{"id":104502,"date":"2026-09-12T16:09:33","date_gmt":"2026-09-12T08:09:33","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/104502.html"},"modified":"2026-09-12T16:09:33","modified_gmt":"2026-09-12T08:09:33","slug":"%e3%80%8a%e5%8a%a8%e6%89%8b%e5%ad%a6%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%ef%bc%88pytorch%e7%89%88%ef%bc%89%e3%80%8b%e7%ac%ac2%e7%ab%a0-%e9%a2%84%e5%a4%87%e7%9f%a5%e8%af%86-%e8%af%bb%e4%b9%a6%e7%ac%94","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/104502.html","title":{"rendered":"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0"},"content":{"rendered":"<p>\u76ee\u5f55<\/p>\n<ul>\n<li>2.1 \u6570\u636e\u64cd\u4f5c<\/li>\n<li>2.2 \u6570\u636e\u9884\u5904\u7406<\/li>\n<li>2.3 \u7ebf\u6027\u4ee3\u6570<\/li>\n<li>2.4 \u5fae\u79ef\u5206<\/li>\n<li>2.5 \u81ea\u52a8\u5fae\u5206<\/li>\n<li>2.6 \u6982\u7387<\/li>\n<li>2.7 \u67e5\u9605\u6587\u6863<\/li>\n<li>\u672c\u7ae0\u6838\u5fc3\u603b\u7ed3&#xff08;\u5fc5\u770b&#xff09;<\/li>\n<li>\u7ed3\u8bed<\/li>\n<\/ul>\n<hr \/>\n<p>\u2003\u2003\u8fd9\u4e00\u7ae0\u662f\u5168\u4e66\u7684&#034;\u5de5\u5177\u7bb1&#034;\u2014\u2014\u6211\u4eec\u8981\u628a\u540e\u9762\u5199\u4ee3\u7801\u9700\u8981\u7684\u57fa\u7840\u64cd\u4f5c\u5168\u90e8\u8fc7\u4e00\u904d\u3002\u522b\u5acc\u57fa\u7840&#xff0c;80%\u7684\u6df1\u5ea6\u5b66\u4e60bug\u90fd\u51fa\u5728\u8fd9\u4e9b\u57fa\u7840\u64cd\u4f5c\u4e0a&#xff08;\u5f20\u91cf\u7ef4\u5ea6\u4e0d\u5bf9\u3001\u7d22\u5f15\u8d8a\u754c\u3001\u68af\u5ea6\u6ca1\u6e05\u96f6\u2026\u2026&#xff09;&#xff0c;\u6240\u4ee5\u8fd9\u4e00\u7ae0\u4e00\u5b9a\u8981\u52a8\u624b\u6572\u4ee3\u7801\u3002<\/p>\n<p>\u2003\u2003\u8fd9\u4e00\u7ae0\u7684\u5185\u5bb9\u5305\u62ec&#xff1a;PyTorch\u5f20\u91cf\u64cd\u4f5c\u3001\u6570\u636e\u9884\u5904\u7406\u3001\u7ebf\u6027\u4ee3\u6570\u3001\u5fae\u79ef\u5206\u3001\u81ea\u52a8\u5fae\u5206\u3001\u6982\u7387\u7edf\u8ba1\u3002\u6bcf\u4e00\u90e8\u5206\u6211\u4eec\u90fd\u914d\u4e86\u53ef\u8fd0\u884c\u7684\u4ee3\u7801\u548c\u771f\u5b9e\u8f93\u51fa\u3002<\/p>\n<h3>2.1 \u6570\u636e\u64cd\u4f5c<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080929-6aa508b96a207.jpg\" alt=\"\u5f20\u91cf\u6570\u636e\u64cd\u4f5c\" \/><\/p>\n<p>\u2003\u2003\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d&#xff0c;\u6240\u6709\u6570\u636e\u90fd\u4ee5**\u5f20\u91cf&#xff08;tensor&#xff09;**\u7684\u5f62\u5f0f\u5b58\u50a8\u548c\u8fd0\u7b97\u3002\u4f60\u53ef\u4ee5\u628a\u5f20\u91cf\u7406\u89e3\u4e3a\u591a\u7ef4\u6570\u7ec4&#xff1a;0\u7ef4\u662f\u6807\u91cf&#xff0c;1\u7ef4\u662f\u5411\u91cf&#xff0c;2\u7ef4\u662f\u77e9\u9635&#xff0c;3\u7ef4\u53ca\u4ee5\u4e0a\u5c31\u662f\u5f20\u91cf\u3002<\/p>\n<h4>2.1.1 \u5165\u95e8<\/h4>\n<p><span class=\"token keyword\">import<\/span> torch<\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u5f20\u91cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">12<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x &#061;&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x.shape &#061;&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u5f62\u72b6<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x.numel() &#061;&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>numel<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u5143\u7d20\u603b\u6570<\/span><\/p>\n<p><span class=\"token comment\"># \u6539\u53d8\u5f62\u72b6&#xff08;\u4e0d\u6539\u53d8\u5143\u7d20\u6570\u91cf\u548c\u503c&#xff09;<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;X &#061; x.reshape(3,4):\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u7279\u6b8a\u5f20\u91cf<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.zeros((2,3,4)):\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>zeros<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.ones((2,3,4)) shape:&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.randn(3,4):\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>x &#061; tensor([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11.])<br \/>\nx.shape &#061; torch.Size([12])<br \/>\nx.numel() &#061; 12<br \/>\nX &#061; x.reshape(3,4):<br \/>\n tensor([[ 0.,  1.,  2.,  3.],<br \/>\n        [ 4.,  5.,  6.,  7.],<br \/>\n        [ 8.,  9., 10., 11.]])<\/p>\n<p>\u2003\u2003\u8981\u70b9&#xff1a;reshape \u53ea\u6539\u53d8\u5f20\u91cf\u7684&#034;\u89c6\u56fe&#034;&#xff0c;\u4e0d\u6539\u53d8\u5e95\u5c42\u6570\u636e\u3002numel() \u8fd4\u56de\u5143\u7d20\u603b\u6570&#xff0c;shape \u8fd4\u56de\u5404\u7ef4\u5ea6\u5927\u5c0f\u3002<\/p>\n<h4>2.1.2 \u8fd0\u7b97\u7b26<\/h4>\n<p>x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x &#043; y:&#034;<\/span><span class=\"token punctuation\">,<\/span> x <span class=\"token operator\">&#043;<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x * y:&#034;<\/span><span class=\"token punctuation\">,<\/span> x <span class=\"token operator\">*<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x ** y:&#034;<\/span><span class=\"token punctuation\">,<\/span> x <span class=\"token operator\">**<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.exp(x):&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>exp<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5f20\u91cf\u62fc\u63a5<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">12<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\nY <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;cat dim&#061;0:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>cat<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> Y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6309\u884c\u62fc\u63a5<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;cat dim&#061;1:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>cat<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> Y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6309\u5217\u62fc\u63a5<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;X &#061;&#061; Y:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> X <span class=\"token operator\">&#061;&#061;<\/span> Y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;X.sum():&#034;<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>x &#043; y: tensor([ 3.,  4.,  6., 10.])<br \/>\nx * y: tensor([ 2.,  4.,  8., 16.])<br \/>\nx ** y: tensor([ 1.,  4., 16., 64.])<br \/>\ntorch.exp(x): tensor([2.7183e&#043;00, 7.3891e&#043;00, 5.4598e&#043;01, 2.9810e&#043;03])<br \/>\nX.sum(): tensor(66.)<\/p>\n<h4>2.1.3 \u5e7f\u64ad\u673a\u5236<\/h4>\n<p>\u2003\u2003\u5f53\u4e24\u4e2a\u5f20\u91cf\u5f62\u72b6\u4e0d\u540c\u65f6&#xff0c;PyTorch\u4f1a\u5c1d\u8bd5\u5e7f\u64ad&#xff08;broadcasting&#xff09;\u2014\u2014\u628a\u5c0f\u7684\u5f20\u91cf&#034;\u590d\u5236\u6269\u5c55&#034;\u5230\u548c\u5927\u7684\u5f20\u91cf\u4e00\u6837\u7684\u5f62\u72b6&#xff0c;\u518d\u8fdb\u884c\u8fd0\u7b97\u3002<\/p>\n<p>a <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># 3\u884c1\u5217<\/span><br \/>\nb <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># 1\u884c2\u5217<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;a &#043; b (broadcast to 3&#215;2):\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> a <span class=\"token operator\">&#043;<\/span> b<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>a &#043; b (broadcast to 3&#215;2):<br \/>\n tensor([[0, 1],<br \/>\n        [1, 2],<br \/>\n        [2, 3]])<\/p>\n<p>\u2003\u2003a&#xff08;3\u00d71&#xff09;\u88ab\u5e7f\u64ad\u62103\u00d72&#xff08;\u6bcf\u5217\u590d\u5236&#xff09;&#xff0c;b&#xff08;1\u00d72&#xff09;\u88ab\u5e7f\u64ad\u62103\u00d72&#xff08;\u6bcf\u884c\u590d\u5236&#xff09;&#xff0c;\u7136\u540e\u9010\u5143\u7d20\u76f8\u52a0\u3002<\/p>\n<h4>2.1.4 \u7d22\u5f15\u548c\u5207\u7247<\/h4>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;X[-1]:&#034;<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span>       <span class=\"token comment\"># \u6700\u540e\u4e00\u884c<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;X[1:3]:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u7b2c2\u30013\u884c<\/span><br \/>\nX<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">9<\/span>                   <span class=\"token comment\"># \u4fee\u6539\u5355\u4e2a\u5143\u7d20<\/span><br \/>\nX<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">12<\/span>                <span class=\"token comment\"># \u4fee\u6539\u533a\u57df<\/span><\/p>\n<h4>2.1.5 \u8282\u7701\u5185\u5b58<\/h4>\n<p>\u2003\u2003Y &#061; Y &#043; X \u4f1a\u65b0\u5206\u914d\u5185\u5b58\u7ed9Y&#xff0c;\u800c Y &#043;&#061; X \u6216 Y[:] &#061; Y &#043; X \u662f\u539f\u5730\u64cd\u4f5c&#xff0c;\u4e0d\u5206\u914d\u65b0\u5185\u5b58\u3002\u8bad\u7ec3\u6a21\u578b\u65f6\u53c2\u6570\u66f4\u65b0\u8981\u7528\u539f\u5730\u64cd\u4f5c&#xff0c;\u5426\u5219\u5185\u5b58\u4f1a\u7206\u3002<\/p>\n<p>before <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">id<\/span><span class=\"token punctuation\">(<\/span>Y<span class=\"token punctuation\">)<\/span><br \/>\nY <span class=\"token operator\">&#061;<\/span> Y <span class=\"token operator\">&#043;<\/span> X<br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;id(Y) changed:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">id<\/span><span class=\"token punctuation\">(<\/span>Y<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">!&#061;<\/span> before<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># True&#xff0c;\u65b0\u5206\u914d\u4e86\u5185\u5b58<\/span><\/p>\n<p>Z <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>zeros_like<span class=\"token punctuation\">(<\/span>Y<span class=\"token punctuation\">)<\/span><br \/>\nZ<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> X <span class=\"token operator\">&#043;<\/span> Y  <span class=\"token comment\"># \u539f\u5730\u64cd\u4f5c&#xff0c;\u4e0d\u5206\u914d\u65b0\u5185\u5b58<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>id(Y) changed after Y &#061; Y &#043; X: True<br \/>\nid(Z) before: 4484860864<br \/>\nid(Z) after Z[:] &#061; X&#043;Y: 4484860864<br \/>\nid(X) unchanged after X &#043;&#061; Y: True<\/p>\n<h4>2.1.6 \u8f6c\u6362\u4e3a\u5176\u4ed6Python\u5bf9\u8c61<\/h4>\n<p>A <span class=\"token operator\">&#061;<\/span> X<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>           <span class=\"token comment\"># \u5f20\u91cf \u2192 numpy\u6570\u7ec4<\/span><br \/>\nB <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>from_numpy<span class=\"token punctuation\">(<\/span>A<span class=\"token punctuation\">)<\/span> <span class=\"token comment\"># numpy\u6570\u7ec4 \u2192 \u5f20\u91cf<\/span><br \/>\na <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">3.5<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;a.item():&#034;<\/span><span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6807\u91cf\u5f20\u91cf \u2192 Python\u6807\u91cf<\/span><\/p>\n<h3>2.2 \u6570\u636e\u9884\u5904\u7406<\/h3>\n<p>\u2003\u2003\u771f\u5b9e\u4e16\u754c\u7684\u6570\u636e\u4e0d\u662f\u5e72\u51c0\u7684\u5f20\u91cf&#xff0c;\u800c\u662fCSV\u3001JSON\u3001\u6570\u636e\u5e93\u91cc\u7684&#034;\u810f\u6570\u636e&#034;\u3002\u6211\u4eec\u9700\u8981\u7528pandas\u8bfb\u53d6\u3001\u6e05\u6d17&#xff0c;\u518d\u8f6c\u6210\u5f20\u91cf\u3002<\/p>\n<h4>2.2.1 \u8bfb\u53d6\u6570\u636e\u96c6<\/h4>\n<p><span class=\"token keyword\">import<\/span> os<br \/>\n<span class=\"token keyword\">import<\/span> pandas <span class=\"token keyword\">as<\/span> pd<\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u4e00\u4e2a\u5c0f\u6570\u636e\u96c6<\/span><br \/>\nos<span class=\"token punctuation\">.<\/span>makedirs<span class=\"token punctuation\">(<\/span>os<span class=\"token punctuation\">.<\/span>path<span class=\"token punctuation\">.<\/span>join<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;..&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;data&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> exist_ok<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\ndata_file <span class=\"token operator\">&#061;<\/span> os<span class=\"token punctuation\">.<\/span>path<span class=\"token punctuation\">.<\/span>join<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;..&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;data&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;house_tiny.csv&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">with<\/span> <span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>data_file<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;w&#039;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">as<\/span> f<span class=\"token punctuation\">:<\/span><br \/>\n    f<span class=\"token punctuation\">.<\/span>write<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;NumRooms,Alley,Price\\\\n&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    f<span class=\"token punctuation\">.<\/span>write<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;NA,Pave,127500\\\\n&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    f<span class=\"token punctuation\">.<\/span>write<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;2,NA,106000\\\\n&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    f<span class=\"token punctuation\">.<\/span>write<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;4,NA,178100\\\\n&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    f<span class=\"token punctuation\">.<\/span>write<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;NA,NA,140000\\\\n&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>data <span class=\"token operator\">&#061;<\/span> pd<span class=\"token punctuation\">.<\/span>read_csv<span class=\"token punctuation\">(<\/span>data_file<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>   NumRooms Alley   Price<br \/>\n0       NaN  Pave  127500<br \/>\n1       2.0   NaN  106000<br \/>\n2       4.0   NaN  178100<br \/>\n3       NaN   NaN  140000<\/p>\n<h4>2.2.2 \u5904\u7406\u7f3a\u5931\u503c<\/h4>\n<p>\u2003\u2003\u5904\u7406\u7f3a\u5931\u503c&#xff08;NaN&#xff09;\u7684\u5e38\u7528\u65b9\u6cd5&#xff1a;\u63d2\u503c&#xff08;\u7528\u5747\u503c\/\u4e2d\u4f4d\u6570\u586b\u5145\u6570\u503c\u578b\u7f3a\u5931&#xff09;\u548c\u5220\u9664\u3002\u5bf9\u4e8e\u7c7b\u522b\u578b\u7f3a\u5931&#xff0c;\u7528 get_dummies \u8f6c\u6210one-hot\u7f16\u7801\u3002<\/p>\n<p>inputs<span class=\"token punctuation\">,<\/span> outputs <span class=\"token operator\">&#061;<\/span> data<span class=\"token punctuation\">.<\/span>iloc<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> data<span class=\"token punctuation\">.<\/span>iloc<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><br \/>\ninputs <span class=\"token operator\">&#061;<\/span> inputs<span class=\"token punctuation\">.<\/span>fillna<span class=\"token punctuation\">(<\/span>inputs<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>numeric_only<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6570\u503c\u5217\u7528\u5747\u503c\u586b\u5145<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;After fillna:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> inputs<span class=\"token punctuation\">)<\/span><br \/>\ninputs <span class=\"token operator\">&#061;<\/span> pd<span class=\"token punctuation\">.<\/span>get_dummies<span class=\"token punctuation\">(<\/span>inputs<span class=\"token punctuation\">,<\/span> dummy_na<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u7c7b\u522b\u5217\u8f6cone-hot<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;After get_dummies:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> inputs<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>After fillna:<br \/>\n    NumRooms Alley<br \/>\n0       3.0  Pave<br \/>\n1       2.0   NaN<br \/>\n2       4.0   NaN<br \/>\n3       3.0   NaN<br \/>\nAfter get_dummies:<br \/>\n    NumRooms  Alley_Pave  Alley_nan<br \/>\n0       3.0        True      False<br \/>\n1       2.0       False       True<br \/>\n2       4.0       False       True<br \/>\n3       3.0       False       True<\/p>\n<h4>2.2.3 \u8f6c\u6362\u4e3a\u5f20\u91cf\u683c\u5f0f<\/h4>\n<p><span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\nX <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>inputs<span class=\"token punctuation\">.<\/span>to_numpy<span class=\"token punctuation\">(<\/span>dtype<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>outputs<span class=\"token punctuation\">.<\/span>to_numpy<span class=\"token punctuation\">(<\/span>dtype<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;X tensor:\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;y tensor:&#034;<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>X tensor:<br \/>\n tensor([[3., 1., 0.],<br \/>\n        [2., 0., 1.],<br \/>\n        [4., 0., 1.],<br \/>\n        [3., 0., 1.]])<br \/>\ny tensor: tensor([127500., 106000., 178100., 140000.])<\/p>\n<h3>2.3 \u7ebf\u6027\u4ee3\u6570<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080930-6aa508ba02867.jpg\" alt=\"\u7ebf\u6027\u4ee3\u6570\u6982\u5ff5\" \/><\/p>\n<p>\u2003\u2003\u7ebf\u6027\u4ee3\u6570\u662f\u6df1\u5ea6\u5b66\u4e60\u7684\u6570\u5b66\u57fa\u7840\u3002\u795e\u7ecf\u7f51\u7edc\u7684\u6bcf\u4e00\u5c42\u672c\u8d28\u4e0a\u90fd\u662f\u77e9\u9635\u4e58\u6cd5\u3002\u6211\u4eec\u5feb\u901f\u8fc7\u4e00\u904d\u6838\u5fc3\u6982\u5ff5\u3002<\/p>\n<h4>2.3.1-2.3.4 \u6807\u91cf\u3001\u5411\u91cf\u3001\u77e9\u9635\u3001\u5f20\u91cf<\/h4>\n<p><span class=\"token comment\"># \u6807\u91cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token number\">3.0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u5411\u91cf<\/span><br \/>\nv <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u77e9\u9635<\/span><br \/>\nA <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;A.T (\u8f6c\u7f6e):\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">.<\/span>T<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u5f20\u91cf<\/span><br \/>\nT <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">24<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>2.3.5 \u5f20\u91cf\u7b97\u6cd5\u7684\u57fa\u672c\u6027\u8d28<\/h4>\n<p>\u2003\u2003\u4e24\u4e2a\u540c\u5f62\u72b6\u5f20\u91cf\u7684\u9010\u5143\u7d20\u8fd0\u7b97&#xff08;Hadamard\u79ef&#xff09;&#xff1a;A * B\u3002\u6807\u91cf\u548c\u5f20\u91cf\u7684\u8fd0\u7b97\u4f1a\u5e7f\u64ad\u5230\u6bcf\u4e2a\u5143\u7d20\u3002<\/p>\n<h4>2.3.6 \u964d\u7ef4<\/h4>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;A.sum():&#034;<\/span><span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>           <span class=\"token comment\"># \u6240\u6709\u5143\u7d20\u6c42\u548c<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;A.sum(axis&#061;0):&#034;<\/span><span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>axis<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6309\u884c\u6c42\u548c&#xff08;\u6d88\u53bb\u884c\u7ef4\u5ea6&#xff09;<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;A.mean():&#034;<\/span><span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>         <span class=\"token comment\"># \u5e73\u5747\u503c<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;A.cumsum(axis&#061;0):\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">.<\/span>cumsum<span class=\"token punctuation\">(<\/span>axis<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u7d2f\u52a0\u6c42\u548c<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>A.sum(): tensor(190.)<br \/>\nA.sum(axis&#061;0): tensor([40., 45., 50., 55.])<br \/>\nA.mean(): tensor(9.5000)<\/p>\n<h4>2.3.7 \u70b9\u79ef<\/h4>\n<p>x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.dot(x, y):&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>dot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># 0*1 &#043; 1*1 &#043; 2*1 &#043; 3*1 &#061; 6<\/span><\/p>\n<h4>2.3.8-2.3.9 \u77e9\u9635-\u5411\u91cf\u79ef\u3001\u77e9\u9635-\u77e9\u9635\u4e58\u6cd5<\/h4>\n<p>A <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.mv(A, x):&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>mv<span class=\"token punctuation\">(<\/span>A<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u77e9\u9635\u00d7\u5411\u91cf<\/span><\/p>\n<p>B <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;torch.mm(A, B) shape:&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>mm<span class=\"token punctuation\">(<\/span>A<span class=\"token punctuation\">,<\/span> B<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u77e9\u9635\u00d7\u77e9\u9635<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>torch.mv(A, x): tensor([ 14.,  38.,  62.,  86., 110.])<br \/>\ntorch.mm(A, B) shape: torch.Size([5, 3])<\/p>\n<h4>2.3.10 \u8303\u6570<\/h4>\n<p>\u2003\u2003\u8303\u6570&#xff08;norm&#xff09;\u8861\u91cf\u5411\u91cf\/\u77e9\u9635\u7684&#034;\u5927\u5c0f&#034;\u3002<\/p>\n<ul>\n<li>L2\u8303\u6570&#xff08;\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb&#xff09;&#xff1a;||x||\u2082 &#061; \u221a(\u03a3x\u1d62\u00b2)<\/li>\n<li>L1\u8303\u6570&#xff1a;||x||\u2081 &#061; \u03a3|x\u1d62|<\/li>\n<li>Frobenius\u8303\u6570&#xff1a;\u77e9\u9635\u7684L2\u8303\u6570<\/li>\n<\/ul>\n<p>u <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">3.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">4.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;L2 norm:&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># 5.0<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;L1 norm:&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>     <span class=\"token comment\"># 7.0<\/span><br \/>\nv <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">9<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Frobenius norm:&#034;<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>    <span class=\"token comment\"># 6.0<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>L2 norm: tensor(5.)<br \/>\nL1 norm: tensor(7.)<br \/>\nFrobenius norm: tensor(6.)<\/p>\n<h3>2.4 \u5fae\u79ef\u5206<\/h3>\n<p>\u2003\u2003\u5fae\u79ef\u5206\u662f\u4f18\u5316\u7b97\u6cd5\u7684\u57fa\u7840\u3002\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u672c\u8d28\u4e0a\u5c31\u662f\u6c42\u635f\u5931\u51fd\u6570\u7684\u6700\u5c0f\u503c&#xff0c;\u800c\u6c42\u6700\u5c0f\u503c\u9700\u8981\u5bfc\u6570\u548c\u68af\u5ea6\u3002<\/p>\n<h4>2.4.1 \u5bfc\u6570\u548c\u5fae\u5206<\/h4>\n<p>\u2003\u2003\u5bfc\u6570 f&#039;(x) \u8861\u91cf\u51fd\u6570\u5728\u67d0\u70b9\u7684\u53d8\u5316\u7387&#xff0c;\u51e0\u4f55\u4e0a\u662f\u5207\u7ebf\u7684\u659c\u7387\u3002<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          f<\/p>\n<p>          \u2032<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           lim<\/p>\n<p>           \u2061<\/p>\n<p>           h<\/p>\n<p>           \u2192<\/p>\n<p>           0<\/p>\n<p>           f<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           &#043;<\/p>\n<p>           h<\/p>\n<p>           )<\/p>\n<p>           \u2212<\/p>\n<p>           f<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           )<\/p>\n<p>          h<\/p>\n<p>         f&#039;(x) &#061; \\\\lim_{h \\\\to 0} \\\\frac{f(x&#043;h) &#8211; f(x)}{h} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1791em;vertical-align: -0.7521em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -2.3479em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7521em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>2.4.2 \u504f\u5bfc\u6570<\/h4>\n<p>\u2003\u2003\u591a\u5143\u51fd\u6570\u5bf9\u67d0\u4e2a\u53d8\u91cf\u6c42\u5bfc&#xff0c;\u5176\u4ed6\u53d8\u91cf\u89c6\u4e3a\u5e38\u6570&#xff0c;\u5c31\u662f\u504f\u5bfc\u6570 \u2202f\/\u2202x\u1d62\u3002<\/p>\n<h4>2.4.3 \u68af\u5ea6<\/h4>\n<p>\u2003\u2003\u68af\u5ea6&#xff08;gradient&#xff09;\u662f\u6240\u6709\u504f\u5bfc\u6570\u7ec4\u6210\u7684\u5411\u91cf&#xff0c;\u6307\u5411\u51fd\u6570\u589e\u957f\u6700\u5feb\u7684\u65b9\u5411\u3002\u4f18\u5316\u65f6\u6211\u4eec\u6cbf\u68af\u5ea6\u53cd\u65b9\u5411\u66f4\u65b0\u53c2\u6570\u3002<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2207<\/p>\n<p>         f<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           [<\/p>\n<p>             \u2202<\/p>\n<p>             f<\/p>\n<p>             \u2202<\/p>\n<p>              x<\/p>\n<p>              1<\/p>\n<p>           ,<\/p>\n<p>             \u2202<\/p>\n<p>             f<\/p>\n<p>             \u2202<\/p>\n<p>              x<\/p>\n<p>              2<\/p>\n<p>           ,<\/p>\n<p>           \u2026<\/p>\n<p>           ,<\/p>\n<p>             \u2202<\/p>\n<p>             f<\/p>\n<p>             \u2202<\/p>\n<p>              x<\/p>\n<p>              n<\/p>\n<p>           ]<\/p>\n<p>          T<\/p>\n<p>         \\\\nabla f(\\\\mathbf{x}) &#061; \\\\left[\\\\frac{\\\\partial f}{\\\\partial x_1}, \\\\frac{\\\\partial f}{\\\\partial x_2}, \\\\ldots, \\\\frac{\\\\partial f}{\\\\partial x_n}\\\\right]^T <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.6313em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6812em\"><span class=\"\" style=\"top: -3.9029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>2.4.4 \u94fe\u5f0f\u6cd5\u5219<\/h4>\n<p>\u2003\u2003\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u7528\u94fe\u5f0f\u6cd5\u5219&#xff1a;dy\/dx &#061; (dy\/du) \u00d7 (du\/dx)\u3002\u8fd9\u662f\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u6570\u5b66\u57fa\u7840\u3002<\/p>\n<h3>2.5 \u81ea\u52a8\u5fae\u5206<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080930-6aa508ba8add1.jpg\" alt=\"\u81ea\u52a8\u5fae\u5206\u4e0e\u53cd\u5411\u4f20\u64ad\" \/><\/p>\n<p>\u2003\u2003\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u53ef\u80fd\u6709\u51e0\u5341\u4ebf\u4e2a\u53c2\u6570&#xff0c;\u624b\u52a8\u6c42\u5bfc\u4e0d\u73b0\u5b9e\u3002PyTorch\u7684\u81ea\u52a8\u5fae\u5206&#xff08;autograd&#xff09; \u80fd\u81ea\u52a8\u8ba1\u7b97\u68af\u5ea6\u2014\u2014\u4f60\u53ea\u9700\u8981\u5199\u524d\u5411\u4f20\u64ad&#xff0c;\u53cd\u5411\u4f20\u64ad\u81ea\u52a8\u641e\u5b9a\u3002<\/p>\n<h4>2.5.1 \u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50<\/h4>\n<p>\u2003\u2003\u5047\u8bbe y &#061; 2x\u00b7x&#xff0c;\u6211\u4eec\u60f3\u6c42 dy\/dx\u3002\u624b\u52a8\u7b97&#xff1a;dy\/dx &#061; 4x\u3002<\/p>\n<p>x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">4.0<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token punctuation\">.<\/span>requires_grad_<span class=\"token punctuation\">(<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u544a\u8bc9PyTorch\u9700\u8981\u8ddf\u8e2ax\u7684\u68af\u5ea6<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> torch<span class=\"token punctuation\">.<\/span>dot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># y &#061; 2*(0\u00b2&#043;1\u00b2&#043;2\u00b2&#043;3\u00b2) &#061; 28<\/span><br \/>\ny<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad&#xff0c;\u8ba1\u7b97\u68af\u5ea6<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x.grad:&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u5e94\u8be5\u7b49\u4e8e 4x &#061; [0, 4, 8, 12]<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x.grad &#061;&#061; 4*x:&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">4<\/span> <span class=\"token operator\">*<\/span> x<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>x.grad (dy\/dx &#061; 4x): tensor([ 0.,  4.,  8., 12.])<br \/>\nx.grad &#061;&#061; 4*x: tensor([True, True, True, True])<\/p>\n<p>\u2003\u2003\u6ce8\u610f&#xff1a;\u68af\u5ea6\u662f\u7d2f\u79ef\u7684&#xff0c;\u6bcf\u6b21\u53cd\u5411\u4f20\u64ad\u524d\u8981 x.grad.zero_() \u6e05\u96f6&#xff0c;\u5426\u5219\u4f1a\u53e0\u52a0\u3002<\/p>\n<h4>2.5.2 \u975e\u6807\u91cf\u53d8\u91cf\u7684\u53cd\u5411\u4f20\u64ad<\/h4>\n<p>\u2003\u2003\u5f53y\u4e0d\u662f\u6807\u91cf\u65f6&#xff0c;y.backward() \u4f1a\u62a5\u9519\u3002\u9700\u8981\u5148\u6c42\u548c&#xff1a;y.sum().backward()\u3002<\/p>\n<p>x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>zero_<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> x <span class=\"token operator\">*<\/span> x<br \/>\ny<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x.grad:&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># [0, 2, 4, 6]<\/span><\/p>\n<h4>2.5.3 \u5206\u79bb\u8ba1\u7b97<\/h4>\n<p>\u2003\u2003\u6709\u65f6\u6211\u4eec\u60f3\u628a\u67d0\u4e9b\u8ba1\u7b97&#034;\u51bb\u7ed3&#034;&#xff0c;\u4e0d\u8ba9\u68af\u5ea6\u4f20\u8fc7\u53bb\u3002\u7528 detach()&#xff1a;<\/p>\n<p>x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>zero_<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> x <span class=\"token operator\">*<\/span> x<br \/>\nu <span class=\"token operator\">&#061;<\/span> y<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># u\u88ab\u5f53\u4f5c\u5e38\u6570&#xff0c;\u68af\u5ea6\u4e0d\u4f1a\u4f20\u5230y<\/span><br \/>\nz <span class=\"token operator\">&#061;<\/span> u <span class=\"token operator\">*<\/span> x<br \/>\nz<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;x.grad &#061;&#061; u:&#034;<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad <span class=\"token operator\">&#061;&#061;<\/span> u<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># True&#xff0c;dz\/dx &#061; u<\/span><\/p>\n<h4>2.5.4 Python\u63a7\u5236\u6d41\u7684\u68af\u5ea6\u8ba1\u7b97<\/h4>\n<p>\u2003\u2003\u81ea\u52a8\u5fae\u5206\u751a\u81f3\u80fd\u5904\u7406\u5305\u542bPython\u63a7\u5236\u6d41&#xff08;if\/while&#xff09;\u7684\u51fd\u6570&#xff1a;<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">f<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    b <span class=\"token operator\">&#061;<\/span> a <span class=\"token operator\">*<\/span> <span class=\"token number\">2<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> b<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        b <span class=\"token operator\">&#061;<\/span> b <span class=\"token operator\">*<\/span> <span class=\"token number\">2<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> b<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        c <span class=\"token operator\">&#061;<\/span> b<br \/>\n    <span class=\"token keyword\">else<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        c <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">100<\/span> <span class=\"token operator\">*<\/span> b<br \/>\n    <span class=\"token keyword\">return<\/span> c<\/p>\n<p>a <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nd <span class=\"token operator\">&#061;<\/span> f<span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">)<\/span><br \/>\nd<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;a.grad &#061;&#061; d\/a:&#034;<\/span><span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">.<\/span>grad <span class=\"token operator\">&#061;&#061;<\/span> d <span class=\"token operator\">\/<\/span> a<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># True<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>a &#061; tensor(1.3310, requires_grad&#061;True)<br \/>\nf(a) &#061; tensor(1362.9602)<br \/>\na.grad &#061; tensor(1024.)<br \/>\na.grad &#061;&#061; d\/a: tensor(True)<\/p>\n<h3>2.6 \u6982\u7387<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080931-6aa508bb27ca4.jpg\" alt=\"\u6982\u7387\u4e0e\u7edf\u8ba1\" \/><\/p>\n<p>\u2003\u2003\u6df1\u5ea6\u5b66\u4e60\u548c\u6982\u7387\u7edf\u8ba1\u5bc6\u4e0d\u53ef\u5206&#xff1a;\u6a21\u578b\u7684\u9884\u6d4b\u672c\u8d28\u4e0a\u662f\u6982\u7387\u5206\u5e03&#xff0c;\u635f\u5931\u51fd\u6570\u5e38\u6765\u81ea\u6700\u5927\u4f3c\u7136\u4f30\u8ba1&#xff0c;\u6b63\u5219\u5316\u5bf9\u5e94\u8d1d\u53f6\u65af\u5148\u9a8c\u3002<\/p>\n<h4>2.6.1 \u57fa\u672c\u6982\u7387\u8bba<\/h4>\n<p>\u2003\u2003\u6211\u4eec\u7528\u63b7\u9ab0\u5b50\u6765\u7406\u89e3\u6982\u7387\u3002\u7406\u8bba\u4e0a\u6bcf\u4e2a\u9762\u7684\u6982\u7387\u662f1\/6 \u2248 0.1667\u3002\u6a21\u62df1000\u6b21\u63b7\u9ab0\u5b50&#xff1a;<\/p>\n<p>fair_probs <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">6<\/span><br \/>\ncounts <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>multinomial<span class=\"token punctuation\">(<\/span>fair_probs<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">,<\/span> replacement<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nroll_counts <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>bincount<span class=\"token punctuation\">(<\/span>counts<span class=\"token punctuation\">,<\/span> minlength<span class=\"token operator\">&#061;<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Counts:&#034;<\/span><span class=\"token punctuation\">,<\/span> roll_counts<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Empirical probs:&#034;<\/span><span class=\"token punctuation\">,<\/span> roll_counts<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>Counts for 1000 rolls: tensor([185, 177, 167, 180, 128, 163])<br \/>\nEmpirical probabilities: tensor([0.1850, 0.1770, 0.1670, 0.1800, 0.1280, 0.1630])<\/p>\n<p>\u2003\u2003\u5927\u6570\u5b9a\u5f8b&#xff1a;\u8bd5\u9a8c\u6b21\u6570\u8d8a\u591a&#xff0c;\u7ecf\u9a8c\u6982\u7387\u8d8a\u63a5\u8fd1\u7406\u8bba\u6982\u7387\u3002<\/p>\n<p>n&#061;     1: P(6)&#061;1.0000, P(1)&#061;0.0000<br \/>\nn&#061;    10: P(6)&#061;0.2000, P(1)&#061;0.2000<br \/>\nn&#061;   100: P(6)&#061;0.2100, P(1)&#061;0.1600<br \/>\nn&#061;  1000: P(6)&#061;0.1720, P(1)&#061;0.1570<br \/>\nn&#061; 10000: P(6)&#061;0.1614, P(1)&#061;0.1732<\/p>\n<h4>2.6.2 \u5904\u7406\u591a\u4e2a\u968f\u673a\u53d8\u91cf<\/h4>\n<p>\u2003\u2003\u8054\u5408\u6982\u7387 P(A,B)&#xff1a;\u4e24\u4e2a\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387\u3002\u6761\u4ef6\u6982\u7387 P(A|B)&#xff1a;\u5728B\u53d1\u751f\u7684\u6761\u4ef6\u4e0bA\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p><span class=\"token comment\"># \u63b7\u4e24\u4e2a\u9ab0\u5b50&#xff0c;P(\u548c\u4e3a7)<\/span><br \/>\nrolls1 <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>multinomial<span class=\"token punctuation\">(<\/span>fair_probs<span class=\"token punctuation\">,<\/span> <span class=\"token number\">10000<\/span><span class=\"token punctuation\">,<\/span> replacement<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nrolls2 <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>multinomial<span class=\"token punctuation\">(<\/span>fair_probs<span class=\"token punctuation\">,<\/span> <span class=\"token number\">10000<\/span><span class=\"token punctuation\">,<\/span> replacement<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nsum7 <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>rolls1 <span class=\"token operator\">&#043;<\/span> rolls2 <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;P(sum&#061;7): <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>sum7<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> (theoretical: 0.1667)&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>P(sum of two dice &#061; 7): 0.1585 (theoretical: 0.1667)<\/p>\n<h4>2.6.3 \u671f\u671b\u548c\u65b9\u5dee<\/h4>\n<p>\u2003\u2003\u671f\u671b E[X]&#xff1a;\u968f\u673a\u53d8\u91cf\u7684\u5e73\u5747\u503c\u3002\u65b9\u5dee Var(X)&#xff1a;\u968f\u673a\u53d8\u91cf\u504f\u79bb\u671f\u671b\u7684\u7a0b\u5ea6\u3002<\/p>\n<p>dice_values <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\nexpected <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>dice_values <span class=\"token operator\">*<\/span> fair_probs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nvariance <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>dice_values <span class=\"token operator\">&#8211;<\/span> expected<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> fair_probs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;E[X] &#061; <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>expected<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> (theoretical: 3.5)&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;Var(X) &#061; <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>variance<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> (theoretical: 2.9167)&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6b63\u6001\u5206\u5e03\u91c7\u6837\u9a8c\u8bc1<\/span><br \/>\nsamples <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">10000<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;Mean: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>samples<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">, Std: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>samples<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>E[X] (dice) &#061; 3.5000 (theoretical: 3.5)<br \/>\nVar(X) (dice) &#061; 2.9167 (theoretical: 2.9167)<br \/>\nStd(X) &#061; 1.7078<br \/>\nMean of 10000 standard normal samples: -0.0096 (theoretical: 0)<br \/>\nStd of 10000 standard normal samples: 0.9949 (theoretical: 1)<\/p>\n<h3>2.7 \u67e5\u9605\u6587\u6863<\/h3>\n<p>\u2003\u2003PyTorch\u6709\u51e0\u767e\u4e2a\u51fd\u6570&#xff0c;\u8bb0\u4e0d\u4f4f\u5f88\u6b63\u5e38\u3002\u5b66\u4f1a\u67e5\u6587\u6863\u662f\u5fc5\u5907\u6280\u80fd\u3002<\/p>\n<p><span class=\"token comment\"># \u67e5\u627e\u6a21\u5757\u4e2d\u7684\u6240\u6709\u51fd\u6570\u548c\u7c7b<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token builtin\">dir<\/span><span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>distributions<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u67e5\u627e\u7279\u5b9a\u51fd\u6570\u7684\u7528\u6cd5<\/span><br \/>\n<span class=\"token builtin\">help<\/span><span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u6216\u5728Jupyter\u4e2d\u7528 ?torch.ones<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c&#xff1a;<\/p>\n<p>torch.distributions modules (first 10):<br \/>\n[&#039;AbsTransform&#039;, &#039;AffineTransform&#039;, &#039;Bernoulli&#039;, &#039;Beta&#039;, &#039;Binomial&#039;, &#8230;]<\/p>\n<p>ones(*size, *, out&#061;None, dtype&#061;None, &#8230;) -&gt; Tensor<br \/>\nReturns a tensor filled with the scalar value &#096;1&#096;&#8230;<\/p>\n<h3>\u672c\u7ae0\u6838\u5fc3\u603b\u7ed3&#xff08;\u5fc5\u770b&#xff09;<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080931-6aa508bbae1ea.jpg\" alt=\"\u7b2c2\u7ae0\u601d\u7ef4\u5bfc\u56fe\" \/><\/p>\n<p>\u2003\u2003\u4e00\u53e5\u8bdd\u6982\u62ec&#xff1a;\u7b2c2\u7ae0\u642d\u5efa\u4e86\u6df1\u5ea6\u5b66\u4e60\u7684&#034;\u5de5\u5177\u7bb1&#034;\u2014\u2014\u5f20\u91cf\u662f\u6570\u636e\u8f7d\u4f53&#xff0c;\u7ebf\u6027\u4ee3\u6570\u662f\u8fd0\u7b97\u8bed\u8a00&#xff0c;\u5fae\u79ef\u5206\u548c\u81ea\u52a8\u5fae\u5206\u662f\u4f18\u5316\u57fa\u7840&#xff0c;\u6982\u7387\u7edf\u8ba1\u662f\u5efa\u6a21\u601d\u7ef4\u3002<\/p>\n<p>\u2003\u2003\u6838\u5fc3\u6982\u5ff5\u6e05\u5355&#xff1a;<\/p>\n<ul>\n<li>\u5f20\u91cf\u64cd\u4f5c&#xff1a;\u521b\u5efa(arange\/zeros\/ones\/randn)\u3001\u53d8\u5f62(reshape)\u3001\u8fd0\u7b97(\u9010\u5143\u7d20\/cat\/sum)\u3001\u5e7f\u64ad\u673a\u5236\u3001\u7d22\u5f15\u5207\u7247\u3001\u539f\u5730\u64cd\u4f5c(&#043;&#061;\/[:])<\/li>\n<li>\u6570\u636e\u9884\u5904\u7406&#xff1a;pandas\u8bfb\u53d6CSV \u2192 \u7f3a\u5931\u503c\u586b\u5145(\u5747\u503c) \u2192 \u7c7b\u522b\u53d8\u91cfone-hot(get_dummies) \u2192 \u8f6c\u5f20\u91cf<\/li>\n<li>\u7ebf\u6027\u4ee3\u6570&#xff1a;\u6807\u91cf\/\u5411\u91cf\/\u77e9\u9635\/\u5f20\u91cf\u3001\u8f6c\u7f6e\u3001\u964d\u7ef4(sum\/mean)\u3001\u70b9\u79ef(dot)\u3001\u77e9\u9635\u4e58\u6cd5(mm\/mv)\u3001\u8303\u6570(norm)<\/li>\n<li>\u5fae\u79ef\u5206&#xff1a;\u5bfc\u6570\u2192\u504f\u5bfc\u6570\u2192\u68af\u5ea6\u2192\u94fe\u5f0f\u6cd5\u5219&#xff0c;\u68af\u5ea6\u4e0b\u964d\u6cbf\u68af\u5ea6\u53cd\u65b9\u5411\u66f4\u65b0<\/li>\n<li>\u81ea\u52a8\u5fae\u5206&#xff1a;requires_grad_(True) \u5f00\u542f\u8ddf\u8e2a \u2192 \u524d\u5411\u8ba1\u7b97 \u2192 backward() \u53cd\u5411\u4f20\u64ad \u2192 .grad \u53d6\u68af\u5ea6&#xff0c;\u8bb0\u5f97 zero_() \u6e05\u96f6<\/li>\n<li>\u6982\u7387&#xff1a;\u5927\u6570\u5b9a\u5f8b\u3001\u8054\u5408\/\u6761\u4ef6\u6982\u7387\u3001\u671f\u671bE[X]\u3001\u65b9\u5deeVar(X)\u3001\u6b63\u6001\u5206\u5e03<\/li>\n<\/ul>\n<h3>\u7ed3\u8bed<\/h3>\n<p>\u2003\u2003\u7b2c2\u7ae0\u7684\u9884\u5907\u77e5\u8bc6\u5c31\u5230\u8fd9\u91cc\u3002\u8fd9\u4e00\u7ae0\u5185\u5bb9\u591a\u4f46\u90fd\u662f\u57fa\u7840&#xff0c;\u5efa\u8bae\u5927\u5bb6\u628a\u4ee3\u7801\u4eb2\u624b\u8dd1\u4e00\u904d\u2014\u2014\u770b\u61c2\u548c\u4f1a\u7528\u4e4b\u95f4\u9694\u7740100\u6b21\u62a5\u9519\u3002<\/p>\n<p>\u2003\u2003\u4e0b\u4e00\u7ae0\u6211\u4eec\u5c06\u8fdb\u5165\u7ebf\u6027\u795e\u7ecf\u7f51\u7edc&#xff0c;\u5f00\u59cb\u771f\u6b63\u7684\u673a\u5668\u5b66\u4e60\u4e4b\u65c5&#xff1a;\u7ebf\u6027\u56de\u5f52\u3001softmax\u56de\u5f52\u3001\u56fe\u50cf\u5206\u7c7b\u3002\u6211\u4eec\u4f1a\u7528\u8fd9\u4e00\u7ae0\u5b66\u7684\u5f20\u91cf\u64cd\u4f5c\u548c\u81ea\u52a8\u5fae\u5206&#xff0c;\u4ece\u96f6\u5b9e\u73b0\u7b2c\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc&#xff01;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u5f55<br \/>\n2.1 \u6570\u636e\u64cd\u4f5c2.2 \u6570\u636e\u9884\u5904\u74062.3 \u7ebf\u6027\u4ee3\u65702.4 \u5fae\u79ef\u52062.5 \u81ea\u52a8\u5fae\u52062.6 \u6982\u73872.7 \u67e5\u9605\u6587\u6863\u672c\u7ae0\u6838\u5fc3\u603b\u7ed3&#xff08;\u5fc5\u770b&#xff09;\u7ed3\u8bed \u8fd9\u4e00\u7ae0\u662f\u5168\u4e66\u7684\\&#8221;\u5de5\u5177\u7bb1\\&#8221;\u2014\u2014\u6211\u4eec\u8981\u628a\u540e\u9762\u5199\u4ee3\u7801\u9700\u8981\u7684\u57fa\u7840\u64cd\u4f5c\u5168\u90e8\u8fc7\u4e00\u904d\u3002\u522b\u5acc\u57fa\u7840&#xff0c;80%\u7684\u6df1\u5ea6\u5b66\u4e60bug\u90fd\u51fa\u5728\u8fd9\u4e9b\u57fa\u7840\u64cd\u4f5c\u4e0a&#xff08;\u5f20\u91cf\u7ef4\u5ea6\u4e0d\u5bf9\u3001\u7d22\u5f15\u8d8a\u754c\u3001\u68af\u5ea6\u6ca1\u6e05\u96f6\u2026\u2026&#xff09;&#xff0c;\u6240\u4ee5\u8fd9\u4e00\u7ae0\u4e00\u5b9a\u8981\u52a8\u624b\u6572\u4ee3\u7801\u3002 \u8fd9\u4e00\u7ae0\u7684\u5185\u5bb9\u5305\u62ec&#xff1a;PyTorch\u5f20\u91cf\u64cd\u4f5c\u3001<\/p>\n","protected":false},"author":2,"featured_media":104497,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11653,6686,8460,152,50,86],"topic":[],"class_list":["post-104502","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-11653","tag-6686","tag-8460","tag-pytorch","tag-50","tag-86"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/104502.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u76ee\u5f55 2.1 \u6570\u636e\u64cd\u4f5c2.2 \u6570\u636e\u9884\u5904\u74062.3 \u7ebf\u6027\u4ee3\u65702.4 \u5fae\u79ef\u52062.5 \u81ea\u52a8\u5fae\u52062.6 \u6982\u73872.7 \u67e5\u9605\u6587\u6863\u672c\u7ae0\u6838\u5fc3\u603b\u7ed3&#xff08;\u5fc5\u770b&#xff09;\u7ed3\u8bed \u8fd9\u4e00\u7ae0\u662f\u5168\u4e66\u7684&quot;\u5de5\u5177\u7bb1&quot;\u2014\u2014\u6211\u4eec\u8981\u628a\u540e\u9762\u5199\u4ee3\u7801\u9700\u8981\u7684\u57fa\u7840\u64cd\u4f5c\u5168\u90e8\u8fc7\u4e00\u904d\u3002\u522b\u5acc\u57fa\u7840&#xff0c;80%\u7684\u6df1\u5ea6\u5b66\u4e60bug\u90fd\u51fa\u5728\u8fd9\u4e9b\u57fa\u7840\u64cd\u4f5c\u4e0a&#xff08;\u5f20\u91cf\u7ef4\u5ea6\u4e0d\u5bf9\u3001\u7d22\u5f15\u8d8a\u754c\u3001\u68af\u5ea6\u6ca1\u6e05\u96f6\u2026\u2026&#xff09;&#xff0c;\u6240\u4ee5\u8fd9\u4e00\u7ae0\u4e00\u5b9a\u8981\u52a8\u624b\u6572\u4ee3\u7801\u3002 \u8fd9\u4e00\u7ae0\u7684\u5185\u5bb9\u5305\u62ec&#xff1a;PyTorch\u5f20\u91cf\u64cd\u4f5c\u3001\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/104502.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-09-12T08:09:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080929-6aa508b96a207.jpg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/104502.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/104502.html\",\"name\":\"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-09-12T08:09:33+00:00\",\"dateModified\":\"2026-09-12T08:09:33+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/104502.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/104502.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/104502.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/104502.html","og_locale":"zh_CN","og_type":"article","og_title":"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u76ee\u5f55 2.1 \u6570\u636e\u64cd\u4f5c2.2 \u6570\u636e\u9884\u5904\u74062.3 \u7ebf\u6027\u4ee3\u65702.4 \u5fae\u79ef\u52062.5 \u81ea\u52a8\u5fae\u52062.6 \u6982\u73872.7 \u67e5\u9605\u6587\u6863\u672c\u7ae0\u6838\u5fc3\u603b\u7ed3&#xff08;\u5fc5\u770b&#xff09;\u7ed3\u8bed \u8fd9\u4e00\u7ae0\u662f\u5168\u4e66\u7684\"\u5de5\u5177\u7bb1\"\u2014\u2014\u6211\u4eec\u8981\u628a\u540e\u9762\u5199\u4ee3\u7801\u9700\u8981\u7684\u57fa\u7840\u64cd\u4f5c\u5168\u90e8\u8fc7\u4e00\u904d\u3002\u522b\u5acc\u57fa\u7840&#xff0c;80%\u7684\u6df1\u5ea6\u5b66\u4e60bug\u90fd\u51fa\u5728\u8fd9\u4e9b\u57fa\u7840\u64cd\u4f5c\u4e0a&#xff08;\u5f20\u91cf\u7ef4\u5ea6\u4e0d\u5bf9\u3001\u7d22\u5f15\u8d8a\u754c\u3001\u68af\u5ea6\u6ca1\u6e05\u96f6\u2026\u2026&#xff09;&#xff0c;\u6240\u4ee5\u8fd9\u4e00\u7ae0\u4e00\u5b9a\u8981\u52a8\u624b\u6572\u4ee3\u7801\u3002 \u8fd9\u4e00\u7ae0\u7684\u5185\u5bb9\u5305\u62ec&#xff1a;PyTorch\u5f20\u91cf\u64cd\u4f5c\u3001","og_url":"https:\/\/www.wsisp.com\/helps\/104502.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-09-12T08:09:33+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260912080929-6aa508b96a207.jpg"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"7 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/104502.html","url":"https:\/\/www.wsisp.com\/helps\/104502.html","name":"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-09-12T08:09:33+00:00","dateModified":"2026-09-12T08:09:33+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/104502.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/104502.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/104502.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\uff08PyTorch\u7248\uff09\u300b\u7b2c2\u7ae0 \u9884\u5907\u77e5\u8bc6 \u8bfb\u4e66\u7b14\u8bb0"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/104502","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=104502"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/104502\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/104497"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=104502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=104502"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=104502"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=104502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}