{"id":96550,"date":"2026-08-27T20:58:16","date_gmt":"2026-08-27T12:58:16","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/96550.html"},"modified":"2026-08-27T20:58:16","modified_gmt":"2026-08-27T12:58:16","slug":"%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%9f%ba%e7%a1%80","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/96550.html","title":{"rendered":"\u795e\u7ecf\u7f51\u7edc\u57fa\u7840"},"content":{"rendered":"<h2>\u795e\u7ecf\u7f51\u7edc\u57fa\u7840<\/h2>\n<h3>\u4e00\u3001\u795e\u7ecf\u7f51\u7edc\u6982\u8ff0<\/h3>\n<h4>1.1 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ANN&#xff09;&#xff0c;\u4e5f\u7b80\u79f0\u4e3a\u795e\u7ecf\u7f51\u7edc&#xff08;NN&#xff09;&#xff0c;\u662f\u4e00\u79cd\u6a21\u4eff\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u548c\u529f\u80fd\u7684\u8ba1\u7b97\u6a21\u578b\u3002\u5b83\u7531\u591a\u4e2a\u4e92\u76f8\u8fde\u63a5\u7684\u4eba\u5de5\u795e\u7ecf\u5143&#xff08;\u4e5f\u79f0\u4e3a\u8282\u70b9&#xff09;\u6784\u6210&#xff0c;\u53ef\u4ee5\u7528\u4e8e\u5904\u7406\u548c\u5b66\u4e60\u590d\u6742\u7684\u6570\u636e\u6a21\u5f0f&#xff0c;\u5c24\u5176\u9002\u5408\u89e3\u51b3\u975e\u7ebf\u6027\u95ee\u9898\u3002\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u662f\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u91cd\u8981\u6a21\u578b&#xff0c;\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u5f97\u5230\u4e86\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n<p>\u4eba\u8111\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u4e2a\u751f\u7269\u795e\u7ecf\u7f51\u7edc&#xff0c;\u7531\u4f17\u591a\u7684\u795e\u7ecf\u5143\u8fde\u63a5\u800c\u6210\u3002\u5404\u4e2a\u795e\u7ecf\u5143\u4f20\u9012\u590d\u6742\u7684\u7535\u4fe1\u53f7&#xff1a;\u6811\u7a81\u63a5\u6536\u5230\u8f93\u5165\u4fe1\u53f7&#xff0c;\u7136\u540e\u5bf9\u4fe1\u53f7\u8fdb\u884c\u5904\u7406&#xff0c;\u901a\u8fc7\u8f74\u7a81\u8f93\u51fa\u4fe1\u53f7\u3002\u4e0b\u56fe\u662f\u751f\u7269\u795e\u7ecf\u5143\u793a\u610f\u56fe&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125807-6a90345f9c7cf.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5f53\u7535\u4fe1\u53f7\u901a\u8fc7\u6811\u7a81\u8fdb\u5165\u7ec6\u80de\u6838\u65f6&#xff0c;\u4f1a\u9010\u6e10\u805a\u96c6\u7535\u8377\u3002\u8fbe\u5230\u4e00\u5b9a\u7684\u7535\u4f4d\u540e&#xff0c;\u7ec6\u80de\u5c31\u4f1a\u88ab\u6fc0\u6d3b&#xff0c;\u901a\u8fc7\u8f74\u7a81\u53d1\u51fa\u7535\u4fe1\u53f7\u3002<\/p>\n<h4>1.2 \u5982\u4f55\u6784\u5efa\u795e\u7ecf\u7f51\u7edc<\/h4>\n<p>\u795e\u7ecf\u7f51\u7edc\u7531\u591a\u4e2a\u795e\u7ecf\u5143\u7ec4\u6210&#xff0c;\u6784\u5efa\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u5728\u6784\u5efa\u795e\u7ecf\u5143\u3002\u4ee5\u4e0b\u662f\u795e\u7ecf\u7f51\u7edc\u4e2d\u795e\u7ecf\u5143\u7684\u6784\u5efa\u8bf4\u660e&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125808-6a90346012236.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8fd9\u4e2a\u6d41\u7a0b\u5c31\u50cf\u6765\u81ea\u4e0d\u540c\u6811\u7a81\u7684\u4fe1\u606f&#xff08;\u6811\u7a81\u90fd\u6709\u4e0d\u540c\u7684\u6743\u91cd&#xff09;\u8fdb\u884c\u52a0\u6743\u8ba1\u7b97&#xff0c;\u8f93\u5165\u5230\u7ec6\u80de\u4e2d\u505a\u52a0\u548c&#xff0c;\u518d\u901a\u8fc7\u6fc0\u6d3b\u51fd\u6570\u8f93\u51fa\u7ec6\u80de\u503c\u3002<\/p>\n<p>\u540c\u4e00\u5c42\u7684\u591a\u4e2a\u795e\u7ecf\u5143\u53ef\u4ee5\u770b\u4f5c\u662f\u901a\u8fc7\u5e76\u884c\u8ba1\u7b97\u6765\u5904\u7406\u76f8\u540c\u7684\u8f93\u5165\u6570\u636e&#xff0c;\u5b66\u4e60\u8f93\u5165\u6570\u636e\u7684\u4e0d\u540c\u7279\u5f81\u3002\u6bcf\u4e2a\u795e\u7ecf\u5143\u53ef\u80fd\u4f1a\u5173\u6ce8\u8f93\u5165\u6570\u636e\u4e2d\u7684\u4e0d\u540c\u90e8\u5206&#xff0c;\u4ece\u800c\u6355\u6349\u5230\u6570\u636e\u7684\u4e0d\u540c\u5c5e\u6027\u3002<\/p>\n<p>\u63a5\u4e0b\u6765&#xff0c;\u6211\u4eec\u4f7f\u7528\u591a\u4e2a\u795e\u7ecf\u5143\u6765\u6784\u5efa\u795e\u7ecf\u7f51\u7edc&#xff0c;\u76f8\u90bb\u5c42\u4e4b\u95f4\u7684\u795e\u7ecf\u5143\u76f8\u4e92\u8fde\u63a5&#xff0c;\u5e76\u7ed9\u6bcf\u4e00\u4e2a\u8fde\u63a5\u5206\u914d\u4e00\u4e2a\u5f3a\u5ea6&#xff0c;\u5982\u4e0b\u56fe\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125808-6a90346031463.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u795e\u7ecf\u7f51\u7edc\u4e2d\u4fe1\u606f\u53ea\u5411\u4e00\u4e2a\u65b9\u5411\u79fb\u52a8&#xff0c;\u5373\u4ece\u8f93\u5165\u8282\u70b9\u5411\u524d\u79fb\u52a8&#xff0c;\u901a\u8fc7\u9690\u85cf\u8282\u70b9&#xff0c;\u518d\u5411\u8f93\u51fa\u8282\u70b9\u79fb\u52a8\u3002\u5176\u4e2d\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\u662f&#xff1a;<\/p>\n<li>\u8f93\u5165\u5c42&#xff08;Input Layer&#xff09;&#xff1a;\u5373\u8f93\u5165 x \u7684\u90a3\u4e00\u5c42&#xff08;\u5982\u56fe\u50cf\u3001\u6587\u672c\u3001\u58f0\u97f3\u7b49&#xff09;\u3002\u6bcf\u4e2a\u8f93\u5165\u7279\u5f81\u5bf9\u5e94\u4e00\u4e2a\u795e\u7ecf\u5143&#xff0c;\u8f93\u5165\u5c42\u5c06\u6570\u636e\u4f20\u9012\u7ed9\u4e0b\u4e00\u5c42\u7684\u795e\u7ecf\u5143\u3002<\/li>\n<li>\u8f93\u51fa\u5c42&#xff08;Output Layer&#xff09;&#xff1a;\u5373\u8f93\u51fa y \u7684\u90a3\u4e00\u5c42\u3002\u8f93\u51fa\u5c42\u7684\u795e\u7ecf\u5143\u6839\u636e\u7f51\u7edc\u7684\u4efb\u52a1&#xff08;\u56de\u5f52\u3001\u5206\u7c7b\u7b49&#xff09;\u751f\u6210\u6700\u7ec8\u7684\u9884\u6d4b\u7ed3\u679c\u3002<\/li>\n<li>\u9690\u85cf\u5c42&#xff08;Hidden Layers&#xff09;&#xff1a;\u8f93\u5165\u5c42\u548c\u8f93\u51fa\u5c42\u4e4b\u95f4\u7684\u90fd\u662f\u9690\u85cf\u5c42&#xff0c;\u795e\u7ecf\u7f51\u7edc\u7684&#034;\u6df1\u5ea6&#034;\u901a\u5e38\u7531\u9690\u85cf\u5c42\u7684\u6570\u91cf\u51b3\u5b9a\u3002\u9690\u85cf\u5c42\u7684\u795e\u7ecf\u5143\u901a\u8fc7\u52a0\u6743\u548c\u4e0e\u6fc0\u6d3b\u51fd\u6570\u5904\u7406\u8f93\u5165&#xff0c;\u5e76\u5c06\u7ed3\u679c\u4f20\u9012\u5230\u4e0b\u4e00\u5c42\u3002<\/li>\n<p>\u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc\u7684\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u540c\u4e00\u5c42\u7684\u795e\u7ecf\u5143\u4e4b\u95f4\u6ca1\u6709\u8fde\u63a5<\/li>\n<li>\u7b2c N \u5c42\u7684\u6bcf\u4e2a\u795e\u7ecf\u5143\u4e0e\u7b2c N-1 \u5c42\u7684\u6240\u6709\u795e\u7ecf\u5143\u76f8\u8fde&#xff08;\u8fd9\u5c31\u662f Fully Connected \u7684\u542b\u4e49&#xff09;&#xff0c;\u5373\u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc&#xff08;FCNN&#xff09;<\/li>\n<li>\u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc\u63a5\u6536\u7684\u6837\u672c\u6570\u636e\u662f\u4e8c\u7ef4\u7684&#xff0c;\u6570\u636e\u5728\u6bcf\u4e00\u5c42\u4e4b\u95f4\u9700\u8981\u4ee5\u4e8c\u7ef4\u7684\u5f62\u5f0f\u4f20\u9012<\/li>\n<li>\u7b2c N-1 \u5c42\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u5c31\u662f\u7b2c N \u5c42\u795e\u7ecf\u5143\u7684\u8f93\u5165<\/li>\n<li>\u6bcf\u4e2a\u8fde\u63a5\u90fd\u6709\u4e00\u4e2a\u6743\u91cd\u503c&#xff08;w \u7cfb\u6570\u548c b \u7cfb\u6570&#xff09;<\/li>\n<\/ul>\n<h4>1.3 \u795e\u7ecf\u7f51\u7edc\u5185\u90e8\u72b6\u6001\u503c\u548c\u6fc0\u6d3b\u503c<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125808-6a90346076092.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u5de5\u4f5c\u65f6&#xff0c;\u524d\u5411\u4f20\u64ad\u4f1a\u4ea7\u751f\u4e24\u4e2a\u503c\u2014\u2014\u5185\u90e8\u72b6\u6001\u503c&#xff08;\u52a0\u6743\u6c42\u548c\u503c&#xff09;\u548c\u6fc0\u6d3b\u503c&#xff1b;\u53cd\u5411\u4f20\u64ad\u65f6\u4f1a\u4ea7\u751f\u6fc0\u6d3b\u503c\u68af\u5ea6\u548c\u5185\u90e8\u72b6\u6001\u503c\u68af\u5ea6\u3002<\/p>\n<p>\u5185\u90e8\u72b6\u6001\u503c<\/p>\n<ul>\n<li>\u795e\u7ecf\u5143\u6216\u9690\u85cf\u5355\u5143\u7684\u5185\u90e8\u5b58\u50a8\u503c&#xff0c;\u53cd\u6620\u4e86\u5f53\u524d\u795e\u7ecf\u5143\u63a5\u6536\u5230\u7684\u8f93\u5165\u3001\u5386\u53f2\u4fe1\u606f\u4ee5\u53ca\u7f51\u7edc\u5185\u90e8\u7684\u6743\u91cd\u8ba1\u7b97\u7ed3\u679c\u3002<\/li>\n<li>\u6bcf\u4e2a\u8f93\u5165 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">xix_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u90fd\u6709\u4e00\u4e2a\u4e0e\u4e4b\u76f8\u4e58\u7684\u6743\u91cd <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">wiw_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8868\u793a\u6bcf\u4e2a\u8f93\u5165\u4fe1\u53f7\u7684\u91cd\u8981\u6027\u3002<\/li>\n<li><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">z&#061;w\u22c5x&#043;bz &#061; w \\\\cdot x &#043; b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4445em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><\/span>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u6743\u91cd\u77e9\u9635<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u8f93\u5165\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bb<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u504f\u7f6e<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u6fc0\u6d3b\u503c<\/p>\n<ul>\n<li>\u901a\u8fc7\u6fc0\u6d3b\u51fd\u6570&#xff08;\u5982 ReLU\u3001Sigmoid\u3001Tanh&#xff09;\u5bf9\u5185\u90e8\u72b6\u6001\u503c\u8fdb\u884c\u975e\u7ebf\u6027\u53d8\u6362\u540e\u5f97\u5230\u7684\u7ed3\u679c&#xff0c;\u51b3\u5b9a\u4e86\u5f53\u524d\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u3002<\/li>\n<li><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">a&#061;f(z)a &#061; f(z)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ff<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u6fc0\u6d3b\u51fd\u6570<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">zz<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u5185\u90e8\u72b6\u6001\u503c<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u901a\u8fc7\u63a7\u5236\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u5185\u90e8\u72b6\u6001\u503c\u3001\u6fc0\u6d3b\u503c\u7684\u5927\u5c0f&#xff0c;\u4ee5\u53ca\u6bcf\u4e00\u5c42\u7684\u5185\u90e8\u72b6\u6001\u503c\u7684\u65b9\u5dee\u3001\u6bcf\u4e00\u5c42\u7684\u6fc0\u6d3b\u503c\u7684\u65b9\u5dee&#xff0c;\u53ef\u4ee5\u8ba9\u6574\u4e2a\u795e\u7ecf\u7f51\u7edc\u66f4\u597d\u5730\u5de5\u4f5c\u3002<\/p>\n<p>\u63a5\u4e0b\u6765&#xff0c;\u6211\u4eec\u5c06\u5b66\u4e60\u795e\u7ecf\u5143\u7684\u6fc0\u6d3b\u51fd\u6570\u548c\u6743\u91cd\u521d\u59cb\u5316\u3002<\/p>\n<hr \/>\n<h3>\u4e8c\u3001\u6fc0\u6d3b\u51fd\u6570<\/h3>\n<h4>2.1 \u7f51\u7edc\u975e\u7ebf\u6027\u56e0\u7d20\u7406\u89e3<\/h4>\n<ul>\n<li>\u6ca1\u6709\u5f15\u5165\u975e\u7ebf\u6027\u56e0\u7d20\u7684\u7f51\u7edc\u7b49\u4ef7\u4e8e\u4f7f\u7528\u4e00\u4e2a\u7ebf\u6027\u6a21\u578b\u6765\u62df\u5408<\/li>\n<li>\u901a\u8fc7\u7ed9\u7f51\u7edc\u8f93\u51fa\u589e\u52a0\u6fc0\u6d3b\u51fd\u6570&#xff0c;\u5b9e\u73b0\u5f15\u5165\u975e\u7ebf\u6027\u56e0\u7d20&#xff0c;\u4f7f\u5f97\u7f51\u7edc\u6a21\u578b\u53ef\u4ee5\u903c\u8fd1\u4efb\u610f\u51fd\u6570&#xff0c;\u63d0\u5347\u7f51\u7edc\u5bf9\u590d\u6742\u95ee\u9898\u7684\u62df\u5408\u80fd\u529b<\/li>\n<\/ul>\n<p>\u6fc0\u6d3b\u51fd\u6570\u7528\u4e8e\u5bf9\u6bcf\u5c42\u7684\u8f93\u51fa\u6570\u636e\u8fdb\u884c\u53d8\u6362&#xff0c;\u8fdb\u800c\u4e3a\u6574\u4e2a\u7f51\u7edc\u6ce8\u5165\u975e\u7ebf\u6027\u56e0\u7d20\u3002\u6b64\u65f6&#xff0c;\u795e\u7ecf\u7f51\u7edc\u5c31\u53ef\u4ee5\u62df\u5408\u5404\u79cd\u66f2\u7ebf\u3002\u5982\u679c\u4e0d\u4f7f\u7528\u6fc0\u6d3b\u51fd\u6570&#xff0c;\u6574\u4e2a\u7f51\u7edc\u867d\u7136\u770b\u8d77\u6765\u590d\u6742&#xff0c;\u5176\u672c\u8d28\u8fd8\u76f8\u5f53\u4e8e\u4e00\u79cd\u7ebf\u6027\u6a21\u578b&#xff0c;\u5982\u4e0b\u516c\u5f0f\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125809-6a903461ec1c2.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125810-6a9034624d1ff.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u53e6\u5916\u901a\u8fc7\u56fe\u50cf\u53ef\u89c6\u5316\u7684\u5f62\u5f0f\u7406\u89e3&#xff1a;<\/p>\n<p>[\u795e\u7ecf\u7f51\u7edc\u53ef\u89c6\u5316\u5de5\u5177]<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125811-6a9034637af41.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u53ef\u4ee5\u53d1\u73b0&#xff0c;\u589e\u52a0\u6fc0\u6d3b\u51fd\u6570\u4e4b\u540e&#xff0c;\u5bf9\u4e8e\u7ebf\u6027\u4e0d\u53ef\u5206\u7684\u573a\u666f&#xff0c;\u795e\u7ecf\u7f51\u7edc\u7684\u62df\u5408\u80fd\u529b\u66f4\u5f3a\u3002<\/p>\n<h4>2.2 \u5e38\u89c1\u6fc0\u6d3b\u51fd\u6570<\/h4>\n<p>\u6fc0\u6d3b\u51fd\u6570\u4e3b\u8981\u7528\u6765\u5411\u795e\u7ecf\u7f51\u7edc\u4e2d\u52a0\u5165\u975e\u7ebf\u6027\u56e0\u7d20&#xff0c;\u4ee5\u89e3\u51b3\u7ebf\u6027\u6a21\u578b\u8868\u8fbe\u80fd\u529b\u4e0d\u8db3\u7684\u95ee\u9898&#xff0c;\u5b83\u5bf9\u795e\u7ecf\u7f51\u7edc\u6709\u7740\u6781\u5176\u91cd\u8981\u7684\u4f5c\u7528\u3002\u7f51\u7edc\u53c2\u6570\u5728\u66f4\u65b0\u65f6\u4f7f\u7528\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5&#xff08;BP&#xff09;&#xff0c;\u8fd9\u5c31\u8981\u6c42\u6fc0\u6d3b\u51fd\u6570\u5fc5\u987b\u53ef\u5fae\u3002<\/p>\n<h5>2.2.1 Sigmoid \u6fc0\u6d3b\u51fd\u6570<\/h5>\n<p>\u6fc0\u6d3b\u51fd\u6570\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a9034650c085.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u6fc0\u6d3b\u51fd\u6570\u6c42\u5bfc\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a9034653a2c2.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>Sigmoid \u51fd\u6570\u56fe\u50cf\u548c\u5bfc\u6570\u56fe\u50cf&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a903465553f7.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>Sigmoid \u7684\u7279\u70b9\u4e0e\u95ee\u9898&#xff1a;<\/p>\n<ul>\n<li>\u4ece\u51fd\u6570\u56fe\u50cf\u53ef\u4ee5\u770b\u51fa&#xff0c;Sigmoid \u51fd\u6570\u53ef\u4ee5\u5c06\u4efb\u610f\u7684\u8f93\u5165\u6620\u5c04\u5230 (0, 1) \u4e4b\u95f4\u3002\u5f53\u8f93\u5165\u7684\u503c\u5927\u81f4 &lt; -6 \u6216\u8005 &gt; 6 \u65f6&#xff0c;\u610f\u5473\u7740\u8f93\u5165\u4efb\u4f55\u503c\u5f97\u5230\u7684\u6fc0\u6d3b\u503c\u90fd\u5dee\u4e0d\u591a&#xff0c;\u8fd9\u6837\u4f1a\u4e22\u5931\u90e8\u5206\u4fe1\u606f\u3002\u4f8b\u5982&#xff1a;\u8f93\u5165 100 \u548c\u8f93\u5165 10000 \u7ecf\u8fc7 Sigmoid \u7684\u6fc0\u6d3b\u503c\u51e0\u4e4e\u90fd\u7b49\u4e8e 1&#xff0c;\u4f46\u8f93\u5165\u6570\u636e\u4e4b\u95f4\u76f8\u5dee 100 \u500d\u7684\u4fe1\u606f\u5c31\u4e22\u5931\u4e86\u3002<\/li>\n<li>\u5bf9\u4e8e Sigmoid \u51fd\u6570\u800c\u8a00&#xff0c;\u8f93\u5165\u503c\u5728 [-6, 6] \u4e4b\u95f4\u8f93\u51fa\u503c\u624d\u4f1a\u6709\u660e\u663e\u5dee\u5f02&#xff0c;\u8f93\u5165\u503c\u5728 [-3, 3] \u4e4b\u95f4\u624d\u4f1a\u6709\u6bd4\u8f83\u597d\u7684\u6548\u679c\u3002<\/li>\n<li>\u901a\u8fc7\u5bfc\u6570\u56fe\u50cf\u53ef\u4ee5\u53d1\u73b0&#xff0c;\u5bfc\u6570\u6570\u503c\u8303\u56f4\u662f (0, 0.25)&#xff0c;\u5f53\u8f93\u5165\u7684\u503c &lt; -6 \u6216\u8005 &gt; 6 \u65f6&#xff0c;Sigmoid \u5bfc\u6570\u63a5\u8fd1\u4e3a 0&#xff0c;\u6b64\u65f6\u7f51\u7edc\u53c2\u6570\u5c06\u66f4\u65b0\u6781\u5176\u7f13\u6162&#xff0c;\u6216\u8005\u65e0\u6cd5\u66f4\u65b0\u3002<\/li>\n<li>\u4e00\u822c\u6765\u8bf4&#xff0c;Sigmoid \u7f51\u7edc\u5728 5 \u5c42\u4e4b\u5185\u5c31\u4f1a\u4ea7\u751f\u68af\u5ea6\u6d88\u5931\u73b0\u8c61\u3002\u800c\u4e14&#xff0c;\u8be5\u6fc0\u6d3b\u51fd\u6570\u7684\u6fc0\u6d3b\u503c\u5e76\u4e0d\u662f\u4ee5 0 \u4e3a\u4e2d\u5fc3\u7684&#xff0c;\u6fc0\u6d3b\u503c\u603b\u662f\u504f\u5411\u6b63\u6570&#xff0c;\u5bfc\u81f4\u68af\u5ea6\u66f4\u65b0\u65f6\u53ea\u4f1a\u5bf9\u67d0\u4e9b\u7279\u5f81\u4ea7\u751f\u76f8\u540c\u65b9\u5411\u7684\u5f71\u54cd\u3002\u56e0\u6b64&#xff0c;\u5728\u5b9e\u8df5\u4e2d\u8fd9\u79cd\u6fc0\u6d3b\u51fd\u6570\u4f7f\u7528\u5f97\u5f88\u5c11\u3002Sigmoid \u51fd\u6570\u4e00\u822c\u53ea\u7528\u4e8e\u4e8c\u5206\u7c7b\u7684\u8f93\u51fa\u5c42\u3002<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 Sigmoid \u7684\u793a\u4f8b\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;font.sans-serif&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;SimHei&#039;<\/span><span class=\"token punctuation\">]<\/span>  <span class=\"token comment\"># \u7528\u6765\u6b63\u5e38\u663e\u793a\u4e2d\u6587\u6807\u7b7e<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;axes.unicode_minus&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">False<\/span>  <span class=\"token comment\"># \u7528\u6765\u6b63\u5e38\u663e\u793a\u8d1f\u53f7<\/span><\/p>\n<p><span class=\"token triple-quoted-string string\">&#034;&#034;&#034;<br \/>\n\u7ed8\u5236\u6fc0\u6d3b\u51fd\u6570\u56fe\u50cf\u65f6\u51fa\u73b0\u4ee5\u4e0b\u63d0\u793a&#xff0c;\u9700\u8981\u5c06 anaconda3\/Lib\/site-packages\/torch\/lib \u76ee\u5f55\u4e0b\u7684 libiomp5md.dll \u6587\u4ef6\u5220\u9664<br \/>\nOMP: Error #15: Initializing libiomp5md.dll, but found libiomp5md.dll already initialized.<br \/>\n&#034;&#034;&#034;<\/span><\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u753b\u5e03\u548c\u5750\u6807\u8f74<\/span><br \/>\n_<span class=\"token punctuation\">,<\/span> axes <span class=\"token operator\">&#061;<\/span> plt<span class=\"token punctuation\">.<\/span>subplots<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u51fd\u6570\u56fe\u50cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u8f93\u5165\u503c x \u901a\u8fc7 sigmoid \u51fd\u6570\u8f6c\u6362\u6210\u6fc0\u6d3b\u503c y<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>sigmoid<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Sigmoid \u51fd\u6570\u56fe\u50cf&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5bfc\u6570\u56fe\u50cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\ntorch<span class=\"token punctuation\">.<\/span>sigmoid<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># x.detach(): \u8f93\u5165\u503c x \u7684 ndarray \u6570\u7ec4<\/span><br \/>\n<span class=\"token comment\"># x.grad: \u8ba1\u7b97\u68af\u5ea6&#xff0c;\u6c42\u5bfc<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Sigmoid \u5bfc\u6570\u56fe\u50cf&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h5>2.2.2 Tanh \u6fc0\u6d3b\u51fd\u6570<\/h5>\n<p>Tanh \u79f0\u4e3a\u53cc\u66f2\u6b63\u5207\u51fd\u6570&#xff0c;\u5176\u516c\u5f0f\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a9034658a9a4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u6c42\u5bfc\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a9034659fc16.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>Tanh \u51fd\u6570\u56fe\u50cf\u548c\u5bfc\u6570\u56fe\u50cf&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a903465b2d1c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>Tanh \u7684\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u7531\u51fd\u6570\u56fe\u50cf\u53ef\u4ee5\u770b\u5230&#xff0c;Tanh \u51fd\u6570\u5c06\u8f93\u5165\u6620\u5c04\u5230 (-1, 1) \u4e4b\u95f4&#xff0c;\u56fe\u50cf\u4ee5 0 \u4e3a\u4e2d\u5fc3&#xff0c;\u6fc0\u6d3b\u503c\u5728 0 \u70b9\u5bf9\u79f0\u3002\u5f53\u8f93\u5165\u7684\u503c\u5927\u6982 &lt; -3 \u6216\u8005 &gt; 3 \u65f6\u5c06\u88ab\u6620\u5c04\u4e3a -1 \u6216 1\u3002\u5176\u5bfc\u6570\u503c\u8303\u56f4 (0, 1)&#xff0c;\u5f53\u8f93\u5165\u7684\u503c\u5927\u6982 &lt; -3 \u6216\u8005 &gt; 3 \u65f6&#xff0c;\u5176\u5bfc\u6570\u8fd1\u4f3c\u4e3a 0\u3002<\/li>\n<li>\u4e0e Sigmoid \u76f8\u6bd4&#xff0c;\u5b83\u662f\u4ee5 0 \u4e3a\u4e2d\u5fc3\u7684&#xff0c;\u4f7f\u5f97\u5176\u6536\u655b\u901f\u5ea6\u8981\u6bd4 Sigmoid \u5feb&#xff0c;\u51cf\u5c11\u8fed\u4ee3\u6b21\u6570\u3002\u7136\u800c&#xff0c;\u4ece\u56fe\u4e2d\u53ef\u4ee5\u770b\u51fa&#xff0c;Tanh \u4e24\u4fa7\u7684\u5bfc\u6570\u4e5f\u4e3a 0&#xff0c;\u540c\u6837\u4f1a\u9020\u6210\u68af\u5ea6\u6d88\u5931\u3002<\/li>\n<li>\u82e5\u4f7f\u7528&#xff0c;\u53ef\u5728\u9690\u85cf\u5c42\u4f7f\u7528 tanh \u51fd\u6570&#xff0c;\u5728\u8f93\u51fa\u5c42\u4f7f\u7528 sigmoid \u51fd\u6570\u3002<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 Tanh \u7684\u793a\u4f8b\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;font.sans-serif&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;SimHei&#039;<\/span><span class=\"token punctuation\">]<\/span>  <span class=\"token comment\"># \u7528\u6765\u6b63\u5e38\u663e\u793a\u4e2d\u6587\u6807\u7b7e<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;axes.unicode_minus&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">False<\/span>  <span class=\"token comment\"># \u7528\u6765\u6b63\u5e38\u663e\u793a\u8d1f\u53f7<\/span><\/p>\n<p>_<span class=\"token punctuation\">,<\/span> axes <span class=\"token operator\">&#061;<\/span> plt<span class=\"token punctuation\">.<\/span>subplots<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u51fd\u6570\u56fe\u50cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tanh<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Tanh \u51fd\u6570\u56fe\u50cf&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5bfc\u6570\u56fe\u50cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\ntorch<span class=\"token punctuation\">.<\/span>tanh<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Tanh \u5bfc\u6570\u56fe\u50cf&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h5>2.2.3 ReLU \u6fc0\u6d3b\u51fd\u6570<\/h5>\n<p>ReLU \u6fc0\u6d3b\u51fd\u6570\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125813-6a903465e6ba4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u6c42\u5bfc\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125814-6a9034660745b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>ReLU \u51fd\u6570\u56fe\u50cf\u548c\u5bfc\u6570\u56fe\u50cf&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125814-6a90346619de2.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>ReLU \u7684\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>ReLU \u6fc0\u6d3b\u51fd\u6570\u5c06\u5c0f\u4e8e 0 \u7684\u503c\u6620\u5c04\u4e3a 0&#xff0c;\u800c\u5927\u4e8e 0 \u7684\u503c\u5219\u4fdd\u6301\u4e0d\u53d8\u3002\u5b83\u66f4\u52a0\u91cd\u89c6\u6b63\u4fe1\u53f7&#xff0c;\u800c\u5ffd\u7565\u8d1f\u4fe1\u53f7&#xff0c;\u8fd9\u79cd\u6fc0\u6d3b\u51fd\u6570\u8fd0\u7b97\u66f4\u4e3a\u7b80\u5355&#xff0c;\u80fd\u591f\u63d0\u9ad8\u6a21\u578b\u7684\u8bad\u7ec3\u6548\u7387\u3002<\/li>\n<li>\u5f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x&lt;0x &lt; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;ReLU \u5bfc\u6570\u4e3a 0&#xff1b;\u800c\u5f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x&gt;0x &gt; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;\u5219\u4e0d\u5b58\u5728\u9971\u548c\u95ee\u9898\u3002\u6240\u4ee5&#xff0c;ReLU \u80fd\u591f\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x&gt;0x &gt; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u65f6\u4fdd\u6301\u68af\u5ea6\u4e0d\u8870\u51cf&#xff0c;\u4ece\u800c\u7f13\u89e3\u68af\u5ea6\u6d88\u5931\u95ee\u9898\u3002\u7136\u800c&#xff0c;\u968f\u7740\u8bad\u7ec3\u7684\u63a8\u8fdb&#xff0c;\u90e8\u5206\u8f93\u5165\u4f1a\u843d\u5165\u5c0f\u4e8e 0 \u7684\u533a\u57df&#xff0c;\u5bfc\u81f4\u5bf9\u5e94\u6743\u91cd\u65e0\u6cd5\u66f4\u65b0&#xff0c;\u8fd9\u79cd\u73b0\u8c61\u88ab\u79f0\u4e3a&#034;\u795e\u7ecf\u5143\u6b7b\u4ea1&#034;\u3002<\/li>\n<li>ReLU \u662f\u76ee\u524d\u6700\u5e38\u7528\u7684\u6fc0\u6d3b\u51fd\u6570\u3002\u4e0e Sigmoid \u76f8\u6bd4&#xff0c;ReLU \u7684\u4f18\u52bf\u662f&#xff1a;\n<ul>\n<li>Sigmoid \u51fd\u6570\u8ba1\u7b97\u91cf\u5927&#xff08;\u6307\u6570\u8fd0\u7b97&#xff09;&#xff0c;\u53cd\u5411\u4f20\u64ad\u6c42\u8bef\u5dee\u68af\u5ea6\u65f6\u8ba1\u7b97\u91cf\u4e5f\u5927&#xff1b;\u800c ReLU \u6fc0\u6d3b\u51fd\u6570\u6574\u4e2a\u8fc7\u7a0b\u7684\u8ba1\u7b97\u91cf\u8282\u7701\u5f88\u591a\u3002<\/li>\n<li>Sigmoid \u51fd\u6570\u53cd\u5411\u4f20\u64ad\u65f6\u5f88\u5bb9\u6613\u51fa\u73b0\u68af\u5ea6\u6d88\u5931&#xff0c;\u4ece\u800c\u65e0\u6cd5\u5b8c\u6210\u6df1\u5c42\u7f51\u7edc\u7684\u8bad\u7ec3&#xff1b;\u800c ReLU \u6fc0\u6d3b\u51fd\u6570\u5f53\u8f93\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x&gt;0x &gt; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;\u68af\u5ea6\u4e3a 1&#xff0c;\u4e0d\u4f1a\u51fa\u73b0\u68af\u5ea6\u6d88\u5931\u7684\u60c5\u51b5\u3002<\/li>\n<li>ReLU \u4f1a\u4f7f\u4e00\u90e8\u5206\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u4e3a 0&#xff0c;\u8fd9\u6837\u5c31\u9020\u6210\u4e86\u7f51\u7edc\u7684\u7a00\u758f\u6027&#xff0c;\u5e76\u4e14\u51cf\u5c11\u4e86\u53c2\u6570\u7684\u76f8\u4e92\u4f9d\u5b58\u5173\u7cfb&#xff0c;\u7f13\u89e3\u4e86\u8fc7\u62df\u5408\u95ee\u9898\u7684\u53d1\u751f\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 ReLU \u7684\u793a\u4f8b\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;font.sans-serif&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;SimHei&#039;<\/span><span class=\"token punctuation\">]<\/span>  <span class=\"token comment\"># \u7528\u6765\u6b63\u5e38\u663e\u793a\u4e2d\u6587\u6807\u7b7e<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>rcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;axes.unicode_minus&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">False<\/span>  <span class=\"token comment\"># \u7528\u6765\u6b63\u5e38\u663e\u793a\u8d1f\u53f7<\/span><\/p>\n<p>_<span class=\"token punctuation\">,<\/span> axes <span class=\"token operator\">&#061;<\/span> plt<span class=\"token punctuation\">.<\/span>subplots<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u51fd\u6570\u56fe\u50cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;ReLU \u51fd\u6570\u56fe\u50cf&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5bfc\u6570\u56fe\u50cf<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1000<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\ntorch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\naxes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;ReLU \u5bfc\u6570\u56fe\u50cf&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h5>2.2.4 SoftMax \u6fc0\u6d3b\u51fd\u6570<\/h5>\n<p>SoftMax \u7528\u4e8e\u591a\u5206\u7c7b\u8fc7\u7a0b\u4e2d&#xff0c;\u5b83\u662f\u4e8c\u5206\u7c7b\u51fd\u6570 Sigmoid \u5728\u591a\u5206\u7c7b\u4e0a\u7684\u63a8\u5e7f&#xff0c;\u76ee\u7684\u662f\u5c06\u591a\u5206\u7c7b\u7684\u7ed3\u679c\u4ee5\u6982\u7387\u7684\u5f62\u5f0f\u5c55\u73b0\u51fa\u6765\u3002<\/p>\n<p>\u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b\u56fe\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125814-6a9034663c7aa.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125814-6a9034666d66f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>SoftMax \u5c31\u662f\u5c06\u7f51\u7edc\u8f93\u51fa\u7684 logits \u901a\u8fc7 softmax \u51fd\u6570&#xff0c;\u6620\u5c04\u6210\u4e3a (0, 1) \u7684\u503c&#xff0c;\u800c\u8fd9\u4e9b\u503c\u7684\u7d2f\u548c\u4e3a 1&#xff08;\u6ee1\u8db3\u6982\u7387\u7684\u6027\u8d28&#xff09;\u3002\u6211\u4eec\u5c06\u5b83\u7406\u89e3\u6210\u6982\u7387&#xff0c;\u9009\u53d6\u6982\u7387\u6700\u5927&#xff08;\u4e5f\u5c31\u662f\u503c\u5bf9\u5e94\u6700\u5927\u7684&#xff09;\u8282\u70b9&#xff0c;\u4f5c\u4e3a\u6211\u4eec\u7684\u9884\u6d4b\u76ee\u6807\u7c7b\u522b\u3002<\/p>\n<p>PyTorch \u5b9e\u73b0 SoftMax \u7684\u793a\u4f8b\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<\/p>\n<p>scores <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.02<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.15<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.15<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.06<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.05<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3.75<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># dim&#061;0, \u6309\u884c\u8ba1\u7b97<\/span><br \/>\nprobabilities <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>softmax<span class=\"token punctuation\">(<\/span>scores<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>probabilities<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7a0b\u5e8f\u8f93\u51fa\u7ed3\u679c&#xff1a;<\/p>\n<p>tensor([0.0212, 0.0177, 0.0202, 0.0202, 0.0638, 0.0287, 0.0185, 0.0522, 0.0183,<br \/>\n        0.7392])<\/p>\n<h4>2.3 \u5982\u4f55\u9009\u62e9\u6fc0\u6d3b\u51fd\u6570<\/h4>\n<p>\u9664\u4e86\u4e0a\u8ff0\u7684\u6fc0\u6d3b\u51fd\u6570&#xff0c;\u8fd8\u5b58\u5728\u5f88\u591a\u5176\u4ed6\u7684\u6fc0\u6d3b\u51fd\u6570&#xff0c;\u5982\u4e0b\u56fe\u6240\u793a&#xff1a;<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125814-6a903466b3087.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5bf9\u4e8e\u9690\u85cf\u5c42&#xff1a;<\/p>\n<li>\u4f18\u5148\u9009\u62e9 ReLU \u6fc0\u6d3b\u51fd\u6570<\/li>\n<li>\u5982\u679c ReLU \u6548\u679c\u4e0d\u597d&#xff0c;\u518d\u5c1d\u8bd5\u5176\u4ed6\u6fc0\u6d3b\u51fd\u6570&#xff0c;\u5982 Leaky ReLU \u7b49<\/li>\n<li>\u5982\u679c\u4f7f\u7528\u4e86 ReLU&#xff0c;\u9700\u8981\u6ce8\u610f Dead ReLU \u95ee\u9898&#xff0c;\u907f\u514d\u51fa\u73b0 0 \u68af\u5ea6\u4ece\u800c\u5bfc\u81f4\u8fc7\u591a\u7684\u795e\u7ecf\u5143\u6b7b\u4ea1<\/li>\n<li>\u5c11\u4f7f\u7528 Sigmoid \u6fc0\u6d3b\u51fd\u6570&#xff0c;\u53ef\u4ee5\u5c1d\u8bd5\u4f7f\u7528 Tanh \u6fc0\u6d3b\u51fd\u6570<\/li>\n<p>\u5bf9\u4e8e\u8f93\u51fa\u5c42&#xff1a;<\/p>\n<li>\u4e8c\u5206\u7c7b\u95ee\u9898\u9009\u62e9 Sigmoid \u6fc0\u6d3b\u51fd\u6570<\/li>\n<li>\u591a\u5206\u7c7b\u95ee\u9898\u9009\u62e9 SoftMax \u6fc0\u6d3b\u51fd\u6570<\/li>\n<li>\u56de\u5f52\u95ee\u9898\u9009\u62e9 Identity \u6fc0\u6d3b\u51fd\u6570<\/li>\n<hr \/>\n<h3>\u4e09\u3001\u53c2\u6570\u521d\u59cb\u5316<\/h3>\n<p>\u6784\u5efa\u7f51\u7edc\u4e4b\u540e&#xff0c;\u7f51\u7edc\u4e2d\u7684\u53c2\u6570\u9700\u8981\u8fdb\u884c\u521d\u59cb\u5316\u3002\u9700\u8981\u521d\u59cb\u5316\u7684\u53c2\u6570\u4e3b\u8981\u6709\u6743\u91cd\u548c\u504f\u7f6e&#xff0c;\u504f\u7f6e\u4e00\u822c\u521d\u59cb\u5316\u4e3a 0 \u5373\u53ef&#xff0c;\u800c\u5bf9\u6743\u91cd\u7684\u521d\u59cb\u5316\u5219\u66f4\u52a0\u91cd\u8981\u3002<\/p>\n<p>\u53c2\u6570\u521d\u59cb\u5316\u7684\u4f5c\u7528&#xff1a;<\/p>\n<ul>\n<li>\u9632\u6b62\u68af\u5ea6\u6d88\u5931\u6216\u7206\u70b8&#xff1a;\u521d\u59cb\u6743\u91cd\u503c\u8fc7\u5927\u6216\u8fc7\u5c0f\u4f1a\u5bfc\u81f4\u68af\u5ea6\u5728\u53cd\u5411\u4f20\u64ad\u4e2d\u6307\u6570\u7ea7\u589e\u5927\u6216\u7f29\u5c0f\u3002<\/li>\n<li>\u63d0\u9ad8\u6536\u655b\u901f\u5ea6&#xff1a;\u5408\u7406\u7684\u521d\u59cb\u5316\u4f7f\u5f97\u7f51\u7edc\u7684\u6fc0\u6d3b\u503c\u5206\u5e03\u9002\u4e2d&#xff0c;\u6709\u52a9\u4e8e\u68af\u5ea6\u9ad8\u6548\u66f4\u65b0\u3002<\/li>\n<li>\u4fdd\u6301\u5bf9\u79f0\u6027\u7834\u9664&#xff1a;\u6743\u91cd\u7684\u521d\u59cb\u5316\u9700\u8981\u6253\u7834\u5bf9\u79f0\u6027&#xff0c;\u5426\u5219\u7f51\u7edc\u7684\u5b66\u4e60\u80fd\u529b\u4f1a\u53d7\u5230\u9650\u5236\u3002<\/li>\n<\/ul>\n<h4>3.1 \u5e38\u89c1\u53c2\u6570\u521d\u59cb\u5316\u65b9\u6cd5<\/h4>\n<h5>\u968f\u673a\u521d\u59cb\u5316<\/h5>\n<ul>\n<li>\n<p>\u5747\u5300\u5206\u5e03\u521d\u59cb\u5316&#xff1a;\u6743\u91cd\u53c2\u6570\u4ece\u533a\u95f4\u5747\u5300\u968f\u673a\u53d6\u503c&#xff0c;\u9ed8\u8ba4\u533a\u95f4\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(0,1)(0, 1)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u53ef\u4ee5\u8bbe\u7f6e\u4e3a\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(\u22121d,1d)(-\\\\frac{1}{\\\\sqrt{d}}, \\\\frac{1}{\\\\sqrt{d}})<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3831em;vertical-align: -0.538em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.5335em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9378em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8978em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1022em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.538em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.5335em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9378em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8978em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1022em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.538em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5747\u5300\u5206\u5e03\u4e2d\u751f\u6210\u5f53\u524d\u795e\u7ecf\u5143\u7684\u6743\u91cd&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dd<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span><\/span> \u4e3a\u795e\u7ecf\u5143\u7684\u8f93\u5165\u6570\u91cf\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/08\/20260827125815-6a903467474b5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<\/li>\n<li>\n<p>\u6b63\u6001\u5206\u5e03\u521d\u59cb\u5316&#xff1a;\u4ece\u5747\u503c\u4e3a 0\u3001\u6807\u51c6\u5dee\u4e3a 1 \u7684\u9ad8\u65af\u5206\u5e03\u4e2d\u53d6\u6837&#xff0c;\u4f7f\u7528\u4e00\u4e9b\u5f88\u5c0f\u7684\u503c\u5bf9\u53c2\u6570 W \u8fdb\u884c\u521d\u59cb\u5316\u3002<\/p>\n<\/li>\n<li>\n<p>\u4f18\u70b9&#xff1a;\u80fd\u6709\u6548\u6253\u7834\u5bf9\u79f0\u6027<\/p>\n<\/li>\n<li>\n<p>\u7f3a\u70b9&#xff1a;\u968f\u673a\u9009\u62e9\u8303\u56f4\u4e0d\u5f53\u53ef\u80fd\u5bfc\u81f4\u68af\u5ea6\u95ee\u9898<\/p>\n<\/li>\n<li>\n<p>\u9002\u7528\u573a\u666f&#xff1a;\u6d45\u5c42\u7f51\u7edc\u6216\u4f4e\u590d\u6742\u5ea6\u6a21\u578b&#xff08;\u9690\u85cf\u5c42 1-3 \u5c42&#xff0c;\u603b\u5c42\u6570\u4e0d\u8d85\u8fc7 5 \u5c42&#xff09;<\/p>\n<\/li>\n<\/ul>\n<h5>\u5168 0 \u521d\u59cb\u5316<\/h5>\n<p>\u5c06\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u6240\u6709\u6743\u91cd\u53c2\u6570\u521d\u59cb\u5316\u4e3a 0\u3002<\/p>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u5b9e\u73b0\u7b80\u5355<\/li>\n<li>\u7f3a\u70b9&#xff1a;\u65e0\u6cd5\u6253\u7834\u5bf9\u79f0\u6027&#xff0c;\u6240\u6709\u795e\u7ecf\u5143\u66f4\u65b0\u65b9\u5411\u76f8\u540c&#xff0c;\u65e0\u6cd5\u6709\u6548\u8bad\u7ec3<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\u51e0\u4e4e\u4e0d\u4f7f\u7528&#xff0c;\u4ec5\u7528\u4e8e\u504f\u7f6e\u9879\u7684\u521d\u59cb\u5316<\/li>\n<\/ul>\n<h5>\u5168 1 \u521d\u59cb\u5316<\/h5>\n<p>\u5c06\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u6240\u6709\u6743\u91cd\u53c2\u6570\u521d\u59cb\u5316\u4e3a 1\u3002<\/p>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u5b9e\u73b0\u7b80\u5355<\/li>\n<li>\u7f3a\u70b9&#xff1a;\n<ul>\n<li>\u65e0\u6cd5\u6253\u7834\u5bf9\u79f0\u6027&#xff0c;\u6240\u6709\u795e\u7ecf\u5143\u66f4\u65b0\u65b9\u5411\u76f8\u540c&#xff0c;\u65e0\u6cd5\u6709\u6548\u8bad\u7ec3<\/li>\n<li>\u4f1a\u5bfc\u81f4\u6fc0\u6d3b\u503c\u5728\u7f51\u7edc\u4e2d\u5448\u6307\u6570\u589e\u957f&#xff0c;\u5bb9\u6613\u51fa\u73b0\u68af\u5ea6\u7206\u70b8<\/li>\n<\/ul>\n<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\n<ul>\n<li>\u6d4b\u8bd5\u6216\u8c03\u8bd5&#xff1a;\u6bd4\u5982\u9a8c\u8bc1\u795e\u7ecf\u7f51\u7edc\u662f\u5426\u80fd\u6b63\u5e38\u524d\u5411\u4f20\u64ad\u548c\u53cd\u5411\u4f20\u64ad<\/li>\n<li>\u7279\u6b8a\u6a21\u578b\u7ed3\u6784&#xff1a;\u67d0\u4e9b\u7a00\u758f\u7f51\u7edc\u6216\u7279\u5b9a\u7684\u81ea\u5b9a\u4e49\u7f51\u7edc\u4e2d\u53ef\u80fd\u9700\u8981\u624b\u52a8\u8bbe\u7f6e\u90e8\u5206\u53c2\u6570\u4e3a 1<\/li>\n<li>\u504f\u7f6e\u521d\u59cb\u5316&#xff1a;\u5076\u5c14\u53ef\u4ee5\u5c06\u504f\u7f6e\u521d\u59cb\u5316\u4e3a\u5c0f\u7684\u6b63\u503c&#xff08;\u5982 0.1&#xff09;&#xff0c;\u4f46\u5f88\u5c11\u7528 1 \u4f5c\u4e3a\u504f\u7f6e\u7684\u521d\u59cb\u503c<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h5>\u56fa\u5b9a\u503c\u521d\u59cb\u5316<\/h5>\n<p>\u5c06\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u6240\u6709\u6743\u91cd\u53c2\u6570\u521d\u59cb\u5316\u4e3a\u67d0\u4e2a\u56fa\u5b9a\u503c\u3002<\/p>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u5b9e\u73b0\u7b80\u5355<\/li>\n<li>\u7f3a\u70b9&#xff1a;\n<ul>\n<li>\u65e0\u6cd5\u6253\u7834\u5bf9\u79f0\u6027&#xff0c;\u6240\u6709\u795e\u7ecf\u5143\u66f4\u65b0\u65b9\u5411\u76f8\u540c&#xff0c;\u65e0\u6cd5\u6709\u6548\u8bad\u7ec3<\/li>\n<li>\u521d\u59cb\u6743\u91cd\u8fc7\u5927\u6216\u8fc7\u5c0f\u53ef\u80fd\u5bfc\u81f4\u68af\u5ea6\u7206\u70b8\u6216\u68af\u5ea6\u6d88\u5931<\/li>\n<\/ul>\n<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\u6d4b\u8bd5\u6216\u8c03\u8bd5<\/li>\n<\/ul>\n<h5>Kaiming \u521d\u59cb\u5316&#xff08;HE \u521d\u59cb\u5316&#xff09;<\/h5>\n<p>\u4e13\u4e3a ReLU \u548c\u5176\u53d8\u4f53\u8bbe\u8ba1&#xff0c;\u8003\u8651\u5230 ReLU \u6fc0\u6d3b\u51fd\u6570\u7684\u7279\u6027&#xff0c;\u5bf9\u8f93\u5165\u7ef4\u5ea6\u8fdb\u884c\u7f29\u653e\u3002<\/p>\n<ul>\n<li>\n<p>HE \u521d\u59cb\u5316\u5206\u4e3a\u6b63\u6001\u5206\u5e03\u7684 HE \u521d\u59cb\u5316\u548c\u5747\u5300\u5206\u5e03\u7684 HE \u521d\u59cb\u5316&#xff1a;<\/p>\n<ul>\n<li>\u6b63\u6001\u5206\u5e03\u7684 HE \u521d\u59cb\u5316&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u6743\u91cd\u503c\u4ece\u5747\u503c\u4e3a 0\u3001\u6807\u51c6\u5dee\u4e3a std \u4e2d\u968f\u673a\u91c7\u6837&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">std&#061;2\/fan_in\\\\text{std} &#061; \\\\sqrt{2 \/ \\\\text{fan\\\\_in}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">std<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.335em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.905em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\">2\/<\/span><span class=\"mord text\"><span class=\"mord\">fan_in<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.865em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.335em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002std \u503c\u8d8a\u5927&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u6743\u91cd\u503c\u79bb\u5747\u503c 0 \u5206\u5e03\u76f8\u5bf9\u8d8a\u5e7f&#xff0c;\u8ba1\u7b97\u5f97\u5230\u7684\u5185\u90e8\u72b6\u6001\u503c\u6709\u8f83\u5927\u7684\u6b63\u503c\u6216\u8d1f\u503c\u3002<\/li>\n<li>\u5747\u5300\u5206\u5e03\u7684 HE \u521d\u59cb\u5316&#xff1a;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[\u2212limit,limit][-\\\\text{limit}, \\\\text{limit}]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord text\"><span class=\"mord\">limit<\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord text\"><span class=\"mord\">limit<\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u5747\u5300\u5206\u5e03\u4e2d\u62bd\u53d6\u6837\u672c&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">limit&#061;6\/fan_in\\\\text{limit} &#061; \\\\sqrt{6 \/ \\\\text{fan\\\\_in}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">limit<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.335em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.905em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\">6\/<\/span><span class=\"mord text\"><span class=\"mord\">fan_in<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.865em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.335em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fan_in\\\\text{fan\\\\_in}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0044em;vertical-align: -0.31em\"><\/span><span class=\"mord text\"><span class=\"mord\">fan_in<\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u8f93\u5165\u795e\u7ecf\u5143\u7684\u4e2a\u6570&#xff0c;\u5373\u5f53\u524d\u5c42\u63a5\u53d7\u7684\u6765\u81ea\u4e0a\u4e00\u5c42\u7684\u795e\u7ecf\u5143\u7684\u6570\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u4f18\u70b9&#xff1a;\u9002\u5408 ReLU&#xff0c;\u80fd\u4fdd\u6301\u68af\u5ea6\u7a33\u5b9a<\/p>\n<\/li>\n<li>\n<p>\u7f3a\u70b9&#xff1a;\u5bf9\u975e ReLU \u6fc0\u6d3b\u51fd\u6570\u6548\u679c\u4e00\u822c<\/p>\n<\/li>\n<li>\n<p>\u9002\u7528\u573a\u666f&#xff1a;\u6df1\u5ea6\u7f51\u7edc&#xff08;10 \u5c42\u53ca\u4ee5\u4e0a&#xff09;&#xff0c;\u4f7f\u7528 ReLU\u3001Leaky ReLU \u6fc0\u6d3b\u51fd\u6570<\/p>\n<\/li>\n<\/ul>\n<h5>Xavier \u521d\u59cb\u5316&#xff08;Glorot \u521d\u59cb\u5316&#xff09;<\/h5>\n<p>\u6839\u636e\u7f51\u7edc\u8f93\u5165\u548c\u8f93\u51fa\u7684\u7ef4\u5ea6\u81ea\u52a8\u9009\u62e9\u6743\u91cd\u8303\u56f4&#xff0c;\u4f7f\u8f93\u5165\u548c\u8f93\u51fa\u7684\u65b9\u5dee\u76f8\u540c\u3002<\/p>\n<ul>\n<li>\n<p>Xavier \u521d\u59cb\u5316\u5206\u4e3a\u6b63\u6001\u5206\u5e03\u7684 Xavier \u521d\u59cb\u5316\u548c\u5747\u5300\u5206\u5e03\u7684 Xavier \u521d\u59cb\u5316&#xff1a;<\/p>\n<ul>\n<li>\u6b63\u6001\u5206\u5e03\u7684 Xavier \u521d\u59cb\u5316&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u6743\u91cd\u503c\u4ece\u5747\u503c\u4e3a 0\u3001\u6807\u51c6\u5dee\u4e3a std \u4e2d\u968f\u673a\u91c7\u6837&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">std&#061;2\/(fan_in&#043;fan_out)\\\\text{std} &#061; \\\\sqrt{2 \/ (\\\\text{fan\\\\_in} &#043; \\\\text{fan\\\\_out})}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">std<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.335em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.905em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\">2\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">fan_in<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord\">fan_out<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.865em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.335em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002std \u503c\u8d8a\u5c0f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u6743\u91cd\u503c\u79bb\u5747\u503c 0 \u5206\u5e03\u76f8\u5bf9\u8d8a\u96c6\u4e2d&#xff0c;\u8ba1\u7b97\u5f97\u5230\u7684\u5185\u90e8\u72b6\u6001\u503c\u6709\u8f83\u5c0f\u7684\u6b63\u503c\u6216\u8d1f\u503c\u3002<\/li>\n<li>\u5747\u5300\u5206\u5e03\u7684 Xavier \u521d\u59cb\u5316&#xff1a;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[\u2212limit,limit][-\\\\text{limit}, \\\\text{limit}]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord text\"><span class=\"mord\">limit<\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord text\"><span class=\"mord\">limit<\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u5747\u5300\u5206\u5e03\u4e2d\u62bd\u53d6\u6837\u672c&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">limit&#061;6\/(fan_in&#043;fan_out)\\\\text{limit} &#061; \\\\sqrt{6 \/ (\\\\text{fan\\\\_in} &#043; \\\\text{fan\\\\_out})}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">limit<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.335em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.905em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\">6\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">fan_in<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord\">fan_out<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.865em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.335em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fan_in\\\\text{fan\\\\_in}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0044em;vertical-align: -0.31em\"><\/span><span class=\"mord text\"><span class=\"mord\">fan_in<\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u8f93\u5165\u795e\u7ecf\u5143\u4e2a\u6570&#xff0c;\u5373\u5f53\u524d\u5c42\u63a5\u53d7\u7684\u6765\u81ea\u4e0a\u4e00\u5c42\u7684\u795e\u7ecf\u5143\u7684\u6570\u91cf\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fan_out\\\\text{fan\\\\_out}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0044em;vertical-align: -0.31em\"><\/span><span class=\"mord text\"><span class=\"mord\">fan_out<\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u8f93\u51fa\u795e\u7ecf\u5143\u4e2a\u6570&#xff0c;\u5373\u5f53\u524d\u5c42\u8f93\u51fa\u7684\u795e\u7ecf\u5143\u7684\u6570\u91cf&#xff0c;\u4e5f\u5c31\u662f\u5f53\u524d\u5c42\u4f1a\u4f20\u9012\u7ed9\u4e0b\u4e00\u5c42\u7684\u795e\u7ecf\u5143\u7684\u6570\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u4f18\u70b9&#xff1a;\u9002\u7528\u4e8e Sigmoid\u3001Tanh \u7b49\u6fc0\u6d3b\u51fd\u6570&#xff0c;\u89e3\u51b3\u68af\u5ea6\u6d88\u5931\u95ee\u9898<\/p>\n<\/li>\n<li>\n<p>\u7f3a\u70b9&#xff1a;\u5bf9 ReLU \u7b49\u6fc0\u6d3b\u51fd\u6570\u8868\u73b0\u6b20\u4f73<\/p>\n<\/li>\n<li>\n<p>\u9002\u7528\u573a\u666f&#xff1a;\u6df1\u5ea6\u7f51\u7edc&#xff08;10 \u5c42\u53ca\u4ee5\u4e0a&#xff09;&#xff0c;\u4f7f\u7528 Sigmoid \u6216 Tanh \u6fc0\u6d3b\u51fd\u6570<\/p>\n<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0\u5404\u79cd\u521d\u59cb\u5316\u7684\u4ee3\u7801\u793a\u4f8b&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token comment\"># 1. \u5747\u5300\u5206\u5e03\u968f\u673a\u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test01<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4ece 0-1 \u5747\u5300\u5206\u5e03\u4ea7\u751f\u53c2\u6570<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>uniform_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>uniform_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>bias<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 2. \u56fa\u5b9a\u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test02<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>constant_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 3. \u5168 0 \u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test03<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>zeros_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 4. \u5168 1 \u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test04<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>ones_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 5. \u6b63\u6001\u5206\u5e03\u968f\u673a\u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test05<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>normal_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> mean<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> std<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 6. Kaiming \u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test06<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># kaiming \u6b63\u6001\u5206\u5e03\u521d\u59cb\u5316<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>kaiming_normal_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> nonlinearity<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># kaiming \u5747\u5300\u5206\u5e03\u521d\u59cb\u5316<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>kaiming_uniform_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> nonlinearity<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 7. Xavier \u521d\u59cb\u5316<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test07<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># xavier \u6b63\u6001\u5206\u5e03\u521d\u59cb\u5316<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>xavier_normal_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># xavier \u5747\u5300\u5206\u5e03\u521d\u59cb\u5316<\/span><br \/>\n    linear <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>xavier_uniform_<span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>linear<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.2 \u5982\u4f55\u9009\u62e9\u53c2\u6570\u521d\u59cb\u5316<\/h4>\n<ul>\n<li>\n<p>\u6839\u636e\u6fc0\u6d3b\u51fd\u6570\u9009\u62e9&#xff1a;<\/p>\n<ul>\n<li>Sigmoid\/Tanh&#xff1a;Xavier \u521d\u59cb\u5316<\/li>\n<li>ReLU\/Leaky ReLU&#xff1a;Kaiming \u521d\u59cb\u5316<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6839\u636e\u7f51\u7edc\u6df1\u5ea6&#xff1a;<\/p>\n<ul>\n<li>\u6d45\u5c42\u7f51\u7edc&#xff1a;\u968f\u673a\u521d\u59cb\u5316\u5373\u53ef<\/li>\n<li>\u6df1\u5c42\u7f51\u7edc&#xff1a;\u9700\u8981\u8003\u8651\u65b9\u5dee\u5e73\u8861&#xff0c;\u5982 Xavier \u6216 Kaiming \u521d\u59cb\u5316<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>\u56db\u3001\u795e\u7ecf\u7f51\u7edc\u642d\u5efa\u548c\u53c2\u6570\u8ba1\u7b97<\/h3>\n<h4>4.1 \u6784\u5efa\u795e\u7ecf\u7f51\u7edc<\/h4>\n<p>\u5728 PyTorch \u4e2d\u5b9a\u4e49\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5176\u5b9e\u5c31\u662f\u5c42\u5806\u53e0\u7684\u8fc7\u7a0b&#xff0c;\u7ee7\u627f\u81ea nn.Module&#xff0c;\u5b9e\u73b0\u4e24\u4e2a\u65b9\u6cd5&#xff1a;<\/p>\n<ul>\n<li>__init__ \u65b9\u6cd5\u4e2d\u5b9a\u4e49\u7f51\u7edc\u4e2d\u7684\u5c42\u7ed3\u6784&#xff0c;\u4e3b\u8981\u662f\u5168\u8fde\u63a5\u5c42&#xff0c;\u5e76\u8fdb\u884c\u521d\u59cb\u5316<\/li>\n<li>forward \u65b9\u6cd5&#xff1a;\u5728\u8c03\u7528\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5bf9\u8c61\u65f6&#xff0c;\u5e95\u5c42\u4f1a\u81ea\u52a8\u8c03\u7528\u8be5\u51fd\u6570&#xff0c;\u4e3a\u521d\u59cb\u5316\u5b9a\u4e49\u7684 layer \u4f20\u5165\u6570\u636e&#xff0c;\u8fdb\u884c\u524d\u5411\u4f20\u64ad\u7b49<\/li>\n<\/ul>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u6784\u5efa\u5982\u4e0b\u56fe\u6240\u793a\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-270zkcpfedze2.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7f16\u7801\u8bbe\u8ba1\u5982\u4e0b&#xff1a;<\/p>\n<ul>\n<li>\u7b2c 1 \u4e2a\u9690\u85cf\u5c42&#xff1a;\u6743\u91cd\u521d\u59cb\u5316\u91c7\u7528\u6807\u51c6\u5316\u7684 Xavier \u521d\u59cb\u5316&#xff0c;\u6fc0\u6d3b\u51fd\u6570\u4f7f\u7528 Sigmoid<\/li>\n<li>\u7b2c 2 \u4e2a\u9690\u85cf\u5c42&#xff1a;\u6743\u91cd\u521d\u59cb\u5316\u91c7\u7528\u6807\u51c6\u5316\u7684 HE \u521d\u59cb\u5316&#xff0c;\u6fc0\u6d3b\u51fd\u6570\u91c7\u7528 ReLU<\/li>\n<li>\u8f93\u51fa\u5c42&#xff1a;\u7ebf\u6027\u5c42&#xff0c;\u82e5\u4e3a\u591a\u5206\u7c7b&#xff0c;\u91c7\u7528 SoftMax \u505a\u6570\u636e\u5f52\u4e00\u5316<\/li>\n<\/ul>\n<p>\u6784\u9020\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<br \/>\n<span class=\"token keyword\">from<\/span> torchsummary <span class=\"token keyword\">import<\/span> summary  <span class=\"token comment\"># \u8ba1\u7b97\u6a21\u578b\u53c2\u6570&#xff0c;\u67e5\u770b\u6a21\u578b\u7ed3\u6784<\/span><\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7c7b<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Model<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u5c5e\u6027\u503c<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u8c03\u7528\u7236\u7c7b\u7684\u521d\u59cb\u5316\u5c5e\u6027\u503c&#xff0c;\u786e\u4fdd nn.Module \u7684\u521d\u59cb\u5316\u4ee3\u7801\u80fd\u591f\u6b63\u786e\u6267\u884c<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span>Model<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u521b\u5efa\u7b2c\u4e00\u4e2a\u9690\u85cf\u5c42\u6a21\u578b&#xff0c;3 \u4e2a\u8f93\u5165\u7279\u5f81&#xff0c;3 \u4e2a\u8f93\u51fa\u7279\u5f81<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear1 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u521d\u59cb\u5316\u6743\u91cd<\/span><br \/>\n        nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>xavier_normal_<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear1<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n        nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>zeros_<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear1<span class=\"token punctuation\">.<\/span>bias<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u521b\u5efa\u7b2c\u4e8c\u4e2a\u9690\u85cf\u5c42\u6a21\u578b&#xff0c;3 \u4e2a\u8f93\u5165\u7279\u5f81&#xff08;\u4e0a\u4e00\u5c42\u7684\u8f93\u51fa\u7279\u5f81&#xff09;&#xff0c;2 \u4e2a\u8f93\u51fa\u7279\u5f81<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear2 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u521d\u59cb\u5316\u6743\u91cd<\/span><br \/>\n        nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>kaiming_normal_<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear2<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> nonlinearity<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>zeros_<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear2<span class=\"token punctuation\">.<\/span>bias<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u521b\u5efa\u8f93\u51fa\u5c42\u6a21\u578b<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>out <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u521b\u5efa\u524d\u5411\u4f20\u64ad\u65b9\u6cd5&#xff0c;\u8c03\u7528\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5bf9\u8c61\u65f6\u81ea\u52a8\u6267\u884c forward() \u65b9\u6cd5<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u6570\u636e\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u7ebf\u6027\u5c42<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>linear1<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u4f7f\u7528 sigmoid \u6fc0\u6d3b\u51fd\u6570<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>sigmoid<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><\/p>\n<p>        <span class=\"token comment\"># \u6570\u636e\u7ecf\u8fc7\u7b2c\u4e8c\u4e2a\u7ebf\u6027\u5c42<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>linear2<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u4f7f\u7528 relu \u6fc0\u6d3b\u51fd\u6570<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><\/p>\n<p>        <span class=\"token comment\"># \u6570\u636e\u7ecf\u8fc7\u8f93\u51fa\u5c42<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>out<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u4f7f\u7528 softmax \u6fc0\u6d3b\u51fd\u6570<\/span><br \/>\n        <span class=\"token comment\"># dim&#061;-1: \u6bcf\u4e00\u7ef4\u5ea6\u884c\u6570\u636e\u76f8\u52a0\u4e3a 1<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>softmax<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> x<\/p>\n<p>\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u6784\u9020\u6a21\u578b\u51fd\u6570<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">train<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u5b9e\u4f8b\u5316 model \u5bf9\u8c61<\/span><br \/>\n    my_model <span class=\"token operator\">&#061;<\/span> Model<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u968f\u673a\u4ea7\u751f\u6570\u636e<\/span><br \/>\n    my_data <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;my_data&#8211;&gt;&#034;<\/span><span class=\"token punctuation\">,<\/span> my_data<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;my_data shape&#034;<\/span><span class=\"token punctuation\">,<\/span> my_data<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u6570\u636e\u7ecf\u8fc7\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u8bad\u7ec3<\/span><br \/>\n    output <span class=\"token operator\">&#061;<\/span> my_model<span class=\"token punctuation\">(<\/span>my_data<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;output&#8211;&gt;&#034;<\/span><span class=\"token punctuation\">,<\/span> output<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;output shape&#8211;&gt;&#034;<\/span><span class=\"token punctuation\">,<\/span> output<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u8ba1\u7b97\u6a21\u578b\u53c2\u6570<\/span><br \/>\n    <span class=\"token comment\"># \u8ba1\u7b97\u6bcf\u5c42\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684 w \u548c b \u4e2a\u6570\u603b\u548c<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;&#061;&#061;&#061;&#061;&#061;&#061;\u8ba1\u7b97\u6a21\u578b\u53c2\u6570&#061;&#061;&#061;&#061;&#061;&#061;&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    summary<span class=\"token punctuation\">(<\/span>my_model<span class=\"token punctuation\">,<\/span> input_size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u67e5\u770b\u6a21\u578b\u53c2\u6570<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;&#061;&#061;&#061;&#061;&#061;&#061;\u67e5\u770b\u6a21\u578b\u53c2\u6570 w \u548c b&#061;&#061;&#061;&#061;&#061;&#061;&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> name<span class=\"token punctuation\">,<\/span> parameter <span class=\"token keyword\">in<\/span> my_model<span class=\"token punctuation\">.<\/span>named_parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>name<span class=\"token punctuation\">,<\/span> parameter<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    train<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>4.2 \u89c2\u5bdf\u6570\u636e\u5f62\u72b6\u53d8\u5316<\/h4>\n<ul>\n<li>\u8f93\u5165 5 \u884c\u6570\u636e&#xff0c;\u8f93\u51fa\u4e5f\u662f 5 \u884c\u6570\u636e<\/li>\n<li>\u8f93\u5165 5 \u884c\u6570\u636e 3 \u4e2a\u7279\u5f81&#xff0c;\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u9690\u85cf\u5c42\u662f 3 \u4e2a\u7279\u5f81&#xff0c;\u7ecf\u8fc7\u7b2c\u4e8c\u4e2a\u9690\u85cf\u5c42\u662f 2 \u4e2a\u7279\u5f81&#xff0c;\u7ecf\u8fc7\u8f93\u51fa\u5c42\u662f 2 \u4e2a\u7279\u5f81<\/li>\n<li>\u6a21\u578b\u6700\u7ec8\u9884\u6d4b\u7ed3\u679c\u662f&#xff1a;5 \u884c 2 \u5217\u6570\u636e<\/li>\n<\/ul>\n<p>mydata.shape&#8212;&gt; torch.Size([5, 3])<br \/>\noutput.shape&#8212;&gt; torch.Size([5, 2])<br \/>\nmydata&#8212;&gt;<br \/>\n  tensor([[-0.3714, -0.8578, -1.6988],<br \/>\n        [ 0.3149,  0.0142, -1.0432],<br \/>\n        [ 0.5374, -0.1479, -2.0006],<br \/>\n        [ 0.4327, -0.3214,  1.0928],<br \/>\n        [ 2.2156, -1.1640,  1.0289]])<br \/>\noutput&#8212;&gt;<br \/>\n  tensor([[0.5095, 0.4905],<br \/>\n        [0.5218, 0.4782],<br \/>\n        [0.5419, 0.4581],<br \/>\n        [0.5163, 0.4837],<br \/>\n        [0.6030, 0.3970]], grad_fn&#061;&lt;SoftmaxBackward&gt;)<\/p>\n<h4>4.3 \u6a21\u578b\u53c2\u6570\u8ba1\u7b97<\/h4>\n<p>\u4ee5\u7b2c\u4e00\u4e2a\u9690\u5c42\u4e3a\u4f8b&#xff1a;\u8be5\u9690\u5c42\u6709 3 \u4e2a\u795e\u7ecf\u5143&#xff0c;\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u53c2\u6570\u4e3a 4 \u4e2a&#xff08;w1, w2, w3, b1&#xff09;&#xff0c;\u6240\u4ee5\u4e00\u5171\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">3\u00d74&#061;123 \\\\times 4 &#061; 12<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/span> \u4e2a\u53c2\u6570\u3002<\/p>\n<p>\u8f93\u5165\u6570\u636e\u548c\u7f51\u7edc\u6743\u91cd\u662f\u4e24\u4e2a\u4e0d\u540c\u7684\u4e8b\u60c5&#xff01;\u5bf9\u4e8e\u521d\u5b66\u8005\u6765\u8bf4&#xff0c;\u7406\u89e3\u8fd9\u4e00\u70b9\u5341\u5206\u91cd\u8981\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27acg3uhe4epj.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<br \/>\n        Layer (type)               Output Shape         Param #<br \/>\n&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;<br \/>\n            Linear-1                     [5, 3]              12<br \/>\n            Linear-2                     [5, 2]               8<br \/>\n            Linear-3                     [5, 2]               6<br \/>\n&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;<br \/>\nTotal params: 26<br \/>\nTrainable params: 26<br \/>\nNon-trainable params: 0<br \/>\n&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<br \/>\nInput size (MB): 0.00<br \/>\nForward\/backward pass size (MB): 0.00<br \/>\nParams size (MB): 0.00<br \/>\nEstimated Total Size (MB): 0.00<br \/>\n&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/p>\n<h4>4.4 \u67e5\u770b\u6a21\u578b\u53c2\u6570<\/h4>\n<p>\u901a\u5e38\u7ee7\u627f nn.Module \u64b0\u5199\u81ea\u5df1\u7684\u7f51\u7edc\u5c42&#xff0c;\u5176\u5f3a\u5927\u7684\u5c01\u88c5\u4e0d\u9700\u8981\u6211\u4eec\u5b9a\u4e49\u53ef\u5b66\u4e60\u7684\u53c2\u6570&#xff08;\u6bd4\u5982\u5377\u79ef\u6838\u7684\u6743\u91cd\u548c\u504f\u7f6e\u53c2\u6570&#xff09;\u3002\u90a3\u4e48&#xff0c;\u5982\u4f55\u67e5\u770b\u5c01\u88c5\u597d\u7684\u53ef\u5b66\u4e60\u7f51\u7edc\u53c2\u6570\u5462&#xff1f;<\/p>\n<p>\u901a\u8fc7 \u6a21\u5757\u5b9e\u4f8b\u540d.named_parameters() \u65b9\u6cd5&#xff0c;\u4f1a\u5206\u522b\u8fd4\u56de name \u548c parameter\u3002<\/p>\n<p><span class=\"token comment\"># \u5b9e\u4f8b\u5316 model \u5bf9\u8c61<\/span><br \/>\nmymodel <span class=\"token operator\">&#061;<\/span> Model<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u67e5\u770b\u7f51\u7edc\u53c2\u6570<\/span><br \/>\n<span class=\"token keyword\">for<\/span> name<span class=\"token punctuation\">,<\/span> parameter <span class=\"token keyword\">in<\/span> mymodel<span class=\"token punctuation\">.<\/span>named_parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># print(&#039;name&#8212;&gt;&#039;, name)<\/span><br \/>\n    <span class=\"token comment\"># print(&#039;parameter&#8212;&gt;&#039;, parameter)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>name<span class=\"token punctuation\">,<\/span> parameter<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u663e\u793a&#xff1a;<\/p>\n<p>linear1.weight Parameter containing:<br \/>\ntensor([[ 0.1715, -0.3711,  0.1692],<br \/>\n        [-0.2497, -0.6156, -0.4235],<br \/>\n        [-0.7090, -0.0380,  0.4790]], requires_grad&#061;True)<br \/>\nlinear1.bias Parameter containing:<br \/>\ntensor([-0.2320,  0.3431,  0.2771], requires_grad&#061;True)<br \/>\nlinear2.weight Parameter containing:<br \/>\ntensor([[-0.5044, -0.7435, -0.6736],<br \/>\n        [ 0.6908, -0.1466, -0.0019]], requires_grad&#061;True)<br \/>\nlinear2.bias Parameter containing:<br \/>\ntensor([0.2340, 0.4730], requires_grad&#061;True)<br \/>\nout.weight Parameter containing:<br \/>\ntensor([[ 0.5185,  0.4019],<br \/>\n        [-0.4313, -0.3438]], requires_grad&#061;True)<br \/>\nout.bias Parameter containing:<br \/>\ntensor([ 0.4521, -0.6339], requires_grad&#061;True)<\/p>\n<hr \/>\n<h3>\u4e94\u3001\u635f\u5931\u51fd\u6570<\/h3>\n<h4>5.1 \u635f\u5931\u51fd\u6570\u6982\u5ff5<\/h4>\n<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d&#xff0c;\u635f\u5931\u51fd\u6570\u662f\u7528\u6765\u8861\u91cf\u6a21\u578b\u53c2\u6570\u8d28\u91cf\u7684\u51fd\u6570&#xff0c;\u8861\u91cf\u7684\u65b9\u5f0f\u662f\u6bd4\u8f83\u7f51\u7edc\u8f93\u51fa&#xff08;\u9884\u6d4b\u503c&#xff09;\u548c\u771f\u5b9e\u8f93\u51fa&#xff08;\u771f\u5b9e\u503c&#xff09;\u7684\u5dee\u5f02\u3002<\/p>\n<p>\u6a21\u578b\u901a\u8fc7\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u7684\u503c\u6765\u8c03\u6574\u53c2\u6570&#xff0c;\u4f7f\u5176\u8f93\u51fa\u66f4\u63a5\u8fd1\u771f\u5b9e\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27fdznlbfsnlq.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u635f\u5931\u51fd\u6570\u5728\u4e0d\u540c\u7684\u6587\u732e\u4e2d\u540d\u79f0\u6709\u6240\u4e0d\u540c&#xff0c;\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u79cd\u547d\u540d\u65b9\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27is3opwzkr1l.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u635f\u5931\u51fd\u6570\u7684\u4f5c\u7528&#xff1a;<\/p>\n<ul>\n<li>\u8bc4\u4f30\u6027\u80fd&#xff1a;\u53cd\u6620\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u4e0e\u76ee\u6807\u503c\u7684\u5339\u914d\u7a0b\u5ea6<\/li>\n<li>\u6307\u5bfc\u4f18\u5316&#xff1a;\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u7b49\u7b97\u6cd5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570&#xff0c;\u4f18\u5316\u6a21\u578b\u53c2\u6570<\/li>\n<\/ul>\n<h4>5.2 \u5206\u7c7b\u4efb\u52a1\u635f\u5931\u51fd\u6570<\/h4>\n<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u7684\u5206\u7c7b\u4efb\u52a1\u4e2d\u4f7f\u7528\u6700\u591a\u7684\u662f\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570&#xff0c;\u8fd9\u91cc\u6211\u4eec\u7740\u91cd\u4ecb\u7ecd\u8fd9\u79cd\u635f\u5931\u51fd\u6570\u3002<\/p>\n<h5>5.2.1 \u591a\u5206\u7c7b\u4efb\u52a1\u635f\u5931\u51fd\u6570<\/h5>\n<p>\u5728\u591a\u5206\u7c7b\u4efb\u52a1\u4e2d&#xff0c;\u901a\u5e38\u4f7f\u7528 SoftMax \u5c06 logits \u8f6c\u6362\u4e3a\u6982\u7387\u7684\u5f62\u5f0f&#xff0c;\u6240\u4ee5\u591a\u5206\u7c7b\u7684\u4ea4\u53c9\u71b5\u635f\u5931\u4e5f\u53eb\u505a SoftMax \u635f\u5931&#xff0c;\u5176\u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27trmzzffrjim.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yiy_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u6837\u672c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5c5e\u4e8e\u67d0\u4e00\u4e2a\u7c7b\u522b\u7684\u771f\u5b9e\u6982\u7387<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f(x)f(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u6837\u672c\u5c5e\u4e8e\u67d0\u4e00\u7c7b\u522b\u7684\u9884\u6d4b\u5206\u6570<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SS<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u662f SoftMax \u6fc0\u6d3b\u51fd\u6570&#xff0c;\u5c06\u5c5e\u4e8e\u67d0\u4e00\u7c7b\u522b\u7684\u9884\u6d4b\u5206\u6570\u8f6c\u6362\u6210\u6982\u7387<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">LL<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u7528\u6765\u8861\u91cf\u771f\u5b9e\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u548c\u9884\u6d4b\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f(x)f(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u5dee\u5f02\u6027\u7684\u635f\u5931\u7ed3\u679c<\/li>\n<\/ul>\n<p>\u4f8b\u5b50&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-272kaln3zfzns.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4e0a\u56fe\u4e2d\u7684\u4ea4\u53c9\u71b5\u635f\u5931\u4e3a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27ya1q03vjsan.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4ece\u6982\u7387\u89d2\u5ea6\u7406\u89e3&#xff0c;\u6211\u4eec\u7684\u76ee\u7684\u662f\u6700\u5c0f\u5316\u6b63\u786e\u7c7b\u522b\u6240\u5bf9\u5e94\u7684\u9884\u6d4b\u6982\u7387\u7684\u5bf9\u6570\u7684\u8d1f\u503c&#xff08;\u635f\u5931\u503c\u6700\u5c0f&#xff09;&#xff0c;\u5982\u4e0b\u56fe\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27zuclpabj0mw.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>PyTorch \u5b9e\u73b0\u591a\u5206\u7c7b\u4ea4\u53c9\u71b5\u635f\u5931&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> nn<\/p>\n<p><span class=\"token comment\"># \u5206\u7c7b\u635f\u5931\u51fd\u6570&#xff1a;\u4ea4\u53c9\u71b5\u635f\u5931\u4f7f\u7528 nn.CrossEntropyLoss() \u5b9e\u73b0<\/span><br \/>\n<span class=\"token comment\"># nn.CrossEntropyLoss() &#061; softmax &#043; \u635f\u5931\u8ba1\u7b97<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test01<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u8bbe\u7f6e\u771f\u5b9e\u503c&#xff1a;\u53ef\u4ee5\u662f one-hot \u7f16\u7801\u540e\u7684\u7ed3\u679c&#xff0c;\u4e5f\u53ef\u4ee5\u4e0d\u8fdb\u884c one-hot \u7f16\u7801<\/span><br \/>\n    <span class=\"token comment\"># y_true &#061; torch.tensor([[0, 1, 0], [0, 0, 1]], dtype&#061;torch.float32)<\/span><br \/>\n    <span class=\"token comment\"># \u6ce8\u610f&#xff1a;\u7c7b\u578b\u5fc5\u987b\u662f 64 \u4f4d\u6574\u578b\u6570\u636e<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>int64<span class=\"token punctuation\">)<\/span><br \/>\n    y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.8<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                          requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u5b9e\u4f8b\u5316\u4ea4\u53c9\u71b5\u635f\u5931&#xff0c;\u9ed8\u8ba4\u6c42\u5e73\u5747\u635f\u5931<\/span><br \/>\n    <span class=\"token comment\"># reduction&#061;&#039;sum&#039;&#xff1a;\u603b\u635f\u5931<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>CrossEntropyLoss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8ba1\u7b97\u635f\u5931\u7ed3\u679c<\/span><br \/>\n    my_loss <span class=\"token operator\">&#061;<\/span> loss<span class=\"token punctuation\">(<\/span>y_pred<span class=\"token punctuation\">,<\/span> y_true<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;loss:&#039;<\/span><span class=\"token punctuation\">,<\/span> my_loss<span class=\"token punctuation\">)<\/span><\/p>\n<h5>5.2.2 \u4e8c\u5206\u7c7b\u4efb\u52a1\u635f\u5931\u51fd\u6570<\/h5>\n<p>\u5728\u5904\u7406\u4e8c\u5206\u7c7b\u4efb\u52a1\u65f6&#xff0c;\u4e0d\u518d\u4f7f\u7528 SoftMax \u6fc0\u6d3b\u51fd\u6570&#xff0c;\u800c\u662f\u4f7f\u7528 Sigmoid \u6fc0\u6d3b\u51fd\u6570&#xff0c;\u635f\u5931\u51fd\u6570\u4e5f\u76f8\u5e94\u8c03\u6574&#xff0c;\u4f7f\u7528\u4e8c\u5206\u7c7b\u7684\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27hu3taccmu00.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u662f\u6837\u672c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5c5e\u4e8e\u67d0\u4e00\u4e2a\u7c7b\u522b\u7684\u771f\u5b9e\u6982\u7387<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">y^\\\\hat{y}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u6837\u672c\u5c5e\u4e8e\u67d0\u4e00\u7c7b\u522b\u7684\u9884\u6d4b\u6982\u7387<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">LL<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u7528\u6765\u8861\u91cf\u771f\u5b9e\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u4e0e\u9884\u6d4b\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">y^\\\\hat{y}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u5dee\u5f02\u6027\u7684\u635f\u5931\u7ed3\u679c<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"2026-08-27mkgzkntqqnb.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>PyTorch \u5b9e\u73b0\u4e8c\u5206\u7c7b\u4ea4\u53c9\u71b5\u635f\u5931&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> nn<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test02<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u8bbe\u7f6e\u771f\u5b9e\u503c\u548c\u9884\u6d4b\u503c<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u9884\u6d4b\u503c\u662f sigmoid \u8f93\u51fa\u7684\u7ed3\u679c<\/span><br \/>\n    y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.6901<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5459<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.2469<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316\u4e8c\u5206\u7c7b\u4ea4\u53c9\u71b5\u635f\u5931<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>BCELoss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n    my_loss <span class=\"token operator\">&#061;<\/span> loss<span class=\"token punctuation\">(<\/span>y_pred<span class=\"token punctuation\">,<\/span> y_true<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;loss&#xff1a;&#039;<\/span><span class=\"token punctuation\">,<\/span> my_loss<span class=\"token punctuation\">)<\/span><\/p>\n<h4>5.3 \u56de\u5f52\u4efb\u52a1\u635f\u5931\u51fd\u6570<\/h4>\n<h5>5.3.1 MAE \u635f\u5931\u51fd\u6570<\/h5>\n<p>Mean Absolute Loss&#xff08;MAE&#xff09; \u4e5f\u88ab\u79f0\u4e3a L1 Loss&#xff0c;\u4ee5\u7edd\u5bf9\u8bef\u5dee\u4f5c\u4e3a\u8ddd\u79bb\u3002<\/p>\n<p>\u635f\u5931\u51fd\u6570\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27bridgotpavx.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u66f2\u7ebf\u56fe&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27nv0sf3lqnn1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u7531\u4e8e L1 loss \u5177\u6709\u7a00\u758f\u6027&#xff0c;\u4e3a\u4e86\u60e9\u7f5a\u8f83\u5927\u7684\u503c&#xff0c;\u5e38\u5e38\u5c06\u5176\u4f5c\u4e3a\u6b63\u5219\u9879\u6dfb\u52a0\u5230\u5176\u4ed6 loss \u4e2d\u4f5c\u4e3a\u7ea6\u675f&#xff08;0 \u70b9\u4e0d\u53ef\u5bfc&#xff0c;\u4ea7\u751f\u7a00\u758f\u77e9\u9635&#xff09;\u3002<\/li>\n<li>L1 loss \u7684\u6700\u5927\u95ee\u9898\u662f\u68af\u5ea6\u5728\u96f6\u70b9\u4e0d\u5e73\u6ed1&#xff0c;\u5bfc\u81f4\u4f1a\u8df3\u8fc7\u6781\u5c0f\u503c\u3002<\/li>\n<li>\u9002\u7528\u4e8e\u56de\u5f52\u95ee\u9898\u4e2d\u5b58\u5728\u5f02\u5e38\u503c\u6216\u566a\u58f0\u6570\u636e\u65f6&#xff0c;\u53ef\u4ee5\u51cf\u5c11\u5bf9\u79bb\u7fa4\u70b9\u7684\u654f\u611f\u6027\u3002<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 MAE \u635f\u5931&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> nn<\/p>\n<p><span class=\"token comment\"># \u8ba1\u7b97 inputs \u4e0e target \u4e4b\u5dee\u7684\u7edd\u5bf9\u503c<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test03<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u8bbe\u7f6e\u771f\u5b9e\u503c\u548c\u9884\u6d4b\u503c<\/span><br \/>\n    y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.9<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316 MAE \u635f\u5931\u5bf9\u8c61<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>L1Loss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n    my_loss <span class=\"token operator\">&#061;<\/span> loss<span class=\"token punctuation\">(<\/span>y_pred<span class=\"token punctuation\">,<\/span> y_true<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;loss:&#039;<\/span><span class=\"token punctuation\">,<\/span> my_loss<span class=\"token punctuation\">)<\/span><\/p>\n<h5>5.3.2 MSE \u635f\u5931\u51fd\u6570<\/h5>\n<p>Mean Squared Loss \/ Quadratic Loss&#xff08;MSE loss&#xff09; \u4e5f\u88ab\u79f0\u4e3a L2 loss \u6216\u6b27\u6c0f\u8ddd\u79bb&#xff0c;\u5b83\u4ee5\u8bef\u5dee\u7684\u5e73\u65b9\u548c\u7684\u5747\u503c\u4f5c\u4e3a\u8ddd\u79bb\u3002<\/p>\n<p>\u635f\u5931\u51fd\u6570\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27cwypxpw4w3d.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u66f2\u7ebf\u56fe&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27jgwggqljxii.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>L2 loss \u4e5f\u5e38\u5e38\u4f5c\u4e3a\u6b63\u5219\u9879&#xff0c;\u5bf9\u4e8e\u79bb\u7fa4\u70b9&#xff08;outliers&#xff09;\u654f\u611f&#xff0c;\u56e0\u4e3a\u5e73\u65b9\u9879\u4f1a\u653e\u5927\u5927\u8bef\u5dee\u3002<\/li>\n<li>\u5f53\u9884\u6d4b\u503c\u4e0e\u76ee\u6807\u503c\u76f8\u5dee\u5f88\u5927\u65f6&#xff0c;\u68af\u5ea6\u5bb9\u6613\u7206\u70b8&#xff08;\u68af\u5ea6\u7206\u70b8&#xff1a;\u7f51\u7edc\u5c42\u4e4b\u95f4\u7684\u68af\u5ea6\u503c\u5927\u4e8e 1.0 \u91cd\u590d\u76f8\u4e58\u5bfc\u81f4\u7684\u6307\u6570\u7ea7\u589e\u957f&#xff09;\u3002<\/li>\n<li>\u9002\u7528\u4e8e\u5927\u591a\u6570\u6807\u51c6\u56de\u5f52\u95ee\u9898&#xff0c;\u5982\u623f\u4ef7\u9884\u6d4b\u3001\u6e29\u5ea6\u9884\u6d4b\u7b49\u3002<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 MSE \u635f\u5931&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> nn<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test04<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u8bbe\u7f6e\u771f\u5b9e\u503c\u548c\u9884\u6d4b\u503c<\/span><br \/>\n    y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.9<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316 MSE \u635f\u5931\u5bf9\u8c61<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>MSELoss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n    my_loss <span class=\"token operator\">&#061;<\/span> loss<span class=\"token punctuation\">(<\/span>y_pred<span class=\"token punctuation\">,<\/span> y_true<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;myloss:&#039;<\/span><span class=\"token punctuation\">,<\/span> my_loss<span class=\"token punctuation\">)<\/span><\/p>\n<h5>5.3.3 Smooth L1 \u635f\u5931\u51fd\u6570<\/h5>\n<p>Smooth L1 \u6307\u7684\u662f\u5149\u6ed1\u4e4b\u540e\u7684 L1&#xff0c;\u662f\u4e00\u79cd\u7ed3\u5408\u4e86\u5747\u65b9\u8bef\u5dee&#xff08;MSE&#xff09;\u548c\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee&#xff08;MAE&#xff09;\u4f18\u70b9\u7684\u635f\u5931\u51fd\u6570\u3002\u5b83\u5728\u8bef\u5dee\u8f83\u5c0f\u65f6\u8868\u73b0\u5f97\u50cf MSE&#xff0c;\u5728\u8bef\u5dee\u8f83\u5927\u65f6\u5219\u66f4\u50cf MAE\u3002<\/p>\n<p>Smooth L1 \u635f\u5931\u51fd\u6570\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27xj0kvm52ypr.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5176\u4e2d&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x&#061;f(x)\u2212yx &#061; f(x) &#8211; y<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u4e3a\u771f\u5b9e\u503c\u548c\u9884\u6d4b\u503c\u7684\u5dee\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27cocuak33cg1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4ece\u4e0a\u56fe\u53ef\u4ee5\u770b\u51fa&#xff0c;\u8be5\u51fd\u6570\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u5206\u6bb5\u51fd\u6570&#xff1a;<\/p>\n<ul>\n<li>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[\u22121,1][-1, 1]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u5b9e\u9645\u4e0a\u5c31\u662f L2 \u635f\u5931&#xff0c;\u8fd9\u6837\u89e3\u51b3\u4e86 L1 \u7684\u4e0d\u5149\u6ed1\u95ee\u9898<\/li>\n<li>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[\u22121,1][-1, 1]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u533a\u95f4\u5916&#xff0c;\u5b9e\u9645\u4e0a\u5c31\u662f L1 \u635f\u5931&#xff0c;\u8fd9\u6837\u5c31\u89e3\u51b3\u4e86\u79bb\u7fa4\u70b9\u68af\u5ea6\u7206\u70b8\u7684\u95ee\u9898<\/li>\n<\/ul>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u5bf9\u79bb\u7fa4\u70b9\u66f4\u52a0\u9c81\u68d2&#xff1a;\u5f53\u8bef\u5dee\u8f83\u5927\u65f6&#xff0c;\u635f\u5931\u51fd\u6570\u4f1a\u7ebf\u6027\u589e\u52a0&#xff08;\u800c\u4e0d\u662f\u50cf MSE \u90a3\u6837\u5e73\u65b9\u589e\u52a0&#xff09;&#xff0c;\u56e0\u6b64\u5b83\u5bf9\u79bb\u7fa4\u70b9\u7684\u60e9\u7f5a\u66f4\u5c0f&#xff0c;\u907f\u514d\u4e86 MSE \u5bf9\u79bb\u7fa4\u70b9\u8fc7\u5ea6\u654f\u611f\u7684\u95ee\u9898\u3002<\/li>\n<li>\u8ba1\u7b97\u68af\u5ea6\u65f6\u66f4\u52a0\u5e73\u6ed1&#xff1a;\u4e0e MAE \u76f8\u6bd4&#xff0c;Smooth L1 \u5728\u5c0f\u8bef\u5dee\u65f6\u8868\u73b0\u5f97\u50cf MSE&#xff0c;\u907f\u514d\u4e86\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u56e0\u4f7f\u7528\u7edd\u5bf9\u8bef\u5dee\u800c\u5bfc\u81f4\u7684\u68af\u5ea6\u4e0d\u8fde\u7eed\u95ee\u9898\u3002<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 Smooth L1 \u635f\u5931&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> nn<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test05<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u8bbe\u7f6e\u771f\u5b9e\u503c\u548c\u9884\u6d4b\u503c<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.4<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316 Smooth L1 \u635f\u5931\u5bf9\u8c61<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>SmoothL1Loss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n    my_loss <span class=\"token operator\">&#061;<\/span> loss<span class=\"token punctuation\">(<\/span>y_pred<span class=\"token punctuation\">,<\/span> y_true<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;loss:&#039;<\/span><span class=\"token punctuation\">,<\/span> my_loss<span class=\"token punctuation\">)<\/span><\/p>\n<hr \/>\n<h3>\u516d\u3001\u795e\u7ecf\u7f51\u7edc\u4f18\u5316\u65b9\u6cd5<\/h3>\n<p>\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u80fd\u529b\u6bd4\u5355\u5c42\u7f51\u7edc\u5f3a\u5f97\u591a\u3002\u60f3\u8981\u8bad\u7ec3\u591a\u5c42\u7f51\u7edc&#xff0c;\u9700\u8981\u66f4\u5f3a\u5927\u7684\u5b66\u4e60\u7b97\u6cd5\u3002\u8bef\u5dee\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5&#xff08;Back Propagation&#xff0c;BP&#xff09; \u662f\u5176\u4e2d\u6700\u6770\u51fa\u7684\u4ee3\u8868&#xff0c;\u5b83\u662f\u76ee\u524d\u6700\u6210\u529f\u7684\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u7b97\u6cd5\u3002\u73b0\u5b9e\u4efb\u52a1\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u65f6&#xff0c;\u5927\u591a\u662f\u5728\u4f7f\u7528 BP \u7b97\u6cd5\u8fdb\u884c\u8bad\u7ec3\u3002\u503c\u5f97\u6307\u51fa\u7684\u662f&#xff0c;BP \u7b97\u6cd5\u4e0d\u4ec5\u53ef\u7528\u4e8e\u591a\u5c42\u524d\u9988\u795e\u7ecf\u7f51\u7edc&#xff0c;\u8fd8\u53ef\u4ee5\u7528\u4e8e\u5176\u4ed6\u7c7b\u578b\u7684\u795e\u7ecf\u7f51\u7edc\u3002\u901a\u5e38\u8bf4 BP \u7f51\u7edc\u65f6&#xff0c;\u4e00\u822c\u662f\u6307\u7528 BP \u7b97\u6cd5\u8bad\u7ec3\u7684\u591a\u5c42\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<p>\u8fd9\u91cc\u9700\u8981\u4e86\u89e3\u4e24\u4e2a\u6982\u5ff5&#xff1a;<\/p>\n<li>\u6b63\u5411\u4f20\u64ad&#xff1a;\u6570\u636e\u901a\u8fc7\u7f51\u7edc\u4ece\u8f93\u5165\u5c42\u5230\u8f93\u51fa\u5c42\u7684\u4f20\u9012\u8fc7\u7a0b&#xff0c;\u76ee\u7684\u662f\u8ba1\u7b97\u7f51\u7edc\u7684\u8f93\u51fa\u503c&#xff08;\u9884\u6d4b\u503c&#xff09;&#xff0c;\u4ece\u800c\u4e0e\u76ee\u6807\u503c&#xff08;\u771f\u5b9e\u503c&#xff09;\u6bd4\u8f83\u4ee5\u8ba1\u7b97\u8bef\u5dee\u3002<\/li>\n<li>\u53cd\u5411\u4f20\u64ad&#xff1a;\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u76f8\u5bf9\u4e8e\u7f51\u7edc\u4e2d\u5404\u53c2\u6570&#xff08;\u6743\u91cd\u548c\u504f\u7f6e&#xff09;\u7684\u68af\u5ea6&#xff0c;\u6307\u5bfc\u4f18\u5316\u5668\u66f4\u65b0\u53c2\u6570&#xff0c;\u4ece\u800c\u4f7f\u795e\u7ecf\u7f51\u7edc\u7684\u9884\u6d4b\u66f4\u63a5\u8fd1\u76ee\u6807\u503c\u3002<\/li>\n<h4>6.1 \u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u56de\u987e<\/h4>\n<p>\u68af\u5ea6\u4e0b\u964d\u6cd5\u7b80\u5355\u6765\u8bf4\u5c31\u662f\u4e00\u79cd\u5bfb\u627e\u4f7f\u635f\u5931\u51fd\u6570\u6700\u5c0f\u5316\u7684\u65b9\u6cd5\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u89d2\u5ea6\u6765\u770b&#xff0c;\u68af\u5ea6\u7684\u65b9\u5411\u662f\u51fd\u6570\u589e\u957f\u901f\u5ea6\u6700\u5feb\u7684\u65b9\u5411&#xff0c;\u90a3\u4e48\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u5c31\u662f\u51fd\u6570\u51cf\u5c11\u6700\u5feb\u7684\u65b9\u5411&#xff0c;\u6240\u4ee5\u6709&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-272acqamqa4cy.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5176\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u662f\u5b66\u4e60\u7387\u3002\u5982\u679c\u5b66\u4e60\u7387\u592a\u5c0f&#xff0c;\u90a3\u4e48\u6bcf\u6b21\u8bad\u7ec3\u4e4b\u540e\u5f97\u5230\u7684\u6548\u679c\u90fd\u592a\u5c0f&#xff0c;\u589e\u52a0\u8bad\u7ec3\u7684\u65f6\u95f4\u6210\u672c\u3002\u5982\u679c\u5b66\u4e60\u7387\u592a\u5927&#xff0c;\u90a3\u5c31\u6709\u53ef\u80fd\u76f4\u63a5\u8df3\u8fc7\u6700\u4f18\u89e3&#xff0c;\u8fdb\u5165\u65e0\u9650\u7684\u8bad\u7ec3\u4e2d\u3002\u89e3\u51b3\u7684\u65b9\u6cd5\u662f&#xff0c;\u5b66\u4e60\u7387\u4e5f\u9700\u8981\u968f\u7740\u8bad\u7ec3\u7684\u8fdb\u884c\u800c\u53d8\u5316\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-271qahqfcysce.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5728\u8fdb\u884c\u6a21\u578b\u8bad\u7ec3\u65f6&#xff0c;\u6709\u4e09\u4e2a\u57fa\u7840\u7684\u6982\u5ff5&#xff1a;<\/p>\n<li>Epoch&#xff1a;\u4f7f\u7528\u5168\u90e8\u6570\u636e\u5bf9\u6a21\u578b\u8fdb\u884c\u4e00\u6b21\u5b8c\u6574\u8bad\u7ec3&#xff0c;\u5373\u8bad\u7ec3\u6b21\u6570\u3002<\/li>\n<li>Batch&#xff1a;\u4f7f\u7528\u8bad\u7ec3\u96c6\u4e2d\u7684\u5c0f\u90e8\u5206\u6837\u672c\u5bf9\u6a21\u578b\u6743\u91cd\u8fdb\u884c\u4e00\u6b21\u53cd\u5411\u4f20\u64ad\u7684\u53c2\u6570\u66f4\u65b0&#xff0c;\u5373\u6bcf\u6b21\u8bad\u7ec3\u6bcf\u6279\u6b21\u6837\u672c\u6570\u91cf\u3002<\/li>\n<li>Iteration&#xff1a;\u4f7f\u7528\u4e00\u4e2a Batch \u6570\u636e\u5bf9\u6a21\u578b\u8fdb\u884c\u4e00\u6b21\u53c2\u6570\u66f4\u65b0\u7684\u8fc7\u7a0b&#xff0c;\u5373\u6bcf\u6b21\u8bad\u7ec3\u6279\u6b21\u6570\u3002<\/li>\n<p>\u5047\u8bbe\u6570\u636e\u96c6\u6709 50000 \u4e2a\u8bad\u7ec3\u6837\u672c&#xff0c;\u73b0\u5728\u9009\u62e9 Batch Size &#061; 256 \u5bf9\u6a21\u578b\u8fdb\u884c\u8bad\u7ec3&#xff1a;<\/p>\n<ul>\n<li>\u6bcf\u4e2a Epoch \u8981\u8bad\u7ec3\u7684\u56fe\u7247\u6570\u91cf&#xff1a;50000<\/li>\n<li>\u8bad\u7ec3\u96c6\u5177\u6709\u7684 Batch \u4e2a\u6570&#xff1a;50000 \/ 256 &#043; 1 &#061; 196<\/li>\n<li>\u6bcf\u4e2a Epoch \u5177\u6709\u7684 Iteration \u4e2a\u6570&#xff1a;196<\/li>\n<li>10 \u4e2a Epoch \u5177\u6709\u7684 Iteration \u4e2a\u6570&#xff1a;1960<\/li>\n<\/ul>\n<h4>6.2 \u53cd\u5411\u4f20\u64ad&#xff08;BP \u7b97\u6cd5&#xff09;<\/h4>\n<p>\u5229\u7528\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u5bf9\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u8bad\u7ec3\u3002\u8be5\u65b9\u6cd5\u4e0e\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u76f8\u7ed3\u5408&#xff0c;\u5bf9\u7f51\u7edc\u4e2d\u6240\u6709\u6743\u91cd\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u7684\u68af\u5ea6&#xff0c;\u5e76\u5229\u7528\u68af\u5ea6\u503c\u6765\u66f4\u65b0\u6743\u503c\u4ee5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u3002<\/p>\n<h5>6.2.1 \u53cd\u5411\u4f20\u64ad\u6982\u5ff5<\/h5>\n<p>\u524d\u5411\u4f20\u64ad&#xff1a;\u6570\u636e\u8f93\u5165\u5230\u795e\u7ecf\u7f51\u7edc\u4e2d&#xff0c;\u9010\u5c42\u5411\u524d\u4f20\u8f93&#xff0c;\u4e00\u76f4\u8fd0\u7b97\u5230\u8f93\u51fa\u5c42\u4e3a\u6b62\u3002<\/p>\n<p>\u53cd\u5411\u4f20\u64ad&#xff08;Back Propagation&#xff09;&#xff1a;\u5229\u7528\u635f\u5931\u51fd\u6570 ERROR \u503c&#xff0c;\u4ece\u540e\u5f80\u524d&#xff0c;\u7ed3\u5408\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5&#xff0c;\u4f9d\u6b21\u6c42\u5404\u4e2a\u53c2\u6570\u7684\u504f\u5bfc&#xff0c;\u5e76\u8fdb\u884c\u53c2\u6570\u66f4\u65b0\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27sngyyylwqdj.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5728\u7f51\u7edc\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e2d&#xff0c;\u7ecf\u8fc7\u524d\u5411\u4f20\u64ad\u540e\u5f97\u5230\u7684\u6700\u7ec8\u7ed3\u679c\u8ddf\u8bad\u7ec3\u6837\u672c\u7684\u771f\u5b9e\u503c\u603b\u662f\u5b58\u5728\u4e00\u5b9a\u8bef\u5dee&#xff0c;\u8fd9\u4e2a\u8bef\u5dee\u4fbf\u662f\u635f\u5931\u51fd\u6570 ERROR\u3002\u60f3\u8981\u51cf\u5c0f\u8fd9\u4e2a\u8bef\u5dee&#xff0c;\u5c31\u7528\u635f\u5931\u51fd\u6570 ERROR&#xff0c;\u4ece\u540e\u5f80\u524d&#xff0c;\u4f9d\u6b21\u6c42\u5404\u4e2a\u53c2\u6570\u7684\u504f\u5bfc&#xff0c;\u8fd9\u5c31\u662f\u53cd\u5411\u4f20\u64ad&#xff08;Back Propagation&#xff09;\u3002<\/p>\n<h5>6.2.2 \u53cd\u5411\u4f20\u64ad\u8be6\u89e3<\/h5>\n<p>\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u5229\u7528\u94fe\u5f0f\u6cd5\u5219\u5bf9\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5404\u4e2a\u8282\u70b9\u7684\u6743\u91cd\u8fdb\u884c\u66f4\u65b0\u3002<\/p>\n<p>\u3010\u4e3e\u4e2a\u6817\u5b50&#x1f330;\u3011<\/p>\n<p>\u5982\u4e0b\u56fe\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u795e\u7ecf\u7f51\u7edc&#xff0c;\u6fc0\u6d3b\u51fd\u6570\u4e3a Sigmoid&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-270uipa1us2fy.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u524d\u5411\u4f20\u64ad\u8fd0\u7b97&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27ntrfu4stzu4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u53cd\u5411\u4f20\u64ad&#xff08;\u6c42\u7f51\u7edc\u8bef\u5dee\u5bf9\u5404\u4e2a\u6743\u91cd\u53c2\u6570\u7684\u68af\u5ea6&#xff09;&#xff1a;<\/p>\n<p>\u6211\u4eec\u5148\u6765\u6c42\u6700\u7b80\u5355\u7684\u2014\u2014\u6c42\u8bef\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w5w_5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570\u3002\u9996\u5148\u660e\u786e\u8fd9\u662f\u4e00\u4e2a\u94fe\u5f0f\u6cd5\u5219\u7684\u6c42\u5bfc\u8fc7\u7a0b&#xff0c;\u8981\u6c42\u8bef\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w5w_5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570&#xff0c;\u9700\u8981\u5148\u6c42\u8bef\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">outo1out_{o1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570&#xff0c;\u518d\u6c42 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">outo1out_{o1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">neto1net_{o1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570&#xff0c;\u6700\u540e\u518d\u6c42 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">neto1net_{o1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w5w_5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570\u3002\u7ecf\u8fc7\u8fd9\u4e2a\u94fe\u5f0f\u6cd5\u5219&#xff0c;\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u51fa\u8bef\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w5w_5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570&#xff08;\u504f\u5bfc&#xff09;&#xff0c;\u5982\u4e0b\u56fe\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27tkttttaf4zt.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5bfc\u6570&#xff08;\u68af\u5ea6&#xff09;\u5df2\u7ecf\u8ba1\u7b97\u51fa\u6765&#xff0c;\u4e0b\u9762\u5c31\u662f\u53cd\u5411\u4f20\u64ad\u4e0e\u53c2\u6570\u66f4\u65b0\u8fc7\u7a0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27jcbsv0qhv0b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5982\u679c\u8981\u6c42\u8bef\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w1w_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570&#xff0c;\u7531\u4e8e\u8bef\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w1w_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6c42\u5bfc\u8def\u5f84\u4e0d\u6b62\u4e00\u6761&#xff0c;\u8fd9\u4f1a\u7a0d\u5fae\u590d\u6742\u4e00\u70b9&#xff0c;\u4f46\u6362\u6c64\u4e0d\u6362\u836f&#xff0c;\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27jmwsl1j5le5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u81f3\u6b64&#xff0c;\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u8fc7\u7a0b\u5c31\u8bb2\u5b8c\u5566&#xff01;<\/p>\n<h4>6.3 \u68af\u5ea6\u4e0b\u964d\u4f18\u5316\u65b9\u6cd5<\/h4>\n<p>\u68af\u5ea6\u4e0b\u964d\u4f18\u5316\u7b97\u6cd5\u4e2d&#xff0c;\u53ef\u80fd\u4f1a\u78b0\u5230\u4ee5\u4e0b\u60c5\u51b5&#xff1a;<\/p>\n<ul>\n<li>\u78b0\u5230\u5e73\u7f13\u533a\u57df&#xff0c;\u68af\u5ea6\u503c\u8f83\u5c0f&#xff0c;\u53c2\u6570\u4f18\u5316\u53d8\u6162<\/li>\n<li>\u78b0\u5230&#034;\u978d\u70b9&#034;&#xff0c;\u68af\u5ea6\u4e3a 0&#xff0c;\u53c2\u6570\u65e0\u6cd5\u4f18\u5316<\/li>\n<li>\u78b0\u5230\u5c40\u90e8\u6700\u5c0f\u503c&#xff0c;\u53c2\u6570\u4e0d\u662f\u6700\u4f18<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u8fd9\u4e9b\u95ee\u9898&#xff0c;\u51fa\u73b0\u4e86\u4e00\u4e9b\u5bf9\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7684\u4f18\u5316\u65b9\u6cd5&#xff0c;\u4f8b\u5982&#xff1a;Momentum\u3001AdaGrad\u3001RMSProp\u3001Adam \u7b49\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27exqjd2k0bee.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h5>6.3.1 \u6307\u6570\u52a0\u6743\u5e73\u5747<\/h5>\n<p>\u6700\u5e38\u89c1\u7684\u7b97\u672f\u5e73\u5747\u6307\u7684\u662f\u5c06\u6240\u6709\u6570\u52a0\u8d77\u6765\u9664\u4ee5\u6570\u7684\u4e2a\u6570&#xff0c;\u6bcf\u4e2a\u6570\u7684\u6743\u91cd\u76f8\u540c\u3002\u6307\u6570\u52a0\u6743\u5e73\u5747\u6307\u7684\u662f\u7ed9\u6bcf\u4e2a\u6570\u8d4b\u4e88\u4e0d\u540c\u7684\u6743\u91cd\u6c42\u5f97\u5e73\u5747\u6570\u3002\u79fb\u52a8\u5e73\u5747\u6570\u6307\u7684\u662f\u8ba1\u7b97\u6700\u8fd1\u90bb\u7684 N \u4e2a\u6570\u6765\u83b7\u5f97\u5e73\u5747\u6570\u3002<\/p>\n<p>\u6307\u6570\u79fb\u52a8\u52a0\u6743\u5e73\u5747\u5219\u662f\u53c2\u8003\u5404\u6570\u503c&#xff0c;\u5e76\u4e14\u5404\u6570\u503c\u7684\u6743\u91cd\u90fd\u4e0d\u540c&#xff0c;\u8ddd\u79bb\u8d8a\u8fdc\u7684\u6570\u5b57\u5bf9\u5e73\u5747\u6570\u8ba1\u7b97\u7684\u8d21\u732e\u5c31\u8d8a\u5c0f&#xff08;\u6743\u91cd\u8f83\u5c0f&#xff09;&#xff0c;\u8ddd\u79bb\u8d8a\u8fd1\u5219\u5bf9\u5e73\u5747\u6570\u7684\u8ba1\u7b97\u8d21\u732e\u5c31\u8d8a\u5927&#xff08;\u6743\u91cd\u8d8a\u5927&#xff09;\u3002<\/p>\n<p>\u6bd4\u5982&#xff1a;\u660e\u5929\u6c14\u6e29\u600e\u4e48\u6837&#xff0c;\u548c\u6628\u5929\u6c14\u6e29\u6709\u5f88\u5927\u5173\u7cfb&#xff0c;\u800c\u548c\u4e00\u4e2a\u6708\u524d\u7684\u6c14\u6e29\u5173\u7cfb\u5c31\u5c0f\u4e00\u4e9b\u3002<\/p>\n<p>\u8ba1\u7b97\u516c\u5f0f&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-275bznv3sgudf.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">StS_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u6307\u6570\u52a0\u6743\u5e73\u5747\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">YtY_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">tt<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u65f6\u523b\u7684\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8c03\u8282\u6743\u91cd\u7cfb\u6570&#xff0c;\u8be5\u503c\u8d8a\u5927\u5e73\u5747\u6570\u8d8a\u5e73\u7f13<\/li>\n<\/ul>\n<p>\u7b2c 100 \u5929\u7684\u6307\u6570\u52a0\u6743\u5e73\u5747\u503c\u4e3a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27vwhoiqdmcwa.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4e0b\u9762\u901a\u8fc7\u4ee3\u7801\u6765\u770b\u7ed3\u679c&#xff0c;\u968f\u673a\u4ea7\u751f 30 \u5929\u7684\u6c14\u6e29\u6570\u636e&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p>ELEMENT_NUMBER <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">30<\/span><\/p>\n<p><span class=\"token comment\"># 1. \u5b9e\u9645\u5e73\u5747\u6e29\u5ea6<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test01<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u56fa\u5b9a\u968f\u673a\u6570\u79cd\u5b50<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4ea7\u751f30\u5929\u7684\u968f\u673a\u6e29\u5ea6<\/span><br \/>\n    temperature <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span>ELEMENT_NUMBER<span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">10<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>temperature<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u7ed8\u5236\u5e73\u5747\u6e29\u5ea6<\/span><br \/>\n    days <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> ELEMENT_NUMBER <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>days<span class=\"token punctuation\">,<\/span> temperature<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;r&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>days<span class=\"token punctuation\">,<\/span> temperature<span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 2. \u6307\u6570\u52a0\u6743\u5e73\u5747\u6e29\u5ea6<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">test02<\/span><span class=\"token punctuation\">(<\/span>beta<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u56fa\u5b9a\u968f\u673a\u6570\u79cd\u5b50<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4ea7\u751f30\u5929\u7684\u968f\u673a\u6e29\u5ea6<\/span><br \/>\n    temperature <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span>ELEMENT_NUMBER<span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">10<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>temperature<span class=\"token punctuation\">)<\/span><\/p>\n<p>    exp_weight_avg <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token comment\"># idx\u4ece1\u5f00\u59cb<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> idx<span class=\"token punctuation\">,<\/span> temp <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">enumerate<\/span><span class=\"token punctuation\">(<\/span>temperature<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u7b2c\u4e00\u4e2a\u5143\u7d20\u7684 EWA \u503c\u7b49\u4e8e\u81ea\u8eab<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> idx <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            exp_weight_avg<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>temp<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">continue<\/span><br \/>\n        <span class=\"token comment\"># \u7b2c\u4e8c\u4e2a\u5143\u7d20\u7684 EWA \u503c\u7b49\u4e8e\u4e0a\u4e00\u4e2a EWA \u4e58\u4ee5 \u03b2 &#043; \u5f53\u524d\u6c14\u6e29\u4e58\u4ee5 (1-\u03b2)<\/span><br \/>\n        <span class=\"token comment\"># idx-2&#xff1a;2-2&#061;0&#xff0c;exp_weight_avg \u5217\u8868\u4e2d\u7b2c\u4e00\u4e2a\u503c\u7684\u4e0b\u6807\u503c<\/span><br \/>\n        new_temp <span class=\"token operator\">&#061;<\/span> exp_weight_avg<span class=\"token punctuation\">[<\/span>idx <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">*<\/span> beta <span class=\"token operator\">&#043;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span> <span class=\"token operator\">&#8211;<\/span> beta<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> temp<br \/>\n        exp_weight_avg<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>new_temp<span class=\"token punctuation\">)<\/span><\/p>\n<p>    days <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> ELEMENT_NUMBER <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>days<span class=\"token punctuation\">,<\/span> exp_weight_avg<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;r&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>days<span class=\"token punctuation\">,<\/span> temperature<span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    test01<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    test02<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    test02<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"2026-08-27ajgr51yu1ct.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4ece\u7a0b\u5e8f\u8fd0\u884c\u7ed3\u679c\u53ef\u4ee5\u770b\u5230&#xff1a;<\/p>\n<ul>\n<li>\u6307\u6570\u52a0\u6743\u5e73\u5747\u7ed8\u5236\u51fa\u7684\u6c14\u6e29\u53d8\u5316\u66f2\u7ebf\u66f4\u52a0\u5e73\u7f13<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u8d8a\u5927&#xff0c;\u5219\u7ed8\u5236\u51fa\u7684\u6298\u7ebf\u8d8a\u52a0\u5e73\u7f13&#xff0c;\u6ce2\u52a8\u8d8a\u5c0f&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\u2212\u03b21-\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u8d8a\u5c0f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">tt<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u65f6\u523b\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">StS_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8d8a\u4e0d\u4f9d\u8d56 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">YtY_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.2222em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u503c&#xff09;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u503c\u4e00\u822c\u9ed8\u8ba4\u90fd\u662f 0.9<\/li>\n<\/ul>\n<h5>6.3.2 \u52a8\u91cf\u7b97\u6cd5 Momentum<\/h5>\n<p>\u5f53\u68af\u5ea6\u4e0b\u964d\u78b0\u5230&#034;\u5ce1\u8c37&#034;\u3001\u201c\u5e73\u7f13\u201d\u3001&#034;\u978d\u70b9&#034;\u533a\u57df\u65f6&#xff0c;\u53c2\u6570\u66f4\u65b0\u901f\u5ea6\u53d8\u6162\u3002Momentum \u901a\u8fc7\u6307\u6570\u52a0\u6743\u5e73\u5747\u6cd5&#xff0c;\u7d2f\u8ba1\u5386\u53f2\u68af\u5ea6\u503c&#xff0c;\u8fdb\u884c\u53c2\u6570\u66f4\u65b0&#xff0c;\u8d8a\u8fd1\u7684\u68af\u5ea6\u503c\u5bf9\u5f53\u524d\u53c2\u6570\u66f4\u65b0\u7684\u91cd\u8981\u6027\u8d8a\u5927\u3002<\/p>\n<p>\u68af\u5ea6\u8ba1\u7b97\u516c\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">st&#061;\u03b2st\u22121&#043;(1\u2212\u03b2)gts_t &#061; \\\\beta s_{t-1} &#043; (1-\\\\beta)g_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em;vertical-align: -0.2083em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53c2\u6570\u66f4\u65b0\u516c\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#061;wt\u22121\u2212\u03b7stw_t &#061; w_{t-1} &#8211; \\\\eta s_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7917em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">sts_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5f53\u524d\u65f6\u523b\u6307\u6570\u52a0\u6743\u5e73\u5747\u68af\u5ea6\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">st\u22121s_{t-1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5386\u53f2\u6307\u6570\u52a0\u6743\u5e73\u5747\u68af\u5ea6\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">gtg_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5f53\u524d\u65f6\u523b\u7684\u68af\u5ea6\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u662f\u8c03\u8282\u6743\u91cd\u7cfb\u6570&#xff0c;\u901a\u5e38\u53d6 0.9 \u6216 0.99<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u662f\u5b66\u4e60\u7387<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wtw_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5f53\u524d\u65f6\u523b\u6a21\u578b\u6743\u91cd\u53c2\u6570<\/li>\n<\/ul>\n<p>\u54b1\u4eec\u4e3e\u4e2a\u4f8b\u5b50&#xff0c;\u5047\u8bbe&#xff1a;\u6743\u91cd \u03b2 \u4e3a 0.9&#xff0c;\u4f8b\u5982&#xff1a;<br \/>\n\u7b2c\u4e00\u6b21\u68af\u5ea6\u503c&#xff1a;s1 &#061; g1 &#061; w1<br \/>\n\u7b2c\u4e8c\u6b21\u68af\u5ea6\u503c&#xff1a;s2 &#061; 0.9 * s1 &#043; g2 * 0.1<br \/>\n\u7b2c\u4e09\u6b21\u68af\u5ea6\u503c&#xff1a;s3 &#061; 0.9 * s2 &#043; g3 * 0.1<br \/>\n\u7b2c\u56db\u6b21\u68af\u5ea6\u503c&#xff1a;s4 &#061; 0.9 * s3 &#043; g4 * 0.1<br \/>\n1. w \u8868\u793a\u521d\u59cb\u68af\u5ea6<br \/>\n2. g \u8868\u793a\u5f53\u524d\u8f6e\u6570\u8ba1\u7b97\u51fa\u7684\u68af\u5ea6\u503c<br \/>\n3. s \u8868\u793a\u5386\u53f2\u68af\u5ea6\u79fb\u52a8\u52a0\u6743\u5e73\u5747\u503c<\/p>\n<p>\u68af\u5ea6\u4e0b\u964d\u516c\u5f0f\u4e2d\u68af\u5ea6\u7684\u8ba1\u7b97&#xff0c;\u5c31\u4e0d\u518d\u662f\u5f53\u524d\u65f6\u523b t \u7684\u68af\u5ea6\u503c&#xff0c;\u800c\u662f\u5386\u53f2\u68af\u5ea6\u503c\u7684\u6307\u6570\u79fb\u52a8\u52a0\u6743\u5e73\u5747\u503c\u3002<br \/>\n\u516c\u5f0f\u4fee\u6539\u4e3a&#xff1a;<br \/>\nWt &#061; Wt-1 &#8211; \u03b7 * St<br \/>\nWt&#xff1a;\u5f53\u524d\u65f6\u523b\u6a21\u578b\u6743\u91cd\u53c2\u6570<br \/>\nSt&#xff1a;\u5f53\u524d\u65f6\u523b\u6307\u6570\u52a0\u6743\u5e73\u5747\u68af\u5ea6\u503c<br \/>\n\u03b7&#xff1a;\u5b66\u4e60\u7387<\/p>\n<p>Momentum \u4f18\u5316\u65b9\u6cd5\u662f\u5982\u4f55\u514b\u670d&#034;\u5e73\u7f13&#034;\u3001\u201c\u978d\u70b9\u201d\u3001&#034;\u5ce1\u8c37&#034;\u95ee\u9898\u7684&#xff1f;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27f2lxd0f4dzh.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li>\u5f53\u5904\u4e8e\u978d\u70b9\u4f4d\u7f6e\u65f6&#xff0c;\u7531\u4e8e\u5f53\u524d\u7684\u68af\u5ea6\u4e3a 0&#xff0c;\u53c2\u6570\u65e0\u6cd5\u66f4\u65b0\u3002\u4f46\u662f Momentum \u52a8\u91cf\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u5df2\u7ecf\u5728\u5148\u524d\u79ef\u7d2f\u4e86\u4e00\u4e9b\u68af\u5ea6\u503c&#xff0c;\u5f88\u6709\u53ef\u80fd\u4f7f\u5f97\u8de8\u8fc7\u978d\u70b9\u3002<\/li>\n<li>\u7531\u4e8e mini-batch \u666e\u901a\u7684\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6bcf\u6b21\u9009\u53d6\u5c11\u6570\u7684\u6837\u672c\u68af\u5ea6\u786e\u5b9a\u524d\u8fdb\u65b9\u5411&#xff0c;\u53ef\u80fd\u4f1a\u51fa\u73b0\u9707\u8361&#xff0c;\u4f7f\u5f97\u8bad\u7ec3\u65f6\u95f4\u53d8\u957f\u3002Momentum \u4f7f\u7528\u79fb\u52a8\u52a0\u6743\u5e73\u5747&#xff0c;\u5e73\u6ed1\u4e86\u68af\u5ea6\u7684\u53d8\u5316&#xff0c;\u4f7f\u5f97\u524d\u8fdb\u65b9\u5411\u66f4\u52a0\u5e73\u7f13&#xff0c;\u6709\u5229\u4e8e\u52a0\u5feb\u8bad\u7ec3\u8fc7\u7a0b&#xff0c;\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u6709\u5229\u4e8e\u964d\u4f4e&#034;\u5ce1\u8c37&#034;\u95ee\u9898\u7684\u5f71\u54cd\u3002<\/li>\n<\/ul>\n<p>PyTorch \u5b9e\u73b0 Momentum \u68af\u5ea6\u4f18\u5316&#xff1a;<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test01<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u521d\u59cb\u5316\u6743\u91cd\u53c2\u6570<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316\u4f18\u5316\u65b9\u6cd5&#xff1a;SGD \u6307\u5b9a\u53c2\u6570 beta&#061;0.9<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>optim<span class=\"token punctuation\">.<\/span>SGD<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">,<\/span> momentum<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u7b2c1\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c1\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u7b2c2\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    <span class=\"token comment\"># \u4f7f\u7528\u66f4\u65b0\u540e\u7684\u53c2\u6570\u8ba1\u7b97\u8f93\u51fa\u7ed3\u679c<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c2\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u663e\u793a&#xff1a;<\/p>\n<p>\u7b2c1\u6b21: \u68af\u5ea6w.grad: 1.000000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.990000<br \/>\n\u7b2c2\u6b21: \u68af\u5ea6w.grad: 0.990000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.971100<\/p>\n<h5>6.3.3 AdaGrad<\/h5>\n<p>AdaGrad \u901a\u8fc7\u5bf9\u4e0d\u540c\u7684\u53c2\u6570\u5206\u91cf\u4f7f\u7528\u4e0d\u540c\u7684\u5b66\u4e60\u7387&#xff0c;AdaGrad \u7684\u5b66\u4e60\u7387\u603b\u4f53\u4f1a\u9010\u6e10\u51cf\u5c0f\u3002\u8fd9\u662f\u56e0\u4e3a AdaGrad \u8ba4\u4e3a&#xff1a;\u5728\u8d77\u521d\u65f6&#xff0c;\u6211\u4eec\u8ddd\u79bb\u6700\u4f18\u76ee\u6807\u4ecd\u8f83\u8fdc&#xff0c;\u53ef\u4ee5\u4f7f\u7528\u8f83\u5927\u7684\u5b66\u4e60\u7387&#xff0c;\u52a0\u5feb\u8bad\u7ec3\u901f\u5ea6&#xff0c;\u968f\u7740\u8fed\u4ee3\u6b21\u6570\u7684\u589e\u52a0&#xff0c;\u5b66\u4e60\u7387\u9010\u6e10\u4e0b\u964d\u3002<\/p>\n<p>\u8ba1\u7b97\u6b65\u9aa4\u5982\u4e0b&#xff1a;<\/p>\n<li>\u521d\u59cb\u5316\u5b66\u4e60\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span>\u3001\u521d\u59cb\u5316\u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span>\u3001\u5c0f\u5e38\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3&#061;1e\u221210\\\\sigma &#061; 1e-10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u521d\u59cb\u5316\u68af\u5ea6\u7d2f\u8ba1\u53d8\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">s&#061;0s &#061; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u4ece\u8bad\u7ec3\u96c6\u4e2d\u91c7\u6837 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6837\u672c\u7684\u5c0f\u6279\u91cf&#xff0c;\u8ba1\u7b97\u68af\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">gtg_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u7d2f\u79ef\u5e73\u65b9\u68af\u5ea6&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">st&#061;st\u22121&#043;gt\u2299gts_t &#061; s_{t-1} &#043; g_t \\\\odot g_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7917em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2299<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2299\\\\odot<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2299<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u5404\u4e2a\u5206\u91cf\u76f8\u4e58<\/li>\n<li>\u5b66\u4e60\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u7684\u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;\u03b7st&#043;\u03c3\\\\eta &#061; \\\\frac{\\\\eta}{\\\\sqrt{s_t} &#043; \\\\sigma}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3064em;vertical-align: -0.5589em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7344em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.6944em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3056em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5589em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6743\u91cd\u53c2\u6570\u66f4\u65b0\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#061;wt\u22121\u2212\u03b7st&#043;\u03c3\u22c5gtw_t &#061; w_{t-1} &#8211; \\\\frac{\\\\eta}{\\\\sqrt{s_t} &#043; \\\\sigma} \\\\cdot g_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7917em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3064em;vertical-align: -0.5589em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7344em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.6944em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3056em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5589em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u91cd\u590d 3-7 \u6b65\u9aa4<\/li>\n<p>AdaGrad \u7684\u7f3a\u70b9&#xff1a; \u53ef\u80fd\u4f1a\u4f7f\u5f97\u5b66\u4e60\u7387\u8fc7\u65e9\u3001\u8fc7\u91cf\u7684\u964d\u4f4e&#xff0c;\u5bfc\u81f4\u6a21\u578b\u8bad\u7ec3\u540e\u671f\u5b66\u4e60\u7387\u592a\u5c0f&#xff0c;\u8f83\u96be\u627e\u5230\u6700\u4f18\u89e3\u3002<\/p>\n<p>PyTorch \u5b9e\u73b0 AdaGrad \u4f18\u5316&#xff1a;<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test02<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u521d\u59cb\u5316\u6743\u91cd\u53c2\u6570<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316\u4f18\u5316\u65b9\u6cd5&#xff1a;adagrad \u4f18\u5316\u65b9\u6cd5<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>optim<span class=\"token punctuation\">.<\/span>Adagrad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u7b2c1\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c1\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u7b2c2\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    <span class=\"token comment\"># \u4f7f\u7528\u66f4\u65b0\u540e\u7684\u53c2\u6570\u8ba1\u7b97\u8f93\u51fa\u7ed3\u679c<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c2\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u663e\u793a&#xff1a;<\/p>\n<p>\u7b2c1\u6b21: \u68af\u5ea6w.grad: 1.000000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.990000<br \/>\n\u7b2c2\u6b21: \u68af\u5ea6w.grad: 0.990000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.982965<\/p>\n<h5>6.3.4 RMSProp<\/h5>\n<p>RMSProp \u4f18\u5316\u7b97\u6cd5\u662f\u5bf9 AdaGrad \u7684\u4f18\u5316\u3002\u6700\u4e3b\u8981\u7684\u4e0d\u540c\u662f&#xff0c;\u5176\u4f7f\u7528\u6307\u6570\u52a0\u6743\u5e73\u5747\u68af\u5ea6\u66ff\u6362\u5386\u53f2\u68af\u5ea6\u7684\u5e73\u65b9\u548c\u3002<\/p>\n<p>\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4e0b&#xff1a;<\/p>\n<li>\u521d\u59cb\u5316\u5b66\u4e60\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span>\u3001\u521d\u59cb\u5316\u6743\u91cd\u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span>\u3001\u5c0f\u5e38\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3&#061;1e\u221210\\\\sigma &#061; 1e-10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u521d\u59cb\u5316\u68af\u5ea6\u7d2f\u8ba1\u53d8\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">s&#061;0s &#061; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u4ece\u8bad\u7ec3\u96c6\u4e2d\u91c7\u6837 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6837\u672c\u7684\u5c0f\u6279\u91cf&#xff0c;\u8ba1\u7b97\u68af\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">gtg_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u4f7f\u7528\u6307\u6570\u52a0\u6743\u5e73\u5747\u7d2f\u8ba1\u5386\u53f2\u68af\u5ea6&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2299\\\\odot<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2299<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u5404\u4e2a\u5206\u91cf\u76f8\u4e58&#xff09;&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">st&#061;\u03b2st\u22121&#043;(1\u2212\u03b2)gt\u2299gts_t &#061; \\\\beta s_{t-1} &#043; (1-\\\\beta) g_t \\\\odot g_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em;vertical-align: -0.2083em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2299<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5b66\u4e60\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u7684\u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;\u03b7st&#043;\u03c3\\\\eta &#061; \\\\frac{\\\\eta}{\\\\sqrt{s_t} &#043; \\\\sigma}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3064em;vertical-align: -0.5589em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7344em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.6944em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3056em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5589em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6743\u91cd\u53c2\u6570\u66f4\u65b0\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#061;wt\u22121\u2212\u03b7st&#043;\u03c3\u22c5gtw_t &#061; w_{t-1} &#8211; \\\\frac{\\\\eta}{\\\\sqrt{s_t} &#043; \\\\sigma} \\\\cdot g_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7917em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3064em;vertical-align: -0.5589em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7344em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.6944em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3056em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5589em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u91cd\u590d 3-7 \u6b65\u9aa4<\/li>\n<p>RMSProp \u4e0e AdaGrad \u6700\u5927\u7684\u533a\u522b\u662f\u5bf9\u68af\u5ea6\u7684\u7d2f\u79ef\u65b9\u5f0f\u4e0d\u540c&#xff0c;\u5bf9\u4e8e\u6bcf\u4e2a\u68af\u5ea6\u5206\u91cf\u4ecd\u7136\u4f7f\u7528\u4e0d\u540c\u7684\u5b66\u4e60\u7387\u3002<\/p>\n<p>RMSProp \u901a\u8fc7\u5f15\u5165\u8870\u51cf\u7cfb\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u63a7\u5236\u5386\u53f2\u68af\u5ea6\u5bf9\u5386\u53f2\u68af\u5ea6\u4fe1\u606f\u83b7\u53d6\u7684\u591a\u5c11&#xff0c;\u88ab\u8bc1\u660e\u5728\u795e\u7ecf\u7f51\u7edc\u975e\u51f8\u6761\u4ef6\u4e0b\u7684\u4f18\u5316\u66f4\u597d&#xff0c;\u5b66\u4e60\u7387\u8870\u51cf\u66f4\u52a0\u5408\u7406\u4e00\u4e9b\u3002<\/p>\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f&#xff1a;AdaGrad \u548c RMSProp \u90fd\u662f\u5bf9\u4e8e\u4e0d\u540c\u7684\u53c2\u6570\u5206\u91cf\u4f7f\u7528\u4e0d\u540c\u7684\u5b66\u4e60\u7387&#xff0c;\u5982\u679c\u67d0\u4e2a\u53c2\u6570\u5206\u91cf\u7684\u68af\u5ea6\u503c\u8f83\u5927&#xff0c;\u5219\u5bf9\u5e94\u7684\u5b66\u4e60\u7387\u5c31\u4f1a\u8f83\u5c0f&#xff0c;\u5982\u679c\u67d0\u4e2a\u53c2\u6570\u5206\u91cf\u7684\u68af\u5ea6\u8f83\u5c0f&#xff0c;\u5219\u5bf9\u5e94\u7684\u5b66\u4e60\u7387\u5c31\u4f1a\u8f83\u5927\u4e00\u4e9b\u3002<\/p>\n<p>PyTorch \u5b9e\u73b0 RMSProp \u4f18\u5316&#xff1a;<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test03<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u521d\u59cb\u5316\u6743\u91cd\u53c2\u6570<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316\u4f18\u5316\u65b9\u6cd5&#xff1a;RMSprop \u7b97\u6cd5&#xff0c;\u5176\u4e2d alpha \u5bf9\u5e94 beta<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>optim<span class=\"token punctuation\">.<\/span>RMSprop<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">,<\/span> alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u7b2c1\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c1\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u7b2c2\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    <span class=\"token comment\"># \u4f7f\u7528\u66f4\u65b0\u540e\u7684\u53c2\u6570\u8ba1\u7b97\u8f93\u51fa\u7ed3\u679c<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c2\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u663e\u793a&#xff1a;<\/p>\n<p>\u7b2c1\u6b21: \u68af\u5ea6w.grad: 1.000000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.968377<br \/>\n\u7b2c2\u6b21: \u68af\u5ea6w.grad: 0.968377, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.945788<\/p>\n<h5>6.3.5 Adam<\/h5>\n<ul>\n<li>Momentum \u4f7f\u7528\u6307\u6570\u52a0\u6743\u5e73\u5747\u8ba1\u7b97\u5f53\u524d\u7684\u68af\u5ea6\u503c<\/li>\n<li>AdaGrad\u3001RMSProp \u4f7f\u7528\u81ea\u9002\u5e94\u7684\u5b66\u4e60\u7387<\/li>\n<li>Adam \u4f18\u5316\u7b97\u6cd5&#xff08;Adaptive Moment Estimation&#xff0c;\u81ea\u9002\u5e94\u77e9\u4f30\u8ba1&#xff09; \u5c06 Momentum \u548c RMSProp \u7b97\u6cd5\u7ed3\u5408\u5728\u4e00\u8d77\n<ul>\n<li>\u4fee\u6b63\u68af\u5ea6&#xff1a;\u4f7f\u7528\u68af\u5ea6\u7684\u6307\u6570\u52a0\u6743\u5e73\u5747<\/li>\n<li>\u4fee\u6b63\u5b66\u4e60\u7387&#xff1a;\u4f7f\u7528\u68af\u5ea6\u5e73\u65b9\u7684\u6307\u6570\u52a0\u6743\u5e73\u5747<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u539f\u7406&#xff1a;Adam \u662f\u7ed3\u5408\u4e86 Momentum \u548c RMSProp \u4f18\u5316\u7b97\u6cd5\u4f18\u70b9\u7684\u81ea\u9002\u5e94\u5b66\u4e60\u7387\u7b97\u6cd5\u3002\u5b83\u8ba1\u7b97\u4e86\u68af\u5ea6\u7684\u4e00\u9636\u77e9&#xff08;\u5e73\u5747\u503c&#xff09;\u548c\u4e8c\u9636\u77e9&#xff08;\u68af\u5ea6\u7684\u65b9\u5dee&#xff09;\u7684\u81ea\u9002\u5e94\u4f30\u8ba1&#xff0c;\u4ece\u800c\u52a8\u6001\u8c03\u6574\u5b66\u4e60\u7387\u3002<\/p>\n<p>\u68af\u5ea6\u8ba1\u7b97\u516c\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">mt&#061;\u03b21mt\u22121&#043;(1\u2212\u03b21)gtm_t &#061; \\\\beta_1 m_{t-1} &#043; (1-\\\\beta_1)g_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">st&#061;\u03b22st\u22121&#043;(1\u2212\u03b22)gt2s_t &#061; \\\\beta_2 s_{t-1} &#043; (1-\\\\beta_2)g_t^2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">mt^&#061;mt1\u2212\u03b21t,st^&#061;st1\u2212\u03b22t\\\\hat{m_t} &#061; \\\\frac{m_t}{1-\\\\beta_1^t}, \\\\quad \\\\hat{s_t} &#061; \\\\frac{s_t}{1-\\\\beta_2^t}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0599em;vertical-align: -0.9523em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7754em\"><span class=\"\" style=\"top: -2.4337em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2663em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9523em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0599em;vertical-align: -0.9523em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7754em\"><span class=\"\" style=\"top: -2.4337em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2663em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9523em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6743\u91cd\u53c2\u6570\u66f4\u65b0\u516c\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#061;wt\u22121\u2212\u03b7st^&#043;\u03f5mt^w_t &#061; w_{t-1} &#8211; \\\\frac{\\\\eta}{\\\\sqrt{\\\\hat{s_t}} &#043; \\\\epsilon} \\\\hat{m_t}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7917em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0376em;vertical-align: -0.93em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.2528em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">\u03f5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mtm_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u68af\u5ea6\u7684\u4e00\u9636\u77e9\u4f30\u8ba1&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">sts_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u68af\u5ea6\u7684\u4e8c\u9636\u77e9\u4f30\u8ba1&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mt^\\\\hat{m_t}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">st^\\\\hat{s_t}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u504f\u5dee\u6821\u6b63\u540e\u7684\u4f30\u8ba1\u3002<\/p>\n<p>PyTorch \u5b9e\u73b0 Adam \u4f18\u5316&#xff1a;<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test04<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u521d\u59cb\u5316\u6743\u91cd\u53c2\u6570<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u5b9e\u4f8b\u5316\u4f18\u5316\u65b9\u6cd5&#xff1a;Adam \u7b97\u6cd5&#xff0c;\u5176\u4e2d betas \u662f\u6307\u6570\u52a0\u6743\u7684\u7cfb\u6570<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>optim<span class=\"token punctuation\">.<\/span>Adam<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">,<\/span> betas<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.99<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u7b2c1\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c1\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u7b2c2\u6b21\u66f4\u65b0&#xff0c;\u8ba1\u7b97\u68af\u5ea6&#xff0c;\u5e76\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0<\/span><br \/>\n    <span class=\"token comment\"># \u4f7f\u7528\u66f4\u65b0\u540e\u7684\u53c2\u6570\u8ba1\u7b97\u8f93\u51fa\u7ed3\u679c<\/span><br \/>\n    loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>w <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u7b2c2\u6b21: \u68af\u5ea6w.grad: %f, \u66f4\u65b0\u540e\u7684\u6743\u91cd:%f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u663e\u793a&#xff1a;<\/p>\n<p>\u7b2c1\u6b21: \u68af\u5ea6w.grad: 1.000000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.990000<br \/>\n\u7b2c2\u6b21: \u68af\u5ea6w.grad: 0.990000, \u66f4\u65b0\u540e\u7684\u6743\u91cd:0.980003<\/p>\n<h5>6.3.6 \u4f18\u5316\u65b9\u6cd5\u5c0f\u7ed3<\/h5>\n<table>\n<tr>\u4f18\u5316\u7b97\u6cd5\u4f18\u70b9\u7f3a\u70b9\u9002\u7528\u573a\u666f<\/tr>\n<tbody>\n<tr>\n<td>SGD<\/td>\n<td>\u7b80\u5355\u3001\u5bb9\u6613\u5b9e\u73b0<\/td>\n<td>\u6536\u655b\u901f\u5ea6\u8f83\u6162&#xff0c;\u5bb9\u6613\u9707\u8361&#xff0c;\u7279\u522b\u662f\u5728\u590d\u6742\u95ee\u9898\u4e2d<\/td>\n<td>\u7528\u4e8e\u7b80\u5355\u4efb\u52a1&#xff0c;\u6216\u8005\u5f53\u6570\u636e\u7279\u5f81\u5206\u5e03\u76f8\u5bf9\u7a33\u5b9a\u65f6<\/td>\n<\/tr>\n<tr>\n<td>Momentum<\/td>\n<td>\u53ef\u4ee5\u52a0\u901f\u6536\u655b&#xff0c;\u51cf\u5c11\u9707\u8361&#xff0c;\u7279\u522b\u662f\u5728\u9ad8\u66f2\u7387\u533a\u57df<\/td>\n<td>\u9700\u8981\u624b\u52a8\u8c03\u6574\u52a8\u91cf\u8d85\u53c2\u6570&#xff0c;\u53ef\u80fd\u4f1a\u5728\u5c0f\u6b65\u957f\u8bad\u7ec3\u4e2d\u8fc7\u5ea6\u66f4\u65b0<\/td>\n<td>\u7528\u4e8e\u975e\u5e73\u7a33\u4f18\u5316\u95ee\u9898&#xff0c;\u5c24\u5176\u662f\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u5e94\u7528<\/td>\n<\/tr>\n<tr>\n<td>AdaGrad<\/td>\n<td>\u81ea\u9002\u5e94\u8c03\u6574\u5b66\u4e60\u7387&#xff0c;\u9002\u7528\u4e8e\u7a00\u758f\u6570\u636e<\/td>\n<td>\u5b66\u4e60\u7387\u4f1a\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u9010\u6e10\u8870\u51cf&#xff0c;\u53ef\u80fd\u5bfc\u81f4\u65e9\u671f\u505c\u6ede<\/td>\n<td>\u9002\u5408\u7a00\u758f\u6570\u636e&#xff0c;\u5982 NLP \u6216\u63a8\u8350\u7cfb\u7edf\u4e2d\u7684\u7279\u5f81<\/td>\n<\/tr>\n<tr>\n<td>RMSProp<\/td>\n<td>\u89e3\u51b3\u4e86 AdaGrad \u5b66\u4e60\u7387\u8fc7\u65e9\u8870\u51cf\u7684\u95ee\u9898&#xff0c;\u9002\u5e94\u6027\u5f3a<\/td>\n<td>\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u8d85\u53c2\u6570&#xff0c;\u66f4\u65b0\u53ef\u80fd\u4f1a\u8fc7\u4e8e\u6fc0\u8fdb<\/td>\n<td>\u9002\u7528\u4e8e\u52a8\u6001\u95ee\u9898\u3001\u975e\u5e73\u7a33\u76ee\u6807\u51fd\u6570&#xff0c;\u5982\u6df1\u5ea6\u5b66\u4e60\u8bad\u7ec3<\/td>\n<\/tr>\n<tr>\n<td>Adam<\/td>\n<td>\u7ed3\u5408\u4e86 Momentum \u548c RMSProp \u7684\u4f18\u70b9&#xff0c;\u9002\u5e94\u6027\u5f3a\u4e14\u7a33\u5b9a<\/td>\n<td>\u9700\u8981\u8c03\u8282\u66f4\u591a\u7684\u8d85\u53c2\u6570&#xff0c;\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u53ef\u80fd\u4f1a\u4ea7\u751f\u8f83\u5927\u6ce2\u52a8<\/td>\n<td>\u5e7f\u6cdb\u9002\u7528\u4e8e\u5404\u79cd\u6df1\u5ea6\u5b66\u4e60\u4efb\u52a1&#xff0c;\u7279\u522b\u662f\u975e\u5e73\u7a33\u548c\u590d\u6742\u95ee\u9898<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u9009\u62e9\u5efa\u8bae&#xff1a;<\/p>\n<ul>\n<li>\u7b80\u5355\u4efb\u52a1\u548c\u8f83\u5c0f\u7684\u6a21\u578b&#xff1a;SGD \u6216 Momentum<\/li>\n<li>\u590d\u6742\u4efb\u52a1\u6216\u6709\u5927\u91cf\u6570\u636e&#xff1a;Adam \u662f\u6700\u5e38\u7528\u7684\u9009\u62e9&#xff0c;\u56e0\u5176\u5728\u5927\u90e8\u5206\u4efb\u52a1\u4e0a\u90fd\u8868\u73b0\u4f18\u79c0<\/li>\n<li>\u9700\u8981\u5904\u7406\u7a00\u758f\u6570\u636e\u6216\u6587\u672c\u6570\u636e&#xff1a;Adagrad \u6216 RMSProp<\/li>\n<\/ul>\n<hr \/>\n<h3>\u4e03\u3001\u5b66\u4e60\u7387\u8870\u51cf\u4f18\u5316\u65b9\u6cd5<\/h3>\n<h4>7.1 \u4e3a\u4ec0\u4e48\u8981\u8fdb\u884c\u5b66\u4e60\u7387\u4f18\u5316<\/h4>\n<p>\u5728\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u65f6&#xff0c;\u4e00\u822c\u60c5\u51b5\u4e0b\u5b66\u4e60\u7387\u90fd\u4f1a\u968f\u7740\u8bad\u7ec3\u800c\u53d8\u5316\u3002\u8fd9\u4e3b\u8981\u662f\u7531\u4e8e&#xff0c;\u5728\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u7684\u540e\u671f&#xff0c;\u5982\u679c\u5b66\u4e60\u7387\u8fc7\u9ad8&#xff0c;\u4f1a\u9020\u6210 loss \u7684\u632f\u8361&#xff0c;\u4f46\u662f\u5982\u679c\u5b66\u4e60\u7387\u51cf\u5c0f\u7684\u8fc7\u6162&#xff0c;\u53c8\u4f1a\u9020\u6210\u6536\u655b\u53d8\u6162\u7684\u60c5\u51b5\u3002<\/p>\n<p>\u8fd0\u884c\u4e0b\u9762\u4ee3\u7801&#xff0c;\u89c2\u5bdf\u5b66\u4e60\u7387\u8bbe\u7f6e\u4e0d\u540c\u5bf9\u7f51\u7edc\u8bad\u7ec3\u7684\u5f71\u54cd&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p><span class=\"token comment\"># x \u770b\u6210\u662f\u6743\u91cd&#xff0c;y \u770b\u6210\u662f loss&#xff0c;\u4e0b\u9762\u901a\u8fc7\u4ee3\u7801\u6765\u7406\u89e3\u5b66\u4e60\u7387\u7684\u4f5c\u7528<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">func<\/span><span class=\"token punctuation\">(<\/span>x_t<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> torch<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">pow<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token operator\">*<\/span>x_t<span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># y &#061; 4 * x^2<\/span><\/p>\n<p><span class=\"token comment\"># \u91c7\u7528\u8f83\u5c0f\u7684\u5b66\u4e60\u7387&#xff0c;\u68af\u5ea6\u4e0b\u964d\u7684\u901f\u5ea6\u6162<\/span><br \/>\n<span class=\"token comment\"># \u91c7\u7528\u8f83\u5927\u7684\u5b66\u4e60\u7387&#xff0c;\u68af\u5ea6\u4e0b\u964d\u592a\u5feb\u8d8a\u8fc7\u4e86\u6700\u5c0f\u503c\u70b9&#xff0c;\u5bfc\u81f4\u4e0d\u6536\u655b&#xff0c;\u751a\u81f3\u9707\u8361<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">dm01<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2.<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8bb0\u5f55 loss \u8fed\u4ee3\u6b21\u6570&#xff0c;\u753b\u66f2\u7ebf<\/span><br \/>\n    iter_rec<span class=\"token punctuation\">,<\/span> loss_rec<span class=\"token punctuation\">,<\/span> x_rec <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u5b9e\u9a8c\u5b66\u4e60\u7387&#xff1a;0.01 0.02 0.03 0.1 0.2 0.3 0.4<\/span><br \/>\n    <span class=\"token comment\"># lr &#061; 0.1       # \u6b63\u5e38\u7684\u68af\u5ea6\u4e0b\u964d<\/span><br \/>\n    <span class=\"token comment\"># lr &#061; 0.125     # \u5f53\u5b66\u4e60\u7387\u8bbe\u7f6e0.125&#xff0c;\u4e00\u4e0b\u5b50\u6c42\u51fa\u4e00\u4e2a\u6700\u4f18\u89e3<\/span><br \/>\n    <span class=\"token comment\">#                # x&#061;0 y&#061;0&#xff0c;\u5728x&#061;0\u5904\u68af\u5ea6\u7b49\u4e8e0&#xff0c;x\u7684\u503c x&#061;x-lr*x.grad \u5c31\u4e0d\u7528\u66f4\u65b0\u4e86<\/span><br \/>\n    <span class=\"token comment\">#                # \u540e\u7eed\u518d\u591a\u5c11\u6b21\u8fed\u4ee3&#xff0c;\u90fd\u56fa\u5b9a\u5728\u6700\u4f18\u70b9<\/span><\/p>\n<p>    lr <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.2<\/span>         <span class=\"token comment\"># x\u4ece2.0\u4e00\u4e0b\u5b50\u8de8\u8fc70\u70b9&#xff0c;\u5230\u4e86\u5de6\u4fa7\u8d1f\u6570\u533a\u57df<\/span><br \/>\n    <span class=\"token comment\"># lr &#061; 0.3       # \u68af\u5ea6\u8d8a\u6765\u8d8a\u5927&#xff0c;\u68af\u5ea6\u7206\u70b8<\/span><br \/>\n    max_iteration <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">4<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>max_iteration<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        y <span class=\"token operator\">&#061;<\/span> func<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u5f97\u51fa loss \u503c<\/span><br \/>\n        y<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8ba1\u7b97 x \u7684\u68af\u5ea6<\/span><br \/>\n        <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Iter:{}, X:{:8}, X.grad:{:8}, loss:{:10}&#034;<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">format<\/span><span class=\"token punctuation\">(<\/span><br \/>\n            i<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        x_rec<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>      <span class=\"token comment\"># \u68af\u5ea6\u4e0b\u964d\u70b9\u5217\u8868<\/span><br \/>\n        <span class=\"token comment\"># \u66f4\u65b0\u53c2\u6570<\/span><br \/>\n        x<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">.<\/span>sub_<span class=\"token punctuation\">(<\/span>lr <span class=\"token operator\">*<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">)<\/span>    <span class=\"token comment\"># x &#061; x &#8211; x.grad<\/span><br \/>\n        x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>zero_<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        iter_rec<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># \u8fed\u4ee3\u6b21\u6570\u5217\u8868<\/span><br \/>\n        loss_rec<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u635f\u5931\u503c\u5217\u8868<\/span><br \/>\n    <span class=\"token comment\"># \u8fed\u4ee3\u6b21\u6570-\u635f\u5931\u503c\u5173\u7cfb\u56fe<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">121<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>iter_rec<span class=\"token punctuation\">,<\/span> loss_rec<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;-ro&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Iteration X&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Loss value Y&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u51fd\u6570\u66f2\u7ebf-\u4e0b\u964d\u8f68\u8ff9\u663e\u793a\u56fe<\/span><br \/>\n    x_t <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">100<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    y <span class=\"token operator\">&#061;<\/span> func<span class=\"token punctuation\">(<\/span>x_t<span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">122<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x_t<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">.<\/span>detach<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;y &#061; 4*x^2&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    y_rec <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span>func<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> x_rec<span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;x_rec&#8212;&gt;&#039;<\/span><span class=\"token punctuation\">,<\/span> x_rec<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;y_rec&#8212;&gt;&#039;<\/span><span class=\"token punctuation\">,<\/span> y_rec<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6307\u5b9a\u7ebf\u7684\u989c\u8272\u548c\u6837\u5f0f&#xff08;-ro&#xff1a;\u7ea2\u8272\u5706\u5708&#xff0c;b-&#xff1a;\u84dd\u8272\u5b9e\u7ebf\u7b49&#xff09;<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>subplot<span class=\"token punctuation\">(<\/span><span class=\"token number\">122<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>x_rec<span class=\"token punctuation\">,<\/span> y_rec<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;-ro&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>dm01<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8fd0\u884c\u6548\u679c\u56fe\u5982\u4e0b&#xff1a;<\/p>\n<p>\u53ef\u4ee5\u770b\u51fa&#xff1a;\u91c7\u7528\u8f83\u5c0f\u7684\u5b66\u4e60\u7387&#xff0c;\u68af\u5ea6\u4e0b\u964d\u7684\u901f\u5ea6\u6162&#xff1b;\u91c7\u7528\u8f83\u5927\u7684\u5b66\u4e60\u7387&#xff0c;\u68af\u5ea6\u4e0b\u964d\u592a\u5feb\u8d8a\u8fc7\u4e86\u6700\u5c0f\u503c\u70b9&#xff0c;\u5bfc\u81f4\u9707\u8361&#xff0c;\u751a\u81f3\u4e0d\u6536\u655b&#xff08;\u68af\u5ea6\u7206\u70b8&#xff09;\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27dddxzoxesu3.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>7.2 \u7b49\u95f4\u9694\u5b66\u4e60\u7387\u8870\u51cf<\/h4>\n<p>\u7b49\u95f4\u9694\u5b66\u4e60\u7387\u8870\u51cf\u65b9\u5f0f\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27cceloknj12w.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>PyTorch \u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token comment\"># step_size&#xff1a;\u8c03\u6574\u95f4\u9694\u6570&#061;50<\/span><br \/>\n<span class=\"token comment\"># gamma&#xff1a;\u8c03\u6574\u7cfb\u6570&#061;0.5<\/span><br \/>\n<span class=\"token comment\"># \u8c03\u6574\u65b9\u5f0f&#xff1a;lr &#061; lr * gamma<\/span><br \/>\noptim<span class=\"token punctuation\">.<\/span>lr_scheduler<span class=\"token punctuation\">.<\/span>StepLR<span class=\"token punctuation\">(<\/span>optimizer<span class=\"token punctuation\">,<\/span> step_size<span class=\"token punctuation\">,<\/span> gamma<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u5177\u4f53\u4f7f\u7528\u65b9\u5f0f&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> optim<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test_StepLR<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 0. \u53c2\u6570\u521d\u59cb\u5316<\/span><br \/>\n    LR <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.1<\/span>  <span class=\"token comment\"># \u8bbe\u7f6e\u5b66\u4e60\u7387\u521d\u59cb\u5316\u503c\u4e3a0.1<\/span><br \/>\n    iteration <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">10<\/span><br \/>\n    max_epoch <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">200<\/span><br \/>\n    <span class=\"token comment\"># 1. \u521d\u59cb\u5316\u53c2\u6570<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u4f18\u5316\u5668<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>SGD<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span>LR<span class=\"token punctuation\">,<\/span> momentum<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8bbe\u7f6e\u5b66\u4e60\u7387\u4e0b\u964d\u7b56\u7565<\/span><br \/>\n    scheduler_lr <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>lr_scheduler<span class=\"token punctuation\">.<\/span>StepLR<span class=\"token punctuation\">(<\/span>optimizer<span class=\"token punctuation\">,<\/span> step_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">50<\/span><span class=\"token punctuation\">,<\/span> gamma<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u83b7\u53d6\u5b66\u4e60\u7387\u7684\u503c\u548c\u5f53\u524d\u7684epoch<\/span><br \/>\n    lr_list<span class=\"token punctuation\">,<\/span> epoch_list <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> epoch <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>max_epoch<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        lr_list<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>scheduler_lr<span class=\"token punctuation\">.<\/span>get_last_lr<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u83b7\u53d6\u5f53\u524dlr<\/span><br \/>\n        epoch_list<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>epoch<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u83b7\u53d6\u5f53\u524d\u7684epoch<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>iteration<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span>  <span class=\"token comment\"># \u904d\u5386\u6bcf\u4e00\u4e2abatch\u6570\u636e<\/span><br \/>\n            loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token operator\">*<\/span>x<span class=\"token operator\">&#8211;<\/span>y_true<span class=\"token punctuation\">)<\/span><span class=\"token operator\">**<\/span><span class=\"token number\">2<\/span>  <span class=\"token comment\"># \u76ee\u6807\u51fd\u6570<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad<\/span><br \/>\n            loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u66f4\u65b0\u4e0b\u4e00\u4e2aepoch\u7684\u5b66\u4e60\u7387<\/span><br \/>\n        scheduler_lr<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 5. \u7ed8\u5236\u5b66\u4e60\u7387\u53d8\u5316\u7684\u66f2\u7ebf<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>epoch_list<span class=\"token punctuation\">,<\/span> lr_list<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;Step LR Scheduler&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Epoch&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Learning rate&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>7.3 \u6307\u5b9a\u95f4\u9694\u5b66\u4e60\u7387\u8870\u51cf<\/h4>\n<p>\u6307\u5b9a\u95f4\u9694\u5b66\u4e60\u7387\u8870\u51cf\u7684\u6548\u679c\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27lzbhdu0klwe.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>PyTorch \u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token comment\"># milestones&#xff1a;\u8bbe\u5b9a\u8c03\u6574\u8f6e\u6b21 [50, 125, 160]<\/span><br \/>\n<span class=\"token comment\"># gamma&#xff1a;\u8c03\u6574\u7cfb\u6570<\/span><br \/>\n<span class=\"token comment\"># \u8c03\u6574\u65b9\u5f0f&#xff1a;lr &#061; lr * gamma<\/span><br \/>\noptim<span class=\"token punctuation\">.<\/span>lr_scheduler<span class=\"token punctuation\">.<\/span>MultiStepLR<span class=\"token punctuation\">(<\/span>optimizer<span class=\"token punctuation\">,<\/span> milestones<span class=\"token punctuation\">,<\/span> gamma<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> last_epoch<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u5177\u4f53\u4f7f\u7528\u65b9\u5f0f&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> optim<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test_MultiStepLR<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    LR <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.1<\/span><br \/>\n    iteration <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">10<\/span><br \/>\n    max_epoch <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">200<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>SGD<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span>LR<span class=\"token punctuation\">,<\/span> momentum<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8bbe\u5b9a\u8c03\u6574\u65f6\u523b\u6570<\/span><br \/>\n    milestones <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">50<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">125<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">160<\/span><span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token comment\"># \u8bbe\u7f6e\u5b66\u4e60\u7387\u4e0b\u964d\u7b56\u7565<\/span><br \/>\n    scheduler_lr <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>lr_scheduler<span class=\"token punctuation\">.<\/span>MultiStepLR<span class=\"token punctuation\">(<\/span>optimizer<span class=\"token punctuation\">,<\/span> milestones<span class=\"token operator\">&#061;<\/span>milestones<span class=\"token punctuation\">,<\/span> gamma<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    lr_list<span class=\"token punctuation\">,<\/span> epoch_list <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> epoch <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>max_epoch<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        lr_list<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>scheduler_lr<span class=\"token punctuation\">.<\/span>get_last_lr<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        epoch_list<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>epoch<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>iteration<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token operator\">*<\/span>x<span class=\"token operator\">&#8211;<\/span>y_true<span class=\"token punctuation\">)<\/span><span class=\"token operator\">**<\/span><span class=\"token number\">2<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad<\/span><br \/>\n            loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53c2\u6570\u66f4\u65b0<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u66f4\u65b0\u4e0b\u4e00\u4e2aepoch\u7684\u5b66\u4e60\u7387<\/span><br \/>\n        scheduler_lr<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>epoch_list<span class=\"token punctuation\">,<\/span> lr_list<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;Multi Step LR Scheduler\\\\nmilestones:{}&#034;<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">format<\/span><span class=\"token punctuation\">(<\/span>milestones<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Epoch&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Learning rate&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>7.4 \u6309\u6307\u6570\u5b66\u4e60\u7387\u8870\u51cf<\/h4>\n<p>\u6309\u6307\u6570\u8870\u51cf\u8c03\u6574\u5b66\u4e60\u7387\u7684\u6548\u679c\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27sd2lh5gxcnx.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>PyTorch \u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token comment\"># gamma&#xff1a;\u6307\u6570\u7684\u5e95<\/span><br \/>\n<span class=\"token comment\"># \u8c03\u6574\u65b9\u5f0f&#xff1a;lr &#061; lr * gamma^epoch<\/span><br \/>\noptim<span class=\"token punctuation\">.<\/span>lr_scheduler<span class=\"token punctuation\">.<\/span>ExponentialLR<span class=\"token punctuation\">(<\/span>optimizer<span class=\"token punctuation\">,<\/span> gamma<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u5177\u4f53\u4f7f\u7528\u65b9\u5f0f&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch <span class=\"token keyword\">import<\/span> optim<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test_ExponentialLR<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 0. \u53c2\u6570\u521d\u59cb\u5316<\/span><br \/>\n    LR <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.1<\/span>  <span class=\"token comment\"># \u8bbe\u7f6e\u5b66\u4e60\u7387\u521d\u59cb\u5316\u503c\u4e3a0.1<\/span><br \/>\n    iteration <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">10<\/span><br \/>\n    max_epoch <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">200<\/span><br \/>\n    <span class=\"token comment\"># 1. \u521d\u59cb\u5316\u53c2\u6570<\/span><br \/>\n    y_true <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u4f18\u5316\u5668<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>SGD<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>w<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span>LR<span class=\"token punctuation\">,<\/span> momentum<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8bbe\u7f6e\u5b66\u4e60\u7387\u4e0b\u964d\u7b56\u7565<\/span><br \/>\n    gamma <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.95<\/span><br \/>\n    scheduler_lr <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>lr_scheduler<span class=\"token punctuation\">.<\/span>ExponentialLR<span class=\"token punctuation\">(<\/span>optimizer<span class=\"token punctuation\">,<\/span> gamma<span class=\"token operator\">&#061;<\/span>gamma<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u83b7\u53d6\u5b66\u4e60\u7387\u7684\u503c\u548c\u5f53\u524d\u7684epoch<\/span><br \/>\n    lr_list<span class=\"token punctuation\">,<\/span> epoch_list <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> epoch <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>max_epoch<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        lr_list<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>scheduler_lr<span class=\"token punctuation\">.<\/span>get_last_lr<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        epoch_list<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>epoch<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>iteration<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span>  <span class=\"token comment\"># \u904d\u5386\u6bcf\u4e00\u4e2abatch\u6570\u636e<\/span><br \/>\n            loss <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>w<span class=\"token operator\">*<\/span>x<span class=\"token operator\">&#8211;<\/span>y_true<span class=\"token punctuation\">)<\/span><span class=\"token operator\">**<\/span><span class=\"token number\">2<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad<\/span><br \/>\n            loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u66f4\u65b0\u4e0b\u4e00\u4e2aepoch\u7684\u5b66\u4e60\u7387<\/span><br \/>\n        scheduler_lr<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 5. \u7ed8\u5236\u5b66\u4e60\u7387\u53d8\u5316\u7684\u66f2\u7ebf<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>epoch_list<span class=\"token punctuation\">,<\/span> lr_list<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;Multi Step LR Scheduler&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Epoch&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Learning rate&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>7.5 \u5b66\u4e60\u7387\u8870\u51cf\u65b9\u6cd5\u5c0f\u7ed3<\/h4>\n<table>\n<tr>\u65b9\u6cd5\u7b49\u95f4\u9694\u5b66\u4e60\u7387\u8870\u51cf (Step Decay)\u6307\u5b9a\u95f4\u9694\u5b66\u4e60\u7387\u8870\u51cf (Multi Step Decay)\u6307\u6570\u5b66\u4e60\u7387\u8870\u51cf (Exponential Decay)<\/tr>\n<tbody>\n<tr>\n<td>\u8870\u51cf\u65b9\u5f0f<\/td>\n<td>\u56fa\u5b9a\u6b65\u957f\u8870\u51cf<\/td>\n<td>\u6307\u5b9a\u6b65\u957f\u8870\u51cf<\/td>\n<td>\u5e73\u6ed1\u6307\u6570\u8870\u51cf&#xff0c;\u5386\u53f2\u5e73\u5747\u8003\u8651<\/td>\n<\/tr>\n<tr>\n<td>\u5b9e\u73b0\u96be\u5ea6<\/td>\n<td>\u7b80\u5355\u6613\u5b9e\u73b0<\/td>\n<td>\u76f8\u5bf9\u7b80\u5355&#xff0c;\u5bb9\u6613\u8c03\u6574<\/td>\n<td>\u9700\u8981\u989d\u5916\u5386\u53f2\u8ba1\u7b97&#xff0c;\u8f83\u590d\u6742<\/td>\n<\/tr>\n<tr>\n<td>\u9002\u7528\u573a\u666f<\/td>\n<td>\u5927\u578b\u6570\u636e\u96c6\u3001\u8f83\u4e3a\u7b80\u5355\u7684\u4efb\u52a1<\/td>\n<td>\u5bf9\u8bad\u7ec3\u5e73\u7a33\u6027\u8981\u6c42\u8f83\u9ad8\u7684\u4efb\u52a1<\/td>\n<td>\u9ad8\u7cbe\u5ea6\u8bad\u7ec3&#xff0c;\u907f\u514d\u8fc7\u5feb\u6536\u655b<\/td>\n<\/tr>\n<tr>\n<td>\u4f18\u70b9<\/td>\n<td>\u76f4\u89c2&#xff0c;\u6613\u4e8e\u8c03\u8bd5&#xff0c;\u9002\u7528\u4e8e\u5927\u6279\u91cf\u6570\u636e<\/td>\n<td>\u6613\u4e8e\u8c03\u8bd5&#xff0c;\u7a33\u5b9a\u8bad\u7ec3\u8fc7\u7a0b<\/td>\n<td>\u5e73\u6ed1\u4e14\u8003\u8651\u5386\u53f2\u66f4\u65b0&#xff0c;\u6536\u655b\u7a33\u5b9a\u6027\u8f83\u5f3a<\/td>\n<\/tr>\n<tr>\n<td>\u7f3a\u70b9<\/td>\n<td>\u5b66\u4e60\u7387\u53d8\u5316\u8f83\u5927&#xff0c;\u53ef\u80fd\u8df3\u8fc7\u6700\u4f18\u70b9<\/td>\n<td>\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u8870\u51cf\u8fc7\u5feb&#xff0c;\u5bfc\u81f4\u4f18\u5316\u63d0\u524d\u505c\u6ede<\/td>\n<td>\u8d85\u53c2\u6570\u8c03\u8282\u8f83\u4e3a\u590d\u6742&#xff0c;\u53ef\u80fd\u9700\u8981\u66f4\u591a\u7684\u8ba1\u7b97\u8d44\u6e90<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u516b\u3001\u6b63\u5219\u5316\u65b9\u6cd5<\/h3>\n<h4>8.1 \u4ec0\u4e48\u662f\u6b63\u5219\u5316<\/h4>\n<p><img decoding=\"async\" src=\"2026-08-272bmussvi0t4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li>\u5728\u8bbe\u8ba1\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u65f6&#xff0c;\u5e0c\u671b\u5728\u65b0\u6837\u672c\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\u5f3a\u3002\u8bb8\u591a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u90fd\u91c7\u7528\u76f8\u5173\u7684\u7b56\u7565\u6765\u51cf\u5c0f\u6d4b\u8bd5\u8bef\u5dee&#xff0c;\u8fd9\u4e9b\u7b56\u7565\u88ab\u7edf\u79f0\u4e3a\u6b63\u5219\u5316\u3002<\/li>\n<li>\u795e\u7ecf\u7f51\u7edc\u5f3a\u5927\u7684\u8868\u793a\u80fd\u529b\u7ecf\u5e38\u9047\u5230\u8fc7\u62df\u5408&#xff0c;\u6240\u4ee5\u9700\u8981\u4f7f\u7528\u4e0d\u540c\u5f62\u5f0f\u7684\u6b63\u5219\u5316\u7b56\u7565\u3002<\/li>\n<li>\u76ee\u524d\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\u4f7f\u7528\u8f83\u591a\u7684\u7b56\u7565\u6709\u8303\u6570\u60e9\u7f5a\u3001Dropout\u3001\u7279\u6b8a\u7684\u7f51\u7edc\u5c42\u7b49&#xff0c;\u63a5\u4e0b\u6765\u6211\u4eec\u5bf9\u5176\u8fdb\u884c\u8be6\u7ec6\u4ecb\u7ecd\u3002<\/li>\n<\/ul>\n<h4>8.2 Dropout \u6b63\u5219\u5316<\/h4>\n<p>\u5728\u8bad\u7ec3\u6df1\u5c42\u795e\u7ecf\u7f51\u7edc\u65f6&#xff0c;\u7531\u4e8e\u6a21\u578b\u53c2\u6570\u8f83\u591a&#xff0c;\u5728\u6570\u636e\u91cf\u4e0d\u8db3\u7684\u60c5\u51b5\u4e0b&#xff0c;\u5f88\u5bb9\u6613\u8fc7\u62df\u5408\u3002Dropout&#xff08;\u4e2d\u6587\u7ffb\u8bd1\u4e3a\u968f\u673a\u5931\u6d3b&#xff09;\u662f\u4e00\u4e2a\u7b80\u5355\u6709\u6548\u7684\u6b63\u5219\u5316\u65b9\u6cd5\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27nx10pd0zgnd.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li>\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d&#xff0c;Dropout \u7684\u5b9e\u73b0\u662f\u8ba9\u795e\u7ecf\u5143\u4ee5\u8d85\u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>&#xff08;\u4e22\u5f03\u6982\u7387&#xff09;\u7684\u6982\u7387\u505c\u6b62\u5de5\u4f5c\u6216\u8005\u6fc0\u6d3b\u88ab\u7f6e\u4e3a 0&#xff0c;\u672a\u88ab\u7f6e\u4e3a 0 \u7684\u8fdb\u884c\u7f29\u653e&#xff0c;\u7f29\u653e\u6bd4\u4f8b\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\/(1\u2212p)1\/(1-p)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u8bad\u7ec3\u8fc7\u7a0b\u53ef\u4ee5\u8ba4\u4e3a\u662f\u5bf9\u5b8c\u6574\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u4e00\u4e9b\u5b50\u96c6\u8fdb\u884c\u8bad\u7ec3&#xff0c;\u6bcf\u6b21\u57fa\u4e8e\u8f93\u5165\u6570\u636e\u53ea\u66f4\u65b0\u5b50\u7f51\u7edc\u7684\u53c2\u6570\u3002<\/li>\n<li>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d&#xff0c;Dropout \u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u7684\u6982\u7387\u901a\u5e38\u53d6\u503c\u5728 0.2 \u5230 0.5 \u4e4b\u95f4&#xff1a;\n<ul>\n<li>\u5bf9\u4e8e\u8f83\u5c0f\u7684\u6a21\u578b\u6216\u8f83\u590d\u6742\u7684\u4efb\u52a1&#xff0c;\u4e22\u5f03\u7387\u53ef\u4ee5\u9009\u62e9 0.3 \u6216\u66f4\u5c0f<\/li>\n<li>\u5bf9\u4e8e\u975e\u5e38\u6df1\u7684\u7f51\u7edc&#xff0c;\u8f83\u5927\u7684\u4e22\u5f03\u7387&#xff08;\u5982 0.5 \u6216 0.6&#xff09;\u53ef\u80fd\u4f1a\u6709\u6548\u9632\u6b62\u8fc7\u62df\u5408<\/li>\n<li>\u5b9e\u9645\u5e94\u7528\u4e2d&#xff0c;\u901a\u5e38\u4f1a\u5728\u5168\u8fde\u63a5\u5c42&#xff08;\u6fc0\u6d3b\u51fd\u6570\u540e&#xff09;\u4e4b\u540e\u6dfb\u52a0 Dropout \u5c42<\/li>\n<\/ul>\n<\/li>\n<li>\u5728\u6d4b\u8bd5\u8fc7\u7a0b\u4e2d&#xff0c;\u968f\u673a\u5931\u6d3b\u4e0d\u8d77\u4f5c\u7528&#xff1a;\n<ul>\n<li>\u5728\u6d4b\u8bd5\u9636\u6bb5&#xff0c;\u4f7f\u7528\u6240\u6709\u7684\u795e\u7ecf\u5143\u8fdb\u884c\u9884\u6d4b&#xff0c;\u4ee5\u83b7\u5f97\u66f4\u7a33\u5b9a\u7684\u7ed3\u679c<\/li>\n<li>\u76f4\u63a5\u4f7f\u7528\u8bad\u7ec3\u597d\u7684\u6a21\u578b\u8fdb\u884c\u6d4b\u8bd5&#xff0c;\u7531\u4e8e\u6240\u6709\u7684\u795e\u7ecf\u5143\u90fd\u53c2\u4e0e\u8ba1\u7b97&#xff0c;\u8f93\u51fa\u7684\u671f\u671b\u503c\u4f1a\u6bd4\u8bad\u7ec3\u9636\u6bb5\u9ad8\u3002\u6d4b\u8bd5\u9636\u6bb5\u7684\u671f\u671b\u8f93\u51fa\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E[xtest]&#061;xE[x_{test}] &#061; x<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mord mathnormal mtight\">es<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6d4b\u8bd5\/\u63a8\u7406\u6a21\u5f0f&#xff1a;model.eval()<\/li>\n<\/ul>\n<\/li>\n<li>\u7f29\u653e\u7684\u5fc5\u8981\u6027&#xff1a;\n<ul>\n<li>\u5728\u8bad\u7ec3\u9636\u6bb5&#xff0c;\u5c06\u53c2\u4e0e\u8ba1\u7b97\u7684\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u9664\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(1\u2212p)(1-p)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u7ecf\u8fc7 Dropout \u540e\u7684\u671f\u671b\u8f93\u51fa\u53d8\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E[xdropout]&#061;[(1\u2212p)\u22c5x]\/(1\u2212p)&#061;xE[x_{dropout}] &#061; [(1-p) \\\\cdot x] \/ (1-p) &#061; x<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">]<\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e0e\u6d4b\u8bd5\u9636\u6bb5\u7684\u671f\u671b\u8f93\u51fa\u4e00\u81f4<\/li>\n<li>\u8bad\u7ec3\u6a21\u5f0f&#xff1a;model.train()<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u89c2\u5bdf Dropout \u6548\u679c\u7684\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u968f\u673a\u5931\u6d3b\u5c42<\/span><br \/>\n    dropout <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Dropout<span class=\"token punctuation\">(<\/span>p<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.4<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u8f93\u5165\u6570\u636e&#xff1a;\u8868\u793a\u67d0\u4e00\u5c42\u7684 weight \u4fe1\u606f<\/span><br \/>\n    inputs <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randint<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    layer <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    y <span class=\"token operator\">&#061;<\/span> layer<span class=\"token punctuation\">(<\/span>inputs<span class=\"token punctuation\">)<\/span><br \/>\n    y <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u672a\u5931\u6d3bFC\u5c42\u7684\u8f93\u51fa\u7ed3\u679c&#xff1a;\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\n    y <span class=\"token operator\">&#061;<\/span> dropout<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u5931\u6d3b\u540eFC\u5c42\u7684\u8f93\u51fa\u7ed3\u679c&#xff1a;\\\\n&#034;<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8f93\u51fa\u7ed3\u679c&#xff1a;<\/p>\n<p>\u672a\u5931\u6d3bFC\u5c42\u7684\u8f93\u51fa\u7ed3\u679c&#xff1a;<br \/>\n tensor([[0.0000, 1.8033, 1.4608, 4.5189, 6.9116]], grad_fn&#061;&lt;ReluBackward0&gt;)<br \/>\n\u5931\u6d3b\u540eFC\u5c42\u7684\u8f93\u51fa\u7ed3\u679c&#xff1a;<br \/>\n tensor([[0.0000,  3.0055,  2.4346,  7.5315, 11.5193]], grad_fn&#061;&lt;MulBackward0&gt;)<\/p>\n<p>\u4e0a\u8ff0\u4ee3\u7801\u5c06 Dropout \u5c42\u7684\u4e22\u5f03\u6982\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u8bbe\u7f6e\u4e3a 0.4&#xff0c;\u6b64\u65f6\u7ecf\u8fc7 Dropout \u5c42\u8ba1\u7b97\u7684\u5f20\u91cf\u4e2d\u51fa\u73b0\u4e86\u5f88\u591a 0&#xff0c;\u672a\u53d8\u4e3a 0 \u7684\u6309\u7167 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\/(1\u22120.4)1\/(1-0.4)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0.4<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u4e86\u7f29\u653e\u5904\u7406\u3002<\/p>\n<h4>8.3 \u6279\u91cf\u5f52\u4e00\u5316&#xff08;Batch Normalization&#xff09;<\/h4>\n<p>\u5728\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e2d&#xff0c;\u6d41\u7ecf\u7f51\u7edc\u7684\u6570\u636e\u90fd\u662f\u4e00\u4e2a batch&#xff0c;\u6bcf\u4e2a batch \u4e4b\u95f4\u7684\u6570\u636e\u5206\u5e03\u53d8\u5316\u975e\u5e38\u5267\u70c8&#xff0c;\u8fd9\u5c31\u4f7f\u5f97\u7f51\u7edc\u53c2\u6570\u9891\u7e41\u5730\u8fdb\u884c\u5927\u7684\u8c03\u6574\u4ee5\u9002\u5e94\u6d41\u7ecf\u7f51\u7edc\u7684\u4e0d\u540c\u5206\u5e03\u7684\u6570\u636e&#xff0c;\u7ed9\u6a21\u578b\u8bad\u7ec3\u5e26\u6765\u975e\u5e38\u5927\u7684\u4e0d\u7a33\u5b9a\u6027&#xff0c;\u4f7f\u5f97\u6a21\u578b\u96be\u4ee5\u6536\u655b\u3002\u5982\u679c\u6211\u4eec\u5bf9\u6bcf\u4e00\u4e2a batch \u7684\u6570\u636e\u8fdb\u884c\u6807\u51c6\u5316\u4e4b\u540e&#xff0c;\u6570\u636e\u5206\u5e03\u5c31\u53d8\u5f97\u7a33\u5b9a&#xff0c;\u53c2\u6570\u7684\u68af\u5ea6\u53d8\u5316\u4e5f\u53d8\u5f97\u7a33\u5b9a&#xff0c;\u6709\u52a9\u4e8e\u52a0\u5feb\u6a21\u578b\u7684\u6536\u655b\u3002<\/p>\n<p>\u901a\u8fc7\u6807\u51c6\u5316\u6bcf\u4e00\u5c42\u7684\u8f93\u5165&#xff0c;\u4f7f\u5176\u5747\u503c\u63a5\u8fd1 0&#xff0c;\u65b9\u5dee\u63a5\u8fd1 1&#xff0c;\u4ece\u800c\u52a0\u901f\u8bad\u7ec3\u5e76\u63d0\u9ad8\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27fknolwbntak.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5148\u5bf9\u6570\u636e\u6807\u51c6\u5316&#xff0c;\u518d\u5bf9\u6570\u636e\u91cd\u6784&#xff08;\u7f29\u653e &#043; \u5e73\u79fb&#xff09;&#xff0c;\u5199\u6210\u516c\u5f0f\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27g2vjf1lzql5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb\\\\lambda<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u662f\u53ef\u5b66\u4e60\u7684\u53c2\u6570&#xff0c;\u76f8\u5f53\u4e8e\u5bf9\u6807\u51c6\u5316\u540e\u7684\u503c\u505a\u4e86\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb\\\\lambda<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7cfb\u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u4e3a\u504f\u7f6e<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03f5\\\\epsilon<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">\u03f5<\/span><\/span><\/span><\/span><\/span> \u901a\u5e38\u53d6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1e\u221251e-5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u907f\u514d\u5206\u6bcd\u4e3a 0<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E(x)E(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u53d8\u91cf\u7684\u5747\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Var(x)Var(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u53d8\u91cf\u7684\u65b9\u5dee<\/li>\n<\/ul>\n<p>\u6279\u91cf\u5f52\u4e00\u5316\u7684\u6b65\u9aa4\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27vsixynkasns.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u6279\u91cf\u5f52\u4e00\u5316\u7684\u4f5c\u7528&#xff1a;<\/p>\n<ul>\n<li>\u51cf\u5c11\u5185\u90e8\u534f\u65b9\u5dee\u504f\u79fb&#xff1a;\u901a\u8fc7\u5bf9\u6bcf\u5c42\u7684\u8f93\u5165\u8fdb\u884c\u6807\u51c6\u5316&#xff0c;\u51cf\u5c11\u4e86\u8f93\u5165\u6570\u636e\u5206\u5e03\u7684\u53d8\u5316&#xff0c;\u4ece\u800c\u52a0\u901f\u4e86\u8bad\u7ec3\u8fc7\u7a0b&#xff0c;\u5e76\u4f7f\u5f97\u7f51\u7edc\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u66f4\u52a0\u7a33\u5b9a\u3002<\/li>\n<li>\u52a0\u901f\u8bad\u7ec3&#xff1a;\n<ul>\n<li>\u5728\u6ca1\u6709\u6279\u91cf\u5f52\u4e00\u5316\u7684\u60c5\u51b5\u4e0b&#xff0c;\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u901a\u5e38\u4f1a\u5f88\u6162&#xff0c;\u5c24\u5176\u662f\u6df1\u5ea6\u7f51\u7edc\u3002\u56e0\u4e3a\u5728\u6bcf\u5c42\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e2d&#xff0c;\u8f93\u5165\u6570\u636e\u7684\u5206\u5e03&#xff08;\u7279\u522b\u662f\u524d\u51e0\u5c42&#xff09;\u4f1a\u4e0d\u65ad\u53d8\u5316&#xff0c;\u8fd9\u4f1a\u5bfc\u81f4\u7f51\u7edc\u5b66\u4e60\u901f\u5ea6\u7f13\u6162\u3002<\/li>\n<li>\u6279\u91cf\u5f52\u4e00\u5316\u901a\u8fc7\u786e\u4fdd\u6bcf\u5c42\u7684\u8f93\u5165\u6570\u636e\u5728\u8bad\u7ec3\u65f6\u5206\u5e03\u7a33\u5b9a&#xff0c;\u6709\u6548\u51cf\u5c11\u4e86\u8fd9\u79cd\u53d8\u5316&#xff0c;\u4ece\u800c\u52a0\u901f\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u8d77\u5230\u6b63\u5219\u5316\u4f5c\u7528&#xff1a;\u6279\u91cf\u5f52\u4e00\u5316\u53ef\u4ee5\u89c6\u4f5c\u4e00\u79cd\u6b63\u5219\u5316\u65b9\u6cd5&#xff0c;\u56e0\u4e3a\u5b83\u5f15\u5165\u4e86\u5bf9\u8bad\u7ec3\u6837\u672c\u7684\u566a\u58f0&#xff08;\u4e0d\u540c\u6279\u6b21\u7684\u7edf\u8ba1\u4fe1\u606f\u4e0d\u540c&#xff0c;\u6279\u6b21\u8f83\u5c0f\u7684\u5747\u503c\u548c\u65b9\u5dee\u4f30\u8ba1\u4f1a\u66f4\u52a0\u4e0d\u51c6\u786e&#xff09;&#xff0c;\u4f7f\u5f97\u6a21\u578b\u4e0d\u5bb9\u6613\u4f9d\u8d56\u7279\u5b9a\u7684\u8f93\u5165\u7279\u5f81&#xff0c;\u4ece\u800c\u8d77\u5230\u4e00\u5b9a\u7684\u6b63\u5219\u5316\u6548\u679c&#xff0c;\u51cf\u5c11\u4e86\u5bf9\u5176\u4ed6\u6b63\u5219\u5316\u6280\u672f&#xff08;\u5982 Dropout&#xff09;\u7684\u9700\u6c42\u3002<\/li>\n<li>\u63d0\u5347\u6cdb\u5316\u80fd\u529b&#xff1a;\u7531\u4e8e\u5176\u6b63\u5219\u5316\u6548\u679c&#xff0c;\u6279\u91cf\u5f52\u4e00\u5316\u80fd\u5e2e\u52a9\u7f51\u7edc\u5728\u6d4b\u8bd5\u96c6\u4e0a\u53d6\u5f97\u66f4\u597d\u7684\u6027\u80fd\u3002<\/li>\n<\/ul>\n<p>\u6279\u91cf\u5f52\u4e00\u5316\u5c42\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\u4f7f\u7528\u8f83\u591a<\/p>\n<p>Batch Normalization \u7684\u4f7f\u7528\u6b65\u9aa4&#xff1a;<\/p>\n<li>\u5728\u7f51\u7edc\u5c42\u540e\u6dfb\u52a0 BN \u5c42&#xff1a;\n<ul>\n<li>\u901a\u5e38&#xff0c;BN \u5c42\u4f1a\u6dfb\u52a0\u5728\u5377\u79ef\u5c42 (Conv2d) \u6216\u5168\u8fde\u63a5\u5c42 (Linear) \u4e4b\u540e&#xff0c;\u6fc0\u6d3b\u51fd\u6570\u4e4b\u524d\u3002<\/li>\n<li>\u4f8b\u5982&#xff1a;Conv2d \u2192 BN \u2192 ReLU \u6216\u8005 Linear \u2192 BN \u2192 ReLU\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u8bad\u7ec3\u65f6&#xff1a;model.train()\n<ul>\n<li>BN \u5c42\u4f1a\u8ba1\u7b97\u5f53\u524d\u6279\u6b21\u7684\u5747\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bc\\\\mu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03bc<\/span><\/span><\/span><\/span><\/span> \u548c\u65b9\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c32\\\\sigma^2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u7136\u540e&#xff0c;\u5229\u7528\u8fd9\u4e24\u4e2a\u7edf\u8ba1\u91cf\u5bf9\u5f53\u524d\u6279\u6b21\u7684\u6570\u636e\u8fdb\u884c\u89c4\u8303\u5316\u3002<\/li>\n<li>\u89c4\u8303\u5316\u540e\u7684\u6570\u636e\u4f1a\u88ab\u7f29\u653e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b3\\\\gamma<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><\/span><\/span><\/span><\/span> \u548c\u5e73\u79fb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u540c\u65f6&#xff0c;BN \u5c42\u8fd8\u4f1a\u7ef4\u62a4\u4e00\u4e2a\u5168\u5c40\u5747\u503c\u548c\u5168\u5c40\u65b9\u5dee\u7684\u79fb\u52a8\u5e73\u5747\u503c&#xff0c;\u7528\u4e8e\u63a8\u7406\u9636\u6bb5\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u63a8\u7406\u65f6&#xff1a;model.eval()\n<ul>\n<li>\u63a8\u7406\u65f6&#xff0c;\u4e0d\u4f1a\u518d\u4f7f\u7528\u5f53\u524d\u6279\u6b21\u7684\u5747\u503c\u548c\u65b9\u5dee&#xff0c;\u800c\u662f\u4f7f\u7528\u8bad\u7ec3\u9636\u6bb5\u8ba1\u7b97\u7684\u5168\u5c40\u5747\u503c\u548c\u5168\u5c40\u65b9\u5dee\u3002<\/li>\n<li>\u540c\u6837&#xff0c;\u89c4\u8303\u5316\u540e\u7684\u6570\u636e\u4f1a\u88ab\u7f29\u653e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b3\\\\gamma<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><\/span><\/span><\/span><\/span> \u548c\u5e73\u79fb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b2\\\\beta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n<p>PyTorch \u5b9e\u73b0\u6279\u91cf\u5f52\u4e00\u5316\u7684\u4ee3\u7801\u793a\u4f8b&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token triple-quoted-string string\">&#034;&#034;&#034;<br \/>\nBatchNorm1d&#xff1a;\u4e3b\u8981\u5e94\u7528\u4e8e\u5168\u8fde\u63a5\u5c42\u6216\u5904\u7406\u4e00\u7ef4\u6570\u636e\u7684\u7f51\u7edc&#xff0c;\u4f8b\u5982\u6587\u672c\u5904\u7406\u3002\u5b83\u63a5\u6536\u5f62\u72b6\u4e3a (N, num_features) \u7684\u5f20\u91cf\u4f5c\u4e3a\u8f93\u5165\u3002<br \/>\nBatchNorm2d&#xff1a;\u4e3b\u8981\u5e94\u7528\u4e8e\u5377\u79ef\u795e\u7ecf\u7f51\u7edc&#xff0c;\u5904\u7406\u4e8c\u7ef4\u56fe\u50cf\u6570\u636e\u6216\u7279\u5f81\u56fe\u3002\u5b83\u63a5\u6536\u5f62\u72b6\u4e3a (N, C, H, W) \u7684\u5f20\u91cf\u4f5c\u4e3a\u8f93\u5165\u3002<br \/>\nBatchNorm3d&#xff1a;\u4e3b\u8981\u7528\u4e8e\u4e09\u7ef4\u5377\u79ef\u795e\u7ecf\u7f51\u7edc (3D CNN)&#xff0c;\u5904\u7406\u4e09\u7ef4\u6570\u636e&#xff0c;\u4f8b\u5982\u89c6\u9891\u6216\u533b\u5b66\u56fe\u50cf\u3002\u5b83\u63a5\u6536\u5f62\u72b6\u4e3a (N, C, D, H, W) \u7684\u5f20\u91cf\u4f5c\u4e3a\u8f93\u5165\u3002<br \/>\n&#034;&#034;&#034;<\/span><\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test01<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u521b\u5efa\u6d4b\u8bd5\u6837\u672c&#xff0c;\u5047\u8bbe\u662f\u7ecf\u8fc7\u5377\u79ef\u5c42 (Conv2d) \u5904\u7406\u540e\u7684\u7279\u5f81\u56fe<\/span><br \/>\n    <span class=\"token comment\"># (N, C, H, W): \u4e00\u5f20\u56fe&#xff0c;\u4e24\u4e2a\u901a\u9053&#xff0c;\u6bcf\u4e2a\u901a\u90533\u884c4\u5217<\/span><br \/>\n    <span class=\"token comment\"># \u53ef\u4ee5\u521b\u5efa1\u4e2a\u6837\u672c&#xff0c;\u56fe\u50cf\u7684BN\u662f\u5bf9\u6bcf\u4e2a\u901a\u9053\u7684\u7279\u5f81\u56fe&#xff08;\u884c\u5217\u6570\u636e&#xff09;\u8fdb\u884c\u6807\u51c6\u5316<\/span><br \/>\n    input_2d <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;input&#8211;&gt;&#034;<\/span><span class=\"token punctuation\">,<\/span> input_2d<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># num_features&#xff1a;\u8f93\u5165\u7279\u5f81\u6570<\/span><br \/>\n    <span class=\"token comment\"># eps&#xff1a;\u975e\u5e38\u5c0f\u7684\u6d6e\u70b9\u6570&#xff0c;\u9632\u6b62\u9664\u4ee50\u7684\u9519\u8bef<\/span><br \/>\n    <span class=\"token comment\"># momentum&#xff1a;\u52a8\u91cf\u7cfb\u6570<\/span><br \/>\n    <span class=\"token comment\"># affine&#xff1a;\u9ed8\u8ba4\u4e3aTrue&#xff0c;\u03b3\u548c\u03b2\u88ab\u4f7f\u7528&#xff0c;\u8ba9BN\u5c42\u66f4\u52a0\u7075\u6d3b<\/span><br \/>\n    bn2d <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>BatchNorm2d<span class=\"token punctuation\">(<\/span>num_features<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> eps<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e-05<\/span><span class=\"token punctuation\">,<\/span> momentum<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> affine<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    output <span class=\"token operator\">&#061;<\/span> bn2d<span class=\"token punctuation\">(<\/span>input_2d<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;output&#8211;&gt;&#034;<\/span><span class=\"token punctuation\">,<\/span> output<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>bn2d<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>bn2d<span class=\"token punctuation\">.<\/span>bias<span class=\"token punctuation\">)<\/span>  <\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test02<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u521b\u5efa\u6d4b\u8bd5\u6837\u672c<\/span><br \/>\n    <span class=\"token comment\"># 2\u4e2a\u6837\u672c&#xff0c;1\u4e2a\u7279\u5f81<\/span><br \/>\n    <span class=\"token comment\"># \u4e0d\u80fd\u521b\u5efa1\u4e2a\u6837\u672c&#xff0c;\u65e0\u6cd5\u7edf\u8ba1\u5747\u503c\u548c\u65b9\u5dee<\/span><br \/>\n    input_1d <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521b\u5efa\u7ebf\u6027\u5c42\u5bf9\u8c61<\/span><br \/>\n    linear1 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>in_features<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> out_features<span class=\"token operator\">&#061;<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521b\u5efaBN\u5c42\u5bf9\u8c61<\/span><br \/>\n    <span class=\"token comment\"># num_features&#xff1a;\u8f93\u5165\u7279\u5f81\u6570<\/span><br \/>\n    bn1d <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>BatchNorm1d<span class=\"token punctuation\">(<\/span>num_features<span class=\"token operator\">&#061;<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    output_1d <span class=\"token operator\">&#061;<\/span> linear1<span class=\"token punctuation\">(<\/span>input_1d<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8fdb\u884c\u6279\u91cf\u5f52\u4e00\u5316<\/span><br \/>\n    output <span class=\"token operator\">&#061;<\/span> bn1d<span class=\"token punctuation\">(<\/span>output_1d<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;output&#8211;&gt;&#034;<\/span><span class=\"token punctuation\">,<\/span> output<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8f93\u51fa\u7ed3\u679c&#xff1a;<\/p>\n<p>test01:<br \/>\ninput_2d&#8211;&gt; tensor([[[[-0.2751, -1.2183, -0.5106, -0.1540],<br \/>\n          [-0.4585, -0.5989, -0.6063,  0.5986],<br \/>\n          [-0.4745,  0.1496, -1.1266, -1.2377]],<\/p>\n<p>         [[ 0.2580,  1.2065,  1.4598,  0.8387],<br \/>\n          [-0.4586,  0.8938, -0.3328,  0.1192],<br \/>\n          [-0.3265, -0.6263,  0.0419, -1.2231]]]])<br \/>\noutput&#8211;&gt; tensor([[[[ 0.4164, -1.3889, -0.0343,  0.6484],<br \/>\n          [ 0.0655, -0.2032, -0.2175,  2.0889],<br \/>\n          [ 0.0349,  1.2294, -1.2134, -1.4262]],<\/p>\n<p>         [[ 0.1340,  1.3582,  1.6853,  0.8835],<br \/>\n          [-0.7910,  0.9546, -0.6287, -0.0452],<br \/>\n          [-0.6205, -1.0075, -0.1449, -1.7779]]]],<br \/>\n       grad_fn&#061;&lt;NativeBatchNormBackward0&gt;)<br \/>\ntorch.Size([1, 2, 3, 4])<br \/>\nParameter containing:<br \/>\ntensor([1., 1.], requires_grad&#061;True)<br \/>\nParameter containing:<br \/>\ntensor([0., 0.], requires_grad&#061;True)<\/p>\n<p>test02:<br \/>\noutput&#8211;&gt; tensor([[-0.9998,  1.0000,  1.0000],<br \/>\n        [ 0.9998, -1.0000, -1.0000]], grad_fn&#061;&lt;NativeBatchNormBackward0&gt;)<br \/>\ntorch.Size([2, 3])<\/p>\n<hr \/>\n<h3>\u4e5d\u3001\u624b\u673a\u4ef7\u683c\u5206\u7c7b\u6848\u4f8b<\/h3>\n<h4>9.1 \u6848\u4f8b\u9700\u6c42\u5206\u6790<\/h4>\n<p>\u5c0f\u660e\u521b\u529e\u4e86\u4e00\u5bb6\u624b\u673a\u516c\u53f8&#xff0c;\u4ed6\u4e0d\u77e5\u9053\u5982\u4f55\u4f30\u7b97\u624b\u673a\u4ea7\u54c1\u7684\u4ef7\u683c\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u4ed6\u6536\u96c6\u4e86\u591a\u5bb6\u516c\u53f8\u7684\u624b\u673a\u9500\u552e\u6570\u636e\u3002\u8be5\u6570\u636e\u4e3a\u4e8c\u624b\u624b\u673a\u7684\u5404\u4e2a\u6027\u80fd\u7684\u6570\u636e&#xff0c;\u6700\u540e\u6839\u636e\u8fd9\u4e9b\u6027\u80fd\u5f97\u5230 4 \u4e2a\u4ef7\u683c\u533a\u95f4&#xff0c;\u4f5c\u4e3a\u8fd9\u4e9b\u4e8c\u624b\u624b\u673a\u552e\u51fa\u7684\u4ef7\u683c\u533a\u95f4\u3002\u4e3b\u8981\u5305\u62ec&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"2026-08-27fufnvi2jw04.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u6211\u4eec\u9700\u8981\u5e2e\u52a9\u5c0f\u660e\u627e\u51fa\u624b\u673a\u7684\u529f\u80fd&#xff08;\u4f8b\u5982&#xff1a;RAM \u7b49&#xff09;\u4e0e\u5176\u552e\u4ef7\u4e4b\u95f4\u7684\u67d0\u79cd\u5173\u7cfb\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u4e5f\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u5168\u8fde\u63a5\u7684\u7f51\u7edc\u3002<\/p>\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f&#xff1a;\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d&#xff0c;\u6211\u4eec\u4e0d\u9700\u8981\u9884\u6d4b\u5b9e\u9645\u4ef7\u683c&#xff0c;\u800c\u662f\u4e00\u4e2a\u4ef7\u683c\u8303\u56f4&#xff0c;\u5b83\u7684\u8303\u56f4\u4f7f\u7528 0\u30011\u30012\u30013 \u6765\u8868\u793a&#xff0c;\u6240\u4ee5\u8be5\u95ee\u9898\u4e5f\u662f\u4e00\u4e2a\u5206\u7c7b\u95ee\u9898\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u8fd8\u662f\u6309\u7167\u56db\u4e2a\u6b65\u9aa4\u6765\u5b8c\u6210\u8fd9\u4e2a\u4efb\u52a1&#xff1a;<\/p>\n<li>\u51c6\u5907\u8bad\u7ec3\u96c6\u6570\u636e<\/li>\n<li>\u6784\u5efa\u8981\u4f7f\u7528\u7684\u6a21\u578b<\/li>\n<li>\u6a21\u578b\u8bad\u7ec3<\/li>\n<li>\u6a21\u578b\u9884\u6d4b\u8bc4\u4f30<\/li>\n<h4>9.2 \u6784\u5efa\u6570\u636e\u96c6<\/h4>\n<p>\u6570\u636e\u5171\u6709 2000 \u6761&#xff0c;\u5176\u4e2d 1600 \u6761\u6570\u636e\u4f5c\u4e3a\u8bad\u7ec3\u96c6&#xff0c;400 \u6761\u6570\u636e\u7528\u4f5c\u6d4b\u8bd5\u96c6\u3002\u6211\u4eec\u4f7f\u7528 sklearn \u7684\u6570\u636e\u96c6\u5212\u5206\u5de5\u4f5c\u6765\u5b8c\u6210&#xff0c;\u5e76\u4f7f\u7528 PyTorch \u7684 TensorDataset \u6765\u5c06\u6570\u636e\u96c6\u6784\u5efa\u4e3a Dataset \u5bf9\u8c61&#xff0c;\u65b9\u4fbf\u6784\u9020\u6570\u636e\u96c6\u52a0\u8f7d\u5bf9\u8c61\u3002<\/p>\n<p><span class=\"token comment\"># \u5bfc\u5165\u76f8\u5173\u6a21\u5757<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torch<span class=\"token punctuation\">.<\/span>utils<span class=\"token punctuation\">.<\/span>data <span class=\"token keyword\">import<\/span> TensorDataset<br \/>\n<span class=\"token keyword\">from<\/span> torch<span class=\"token punctuation\">.<\/span>utils<span class=\"token punctuation\">.<\/span>data <span class=\"token keyword\">import<\/span> DataLoader<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<br \/>\n<span class=\"token keyword\">from<\/span> torchsummary <span class=\"token keyword\">import<\/span> summary<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>optim <span class=\"token keyword\">as<\/span> optim<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> pandas <span class=\"token keyword\">as<\/span> pd<br \/>\n<span class=\"token keyword\">import<\/span> time<\/p>\n<p><span class=\"token comment\"># \u6784\u5efa\u6570\u636e\u96c6<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">create_dataset<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u4f7f\u7528pandas\u8bfb\u53d6\u6570\u636e<\/span><br \/>\n    data <span class=\"token operator\">&#061;<\/span> pd<span class=\"token punctuation\">.<\/span>read_csv<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;data\/\u624b\u673a\u4ef7\u683c\u9884\u6d4b.csv&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u7279\u5f81\u503c\u548c\u76ee\u6807\u503c<\/span><br \/>\n    x<span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> data<span class=\"token punctuation\">.<\/span>iloc<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> data<span class=\"token punctuation\">.<\/span>iloc<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token comment\"># \u7c7b\u578b\u8f6c\u6362&#xff1a;\u7279\u5f81\u503c<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>astype<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6570\u636e\u96c6\u5212\u5206<\/span><br \/>\n    x_train<span class=\"token punctuation\">,<\/span> x_valid<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> y_valid <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> train_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.8<\/span><span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">88<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6784\u5efa\u6570\u636e\u96c6&#xff0c;\u8f6c\u6362\u4e3a pytorch \u7684\u5f62\u5f0f<\/span><br \/>\n    train_dataset <span class=\"token operator\">&#061;<\/span> TensorDataset<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>from_numpy<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">.<\/span>values<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>y_train<span class=\"token punctuation\">.<\/span>values<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    valid_dataset <span class=\"token operator\">&#061;<\/span> TensorDataset<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>from_numpy<span class=\"token punctuation\">(<\/span>x_valid<span class=\"token punctuation\">.<\/span>values<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>y_valid<span class=\"token punctuation\">.<\/span>values<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8fd4\u56de\u7ed3\u679c<\/span><br \/>\n    <span class=\"token comment\"># x_train.shape[1]: \u7279\u5f81\u6570<\/span><br \/>\n    <span class=\"token comment\"># len(np.unique(y)): \u7c7b\u522b\u6570<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> x_train<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span>unique<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u83b7\u53d6\u6570\u636e<\/span><br \/>\n    train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num <span class=\"token operator\">&#061;<\/span> create_dataset<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u8f93\u5165\u7279\u5f81\u6570&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u5206\u7c7b\u4e2a\u6570&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8f93\u51fa\u7ed3\u679c&#xff1a;<\/p>\n<p>\u8f93\u5165\u7279\u5f81\u6570&#xff1a; 20<br \/>\n\u5206\u7c7b\u4e2a\u6570&#xff1a; 4<\/p>\n<h4>9.3 \u6784\u5efa\u5206\u7c7b\u7f51\u7edc\u6a21\u578b<\/h4>\n<p>\u6784\u5efa\u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc\u6765\u8fdb\u884c\u624b\u673a\u4ef7\u683c\u5206\u7c7b&#xff0c;\u8be5\u7f51\u7edc\u4e3b\u8981\u7531\u4e09\u4e2a\u7ebf\u6027\u5c42\u6765\u6784\u5efa&#xff0c;\u4f7f\u7528 ReLU \u6fc0\u6d3b\u51fd\u6570\u3002<\/p>\n<p>\u7f51\u7edc\u5171\u6709 3 \u4e2a\u5168\u8fde\u63a5\u5c42&#xff0c;\u5177\u4f53\u4fe1\u606f\u5982\u4e0b&#xff1a;<\/p>\n<ul>\n<li>\u7b2c\u4e00\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 20&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 128<\/li>\n<li>\u7b2c\u4e8c\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 128&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 256<\/li>\n<li>\u7b2c\u4e09\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 256&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 4<\/li>\n<\/ul>\n<p><span class=\"token comment\"># \u6784\u5efa\u7f51\u7edc\u6a21\u578b<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">PhonePriceModel<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> output_dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span>PhonePriceModel<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 1. \u7b2c\u4e00\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 20&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 128<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear1 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 2. \u7b2c\u4e8c\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 128&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 256<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear2 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">256<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 3. \u7b2c\u4e09\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 256&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 4<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear3 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">256<\/span><span class=\"token punctuation\">,<\/span> output_dim<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u524d\u5411\u4f20\u64ad\u8fc7\u7a0b<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear1<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear2<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u540e\u7eed CrossEntropyLoss \u635f\u5931\u51fd\u6570\u4e2d\u5305\u542b softmax \u8fc7\u7a0b&#xff0c;\u6240\u4ee5\u5f53\u524d\u6b65\u9aa4\u4e0d\u8fdb\u884c softmax \u64cd\u4f5c<\/span><br \/>\n        output <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>linear3<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u83b7\u53d6\u6570\u636e\u7ed3\u679c<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> output<\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num <span class=\"token operator\">&#061;<\/span> create_dataset<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6a21\u578b\u5b9e\u4f8b\u5316<\/span><br \/>\n    model <span class=\"token operator\">&#061;<\/span> PhonePriceModel<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><br \/>\n    summary<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">,<\/span> input_size<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">16<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"2026-08-272s0g3e25pzc.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>9.4 \u6a21\u578b\u8bad\u7ec3<\/h4>\n<p>\u7f51\u7edc\u7f16\u5199\u5b8c\u6210\u4e4b\u540e&#xff0c;\u6211\u4eec\u9700\u8981\u7f16\u5199\u8bad\u7ec3\u51fd\u6570\u3002\u6240\u8c13\u7684\u8bad\u7ec3\u51fd\u6570&#xff0c;\u6307\u7684\u662f\u8f93\u5165\u6570\u636e\u8bfb\u53d6\u3001\u9001\u5165\u7f51\u7edc\u3001\u8ba1\u7b97\u635f\u5931\u3001\u66f4\u65b0\u53c2\u6570\u7684\u6d41\u7a0b&#xff0c;\u8be5\u6d41\u7a0b\u8f83\u4e3a\u56fa\u5b9a\u3002\u6211\u4eec\u4f7f\u7528\u591a\u5206\u7c7b\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570\u3001\u4f7f\u7528 SGD \u4f18\u5316\u65b9\u6cd5\u3002\u6700\u7ec8&#xff0c;\u5c06\u8bad\u7ec3\u597d\u7684\u6a21\u578b\u6301\u4e45\u5316\u5230\u78c1\u76d8\u4e2d\u3002<\/p>\n<p><span class=\"token comment\"># \u6a21\u578b\u8bad\u7ec3\u8fc7\u7a0b<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">train<\/span><span class=\"token punctuation\">(<\/span>train_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u56fa\u5b9a\u968f\u673a\u6570\u79cd\u5b50<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u6570\u636e\u52a0\u8f7d\u5668<\/span><br \/>\n    dataloader <span class=\"token operator\">&#061;<\/span> DataLoader<span class=\"token punctuation\">(<\/span>train_dataset<span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u6a21\u578b<\/span><br \/>\n    model <span class=\"token operator\">&#061;<\/span> PhonePriceModel<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u635f\u5931\u51fd\u6570 CrossEntropyLoss &#061; softmax &#043; \u635f\u5931\u8ba1\u7b97<\/span><br \/>\n    criterion <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>CrossEntropyLoss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4f18\u5316\u65b9\u6cd5<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>SGD<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e-3<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8bad\u7ec3\u8f6e\u6570<\/span><br \/>\n    num_epoch <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">50<\/span><br \/>\n    <span class=\"token comment\"># \u904d\u5386\u6bcf\u4e2a\u8f6e\u6b21\u7684\u6570\u636e<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> epoch_idx <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>num_epoch<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u8bad\u7ec3\u65f6\u95f4<\/span><br \/>\n        start <span class=\"token operator\">&#061;<\/span> time<span class=\"token punctuation\">.<\/span>time<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n        total_loss <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.0<\/span><br \/>\n        total_num <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n        <span class=\"token comment\"># \u904d\u5386\u6bcf\u4e2a batch \u6570\u636e\u8fdb\u884c\u5904\u7406<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> x<span class=\"token punctuation\">,<\/span> y <span class=\"token keyword\">in<\/span> dataloader<span class=\"token punctuation\">:<\/span><br \/>\n            <span class=\"token comment\"># \u5c06\u6570\u636e\u9001\u5165\u7f51\u7edc\u4e2d\u8fdb\u884c\u9884\u6d4b<\/span><br \/>\n            model<span class=\"token punctuation\">.<\/span>train<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4f7f\u7528\u8bad\u7ec3\u6a21\u5f0f<\/span><br \/>\n            output <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n            loss <span class=\"token operator\">&#061;<\/span> criterion<span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u68af\u5ea6\u6e05\u96f6<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad<\/span><br \/>\n            loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53c2\u6570\u66f4\u65b0<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u635f\u5931\u8ba1\u7b97<\/span><br \/>\n            total_num <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token number\">1<\/span><br \/>\n            total_loss <span class=\"token operator\">&#043;&#061;<\/span> loss<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u6253\u5370\u635f\u5931\u53d8\u6362\u7ed3\u679c<\/span><br \/>\n        <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;epoch: %4s loss: %.2f, time: %.2fs&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>epoch_idx <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> total_loss <span class=\"token operator\">\/<\/span> total_num<span class=\"token punctuation\">,<\/span> time<span class=\"token punctuation\">.<\/span>time<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> start<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6a21\u578b\u4fdd\u5b58<\/span><br \/>\n    <span class=\"token comment\"># state_dict(): \u5c06\u6a21\u578b\u7684\u53c2\u6570\u4fdd\u5b58\u5230\u5b57\u5178\u4e2d<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>save<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>state_dict<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;model\/phone-price-model.pth&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u83b7\u53d6\u6570\u636e<\/span><br \/>\n    train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num <span class=\"token operator\">&#061;<\/span> create_dataset<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6a21\u578b\u8bad\u7ec3\u8fc7\u7a0b<\/span><br \/>\n    train<span class=\"token punctuation\">(<\/span>train_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"2026-08-27jyd4kqbhjux.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>9.5 \u6a21\u578b\u8bc4\u4f30<\/h4>\n<p>\u4f7f\u7528\u8bad\u7ec3\u597d\u7684\u6a21\u578b&#xff0c;\u5bf9\u672a\u77e5\u7684\u6837\u672c\u8fdb\u884c\u9884\u6d4b\u3002\u6211\u4eec\u8fd9\u91cc\u4f7f\u7528\u524d\u9762\u5355\u72ec\u5212\u5206\u51fa\u6765\u7684\u9a8c\u8bc1\u96c6\u6765\u8fdb\u884c\u8bc4\u4f30\u3002<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test<\/span><span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u52a0\u8f7d\u6a21\u578b\u548c\u8bad\u7ec3\u597d\u7684\u7f51\u7edc\u53c2\u6570<\/span><br \/>\n    model <span class=\"token operator\">&#061;<\/span> PhonePriceModel<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># load_state_dict: \u5c06\u52a0\u8f7d\u7684\u53c2\u6570\u5b57\u5178\u5e94\u7528\u5230\u6a21\u578b\u4e0a<\/span><br \/>\n    <span class=\"token comment\"># load: \u52a0\u8f7d\u7528\u6765\u4fdd\u5b58\u6a21\u578b\u53c2\u6570\u7684\u6587\u4ef6<\/span><br \/>\n    model<span class=\"token punctuation\">.<\/span>load_state_dict<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>load<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;model\/phone-price-model.pth&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6784\u5efa\u52a0\u8f7d\u5668<\/span><br \/>\n    dataloader <span class=\"token operator\">&#061;<\/span> DataLoader<span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8bc4\u4f30\u6d4b\u8bd5\u96c6<\/span><br \/>\n    correct <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n    <span class=\"token comment\"># \u904d\u5386\u6d4b\u8bd5\u96c6\u4e2d\u7684\u6570\u636e<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> x<span class=\"token punctuation\">,<\/span> y <span class=\"token keyword\">in<\/span> dataloader<span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u5c06\u5176\u9001\u5165\u7f51\u7edc\u4e2d<\/span><br \/>\n        model<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">eval<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4f7f\u7528\u63a8\u7406\u6a21\u5f0f<\/span><br \/>\n        output <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u83b7\u53d6\u7c7b\u522b\u7ed3\u679c<\/span><br \/>\n        <span class=\"token comment\"># argmax: \u6700\u5927\u503c\u5bf9\u5e94\u7684\u4e0b\u6807&#xff0c;\u5373\u7c7b\u522b\u7f16\u7801<\/span><br \/>\n        y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>argmax<span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u83b7\u53d6\u9884\u6d4b\u6b63\u786e\u7684\u4e2a\u6570<\/span><br \/>\n        correct <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token punctuation\">(<\/span>y_pred <span class=\"token operator\">&#061;&#061;<\/span> y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6c42\u9884\u6d4b\u7cbe\u5ea6<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Acc: %.5f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>correct<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u83b7\u53d6\u6570\u636e<\/span><br \/>\n    train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num <span class=\"token operator\">&#061;<\/span> create_dataset<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6a21\u578b\u9884\u6d4b\u7ed3\u679c<\/span><br \/>\n    test<span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u8f93\u51fa\u7ed3\u679c&#xff1a;<\/p>\n<p>Acc: 0.64250<\/p>\n<h4>9.6 \u7f51\u7edc\u6027\u80fd\u4f18\u5316<\/h4>\n<p>\u6211\u4eec\u524d\u9762\u7684\u7f51\u7edc\u6a21\u578b\u5728\u6d4b\u8bd5\u96c6\u7684\u51c6\u786e\u7387\u4e3a 0.64250&#xff0c;\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u9762\u8fdb\u884c\u8c03\u4f18&#xff1a;<\/p>\n<li>\u5bf9\u8f93\u5165\u6570\u636e\u8fdb\u884c\u6807\u51c6\u5316<\/li>\n<li>\u8c03\u6574\u4f18\u5316\u65b9\u6cd5<\/li>\n<li>\u8c03\u6574\u5b66\u4e60\u7387<\/li>\n<li>\u589e\u52a0\u6279\u91cf\u5f52\u4e00\u5316\u5c42<\/li>\n<li>\u589e\u52a0\u7f51\u7edc\u5c42\u6570\u3001\u795e\u7ecf\u5143\u4e2a\u6570<\/li>\n<li>\u589e\u52a0\u8bad\u7ec3\u8f6e\u6570<\/li>\n<li>\u7b49\u7b49\u2026\u2026<\/li>\n<p>\u8fdb\u884c\u5982\u4e0b\u8c03\u6574&#xff1a;<\/p>\n<li>\u4f18\u5316\u65b9\u6cd5\u7531 SGD \u8c03\u6574\u4e3a Adam<\/li>\n<li>\u5b66\u4e60\u7387\u7531 1e-3 \u8c03\u6574\u4e3a 1e-4<\/li>\n<li>\u5bf9\u6570\u636e\u8fdb\u884c\u6807\u51c6\u5316<\/li>\n<li>\u589e\u52a0\u7f51\u7edc\u6df1\u5ea6&#xff0c;\u5373\u589e\u52a0\u7f51\u7edc\u53c2\u6570\u91cf<\/li>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<br \/>\n<span class=\"token keyword\">import<\/span> pandas <span class=\"token keyword\">as<\/span> pd<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token keyword\">from<\/span> torch<span class=\"token punctuation\">.<\/span>utils<span class=\"token punctuation\">.<\/span>data <span class=\"token keyword\">import<\/span> TensorDataset<br \/>\n<span class=\"token keyword\">from<\/span> torch<span class=\"token punctuation\">.<\/span>utils<span class=\"token punctuation\">.<\/span>data <span class=\"token keyword\">import<\/span> DataLoader<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>optim <span class=\"token keyword\">as<\/span> optim<br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> time<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>preprocessing <span class=\"token keyword\">import<\/span> StandardScaler<\/p>\n<p><span class=\"token comment\"># \u6784\u5efa\u6570\u636e\u96c6<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">create_dataset<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u4f7f\u7528pandas\u8bfb\u53d6\u6570\u636e<\/span><br \/>\n    data <span class=\"token operator\">&#061;<\/span> pd<span class=\"token punctuation\">.<\/span>read_csv<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;.\/data\/\u624b\u673a\u4ef7\u683c\u9884\u6d4b.csv&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u7279\u5f81\u503c\u548c\u76ee\u6807\u503c<\/span><br \/>\n    x<span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> data<span class=\"token punctuation\">.<\/span>iloc<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">:<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> data<span class=\"token punctuation\">.<\/span>iloc<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token comment\"># \u7c7b\u578b\u8f6c\u6362&#xff1a;\u7279\u5f81\u503c&#xff0c;\u76ee\u6807\u503c<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>astype<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span>float32<span class=\"token punctuation\">)<\/span><br \/>\n    y <span class=\"token operator\">&#061;<\/span> y<span class=\"token punctuation\">.<\/span>astype<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span>int64<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6570\u636e\u96c6\u5212\u5206<\/span><br \/>\n    x_train<span class=\"token punctuation\">,<\/span> x_valid<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> y_valid <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> train_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.8<\/span><span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">88<\/span><span class=\"token punctuation\">,<\/span> stratify<span class=\"token operator\">&#061;<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4f18\u5316\u2460: \u6570\u636e\u6807\u51c6\u5316<\/span><br \/>\n    transfer <span class=\"token operator\">&#061;<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    x_train <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><br \/>\n    x_valid <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>x_valid<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6784\u5efa\u6570\u636e\u96c6&#xff0c;\u8f6c\u6362\u4e3a pytorch \u7684\u5f62\u5f0f<\/span><br \/>\n    train_dataset <span class=\"token operator\">&#061;<\/span> TensorDataset<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>from_numpy<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>y_train<span class=\"token punctuation\">.<\/span>values<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    valid_dataset <span class=\"token operator\">&#061;<\/span> TensorDataset<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>from_numpy<span class=\"token punctuation\">(<\/span>x_valid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>tensor<span class=\"token punctuation\">(<\/span>y_valid<span class=\"token punctuation\">.<\/span>values<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8fd4\u56de\u7ed3\u679c<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> x_train<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span>unique<span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6784\u5efa\u7f51\u7edc\u6a21\u578b<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">PhonePriceModel<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> output_dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span>PhonePriceModel<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u4f18\u5316\u2461: \u589e\u52a0\u7f51\u7edc\u6df1\u5ea6<\/span><br \/>\n        <span class=\"token comment\"># 1. \u7b2c\u4e00\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 20&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 128<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear1 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 2. \u7b2c\u4e8c\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 128&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 256<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear2 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">256<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 3. \u7b2c\u4e09\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 256&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 512<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear3 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">256<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">512<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 4. \u7b2c\u56db\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 512&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 128<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear4 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">512<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># 5. \u8f93\u51fa\u5c42&#xff1a;\u8f93\u5165\u7ef4\u5ea6\u4e3a 128&#xff0c;\u8f93\u51fa\u7ef4\u5ea6\u4e3a 4<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>linear5 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> output_dim<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u524d\u5411\u4f20\u64ad\u8fc7\u7a0b<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear1<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear2<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear3<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>relu<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>linear4<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u540e\u7eed CrossEntropyLoss \u635f\u5931\u51fd\u6570\u4e2d\u5305\u542b softmax \u8fc7\u7a0b&#xff0c;\u6240\u4ee5\u5f53\u524d\u6b65\u9aa4\u4e0d\u8fdb\u884c softmax \u64cd\u4f5c<\/span><br \/>\n        output <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>linear5<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u83b7\u53d6\u6570\u636e\u7ed3\u679c<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> output<\/p>\n<p><span class=\"token comment\"># \u7f16\u5199\u8bad\u7ec3\u51fd\u6570<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">train<\/span><span class=\"token punctuation\">(<\/span>train_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u56fa\u5b9a\u968f\u673a\u6570\u79cd\u5b50<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u6570\u636e\u52a0\u8f7d\u5668<\/span><br \/>\n    dataloader <span class=\"token operator\">&#061;<\/span> DataLoader<span class=\"token punctuation\">(<\/span>train_dataset<span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u521d\u59cb\u5316\u6a21\u578b<\/span><br \/>\n    model <span class=\"token operator\">&#061;<\/span> PhonePriceModel<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u635f\u5931\u51fd\u6570 CrossEntropyLoss &#061; softmax &#043; \u635f\u5931\u8ba1\u7b97<\/span><br \/>\n    criterion <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>CrossEntropyLoss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4f18\u5316\u2462: \u4f7f\u7528Adam\u4f18\u5316\u65b9\u6cd5&#xff0c;\u4f18\u5316\u2463: \u5b66\u4e60\u7387\u53d8\u4e3a1e-4<\/span><br \/>\n    optimizer <span class=\"token operator\">&#061;<\/span> optim<span class=\"token punctuation\">.<\/span>Adam<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e-4<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u904d\u5386\u6bcf\u4e2a\u8f6e\u6b21\u7684\u6570\u636e<\/span><br \/>\n    num_epoch <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">50<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> epoch_idx <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>num_epoch<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u8bad\u7ec3\u65f6\u95f4<\/span><br \/>\n        start <span class=\"token operator\">&#061;<\/span> time<span class=\"token punctuation\">.<\/span>time<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n        total_loss <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.0<\/span><br \/>\n        total_num <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n        <span class=\"token comment\"># \u904d\u5386\u6bcf\u4e2a batch \u6570\u636e\u8fdb\u884c\u5904\u7406<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> x<span class=\"token punctuation\">,<\/span> y <span class=\"token keyword\">in<\/span> dataloader<span class=\"token punctuation\">:<\/span><br \/>\n            model<span class=\"token punctuation\">.<\/span>train<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            output <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n            loss <span class=\"token operator\">&#061;<\/span> criterion<span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u68af\u5ea6\u6e05\u96f6<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>zero_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad<\/span><br \/>\n            loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u53c2\u6570\u66f4\u65b0<\/span><br \/>\n            optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token comment\"># \u635f\u5931\u8ba1\u7b97<\/span><br \/>\n            total_num <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n            total_loss <span class=\"token operator\">&#043;&#061;<\/span> loss<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u6253\u5370\u635f\u5931\u53d8\u6362\u7ed3\u679c<\/span><br \/>\n        <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;epoch: %4s loss: %.2f, time: %.2fs&#039;<\/span> <span class=\"token operator\">%<\/span><br \/>\n              <span class=\"token punctuation\">(<\/span>epoch_idx <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> total_loss <span class=\"token operator\">\/<\/span> total_num<span class=\"token punctuation\">,<\/span> time<span class=\"token punctuation\">.<\/span>time<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> start<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6a21\u578b\u4fdd\u5b58<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>save<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>state_dict<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;.\/model\/phone-price-model2.pth&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test<\/span><span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u52a0\u8f7d\u6a21\u578b\u548c\u8bad\u7ec3\u597d\u7684\u7f51\u7edc\u53c2\u6570<\/span><br \/>\n    model <span class=\"token operator\">&#061;<\/span> PhonePriceModel<span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span> class_num<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># load_state_dict: \u5c06\u52a0\u8f7d\u7684\u53c2\u6570\u5b57\u5178\u5e94\u7528\u5230\u6a21\u578b\u4e0a<\/span><br \/>\n    model<span class=\"token punctuation\">.<\/span>load_state_dict<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>load<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;.\/model\/phone-price-model2.pth&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6784\u5efa\u52a0\u8f7d\u5668<\/span><br \/>\n    dataloader <span class=\"token operator\">&#061;<\/span> DataLoader<span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8bc4\u4f30\u6d4b\u8bd5\u96c6<\/span><br \/>\n    correct <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\n    <span class=\"token comment\"># \u904d\u5386\u6d4b\u8bd5\u96c6\u4e2d\u7684\u6570\u636e<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> x<span class=\"token punctuation\">,<\/span> y <span class=\"token keyword\">in<\/span> dataloader<span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u5c06\u5176\u9001\u5165\u7f51\u7edc\u4e2d<\/span><br \/>\n        <span class=\"token comment\"># model.eval()<\/span><br \/>\n        output <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u83b7\u53d6\u9884\u6d4b\u7c7b\u522b\u7ed3\u679c<\/span><br \/>\n        y_pred <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>argmax<span class=\"token punctuation\">(<\/span>output<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token comment\"># \u83b7\u53d6\u9884\u6d4b\u6b63\u786e\u7684\u4e2a\u6570<\/span><br \/>\n        correct <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token punctuation\">(<\/span>y_pred <span class=\"token operator\">&#061;&#061;<\/span> y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u6c42\u9884\u6d4b\u7cbe\u5ea6<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Acc: %.5f&#039;<\/span> <span class=\"token operator\">%<\/span> <span class=\"token punctuation\">(<\/span>correct <span class=\"token operator\">\/<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>valid_dataset<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#039;__main__&#039;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    train_dataset<span class=\"token punctuation\">,<\/span> valid_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token punctuation\">,<\/span> class_num <span class=\"token operator\">&#061;<\/span> create_dataset<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    train<span class=\"token punctuation\">(<\/span>train_dataset<span class=\"token punctuation\">,<\/span> input_dim<span class=\"token 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