49dbe2a42afa4dc2192783769aae01c9d1e400.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><strong>\u5411\u91cf\u957f\u5ea6\u901a\u5e38\u79f0\u4e3a\u5411\u91cf\u7684\u7ef4\u5ea6<\/strong>\uff0c\u4e0e\u666e\u901a\u7684Python\u6570\u7ec4\u4e00\u6837\uff0c\u53ef\u4ee5\u901a\u8fc7\u8c03\u7528Python\u7684\u5185\u7f6e<code>len()<\/code>\u51fd\u6570\u6765\u8bbf\u95ee\u5f20\u91cf\u7684\u957f\u5ea6\u3002<\/p>\n<p>\u5f53\u7528\u5f20\u91cf\u8868\u793a\u4e00\u4e2a\u5411\u91cf\uff08\u53ea\u6709\u4e00\u4e2a\u8f74\uff09\u65f6\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7<code>.shape<\/code>\u5c5e\u6027\u8bbf\u95ee\u5411\u91cf\u7684\u957f\u5ea6\u3002 \u5f62\u72b6\uff08shape\uff09\u662f\u4e00\u4e2a\u5143\u7d20\u7ec4\uff0c\u5217\u51fa\u4e86\u5f20\u91cf\u6cbf\u6bcf\u4e2a\u8f74\u7684\u957f\u5ea6\uff08\u7ef4\u6570\uff09\u3002 \u5bf9\u4e8e\u53ea\u6709\u4e00\u4e2a\u8f74\u7684\u5f20\u91cf\uff0c\u5f62\u72b6\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_2\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">x.shape\r\n# \u7ed3\u679c\uff1atorch.Size([4])<\/code><\/pre>\n<ul id=\"code_id_2\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u6ce8\u610f\uff0c\u7ef4\u5ea6\uff08dimension\uff09\u8fd9\u4e2a\u8bcd\u5728\u4e0d\u540c\u4e0a\u4e0b\u6587\u65f6\u5f80\u5f80\u4f1a\u6709\u4e0d\u540c\u7684\u542b\u4e49\uff0c\u8fd9\u7ecf\u5e38\u4f1a\u4f7f\u4eba\u611f\u5230\u56f0\u60d1\u3002 \u4e3a\u4e86\u6e05\u695a\u8d77\u89c1\uff0c\u660e\u786e\uff1a<strong>\u5411\u91cf\u6216\u8f74\u7684\u7ef4\u5ea6\u88ab\u7528\u6765\u8868\u793a\u5411\u91cf\u6216\u8f74\u7684\u957f\u5ea6<\/strong>\uff0c\u5373\u5411\u91cf\u6216\u8f74\u7684\u5143\u7d20\u6570\u91cf\u3002 \u7136\u800c\uff0c\u5f20\u91cf\u7684\u7ef4\u5ea6\u7528\u6765\u8868\u793a\u5f20\u91cf\u5177\u6709\u7684\u8f74\u6570\u3002 \u5728\u8fd9\u4e2a\u610f\u4e49\u4e0a\uff0c<strong>\u5f20\u91cf\u7684\u67d0\u4e2a\u8f74\u7684\u7ef4\u6570\u5c31\u662f\u8fd9\u4e2a\u8f74\u7684\u957f\u5ea6<\/strong>\u3002<\/p>\n<h3>3\u3001\u77e9\u9635<\/h3>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u662f<strong>\u5411\u91cf\u4ece\u4e00\u9636\u5230\u4e8c\u9636\u7684\u63a8\u5e7f<\/strong>\uff0c\u901a\u5e38\u7528\u7c97\u4f53\u3001\u5927\u5199\u5b57\u6bcd\uff08\u5982<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202504\/27\/b8b003573c6f405e6ba15481373b8e82cec8bc.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><strong>\u8868\u793a<\/strong>\uff1a\u77e9\u9635\u5143\u7d20\u7528<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202504\/27\/b91e43d57d7be247482202d14f904adb27e54d.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u8868\u793a\uff0c\u53ef\u901a\u8fc7\u884c\u3001\u5217\u7d22\u5f15\u8bbf\u95ee\u3002<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s4.51cto.com\/oss\/202504\/27\/d73c2a7207c9e75f9a9685618d42bcb0edba98.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u5f53\u8c03\u7528\u51fd\u6570\u6765\u5b9e\u4f8b\u5316\u5f20\u91cf\u65f6\uff0c \u53ef\u4ee5\u901a\u8fc7\u6307\u5b9a\u4e24\u4e2a\u5206\u91cfm\u548cn\u6765\u521b\u5efa\u4e00\u4e2a\u5f62\u72b6\u4e3a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202504\/27\/717d5e808a6d0c78474284058d801d7923b0cd.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u7684\u77e9\u9635\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_3\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A = torch.arange(20).reshape(5, 4)\r\nA<\/code><\/pre>\n<ul id=\"code_id_3\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u7ed3\u679c\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s5.51cto.com\/oss\/202504\/27\/27c1a3b23a7007a3972805017943580072ac63.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u4ea4\u6362\u77e9\u9635\u7684\u884c\u548c\u5217\u65f6\uff0c\u7ed3\u679c\u79f0\u4e3a\u77e9\u9635\u7684<strong>\u8f6c\u7f6e\uff08transpose\uff09<\/strong>\u3002 \u901a\u5e38\u7528<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s4.51cto.com\/oss\/202504\/27\/a26bf07927b9950d1bd218f2abe84ac3ff9de5.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u6765\u8868\u793a\u77e9\u9635\u7684\u8f6c\u7f6e\uff1a<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_4\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A.T<\/code><\/pre>\n<ul id=\"code_id_4\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u7ed3\u679c\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s4.51cto.com\/oss\/202504\/27\/743c11b423a06c97dc6639c723889e6777acb6.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<h3>4\u3001\u5f20\u91cf<\/h3>\n<p><strong>\u5b9a\u4e49\uff1a\u5c31\u50cf\u5411\u91cf\u662f\u6807\u91cf\u7684\u63a8\u5e7f\uff0c\u77e9\u9635\u662f\u5411\u91cf\u7684\u63a8\u5e7f\u4e00\u6837\uff0c\u5f20\u91cf\u662f\u63cf\u8ff0\u5177\u6709\u4efb\u610f\u6570\u91cf\u8f74\u7684n\u7ef4\u6570\u7ec4\u7684\u901a\u7528\u65b9\u6cd5<\/strong>\uff0c\u53ef\u4ee5\u6784\u5efa\u5177\u6709\u66f4\u591a\u8f74\u7684\u6570\u636e\u7ed3\u6784\u3002 \u4f8b\u5982\uff0c\u5411\u91cf\u662f\u4e00\u9636\u5f20\u91cf\uff0c\u77e9\u9635\u662f\u4e8c\u9636\u5f20\u91cf\u3002<\/p>\n<p><strong>\u8868\u793a\u4e0e\u8fd0\u7b97<\/strong>\uff1a\u5c24\u5176\u5728\u5904\u7406\u56fe\u50cf\u7b49\u6570\u636e\u65f6\uff0c\u5f20\u91cf\u53d8\u5f97\u66f4\u52a0\u91cd\u8981\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u56fe\u50cf\u4ee5n\u7ef4\u6570\u7ec4\u5f62\u5f0f\u51fa\u73b0\uff0c \u5176\u4e2d3\u4e2a\u8f74\u5bf9\u5e94\u4e8e\u9ad8\u5ea6\u3001\u5bbd\u5ea6\uff0c\u4ee5\u53ca\u4e00\u4e2a\u901a\u9053\uff08channel\uff09\u8f74\uff0c \u7528\u4e8e\u8868\u793a\u989c\u8272\u901a\u9053\uff08\u7ea2\u8272\u3001\u7eff\u8272\u548c\u84dd\u8272\uff09\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_5\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">X = torch.arange(24).reshape(2, 3, 4)\r\nX<\/code><\/pre>\n<ul id=\"code_id_5\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u7ed3\u679c\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s5.51cto.com\/oss\/202504\/27\/c1e7c6c94de88484a47128f314a65c4c8644c7.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<h3>5\u3001\u5f20\u91cf\u7b97\u6cd5\u7684\u57fa\u672c\u6027\u8d28<\/h3>\n<p>\u5f20\u91cf\u7b97\u6cd5\u7684\u57fa\u672c\u6027\u8d28\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\u81f3\u5173\u91cd\u8981\uff0c\u5b83\u5305\u62ec\u6309\u5143\u7d20\u8fd0\u7b97\u7684\u5f62\u72b6\u4e0d\u53d8\u6027\u3001\u5f20\u91cf\u95f4\u8fd0\u7b97\u7ed3\u679c\u7684\u5f62\u72b6\u89c4\u5f8b\u3001\u4e0e\u6807\u91cf\u8fd0\u7b97\u7684\u7279\u70b9\uff0c\u4ee5\u53ca\u964d\u7ef4\u3001\u975e\u964d\u7ef4\u6c42\u548c\u4e0e\u7d2f\u79ef\u6c42\u548c\u7b49\u64cd\u4f5c\u7279\u6027\u3002\u8fd9\u4e9b\u6027\u8d28\u8d2f\u7a7f\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u5404\u7c7b\u8ba1\u7b97\u4e2d\uff0c\u5bf9\u7406\u89e3\u548c\u8fd0\u7528\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u8d77\u7740\u5173\u952e\u4f5c\u7528\uff0c\u5177\u4f53\u5982\u4e0b\uff1a<\/p>\n<h4>\u6309\u5143\u7d20\u8fd0\u7b97\u7684\u5f62\u72b6\u4e0d\u53d8\u6027<\/h4>\n<p>\u4ece\u6309\u5143\u7d20\u64cd\u4f5c\u7684\u5b9a\u4e49\u53ef\u77e5\uff0c\u4efb\u4f55\u6309\u5143\u7d20\u7684\u4e00\u5143\u8fd0\u7b97\u90fd\u4e0d\u4f1a\u6539\u53d8\u5176\u64cd\u4f5c\u6570\u7684\u5f62\u72b6\u3002\u4f8b\u5982\uff0c\u5bf9\u4e00\u4e2a\u5f20\u91cf\u8fdb\u884c\u53d6\u7edd\u5bf9\u503c\u3001\u5e73\u65b9\u7b49\u4e00\u5143\u8fd0\u7b97\uff0c\u8fd0\u7b97\u540e\u7684\u5f20\u91cf\u5f62\u72b6\u4e0e\u539f\u5f20\u91cf\u4fdd\u6301\u4e00\u81f4\u3002\u8fd9\u4e00\u6027\u8d28\u786e\u4fdd\u4e86\u5728\u5bf9\u5f20\u91cf\u7684\u6bcf\u4e2a\u5143\u7d20\u8fdb\u884c\u5355\u72ec\u64cd\u4f5c\u65f6\uff0c\u6570\u636e\u7684\u7ed3\u6784\u4e0d\u4f1a\u88ab\u7834\u574f\uff0c\u4e3a\u540e\u7eed\u57fa\u4e8e\u5f20\u91cf\u5f62\u72b6\u7684\u8ba1\u7b97\u548c\u5904\u7406\u63d0\u4f9b\u4e86\u7a33\u5b9a\u6027\u3002<\/p>\n<h4>\u5f20\u91cf\u95f4\u8fd0\u7b97\u7ed3\u679c\u7684\u5f62\u72b6\u89c4\u5f8b<\/h4>\n<p>\u7ed9\u5b9a<strong>\u5177\u6709\u76f8\u540c\u5f62\u72b6\u7684\u4efb\u610f\u4e24\u4e2a\u5f20\u91cf\uff0c\u4efb\u4f55\u6309\u5143\u7d20\u4e8c\u5143\u8fd0\u7b97\u7684\u7ed3\u679c\u90fd\u5c06\u662f\u76f8\u540c\u5f62\u72b6\u7684\u5f20\u91cf<\/strong>\u3002<\/p>\n<p>\u4e24\u4e2a\u76f8\u540c\u5f62\u72b6\u7684\u77e9\u9635\u76f8\u52a0\uff0c\u4f1a\u5728\u8fd9\u4e24\u4e2a\u77e9\u9635\u4e0a\u6267\u884c\u5143\u7d20\u52a0\u6cd5\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u77e9\u9635\u5f62\u72b6\u4e0e\u539f\u77e9\u9635\u76f8\u540c\u3002\u8fd9\u4e00\u6027\u8d28\u4f7f\u5f97<strong>\u5728\u8fdb\u884c\u5f20\u91cf\u95f4\u7684\u6279\u91cf\u8fd0\u7b97\u65f6\uff0c\u65e0\u9700\u62c5\u5fc3\u5f62\u72b6\u4e0d\u5339\u914d\u7684\u95ee\u9898<\/strong>\uff0c\u63d0\u9ad8\u4e86\u8ba1\u7b97\u7684\u6548\u7387\u548c\u51c6\u786e\u6027\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_6\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A = torch.arange(20, dtype=torch.float32).reshape(5, 4)\r\nB = A.clone()  # \u901a\u8fc7\u5206\u914d\u65b0\u5185\u5b58\uff0c\u5c06A\u7684\u4e00\u4e2a\u526f\u672c\u5206\u914d\u7ed9B\r\nA, A + B<\/code><\/pre>\n<ul id=\"code_id_6\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s4.51cto.com\/oss\/202504\/27\/454412f79f636af65fc1073ef3c35b27fee664.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<h4>\u4e0e\u6807\u91cf\u8fd0\u7b97\u7684\u7279\u70b9<\/h4>\n<p><strong>\u5c06\u5f20\u91cf\u4e58\u4ee5\u6216\u52a0\u4e0a\u4e00\u4e2a\u6807\u91cf\u4e0d\u4f1a\u6539\u53d8\u5f20\u91cf\u7684\u5f62\u72b6\uff0c\u5176\u4e2d\u5f20\u91cf\u7684\u6bcf\u4e2a\u5143\u7d20\u90fd\u5c06\u4e0e\u6807\u91cf\u76f8\u52a0\u6216\u76f8\u4e58<\/strong>\u3002\u8fd9\u79cd\u7279\u6027\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d<strong>\u5e38\u7528\u4e8e\u5bf9\u5f20\u91cf\u8fdb\u884c\u7f29\u653e\u6216\u5e73\u79fb\u64cd\u4f5c<\/strong>\uff0c\u4ee5\u8c03\u6574\u6570\u636e\u7684\u5206\u5e03\u6216\u7279\u5f81\u7684\u5f3a\u5ea6\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_7\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">a = 2\r\nX = torch.arange(24).reshape(2, 3, 4)\r\na + X, (a * X).shape<\/code><\/pre>\n<ul id=\"code_id_7\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/f79f8f8539c1417a38d57285d66f4b3508f87b.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><strong>\u964d\u7ef4\u64cd\u4f5c<\/strong><\/p>\n<p>\u6c42\u548c\u964d\u7ef4\uff1a\u53ef\u4ee5\u5bf9\u4efb\u610f\u5f20\u91cf\u8fdb\u884c\u5143\u7d20\u6c42\u548c\u64cd\u4f5c\uff0c\u9ed8\u8ba4\u60c5\u51b5\u4e0b\uff0c\u8c03\u7528\u6c42\u548c\u51fd\u6570\u4f1a\u6cbf\u6240\u6709\u7684\u8f74\u964d\u4f4e\u5f20\u91cf\u7684\u7ef4\u5ea6\uff0c\u4f7f\u5b83\u53d8\u4e3a\u4e00\u4e2a\u6807\u91cf\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_8\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A = torch.arange(20, dtype=torch.float32).reshape(5, 4)\r\nA.sum()\r\n# \u7ed3\u679c\uff1atensor(190.))<\/code><\/pre>\n<ul id=\"code_id_8\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u4e5f\u53ef\u6307\u5b9a\u5f20\u91cf\u6cbf\u67d0\u4e00\u4e2a\u8f74\u6765\u901a\u8fc7\u6c42\u548c\u964d\u4f4e\u7ef4\u5ea6\uff0c \u4ee5\u77e9\u9635\u4e3a\u4f8b\uff0c\u4e3a\u4e86\u901a\u8fc7\u6c42\u548c\u6240\u6709\u884c\u7684\u5143\u7d20\u6765\u964d\u7ef4\uff08\u8f740\uff09\uff0c\u53ef\u4ee5\u5728\u8c03\u7528\u51fd\u6570\u65f6\u6307\u5b9a<code>axis=0<\/code>\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_9\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A_sum_axis0 = A.sum(axis=0)\r\nA_sum_axis0, A_sum_axis0.shape\r\n# \u7ed3\u679c\uff1a(tensor([40., 45., 50., 55.]), torch.Size([4]))<\/code><\/pre>\n<ul id=\"code_id_9\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u6307\u5b9aaxis=1\u5c06\u901a\u8fc7\u6c47\u603b\u6240\u6709\u5217\u7684\u5143\u7d20\u964d\u7ef4\uff08\u8f741\uff09<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_10\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A_sum_axis1 = A.sum(axis=1)\r\nA_sum_axis1, A_sum_axis1.shape\r\n# \u7ed3\u679c\uff1a(tensor([ 6., 22., 38., 54., 70.]), torch.Size([5]))<\/code><\/pre>\n<ul id=\"code_id_10\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u4e09\u7ef4\u5f20\u91cf\uff0c\u8f74\uff08axis\uff09\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p>\u8f740\uff08axis=0\uff09\uff1a\u901a\u5e38\u8868\u793a\u5f20\u91cf\u4e2d\u7684\u7b2c\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e0d\u540c\u7684\u6570\u636e\u6837\u672c\u6216\u8005\u6279\u6b21\uff08batch\uff09\u3002<\/p>\n<p>\u8f741\uff08axis=1\uff09\uff1a\u901a\u5e38\u8868\u793a\u5f20\u91cf\u4e2d\u7684\u7b2c\u4e8c\u4e2a\u7ef4\u5ea6\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u6570\u636e\u7684\u884c\u3002<\/p>\n<p>\u8f742\uff08axis=2\uff09\uff1a\u901a\u5e38\u8868\u793a\u5f20\u91cf\u4e2d\u7684\u7b2c\u4e09\u4e2a\u7ef4\u5ea6\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u6570\u636e\u7684\u5217\u3002<\/p>\n<p>\u5e73\u5747\u503c\u8ba1\u7b97\uff1a\u5e73\u5747\u503c\u662f\u4e0e\u6c42\u548c\u76f8\u5173\u7684\u91cf\uff0c\u901a\u8fc7\u5c06\u603b\u548c\u9664\u4ee5\u5143\u7d20\u603b\u6570\u6765\u8ba1\u7b97\u3002\u8ba1\u7b97\u5e73\u5747\u503c\u7684\u51fd\u6570\u4e5f\u53ef\u6cbf\u6307\u5b9a\u8f74\u964d\u4f4e\u5f20\u91cf\u7684\u7ef4\u5ea6\u3002\u5982A.mean(axis = 0)\u8ba1\u7b97\u77e9\u9635 A \u6309\u5217\u7684\u5e73\u5747\u503c\uff0cA.mean()\u8ba1\u7b97\u6240\u6709\u5143\u7d20\u7684\u5e73\u5747\u503c\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_11\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A.mean(), A.sum() \/ A.numel() # \u7ed3\u679c\uff1a(tensor(9.5000), tensor(9.5000))\r\nA.mean(axis=0), A.sum(axis=0) \/ A.shape[0] # \u7ed3\u679c\uff1a(tensor([ 8.,  9., 10., 11.]), tensor([ 8.,  9., 10., 11.]))<\/code><\/pre>\n<ul id=\"code_id_11\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h4>\u975e\u964d\u7ef4\u6c42\u548c\u4e0e\u7d2f\u79ef\u6c42\u548c<\/h4>\n<p><strong>\u975e\u964d\u7ef4\u6c42\u548c<\/strong>\uff1a\u6709\u65f6\u5728\u8c03\u7528\u51fd\u6570\u8ba1\u7b97\u603b\u548c\u6216\u5747\u503c\u65f6\u4fdd\u6301\u8f74\u6570\u4e0d\u53d8\u5f88\u6709\u7528\u3002<\/p>\n<p>\u4f8b\u5982<code>sum_A = A.sum(axis = 1, keepdims = True)<\/code>\uff0c\u5bf9\u77e9\u9635 A \u6309\u884c\u6c42\u548c\u540e\u4ecd\u4fdd\u6301\u4e24\u4e2a\u8f74\uff0c\u7ed3\u679c\u5f62\u72b6\u4e3a (5, 1) \u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_12\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">sum_A = A.sum(axis=1, keepdims=True)\r\nsum_A<\/code><\/pre>\n<ul id=\"code_id_12\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_13\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">\u7531\u4e8e sum_A \u5728\u5bf9\u6bcf\u884c\u8fdb\u884c\u6c42\u548c\u540e\u4ecd\u4fdd\u6301\u4e24\u4e2a\u8f74\uff0c\u8fd9\u6837\u53ef\u4ee5\u901a\u8fc7\u5e7f\u64ad\u5c06 A \u9664\u4ee5 sum_A\uff0c\u5b9e\u73b0\u6309\u884c\u7684\u5f52\u4e00\u5316\u7b49\u64cd\u4f5c\u3002<\/code><\/pre>\n<ul id=\"code_id_13\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_14\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A \/ sum_A<\/code><\/pre>\n<ul id=\"code_id_14\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_15\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">\u6cbf\u67d0\u4e2a\u8f74\u8ba1\u7b97 A \u5143\u7d20\u7684\u7d2f\u79ef\u603b\u548c\uff0c \u6bd4\u5982 axis=0 \uff08\u6309\u884c\u8ba1\u7b97\uff09\uff0c\u53ef\u4ee5\u8c03\u7528 cumsum \u51fd\u6570\u3002 \u6b64\u51fd\u6570\u4e0d\u4f1a\u6cbf\u4efb\u4f55\u8f74\u964d\u4f4e\u8f93\u5165\u5f20\u91cf\u7684\u7ef4\u5ea6\u3002<\/code><\/pre>\n<ul id=\"code_id_15\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u7d2f\u79ef\u6c42\u548c\uff1a\u6cbf\u67d0\u4e2a\u8f74\u8ba1\u7b97\u5f20\u91cf\u5143\u7d20\u7684\u7d2f\u79ef\u603b\u548c\uff0c\u5982A.cumsum(axis = 0)\u6309\u884c\u8ba1\u7b97\u7d2f\u79ef\u603b\u548c\uff0c\u6b64\u51fd\u6570\u4e0d\u4f1a\u6cbf\u4efb\u4f55\u8f74\u964d\u4f4e\u8f93\u5165\u5f20\u91cf\u7684\u7ef4\u5ea6\u3002\u5728\u5206\u6790\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u6216\u9010\u6b65\u7d2f\u52a0\u7684\u7279\u5f81\u65f6\uff0c\u7d2f\u79ef\u6c42\u548c\u64cd\u4f5c\u80fd\u5e2e\u52a9\u83b7\u53d6\u6570\u636e\u7684\u7d2f\u79ef\u8d8b\u52bf\u548c\u72b6\u6001\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_16\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A.cumsum(axis=0)<\/code><\/pre>\n<ul id=\"code_id_16\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202504\/27\/a3cd91d51bcd42eb22471872c208b56dbb43da.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<h4>\u70b9\u79ef\uff08Dot Product\uff09<\/h4>\n<p>\u7ed9\u5b9a\u4e24\u4e2a\u5411\u91cf<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202504\/27\/628f31189f093a8bc19654d6e13df0ff00cab7.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c \u5b83\u4eec\u7684\u70b9\u79ef\uff08dot product\uff09\uff08<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/994334e80a3e97d2efd5838cc5af8a64ccd7ec.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u6216<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s4.51cto.com\/oss\/202504\/27\/d96fc4624e6315dc2c48299a1154db4a506879.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff09 \u662f\u76f8\u540c\u4f4d\u7f6e\u7684\u6309\u5143\u7d20\u4e58\u79ef\u7684\u548c\uff1a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202504\/27\/f6359ac992b3b46a5ad413a22f6000ff267880.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<\/p>\n<p><code><strong>1.torch.dot<\/strong><\/code><\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_17\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">\u529f\u80fd\uff1atorch.dot\u7528\u4e8e\u8ba1\u7b97\u4e24\u4e2a\u4e00\u7ef4\u5411\u91cf\u7684\u70b9\u79ef\uff08Dot Product\uff09\u3002\r\n \u8f93\u5165\u8981\u6c42\uff1a\u4e24\u4e2a\u8f93\u5165\u5fc5\u987b\u662f\u4e00\u7ef4\u5411\u91cf\uff08\u5373\u5f62\u72b6\u4e3a(n,)\u7684\u5f20\u91cf\uff09\uff0c\u4e14\u957f\u5ea6\u76f8\u540c\u3002\r\n \u8f93\u51fa\uff1a\u8fd4\u56de\u4e00\u4e2a\u6807\u91cf\uff0c\u8868\u793a\u4e24\u4e2a\u5411\u91cf\u7684\u70b9\u79ef\u3002\r\n \r\n \r\n \r\n \r\n \r\n import torcha = torch.tensor([1, 2, 3])b = torch.tensor([4, 5, 6])dot_product = torch.dot(a, b)print(\"\u70b9\u79ef\u7ed3\u679c\uff1a\", dot_product)  # \u8f93\u51fa\uff1a32\r\n\r\ntorch.dot\u7528\u4e8e\u8ba1\u7b97\u4e24\u4e2a\u4e00\u7ef4\u5411\u91cf\u7684\u70b9\u79ef\uff08Dot Product\uff09\u3002\r\nimport torch\r\na = torch.tensor([1, 2, 3])\r\nb = torch.tensor([4, 5, 6])\r\ndot_product = torch.dot(a, b)\r\nprint(\"\u70b9\u79ef\u7ed3\u679c\uff1a\", dot_product)  # \u8f93\u51fa\uff1a32<\/code><\/pre>\n<ul id=\"code_id_17\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<li>16.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><code><strong>2.torch.matmul<\/strong><\/code><\/p>\n<ul data-id=\"udcdd064-gOV94AkP\">\n<li data-id=\"ld70c578-gccZA35c\"><strong>\u529f\u80fd<\/strong>\uff1a<code>torch.matmul<\/code>\u7528\u4e8e\u8ba1\u7b97\u4e24\u4e2a\u5f20\u91cf\u7684\u77e9\u9635\u4e58\u79ef\uff08Matrix Product\uff09\uff0c\u652f\u6301\u4e00\u7ef4\u5411\u91cf\u3001\u4e8c\u7ef4\u77e9\u9635\u4ee5\u53ca\u66f4\u9ad8\u7ef4\u5ea6\u5f20\u91cf\u7684\u4e58\u6cd5\u3002<\/li>\n<li data-id=\"ld70c578-M99cTlGU\"><strong>\u8f93\u5165\u8981\u6c42<\/strong>\uff1a<br \/>\n\u5bf9\u4e8e\u4e00\u7ef4\u5411\u91cf\uff0c<code>torch.matmul<\/code>\u4f1a\u5c06\u5b83\u4eec\u89c6\u4e3a\u884c\u5411\u91cf\u548c\u5217\u5411\u91cf\uff0c\u8ba1\u7b97\u5b83\u4eec\u7684\u77e9\u9635\u4e58\u79ef\u3002<br \/>\n\u5bf9\u4e8e\u4e8c\u7ef4\u77e9\u9635\uff0c<code>torch.matmul<\/code>\u8ba1\u7b97\u77e9\u9635\u4e58\u6cd5\u3002<br \/>\n\u5bf9\u4e8e\u9ad8\u7ef4\u5ea6\u5f20\u91cf\uff0c<code>torch.matmul<\/code>\u4f1a\u8ba1\u7b97\u6279\u91cf\u77e9\u9635\u4e58\u79ef\u3002<\/li>\n<li data-id=\"ld70c578-EjNdNc54\"><strong>\u8f93\u51fa<\/strong>\uff1a\u8fd4\u56de\u4e00\u4e2a\u5f20\u91cf\uff0c\u5f62\u72b6\u6839\u636e\u8f93\u5165\u5f20\u91cf\u7684\u5f62\u72b6\u51b3\u5b9a\u3002<\/li>\n<\/ul>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_18\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">import torch\r\n# \u4e00\u7ef4\u5411\u91cf\r\na = torch.tensor([1, 2, 3])\r\nb = torch.tensor([4, 5, 6])\r\n# torch.matmul \u4f1a\u5c06\u4e00\u7ef4\u5411\u91cf\u89c6\u4e3a\u884c\u5411\u91cf\u548c\u5217\u5411\u91cf\uff0c\u8ba1\u7b97\u77e9\u9635\u4e58\u79ef\r\nmatmul_result = torch.matmul(a, b)\r\nprint(\"\u77e9\u9635\u4e58\u79ef\u7ed3\u679c\uff1a\", matmul_result)  # \u8f93\u51fa\uff1a32\r\n# \u4e8c\u7ef4\u77e9\u9635\r\nA = torch.tensor([[1, 2], [3, 4]])\r\nB = torch.tensor([[5, 6], [7, 8]])\r\nmatrix_product = torch.matmul(A, B)\r\nprint(\"\u77e9\u9635\u4e58\u79ef\u7ed3\u679c\uff1a\\n\", matrix_product)\r\n# \u8f93\u51fa\uff1a\r\n# tensor([[19, 22],\r\n#         [43, 50]])<\/code><\/pre>\n<ul id=\"code_id_18\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_19\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">\u5bf9\u4e8e\u4e00\u7ef4\u5411\u91cf\r\ntorch.dot(a, b)\r\ntorch.matmul(a, b)\r\ntorch.dot\r\ntorch.matmul\r\n(1,)<\/code><\/pre>\n<ul id=\"code_id_19\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><strong>\u5bf9\u4e8e\u4e8c\u7ef4\u53ca\u9ad8\u7ef4\u77e9\u9635<\/strong>\uff1a<code>torch.matmul<\/code>\u53ef\u4ee5\u8ba1\u7b97\u77e9\u9635\u4e58\u79ef\uff0c\u4f46<code>torch.dot<\/code>\u4e0d\u80fd\u7528\u4e8e\u4e8c\u7ef4\u77e9\u9635\u3002<\/p>\n<h4>Hadamard\u79ef<\/h4>\n<p>\u4e24\u4e2a\u77e9\u9635\u7684\u6309\u5143\u7d20\u4e58\u6cd5\u79f0\u4e3aHadamard\u79ef\uff08Hadamard product\uff09\uff08\u6570\u5b66\u7b26\u53f7<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/d48d09e2840d2e99d06842a30ddb4385c35717.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_20\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">A * B<\/code><\/pre>\n<ul id=\"code_id_20\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202504\/27\/390fd9f0804173dfb8159698fa5c910c2f43cd.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<h4>\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\uff0cHadamard \u79ef\u548c\u70b9\u79ef\u7684\u5e94\u7528\u573a\u666f<\/h4>\n<p>Hadamard \u79ef\u662f\u6307\u4e24\u4e2a\u76f8\u540c\u7ef4\u5ea6\u7684\u5f20\u91cf\u9010\u5143\u7d20\u76f8\u4e58\uff0c\u901a\u5e38\u7528\u4e8e\u4ee5\u4e0b\u573a\u666f\uff1a<\/p>\n<ol class=\"list-paddingleft-1\" data-id=\"odd3d8fc-WLBYFjTH\">\n<li data-id=\"ld70c578-JM0QhUIP\">\u6fc0\u6d3b\u51fd\u6570\u7684\u9010\u5143\u7d20\u64cd\u4f5c\uff1a\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u6fc0\u6d3b\u51fd\u6570\uff08\u5982 ReLU\u3001Sigmoid \u6216 Tanh\uff09\u901a\u5e38\u5bf9\u8f93\u5165\u5f20\u91cf\u9010\u5143\u7d20\u5e94\u7528\u3002\u8fd9\u79cd\u64cd\u4f5c\u53ef\u4ee5\u770b\u4f5c\u662f\u8f93\u5165\u5f20\u91cf\u4e0e\u4e00\u4e2a\u9010\u5143\u7d20\u7684\u975e\u7ebf\u6027\u51fd\u6570\u7684 Hadamard \u79ef\u3002\u4f8b\u5982\uff0c<code>output = activation(input)<\/code>\uff0c\u5176\u4e2d<code>activation<\/code>\u662f\u9010\u5143\u7d20\u7684\u975e\u7ebf\u6027\u51fd\u6570\u3002<\/li>\n<li data-id=\"ld70c578-6ia7qZ3V\">\u7279\u5f81\u878d\u5408\uff1a\u5728\u591a\u7279\u5f81\u878d\u5408\u65f6\uff0cHadamard \u79ef\u53ef\u4ee5\u7528\u4e8e\u5c06\u4e0d\u540c\u6765\u6e90\u7684\u7279\u5f81\u9010\u5143\u7d20\u76f8\u4e58\uff0c\u4ece\u800c\u5b9e\u73b0\u7279\u5f81\u7684\u52a0\u6743\u878d\u5408\u3002\u4f8b\u5982\uff0c\u5728\u67d0\u4e9b\u6ce8\u610f\u529b\u673a\u5236\u4e2d\uff0c\u901a\u8fc7 Hadamard \u79ef\u5bf9\u7279\u5f81\u8fdb\u884c\u52a0\u6743\uff0c\u4ee5\u7a81\u51fa\u91cd\u8981\u7279\u5f81\u3002<\/li>\n<li data-id=\"ld70c578-bij9c34X\">LSTM \u95e8\u63a7\u673a\u5236\uff1a\u5728\u957f\u77ed\u671f\u8bb0\u5fc6\u7f51\u7edc\uff08LSTM\uff09\u4e2d\uff0cHadamard \u79ef\u7528\u4e8e\u8ba1\u7b97\u9057\u5fd8\u95e8\u548c\u8f93\u5165\u95e8\u7684\u8f93\u51fa\u3002\u9057\u5fd8\u95e8\u548c\u8f93\u5165\u95e8\u7684\u8f93\u51fa\u901a\u8fc7 Hadamard \u79ef\u9010\u5143\u7d20\u4f5c\u7528\u4e8e\u7ec6\u80de\u72b6\u6001\u3002\u5177\u4f53\u516c\u5f0f\u4e3a\uff1a<img data-dominant-color=\"f3f3f3\" data-has-transparency=\"false\" style=\"--dominant-color: #f3f3f3;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-25630\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e4eaca404f0d68634689404ab17552c2d080aa.png\" width=\"293\" height=\"43\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e4eaca404f0d68634689404ab17552c2d080aa.png 293w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/04\/e4eaca404f0d68634689404ab17552c2d080aa-150x22.png 150w\" sizes=\"auto, (max-width: 293px) 100vw, 293px\" \/>\u3002<\/li>\n<li data-id=\"ld70c578-XseOc2e7\">\u56fe\u50cf\u5904\u7406\uff1a\u5728\u56fe\u50cf\u5904\u7406\u4e2d\uff0cHadamard \u79ef\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u878d\u5408\u3002\u4f8b\u5982\uff0c\u5c06\u4e0d\u540c\u6ce2\u6bb5\u7684\u56fe\u50cf\u9010\u5143\u7d20\u76f8\u4e58\uff0c\u4ee5\u589e\u5f3a\u7279\u5b9a\u7684\u5149\u8c31\u7279\u5f81\u3002\u6b64\u5916\uff0cHadamard \u79ef\u8fd8\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u6ee4\u6ce2\uff0c\u901a\u8fc7\u9010\u5143\u7d20\u76f8\u4e58\u5b9e\u73b0\u7279\u5b9a\u7684\u6ee4\u6ce2\u6548\u679c\u3002<\/li>\n<\/ol>\n<p>\u70b9\u79ef\u901a\u5e38\u7528\u4e8e\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u7684\u76f8\u4f3c\u5ea6\u6216\u8fdb\u884c\u7ebf\u6027\u53d8\u6362\uff0c\u5e38\u89c1\u4e8e\u4ee5\u4e0b\u573a\u666f\uff1a<\/p>\n<ol class=\"list-paddingleft-1\" data-id=\"odd3d8fc-BL65N3Va\">\n<li data-id=\"ld70c578-b5q13aLZ\">\u6ce8\u610f\u529b\u673a\u5236\uff1a\u70b9\u79ef\u5728\u6ce8\u610f\u529b\u673a\u5236\u4e2d\u5e7f\u6cdb\u4f7f\u7528\uff0c\u7528\u4e8e\u8ba1\u7b97\u67e5\u8be2\uff08query\uff09\u548c\u952e\uff08key\uff09\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6\u3002\u4f8b\u5982\uff0c\u5728\u70b9\u79ef\u6ce8\u610f\u529b\u673a\u5236\u4e2d\uff0c\u901a\u8fc7\u8ba1\u7b97\u67e5\u8be2\u548c\u952e\u7684\u70b9\u79ef\u6765\u751f\u6210\u6ce8\u610f\u529b\u6743\u91cd\u3002\u5177\u4f53\u516c\u5f0f\u4e3a\uff1a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202504\/27\/42990c751e2c2c4a8d5538d367c4cb82e6ed28.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<\/li>\n<li data-id=\"ld70c578-QJ2WDXjV\">\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08CNN\uff09\uff1a\u5728\u5377\u79ef\u5c42\u4e2d\uff0c\u5377\u79ef\u6838\u4e0e\u8f93\u5165\u7279\u5f81\u56fe\u7684\u5377\u79ef\u64cd\u4f5c\u672c\u8d28\u4e0a\u662f\u70b9\u79ef\u8ba1\u7b97\u3002\u6bcf\u4e2a\u795e\u7ecf\u5143\u4e0e\u8f93\u5165\u7279\u5f81\u56fe\u4e0a\u7684\u4e00\u4e2a\u5c0f\u533a\u57df\u8fdb\u884c\u70b9\u79ef\u8fd0\u7b97\uff0c\u4ece\u800c\u63d0\u53d6\u51fa\u6709\u7528\u7684\u7279\u5f81\u3002<\/li>\n<li data-id=\"ld70c578-rSIa0N3U\">\u7279\u5f81\u5411\u91cf\u7684\u76f8\u4f3c\u5ea6\u8ba1\u7b97\uff1a\u5728\u81ea\u7136\u8bed\u8a00\u5904\u7406\uff08NLP\uff09\u4e2d\uff0c\u8bcd\u5411\u91cf\u4e4b\u95f4\u7684\u70b9\u79ef\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u8bcd\u4e0e\u8bcd\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6\u3002\u4f8b\u5982\uff0c\u901a\u8fc7\u70b9\u79ef\u8ba1\u7b97\u4e24\u4e2a\u8bcd\u5411\u91cf\u7684\u76f8\u4f3c\u5ea6\uff0c\u8fdb\u800c\u5b9e\u73b0\u6587\u672c\u5206\u7c7b\u548c\u60c5\u611f\u5206\u6790\u3002<\/li>\n<li data-id=\"ld70c578-WihGivw6\">\u6b63\u5219\u5316\uff1a\u5728 L2 \u6b63\u5219\u5316\uff08\u6743\u91cd\u8870\u51cf\uff09\u4e2d\uff0c\u70b9\u79ef\u7528\u4e8e\u8ba1\u7b97\u6743\u91cd\u77e9\u9635\u7684 Frobenius \u8303\u6570\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6743\u91cd\u77e9\u9635\u4e0e\u81ea\u8eab\u7684\u70b9\u79ef\uff08\u5373 Frobenius \u5185\u79ef\uff09\u7528\u4e8e\u6b63\u5219\u5316\u9879\u3002<\/li>\n<\/ol>\n<p>\u603b\u7ed3\uff1a<\/p>\n<ul data-id=\"u738a58b-Z2269KdS\">\n<li data-id=\"ld70c578-P6U0H9Pp\">Hadamard \u79ef\uff1a\u9002\u7528\u4e8e\u9010\u5143\u7d20\u64cd\u4f5c\uff0c\u5982\u6fc0\u6d3b\u51fd\u6570\u3001\u7279\u5f81\u878d\u5408\u3001LSTM \u95e8\u63a7\u673a\u5236\u548c\u56fe\u50cf\u5904\u7406\u3002<\/li>\n<li data-id=\"ld70c578-fJ3qcLMN\">\u70b9\u79ef\uff1a\u9002\u7528\u4e8e\u8ba1\u7b97\u5411\u91cf\u76f8\u4f3c\u5ea6\u3001\u5377\u79ef\u64cd\u4f5c\u3001\u6ce8\u610f\u529b\u673a\u5236\u548c\u6b63\u5219\u5316\u3002<\/li>\n<\/ul>\n<h4>\u77e9\u9635-\u5411\u91cf\u79ef<\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u8bbe\u77e9\u9635<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202504\/27\/2139a468385b0739a7223513a8c6aaf27d4263.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u5411\u91cf<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202504\/27\/05a88e94571a451c0fb415b077aae536d36a22.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u90a3\u4e48\u77e9\u9635 &#8211; \u5411\u91cf\u79ef<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/6242ed3648fcf69aa0f920be685701bd68407b.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u662f\u4e00\u4e2am\u7ef4\u5411\u91cf<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202504\/27\/028696140b94d41052f0502b07af32e43590a1.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002\u5176\u8ba1\u7b97\u65b9\u5f0f\u662fy\u7684\u7b2ci\u4e2a\u5143\u7d20<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202504\/27\/07b97b50236114c7abb2134ae9ee68f2d5d401.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u5176\u4e2d<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202504\/27\/93fa6e2606a281fc50d235b0f12bd24cb182d9.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u662f\u77e9\u9635A\u7684\u7b2ci\u884c\u7b2cj\u5217\u7684\u5143\u7d20\uff0c<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202504\/27\/24b5ba405cd35e0331e7823a9a06d8314075f7.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u662f\u5411\u91cfx\u7684\u7b2cj\u4e2a\u5143\u7d20\u3002<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202504\/27\/368cc0d71a9d4ccf2857988decf526146ad7bf.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><strong>\u51e0\u4f55\u610f\u4e49<\/strong>\uff1a<strong>\u77e9\u9635 &#8211; \u5411\u91cf\u79ef\u53ef\u4ee5\u770b\u4f5c\u662f\u5bf9\u5411\u91cfx\u8fdb\u884c\u7ebf\u6027\u53d8\u6362<\/strong>\uff0c\u5c06\u5176\u4ecen\u7ef4\u7a7a\u95f4\u6620\u5c04\u5230m\u7ef4\u7a7a\u95f4\u3002\u4f8b\u5982\uff0c\u5728\u4e8c\u7ef4\u5e73\u9762\u4e2d\uff0c\u4e00\u4e2a2\u00d72\u7684\u77e9\u9635\u53ef\u4ee5\u5bf9\u5e73\u9762\u4e0a\u7684\u5411\u91cf\u8fdb\u884c\u65cb\u8f6c\u3001\u7f29\u653e\u7b49\u64cd\u4f5c\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u793a\u4f8b<\/strong>\uff1a<\/p>\n<ul data-id=\"u738a58b-Skhn1JZf\">\n<li data-id=\"ld70c578-Af5DGBNq\">\u8bbe\u77e9\u9635<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202504\/27\/e7e4a38413b5adbbb90668f92f71531223f921.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u5411\u91cf<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202504\/27\/529febc575e417522de410b3f90201d75a9ffa.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<\/li>\n<li data-id=\"ld70c578-XA1Jkk2c\">\u5219<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202504\/27\/761488037c6696e02349922f8aba655475acea.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<\/li>\n<\/ul>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_21\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">torch.mv(A, x)<\/code><\/pre>\n<ul id=\"code_id_21\" class=\"pre-numbering\">\n<li>1.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h4>\u77e9\u9635-\u77e9\u9635\u4e58\u6cd5<\/h4>\n<p>\u5b9a\u4e49\uff1a\u8bbe\u77e9\u9635<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202504\/27\/e5a36cd813951ba87979038bc86fe1abd039b4.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u77e9\u9635<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202504\/27\/e374815174d6c6c6378421c77cab59533bfab9.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u5219\u77e9\u9635C=AB\u662f\u4e00\u4e2am\u00d7p\u7684\u77e9\u9635\uff0c\u5176\u4e2dC\u7684\u7b2ci\u884c\u7b2cj\u5217\u7684\u5143\u7d20<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s5.51cto.com\/oss\/202504\/27\/28797b988b2a3604a192087138586792ae67cb.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002\u8fd9\u610f\u5473\u7740C\u7684\u6bcf\u4e2a\u5143\u7d20\u662fA\u7684\u5bf9\u5e94\u884c\u4e0eB\u7684\u5bf9\u5e94\u5217\u7684\u5143\u7d20\u4e58\u79ef\u4e4b\u548c\u3002<\/p>\n<h3><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/586f6ef8329380f981a2646cf8f4e1c9a4ba24.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/h3>\n<h3><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202504\/27\/45d8c3d55db1f64f32a6584531c41d134ac53d.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/h3>\n<h3><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202504\/27\/d56ca7695e3d411064a0784670c7881af293dd.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/h3>\n<p><strong>\u51e0\u4f55\u610f\u4e49<\/strong>\uff1a\u77e9\u9635 &#8211; \u77e9\u9635\u4e58\u6cd5\u53ef\u4ee5\u8868\u793a\u591a\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u590d\u5408\u3002\u4f8b\u5982\uff0c\u5148\u8fdb\u884c\u4e00\u4e2a\u65cb\u8f6c\u53d8\u6362\uff0c\u518d\u8fdb\u884c\u4e00\u4e2a\u7f29\u653e\u53d8\u6362\uff0c\u8fd9\u4e24\u4e2a\u53d8\u6362\u5bf9\u5e94\u7684\u77e9\u9635\u76f8\u4e58\u5c31\u5f97\u5230\u4e86\u8868\u793a\u8fd9\u4e24\u4e2a\u53d8\u6362\u590d\u5408\u6548\u679c\u7684\u77e9\u9635\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u793a\u4f8b<\/strong>\uff1a<\/p>\n<ul data-id=\"u738a58b-BFJj2GIW\">\n<li data-id=\"ld70c578-Pw4Axh6n\">\u8bbe\u77e9\u9635<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202504\/27\/a94e0646442747f2c7564966e9d91df7bb267f.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u77e9\u9635<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202504\/27\/a27f51466a7f11f1376234d8da47554349d7ef.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<\/li>\n<li data-id=\"ld70c578-Easr80IR\">\u5219<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202504\/27\/c6a3f0c45e910c203f7145ee8377cdf380ad89.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002<\/li>\n<\/ul>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_22\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-plain\" tabindex=\"0\"><code class=\"language-plain\">torch.mm(A, B)<\/code><\/pre>\n<ul id=\"code_id_22\" class=\"pre-numbering\">\n<li><\/li>\n<\/ul>\n<div class=\"toolbar\">\u6587\u7ae0\u6765\u81ea\uff1a51CTO<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_25626\" class=\"pvc_stats total_only  \" data-element-id=\"25626\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" version=\"1.0\" 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class=\"pvc_clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\uff0c\u6807\u91cf\u3001\u5411\u91cf\u3001\u77e9\u9635\u548c\u5f20\u91cf\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u57fa\u672c\u6982\u5ff5\u3002\u672c\u6587\u5c06\u7b80\u8981\u4ecb\u7ecd\u8fd9\u4e9b\u6570\u5b66\u57fa\u7840\uff0c\u5e2e\u52a9\u8bfb\u8005\u66f4\u597d\u5730\u7406\u89e3\u5b83\u4eec [&hellip;]<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_25626\" class=\"pvc_stats total_only  \" data-element-id=\"25626\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" version=\"1.0\" viewBox=\"0 0 502 315\" preserveAspectRatio=\"xMidYMid meet\"><g transform=\"translate(0,332) scale(0.1,-0.1)\" fill=\"\" stroke=\"none\"><path d=\"M2394 3279 l-29 -30 -3 -207 c-2 -182 0 -211 15 -242 39 -76 157 -76 196 0 15 31 17 60 15 243 l-3 209 -33 29 c-26 23 -41 29 -80 29 -41 0 -53 -5 -78 -31z\"\/><path d=\"M3085 3251 c-45 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class=\"pvc_clear\"><\/div>\n","protected":false},"author":56,"featured_media":25628,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,23,20,80],"tags":[124,113,1393],"class_list":["post-25626","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai","category-23","category-20","category-80","tag-ai","tag-113","tag-1393"],"_links":{"self":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts\/25626","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/comments?post=25626"}],"version-history":[{"count":1,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts\/25626\/revisions"}],"predecessor-version":[{"id":25631,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts\/25626\/revisions\/25631"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/media\/25628"}],"wp:attachment":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/media?parent=25626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/categories?post=25626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/tags?post=25626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}