{"id":2435,"date":"2024-10-29T09:39:49","date_gmt":"2024-10-29T01:39:49","guid":{"rendered":"https:\/\/sanlangcode.com\/?p=2435"},"modified":"2024-10-29T09:39:49","modified_gmt":"2024-10-29T01:39:49","slug":"pytorch%e7%9a%84%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%92%8c%e5%bc%a0%e9%87%8f%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/sanlangcode.com\/index.php\/2024\/10\/29\/pytorch%e7%9a%84%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%92%8c%e5%bc%a0%e9%87%8f%e8%ae%a1%e7%ae%97\/","title":{"rendered":"Pytorch\u7684\u795e\u7ecf\u7f51\u7edc\u548c\u5f20\u91cf\u8ba1\u7b97"},"content":{"rendered":"\n<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u6838\u5fc3\u5c31\u662f\u5229\u7528\u5f20\u91cf\u8ba1\u7b97\uff08\u77e9\u9635\u8fd0\u7b97\uff09\u6765\u5904\u7406\u6570\u636e\uff0c\u8c03\u6574\u53c2\u6570\u5e76\u4f18\u5316\u7ed3\u679c\u3002\u5728 PyTorch \u4e2d\uff0c\u5f20\u91cf\u548c\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u662f\u6df1\u5ea6\u5b66\u4e60\u7684\u57fa\u7840\uff0c\u4e0b\u9762\u6211\u4eec\u4ece\u5b83\u4eec\u7684\u6982\u5ff5\u548c\u5e94\u7528\u8fdb\u884c\u6df1\u5165\u4e86\u89e3\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u5f20\u91cf\uff08Tensor\uff09<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u5b9a\u4e49<\/strong>\uff1a\u5f20\u91cf\u662f\u591a\u7ef4\u6570\u7ec4\u7684\u6cdb\u5316\uff0c\u53ef\u4ee5\u662f\u6807\u91cf\uff080D\uff09\u3001\u5411\u91cf\uff081D\uff09\u3001\u77e9\u9635\uff082D\uff09\u4ee5\u53ca\u66f4\u9ad8\u7ef4\u7684\u6570\u7ec4\u3002\u6bd4\u5982\uff1a<ul><li>0D \u5f20\u91cf\uff1a\u6807\u91cf\uff0c\u5982 <code>torch.tensor(3)<\/code><\/li><li>1D \u5f20\u91cf\uff1a\u5411\u91cf\uff0c\u5982 <code>torch.tensor([1, 2, 3])<\/code><\/li><li>2D \u5f20\u91cf\uff1a\u77e9\u9635\uff0c\u5982 <code>torch.tensor([[1, 2], [3, 4]])<\/code><\/li><\/ul><\/li><li><strong>\u5f20\u91cf\u64cd\u4f5c<\/strong>\uff1aPyTorch \u63d0\u4f9b\u5927\u91cf\u5f20\u91cf\u64cd\u4f5c\uff0c\u5305\u62ec\u52a0\u6cd5\u3001\u51cf\u6cd5\u3001\u70b9\u79ef\u3001\u77e9\u9635\u4e58\u6cd5\u7b49\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u53ef\u4ee5\u5728 GPU \u4e0a\u52a0\u901f\u8fd0\u884c\u3002<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u5f20\u91cf\u8ba1\u7b97\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5e94\u7528<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u6743\u91cd\u548c\u504f\u7f6e\u8868\u793a<\/strong>\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u53c2\u6570\uff08\u6743\u91cd\u548c\u504f\u7f6e\uff09\u901a\u5e38\u7528\u5f20\u91cf\u8868\u793a\u3002\u6bd4\u5982\uff0c\u5168\u8fde\u63a5\u5c42\u7684\u6743\u91cd\u53ef\u4ee5\u8868\u793a\u4e3a\u4e8c\u7ef4\u5f20\u91cf\uff08\u5f62\u72b6\u4e3a <code>[\u8f93\u51fa\u8282\u70b9\u6570, \u8f93\u5165\u8282\u70b9\u6570]<\/code>\uff09\u3002<\/li><li><strong>\u6570\u636e\u8f93\u5165\u4e0e\u6279\u5904\u7406<\/strong>\uff1a\u8f93\u5165\u6570\u636e\u901a\u5e38\u8868\u793a\u4e3a\u5f20\u91cf\uff0c\u6bd4\u5982\u4e00\u6279 32 \u4e2a\u56fe\u7247\u6570\u636e\uff0c\u6bcf\u4e2a\u56fe\u7247\u7684\u5927\u5c0f\u4e3a 28&#215;28\uff0c\u90a3\u4e48\u8f93\u5165\u5f20\u91cf\u7684\u5f62\u72b6\u662f <code>[32, 28, 28]<\/code>\u3002\u5229\u7528\u8fd9\u79cd\u7ed3\u6784\u5316\u7684\u5f20\u91cf\u53ef\u4ee5\u9ad8\u6548\u5730\u8fdb\u884c\u6279\u91cf\u5904\u7406\u3002<\/li><li><strong>\u77e9\u9635\u4e58\u6cd5<\/strong>\uff1a\u5728\u795e\u7ecf\u7f51\u7edc\u7684\u524d\u5411\u4f20\u64ad\u4e2d\uff0c\u6570\u636e\u4ece\u4e00\u5c42\u4f20\u64ad\u5230\u4e0b\u4e00\u5c42\u7684\u8ba1\u7b97\u901a\u5e38\u662f\u77e9\u9635\u4e58\u6cd5\u3002\u4f8b\u5982\uff0c\u5168\u8fde\u63a5\u5c42\u4e2d\uff0c\u6bcf\u5c42\u7684\u8f93\u51fa\u662f\u8f93\u5165\u5f20\u91cf\u548c\u6743\u91cd\u5f20\u91cf\u7684\u77e9\u9635\u4e58\u79ef\u52a0\u4e0a\u504f\u7f6e\u5f20\u91cf\u3002<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. PyTorch \u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u795e\u7ecf\u7f51\u7edc\u5c42<\/strong>\uff1aPyTorch \u63d0\u4f9b\u4e86\u8bb8\u591a\u5e38\u89c1\u7684\u795e\u7ecf\u7f51\u7edc\u5c42\u6a21\u5757\uff0c\u5982 <code>torch.nn.Linear<\/code>\uff08\u5168\u8fde\u63a5\u5c42\uff09\u3001<code>torch.nn.Conv2d<\/code>\uff08\u5377\u79ef\u5c42\uff09\u3001<code>torch.nn.RNN<\/code>\uff08\u5faa\u73af\u5c42\uff09\u7b49\uff0c\u8fd9\u4e9b\u5c42\u6a21\u5757\u90fd\u662f\u57fa\u4e8e\u5f20\u91cf\u8fd0\u7b97\u7684\u3002<\/li><li><strong>\u6fc0\u6d3b\u51fd\u6570<\/strong>\uff1a\u5728\u6bcf\u4e00\u5c42\u7684\u8f93\u51fa\u4e0a\uff0c\u901a\u5e38\u4f1a\u5e94\u7528\u4e00\u4e2a\u6fc0\u6d3b\u51fd\u6570\uff0c\u4f8b\u5982 <code>torch.nn.ReLU()<\/code>\uff0c\u5b83\u4f1a\u6267\u884c\u5143\u7d20\u7ea7\u64cd\u4f5c\uff0c\u5c06\u8d1f\u503c\u53d8\u4e3a\u96f6\uff0c\u800c\u4e0d\u6539\u53d8\u5f20\u91cf\u7684\u7ef4\u5ea6\u3002<\/li><li><strong>\u635f\u5931\u8ba1\u7b97<\/strong>\uff1a\u5728\u8bad\u7ec3\u4e2d\uff0c\u9884\u6d4b\u8f93\u51fa\u4e0e\u771f\u5b9e\u6807\u7b7e\u4e4b\u95f4\u7684\u635f\u5931\u503c\u4e5f\u662f\u57fa\u4e8e\u5f20\u91cf\u8ba1\u7b97\u7684\u3002PyTorch \u4e2d\u5e38\u7528\u7684\u635f\u5931\u51fd\u6570\u5982\u5747\u65b9\u8bef\u5dee\uff08<code>torch.nn.MSELoss<\/code>\uff09\u3001\u4ea4\u53c9\u71b5\u635f\u5931\uff08<code>torch.nn.CrossEntropyLoss<\/code>\uff09\u7b49\u3002<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. \u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u524d\u5411\u4f20\u64ad\uff08Forward Pass\uff09<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u8ba1\u7b97\u8fc7\u7a0b<\/strong>\uff1a\u524d\u5411\u4f20\u64ad\u662f\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u6570\u636e\u901a\u8fc7\u4e00\u5c42\u5c42\u7684\u8ba1\u7b97\u540e\u5f97\u5230\u8f93\u51fa\u7684\u8fc7\u7a0b\u3002\u6bcf\u4e00\u5c42\u8ba1\u7b97\u7684\u7ed3\u679c\uff08\u5f20\u91cf\uff09\u4f5c\u4e3a\u4e0b\u4e00\u5c42\u7684\u8f93\u5165\u3002<\/li><li><strong>\u52a8\u6001\u8ba1\u7b97\u56fe<\/strong>\uff1aPyTorch \u5728\u6bcf\u6b21\u524d\u5411\u4f20\u64ad\u4e2d\u81ea\u52a8\u6784\u5efa\u8ba1\u7b97\u56fe\uff0c\u4e3a\u53cd\u5411\u4f20\u64ad\u63d0\u4f9b\u4f9d\u8d56\u3002\u5f20\u91cf\u7684\u6bcf\u4e2a\u64cd\u4f5c\uff08\u5982\u52a0\u6cd5\u3001\u4e58\u6cd5\u7b49\uff09\u90fd\u4f1a\u8bb0\u5f55\u5728\u8ba1\u7b97\u56fe\u4e2d\uff0c\u65b9\u4fbf\u540e\u7eed\u7684\u68af\u5ea6\u8ba1\u7b97\u3002<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5. \u81ea\u52a8\u6c42\u5bfc\u548c\u53cd\u5411\u4f20\u64ad\uff08Backward Pass\uff09<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u68af\u5ea6\u8ba1\u7b97<\/strong>\uff1a\u5728\u524d\u5411\u4f20\u64ad\u4e4b\u540e\uff0c\u6211\u4eec\u4f1a\u901a\u8fc7\u81ea\u52a8\u6c42\u5bfc\uff08Autograd\uff09\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5173\u4e8e\u6bcf\u4e2a\u53c2\u6570\u7684\u68af\u5ea6\u3002PyTorch \u4e2d\u7684 <code>tensor.backward()<\/code> \u51fd\u6570\u4f1a\u57fa\u4e8e\u8ba1\u7b97\u56fe\u53cd\u5411\u4f20\u64ad\uff0c\u66f4\u65b0\u53c2\u6570\u7684\u68af\u5ea6\u4fe1\u606f\u3002<\/li><li><strong>\u53c2\u6570\u66f4\u65b0<\/strong>\uff1a\u57fa\u4e8e\u8ba1\u7b97\u7684\u68af\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4f18\u5316\u5668\uff08\u5982 SGD\u3001Adam\uff09\u66f4\u65b0\u6743\u91cd\u548c\u504f\u7f6e\uff0c\u8c03\u6574\u6a21\u578b\uff0c\u4f7f\u5176\u635f\u5931\u6700\u5c0f\u5316\u3002<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u793a\u4f8b\uff1a\u7b80\u5355\u7684\u795e\u7ecf\u7f51\u7edc\u5f20\u91cf\u8ba1\u7b97<\/h3>\n\n\n\n<p>\u4e0b\u9762\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u795e\u7ecf\u7f51\u7edc\u524d\u5411\u4f20\u64ad\u7684\u4f8b\u5b50\uff0c\u5e2e\u52a9\u7406\u89e3\u5f20\u91cf\u8ba1\u7b97\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u4f5c\u7528\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><code>import torch\nimport torch.nn as nn\n\n# \u8f93\u5165\u6570\u636e\u5f20\u91cf\nx = torch.tensor(&#91;&#91;0.5, -1.5], &#91;1.0, 1.0]], requires_grad=True) <\/code>\n<code># \u8f93\u5165\u6709\u4e24\u4e2a\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c\u6709\u4e24\u4e2a\u7279\u5f81\n\n# \u5b9a\u4e49\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u5c42\nlinear = nn.Linear(2, 1)  # \u8f93\u5165\u5927\u5c0f\u4e3a2\uff0c\u8f93\u51fa\u5927\u5c0f\u4e3a1\n\n# \u524d\u5411\u4f20\u64ad\ny_pred = linear(x)  # \u8ba1\u7b97\u8f93\u51fa\uff08\u9884\u6d4b\u503c\uff09\n\n# \u5b9a\u4e49\u4e00\u4e2a\u76ee\u6807\u503c\u5f20\u91cf\u548c\u635f\u5931\u51fd\u6570\ny_true = torch.tensor(&#91;&#91;1.0], &#91;0.0]])\nloss_fn = nn.MSELoss()\nloss = loss_fn(y_pred, y_true)  # \u8ba1\u7b97\u635f\u5931\n\n# \u53cd\u5411\u4f20\u64ad\nloss.backward()  # \u81ea\u52a8\u8ba1\u7b97\u68af\u5ea6\n\n# \u67e5\u770b\u68af\u5ea6\nprint(f\"Loss: {loss.item()}\")\nprint(f\"Gradients: {linear.weight.grad}, {linear.bias.grad}\")\n<\/code><\/code><\/pre>\n\n\n\n<p>\u4f7f\u7528 <code>nn.Linear<\/code> \u5b9a\u4e49\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u5c42\u3002\u524d\u5411\u4f20\u64ad\u540e\uff0c\u4f7f\u7528 <code>loss.backward()<\/code> \u8ba1\u7b97\u68af\u5ea6\uff0c\u5373\u4e3a\u53cd\u5411\u4f20\u64ad\u7684\u6838\u5fc3\u3002\u901a\u8fc7\u8fd9\u6837\u7684\u5f20\u91cf\u8ba1\u7b97\u548c\u81ea\u52a8\u6c42\u5bfc\uff0c\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u9010\u6b65\u4f18\u5316\u5176\u53c2\u6570\u3002<\/p>\n\n\n\n<!doctype html>\n<html style='font-size:20px !important'>\n<head>\n<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>\n<title>\u6a21\u578b (copy)<\/title><link href='https:\/\/fonts.loli.net\/css?family=Open+Sans:400italic,700italic,700,400&#038;subset=latin,latin-ext' rel='stylesheet' type='text\/css' \/><style type='text\/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:\"Lucida Console\",Consolas,\"Courier\",monospace; --title-bar-height:20px; }\n.mac-os-11 { --title-bar-height:28px; }\nhtml { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: \"Helvetica Neue\", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }\nbody { margin: 0px; padding: 0px; height: auto; bottom: 0px; top: 0px; left: 0px; right: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }\niframe { margin: auto; }\na.url { word-break: break-all; }\na:active, a:hover { outline: 0px; }\n.in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }\n#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }\n#write.first-line-indent p { text-indent: 2em; }\n#write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }\n#write.first-line-indent li { margin-left: 2em; }\n.for-image #write { padding-left: 8px; padding-right: 8px; }\nbody.typora-export { padding-left: 30px; padding-right: 30px; }\n.typora-export .footnote-line, .typora-export li, .typora-export p { white-space: pre-wrap; }\n.typora-export .task-list-item input { pointer-events: none; }\n@media screen and (max-width: 500px) {\n  body.typora-export { padding-left: 0px; padding-right: 0px; }\n  #write { padding-left: 20px; padding-right: 20px; }\n  .CodeMirror-sizer { margin-left: 0px !important; }\n  .CodeMirror-gutters { display: none !important; }\n}\n#write li > figure:last-child { margin-bottom: 0.5rem; }\n#write ol, #write ul { position: relative; }\nimg { max-width: 100%; vertical-align: middle; image-orientation: from-image; }\nbutton, input, select, textarea { color: inherit; font: inherit; }\ninput[type=\"checkbox\"], input[type=\"radio\"] { line-height: normal; padding: 0px; }\n*, ::after, ::before { box-sizing: border-box; }\n#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p, #write pre { width: inherit; }\n#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p { position: relative; }\np { line-height: inherit; }\nh1, h2, h3, h4, h5, h6 { break-after: avoid-page; break-inside: avoid; orphans: 4; }\np { orphans: 4; }\nh1 { font-size: 2rem; }\nh2 { font-size: 1.8rem; }\nh3 { font-size: 1.6rem; }\nh4 { font-size: 1.4rem; }\nh5 { 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32px; }\n.CodeMirror-gutters { border-right: 0px; background-color: inherit; }\n.CodeMirror-linenumber { user-select: none; }\n.CodeMirror { text-align: left; }\n.CodeMirror-placeholder { opacity: 0.3; }\n.CodeMirror pre { padding: 0px 4px; }\n.CodeMirror-lines { padding: 0px; }\ndiv.hr:focus { cursor: none; }\n#write pre { white-space: pre-wrap; }\n#write.fences-no-line-wrapping pre { white-space: pre; }\n#write pre.ty-contain-cm { white-space: normal; }\n.CodeMirror-gutters { margin-right: 4px; }\n.md-fences { font-size: 0.9rem; display: block; break-inside: avoid; text-align: left; overflow: visible; white-space: pre; background: inherit; position: relative !important; }\n.md-diagram-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }\n#write .md-fences.mock-cm { white-space: pre-wrap; }\n.md-fences.md-fences-with-lineno { padding-left: 0px; }\n#write.fences-no-line-wrapping .md-fences.mock-cm { white-space: pre; overflow-x: auto; }\n.md-fences.mock-cm.md-fences-with-lineno { padding-left: 8px; }\n.CodeMirror-line, twitterwidget { break-inside: avoid; }\n.footnotes { opacity: 0.8; font-size: 0.9rem; margin-top: 1em; margin-bottom: 1em; }\n.footnotes + .footnotes { margin-top: 0px; }\n.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }\nli div { padding-top: 0px; }\nblockquote { margin: 1rem 0px; }\nli .mathjax-block, li p { margin: 0.5rem 0px; }\nli blockquote { margin: 1rem 0px; }\nli { margin: 0px; position: relative; }\nblockquote > :last-child { margin-bottom: 0px; }\nblockquote > :first-child, li > :first-child { margin-top: 0px; }\n.footnotes-area { color: rgb(136, 136, 136); margin-top: 0.714rem; padding-bottom: 0.143rem; white-space: normal; }\n#write .footnote-line { white-space: pre-wrap; }\n@media print {\n  body, html { border: 1px solid transparent; height: 99%; break-after: avoid; break-before: avoid; font-variant-ligatures: no-common-ligatures; }\n  #write { margin-top: 0px; padding-top: 0px; border-color: transparent !important; }\n  .typora-export * { -webkit-print-color-adjust: exact; }\n  .typora-export #write { break-after: avoid; }\n  .typora-export #write::after { height: 0px; }\n  .is-mac table { break-inside: avoid; }\n}\n.footnote-line { margin-top: 0.714em; font-size: 0.7em; }\na img, img a { cursor: pointer; }\npre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }\np > .md-image:only-child:not(.md-img-error) img, p > img:only-child { display: block; margin: auto; }\n#write.first-line-indent p > .md-image:only-child:not(.md-img-error) img { left: -2em; position: relative; }\np > .md-image:only-child { display: inline-block; width: 100%; }\n#write .MathJax_Display { margin: 0.8em 0px 0px; }\n.md-math-block { width: 100%; }\n.md-math-block:not(:empty)::after { display: none; }\n.MathJax_ref { fill: currentcolor; }\n[contenteditable=\"true\"]:active, [contenteditable=\"true\"]:focus, [contenteditable=\"false\"]:active, [contenteditable=\"false\"]:focus { outline: 0px; box-shadow: none; }\n.md-task-list-item { position: relative; list-style-type: none; }\n.task-list-item.md-task-list-item { padding-left: 0px; }\n.md-task-list-item > input { position: absolute; top: 0px; left: 0px; margin-left: -1.2em; margin-top: calc(1em - 10px); border: none; }\n.math { font-size: 1rem; }\n.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }\n.md-toc-content { position: relative; margin-left: 0px; }\n.md-toc-content::after, .md-toc::after { display: none; }\n.md-toc-item { display: block; color: rgb(65, 131, 196); }\n.md-toc-item a { text-decoration: none; }\n.md-toc-inner:hover { text-decoration: underline; }\n.md-toc-inner { display: inline-block; cursor: pointer; }\n.md-toc-h1 .md-toc-inner { margin-left: 0px; font-weight: 700; }\n.md-toc-h2 .md-toc-inner { margin-left: 2em; }\n.md-toc-h3 .md-toc-inner { margin-left: 4em; }\n.md-toc-h4 .md-toc-inner { margin-left: 6em; }\n.md-toc-h5 .md-toc-inner { margin-left: 8em; }\n.md-toc-h6 .md-toc-inner { margin-left: 10em; }\n@media screen and (max-width: 48em) {\n  .md-toc-h3 .md-toc-inner { margin-left: 3.5em; }\n  .md-toc-h4 .md-toc-inner { margin-left: 5em; }\n  .md-toc-h5 .md-toc-inner { margin-left: 6.5em; }\n  .md-toc-h6 .md-toc-inner { margin-left: 8em; }\n}\na.md-toc-inner { font-size: inherit; font-style: inherit; font-weight: inherit; line-height: inherit; }\n.footnote-line a:not(.reversefootnote) { color: inherit; }\n.md-attr { display: none; }\n.md-fn-count::after { content: \".\"; }\ncode, pre, samp, tt { font-family: var(--monospace); }\nkbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }\n.md-comment { color: rgb(162, 127, 3); opacity: 0.8; font-family: var(--monospace); }\ncode { text-align: left; vertical-align: initial; }\na.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }\n.md-inline-math .MathJax_SVG .noError { display: none !important; }\n.html-for-mac 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}\n.cm-s-inner .cm-variable-2 { color: rgb(0, 85, 170); }\n.cm-s-inner .cm-variable-3 { color: rgb(0, 136, 85); }\n.cm-s-inner .cm-string { color: rgb(170, 17, 17); }\n.cm-s-inner .cm-property { color: rgb(0, 0, 0); }\n.cm-s-inner .cm-operator { color: rgb(152, 26, 26); }\n.cm-s-inner .cm-comment, .cm-s-inner.cm-comment { color: rgb(170, 85, 0); }\n.cm-s-inner .cm-string-2 { color: rgb(255, 85, 0); }\n.cm-s-inner .cm-meta { color: rgb(85, 85, 85); }\n.cm-s-inner .cm-qualifier { color: rgb(85, 85, 85); }\n.cm-s-inner .cm-builtin { color: rgb(51, 0, 170); }\n.cm-s-inner .cm-bracket { color: rgb(153, 153, 119); }\n.cm-s-inner .cm-tag { color: rgb(17, 119, 0); }\n.cm-s-inner .cm-attribute { color: rgb(0, 0, 204); }\n.cm-s-inner .cm-header, .cm-s-inner.cm-header { color: rgb(0, 0, 255); }\n.cm-s-inner .cm-quote, .cm-s-inner.cm-quote { color: rgb(0, 153, 0); }\n.cm-s-inner .cm-hr, .cm-s-inner.cm-hr { color: rgb(153, 153, 153); }\n.cm-s-inner .cm-link, .cm-s-inner.cm-link { color: rgb(0, 0, 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}\n.CodeMirror-vscrollbar { right: 0px; top: 0px; overflow: hidden; }\n.CodeMirror-hscrollbar { bottom: 0px; left: 0px; overflow: hidden; }\n.CodeMirror-scrollbar-filler { right: 0px; bottom: 0px; }\n.CodeMirror-gutter-filler { left: 0px; bottom: 0px; }\n.CodeMirror-gutters { position: absolute; left: 0px; top: 0px; padding-bottom: 30px; z-index: 3; }\n.CodeMirror-gutter { white-space: normal; height: 100%; box-sizing: content-box; padding-bottom: 30px; margin-bottom: -32px; display: inline-block; }\n.CodeMirror-gutter-wrapper { position: absolute; z-index: 4; background: 0px 0px !important; border: none !important; }\n.CodeMirror-gutter-background { position: absolute; top: 0px; bottom: 0px; z-index: 4; }\n.CodeMirror-gutter-elt { position: absolute; cursor: default; z-index: 4; }\n.CodeMirror-lines { cursor: text; }\n.CodeMirror pre { border-radius: 0px; border-width: 0px; background: 0px 0px; font-family: inherit; font-size: inherit; margin: 0px; white-space: pre; overflow-wrap: normal; color: inherit; z-index: 2; position: relative; overflow: visible; }\n.CodeMirror-wrap pre { overflow-wrap: break-word; white-space: pre-wrap; word-break: normal; }\n.CodeMirror-code pre { border-right: 30px solid transparent; width: fit-content; }\n.CodeMirror-wrap .CodeMirror-code pre { border-right: none; width: auto; }\n.CodeMirror-linebackground { position: absolute; left: 0px; right: 0px; top: 0px; bottom: 0px; z-index: 0; }\n.CodeMirror-linewidget { position: relative; z-index: 2; overflow: auto; }\n.CodeMirror-wrap .CodeMirror-scroll { overflow-x: hidden; }\n.CodeMirror-measure { position: absolute; width: 100%; height: 0px; overflow: hidden; visibility: hidden; }\n.CodeMirror-measure pre { position: static; }\n.CodeMirror div.CodeMirror-cursor { position: absolute; visibility: hidden; border-right: none; width: 0px; }\n.CodeMirror div.CodeMirror-cursor { visibility: hidden; }\n.CodeMirror-focused div.CodeMirror-cursor { visibility: inherit; }\n.cm-searching { background: rgba(255, 255, 0, 0.4); }\n@media print {\n  .CodeMirror div.CodeMirror-cursor { visibility: hidden; }\n}\n\n\n:root {\n    --side-bar-bg-color: #fafafa;\n    --control-text-color: #777;\n}\n\n@include-when-export url(https:\/\/fonts.loli.net\/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext);\n\n\/* open-sans-regular - latin-ext_latin *\/\n  \/* open-sans-italic - latin-ext_latin *\/\n    \/* open-sans-700 - latin-ext_latin *\/\n    \/* open-sans-700italic - latin-ext_latin *\/\n  html {\n    font-size: 16px;\n}\n\nbody {\n    font-family: \"Open Sans\",\"Clear Sans\", \"Helvetica Neue\", Helvetica, Arial, sans-serif;\n    color: rgb(51, 51, 51);\n    line-height: 1.6;\n}\n\n#write {\n    max-width: 860px;\n  \tmargin: 0 auto;\n  \tpadding: 30px;\n    padding-bottom: 100px;\n}\n\n@media only screen and (min-width: 1400px) {\n\t#write {\n\t\tmax-width: 1024px;\n\t}\n}\n\n@media only screen and (min-width: 1800px) {\n\t#write {\n\t\tmax-width: 1200px;\n\t}\n}\n\n#write > ul:first-child,\n#write > ol:first-child{\n    margin-top: 30px;\n}\n\na {\n    color: #4183C4;\n}\nh1,\nh2,\nh3,\nh4,\nh5,\nh6 {\n    position: relative;\n    margin-top: 1rem;\n    margin-bottom: 1rem;\n    font-weight: bold;\n    line-height: 1.4;\n    cursor: text;\n}\nh1:hover a.anchor,\nh2:hover a.anchor,\nh3:hover a.anchor,\nh4:hover a.anchor,\nh5:hover a.anchor,\nh6:hover a.anchor {\n    text-decoration: none;\n}\nh1 tt,\nh1 code {\n    font-size: inherit;\n}\nh2 tt,\nh2 code {\n    font-size: inherit;\n}\nh3 tt,\nh3 code {\n    font-size: inherit;\n}\nh4 tt,\nh4 code {\n    font-size: inherit;\n}\nh5 tt,\nh5 code {\n    font-size: inherit;\n}\nh6 tt,\nh6 code {\n    font-size: inherit;\n}\nh1 {\n    font-size: 2.25em;\n    line-height: 1.2;\n    border-bottom: 1px solid #eee;\n}\nh2 {\n    font-size: 1.75em;\n    line-height: 1.225;\n    border-bottom: 1px solid #eee;\n}\n\n\/*@media print {\n    .typora-export h1,\n    .typora-export h2 {\n        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color: #777777;\n}\nblockquote blockquote {\n    padding-right: 0;\n}\ntable {\n    padding: 0;\n    word-break: initial;\n}\ntable tr {\n    border-top: 1px solid #dfe2e5;\n    margin: 0;\n    padding: 0;\n}\ntable tr:nth-child(2n),\nthead {\n    background-color: #f8f8f8;\n}\ntable th {\n    font-weight: bold;\n    border: 1px solid #dfe2e5;\n    border-bottom: 0;\n    margin: 0;\n    padding: 6px 13px;\n}\ntable td {\n    border: 1px solid #dfe2e5;\n    margin: 0;\n    padding: 6px 13px;\n}\ntable th:first-child,\ntable td:first-child {\n    margin-top: 0;\n}\ntable th:last-child,\ntable td:last-child {\n    margin-bottom: 0;\n}\n\n.CodeMirror-lines {\n    padding-left: 4px;\n}\n\n.code-tooltip {\n    box-shadow: 0 1px 1px 0 rgba(0,28,36,.3);\n    border-top: 1px solid #eef2f2;\n}\n\n.md-fences,\ncode,\ntt {\n    border: 1px solid #e7eaed;\n    background-color: #f8f8f8;\n    border-radius: 3px;\n    padding: 0;\n    padding: 2px 4px 0px 4px;\n    font-size: 0.9em;\n}\n\ncode {\n    background-color: #f3f4f4;\n    padding: 0 2px 0 2px;\n}\n\n.md-fences {\n    margin-bottom: 15px;\n    margin-top: 15px;\n    padding-top: 8px;\n    padding-bottom: 6px;\n}\n\n\n.md-task-list-item > input {\n  margin-left: -1.3em;\n}\n\n@media print {\n    html {\n        font-size: 13px;\n    }\n    table,\n    pre {\n        page-break-inside: avoid;\n    }\n    pre {\n        word-wrap: break-word;\n    }\n}\n\n.md-fences {\n\tbackground-color: #f8f8f8;\n}\n#write pre.md-meta-block {\n\tpadding: 1rem;\n    font-size: 85%;\n    line-height: 1.45;\n    background-color: #f7f7f7;\n    border: 0;\n    border-radius: 3px;\n    color: #777777;\n    margin-top: 0 !important;\n}\n\n.mathjax-block>.code-tooltip {\n\tbottom: .375rem;\n}\n\n.md-mathjax-midline {\n    background: #fafafa;\n}\n\n#write>h3.md-focus:before{\n\tleft: -1.5625rem;\n\ttop: .375rem;\n}\n#write>h4.md-focus:before{\n\tleft: -1.5625rem;\n\ttop: .285714286rem;\n}\n#write>h5.md-focus:before{\n\tleft: -1.5625rem;\n\ttop: .285714286rem;\n}\n#write>h6.md-focus:before{\n\tleft: -1.5625rem;\n\ttop: .285714286rem;\n}\n.md-image>.md-meta {\n    \/*border: 1px solid #ddd;*\/\n    border-radius: 3px;\n    padding: 2px 0px 0px 4px;\n    font-size: 0.9em;\n    color: inherit;\n}\n\n.md-tag {\n    color: #a7a7a7;\n    opacity: 1;\n}\n\n.md-toc { \n    margin-top:20px;\n    padding-bottom:20px;\n}\n\n.sidebar-tabs {\n    border-bottom: none;\n}\n\n#typora-quick-open {\n    border: 1px solid #ddd;\n    background-color: #f8f8f8;\n}\n\n#typora-quick-open-item {\n    background-color: #FAFAFA;\n    border-color: #FEFEFE #e5e5e5 #e5e5e5 #eee;\n    border-style: solid;\n    border-width: 1px;\n}\n\n\/** focus mode *\/\n.on-focus-mode blockquote {\n    border-left-color: rgba(85, 85, 85, 0.12);\n}\n\nheader, .context-menu, .megamenu-content, footer{\n    font-family: \"Segoe UI\", \"Arial\", sans-serif;\n}\n\n.file-node-content:hover .file-node-icon,\n.file-node-content:hover .file-node-open-state{\n    visibility: visible;\n}\n\n.mac-seamless-mode #typora-sidebar {\n    background-color: #fafafa;\n    background-color: var(--side-bar-bg-color);\n}\n\n.md-lang {\n    color: #b4654d;\n}\n\n.html-for-mac .context-menu {\n    --item-hover-bg-color: #E6F0FE;\n}\n\n#md-notification .btn {\n    border: 0;\n}\n\n.dropdown-menu .divider {\n    border-color: #e5e5e5;\n}\n\n.ty-preferences .window-content {\n    background-color: #fafafa;\n}\n\n.ty-preferences .nav-group-item.active {\n    color: white;\n    background: #999;\n}\n\n :root {--mermaid-font-zoom:1.25em ;} \n<\/style>\n<\/head>\n<body class='typora-export os-windows'>\n<div id='write'  class=''><h3><a name=\"1-\u8f93\u5165\u6570\u636e\u548c\u7ebf\u6027\u5c42\u7684\u53c2\u6570\" class=\"md-header-anchor\"><\/a><span>1. \u8f93\u5165\u6570\u636e\u548c\u7ebf\u6027\u5c42\u7684\u53c2\u6570<\/span><\/h3><p><span>\u9996\u5148\uff0c\u6211\u4eec\u5b9a\u4e49\u8f93\u5165\u6570\u636e <\/span><code>x<\/code><span> \u548c\u7ebf\u6027\u5c42\u7684\u6743\u91cd\u548c\u504f\u7f6e\uff1a<\/span><\/p><pre spellcheck=\"false\" class=\"md-fences md-end-block ty-contain-cm modeLoaded\" lang=\"python\"><div class=\"CodeMirror cm-s-inner CodeMirror-wrap\" lang=\"python\"><div style=\"overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;\"><textarea autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" tabindex=\"0\" style=\"position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;\"><\/textarea><\/div><div class=\"CodeMirror-scrollbar-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-gutter-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-scroll\" tabindex=\"-1\"><div class=\"CodeMirror-sizer\" style=\"margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;\"><div style=\"position: relative; top: 0px;\"><div class=\"CodeMirror-lines\" role=\"presentation\"><div role=\"presentation\" style=\"position: relative; outline: none;\"><div class=\"CodeMirror-measure\"><pre><span>xxxxxxxxxx<\/span><\/pre><\/div><div class=\"CodeMirror-measure\"><\/div><div style=\"position: relative; z-index: 1;\"><\/div><div class=\"CodeMirror-code\" role=\"presentation\" style=\"\"><div class=\"CodeMirror-activeline\" style=\"position: relative;\"><div class=\"CodeMirror-activeline-background CodeMirror-linebackground\"><\/div><div class=\"CodeMirror-gutter-background CodeMirror-activeline-gutter\" style=\"left: 0px; width: 0px;\"><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-comment\"># \u8f93\u5165\u6570\u636e\u5f20\u91cf<\/span><\/span><\/pre><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">x<\/span> = <span class=\"cm-variable\">torch<\/span>.<span class=\"cm-property\">tensor<\/span>([[<span class=\"cm-number\">0.5<\/span>, <span class=\"cm-operator\">-<\/span><span class=\"cm-number\">1.5<\/span>], [<span class=\"cm-number\">1.0<\/span>, <span class=\"cm-number\">1.0<\/span>]], <span class=\"cm-variable\">requires_grad<\/span>=<span class=\"cm-keyword\">True<\/span>) &nbsp;<span class=\"cm-comment\"># 2\u4e2a\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c2\u4e2a\u7279\u5f81<\/span><\/span><\/pre><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span cm-text=\"\">\u200b<\/span><\/span><\/pre><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-comment\"># \u5b9a\u4e49\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u5c42<\/span><\/span><\/pre><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">linear<\/span> = <span class=\"cm-variable\">nn<\/span>.<span class=\"cm-property\">Linear<\/span>(<span class=\"cm-number\">2<\/span>, <span class=\"cm-number\">1<\/span>) &nbsp;<span class=\"cm-comment\"># \u8f93\u5165\u5927\u5c0f\u4e3a2\uff0c\u8f93\u51fa\u5927\u5c0f\u4e3a1<\/span><\/span><\/pre><\/div><\/div><\/div><\/div><\/div><div style=\"position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 144px;\"><\/div><div class=\"CodeMirror-gutters\" style=\"display: none; height: 144px;\"><\/div><\/div><\/div><\/pre><ul><li><p><span>\u8f93\u5165\u5f20\u91cf <\/span><code>x<\/code><span> \u6709\u4e24\u4e2a\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c\u6709\u4e24\u4e2a\u7279\u5f81\u3002<\/span><\/p><\/li><li><p><code>linear<\/code><span> \u662f\u4e00\u4e2a\u7ebf\u6027\u5c42\uff0c\u5176\u6743\u91cd <\/span><code>W<\/code><span> \u548c\u504f\u7f6e <\/span><code>b<\/code><span> \u5728\u521d\u59cb\u5316\u65f6\u662f\u968f\u673a\u751f\u6210\u7684\uff0c\u5047\u8bbe\u5982\u4e0b\uff1a<\/span><\/p><ul><li><span>\u6743\u91cd\uff1a<\/span><code>W = [[w1, w2]]<\/code><\/li><li><span>\u504f\u7f6e\uff1a<\/span><code>b = [b]<\/code><\/li><\/ul><\/li><\/ul><h3><a name=\"2-\u524d\u5411\u4f20\u64ad\" class=\"md-header-anchor\"><\/a><span>2. \u524d\u5411\u4f20\u64ad<\/span><\/h3><p><span>\u524d\u5411\u4f20\u64ad\u8fc7\u7a0b\u8ba1\u7b97\u6a21\u578b\u7684\u8f93\u51fa\uff08\u9884\u6d4b\u503c\uff09\uff1a<\/span><\/p><pre spellcheck=\"false\" class=\"md-fences md-end-block ty-contain-cm modeLoaded\" lang=\"python\"><div class=\"CodeMirror cm-s-inner CodeMirror-wrap\" lang=\"python\"><div style=\"overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;\"><textarea autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" tabindex=\"0\" style=\"position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;\"><\/textarea><\/div><div class=\"CodeMirror-scrollbar-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-gutter-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-scroll\" tabindex=\"-1\"><div class=\"CodeMirror-sizer\" style=\"margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;\"><div style=\"position: relative; top: 0px;\"><div class=\"CodeMirror-lines\" role=\"presentation\"><div role=\"presentation\" style=\"position: relative; outline: none;\"><div class=\"CodeMirror-measure\"><pre><span>xxxxxxxxxx<\/span><\/pre><\/div><div class=\"CodeMirror-measure\"><\/div><div style=\"position: relative; z-index: 1;\"><\/div><div class=\"CodeMirror-code\" role=\"presentation\"><div class=\"CodeMirror-activeline\" style=\"position: relative;\"><div class=\"CodeMirror-activeline-background CodeMirror-linebackground\"><\/div><div class=\"CodeMirror-gutter-background CodeMirror-activeline-gutter\" style=\"left: 0px; width: 0px;\"><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-comment\"># \u524d\u5411\u4f20\u64ad<\/span><\/span><\/pre><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">y_pred<\/span> = <span class=\"cm-variable\">linear<\/span>(<span class=\"cm-variable\">x<\/span>) &nbsp;<span class=\"cm-comment\"># \u8ba1\u7b97\u8f93\u51fa\uff08\u9884\u6d4b\u503c\uff09<\/span><\/span><\/pre><\/div><\/div><\/div><\/div><\/div><div style=\"position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 58px;\"><\/div><div class=\"CodeMirror-gutters\" style=\"display: none; height: 58px;\"><\/div><\/div><\/div><\/pre><p><span>\u5bf9\u4e8e\u6bcf\u4e2a\u6837\u672c\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" 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138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E218-MJMATHI-79\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(490,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E218-MJMAIN-70\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E218-MJMAIN-72\" x=\"556\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E218-MJMAIN-65\" x=\"948\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E218-MJMAIN-64\" x=\"1392\" y=\"0\"><\/use><\/g><use xlink:href=\"#E218-MJMAIN-3D\" x=\"2245\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMATHI-78\" x=\"3300\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMAIN-22C5\" x=\"4095\" y=\"0\"><\/use><g transform=\"translate(4595,0)\"><use xlink:href=\"#E218-MJMATHI-57\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E218-MJMATHI-54\" x=\"1526\" y=\"583\"><\/use><\/g><use xlink:href=\"#E218-MJMAIN-2B\" x=\"6494\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMATHI-62\" x=\"7494\" y=\"0\"><\/use><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-103\">\ny_{\\text{pred}} = x \\cdot W^T + b<\/script><\/div><\/div><p><span>\u5047\u8bbe\u6743\u91cd\u548c\u504f\u7f6e\u521d\u59cb\u5316\u4e3a\uff1a<\/span><\/p><p><span>\u5047\u8bbe\u6743\u91cd\u548c\u504f\u7f6e\u521d\u59cb\u5316\u4e3a\uff1a<\/span><\/p><ul><li><span>\u6743\u91cd\uff1a<\/span><code>W = [[0.3, -0.2]]<\/code><span>\uff08\u5177\u4f53\u503c\u53d6\u51b3\u4e8e\u521d\u59cb\u5316\uff09<\/span><\/li><li><span>\u504f\u7f6e\uff1a<\/span><code>b = [0.1]<\/code><\/li><\/ul><h4><a name=\"\u8ba1\u7b97\u8fc7\u7a0b\" class=\"md-header-anchor\"><\/a><span>\u8ba1\u7b97\u8fc7\u7a0b<\/span><\/h4><p><span>\u5bf9\u4e8e\u7b2c\u4e00\u4e2a\u6837\u672c <\/span><code>x[0] = [0.5, -1.5]<\/code><span>\uff1a<\/span><\/p><div contenteditable=\"false\" 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x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMAIN-31\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E219-MJMAIN-3D\" x=\"26138\" y=\"0\"><\/use><g transform=\"translate(27194,0)\"><use xlink:href=\"#E219-MJMAIN-30\"><\/use><use xlink:href=\"#E219-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMAIN-35\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMAIN-35\" x=\"1278\" y=\"0\"><\/use><\/g><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-104\">\ny_{\\text{pred}}[0] = 0.5 \\cdot 0.3 + (-1.5) \\cdot (-0.2) + 0.1\n\n= 0.15 + 0.3 + 0.1 = 0.55\n<\/script><\/div><\/div><p><span>\u5bf9\u4e8e\u7b2c\u4e8c\u4e2a\u6837\u672c <\/span><code>x[1] = [1.0, 1.0]<\/code><span>\uff1a<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n642\" cid=\"n642\" mdtype=\"math_block\"><div class=\"md-rawblock-container md-math-container\" tabindex=\"-1\"><div 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xlink:href=\"#E220-MJMAIN-2B\" x=\"13914\" y=\"0\"><\/use><g transform=\"translate(14914,0)\"><use xlink:href=\"#E220-MJMAIN-30\"><\/use><use xlink:href=\"#E220-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-31\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E220-MJMAIN-3D\" x=\"16470\" y=\"0\"><\/use><g transform=\"translate(17526,0)\"><use xlink:href=\"#E220-MJMAIN-30\"><\/use><use xlink:href=\"#E220-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-33\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E220-MJMAIN-2212\" x=\"19026\" y=\"0\"><\/use><g transform=\"translate(20026,0)\"><use xlink:href=\"#E220-MJMAIN-30\"><\/use><use xlink:href=\"#E220-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-32\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E220-MJMAIN-2B\" x=\"21526\" y=\"0\"><\/use><g transform=\"translate(22527,0)\"><use xlink:href=\"#E220-MJMAIN-30\"><\/use><use xlink:href=\"#E220-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-31\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E220-MJMAIN-3D\" x=\"24082\" y=\"0\"><\/use><g transform=\"translate(25138,0)\"><use xlink:href=\"#E220-MJMAIN-30\"><\/use><use xlink:href=\"#E220-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-32\" x=\"778\" y=\"0\"><\/use><\/g><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-105\">y_{\\text{pred}}[1] = 1.0 \\cdot 0.3 + 1.0 \\cdot (-0.2) + 0.1\n\n= 0.3 - 0.2 + 0.1 = 0.2<\/script><\/div><\/div><p><span>\u6240\u4ee5\u8f93\u51fa <\/span><code>y_pred<\/code><span> \u4e3a\uff1a<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n644\" cid=\"n644\" mdtype=\"math_block\"><div class=\"md-rawblock-container md-math-container\" tabindex=\"-1\"><div class=\"MathJax_SVG_Display\" style=\"text-align: center;\"><span class=\"MathJax_SVG\" 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xlink:href=\"#E221-MJMAIN-65\" x=\"948\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E221-MJMAIN-64\" x=\"1392\" y=\"0\"><\/use><\/g><use xlink:href=\"#E221-MJMAIN-3D\" x=\"2245\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-5B\" x=\"3300\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-5B\" x=\"3578\" y=\"0\"><\/use><g transform=\"translate(3856,0)\"><use xlink:href=\"#E221-MJMAIN-30\"><\/use><use xlink:href=\"#E221-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-35\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-35\" x=\"1278\" y=\"0\"><\/use><\/g><use xlink:href=\"#E221-MJMAIN-5D\" x=\"5634\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-2C\" x=\"5912\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-5B\" x=\"6357\" y=\"0\"><\/use><g transform=\"translate(6635,0)\"><use xlink:href=\"#E221-MJMAIN-30\"><\/use><use xlink:href=\"#E221-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-32\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E221-MJMAIN-5D\" x=\"7913\" y=\"0\"><\/use><use xlink:href=\"#E221-MJMAIN-5D\" x=\"8191\" y=\"0\"><\/use><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-106\">y_{\\text{pred}} = [[0.55], [0.2]]<\/script><\/div><\/div><h3><a name=\"3-\u635f\u5931\u8ba1\u7b97\" class=\"md-header-anchor\"><\/a><span>3. \u635f\u5931\u8ba1\u7b97<\/span><\/h3><p><span>\u63a5\u4e0b\u6765\uff0c\u8ba1\u7b97\u635f\u5931\uff1a<\/span><\/p><pre spellcheck=\"false\" class=\"md-fences md-end-block ty-contain-cm modeLoaded\" lang=\"python\"><div class=\"CodeMirror cm-s-inner CodeMirror-wrap\" lang=\"python\"><div style=\"overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;\"><textarea autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" tabindex=\"0\" style=\"position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;\"><\/textarea><\/div><div class=\"CodeMirror-scrollbar-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-gutter-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-scroll\" tabindex=\"-1\"><div class=\"CodeMirror-sizer\" style=\"margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;\"><div style=\"position: relative; top: 0px;\"><div class=\"CodeMirror-lines\" role=\"presentation\"><div role=\"presentation\" style=\"position: relative; outline: none;\"><div class=\"CodeMirror-measure\"><pre><span>xxxxxxxxxx<\/span><\/pre><\/div><div class=\"CodeMirror-measure\"><\/div><div style=\"position: relative; z-index: 1;\"><\/div><div class=\"CodeMirror-code\" role=\"presentation\"><div class=\"CodeMirror-activeline\" style=\"position: relative;\"><div class=\"CodeMirror-activeline-background CodeMirror-linebackground\"><\/div><div class=\"CodeMirror-gutter-background CodeMirror-activeline-gutter\" style=\"left: 0px; width: 0px;\"><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-comment\"># \u5b9a\u4e49\u76ee\u6807\u503c\u5f20\u91cf\u548c\u635f\u5931\u51fd\u6570<\/span><\/span><\/pre><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">y_true<\/span> = <span class=\"cm-variable\">torch<\/span>.<span class=\"cm-property\">tensor<\/span>([[<span class=\"cm-number\">1.0<\/span>], [<span class=\"cm-number\">0.0<\/span>]])<\/span><\/pre><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">loss_fn<\/span> = <span class=\"cm-variable\">nn<\/span>.<span class=\"cm-property\">MSELoss<\/span>()<\/span><\/pre><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">loss<\/span> = <span class=\"cm-variable\">loss_fn<\/span>(<span class=\"cm-variable\">y_pred<\/span>, <span class=\"cm-variable\">y_true<\/span>) &nbsp;<span class=\"cm-comment\"># \u8ba1\u7b97\u635f\u5931<\/span><\/span><\/pre><\/div><\/div><\/div><\/div><\/div><div style=\"position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 115px;\"><\/div><div class=\"CodeMirror-gutters\" style=\"display: none; height: 115px;\"><\/div><\/div><\/div><\/pre><p><span>\u4f7f\u7528\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u635f\u5931\u51fd\u6570\uff0c\u8ba1\u7b97\u65b9\u6cd5\u4e3a\uff1a<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n650\" cid=\"n650\" mdtype=\"math_block\"><div class=\"md-rawblock-container md-math-container\" tabindex=\"-1\"><div class=\"MathJax_SVG_Display\" style=\"text-align: center;\"><span class=\"MathJax_SVG\" id=\"MathJax-Element-107-Frame\" tabindex=\"-1\" 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y=\"0\"><\/use><g transform=\"translate(37440,0)\"><g transform=\"translate(397,0)\"><rect stroke=\"none\" width=\"620\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use xlink:href=\"#E223-MJMAIN-31\" x=\"60\" y=\"676\"><\/use><use xlink:href=\"#E223-MJMAIN-32\" x=\"60\" y=\"-686\"><\/use><\/g><\/g><use xlink:href=\"#E223-MJMAIN-D7\" x=\"38800\" y=\"0\"><\/use><g transform=\"translate(39801,0)\"><use xlink:href=\"#E223-MJMAIN-30\"><\/use><use xlink:href=\"#E223-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-32\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-34\" x=\"1278\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-32\" x=\"1778\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-35\" x=\"2278\" y=\"0\"><\/use><\/g><use xlink:href=\"#E223-MJMAIN-3D\" x=\"42856\" y=\"0\"><\/use><g transform=\"translate(43912,0)\"><use xlink:href=\"#E223-MJMAIN-30\"><\/use><use xlink:href=\"#E223-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-31\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-32\" x=\"1278\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-31\" x=\"1778\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-32\" x=\"2278\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-35\" x=\"2778\" y=\"0\"><\/use><\/g><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-108\">\\text{MSE} = \\frac{1}{2} \\left( (0.55 - 1.0)^2 + (0.2 - 0.0)^2 \\right)\n\n= \\frac{1}{2} \\left( (-0.45)^2 + (0.2)^2 \\right)\n\n= \\frac{1}{2} \\left( 0.2025 + 0.04 \\right) = \\frac{1}{2} \\times 0.2425 = 0.12125<\/script><\/div><\/div><p><span>\u6240\u4ee5 <\/span><code>loss<\/code><span> \u7684\u503c\u4e3a <\/span><code>0.12125<\/code><span>\u3002<\/span><\/p><h3><a name=\"4-\u53cd\u5411\u4f20\u64ad\" class=\"md-header-anchor\"><\/a><span>4. \u53cd\u5411\u4f20\u64ad<\/span><\/h3><p><span>\u53cd\u5411\u4f20\u64ad\u8fc7\u7a0b\u8ba1\u7b97\u635f\u5931\u76f8\u5bf9\u4e8e\u6a21\u578b\u53c2\u6570\u7684\u68af\u5ea6\uff1a<\/span><\/p><pre spellcheck=\"false\" class=\"md-fences md-end-block ty-contain-cm modeLoaded\" lang=\"python\"><div class=\"CodeMirror cm-s-inner CodeMirror-wrap\" lang=\"python\"><div style=\"overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;\"><textarea autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" tabindex=\"0\" style=\"position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;\"><\/textarea><\/div><div class=\"CodeMirror-scrollbar-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-gutter-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-scroll\" tabindex=\"-1\"><div class=\"CodeMirror-sizer\" style=\"margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;\"><div style=\"position: relative; top: 0px;\"><div class=\"CodeMirror-lines\" role=\"presentation\"><div role=\"presentation\" style=\"position: relative; outline: none;\"><div class=\"CodeMirror-measure\"><pre><span>xxxxxxxxxx<\/span><\/pre><\/div><div class=\"CodeMirror-measure\"><\/div><div style=\"position: relative; z-index: 1;\"><\/div><div class=\"CodeMirror-code\" role=\"presentation\"><div class=\"CodeMirror-activeline\" style=\"position: relative;\"><div class=\"CodeMirror-activeline-background CodeMirror-linebackground\"><\/div><div class=\"CodeMirror-gutter-background CodeMirror-activeline-gutter\" style=\"left: 0px; width: 0px;\"><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-comment\"># \u53cd\u5411\u4f20\u64ad<\/span><\/span><\/pre><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">loss<\/span>.<span class=\"cm-property\">backward<\/span>() &nbsp;<span class=\"cm-comment\"># \u81ea\u52a8\u8ba1\u7b97\u68af\u5ea6<\/span><\/span><\/pre><\/div><\/div><\/div><\/div><\/div><div style=\"position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 58px;\"><\/div><div class=\"CodeMirror-gutters\" style=\"display: none; height: 58px;\"><\/div><\/div><\/div><\/pre><p><span>\u5728\u8fd9\u4e00\u6b65\uff0cPyTorch \u81ea\u52a8\u8ba1\u7b97 <\/span><code>linear.weight<\/code><span> \u548c <\/span><code>linear.bias<\/code><span> \u7684\u68af\u5ea6\u3002\u4ee5\u4e0b\u662f\u5177\u4f53\u8ba1\u7b97\u8fc7\u7a0b\u3002<\/span><\/p><h4><a name=\"\u68af\u5ea6\u8ba1\u7b97\" class=\"md-header-anchor\"><\/a><span>\u68af\u5ea6\u8ba1\u7b97<\/span><\/h4><ul><li><p><strong><span>\u5bf9\u4e8e\u6743\u91cd\u7684\u68af\u5ea6<\/span><\/strong><span>\uff1a<\/span>\n<span>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\uff0c\u53ef\u4ee5\u5c06\u635f\u5931\u5bf9\u6743\u91cd\u7684\u68af\u5ea6\u8868\u793a\u4e3a\uff1a<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n662\" cid=\"n662\" mdtype=\"math_block\"><div class=\"md-rawblock-container md-math-container\" tabindex=\"-1\"><div class=\"MathJax_SVG_Display\" style=\"text-align: center;\"><span class=\"MathJax_SVG\" id=\"MathJax-Element-109-Frame\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"24.011ex\" height=\"5.897ex\" viewBox=\"0 -1490.8 10337.9 2539\" role=\"img\" focusable=\"false\" style=\"vertical-align: -2.435ex; max-width: 100%;\"><defs><path 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y=\"0\"><\/use><use xlink:href=\"#E235-MJMATHI-62\" x=\"567\" y=\"0\"><\/use><\/g><\/g><\/g><use xlink:href=\"#E235-MJMAIN-3D\" x=\"10615\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-5B\" x=\"11671\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-2212\" x=\"11949\" y=\"0\"><\/use><g transform=\"translate(12727,0)\"><use xlink:href=\"#E235-MJMAIN-30\"><\/use><use xlink:href=\"#E235-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-34\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-35\" x=\"1278\" y=\"0\"><\/use><\/g><use xlink:href=\"#E235-MJMAIN-2B\" x=\"14727\" y=\"0\"><\/use><g transform=\"translate(15727,0)\"><use xlink:href=\"#E235-MJMAIN-30\"><\/use><use xlink:href=\"#E235-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-32\" x=\"778\" y=\"0\"><\/use><\/g><use xlink:href=\"#E235-MJMAIN-5D\" x=\"17005\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-3D\" x=\"17561\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-5B\" x=\"18617\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-2212\" x=\"18895\" y=\"0\"><\/use><g transform=\"translate(19673,0)\"><use xlink:href=\"#E235-MJMAIN-30\"><\/use><use xlink:href=\"#E235-MJMAIN-2E\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-32\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-35\" x=\"1278\" y=\"0\"><\/use><\/g><use xlink:href=\"#E235-MJMAIN-5D\" x=\"21451\" y=\"0\"><\/use><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-120\">\\frac{\\partial \\text{loss}}{\\partial b} = \\frac{\\partial \\text{loss}}{\\partial y_{\\text{pred}}} \\cdot \\frac{\\partial y_{\\text{pred}}}{\\partial b} = [-0.45 + 0.2] = [-0.25]<\/script><\/div><\/div><\/li><\/ul><h3><a name=\"5-\u67e5\u770b\u68af\u5ea6\" class=\"md-header-anchor\"><\/a><span>5. \u67e5\u770b\u68af\u5ea6<\/span><\/h3><p><span>\u6700\u540e\uff0c\u8f93\u51fa\u8ba1\u7b97\u7684\u635f\u5931\u548c\u68af\u5ea6\uff1a<\/span><\/p><pre spellcheck=\"false\" class=\"md-fences md-end-block ty-contain-cm modeLoaded\" lang=\"python\"><div class=\"CodeMirror cm-s-inner CodeMirror-wrap\" lang=\"python\"><div style=\"overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;\"><textarea autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" tabindex=\"0\" style=\"position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;\"><\/textarea><\/div><div class=\"CodeMirror-scrollbar-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-gutter-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-scroll\" tabindex=\"-1\"><div class=\"CodeMirror-sizer\" style=\"margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;\"><div style=\"position: relative; top: 0px;\"><div class=\"CodeMirror-lines\" role=\"presentation\"><div role=\"presentation\" style=\"position: relative; outline: none;\"><div class=\"CodeMirror-measure\"><pre><span>xxxxxxxxxx<\/span><\/pre><\/div><div class=\"CodeMirror-measure\"><\/div><div style=\"position: relative; z-index: 1;\"><\/div><div class=\"CodeMirror-code\" role=\"presentation\"><div class=\"CodeMirror-activeline\" style=\"position: relative;\"><div class=\"CodeMirror-activeline-background CodeMirror-linebackground\"><\/div><div class=\"CodeMirror-gutter-background CodeMirror-activeline-gutter\" style=\"left: 0px; width: 0px;\"><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-builtin\">print<\/span>(<span class=\"cm-string\">f\"Loss: {loss.item()}\"<\/span>)<\/span><\/pre><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-builtin\">print<\/span>(<span class=\"cm-string\">f\"Gradients: {linear.weight.grad}, {linear.bias.grad}\"<\/span>)<\/span><\/pre><\/div><\/div><\/div><\/div><\/div><div style=\"position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 58px;\"><\/div><div class=\"CodeMirror-gutters\" style=\"display: none; height: 58px;\"><\/div><\/div><\/div><\/pre><ul><li><code>linear.weight.grad<\/code><span> \u5c06\u8f93\u51fa <\/span><code>[-0.0125, 0.4375]<\/code><span>\uff0c\u8868\u793a\u6743\u91cd\u5728\u8fd9\u4e00\u8f6e\u7684\u68af\u5ea6\u3002<\/span><\/li><li><code>linear.bias.grad<\/code><span> \u5c06\u8f93\u51fa <\/span><code>[-0.25]<\/code><span>\uff0c\u8868\u793a\u504f\u7f6e\u7684\u68af\u5ea6\u3002<\/span><\/li><\/ul><h3><a name=\"6-\u66f4\u65b0\u53c2\u6570\" class=\"md-header-anchor\"><\/a><span>6. \u66f4\u65b0\u53c2\u6570<\/span><\/h3><p><span>\u5728\u5b9e\u9645\u8bad\u7ec3\u4e2d\uff0c\u4f7f\u7528\u4f18\u5316\u5668\uff08\u5982 SGD \u6216 Adam\uff09\u4f1a\u6839\u636e\u8ba1\u7b97\u5f97\u5230\u7684\u68af\u5ea6\u66f4\u65b0\u53c2\u6570\uff1a<\/span><\/p><pre spellcheck=\"false\" class=\"md-fences md-end-block ty-contain-cm modeLoaded\" lang=\"python\"><div class=\"CodeMirror cm-s-inner CodeMirror-wrap\" lang=\"python\"><div style=\"overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;\"><textarea autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" tabindex=\"0\" style=\"position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;\"><\/textarea><\/div><div class=\"CodeMirror-scrollbar-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-gutter-filler\" cm-not-content=\"true\"><\/div><div class=\"CodeMirror-scroll\" tabindex=\"-1\"><div class=\"CodeMirror-sizer\" style=\"margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;\"><div style=\"position: relative; top: 0px;\"><div class=\"CodeMirror-lines\" role=\"presentation\"><div role=\"presentation\" style=\"position: relative; outline: none;\"><div class=\"CodeMirror-measure\"><pre><span>xxxxxxxxxx<\/span><\/pre><\/div><div class=\"CodeMirror-measure\"><\/div><div style=\"position: relative; z-index: 1;\"><\/div><div class=\"CodeMirror-code\" role=\"presentation\"><div class=\"CodeMirror-activeline\" style=\"position: relative;\"><div class=\"CodeMirror-activeline-background CodeMirror-linebackground\"><\/div><div class=\"CodeMirror-gutter-background CodeMirror-activeline-gutter\" style=\"left: 0px; width: 0px;\"><\/div><pre class=\" CodeMirror-line \" role=\"presentation\"><span role=\"presentation\" style=\"padding-right: 0.1px;\"><span class=\"cm-variable\">optimizer<\/span>.<span class=\"cm-property\">step<\/span>() &nbsp;<span class=\"cm-comment\"># \u6839\u636e\u68af\u5ea6\u66f4\u65b0\u6743\u91cd\u548c\u504f\u7f6e<\/span><\/span><\/pre><\/div><\/div><\/div><\/div><\/div><\/div><div style=\"position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 29px;\"><\/div><div class=\"CodeMirror-gutters\" style=\"display: none; height: 29px;\"><\/div><\/div><\/div><\/pre><p><span>\u53c2\u6570\u66f4\u65b0\u89c4\u5219\u901a\u5e38\u662f\uff1a<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n707\" cid=\"n707\" mdtype=\"math_block\"><div class=\"md-rawblock-container md-math-container\" tabindex=\"-1\"><div class=\"MathJax_SVG_Display\" style=\"text-align: center;\"><span class=\"MathJax_SVG\" id=\"MathJax-Element-121-Frame\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"39.316ex\" height=\"5.149ex\" viewBox=\"0 -1450.6 16927.8 2217.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.78ex; max-width: 100%;\"><defs><path stroke-width=\"0\" id=\"E236-MJMATHI-57\" d=\"M436 683Q450 683 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