{"id":49794,"date":"2025-07-30T19:51:38","date_gmt":"2025-07-30T11:51:38","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/49794.html"},"modified":"2025-07-30T19:51:38","modified_gmt":"2025-07-30T11:51:38","slug":"%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0-%e8%bf%87%e6%8b%9f%e5%90%88%e4%b8%8e%e6%ac%a0%e6%8b%9f%e5%90%88","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/49794.html","title":{"rendered":"\u6df1\u5ea6\u5b66\u4e60 --- \u8fc7\u62df\u5408\u4e0e\u6b20\u62df\u5408"},"content":{"rendered":"<h2>\u6df1\u5ea6\u5b66\u4e60 \u2014 \u8fc7\u62df\u5408\u4e0e\u6b20\u62df\u5408<\/h2>\n<hr \/>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u6df1\u5ea6\u5b66\u4e60 &#8212; \u8fc7\u62df\u5408\u4e0e\u6b20\u62df\u5408<\/li>\n<li>\u4e00.\u6982\u5ff5<\/li>\n<li>\n<ul>\n<li>1.1 \u8fc7\u62df\u5408<\/li>\n<li>1.2 \u6b20\u62df\u5408<\/li>\n<li>1.3 \u5224\u65ad\u65b9\u5f0f<\/li>\n<\/ul>\n<\/li>\n<li>\u4e8c&#xff0c;\u89e3\u51b3\u6b20\u62df\u5408<\/li>\n<li>\u4e09&#xff0c;\u89e3\u51b3\u8fc7\u62df\u5408<\/li>\n<li>\n<ul>\n<li>3.1 L2\u6b63\u5219\u5316<\/li>\n<li>\n<ul>\n<li>3.1.1 \u5b9a\u4e49\u4ee5\u53ca\u4f5c\u7528<\/li>\n<li>3.1.2 \u4ee3\u7801<\/li>\n<\/ul>\n<\/li>\n<li>3.2 L1\u6b63\u5219\u5316<\/li>\n<li>3.3 L1\u4e0eL2\u5bf9\u6bd4<\/li>\n<li>3.4 Dropout<\/li>\n<li>\n<ul>\n<li>\u793a\u4f8b<\/li>\n<\/ul>\n<\/li>\n<li>3.5 \u6570\u636e\u589e\u5f3a<\/li>\n<li>\n<ul>\n<li>3.5.1 \u56fe\u7247\u7f29\u653e<\/li>\n<li>3.5.2 \u968f\u673a\u88c1\u526a<\/li>\n<li>3.5.3 \u968f\u673a\u6c34\u5e73\u7ffb\u8f6c<\/li>\n<li>3.5.4 \u8c03\u6574\u56fe\u7247\u989c\u8272<\/li>\n<li>3.5.5 \u968f\u673a\u65cb\u8f6c<\/li>\n<li>3.5.6 \u56fe\u7247\u8f6cTensor<\/li>\n<li>3.5.7 Tensor\u8f6c\u56fe\u7247<\/li>\n<li>3.5.8 \u5f52\u4e00\u5316<\/li>\n<li>3.5.9 \u6570\u636e\u589e\u5f3a\u6574\u5408<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h2>\u4e00.\u6982\u5ff5<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730115134-688a07463e28c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.1 \u8fc7\u62df\u5408<\/h3>\n<p>\u8fc7\u62df\u5408\u662f\u6307\u6a21\u578b\u5bf9\u8bad\u7ec3\u6570\u636e\u62df\u5408\u80fd\u529b\u5f88\u5f3a\u5e76\u8868\u73b0\u5f88\u597d&#xff0c;\u4f46\u5728\u6d4b\u8bd5\u6570\u636e\u4e0a\u8868\u73b0\u8f83\u5dee\u3002<\/p>\n<p>\u8fc7\u62df\u5408\u5e38\u89c1\u539f\u56e0\u6709&#xff1a;<\/p>\n<li>\u6570\u636e\u91cf\u4e0d\u8db3&#xff1a;\u5f53\u8bad\u7ec3\u6570\u636e\u8f83\u5c11\u65f6&#xff0c;\u6a21\u578b\u53ef\u80fd\u4f1a\u8fc7\u5ea6\u5b66\u4e60\u6570\u636e\u4e2d\u7684\u566a\u58f0\u548c\u7ec6\u8282\u3002<\/li>\n<li>\u6a21\u578b\u592a\u590d\u6742&#xff1a;\u5982\u679c\u6a21\u578b\u5f88\u590d\u6742&#xff0c;\u4e5f\u4f1a\u8fc7\u5ea6\u5b66\u4e60\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u7ec6\u8282\u548c\u566a\u58f0\u3002<\/li>\n<li>\u6b63\u5219\u5316\u5f3a\u5ea6\u4e0d\u8db3&#xff1a;\u5982\u679c\u6b63\u5219\u5316\u5f3a\u5ea6\u4e0d\u8db3&#xff0c;\u53ef\u80fd\u4f1a\u5bfc\u81f4\u6a21\u578b\u8fc7\u5ea6\u5b66\u4e60\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u7ec6\u8282\u548c\u566a\u58f0\u3002<\/li>\n<h3>1.2 \u6b20\u62df\u5408<\/h3>\n<p>\u6b20\u62df\u5408\u662f\u7531\u4e8e\u6a21\u578b\u5b66\u4e60\u80fd\u529b\u4e0d\u8db3&#xff0c;\u65e0\u6cd5\u5145\u5206\u6355\u6349\u6570\u636e\u4e2d\u7684\u590d\u6742\u5173\u7cfb\u3002<\/p>\n<h3>1.3 \u5224\u65ad\u65b9\u5f0f<\/h3>\n<p>\u8fc7\u62df\u5408<\/p>\n<p>\u200b \u8bad\u7ec3\u8bef\u5dee\u4f4e&#xff0c;\u4f46\u9a8c\u8bc1\u65f6\u8bef\u5dee\u9ad8\u3002\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8868\u73b0\u5f88\u597d&#xff0c;\u4f46\u5728\u9a8c\u8bc1\u6570\u636e\u4e0a\u8868\u73b0\u4e0d\u4f73&#xff0c;\u8bf4\u660e\u6a21\u578b\u53ef\u80fd\u8fc7\u5ea6\u62df\u5408\u4e86\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u566a\u58f0\u6216\u7279\u5b9a\u6a21\u5f0f\u3002<\/p>\n<p>\u6b20\u62df\u5408<\/p>\n<p>\u200b \u8bad\u7ec3\u8bef\u5dee\u548c\u6d4b\u8bd5\u8bef\u5dee\u90fd\u9ad8\u3002\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u548c\u6d4b\u8bd5\u6570\u636e\u4e0a\u7684\u8868\u73b0\u90fd\u4e0d\u597d&#xff0c;\u8bf4\u660e\u6a21\u578b\u53ef\u80fd\u592a\u7b80\u5355&#xff0c;\u65e0\u6cd5\u6355\u6349\u5230\u6570\u636e\u4e2d\u7684\u590d\u6742\u6a21\u5f0f\u3002<\/p>\n<h2>\u4e8c&#xff0c;\u89e3\u51b3\u6b20\u62df\u5408<\/h2>\n<p>\u6b20\u62df\u5408\u7684\u89e3\u51b3\u601d\u8def\u6bd4\u8f83\u76f4\u63a5&#xff1a;<\/p>\n<li>\u589e\u52a0\u6a21\u578b\u590d\u6742\u5ea6&#xff1a;\u5f15\u5165\u66f4\u591a\u7684\u53c2\u6570\u3001\u589e\u52a0\u795e\u7ecf\u7f51\u7edc\u7684\u5c42\u6570\u6216\u8282\u70b9\u6570\u91cf&#xff0c;\u4f7f\u6a21\u578b\u80fd\u591f\u6355\u6349\u5230\u6570\u636e\u4e2d\u7684\u590d\u6742\u6a21\u5f0f\u3002<\/li>\n<li>\u589e\u52a0\u7279\u5f81&#xff1a;\u901a\u8fc7\u7279\u5f81\u5de5\u7a0b\u6dfb\u52a0\u66f4\u591a\u6709\u610f\u4e49\u7684\u7279\u5f81&#xff0c;\u4f7f\u6a21\u578b\u80fd\u591f\u66f4\u597d\u5730\u7406\u89e3\u6570\u636e\u3002<\/li>\n<li>\u51cf\u5c11\u6b63\u5219\u5316\u5f3a\u5ea6&#xff1a;\u9002\u5f53\u51cf\u5c0f L1\u3001L2 \u6b63\u5219\u5316\u5f3a\u5ea6&#xff0c;\u5141\u8bb8\u6a21\u578b\u6709\u66f4\u591a\u81ea\u7531\u5ea6\u6765\u62df\u5408\u6570\u636e\u3002<\/li>\n<li>\u8bad\u7ec3\u66f4\u957f\u65f6\u95f4&#xff1a;\u5982\u679c\u662f\u56e0\u4e3a\u8bad\u7ec3\u4e0d\u8db3\u5bfc\u81f4\u7684\u6b20\u62df\u5408&#xff0c;\u53ef\u4ee5\u589e\u52a0\u8bad\u7ec3\u7684\u8f6e\u6570\u6216\u65f6\u95f4.<\/li>\n<h2>\u4e09&#xff0c;\u89e3\u51b3\u8fc7\u62df\u5408<\/h2>\n<p>\u907f\u514d\u6a21\u578b\u53c2\u6570\u8fc7\u5927\u662f\u9632\u6b62\u8fc7\u62df\u5408\u7684\u5173\u952e\u6b65\u9aa4\u4e4b\u4e00\u3002<\/p>\n<p>\u6a21\u578b\u7684\u590d\u6742\u5ea6\u4e3b\u8981\u7531\u6743\u91cdw\u51b3\u5b9a&#xff0c;\u800c\u4e0d\u662f\u504f\u7f6eb\u3002\u504f\u7f6e\u53ea\u662f\u5bf9\u6a21\u578b\u8f93\u51fa\u7684\u5e73\u79fb&#xff0c;\u4e0d\u4f1a\u5bfc\u81f4\u6a21\u578b\u8fc7\u5ea6\u62df\u5408\u6570\u636e\u3002<\/p>\n<p>\u600e\u4e48\u63a7\u5236\u6743\u91cdw&#xff0c;\u4f7fw\u5728\u6bd4\u8f83\u5c0f\u7684\u8303\u56f4\u5185&#xff1f;<\/p>\n<p>\u8003\u8651\u635f\u5931\u51fd\u6570&#xff0c;\u635f\u5931\u51fd\u6570\u7684\u76ee\u7684\u662f\u4f7f\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u65e0\u9650\u63a5\u8fd1&#xff0c;\u5982\u679c\u5728\u539f\u6765\u7684\u635f\u5931\u51fd\u6570\u4e0a\u6dfb\u52a0\u4e00\u4e2a\u975e0\u7684\u53d8\u91cf <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          L<\/p>\n<p>          1<\/p>\n<p>         (<\/p>\n<p>          y<\/p>\n<p>          ^<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         L<\/p>\n<p>         (<\/p>\n<p>          y<\/p>\n<p>          ^<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#043;<\/p>\n<p>         f<\/p>\n<p>         (<\/p>\n<p>         w<\/p>\n<p>         )<\/p>\n<p>         L_1(\\\\hat{y},y) &#061; L(\\\\hat{y},y) &#043; f(w) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/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 class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/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 class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose\">)<\/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=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        f<\/p>\n<p>        (<\/p>\n<p>        w<\/p>\n<p>        )<\/p>\n<p>       f(w)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u662f\u5173\u4e8e\u6743\u91cdw\u7684\u51fd\u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        f<\/p>\n<p>        (<\/p>\n<p>        w<\/p>\n<p>        )<\/p>\n<p>        &gt;<\/p>\n<p>        0<\/p>\n<p>       f(w)&gt;0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/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><\/p>\n<p>\u8981\u4f7fL1\u53d8\u5c0f&#xff0c;\u5c31\u8981\u4f7fL\u53d8\u5c0f\u7684\u540c\u65f6&#xff0c;\u4e5f\u8981\u4f7f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        f<\/p>\n<p>        (<\/p>\n<p>        w<\/p>\n<p>        )<\/p>\n<p>       f(w)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u53d8\u5c0f\u3002\u4ece\u800c\u63a7\u5236\u6743\u91cdw\u5728\u8f83\u5c0f\u7684\u8303\u56f4\u5185\u3002<\/p>\n<h3>3.1 L2\u6b63\u5219\u5316<\/h3>\n<p>L2 \u6b63\u5219\u5316\u901a\u8fc7\u5728\u635f\u5931\u51fd\u6570\u4e2d\u6dfb\u52a0\u6743\u91cd\u53c2\u6570\u7684\u5e73\u65b9\u548c\u6765\u5b9e\u73b0&#xff0c;\u76ee\u6807\u662f\u60e9\u7f5a\u8fc7\u5927\u7684\u53c2\u6570\u503c\u3002<\/p>\n<h4>3.1.1 \u5b9a\u4e49\u4ee5\u53ca\u4f5c\u7528<\/h4>\n<table>\n<tr>\u7ef4\u5ea6\u5185\u5bb9\u6570\u5b66\u8868\u8fbe\u5f0f\u89e3\u91ca\u4e0e\u4f5c\u7528<\/tr>\n<tbody>\n<tr>\n<td>\u539f\u59cb\u635f\u5931\u51fd\u6570<\/td>\n<td>\u6a21\u578b\u672a\u52a0\u6b63\u5219\u5316\u7684\u635f\u5931\u51fd\u6570&#xff08;\u5982 MSE\u3001\u4ea4\u53c9\u71b5&#xff09;<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           L<\/p>\n<p>           (<\/p>\n<p>           \u03b8<\/p>\n<p>           )<\/p>\n<p>          L(\\\\theta)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u4ec5\u8861\u91cf\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u7684\u8bef\u5dee\u3002<\/td>\n<\/tr>\n<tr>\n<td>L2 \u6b63\u5219\u5316\u9879<\/td>\n<td>\u6240\u6709\u6743\u91cd\u53c2\u6570\u7684\u5e73\u65b9\u548c<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            1<\/p>\n<p>            2<\/p>\n<p>            \u2211<\/p>\n<p>            i<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>            2<\/p>\n<p>          \\\\frac{1}{2} \\\\sum_i \\\\theta_i^2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/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: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/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: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;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: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0278em;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 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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u60e9\u7f5a\u5927\u6743\u91cd&#xff0c;\u9632\u6b62\u6a21\u578b\u590d\u6742\u5ea6\u8fc7\u9ad8\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u603b\u635f\u5931\u51fd\u6570<\/td>\n<td>\u539f\u59cb\u635f\u5931 &#043; L2 \u6b63\u5219\u5316\u9879<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            L<\/p>\n<p>            total<\/p>\n<p>           (<\/p>\n<p>           \u03b8<\/p>\n<p>           )<\/p>\n<p>           &#061;<\/p>\n<p>           L<\/p>\n<p>           (<\/p>\n<p>           \u03b8<\/p>\n<p>           )<\/p>\n<p>           &#043;<\/p>\n<p>            \u03bb<\/p>\n<p>            2<\/p>\n<p>            \u2211<\/p>\n<p>            i<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>            2<\/p>\n<p>          L_{\\\\text{total}}(\\\\theta) &#061; L(\\\\theta) &#043; \\\\frac{\\\\lambda}{2} \\\\sum_i \\\\theta_i^2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/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 text mtight\"><span class=\"mord mtight\">total<\/span><\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose\">)<\/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: 1.2251em;vertical-align: -0.345em\"><\/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: 0.8801em\"><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 mtight\">2<\/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 mathnormal mtight\">\u03bb<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;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: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0278em;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 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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u52a0\u5165\u60e9\u7f5a\u9879&#xff0c;\u5e73\u8861\u62df\u5408\u80fd\u529b\u4e0e\u590d\u6742\u5ea6\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u68af\u5ea6\u66f4\u65b0\u89c4\u5219<\/td>\n<td>\u53c2\u6570\u66f4\u65b0\u65f6\u8003\u8651\u539f\u59cb\u68af\u5ea6 &#043; L2 \u9879\u7684\u68af\u5ea6<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            \u03b8<\/p>\n<p>             t<\/p>\n<p>             &#043;<\/p>\n<p>             1<\/p>\n<p>           &#061;<\/p>\n<p>            \u03b8<\/p>\n<p>            t<\/p>\n<p>           \u2212<\/p>\n<p>           \u03b7<\/p>\n<p>            (<\/p>\n<p>            \u2207<\/p>\n<p>            L<\/p>\n<p>            (<\/p>\n<p>             \u03b8<\/p>\n<p>             t<\/p>\n<p>            )<\/p>\n<p>            &#043;<\/p>\n<p>            \u03bb<\/p>\n<p>             \u03b8<\/p>\n<p>             t<\/p>\n<p>            )<\/p>\n<p>          \\\\theta_{t&#043;1} &#061; \\\\theta_t &#8211; \\\\eta \\\\left( \\\\nabla L(\\\\theta_t) &#043; \\\\lambda \\\\theta_t \\\\right)<\/p>\n<p>       <\/span><span class=\"katex-html\"><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: 0.0278em\">\u03b8<\/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: -0.0278em;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\">&#043;<\/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: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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\">\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: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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=\"mclose\">)<\/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\">\u03bb<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u6bcf\u6b21\u66f4\u65b0\u90fd\u201c\u8870\u51cf\u201d\u53c2\u6570&#xff08;\u4e58\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>           \u2212<\/p>\n<p>           \u03b7<\/p>\n<p>           \u03bb<\/p>\n<p>          1 &#8211; \\\\eta \\\\lambda<\/p>\n<p>       <\/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: 0.0359em\">\u03b7<\/span><span class=\"mord mathnormal\">\u03bb<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u9632\u6b62\u6743\u91cd\u8fc7\u5927\u3002<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             1<\/p>\n<p>             2<\/p>\n<p>           \\\\frac{1}{2}<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/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: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/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: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u4f5c\u7528<\/td>\n<td>\u7b80\u5316\u68af\u5ea6\u8ba1\u7b97<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            \u2202<\/p>\n<p>             \u2202<\/p>\n<p>              \u03b8<\/p>\n<p>              i<\/p>\n<p>            (<\/p>\n<p>             1<\/p>\n<p>             2<\/p>\n<p>             \u03b8<\/p>\n<p>             i<\/p>\n<p>             2<\/p>\n<p>            )<\/p>\n<p>           &#061;<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>          \\\\frac{\\\\partial}{\\\\partial \\\\theta_i} \\\\left( \\\\frac{1}{2} \\\\theta_i^2 \\\\right) &#061; \\\\theta_i<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3252em;vertical-align: -0.4451em\"><\/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: 0.8801em\"><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 mtight\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0278em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/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\" style=\"margin-right: 0.0556em\">\u2202<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><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 mtight\">2<\/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: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0278em;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 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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/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: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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><\/td>\n<td>\u6d88\u53bb\u7cfb\u6570 2&#xff0c;\u4f7f\u68af\u5ea6\u66f4\u65b0\u516c\u5f0f\u66f4\u7b80\u6d01&#xff08;\u907f\u514d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>           \u03bb<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>          2\\\\lambda \\\\theta_i<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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>&#xff09;\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u9632\u6b62\u8fc7\u62df\u5408<\/td>\n<td>\u6291\u5236\u6743\u91cd\u8fc7\u5927&#xff0c;\u964d\u4f4e\u6a21\u578b\u5bf9\u8bad\u7ec3\u566a\u58f0\u7684\u654f\u611f\u6027<\/td>\n<td>&#8211;<\/td>\n<td>\u6743\u91cd\u8d8a\u5c0f&#xff0c;\u6a21\u578b\u5bf9\u8f93\u5165\u6270\u52a8\u8d8a\u4e0d\u654f\u611f&#xff0c;\u6cdb\u5316\u80fd\u529b\u589e\u5f3a\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u9650\u5236\u6a21\u578b\u590d\u6742\u5ea6<\/td>\n<td>\u5f3a\u5236\u6743\u91cd\u63a5\u8fd1 0&#xff0c;\u907f\u514d\u8fc7\u62df\u5408<\/td>\n<td>&#8211;<\/td>\n<td>\u901a\u8fc7\u60e9\u7f5a\u5927\u6743\u91cd&#xff0c;\u51cf\u5c11\u6a21\u578b\u81ea\u7531\u5ea6&#xff0c;\u964d\u4f4e VC \u7ef4\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u63d0\u9ad8\u6cdb\u5316\u80fd\u529b<\/td>\n<td>\u5728\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u4e0a\u8868\u73b0\u66f4\u5747\u8861<\/td>\n<td>&#8211;<\/td>\n<td>\u6b63\u5219\u5316\u9879\u4f7f\u6a21\u578b\u66f4\u5173\u6ce8\u6570\u636e\u7684\u771f\u5b9e\u89c4\u5f8b&#xff0c;\u800c\u975e\u566a\u58f0\u3002<\/td>\n<\/tr>\n<tr>\n<td>\u5e73\u6ed1\u6743\u91cd\u5206\u5e03<\/td>\n<td>\u6743\u91cd\u9010\u6e10\u7f29\u5c0f\u4f46\u4e0d\u76f4\u63a5\u4e3a 0<\/td>\n<td>&#8211;<\/td>\n<td>\u4fdd\u7559\u6240\u6709\u7279\u5f81\u8d21\u732e&#xff0c;\u907f\u514d\u7a00\u758f\u6027&#xff08;\u4e0e L1 \u4e0d\u540c&#xff09;&#xff0c;\u4f7f\u6a21\u578b\u66f4\u5e73\u6ed1\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>3.1.2 \u4ee3\u7801<\/h4>\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> torch<span class=\"token punctuation\">.<\/span>optim <span class=\"token keyword\">as<\/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 comment\"># \u8bbe\u7f6e\u968f\u673a\u79cd\u5b50\u4ee5\u4fdd\u8bc1\u53ef\u91cd\u590d\u6027<\/span><br \/>\ntorch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u751f\u6210\u968f\u673a\u6570\u636e<\/span><br \/>\nn_samples <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">100<\/span><br \/>\nn_features <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">20<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>n_samples<span class=\"token punctuation\">,<\/span> n_features<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8f93\u5165\u6570\u636e<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>n_samples<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u76ee\u6807\u503c<\/span><\/p>\n<p><span class=\"token comment\"># \u5b9a\u4e49\u4e00\u4e2a\u7b80\u5355\u7684\u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">SimpleNet<\/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><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span>SimpleNet<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        self<span class=\"token punctuation\">.<\/span>fc1 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>n_features<span class=\"token punctuation\">,<\/span> <span class=\"token number\">50<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>fc2 <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">50<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><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        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>fc1<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> self<span class=\"token punctuation\">.<\/span>fc2<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u8bad\u7ec3\u51fd\u6570<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">train_model<\/span><span class=\"token punctuation\">(<\/span>use_l2<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">,<\/span> weight_decay<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">,<\/span> n_epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">)<\/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> SimpleNet<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    criterion <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>MSELoss<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u635f\u5931\u51fd\u6570&#xff08;\u5747\u65b9\u8bef\u5dee&#xff09;<\/span><\/p>\n<p>    <span class=\"token comment\"># \u9009\u62e9\u4f18\u5316\u5668<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> use_l2<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>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\">0.01<\/span><span class=\"token punctuation\">,<\/span> weight_decay<span class=\"token operator\">&#061;<\/span>weight_decay<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4f7f\u7528 L2 \u6b63\u5219\u5316<\/span><br \/>\n    <span class=\"token keyword\">else<\/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>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\">0.01<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4e0d\u4f7f\u7528 L2 \u6b63\u5219\u5316<\/span><\/p>\n<p>    <span class=\"token comment\"># \u8bb0\u5f55\u8bad\u7ec3\u635f\u5931<\/span><br \/>\n    train_losses <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<p>    <span class=\"token comment\"># \u8bad\u7ec3\u8fc7\u7a0b<\/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>n_epochs<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>  <span class=\"token comment\"># \u6e05\u7a7a\u68af\u5ea6<\/span><br \/>\n        outputs <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u524d\u5411\u4f20\u64ad<\/span><br \/>\n        loss <span class=\"token operator\">&#061;<\/span> criterion<span class=\"token punctuation\">(<\/span>outputs<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8ba1\u7b97\u635f\u5931<\/span><br \/>\n        loss<span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u53cd\u5411\u4f20\u64ad<\/span><br \/>\n        optimizer<span class=\"token punctuation\">.<\/span>step<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u66f4\u65b0\u53c2\u6570<\/span><\/p>\n<p>        train_losses<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span>loss<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\"># \u8bb0\u5f55\u635f\u5931<\/span><\/p>\n<p>        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>epoch <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">%<\/span> <span class=\"token number\">10<\/span> <span class=\"token operator\">&#061;&#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><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;Epoch [<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>epoch <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">\/<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>n_epochs<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">], Loss: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>loss<span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#039;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">return<\/span> train_losses<\/p>\n<p><span class=\"token comment\"># \u8bad\u7ec3\u5e76\u6bd4\u8f83\u4e24\u79cd\u6a21\u578b<\/span><br \/>\ntrain_losses_no_l2 <span class=\"token operator\">&#061;<\/span> train_model<span class=\"token punctuation\">(<\/span>use_l2<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4e0d\u4f7f\u7528 L2 \u6b63\u5219\u5316<\/span><br \/>\ntrain_losses_with_l2 <span class=\"token operator\">&#061;<\/span> train_model<span class=\"token punctuation\">(<\/span>use_l2<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> weight_decay<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4f7f\u7528 L2 \u6b63\u5219\u5316<\/span><\/p>\n<p><span class=\"token comment\"># \u7ed8\u5236\u8bad\u7ec3\u635f\u5931\u66f2\u7ebf<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>train_losses_no_l2<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;Without L2 Regularization&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>train_losses_with_l2<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;With L2 Regularization&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Epoch&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Loss&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Training Loss: L2 Regularization vs No Regularization&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h3>3.2 L1\u6b63\u5219\u5316<\/h3>\n<p>\u8bbe\u6a21\u578b\u7684\u539f\u59cb\u635f\u5931\u51fd\u6570\u4e3a <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         L<\/p>\n<p>         (<\/p>\n<p>         \u03b8<\/p>\n<p>         )<\/p>\n<p>         L(\\\\theta)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03b8<\/p>\n<p>        \\\\theta<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u6a21\u578b\u6743\u91cd\u53c2\u6570&#xff0c;\u5219\u52a0\u5165 L1 \u6b63\u5219\u5316\u540e\u7684\u635f\u5931\u51fd\u6570\u8868\u793a\u4e3a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          L<\/p>\n<p>          total<\/p>\n<p>         (<\/p>\n<p>         \u03b8<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         L<\/p>\n<p>         (<\/p>\n<p>         \u03b8<\/p>\n<p>         )<\/p>\n<p>         &#043;<\/p>\n<p>         \u03bb<\/p>\n<p>          \u2211<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>          \u03b8<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>         L_{\\\\text{total}}(\\\\theta) &#061; L(\\\\theta) &#043; \\\\lambda \\\\sum_{i} |\\\\theta_i| <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/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 text mtight\"><span class=\"mord mtight\">total<\/span><\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose\">)<\/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: 2.3277em;vertical-align: -1.2777em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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 class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u68af\u5ea6\u66f4\u65b0 \u5728 L1 \u6b63\u5219\u5316\u4e0b&#xff0c;\u68af\u5ea6\u66f4\u65b0\u65f6\u7684\u516c\u5f0f\u662f&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           \u03b8<\/p>\n<p>            t<\/p>\n<p>            &#043;<\/p>\n<p>            1<\/p>\n<p>          &#061;<\/p>\n<p>           \u03b8<\/p>\n<p>           t<\/p>\n<p>          \u2212<\/p>\n<p>          \u03b7<\/p>\n<p>           (<\/p>\n<p>           \u2207<\/p>\n<p>           L<\/p>\n<p>           (<\/p>\n<p>            \u03b8<\/p>\n<p>            t<\/p>\n<p>           )<\/p>\n<p>           &#043;<\/p>\n<p>           \u03bb<\/p>\n<p>           \u22c5<\/p>\n<p>           sign<\/p>\n<p>           (<\/p>\n<p>            \u03b8<\/p>\n<p>            t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          \\\\theta_{t&#043;1} &#061; \\\\theta_t &#8211; \\\\eta \\\\left( \\\\nabla L(\\\\theta_t) &#043; \\\\lambda \\\\cdot \\\\text{sign}(\\\\theta_t) \\\\right) <\/p>\n<p>      <\/span><span class=\"katex-html\"><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: 0.0278em\">\u03b8<\/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: -0.0278em;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\">&#043;<\/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: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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\">\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: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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=\"mclose\">)<\/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\">\u03bb<\/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 class=\"mord text\"><span class=\"mord\">sign<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u4f5c\u7528&#xff1a;<\/li>\n<\/ul>\n<li>\n<p>\u7a00\u758f\u6027&#xff1a;L1 \u6b63\u5219\u5316\u7684\u4e00\u4e2a\u663e\u8457\u7279\u6027\u662f\u5b83\u4f1a\u4fc3\u4f7f\u8bb8\u591a\u6743\u91cd\u53c2\u6570\u53d8\u4e3a \u96f6\u3002\u8fd9\u662f\u56e0\u4e3a L1 \u6b63\u5219\u5316\u503e\u5411\u4e8e\u5c06\u6743\u91cd\u7edd\u5bf9\u503c\u7f29\u5c0f\u5230\u96f6&#xff0c;\u4f7f\u5f97\u6a21\u578b\u53ea\u4fdd\u7559\u5bf9\u7ed3\u679c\u6700\u91cd\u8981\u7684\u7279\u5f81&#xff0c;\u800c\u5c06\u5176\u4ed6\u4e0d\u76f8\u5173\u7684\u7279\u5f81\u6743\u91cd\u8bbe\u4e3a\u96f6&#xff0c;\u4ece\u800c\u5b9e\u73b0 \u7279\u5f81\u9009\u62e9 \u7684\u529f\u80fd\u3002<\/p>\n<\/li>\n<li>\n<p>\u9632\u6b62\u8fc7\u62df\u5408&#xff1a;\u901a\u8fc7\u9650\u5236\u6743\u91cd\u7684\u7edd\u5bf9\u503c&#xff0c;L1 \u6b63\u5219\u5316\u51cf\u5c11\u4e86\u6a21\u578b\u7684\u590d\u6742\u5ea6&#xff0c;\u4f7f\u5176\u4e0d\u5bb9\u6613\u8fc7\u62df\u5408\u8bad\u7ec3\u6570\u636e\u3002\u76f8\u6bd4\u4e8e L2 \u6b63\u5219\u5316&#xff0c;L1 \u6b63\u5219\u5316\u66f4\u503e\u5411\u4e8e\u5c06\u67d0\u4e9b\u6743\u91cd\u5b8c\u5168\u79fb\u9664&#xff0c;\u800c\u4e0d\u662f\u51cf\u5c0f\u5b83\u4eec\u7684\u503c\u3002<\/p>\n<\/li>\n<li>\n<p>\u7b80\u5316\u6a21\u578b&#xff1a;\u7531\u4e8e L1 \u6b63\u5219\u5316\u4f1a\u5c06\u4e00\u4e9b\u6743\u91cd\u53d8\u4e3a\u96f6&#xff0c;\u56e0\u6b64\u6a21\u578b\u6700\u7ec8\u4f1a\u53d8\u5f97\u66f4\u52a0\u7b80\u5355&#xff0c;\u4ec5\u4f9d\u8d56\u4e8e\u5c11\u6570\u91cd\u8981\u7279\u5f81\u3002\u8fd9\u5bf9\u4e8e\u9ad8\u7ef4\u5ea6\u6570\u636e\u7279\u522b\u6709\u7528&#xff0c;\u5c24\u5176\u662f\u5728\u7279\u5f81\u6570\u91cf\u8fdc\u591a\u4e8e\u6837\u672c\u6570\u91cf\u7684\u60c5\u51b5\u4e0b\u3002<\/p>\n<\/li>\n<li>\n<p>\u7279\u5f81\u9009\u62e9&#xff1a;\u56e0\u4e3a L1 \u6b63\u5219\u5316\u4f1a\u5c06\u90e8\u5206\u6743\u91cd\u7f6e\u96f6&#xff0c;\u56e0\u6b64\u5b83\u5929\u7136\u5177\u6709\u7279\u5f81\u9009\u62e9\u7684\u80fd\u529b&#xff0c;\u6709\u52a9\u4e8e\u81ea\u52a8\u7b5b\u9009\u51fa\u5bf9\u6a21\u578b\u9884\u6d4b\u6700\u91cd\u8981\u7684\u7279\u5f81\u3002<\/p>\n<\/li>\n<h3>3.3 L1\u4e0eL2\u5bf9\u6bd4<\/h3>\n<table>\n<tr>\u7279\u6027L2 \u6b63\u5219\u5316&#xff08;Ridge&#xff09;L1 \u6b63\u5219\u5316&#xff08;Lasso&#xff09;<\/tr>\n<tbody>\n<tr>\n<td>\u60e9\u7f5a\u9879<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            \u2211<\/p>\n<p>            i<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>            2<\/p>\n<p>          \\\\sum_i \\\\theta_i^2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1138em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;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: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0278em;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 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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u2211<\/p>\n<p>           _<\/p>\n<p>           i<\/p>\n<p>           \u03b8<\/p>\n<p>           _<\/p>\n<p>           i<\/p>\n<p>          \\\\sum\\\\_i \\\\theta\\\\_i<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.06em;vertical-align: -0.31em\"><\/span><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\" style=\"margin-right: 0.0278em\">_<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mord\" style=\"margin-right: 0.0278em\">_<\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u6548\u679c<\/td>\n<td>\u6743\u91cd\u5e73\u6ed1\u8d8b\u8fd1\u4e8e 0<\/td>\n<td>\u6743\u91cd\u7a00\u758f&#xff08;\u90e8\u5206\u53d8\u4e3a 0&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u68af\u5ea6<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u03bb<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>          \\\\lambda \\\\theta_i<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u03bb<\/p>\n<p>           \u22c5<\/p>\n<p>           sign<\/p>\n<p>           (<\/p>\n<p>            \u03b8<\/p>\n<p>            i<\/p>\n<p>           )<\/p>\n<p>          \\\\lambda \\\\cdot \\\\text{sign}(\\\\theta_i)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/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 text\"><span class=\"mord\">sign<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: -0.0278em;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 class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u9002\u7528\u573a\u666f<\/td>\n<td>\u7279\u5f81\u5171\u7ebf\u6027\u5f3a\u3001\u9700\u8981\u4fdd\u7559\u6240\u6709\u7279\u5f81<\/td>\n<td>\u7279\u5f81\u9009\u62e9&#xff08;\u81ea\u52a8\u5ffd\u7565\u65e0\u5173\u7279\u5f81&#xff09;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>3.4 Dropout<\/h3>\n<p>Dropout \u7684\u5de5\u4f5c\u6d41\u7a0b\u5982\u4e0b&#xff1a;<\/p>\n<li>\u5728\u6bcf\u6b21\u8bad\u7ec3\u8fed\u4ee3\u4e2d&#xff0c;\u968f\u673a\u9009\u62e9\u4e00\u90e8\u5206\u795e\u7ecf\u5143&#xff08;\u901a\u5e38\u4ee5\u6982\u7387 p\u4e22\u5f03&#xff0c;\u6bd4\u5982 p&#061;0.5&#xff09;\u3002<\/li>\n<li>\u88ab\u9009\u4e2d\u7684\u795e\u7ecf\u5143\u5728\u5f53\u524d\u8fed\u4ee3\u4e2d\u4e0d\u53c2\u4e0e\u524d\u5411\u4f20\u64ad\u548c\u53cd\u5411\u4f20\u64ad\u3002<\/li>\n<li>\u5728\u6d4b\u8bd5\u9636\u6bb5&#xff0c;\u6240\u6709\u795e\u7ecf\u5143\u90fd\u53c2\u4e0e\u8ba1\u7b97&#xff0c;\u4f46\u9700\u8981\u5bf9\u6743\u91cd\u8fdb\u884c\u7f29\u653e&#xff08;\u901a\u5e38\u4e58\u4ee5 1\u2212p&#xff09;&#xff0c;\u4ee5\u4fdd\u6301\u8f93\u51fa\u7684\u671f\u671b\u503c\u4e00\u81f4\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730115135-688a0747b36b6.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> Dropout \u662f\u4e00\u79cd\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u968f\u673a\u4e22\u5f03\u90e8\u5206\u795e\u7ecf\u5143\u7684\u6280\u672f\u3002\u5b83\u901a\u8fc7\u51cf\u5c11\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u4f9d\u8d56\u6765\u9632\u6b62\u6a21\u578b\u8fc7\u4e8e\u590d\u6742&#xff0c;\u4ece\u800c\u907f\u514d\u8fc7\u62df\u5408\u3002<\/li>\n<p><span class=\"token keyword\">import<\/span> torch<\/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 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    x<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>randint<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>dtype<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    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\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>dropout<span class=\"token punctuation\">(<\/span>x<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><\/p>\n<h4>\u793a\u4f8b<\/h4>\n<p>\u5bf9\u56fe\u7247\u8fdb\u884c\u968f\u673a\u4e22\u5f03<\/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<br \/>\n<span class=\"token keyword\">from<\/span> PIL <span class=\"token keyword\">import<\/span> Image<br \/>\n<span class=\"token keyword\">from<\/span> torchvision <span class=\"token keyword\">import<\/span> transforms<br \/>\n<span class=\"token keyword\">import<\/span> os<\/p>\n<p><span class=\"token keyword\">from<\/span> matplotlib <span class=\"token keyword\">import<\/span> pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p>torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">load_img<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">,<\/span> resize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">224<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    pil_img <span class=\"token operator\">&#061;<\/span> Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>convert<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;RGB&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Original image size:&#034;<\/span><span class=\"token punctuation\">,<\/span> pil_img<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u6253\u5370\u539f\u59cb\u5c3a\u5bf8<\/span><br \/>\n    transform <span class=\"token operator\">&#061;<\/span> transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>Resize<span class=\"token punctuation\">(<\/span>resize<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8f6c\u6362\u4e3aTensor\u5e76\u81ea\u52a8\u5f52\u4e00\u5316\u5230[0,1]<\/span><br \/>\n    <span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> transform<span class=\"token punctuation\">(<\/span>pil_img<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u8fd4\u56de[C,H,W]\u683c\u5f0f\u7684tensor<\/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    dirpath <span class=\"token operator\">&#061;<\/span> os<span class=\"token punctuation\">.<\/span>path<span class=\"token punctuation\">.<\/span>dirname<span class=\"token punctuation\">(<\/span>__file__<span class=\"token punctuation\">)<\/span><br \/>\n    path <span class=\"token operator\">&#061;<\/span> os<span class=\"token punctuation\">.<\/span>path<span class=\"token punctuation\">.<\/span>join<span class=\"token punctuation\">(<\/span>dirpath<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;img&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;torch-fcnn\/fcnn-demo\/100.jpg&#039;<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u4f7f\u7528os.path.join\u66f4\u5b89\u5168<\/span><\/p>\n<p>    <span class=\"token comment\"># \u52a0\u8f7d\u56fe\u50cf (\u5df2\u7ecf\u662f[0,1]\u8303\u56f4\u7684Tensor)<\/span><br \/>\n    trans_img <span class=\"token operator\">&#061;<\/span> load_img<span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u6dfb\u52a0batch\u7ef4\u5ea6 [1, C, H, W]&#xff0c;\u56e0\u4e3aDropout\u9ed8\u8ba4\u9700\u89814D\u8f93\u5165<\/span><br \/>\n    trans_img <span class=\"token operator\">&#061;<\/span> trans_img<span class=\"token punctuation\">.<\/span>unsqueeze<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u521b\u5efaDropout\u5c42<\/span><br \/>\n    dropout <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Dropout2d<span class=\"token punctuation\">(<\/span>p<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    drop_img <span class=\"token operator\">&#061;<\/span> dropout<span class=\"token punctuation\">(<\/span>trans_img<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u79fb\u9664batch\u7ef4\u5ea6\u5e76\u8f6c\u6362\u4e3a[H,W,C]\u683c\u5f0f\u4f9bmatplotlib\u663e\u793a<\/span><br \/>\n    trans_img <span class=\"token operator\">&#061;<\/span> trans_img<span class=\"token punctuation\">.<\/span>squeeze<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>permute<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\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    drop_img <span class=\"token operator\">&#061;<\/span> drop_img<span class=\"token punctuation\">.<\/span>squeeze<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>permute<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\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>numpy<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u786e\u4fdd\u6570\u636e\u5728[0,1]\u8303\u56f4\u5185<\/span><br \/>\n    drop_img <span class=\"token operator\">&#061;<\/span> drop_img<span class=\"token punctuation\">.<\/span>clip<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><\/p>\n<p>    <span class=\"token comment\"># \u663e\u793a\u56fe\u50cf<\/span><br \/>\n    fig <span class=\"token operator\">&#061;<\/span> plt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    ax1 <span class=\"token operator\">&#061;<\/span> fig<span class=\"token punctuation\">.<\/span>add_subplot<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\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    ax1<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>trans_img<span class=\"token punctuation\">)<\/span><\/p>\n<p>    ax2 <span class=\"token operator\">&#061;<\/span> fig<span class=\"token punctuation\">.<\/span>add_subplot<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\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    ax2<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>drop_img<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<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730115136-688a0748688bd.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>3.5 \u6570\u636e\u589e\u5f3a<\/h3>\n<p>\u6837\u672c\u6570\u91cf\u4e0d\u8db3&#xff08;\u5373\u8bad\u7ec3\u6570\u636e\u8fc7\u5c11&#xff09;\u662f\u5bfc\u81f4\u8fc7\u62df\u5408&#xff08;Overfitting&#xff09;\u7684\u5e38\u89c1\u539f\u56e0\u4e4b\u4e00&#xff0c;\u53ef\u4ee5\u4ece\u4ee5\u4e0b\u89d2\u5ea6\u7406\u89e3&#xff1a;<\/p>\n<ul>\n<li>\u5f53\u8bad\u7ec3\u6570\u636e\u8fc7\u5c11\u65f6&#xff0c;\u6a21\u578b\u5bb9\u6613\u201c\u8bb0\u4f4f\u201d\u6709\u9650\u7684\u6837\u672c&#xff08;\u5305\u62ec\u566a\u58f0\u548c\u65e0\u5173\u7ec6\u8282&#xff09;&#xff0c;\u800c\u975e\u5b66\u4e60\u901a\u7528\u7684\u89c4\u5f8b\u3002<\/li>\n<li>\u7b80\u5355\u6a21\u578b\u66f4\u53ef\u80fd\u6355\u6349\u771f\u5b9e\u89c4\u5f8b&#xff0c;\u4f46\u6570\u636e\u4e0d\u8db3\u65f6&#xff0c;\u590d\u6742\u6a21\u578b\u4f1a\u503e\u5411\u4e8e\u62df\u5408\u8bad\u7ec3\u96c6\u4e2d\u7684\u5076\u7136\u6027\u6a21\u5f0f&#xff08;\u566a\u58f0&#xff09;\u3002<\/li>\n<li>\u6837\u672c\u4e0d\u8db3\u65f6&#xff0c;\u8bad\u7ec3\u96c6\u7684\u5206\u5e03\u53ef\u80fd\u4e0e\u771f\u5b9e\u5206\u5e03\u504f\u5dee\u8f83\u5927&#xff0c;\u5bfc\u81f4\u6a21\u578b\u5b66\u5230\u9519\u8bef\u7684\u89c4\u5f8b\u3002<\/li>\n<li>\u5c0f\u6570\u636e\u96c6\u4e2d&#xff0c;\u4e2a\u522b\u6837\u672c\u7684\u566a\u58f0&#xff08;\u5982\u6807\u6ce8\u9519\u8bef\u3001\u5f02\u5e38\u503c&#xff09;\u4f1a\u88ab\u653e\u5927&#xff0c;\u6a21\u578b\u53ef\u80fd\u5c06\u566a\u58f0\u8bef\u8ba4\u4e3a\u89c4\u5f8b\u3002<\/li>\n<\/ul>\n<p>\u6570\u636e\u589e\u5f3a&#xff08;Data Augmentation&#xff09;\u662f\u4e00\u79cd\u901a\u8fc7\u4eba\u5de5\u751f\u6210\u6216\u4fee\u6539\u8bad\u7ec3\u6570\u636e\u6765\u589e\u52a0\u6570\u636e\u96c6\u591a\u6837\u6027\u7684\u6280\u672f&#xff0c;\u5e38\u7528\u4e8e\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\u3002\u6570\u636e\u589e\u5f3a\u901a\u8fc7\u201c\u6a21\u62df\u201d\u66f4\u591a\u8bad\u7ec3\u6570\u636e&#xff0c;\u8feb\u4f7f\u6a21\u578b\u5b66\u4e60\u6cdb\u5316\u6027\u66f4\u5f3a\u7684\u89c4\u5f8b&#xff0c;\u800c\u975e\u8bad\u7ec3\u96c6\u4e2d\u7684\u5076\u7136\u6027\u6a21\u5f0f\u3002\u5176\u672c\u8d28\u662f\u4e00\u79cd\u4f4e\u6210\u672c\u7684\u6b63\u5219\u5316\u624b\u6bb5&#xff0c;\u5c24\u5176\u5728\u6570\u636e\u7a00\u7f3a\u65f6\u6548\u679c\u663e\u8457\u3002<\/p>\n<p>\u5728\u4e86\u89e3\u8ba1\u7b97\u673a\u5982\u4f55\u5904\u7406\u56fe\u50cf\u4e4b\u524d&#xff0c;\u9700\u8981\u5148\u4e86\u89e3\u56fe\u50cf\u7684\u6784\u6210\u5143\u7d20\u3002<\/p>\n<p>\u56fe\u50cf\u662f\u7531\u50cf\u7d20\u70b9\u7ec4\u6210\u7684&#xff0c;\u6bcf\u4e2a\u50cf\u7d20\u70b9\u7684\u503c\u8303\u56f4\u4e3a: [0, 255], \u50cf\u7d20\u503c\u8d8a\u5927\u610f\u5473\u7740\u8f83\u4eae\u3002\u6bd4\u5982\u4e00\u5f20 200&#215;200 \u7684\u56fe\u50cf, \u5219\u662f\u7531 40000 \u4e2a\u50cf\u7d20\u70b9\u7ec4\u6210, \u5982\u679c\u6bcf\u4e2a\u50cf\u7d20\u70b9\u90fd\u662f 0 \u7684\u8bdd, \u610f\u5473\u7740\u8fd9\u662f\u4e00\u5f20\u5168\u9ed1\u7684\u56fe\u50cf\u3002<\/p>\n<p>\u6211\u4eec\u770b\u5230\u7684\u5f69\u8272\u56fe\u4e00\u822c\u90fd\u662f\u591a\u901a\u9053\u7684\u56fe\u50cf, \u6240\u8c13\u591a\u901a\u9053\u53ef\u4ee5\u7406\u89e3\u4e3a\u56fe\u50cf\u7531\u591a\u4e2a\u4e0d\u540c\u7684\u56fe\u50cf\u5c42\u53e0\u52a0\u800c\u6210, \u4f8b\u5982\u6211\u4eec\u770b\u5230\u7684\u5f69\u8272\u56fe\u50cf\u4e00\u822c\u90fd\u662f\u7531 RGB \u4e09\u4e2a\u901a\u9053\u7ec4\u6210\u7684&#xff0c;\u8fd8\u6709\u4e00\u4e9b\u56fe\u50cf\u5177\u6709 RGBA \u56db\u4e2a\u901a\u9053&#xff0c;\u6700\u540e\u4e00\u4e2a\u901a\u9053\u4e3a\u900f\u660e\u901a\u9053&#xff0c;\u8be5\u503c\u8d8a\u5c0f&#xff0c;\u5219\u56fe\u50cf\u8d8a\u900f\u660e\u3002<\/p>\n<p>\u6570\u636e\u589e\u5f3a\u662f\u63d0\u9ad8\u6a21\u578b\u6cdb\u5316\u80fd\u529b&#xff08;\u9c81\u68d2\u6027&#xff09;\u7684\u4e00\u79cd\u6709\u6548\u65b9\u6cd5&#xff0c;\u5c24\u5176\u5728\u56fe\u50cf\u5206\u7c7b\u3001\u76ee\u6807\u68c0\u6d4b\u7b49\u4efb\u52a1\u4e2d\u3002\u6570\u636e\u589e\u5f3a\u53ef\u4ee5\u6a21\u62df\u66f4\u591a\u7684\u8bad\u7ec3\u6837\u672c&#xff0c;\u4ece\u800c\u51cf\u5c11\u8fc7\u62df\u5408\u98ce\u9669\u3002\u6570\u636e\u589e\u5f3a\u901a\u8fc7torchvision.transforms\u6a21\u5757\u6765\u5b9e\u73b0\u3002<\/p>\n<h4>3.5.1 \u56fe\u7247\u7f29\u653e<\/h4>\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    path<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;torch-fcnn\/fcnn-demo\/datasets\/100.jpg&#034;<\/span><br \/>\n    img<span class=\"token operator\">&#061;<\/span>Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">)<\/span><\/p>\n<p>    transform<span class=\"token operator\">&#061;<\/span>transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>Resize<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    t_img<span class=\"token operator\">&#061;<\/span>transform<span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>t_img<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span><\/p>\n<p>    t_img <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span>t_img<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>t_img<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>3.5.2 \u968f\u673a\u88c1\u526a<\/h4>\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    path<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;torch-fcnn\/fcnn-demo\/datasets\/100.jpg&#034;<\/span><br \/>\n    img<span class=\"token operator\">&#061;<\/span>Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">)<\/span><\/p>\n<p>    transform<span class=\"token operator\">&#061;<\/span>transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>RandomCrop<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    t_img<span class=\"token operator\">&#061;<\/span>transform<span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># print(t_img.shape)<\/span><\/p>\n<p>    t_img <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span>t_img<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>t_img<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>3.5.3 \u968f\u673a\u6c34\u5e73\u7ffb\u8f6c<\/h4>\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    path<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;torch-fcnn\/fcnn-demo\/datasets\/100.jpg&#034;<\/span><br \/>\n    img<span class=\"token operator\">&#061;<\/span>Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">)<\/span><\/p>\n<p>    transform<span class=\"token operator\">&#061;<\/span>transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>RandomHorizontalFlip<span class=\"token punctuation\">(<\/span>p<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    t_img<span class=\"token operator\">&#061;<\/span>transform<span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># print(t_img.shape)<\/span><\/p>\n<p>    t_img <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span>t_img<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>t_img<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>3.5.4 \u8c03\u6574\u56fe\u7247\u989c\u8272<\/h4>\n<p>img <span class=\"token operator\">&#061;<\/span> Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;.\/img\/100.jpg&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    transform <span class=\"token operator\">&#061;<\/span> transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>transforms<span class=\"token punctuation\">.<\/span>ColorJitter<span class=\"token punctuation\">(<\/span>brightness<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> contrast<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> saturation<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> hue<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    r_img <span class=\"token operator\">&#061;<\/span> transform<span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>r_img<span class=\"token punctuation\">.<\/span>shape<span class=\"token punctuation\">)<\/span><\/p>\n<p>    r_img <span class=\"token operator\">&#061;<\/span> r_img<span class=\"token punctuation\">.<\/span>permute<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\">0<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>r_img<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>3.5.5 \u968f\u673a\u65cb\u8f6c<\/h4>\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    path<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;torch-fcnn\/fcnn-demo\/datasets\/100.jpg&#034;<\/span><br \/>\n    img<span class=\"token operator\">&#061;<\/span>Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">)<\/span><\/p>\n<p>    transform<span class=\"token operator\">&#061;<\/span>transforms<span class=\"token punctuation\">.<\/span>RandomRotation<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">30<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">60<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    expand<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    center<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    fill<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><\/p>\n<p><span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.5.6 \u56fe\u7247\u8f6cTensor<\/h4>\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    t<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    transform<span class=\"token operator\">&#061;<\/span>transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n        <span class=\"token comment\"># \u8f6c\u6362\u4e3aPIL\u56fe\u7247<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToPILImage<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    t_img<span class=\"token operator\">&#061;<\/span>transform<span class=\"token punctuation\">(<\/span>t<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># print(t_img.shape)<\/span><br \/>\n    t_img <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span>t_img<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>t_img<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>3.5.7 Tensor\u8f6c\u56fe\u7247<\/h4>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> PIL <span class=\"token keyword\">import<\/span> Image<br \/>\n<span class=\"token keyword\">from<\/span> torchvision <span class=\"token keyword\">import<\/span> transforms<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">test002<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># 1. \u968f\u673a\u4e00\u4e2a\u6570\u636e\u8868\u793a\u56fe\u7247<\/span><br \/>\n    img_tensor <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">224<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">224<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 2. \u521b\u5efa\u4e00\u4e2atransforms<\/span><br \/>\n    transform <span class=\"token operator\">&#061;<\/span> transforms<span class=\"token punctuation\">.<\/span>ToPILImage<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 3. \u8f6c\u6362\u4e3a\u56fe\u7247<\/span><br \/>\n    img <span class=\"token operator\">&#061;<\/span> transform<span class=\"token punctuation\">(<\/span>img_tensor<span class=\"token punctuation\">)<\/span><br \/>\n    img<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># 4. \u4fdd\u5b58\u56fe\u7247<\/span><br \/>\n    img<span class=\"token punctuation\">.<\/span>save<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;.\/test.jpg&#034;<\/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\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    test002<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.5.8 \u5f52\u4e00\u5316<\/h4>\n<p><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    path<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;torch-fcnn\/fcnn-demo\/datasets\/100.jpg&#034;<\/span><br \/>\n    img<span class=\"token operator\">&#061;<\/span>Image<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">open<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">.<\/span>size<span class=\"token punctuation\">)<\/span><\/p>\n<p>    t<span class=\"token operator\">&#061;<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">224<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    transform <span class=\"token operator\">&#061;<\/span> transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token comment\"># \u5f52\u4e00\u5316<\/span><br \/>\n        transforms<span class=\"token punctuation\">.<\/span>Normalize<span class=\"token punctuation\">(<\/span>mean<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.485<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.456<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.406<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                              std<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.229<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.224<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.225<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                              <span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    t_img<span class=\"token operator\">&#061;<\/span>transform<span class=\"token punctuation\">(<\/span>t<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># print(t_img.shape)<\/span><br \/>\n    t_img <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>permute<span class=\"token punctuation\">(<\/span>t_img<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>t_img<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>3.5.9 \u6570\u636e\u589e\u5f3a\u6574\u5408<\/h4>\n<p><span class=\"token keyword\">from<\/span> PIL <span class=\"token keyword\">import<\/span> Image<br \/>\n<span class=\"token keyword\">from<\/span> pathlib <span class=\"token keyword\">import<\/span> Path<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">from<\/span> torchvision <span class=\"token keyword\">import<\/span> transforms<span class=\"token punctuation\">,<\/span> datasets<span class=\"token punctuation\">,<\/span> utils<\/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\"># \u5b9a\u4e49\u6570\u636e\u589e\u5f3a\u548c\u5f52\u4e00\u5316<\/span><br \/>\n    transform <span class=\"token operator\">&#061;<\/span> transforms<span class=\"token punctuation\">.<\/span>Compose<span class=\"token punctuation\">(<\/span><br \/>\n        <span class=\"token punctuation\">[<\/span><br \/>\n            transforms<span class=\"token punctuation\">.<\/span>RandomHorizontalFlip<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u968f\u673a\u6c34\u5e73\u7ffb\u8f6c<\/span><br \/>\n            transforms<span class=\"token punctuation\">.<\/span>RandomRotation<span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u968f\u673a\u65cb\u8f6c \u00b110 \u5ea6<\/span><br \/>\n            transforms<span class=\"token punctuation\">.<\/span>RandomResizedCrop<span class=\"token punctuation\">(<\/span><br \/>\n                <span class=\"token number\">32<\/span><span class=\"token punctuation\">,<\/span> scale<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0.8<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u968f\u673a\u88c1\u526a\u5230 32&#215;32&#xff0c;\u7f29\u653e\u6bd4\u4f8b\u57280.8\u52301.0\u4e4b\u95f4<\/span><br \/>\n            transforms<span class=\"token punctuation\">.<\/span>ColorJitter<span class=\"token punctuation\">(<\/span><br \/>\n                brightness<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> contrast<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> saturation<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> hue<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><br \/>\n            <span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u968f\u673a\u8c03\u6574\u4eae\u5ea6\u3001\u5bf9\u6bd4\u5ea6\u3001\u9971\u548c\u5ea6\u3001\u8272\u8c03<\/span><br \/>\n            transforms<span class=\"token punctuation\">.<\/span>ToTensor<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u8f6c\u6362\u4e3a Tensor<\/span><br \/>\n            transforms<span class=\"token punctuation\">.<\/span>Normalize<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u5f52\u4e00\u5316&#xff0c;\u8fd9\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u7ecf\u9a8c\u8bbe\u7f6e&#xff0c;\u9002\u7528\u4e8e\u6570\u636e\u8303\u56f4 [0, 1]&#xff0c;\u4f7f\u5176\u6620\u5c04\u5230 [-1, 1]<\/span><br \/>\n        <span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u52a0\u8f7d CIFAR-10 \u6570\u636e\u96c6&#xff0c;\u5e76\u5e94\u7528\u6570\u636e\u589e\u5f3a<\/span><br \/>\n    trainset <span class=\"token operator\">&#061;<\/span> datasets<span class=\"token punctuation\">.<\/span>CIFAR10<span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;.\/cifar10_data&#034;<\/span><span class=\"token punctuation\">,<\/span> train<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> download<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> transform<span class=\"token operator\">&#061;<\/span>transform<span class=\"token punctuation\">)<\/span><br \/>\n    dataloader <span class=\"token operator\">&#061;<\/span> DataLoader<span class=\"token punctuation\">(<\/span>trainset<span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u83b7\u53d6\u4e00\u4e2a\u6279\u6b21\u7684\u6570\u636e<\/span><br \/>\n    images<span class=\"token punctuation\">,<\/span> labels <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">next<\/span><span class=\"token punctuation\">(<\/span><span class=\"token builtin\">iter<\/span><span class=\"token punctuation\">(<\/span>dataloader<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># \u8fd8\u539f\u56fe\u7247\u5e76\u663e\u793a<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><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><span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token comment\"># \u53cd\u5f52\u4e00\u5316&#xff1a;\u5c06\u50cf\u7d20\u503c\u4ece [-1, 1] \u8fd8\u539f\u5230 [0, 1]<\/span><br \/>\n        img <span class=\"token operator\">&#061;<\/span> images<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">0.5<\/span><\/p>\n<p>        <span class=\"token comment\"># \u8f6c\u6362\u4e3a PIL \u56fe\u50cf<\/span><br \/>\n        img_pil <span class=\"token operator\">&#061;<\/span> transforms<span class=\"token punctuation\">.<\/span>ToPILImage<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">(<\/span>img<span class=\"token punctuation\">)<\/span><\/p>\n<p>        <span class=\"token comment\"># \u663e\u793a\u56fe\u7247<\/span><br \/>\n        plt<span class=\"token punctuation\">.<\/span>subplot<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> i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        plt<span class=\"token punctuation\">.<\/span>imshow<span class=\"token punctuation\">(<\/span>img_pil<span class=\"token punctuation\">)<\/span><br \/>\n        plt<span class=\"token punctuation\">.<\/span>axis<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;off&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        plt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;Label: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>labels<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#039;<\/span><\/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<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token 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