{"id":4069,"date":"2025-06-10T21:21:22","date_gmt":"2025-06-10T13:21:22","guid":{"rendered":"https:\/\/www.haruhi.fans\/?p=4069"},"modified":"2025-06-12T23:35:18","modified_gmt":"2025-06-12T15:35:18","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/www.haruhi.fans\/?p=4069","title":{"rendered":"\u673a\u5668\u5b66\u4e60"},"content":{"rendered":"<div class='admonition shadow-sm admonition-primary'><div class='admonition-title'><i class='fa fa-flag'><\/i> \u8003\u8bd5\u5185\u5bb9<\/div><div class='admonition-body'>\u8003\u8bd5\u5f62\u5f0f\uff1a\u5f00\u5377\uff0c\u53ef\u5e26\u4efb\u4f55\u7eb8\u8d28\u8d44\u6599<br \/>\n\u8003\u8bd5\u8bed\u8a00\uff1a\u4e2d\u6587<br \/>\n\u8003\u8bd5\u9898\u578b\uff1a\u5224\u65ad\u3001\u9009\u62e9\u3001\u7b80\u7b54\u3001\u8ba1\u7b97\u3001\u7cfb\u7edf\u8bbe\u8ba1<br \/>\n\u6ce8\u610f\u4e8b\u9879\uff1a\u5e26\u8ba1\u7b97\u5668<br \/>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">\u5f15\u8a00<\/h2>\n\n\n\n<p>\u5b9a\u4e49\uff1a\u4e00\u79cd\u4eba\u5de5\u667a\u80fd\u6280\u672f\uff0c\u53ef\u4ee5\u8ba9\u673a\u5668\u901a\u8fc7\u6570\u636e\u81ea\u52a8\u53d1\u73b0\u7edf\u8ba1\u89c4\u5f8b\uff08\u6a21\u578b\uff09\uff0c\u5e76\u4e0d\u65ad\u4f18\u5316\u81ea\u8eab\u6027\u80fd\uff08\u4f18\u5316\uff09\uff0c\u4ee5\u5b9e\u73b0\u7279\u5b9a\u76ee\u6807\uff08\u5982\u6700\u5c0f\u635f\u5931\uff09<\/p>\n\n\n\n<p>\u6d41\u7a0b\uff1a\u6570\u636e\u51c6\u5907\uff08\u6570\u636e\u6536\u96c6\u3001\u7279\u5f81\u63d0\u53d6\uff09\u2192 \u8bad\u7ec3\uff08\u8bad\u7ec3\u3001\u9a8c\u8bc1\uff09\u2192 \u8bc4\u4f30\uff08\u9884\u6d4b\u3001\u8bc4\u4f30\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u673a\u5668\u5b66\u4e60\u5206\u7c7b<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u76d1\u7763\u5b66\u4e60\n<ul class=\"wp-block-list\">\n<li>\u6570\u636e\uff1a\uff08x\uff0cy\uff09\u5176\u4e2dx\u8868\u793a\u8f93\u5165\u6570\u636e\uff08\u7279\u5f81\uff09\uff0cy\u8868\u793a\u6807\u7b7e\uff08\u76ee\u6807\u503c\uff09<\/li>\n\n\n\n<li>\u76ee\u6807\uff1a\u5b66\u4f1a\u6620\u5c04\u51fd\u6570 f(x) -&gt; y \uff0c\u5373\u901a\u8fc7x\u9884\u6d4by\u3002\u6620\u5c04\u51fd\u6570\u53ef\u4ee5\u4e3a\u7ebf\u6027\u975e\u7ebf\u6027or\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u3002<\/li>\n\n\n\n<li>\u5178\u578b\u4efb\u52a1\uff1a\u5206\u7c7b\uff08\u5982\u5224\u65ad\u662f\u5426\u4e3a\u5783\u573e\u90ae\u7bb1\uff0c\u732b\u72d7\u7b49\uff09\uff0c\u56de\u5f52\uff08\u9884\u6d4b\u80a1\u7968\uff09\uff0c\u76ee\u6807\u68c0\u6d4b\uff08\u8bc6\u522b\u7279\u5b9a\u76ee\u6807\uff0c\u5e76\u7528\u8fb9\u754c\u6846\u6807\u8bb0\u4f4d\u7f6e\uff09\uff0c\u8bed\u4e49\u5206\u5272\uff08\u5bf9\u56fe\u50cf\u6bcf\u4e00\u4e2a\u50cf\u7d20\u90fd\u5206\u7c7b\uff0c\u5982\u81ea\u52a8\u9a7e\u9a76\u5206\u5272\u9053\u8def\u8f66\u8f86\u884c\u4eba\u6807\u5fd7\u5404\u4e2a\u533a\u57df\uff09<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u65e0\u76d1\u7763\u5b66\u4e60\n<ul class=\"wp-block-list\">\n<li>\u6570\u636e\uff1ax<\/li>\n\n\n\n<li>\u76ee\u6807\uff1a\u65e0\u76d1\u7763\u5b66\u4e60\u901a\u8fc7\u5206\u6790\u6570\u636e\u7684\u5206\u5e03\u6216\u7ed3\u6784\uff0c\u627e\u51fa\u6570\u636e\u6f5c\u5728\u7684\u89c4\u5f8b\u7279\u70b9<\/li>\n\n\n\n<li>\u7279\u70b9\uff1a\u805a\u7c7b\uff08\u628a\u6570\u636e\u5206\u7ec4\uff0c\u7c7b\u4f3c\u6570\u636e\u5206\u4e3a\u4e00\u7c7b\uff09\uff0c\u964d\u7ef4\uff08PCA\u4e4b\u7c7b\u7684\uff0c\u7528\u6765\u7b80\u5316\u7ed3\u6784\u5e76\u5c3d\u53ef\u80fd\u4fdd\u7559\u7279\u5f81\uff09\uff0c\u6982\u7387\u5bc6\u5ea6\u4f30\u8ba1\uff08\u98ce\u9669\u8bc4\u4f30\uff09\uff0c\u6570\u636e\u751f\u6210\uff08\u4ece\u539f\u59cb\u6570\u636e\u4e2d\u5b66\u4e60\u5206\u5e03\u5e76\u751f\u6210\u7c7b\u4f3c\u7684\u65b0\u6570\u636e\uff09\uff0c\u5f02\u5e38\u68c0\u6d4b\uff08\u8bc6\u522b\u6570\u636e\u4e2d\u5f02\u5e38\u7684\u70b9or\u5f02\u5e38\u6a21\u5f0f\uff09<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5f3a\u5316\u5b66\u4e60\n<ul class=\"wp-block-list\">\n<li>\u6570\u636e\uff1a\u6765\u6e90\u4e8e\u548c\u73af\u5883\u7684\u4ea4\u4e92\uff0c\u5305\u62ec\n<ul class=\"wp-block-list\">\n<li>\u72b6\u6001\uff1a\u667a\u80fd\u4f53\u5f53\u524d\u72b6\u6001<\/li>\n\n\n\n<li>\u89c2\u5bdf\uff1a\u667a\u80fd\u4f53\u5bf9\u73af\u5883\u7684\u89c2\u5bdf<\/li>\n\n\n\n<li>\u52a8\u4f5c\uff1a\u667a\u80fd\u4f53\u7684\u884c\u4e3a\u9009\u62e9<\/li>\n\n\n\n<li>\u5956\u52b1\uff1a\u6267\u884c\u67d0\u4e00\u4e2a\u52a8\u4f5c\u540e\u7684\u53cd\u9988\uff0c\u7528\u6765\u6307\u5bfc\u5b66\u4e60<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u76ee\u6807\uff1a\u628a\u72b6\u6001state\u6620\u5c04\u5230\u52a8\u4f5caction\uff0c\u4ee5\u6700\u5927\u5316\u957f\u671f\u6536\u76ca<\/li>\n\n\n\n<li>\u5178\u578b\u4efb\u52a1\uff1a\u7b56\u7565\u4f18\u5316\uff0c\u8499\u7279\u5361\u6d1b\u5f3a\u5316\u5b66\u4e60\uff08\u6a21\u62df\u73af\u5883\u548c\u667a\u80fd\u4f53\u7684\u4ea4\u4e92\u6765\u4f18\u5316\u7b56\u7565\uff09\uff0c\u503c\u51fd\u6570\u4f30\u8ba1\uff08\u80a1\u7968\u957f\u671f\u6536\u76ca\uff09\uff0c\u6e38\u620fAI\uff08AlphaGo\uff09\uff0c\u673a\u5668\u4eba\u63a7\u5236<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u6cdb\u5316\u80fd\u529b<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-26.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"287\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-26.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4079\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u6b20\u62df\u5408\uff1a\u6a21\u578b\u4e0d\u591f\u590d\u6742\uff0c\u6ca1\u529e\u6cd5\u523b\u753b\u771f\u5b9e\u89c4\u5f8b\uff0c\u6a21\u578b\u5047\u8bbe\u4e0d\u6210\u7acb<br>\u8fc7\u62df\u5408\uff1a\u6a21\u578b\u8fc7\u4e8e\u590d\u6742\u5bfc\u81f4\u8bb0\u4f4f\u7684\u7ec6\u8282\u4e0d\u662f\u6f5c\u5728\u89c4\u5f8b\uff08\u968f\u673a\u566a\u58f0\u4e4b\u7c7b\uff09<br>\u6b20\u62df\u5408\u548c\u8fc7\u62df\u5408\u672c\u8d28\uff1a\u6a21\u578b\u7684\u590d\u6742\u5ea6\uff0c\u6a21\u578b\u9700\u8981\u5728\u4e8c\u8005\u4e4b\u95f4\u5e73\u8861<\/p>\n\n\n\n<p>\u907f\u514d\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u589e\u52a0\u8bad\u7ec3\u6570\u636e\n<ul class=\"wp-block-list\">\n<li>\u901a\u8fc7\u5927\u91cf\u6570\u636e\u6291\u5236\u6a21\u578b\u8bb0\u5fc6\u6bcf\u4e2a\u6570\u636e\u7684\u7ec6\u8282<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6b63\u5219\u5316\n<ul class=\"wp-block-list\">\n<li>\u5728\u635f\u5931\u51fd\u6570\u4e2d\u5f15\u5165\u5bf9\u6a21\u578b\u53c2\u6570\u7684\u60e9\u7f5a\u9879\uff0c\u9650\u5236\u53c2\u6570\u5927\u5c0f\u6216\u7a00\u758f\u6027\u3002\u539f\u7406\u53ef\u4ee5\u901a\u8fc7\u5bf9\u635f\u5931\u51fd\u6570\u6c42\u68af\u5ea6\uff0c<a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzU0MDQ1NjAzNg==&amp;mid=2247583952&amp;idx=2&amp;sn=62a5f02bc985b078ecb8e9ca7bc24ac7&amp;chksm=fae76ad0e83c35402c6e2994ca407ee8605c0f0c527129a6969f5afd51a9a4d13e4d1de5e7e3&amp;scene=27\">\u53c2\u8003\u6587\u7ae0<\/a>\n<ul class=\"wp-block-list\">\n<li>$ L(W, \\lambda_1, \\lambda_2) = ||y &#8211; WX||_2^2 + \\lambda_2 ||W||_2^2 + \\lambda_1 ||W||_1 $\n<ul class=\"wp-block-list\">\n<li>L1\u6b63\u5219\u5316\uff1a\u60e9\u7f5a\u6a21\u578b\u53c2\u6570\u7684\u7edd\u5bf9\u503c\uff0c\u4f7f\u5f97\u90e8\u5206\u53c2\u6570\u8d8b\u4e8e\u96f6\uff08\u7a00\u758f\u5316\uff09\uff0c\u4fbf\u4e8e\u7b5b\u9009\u51fa\u91cd\u8981\u7279\u5f81<\/li>\n\n\n\n<li>L2\u6b63\u5219\u5316\uff1a\u60e9\u7f5a\u6a21\u578b\u53c2\u6570\u7684\u5e73\u65b9\uff0c\u4f7f\u5f97\u53c2\u6570\u503c\u8f83\u5c0f\u4f46\u4e0d\u4e3a\u96f6\uff08\u5e73\u6ed1\u5316\uff09\uff0c\u4ee5\u6b64\u6765\u964d\u4f4e\u566a\u58f0\u654f\u611f\u5ea6\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6570\u636e\u5212\u5206&amp;\u4ea4\u53c9\u9a8c\u8bc1\n<ul class=\"wp-block-list\">\n<li>\u901a\u8fc7\u5c06\u6570\u636e\u5212\u5206\u4e3a\u8bad\u7ec3\u96c6\u3001\u9a8c\u8bc1\u96c6\u548c\u6d4b\u8bd5\u96c6\uff0c\u786e\u4fdd\u6a21\u578b\u4e0d\u4ec5\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8868\u73b0\u597d\uff0c\u8fd8\u5728\u672a\u77e5\u6570\u636e\u4e0a\u8868\u73b0\u597d\u3002<\/li>\n\n\n\n<li>e.g. K\u6298\u4ea4\u53c9\u9a8c\u8bc1\uff1a\u5c06\u6570\u636e\u5206\u4e3aK\u4efd\uff0c\u6bcf\u6b21\u7528\u5176\u4e2d\u4e00\u4efd\u4f5c\u4e3a\u9a8c\u8bc1\u96c6\uff0c\u5176\u4ed6K-1\u4efd\u4f5c\u4e3a\u8bad\u7ec3\u96c6\uff0c\u5faa\u73afK\u6b21\u3002<br><img decoding=\"async\" src=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-29-1024x394.png\" alt=\"\"><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u65e9\u505c\uff1a\u6a21\u578b\u5f00\u59cb\u53d8\u5dee\u5c31\u505c\u6b62\u8bad\u7ec3<\/li>\n\n\n\n<li>\u5f15\u5165\u5148\u9a8c\u77e5\u8bc6\uff08\u5982\u8d1d\u53f6\u65af\u5148\u9a8c\uff09\n<ul class=\"wp-block-list\">\n<li>\u7ea6\u675f\u6a21\u578b\u7684\u5b66\u4e60\u8fc7\u7a0b\uff0c\u4f7f\u5176\u66f4\u7b26\u5408\u5b9e\u9645\u95ee\u9898\u7684\u89c4\u5f8b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u8bbe\u8ba1\u597d\u7684\u635f\u5931\u51fd\u6570<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ebf\u6027\u56de\u5f52<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u56de\u5f52\u95ee\u9898<\/h3>\n\n\n\n<p>\u901a\u8fc7\u5b9e\u9a8c\u89c2\u6d4b\u6570\u636e\uff0c\u63ed\u793a\u53d8\u91cf\u4e4b\u95f4\u7684\u7edf\u8ba1\u5173\u7cfb\uff0c\u56de\u5f52\u53d8\u91cf\u7684\u771f\u5b9e\u503c\u3002<\/p>\n\n\n\n<p>\u5373\uff1a\u5efa\u7acb\u6570\u5b66\u5173\u7cfb y= f(X)+\u03f5\u3002\u5176\u4e2dX\u4e3a\u81ea\u53d8\u91cf\uff0cy\u4e3a\u56e0\u53d8\u91cf\uff0cf(X)\u4e3a\u56de\u5f52\u6a21\u578b\uff08\u62df\u5408\u6a21\u578b\uff09\uff0c\u03f5\u4e3a\u968f\u673a\u8bef\u5dee\uff08\u65e0\u6cd5\u88ab\u89e3\u91ca\u7684\u90e8\u5206\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7ebf\u6027\u56de\u5f52<\/h3>\n\n\n\n<p>\u56de\u5f52\u51fd\u6570\u4e3a\u7ebf\u6027\u8868\u8fbe\u5f0f\uff0c\u5373 y=f(X)=w<sup>T<\/sup>X+w<sub>0<\/sub><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>X = [x<sub>1<\/sub>,x<sub>2<\/sub>,&#8230;&#8230;,x<sub>d<\/sub>]\uff1a\u8f93\u5165\u7279\u5f81\u5411\u91cf\uff08\u81ea\u53d8\u91cf\uff09\u3002<\/li>\n\n\n\n<li>W = [w<sub>1<\/sub>,w<sub>2<\/sub>,&#8230;&#8230;,w<sub>d<\/sub>]\uff1a\u6a21\u578b\u7684\u53c2\u6570\uff08\u6743\u91cd\uff09\u3002<\/li>\n\n\n\n<li>w<sub>0<\/sub>\uff1a\u504f\u7f6e\u9879<\/li>\n\n\n\n<li>f(X)\uff1a\u9884\u6d4b\u503c<\/li>\n<\/ul>\n\n\n\n<p>\u5bf9\u4e8e\u8bad\u7ec3\u8fc7\u7a0b\uff0c\u662f\u6839\u636e\u8bef\u5dee\uff0c\u4e0d\u65ad\u8c03\u6574\u53c2\u6570w<sup>T<\/sup>\u548cw<sub>0<\/sub><br>\u5bf9\u4e8e\u9884\u6d4b\u8fc7\u7a0b\uff0c\u662f\u5bf9\u4e8e\u65b0\u6570\u636ex\uff0c\u8ba1\u7b97f(x)\uff0c\u5f97\u5230\u56de\u5f52\u503cy<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u635f\u5931\u51fd\u6570<\/h3>\n\n\n\n<p>\u5355\u4e2a\u6837\u672c\u7684\u5e73\u65b9\u65b9\u5dee\uff0c\u5176\u4e2dx\u4e3a\u8f93\u5165\u6837\u672c\uff0cy\u4e3a\u6a21\u578b\u8f93\u51fa\uff0c\u771f\u5b9e\u503c\u4e3ar\uff1a<\/p>\n\n\n\n<p>$$l(w, w_0 \\mid x, r) = (r &#8211; y)^2$$<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u6574\u4e2a\u6570\u636e\u96c6D={(x<sup>(1)<\/sup>,r<sup>(1)<\/sup>),\u2026,(x<sup>(n)<\/sup>,r<sup>(n)<\/sup>)}\uff08N\u4e2a\u6837\u672c\uff09\u7684\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<p>$$L(w, w_0 \\mid D) = \\frac{1}{2N} \\sum_{i=1}^N (r^{(i)} &#8211; \\hat{y}^{(i)})^2$$<\/p>\n\n\n\n<p>\u9664\u4ee52\u662f\u4e3a\u4e86\u7b80\u5316\u540e\u7eed\u68af\u5ea6\u516c\u5f0f\u63a8\u5bfc\uff0c\u5e38\u6570\u7cfb\u6570\u4e0d\u4f1a\u5f71\u54cd\u6a21\u578b\u4f18\u5316\u65b9\u5411\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f18\u5316<\/h3>\n\n\n\n<p>\u4f18\u5316\u7684\u76ee\u6807\u4e3a\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\uff1a $ \\min_w L(w) $<br>\u8fed\u4ee3\u6b65\u9aa4\uff1a$ w_{t+1} = w_t &#8211; \\eta_t \\frac{\\partial L}{\\partial w} $<\/p>\n\n\n\n<p>\u8ba1\u7b97$ \\frac{\\partial L}{\\partial w} $:<br>\u5bf9\u4e8e\u4efb\u610f\u53c2\u6570w<sub>j<\/sub>\uff1a$ \\frac{\\partial L}{\\partial w_j} = -\\frac{1}{N} \\sum_{i=1}^N (r^{(i)} &#8211; \\hat{y}^{(i)}) \\frac{\\partial L^{(i)}}{\\partial w_j} = -\\frac{1}{N} \\sum_{i=1}^N (r^{(i)} &#8211; \\hat{y}^{(i)}) x_j^{(i)}  $<\/p>\n\n\n\n<p>\u8fed\u4ee3\u89c4\u5219\uff1a$ w_{\\text{new}} = w_{\\text{old}} &#8211; \\frac{1}{N} \\sum_{i=1}^N (r^{(i)} &#8211; \\hat{y}^{(i)}) x_j^{(i)} $<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u5f62\u5f0f<\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u68af\u5ea6\u4e0b\u964d\u6cd5\u6c42\u7ebf\u6027\u56de\u5f52\u5176\u5b9e\u6ca1\u5fc5\u8981\uff0c\u56e0\u4e3a\u901a\u8fc7\u6570\u5b66\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230\u6700\u4f18\u503c\u3002<\/p>\n\n\n\n<p>\u4ee4\uff1a<\/p>\n\n\n\n<p>$$<br>X =<br>\\begin{bmatrix}<br>x^{(1)} \\\\<br>x^{(2)} \\\\<br>\\vdots \\\\<br>x^{(N)}<br>\\end{bmatrix} =<br>\\begin{bmatrix}<br>x_0^{(1)} &amp; x_1^{(1)} &amp; x_2^{(1)} &amp; \\dots &amp; x_d^{(1)} \\\\<br>x_0^{(2)} &amp; x_1^{(2)} &amp; x_2^{(2)} &amp; \\dots &amp; x_d^{(2)} \\\\<br>\\vdots &amp; \\vdots &amp; \\ddots &amp; \\ddots &amp; \\vdots \\\\<br>x_0^{(N)} &amp; x_1^{(N)} &amp; x_2^{(N)} &amp; \\dots &amp; x_d^{(N)}<br>\\end{bmatrix},<br>\\quad<br>w =<br>\\begin{bmatrix}<br>w_1 \\\\<br>w_2 \\\\<br>\\vdots \\\\<br>w_d<br>\\end{bmatrix},<br>\\quad<br>r =<br>\\begin{bmatrix}<br>r^{(1)} \\\\<br>r^{(2)} \\\\<br>\\vdots \\\\<br>r^{(N)}<br>\\end{bmatrix}<br>$$<\/p>\n\n\n\n<p>\u90a3\u4e48\u6b64\u65f6\uff0c\u9884\u6d4b\u503c\uff1a$ y = Xw =<br>\\begin{bmatrix}<br>x^{(1)} w \\\\<br>x^{(2)} w \\\\<br>\\vdots \\\\<br>x^{(N)} w<br>\\end{bmatrix} $<br>\u635f\u5931\u51fd\u6570\uff1a$ L(w) = \\frac{1}{2} (r &#8211; y)^T (r &#8211; y) = \\frac{1}{2} (r &#8211; Xw)^T (r &#8211; Xw) $<br>\u68af\u5ea6\uff1a $ L(w) = \\frac{1}{2} (r &#8211; y)^T (r &#8211; y) = \\frac{1}{2} (r &#8211; Xw)^T (r &#8211; Xw) $<br>\u4ee4\u68af\u5ea6\u4e3a0\uff0c\u5f97\u5230\uff1a$ \\frac{\\partial L(w)}{\\partial w} = 0 \\implies X^T (r &#8211; Xw) = 0 \\implies X^T r = X^T X w $<br>\u4ece\u800c\u5f97\u5230\uff1a$ w^* = (X^T X)^{-1} X^T r $<br>\u5e26\u5165$ w^* $\uff0c\u6700\u540e\u5f97\u5230\u9884\u6d4b\u503c $ y = X (X^T X)^{-1} X^T r = H r $<br>\u6211\u4eec\u6b64\u65f6\u53ea\u9700\u8981\u7b97\u51faH\u5373\u53ef<\/p>\n\n\n\n<p>\u95ee\u9898\uff1aX<sup>T<\/sup>X\u53ef\u80fd\u4e0d\u53ef\u9006\uff08\u5982x<sub>2<\/sub>=3x<sub>1<\/sub>\uff09\uff0c\u5bfc\u81f4\u6211\u4eec\u8fd8\u662f\u53ea\u80fd\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5<br>\u89e3\u51b3\uff1a\u4f7f\u7528\u6b63\u5219\u5316\uff0c\u5bf9\u635f\u5931\u51fd\u6570\u5f15\u5165\u60e9\u7f5a\u9879<\/p>\n\n\n\n<p>\u65b0\u7684\u635f\u5931\u51fd\u6570\uff1a$ L(w) = \\frac{1}{2} (r &#8211; y)^T (r &#8211; y) = \\frac{1}{2} (r &#8211; Xw)^T (r &#8211; Xw) + \\frac{\\lambda}{2} |w|_2^2 $<br>\u65b0\u7684\u68af\u5ea6\uff1a$ \\frac{\\partial L(w)}{\\partial w} = -X^T (r &#8211; Xw) + \\lambda w $<br>\u65b0\u7684\u6700\u4f18\u89e3\uff1a$ \\frac{\\partial L(w)}{\\partial w} = 0 \\implies -X^T (r &#8211; Xw) + \\lambda w = 0 \\implies X^T r = (X^T X + \\lambda I) w $<br>\u4ece\u800c\u5f97\u5230\uff1a$ w^* = (X^T X + \\lambda I)^{-1} X^T r $<br>\u56e0\u4e3aX<sup>T<\/sup>X + \u03bbI\u4e00\u5b9a\u662f\u6ee1\u79e9\u7684\uff0c\u6240\u4ee5\u4e00\u5b9a\u53ef\u9006<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u51b3\u7b56\u6811<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u56de\u5f52\uff08\u9884\u6d4b\u8fde\u7eed\u503c\u6807\u7b7e\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u6570\u636e\u70b9\u5728\uff08d+1\uff09\u7ef4\u7a7a\u95f4\uff08d \u662f\u7279\u5f81\u7ef4\u5ea6\uff0c+1 \u7ef4\u662f\u6807\u7b7e\u8f74 y\uff09\u4e2d\u7684\u5206\u5e03\u8fdb\u884c\u5efa\u6a21\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5206\u7c7b\uff08\u9884\u6d4b\u7c7b\u522b\u6807\u7b7e\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5bf9 d \u7ef4\u7a7a\u95f4\u4e2d\u4e0d\u540c\u7c7b\u522b\u6570\u636e\u7684\u5206\u754c\u8fb9\u754c\u8fdb\u884c\u5efa\u6a21\uff0c\u901a\u8fc7\u51b3\u7b56\u8fb9\u754c\u5212\u5206\u4e0d\u540c\u7c7b\u522b\u533a\u57df\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u5206\u7c7b\u95ee\u9898\u4e2d\uff0c\u53ef\u80fd\u9047\u5230\u65e0\u6cd5\u7ebf\u6027\u5206\u5272\u7684\u95ee\u9898\uff0c\u6216\u8005\u5c5e\u6027\u975e\u6570\u5b57\uff0c\u4f46\u662f\u6cbf\u7740\u67d0\u4e9b\u7ef4\u5ea6\u5c40\u90e8\u7ebf\u6027\u53ef\u5206<br>\u89e3\u51b3\u601d\u60f3\uff1a\u5206\u800c\u6cbb\u4e4b\uff08\u521b\u5efa\u4e00\u7cfb\u5217if then\u6761\u4ef6\uff09\uff0c\u901a\u8fc7\u51b3\u7b56\u6811\u5efa\u7acb\u4e00\u7cfb\u5217\u51b3\u7b56\u89c4\u5219\u5bf9\u6570\u636e\u8fdb\u884c\u5206\u7c7b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-30.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"526\" height=\"522\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-30.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4150\" style=\"width:348px;height:auto\"  sizes=\"auto, (max-width: 526px) 100vw, 526px\" \/><\/div><\/figure>\n\n\n\n<p>\u6784\u9020\u51b3\u7b56\u6811\u7684\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6784\u9020\u4e00\u4e2a\u6839\u8282\u70b9\uff0c\u5305\u542b\u6574\u4e2a\u6570\u636e\u96c6<\/li>\n\n\n\n<li>\u9009\u62e9\u4e00\u4e2a\u6700\u5408\u9002\u7684\u5c5e\u6027<\/li>\n\n\n\n<li>\u6839\u636e\u9009\u62e9\u5c5e\u6027\u7684\u4e0d\u540c\u53d6\u503c\uff0c\u5c06\u5f53\u524d\u8282\u70b9\u7684\u6837\u672c\u5212\u5206\u6210\u82e5\u5e72\u5b50\u96c6<\/li>\n\n\n\n<li>\u5bf9\u6bcf\u4e2a\u5212\u5206\u540e\u7684\u5b50\u96c6\u521b\u5efa\u4e00\u4e2a\u5b69\u5b50\u8282\u70b9\uff0c\u5e76\u5c06\u5b50\u96c6\u7684\u6570\u636e\u4f20\u7ed9\u8be5\u5b69\u5b50\u8282\u70b9<\/li>\n\n\n\n<li>\u9012\u5f52\u91cd\u590d2~4\u76f4\u5230\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6<\/li>\n<\/ul>\n\n\n\n<p>\u5982\u4f55\u9ad8\u6548\u6784\u5efa\u51b3\u7b56\u6811\uff1f<br>\u9009\u62e9\u6bcf\u4e2a\u5c5e\u6027X\u7684\u65f6\u5019\uff0c\u5c3d\u53ef\u80fd\u6700\u5927\u5316\u6807\u7b7eY\u7684\u7eaf\u5ea6\u3002<\/p>\n\n\n\n<p>\u5982\u4f55\u9009\u62e9\u5c5e\u6027\u4ee5\u6700\u5927\u5316\u6807\u7b7e\u7684\u7eaf\u5ea6\uff1f<br>\u9009\u62e9X\u4ee5\u6700\u5927\u5316\u4fe1\u606f\u589e\u76ca\u3001Gini\u7cfb\u6570\u7b49<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">ID3\u7b97\u6cd5<\/h3>\n\n\n\n<p>\u6839\u636e\u4fe1\u606f\u589e\u76ca\u8fdb\u884c\u5212\u5206\uff0c\u76ee\u6807\u662f\u4f7f\u4fe1\u606f\u589e\u76ca\uff08Information Gain\uff09\u6700\u5927\u5316<\/p>\n\n\n\n<p>\u4fe1\u606f\u71b5<strong>\u8868\u793a\u6570\u636e\u96c6\u5408\u7684\u4e0d\u7eaf\u51c0\u5ea6<\/strong>\uff0c\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p>$$H(D) = -\\sum_{k=1}^{K} p_k \\log p_k = -\\sum_{k=1}^{K} \\frac{|C_k|}{|D|} \\log \\frac{|C_k|}{|D|}$$<\/p>\n\n\n\n<p>$ |C_k| $\uff1a\u6570\u636e\u96c6\u4e2d\u5c5e\u4e8e\u7c7b\u522b$ C_k $\u7684\u6837\u672c\u6570\u91cf<br>$ |D| $\uff1a\u6570\u636e\u96c6\u7684\u603b\u6837\u672c\u6570\u91cf<\/p>\n\n\n\n<p>\u6761\u4ef6\u71b5\u8868\u793a\u6570\u636e\u96c6\u5728\u67d0\u4e2a\u5c5e\u6027&nbsp;<em>A<\/em>&nbsp;\u6761\u4ef6\u4e0b\u7684\u4e0d\u7eaf\u51c0\u5ea6\uff0c\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p>$$H(D|A) = \\sum_{i=1}^{n} \\frac{|D_i|}{|D|} H(D_i) = -\\sum_{i=1}^{n} \\frac{|D_i|}{|D|} \\left( \\sum_{k=1}^{K} \\frac{|D_{ik}|}{|D_i|} \\log \\frac{|D_{ik}|}{|D_i|} \\right)$$<\/p>\n\n\n\n<p>$ |D_i| $\uff1a\u6570\u636e\u96c6\u4e2d\u5c5e\u6027&nbsp;<strong>A<\/strong>&nbsp;\u53d6\u7b2c&nbsp;<strong>i<\/strong>&nbsp;\u4e2a\u503c\u7684\u6837\u672c\u6570\u91cf\uff1b<br>$ |D_{ik}| $\uff1a\u5728&nbsp;D<sub>i&nbsp;<\/sub>\u4e2d\u5c5e\u4e8e\u7c7b\u522b&nbsp;C<sub>k<\/sub>&nbsp;\u7684\u6837\u672c\u6570\u91cf\u3002<\/p>\n\n\n\n<p>\u4fe1\u606f\u589e\u76ca\u8868\u793a\u9009\u62e9\u67d0\u4e2a\u5c5e\u6027&nbsp;<em>A<\/em>&nbsp;\u540e\uff0c\u4fe1\u606f\u71b5\u7684\u51cf\u5c11\u7a0b\u5ea6\uff1a<\/p>\n\n\n\n<p>$$Gain(D, A) = H(D) &#8211; H(D|A)$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f8b\u9898<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-31-1024x363.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"363\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-31-1024x363.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4157\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-32.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"441\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-32.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4159\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-33.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"623\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-33.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4160\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-34.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"666\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-34.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4161\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u505c\u6b62\u5212\u5206\u6761\u4ef6\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7eaf\u5ea6\uff1a\u53f6\u5b50\u8282\u70b9\u5305\u542b\u7684\u6837\u672c\u5747\u5c5e\u4e8e\u540c\u4e00\u7c7b<\/li>\n\n\n\n<li>\u6570\u636e\u91cf\u8fc7\u5c0f\uff1a\u53f6\u5b50\u8282\u70b9\u5305\u542b\u7684\u6837\u672c\u6570\u5c0f\u4e8e\u4e00\u4e2a\u9608\u503c<\/li>\n\n\n\n<li>\u6ca1\u6709\u5c5e\u6027\u53ef\u5206\uff08ID3\uff09\uff1aID3\u5bf9\u6bcf\u4e2a\u5c5e\u6027\u53ea\u5212\u5206\u4e00\u6b21<\/li>\n<\/ul>\n\n\n\n<p>\u4f18\u70b9\uff1a\u7b80\u5355\uff0c\u4fbf\u4e8e\u53ef\u89c6\u5316\u5206\u6790\uff1b\u5bf9\u6570\u636e\u9884\u5904\u7406\u8981\u6c42\u4f4e\uff0c\u53ef\u4ee5\u5bb9\u6613\u5904\u7406\u975e\u7ebf\u6027\u8fb9\u754c\uff0c\u6570\u636e\u9a71\u52a8\uff0c\u53ef\u4ee5\u4efb\u610f\u62df\u5408\u6570\u636e\u96c6<br>\u7f3a\u70b9\uff1a\u8fc7\u62df\u5408\uff08\u566a\u58f0\u6837\u4f8b\u4e5f\u4f1a\u88ab\u5b66\u4e60\uff09<\/p>\n\n\n\n<p>\u89e3\u51b3\uff1a\u968f\u673a\u68ee\u6797<\/p>\n\n\n\n<p>\u5c06\u6570\u636e\u968f\u673a\u5212\u5206\u5b50\u96c6\uff0c\u5404\u81ea\u6784\u5efa\u51b3\u7b56\u6811\uff0c\u6309\u591a\u4e2a\u51b3\u7b56\u6811\u7684\u7ed3\u679c\u6295\u7968\u51b3\u5b9a\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4f18\u70b9\uff08\u7528\u968f\u673a\u6027\u6362\u7a33\u5b9a\u6027\uff0c\u7528\u96c6\u6210\u6362\u7cbe\u5ea6\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u901a\u8fc7\u53cc\u91cd\u968f\u673a\u6027\uff08\u6570\u636e\u81ea\u52a9\u91c7\u6837&nbsp;+&nbsp;\u7279\u5f81\u5b50\u96c6\u968f\u673a\u9009\u62e9\uff09\u964d\u4f4e\u8fc7\u62df\u5408\u98ce\u9669\uff0c\u6bd4\u5355\u68f5\u51b3\u7b56\u6811\u66f4\u51c6\u786e\uff1b<\/li>\n\n\n\n<li>\u53ef\u4ee5\u5904\u7406\u9ad8\u7ef4\u6570\u636e\uff0c\u5e76\u4e14\u4e0d\u7528\u505a\u7279\u5f81\u9009\u62e9 (\u56e0\u4e3a\u7279\u5f81\u5b50\u96c6\u662f\u968f\u673a\u9009\u62e9\u7684)\uff1b<\/li>\n\n\n\n<li>\u8bad\u7ec3\u901f\u5ea6\u5feb\uff08\u6811\u4e0e\u6811\u72ec\u7acb\u751f\u6210\uff0c\u5929\u7136\u652f\u6301\u5e76\u884c\u5316\uff09\uff1b<\/li>\n\n\n\n<li>\u53ef\u5904\u7406\u7f3a\u5931\u503c\u3001\u4e0d\u5e73\u8861\u6570\u636e\uff08\u901a\u8fc7\u91c7\u6837\u5e73\u8861\u8bef\u5dee\uff09\u548c\u7279\u5f81\u4ea4\u4e92\uff08\u81ea\u52a8\u68c0\u6d4b\u7279\u5f81\u95f4\u5173\u7cfb\uff09\uff1b<\/li>\n\n\n\n<li>\u63d0\u4f9b\u7279\u5f81\u91cd\u8981\u6027\u6392\u5e8f\uff0c\u540c\u65f6\u4fdd\u6301\u96c6\u6210\u6a21\u578b\u7684\u76f4\u89c2\u89e3\u91ca\u6027\uff08i.e.,\u5728\u8bad\u7ec3\u5b8c\u540e\uff0c\u80fd\u591f\u7ed9\u51fa\u54ea\u4e9bfeature\u6bd4\u8f83\u91cd\u8981\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u8d1d\u53f6\u65af\u5206\u7c7b<\/h2>\n\n\n\n<p>\u5bf9\u4e8e\u6570\u636e\u4ea4\u878d\u5728\u4e00\u8d77\uff0c\u51b3\u7b56\u6811\u6ca1\u6709\u529e\u6cd5\u7cbe\u51c6\u533a\u5206<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-35.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"494\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-35.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4163\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u89e3\u51b3\uff1a\u4f9d\u9760\u6982\u7387\u8bba\uff0c\u901a\u8fc7\u8ba1\u7b97\u67d0\u4e2a\u70b9\u5c5e\u4e8e\u67d0\u4e00\u7c7b\u7684\u6982\u7387\u89e3\u51b3\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u516c\u5f0f\uff1a$ P(C_i|x)=\\frac{p(x|C_i)P(C_i)}{p(x)}, \\ i=1,2,\\dots,N $<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>C<sub>i<\/sub> \u662f\u7b2c i \u4e2a\u7c7b\u522b\uff08\u5171N\u4e2a\uff09\uff0cx \u6570\u636e\u7279\u5f81\u5411\u91cf\uff1b<\/li>\n\n\n\n<li>P(C<sub>i<\/sub>) \u5148\u9a8c\u6982\u7387\uff0c\u5728\u672a\u89c2\u6d4b\u6570\u636e\u65f6\uff0c\u7c7b\u522b P(C<sub>i<\/sub>) \u7684\u521d\u59cb\u6982\u7387\uff08\u53ef\u901a\u8fc7\u8bad\u7ec3\u96c6\u9891\u7387\u4f30\u8ba1\uff09\uff1b<\/li>\n\n\n\n<li>p(x|C<sub>i<\/sub>) \u4f3c\u7136\u6982\u7387\uff0c\u5728\u7c7b\u522b Ci \u6210\u7acb\u7684\u6761\u4ef6\u4e0b\uff0c\u89c2\u6d4b\u5230\u6570\u636e x \u7684\u6982\u7387\uff1b<\/li>\n\n\n\n<li>p(x) \u8bc1\u636e\u6982\u7387\uff0c\u662f\u6240\u6709\u7c7b\u522b\u4e0b\u751f\u6210\u7279\u5f81 x \u7684\u603b\u6982\u7387\uff0c\u7528\u4e8e\u5f52\u4e00\u5316\uff1b<\/li>\n\n\n\n<li>p(x)=\u2211N<sub>i<\/sub>=1P(C<sub>i<\/sub>)p(x|C<sub>i<\/sub>)<\/li>\n\n\n\n<li>p(C<sub>i<\/sub>|x) \u540e\u9a8c\u6982\u7387\uff0c\u89c2\u5bdf\u5230\u6570\u636e x \u540e\uff0c\u6837\u672c\u5c5e\u4e8e\u7c7b\u522bC<sub>i<\/sub>\u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5bf9\u4e8e\u591a\u4e2a\u7279\u5f81\uff0c\u516c\u5f0f\u53d8\u4e3a\uff1a<\/p>\n\n\n\n<p>$$ P(C_i | x_1, x_2, \\dots, x_d) = \\frac{p(x_1, x_2, \\dots, x_d | C_i) P(C_i)}{p(x_1, x_2, \\dots, x_d)} $$<\/p>\n\n\n\n<p>\u7531\u4e8e\u6211\u4eec\u53ea\u8003\u8651\u6982\u7387\u7684\u76f8\u5bf9\u5927\u5c0f\uff0c\u56e0\u6b64\u53ea\u7528\u8ba1\u7b97\u5206\u5b50\u7684\u90e8\u5206\uff1a<\/p>\n\n\n\n<p>$$ P(C_i | x_1, x_2, \\dots, x_d) \\propto p(x_1, x_2, \\dots, x_d | C_i) P(C_i) $$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u72ec\u7acb\u6027\u5047\u8bbe\uff08\u6734\u7d20\u8d1d\u53f6\u65af\u5047\u8bbe\uff09<\/h3>\n\n\n\n<p>\u5982\u679c\u5404\u4e2a\u7279\u5f81\u4e4b\u95f4x<sub>j<\/sub>\u90fd\u662f\u72ec\u7acb\u7684\uff0c\u5219\uff1a<\/p>\n\n\n\n<p>$ p(x_1,x_2,\\dots,x_d|C) = P(x_1|C) \\cdot P(x_2|x_1,C) \\dots P(x_d|x_1,\\dots,x_{d-1},C)$<br>$ \\approx P(x_1|C) \\cdot P(x_2|C) \\dots P(x_d|C) $<\/p>\n\n\n\n<p>\u6b64\u65f6\uff0c\u8d1d\u53f6\u65af\u516c\u5f0f\u53ef\u4ee5\u7b80\u5316\u4e3a<\/p>\n\n\n\n<p>$$ P(C_i | x_1, x_2, \\dots, x_d) \\propto P(C_i) \\prod_{j=1}^d p(x_j | C_i) $$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u865a\u62df\u8ba1\u6570\u4fee\u6b63<\/h3>\n\n\n\n<p>\u8ba1\u7b97&nbsp;\ud835\udc43(\ud835\udc65<sub>\ud835\udc57<\/sub>\u2223\ud835\udc36<sub>\ud835\udc56<\/sub>)&nbsp;\u65f6\uff0c\u53ef\u80fd\u51fa\u73b0\u67d0\u4e9b\u503c\u4e3a 0 \u7684\u60c5\u51b5\uff0c\u53ef\u4ee5\u901a\u8fc7\u865a\u62df\u8ba1\u6570\uff08\u5e73\u6ed1\u5904\u7406\uff09\u4fee\u6b63\uff1a<\/p>\n\n\n\n<p>$$ P(x_j | C_i) = \\frac{\\text{count}(x_j, C_i) + \\alpha}{\\text{count}(C_i) + \\alpha \\cdot |\\text{X}|} $$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>\u03b1<\/em>&nbsp;\u662f\u5e73\u6ed1\u53c2\u6570\uff08\u5982\u62c9\u666e\u62c9\u65af\u5e73\u6ed1\u4e2d <em>\u03b1<\/em>=1\uff09\u3002<\/li>\n\n\n\n<li>\u2223X\u2223\u662f\u6240\u6709\u7279\u5f81\u53d6\u503c\u7684\u6570\u91cf\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u603b\u7ed3\u4f18\u7f3a\u70b9<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4f18\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8bad\u7ec3\u548c\u6d4b\u8bd5\u901f\u5ea6\u5feb\u3002<\/li>\n\n\n\n<li>\u8868\u73b0\u597d\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5f53\u72ec\u7acb\u6027\u5047\u8bbe\u6210\u7acb\u65f6\uff0c\u6548\u679c\u975e\u5e38\u597d\u3002<\/li>\n\n\n\n<li>\u5728\u591a\u5206\u7c7b\u95ee\u9898\u4e2d\u8868\u73b0\u826f\u597d\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6613\u4e8e\u5728\u6570\u636e\u96c6\u66f4\u65b0\u65f6\u8fdb\u884c\u8bad\u7ec3\uff0c\u7b97\u6cd5\u6613\u7ef4\u62a4\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7f3a\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4f9d\u8d56\u4e8e\u72ec\u7acb\u6027\u5047\u8bbe\uff0c\u5982\u679c\u7279\u5f81\u4e4b\u95f4\u5b58\u5728\u8f83\u5f3a\u7684\u76f8\u5173\u6027\uff0c\u6a21\u578b\u6548\u679c\u53ef\u80fd\u53d7\u5f71\u54cd\u3002<\/li>\n\n\n\n<li>\u5bb9\u6613\u6b20\u62df\u5408\uff1a\u7531\u4e8e\u6a21\u578b\u7684\u7b80\u5355\u6027\uff0c\u53ef\u80fd\u65e0\u6cd5\u6355\u6349\u6570\u636e\u7684\u590d\u6742\u6a21\u5f0f\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">K-\u8fd1\u90bb KNN<\/h2>\n\n\n\n<p>\u57fa\u672c\u539f\u5219\uff1a\u6839\u636e\u8ddd\u79bb\u81ea\u5df1\u6700\u8fd1\u7684\u51e0\u4e2a\u70b9\u7684\u6240\u5c5e\u7c7b\u522b\u8fdb\u884c\u6295\u7968<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-36.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"433\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-36.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4181\"  sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u9009\u53d6\u6307\u6807<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8ddd\u79bb\u6307\u6807\n<ul class=\"wp-block-list\">\n<li>\u6b27\u6c0f\u8ddd\u79bb\uff1aL2\u6cdb\u6570\uff0c\u5e73\u65b9\u8ddd\u79bb$ D(x,y) = \\sqrt{\\sum_{i=1}^n(x_i-y_i)^2} $<\/li>\n\n\n\n<li>\u66fc\u54c8\u987f\u8ddd\u79bb\uff1aL1\u6cdb\u6570$ D(x,y) = \\sqrt{\\sum_{i=1}^n|x_i-y_i|} $<\/li>\n\n\n\n<li>\u95f5\u5f0f\u8ddd\u79bb\uff1a$ D(x,y) = \\big( {\\sum_{i=1}^n(x_i-y_i)^p} \\big) ^\\frac{1}{p} $<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5f52\u4e00\u5316\uff1a\u4fdd\u8bc1\u5404\u4e2a\u5c5e\u6027\u5c3a\u5ea6\u4e00\u81f4\uff0c\u4fbf\u4e8e\u5904\u7406\n<ul class=\"wp-block-list\">\n<li>Z-score\u6807\u51c6\u5316\uff1a$ x_{\\text{norm}} = \\frac{x \u2013 \\mu}{\\sigma} $\uff0c\u628a\u7279\u5f81\u7f29\u653e\u5230\u8ddd\u79bb\u4e3a0\uff0c\u6807\u51c6\u5dee\u4e3a1\u7684\u5206\u5e03<\/li>\n\n\n\n<li>Min-Max\u5f52\u4e00\u5316\uff1a$ x_{\\text{norm}} = \\frac{x \u2013 x_{\\text{min}}}{x_{\\text{max}} \u2013 x_{\\text{min}}} $\uff0c\u628a\u7279\u5f81\u7f29\u653e\u5230&nbsp;[0, 1] \u6216 [-1, 1] \u533a\u95f4\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u76f8\u4f3c\u5ea6\uff1a\u4e0d\u4e00\u5b9a\u8981\u7528\u8ddd\u79bb\u4f5c\u4e3a\u9650\u5236\uff0c\u7528\u76f8\u4f3c\u5ea6\u4e5f\u53ef\u4ee5\n<ul class=\"wp-block-list\">\n<li>\u4f59\u5f26\u76f8\u4f3c\u5ea6<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b97\u6cd5\u8fc7\u7a0b<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9884\u5904\u7406\u6570\u636e\uff08\u7279\u5f81\u6807\u7b7e\u5f52\u4e00\u5316\uff09<\/li>\n\n\n\n<li>\u8ba1\u7b97\u8f93\u5165\u6837\u672c\u4e0e\u8bad\u7ec3\u6837\u672c\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u6216\u76f8\u4f3c\u5ea6\uff09<\/li>\n\n\n\n<li>\u5bf9\u8ddd\u79bb\u6392\u5e8f\u5e76\u9009\u53d6 K \u4e2a\u6700\u8fd1\u90bb\u6837\u672c<\/li>\n\n\n\n<li>\u6839\u636e K \u4e2a\u90bb\u5c45\u7684\u591a\u6570\u6295\u7968\u7ed3\u679c\u786e\u5b9a\u6d4b\u8bd5\u6837\u672c\u7c7b\u522b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">K\u503c\u9009\u53d6<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-38.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"563\" height=\"287\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-38.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4189\"  sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/div><\/figure>\n\n\n\n<p>\u4e0a\u9762\u662f\u7ef4\u8bfa\u56fe\uff0c\u662f\u628a\u7a7a\u95f4\u5212\u5206\u7ed9\u5b9a\u70b9\u6700\u8fd1\u7684\u533a\u57df\uff1b\u8fb9\u754c\u8868\u793a\u4e8c\u8005\u76f8\u5f53\uff0c\u53ef\u4ee5\u6e05\u695a\u770b\u5230K\u503c\u5f71\u54cd<\/p>\n\n\n\n<p>K\u503c\u8fc7\u5c0f\uff1a\u66f4\u80fd\u53cd\u6620\u5c40\u90e8\u7ec6\u8282\uff0c\u4f46\u4f1a\u5bfc\u81f4\u8fc7\u62df\u5408\uff0c\u5bb9\u6613\u88ab\u566a\u58f0\u5f71\u54cd<br>K\u503c\u8f83\u5927\uff1a\u8fb9\u754c\u66f4\u52a0\u5e73\u6ed1\uff0c\u4e5f\u53ef\u80fd\u5bfc\u81f4\u6b20\u62df\u5408\uff0c\u5bb9\u6613\u5ffd\u89c6\u7ec6\u8282<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f18\u7f3a\u70b9<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4f18\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6613\u4e8e\u7406\u89e3\u3001\u89e3\u91ca\u548c\u5b9e\u73b0\uff0c\u8bad\u7ec3\u96be\u5ea6\u4f4e<\/li>\n\n\n\n<li>\u53ef\u4ee5\u65e0\u7f1d\u6dfb\u52a0\u65b0\u6570\u636e\uff0c\u800c\u4e0d\u4f1a\u5f71\u54cd\u6a21\u578b\u7684\u51c6\u786e\u6027<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7f3a\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4e0d\u9002\u7528\u4e8e\u5927\u578b\u6570\u636e\u96c6\uff08\u8ba1\u7b97\u8ddd\u79bb\u7684\u8ba1\u7b97\u6210\u672c\u5f88\u9ad8\uff09<\/li>\n\n\n\n<li>\u6781\u6613\u53d7\u5230\u7ef4\u5ea6\u7684\u5f71\u54cd\uff08\u9ad8\u7ef4\u6570\u636e\u5931\u6548\uff09<\/li>\n\n\n\n<li>\u9700\u8981\u5927\u91cf\u5b58\u50a8\uff0c\u9700\u8981\u6570\u636e\u5f52\u4e00\u5316<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u903b\u8f91\u56de\u5f52LR<\/h2>\n\n\n\n<p>\u5229\u7528\u5224\u522b\u51fd\u6570\uff0c\u6839\u636e\u6b63\u8d1f\u6765\u51b3\u5b9a\u5206\u7c7b\u3002\u6b64\u65f6\uff0c\u903b\u8f91\u56de\u5f52<strong>\u5b66\u4e60<\/strong>\u8fd9\u4e2a\u5224\u51b3\u51fd\u6570<strong>\u76f4\u63a5\u5efa\u6a21\u51b3\u7b56\u8fb9\u754c<\/strong>\uff0c\u800c\u4e0d\u9700\u8981\u4f30\u8ba1\u6570\u636e\u7684\u6982\u7387\u5206\u5e03\u3002<\/p>\n\n\n\n<p>\u4f18\u52bf\uff1a\u901a\u5e38\u6548\u7387\u6bd4\u8f83\u9ad8<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u611f\u77e5\u673a<\/h3>\n\n\n\n<p>\u7ed3\u6784\u975e\u5e38\u7b80\u5355\uff0c\u6734\u7d20\u5206\u7c7b\uff08\u53ea\u6709-1\u548c1\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-39.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"259\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-39.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4190\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8bad\u7ec3\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u89c4\u5b9a\u6570\u636e\u96c6D={(x(1),r(1)),...,x(d)r(d)};\nfor (x(l),r(l)) in D:\uff08\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u6570\u636e\u548c\u6807\u7b7e\uff09\n| if r(l)g(x(l))\u22640:\uff08\u9884\u6d4b\u4e0e\u5b9e\u9645\u4e0d\u4e00\u81f4\uff09\n| | w=w+\u03b7r(l)x(l)\uff08\u5c06\u8d85\u5e73\u9762\u5411\u88ab\u9519\u8bef\u5206\u7c7b\u7684\u70b9\u79fb\u52a8\uff0c\u03b7\u4e3a\u5b66\u4e60\u7387\uff09\n\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u76f4\u81f3\u5168\u90e8\u6570\u636e\u96c6\u90fd\u88ab\u6b63\u786e\u5206\u7c7b<\/code><\/pre>\n\n\n\n<p>\u611f\u77e5\u673a\u9650\u5236\uff1a\u53d6\u503c\u53ea\u6709-1\u548c1\uff0c\u5bf9\u4e8e\u4f18\u5316\u6765\u8bf4\u975e\u5e38\u56f0\u96be<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">sigmoid<\/h3>\n\n\n\n<p>\u5b9a\u4e49y\u4e3a\u6570\u636e\u70b9x\u5c5e\u4e8e\u7c7b\u522bC<sub>1<\/sub>\u7684\u6982\u7387\uff0c\u90a3\u4e48\u5bf9\u5e94C<sub>2<\/sub>\u6982\u7387\u5c31\u662f1-y<br>\u6b64\u65f6\uff0c\u6839\u636e$ \\log \\frac{y}{1 \u2013 y} $\u5224\u65ad\uff0c\u5e94\u8be5\u5c5e\u4e8e\u54ea\u4e00\u7c7b\uff0c\u7136\u540e\u63a8\u5bfc\u5f97\u5230\uff1a<\/p>\n\n\n\n<p>$ \\log \\frac{y}{1 \u2013 y} = \\mathbf{w}^T\\mathbf{x} + w_0 \\Rightarrow y = \\text{sigmoid}(\\mathbf{w}^T\\mathbf{x} + w_0) = \\frac{1}{1 + \\exp [-(\\mathbf{w}^T\\mathbf{x} + w_0)]} $<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-40.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"233\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-40.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4194\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8bad\u7ec3\uff1a\u4ece\u6570\u636e\u4e2d\u9884\u6d4b\u53c2\u6570 <strong>w<\/strong>,w0 \u3002<br>\u9884\u6d4b\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u65b0 x\uff0c\u8ba1\u7b97$ y = \\text{sigmoid}(\\mathbf{w}^T \\mathbf{x} + w_0) $\uff0c\u9009\u62e9$ C_1 \\ \\text{if} \\ y &gt; 0.5 \\ \\text{otherwise} \\ C_2 $\uff08y\u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u662f\u540e\u9a8c\u6982\u7387\uff09<\/p>\n\n\n\n<p>\u635f\u5931\u51fd\u6570\uff1a\u56e0\u4e3a\u662f\u4e8c\u5206\u95ee\u9898\uff0c\u6240\u4ee5\u6700\u540e\u5bf9\u4e8er\u4e3a0\u62161\uff0c\u5219\u5bf9\u5e94\u8fc7\u6765<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c&nbsp;<em>r<\/em>=1\uff0c\u6700\u5927\u5316&nbsp;log<em>P<\/em>(<em>C<\/em>1\u200b\u2223<em>x<\/em>)=log<em>y<\/em>\uff08\u635f\u5931\u4e3a-log<em>y<\/em> \uff09\u3002<\/li>\n\n\n\n<li>\u5982\u679c&nbsp;<em>r<\/em>=0\uff0c\u6700\u5927\u5316&nbsp;log<em>P<\/em>(<em>C<\/em>2\u200b\u2223<em>x<\/em>)=log(1\u2212<em>y<\/em>)\uff08\u635f\u5931\u4e3a-log(1-y) \uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4e3a\u4e86\u628a\u4e8c\u8005\u7edf\u4e00\u8d77\u6765\uff0c\u5b9a\u4e49\u4e00\u4e2a\u65b0\u635f\u5931\u51fd\u6570\uff0c\u5373\u4ea4\u53c9\u71b5\u635f\u5931CE\uff1a<\/p>\n\n\n\n<p>$ \\ell(w, w_0 | x, r) = -r \\log y &#8211; (1 &#8211; r) \\log (1 &#8211; y) $<\/p>\n\n\n\n<p>\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u7b49\u4ef7\u4e8e\u6700\u5927\u5316\u4f3c\u7136<\/p>\n\n\n\n<p>$ p(r \\mid x) = y^r(1-y)^{(1-r)}=\\begin{cases} y \\quad \\text{if} \\ r = 1 \\\\ 1-y \\quad \\text{if} \\ r = 0 \\end{cases} $<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8bad\u7ec3\u8fc7\u7a0b<\/h4>\n\n\n\n<p>\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u6cd5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570 $ w_{t+1} = w_t &#8211; \\eta \\frac{\\partial L}{\\partial w} $<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u6574\u4e2a\u6570\u636e\u96c6 D \u800c\u8a00\uff1a$ L(w, w_0 \\mid D) = -\\sum_{l=1}^N \\left( r^{(l)} \\log y^{(l)} + (1 &#8211; r^{(l)}) \\log(1 &#8211; y^{(l)}) \\right) $<\/p>\n\n\n\n<p>\u6211\u4eec\u5b9a\u4e49\uff1a$ a = w^T x + w_0 $<\/p>\n\n\n\n<p>\u90a3\u4e48\u5e26\u5165\u5230\u4e0a\u9762\u7684\u516c\u5f0f\uff0c\u53ef\u4ee5\u5f97\u5230$ y = \\text{sigmoid}(a) $\uff0c$ \\frac{\\partial a}{\\partial w_j} = x_j^{(l)} $\u548c$ \\frac{\\partial y}{\\partial a} = y(1 &#8211; y) $<\/p>\n\n\n\n<p>\u6700\u540e\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n<p>$ \\frac{\\partial L}{\\partial w_j} = -\\sum_{l=1}^N \\left( \\frac{\\partial L}{\\partial y^{(l)}} \\cdot \\frac{\\partial y^{(l)}}{\\partial a^{(l)}} \\cdot \\frac{\\partial a^{(l)}}{\\partial w_j} \\right) = -\\sum_l \\Big( r^{(l)} &#8211; y^{(l)} \\Big) x_j^{(l)} $<\/p>\n\n\n\n<p>\u5176\u4e2dr<sup>(l)<\/sup>\u662f\u771f\u5b9e\u6807\u7b7e\uff0cy<sup>(l)<\/sup>\u662f\u9884\u6d4b\u503c\uff0cx<sub>j<\/sub>\u8868\u793a\u7279\u5f81\u503c<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u591a\u5206\u7c7b\u95ee\u9898<\/h3>\n\n\n\n<p>\u6709\u65f6\u6211\u4eec\u9700\u8981\u9884\u6d4b\u591a\u4e2a\u7c7b\uff0c\u5982\u679c\u6211\u4eec\u60f3\u7edf\u4e00\u5904\u7406\u6240\u6709\u7c7b\u800c\u4e0d\u5fc5\u9009\u62e9\u53c2\u8003\u7c7b\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 softmax \u51fd\u6570\u6765\u4ee3\u66ff\u540e\u9a8c\u7c7b\u6982\u7387y<\/p>\n\n\n\n<p>$ y_i = \\text{softmax}(a_1, \\dots, a_K)i = \\frac{e^{a_i}}{\\sum{j=1}^K e^{a_j}} $<\/p>\n\n\n\n<p>\u5176\u4e2d $ a_i = W_i x + w_{i0} $\uff0c\u88ab\u79f0\u4e3alogits\uff0cW<sub>i<\/sub>\uff0cw<sub>i0<\/sub>\u4e3a\u53ef\u8bad\u7ec3\u53c2\u6570<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-41.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"653\" height=\"330\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-41.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4216\"  sizes=\"auto, (max-width: 653px) 100vw, 653px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-42.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"237\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-42.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4217\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570\u53ca\u68af\u5ea6\uff1a<\/p>\n\n\n\n<p>$ L_{CE}(y, r) = -\\sum_{i=1}^{k} r_i \\log y_i = -r^T (\\log y) $ <br>$ \\frac{\\partial L}{\\partial w_j} = -\\sum_l \\Big(r_j^{(l)} &#8211; y_j^{(l)}\\Big) x_j^{(l)} $<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u652f\u6301\u5411\u91cfSVM<\/h2>\n\n\n\n<p>\u5bf9\u4e8e\u4e4b\u524d\u7684\u5206\u88c2\u65b9\u6cd5\uff0c\u76ee\u6807\u53ea\u662f\u4e00\u4e2a\u6b63\u786e\u7684\u7ed3\u679c\u3002\u5f53\u7136\u8fd9\u4e2a\u7ed3\u679c\u4e5f\u53ef\u4ee5\u66f4\u8fdb\u4e00\u6b65\u4f18\u5316\uff0c\u8ffd\u6c42\u6548\u679c\u5e94\u8be5\u662f\u6700\u5927\u5316\u4e24\u4e2a\u8fb9\u754c\u8ddd\u79bb\u7684<strong>\u51b3\u7b56\u8fb9\u754c<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-43.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"635\" height=\"586\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-43.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4225\" style=\"width:323px;height:auto\"  sizes=\"auto, (max-width: 635px) 100vw, 635px\" \/><\/div><\/figure>\n\n\n\n<p>\u4e0a\u5f0f\u76f8\u51cf\uff0c\u6700\u540e\u5f97\u5230\u95f4\u8ddd\uff1a<\/p>\n\n\n\n<p>$ margin = \\frac{2}{||w||} $<\/p>\n\n\n\n<p>\u6700\u5927\u5316margin\u5219\u7b49\u4ef7\u4e8e\u6700\u5c0f\u5316 $ 0.5 ||w|| $<\/p>\n\n\n\n<p>\u90a3\u4e48\u5199\u51fa\u4e00\u4e2a\u6700\u4f18\u5316\u95ee\u9898\u7684\u5f62\u5f0f\uff1a<br>minimize $ \\frac{1}{2} |\\mathbf{w}|^2 $<br>subject to $ y^{(\\ell)} (\\mathbf{w}^T x^{(\\ell)} + w_0) \\ge 1, \\ell=1,\\dots,N $<\/p>\n\n\n\n<p>\u56e0\u4e3ay\u7684\u53d6\u503c\u53ea\u6709\u00b11\uff0c\u6240\u4ee5\u4fdd\u8bc1\u4e86\u6240\u6709\u70b9\u5728\u4e24\u6761\u865a\u7ebf\u5916\uff0c\u91c7\u7528\u611f\u77e5\u673a\u4f5c\u4e3a\u6a21\u578b<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-45.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"992\" height=\"254\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-45.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4232\"  sizes=\"auto, (max-width: 992px) 100vw, 992px\" \/><\/div><\/figure>\n\n\n\n<p>\u5bf9\u4e8e\u8fd9\u4e2a\uff0c\u6211\u4eec\u9996\u5148\u5e0c\u671by(w<sup>T<\/sup>x+w<sub>0<\/sub>)&gt;1\uff0c\u6240\u4ee5\u9700\u8981\u4f18\u5316\u5176\u4e2d\u6700\u5c0f\u7684\u503c\uff0c\u76f4\u81f3\u5176\u5927\u4e8e1<br>\u5f53\u6240\u6709\u70b9\u90fd\u5728\u865a\u7ebf\u5916\uff0c\u6211\u4eec\u5f00\u59cb\u8c03\u6574w\u4f7f\u5176\u6700\u7ec8\u5361\u5728\u8fb9\u754c\u4e0a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-47.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"641\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-47.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4236\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u591a\u5c42\u611f\u77e5\u673a\u5236<\/h2>\n\n\n\n<p>\u6a21\u4eff\u4e86\u4eba\u7c7b\u5927\u8111\u7684\u67d0\u4e9b\u7279\u6027\uff0c\u6839\u636e\u4eba\u7c7b\u7684\u795e\u7ecf\u7ed3\u6784\uff0c\u79d1\u5b66\u5bb6\u6784\u5efa\u51fa\u4eba\u5de5\u795e\u7ecf\u7f51\u7edcANN\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-48.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"549\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-48.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4238\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5982\u679c\u5176\u4e2d\u7684\u6fc0\u6d3b\u51fd\u6570\u03c3 ()\u662fsign()\u7b26\u53f7\u51fd\u6570\u7684\u8bdd\uff0c\u8fd9\u4e2a\u795e\u7ecf\u5143\u5c31\u662f\u4e4b\u524d\u5b66\u8fc7\u7684\u611f\u77e5\u673a\u3002<br>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u611f\u77e5\u673a\u6765\u6a21\u62df\u4e0e\u6216\u8fd0\u7b97\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-49.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"596\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-49.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4239\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5982\u679c\u7ee7\u7eed\u6dfb\u52a0\u9690\u85cf\u5c42\uff0c\u5c31\u53ef\u4ee5\u6a21\u62df\u4e00\u4e9b\u975e\u7ebf\u6027\u64cd\u4f5c\uff0c\u6bd4\u5982\u8bf4XOR<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-50.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"288\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-50.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4240\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8fd8\u6709\u5f88\u591a\u5176\u5b83\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u8fd9\u4e9b\u90fd\u4e3a\u975e\u7ebf\u6027<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-51.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"477\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-51.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4241\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u4e5f\u53ef\u4ee5\u6784\u5efa\u591a\u5c42\u611f\u77e5\u673a\u7ed3\u6784\uff0c\u5b9e\u73b0\u8fde\u7eed\u7684\uff08\u53ef\u5fae\u5206\u7684\uff09\u51b3\u7b56<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-52.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"701\" height=\"375\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-52.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4242\"  sizes=\"auto, (max-width: 701px) 100vw, 701px\" \/><\/div><\/figure>\n\n\n\n<p>\u8bad\u7ec3\u7684\u6838\u5fc3\u5c31\u5728\u4e8e\u7b97\u68af\u5ea6\uff1a\u901a\u8fc7\u8bef\u5dee\u627e\u5c40\u90e8\u6781\u5c0f\u503c\u70b9\uff0c\u8ba9&nbsp;\u03b8&nbsp;\u671d\u7740\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u79fb\u52a8\u6b65\u957f\uff08\u68af\u5ea6\u4e0b\u964d\u6cd5\uff09\u3002<\/p>\n\n\n\n<p>\u53ef\u4ee5\u5f97\u5230\u635f\u5931\u51fd\u6570\uff0cm\u662f\u8f93\u51fa\u7684\u503c\u7684\u7ef4\u5ea6\u3002\u6211\u4eec\u9700\u8981\u6700\u5c0f\u5316\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u635f\u5931\uff1a $ \\mathcal{L}(\\theta \\mid D) = \\frac{1}{2} \\sum_{\\ell=1}^N \\sum_{i=1}^m \\left( r_i^{(\\ell)} \u2013 y_i^{(\\ell)} \\right)^2 $<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u5355\u4e2a\u6837\u672c\uff08x\uff0cr\uff09\u8bef\u5dee\uff1a$ \\ell(x, r) = \\frac{1}{2} \\sum_{i=1}^m \\left( r_i \u2013 y_i \\right)^2 $<\/p>\n\n\n\n<p>\u7531\u4e8e\u76f4\u63a5\u8ba1\u7b97\u8fc7\u4e8e\u590d\u6742\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u4f7f\u7528<strong>\u53cd\u5411\u4f20\u64ad<\/strong>\u8ba1\u7b97\u68af\u5ea6<\/p>\n\n\n\n<p>\u8bef\u5dee\u53cd\u5411\u4f20\u64ad\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u524d\u5411\u4f20\u64ad\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5728\u524d\u5411\u4f20\u64ad\u8fc7\u7a0b\u4e2d\uff0c\u8f93\u5165\u6570\u636e\u4ece\u8f93\u5165\u5c42\u7ecf\u8fc7\u9690\u85cf\u5c42\u4f20\u9012\u5230\u8f93\u51fa\u5c42\uff0c\u8ba1\u7b97\u51fa\u6a21\u578b\u7684\u9884\u6d4b\u503c&nbsp;y<sub>pred<\/sub>\u548c\u635f\u5931\u503c&nbsp;L\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u53cd\u5411\u4f20\u64ad\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6839\u636e\u94fe\u5f0f\u6cd5\u5219\uff08\u7528\u4e8e\u5904\u7406\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u7684\u91cd\u8981\u89c4\u5219\uff09\uff0c\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u76f8\u5bf9\u4e8e\u6bcf\u4e2a\u53c2\u6570\u7684\u68af\u5ea6&nbsp;\u2202L\/\u2202w\uff0c\u4ece\u8f93\u51fa\u5c42\u5411\u8f93\u5165\u5c42\u9010\u5c42\u53cd\u5411\u4f20\u64ad\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u53c2\u6570\u66f4\u65b0\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5229\u7528\u68af\u5ea6\u4e0b\u964d\u7b49\u4f18\u5316\u7b97\u6cd5\uff0c\u901a\u8fc7\u68af\u5ea6\u4fe1\u606f\u66f4\u65b0\u6bcf\u5c42\u7684\u6743\u91cd\u548c\u504f\u7f6e\uff1aw=w\u2212\u03b7\u22c5\u2202w\/\u2202L\uff0c\u5176\u4e2dw\u4e3a\u53c2\u6570\uff0c\u03b7\u4e3a\u5b66\u4e60\u7387<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u53cd\u5411\u4f20\u64ad\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<p>\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u7684<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-66e2ff5b17b4b4c4b0355a0de8b4c783_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-66e2ff5b17b4b4c4b0355a0de8b4c783_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial L}{\\partial w_{i,j}^k} \\quad i \\in {1,2,\\cdots,n}; j\\in {1,2,\\cdots,n}; k\\in {1,2,\\cdots\\,L+1}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u6211\u4eec\u5148\u5173\u5fc3\u8f93\u51fa\u5c42\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u7684<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-942cfbee08cb726b9cb566dd1fbfce2c_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-942cfbee08cb726b9cb566dd1fbfce2c_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial L}{\\partial w_{i,1}^{L+1}} \\quad i \\in {1,2,\\cdots,n}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u5bb9\u6613\u5f97\u5230<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cf527985cf6b2dddb70ba742cb9af792_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cf527985cf6b2dddb70ba742cb9af792_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial L}{\\partial w_{i,1}^{L+1}}=\\frac{\\partial L}{\\partial a_{1}^{L+2}}\\frac{\\partial a_{1}^{L+2}}{\\partial w_{i,1}^{L+1}}=\\frac{\\partial L}{\\partial a_{1}^{L+2}}x_{1}^{L+1}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u6211\u4eec\u518d\u8003\u8651\u4f4d\u4e8eL\u5c42\u7684\u7b2cj\u4e2a\u795e\u7ecf\u5143<br>\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u7684<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-ac6a40bb379baf579b6dd0f457cc6b46_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-ac6a40bb379baf579b6dd0f457cc6b46_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial x_{j}^{L}}{\\partial w_{i,j}^{L-1}} \\quad i\\in {1,2,\\cdots,n}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u53ef\u4ee5\u5f97\u5230<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-7f124da5943e7c6354c5d2035e46ab15_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-7f124da5943e7c6354c5d2035e46ab15_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial x_{j}^{L}}{\\partial w_{i,j}^{L-1}}=\\frac{\\partial x_{j}^{L}}{\\partial a_{j}^{L}}\\frac{\\partial a_{j}^{L}}{\\partial w_{i,j}^{L-1}}=\\frac{\\partial x_{j}^{L}}{\\partial a_{j}^{L}}x_{i}^{L-1}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u73b0\u5728\uff0c\u5982\u679c\u80fd\u8ba1\u7b97\u51fa\u2202L\/\u2202x\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u80fd\u8ba1\u7b97\u51fa\u6211\u4eec\u60f3\u5f97\u5230\u7684\u6240\u6709\u6570\u636e\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u8003\u8651\u8f93\u51fa\u5c42\u795e\u7ecf\u5143<br>\u6211\u4eec\u9700\u8981\u8ba1\u7b97\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-b790d58b87be72141614d4ef1ed13864_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-b790d58b87be72141614d4ef1ed13864_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial L}{\\partial x_{i}^{L+1}} \\quad i \\in {1,2,\\cdots,n}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u6ce8\u610f\u5230<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-03afdd1a0856f894a59813f3aa1d0128_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-03afdd1a0856f894a59813f3aa1d0128_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial L}{\\partial x_{i}^{L+1}}=\\frac{\\partial L}{\\partial a_{1}^{L+2}}\\frac{\\partial a_{1}^{L+2}}{\\partial x_{i}^{L+1}}=\\frac{\\partial L}{\\partial a_{1}^{L+2}}w_{i,1}^{L+1}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u6ce8\u610f\uff0c\u5982\u679c\u662f\u4e2d\u95f4\u5c42\uff0c\u5219\u6700\u540e\u662f\u6c42\u548c\u7684\u5f62\u5f0f\uff0c\u56e0\u4e3ax\u88ab\u4f7f\u7528n\u6b21<\/p>\n\n\n\n<p>\u4e0a\u9762\u7684\u63a8\u5bfc\u975e\u5e38\u590d\u6742\uff0c\u4f46\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-4bfb36e2664a318da2bcbf96766f9952_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-4bfb36e2664a318da2bcbf96766f9952_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{\\partial L}{\\partial w_{i,j}^{L}}=\\frac{\\partial a_{j}^{L}}{\\partial w_{i,j}^{L}} \\frac{\\partial L}{\\partial a_{j}^{L}}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u6211\u4eec\u5c06\u7b2c\u4e00\u90e8\u5206\u79f0\u4e3a\u8f93\u5165\uff0c\u540e\u4e00\u90e8\u5206\u79f0\u4e3a\u8bef\u5dee\uff1b\u8f93\u5165\u662fw<sub>i,j<\/sub><sup>L<\/sup>\u4e0a\u5bf9\u5e94\u7684x<sub>i<\/sub><sup>L<\/sup>\uff0c\u800c\u8bef\u5dee\u03b4<sub>j<\/sub><sup>L<\/sup>\u53ef\u4ee5\u6839\u636e\u4e0b\u9762\u7684\u5f0f\u5b50\u9012\u5f52\u8ba1\u7b97<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-aab8c781f0134ae12b7e0277397c26e5_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-aab8c781f0134ae12b7e0277397c26e5_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\delta^{L}=\\sigma'(x^L)\\cdot (r-y)\\\\\\delta^{L-1}=\\sigma'(x^{L-1})\\cdot (W^L)^T \\delta^L \\\\\\cdots\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u9012\u5f52\u8ba1\u7b97\u68af\u5ea6\u7684\u65f6\u5019\u4f1a\u7ecf\u5e38\u91cd\u590d\uff0c\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u4f18\u5316<\/p>\n\n\n\n<p>\u6df1\u5ea6\u5b66\u4e60\u7684\u7279\u70b9\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u81ea\u52a8\u5b66\u4e60\u6570\u636e\u8868\u5f81<\/li>\n\n\n\n<li>\u5b66\u4e60\u5c42\u6b21\u5316\u8868\u5f81<\/li>\n\n\n\n<li>\u7aef\u5230\u7aef\u5b66\u4e60<\/li>\n<\/ul>\n\n\n\n<p>\u9898\u76ee\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-53.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"120\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-53.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4250\"\/><\/div><\/figure>\n\n\n\n<p>\u03c3\u8fd9\u91cc\u662fSIgmoid\u51fd\u6570\uff0c\u5373\u6fc0\u6d3b\u51fd\u6570<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-54.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"631\" height=\"454\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-54.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4251\"  sizes=\"auto, (max-width: 631px) 100vw, 631px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-55.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"761\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-55.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4252\"  sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u8bed\u8a00\u6a21\u578b<\/h2>\n\n\n\n<p>Word2vec<\/p>\n\n\n\n<p>\u5355\u7eaf\u4f7f\u7528ASCII\u7801\uff0c\u673a\u5668\u65e0\u6cd5\u7406\u89e3\u6570\u5b57\u7684\u610f\u4e49\uff0c\u65e0\u6cd5\u7406\u89e3\u5355\u8bcd\u4e0e\u5355\u8bcd\u95f4\u7684\u5173\u7cfb<br>one-hot\u7f16\u7801\uff1a\u6bcf\u4e2a\u5355\u8bcd\u5360\u6709\u5411\u91cf\u4e2d\u7684\u4e00\u4f4d\uff0c\u8fd9\u4e00\u4f4d\u4e3a1\uff0c\u5176\u4f59\u4e3a0\uff1b\u975e\u5e38\u5360\u7528\u7a7a\u95f4\uff0c\u5e76\u4e14\u4e0d\u80fd\u53cd\u6620\u8bcd\u95f4\u5173\u7cfb<br>\u6211\u4eec\u5e0c\u671b\u4f7f\u7528\u4e00\u79cd\u538b\u7f29\u7684\u5411\u91cf\uff0c\u5e76\u4e14\u80fd\u591f\u53cd\u6620\u8bcd\u95f4\u5173\u7cfb<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-56.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"413\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-56.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4253\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5982\u4f55\u83b7\u53d6\u5355\u8bcd\u7f16\u7801\u5462\uff1f\u57fa\u672c\u60f3\u6cd5\uff0c\u5982\u679c\u672a\u77e5\u5355\u8bcd\u548c\u5df2\u77e5\u5355\u8bcd\u6709\u76f8\u4f3c\u7684\u4e0a\u4e0b\u6587\uff0c\u5219\u8ba4\u4e3a\u4e8c\u8005\u76f8\u4f3c\uff0c\u5bf9\u5e94\u7b97\u6cd5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u51c6\u5907\u4e00\u4e2a\u5927\u89c4\u6a21\u7684\u6587\u672c\u5e93<\/li>\n\n\n\n<li>\u7ed9\u6bcf\u4e2a\u5355\u8bcd\u5206\u914d\u4e00\u4e2a\u8bcd\u5411\u91cf<\/li>\n\n\n\n<li>\u904d\u5386\u6587\u672c\uff0c\u83b7\u53d6\u5355\u8bcdw\u53ca\u5176\u4e24\u8fb9\u7684\u8bcdc<\/li>\n\n\n\n<li>\u6839\u636e\u5411\u91cf\u76f8\u4f3c\u5ea6\u8ba1\u7b97\u7ed9\u5b9ac\u540e\u4e2d\u95f4\u4e3aw\u7684\u6982\u7387<\/li>\n\n\n\n<li>\u66f4\u65b0\u8bcd\u5411\u91cf\uff0c\u76f4\u81f3\u6982\u7387\u6700\u5927\u5316<\/li>\n<\/ul>\n\n\n\n<p>\u6b64\u65f6\u5f97\u5230\u4e86\u8bcd\u5411\u91cf\uff0c\u5982\u679c\u8ba9\u8ba1\u7b97\u673a\u8f93\u51fa\u8bed\u53e5\uff1f<br>\u5982\u679c\u4e00\u53e5\u8bdd\u7531w<sub>1<\/sub>,..,w<sub>n<\/sub>\u6784\u6210\uff0c\u90a3\u4e48\u6700\u540e\u7684\u6982\u7387p(x)=p(w<sub>1<\/sub>,w<sub>2<\/sub>,\u2026,w<sub>n<\/sub>)\u5982\u4f55\u8ba1\u7b97\uff1f<\/p>\n\n\n\n<p>\u57fa\u4e8e\u6761\u4ef6\u6982\u7387\uff0c\u53ef\u4ee5\u5f97\u5230p(w<sub>1<\/sub>,w<sub>2<\/sub>,\u2026,w<sub>n<\/sub>)=p(w<sub>1<\/sub>)p(w<sub>2<\/sub>|w<sub>1<\/sub>)\u2026p(w<sub>n<\/sub>|w<sub>1<\/sub>,w<sub>2<\/sub>\u2026)\uff0c\u800c\u5355\u8bcd\u4e00\u822c\u53ea\u548c\u76f8\u8fd1\u7684\u5355\u8bcd\u6709\u5173\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5316\u7b80\u6210\u53ea\u8003\u8651\u524dk\u4e2a\u5355\u8bcd<\/p>\n\n\n\n<p>\u90a3\u4e48\u6211\u4eec\u5982\u4f55\u83b7\u5f97\u8fd9\u4e2a\u6761\u4ef6\u6982\u7387\uff1f<br>\u6700\u7b80\u5355\u7684\u60f3\u6cd5\u662f\u8ba1\u6570\u3002\u7f3a\u70b9\uff1a\u4f9d\u8d56\u79bb\u6563\u7b26\u53f7\u8868\u793a\uff0c\u9762\u4e34\u6570\u636e\u7a00\u758f\u95ee\u9898\uff08Data Sparsity\uff09\uff1b\u5b9e\u9645\u6ca1\u6709\u5b66\u4e60\u5230\u8bed\u4e49\uff1b\u5bf9\u76f8\u5173\u8bcd\u548c\u53e5\u5b50\u4e0d\u654f\u611f\uff0c\u5bf9\u524d\u7f00\u53d8\u5316\u6781\u5176\u654f\u611f\u3002<\/p>\n\n\n\n<p>\u56e0\u6b64\u6211\u4eec\u4f7f\u7528\u8bcd\u5411\u91cf\u4ee3\u66ff\u5355\u8bcd\u3002\u8bcd\u5411\u91cf\u53ef\u4ee5\u53cd\u6620\u76f8\u4f3c\u5ea6\uff0c\u4f46\u662f\u8fd9\u79cd\u65b9\u5f0f\u8fd8\u4e0d\u80fd\u53cd\u6620\u8bcd\u4e0e\u8bcd\u95f4\u7684\u987a\u5e8f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06\u591a\u4e2a\u8bcd\u5411\u91cf\u8fdb\u884c\u62fc\u63a5\u3002\u8fd9\u79cd\u65b9\u5f0f\u7684\u95ee\u9898\u662f\u8f93\u5165\u7684\u957f\u5ea6\u4e0d\u53ef\u53d8\uff0c\u5e76\u4e14\u6807\u70b9\u7b26\u53f7\u7b49\u4f1a\u5bf9\u5176\u4ea7\u751f\u5f88\u5927\u5f71\u54cd\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u7684\u8981\u6c42\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5904\u7406\u53d8\u957f\u5e8f\u5217<\/li>\n\n\n\n<li>\u8ddf\u8e2a\u957f\u671f\u4f9d\u8d56\u5173\u7cfb<\/li>\n\n\n\n<li>\u4fdd\u5b58\u6709\u5173\u987a\u5e8f\u7684\u4fe1\u606f<\/li>\n\n\n\n<li>\u5728\u8bed\u53e5\u95f4\u5171\u4eab\u53c2\u6570<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u5faa\u73af\u795e\u7ecf\u7f51\u7edcRNN<\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u6807\u51c6\u795e\u7ecf\u7f51\u7edc\u6765\u8bf4\uff0c\u4e00\u6b21\u53ea\u80fd\u5904\u7406\u4e00\u4e2a\u5355\u8bcd\u3002<br>\u8bbe\u60f3\u662f\u5426\u53ef\u4ee5\u8ba9\u795e\u7ecf\u7f51\u7edc\u8bb0\u5f55\u5904\u7406\u8fc7\u7684\u5355\u8bcd\uff1a\u4e3a\u9690\u85cf\u5c42\u6dfb\u52a0\u56de\u8def\u4ee5\u5b9e\u73b0\u8bb0\u5fc6\u80fd\u529b\u3002<br>\u6838\u5fc3\u601d\u60f3\uff1a\u901a\u8fc7<strong>\u9012\u5f52\u5173\u7cfb<\/strong>\u5c06\u5f53\u524d\u65f6\u95f4\u6b65\u7684\u8f93\u5165\u4e0e\u4e0a\u4e00\u65f6\u95f4\u6b65\u7684\u9690\u85cf\u72b6\u6001\u7ed3\u5408\uff0c\u66f4\u65b0\u9690\u85cf\u72b6\u6001\uff0c\u4ece\u800c\u9010\u6b65\u5904\u7406\u5e8f\u5217\u6570\u636e\u5e76\u6355\u83b7\u65f6\u95f4\u5e8f\u5217\u4e2d\u7684\u4e0a\u4e0b\u6587\u548c\u4f9d\u8d56\u5173\u7cfb\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-57.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"381\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-57.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4254\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8bad\u7ec3\u65b9\u6cd5\uff1a\u901a\u8fc7\u65f6\u95f4\u7684\u53cd\u5411\u4f20\u64ad<\/p>\n\n\n\n<p>\u5e94\u7528\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8bed\u53e5\u5206\u7c7b\uff1a\u5206\u6790\u4e00\u4e2a\u5355\u8bcd\u5e8f\u5217\u7684\u60c5\u611f\uff08<strong>Many-to-One<\/strong>\uff09<\/li>\n\n\n\n<li>\u6587\u672c\u751f\u6210\uff1a\u9884\u6d4b\u751f\u6210\u6587\u672c<\/li>\n\n\n\n<li>\u673a\u5668\u7ffb\u8bd1\uff1a\u4f7f\u7528\u7f16\u7801\u5668-\u89e3\u7801\u5668\u67b6\u6784\u5904\u7406\u6761\u4ef6\u5e8f\u5217\u751f\u6210\u4efb\u52a1\u3002\uff08<strong>Many-to-Many<\/strong>\uff09<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-58.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"656\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-58.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4255\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u7f3a\u70b9\uff1a\u65f6\u95f4\u6b65\u4e4b\u95f4\u5b58\u5728\u4f9d\u8d56\uff0c\u56e0\u6b64\u65e0\u6cd5\u5e76\u884c\u5316\u5904\u7406\u3002\u540c\u65f6\u5bf9\u4e8e\u8f83\u957f\u65f6\u95f4\u7684\u8fdc\u7a0b\u4f9d\u8d56\u5173\u7cfb\u8868\u73b0\u4e0d\u597d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Transformer<\/h2>\n\n\n\n<p><strong>RNN\u7684\u7f16\u89e3\u7801\u5668<\/strong><\/p>\n\n\n\n<p>\u4f7f\u7528\u4e24\u4e2aRNN\uff0c\u4e00\u4e2a\u4f5c\u4e3a\u7f16\u7801\u5668\uff0c\u5904\u7406\u8f93\u5165\u5e8f\u5217\uff0c\u4e00\u4e2a\u4f5c\u4e3a\u89e3\u7801\u5668\uff0c\u751f\u6210\u8f93\u51fa\u5e8f\u5217\u3002\u901a\u8fc7\u8fd9\u4e2a\u901a\u7528\u7684\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u5b8c\u6210\u8bed\u97f3\u8f6c\u6587\u5b57\u3001\u7ffb\u8bd1\u7b49\u5de5\u4f5c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-59.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"598\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-59.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4258\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u7f16\u7801\u5668\u5427\u8f93\u5165\u7684\u5e8f\u5217\u538b\u7f29\u6210\u4e3a\u4e00\u4e2a\u5411\u91cfc\uff0c\u89e3\u7801\u5668\u7684\u4efb\u52a1\u662f\u57fa\u4e8e\u5411\u91cfc\u751f\u6210\u5e8f\u5217\uff0c\u5e76\u901a\u8fc7\u5206\u7c7b\u5668\u628a\u751f\u6210\u7684\u5e8f\u5217\u8f6c\u5316\u4e3a\u81ea\u7136\u8bed\u8a00\u3002<\/p>\n\n\n\n<p>\u8bad\u7ec3\u8fc7\u7a0b\uff1a\u901a\u8fc7\u751f\u6210\u7684y\u548c\u771f\u5b9e\u503c\u505a\u6bd4\u5bf9\uff0c\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u6700\u5c0f\u5316\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570<\/p>\n\n\n\n<p>\u7528\u9014\uff1a\u9664\u4e86\u6587\u672c\u751f\u6210\u3001\u7ffb\u8bd1\u7b49\u529f\u80fd\uff0c\u8fd8\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u751f\u6210\u7b49\u3002<\/p>\n\n\n\n<p>\u7f3a\u70b9\uff1a\u65e0\u6cd5\u7406\u89e3\u957f\u6587\u672c\uff0c\u56e0\u4e3a\u5411\u91cfc\u7684\u8868\u8fbe\u80fd\u529b\u662f\u6709\u9650\u7684\uff0c\u4f1a\u5e26\u6765\u5f88\u5927\u7684\u4fe1\u606f\u635f\u5931\u3002\u6240\u6709\u4fe1\u606f\u90fd\u88ab\u7b49\u540c\u5bf9\u5f85\uff0c\u5bf9\u4e8e\u91cd\u8981\u4fe1\u606f\u5173\u6ce8\u4e0d\u591f\u3002<br>\u6539\u8fdb\uff1a\u52a8\u6001\u7f16\u7801\u5668<\/p>\n\n\n\n<p>\u52a8\u6001\u7f16\u7801\u5668\u4f1a\u751f\u6210\u591a\u4e2ac<sub>i<\/sub>\uff0c\u89e3\u7801\u5668\u9700\u8981\u6839\u636e\u5f53\u524d\u751f\u6210\u7684\u5e8f\u5217\uff0c\u81ea\u884c\u9009\u62e9\u5173\u8054\u5ea6\u66f4\u9ad8\u7684c<sub>i<\/sub>\uff0c\u8fd9\u4e5f\u88ab\u79f0\u4e3a\u6ce8\u610f\u529b\u673a\u5236<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6ce8\u610f\u529b\u673a\u5236\uff08Attetion\uff09<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-60.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"639\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-60.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4259\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5982\u4f55\u9009\u62e9\u6700\u5408\u7406\u7684c\uff1f<br>\u2014\u2014\u8bad\u7ec3\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\uff0c\u8f93\u5165\u4e3a\u89e3\u7801\u5668\u7684\u72b6\u6001\u53ca\u6240\u6709c\uff0c\u8f93\u51fa\u6240\u6709c\u7684\u5206\u6570\uff0c\u9009\u62e9\u5206\u6570\u6700\u9ad8\u7684<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Transformer<\/h3>\n\n\n\n<p>\u5177\u4f53\u6b65\u9aa4\uff1a<br>\u8f93\u5165\u4e3ax={x<sub>1<\/sub>,x<sub>2<\/sub>,\u2026,x<sub>n<\/sub>}<\/p>\n\n\n\n<p>\u5c06\u6ce8\u610f\u529b\u673a\u5236\u8fdb\u884c\u62d3\u5c55\uff0c\u6211\u4eec\u5e0c\u671b\u5728\u7f16\u7801\u8fc7\u7a0b\u4e2d\u4e5f\u4f7f\u7528\u6ce8\u610f\u529b\u673a\u5236\uff0c\u514b\u670d\u6389RNN\u4e0d\u80fd\u5e76\u884c\u7684\u7f3a\u70b9\u3002<\/p>\n\n\n\n<p>1.\u7f16\u7801<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-62.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"741\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-62.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4261\" style=\"width:438px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>2.\u63a5\u7740\u8ba1\u7b97Q,K,V\uff0c\u5176\u4e2dW<sup>q<\/sup>\uff0cW<sup>k<\/sup>\uff0cW<sup>v<\/sup>\u4e3a\u4e09\u4e2a\u53ef\u5b66\u4e60\u77e9\u9635<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-63.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"489\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-63.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4262\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>3.\u8ba1\u7b97\u5206\u6570\u5e76\u5f52\u4e00\u5316<\/p>\n\n\n\n<p>\u8fd9\u91cc\u4ee5h1\u505aquery\uff0c\u7528h1\u81ea\u5df1\u7684q1\u5206\u522b\u4e8e\u5269\u4e0b\u7684k<sub>1<\/sub>-k<sub>i<\/sub>\u8ba1\u7b97a\uff0c\u7136\u540e\u901a\u8fc7softmax\u5f52\u4e00\u5316\uff08\u4e0b\u9762\u7684\u516c\u5f0f\uff09\u5f97\u5230a<sub>1,i<\/sub>\uff0c\u5176\u4e2dd\u4e3aq\u548ck\u7684\u7ef4\u5ea6<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-64.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"744\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-64.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4263\" style=\"width:640px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>4.\u628a\u5f97\u5230\u7684\u5206\u6570\uff0cvalue\u7ed3\u5408\u5f97\u5230h<sub>1<\/sub>\u2018-h<sub>i<\/sub>\u2019 \uff0c\u6700\u540e\u5408\u6210\u5927\u77e9\u9635<\/p>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-66-1024x633.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"633\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-66-1024x633.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4265\" style=\"width:399px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-66-1024x633.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"633\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-66-1024x633.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4265\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n<\/div>\n\n\n\n<p>\u5bf9\u4e0a\u9762\u51e0\u6b65\u62bd\u8c61\u6210\u77e9\u9635\u8ba1\u7b97\uff1a<\/p>\n\n\n\n<p>\u7b2c\u4e00\u6b65\uff1aH=WX<br>\u7b2c\u4e8c\u6b65\uff1aQ=W<sup>q<\/sup>H\uff1bK=W<sup>k<\/sup>H\uff1bV=W<sup>v<\/sup>H<br>\u7b2c\u4e09\u6b65\uff1aA=K<sup>T<\/sup>Q\/\\sqrt{d} ; 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src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4270\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8fd9\u4e9b\u77e9\u9635\u8fd0\u7b97\u53ef\u4ee5\u7528gpu\u52a0\u901f\uff0c\u4f46\u662f\u4e0a\u9762\u7684\u8fc7\u7a0b\u4e22\u5931\u4e86\u8bcd\u8bed\u95f4\u7684\u987a\u5e8f\uff0c\u6211\u4eec\u9700\u8981\u8865\u5145\u4e00\u4e2a\u4f4d\u7f6e\u7f16\u7801\uff0c\u5c06\u987a\u5e8f\u4f5c\u4e3a\u6a21\u578b\u8f93\u5165\uff08onehot\u7f16\u7801\uff0c\u5728\u54ea\u4e00\u4f4d\u54ea\u4e00\u4f4d\u5c31\u662f1\uff09<\/p>\n\n\n\n<h2 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loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"503\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-68.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4271\" style=\"width:613px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8fd9\u4e2a\u8fc7\u7a0b\u5b9e\u9645\u53ef\u4ee5\u7528\u5377\u79ef\u5b8c\u6210\uff0c\u5c06\u51e0\u4e2a\u70b9\u7684\u6570\u636e\u901a\u8fc7\u5377\u79ef\u5408\u5e76\u6210\u4e00\u4e2a\u6570\u636e<\/p>\n\n\n\n<p>\u5b9e\u9645\u60c5\u51b5\u4e0b\uff0c\u56e0\u4e3a\u56fe\u7247\u6709RGB\u4e09\u901a\u9053\uff0c\u6240\u4ee5\u5b9e\u9645\u6211\u4eec\u505a\u7684\u662f3\u7ef4\u5377\u79ef\u3002\u6bd4\u59823*5*5\u7684\u5377\u79ef\u6838\u5c31\u4f1a\u5c0675\u4e2a\u503c\u5408\u5e76\u62101\u4e2a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-69.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"439\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-69.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4272\" style=\"width:699px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" 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class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-73.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"409\" height=\"201\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-73.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4276\"  sizes=\"auto, (max-width: 409px) 100vw, 409px\" \/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u673a\u5668\u89c6\u89c9CV<\/h2>\n\n\n\n<p>\u673a\u5668\u89c6\u89c9\u7684\u4efb\u52a1\uff1a\u56fe\u7247\u5206\u7c7b\u3001\u56fe\u7247\u5206\u5272\u3001\u7269\u4f53\u8bc6\u522b\u3001\u56fe\u5347\u6587\u3001\u6587\u751f\u56fe<\/p>\n\n\n\n<p>\u56fe\u7247\u5206\u5272<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-74.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"442\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-74.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4277\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u663e\u7136\u6211\u4eec\u4e0d\u80fd\u8ba9\u6a21\u578b\u5bf9\u5355\u72ec\u7684\u4e00\u4e2a\u50cf\u7d20\u8fdb\u884c\u5206\u7c7b\uff0c\u56e0\u4e3a\u51e0\u5343\u4e07\u50cf\u7d20\u4e0d\u80fd\u9010\u4e00\u8fdb\u884c\u5206\u7c7b<br>\u2014\u2014\u6211\u4eec\u80fd\u5426\u901a\u8fc7\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff0c\u5f97\u5230\u7279\u5f81\uff0c\u7136\u540e\u5f97\u51fa\u5206\u7c7b<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-75.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"337\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-75.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4278\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u6211\u4eec\u4f3c\u4e4e\u6ca1\u6709\u5fc5\u8981\u5bf9\u6574\u4e2a\u56fe\u7247\u8fdb\u884c\u5212\u5206\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u5728\u5c0f\u56fe\u7247\u4e0a\u5212\u51fa\u8f6e\u5ed3\uff0c\u518d\u590d\u539f\u5927\u56fe\u7247<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-76.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"287\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-76.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4279\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u73b0\u5728\u6211\u4eec\u8003\u8651\u5982\u4f55\u590d\u539f\u56fe\u7247(unpooling)\uff1a<br>\u4ece\u6b63\u5411\u7684\u5377\u79ef\u6765\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06\u56fe\u7247\u53ca\u5377\u79ef\u6838\u94fa\u5f00\uff0c\u5c06\u5377\u79ef\u64cd\u4f5c\u53d8\u6210\u77e9\u9635C<sub>m\u00d7n<\/sub>\u4e0e\u5411\u91cfi\u7684\u4e58\u6cd5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-77.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"496\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-77.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4280\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u53ef\u4ee5\u901a\u8fc7\u53cd\u5411\u4e58\u4e00\u4e2an\u00d7m\u7684\u77e9\u9635\uff0c\u5c06\u5377\u79ef\u540e\u7684\u7ed3\u679c\u590d\u539f\u6210\u539f\u59cb\u56fe\u7247\u7684\u5927\u5c0f\uff08\u6ce8\u610f\u4e0d\u80fd\u5b8c\u5168\u590d\u539f\u6210\u539f\u59cb\u56fe\u7247\uff0c\u9700\u8981\u5b66\u4e60\u77e9\u9635\u53c2\u6570\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-78.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"534\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-78.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4281\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong>\u7269\u4f53\u8bc6\u522b<\/strong><\/p>\n\n\n\n<p>\u8bc6\u522b=\u5206\u7c7b+\u5b9a\u4f4d<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-79.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"252\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-79.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4282\"\/><\/div><\/figure>\n\n\n\n<p>\u5206\u7c7b\u5f88\u597d\u89e3\u51b3\uff0c\u53ea\u9700\u8981\u8bad\u7ec3\u4e00\u4e2a\u5206\u7c7b\u5668\uff1b\u4e3b\u8981\u95ee\u9898\u662f\u5982\u4f55\u5212\u5206\u56fe\u7247\uff1f<\/p>\n\n\n\n<p>\u6211\u4eec\u4f7f\u7528\u201cselective search\u201d\u2014\u2014\u4e00\u4e2a\u4f20\u7edf\u7684\u673a\u5668\u89c6\u89c9\u7b97\u6cd5\uff0c\u80fd\u591f\u7ed9\u51fa\u53ef\u80fd\u51fa\u73b0\u76ee\u6807\u7684\u8303\u56f4<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-80.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"323\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-80.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4283\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5f53\u6211\u4eec\u83b7\u5f97\u8fd9\u4e9b\u5206\u5757\u7684\u5c0f\u56fe\u7247\uff0c\u6211\u4eec\u5bf9\u8fd9\u4e9b\u56fe\u7247\u8fdb\u884c\u5377\u79ef\u53ef\u4ee5\u5b8c\u6210\u76ee\u6807(slow r-cnn)\uff0c\u4f46\u6211\u4eec\u4ecd\u89c9\u5f97\u5206\u5757\u8fc7\u4e8e\u591a\uff0c\u6240\u4ee5\u6211\u4eec\u5148\u5bf9\u6574\u5f20\u56fe\u8fdb\u884c\u4e00\u6b21\u5377\u79ef\uff0c\u518d\u6839\u636e\u5c0f\u5206\u5757\u88c1\u526a\u5377\u79ef\u7ed3\u679c\uff0c\u63d0\u5347\u8fd0\u884c\u901f\u5ea6(fast r-cnn)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-81.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"544\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-81.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4284\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u9664\u6b64\u4e4b\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u56fe\u7247\u5212\u5206(faster r-cnn)\uff0c\u8fd8\u6709\u4e00\u4e9b\u5176\u4ed6\u7b97\u6cd5\u53ef\u4ee5\u63d0\u5347\u901f\u5ea6\uff08YOLO\uff09<\/p>\n\n\n\n<p><strong>\u56fe\u751f\u6587<\/strong><\/p>\n\n\n\n<p>\u7c7b\u4f3c\u4e8e\u7ffb\u8bd1\u95ee\u9898\uff0c\u6211\u4eec\u4ecd\u62c6\u5206\u6210\u7f16\u89e3\u7801\u5668\uff0c\u53c2\u7167transformer\uff0c\u5c06\u56fe\u7247\u901a\u8fc7\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u63d0\u53d6\u7279\u5f81\uff0c\u7136\u540e\u63a5\u5165\u81ea\u6ce8\u610f\u529b\u673a\u5236\uff1b\u751a\u81f3\u53ef\u4ee5\u76f4\u63a5\u5c06\u5206\u5757\u7684\u539f\u59cb\u56fe\u7247\u8f93\u5165\u7ed9transformer\uff0c\u4e0d\u4f7f\u7528\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08Vision Transformer-ViT\uff09<\/p>\n\n\n\n<p><strong>\u89c6\u89c9\u8bed\u8a00\u6a21\u578bVLM<\/strong><\/p>\n\n\n\n<p>\u5728ViT\u4e2d\u6211\u4eec\u53d1\u73b0transformer\u4e0d\u4ec5\u80fd\u7406\u89e3\u6587\u5b57\uff0c\u8fd8\u80fd\u7406\u89e3\u56fe\u7247\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8bad\u7ec3\u4e00\u4e2a\u652f\u6301\u591a\u79cd\u7c7b\u578b\u8f93\u5165\u8f93\u51fa\u7684transformer<\/p>\n\n\n\n<p>clip\uff1a\u5bf9\u6587\u5b57\u548c\u4e0e\u4e4b\u5bf9\u5e94\u7684\u56fe\u7247\u91c7\u7528\u4e24\u4e2aencoder\u8fdb\u884c\u7f16\u7801\uff0c\u6700\u5927\u5316\u4e24\u7ec4\u7f16\u7801\u7684\u76f8\u4f3c\u5ea6<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-82.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"507\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-82.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4285\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>CLIP\u5bf9\u5e94\u4e0b\u56fe\u4e2d\u7684\u5de6\u4e0a\u89d2\uff0c\u8fd8\u6709\u4e9b\u4e0d\u540c\u7684\u67b6\u6784<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-83.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"621\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-83.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4286\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u805a\u7c7b<\/h2>\n\n\n\n<p>\u5e0c\u671b\u5728\u6ca1\u6709\u6807\u7b7e\u7684\u60c5\u51b5\u4e0b\uff0c\u8ba9\u6a21\u578b\u81ea\u884c\u5c06\u6570\u636e\u5206\u7c7b\u3002\u5728\u5927\u89c4\u6a21\u6570\u636e\u4e2d\uff0c\u6211\u4eec\u65e0\u6cd5\u4f7f\u7528k-\u8fd1\u90bb\u7b97\u6cd5\uff0c\u56e0\u4e3a\u5b58\u50a8\u96be\u5ea6\u592a\u5927\uff0c\u6211\u4eec\u9009\u62e9\u8bb0\u5f55\u53ea\u6bcf\u4e2a\u7c07\u7684\u5706\u5fc3\u3002<\/p>\n\n\n\n<p>k-means\u628a\u7c07\u7684\u5706\u5fc3\u5b9a\u4e49\u4e3a\u7c07\u5185\u70b9\u7684\u5747\u503c\uff0c\u9700\u8981\u4eba\u4e3a\u7ed9\u5b9ak<\/p>\n\n\n\n<p>k-\u5747\u503c\u7b97\u6cd5\u7531\u4ee5\u4e0b\u56db\u6b65\u6765\u5b8c\u6210:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u968f\u673a\u7684\u9009\u62e9k\u4e2a\u5bf9\u8c61\u4f5c\u4e3a\u76ee\u524d\u5212\u5206\u7684\u7c07\u7684\u521d\u59cb\u7c07\u4e2d\u5fc3<\/li>\n\n\n\n<li>\u5bf9\u5269\u4e0b\u7684\u6bcf\u4e2a\u5bf9\u8c61\uff0c\u8ba1\u7b97\u4e0e\u5404\u7c07\u4e2d\u5fc3\u7684\u6b27\u6c0f\u8ddd\u79bb\uff0c\u5c06\u5b83\u5206\u914d\u5230\u6700\u76f8\u4f3c\u7684\u7c07<\/li>\n\n\n\n<li>\u4f7f\u7528\u4e0a\u6b21\u8fed\u4ee3\u5206\u914d\u5230\u8be5\u7c07\u7684\u5bf9\u8c61\uff0c\u8ba1\u7b97\u65b0\u7684\u5747\u503c<\/li>\n\n\n\n<li>\u4f7f\u7528\u65b0\u7684\u5747\u503c\u4f5c\u4e3a\u65b0\u7684\u7c07\u4e2d\u5fc3\uff0c\u91cd\u65b0\u5206\u914d\u6240\u6709\u5bf9\u8c61\uff0c\u76f4\u5230\u5206\u914d\u7a33\u5b9a<\/li>\n<\/ul>\n\n\n\n<p>\u590d\u6742\u5ea6\uff1aO(Iknd)\uff1b\u5176\u4e2dn \u662f\u5bf9\u8c61\u7684\u6570\u76ee, k \u662f\u7c07\u7684\u6570\u76ee, I \u662f\u8fed\u4ee3\u7684\u6b21\u6570, d\u662f\u5411\u91cf\u7684\u7ef4\u6570<\/p>\n\n\n\n<p>\u53d7\u521d\u59cb\u4e2d\u5fc3\u7684\u5f71\u54cd\uff0c\u53ef\u80fd\u5bfc\u81f4\u8fed\u4ee3\u6b21\u6570\u589e\u52a0\u6216\u9677\u5165\u5c40\u90e8\u6700\u4f18<\/p>\n\n\n\n<p>\u4f18\u70b9\uff1a\u6709\u53ef\u89e3\u91ca\u6027\uff0c\u6548\u7387\u9ad8<br>\u7f3a\u70b9\uff1a\u6bcf\u4e2a\u7c07\u90fd\u662f\u7403\u5f62\uff0c\u5728\u4e00\u4e9b\u62bd\u8c61\u6570\u636e\u4e2d\uff0c\u201c\u5747\u503c\u201d\u96be\u4ee5\u5b9a\u4e49\uff0ck\u9700\u8981\u4eba\u5de5\u6307\u5b9a\uff0c\u4e0d\u4e00\u5b9a\u5408\u9002\uff0c\u5bf9\u5f02\u5e38\u503c\u654f\u611f<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u964d\u7ef4<\/h2>\n\n\n\n<p>\u964d\u7ef4\u65b9\u6cd5\uff1aPCA\u4e3b\u6210\u5206\u5206\u6790\uff08\u7ebf\u6027\uff09Autoencoder\u81ea\u7f16\u7801\u5668\uff08\u975e\u7ebf\u6027\uff09<\/p>\n\n\n\n<p>\u4ee5\u4ee5\u4e0b\u6570\u636e\u4e3a\u4f8b<br>A = [2.5, 2.4]<br>B = [0.4, 0.7]<br>C = [2.2, 2.9]<\/p>\n\n\n\n<p>1.\u8ba1\u7b97\u6837\u672c\u5747\u503cX\u53ca\u534f\u65b9\u5dee\u77e9\u9635S<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-225238689e8622c6e1cd7bf35da44d33_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-225238689e8622c6e1cd7bf35da44d33_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\bar{x}=\\begin{bmatrix}\\frac{2.5+0.4+2.2}{3} &amp; \\frac{2.4+0.7+2.9}{3}\\end{bmatrix}=\\begin{bmatrix}1.7 &amp; 2\\end{bmatrix}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u5b9a\u4e49\u534f\u65b9\u5dee\u53ca\u534f\u65b9\u5dee\u77e9\u9635(\u4ee52\u7ef4\u4e3a\u4f8b\uff0c\u82e5\u4e09\u7ef4\u5219\u4e3axyz)\uff0c(n\u4e3a\u6837\u672c\u6570\u91cf)<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-7f801cae1d26e6d5ea821bcfcf864582_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-7f801cae1d26e6d5ea821bcfcf864582_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"cov(X,Y)=\\frac{\\sum_{i=1}^{n}(X_i-\\bar{X})(Y_i-\\bar{Y})}{n-1}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cd825bc6e165b82383b45c3e0693befe_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cd825bc6e165b82383b45c3e0693befe_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"S_{n\\times n}=\\begin{bmatrix}cov(x,x) &amp; cov(x,y) \\\\ cov(y,x) &amp; cov(y,y)\\end{bmatrix}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u5728\u4f8b\u5b50\u4e2d\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cfc60548ca1ce6c400aef5c0404e8a82_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-cfc60548ca1ce6c400aef5c0404e8a82_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"cov(x,x)=\\frac{(2.5-1.7)^2+(0.4-1.7)^2+(2.2-1.7)^2}{3-1}=1.26 \\\\cov(x,y)=cov(y,x)=\\frac{(2.5-1.7)*(2.4-2)+(0.4-1.7)*(0.7-2)+(2.2-1.7)*(2.9-2)}{3-1}=1.23 \\\\cov(y,y)=\\frac{(2.4-2)^2+(0.7-2)^2+(2.9-2)^2}{3-1}=1.33\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-2a268ccd9b4a030b91c7f106684e7240_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-2a268ccd9b4a030b91c7f106684e7240_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"S=\\begin{bmatrix}1.26 &amp; 1.23 \\\\1.23 &amp; 1.33 \\\\\\end{bmatrix}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>2.\u89e3\u51fa\u534f\u65b9\u5dee\u77e9\u9635S\u7684\u7279\u5f81\u503c\u03bb\uff0c\u5373|S-\u03bbI|=0\u7684\u89e3<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-a3c8d7ae382418bf7a8bbd0c919947b0_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-a3c8d7ae382418bf7a8bbd0c919947b0_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\mid S-\\lambda I\\mid =\\begin{vmatrix}1.26-\\lambda &amp; 1.23 \\\\1.23 &amp; 1.33-\\lambda \\end{vmatrix}=(1.26-\\lambda)(1.33-\\lambda)-1.23^2=0\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u89e3\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u5f97<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-054bf46b5a98cc9dbfe87a71476124fe_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-054bf46b5a98cc9dbfe87a71476124fe_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\lambda_1={0.06}\\quad \\lambda_2={2.53}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u8fdb\u800c\u5f97\u5230\u4e0e\u03bb\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf\uff08\u5373Sv=\u03bbv\uff09<\/p>\n\n\n\n<p>\u7279\u5f81\u5411\u91cf\u6ee1\u8db3\u5982\u4e0b\u5f0f\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-04c51f85daea1aca18fd282d2db1def9_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-04c51f85daea1aca18fd282d2db1def9_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"Sv=\\lambda v\\\\(S-\\lambda I)v=0\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u9700\u8981\u8bbev=[x,y]\u7136\u540e\u89e3\u51fax,y\u7684\u6bd4\u4f8b\uff0c\u518d\u5f52\u4e00\u5316\u5230\u5355\u4f4d\u957f\u5ea6<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u03bb<sub>1<\/sub>\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-6f3a3a97855d7bada0d993f08578d553_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-6f3a3a97855d7bada0d993f08578d553_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\begin{bmatrix}1.26-0.06 &amp; 1.23 \\\\1.23 &amp; 1.33-0.06 \\\\\\end{bmatrix} \\begin{bmatrix}x \\\\y \\\\\\end{bmatrix} =0\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u89e3\u5f97<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-d9de567faba1e0319382b03dbc0d57e4_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-d9de567faba1e0319382b03dbc0d57e4_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\\frac{x}{y}\\approx -\\frac{1.23}{1.2} \\approx -\\frac{1.27}{1.23}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u4ee5\u4e0a\u4e24\u4e2a\u7ea6\u7b49\u4e8e\u662f\u56e0\u4e3a\u8ba1\u7b97\u8bef\u5dee\u5bfc\u81f4\u7684\uff0c\u5b9e\u9645\u4e0a\u4f1a\u662f\u4e00\u4e2a\u503c\u3002<br>\u518d\u8fdb\u884c\u5f52\u4e00\u5316\uff0cv<sub>1<\/sub>=[0.713,-0.696]<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u03bb<sub>2<\/sub>\u540c\u7406\uff0cv<sub>2<\/sub>=[0.696,0.713]\uff08\u56e0\u4e3a\u662f2\u7ef4\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u770b\u51fa\u6765\uff0c\u4e09\u7ef4\u4e0d\u884c\uff09<\/p>\n\n\n\n<p>\u4e24\u4e2a\u4e3b\u6210\u5206\u7684\u8868\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-6c47b65a087f1c782908ec4c2e018582_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-6c47b65a087f1c782908ec4c2e018582_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"F_1=v_{11}(x-\\bar{x})+v_{21}(y-\\bar{y}) = 0.713(x-1.7)-0.696(y-2)\\\\F_2=v_{12}(x-\\bar{x})+v_{22}(y-\\bar{y}) = 0.696(x-1.7)+0.713(y-2)\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u4e3b\u6210\u5206\u7684\u8d21\u732e\u5ea6p\uff1a\uff08\u7ecf\u8bc1\u660e\u4e3b\u6210\u5206\u7684\u65b9\u5dee\u5c31\u662f\u7279\u5f81\u503c\u5927\u5c0f\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-6d7174bf1363a291bbdb013bea7f2301_l3.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/ql-cache\/quicklatex.com-6d7174bf1363a291bbdb013bea7f2301_l3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"p_i=\\frac{\\lambda_i}{\\sum \\lambda_i}\" title=\"Rendered by QuickLaTeX.com\"\/><\/div><\/figure>\n\n\n\n<p>\u5bf9\u793a\u4f8b\u60c5\u51b5\uff1a<\/p>\n\n\n\n<p>F<sub>1<\/sub>\u8d21\u732e\u5ea6=0.06\/(0.06+2.53)=0.02<br>F<sub>2<\/sub>\u8d21\u732e\u5ea6=2.53\/(0.06+2.53)=0.98<\/p>\n\n\n\n<p>\u53ef\u4ee5\u6839\u636e\u8d21\u732e\u5ea6\u4ece\u5927\u5230\u5c0f\uff0c\u5bf9\u6240\u6709\u4e3b\u6210\u5206\u8fdb\u884c\u6392\u5e8f\uff0c\u7136\u540e\u6839\u636e\u7d2f\u8ba1\u8d21\u732e\u5ea6\u8981\u6c42\u9009\u51fa\u524d\u51e0\u4e2a\u4e3b\u6210\u5206<\/p>\n\n\n\n<p><strong>Autoencoder\u81ea\u7f16\u7801\u5668<\/strong><\/p>\n\n\n\n<p>\u81ea\u7f16\u7801\u5668\u662f\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\uff0c\u5176\u8f93\u51fa\u76ee\u6807\u662f\u8fd8\u539f\u8f93\u5165<\/p>\n\n\n\n<p>PCA\u7b97\u6cd5\u53ef\u4ee5\u62bd\u8c61\u6210\u4e00\u5bf9\u7f16\u89e3\u7801\u5668<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-68.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-68.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u5b9e\u9645\u7684\u81ea\u7f16\u7801\u5668\uff0c\u7f16\u89e3\u7801\u5668\u662f\u9700\u8981\u8bad\u7ec3\u7684\u795e\u7ecf\u7f51\u7edc<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-67-1024x510.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-67-1024x510.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u81ea\u7f16\u7801\u5668\u5b8c\u6210\u56fe\u7247\u590d\u539f\u3001\u76f8\u4f3c\u56fe\u7247\u641c\u7d22\u7b49\u529f\u80fd\uff0c\u4ee5\u53ca\u7528\u4e8eCNN<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u751f\u6210\u5f0f\u6a21\u578b<\/h2>\n\n\n\n<p>GAN<\/p>\n\n\n\n<p>\u56de\u5fc6\uff1a\u8bed\u8a00\u6a21\u578b\u4e5f\u662f\u751f\u6210\u5f0f\u6a21\u578b\uff0c\u6211\u4eec\u5b66\u4e60\u7684\u662f\u4e0b\u4e00\u4e2a\u8bcd\u8bed\u7684\u6982\u7387<br>\u4eff\u7167\u8bed\u8a00\u6a21\u578b\uff0c\u6211\u4eec\u5728\u751f\u6210\u5176\u4ed6\u6570\u636e\u5982\u56fe\u7247\u65f6\uff0c\u5b66\u4e60\u7684\u4e5f\u662f\u6982\u7387<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-84.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"718\" height=\"347\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-84.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4287\"  sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/div><\/figure>\n\n\n\n<p>\u95ee\u9898\uff1a<br>\u6211\u4eec\u5982\u4f55\u8868\u793a\u56fe\u7247\u7684\u6982\u7387<br>\u6211\u4eec\u5982\u4f55\u4f7fp<sub>model<\/sub>\u63a5\u8fd1p<sub>data<\/sub><\/p>\n\n\n\n<p>\u8868\u793a\u56fe\u7247\u7684\u6982\u7387\uff1a<\/p>\n\n\n\n<p>\u6211\u4eec\u901a\u8fc7\u968f\u673a\u6570\u8ba9\u751f\u6210\u5668G\u4ea7\u751f\u56fe\u7247\uff0c\u5c31\u5982\u540c\u63b7\u8272\u5b50\uff0c\u901a\u8fc7\u5927\u91cf\u7684\u751f\u6210\u7684\u56fe\u7247\u7684\u5206\u5e03\u53cd\u6620\u6982\u7387\u5206\u5e03<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-85.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"381\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-85.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4288\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u4f7fp<sub>model<\/sub>\u63a5\u8fd1p<sub>data<\/sub>\uff1a<\/p>\n\n\n\n<p>\u5373\u5e0c\u671b\u6a21\u578b\u53ea\u751f\u6210\u771f\u56fe\u7247\uff0c\u4e0d\u751f\u6210\u5047\u56fe\u7247\uff0c\u751f\u6210\u7684\u5047\u56fe\u7247\u8d8a\u5c11\uff0c\u8bf4\u660e\u4e8c\u8005\u7684\u6982\u7387\u5206\u5e03\u8d8a\u63a5\u8fd1<\/p>\n\n\n\n<p>\u5f15\u5165\u4e00\u4e2a\u5224\u522b\u5668\uff1a\u5224\u65ad\u4e00\u5f20\u56fe\u7247\u662f\u5426\u7531ai\u751f\u6210\uff0c\u5f53\u751f\u6210\u6a21\u578b\u53ef\u4ee5\u4ee5\u5047\u4e71\u771f\uff0c\u90a3\u4e48\u8bf4\u660e\u5206\u5e03\u662f\u4e00\u81f4\u7684\u3002<br>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u751f\u6210\u5668\u548c\u5224\u522b\u5668\u7684\u76ee\u6807\u662f\u76f8\u53cd\u7684\uff0c\u4e8c\u8005\u6784\u6210\u4e86\u201c\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u201dGAN<\/p>\n\n\n\n<p>\u5224\u522b\u5668\u7684\u8bad\u7ec3\uff1a\uff08\u635f\u5931\u51fd\u6570\u4f7f\u7528\u4ea4\u53c9\u71b5\u5b9a\u4e49\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-71-1024x520.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-71-1024x520.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u751f\u6210\u5668\u7684\u8bad\u7ec3\uff1a\uff08\u635f\u5931\u51fd\u6570\u4e0e\u5224\u522b\u5668\u76f8\u53cd\uff09<\/p>\n\n\n\n<p>\u56e0\u4e3a\u751f\u6210\u5668\u770b\u4e0d\u5230\u771f\u5b9e\u56fe\u7247\uff0c\u6240\u4ee5\u5c11\u4e86\u4e00\u9879<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-72.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-72.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8bad\u7ec3\u5f00\u59cb\u65f6\uff0c\u9700\u8981\u6709\u4e00\u4e2a\u5df2\u7ecf\u9884\u8bad\u7ec3\u8fc7\u7684\u5224\u522b\u5668\uff0c\u5426\u5219\u8bad\u7ec3\u7ed3\u679c\u4e0d\u597d\u3002<\/p>\n\n\n\n<p><strong>\u6df1\u5ea6\u5377\u79ef\u751f\u6210\u5bf9\u6297\u7f51\u7edcDCGAN<\/strong><\/p>\n\n\n\n<p>\u4f7f\u7528\u9006\u5411\u5377\u79ef\u4f5c\u4e3a\u751f\u6210\u5668\uff0c\u4f7f\u7528\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u4f5c\u4e3a\u5224\u522b\u5668<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-90-1024x555.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-90-1024x555.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u9488\u5bf9DCGAN\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u4e86\u4e00\u4e9b\u6709\u8da3\u7684\u73b0\u8c61\u3002<br>\u52a0\u4e0a\u6211\u4eec\u8bad\u7ec3\u597d\u4e86\u4e00\u4e2a\u751f\u6210\u5668\uff0c\u7136\u540e\u6211\u4eec\u5df2\u77e5\u67d0\u4e9b\u968f\u673a\u79cd\u5b50\u5bf9\u5e94\u7740\u751f\u6210\u67d0\u7c7b\u56fe\u7247\uff1b\u5f53\u6211\u4eec\u7ed9\u8fd9\u4e9b\u79cd\u5b50\u8fdb\u884c\u7ebf\u6027\u7ec4\u5408\uff0c\u751f\u6210\u7684\u56fe\u7247\u4ecd\u662f\u8fd9\u4e2a\u7c7b\u578b\uff1b\u751a\u81f3\uff0c\u7c7b\u95f4\u7684\u968f\u673a\u79cd\u5b50\u52a0\u51cf\u540e\u7684\u7ed3\u679c\u80fd\u53cd\u6620\u51fa\u56fe\u7247\u7c7b\u578b\u7684\u589e\u5220<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-91-1024x508.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-91-1024x508.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p><strong>Conditional GAN<\/strong><\/p>\n\n\n\n<p>\u80fd\u591f\u6309\u7167\u9700\u6c42\u751f\u6210\u56fe\u7247<\/p>\n\n\n\n<p>\u6211\u4eec\u628a\u6761\u4ef6\u5206\u522b\u8f93\u5165\u751f\u6210\u5668\u548c\u5224\u522b\u5668\uff0c\u7136\u540e\u8fdb\u884c\u8bad\u7ec3\uff0c\u4e5f\u53ef\u4ee5\u770b\u4f5c\u4e00\u79cd\u7ffb\u8bd1\u5668<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-92-1024x521.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-92-1024x521.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p><strong>CycleGAN<\/strong><\/p>\n\n\n\n<p>Conditional GAN\u662f\u76d1\u7763\u5b66\u4e60\uff0c\u9700\u8981\u5927\u91cf\u7684\u6210\u5bf9\u6570\u636e\uff0c\u800ccycleGAN\u7684\u76ee\u6807\u662f\u65e0\u76d1\u7763\u5b66\u4e60\u3002\u5728\u6ca1\u6709\u6210\u5bf9\u793a\u4f8b\u7684\u60c5\u51b5\u4e0b\u5c06\u56fe\u50cf\u4ece\u6e90\u57df A \u4f20\u8f93\u5230\u76ee\u6807\u57df B\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-73-1024x463.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-73-1024x463.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>GAN\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u4ece\u968f\u673a\u5206\u5e03\u5230\u56fe\u7247\u6982\u7387\u5206\u5e03\u7684\u6982\u7387\u8f6c\u6362\u5668\uff1b\u800cCycleGAN\u9700\u8981\u7684\u662f\u4ece\u56fe\u7247\u6982\u7387\u5206\u5e03\u5230\u56fe\u7247\u6982\u7387\u5206\u5e03\u7684\u6982\u7387\u8f6c\u6362\u5668<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-74-1024x541.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-74-1024x541.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u6a21\u578b\u7ed3\u6784\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-75-1024x608.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-75-1024x608.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u901a\u8fc7\u53cd\u5411\u751f\u6210\u5668G<sub>BA<\/sub>\u5c1d\u8bd5\u590d\u539f\u56fe\u7247\uff0c\u6700\u5927\u5316\u590d\u539f\u56fe\u4e0e\u539f\u56fe\u7684\u76f8\u4f3c\u5ea6\uff1bG<sub>AB<\/sub>\u8bad\u7ec3\u76ee\u6807\u4e0d\u53d8\u3002\u5982\u679cG<sub>BA<\/sub>\u80fd\u590d\u539f\u56fe\u7247\uff0c\u8bf4\u660e\u751f\u6210\u7684\u5047\u56fe\u7247\u4e00\u5b9a\u5305\u542b\u4e86\u539f\u56fe\u7684\u4fe1\u606f<\/p>\n\n\n\n<p><strong>\u53d8\u5206\u81ea\u7f16\u7801\u5668Variational Autoencoder-VAE<\/strong><\/p>\n\n\n\n<p>GAN\u751f\u6210\u56fe\u7247\u9700\u8981\u968f\u673a\u53d8\u91cfz\uff0c\u4f46\u662f\u6211\u4eec\u627e\u4e0d\u5230z\u7684\u89c4\u5f8b\uff0c\u65e0\u6cd5\u901a\u8fc7\u5b9a\u5411\u9700\u6c42\u4ea7\u751f\u56fe\u7247<br>\u6211\u4eec\u60f3\u5230\u4f7f\u7528Autoencoder\uff0c\u4f7fz\u662f\u4e00\u5f20\u539f\u59cb\u56fe\u7247\u7684\u538b\u7f29\u8868\u793a\uff0c\u8fd9\u6837\u7684z\u662f\u6709\u610f\u4e49\u7684\uff0c\u53ef\u4ee5\u7528\u6765\u5b9a\u5411\u751f\u6210\u56fe\u7247\uff0c\u4f46\u662fAutoencoder\u4e2dz\u662f\u79bb\u6563\u5206\u5e03\u7684\uff0c\u6211\u4eec\u8981\u60f3\u529e\u6cd5\u8ba9z\u7684\u5206\u5e03\u5f0f\u8fde\u7eed\u7684\uff0c\u6bd4\u5982\u7b26\u5408\u9ad8\u65af\u5206\u5e03<\/p>\n\n\n\n<p>VAE\uff1a\u5f3a\u5236\u7f16\u7801\u5668\u8f93\u51fa\u5747\u503c\u548c\u6807\u51c6\u5dee\uff08\u53ef\u4ee5\u786e\u5b9a\u4e3a\u4e00\u4e2a\u9ad8\u65af\u5206\u5e03\uff09\uff0c\u89e3\u7801\u5668\u7684\u8f93\u5165\u662f\u7b26\u5408\u8fd9\u4e2a\u9ad8\u65af\u5206\u5e03\u7684\u4e00\u4e2a\u968f\u673a\u503c\uff1b\u8fd9\u6837\u8bad\u7ec3\u51fa\u7684\u6a21\u578b\u4f1a\u5c06\u7279\u5f81\u9690\u85cf\u5728\u9ad8\u65af\u5206\u5e03\u4e2d\uff0c\u800c\u6ee1\u8db3\u8fd9\u79cd\u9ad8\u65af\u5206\u5e03\u7684\u968f\u673a\u79cd\u5b50\u751f\u6210\u7684\u56fe\u7247\u5177\u6709\u76f8\u540c\u7684\u7279\u5f81\uff0c\u4f46\u53c8\u5404\u4e0d\u76f8\u540c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-93-1024x387.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-93-1024x387.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>GAN\u548cVAE\u7684\u5c40\u9650\u6027\uff1a\u964d\u7ef4\u540e\u7684z\u7684\u8868\u8fbe\u80fd\u529b\u6709\u9650\uff0c\u548c\u539f\u59cb\u56fe\u7247\u5dee\u522b\u975e\u5e38\u5927\uff1b\u6240\u6709\u5185\u5bb9\u90fd\u662f\u4e00\u6b21\u751f\u6210\u7684<\/p>\n\n\n\n<p><strong>\u53bb\u566a\u6269\u6563\u6a21\u578b<\/strong><\/p>\n\n\n\n<p>\u5e0c\u671b\u6a21\u4eff\u4eba\u7c7b\u7684\u7ed8\u753b\u8fc7\u7a0b\uff0c\u4e00\u6b65\u6b65\u751f\u6210\u56fe\u7247<\/p>\n\n\n\n<p>\u6a21\u578b\u7ed3\u6784\uff1a\u539f\u59cb\u56fe\u7247\u662f\u968f\u673a\u566a\u58f0\uff0c\u7ecf\u8fc7\u591a\u5c42\u751f\u6210\u5668\u5f97\u5230\u56fe\u7247<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-94-1024x579.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-94-1024x579.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u8bad\u7ec3\u8fc7\u7a0b\uff1a\u5728\u4e00\u5f20\u56fe\u7247\u4e0a\u968f\u673a\u6dfb\u52a0\u566a\u58f0\u70b9\uff0c\u518d\u8bad\u7ec3\u6a21\u578b\u5c06\u5176\u590d\u539f\uff08\u5bf9\u6bcf\u4e00\u5c42\u5206\u522b\u8bad\u7ec3\uff0c\u800c\u4e0d\u662f\u4e00\u8d77\u8bad\u7ec3\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-95-1024x239.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-95-1024x239.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u5f3a\u5316\u5b66\u4e60RL<\/h2>\n\n\n\n<p>agent\u751f\u6210\u4e00\u4e2aaction\uff0c\u73af\u5883\u8fd4\u56destate\u548creward\uff1bagent\u518d\u6839\u636estate\u751f\u6210\u65b0\u7684action<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-86.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"555\" height=\"382\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-86.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4291\"  sizes=\"auto, (max-width: 555px) 100vw, 555px\" \/><\/div><\/figure>\n\n\n\n<p>\u5b9a\u4e49\u9a6c\u5c14\u79d1\u592b\u51b3\u7b56\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<p>\u628a\u8bad\u7ec3\u62bd\u8c61\u4e3a\u5982\u4e0b\u591a\u6b21\u51b3\u7b56\uff0c\u6bcf\u6b21\u51b3\u7b56\u4f1a\u5e26\u6765\u72b6\u6001\u4e13\u4e1a\uff0c\u5e76\u83b7\u5f97\u4e00\u5b9a\u5956\u52b1\u6216\u8005\u60e9\u7f5a\uff0c\u6211\u4eec\u6700\u7ec8\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u6761\u5956\u52b1\u6700\u5927\u7684\u8def\u5f84<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-87.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"654\" height=\"386\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-87.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4292\"  sizes=\"auto, (max-width: 654px) 100vw, 654px\" \/><\/div><\/figure>\n\n\n\n<p>RL\u7684\u5b66\u4e60\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-88.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"587\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-88.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4293\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Q-Learning<\/h3>\n\n\n\n<p>\u5b9a\u4e49\uff1aQ\u51fd\u6570\uff1a\u8f93\u5165\u4e3a\u5f53\u524d\u72b6\u6001\u548c\u884c\u4e3a\uff0c\u8f93\u51fa\u4e3a\u672a\u6765\u53ef\u83b7\u5f97\u5956\u52b1\u7684\u671f\u671b<\/p>\n\n\n\n<p>\u5982\u4f55\u5f97\u5230Q\u503c\uff1a<br>1.\u8499\u7279\u5361\u6d1b\uff1a\u901a\u8fc7\u904d\u5386\u540e\u7eed\u6240\u6709\u60c5\u51b5\/\u968f\u673a\u8ba1\u7b97\u51e0\u79cd\u540e\u7eed\u60c5\u51b5\uff0c\u8ba1\u7b97\u5e73\u5747\u7684\u5956\u52b1\u503c\uff1b\u4f46\u662f\u4f1a\u8017\u8d39\u5927\u91cf\u65f6\u95f4<br>2.\u9012\u5f52\u4f30\u8ba1\uff1a\u6839\u636e\u9012\u63a8\u5173\u7cfbQt=rt+\u03b3maxa{Qt+1}\uff0c\u91c7\u7528\u52a8\u6001\u89c4\u5212\u7684\u65b9\u5f0f\uff0c\u586b\u5199\u4e00\u4e2aQ\u503c\u8868\uff0c\u76f4\u81f3\u8868\u586b\u6ee1\uff08\u9012\u5f52\u5173\u7cfb\u4e0d\u552f\u4e00\uff09<\/p>\n\n\n\n<p>Q\u51fd\u6570\u7684\u95ee\u9898\uff1a\u53ea\u80fd\u9002\u7528\u4e8e\u8d70\u683c\u5b50\u8fd9\u79cd\u7b80\u5355\u7684\u6e38\u620f\uff0c\u6211\u4eec\u65e0\u6cd5\u5c06Q\u503c\u8868\u771f\u6b63\u586b\u6ee1\uff0c\u56e0\u6b64\u6211\u4eec\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u6765\u62df\u5408Q\u51fd\u6570<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>DQN<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-85-1024x235.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-85-1024x235.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-81-1024x149.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-81-1024x149.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p>\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5b58\u50a8\u72b6\u6001\u8f6c\u79fb\u7684\u56db\u5143\u7ec4D = {(s<sup>(1)<\/sup>,a<sup>(1)<\/sup>, r<sup>(1)<\/sup>, s\u2019<sup>(1)<\/sup>), \u2026, (s<sup>(N)<\/sup>&nbsp;, a<sup>(N)<\/sup>, r<sup>(N)<\/sup>, s\u2019<sup>(N)<\/sup>)}\uff0cDQN\u5728\u5bf9\u6574\u4e2aD\u8fdb\u884c\u4f18\u5316\u65f6\u7684\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-82-1024x191.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-82-1024x191.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>mini-batch&nbsp;: DQN \u4f1a\u968f\u673a\u62bd\u53d6\u4e00\u6279\u7ecf\u9a8c\u8fdb\u884c\u8bad\u7ec3\uff0c\u800c\u4e0d\u662f\u4f7f\u7528\u6700\u65b0\u7684\u7ecf\u9a8c\uff0c\u5373minibatch<\/li>\n\n\n\n<li><\/li>\n<\/ul>\n\n\n\n<p>\u95ee\u9898\uff1aQ\u4e5f\u662f\u6839\u636e\u6a21\u578b\u53d8\u5316\u7684\uff0c\u76ee\u6807\u503c\u4e0d\u7a33\u5b9a\uff0c\u4e8e\u662f\u6211\u4eec\u53e6\u5916\u6307\u5b9a\u4e00\u4e2a\u7f51\u7edc\uff08target Net\uff09\uff0c\u4e13\u95e8\u7528\u4e8e\u751f\u6210Q\uff0c\u6574\u4e2a\u7f51\u7edc\u7684\u53c2\u6570\u662f\u56fa\u5b9a\u7684\uff0c\u6bcf\u9694\u4e00\u6bb5\u65f6\u95f4\u5c06Q Net\u7684\u53c2\u6570\u590d\u5236\u8fc7\u53bb\u3002<\/p>\n\n\n\n<p>\u8bad\u7ec3\u6d41\u7a0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u521d\u59cb\u5316\uff1a\u521d\u59cb\u5316Q\u7f51\u7edc\u548c\u53c2\u6570\u03b8\uff1a<\/li>\n\n\n\n<li>\u667a\u80fd\u4f53\u4e0e\u73af\u5883\u4ea4\u4e92\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5728\u5f53\u524d\u72b6\u6001s\uff0c\u667a\u80fd\u4f53\uff0c\u4f7f\u7528\u8d2a\u5a6a\u7b56\u7565\u9009\u62e9\u52a8\u4f5ca<\/li>\n\n\n\n<li>\u6267\u884c\u52a8\u4f5ca\uff0c\u89c2\u5bdf\u5956\u52b1r\u548c\u4e0b\u4e00\u72b6\u6001s\u2018\u3002<\/li>\n\n\n\n<li>\u628a(<em>s<\/em>,<em>a<\/em>,<em>r<\/em>,<em>s<\/em>\u2032)&nbsp;\u5b58\u5165\u7ecf\u9a8c\u56de\u653e\u7f13\u51b2\u533a\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u8bad\u7ec3Q\u7f51\u7edc\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4ece\u56de\u653e\u7f13\u51b2\u533a\u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u6279\u7ecf\u9a8c&nbsp;(\ud835\udc60,\ud835\udc4e,\ud835\udc5f,\ud835\udc60\u2032)\u3002<\/li>\n\n\n\n<li>\u8ba1\u7b97\u76ee\u6807\u7684Q\u503c\uff0c\u4e0b\u56feTarget Qvalue<\/li>\n\n\n\n<li>\u6700\u5c0f\u5316Q\u7f51\u7edc\u7684\u9884\u6d4b\u8bef\u5dee\uff0c\u901a\u8fc7lossfunction<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u66f4\u65b0\u76ee\u6807\u7f51\u7edc\uff1a\u5b9a\u671f\u5c06 Q \u7f51\u7edc\u7684\u53c2\u6570&nbsp;<em>\u03b8<\/em>&nbsp;\u590d\u5236\u5230\u76ee\u6807\u7f51\u7edc&nbsp;<em>\u03b8<\/em>\u2212\u3002<\/li>\n\n\n\n<li>\u518d\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-83-1024x591.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-83-1024x591.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4f18\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u80fd\u591f\u5904\u7406\u9ad8\u7ef4\u72b6\u6001\u7a7a\u95f4\uff08\u6bd4\u5982\u56fe\u50cf\uff09\u3002<\/li>\n\n\n\n<li>\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u6765\u8fd1\u4f3c Q \u51fd\u6570\uff0c\u89e3\u51b3\u4e86\u4f20\u7edf Q-Learning \u7684\u5c40\u9650\u6027\u3002<\/li>\n\n\n\n<li>\u5f15\u5165\u4e86\u76ee\u6807\u7f51\u7edc\u548c\u7ecf\u9a8c\u56de\u653e\uff0c\u63d0\u5347\u4e86\u8bad\u7ec3\u7684\u7a33\u5b9a\u6027\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7f3a\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u8d85\u53c2\u6570\u654f\u611f\uff08\u6bd4\u5982\u5b66\u4e60\u7387\u3001\u6298\u6263\u56e0\u5b50\u7b49\uff09\u3002<\/li>\n\n\n\n<li>\u8bad\u7ec3\u8fc7\u7a0b\u53ef\u80fd\u4e0d\u7a33\u5b9a\uff0c\u5c24\u5176\u662f\u5728\u590d\u6742\u73af\u5883\u4e2d\u3002<\/li>\n\n\n\n<li>\u8ba1\u7b97\u8d44\u6e90\u9700\u6c42\u8f83\u9ad8\uff0c\u56e0\u4e3a\u9700\u8981\u591a\u6b21\u66f4\u65b0\u795e\u7ecf\u7f51\u7edc\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b56\u7565\u5b66\u4e60<\/h3>\n\n\n\n<p>\u6211\u4eec\u5e0c\u671b\u76f4\u63a5\u901a\u8fc7\u73af\u5883S\u5f97\u51fa\u884c\u52a8a\uff0c\u6216\u8005\u8bf4\u7ed9\u51fa\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u884c\u52a8ai\u7684\u6982\u7387\uff0c\u5373 $ \\pi_\\theta(s) \\sim P(a|s) $<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-89.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"284\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-89.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4294\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u8f6c\u6362\u6210\u4e86\u4e00\u4e2a\u5206\u7c7b\u95ee\u9898\uff0c\u6211\u4eec\u4f7f\u7528\u672a\u6765\u80fd\u83b7\u5f97\u6700\u5927\u8bc4\u4ef7\u5956\u52b1\u7684a\u4f5c\u4e3a\u76ee\u6807\u503c\u3002<br>\u6211\u4eec\u8fd8\u662f\u901a\u8fc7\u591a\u6b21\u5b9e\u9a8c\u7684\u65b9\u5f0f\u5f97\u5230\u5e73\u5747\u7684reward<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-90.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"941\" height=\"193\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-90.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4295\"  sizes=\"auto, (max-width: 941px) 100vw, 941px\" \/><\/div><\/figure>\n\n\n\n<p>\u7b56\u7565\u68af\u5ea6\u7684\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n<p>$ L = -\\sum_{\\tau} R_\\tau \\log p_\\theta(a_t|s_t) $<\/p>\n\n\n\n<p>\u5bf9\u5176\u6c42\u68af\u5ea6\uff0c\u53ef\u4ee5\u5f97\u5230<\/p>\n\n\n\n<p>$ \\nabla_\\theta L = -\\sum_\\tau R_\\tau \\nabla_\\theta \\log p_\\theta(a_t|s_t) $<\/p>\n\n\n\n<p>\u90a3\u4e48\u6700\u540e\u53c2\u6570\u66f4\u65b0\u53ca\u68af\u5ea6\u8868\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-97-1024x290.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.smzytyzg.tw.cn\/wp-content\/uploads\/2025\/06\/image-97-1024x290.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p><strong>\u57fa\u4e8eRL\u7684\u6587\u672c\u751f\u6210<\/strong><\/p>\n\n\n\n<p>\u4f20\u7edf\u7684\u6587\u672c\u751f\u6210\u65b9\u6cd5\uff08\u5982\u57fa\u4e8e RNN\u3001LSTM \u6216 Transformer \u7684\u8bed\u8a00\u6a21\u578b\uff09\u4e3b\u8981\u901a\u8fc7\u6700\u5927\u5316\u6761\u4ef6\u6982\u7387\u6765\u751f\u6210\u4e0b\u4e00\u4e2a\u8bcd\u8bed\uff1b\u5f3a\u5316\u5b66\u4e60\u63d0\u4f9b\u4e86\u4e00\u79cd\u673a\u5236\uff0c\u53ef\u4ee5\u6839\u636e\u751f\u6210\u6587\u672c\u7684\u5168\u5c40\u8d28\u91cf\u6765\u4f18\u5316\u6a21\u578b\u3002\u6211\u4eec\u5e0c\u671b\u6700\u5927\u5316\u6574\u4e2a\u751f\u6210\u5e8f\u5217\u7684\u603b\u5956\u52b1R\uff0c\u800c\u4e0d\u662f\u5355\u7eaf\u7684\u6700\u5927\u5316\u8bcd\u8bed\u7684\u6761\u4ef6\u6982\u7387\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4f5c\u4e1a\u89e3\u6790<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f5c\u4e1a\u4e00<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e00\u9898<\/h4>\n\n\n\n<p>\u8003\u8651\u4e00\u4e0b\u6839\u636e\u5e74\u9f84\u548c\u85aa\u6c34\u9884\u6d4b\u4e00\u4e2a\u4eba\u662f\u5426\u62e5\u6709\u5927\u5b66\u5b66\u4f4d\u7684\u95ee\u9898\u3002\u4e0b\u8868\u548c\u56fe\u8868\u5305\u542b10\u4e2a\u4eba\u7684\u8bad\u7ec3\u6570\u636e\u3002<\/p>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-91.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"565\" height=\"455\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-91.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4306\" style=\"width:367px;height:auto\"  sizes=\"auto, (max-width: 565px) 100vw, 565px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-92.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"867\" height=\"724\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-92.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4307\"  sizes=\"auto, (max-width: 867px) 100vw, 867px\" \/><\/div><\/figure>\n<\/div>\n\n\n\n<h5 class=\"wp-block-heading\">\u6784\u5efa\u51b3\u7b56\u6811<\/h5>\n\n\n\n<p>\u901a\u8fc7\u8d2a\u5a6a\u5730\u5206\u5272\u5c5e\u6027\u6765\u6700\u5927\u5316\u4fe1\u606f\u83b7\u53d6\uff0c\u6784\u5efa\u4e00\u4e2a\u51b3\u7b56\u6811\u6765\u5206\u7c7b\u4e00\u4e2a\u4eba\u662f\u5426\u62e5\u6709\u5927\u5b66\u5b66\u4f4d\u3002\u5047\u8bbe\u6bcf\u4e2a\u5206\u5272\u7684\u9608\u503c\u662f\u5f53\u524d\u5b50\u96c6\u4e2d\u5c5e\u6027\u7684\u4e2d\u95f4\u503c\uff0c\u5373\u00bd\uff08min+max\uff09\u3002\u663e\u793a\u6bcf\u6b21\u5206\u5272\u7684\u4fe1\u606f\u589e\u76ca\uff0c\u5e76\u5728\u56fe\u4e2d\u7ed8\u5236\u6240\u5b66\u6811\u7684\u51b3\u7b56\u8fb9\u754c\u3002<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/3fbfa6756740a257f5ac5f32494be88-636x1024.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"636\" height=\"1024\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/3fbfa6756740a257f5ac5f32494be88-636x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4309\"  sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u591a\u5143\u51b3\u7b56\u6811<\/h5>\n\n\n\n<p>\u591a\u5143\u51b3\u7b56\u6811\u662f\u5355\u53d8\u91cf\u51b3\u7b56\u6811\u7684\u63a8\u5e7f\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5206\u5272\u7684\u51b3\u7b56\u89c4\u5219\u4e2d\u53ef\u4ee5\u4f7f\u7528\u591a\u4e2a\u5c5e\u6027\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5206\u5272\u4e0d\u9700\u8981\u4e0e\u7279\u5f81\u7684\u8f74\u6b63\u4ea4\u3002<br>\u5bf9\u4e8e\u76f8\u540c\u7684\u6570\u636e\uff0c\u63d0\u4f9b\u4e00\u4e2a\u591a\u5143\u51b3\u7b56\u6811\uff0c\u5176\u4e2d\u6bcf\u4e2a\u51b3\u7b56\u89c4\u5219\u90fd\u662f\u4e00\u4e2a\u7ebf\u6027\u5206\u7c7b\u5668\uff0c\u6839\u636e\u03b1xage+\u03b2xincome-1\u7684\u7b26\u53f7\u505a\u51fa\u51b3\u7b56\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-93.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"884\" height=\"669\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-93.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4310\"  sizes=\"auto, (max-width: 884px) 100vw, 884px\" \/><\/div><\/figure>\n\n\n\n<p>\u89e3\u7b54\uff1a\u53ea\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u5408\u9002\u7684\u53c2\u6570\uff0c\u4f7f\u5f97\u7ebf\u6ee1\u8db3\u628a\u4e24\u7c7b\u5b8c\u5168\u5206\u5f00<\/p>\n\n\n\n<p>\u4f8b\u5982\u03b1=-0.1\uff0c\u03b2=-0.0001\uff0c\u90a3\u4e48\u4fe1\u606f\u589e\u76ca\u8ba1\u7b97\u4e3a IG=0.97-0=0.97<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">k-\u6700\u8fd1\u90bb<\/h5>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u4f7f\u7528\u6807\u51c6\u6b27\u51e0\u91cc\u5fb7\u8ddd\u79bb\u6765\u8ba1\u7b97\u6700\u8fd1\u90bb\uff0c\u5219\u7ed8\u52361-\u6700\u8fd1\u90bb\u5206\u7c7b\u5668\u7684\u51b3\u7b56\u8fb9\u754c\u3002<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a\u505a\u5782\u76f4\u5e73\u5206\u7ebf\uff0c\u8fde\u63a5\u5408\u5e76\uff0c\u6df1\u8272\u7684\u5c31\u662f\u6700\u540e\u7ed3\u679c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-94.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"991\" height=\"691\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-94.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4311\"  sizes=\"auto, (max-width: 991px) 100vw, 991px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e8c\u9898<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b<\/h5>\n\n\n\n<p>\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6587\u672c\u5206\u7c7b\u3002\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u4f60\u4f1a\u5f97\u5230\u4e00\u7ec4\u5b66\u751f\u5bf9\u98df\u5802\u7684\u53cd\u9988\uff0c\u5e76\u9644\u6709\u76f8\u5e94\u7684\u6807\u7b7e\uff0c\u8868\u660e\u5b66\u751f\u662f\u559c\u6b22\u8fd8\u662f\u4e0d\u559c\u6b22\u5b83\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-95.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"709\" height=\"432\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-95.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4312\"  sizes=\"auto, (max-width: 709px) 100vw, 709px\" \/><\/div><\/figure>\n\n\n\n<p>\u73b0\u5728\u7ed9\u51fa\u4e00\u4e2a\u65b0\u7684\u8bc4\u8bba\u201cvery delicious and cheap\u201d\uff0c\u6211\u4eec\u60f3\u4f7f\u7528\u6734\u7d20\u8d1d\u53f6\u65af\u7b97\u6cd5\u5c06\u5b83\u4eec\u5206\u4e3a\u4e24\u7c7b\u3002\u8bf7\u63d0\u4f9b\u6574\u4e2a\u8ba1\u7b97\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-96.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"777\" height=\"454\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-96.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4313\" style=\"width:491px;height:auto\"  sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/div><\/figure>\n\n\n\n<p>\u5e26 Laplace \u5e73\u6ed1\u7684\u6761\u4ef6\u6982\u7387\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-97.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"90\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-97.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4314\" style=\"width:161px;height:auto\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-98.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"879\" height=\"295\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-98.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4315\" style=\"width:431px;height:auto\"  sizes=\"auto, (max-width: 879px) 100vw, 879px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-99.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"737\" height=\"575\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-99.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4318\" style=\"width:367px;height:auto\"  sizes=\"auto, (max-width: 737px) 100vw, 737px\" \/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f5c\u4e1a\u4e8c<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e00\u9898<\/h4>\n\n\n\n<p>\u8bbe\u8ba1\u4e00\u4e2a\u4e24\u5c42\u591a\u5c42\u611f\u77e5\u5668\uff08MLP\uff09\uff0c\u7528\u4e8e\u68c0\u6d4b\u8f93\u5165 x1, x2, x3, x4 \u2208 R \u4e2d \u662f\u5426\u5b58\u5728\u4e00\u5bf9 xi + xj = 0\uff08\u5176\u4e2d i = j\uff09\u3002\u5982\u679c\u5b58\u5728\u8fd9\u6837\u7684\u6570\u5bf9\uff0c\u7f51\u7edc\u8f93\u51fa 1\uff1b\u5426\u5219\u8f93\u51fa 0\u3002 \u9690\u85cf\u5c42\u4f7f\u7528\u51b2\u6fc0\u6fc0\u6d3b\u51fd\u6570\u03c3 \uff1a<\/p>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-100.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"184\" height=\"69\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-100.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4319\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-101.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"75\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-101.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4320\"\/><\/div><\/figure>\n<\/div>\n\n\n\n<p>\u8f93\u51fa\u5c42\u9009\u62e9\u4f7f\u7528\u9636\u8dc3\u6fc0\u6d3b\u51fd\u6570\u03c3 \u2032 <\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u9690\u85cf\u5355\u5143\u6570\u91cf<\/h5>\n\n\n\n<p>n\u7684\u5408\u9002\u503c\u662f\u591a\u5c11\uff08\u5373\u9690\u85cf\u5355\u5143\u7684\u6570\u91cf\uff09\uff1f\u89e3\u91ca\u539f\u56e0<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<p>\u95ee\u9898\u8981\u6c42\u68c0\u6d4b x1, x2, x3, x4 \u4e2d\u662f\u5426\u5b58\u5728\u4e00\u5bf9 x<sub>i<\/sub> + x<sub>j<\/sub> = 0\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u9700\u8981\u68c0\u67e5\u6240\u6709\u53ef\u80fd\u7684\u6570\u5bf9\u7ec4\u5408\u00a0(\ud835\udc65<sub>\ud835\udc56<\/sub>,\ud835\udc65<sub>\ud835\udc57<\/sub>)\uff0c\u5e76\u5224\u65ad\u5b83\u4eec\u7684\u548c\u662f\u5426\u4e3a\u96f6\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u56db\u4e2a\u8f93\u5165\uff0c\u53ef\u80fd\u7684\u6570\u5bf9\uff08i \u2260 j\uff09\u6709\uff1a(x1, x2),(x1, x3),(x1, x4),(x2, x3),(x2, x4),(x3, x4)<br>\u6240\u4ee5\u8bbe\u8ba1\u7f51\u7edc\uff0c\u4f7f\u5f97\u6bcf\u4e2a\u9690\u85cf\u5355\u5143\u8d1f\u8d23\u68c0\u67e5\u4e00\u4e2a\u6570\u5bf9\uff0c\u8ba1\u7b97 x<sub>i<\/sub> + x<sub>j<\/sub> \u5e76 \u5e94\u7528\u51b2\u6fc0\u6fc0\u6d3b\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u9700\u8981 6 \u4e2a\u9690\u85cf\u5355\u5143\uff0c\u6bcf\u4e2a\u5bf9\u5e94\u4e00\u4e2a\u6570\u5bf9\uff1an=6<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u6743\u91cd\u548c\u504f\u7f6e<\/h5>\n\n\n\n<p>\u9009\u62e9\u4e00\u7ec4\u6743\u91cd\u548c\u504f\u5dee\uff0c\u4ee5\u4fbf\u7f51\u7edc\u6b63\u786e\u5b9e\u73b0\u6240\u9700\u529f\u80fd\u3002<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<p>\u8bbe\u8ba1\u4e00\u4e2a\u5177\u6709 n = 6 \u4e2a\u9690\u85cf\u5355\u5143\u7684\u7f51\u7edc\uff0c\u6bcf\u4e2a\u9690\u85cf\u5355\u5143\u5bf9\u5e94\u4e00\u4e2a\u6570\u5bf9\u3002 <br>\u8bbe\u9690\u85cf\u5355\u5143\u4e3a h1, h2, . . . , h6\uff0c\u5206\u522b\u5bf9\u5e94\u6570\u5bf9 (x1, x2),(x1, x3),(x1, x4),(x2, x3),(x2, x4),(x3, x4)\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u9690\u85cf\u5355\u5143 h<sub>k<\/sub>\uff0c\u5176\u9884\u6fc0\u6d3b\u503ca<sub>k<\/sub>\u662f\u8f93\u5165\u7684\u52a0\u6743\u548c\u52a0\u504f\u7f6e\uff0c\u5373\uff1a<\/p>\n\n\n\n<p>a<sub>k\u200b<\/sub>=<em>w<\/em><sub>k1<\/sub>\u200b<em>x<\/em><sub>1<\/sub>\u200b+w<sub>k2<\/sub>\u200b<em>x<\/em><sub>2<\/sub>\u200b+w<sub>k3<\/sub>\u200b<em>x<\/em><sub>3<\/sub>\u200b+w<sub>k4<\/sub>\u200b<em>x<\/em><sub>4<\/sub>\u200b+b<sub>k\u200b<\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-102.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"525\" height=\"535\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-102.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4323\"  sizes=\"auto, (max-width: 525px) 100vw, 525px\" \/><\/div><\/figure>\n\n\n\n<p>\u5bf9\u4e8e\u8f93\u51fa\u5c42\uff1a<\/p>\n\n\n\n<p>\u8f93\u51fa\u5c42\u9700\u8981\u6839\u636e\u9690\u85cf\u5c42\u7684\u8f93\u51fa\u00a0\u210e1,\u210e2,\u2026,\u210e6\u200b\u00a0\u5224\u65ad\u662f\u5426\u5b58\u5728\u81f3\u5c11\u4e00\u4e2a\u6570\u5bf9\u6ee1\u8db3\u00a0\ud835\udc65\ud835\udc56+\ud835\udc65\ud835\udc57=0\u3002\u5982\u679c\u5b58\u5728\uff0c\u8f93\u51fa\u00a0\ud835\udc66=1\uff1b\u5426\u5219\u8f93\u51fa\u00a0\ud835\udc66=0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-103.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"224\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-103.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4324\"  sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-104.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"101\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-104.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4325\"  sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/div><\/figure>\n\n\n\n<p>\u8fd9\u6b63\u662f\u6211\u4eec\u9700\u8981\u7684\u903b\u8f91\uff1a\u5f53\u5b58\u5728\u81f3\u5c11\u4e00\u4e2a\u6570\u5bf9\u6ee1\u8db3\u00a0\ud835\udc65\ud835\udc56+\ud835\udc65\ud835\udc57=0\uff0c\u9690\u85cf\u5c42\u7684\u67d0\u4e2a\u00a0\u210e\ud835\udc58=1\uff0c\u4ece\u800c\u00a0\ud835\udc67>0\uff0c\u8f93\u51fa\u00a0\ud835\udc66=1\u3002\u5426\u5219\uff0c\u6240\u6709\u00a0\u210e\ud835\udc58=0\uff0c\u4ece\u800c\u00a0\ud835\udc67=0\uff0c\u8f93\u51fa\u00a0\ud835\udc66=0\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u9a8c\u8bc1\u5206\u7c7b<\/h5>\n\n\n\n<p>\u9a8c\u8bc1\u4e09\u4e2a\u6d4b\u8bd5\u7f51\u7edc\uff1a <br>&#8211; \u8f93\u5165 1\uff1ax1 = 1, x2 = \u22121, x3 = 2, x4 = 3 <br>&#8211; \u8f93\u5165 2\uff1ax1 = 2, x2 = 3, x3 = 4, x4 = 5 <br>&#8211; \u8f93\u5165 3\uff1ax1 = 0, x2 = 5, x3 = \u22125, x4 = 0<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<p>\u903b\u8f91\u90fd\u7c7b\u4f3c\uff0c\u9010\u4e2a\u9a8c\u8bc1\u5c55\u793a\u5373\u53ef<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-105.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"421\" height=\"222\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-105.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4326\"  sizes=\"auto, (max-width: 421px) 100vw, 421px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-106.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"410\" height=\"219\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-106.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4327\"  sizes=\"auto, (max-width: 410px) 100vw, 410px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-107.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"411\" height=\"222\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-107.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4328\"  sizes=\"auto, (max-width: 411px) 100vw, 411px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e8c\u9898<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-108.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"789\" height=\"443\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-108.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4329\"  sizes=\"auto, (max-width: 789px) 100vw, 789px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-109.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"238\" height=\"185\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-109.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4330\"\/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u524d\u5411\u4f20\u64ad<\/h5>\n\n\n\n<p>\u8981\u8ba1\u7b97\u524d\u5411\u4f20\u64ad\uff0c\u5c31\u9700\u8981\u7b97\u51fa\u5b9e\u9645\u7684a1\uff0ca2\uff0c\u7136\u540e\u6309\u7167\u8981\u6c42\u4f7f\u7528\u6fc0\u6d3b\u51fd\u6570\u5f97\u51fa\u9690\u85cf\u5c42h1h2\u3002<\/p>\n\n\n\n<p>\u505a\u9898\u5c31\u662f\u6309\u7167\u516c\u5f0f\u7ec4\u5408\uff0c\u6bd4\u5982\u8bf4\u7b2c\u4e00\u4e2a\u53ef\u4ee5\u770b\u5230h1\u662f\u7531x1,x2,w0,W\u5171\u540c\u7ec4\u5408\u6210\uff0c\u56e0\u6b64\u6211\u4eec\u5c31\u53ef\u4ee5\u5148\u8ba1\u7b97\u51faa1\uff0c\u7136\u540e\u6fc0\u6d3b\u540e\u4f5c\u4e3ah1\uff0c\u540c\u7406\uff0c\u5bf9\u4e8ey\uff0c\u7531h1,h2,v0,V\u8fd9\u4e2a\u7ec4\u6210\uff0c\u8fd8\u662f\u7ec4\u5408\u540e\u6fc0\u6d3b\u5f97\u5230y<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-110.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"613\" height=\"102\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-110.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4332\" style=\"width:577px;height:auto\"  sizes=\"auto, (max-width: 613px) 100vw, 613px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-111.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"588\" height=\"828\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-111.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4333\" style=\"width:584px;height:auto\"  sizes=\"auto, (max-width: 588px) 100vw, 588px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-112.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"503\" height=\"276\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-112.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4334\"  sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u53cd\u5411\u4f20\u64ad<\/h5>\n\n\n\n<p>\u4f7f\u7528\u7b2c 4 \u4e2a\u6837\u672c (x = [0.7, 0.6],t = 1)\uff0c\u57fa\u4e8e\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570\u8ba1\u7b97\u6bcf\u4e2a\u53c2\u6570\u7684\u504f\u5bfc\u6570<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<p>\u901a\u8fc7\u67e5\u8be2\u53ef\u77e5\uff0c\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570L = \u2212tlog y \u2212 (1 \u2212 t)log(1 \u2212 y)\uff0c\u56e0\u4e3at=1\uff0c\u6240\u4ee5L=-logy<\/p>\n\n\n\n<p><strong>\uff081\uff09\u5bf9\u4e8e\u8bef\u5dee\u4fe1\u53f7\u03b4y<\/strong>\uff0c\u4e3a\u635f\u5931\u51fd\u6570\u5bf9\u8f93\u51fay\u7684\u504f\u5bfc\u6570\uff1a<\/p>\n\n\n\n<p>$ \\delta_y = \\frac{\\partial L}{\\partial y} $<\/p>\n\n\n\n<p>\u5e26\u5165\u4e0a\u9762\u7684\u4ea4\u53c9\u71b5\u635f\u5931\u51fd\u6570L=-logy\uff0c\u53ef\u4ee5\u5f97\u5230<br>$ \\delta_y = \\frac{\\partial (-\\log y)}{\\partial y} = -\\frac{1}{y} = -\\frac{1}{0.470} \\approx -2.128 $<\/p>\n\n\n\n<p><strong>\uff082\uff09\u63a5\u7740\u5bf9\u4e8e\u03b4z<\/strong>\uff0c\u7531\u4e4b\u524d\u53ef\u5f97z\u6fc0\u6d3b\u540e\u5f97\u5230\u8f93\u51fa\u7684y\uff0c\u5373\uff1a<\/p>\n\n\n\n<p>$ y = \\text{sigmoid}(z) = \\frac{1}{1 + e^{-z}} $<\/p>\n\n\n\n<p>\u5bf9z\u6c42\u5bfc\uff0c\u5f97\u5230\uff1a<br>$ \\frac{\\partial y}{\\partial z} = y(1 &#8211; y)  $<\/p>\n\n\n\n<p>\u8bef\u5dee\u4fe1\u53f7\u4ece\u00a0<em>y<\/em>\u00a0\u4f20\u9012\u5230\u00a0<em>z<\/em>\u00a0\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\uff1a<br>$ \\delta_z = \\frac{\\partial L}{\\partial z} = \\delta_y \\cdot \\frac{\\partial y}{\\partial z} = \\delta_y \\cdot y(1 &#8211; y) $<\/p>\n\n\n\n<p>\u4e0a\u4e00\u95ee\u5f97\u5230\u7684y\u548c\u521a\u624d\u7684\u03b4y\u4ee3\u5165\u540e\uff0c\u5f97\u5230\uff1a<br>$ \\delta_z = -2.128 \\cdot 0.470 \\cdot 0.530 \\approx -0.530 $<\/p>\n\n\n\n<p><strong>\uff083\uff09\u5bf9\u4e8e\u8f93\u51fa\u5c42\u6743\u91cdv<sub>k<\/sub>V<sub>0<\/sub>\u7684\u504f\u5bfc\u6570<\/strong><\/p>\n\n\n\n<p>\u8f93\u51fa\u5c42\u7684\u9884\u6fc0\u6d3b\u503c\u00a0<em>z<\/em>\u00a0\u662f\u9690\u85cf\u5c42\u7684\u52a0\u6743\u548c\u52a0\u504f\u7f6e\uff1a<br>$ z = v_1 h_1 + v_2 h_2  + v_0 $<\/p>\n\n\n\n<p>\u6bcf\u4e2a\u6743\u91cd\u00a0\ud835\udc63<sub>\ud835\udc58<\/sub>\u200b\u00a0\u7684\u504f\u5bfc\u6570\u4e3a\uff1a<br>$ \\delta v_k = \\frac{\\partial L}{\\partial v_k} = \\delta_z \\cdot \\frac{\\partial z}{\\partial v_k} $<\/p>\n\n\n\n<p>\u6c42\u5bfc\u540e\u53ef\u4ee5\u53d1\u73b0\uff1a<br>$ \\frac{\\partial z}{\\partial v_k} = h_k $<\/p>\n\n\n\n<p>\u90a3\u4e48\uff1a<br>$ \\delta v_k = \\delta_z \\cdot h_k $<\/p>\n\n\n\n<p>\u90a3\u4e48\u518d\u7528\u5230\u4e0a\u9762\u7684h1\uff0ch2\uff0c\u548c\u4e0a\u4e00\u95ee\u7684\u03b4z\uff0c\u53ef\u4ee5\u5f97\u5230<br>$ \\delta v_1 = \\delta_z \\cdot h_1 = -0.530 \\cdot 0.07 \\approx -0.0371 $<br>$ \\delta v_2 = \\delta_z \\cdot h_2 = -0.530 \\cdot 0.58 \\approx -0.3074 $<br>$ \\delta v_0 = \\frac{\\partial L}{\\partial v_0} = \\delta_z \\cdot \\frac{\\partial z}{\\partial v_0} = \\delta_z \\cdot 1 = -0.530 $<\/p>\n\n\n\n<p><strong>\uff084\uff09\u5bf9\u9690\u85cf\u5c42\u8f93\u51fa<em>h<sub>k<\/sub><\/em>\u200b\u00a0\u7684\u504f\u5bfc\u6570<\/strong><\/p>\n\n\n\n<p>$ \\delta h_k =  \\frac{\\partial L}{\\partial h_k} = \\delta_z \\cdot \\frac{\\partial z}{\\partial h_k} $<\/p>\n\n\n\n<p>\u5176\u4e2d\u4ece\u4e0a\u4e00\u95ee\u5f0f\u5b50\u4e2d\u4e5f\u53ef\u4ee5\u770b\u5230\uff0c$ \\frac{\\partial z}{\\partial h_k} = v_k $<\/p>\n\n\n\n<p>\u4ee3\u5165\u9898\u76ee\u4e2d\u6700\u5f00\u59cb\u7ed9\u7684v1\uff0cv0\uff0c\u8fd8\u6709\u4e0a\u4e0a\u4e00\u95ee\u7684\u03b4z\uff0c\u6700\u540e\u5f97\u5230<br>$ \\delta h_1 = \\delta_z \\cdot v_1 = -0.530 \\cdot 1.0 = -0.530 $<br>$ \\delta h_2 = \\delta_z \\cdot v_2 = -0.530 \\cdot (-0.5) = 0.265 $<\/p>\n\n\n\n<p><strong>\uff085\uff09\u5bf9\u9690\u85cf\u5c42\u6fc0\u6d3b\u503ca<sub>k<\/sub>\u7684\u504f\u5bfc\u6570<\/strong><\/p>\n\n\n\n<p>\u9690\u85cf\u5c42\u6fc0\u6d3b\u503c\u00a0<em>ak<\/em>\u200b\u00a0\u662f\u9690\u85cf\u5c42\u8f93\u51fa\u00a0<em>hk<\/em>\u200b\u00a0\u7684\u8f93\u5165\u3002\u9690\u85cf\u5c42\u7684\u6fc0\u6d3b\u51fd\u6570\u662f ReLU\uff0c\u5b9a\u4e49\u4e3a\uff1a<br>$ h_k = \\text{ReLU}(a_k) =<br>\\begin{cases}<br>a_k, &amp; \\text{\u5982\u679c } a_k > 0 \\\\<br>0, &amp; \\text{\u5426\u5219}<br>\\end{cases} $<\/p>\n\n\n\n<p>ReLU \u7684\u5bfc\u6570\u4e3a\uff1a<br>$ \\frac{\\partial h_k}{\\partial a_k} =<br>\\begin{cases}<br>1, &amp; \\text{\u5982\u679c } a_k > 0 \\\\<br>0, &amp; \\text{\u5426\u5219}<br>\\end{cases} $<\/p>\n\n\n\n<p><em>a<\/em>1\u200b=0.07>0,\u00a0\ud835\udc4e2=0.58>0:<br>$ \\delta a_1 = \\delta h_1 \\cdot \\frac{\\partial h_1}{\\partial a_1} = -0.530 \\cdot 1 = -0.530 $<br>$ \\delta a_2 = \\delta h_2 \\cdot \\frac{\\partial h_2}{\\partial a_2} = 0.265 \\cdot 1 = 0.265 $<\/p>\n\n\n\n<p><strong>\uff086\uff09\u5bf9\u9690\u85cf\u5c42\u6743\u91cd\u00a0<em>w<\/em><sub><em>jk<\/em>\u200b<\/sub>\u00a0\u7684\u504f\u5bfc\u6570<\/strong><\/p>\n\n\n\n<p>\u9690\u85cf\u5c42\u7684\u6fc0\u6d3b\u503c\u00a0<em>ak<\/em>\u200b\u00a0\u662f\u8f93\u5165\u7684\u52a0\u6743\u548c\u52a0\u504f\u7f6e\uff1a<br>$ a_k = w_{k1} x_1 + w_{k2} x_2 + w_{k3} x_3 + w_{k4} x_4 + w_{0k} $<\/p>\n\n\n\n<p>\u6bcf\u4e2a\u6743\u91cd\u00a0<em>w<sub>jk<\/sub><\/em>\u200b\u00a0\u7684\u504f\u5bfc\u6570\u4e3a\uff1a<br>$ \\frac{\\partial L}{\\partial w_{jk}} = \\delta a_k \\cdot \\frac{\\partial a_k}{\\partial w_{jk}} $<\/p>\n\n\n\n<p>\u53ef\u4ee5\u5f97\u5230$ \\frac{\\partial a_k}{\\partial w_{jk}} = x_j $\uff0c\u6240\u4ee5\uff1a<br>$ \\delta w_{jk} = \\delta a_k \\cdot x_j $<\/p>\n\n\n\n<p>\u4ee3\u5165\uff0c\u6700\u540e\u53ef\u4ee5\u5f97\u5230\u8fd9\u56db\u4e2a\u6570<br>$ \\delta w_{11} = \\delta a_1 \\cdot x_1 = -0.530 \\cdot 0.7 \\approx -0.371 $<br>$ \\delta w_{12} = \\delta a_1 \\cdot x_2 = -0.530 \\cdot 0.6 \\approx -0.318 $<br>$ \\delta w_{21} = \\delta a_2 \\cdot x_1 = 0.265 \\cdot 0.7 \\approx 0.1855 $<br>$ \\delta w_{22} = \\delta a_2 \\cdot x_2 = 0.265 \\cdot 0.6 \\approx 0.159 $<\/p>\n\n\n\n<p>\u540c\u7406<em>w<\/em><sub>0<em>k<\/em><\/sub>\u504f\u5bfc\u6570<\/p>\n\n\n\n<p>$ \\frac{\\partial L}{\\partial w_{0k}} = \\delta a_k \\cdot \\frac{\\partial a_k}{\\partial w_{0k}} = \\delta a_k $<\/p>\n\n\n\n<p>\u6240\u4ee5\u6700\u540e\uff1a<br>$ \\delta w_{01} = \\delta a_1 = -0.530 $<br>$ \\delta w_{02} = \\delta a_2 = 0.265 $<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u6743\u91cd\u66f4\u65b0<\/h5>\n\n\n\n<p>\u8bbe\u5b66\u4e60\u7387\u4e3a \u03b7 = 0.5\uff0c\u66f4\u65b0\u6bcf\u4e2a\u53c2\u6570<\/p>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<p>\u68af\u5ea6\u4e0b\u964d\u7684\u66f4\u65b0\u516c\u5f0f\u4e3a\uff1a<br>$ \\theta \\leftarrow \\theta  &#8211;  \\eta \\cdot \\frac{\\partial L}{\\partial \\theta} $<\/p>\n\n\n\n<p>\u6309\u7167\u4e4b\u524d\u8ba1\u7b97\u7684\u68af\u5ea6\u4e00\u4e2a\u4e2a\u4ee3\u5165\u5373\u53ef\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-113.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"517\" height=\"114\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-113.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4389\"  sizes=\"auto, (max-width: 517px) 100vw, 517px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-114.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"489\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-114.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4390\"  sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f5c\u4e1a3<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e00\u9898<\/h4>\n\n\n\n<p>\u6211\u4eec\u6709\u4e00\u4e2a\u56db\u4e2a\u5355\u8bcd\u7684\u53e5\u5b50\u3002\u5bf9\u5e94\u7684\u8bcd\u5d4c\u5165a1\u3001a2\u3001a3\u548ca4\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-115.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"181\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-115.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4398\" style=\"width:231px;height:auto\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-118-1024x561.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"561\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-118-1024x561.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4401\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n<\/div>\n\n\n\n<p>\u73b0\u5728\u6211\u4eec\u4f7f\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u81ea\u6211\u5173\u6ce8\u5c42\u6765\u5904\u7406\u8fd9\u4e9b\u8f93\u5165\uff0c\u8bf7\u8ba1\u7b97\u7b2c\u4e00\u4e2a\u5355\u8bcd\u7684\u65b0\u9690\u85cf\u72b6\u6001b1\u3002\uff08\u5047\u8bbe\u6240\u6709\u7684\u6a21\u578b\u9700\u8981\u7684\u53c2\u6570\u5df2\u521d\u59cb\u5316\u4e3a1\uff09<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u81ea\u6ce8\u610f\u529b<\/h5>\n\n\n\n<p>\u7b2c\u4e00\u6b65\uff1aH=WX<br>\u7b2c\u4e8c\u6b65\uff1aQ=WqH\uff1bK=WkH\uff1bV=WvH<br>\u7b2c\u4e09\u6b65\uff1a$ A=\\frac{KTQ}{\\sqrt{d}} $ ; A\u2019=softmax(A)\u6ce8\u610f\u8fd9\u91cc\u4e00\u5b9a\u8981\u9664$ \\sqrt{d} $\uff0cd\u4e3aq\u548ck\u7684\u7ef4\u5ea6<br>\u7b2c\u56db\u6b65\uff1aH\u2019=VA\u2019<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-119-1024x251.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"251\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-119-1024x251.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4402\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e8c\u9898<\/h4>\n\n\n\n<p>\u4e0b\u9762\u662f\u4e00\u4e2a\u5c0f\u578b\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u7684\u793a\u610f\u56fe\uff0c\u5b83\u5c0613&#215;13\u56fe\u50cf\u8f6c\u6362\u4e3a4\u4e2a\u8f93\u51fa\u503c\u3002\u8be5\u7f51\u7edc\u4ece\u8f93\u5165\u5230\u8f93\u51fa\u6709\u4ee5\u4e0b\u5c42\/\u64cd\u4f5c\uff1a3\u4e2a\u8fc7\u6ee4\u5668\u7684\u5377\u79ef\u3001\u6700\u5927\u6c60\u5316\u3001ReLU\uff0c\u6700\u540e\u662f\u4e00\u4e2a\u5b8c\u5168\u8fde\u63a5\u7684\u5c42\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u7f51\u7edc\uff0c\u6211\u4eec\u5c06\u4e0d\u4f7f\u7528\u4efb\u4f55\u504f\u7f6e\/\u504f\u79fb\u53c2\u6570\uff08w0\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-120.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"554\" height=\"225\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-120.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4403\"  sizes=\"auto, (max-width: 554px) 100vw, 554px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u6bcf\u5c42\u540e\u56fe\u50cf\/\u7279\u5f81\u56fe\u7684\u5927\u5c0f\u662f\u591a\u5c11\uff1f<\/h5>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-121.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"694\" height=\"820\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-121.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4404\" style=\"width:499px;height:auto\"  sizes=\"auto, (max-width: 694px) 100vw, 694px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-122-1024x226.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"226\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-122-1024x226.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4405\" style=\"width:504px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>\u6211\u4eec\u9700\u8981\u5b66\u4e60\u5377\u79ef\u5c42\u4e2d\u7684\u591a\u5c11\u6743\u91cd\uff1f<\/strong><\/h5>\n\n\n\n<p>\u5377\u79ef\u5c42\u6709 3 \u4e2a\u8fc7\u6ee4\u5668\uff0c\u6bcf\u4e2a\u8fc7\u6ee4\u5668\u7684\u5927\u5c0f\u662f\u00a04\u00d74\u3002\u8f93\u5165\u56fe\u50cf\u53ea\u6709 1 \u4e2a\u901a\u9053\uff0c\u5219\u6bcf\u4e2a\u8fc7\u6ee4\u5668\u6709\u00a04\u00d74=16\u00a0\u4e2a\u6743\u91cd\u3002<\/p>\n\n\n\n<p>\u603b\u7684\u5377\u79ef\u6743\u91cd\u6570\u4e3a\uff1a<br>\u603b\u6743\u91cd=\u8fc7\u6ee4\u5668\u6570\u00d7\u8fc7\u6ee4\u5668\u5927\u5c0f=3\u00d716=48<\/p>\n\n\n\n<p>\u5377\u79ef\u5c42\u4e2d\u9700\u8981\u5b66\u4e60&nbsp;<strong>48 \u4e2a\u6743\u91cd<\/strong>\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>\u5bf9\u6b63\u5411\u4f20\u9012\u6267\u884c\u4e86\u591a\u5c11\u6b21 ReLU \u64cd\u4f5c\uff1f<\/strong><\/h5>\n\n\n\n<p>ReLU \u662f\u9010\u5143\u7d20\u64cd\u4f5c\uff0c\u5bf9\u6bcf\u4e2a\u7279\u5f81\u56fe\u4e2d\u7684\u6bcf\u4e2a\u503c\u6267\u884c\u4e00\u6b21\u3002ReLU \u5c42\u7684\u8f93\u5165\u662f 3 \u4e2a\u00a05\u00d75\u00a0\u7684\u7279\u5f81\u56fe\uff0c\u56e0\u6b64\u603b\u5171\u6709\uff1aReLU\u00a0\u64cd\u4f5c\u6570=3\u00d75\u00d75=75<\/p>\n\n\n\n<p>\u6b63\u5411\u4f20\u9012\u4e2d\u6267\u884c\u4e86&nbsp;<strong>75 \u6b21 ReLU \u64cd\u4f5c<\/strong><\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u6574\u4e2a\u7f51\u7edc\u8981\u5b66\u4e60\u591a\u5c11\u6743\u91cd<\/h5>\n\n\n\n<p>\u5b8c\u5168\u8fde\u63a5\u5c42\u7684\u8f93\u51fa\u662f 4 \u4e2a\u503c\u3002\u6bcf\u4e2a\u8f93\u51fa\u503c\u4e0e\u8f93\u5165\u6240\u6709 75 \u4e2a\u503c\u76f8\u8fde\uff0c\u56e0\u6b64\u5b8c\u5168\u8fde\u63a5\u5c42\u7684\u6743\u91cd\u6570\u4e3a\uff1a<br>\u5b8c\u5168\u8fde\u63a5\u5c42\u6743\u91cd\u6570=\u8f93\u5165\u5927\u5c0f\u00d7\u8f93\u51fa\u5927\u5c0f=75\u00d74=300<\/p>\n\n\n\n<p>\u603b\u6743\u91cd\u6570=\u5377\u79ef\u5c42\u6743\u91cd\u6570+\u5b8c\u5168\u8fde\u63a5\u5c42\u6743\u91cd\u6570=48+300=348<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6837\u5377<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-125.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"742\" height=\"869\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-125.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4410\"  sizes=\"auto, (max-width: 742px) 100vw, 742px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-124.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"734\" height=\"628\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-124.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4407\"  sizes=\"auto, (max-width: 734px) 100vw, 734px\" \/><\/div><\/figure>\n\n\n\n<p>\u89e3\u7b54\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5224\u65ad\u9898<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9519\u8bef\n<ul class=\"wp-block-list\">\n<li><strong>\u903b\u8f91\u56de\u5f52\u662f\u4e00\u79cd\u7ebf\u6027\u6a21\u578b\uff0c\u9002\u7528\u4e8e\u7ebf\u6027\u51b3\u7b56\u8fb9\u754c\u3002<\/strong>\u5f53\u6570\u636e\u7279\u5f81\u7a7a\u95f4\u662f\u975e\u7ebf\u6027\u51b3\u7b56\u8fb9\u754c\u65f6\uff0c\u903b\u8f91\u56de\u5f52\u6a21\u578b\u65e0\u6cd5\u76f4\u63a5\u8fdb\u884c\u5206\u7c7b\uff0c\u901a\u5e38\u9700\u8981\u901a\u8fc7\u7279\u5f81\u8f6c\u6362\u6216\u4f7f\u7528\u6838\u65b9\u6cd5\u6765\u5904\u7406\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6b63\u786e\n<ul class=\"wp-block-list\">\n<li>K-means\u7684\u521d\u59cb\u72b6\u6001\uff08\u521d\u59cb\u8d28\u5fc3\u7684\u9009\u62e9\uff09\u4f1a\u5f71\u54cd\u6700\u7ec8\u7684\u805a\u7c7b\u7ed3\u679c\uff0c\u56e0\u4e3aK-means\u53ef\u80fd\u6536\u655b\u5230\u5c40\u90e8\u6700\u4f18\u89e3\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u9519\u8bef\n<ul class=\"wp-block-list\">\n<li>\u5f3a\u5316\u5b66\u4e60\u901a\u8fc7\u4e0e\u73af\u5883\u4ea4\u4e92\u83b7\u5f97\u5956\u52b1\u4fe1\u53f7\u6765\u5b66\u4e60\u7b56\u7565\uff0c\u662f\u4e00\u79cd\u6709\u76d1\u7763\u5b66\u4e60\u65b9\u6cd5\uff0c\u4e0d\u662f\u65e0\u76d1\u7763\u5b66\u4e60\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6b63\u786e\n<ul class=\"wp-block-list\">\n<li>\u589e\u52a0\u795e\u7ecf\u7f51\u7edc\u7684\u5c42\u6570\u53ef\u4ee5\u6355\u83b7\u66f4\u590d\u6742\u7684\u7279\u5f81\uff0c\u56e0\u6b64\u5177\u6709\u66f4\u5f3a\u7684\u8868\u5f81\u5b66\u4e60\u80fd\u529b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6b63\u786e\n<ul class=\"wp-block-list\">\n<li>\u6c60\u5316\u5c42\u901a\u8fc7\u51cf\u5c11\u7279\u5f81\u56fe\u7684\u5927\u5c0f\u964d\u4f4e\u53c2\u6570\u91cf\uff0c\u540c\u65f6\u4fdd\u7559\u91cd\u8981\u7684\u7279\u5f81\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u9519\u8bef\n<ul class=\"wp-block-list\">\n<li>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6536\u655b\u901f\u5ea6\u5feb\uff0c\u4f46\u5b83\u7684\u66f4\u65b0\u65b9\u5411\u6709\u566a\u58f0\uff0c\u53ef\u80fd\u4e0d\u7a33\u5b9a\u3002\u6279\u68af\u5ea6\u4e0b\u964d\u66f4\u7a33\u5b9a\uff0c\u4f46\u901f\u5ea6\u8f83\u6162\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u9009\u62e9\u9898<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\uff1f<\/li>\n\n\n\n<li>C      Adam\u4f18\u5316\u7b97\u6cd5\u5f15\u5165\u4e86\u201c\u52a8\u91cf\u201d\uff08momentum\uff09\u6982\u5ff5\u3002<\/li>\n\n\n\n<li>B      \u589e\u52a0\u9690\u85cf\u5c42\u795e\u7ecf\u5143\u6570\u91cf\u53ef\u80fd\u5bfc\u81f4\u6a21\u578b\u590d\u6742\u5ea6\u589e\u52a0\uff0c\u4ece\u800c\u52a0\u91cd\u8fc7\u62df\u5408\u3002<\/li>\n\n\n\n<li>A      \u975e\u7ebf\u6027\u5206\u7c7b\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u7279\u5f81\u8f6c\u6362\uff08\u5982\u6838\u65b9\u6cd5\uff09\u8f6c\u5316\u4e3a\u7ebf\u6027\u53ef\u5206\u95ee\u9898\u3002<\/li>\n\n\n\n<li>C      LSTM\uff08\u957f\u77ed\u671f\u8bb0\u5fc6\u7f51\u7edc\uff09\u662f\u5904\u7406\u5e8f\u5217\u9884\u6d4b\u4efb\u52a1\u7684\u6700\u4f73\u9009\u62e9\uff0c\u56e0\u4e3a\u5b83\u80fd\u6709\u6548\u6355\u83b7\u957f\u671f\u4f9d\u8d56\u5173\u7cfb\u3002<\/li>\n\n\n\n<li>C      \u6bcf\u5c42\u5377\u79ef\u6838\u5927\u5c0f\u4e3a3\u00d73\uff0cstride\u4e3a1\uff0c\u4e0d\u4f7f\u7528padding\u3002\u4e09\u5c42\u7f51\u7edc\u7684\u611f\u53d7\u91ce\u5927\u5c0f\u4e3a7\u00d77\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b80\u7b54\u9898<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8bef\u5dee\u53cd\u5411\u4f20\u64ad\u7684\u89d2\u5ea6\u8c08LSTM\u76f8\u6bd4RNN\u7684\u4f18\u70b9<br>LSTM\u901a\u8fc7\u5f15\u5165\u8bb0\u5fc6\u5355\u5143\u548c\u95e8\u673a\u5236\uff08\u8f93\u5165\u95e8\u3001\u9057\u5fd8\u95e8\u3001\u8f93\u51fa\u95e8\uff09\uff0c\u89e3\u51b3\u4e86RNN\u4e2d\u8bef\u5dee\u53cd\u5411\u4f20\u64ad\u65f6\u68af\u5ea6\u6d88\u5931\u6216\u68af\u5ea6\u7206\u70b8\u7684\u95ee\u9898\u3002\u5b83\u80fd\u591f\u901a\u8fc7\u8bb0\u5fc6\u5355\u5143\u6709\u6548\u4fdd\u5b58\u957f\u671f\u4f9d\u8d56\u4fe1\u606f\uff0c\u5e76\u901a\u8fc7\u95e8\u673a\u5236\u9009\u62e9\u6027\u5730\u66f4\u65b0\u6216\u9057\u5fd8\u4fe1\u606f\uff0c\u4ece\u800c\u5728\u957f\u5e8f\u5217\u4efb\u52a1\u4e2d\u8868\u73b0\u4f18\u4e8e\u4f20\u7edfRNN\u3002<\/li>\n\n\n\n<li>Self-Attention\u5c42\u7684\u8bcd\u5411\u91cf\u672c\u8d28\u533a\u522b<br>\u7b2c\u4e00\u5c42\u7684\u8bcd\u5411\u91cf\u662f\u57fa\u4e8e\u521d\u59cb\u8bcd\u5d4c\u5165\u751f\u6210\u7684\uff0c\u800c\u6700\u540e\u4e00\u5c42\u7684\u8bcd\u5411\u91cf\u901a\u8fc7\u591a\u5c42Self-Attention\u673a\u5236\u63d0\u53d6\u4e86\u66f4\u9ad8\u7ea7\u7684\u8bed\u4e49\u4fe1\u606f\uff0c\u80fd\u66f4\u597d\u5730\u8868\u793a\u8bcd\u5728\u6574\u4e2a\u4e0a\u4e0b\u6587\u4e2d\u7684\u610f\u4e49\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u8ba1\u7b97\u9898<\/h3>\n\n\n\n<p><strong>1.(a) \u5199\u51fa\u540e\u9a8c\u6982\u7387\u8868\u8fbe\u5f0f<\/strong><br>$ P(y|x_1, x_2, x_3) = \\frac{P(y) \\cdot P(x_1|y) \\cdot P(x_2|y) \\cdot P(x_3|y)}{P(x_1, x_2, x_3)} $<\/p>\n\n\n\n<p><strong>(b) \u8ba1\u7b97\u540e\u9a8c\u6982\u7387<\/strong><br>\u8868\u683c\u6570\u636e<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-126.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"842\" height=\"286\" data-original=\"https:\/\/www.haruhi.fans\/wp-content\/uploads\/2025\/06\/image-126.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-4413\"  sizes=\"auto, (max-width: 842px) 100vw, 842px\" \/><\/div><\/figure>\n\n\n\n<p>\u8ba1\u7b97\u540e\u9a8c\u6982\u7387\uff1a<br>$ P(y=0|x_1=0, x_2=0, x_3=1) = \\frac{P(y=0) \\cdot P(x_1=0|y=0) \\cdot P(x_2=0|y=0) \\cdot P(x_3=1|y=0)}{P(x_1=0, x_2=0, x_3=1)} $<br>$ P(y=0|x_1=0, x_2=0, x_3=1) = \\frac{0.5 \\cdot 0.75 \\cdot 0.75 \\cdot 0.5}{Z} = \\frac{0.140625}{Z} $<br>$ P(y=1|x_1=0, x_2=0, x_3=1) = \\frac{P(y=1) \\cdot P(x_1=0|y=1) \\cdot P(x_2=0|y=1) \\cdot P(x_3=1|y=1)}{P(x_1=0, x_2=0, x_3=1)} $<br>$ P(y=1|x_1=0, x_2=0, x_3=1) = \\frac{0.5 \\cdot 0.25 \\cdot 0.5 \\cdot 0.75}{Z} = \\frac{0.046875}{Z} $<\/p>\n\n\n\n<p>\u8fdb\u8fc7\u5f52\u4e00\u5316\uff0c\u6700\u540e\u5f97\u5230<br>$ P(y=0|x_1=0, x_2=0, x_3=1) = \\frac{0.140625}{0.140625 + 0.046875} = 0.75 $<br>$ P(y=1|x_1=0, x_2=0, x_3=1) = \\frac{0.046875}{0.140625 + 0.046875} = 0.25 $<\/p>\n\n\n\n<p>\u6240\u4ee5\u9884\u6d4by=0<\/p>\n\n\n\n<p>2. <strong>\u6279\u68af\u5ea6\u4e0b\u964d\u8fc7\u7a0b<\/strong><\/p>\n\n\n\n<p>\u6570\u636e\u70b9\u4e3a\u00a0(1,3),(2,5),(3,7)\uff0c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4e3a\u00a0\ud835\udc66=\ud835\udc64\u22c5\ud835\udc65+\ud835\udc4f\u3002\u521d\u59cb\u503c\u4e3a\u00a0\ud835\udc64=0,\ud835\udc4f=0\uff0c\u5b66\u4e60\u7387\u4e3a\u00a0\ud835\udefc=0.1\u3002<\/p>\n\n\n\n<p>\u8ba1\u7b97\u68af\u5ea6\uff1a <br>$ \\frac{\\partial L}{\\partial w} = -\\frac{2}{3} \\left[ (3 &#8211; (0 \\cdot 1 + 0)) \\cdot 1 + (5 &#8211; (0 \\cdot 2 + 0)) \\cdot 2 + (7 &#8211; (0 \\cdot 3 + 0)) \\cdot 3 \\right] $<br>$ \\frac{\\partial L}{\\partial w} = -\\frac{2}{3} \\left[ 3 \\cdot 1 + 5 \\cdot 2 + 7 \\cdot 3 \\right] = -\\frac{2}{3} \\cdot 38 = -25.33 $<br>$ \\frac{\\partial L}{\\partial b} = -\\frac{2}{3} \\left[ (3 &#8211; (0 \\cdot 1 + 0)) + (5 &#8211; (0 \\cdot 2 + 0)) + (7 &#8211; (0 \\cdot 3 + 0)) \\right] $<br>$ \\frac{\\partial L}{\\partial b} = -\\frac{2}{3} \\cdot (3 + 5 + 7) = -\\frac{2}{3} \\cdot 15 = -10 $<\/p>\n\n\n\n<p>\u66f4\u65b0\u53c2\u6570<br>$ w_{\\text{new}} = w_{\\text{old}} &#8211; \\alpha \\cdot \\frac{\\partial L}{\\partial w} = 0 &#8211; 0.1 \\cdot (-25.33) = 2.533 $<br>$ b_{\\text{new}} = b_{\\text{old}} &#8211; \\alpha \\cdot \\frac{\\partial L}{\\partial b} = 0 &#8211; 0.1 \\cdot (-10) = 1 $<\/p>\n\n\n\n<p>\u66f4\u65b0\u5230w\u548cb\u540e\uff0c\u7ee7\u7eed\u4e09\u6b21<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7cfb\u7edf\u8bbe\u8ba1\u9898<\/h3>\n\n\n\n<p>1. \u56fe\u4e66\u4ef7\u683c\u533a\u95f4\u9884\u6d4b<\/p>\n\n\n\n<p><strong>(1) \u4ef7\u683c\u533a\u95f4\u9884\u6d4b\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7279\u5f81\uff1a\u6807\u9898\u3001\u7b80\u4ecb\uff08\u6587\u672c\u5411\u91cf\u5316\u5904\u7406\u5982 TF-IDF\uff09\u3001\u51fa\u7248\u65e5\u671f\uff08\u65f6\u95f4\u7279\u5f81\uff09\u3001\u5b9a\u4ef7\u3002<\/li>\n\n\n\n<li>\u6a21\u578b\uff1a\u4f7f\u7528\u5206\u7c7b\u6a21\u578b\uff08\u5982\u903b\u8f91\u56de\u5f52\u3001\u968f\u673a\u68ee\u6797\u6216\u795e\u7ecf\u7f51\u7edc\uff09\u3002<\/li>\n\n\n\n<li>\u8bad\u7ec3\uff1a\u8f93\u5165\u5386\u53f2\u56fe\u4e66\u6570\u636e\uff0c\u6807\u7b7e\u4e3a\u4ef7\u683c\u533a\u95f4\u3002<\/li>\n\n\n\n<li>\u9884\u6d4b\uff1a\u5bf9\u65b0\u56fe\u4e66\u5206\u7c7b\u4e3a\u4f4e\u4ef7\u3001\u4e2d\u4ef7\u6216\u9ad8\u4ef7\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>(2) \u5b9a\u5411\u4e66\u7c4d\u63a8\u8350\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7279\u5f81\uff1a\u7528\u6237\u7684\u9605\u8bfb\u5e8f\u5217\u4f5c\u4e3a\u8f93\u5165\u3002<\/li>\n\n\n\n<li>\u6a21\u578b\uff1a\u4f7f\u7528\u5e8f\u5217\u6a21\u578b\uff08\u5982 LSTM \u6216 Transformer\uff09\u3002<\/li>\n\n\n\n<li>\u8bad\u7ec3\uff1a\u8f93\u5165\u7528\u6237\u5386\u53f2\u9605\u8bfb\u5e8f\u5217\uff0c\u9884\u6d4b\u4e0b\u4e00\u672c\u4e66\u3002<\/li>\n\n\n\n<li>\u63a8\u8350\uff1a\u8f93\u51fa\u6982\u7387\u6700\u9ad8\u7684\u4e66\u7c4d\u4f5c\u4e3a\u63a8\u8350\u7ed3\u679c\u3002<\/li>\n<\/ul>\n\n\n\n<p>2. \u81ea\u52a8\u9a7e\u9a76\u8bbe\u8ba1<\/p>\n\n\n\n<p><strong>(1) \u969c\u788d\u7269\u8bc6\u522b\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6570\u636e\u6536\u96c6\uff1a\u91c7\u96c6\u9053\u8def\u56fe\u50cf\uff0c\u6807\u6ce8\u969c\u788d\u7269\u3002<\/li>\n\n\n\n<li>\u6a21\u578b\uff1a\u4f7f\u7528 CNN\uff08\u5982 ResNet\uff09\u8fdb\u884c\u56fe\u50cf\u5206\u7c7b\u3002<\/li>\n\n\n\n<li>\u8bad\u7ec3\uff1a\u5c06\u56fe\u50cf\u8f93\u5165 CNN\uff0c\u8f93\u51fa\u969c\u788d\u7269\u7c7b\u522b\u3002<\/li>\n\n\n\n<li>\u90e8\u7f72\uff1a\u5b9e\u65f6\u9884\u6d4b\u969c\u788d\u7269\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>(2) \u5f3a\u5316\u5b66\u4e60\u63a7\u5236\u7cfb\u7edf\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u72b6\u6001\uff1a\u8f66\u8f86\u4f4d\u7f6e\u3001\u901f\u5ea6\u3001\u73af\u5883\u4fe1\u606f\u3002<\/li>\n\n\n\n<li>\u52a8\u4f5c\uff1a\u52a0\u901f\u3001\u51cf\u901f\u3001\u8f6c\u5411\u7b49\u3002<\/li>\n\n\n\n<li>\u5956\u52b1\uff1a\u6839\u636e\u884c\u9a76\u5b89\u5168\u6027\u548c\u6548\u7387\u8bbe\u8ba1\u5956\u52b1\u51fd\u6570\u3002<\/li>\n\n\n\n<li>\u4f7f\u7528 Q \u5b66\u4e60\u6216 PPO \u7b97\u6cd5\u4f18\u5316\u7b56\u7565\u4ee5\u6700\u5927\u5316\u5956\u52b1\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5f15\u8a00 \u5b9a\u4e49\uff1a\u4e00\u79cd\u4eba\u5de5\u667a\u80fd\u6280\u672f\uff0c\u53ef\u4ee5\u8ba9\u673a\u5668\u901a\u8fc7\u6570\u636e\u81ea\u52a8\u53d1\u73b0\u7edf\u8ba1\u89c4\u5f8b\uff08\u6a21\u578b\uff09\uff0c\u5e76\u4e0d\u65ad\u4f18\u5316\u81ea\u8eab\u6027\u80fd\uff08\u4f18\u5316\uff09\uff0c\u4ee5\u5b9e\u73b0\u7279 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