{"id":2149,"date":"2024-06-11T17:46:32","date_gmt":"2024-06-11T09:46:32","guid":{"rendered":"https:\/\/17aitech.com\/?p=2149"},"modified":"2024-10-08T15:20:44","modified_gmt":"2024-10-08T07:20:44","slug":"%e3%80%90%e8%af%be%e7%a8%8b%e6%80%bb%e7%bb%93%e3%80%91day7%ef%bc%9a%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%e6%a6%82%e8%bf%b0","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=2149","title":{"rendered":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 ez-toc-wrap-left-text counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u6587\u7ae0\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E5%89%8D%E8%A8%80\" >\u524d\u8a00<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92\" >\u7ebf\u6027\u56de\u5f52<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92%E5%86%85%E5%AE%B9%E5%9B%9E%E9%A1%BE\" >\u7ebf\u6027\u56de\u5f52\u5185\u5bb9\u56de\u987e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92%E6%96%B9%E7%A8%8B%E7%9A%84%E8%A7%A3%E6%9E%90\" >\u7ebf\u6027\u56de\u5f52\u65b9\u7a0b\u7684\u89e3\u6790<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92%E6%B1%82%E6%8D%9F%E5%A4%B1loss%E5%87%BD%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC\" >\u7ebf\u6027\u56de\u5f52=\u6c42\u635f\u5931loss\u51fd\u6570\u7684\u6700\u5c0f\u503c<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E8%AE%AD%E7%BB%83%E8%BF%87%E7%A8%8B\" >\u8bad\u7ec3\u8fc7\u7a0b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E8%AE%AD%E7%BB%83%E7%9A%84%E6%9C%AC%E8%B4%A8\" >\u8bad\u7ec3\u7684\u672c\u8d28<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E5%A6%82%E4%BD%95%E6%B1%82%E5%87%BD%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%EF%BC%9F\" >\u5982\u4f55\u6c42\u51fd\u6570\u7684\u6700\u5c0f\u503c\uff1f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E4%B8%80%E4%B8%AA%E4%BE%8B%E5%AD%90\" >\u4e00\u4e2a\u4f8b\u5b50<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E6%B1%82%E8%A7%A3%E6%96%B9%E6%B3%95%E7%90%86%E8%AE%BA%E6%96%B9%E6%B3%95\" >\u6c42\u89e3\u65b9\u6cd5(\u7406\u8bba\u65b9\u6cd5)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E6%B1%82%E8%A7%A3%E7%9A%84%E9%97%AE%E9%A2%98\" >\u6c42\u89e3\u7684\u95ee\u9898<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E6%B1%82%E8%A7%A3%E6%96%B9%E6%B3%95%E8%BF%AD%E4%BB%A3%E6%B3%95\" >\u6c42\u89e3\u65b9\u6cd5(\u8fed\u4ee3\u6cd5)<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E6%A6%82%E5%BF%B5%E8%A1%A5%E5%85%85\" >\u6982\u5ff5\u8865\u5145<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E6%89%8B%E5%8A%A8%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E5%80%BC\" >\u4ee3\u7801\u5b9e\u73b0(\u624b\u52a8\u6c42\u51fd\u6570\u6700\u5c0f\u503c)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E4%BD%BF%E7%94%A8pytorch%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E5%80%BC\" >\u4ee3\u7801\u5b9e\u73b0(\u4f7f\u7528pytorch\u6c42\u51fd\u6570\u6700\u5c0f\u503c)<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/17aitech.com\/?p=2149\/#%E5%86%85%E5%AE%B9%E5%B0%8F%E7%BB%93\" >\u5185\u5bb9\u5c0f\u7ed3<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E5%89%8D%E8%A8%80\"><\/span>\u524d\u8a00<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u7bc7\u6587\u7ae0\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u793a\u4f8b\u6765\u9010\u6b65\u5b66\u4e60\u7406\u89e3\u5bfc\u6570\u3001\u6c42\u51fd\u6570\u6700\u5c0f\u503c\u3001\u6df1\u5ea6\u5b66\u4e60\u7684\u672c\u8d28\u3001\u4ee5\u53ca\u4f7f\u7528numpy\u548cpytorch\u5b9e\u64cd\u6df1\u5ea6\u5b66\u4e60\u8bad\u7ec3\u8fc7\u7a0b\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92\"><\/span>\u7ebf\u6027\u56de\u5f52<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92%E5%86%85%E5%AE%B9%E5%9B%9E%E9%A1%BE\"><\/span>\u7ebf\u6027\u56de\u5f52\u5185\u5bb9\u56de\u987e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728<a href=\"https:\/\/17aitech.com\/?p=2040#toc-2\">\u300a\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day5(\u4e0b)\uff1aPCA\u964d\u7ef4\u3001SVD\u5206\u89e3\u3001\u805a\u7c7b\u7b97\u6cd5\u548c\u96c6\u6210\u5b66\u4e60\u300b<\/a>\u4e2d\uff0c\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u5230\u7ebf\u6027\u56de\u5f52\u4ee5\u53ca\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n<p><code class=\"katex-inline\">y=f(x)=x_1w_1 + x_2w_2 + ... + x_{13}w_{13} + b<\/code><\/p>\n<blockquote>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>( x<em><em>1, x<\/em><\/em>2, &#8230;, x<em>_{13} )\uff1a\u8f93\u5165\u7279\u5f81\u5411\u91cf ( x ) \u7684\u5404\u4e2a\u7279\u5f81\u503c\uff0c\u4ee3\u8868\u8f93\u5165\u6570\u636e\u7684\u5404\u4e2a\u7279\u5f81\u3002<\/em><\/li>\n<li><em>( w_<\/em>1, w<em><em>2, &#8230;, w<\/em><\/em>{13} )\uff1a\u6743\u91cd\u5411\u91cf ( w ) \u7684\u5404\u4e2a\u6743\u91cd\u503c\uff0c\u7528\u6765\u8861\u91cf\u6bcf\u4e2a\u7279\u5f81\u5bf9\u8f93\u51fa\u7684\u5f71\u54cd\u7a0b\u5ea6\u3002<\/li>\n<li>( b )\uff1a\u504f\u7f6e\u9879\uff0c\u4e5f\u79f0\u4e3a\u622a\u8ddd\u9879\uff0c\u7528\u6765\u8c03\u6574\u6a21\u578b\u7684\u8f93\u51fa\u503c\uff0c\u5373\u5728\u6ca1\u6709\u7279\u5f81\u8f93\u5165\u65f6\u7684\u8f93\u51fa\u503c\u3002<\/li>\n<li>( y )\uff1a\u6a21\u578b\u7684\u8f93\u51fa\u503c\uff0c\u5373\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5bf9\u8f93\u5165\u7279\u5f81\u7684\u9884\u6d4b\u503c\u3002<\/li>\n<\/ul>\n<\/blockquote>\n<p>\u8be5\u516c\u5f0f\u4e5f\u53ef\u4ee5\u8868\u793a\u4e3a\u5185\u79ef\u76f8\u4e58\u7684\u65b9\u5f0f\uff0c\u5982\u4e0b\uff1a<\/p>\n<p><code class=\"katex-inline\">y=f(x)=x@w+b<\/code><\/p>\n<blockquote>\n<p>\u5176\u4e2d\uff1a<\/p>\n<p>x@w\uff1a\u7279\u5f81\u5411\u91cf ( x ) \u4e0e \u6743\u91cd\u5411\u91cf( w ) \u7684\u5185\u79ef<\/p>\n<\/blockquote>\n<p>\u5982\u679c\u6709\u591a\u4e2a\u6837\u672c\u7684\u8bdd\uff0c\u90a3\u4e48\u4e0a\u9762\u7684\u516c\u793a\u53ef\u4ee5\u8fdb\u4e00\u6b65\u8868\u793a\u4e3a\uff1a<\/p>\n<p><code class=\"katex-inline\">y=f(X)=X@w+b<\/code><\/p>\n<blockquote>\n<p>\u5176\u4e2d\uff1a<\/p>\n<p>X\u4ee3\u8868\u7279\u5f81\u77e9\u9635\uff0c\u77e9\u9635\u7684\u884c\u4e3a\u4e00\u6761\u4e00\u6761\u7684\u6837\u672c\uff0c\u77e9\u9635\u7684\u5217\u4e3a\u591a\u4e2a\u7279\u5f81\u5411\u91cf\u3002<\/p>\n<\/blockquote>\n<h3><span class=\"ez-toc-section\" id=\"%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92%E6%96%B9%E7%A8%8B%E7%9A%84%E8%A7%A3%E6%9E%90\"><\/span>\u7ebf\u6027\u56de\u5f52\u65b9\u7a0b\u7684\u89e3\u6790<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611153732879.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611153732879.png\" alt=\"\" \/><\/a><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611154512030.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611154512030.png\" alt=\"\" \/><\/a><\/p>\n<ul>\n<li>\u5728\u8bad\u7ec3\u65f6\uff0c<code>x<\/code>\u548c<code>y<\/code>\u662f\u8bad\u7ec3\u96c6\u4e2d\u7684\u7279\u5f81\u548c\u6807\u7b7e\uff0c\u770b\u4f5c\u662f<strong>\u5e38\u91cf<\/strong>\uff1b<code>w<\/code>\u548cb\u662f\u5f85\u4f18\u5316\u7684\u53c2\u6570\u503c\uff0c\u770b\u4f5c\u662f<strong>\u53d8\u91cf<\/strong>\u3002<\/li>\n<li>\u5728\u63a8\u7406\u65f6\uff0c<code>w<\/code>\u548c<code>b<\/code>\u5df2\u7ecf\u627e\u5230\u4e86\u6bd4\u8f83\u5408\u9002\u7684\u503c\u56fa\u5b9a\u4e0b\u6765\uff0c\u770b\u4f5c<strong>\u5e38\u91cf<\/strong>\uff1b\u6b64\u65f6<code>x<\/code>\u662f\u5f85\u9884\u6d4b\u7684\u6837\u672c\u7684\u7279\u5f81\uff0c\u662f<strong>\u53d8\u91cf<\/strong>\uff1b<\/li>\n<li>\u9884\u6d4b\u7684\u672c\u8d28\uff1a\u628ax\u5e26\u5165\uff0c\u6c42\u89e3y\u3002<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92%E6%B1%82%E6%8D%9F%E5%A4%B1loss%E5%87%BD%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC\"><\/span>\u7ebf\u6027\u56de\u5f52=\u6c42\u635f\u5931loss\u51fd\u6570\u7684\u6700\u5c0f\u503c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E8%AE%AD%E7%BB%83%E8%BF%87%E7%A8%8B\"><\/span>\u8bad\u7ec3\u8fc7\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u7531\u4e0a\u56fe\u53ef\u77e5\uff0c\u8bad\u7ec3\u7684\u5927\u81f4\u8fc7\u7a0b\u662f\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611155946301.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611155946301.png\" alt=\"\" \/><\/a><\/p>\n<ol>\n<li>\u4ece\u8bad\u7ec3\u96c6\u4e2d\u53d6\u51fa\u4e00\u5bf9x \u548cy<\/li>\n<li>\u628ax\u5e26\u5165\u6a21\u578b\uff0c\u6c42\u89e3\u9884\u6d4b\u7ed3\u679cy_pred<\/li>\n<li>\u627e\u5230\u4e00\u79cd\u65b9\u6cd5\uff0c\u5ea6\u91cfy\u548cy_pred\u7684\u8bef\u5deeloss<\/li>\n<li>\u7531\u6b64\u63a8\u5bfc\uff1a\n<ul>\n<li>loss\u662fy\u548cy_pred\u7684\u51fd\u6570\uff1b<\/li>\n<li>y_pred\u662f\u6a21\u578b\u9884\u6d4b\u7684\u7ed3\u679c\uff0c\u662fw\u548cb\u7684\u51fd\u6570\uff1b<\/li>\n<li>\u6240\u4ee5\u7b80\u5355\u6765\u8bf4\uff0closs\u4e5f\u662fw\u548cb\u7684\u51fd\u6570<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h4><span class=\"ez-toc-section\" id=\"%E8%AE%AD%E7%BB%83%E7%9A%84%E6%9C%AC%E8%B4%A8\"><\/span>\u8bad\u7ec3\u7684\u672c\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u7531\u4e0a\u56fe\u63a8\u5bfc\u7ed3\u679c\u53ef\u77e5\uff0c\u8bad\u7ec3\u7684\u672c\u8d28\uff1a\u6c42\u89e3loss\u4ec0\u4e48\u65f6\u5019\u662f\u6700\u5c0f\u503c\u3002<\/p>\n<blockquote>\n<p>\u6570\u5b66\u8868\u8fbe\uff1a\u5f53w\u548cb\u53d6\u5f97\u4ec0\u4e48\u503c\u7684\u65f6\u5019\uff0closs\u6700\u5c0f<\/p>\n<p>\u901a\u4fd7\u8868\u8fbe\uff1a\u6c42loss\u51fd\u6570\u7684\u6700\u5c0f\u503c<\/p>\n<\/blockquote>\n<h2><span class=\"ez-toc-section\" id=\"%E5%A6%82%E4%BD%95%E6%B1%82%E5%87%BD%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%EF%BC%9F\"><\/span>\u5982\u4f55\u6c42\u51fd\u6570\u7684\u6700\u5c0f\u503c\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"%E4%B8%80%E4%B8%AA%E4%BE%8B%E5%AD%90\"><\/span>\u4e00\u4e2a\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u200b   <code class=\"katex-inline\">y = 2x^2<\/code><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611102202488.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611102202488.png\" alt=\"\" \/><\/a><\/p>\n<p>\u4e0a\u8ff0\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6c42y\u6700\u5c0f\u503c\u662f\u6bd4\u8f83\u7b80\u5355\u7684\uff0c\u4ece\u56fe\u5f62\u4e2d\u53ef\u4ee5\u770b\u5230x=0\u65f6\uff0cy=0\u4e3a\u6700\u5c0f\u503c\u3002\u4f46\u662f\u5b9e\u9645\u5de5\u7a0b\u4e2d\uff0c\u5e76\u4e0d\u662f\u6240\u6709\u7684\u51fd\u6570y=f(x)\u90fd\u80fd\u753b\u51fa\u6765\uff0c\u7b80\u5355\u5730\u627e\u5230\u6700\u5c0f\u503c\uff0c\u6b64\u65f6\u5c31\u9700\u8981\u4f7f\u7528\u5bfc\u6570\u6c42\u6700\u5c0f\u503c\u3002<\/p>\n<blockquote>\n<p>\u5982\u679c\u4f60\u548c\u6211\u4e00\u6837\u5fd8\u4e86\u5bfc\u6570\u76f8\u5173\u7684\u77e5\u8bc6\uff0c\u53ef\u4ee5\u67e5\u770b<a href=\"https:\/\/17aitech.com\/?p=2138\">\u300a\u3010\u91cd\u62fe\u6570\u5b66\u77e5\u8bc6\u3011\u5bfc\u6570\u3001\u6781\u503c\u548c\u6700\u503c\u300b<\/a>\u56de\u987e\u4e00\u4e0b\u3002<\/p>\n<\/blockquote>\n<h3><span class=\"ez-toc-section\" id=\"%E6%B1%82%E8%A7%A3%E6%96%B9%E6%B3%95%E7%90%86%E8%AE%BA%E6%96%B9%E6%B3%95\"><\/span>\u6c42\u89e3\u65b9\u6cd5(\u7406\u8bba\u65b9\u6cd5)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u901a\u8fc7\u56de\u5f52\u5bfc\u6570\u6c42\u6781\u503c\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u77e5\u9053\u5927\u81f4\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u7b2c\u4e00\u6b65\uff1a\u6c42\u51fd\u6570\u7684\u5bfc\u6570<\/li>\n<li>\u7b2c\u4e8c\u6b65\uff1a\u4ee4\u5bfc\u6570\u7b49\u4e8e\u96f6<\/li>\n<li>\u7b2c\u4e09\u6b65\uff1a\u89e3\u65b9\u7a0b\uff0c\u6c42\u51fa\u7591\u4f3c\u6781\u503c\u70b9<\/li>\n<li>\u7b2c\u56db\u6b65\uff1a\u9a8c\u8bc1\u8be5\u70b9\u662f\u5426\u662f\u6781\u503c\u70b9\u4ee5\u53ca\u662f\u4ec0\u4e48\u6781\u503c\u70b9<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"%E6%B1%82%E8%A7%A3%E7%9A%84%E9%97%AE%E9%A2%98\"><\/span>\u6c42\u89e3\u7684\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e0a\u8ff0\u7684\u65b9\u6cd5\u662f\u6709\u4e00\u5b9a\u524d\u63d0\u6761\u4ef6\u7684\uff0c\u5373\uff1a<\/p>\n<ul>\n<li>\u7b2c\u4e00\u6b65\u7684\u6c42(\u504f)\u5bfc\u6570\u662f\u53ef\u4ee5\u6c42\u5f97\u7684\uff1b<\/li>\n<li>\u7b2c\u4e09\u6b65(\u504f)\u5bfc\u6570\u4e3a\u96f6\u540e\uff0c\u65b9\u7a0b(\u7ec4)\u662f\u53ef\u4ee5\u89e3\u7684\u3002<\/li>\n<\/ul>\n<p>\u5b9e\u9645\u5de5\u7a0b\u4e2d\uff0c\u4e0a\u8ff0\u65b9\u6cd5\u662f\u4e0d\u53ef\u884c\u7684\u3002\u4ee5<a href=\"https:\/\/modelscope.cn\/models\/LLM-Research\/Meta-Llama-3-8B-Instruct\/summary\">Llama3-8B\u6a21\u578b<\/a>\u4e3a\u4f8b\uff0c\u5176\u670980\u4ebf\u4e2a\u8f93\u5165\u53c2\u6570x\uff0c\u6309\u7167\u4e0a\u8ff0\u7684\u6c42\u89e3\u65b9\u6cd5\u662f\u65e0\u6cd5\u6c42\u5f97\u6700\u5c0f\u503c\u7684\uff01<\/p>\n<p>\u7531\u6b64\u53ef\u77e5\uff0c\u901a\u8fc7\u63a8\u5bfc\u516c\u5f0f\u671f\u671b\u4e00\u6b21\u6027\u6c42\u5f97\u6700\u5c0f\u503c\u662f\u4e0d\u73b0\u5b9e\u7684\uff1b\u800c\u6211\u4eec\u53ef\u4ee5\u501f\u9274\u4eba\u5de5\u667a\u80fd\u4e2d\u4e00\u4e2a\u91cd\u8981\u7684\u601d\u60f3\uff1a\u8fed\u4ee3\u6cd5\u6765\u9010\u6b65\u6c42\u89e3\u6700\u5c0f\u503c\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E6%B1%82%E8%A7%A3%E6%96%B9%E6%B3%95%E8%BF%AD%E4%BB%A3%E6%B3%95\"><\/span>\u6c42\u89e3\u65b9\u6cd5(\u8fed\u4ee3\u6cd5)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4ecd\u7136\u4ee5<code class=\"katex-inline\">y = 2x^2<\/code>\u4e3a\u4f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u6cd5\u6c42\u5f97\u6700\u5c0f\u503c\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/gradient_descent_animation_1000-1.gif\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/gradient_descent_animation_1000-1.gif\" alt=\"\" \/><\/a><\/p>\n<p>\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u51fa\u751f\u70b9<code class=\"katex-inline\">x_0<\/code>\uff0c<\/p>\n<ul>\n<li>\u5f53<code class=\"katex-inline\">x_0<\/code>\u5728\u6700\u5c0f\u503c\u7684\u5de6\u4fa7\u65f6\uff0c<code class=\"katex-inline\">x_0<\/code> + \u6b63\u6570(\u4e00\u4e2a\u975e\u5e38\u5c0f\u7684\u6b63\u6570)\u5411\u53f3\u4fa7\u79fb\u52a8\uff1b<\/li>\n<li>\u5f53<code class=\"katex-inline\">x_0<\/code>\u5728\u6700\u5c0f\u503c\u7684\u53f3\u4fa7\u65f6\uff0c<code class=\"katex-inline\">x_0<\/code> &#8211; \u6b63\u6570(\u4e00\u4e2a\u975e\u5e38\u5c0f\u7684\u6b63\u6570)\u5411\u5de6\u4fa7\u79fb\u52a8\uff1b<\/li>\n<li>\u5f53<code class=\"katex-inline\">x_0<\/code>\u5728\u6700\u5c0f\u503c\u7684\u65f6\u5019\uff0c\u4e0d\u7528\u79fb\u52a8\uff0c\u6b64\u65f6\u5c31\u662f\u6700\u5c0f\u503c\u3002<\/li>\n<\/ul>\n<p>\u7531\u5bfc\u6570\u7684\u5355\u8c03\u6027\u53ef\u77e5\uff1a<\/p>\n<ul>\n<li>\u5f53<code class=\"katex-inline\">x_0<\/code>\u5728\u5de6\u4fa7\u65f6\uff0c\u7531\u4e8e\u51fd\u6570\u662f\u5355\u8c03\u9012\u51cf\u7684\uff0c\u6240\u4ee5\u5bfc\u6570&lt;0<\/li>\n<li>\u5f53<code class=\"katex-inline\">x_0<\/code>\u5728\u53f3\u4fa7\u65f6\uff0c\u7531\u4e8e\u51fd\u6570\u662f\u5355\u8c03\u9012\u589e\u7684\uff0c\u6240\u4ee5\u5bfc\u6570&gt;0<\/li>\n<\/ul>\n<p>\u56e0\u6b64\u4e0a\u8ff0\u7684\u8ba1\u7b97\u65b9\u6cd5\u53ef\u4ee5\u63a8\u5bfc\u5f97\u5230\uff1a<\/p>\n<ul>\n<li>\n<p>\u5f53<code class=\"katex-inline\">x_0<\/code>\u57280\u7684\u5de6\u4fa7\u65f6\uff0c<code class=\"katex-inline\">x_0<\/code> + \u6b63\u6570 \u2192 <code class=\"katex-inline\">x_0<\/code> + \u5bfc\u6570 \u2192  <code class=\"katex-inline\">x_0<\/code> &#8211; \u5bfc\u6570   <\/p>\n<blockquote>\n<p>\u56e0\u4e3a\u5bfc\u6570&lt;0\uff0c\u52a0\u4e0a\u4e00\u4e2a\u5c0f\u4e8e\u7684\u5bfc\u6570\u76f8\u5f53\u4e8e\u51cf\u53bb\u5bfc\u6570<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<p>\u5f53<code class=\"katex-inline\">x_0<\/code>\u57280\u7684\u53f3\u4fa7\u65f6\uff0c<code class=\"katex-inline\">x_0<\/code> &#8211; \u6b63\u6570 \u2192 <code class=\"katex-inline\">x_0<\/code> &#8211; \u5bfc\u6570 <\/p>\n<blockquote>\n<p>\u56e0\u4e3a\u5bfc\u6570&gt;0\uff0c\u51cf\u53bb\u4e00\u4e2a\u5927\u4e8e\u7684\u5bfc\u6570\u76f8\u5f53\u4e8e\u51cf\u53bb\u5bfc\u6570<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<p>\u5f53<code class=\"katex-inline\">x_0<\/code>=0\u65f6\uff0c\u4e5f\u53ef\u4ee5\u770b\u4f5c\u662f<code class=\"katex-inline\">x_0<\/code> &#8211; \u5bfc\u6570 <\/p>\n<\/li>\n<\/ul>\n<p>\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7ed3\u8bba\uff1a<font color=\"red\">\u4e0d\u7ba1<code class=\"katex-inline\">x_0<\/code>\u5728\u4f55\u5904\uff0c\u6c42\u6700\u5c0f\u503c\u65f6\u51cf\u53bb\u5bfc\u6570\u5373\u5411\u6781\u503c\u903c\u8fd1\u3002<\/font><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%A6%82%E5%BF%B5%E8%A1%A5%E5%85%85\"><\/span>\u6982\u5ff5\u8865\u5145<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u5728\u4e00\u5143\u51fd\u6570\u4e2d\uff0c\u6c42\u51fd\u6570f(x)\u5728\u67d0\u4e00\u70b9\u7684\u659c\u7387\u4e3a\u5bfc\u6570\uff1b\u5728\u591a\u5143\u51fd\u6570\u4e2d\uff0c\u79f0\u4e3a\u504f\u5bfc\u6570\uff0c\u4e5f\u5c31\u662f\u68af\u5ea6\u3002<\/li>\n<li>\n<p>\u51cf\u53bb\u5bfc\u6570\u4e5f\u5c31\u662f\u51cf\u53bb\u68af\u5ea6\uff0c\u8fd9\u5c31\u662f\u68af\u5ea6\u4e0b\u964d\u6cd5\uff01<\/p>\n<blockquote>\n<p>\u5907\u6ce8\uff1a\u6df1\u5ea6\u5b66\u4e60\u5728\u5174\u8d77\u4e4b\u524d\uff0c\u4eba\u5de5\u667a\u80fd\u53ea\u80fd\u9760\u652f\u6301\u5411\u91cf\u673a\u6491\u95e8\u9762\uff1b\u4f34\u968f\u7740\u4e92\u8054\u7f51+GPU\u82af\u7247\u7684\u5174\u8d77\uff0c\u68af\u5ea6\u4e0b\u964d\u6cd5\u62e5\u6709\u4e86\u4f7f\u7528\u7684\u571f\u58e4\uff0c\u4ee5\u6b64\u4eba\u5de5\u667a\u80fd\u624d\u771f\u6b63\u5174\u8d77\u3002<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E6%89%8B%E5%8A%A8%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E5%80%BC\"><\/span>\u4ee3\u7801\u5b9e\u73b0(\u624b\u52a8\u6c42\u51fd\u6570\u6700\u5c0f\u503c)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u4ee5<code class=\"katex-inline\">y = 2x^2<\/code>\u4e3a\u4f8b<\/p>\n<pre><code class=\"language-python\">import numpy as np\n\ndef fn(x):\n    &quot;&quot;&quot;\n    \u539f\u59cb\u51fd\u6570\n    &quot;&quot;&quot;\n    return 2 * x ** 2\n\ndef dfn(x):\n    &quot;&quot;&quot;\n    \u5bfc\u51fd\u6570\n    &quot;&quot;&quot;\n    return 4 * x\n\ndef gradient_descent(x0, learning_rate, dfn, epochs):\n    &quot;&quot;&quot;\n    \u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u6c42\u51fd\u6570\u7684\u6700\u5c0f\u503c\n\n    Parameters:\n        x0 (float): \u521d\u59cb\u70b9\u7684\u4f4d\u7f6e\n        learning_rate (float): \u5b66\u4e60\u7387\n        dfn (function): \u5bfc\u51fd\u6570\n        epochs (int): \u8fed\u4ee3\u6b21\u6570\n\n    Returns:\n        x_min (float): \u6700\u5c0f\u503c\u70b9\u7684\u4f4d\u7f6e\n    &quot;&quot;&quot;\n    for _ in range(epochs):\n        x0 = x0 - learning_rate * dfn(x0)\n\n    return x0\n\n# \u968f\u673a\u9009\u62e9\u4e00\u4e2a\u51fa\u751f\u70b9\nx0 = np.random.randint(low=-1000, high=1000, size=1)\n\n# \u8fed\u4ee3\u6b21\u6570\nepochs = 1000\n\n# \u5b66\u4e60\u7387\nlearning_rate = 1e-2\n\n# \u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u6c42\u6700\u5c0f\u503c\nx_min = gradient_descent(x0, learning_rate, dfn, epochs)\n\n# \u8f93\u51fa\u6700\u5c0f\u503c\nprint(&quot;\u6700\u5c0f\u503c\u70b9\u7684\u4f4d\u7f6e\uff1a&quot;, x_min)<\/code><\/pre>\n<p>\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170037157.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170037157.png\" alt=\"\" \/><\/a><\/p>\n<p>\u4ee5<code class=\"katex-inline\">f(x,y,z) = x^2 + y^2 + z^2<\/code>\u4e3a\u4f8b<\/p>\n<pre><code class=\"language-py\">import numpy as np\n\ndef df_x(x, y, z):\n    &quot;&quot;&quot;\n    f \u5bf9 x \u6c42\u504f\u5bfc\n    &quot;&quot;&quot;\n    return 2 * x\n\ndef df_y(x, y, z):\n    &quot;&quot;&quot;\n    f \u5bf9 y \u6c42\u504f\u5bfc\n    &quot;&quot;&quot;\n    return 2 * y\n\ndef df_z(x, y, z):\n    &quot;&quot;&quot;\n    f \u5bf9 z \u6c42\u504f\u5bfc\n    &quot;&quot;&quot;\n    return 2 * z\n\n# \u968f\u673a\u9009\u62e9\u51fa\u751f\u70b9\nx0 = np.random.randint(low=-1000, high=1000, size=(1,))\ny0 = np.random.randint(low=-1000, high=1000, size=(1,))\nz0 = np.random.randint(low=-1000, high=1000, size=(1,))\n\n# \u8fed\u4ee3\u6b21\u6570\nepochs = 1000\n\n# \u5b66\u4e60\u7387\nlearning_rate = 1e-2\n\nfor _ in range(epochs):\n    # \u6c42\u89e3\u6bcf\u4e2a\u53d8\u91cf\u7684\u504f\u5bfc\n    fx = df_x(x0, y0, z0)\n    fy = df_y(x0, y0, z0)\n    fz = df_z(x0, y0, z0)\n\n    # \u6bcf\u4e2a\u53d8\u91cf\u90fd\u51cf\u53bb\u81ea\u5df1\u7684\u504f\u5bfc\n    x0 = x0 - learning_rate * fx\n    y0 = y0 - learning_rate * fy\n    z0 = z0 - learning_rate * fz\n\n# \u8f93\u51fa\u66f4\u65b0\u540e\u7684\u53d8\u91cf\u503c\nprint(&quot;\u66f4\u65b0\u540e\u7684 x \u503c\uff1a&quot;, x0)\nprint(&quot;\u66f4\u65b0\u540e\u7684 y \u503c\uff1a&quot;, y0)\nprint(&quot;\u66f4\u65b0\u540e\u7684 z \u503c\uff1a&quot;, z0)<\/code><\/pre>\n<p>\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170054557.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170054557.png\" alt=\"\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E4%BD%BF%E7%94%A8pytorch%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E5%80%BC\"><\/span>\u4ee3\u7801\u5b9e\u73b0(\u4f7f\u7528pytorch\u6c42\u51fd\u6570\u6700\u5c0f\u503c)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u4e0a\u8ff0\u901a\u8fc7\u6c42\u5bfc\u6570\u5f97\u5230\u51fd\u6570\u6700\u5c0f\u503c\u7684\u65b9\u6cd5\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7pytorch\u6765\u5b9e\u73b0\uff0c\u5177\u4f53\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<p>\u4ee5<code class=\"katex-inline\">y = 2x^2<\/code>\u4e3a\u4f8b<\/p>\n<pre><code class=\"language-py\">import torch\n\n# \u5b9a\u4e49\u539f\u59cb\u51fd\u6570\u548c\u5bfc\u51fd\u6570\ndef fn(x):\n    return 2 * x ** 2\n\n# \u8bf4\u660e\uff1apytorch\u53ef\u4ee5\u901a\u8fc7grad\u51fd\u6570\u6c42\u5bfc\uff0c\u6240\u4ee5\u53ef\u4ee5\u7701\u53bb\u5199\u5bfc\u51fd\u6570\n# def dfn(x):\n#     return 4 * x\n\n# \u968f\u673a\u9009\u62e9\u51fa\u751f\u70b9\n# requires_grad=True\u7528\u6765\u544a\u8bc9\u6846\u67b6\u8be5\u53d8\u91cf\u662f\u4e00\u4e2a\u5f20\u91cf\uff0c\u9700\u8981\u8ba1\u7b97\u68af\u5ea6\u3002\nx0 = torch.randint(low=-1000, high=1001, size=(1,), \n                   dtype=torch.float32, \n                   requires_grad=True)\n\n# \u8fed\u4ee3\u6b21\u6570\nepochs = 1000\n\n# \u5b66\u4e60\u7387\nlearning_rate = 1e-2\n\n# \u4f7f\u7528 PyTorch \u8fdb\u884c\u68af\u5ea6\u4e0b\u964d\nfor _ in range(epochs):\n    # \u6b63\u5411\u4f20\u64ad\u8ba1\u7b97\u635f\u5931\n    loss = fn(x0)\n\n    # \u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\u68af\u5ea6\n    loss.backward()\n\n    # \u83b7\u53d6\u68af\u5ea6\u5e76\u66f4\u65b0\u53c2\u6570\n    with torch.no_grad():\n        grad = x0.grad\n        x0 -= learning_rate * grad\n\n    # \u68af\u5ea6\u6e05\u96f6\n    x0.grad.zero_()\n\n# \u8f93\u51fa\u6700\u5c0f\u503c\u70b9\u7684\u4f4d\u7f6e\nprint(&quot;\u6700\u5c0f\u503c\u70b9\u7684\u4f4d\u7f6e\uff1a&quot;, x0.item())<\/code><\/pre>\n<p>\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170246071.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170246071.png\" alt=\"\" \/><\/a><\/p>\n<p>\u4ee5<code class=\"katex-inline\">f(x,y,z) = x^2 + y^2 + z^2<\/code>\u4e3a\u4f8b<\/p>\n<pre><code class=\"language-py\">import torch\n\ndef fn(x, y, z):\n    &quot;&quot;&quot;\n        \u51fd\u6570\u5b9a\u4e49\n    &quot;&quot;&quot;\n    return x**2 + y**2 + z**2\n\n# \u8bf4\u660e\uff1apytorch\u53ef\u4ee5\u901a\u8fc7grad\u51fd\u6570\u6c42\u5bfc\uff0c\u6240\u4ee5\u53ef\u4ee5\u7701\u53bb\u5199\u5bfc\u51fd\u6570\n# def df_x(x, y, z):\n#     return 2 * x\n\n# def df_y(x, y, z):\n#     return 2 * y\n\n# def df_z(x, y, z):\n#     return 2 * z\n\n# \u968f\u673a\u9009\u62e9\u51fa\u751f\u70b9\nx0 = torch.randint(low=-1000, high=1001, size=(1,), \n                   dtype=torch.float32, \n                   requires_grad=True)\ny0 = torch.randint(low=-1000, high=1001, size=(1,), \n                   dtype=torch.float32, \n                   requires_grad=True)\nz0 = torch.randint(low=-1000, high=1001, size=(1,), \n                   dtype=torch.float32, \n                   requires_grad=True)\n\n# \u8fed\u4ee3\u6b21\u6570\nepochs = 1000\n\n# \u5b66\u4e60\u7387\nlearning_rate = 1e-2\n\n# \u4f7f\u7528 PyTorch \u8fdb\u884c\u68af\u5ea6\u4e0b\u964d\nfor _ in range(epochs):\n    # \u6b63\u5411\u4f20\u64ad\u8ba1\u7b97\u635f\u5931\n    loss = fn(x0, y0, z0)\n\n    # \u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\u68af\u5ea6\n    loss.backward()\n\n    # \u83b7\u53d6\u68af\u5ea6\u5e76\u66f4\u65b0\u53c2\u6570\n    # \u5728\u6d4b\u8bd5\u9636\u6bb5\u6216\u8005\u4e0d\u9700\u8981\u8ba1\u7b97\u68af\u5ea6\u7684\u60c5\u51b5\u4e0b\u4f7f\u7528 torch.no_grad()\n    # \u4ee5\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u5e76\u907f\u514d\u4e0d\u5fc5\u8981\u7684\u68af\u5ea6\u8ba1\u7b97\u3002\n    with torch.no_grad():\n        x0 -= learning_rate * x0.grad\n        y0 -= learning_rate * y0.grad\n        z0 -= learning_rate * z0.grad\n\n    # \u68af\u5ea6\u6e05\u96f6\n    x0.grad.zero_()\n    y0.grad.zero_()\n    z0.grad.zero_()\n\n# \u8f93\u51fa\u66f4\u65b0\u540e\u7684\u53d8\u91cf\u503c\nprint(&quot;\u66f4\u65b0\u540e\u7684 x \u503c\uff1a&quot;, x0.item())\nprint(&quot;\u66f4\u65b0\u540e\u7684 y \u503c\uff1a&quot;, y0.item())\nprint(&quot;\u66f4\u65b0\u540e\u7684 z \u503c\uff1a&quot;, z0.item())<\/code><\/pre>\n<p>\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170402142.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611170402142.png\" alt=\"\" \/><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%86%85%E5%AE%B9%E5%B0%8F%E7%BB%93\"><\/span>\u5185\u5bb9\u5c0f\u7ed3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\n<p>\u7ebf\u6027\u56de\u5f52<\/p>\n<ul>\n<li>\u5728\u8bad\u7ec3\u65f6\uff0c<code>x<\/code>\u548c<code>y<\/code>\u662f\u8bad\u7ec3\u96c6\u4e2d\u7684\u7279\u5f81\u548c\u6807\u7b7e\uff0c\u770b\u4f5c\u662f<strong>\u5e38\u91cf<\/strong>\uff1b<code>w<\/code>\u548cb\u662f\u5f85\u4f18\u5316\u7684\u53c2\u6570\u503c\uff0c\u770b\u4f5c\u662f<strong>\u53d8\u91cf<\/strong>\u3002<\/li>\n<li>\u5728\u63a8\u7406\u65f6\uff0c<code>w<\/code>\u548c<code>b<\/code>\u5df2\u7ecf\u627e\u5230\u4e86\u6bd4\u8f83\u5408\u9002\u7684\u503c\u56fa\u5b9a\u4e0b\u6765\uff0c\u770b\u4f5c<strong>\u5e38\u91cf<\/strong>\uff1b\u6b64\u65f6<code>x<\/code>\u662f\u5f85\u9884\u6d4b\u7684\u6837\u672c\u7684\u7279\u5f81\uff0c\u662f<strong>\u53d8\u91cf<\/strong>\uff1b<\/li>\n<li>\u9884\u6d4b\u7684\u672c\u8d28\uff1a\u628ax\u5e26\u5165\uff0c\u6c42\u89e3y\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6c42\u635f\u5931loss\u51fd\u6570<\/p>\n<ul>\n<li>\u7531\u8bad\u7ec3\u7684\u8fc7\u7a0b\u53ef\u77e5\uff1a\u635f\u5931\u51fd\u6570loss\u4e5f\u662fw\u548cb\u7684\u51fd\u6570<\/li>\n<li>\u8bad\u7ec3\u7684\u672c\u8d28\uff1a\u6c42\u635f\u5931loss\u51fd\u6570\u7684\u6700\u5c0f\u503c<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6c42\u51fd\u6570\u6700\u5c0f\u503c<\/p>\n<ul>\n<li>\u7406\u8bba\u7684\u6c42\u89e3\u65b9\u6cd5\uff0c\u5728\u73b0\u5b9e\u5de5\u7a0b\u4e2d\u7531\u4e8e\u53c2\u6570\u5de8\u5927\uff0c\u5b9e\u9645\u4e0d\u53ef\u884c\u3002<\/li>\n<li>\u5b9e\u9645\u7684\u6c42\u89e3\u65b9\u5f0f\u662f\u4f7f\u7528\u8fed\u4ee3\u601d\u60f3\u9010\u6b65\u6c42\u89e3\u3002<\/li>\n<li>\u4e0d\u7ba1$x_0$\u5728\u4f55\u5904\uff0c\u6c42\u6700\u5c0f\u503c\u65f6\u51cf\u53bb\u5bfc\u6570\u5373\u5411\u6781\u503c\u903c\u8fd1\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8fed\u4ee3\u6cd5+\u8fed\u4ee3\u4e2d\u51cf\u53bb\u5bfc\u6570\u6c42\u6700\u5c0f\u503c\uff0c\u8fd9\u5c31\u662f\u68af\u5ea6\u4e0b\u964d\u6cd5\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6c42\u5bfc\u5373\u53ef\u4f7f\u7528numpy\u65b9\u6cd5\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528pytorch<\/p>\n<ul>\n<li>\u68af\u5ea6\u4e0b\u964d\u6cd5\u4f7f\u7528\u8fc7\u7a0b\u4e2d\uff0c\u4e00\u822c\u9700\u8981\u5b9a\u4e49epochs\u8fed\u4ee3\u6b21\u6570\u3001learning_rate\u5b66\u4e60\u7387<\/li>\n<li>\u68af\u5ea6\u4e0b\u964d\u6cd5\u7684\u4e00\u822c\u8fc7\u7a0b\u4e3a\uff1a\u6b63\u5411\u4f20\u64ad\u8ba1\u7b97\u635f\u5931\u2192\u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\u68af\u5ea6\u2192\u83b7\u53d6\u68af\u5ea6\u5e76\u66f4\u65b0\u53c2\u6570\u2192\u68af\u5ea6\u6e05\u96f6<\/li>\n<li>\u5728\u5faa\u73af\u51cf\u53bb\u68af\u5ea6\u7684\u8fc7\u7a0b\u4e2d\uff0c\u9700\u8981\u8bb0\u5f97\u4f7f\u7528.grad.zero_()\u8fdb\u884c\u68af\u5ea6\u6e05\u96f6<\/li>\n<\/ul>\n<p align=\"center\">\u6b22\u8fce\u5173\u6ce8\u516c\u4f17\u53f7\u4ee5\u83b7\u5f97\u6700\u65b0\u7684\u6587\u7ae0\u548c\u65b0\u95fb<\/p>\n<\/li>\n<\/ul>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/09\/\u626b\u7801_\u641c\u7d22\u8054\u5408\u4f20\u64ad\u6837\u5f0f-\u767d\u8272\u7248.bmp\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/09\/\u626b\u7801_\u641c\u7d22\u8054\u5408\u4f20\u64ad\u6837\u5f0f-\u767d\u8272\u7248.bmp\" alt=\"\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u8a00 \u672c\u7bc7\u6587\u7ae0\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u793a\u4f8b\u6765\u9010\u6b65\u5b66\u4e60 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2161,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"aside","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[28],"tags":[65],"class_list":["post-2149","post","type-post","status-publish","format-aside","has-post-thumbnail","hentry","category-blog","tag-65","post_format-post-format-aside"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0 - \u4e00\u8d77AI\u6280\u672f<\/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:\/\/17aitech.com\/?p=2149\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149\"},\"author\":{\"name\":\"Dongming\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/#\\\/schema\\\/person\\\/3d23bb6f7f115fcefc9ae7803a691739\"},\"headline\":\"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0\",\"datePublished\":\"2024-06-11T09:46:32+00:00\",\"dateModified\":\"2024-10-08T07:20:44+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149\"},\"wordCount\":90,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/2024\\\/06\\\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png\",\"keywords\":[\"\u6df1\u5ea6\u5b66\u4e60\"],\"articleSection\":[\"\u535a\u5ba2\u6587\u7ae0\"],\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/17aitech.com\\\/?p=2149#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149\",\"url\":\"https:\\\/\\\/17aitech.com\\\/?p=2149\",\"name\":\"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0 - \u4e00\u8d77AI\u6280\u672f\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/2024\\\/06\\\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png\",\"datePublished\":\"2024-06-11T09:46:32+00:00\",\"dateModified\":\"2024-10-08T07:20:44+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/#\\\/schema\\\/person\\\/3d23bb6f7f115fcefc9ae7803a691739\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/17aitech.com\\\/?p=2149\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#primaryimage\",\"url\":\"https:\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/2024\\\/06\\\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png\",\"contentUrl\":\"https:\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/2024\\\/06\\\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png\",\"width\":1292,\"height\":902},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/?p=2149#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\\\/\\\/17aitech.com\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/#website\",\"url\":\"https:\\\/\\\/17aitech.com\\\/\",\"name\":\"\u4e00\u8d77AI\u6280\u672f\",\"description\":\"\u8ba9AI\u77e5\u8bc6\u89e6\u624b\u53ef\u53ca\",\"alternateName\":\"\u4e00\u8d77AI\u6280\u672f\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/17aitech.com\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/17aitech.com\\\/#\\\/schema\\\/person\\\/3d23bb6f7f115fcefc9ae7803a691739\",\"name\":\"Dongming\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/member\\\/avatars\\\/238a0b923820dcc5.1732798681.jpg\",\"url\":\"\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/member\\\/avatars\\\/238a0b923820dcc5.1732798681.jpg\",\"contentUrl\":\"\\\/\\\/17aitech.com\\\/wp-content\\\/uploads\\\/member\\\/avatars\\\/238a0b923820dcc5.1732798681.jpg\",\"caption\":\"Dongming\"},\"description\":\"\u89c1\u5929\u5730\uff0c\u89c1\u4f17\u751f\uff0c\u89c1\u81ea\u5df1\u3002\",\"sameAs\":[\"http:\\\/\\\/17aitech.com\"],\"url\":\"https:\\\/\\\/17aitech.com\\\/?page_id=33738&user=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0 - \u4e00\u8d77AI\u6280\u672f","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:\/\/17aitech.com\/?p=2149","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/17aitech.com\/?p=2149#article","isPartOf":{"@id":"https:\/\/17aitech.com\/?p=2149"},"author":{"name":"Dongming","@id":"https:\/\/17aitech.com\/#\/schema\/person\/3d23bb6f7f115fcefc9ae7803a691739"},"headline":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0","datePublished":"2024-06-11T09:46:32+00:00","dateModified":"2024-10-08T07:20:44+00:00","mainEntityOfPage":{"@id":"https:\/\/17aitech.com\/?p=2149"},"wordCount":90,"commentCount":0,"image":{"@id":"https:\/\/17aitech.com\/?p=2149#primaryimage"},"thumbnailUrl":"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png","keywords":["\u6df1\u5ea6\u5b66\u4e60"],"articleSection":["\u535a\u5ba2\u6587\u7ae0"],"inLanguage":"zh-Hans","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/17aitech.com\/?p=2149#respond"]}]},{"@type":"WebPage","@id":"https:\/\/17aitech.com\/?p=2149","url":"https:\/\/17aitech.com\/?p=2149","name":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0 - \u4e00\u8d77AI\u6280\u672f","isPartOf":{"@id":"https:\/\/17aitech.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/17aitech.com\/?p=2149#primaryimage"},"image":{"@id":"https:\/\/17aitech.com\/?p=2149#primaryimage"},"thumbnailUrl":"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png","datePublished":"2024-06-11T09:46:32+00:00","dateModified":"2024-10-08T07:20:44+00:00","author":{"@id":"https:\/\/17aitech.com\/#\/schema\/person\/3d23bb6f7f115fcefc9ae7803a691739"},"breadcrumb":{"@id":"https:\/\/17aitech.com\/?p=2149#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/17aitech.com\/?p=2149"]}]},{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/17aitech.com\/?p=2149#primaryimage","url":"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png","contentUrl":"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/\u6df1\u5ea6\u5b66\u4e60\u5c01\u9762.png","width":1292,"height":902},{"@type":"BreadcrumbList","@id":"https:\/\/17aitech.com\/?p=2149#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/17aitech.com\/"},{"@type":"ListItem","position":2,"name":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day7\uff1a\u6df1\u5ea6\u5b66\u4e60\u6982\u8ff0"}]},{"@type":"WebSite","@id":"https:\/\/17aitech.com\/#website","url":"https:\/\/17aitech.com\/","name":"\u4e00\u8d77AI\u6280\u672f","description":"\u8ba9AI\u77e5\u8bc6\u89e6\u624b\u53ef\u53ca","alternateName":"\u4e00\u8d77AI\u6280\u672f","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/17aitech.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/17aitech.com\/#\/schema\/person\/3d23bb6f7f115fcefc9ae7803a691739","name":"Dongming","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"\/\/17aitech.com\/wp-content\/uploads\/member\/avatars\/238a0b923820dcc5.1732798681.jpg","url":"\/\/17aitech.com\/wp-content\/uploads\/member\/avatars\/238a0b923820dcc5.1732798681.jpg","contentUrl":"\/\/17aitech.com\/wp-content\/uploads\/member\/avatars\/238a0b923820dcc5.1732798681.jpg","caption":"Dongming"},"description":"\u89c1\u5929\u5730\uff0c\u89c1\u4f17\u751f\uff0c\u89c1\u81ea\u5df1\u3002","sameAs":["http:\/\/17aitech.com"],"url":"https:\/\/17aitech.com\/?page_id=33738&user=1"}]}},"_links":{"self":[{"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/posts\/2149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/17aitech.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2149"}],"version-history":[{"count":12,"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/posts\/2149\/revisions"}],"predecessor-version":[{"id":33248,"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/posts\/2149\/revisions\/33248"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/17aitech.com\/index.php?rest_route=\/wp\/v2\/media\/2161"}],"wp:attachment":[{"href":"https:\/\/17aitech.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/17aitech.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/17aitech.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}