{"id":112440,"date":"2026-10-03T16:33:18","date_gmt":"2026-10-03T08:33:18","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/112440.html"},"modified":"2026-10-03T16:33:18","modified_gmt":"2026-10-03T08:33:18","slug":"transformer%e5%8e%9f%e7%90%86-%e6%b7%b1%e5%b1%82%e7%bd%91%e7%bb%9c%e7%9a%84%e7%a8%b3%e5%8e%8b%ef%bc%9a%e5%bd%92%e4%b8%80%e5%8c%96%e4%b8%8e%e6%ae%8b%e5%b7%ae","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/112440.html","title":{"rendered":"Transformer\u539f\u7406--\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261003083317-6ac0bdcd410fa.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>\u76ee\u5f55<\/h3>\n<ul>\n<li>1. \u6df1\u7f51\u7edc\u4e3a\u4ec0\u4e48\u9700\u8981\u5f52\u4e00\u5316\n<ul>\n<li>1.1 \u5206\u5e03\u6f02\u79fb\u4e0e\u68af\u5ea6\u5931\u63a7&#xff1a;\u4e24\u6761\u5e76\u884c\u7684\u75c5\u7076<\/li>\n<li>1.2 BatchNorm \u5728 NLP \u7684\u4e09\u5904\u5931\u6548<\/li>\n<li>1.3 LayerNorm \u516c\u5f0f\u62c6\u89e3&#xff1a;\u5355\u6837\u672c\u5185\u7edf\u8ba1<\/li>\n<\/ul>\n<\/li>\n<li>2. \u4f4d\u7f6e\u4e4b\u4e89&#xff1a;Post-LN \u4e0e Pre-LN\n<ul>\n<li>2.1 \u4e24\u79cd\u5199\u6cd5\u7684\u7cbe\u786e\u5b9a\u4e49<\/li>\n<li>2.2 \u68af\u5ea6\u89c6\u89d2&#xff1a;\u6b8b\u5dee\u4e3b\u5e72\u4e0a\u7684\u76f4\u901a\u8def\u5f84<\/li>\n<li>2.3 \u8bad\u7ec3\u66f2\u7ebf\u4e0e\u5b66\u4e60\u7387\u654f\u611f\u5ea6<\/li>\n<li>2.4 \u4e3b\u6d41\u6a21\u578b\u7684\u4e8b\u5b9e\u8868<\/li>\n<\/ul>\n<\/li>\n<li>3. RMSNorm \u7684\u51cf\u6cd5\n<ul>\n<li>3.1 \u53bb\u6389\u5747\u503c\u4e2d\u5fc3\u5316\u4e0e bias<\/li>\n<li>3.2 \u8bba\u6587\u5b9e\u9a8c&#xff1a;\u8d28\u91cf\u6301\u5e73\u4e0e 7% \u5230 64% \u63d0\u901f<\/li>\n<li>3.3 \u6570\u503c\u5b9e\u9a8c&#xff1a;\u8f93\u51fa\u5747\u503c\u975e\u96f6<\/li>\n<li>3.4 \u81ea\u5b9e\u73b0 RMSNorm \u4e0e\u901f\u5ea6\u57fa\u51c6<\/li>\n<\/ul>\n<\/li>\n<li>4. \u6b8b\u5dee\u8fde\u63a5&#xff1a;\u68af\u5ea6\u7684\u9ad8\u901f\u51fa\u53e3\n<ul>\n<li>4.1 ResNet \u601d\u60f3\u7684\u8fc1\u79fb<\/li>\n<li>4.2 \u6052\u7b49\u9879\u7684\u6570\u503c\u9a8c\u8bc1<\/li>\n<li>4.3 \u6b8b\u5dee\u6d41&#xff1a;\u4fe1\u606f\u9ad8\u901f\u516c\u8def\u89c6\u89d2<\/li>\n<li>4.4 \u5c42\u95f4\u8303\u6570\u589e\u957f\u73b0\u8c61<\/li>\n<\/ul>\n<\/li>\n<li>5. \u73b0\u4ee3\u53d8\u4f53&#xff1a;QK-Norm \u4e0e Sandwich\n<ul>\n<li>5.1 QK-Norm&#xff1a;\u628a\u5f52\u4e00\u5316\u63a8\u8fdb\u6ce8\u610f\u529b\u5185\u90e8<\/li>\n<li>5.2 DeepNorm \u4e0e Sandwich Norm<\/li>\n<li>5.3 \u53d8\u4f53\u9009\u62e9\u7684\u51b3\u7b56\u8868<\/li>\n<\/ul>\n<\/li>\n<li>6. \u5b9e\u9a8c\u5bf9\u6bd4&#xff1a;\u6df1\u5ea6\u3001\u5f52\u4e00\u5316\u4e0e\u4f4d\u7f6e\n<ul>\n<li>6.1 \u5b9e\u9a8c\u8bbe\u7f6e&#xff1a;\u73a9\u5177\u4efb\u52a1\u4e0e 20 \u5c42\u7f51\u7edc<\/li>\n<li>6.2 \u65e0\u5f52\u4e00\u5316\u7684 20 \u5c42\u5d29\u6e83\u5b9e\u9a8c<\/li>\n<li>6.3 Pre-LN \u4e0e Post-LN \u7684\u5b66\u4e60\u7387\u654f\u611f\u5ea6<\/li>\n<li>6.4 LN \u4e0e RMSNorm \u7684\u901f\u5ea6\u5bf9\u6bd4<\/li>\n<\/ul>\n<\/li>\n<li>7. \u8fb9\u754c\u4e0e\u5751\n<ul>\n<li>7.1 \u5f52\u4e00\u5316\u4e0d\u662f\u4e07\u80fd\u5f00\u5173<\/li>\n<li>7.2 \u5b9e\u73b0\u7ec6\u8282&#xff1a;final norm \u4e0e\u547d\u540d<\/li>\n<li>7.3 checkpoint \u4e0d\u517c\u5bb9&#xff1a;LN \u6743\u91cd\u8f6c RMSNorm<\/li>\n<li>7.4 \u7a33\u5b9a\u4e0e\u8d28\u91cf\u7684\u6743\u8861<\/li>\n<\/ul>\n<\/li>\n<li>\u603b\u7ed3<\/li>\n<\/ul>\n<h3>\u6458\u8981<\/h3>\n<p>\u672c\u7bc7\u662f\u7cfb\u5217\u7b2c 6 \u7bc7&#xff0c;\u62c6\u89e3\u6df1\u5c42 Transformer \u7684\u4e24\u4ef6\u7a33\u5b9a\u88c5\u7f6e&#xff1a;\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee\u3002\u5148\u8bb2\u5206\u5e03\u6f02\u79fb\u4e0e\u68af\u5ea6\u5931\u63a7&#xff0c;\u518d\u8bb2\u4e24\u79cd LN \u6446\u4f4d\u7684\u68af\u5ea6\u8def\u5f84\u5dee\u522b\u3002\u6587\u672b\u7528 20 \u5c42\u73a9\u5177\u7f51\u7edc\u590d\u73b0\u65e0\u5f52\u4e00\u5316\u5d29\u6e83\u4e0e RMSNorm \u7684\u901f\u5ea6\u4f18\u52bf\u3002<\/p>\n<h3>1. \u6df1\u7f51\u7edc\u4e3a\u4ec0\u4e48\u9700\u8981\u5f52\u4e00\u5316<\/h3>\n<p>\u4e0a\u4e00\u7bc7\u8bb2 FFN&#xff1a;\u5b83\u5360 Transformer \u53c2\u6570\u5927\u5934&#xff0c;\u662f\u77e5\u8bc6\u5b58\u50a8\u7684\u4e3b\u8981\u5bb9\u5668\u3002\u8fd9\u4e00\u7bc7\u5f80\u4e0b\u8d70\u4e00\u5c42&#xff0c;\u95ee\u4e00\u4e2a\u95ee\u9898&#xff1a;\u53c2\u6570\u5806\u5230\u51e0\u5341\u5c42&#xff0c;\u4fe1\u53f7\u9760\u4ec0\u4e48\u4e0d\u5931\u771f\u3002<\/p>\n<p>\u7b54\u6848\u5728\u4e24\u4e2a\u90e8\u4ef6\u91cc&#xff1a;\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee\u8fde\u63a5\u3002\u524d\u8005\u63a7\u4f4f\u6bcf\u5c42\u7684\u8f93\u51fa\u5e45\u5ea6&#xff0c;\u540e\u8005\u7ed9\u68af\u5ea6\u7559\u4e00\u6761\u4e0d\u8870\u51cf\u7684\u901a\u9053\u3002\u672c\u8282\u5148\u8bb2\u524d\u8005\u3002<\/p>\n<h4>1.1 \u5206\u5e03\u6f02\u79fb\u4e0e\u68af\u5ea6\u5931\u63a7&#xff1a;\u4e24\u6761\u5e76\u884c\u7684\u75c5\u7076<\/h4>\n<p>\u767d\u8bdd\u7248&#xff1a;\u6df1\u7f51\u7edc\u50cf\u4e00\u6392\u63a5\u529b\u4f20\u8bdd\u7684\u4eba\u3002\u7b2c\u4e00\u4e2a\u4eba\u97f3\u91cf\u5408\u9002&#xff0c;\u4f20\u5230\u7b2c\u5341\u4e2a\u4eba\u65f6\u8981\u4e48\u558a\u6210\u566a\u58f0&#xff0c;\u8981\u4e48\u5c0f\u5230\u542c\u4e0d\u89c1\u3002<\/p>\n<p>\u672f\u8bed\u7248&#xff1a;\u8fd9\u5bf9\u5e94\u4e24\u4e2a\u95ee\u9898\u3002\u4e00\u662f\u5185\u90e8\u534f\u53d8\u91cf\u504f\u79fb&#xff08;internal covariate shift&#xff09;\u3002\u6307\u8bad\u7ec3\u4e2d\u6bcf\u5c42\u8f93\u5165\u5206\u5e03\u968f\u4e0a\u6e38\u66f4\u65b0\u800c\u6f02\u79fb&#xff0c;\u4e0b\u5c42\u8981\u4e0d\u505c\u8ffd\u7740\u65b0\u5206\u5e03\u8c03\u53c2\u3002\u4e8c\u662f\u68af\u5ea6\u7206\u70b8\u4e0e\u6d88\u5931\u3002\u6307\u8bef\u5dee\u4fe1\u53f7\u53cd\u4f20\u65f6\u9010\u5c42\u76f8\u4e58&#xff0c;\u5e45\u5ea6\u504f\u79bb\u4e00\u5c31\u6307\u6570\u53d1\u6563\u3002<\/p>\n<p>\u7b2c\u4e00\u7bc7\u63a8\u8fc7\u8def\u5f84\u957f\u5ea6\u7684\u8d26&#xff0c;\u8fd9\u91cc\u662f\u540c\u4e00\u7b14\u8d26\u7684\u53e6\u4e00\u9762\u3002\u524d\u5411\u662f\u4e58\u6cd5\u94fe&#xff0c;\u53cd\u5411\u4e5f\u662f\u4e58\u6cd5\u94fe\u3002\u5c42\u6570 L \u8d8a\u5927&#xff0c;\u94fe\u8d8a\u957f&#xff0c;\u5e45\u5ea6\u8d8a\u96be\u5b88\u4f4f\u3002<\/p>\n<p>\u5f52\u4e00\u5316\u7684\u4f5c\u7528\u53ef\u4ee5\u6982\u62ec\u6210\u7a33\u538b\u3002\u5b83\u4e0d\u4fdd\u8bc1\u6bcf\u5c42\u5b66\u5230\u4ec0\u4e48&#xff0c;\u53ea\u4fdd\u8bc1\u8fdb\u6bcf\u5c42\u7684\u4fe1\u53f7\u5e45\u5ea6\u88ab\u538b\u56de\u56fa\u5b9a\u8303\u56f4\u3002\u4e0b\u6e38\u66f4\u65b0\u518d\u731b&#xff0c;\u4e0b\u4e00\u5c42\u7684\u8f93\u5165\u7edf\u8ba1\u4e0d\u4f1a\u8dd1\u8fdc\u3002<\/p>\n<p><span class=\"token comment\"># \u81ea\u5b9e\u73b0&#xff1a;\u89c2\u5bdf\u65e0\u5f52\u4e00\u5316\u6df1\u7f51\u7edc\u7684\u524d\u5411\u5e45\u5ea6\u6f02\u79fb&#xff08;\u672c\u7bc7\u5b9e\u9a8c\u73af\u5883 PyTorch 2.13 CPU&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\ntorch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>d<span class=\"token punctuation\">,<\/span> L <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">20<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">16<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># batch&#061;4, seq&#061;16, dim&#061;64<\/span><br \/>\nmags <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>L<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    w <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">0.3<\/span>    <span class=\"token comment\"># \u6bcf\u5c42\u4e00\u4e2a\u968f\u673a\u7ebf\u6027\u53d8\u6362&#xff0c;\u6a21\u62df\u6743\u91cd<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> x &#064; w                      <span class=\"token comment\"># \u65e0\u5f52\u4e00\u5316\u3001\u65e0\u6b8b\u5dee&#xff0c;\u7eaf\u5806\u53e0<\/span><br \/>\n    mags<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span><span class=\"token builtin\">round<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>mags<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># [8.0, 2.45, 0.77, 0.25, 0.08, 0.03, 0.01, 0.0, 0.0, &#8230; ]  \u4fe1\u53f7 3 \u5c42\u5185\u6d88\u5931<\/span><\/p>\n<p>\u8fd9\u6bb5\u4ee3\u7801\u8dd1 20 \u5c42\u968f\u673a\u7ebf\u6027\u5806\u53e0&#xff0c;\u6bcf\u5c42\u8f93\u51fa\u8303\u6570\u88ab\u6253\u5370\u3002dim&#061;64 \u65f6\u7ea6 3 \u5c42\u540e\u5e45\u5ea6\u8dcc\u5230 0.01 \u91cf\u7ea7&#xff0c;\u7b2c 7 \u5c42\u8d77\u76f4\u63a5\u4e0b\u6ea2\u4e3a 0\u3002<\/p>\n<p>\u628a\u6743\u91cd\u653e\u5927\u5230 1.2 \u500d&#xff0c;\u65b9\u5411\u53cd\u8fc7\u6765&#xff0c;\u5e45\u5ea6 4 \u5c42\u5185\u6da8\u5230 1e4 \u91cf\u7ea7\u3002\u4e24\u4e2a\u65b9\u5411\u90fd\u4e0d\u53ef\u8bad\u3002<\/p>\n<p>\u518d\u770b\u5f52\u4e00\u5316\u63d2\u5165\u540e\u7684\u540c\u4e00\u5b9e\u9a8c\u3002\u6bcf\u5c42\u7ebf\u6027\u53d8\u6362\u540e\u63a5\u4e00\u6b21 LayerNorm&#xff0c;\u5e45\u5ea6\u88ab\u9489\u5728 sqrt(d) \u9644\u8fd1\u300220 \u5c42\u4e0b\u6765\u7eb9\u4e1d\u4e0d\u52a8\u3002\u8fd9\u5c31\u662f\u7a33\u538b\u4e24\u4e2a\u5b57\u7684\u76f4\u89c2\u6570\u636e\u3002<\/p>\n<p>\u75c5\u7076\u7684\u56e0\u679c\u94fe\u5982\u4e0b\u3002\u5206\u5e03\u6f02\u79fb\u8ba9\u635f\u5931\u9762\u5f62\u72b6\u968f\u8bad\u7ec3\u8fdb\u7a0b\u53d8\u5316&#xff0c;\u68af\u5ea6\u5931\u63a7\u8ba9\u4e00\u6b65\u66f4\u65b0\u8fc7\u5927\u5f15\u7206\u6574\u4e2a\u94fe\u3002\u5f52\u4e00\u5316\u540c\u65f6\u538b\u4f4f\u8fd9\u4e24\u5934\u3002<\/p>\n<p>\u4e0a\u6e38\u6743\u91cd\u66f4\u65b0<br \/>\n    -&gt; \u7b2c l \u5c42\u8f93\u5165\u5206\u5e03\u6f02\u79fb&#xff08;\u5185\u90e8\u534f\u53d8\u91cf\u504f\u79fb&#xff09;<br \/>\n    -&gt; \u7b2c l&#043;1 \u5c42\u6700\u4f18\u70b9\u4f4d\u7f6e\u79fb\u52a8&#xff0c;\u65e7\u53c2\u6570\u77ac\u95f4\u53d8\u5dee<br \/>\n    -&gt; \u53cd\u5411\u94fe\u4e58\u79ef\u5e45\u5ea6\u504f\u79bb 1<br \/>\n    -&gt; \u68af\u5ea6\u7206\u70b8\u6216\u6d88\u5931<br \/>\n    -&gt; \u8bad\u7ec3\u4e0d\u6536\u655b<\/p>\n<p>LayerNorm \u8bba\u6587&#xff08;arXiv:1607.06450&#xff09;\u7684\u539f\u59cb\u52a8\u673a\u6b63\u662f\u8fd9\u4e2a\u3002\u6458\u8981\u662f\u8bf4&#xff0c;\u6279\u5f52\u4e00\u5316\u6709\u6548\u4f46\u4f9d\u8d56\u6279\u5927\u5c0f&#xff0c;\u4e14\u4e0d\u9002\u7528\u4e8e\u5faa\u73af\u7f51\u7edc\u3002\u4ed6\u4eec\u628a\u7edf\u8ba1\u6765\u6e90\u4ece\u6279\u7ef4\u5ea6\u6362\u5230\u5c42\u7ef4\u5ea6\u3002<\/p>\n<p>\u8bba\u6587\u7ed9\u51fa\u4e09\u4e2a\u53ef\u6838\u5bf9\u7684\u70b9\u3002\u4e00\u662f\u8bad\u7ec3\u6d4b\u8bd5\u8ba1\u7b97\u4e00\u81f4&#xff0c;\u6ca1\u6709 running mean \u7684\u62d6\u5c3e\u95ee\u9898\u3002\u4e8c\u662f\u5929\u7136\u9002\u914d\u5faa\u73af\u7ed3\u6784&#xff0c;\u6bcf\u4e2a\u65f6\u95f4\u6b65\u5206\u522b\u7edf\u8ba1\u3002\u4e09\u662f\u5728\u5faa\u73af\u7f51\u7edc\u4e0a\u7a33\u5b9a\u4e86\u9690\u72b6\u6001\u52a8\u6001\u3002<\/p>\n<p>\u9700\u8981\u6f84\u6e05\u4e00\u70b9\u3002\u5185\u90e8\u534f\u53d8\u91cf\u504f\u79fb\u8fd9\u4e2a\u89e3\u91ca\u540e\u6765\u6709\u4e89\u8bae&#xff0c;BN \u7684\u673a\u5236\u5206\u6790\u4e5f\u88ab\u4fee\u6b63\u8fc7\u3002\u4f46\u5de5\u7a0b\u7ed3\u8bba\u6ca1\u53d8&#xff1a;\u5f52\u4e00\u5316\u8ba9\u6df1\u7f51\u7edc\u53ef\u8bad\u3002\u8fd9\u4e00\u70b9\u88ab\u540e\u9762\u6240\u6709\u67b6\u6784\u53cd\u590d\u9a8c\u8bc1\u3002<\/p>\n<p>  #mermaid-svg-tsvhb3tDsgkx0Rri{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-tsvhb3tDsgkx0Rri .error-icon{fill:#552222;}#mermaid-svg-tsvhb3tDsgkx0Rri .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-tsvhb3tDsgkx0Rri .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-tsvhb3tDsgkx0Rri .marker{fill:#333333;stroke:#333333;}#mermaid-svg-tsvhb3tDsgkx0Rri .marker.cross{stroke:#333333;}#mermaid-svg-tsvhb3tDsgkx0Rri svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-tsvhb3tDsgkx0Rri p{margin:0;}#mermaid-svg-tsvhb3tDsgkx0Rri .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri .cluster-label text{fill:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri .cluster-label span{color:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri .cluster-label span p{background-color:transparent;}#mermaid-svg-tsvhb3tDsgkx0Rri .label text,#mermaid-svg-tsvhb3tDsgkx0Rri span{fill:#333;color:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri .node rect,#mermaid-svg-tsvhb3tDsgkx0Rri .node circle,#mermaid-svg-tsvhb3tDsgkx0Rri .node ellipse,#mermaid-svg-tsvhb3tDsgkx0Rri .node polygon,#mermaid-svg-tsvhb3tDsgkx0Rri .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-tsvhb3tDsgkx0Rri .rough-node .label text,#mermaid-svg-tsvhb3tDsgkx0Rri .node .label text,#mermaid-svg-tsvhb3tDsgkx0Rri .image-shape .label,#mermaid-svg-tsvhb3tDsgkx0Rri .icon-shape .label{text-anchor:middle;}#mermaid-svg-tsvhb3tDsgkx0Rri .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-tsvhb3tDsgkx0Rri .rough-node .label,#mermaid-svg-tsvhb3tDsgkx0Rri .node .label,#mermaid-svg-tsvhb3tDsgkx0Rri .image-shape .label,#mermaid-svg-tsvhb3tDsgkx0Rri .icon-shape .label{text-align:center;}#mermaid-svg-tsvhb3tDsgkx0Rri .node.clickable{cursor:pointer;}#mermaid-svg-tsvhb3tDsgkx0Rri .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-tsvhb3tDsgkx0Rri .arrowheadPath{fill:#333333;}#mermaid-svg-tsvhb3tDsgkx0Rri .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-tsvhb3tDsgkx0Rri .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-tsvhb3tDsgkx0Rri .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-tsvhb3tDsgkx0Rri .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-tsvhb3tDsgkx0Rri .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-tsvhb3tDsgkx0Rri .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-tsvhb3tDsgkx0Rri .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-tsvhb3tDsgkx0Rri .cluster text{fill:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri .cluster span{color:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-tsvhb3tDsgkx0Rri .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-tsvhb3tDsgkx0Rri rect.text{fill:none;stroke-width:0;}#mermaid-svg-tsvhb3tDsgkx0Rri .icon-shape,#mermaid-svg-tsvhb3tDsgkx0Rri .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-tsvhb3tDsgkx0Rri .icon-shape p,#mermaid-svg-tsvhb3tDsgkx0Rri .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-tsvhb3tDsgkx0Rri .icon-shape .label rect,#mermaid-svg-tsvhb3tDsgkx0Rri .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-tsvhb3tDsgkx0Rri .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-tsvhb3tDsgkx0Rri .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-tsvhb3tDsgkx0Rri :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-tsvhb3tDsgkx0Rri .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-tsvhb3tDsgkx0Rri .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-tsvhb3tDsgkx0Rri .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e0a\u6e38\u5c42\u6743\u91cd\u66f4\u65b0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b2c l \u5c42\u8f93\u5165\u5206\u5e03\u6f02\u79fb<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e0b\u5c42\u6700\u4f18\u70b9\u79fb\u52a8<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u635f\u5931\u9762\u968f\u8bad\u7ec3\u8fdb\u7a0b\u53d8\u5f62<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53cd\u5411\u94fe\u4e58\u79ef\u5e45\u5ea6\u504f\u79bb 1<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u68af\u5ea6\u7206\u70b8\u6216\u6d88\u5931<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u4e0d\u6536\u655b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u63d2\u5165\u5f52\u4e00\u5316<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6bcf\u5c42\u8f93\u5165\u5e45\u5ea6\u88ab\u9489\u56de\u56fa\u5b9a\u8303\u56f4<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53cd\u5411\u94fe\u5e45\u5ea6\u53d7\u63a7<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u53ef\u6536\u655b<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u5de6\u53f3\u4e24\u6761\u75c5\u56e0\u94fe\u6700\u7ec8\u6c47\u5165\u540c\u4e00\u4e2a\u7ed3\u5c40\u3002\u5f52\u4e00\u5316\u4e0d\u662f\u6cbb\u67d0\u4e00\u4e2a\u75c5\u56e0&#xff0c;\u662f\u628a\u4e24\u6761\u94fe\u7684\u516c\u5171\u524d\u63d0&#xff08;\u5e45\u5ea6\u4e0d\u53d7\u63a7&#xff09;\u62ff\u6389\u3002<\/p>\n<p>\u672c\u8282\u8bb2\u4e86\u4e3a\u4ec0\u4e48\u3002\u4e0b\u4e00\u8282\u8bb2\u7b2c\u4e00\u4e2a\u5de5\u4e1a\u65b9\u6848 BatchNorm \u4e3a\u4f55\u5728 NLP \u6c34\u571f\u4e0d\u670d\u3002<\/p>\n<h4>1.2 BatchNorm \u5728 NLP \u7684\u4e09\u5904\u5931\u6548<\/h4>\n<p>\u767d\u8bdd\u7248&#xff1a;BatchNorm \u662f\u5168\u73ed\u540c\u4e00\u6b21\u8003\u8bd5\u653e\u5728\u4e00\u8d77\u7b97\u5e73\u5747\u5206\u3002NLP \u7684\u8003\u5377\u957f\u5ea6\u4e0d\u4e00&#xff0c;\u8fd8\u6709\u4eba\u5077\u770b\u540e\u9762\u9898\u76ee\u3002<\/p>\n<p>\u7b2c\u4e00\u5904\u5931\u6548\u662f\u53d8\u957f\u5e8f\u5217\u3002\u540c\u4e00\u6279\u5185\u53e5\u5b50\u957f\u5ea6\u4ece 5 \u5230 200 \u4e0d\u7b49&#xff0c;\u77ed\u53e5\u9760 padding \u8865\u9f50\u3002padding \u4f4d\u7f6e\u662f\u5426\u8ba1\u5165\u7edf\u8ba1&#xff0c;\u76f4\u63a5\u6539\u53d8\u5747\u503c\u65b9\u5dee\u7684\u6570\u503c\u3002CNN \u5904\u7406\u56fe\u50cf\u6ca1\u6709\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u6240\u6709\u6837\u672c\u540c\u5c3a\u5bf8\u3002<\/p>\n<p>\u7b2c\u4e8c\u5904\u5931\u6548\u662f\u6279\u5185\u7edf\u8ba1\u4e0d\u7a33\u3002\u7edf\u8ba1\u91cf\u968f batch \u5185\u6837\u672c\u7ec4\u5408\u53d8\u5316&#xff0c;batch \u4ece 32 \u964d\u5230 8 \u566a\u58f0\u663e\u8457\u53d8\u5927\u3002\u63a8\u7406\u65f6\u6539\u7528 running statistics&#xff0c;\u4e0e\u8bad\u7ec3\u65f6\u7684\u6279\u7edf\u8ba1\u5b58\u5728\u5206\u5e03\u5dee\u3002\u5c0f batch \u573a\u666f\u4e0b\u8fd9\u4e2a\u5dee\u4e0d\u53ef\u5ffd\u7565\u3002<\/p>\n<p>\u7b2c\u4e09\u5904\u6700\u81f4\u547d&#xff1a;\u81ea\u56de\u5f52\u6cc4\u6f0f\u98ce\u9669\u3002\u89e3\u7801\u5668\u91cc\u7b2c t \u6b65\u53ea\u80fd\u770b\u89c1\u524d t \u4e2a token\u3002\u82e5\u7edf\u8ba1\u5728\u5b8c\u6574\u5e8f\u5217\u4e0a\u7b97&#xff0c;\u7b2c t \u6b65\u7684\u5f52\u4e00\u5316\u7ed3\u679c\u5c31\u4f9d\u8d56\u672a\u6765\u4f4d\u7f6e\u3002\u8fd9\u7b49\u4e8e\u628a\u7b54\u6848\u6f0f\u7ed9\u5f53\u524d\u6b65\u3002<\/p>\n<p><span class=\"token comment\"># \u81ea\u5b9e\u73b0&#xff1a;\u6f14\u793a batch \u7ef4\u7edf\u8ba1\u5728\u53d8\u957f\u5e8f\u5217\u4e0b\u7684\u4e0d\u7a33\u5b9a&#xff08;PyTorch 2.13&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\ntorch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>d<span class=\"token punctuation\">,<\/span> lens <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">12<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">30<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">200<\/span><span class=\"token punctuation\">]<\/span><br \/>\nxs <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">2.0<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1.0<\/span> <span class=\"token keyword\">for<\/span> n <span class=\"token keyword\">in<\/span> lens<span class=\"token punctuation\">]<\/span>   <span class=\"token comment\"># 4 \u6761\u4e0d\u540c\u957f\u5ea6\u5e8f\u5217<\/span><\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">batch_stats<\/span><span class=\"token punctuation\">(<\/span>x_list<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u628a\u6240\u6709 token \u62fc\u5728\u4e00\u8d77\u7b97&#034;batch \u7ef4&#034;\u7edf\u8ba1&#xff08;padding \u7b80\u5316\u4e3a\u62fc\u63a5&#xff09;<\/span><br \/>\n    alltok <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>cat<span class=\"token punctuation\">(<\/span>x_list<span class=\"token punctuation\">,<\/span> dim<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> alltok<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> alltok<span class=\"token punctuation\">.<\/span>var<span class=\"token punctuation\">(<\/span>unbiased<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> keep <span class=\"token keyword\">in<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">:<\/span>                                <span class=\"token comment\"># \u4f9d\u6b21\u4e22\u6389\u957f\u53e5\u518d\u7b97<\/span><br \/>\n    m<span class=\"token punctuation\">,<\/span> v <span class=\"token operator\">&#061;<\/span> batch_stats<span class=\"token punctuation\">(<\/span>xs<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span>keep<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;\u4fdd\u7559 <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>keep<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> \u6761: mean&#061;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>m<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.3f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> var&#061;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>v<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.3f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u4fdd\u7559 4 \u6761: mean&#061;0.998 var&#061;4.004<\/span><br \/>\n<span class=\"token comment\"># \u4fdd\u7559 2 \u6761: mean&#061;0.996 var&#061;3.997<\/span><br \/>\n<span class=\"token comment\"># \u4fdd\u7559 1 \u6761: mean&#061;0.992 var&#061;3.981   &#xff08;\u672c\u4f8b\u5206\u5e03\u540c\u6784\u6240\u4ee5\u7a33\u5b9a&#xff09;<\/span><\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">layer_stats<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># LayerNorm&#xff1a;\u6bcf\u6761\u5e8f\u5217\u5355\u72ec\u7edf\u8ba1&#xff0c;\u4e0e\u6279\u5185\u5176\u4ed6\u6837\u672c\u65e0\u5173<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> x<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">.<\/span>var<span class=\"token punctuation\">(<\/span>unbiased<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token builtin\">tuple<\/span><span class=\"token punctuation\">(<\/span><span class=\"token builtin\">round<\/span><span class=\"token punctuation\">(<\/span>z<span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> z <span class=\"token keyword\">in<\/span> layer_stats<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> x <span class=\"token keyword\">in<\/span> xs<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># [(0.994, 4.076), (1.006, 3.918)]  \u6bcf\u6761\u5404\u81ea\u7edf\u8ba1&#xff0c;\u4e92\u4e0d\u5f71\u54cd<\/span><\/p>\n<p>\u4e0a\u9762\u6784\u9020\u7684\u662f\u7406\u60f3\u60c5\u51b5&#xff1a;\u5404\u53e5\u5206\u5e03\u540c\u6784&#xff0c;\u6240\u4ee5 batch \u7edf\u8ba1\u770b\u8d77\u6765\u7a33\u5b9a\u3002\u771f\u5b9e\u8bed\u6599\u91cc\u77ed\u53e5\u4e0e\u957f\u53e5\u7684 token \u5206\u5e03\u4e0d\u540c\u6784&#xff0c;batch \u7ec4\u5408\u4e00\u53d8\u7edf\u8ba1\u5c31\u8df3\u3002<\/p>\n<p>\u6700\u540e\u4e24\u884c\u662f LayerNorm \u7684\u53e3\u5f84\u3002\u6bcf\u6761\u5e8f\u5217\u81ea\u5df1\u7b97 mean \u4e0e var&#xff0c;\u6279\u91cc\u6709\u8c01\u3001\u6709\u51e0\u6761&#xff0c;\u90fd\u4e0d\u8fdb\u5165\u516c\u5f0f\u3002\u8fd9\u4e5f\u662f\u5b83\u63a8\u7406\u65f6\u65e0\u9700 running statistics \u7684\u539f\u56e0\u3002<\/p>\n<p>\u4e24\u6761\u8def\u7ebf\u7684\u5dee\u5f02\u53ef\u4ee5\u7528\u4e00\u5f20\u8868\u9489\u6b7b\u3002<\/p>\n<table>\n<tr>\u7ef4\u5ea6BatchNormLayerNorm<\/tr>\n<tbody>\n<tr>\n<td>\u7edf\u8ba1\u8303\u56f4<\/td>\n<td>\u540c\u4e00\u901a\u9053\u8de8 batch \u4e0e\u5e8f\u5217\u4f4d\u7f6e<\/td>\n<td>\u5355\u6837\u672c\u5355 token \u7684\u6574\u4e2a\u7279\u5f81\u7ef4<\/td>\n<\/tr>\n<tr>\n<td>\u53d8\u957f\u5e8f\u5217<\/td>\n<td>\u9700 padding \u7b56\u7565&#xff0c;\u7edf\u8ba1\u53d7\u5f71\u54cd<\/td>\n<td>\u4e0d\u6d89\u53ca&#xff0c;\u9010 token \u8ba1\u7b97<\/td>\n<\/tr>\n<tr>\n<td>\u8bad\u7ec3\u63a8\u7406\u4e00\u81f4<\/td>\n<td>\u8bad\u7ec3\u7528\u6279\u7edf\u8ba1&#xff0c;\u63a8\u7406\u7528 running \u503c<\/td>\n<td>\u5b8c\u5168\u4e00\u81f4<\/td>\n<\/tr>\n<tr>\n<td>\u81ea\u56de\u5f52\u5b89\u5168<\/td>\n<td>\u5e8f\u5217\u7ea7\u7edf\u8ba1\u6709\u6cc4\u6f0f\u98ce\u9669<\/td>\n<td>\u53ea\u770b\u5f53\u524d token&#xff0c;\u5b89\u5168<\/td>\n<\/tr>\n<tr>\n<td>batch \u4f9d\u8d56<\/td>\n<td>\u5f3a&#xff0c;\u5c0f batch \u566a\u58f0\u5927<\/td>\n<td>\u65e0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>LayerNorm \u8bba\u6587\u7684\u8868\u8ff0\u53ef\u4ee5\u76f4\u63a5\u5f15\u7528\u3002\u7edf\u8ba1\u6765\u81ea single training case \u7684\u5168\u90e8 summed inputs\u3002\u8bad\u7ec3\u4e0e\u6d4b\u8bd5\u8ba1\u7b97\u5b8c\u5168\u76f8\u540c\u3002\u8fd9\u53e5\u662f LN \u4e0e BN \u7684\u5206\u6c34\u5cad\u3002<\/p>\n<p>  #mermaid-svg-8jfGv3HKBsE29gfC{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-8jfGv3HKBsE29gfC .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-8jfGv3HKBsE29gfC .error-icon{fill:#552222;}#mermaid-svg-8jfGv3HKBsE29gfC .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-8jfGv3HKBsE29gfC .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-8jfGv3HKBsE29gfC .marker{fill:#333333;stroke:#333333;}#mermaid-svg-8jfGv3HKBsE29gfC .marker.cross{stroke:#333333;}#mermaid-svg-8jfGv3HKBsE29gfC svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-8jfGv3HKBsE29gfC p{margin:0;}#mermaid-svg-8jfGv3HKBsE29gfC .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-8jfGv3HKBsE29gfC .cluster-label text{fill:#333;}#mermaid-svg-8jfGv3HKBsE29gfC .cluster-label span{color:#333;}#mermaid-svg-8jfGv3HKBsE29gfC .cluster-label span p{background-color:transparent;}#mermaid-svg-8jfGv3HKBsE29gfC .label text,#mermaid-svg-8jfGv3HKBsE29gfC span{fill:#333;color:#333;}#mermaid-svg-8jfGv3HKBsE29gfC .node rect,#mermaid-svg-8jfGv3HKBsE29gfC .node circle,#mermaid-svg-8jfGv3HKBsE29gfC .node ellipse,#mermaid-svg-8jfGv3HKBsE29gfC .node polygon,#mermaid-svg-8jfGv3HKBsE29gfC .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-8jfGv3HKBsE29gfC .rough-node .label text,#mermaid-svg-8jfGv3HKBsE29gfC .node .label text,#mermaid-svg-8jfGv3HKBsE29gfC .image-shape .label,#mermaid-svg-8jfGv3HKBsE29gfC .icon-shape .label{text-anchor:middle;}#mermaid-svg-8jfGv3HKBsE29gfC .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-8jfGv3HKBsE29gfC .rough-node .label,#mermaid-svg-8jfGv3HKBsE29gfC .node .label,#mermaid-svg-8jfGv3HKBsE29gfC .image-shape .label,#mermaid-svg-8jfGv3HKBsE29gfC .icon-shape .label{text-align:center;}#mermaid-svg-8jfGv3HKBsE29gfC .node.clickable{cursor:pointer;}#mermaid-svg-8jfGv3HKBsE29gfC .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-8jfGv3HKBsE29gfC .arrowheadPath{fill:#333333;}#mermaid-svg-8jfGv3HKBsE29gfC .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-8jfGv3HKBsE29gfC .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-8jfGv3HKBsE29gfC .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-8jfGv3HKBsE29gfC .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-8jfGv3HKBsE29gfC .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-8jfGv3HKBsE29gfC .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-8jfGv3HKBsE29gfC .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-8jfGv3HKBsE29gfC .cluster text{fill:#333;}#mermaid-svg-8jfGv3HKBsE29gfC .cluster span{color:#333;}#mermaid-svg-8jfGv3HKBsE29gfC div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-8jfGv3HKBsE29gfC .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-8jfGv3HKBsE29gfC rect.text{fill:none;stroke-width:0;}#mermaid-svg-8jfGv3HKBsE29gfC .icon-shape,#mermaid-svg-8jfGv3HKBsE29gfC .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-8jfGv3HKBsE29gfC .icon-shape p,#mermaid-svg-8jfGv3HKBsE29gfC .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-8jfGv3HKBsE29gfC .icon-shape .label rect,#mermaid-svg-8jfGv3HKBsE29gfC .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-8jfGv3HKBsE29gfC .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-8jfGv3HKBsE29gfC .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-8jfGv3HKBsE29gfC :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-8jfGv3HKBsE29gfC .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-8jfGv3HKBsE29gfC .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-8jfGv3HKBsE29gfC .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316\u7edf\u8ba1\u6765\u6e90<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8de8\u6837\u672c: BatchNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6837\u672c\u5185: LayerNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8981\u6c42\u540c\u5c3a\u5bf8\u8f93\u5165<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53d8\u957f\u5e8f\u5217\u9700 padding<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7edf\u8ba1\u53d7 batch \u7ec4\u5408\u5f71\u54cd<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u63a8\u7406\u53e3\u5f84\u4e0d\u4e00<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9010 token \u5168\u7279\u5f81\u7ef4\u7edf\u8ba1<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e0e batch \u65e0\u5173<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u63a8\u7406\u540c\u516c\u5f0f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9002\u914d NLP \u53d8\u957f\u4e0e\u81ea\u56de\u5f52<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>NLP \u573a\u666f\u5931\u6548<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u5de6\u8fb9 BN \u7684\u4e09\u5904\u786c\u4f24&#xff08;padding\u3001\u6279\u4f9d\u8d56\u3001\u53e3\u5f84\u4e0d\u4e00&#xff09;\u90fd\u6e90\u81ea\u540c\u4e00\u4e2a\u51b3\u5b9a&#xff1a;\u8de8\u6837\u672c\u501f\u7edf\u8ba1\u3002LN \u628a\u7edf\u8ba1\u642c\u56de\u6837\u672c\u5185\u90e8&#xff0c;\u4e09\u5904\u540c\u65f6\u89e3\u5f00\u3002<\/p>\n<p>BN \u5e76\u975e\u4e00\u65e0\u662f\u5904\u3002\u89c6\u89c9\u4efb\u52a1\u91cc batch \u5927\u4e14\u56fe\u50cf\u540c\u5c3a\u5bf8&#xff0c;\u5b83\u81f3\u4eca\u4ecd\u662f\u9ed8\u8ba4\u9009\u9879\u3002\u5931\u6548\u662f\u6709\u6761\u4ef6\u7684&#xff1a;\u6761\u4ef6\u5c31\u662f NLP \u7684\u53d8\u957f\u4e0e\u81ea\u56de\u5f52\u3002<\/p>\n<p>\u4e0b\u4e00\u8282\u628a LN \u7684\u516c\u5f0f\u9010\u9879\u62c6\u5f00&#xff0c;\u770b\u6e05\u5b83\u5230\u5e95\u5bf9\u54ea\u4e2a\u7ef4\u5ea6\u505a\u4e86\u7edf\u8ba1\u3002<\/p>\n<h4>1.3 LayerNorm \u516c\u5f0f\u62c6\u89e3&#xff1a;\u5355\u6837\u672c\u5185\u7edf\u8ba1<\/h4>\n<p>\u767d\u8bdd\u7248&#xff1a;LayerNorm \u5bf9\u6bcf\u4e2a token \u7684\u7279\u5f81\u5411\u91cf\u505a\u4e09\u4ef6\u4e8b\u3002\u51cf\u5747\u503c\u3001\u9664\u6807\u51c6\u5dee\u3001\u518d\u4e58\u52a0\u4e00\u7ec4\u53ef\u5b66\u53c2\u6570\u3002<\/p>\n<p>\u516c\u5f0f\u5199\u6210\u4e09\u6b65\u3002\u7b2c\u4e00\u6b65\u7b97\u5747\u503c\u4e0e\u65b9\u5dee&#xff0c;\u7edf\u8ba1\u8303\u56f4\u662f\u7279\u5f81\u7ef4 d&#xff1a;<\/p>\n<p>mean &#061; (1\/d) * sum_i x_i<br \/>\nvar  &#061; (1\/d) * sum_i (x_i &#8211; mean)^2<\/p>\n<p>\u7b2c\u4e8c\u6b65\u6807\u51c6\u5316&#xff0c;eps \u662f\u9632\u9664\u96f6\u7684\u5c0f\u5e38\u6570&#xff0c;\u901a\u5e38 1e-5&#xff1a;<\/p>\n<p>x_hat_i &#061; (x_i &#8211; mean) \/ sqrt(var &#043; eps)<\/p>\n<p>\u7b2c\u4e09\u6b65\u4eff\u5c04&#xff08;affine&#xff0c;\u6307\u4e58\u52a0\u7ebf\u6027\u53d8\u6362&#xff09;\u3002gamma \u4e0e beta \u662f\u6bcf\u4e2a\u7ef4\u5ea6\u4e00\u4efd\u7684\u53ef\u5b66\u53c2\u6570&#xff1a;<\/p>\n<p>y_i &#061; gamma_i * x_hat_i &#043; beta_i<\/p>\n<p>\u4e09\u6b65\u5404\u6709\u5206\u5de5\u3002\u51cf\u5747\u503c\u53bb\u6389\u516c\u5171\u504f\u79fb&#xff0c;\u9664 std \u628a\u5e45\u5ea6\u9489\u4f4f\u3002\u4eff\u5c04\u628a\u9489\u4f4f\u7684\u7ea6\u675f\u653e\u677e\u56de\u6765&#xff0c;\u5141\u8bb8\u7f51\u7edc\u81ea\u5df1\u5b66\u6bcf\u7ef4\u7684\u5c3a\u5ea6\u4e0e\u504f\u79fb\u3002<\/p>\n<p>\u5173\u952e\u5728\u7edf\u8ba1\u8f74\u3002PyTorch \u7684 nn.LayerNorm \u9ed8\u8ba4\u5bf9\u6700\u540e\u4e00\u7ef4\u5f52\u4e00\u5316\u3002\u5373 shape \u4e3a (batch, seq, d) \u65f6\u5bf9 d \u7edf\u8ba1\u3002batch \u4e0e seq \u4e24\u4e2a\u7ef4\u5ea6\u53ea\u88ab\u5e7f\u64ad&#xff0c;\u4e0d\u53c2\u4e0e\u7edf\u8ba1\u3002<\/p>\n<p><span class=\"token comment\"># \u81ea\u5b9e\u73b0 LayerNorm&#xff1a;\u624b\u5199\u516c\u5f0f\u4e0e nn.LayerNorm \u5bf9\u7167&#xff08;PyTorch 2.13 CPU&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MyLayerNorm<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> dim<span class=\"token punctuation\">,<\/span> eps<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e-5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>gamma <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u7f29\u653e\u53c2\u6570<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>beta <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>zeros<span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u5e73\u79fb\u53c2\u6570<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>eps <span class=\"token operator\">&#061;<\/span> eps<\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        mean <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> keepdim<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>                    <span class=\"token comment\"># \u7b2c\u4e00\u6b65&#xff1a;\u5747\u503c<\/span><br \/>\n        var <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>var<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> unbiased<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">,<\/span> keepdim<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>      <span class=\"token comment\"># \u65b9\u5dee&#xff08;\u6709\u504f\u53e3\u5f84&#xff09;<\/span><br \/>\n        x_hat <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">&#8211;<\/span> mean<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> torch<span class=\"token punctuation\">.<\/span>sqrt<span class=\"token punctuation\">(<\/span>var <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>eps<span class=\"token punctuation\">)<\/span>        <span class=\"token comment\"># \u7b2c\u4e8c\u6b65&#xff1a;\u6807\u51c6\u5316<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> self<span class=\"token punctuation\">.<\/span>gamma <span class=\"token operator\">*<\/span> x_hat <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>beta                  <span class=\"token comment\"># \u7b2c\u4e09\u6b65&#xff1a;\u4eff\u5c04<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    dim <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">256<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">32<\/span><span class=\"token punctuation\">,<\/span> dim<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">3.0<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">2.0<\/span>        <span class=\"token comment\"># \u6545\u610f\u504f\u79fb\u5e76\u653e\u5927<\/span><br \/>\n    ref <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span>                     <span class=\"token comment\"># \u5b98\u65b9\u5b9e\u73b0\u505a\u53c2\u7167<\/span><br \/>\n    mine <span class=\"token operator\">&#061;<\/span> MyLayerNorm<span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span>                     <span class=\"token comment\"># \u624b\u5199\u5b9e\u73b0<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u5927\u7edd\u5bf9\u8bef\u5dee:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span>ref <span class=\"token operator\">&#8211;<\/span> mine<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">max<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># 0.0<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u8f93\u51fa\u5747\u503c:&#034;<\/span><span class=\"token punctuation\">,<\/span> mine<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>                    <span class=\"token comment\"># \u63a5\u8fd1 0<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u8f93\u51fastd:&#034;<\/span><span class=\"token punctuation\">,<\/span> mine<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>                      <span class=\"token comment\"># \u63a5\u8fd1 1<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u53c2\u6570\u91cf:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">.<\/span>numel<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> p <span class=\"token keyword\">in<\/span> MyLayerNorm<span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># 512<\/span><\/p>\n<p>\u5bf9\u7167\u7ed3\u679c\u6700\u5927\u7edd\u5bf9\u8bef\u5dee\u5728 1e-6 \u91cf\u7ea7&#xff0c;\u5c5e\u6d6e\u70b9\u8bef\u5dee\u3002\u4e24\u5b9e\u73b0\u6570\u503c\u4e00\u81f4\u3002\u6ce8\u610f var \u7528 unbiased&#061;False&#xff0c;\u5b98\u65b9\u5b9e\u73b0\u540c\u6837\u7528\u6709\u504f\u53e3\u5f84\u3002\u8fd9\u662f\u6700\u5e38\u89c1\u7684\u8e29\u5751\u70b9\u3002<\/p>\n<p>\u53c2\u6570\u91cf\u4e00\u884c\u4e3a\u540e\u9762 RMSNorm \u7684\u5bf9\u6bd4\u57cb\u4e86\u4f0f\u7b14\u3002dim&#061;256 \u65f6 LN \u5e26 512 \u4e2a\u53c2\u6570\u3002\u4e00\u534a\u662f gamma&#xff0c;\u4e00\u534a\u662f beta\u3002<\/p>\n<p>\u7edf\u8ba1\u8f74\u7684\u9009\u62e9\u4e5f\u51b3\u5b9a\u4e86\u7b97\u529b\u53bb\u5411\u3002\u5bf9 d \u7ef4\u7edf\u8ba1\u610f\u5473\u7740\u6bcf\u4e2a token \u5355\u72ec\u4e00\u6b21\u5f52\u4e00\u5316&#xff0c;\u5e8f\u5217\u5185\u4e92\u76f8\u72ec\u7acb\u3002\u8fd9\u4e2a\u6027\u8d28\u8ba9 LN \u53ef\u4ee5\u9010 token \u5e76\u884c&#xff0c;\u4e5f\u662f\u5b83\u80fd\u585e\u8fdb\u81ea\u56de\u5f52\u89e3\u7801\u5668\u7684\u539f\u56e0\u3002<\/p>\n<p>eps \u7684\u53d6\u503c\u4e0d\u662f\u7eaf\u6280\u672f\u7ec6\u8282\u3002fp16 \u8bad\u7ec3\u91cc var \u53ef\u80fd\u4e0b\u6ea2&#xff0c;eps \u5e38\u88ab\u8c03\u5927\u3002RMSNorm \u539f\u6587\u5b9e\u73b0\u540c\u6837\u5e26 eps\u3002<\/p>\n<p>\u6700\u540e\u56de\u5230\u7a33\u538b\u7684\u6bd4\u55bb\u3002LN \u4e0d\u6539\u53d8\u4fe1\u606f\u5185\u5bb9&#xff0c;\u53ea\u6539\u53d8\u8f7d\u4f53\u5e45\u5ea6\u3002\u7c7b\u6bd4\u6c34\u7ba1&#xff1a;\u6c34\u6d41\u5927\u5c0f\u88ab\u9650\u5b9a&#xff0c;\u6c34\u91cc\u5e26\u4ec0\u4e48\u6d88\u606f\u5b83\u4e0d\u7ba1\u3002<\/p>\n<p>  #mermaid-svg-WwXURVl7lDfH6iWA{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-WwXURVl7lDfH6iWA .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-WwXURVl7lDfH6iWA .error-icon{fill:#552222;}#mermaid-svg-WwXURVl7lDfH6iWA .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-WwXURVl7lDfH6iWA .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-WwXURVl7lDfH6iWA .marker{fill:#333333;stroke:#333333;}#mermaid-svg-WwXURVl7lDfH6iWA .marker.cross{stroke:#333333;}#mermaid-svg-WwXURVl7lDfH6iWA svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-WwXURVl7lDfH6iWA p{margin:0;}#mermaid-svg-WwXURVl7lDfH6iWA .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-WwXURVl7lDfH6iWA .cluster-label text{fill:#333;}#mermaid-svg-WwXURVl7lDfH6iWA .cluster-label span{color:#333;}#mermaid-svg-WwXURVl7lDfH6iWA .cluster-label span p{background-color:transparent;}#mermaid-svg-WwXURVl7lDfH6iWA .label text,#mermaid-svg-WwXURVl7lDfH6iWA span{fill:#333;color:#333;}#mermaid-svg-WwXURVl7lDfH6iWA .node rect,#mermaid-svg-WwXURVl7lDfH6iWA .node circle,#mermaid-svg-WwXURVl7lDfH6iWA .node ellipse,#mermaid-svg-WwXURVl7lDfH6iWA .node polygon,#mermaid-svg-WwXURVl7lDfH6iWA .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-WwXURVl7lDfH6iWA .rough-node .label text,#mermaid-svg-WwXURVl7lDfH6iWA .node .label text,#mermaid-svg-WwXURVl7lDfH6iWA .image-shape .label,#mermaid-svg-WwXURVl7lDfH6iWA .icon-shape .label{text-anchor:middle;}#mermaid-svg-WwXURVl7lDfH6iWA .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-WwXURVl7lDfH6iWA .rough-node .label,#mermaid-svg-WwXURVl7lDfH6iWA .node .label,#mermaid-svg-WwXURVl7lDfH6iWA .image-shape .label,#mermaid-svg-WwXURVl7lDfH6iWA .icon-shape .label{text-align:center;}#mermaid-svg-WwXURVl7lDfH6iWA .node.clickable{cursor:pointer;}#mermaid-svg-WwXURVl7lDfH6iWA .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-WwXURVl7lDfH6iWA .arrowheadPath{fill:#333333;}#mermaid-svg-WwXURVl7lDfH6iWA .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-WwXURVl7lDfH6iWA .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-WwXURVl7lDfH6iWA .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-WwXURVl7lDfH6iWA .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-WwXURVl7lDfH6iWA .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-WwXURVl7lDfH6iWA .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-WwXURVl7lDfH6iWA .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-WwXURVl7lDfH6iWA .cluster text{fill:#333;}#mermaid-svg-WwXURVl7lDfH6iWA .cluster span{color:#333;}#mermaid-svg-WwXURVl7lDfH6iWA div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-WwXURVl7lDfH6iWA .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-WwXURVl7lDfH6iWA rect.text{fill:none;stroke-width:0;}#mermaid-svg-WwXURVl7lDfH6iWA .icon-shape,#mermaid-svg-WwXURVl7lDfH6iWA .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-WwXURVl7lDfH6iWA .icon-shape p,#mermaid-svg-WwXURVl7lDfH6iWA .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-WwXURVl7lDfH6iWA .icon-shape .label rect,#mermaid-svg-WwXURVl7lDfH6iWA .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-WwXURVl7lDfH6iWA .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-WwXURVl7lDfH6iWA .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-WwXURVl7lDfH6iWA :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-WwXURVl7lDfH6iWA .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-WwXURVl7lDfH6iWA .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-WwXURVl7lDfH6iWA .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u5165 x \u5f62\u72b6 batch seq d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5bf9\u6700\u540e\u4e00\u7ef4 d \u6c42 mean<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5bf9\u6700\u540e\u4e00\u7ef4 d \u6c42 var<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>x \u51cf mean \u53bb\u516c\u5171\u504f\u79fb<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9664 sqrt var \u52a0 eps<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6807\u51c6\u5316\u7ed3\u679c x_hat<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e58\u53ef\u5b66 gamma<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u52a0\u53ef\u5b66 beta<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa y \u540c\u5f62\u72b6<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u53ea\u6709 B \u4e0e C \u4e24\u5904\u771f\u6b63\u505a\u7edf\u8ba1&#xff0c;\u5176\u4f59\u5168\u662f\u9010\u5143\u7d20\u64cd\u4f5c\u3002\u7edf\u8ba1\u8f74\u662f\u6700\u540e\u4e00\u7ef4&#xff0c;batch \u4e0e seq \u53ea\u88ab\u5e7f\u64ad\u3002<\/p>\n<p>LN \u89e3\u51b3\u4e86&#034;\u5f52\u4e0d\u5f52\u4e00\u5316&#034;&#xff0c;\u6ca1\u89e3\u51b3&#034;\u5728\u54ea\u5f52\u4e00\u5316&#034;\u3002\u4e0b\u4e00\u8282\u8fdb\u5165\u4f4d\u7f6e\u4e4b\u4e89\u3002<\/p>\n<h3>2. \u4f4d\u7f6e\u4e4b\u4e89&#xff1a;Post-LN \u4e0e Pre-LN<\/h3>\n<h4>2.1 \u4e24\u79cd\u5199\u6cd5\u7684\u7cbe\u786e\u5b9a\u4e49<\/h4>\n<p>\u5148\u628a\u7b26\u53f7\u9489\u6b7b\u3002Sublayer \u6307\u5b50\u5c42&#xff0c;\u5373\u591a\u5934\u6ce8\u610f\u529b\u6216 FFN\u3002LN \u653e\u5728\u5b50\u5c42\u5916\u9762\u8fd8\u662f\u91cc\u9762&#xff0c;\u5c31\u662f Post-LN \u4e0e Pre-LN \u7684\u5168\u90e8\u533a\u522b\u3002<\/p>\n<p>\u539f\u8bba\u6587&#xff08;arXiv:1706.03762&#xff09;\u662f Post-LN&#xff0c;LN \u5728\u6b8b\u5dee\u5408\u6d41\u4e4b\u540e\u3002\u6bcf\u5c42\u8f93\u51fa\u4e3a&#xff1a;<\/p>\n<p>Post-LN:  y &#061; LN(x &#043; Sublayer(x))<\/p>\n<p>\u5b50\u5c42\u8f93\u51fa\u4e0e\u8f93\u5165\u76f8\u52a0&#xff0c;\u518d\u6574\u4f53\u8fc7\u4e00\u6b21 LN\u3002LN \u4f4d\u4e8e\u4e24\u5c42\u4e4b\u95f4\u7684\u4e3b\u5e72\u4e0a&#xff0c;\u6240\u4ee5\u539f\u6587\u63cf\u8ff0\u4e3a&#034;LN \u653e\u5728\u6b8b\u5dee\u5757\u4e4b\u95f4&#034;\u3002<\/p>\n<p>Pre-LN&#xff08;arXiv:2002.04745&#xff09;\u628a LN \u632a\u8fdb\u5b50\u5c42\u5185\u90e8\u3002\u6b8b\u5dee\u4e3b\u5e72\u4e0a\u4e0d\u518d\u6709\u4efb\u4f55\u64cd\u4f5c\u3002\u6bcf\u5c42\u8f93\u51fa\u4e3a&#xff1a;<\/p>\n<p>Pre-LN:   y &#061; x &#043; Sublayer(LN(x))<\/p>\n<p>\u4e24\u79cd\u5199\u6cd5\u7684\u6a21\u5757\u4ee3\u7801\u5bf9\u7167\u5982\u4e0b&#xff0c;\u5f62\u72b6\u6807\u6ce8\u5728\u524d\u5411\u6ce8\u91ca\u91cc\u3002<\/p>\n<p><span class=\"token comment\"># Pre-LN \u4e0e Post-LN \u6a21\u5757\u5bf9\u7167&#xff08;PyTorch 2.13&#xff0c;\u5f62\u72b6 batch seq d&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">PostLNBlock<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;Post-LN&#xff1a;LN \u5728\u6b8b\u5dee\u5408\u6d41\u4e4b\u540e&#034;&#034;&#034;<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>sub <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Sequential<span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> nn<span class=\"token punctuation\">.<\/span>GELU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                 nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>hidden<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>     <span class=\"token comment\"># Sublayer \u5360\u4f4d<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>ln <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> self<span class=\"token punctuation\">.<\/span>ln<span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>sub<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">PreLNBlock<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;Pre-LN&#xff1a;LN \u8fdb\u5b50\u5c42&#xff0c;\u6b8b\u5dee\u4e3b\u5e72\u65e0\u4efb\u4f55\u64cd\u4f5c&#034;&#034;&#034;<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>ln <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>sub <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Sequential<span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> nn<span class=\"token punctuation\">.<\/span>GELU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                 nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>hidden<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> x <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>sub<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>ln<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u4e24\u79cd\u5199\u6cd5\u53ea\u5dee\u4e00\u4e2a\u62ec\u53f7\u4f4d\u7f6e\u3002\u524d\u5411\u5f62\u72b6\u90fd\u662f batch\u3001seq\u3001d \u4e09\u7ef4\u4e0d\u53d8\u3002\u4e0b\u9762\u8dd1\u4e00\u6b21\u5bf9\u7167&#xff0c;\u770b\u51fa\u53e3\u8303\u6570\u7684\u5dee\u522b\u3002<\/p>\n<p><span class=\"token comment\"># Post-LN \u4e0e Pre-LN \u7684\u51fa\u53e3\u8303\u6570\u5bf9\u7167&#xff08;\u63a5\u4e0a\u5757\u5b9a\u4e49&#xff0c;\u9700\u5148\u6267\u884c\u4e0a\u5757&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">64<\/span><span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># batch&#061;2, seq&#061;8, d&#061;64<\/span><br \/>\n    post <span class=\"token operator\">&#061;<\/span> PostLNBlock<span class=\"token punctuation\">(<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span>     <span class=\"token comment\"># \u524d\u5411\u5f62\u72b6 2 8 64 \u4e0d\u53d8<\/span><br \/>\n    pre <span class=\"token operator\">&#061;<\/span> PreLNBlock<span class=\"token punctuation\">(<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Post-LN \u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> post<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Pre-LN \u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> pre<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u8f93\u51fa&#xff1a;8.0000 \u4e0e 8.3924&#xff0c;Post-LN \u88ab\u9489\u5728 sqrt(64)&#061;8 \u9644\u8fd1<\/span><\/p>\n<p>\u8f93\u51fa\u8303\u6570\u4e00\u884c\u7684\u6570\u5b57\u662f\u7406\u89e3\u4e24\u79cd\u67b6\u6784\u7684\u94a5\u5319\u3002Post-LN \u6bcf\u5c42\u51fa\u53e3\u90fd\u88ab\u538b\u56de sqrt(d)&#xff0c;\u4e3b\u5e72\u5e45\u5ea6\u6052\u5b9a\u3002Pre-LN \u4e3b\u5e72\u4e0a\u53ea\u6709\u52a0\u6cd5&#xff0c;\u5e45\u5ea6\u9010\u5c42\u589e\u957f\u3002Post-LN \u88ab\u9489\u5728 sqrt(64)&#061;8 \u9644\u8fd1&#xff1b;Pre-LN \u5355\u5c42\u5373\u5f00\u59cb\u7d2f\u52a0\u3002<\/p>\n<p>Pre-LN \u8fd8\u6709\u4e00\u4e2a\u5e38\u88ab\u6f0f\u6389\u7684\u90e8\u4ef6&#xff1a;final norm\u3002\u539f\u6587\u660e\u786e\u8bf4&#xff0c;Pre-LN \u5728\u9884\u6d4b\u5934\u524d\u52a0\u4e86\u4e00\u6b21 final layer normalization\u3002\u4e3b\u5e72\u5e45\u5ea6\u5728\u6da8&#xff0c;\u4e0d\u8865\u4e00\u6b21 LN&#xff0c;\u8f93\u51fa\u5934\u62ff\u5230\u7684\u5c31\u662f\u4e00\u8def\u81a8\u80c0\u7684\u5411\u91cf\u3002<\/p>\n<p>  #mermaid-svg-w5dUFjitgFhR521L{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-w5dUFjitgFhR521L .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-w5dUFjitgFhR521L .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-w5dUFjitgFhR521L .error-icon{fill:#552222;}#mermaid-svg-w5dUFjitgFhR521L .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-w5dUFjitgFhR521L .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-w5dUFjitgFhR521L .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-w5dUFjitgFhR521L .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-w5dUFjitgFhR521L .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-w5dUFjitgFhR521L .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-w5dUFjitgFhR521L .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-w5dUFjitgFhR521L .marker{fill:#333333;stroke:#333333;}#mermaid-svg-w5dUFjitgFhR521L .marker.cross{stroke:#333333;}#mermaid-svg-w5dUFjitgFhR521L svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-w5dUFjitgFhR521L p{margin:0;}#mermaid-svg-w5dUFjitgFhR521L .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-w5dUFjitgFhR521L .cluster-label text{fill:#333;}#mermaid-svg-w5dUFjitgFhR521L .cluster-label span{color:#333;}#mermaid-svg-w5dUFjitgFhR521L .cluster-label span p{background-color:transparent;}#mermaid-svg-w5dUFjitgFhR521L .label text,#mermaid-svg-w5dUFjitgFhR521L span{fill:#333;color:#333;}#mermaid-svg-w5dUFjitgFhR521L .node rect,#mermaid-svg-w5dUFjitgFhR521L .node circle,#mermaid-svg-w5dUFjitgFhR521L .node ellipse,#mermaid-svg-w5dUFjitgFhR521L .node polygon,#mermaid-svg-w5dUFjitgFhR521L .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-w5dUFjitgFhR521L .rough-node .label text,#mermaid-svg-w5dUFjitgFhR521L .node .label text,#mermaid-svg-w5dUFjitgFhR521L .image-shape .label,#mermaid-svg-w5dUFjitgFhR521L .icon-shape .label{text-anchor:middle;}#mermaid-svg-w5dUFjitgFhR521L .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-w5dUFjitgFhR521L .rough-node .label,#mermaid-svg-w5dUFjitgFhR521L .node .label,#mermaid-svg-w5dUFjitgFhR521L .image-shape .label,#mermaid-svg-w5dUFjitgFhR521L .icon-shape .label{text-align:center;}#mermaid-svg-w5dUFjitgFhR521L .node.clickable{cursor:pointer;}#mermaid-svg-w5dUFjitgFhR521L .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-w5dUFjitgFhR521L .arrowheadPath{fill:#333333;}#mermaid-svg-w5dUFjitgFhR521L .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-w5dUFjitgFhR521L .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-w5dUFjitgFhR521L .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-w5dUFjitgFhR521L .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-w5dUFjitgFhR521L .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-w5dUFjitgFhR521L .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-w5dUFjitgFhR521L .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-w5dUFjitgFhR521L .cluster text{fill:#333;}#mermaid-svg-w5dUFjitgFhR521L .cluster span{color:#333;}#mermaid-svg-w5dUFjitgFhR521L div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-w5dUFjitgFhR521L .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-w5dUFjitgFhR521L rect.text{fill:none;stroke-width:0;}#mermaid-svg-w5dUFjitgFhR521L .icon-shape,#mermaid-svg-w5dUFjitgFhR521L .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-w5dUFjitgFhR521L .icon-shape p,#mermaid-svg-w5dUFjitgFhR521L .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-w5dUFjitgFhR521L .icon-shape .label rect,#mermaid-svg-w5dUFjitgFhR521L .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-w5dUFjitgFhR521L .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-w5dUFjitgFhR521L .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-w5dUFjitgFhR521L :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-w5dUFjitgFhR521L .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-w5dUFjitgFhR521L .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-w5dUFjitgFhR521L .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>Post-LN<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>Pre-LN<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6bcf\u5c42\u8f93\u5165 x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>LN \u653e\u54ea<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Sublayer \u76f4\u63a5\u5403 x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>x \u52a0 Sublayer x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6574\u4f53\u8fc7 LN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5e45\u5ea6\u9489\u5728 sqrt d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>x \u5148\u8fc7 LN \u8fdb\u5b50\u5c42<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Sublayer LN x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>x \u52a0\u7ed3\u679c<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e3b\u5e72\u4e0a\u53ea\u6709\u52a0\u6cd5<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5e45\u5ea6\u9010\u5c42\u589e\u957f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9700\u5728\u9884\u6d4b\u5934\u524d\u8865 final LN<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u91cc\u4e24\u6761\u652f\u7ebf\u7684\u7ec8\u70b9\u5dee\u5f02&#xff08;\u5e45\u5ea6\u9489\u4f4f\u8fd8\u662f\u9010\u5c42\u589e\u957f&#xff09;\u4f1a\u5728\u7b2c 4 \u8282\u518d\u6b21\u51fa\u73b0\u3002\u90a3\u662f\u6b8b\u5dee\u6d41\u89c6\u89d2\u4e0b\u540c\u4e00\u4e2a\u73b0\u8c61\u7684\u4e24\u79cd\u8bb2\u6cd5\u3002<\/p>\n<p>\u5199\u6cd5\u53ea\u5dee\u4e00\u4e2a\u62ec\u53f7\u4f4d\u7f6e&#xff0c;\u8bad\u7ec3\u52a8\u529b\u5b66\u5374\u5b8c\u5168\u4e0d\u540c\u3002\u4e0b\u4e00\u8282\u4ece\u68af\u5ea6\u89d2\u5ea6\u89e3\u91ca\u4e3a\u4ec0\u4e48\u3002<\/p>\n<h4>2.2 \u68af\u5ea6\u89c6\u89d2&#xff1a;\u6b8b\u5dee\u4e3b\u5e72\u4e0a\u7684\u76f4\u901a\u8def\u5f84<\/h4>\n<p>Pre-LN \u8bba\u6587&#xff08;arXiv:2002.04745&#xff09;\u7684\u7406\u8bba\u7ed3\u8bba\u53ef\u4ee5\u76f4\u8bd1\u6210\u4e00\u53e5\u3002\u521d\u59cb\u5316\u65f6&#xff0c;Post-LN \u9760\u8fd1\u8f93\u51fa\u5c42\u90a3\u4e9b\u5c42\u7684\u53c2\u6570\u68af\u5ea6\u671f\u671b\u5927\u3002\u5927\u5b66\u4e60\u7387\u4e00\u538b\u5c31\u8bad\u5d29\u3002Pre-LN \u7684\u68af\u5ea6\u5728\u521d\u59cb\u5316\u65f6\u8868\u73b0\u826f\u597d&#xff08;well-behaved&#xff09;\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48\u5dee\u4e00\u4e2a LN \u4f4d\u7f6e\u5c31\u6709\u8fd9\u4e48\u5927\u7684\u533a\u522b\u3002\u770b\u53cd\u5411\u8def\u5f84\u3002<\/p>\n<p>Pre-LN \u7684\u4e3b\u5e72\u662f y &#061; x &#043; f(LN(x))\u3002\u4ece y \u53cd\u4f20\u5230 x \u65f6&#xff0c;\u68af\u5ea6\u8981\u8fc7\u52a0\u6cd5\u8282\u70b9\u3002\u52a0\u6cd5\u5bf9\u4e24\u4e2a\u8f93\u5165\u7684\u504f\u5bfc\u90fd\u662f 1&#xff0c;\u6240\u4ee5\u68af\u5ea6\u88ab\u539f\u6837\u590d\u5236\u4e00\u4efd\u76f4\u8fbe x\u3002\u8fd9\u6761\u8def\u4e0d\u7ecf\u8fc7\u4efb\u4f55\u6743\u91cd\u77e9\u9635\u3002<\/p>\n<p>Post-LN \u7684\u4e3b\u5e72\u662f y &#061; LN(x &#043; f(x))\u3002\u4ece y \u53cd\u4f20\u5230 x&#xff0c;\u5fc5\u987b\u5148\u8fdb LN \u7684\u96c5\u53ef\u6bd4&#xff0c;\u518d\u62c6\u5230\u52a0\u6cd5\u3002LN \u7684\u96c5\u53ef\u6bd4\u4e0e\u5f53\u524d\u8f93\u5165\u76f8\u5173&#xff0c;\u521d\u59cb\u5316\u65f6\u5b83\u5bf9\u9760\u8fd1\u8f93\u51fa\u7684\u5c42\u653e\u5927\u660e\u663e\u3002<\/p>\n<p>\u9010\u5c42\u7d2f\u4e58\u540e\u5dee\u522b\u88ab\u6307\u6570\u653e\u5927\u3002Pre-LN \u7684\u6052\u7b49\u8def\u5f84\u63d0\u4f9b\u4e00\u6761\u5e45\u5ea6\u4e3a 1 \u7684\u76f4\u901a\u9879\u3002L \u5c42\u76f8\u4e58\u91cc\u59cb\u7ec8\u6709 1 \u515c\u5e95&#xff0c;Post-LN \u6ca1\u6709\u8fd9\u6761\u515c\u5e95\u3002<\/p>\n<p>\u8bba\u6587\u5b9e\u9a8c\u91cc\u6709\u53ef\u76f4\u63a5\u5f15\u7528\u7684\u5bf9\u7167\u3002IWSLT14 \u5fb7\u82f1\u4efb\u52a1\u4e0a&#xff0c;Pre-LN \u7b2c 9 \u4e2a checkpoint \u8ffd\u5e73 Post-LN \u7b2c 15 \u4e2a\u3002\u540c\u4e00\u5b66\u4e60\u7387\u4e0b Pre-LN \u6536\u655b\u66f4\u5feb\u3002<\/p>\n<p>\u518d\u52a0\u4e00\u6761\u3002\u8bba\u6587\u5b9e\u9a8c\u8868\u660e Pre-LN \u53bb\u6389 warm-up \u540e\u4ecd\u80fd\u8fbe\u5230\u4e0e\u57fa\u7ebf\u76f8\u5f53\u7684\u7ed3\u679c\u3002\u540c\u65f6\u8bad\u7ec3\u65f6\u95f4\u4e0e\u8c03\u53c2\u6210\u672c\u663e\u8457\u4e0b\u964d\u3002<\/p>\n<table>\n<tr>\u5bf9\u6bd4\u9879Post-LNPre-LN<\/tr>\n<tbody>\n<tr>\n<td>\u521d\u59cb\u5316\u68af\u5ea6<\/td>\n<td>\u9760\u8fd1\u8f93\u51fa\u5c42\u504f\u5927<\/td>\n<td>\u8868\u73b0\u826f\u597d<\/td>\n<\/tr>\n<tr>\n<td>warm-up<\/td>\n<td>\u57fa\u672c\u5fc5\u9700<\/td>\n<td>\u53ef\u53bb\u6389<\/td>\n<\/tr>\n<tr>\n<td>\u6536\u655b\u901f\u5ea6<\/td>\n<td>\u6162<\/td>\n<td>\u540c lr \u4e0b\u66f4\u5feb<\/td>\n<\/tr>\n<tr>\n<td>\u6df1\u5c42\u53ef\u8bad\u6027<\/td>\n<td>\u5c42\u6570\u4e0a\u53bb\u540e\u96be\u8c03<\/td>\n<td>\u6df1\u5c42\u7a33\u5b9a<\/td>\n<\/tr>\n<tr>\n<td>\u8f93\u51fa\u5e45\u5ea6<\/td>\n<td>\u6bcf\u5c42\u9489\u4f4f sqrt d<\/td>\n<td>\u9010\u5c42\u589e\u957f\u9700 final LN<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>  #mermaid-svg-FCpF2n2pfM1brOqm{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-FCpF2n2pfM1brOqm .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-FCpF2n2pfM1brOqm .error-icon{fill:#552222;}#mermaid-svg-FCpF2n2pfM1brOqm .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-FCpF2n2pfM1brOqm .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-FCpF2n2pfM1brOqm .marker{fill:#333333;stroke:#333333;}#mermaid-svg-FCpF2n2pfM1brOqm .marker.cross{stroke:#333333;}#mermaid-svg-FCpF2n2pfM1brOqm svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-FCpF2n2pfM1brOqm p{margin:0;}#mermaid-svg-FCpF2n2pfM1brOqm .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-FCpF2n2pfM1brOqm .cluster-label text{fill:#333;}#mermaid-svg-FCpF2n2pfM1brOqm .cluster-label span{color:#333;}#mermaid-svg-FCpF2n2pfM1brOqm .cluster-label span p{background-color:transparent;}#mermaid-svg-FCpF2n2pfM1brOqm .label text,#mermaid-svg-FCpF2n2pfM1brOqm span{fill:#333;color:#333;}#mermaid-svg-FCpF2n2pfM1brOqm .node rect,#mermaid-svg-FCpF2n2pfM1brOqm .node circle,#mermaid-svg-FCpF2n2pfM1brOqm .node ellipse,#mermaid-svg-FCpF2n2pfM1brOqm .node polygon,#mermaid-svg-FCpF2n2pfM1brOqm .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-FCpF2n2pfM1brOqm .rough-node .label text,#mermaid-svg-FCpF2n2pfM1brOqm .node .label text,#mermaid-svg-FCpF2n2pfM1brOqm .image-shape .label,#mermaid-svg-FCpF2n2pfM1brOqm .icon-shape .label{text-anchor:middle;}#mermaid-svg-FCpF2n2pfM1brOqm .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-FCpF2n2pfM1brOqm .rough-node .label,#mermaid-svg-FCpF2n2pfM1brOqm .node .label,#mermaid-svg-FCpF2n2pfM1brOqm .image-shape .label,#mermaid-svg-FCpF2n2pfM1brOqm .icon-shape .label{text-align:center;}#mermaid-svg-FCpF2n2pfM1brOqm .node.clickable{cursor:pointer;}#mermaid-svg-FCpF2n2pfM1brOqm .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-FCpF2n2pfM1brOqm .arrowheadPath{fill:#333333;}#mermaid-svg-FCpF2n2pfM1brOqm .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-FCpF2n2pfM1brOqm .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-FCpF2n2pfM1brOqm .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-FCpF2n2pfM1brOqm .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-FCpF2n2pfM1brOqm .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-FCpF2n2pfM1brOqm .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-FCpF2n2pfM1brOqm .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-FCpF2n2pfM1brOqm .cluster text{fill:#333;}#mermaid-svg-FCpF2n2pfM1brOqm .cluster span{color:#333;}#mermaid-svg-FCpF2n2pfM1brOqm div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-FCpF2n2pfM1brOqm .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-FCpF2n2pfM1brOqm rect.text{fill:none;stroke-width:0;}#mermaid-svg-FCpF2n2pfM1brOqm .icon-shape,#mermaid-svg-FCpF2n2pfM1brOqm .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-FCpF2n2pfM1brOqm .icon-shape p,#mermaid-svg-FCpF2n2pfM1brOqm .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-FCpF2n2pfM1brOqm .icon-shape .label rect,#mermaid-svg-FCpF2n2pfM1brOqm .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-FCpF2n2pfM1brOqm .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-FCpF2n2pfM1brOqm .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-FCpF2n2pfM1brOqm :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-FCpF2n2pfM1brOqm .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-FCpF2n2pfM1brOqm .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-FCpF2n2pfM1brOqm .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>Pre-LN<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>Post-LN<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53cd\u5411\u4f20\u64ad\u4ece\u635f\u5931\u51fa\u53d1<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u67b6\u6784\u662f\u54ea\u79cd<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e3b\u5e72\u53ea\u6709\u52a0\u6cd5<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u52a0\u6cd5\u504f\u5bfc\u4e3a 1<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u68af\u5ea6\u539f\u6837\u76f4\u8fbe\u4e0b\u5c42<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6052\u7b49\u76f4\u901a\u8def\u5f84\u515c\u5e95<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6df1\u5c42\u6570\u68af\u5ea6\u4e0d\u6d88\u5931<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e3b\u5e72\u4e0a\u6709 LN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u68af\u5ea6\u5148\u8fc7 LN \u96c5\u53ef\u6bd4<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9760\u8fd1\u8f93\u51fa\u5c42\u88ab\u653e\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u521d\u59cb\u5316\u68af\u5ea6\u504f\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9700 warmup \u964d\u5b66\u4e60\u7387<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d G \u4e0e L \u662f\u4e24\u79cd\u67b6\u6784\u8bad\u7ec3\u884c\u4e3a\u5dee\u5f02\u7684\u6839\u6e90\u3002\u7b2c 4 \u8282\u4f1a\u628a\u8fd9\u6761\u76f4\u901a\u8def\u5f84\u4e0e ResNet \u7684\u6052\u7b49\u9879\u7edf\u4e00\u6210\u540c\u4e00\u4ef6\u4e8b\u3002<\/p>\n<p>\u4e00\u53e5\u8bdd\u6536\u675f\u3002Pre-LN \u628a\u5f52\u4e00\u5316\u4ece\u4e3b\u5e72\u632a\u5230\u652f\u8def&#xff0c;\u7b49\u4e8e\u7ed9\u68af\u5ea6\u4fee\u4e86\u4e00\u6761\u4e0d\u9650\u901f\u7684\u5e94\u6025\u8f66\u9053\u3002<\/p>\n<h4>2.3 \u8bad\u7ec3\u66f2\u7ebf\u4e0e\u5b66\u4e60\u7387\u654f\u611f\u5ea6<\/h4>\n<p>\u4e24\u8fb9\u7684\u4f18\u52a3\u8981\u6309\u53e3\u5f84\u5206\u5f00\u8bf4&#xff0c;\u4e0d\u80fd\u4e00\u53e5&#034;\u8c01\u66f4\u597d&#034;\u5e26\u8fc7\u3002<\/p>\n<p>Pre-LN \u7684\u4f18\u52bf\u96c6\u4e2d\u5728\u8bad\u7ec3\u6548\u7387\u4e0e\u7a33\u5b9a\u6027\u3002\u4e0d\u9700\u8981 warm-up&#xff0c;\u5bf9\u5cf0\u503c\u5b66\u4e60\u7387\u4e0d\u654f\u611f&#xff0c;\u6df1\u5c42\u7f51\u7edc&#xff08;\u5982 30 \u5c42\u4ee5\u4e0a&#xff09;\u80fd\u76f4\u63a5\u8bad\u3002\u5de5\u7a0b\u4e0a\u7701\u6389\u7684\u662f\u8c03\u53c2\u6210\u672c&#xff0c;\u8fd9\u5728\u4e07\u4ebf token \u9884\u8bad\u7ec3\u91cc\u662f\u771f\u91d1\u767d\u94f6\u3002<\/p>\n<p>Post-LN \u7684\u4f18\u52bf\u5728\u6700\u7ec8\u8d28\u91cf\u7684\u53ef\u80fd\u4e0a\u9650\u3002\u5f52\u4e00\u5316\u538b\u5728\u4e3b\u5e72\u4e0a&#xff0c;\u7b49\u4e8e\u5bf9\u6bcf\u5c42\u8f93\u51fa\u52a0\u4e86\u4e00\u4e2a\u786c\u7ea6\u675f&#xff0c;\u9690\u5f0f\u8d77\u5230\u6b63\u5219\u4f5c\u7528\u3002\u90e8\u5206\u4efb\u52a1\u4e0a Post-LN \u7cbe\u8c03\u540e\u80fd\u7565\u4f18\u3002\u524d\u63d0\u662f warm-up \u4e0e\u5b66\u4e60\u7387\u8c03\u5f97\u5bf9\u3002<\/p>\n<p>\u9700\u8981\u5f3a\u8c03\u53e3\u5f84\u3002\u8fd9\u662f\u8c03\u53c2\u5230\u4f4d\u7684 Post-LN \u53ef\u80fd\u7565\u4f18&#xff0c;\u4e0d\u662f Post-LN \u4e00\u5b9a\u66f4\u51c6\u3002Xiong \u7b49\u4eba\u7684\u5b9e\u9a8c\u91cc\u4e24\u8005\u6700\u7ec8\u6307\u6807\u76f8\u5f53\u3002\u5dee\u522b\u5728\u5230\u8fbe\u540c\u6837\u6307\u6807\u6240\u9700\u6b65\u6570\u3002<\/p>\n<p>\u8bad\u7ec3\u66f2\u7ebf\u7684\u5178\u578b\u5f62\u6001\u53ef\u4ee5\u7528\u6570\u636e\u8868\u63cf\u8ff0&#xff08;\u53e3\u5f84&#xff1a;\u73a9\u5177\u4efb\u52a1 12 \u5c42&#xff0c;\u7ec6\u8282\u89c1\u7b2c 6 \u8282&#xff09;\u3002<\/p>\n<table>\n<tr>\u6b65\u6570Post-LN \u65e0 warmupPre-LN \u65e0 warmupPost-LN \u5e26 warmup<\/tr>\n<tbody>\n<tr>\n<td>200<\/td>\n<td>\u53d1\u6563 NaN<\/td>\n<td>2.41<\/td>\n<td>3.05<\/td>\n<\/tr>\n<tr>\n<td>500<\/td>\n<td>\u53d1\u6563 NaN<\/td>\n<td>1.62<\/td>\n<td>2.20<\/td>\n<\/tr>\n<tr>\n<td>1000<\/td>\n<td>\u53d1\u6563 NaN<\/td>\n<td>1.18<\/td>\n<td>1.51<\/td>\n<\/tr>\n<tr>\n<td>2000<\/td>\n<td>\u53d1\u6563 NaN<\/td>\n<td>0.86<\/td>\n<td>0.94<\/td>\n<\/tr>\n<tr>\n<td>3000<\/td>\n<td>\u53d1\u6563 NaN<\/td>\n<td>0.71<\/td>\n<td>0.73<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8868\u91cc\u4e09\u4e2a\u4fe1\u606f\u3002Post-LN \u4e0d\u5e26 warmup \u76f4\u63a5 NaN\u3002\u8fd9\u662f\u521d\u59cb\u5316\u68af\u5ea6\u5927\u52a0\u5e38\u89c4\u5b66\u4e60\u7387\u7684\u5178\u578b\u7ed3\u5c40\u3002Pre-LN \u4ece\u7b2c\u4e00\u6b65\u5c31\u5e73\u7a33\u4e0b\u964d\u3002\u8c03\u597d warm-up \u7684 Post-LN \u6700\u7ec8\u8ffd\u5e73&#xff0c;\u4f46\u524d\u671f\u6162\u3002<\/p>\n<p>\u5b66\u4e60\u7387\u654f\u611f\u5ea6\u662f\u53e6\u4e00\u7ec4\u8bc1\u636e\u3002\u540c\u4e00\u6a21\u578b\u626b\u5b66\u4e60\u7387&#xff0c;Pre-LN \u5728\u4e00\u4e2a\u6570\u91cf\u7ea7\u8303\u56f4\u5185\u90fd\u80fd\u6536\u655b\u3002Post-LN \u53ea\u5728\u7a84\u7a97\u53e3\u5185\u6d3b\u7740\u3002\u7b2c 6.3 \u8282\u7ed9\u51fa\u5b8c\u6574\u626b\u63cf\u8868\u3002<\/p>\n<p>  #mermaid-svg-CSzYfuEPxwPybutm{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-CSzYfuEPxwPybutm .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-CSzYfuEPxwPybutm .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-CSzYfuEPxwPybutm .error-icon{fill:#552222;}#mermaid-svg-CSzYfuEPxwPybutm .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-CSzYfuEPxwPybutm .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-CSzYfuEPxwPybutm .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-CSzYfuEPxwPybutm .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-CSzYfuEPxwPybutm .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-CSzYfuEPxwPybutm .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-CSzYfuEPxwPybutm .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-CSzYfuEPxwPybutm .marker{fill:#333333;stroke:#333333;}#mermaid-svg-CSzYfuEPxwPybutm .marker.cross{stroke:#333333;}#mermaid-svg-CSzYfuEPxwPybutm svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-CSzYfuEPxwPybutm p{margin:0;}#mermaid-svg-CSzYfuEPxwPybutm .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-CSzYfuEPxwPybutm .cluster-label text{fill:#333;}#mermaid-svg-CSzYfuEPxwPybutm .cluster-label span{color:#333;}#mermaid-svg-CSzYfuEPxwPybutm .cluster-label span p{background-color:transparent;}#mermaid-svg-CSzYfuEPxwPybutm .label text,#mermaid-svg-CSzYfuEPxwPybutm span{fill:#333;color:#333;}#mermaid-svg-CSzYfuEPxwPybutm .node rect,#mermaid-svg-CSzYfuEPxwPybutm .node circle,#mermaid-svg-CSzYfuEPxwPybutm .node ellipse,#mermaid-svg-CSzYfuEPxwPybutm .node polygon,#mermaid-svg-CSzYfuEPxwPybutm .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-CSzYfuEPxwPybutm .rough-node .label text,#mermaid-svg-CSzYfuEPxwPybutm .node .label text,#mermaid-svg-CSzYfuEPxwPybutm .image-shape .label,#mermaid-svg-CSzYfuEPxwPybutm .icon-shape .label{text-anchor:middle;}#mermaid-svg-CSzYfuEPxwPybutm .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-CSzYfuEPxwPybutm .rough-node .label,#mermaid-svg-CSzYfuEPxwPybutm .node .label,#mermaid-svg-CSzYfuEPxwPybutm .image-shape .label,#mermaid-svg-CSzYfuEPxwPybutm .icon-shape .label{text-align:center;}#mermaid-svg-CSzYfuEPxwPybutm .node.clickable{cursor:pointer;}#mermaid-svg-CSzYfuEPxwPybutm .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-CSzYfuEPxwPybutm .arrowheadPath{fill:#333333;}#mermaid-svg-CSzYfuEPxwPybutm .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-CSzYfuEPxwPybutm .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-CSzYfuEPxwPybutm .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-CSzYfuEPxwPybutm .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-CSzYfuEPxwPybutm .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-CSzYfuEPxwPybutm .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-CSzYfuEPxwPybutm .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-CSzYfuEPxwPybutm .cluster text{fill:#333;}#mermaid-svg-CSzYfuEPxwPybutm .cluster span{color:#333;}#mermaid-svg-CSzYfuEPxwPybutm div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-CSzYfuEPxwPybutm .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-CSzYfuEPxwPybutm rect.text{fill:none;stroke-width:0;}#mermaid-svg-CSzYfuEPxwPybutm .icon-shape,#mermaid-svg-CSzYfuEPxwPybutm .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-CSzYfuEPxwPybutm .icon-shape p,#mermaid-svg-CSzYfuEPxwPybutm .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-CSzYfuEPxwPybutm .icon-shape .label rect,#mermaid-svg-CSzYfuEPxwPybutm .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-CSzYfuEPxwPybutm .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-CSzYfuEPxwPybutm .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-CSzYfuEPxwPybutm :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-CSzYfuEPxwPybutm .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-CSzYfuEPxwPybutm .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-CSzYfuEPxwPybutm .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u65e0<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u6709<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u5f00\u59cb<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6709\u65e0 warmup<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN \u521d\u59cb\u68af\u5ea6\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u524d\u51e0\u6b65\u66f4\u65b0\u8fc7\u731b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u635f\u5931\u53d1\u6563\u6216 NaN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5b66\u4e60\u7387\u4ece 0 \u7f13\u5347<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u907f\u5f00\u521d\u671f\u5371\u9669\u533a<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN \u5e73\u7a33\u6536\u655b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN \u521d\u59cb\u68af\u5ea6\u826f\u597d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u76f4\u63a5\u7528\u76ee\u6807\u5b66\u4e60\u7387<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4ece\u7b2c\u4e00\u6b65\u7a33\u5b9a\u4e0b\u964d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7701\u53bb\u8c03 warmup \u6210\u672c<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d E \u4e0e K \u662f\u4e24\u6761\u66f2\u7ebf\u7684\u8d77\u70b9\u5206\u6b67&#xff0c;\u4e4b\u540e\u7684\u4e00\u5207\u5dee\u522b\u90fd\u4ece\u8fd9\u91cc\u957f\u51fa\u6765\u3002warm-up \u672c\u8d28\u662f\u7528\u65f6\u95f4\u6362\u5b89\u5168&#xff0c;Pre-LN \u7528\u7ed3\u6784\u6362\u5b89\u5168\u3002<\/p>\n<h4>2.4 \u4e3b\u6d41\u6a21\u578b\u7684\u4e8b\u5b9e\u8868<\/h4>\n<p>\u628a\u8bba\u6587\u4e0e\u5f00\u6e90\u5b9e\u73b0\u62fc\u6210\u4e00\u5f20\u4e8b\u5b9e\u8868\u3002\u53e3\u5f84\u4ee5\u5404\u6a21\u578b\u6280\u672f\u62a5\u544a\u4e0e\u5f00\u6e90\u4ee3\u7801\u4e3a\u51c6\u3002<\/p>\n<table>\n<tr>\u6a21\u578b\u5e74\u4efdLN \u4f4d\u7f6e\u5f52\u4e00\u5316\u7c7b\u578b\u5907\u6ce8<\/tr>\n<tbody>\n<tr>\n<td>\u539f\u59cb Transformer<\/td>\n<td>2017<\/td>\n<td>Post-LN<\/td>\n<td>LayerNorm<\/td>\n<td>\u8bba\u6587\u516c\u5f0f 1 \u4e0e\u56fe 1 \u5de6<\/td>\n<\/tr>\n<tr>\n<td>BERT<\/td>\n<td>2018<\/td>\n<td>Post-LN<\/td>\n<td>LayerNorm<\/td>\n<td>\u8bad\u7ec3\u5e26 warmup<\/td>\n<\/tr>\n<tr>\n<td>GPT-2<\/td>\n<td>2019<\/td>\n<td>Pre-LN<\/td>\n<td>LayerNorm<\/td>\n<td>final norm \u5728\u8f93\u51fa\u524d<\/td>\n<\/tr>\n<tr>\n<td>GPT-3<\/td>\n<td>2020<\/td>\n<td>Pre-LN<\/td>\n<td>LayerNorm<\/td>\n<td>\u6280\u672f\u62a5\u544a\u53e3\u5f84<\/td>\n<\/tr>\n<tr>\n<td>T5<\/td>\n<td>2019<\/td>\n<td>Pre-LN&#xff08;\u7b80\u5316\u5c42&#xff09;<\/td>\n<td>\u7b80\u5316 LayerNorm<\/td>\n<td>\u53bb bias\u3001\u53bb mean \u4e2d\u5fc3\u5316\u7684\u8fc7\u6e21\u5f62\u6001<\/td>\n<\/tr>\n<tr>\n<td>LLaMA<\/td>\n<td>2023<\/td>\n<td>Pre-LN<\/td>\n<td>RMSNorm<\/td>\n<td>final norm \u540c\u6837\u4e3a RMSNorm<\/td>\n<\/tr>\n<tr>\n<td>Qwen3<\/td>\n<td>2025<\/td>\n<td>Pre-RMSNorm<\/td>\n<td>RMSNorm \u52a0 QK-Norm<\/td>\n<td>\u6280\u672f\u62a5\u544a\u660e\u8bf4 pre-normalization<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8fd9\u5f20\u8868\u7684\u65f6\u95f4\u7ebf\u5f88\u6e05\u695a\u30022017 \u5230 2019 \u662f Post-LN \u5230 Pre-LN \u7684\u8fc1\u79fb\u30022020 \u4e4b\u540e RMSNorm \u9010\u6b65\u66ff\u6362 LN\u3002\u4e24\u4e2a\u53d8\u5316\u53e0\u52a0&#xff0c;\u5f97\u5230\u4eca\u5929\u7684\u4e3b\u6d41\u5f62\u6001&#xff1a;Pre-RMSNorm \u52a0 final RMSNorm\u3002<\/p>\n<p>Qwen3 \u6280\u672f\u62a5\u544a\u7684\u539f\u8bdd\u503c\u5f97\u6458\u5f55\u3002\u67b6\u6784\u6cbf\u7528 RMSNorm \u52a0 pre-normalization\u3002\u5e76\u5f15\u5165 QK-Norm \u5230\u6ce8\u610f\u529b\u673a\u5236\u4ee5\u4fdd\u8bc1\u8bad\u7ec3\u7a33\u5b9a\u3002\u7b2c 5 \u8282\u5c55\u5f00 QK-Norm\u3002<\/p>\n<p>\u66ff\u6362\u7684\u52a8\u673a\u4e0d\u662f\u7cbe\u5ea6&#xff0c;\u800c\u662f\u901f\u5ea6\u4e0e\u5b9e\u73b0\u7b80\u5355\u3002RMSNorm \u5c11\u4e00\u6b21\u5747\u503c\u8ba1\u7b97\u3001\u5c11\u4e00\u4efd\u53c2\u6570&#xff0c;\u5728\u8d85\u5927\u6a21\u578b\u4e0a\u7d2f\u79ef\u6210\u53ef\u89c2\u7684\u8282\u7701\u3002\u7b2c 3 \u8282\u7ed9\u51fa\u6570\u5b57\u3002<\/p>\n<p>  #mermaid-svg-P8pCIzVhSWe37ftS{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-P8pCIzVhSWe37ftS .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-P8pCIzVhSWe37ftS .error-icon{fill:#552222;}#mermaid-svg-P8pCIzVhSWe37ftS .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-P8pCIzVhSWe37ftS .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-P8pCIzVhSWe37ftS .marker{fill:#333333;stroke:#333333;}#mermaid-svg-P8pCIzVhSWe37ftS .marker.cross{stroke:#333333;}#mermaid-svg-P8pCIzVhSWe37ftS svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-P8pCIzVhSWe37ftS p{margin:0;}#mermaid-svg-P8pCIzVhSWe37ftS .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-P8pCIzVhSWe37ftS .cluster-label text{fill:#333;}#mermaid-svg-P8pCIzVhSWe37ftS .cluster-label span{color:#333;}#mermaid-svg-P8pCIzVhSWe37ftS .cluster-label span p{background-color:transparent;}#mermaid-svg-P8pCIzVhSWe37ftS .label text,#mermaid-svg-P8pCIzVhSWe37ftS span{fill:#333;color:#333;}#mermaid-svg-P8pCIzVhSWe37ftS .node rect,#mermaid-svg-P8pCIzVhSWe37ftS .node circle,#mermaid-svg-P8pCIzVhSWe37ftS .node ellipse,#mermaid-svg-P8pCIzVhSWe37ftS .node polygon,#mermaid-svg-P8pCIzVhSWe37ftS .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-P8pCIzVhSWe37ftS .rough-node .label text,#mermaid-svg-P8pCIzVhSWe37ftS .node .label text,#mermaid-svg-P8pCIzVhSWe37ftS .image-shape .label,#mermaid-svg-P8pCIzVhSWe37ftS .icon-shape .label{text-anchor:middle;}#mermaid-svg-P8pCIzVhSWe37ftS .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-P8pCIzVhSWe37ftS .rough-node .label,#mermaid-svg-P8pCIzVhSWe37ftS .node .label,#mermaid-svg-P8pCIzVhSWe37ftS .image-shape .label,#mermaid-svg-P8pCIzVhSWe37ftS .icon-shape .label{text-align:center;}#mermaid-svg-P8pCIzVhSWe37ftS .node.clickable{cursor:pointer;}#mermaid-svg-P8pCIzVhSWe37ftS .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-P8pCIzVhSWe37ftS .arrowheadPath{fill:#333333;}#mermaid-svg-P8pCIzVhSWe37ftS .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-P8pCIzVhSWe37ftS .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-P8pCIzVhSWe37ftS .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-P8pCIzVhSWe37ftS .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-P8pCIzVhSWe37ftS .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-P8pCIzVhSWe37ftS .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-P8pCIzVhSWe37ftS .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-P8pCIzVhSWe37ftS .cluster text{fill:#333;}#mermaid-svg-P8pCIzVhSWe37ftS .cluster span{color:#333;}#mermaid-svg-P8pCIzVhSWe37ftS div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-P8pCIzVhSWe37ftS .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-P8pCIzVhSWe37ftS rect.text{fill:none;stroke-width:0;}#mermaid-svg-P8pCIzVhSWe37ftS .icon-shape,#mermaid-svg-P8pCIzVhSWe37ftS .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-P8pCIzVhSWe37ftS .icon-shape p,#mermaid-svg-P8pCIzVhSWe37ftS .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-P8pCIzVhSWe37ftS .icon-shape .label rect,#mermaid-svg-P8pCIzVhSWe37ftS .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-P8pCIzVhSWe37ftS .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-P8pCIzVhSWe37ftS .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-P8pCIzVhSWe37ftS :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-P8pCIzVhSWe37ftS .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-P8pCIzVhSWe37ftS .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-P8pCIzVhSWe37ftS .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>Post-LN LayerNorm<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u7ed3\u6784\u6cbf\u7528<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>LN \u79fb\u8fdb\u5b50\u5c42<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u53bb mean \u53bb bias<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u6df1\u5c42\u96be\u8bad\u63a8\u52a8\u8fc1\u79fb<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>2017 \u539f\u59cb Transformer<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>BERT 2018<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>GPT-2 2019<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN LayerNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>GPT-3 \u4e0e T5<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>LLaMA 2023 Pre-RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Qwen3 2025 \u52a0 QK-Norm<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u4e24\u6b21\u62d0\u70b9\u5404\u5bf9\u5e94\u4e00\u7bc7\u8bba\u6587\u30022002.04745 \u63a8\u52a8 Pre-LN&#xff0c;1910.07467 \u63a8\u52a8 RMSNorm\u3002\u4e0b\u4e00\u8282\u8fdb\u5165\u540e\u8005\u3002<\/p>\n<h3>3. RMSNorm \u7684\u51cf\u6cd5<\/h3>\n<h4>3.1 \u53bb\u6389\u5747\u503c\u4e2d\u5fc3\u5316\u4e0e bias<\/h4>\n<p>RMSNorm&#xff08;arXiv:1910.07467&#xff09;\u7684\u505a\u6cd5\u662f\u505a\u51cf\u6cd5\u3002\u5b83\u4e0e LN \u7684\u5dee\u522b\u53ea\u6709\u4e24\u5904&#xff0c;\u4f46\u6bcf\u5904\u90fd\u6709\u660e\u786e\u7406\u7531\u3002<\/p>\n<p>\u516c\u5f0f\u5bf9\u7167\u5982\u4e0b\u3002LN \u7684\u4e09\u6b65&#xff1a;<\/p>\n<p>x_hat_i &#061; (x_i &#8211; mean) \/ sqrt(var &#043; eps)<br \/>\ny_i     &#061; gamma_i * x_hat_i &#043; beta_i<\/p>\n<p>RMSNorm \u53ea\u4fdd\u7559\u9664\u6cd5&#xff1a;<\/p>\n<p>rms    &#061; sqrt((1\/d) * sum_i x_i^2 &#043; eps)<br \/>\ny_i    &#061; x_i \/ rms * gamma_i<\/p>\n<p>\u51cf\u6389\u7684\u7b2c\u4e00\u6837\u662f\u5747\u503c\u4e2d\u5fc3\u5316\u3002\u4e0d\u518d\u7b97 mean&#xff0c;\u76f4\u63a5\u7528\u5747\u65b9\u6839&#xff08;root mean square&#xff0c;\u5404\u5143\u7d20\u5e73\u65b9\u5e73\u5747\u540e\u5f00\u65b9&#xff09;\u505a\u5206\u6bcd\u3002<\/p>\n<p>\u8bba\u6587\u7684\u52a8\u673a\u8868\u8ff0\u5206\u4e24\u53e5\u3002re-centering invariance&#xff08;\u5bf9\u8f93\u5165\u4e0e\u6743\u91cd\u5e73\u79fb\u7684\u4e0d\u53d8\u6027&#xff09;\u5e76\u975e\u5fc5\u8981\u3002\u800c\u4e14 mean normalization \u5e76\u4e0d\u964d\u4f4e\u9690\u72b6\u6001\u6216\u68af\u5ea6\u7684\u65b9\u5dee\u3002\u6362\u53e5\u8bdd\u8bf4&#xff0c;\u51cf mean \u8fd9\u4e00\u6b65\u7684\u6536\u76ca\u914d\u4e0d\u4e0a\u5b83\u7684\u8ba1\u7b97\u6210\u672c\u3002<\/p>\n<p>\u51cf\u6389\u7684\u7b2c\u4e8c\u6837\u662f beta\u3002\u53ea\u7559 gamma \u4e00\u4e2a\u53ef\u5b66\u53c2\u6570&#xff0c;bias \u9879\u6574\u4f53\u6d88\u5931\u3002\u8bba\u6587\u7684\u9690\u5c42\u5b9e\u9a8c\u663e\u793a\u8d28\u91cf\u4e0d\u53d7\u5f71\u54cd&#xff0c;\u901f\u5ea6\u53cd\u800c\u63d0\u5347\u3002<\/p>\n<p>\u6536\u76ca\u53ef\u4ee5\u91cf\u5316\u3002\u8ba1\u7b97\u4e0a\u5c11\u4e00\u6b21\u5168\u7ef4 mean \u89c4\u7ea6&#xff0c;\u53c2\u6570\u4e0a\u4ece 2d \u964d\u5230 d\u3002d&#061;4096 \u65f6\u6bcf\u5904\u5f52\u4e00\u5316\u7701 4096 \u4e2a\u53c2\u6570\u3002\u5f52\u4e00\u5316\u5728\u6bcf\u5c42\u51fa\u73b0\u4e24\u5230\u4e09\u6b21&#xff0c;\u8fd9\u4e2a\u7701\u662f\u7eaf\u51cf\u6cd5&#xff0c;\u7d2f\u79ef\u53ef\u89c2\u3002<\/p>\n<p>\u8fd8\u6709\u4e00\u4e2a\u5e38\u88ab\u5ffd\u7565\u7684\u6027\u8d28\u5dee\u5f02\u3002LN \u7684\u8f93\u51fa\u5747\u503c\u6052\u4e3a 0&#xff08;\u5ffd\u7565 beta&#xff09;&#xff0c;RMSNorm \u7684\u8f93\u51fa\u5747\u503c\u975e\u96f6\u3002\u7b2c 3.3 \u8282\u7528\u6570\u503c\u5b9e\u9a8c\u5c55\u793a\u8fd9\u4e00\u70b9\u3002<\/p>\n<p>  #mermaid-svg-uvZxZz9sDcO8s2Ga{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-uvZxZz9sDcO8s2Ga .error-icon{fill:#552222;}#mermaid-svg-uvZxZz9sDcO8s2Ga .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-uvZxZz9sDcO8s2Ga .marker{fill:#333333;stroke:#333333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .marker.cross{stroke:#333333;}#mermaid-svg-uvZxZz9sDcO8s2Ga svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-uvZxZz9sDcO8s2Ga p{margin:0;}#mermaid-svg-uvZxZz9sDcO8s2Ga .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .cluster-label text{fill:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .cluster-label span{color:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .cluster-label span p{background-color:transparent;}#mermaid-svg-uvZxZz9sDcO8s2Ga .label text,#mermaid-svg-uvZxZz9sDcO8s2Ga span{fill:#333;color:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .node rect,#mermaid-svg-uvZxZz9sDcO8s2Ga .node circle,#mermaid-svg-uvZxZz9sDcO8s2Ga .node ellipse,#mermaid-svg-uvZxZz9sDcO8s2Ga .node polygon,#mermaid-svg-uvZxZz9sDcO8s2Ga .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .rough-node .label text,#mermaid-svg-uvZxZz9sDcO8s2Ga .node .label text,#mermaid-svg-uvZxZz9sDcO8s2Ga .image-shape .label,#mermaid-svg-uvZxZz9sDcO8s2Ga .icon-shape .label{text-anchor:middle;}#mermaid-svg-uvZxZz9sDcO8s2Ga .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .rough-node .label,#mermaid-svg-uvZxZz9sDcO8s2Ga .node .label,#mermaid-svg-uvZxZz9sDcO8s2Ga .image-shape .label,#mermaid-svg-uvZxZz9sDcO8s2Ga .icon-shape .label{text-align:center;}#mermaid-svg-uvZxZz9sDcO8s2Ga .node.clickable{cursor:pointer;}#mermaid-svg-uvZxZz9sDcO8s2Ga .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .arrowheadPath{fill:#333333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-uvZxZz9sDcO8s2Ga .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-uvZxZz9sDcO8s2Ga .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-uvZxZz9sDcO8s2Ga .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-uvZxZz9sDcO8s2Ga .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .cluster text{fill:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga .cluster span{color:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-uvZxZz9sDcO8s2Ga .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-uvZxZz9sDcO8s2Ga rect.text{fill:none;stroke-width:0;}#mermaid-svg-uvZxZz9sDcO8s2Ga .icon-shape,#mermaid-svg-uvZxZz9sDcO8s2Ga .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-uvZxZz9sDcO8s2Ga .icon-shape p,#mermaid-svg-uvZxZz9sDcO8s2Ga .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-uvZxZz9sDcO8s2Ga .icon-shape .label rect,#mermaid-svg-uvZxZz9sDcO8s2Ga .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-uvZxZz9sDcO8s2Ga .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-uvZxZz9sDcO8s2Ga .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-uvZxZz9sDcO8s2Ga :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-uvZxZz9sDcO8s2Ga .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-uvZxZz9sDcO8s2Ga .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-uvZxZz9sDcO8s2Ga .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>LayerNorm \u5b8c\u6574\u6d41\u7a0b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u51cf mean \u4e2d\u5fc3\u5316<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9664 std \u7f29\u653e<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e58 gamma \u52a0 beta<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u780d\u6389<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u53ea\u7559 gamma<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u6539\u7528\u5747\u65b9\u6839 rms<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5c11\u4e00\u6b21\u5168\u7ef4\u89c4\u7ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53c2\u6570\u4ece 2d \u964d\u5230 d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5747\u503c\u4e0d\u518d\u6052\u4e3a 0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u4e0e\u63a8\u7406\u66f4\u5feb<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u7684\u4e09\u6761\u6539\u52a8\u7ebf\u5404\u81ea\u5bf9\u5e94\u4e00\u4e2a\u53ef\u9a8c\u8bc1\u540e\u679c&#xff1a;\u5c11\u7b97\u4e00\u6b21\u3001\u5c11\u5b58\u4e00\u4efd\u3001\u8f93\u51fa\u7edf\u8ba1\u53d8\u5316\u3002\u7b2c\u4e09\u6761\u5728\u4e0b\u4e00\u8282\u7684\u6570\u503c\u5b9e\u9a8c\u91cc\u76f4\u63a5\u770b\u5230\u3002<\/p>\n<h4>3.2 \u8bba\u6587\u5b9e\u9a8c&#xff1a;\u8d28\u91cf\u6301\u5e73\u4e0e 7% \u5230 64% \u63d0\u901f<\/h4>\n<p>\u8bba\u6587\u7684\u5b9e\u9a8c\u7ed3\u8bba\u5206\u4e24\u5c42&#xff0c;\u5f15\u7528\u65f6\u4e0d\u80fd\u6df7\u3002<\/p>\n<p>\u7b2c\u4e00\u5c42\u662f\u603b\u53e3\u5f84\u3002\u8de8\u591a\u4e2a\u4efb\u52a1\u4e0e\u67b6\u6784&#xff0c;RMSNorm \u4e0e LayerNorm \u8d28\u91cf\u76f8\u5f53\u3002\u8fd0\u884c\u65f6\u95f4\u51cf\u5c11 7% \u5230 64%\u3002\u6ce8\u610f\u8fd9\u662f\u6574\u6a21\u578b\u7684\u63d0\u901f&#xff0c;\u4e0d\u662f\u5f52\u4e00\u5316\u7b97\u5b50\u672c\u8eab\u63d0\u901f\u3002<\/p>\n<p>\u7b2c\u4e8c\u5c42\u662f\u5206\u573a\u666f\u6570\u5b57\u3002RNN \u4e0a\u6536\u76ca\u6700\u5927\u3002TensorFlow \u7248 RNNSearch \u91cc LayerNorm \u6bd4\u57fa\u7ebf\u6162\u7ea6 67%\u3002RMSNorm \u76f8\u5bf9 LayerNorm \u63d0\u901f\u7ea6 25%\u3002Theano \u4e0e PyTorch \u5b9e\u73b0\u4e0b\u63d0\u901f 11% \u5230 34%\u3002<\/p>\n<p>Transformer \u4e0a\u6536\u76ca\u6700\u5c0f\u3002\u8bba\u6587 Table 5 \u7ed9\u51fa&#xff1a;\u65e0\u5f52\u4e00\u5316\u57fa\u7ebf\u8bad\u4e0d\u52a8\u3002LayerNorm \u5f97 Test14 BLEU 26.6\u3001Test17 27.7\u3002RMSNorm \u76f8\u5e94\u4e3a 26.5\u300127.6&#xff0c;\u8d28\u91cf\u76f8\u5f53\u3002\u65f6\u95f4\u4ece\u6bcf\u5343\u6b65 248 \u79d2\u964d\u5230\u7ea6 230 \u79d2&#xff0c;\u63d0\u901f 7% \u5230 9%\u3002<\/p>\n<table>\n<tr>\u573a\u666fLN \u8d28\u91cfRMSNorm \u8d28\u91cfRMSNorm \u63d0\u901f<\/tr>\n<tbody>\n<tr>\n<td>RNNSearch&#xff08;TF \u5b9e\u73b0&#xff09;<\/td>\n<td>Test14 22.6<\/td>\n<td>22.4<\/td>\n<td>\u7ea6 25%<\/td>\n<\/tr>\n<tr>\n<td>RNNSearch&#xff08;Theano\/PyTorch&#xff09;<\/td>\n<td>\u76f8\u5f53<\/td>\n<td>\u76f8\u5f53<\/td>\n<td>11% \u5230 34%<\/td>\n<\/tr>\n<tr>\n<td>Transformer \u7ffb\u8bd1<\/td>\n<td>Test14 26.6<\/td>\n<td>Test14 26.5<\/td>\n<td>7% \u5230 9%<\/td>\n<\/tr>\n<tr>\n<td>CIFAR-10 CNN<\/td>\n<td>\u8bef\u5dee\u76f8\u5f53<\/td>\n<td>\u8bef\u5dee\u76f8\u5f53<\/td>\n<td>20% \u4e0a\u4e0b<\/td>\n<\/tr>\n<tr>\n<td>\u56fe\u6587\u68c0\u7d22<\/td>\n<td>\u76f8\u5f53<\/td>\n<td>\u6cdb\u5316\u7565\u597d<\/td>\n<td>40% \u5230 64%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8868\u91cc\u6700\u6709\u4fe1\u606f\u91cf\u7684\u662f\u5012\u6570\u7b2c\u4e09\u884c\u3002Transformer \u4e0a\u63d0\u901f\u5e45\u5ea6\u6700\u5c0f\u3002\u8bba\u6587\u81ea\u5df1\u7684\u89e3\u91ca\u662f&#xff1a;Transformer \u91cc\u987a\u5e8f\u6267\u884c\u7684\u5f52\u4e00\u5316\u64cd\u4f5c\u6bd4 RNN \u5c11\u5f97\u591a&#xff0c;\u5f52\u4e00\u5316\u5360\u603b\u8017\u65f6\u6bd4\u4f8b\u4f4e\u3002<\/p>\n<p>\u53cd\u8fc7\u6765\u8bf4&#xff0c;RNN \u91cc\u5f52\u4e00\u5316\u662f\u74f6\u9888&#xff0c;\u6240\u4ee5\u780d\u4e00\u534a\u8ba1\u7b97\u80fd\u6362\u6765\u56db\u5206\u4e4b\u4e00\u63d0\u901f\u3002\u8fd9\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u8bba\u6587\u7684\u573a\u666f\u5206\u5e03\u5982\u6b64\u4e0d\u5747\u3002<\/p>\n<p>\u5bf9\u4eca\u5929\u7684\u5927\u6a21\u578b&#xff0c;7% \u5230 9% \u8fd9\u4e2a Transformer \u53e3\u5f84\u66f4\u76f8\u5173\u3002\u4f46 LLaMA \u9009 RMSNorm \u8fd8\u6709\u4e00\u4e2a\u7b97\u5b50\u4e4b\u5916\u7684\u52a8\u673a\u3002\u5b9e\u73b0\u53ea\u6709\u51e0\u884c&#xff0c;\u4e0e RoPE\u3001SwiGLU \u7ec4\u5408\u65f6\u6ca1\u6709\u989d\u5916\u5206\u652f&#xff0c;kernel \u878d\u5408\u66f4\u5bb9\u6613\u3002<\/p>\n<p>  #mermaid-svg-oGAEOYeTG203yHq8{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-oGAEOYeTG203yHq8 .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-oGAEOYeTG203yHq8 .error-icon{fill:#552222;}#mermaid-svg-oGAEOYeTG203yHq8 .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-oGAEOYeTG203yHq8 .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-oGAEOYeTG203yHq8 .marker{fill:#333333;stroke:#333333;}#mermaid-svg-oGAEOYeTG203yHq8 .marker.cross{stroke:#333333;}#mermaid-svg-oGAEOYeTG203yHq8 svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-oGAEOYeTG203yHq8 p{margin:0;}#mermaid-svg-oGAEOYeTG203yHq8 .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-oGAEOYeTG203yHq8 .cluster-label text{fill:#333;}#mermaid-svg-oGAEOYeTG203yHq8 .cluster-label span{color:#333;}#mermaid-svg-oGAEOYeTG203yHq8 .cluster-label span p{background-color:transparent;}#mermaid-svg-oGAEOYeTG203yHq8 .label text,#mermaid-svg-oGAEOYeTG203yHq8 span{fill:#333;color:#333;}#mermaid-svg-oGAEOYeTG203yHq8 .node rect,#mermaid-svg-oGAEOYeTG203yHq8 .node circle,#mermaid-svg-oGAEOYeTG203yHq8 .node ellipse,#mermaid-svg-oGAEOYeTG203yHq8 .node polygon,#mermaid-svg-oGAEOYeTG203yHq8 .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-oGAEOYeTG203yHq8 .rough-node .label text,#mermaid-svg-oGAEOYeTG203yHq8 .node .label text,#mermaid-svg-oGAEOYeTG203yHq8 .image-shape .label,#mermaid-svg-oGAEOYeTG203yHq8 .icon-shape .label{text-anchor:middle;}#mermaid-svg-oGAEOYeTG203yHq8 .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-oGAEOYeTG203yHq8 .rough-node .label,#mermaid-svg-oGAEOYeTG203yHq8 .node .label,#mermaid-svg-oGAEOYeTG203yHq8 .image-shape .label,#mermaid-svg-oGAEOYeTG203yHq8 .icon-shape .label{text-align:center;}#mermaid-svg-oGAEOYeTG203yHq8 .node.clickable{cursor:pointer;}#mermaid-svg-oGAEOYeTG203yHq8 .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-oGAEOYeTG203yHq8 .arrowheadPath{fill:#333333;}#mermaid-svg-oGAEOYeTG203yHq8 .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-oGAEOYeTG203yHq8 .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-oGAEOYeTG203yHq8 .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-oGAEOYeTG203yHq8 .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-oGAEOYeTG203yHq8 .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-oGAEOYeTG203yHq8 .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-oGAEOYeTG203yHq8 .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-oGAEOYeTG203yHq8 .cluster text{fill:#333;}#mermaid-svg-oGAEOYeTG203yHq8 .cluster span{color:#333;}#mermaid-svg-oGAEOYeTG203yHq8 div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-oGAEOYeTG203yHq8 .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-oGAEOYeTG203yHq8 rect.text{fill:none;stroke-width:0;}#mermaid-svg-oGAEOYeTG203yHq8 .icon-shape,#mermaid-svg-oGAEOYeTG203yHq8 .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-oGAEOYeTG203yHq8 .icon-shape p,#mermaid-svg-oGAEOYeTG203yHq8 .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-oGAEOYeTG203yHq8 .icon-shape .label rect,#mermaid-svg-oGAEOYeTG203yHq8 .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-oGAEOYeTG203yHq8 .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-oGAEOYeTG203yHq8 .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-oGAEOYeTG203yHq8 :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-oGAEOYeTG203yHq8 .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-oGAEOYeTG203yHq8 .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-oGAEOYeTG203yHq8 .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u63d0\u901f\u6765\u6e90\u62c6\u89e3<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u573a\u666f\u4e00 RNN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u573a\u666f\u4e8c Transformer<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u573a\u666f\u4e09 CNN \u4e0e\u68c0\u7d22<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6bcf\u65f6\u95f4\u6b65\u90fd\u8981\u5f52\u4e00\u5316<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316\u5360\u8017\u65f6\u6bd4\u4f8b\u9ad8<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u63d0\u901f 25% \u5230 34%<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6bcf\u5c42\u53ea\u5f52\u4e00\u5316\u4e24\u4e09\u6b21<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316\u5360\u6bd4\u4f4e<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u63d0\u901f 7% \u5230 9%<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316\u76f8\u5bf9\u5176\u4ed6\u7b97\u5b50\u8d35<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u63d0\u901f 40% \u5230 64%<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u7684\u6838\u5fc3\u4fe1\u606f\u662f&#xff1a;\u63d0\u901f\u767e\u5206\u6bd4\u53d6\u51b3\u4e8e\u5f52\u4e00\u5316\u5728\u603b\u8ba1\u7b97\u91cc\u7684\u5360\u6bd4&#xff0c;\u800c\u4e0d\u662f\u7b97\u5b50\u672c\u8eab\u5feb\u4e86\u591a\u5c11\u500d\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u8bba\u6587\u53cd\u590d\u5f3a\u8c03\u5b9e\u9645\u63d0\u5347\u4f9d\u6846\u67b6\u3001\u786c\u4ef6\u4e0e\u67b6\u6784\u800c\u53d8\u3002<\/p>\n<h4>3.3 \u6570\u503c\u5b9e\u9a8c&#xff1a;\u8f93\u51fa\u5747\u503c\u975e\u96f6<\/h4>\n<p>\u780d\u6389 mean \u4e2d\u5fc3\u5316\u6709\u4e00\u4e2a\u76f4\u63a5\u53ef\u89c1\u7684\u540e\u679c&#xff1a;\u8f93\u51fa\u5747\u503c\u4e0d\u518d\u4e3a\u96f6\u3002\u8fd9\u4e00\u8282\u7528\u6570\u503c\u5b9e\u9a8c\u628a\u5b83\u91cf\u5316\u3002<\/p>\n<p>\u5b9e\u9a8c\u8bbe\u8ba1\u5f88\u7b80\u5355\u3002\u53d6\u4e00\u6279\u968f\u673a\u5f20\u91cf&#xff0c;\u5206\u522b\u8fc7 LN \u4e0e RMSNorm&#xff0c;\u7edf\u8ba1\u8f93\u51fa\u5747\u503c\u4e0e\u6807\u51c6\u5dee\u7684\u5206\u5e03\u3002<\/p>\n<p><span class=\"token comment\"># \u6570\u503c\u5b9e\u9a8c&#xff1a;LN \u4e0e RMSNorm \u8f93\u51fa\u7edf\u8ba1\u5bf9\u6bd4&#xff08;PyTorch 2.13 CPU&#xff09;<\/span><br \/>\n<span class=\"token comment\"># RMSNorm \u7c7b\u5b9a\u4e49\u89c1 3.4 \u8282&#xff0c;\u6b64\u5904 import \u590d\u7528<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">from<\/span> rmsnorm <span class=\"token keyword\">import<\/span> RMSNorm                       <span class=\"token comment\"># 3.4 \u8282\u7684\u81ea\u5b9e\u73b0<\/span><\/p>\n<p>torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">)<\/span><br \/>\nd <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">512<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">1024<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">3.0<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1.5<\/span>          <span class=\"token comment\"># \u5747\u503c 1.5&#xff0c;\u6807\u51c6\u5dee 3<\/span><br \/>\nln<span class=\"token punctuation\">,<\/span> rms <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> RMSNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># LN \u5b98\u65b9\u4e0e RMSNorm \u81ea\u5b9e\u73b0<\/span><\/p>\n<p>y_ln<span class=\"token punctuation\">,<\/span> y_rms <span class=\"token operator\">&#061;<\/span> ln<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> rms<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\nrow_mean_ln <span class=\"token operator\">&#061;<\/span> y_ln<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span>                <span class=\"token comment\"># \u6bcf\u884c\u8f93\u51fa\u7684\u5747\u503c<\/span><br \/>\nrow_mean_rms <span class=\"token operator\">&#061;<\/span> y_rms<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;LN      \u8f93\u51fa\u884c\u5747\u503c: \u5747\u503c <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>row_mean_ln<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">  \u6807\u51c6\u5dee <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>row_mean_ln<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;RMSNorm \u8f93\u51fa\u884c\u5747\u503c: \u5747\u503c <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>row_mean_rms<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">  \u6807\u51c6\u5dee <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>row_mean_rms<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;LN      \u8f93\u51fa\u884c\u6807\u51c6\u5dee: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>y_ln<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;RMSNorm \u8f93\u51fa\u884c\u6807\u51c6\u5dee: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>y_rms<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># LN      \u8f93\u51fa\u884c\u5747\u503c: \u5747\u503c 0.0000  \u6807\u51c6\u5dee 0.0000<\/span><br \/>\n<span class=\"token comment\"># RMSNorm \u8f93\u51fa\u884c\u5747\u503c: \u5747\u503c 0.4475  \u6807\u51c6\u5dee 0.0324<\/span><br \/>\n<span class=\"token comment\"># LN      \u8f93\u51fa\u884c\u6807\u51c6\u5dee: 1.0010<\/span><br \/>\n<span class=\"token comment\"># RMSNorm \u8f93\u51fa\u884c\u6807\u51c6\u5dee: 0.8944<\/span><\/p>\n<p>\u4e24\u4e2a\u6570\u5b57\u503c\u5f97\u9010\u6761\u89e3\u91ca\u3002<\/p>\n<p>\u7b2c\u4e00&#xff0c;LN \u7684\u884c\u5747\u503c\u6052\u4e3a 0&#xff0c;\u8fd9\u662f\u6784\u9020\u4f7f\u7136\u3002RMSNorm \u7684\u884c\u5747\u503c\u7ea6 0.4475&#xff0c;\u660e\u663e\u975e\u96f6\u3002\u8fd9\u4e2a\u6570\u6765\u81ea\u8f93\u5165\u5747\u503c 1.5&#xff1a;\u5f52\u4e00\u5316\u53ea\u7ea6\u675f\u5e73\u65b9\u548c&#xff0c;\u516c\u5171\u504f\u79fb\u88ab\u4fdd\u7559\u4e0b\u6765\u3002\u8f93\u5165\u5747\u503c\u8d8a\u5927&#xff0c;\u8fd9\u4e2a\u6570\u8d8a\u5927\u3002<\/p>\n<p>\u7b2c\u4e8c&#xff0c;RMSNorm \u8f93\u51fa\u884c\u6807\u51c6\u5dee\u7ea6 0.8944\u3002\u6ce8\u610f\u5b83\u4e0d\u7b49\u4e8e 1\u3002\u539f\u56e0\u662f\u8f93\u51fa\u7684\u603b\u5e73\u65b9\u91cf\u88ab\u9489\u4f4f\u540e&#xff0c;\u5747\u503c\u5360\u8d70\u4e86\u4e00\u90e8\u5206&#xff0c;\u79bb\u6563\u90e8\u5206\u5c31\u4e0d\u8db3 1\u3002LN \u5219\u56e0\u51cf\u6389\u4e86\u5747\u503c&#xff0c;\u6807\u51c6\u5dee\u6052\u4e3a 1\u3002<\/p>\n<p>\u8fd9\u4e2a\u5dee\u5f02\u4e0d\u81f4\u547d&#xff0c;\u4f46\u8981\u7559\u610f\u4e24\u70b9\u3002\u4e00\u662f\u4e0b\u6e38\u82e5\u5bf9\u8f93\u5165\u5206\u5e03\u654f\u611f&#xff08;\u5982\u67d0\u4e9b\u6fc0\u6d3b\u51fd\u6570&#xff09;&#xff0c;\u9700\u8981\u786e\u8ba4\u3002\u4e8c\u662f fp16 \u4e0b RMSNorm \u7684\u6570\u503c\u8303\u56f4\u6bd4 LN \u5bbd&#xff0c;eps \u4e0e\u7cbe\u5ea6\u8981\u5355\u72ec\u9a8c\u4e00\u904d\u3002<\/p>\n<p>\u7ed3\u8bba&#xff1a;RMSNorm \u8f93\u51fa\u7684\u7edf\u8ba1\u4e0e LN \u4e0d\u540c\u6784\u3002\u66ff\u6362\u4e0d\u662f\u7eaf\u65e0\u635f\u7684\u7b97\u5b50\u7ea7\u66ff\u6362\u3002\u7b2c 7.3 \u8282\u4f1a\u56de\u5230 checkpoint \u517c\u5bb9\u95ee\u9898\u3002<\/p>\n<h4>3.4 \u81ea\u5b9e\u73b0 RMSNorm \u4e0e\u901f\u5ea6\u57fa\u51c6<\/h4>\n<p>\u5b8c\u6574\u5b9e\u73b0\u4e0e\u901f\u5ea6\u5bf9\u6bd4\u653e\u5728\u4e00\u8282\u3002\u4ee3\u7801\u5e26 __main__&#xff0c;\u53ef\u76f4\u63a5\u8dd1\u3002<\/p>\n<p><span class=\"token comment\"># \u81ea\u5b9e\u73b0 RMSNorm&#xff1a;\u4e0e LayerNorm \u7684\u53c2\u6570\u91cf\u4e0e\u8ba1\u7b97\u91cf\u5bf9\u6bd4&#xff08;PyTorch 2.13 CPU&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> time<span class=\"token punctuation\">,<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">RMSNorm<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> dim<span class=\"token punctuation\">,<\/span> eps<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e-6<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>weight <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u53ea\u6709 gamma&#xff0c;\u65e0 beta<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>eps <span class=\"token operator\">&#061;<\/span> eps<\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        ms <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">pow<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> keepdim<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>      <span class=\"token comment\"># \u5747\u65b9&#xff0c;\u5c11\u4e00\u6b21 mean \u89c4\u7ea6<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> x <span class=\"token operator\">*<\/span> torch<span class=\"token punctuation\">.<\/span>rsqrt<span class=\"token punctuation\">(<\/span>ms <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>eps<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>weight<\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    d <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1024<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\n    ln<span class=\"token punctuation\">,<\/span> rms <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> RMSNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;LN \u53c2\u6570\u91cf:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">.<\/span>numel<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> p <span class=\"token keyword\">in<\/span> ln<span class=\"token punctuation\">.<\/span>parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>       <span class=\"token comment\"># 2048<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;RMSNorm \u53c2\u6570\u91cf:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">.<\/span>numel<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> p <span class=\"token keyword\">in<\/span> rms<span class=\"token punctuation\">.<\/span>parameters<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\"># 1024<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u8f93\u51fa\u5e73\u65b9\u5747\u503c:&#034;<\/span><span class=\"token punctuation\">,<\/span> rms<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">pow<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u7ea6 1.0<\/span><br \/>\n    <span class=\"token comment\"># \u901f\u5ea6\u57fa\u51c6&#xff1a;\u9884\u70ed\u540e\u8dd1 2000 \u6b21\u53d6\u4e2d\u4f4d<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">bench<\/span><span class=\"token punctuation\">(<\/span>mod<span class=\"token punctuation\">,<\/span> n<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2000<\/span><span class=\"token punctuation\">,<\/span> warm<span class=\"token operator\">&#061;<\/span><span class=\"token number\">50<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>warm<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span> mod<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        ts <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">(<\/span>time<span class=\"token punctuation\">.<\/span>perf_counter<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> mod<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> time<span class=\"token punctuation\">.<\/span>perf_counter<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token builtin\">sorted<\/span><span class=\"token punctuation\">(<\/span>b <span class=\"token operator\">&#8211;<\/span> a <span class=\"token keyword\">for<\/span> a<span class=\"token punctuation\">,<\/span> _<span class=\"token punctuation\">,<\/span> b <span class=\"token keyword\">in<\/span> ts<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span>n <span class=\"token operator\">\/\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">1e6<\/span><\/p>\n<p>    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;nn.LayerNorm \u4e2d\u4f4d\u8017\u65f6: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>bench<span class=\"token punctuation\">(<\/span>ln<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.1f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> us&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span>   <span class=\"token comment\"># \u7ea6 96 us<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;RMSNorm   \u4e2d\u4f4d\u8017\u65f6: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>bench<span class=\"token punctuation\">(<\/span>rms<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.1f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> us&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span>     <span class=\"token comment\"># \u7ea6 78 us&#xff08;\u672c\u673a CPU&#xff09;<\/span><\/p>\n<p>\u53c2\u6570\u91cf\u4e00\u884c\u662f\u786c\u4e8b\u5b9e&#xff1a;2048 \u5bf9 1024&#xff0c;\u6070\u597d\u51cf\u534a\u3002\u901f\u5ea6\u4e00\u884c\u8981\u52a0\u6761\u4ef6\u3002\u8fd9\u662f Python \u5c42\u4e0e\u5b98\u65b9\u4f18\u5316 kernel \u7684\u5bf9\u6bd4\u3002\u6570\u5b57\u53ea\u8bf4\u660e\u8d8b\u52bf&#xff0c;\u5177\u4f53\u6570\u503c\u968f\u786c\u4ef6\u4e0e\u5f62\u72b6\u53d8\u3002<\/p>\n<p>\u4e00\u4e2a\u53cd\u76f4\u89c9\u7684\u7ec6\u8282\u3002torch \u5b98\u65b9 nn.LayerNorm \u8d70\u9ad8\u5ea6\u4f18\u5316\u7684 kernel&#xff0c;\u624b\u5199 RMSNorm \u5728 Python \u5c42\u53cd\u800c\u53ef\u80fd\u66f4\u6162\u3002\u771f\u5b9e\u6536\u76ca\u6765\u81ea\u878d\u5408\u5b9e\u73b0&#xff08;\u5982 Apex\u3001LLaMA \u6e90\u7801&#xff09;\u4e0e\u53c2\u6570\u91cf\u51cf\u534a\u3002\u4e0d\u662f\u88f8 Python \u5bf9\u6bd4\u3002<\/p>\n<p>\u7b2c 6.4 \u8282\u4f1a\u5728\u66f4\u8d34\u8fd1\u5b9e\u9645\u7684\u8bbe\u7f6e\u4e0b\u91cd\u8dd1\u8fd9\u7ec4\u57fa\u51c6&#xff0c;\u5e76\u7ed9\u51fa\u5f62\u72b6\u626b\u63a0\u8868\u3002<\/p>\n<p>  #mermaid-svg-EA5gT0sB4V2GwkJV{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-EA5gT0sB4V2GwkJV .error-icon{fill:#552222;}#mermaid-svg-EA5gT0sB4V2GwkJV .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-EA5gT0sB4V2GwkJV .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-EA5gT0sB4V2GwkJV .marker{fill:#333333;stroke:#333333;}#mermaid-svg-EA5gT0sB4V2GwkJV .marker.cross{stroke:#333333;}#mermaid-svg-EA5gT0sB4V2GwkJV svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-EA5gT0sB4V2GwkJV p{margin:0;}#mermaid-svg-EA5gT0sB4V2GwkJV .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV .cluster-label text{fill:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV .cluster-label span{color:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV .cluster-label span p{background-color:transparent;}#mermaid-svg-EA5gT0sB4V2GwkJV .label text,#mermaid-svg-EA5gT0sB4V2GwkJV span{fill:#333;color:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV .node rect,#mermaid-svg-EA5gT0sB4V2GwkJV .node circle,#mermaid-svg-EA5gT0sB4V2GwkJV .node ellipse,#mermaid-svg-EA5gT0sB4V2GwkJV .node polygon,#mermaid-svg-EA5gT0sB4V2GwkJV .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-EA5gT0sB4V2GwkJV .rough-node .label text,#mermaid-svg-EA5gT0sB4V2GwkJV .node .label text,#mermaid-svg-EA5gT0sB4V2GwkJV .image-shape .label,#mermaid-svg-EA5gT0sB4V2GwkJV .icon-shape .label{text-anchor:middle;}#mermaid-svg-EA5gT0sB4V2GwkJV .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-EA5gT0sB4V2GwkJV .rough-node .label,#mermaid-svg-EA5gT0sB4V2GwkJV .node .label,#mermaid-svg-EA5gT0sB4V2GwkJV .image-shape .label,#mermaid-svg-EA5gT0sB4V2GwkJV .icon-shape .label{text-align:center;}#mermaid-svg-EA5gT0sB4V2GwkJV .node.clickable{cursor:pointer;}#mermaid-svg-EA5gT0sB4V2GwkJV .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-EA5gT0sB4V2GwkJV .arrowheadPath{fill:#333333;}#mermaid-svg-EA5gT0sB4V2GwkJV .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-EA5gT0sB4V2GwkJV .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-EA5gT0sB4V2GwkJV .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-EA5gT0sB4V2GwkJV .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-EA5gT0sB4V2GwkJV .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-EA5gT0sB4V2GwkJV .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-EA5gT0sB4V2GwkJV .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-EA5gT0sB4V2GwkJV .cluster text{fill:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV .cluster span{color:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-EA5gT0sB4V2GwkJV .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-EA5gT0sB4V2GwkJV rect.text{fill:none;stroke-width:0;}#mermaid-svg-EA5gT0sB4V2GwkJV .icon-shape,#mermaid-svg-EA5gT0sB4V2GwkJV .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-EA5gT0sB4V2GwkJV .icon-shape p,#mermaid-svg-EA5gT0sB4V2GwkJV .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-EA5gT0sB4V2GwkJV .icon-shape .label rect,#mermaid-svg-EA5gT0sB4V2GwkJV .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-EA5gT0sB4V2GwkJV .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-EA5gT0sB4V2GwkJV .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-EA5gT0sB4V2GwkJV :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-EA5gT0sB4V2GwkJV .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-EA5gT0sB4V2GwkJV .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-EA5gT0sB4V2GwkJV .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u51cf\u6cd5\u6e05\u5355<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u780d mean \u89c4\u7ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u780d beta \u53c2\u6570<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5206\u6bcd\u6539\u5747\u65b9\u6839<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6bcf\u6b21\u524d\u5411\u5c11\u4e00\u6b21\u5168\u7ef4\u89c4\u7ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53c2\u6570\u4ece 2d \u51cf\u5230 d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5747\u503c\u4e0d\u518d\u6052\u4e3a 0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5927\u6a21\u578b\u4e0a\u7d2f\u79ef\u6210 7 \u5230 9 \u6574\u4f53\u63d0\u901f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9700\u5355\u72ec\u9a8c\u8bc1\u6570\u503c\u8303\u56f4<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u6700\u4e0b\u9762\u4e00\u884c\u7684\u63d0\u901f\u6570\u5b57\u662f Transformer \u573a\u666f\u7684\u8bba\u6587\u53e3\u5f84\u3002RNN \u573a\u666f\u66f4\u9ad8&#xff0c;\u89c1 3.2 \u8282\u7684\u8868\u3002<\/p>\n<p>\u81f3\u6b64\u5f52\u4e00\u5316\u4fa7\u8bb2\u5b8c\u3002\u4e0b\u4e00\u8282\u628a\u89c6\u89d2\u5207\u5230\u6b8b\u5dee&#xff0c;\u770b\u90a3\u6761\u88ab Pre-LN \u4fdd\u62a4\u7684\u4e3b\u5e72\u5230\u5e95\u662f\u4ec0\u4e48\u3002<\/p>\n<h3>4. \u6b8b\u5dee\u8fde\u63a5&#xff1a;\u68af\u5ea6\u7684\u9ad8\u901f\u51fa\u53e3<\/h3>\n<h4>4.1 ResNet \u601d\u60f3\u7684\u8fc1\u79fb<\/h4>\n<p>\u6b8b\u5dee\u8fde\u63a5\u4e0d\u662f Transformer \u7684\u53d1\u660e\u3002\u5b83\u6765\u81ea ResNet&#xff08;arXiv:1512.03385&#xff09;&#xff0c;2015 \u5e74\u7684\u56fe\u50cf\u5206\u7c7b\u5de5\u4f5c\u3002<\/p>\n<p>ResNet \u89e3\u51b3\u7684\u95ee\u9898\u662f&#xff1a;\u7f51\u7edc\u52a0\u6df1\u540e&#xff0c;\u666e\u901a\u5806\u53e0\u7684\u6a21\u578b\u8bad\u7ec3\u8bef\u5dee\u53cd\u800c\u4e0a\u5347\u300256 \u5c42\u7f51\u7edc\u6bd4 20 \u5c42\u66f4\u5dee\u3002\u8fd9\u4e0d\u662f\u8fc7\u62df\u5408&#xff08;\u6d4b\u8bd5\u8bef\u5dee\u4e0e\u8bad\u7ec3\u8bef\u5dee\u540c\u6da8&#xff09;&#xff0c;\u662f\u4f18\u5316\u4e0d\u52a8\u3002<\/p>\n<p>\u89e3\u6cd5\u662f\u628a\u5c42\u7684\u76ee\u6807\u6539\u5199\u3002\u4e0d\u8ba9\u5c42\u5b66\u5b8c\u6574\u7684\u6620\u5c04 H(x)&#xff0c;\u6539\u5b66\u6b8b\u5dee F(x) &#061; H(x) &#8211; x&#xff0c;\u8f93\u51fa\u4e3a&#xff1a;<\/p>\n<p>y &#061; F(x) &#043; x<\/p>\n<p>\u5982\u679c\u6700\u4f18\u6620\u5c04\u63a5\u8fd1\u6052\u7b49&#xff0c;\u628a F \u7684\u6743\u91cd\u63a8\u5411\u96f6\u5373\u53ef&#xff0c;\u6bd4\u4ece\u5934\u5b66\u4e00\u4e2a\u6052\u7b49\u6620\u5c04\u5bb9\u6613\u5f97\u591a\u3002\u8bba\u6587\u5b9e\u9a8c\u91cc\u6700\u6df1\u505a\u5230 152 \u5c42\u3002\u96c6\u6210\u6a21\u578b\u5728 ImageNet \u6d4b\u8bd5\u96c6\u9519\u8bef\u7387 3.57%&#xff0c;\u5355\u6a21\u578b\u4e5f\u7cfb\u7edf\u4f18\u4e8e\u66f4\u6d45\u7684\u7f51\u7edc\u3002<\/p>\n<p>Transformer \u76f4\u63a5\u7ee7\u627f\u4e86\u8fd9\u4e2a\u7ed3\u6784\u3002\u539f\u8bba\u6587\u6bcf\u4e2a\u5b50\u5c42\u90fd\u5957\u6b8b\u5dee&#xff0c;\u914d LN \u4f7f\u7528\u3002attention \u5c42\u4e0e FFN \u5c42\u7684\u8f93\u51fa\u90fd\u8d70 x \u52a0 Sublayer(x) \u7684\u5f62\u5f0f\u3002<\/p>\n<p>\u5bf9\u5e8f\u5217\u6a21\u578b&#xff0c;\u6b8b\u5dee\u8fd8\u6709\u4e00\u5c42\u989d\u5916\u542b\u4e49\u3002\u7b2c l \u5c42\u5b66\u5230\u7684\u7279\u5f81&#xff0c;\u901a\u8fc7\u52a0\u6cd5\u539f\u6837\u4fdd\u7559\u5230\u7b2c l&#043;1 \u5c42\u3002\u4fe1\u606f\u4e0d\u4f1a\u88ab\u540e\u7eed\u5c42\u8986\u76d6&#xff0c;\u53ea\u4f1a\u88ab\u8ffd\u52a0\u4fee\u6539\u3002<\/p>\n<p>\u8fd9\u4e0e\u7b2c 2 \u8282\u7684\u68af\u5ea6\u5206\u6790\u95ed\u73af\u3002\u524d\u5411\u7684\u6052\u7b49\u901a\u9053\u5bf9\u5e94\u53cd\u5411\u7684\u6052\u7b49\u68af\u5ea6&#xff0c;\u6b8b\u5dee\u540c\u65f6\u4fdd\u4f4f\u4e24\u5934\u3002<\/p>\n<table>\n<tr>\u9879\u666e\u901a\u5806\u53e0\u6b8b\u5dee\u5806\u53e0<\/tr>\n<tbody>\n<tr>\n<td>\u524d\u5411<\/td>\n<td>y &#061; F(x)<\/td>\n<td>y &#061; F(x) &#043; x<\/td>\n<\/tr>\n<tr>\n<td>\u53cd\u4f20\u5230 x \u7684\u68af\u5ea6<\/td>\n<td>dF\/dx \u4e58\u68af\u5ea6<\/td>\n<td>1 \u52a0 dF\/dx \u4e58\u68af\u5ea6<\/td>\n<\/tr>\n<tr>\n<td>\u5b66\u6052\u7b49\u6620\u5c04<\/td>\n<td>\u9700\u903c\u8fd1\u6743\u91cd<\/td>\n<td>F \u7f6e\u96f6\u5373\u5f97<\/td>\n<\/tr>\n<tr>\n<td>\u6df1\u5c42\u53ef\u8bad\u6027<\/td>\n<td>\u8bef\u5dee\u968f\u6df1\u5ea6\u4e0a\u5347<\/td>\n<td>152 \u5c42\u4ecd\u53ef\u4f18\u5316<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>  #mermaid-svg-AghaFIAYRyuUfxml{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-AghaFIAYRyuUfxml .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-AghaFIAYRyuUfxml .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-AghaFIAYRyuUfxml .error-icon{fill:#552222;}#mermaid-svg-AghaFIAYRyuUfxml .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-AghaFIAYRyuUfxml .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-AghaFIAYRyuUfxml .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-AghaFIAYRyuUfxml .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-AghaFIAYRyuUfxml .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-AghaFIAYRyuUfxml .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-AghaFIAYRyuUfxml .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-AghaFIAYRyuUfxml .marker{fill:#333333;stroke:#333333;}#mermaid-svg-AghaFIAYRyuUfxml .marker.cross{stroke:#333333;}#mermaid-svg-AghaFIAYRyuUfxml svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-AghaFIAYRyuUfxml p{margin:0;}#mermaid-svg-AghaFIAYRyuUfxml .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-AghaFIAYRyuUfxml .cluster-label text{fill:#333;}#mermaid-svg-AghaFIAYRyuUfxml .cluster-label span{color:#333;}#mermaid-svg-AghaFIAYRyuUfxml .cluster-label span p{background-color:transparent;}#mermaid-svg-AghaFIAYRyuUfxml .label text,#mermaid-svg-AghaFIAYRyuUfxml span{fill:#333;color:#333;}#mermaid-svg-AghaFIAYRyuUfxml .node rect,#mermaid-svg-AghaFIAYRyuUfxml .node circle,#mermaid-svg-AghaFIAYRyuUfxml .node ellipse,#mermaid-svg-AghaFIAYRyuUfxml .node polygon,#mermaid-svg-AghaFIAYRyuUfxml .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-AghaFIAYRyuUfxml .rough-node .label text,#mermaid-svg-AghaFIAYRyuUfxml .node .label text,#mermaid-svg-AghaFIAYRyuUfxml .image-shape .label,#mermaid-svg-AghaFIAYRyuUfxml .icon-shape .label{text-anchor:middle;}#mermaid-svg-AghaFIAYRyuUfxml .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-AghaFIAYRyuUfxml .rough-node .label,#mermaid-svg-AghaFIAYRyuUfxml .node .label,#mermaid-svg-AghaFIAYRyuUfxml .image-shape .label,#mermaid-svg-AghaFIAYRyuUfxml .icon-shape .label{text-align:center;}#mermaid-svg-AghaFIAYRyuUfxml .node.clickable{cursor:pointer;}#mermaid-svg-AghaFIAYRyuUfxml .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-AghaFIAYRyuUfxml .arrowheadPath{fill:#333333;}#mermaid-svg-AghaFIAYRyuUfxml .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-AghaFIAYRyuUfxml .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-AghaFIAYRyuUfxml .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-AghaFIAYRyuUfxml .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-AghaFIAYRyuUfxml .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-AghaFIAYRyuUfxml .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-AghaFIAYRyuUfxml .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-AghaFIAYRyuUfxml .cluster text{fill:#333;}#mermaid-svg-AghaFIAYRyuUfxml .cluster span{color:#333;}#mermaid-svg-AghaFIAYRyuUfxml div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-AghaFIAYRyuUfxml .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-AghaFIAYRyuUfxml rect.text{fill:none;stroke-width:0;}#mermaid-svg-AghaFIAYRyuUfxml .icon-shape,#mermaid-svg-AghaFIAYRyuUfxml .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-AghaFIAYRyuUfxml .icon-shape p,#mermaid-svg-AghaFIAYRyuUfxml .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-AghaFIAYRyuUfxml .icon-shape .label rect,#mermaid-svg-AghaFIAYRyuUfxml .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-AghaFIAYRyuUfxml .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-AghaFIAYRyuUfxml .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-AghaFIAYRyuUfxml :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-AghaFIAYRyuUfxml .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-AghaFIAYRyuUfxml .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-AghaFIAYRyuUfxml .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u5165 x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6743\u91cd\u5c42 F<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>F x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6052\u7b49\u76f4\u901a<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u76f8\u52a0\u5f97 y<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53cd\u5411\u65f6\u68af\u5ea6\u5206\u4e24\u8def<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ecf F \u7684\u8def\u5e45\u5ea6\u53ef\u80fd\u8870\u51cf<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ecf\u52a0\u6cd5\u7684\u8def\u539f\u6837\u8fd4\u56de<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u68af\u5ea6\u603b\u91cf\u6709 1 \u515c\u5e95<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6df1\u5c42\u6570\u68af\u5ea6\u4e0d\u6d88\u5931<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u53f3\u4fa7\u90a3\u6761\u4e0d\u7ecf\u6743\u91cd\u7684\u8def&#xff0c;\u5c31\u662f 4.2 \u8282\u8981\u6570\u503c\u9a8c\u8bc1\u7684\u6052\u7b49\u9879\u3002<\/p>\n<h4>4.2 \u6052\u7b49\u9879\u7684\u6570\u503c\u9a8c\u8bc1<\/h4>\n<p>\u6b8b\u5dee\u7684\u68af\u5ea6\u516c\u5f0f\u53ef\u4ee5\u5199\u6210&#xff1a;<\/p>\n<p>dy\/dx &#061; 1 &#043; dF\/dx<\/p>\n<p>\u94fe\u5f0f\u6cd5\u5219\u4e0b&#xff0c;\u635f\u5931 L \u5bf9 x \u7684\u68af\u5ea6\u4e3a&#xff1a;<\/p>\n<p>dL\/dx &#061; dL\/dy * (1 &#043; dF\/dx)<br \/>\n       &#061; dL\/dy &#043; dL\/dy * dF\/dx<\/p>\n<p>\u7b2c\u4e00\u9879 dL\/dy \u5c31\u662f\u6052\u7b49\u9879\u8d21\u732e&#xff0c;\u4e0e F \u7684\u6743\u91cd\u65e0\u5173\u3002\u7b2c\u4e8c\u9879\u7ecf\u6743\u91cd\u53cd\u4f20&#xff0c;\u53ef\u80fd\u8870\u51cf\u4e5f\u53ef\u80fd\u653e\u5927\u3002<\/p>\n<p>\u4e0b\u9762\u7528\u81ea\u52a8\u5fae\u5206\u9a8c\u8bc1\u8fd9\u4e2a\u5206\u89e3\u3002<\/p>\n<p><span class=\"token comment\"># \u6b8b\u5dee\u76f4\u901a\u68af\u5ea6\u7684\u6570\u503c\u9a8c\u8bc1&#xff08;PyTorch 2.13 CPU&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p>torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span><br \/>\nd <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">64<\/span><br \/>\nFnet <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Sequential<span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> nn<span class=\"token punctuation\">.<\/span>GELU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>        <span class=\"token comment\"># \u5bf9 x \u6c42\u68af\u5ea6<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> Fnet<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> x                                   <span class=\"token comment\"># \u6b8b\u5dee\u7ed3\u6784<\/span><br \/>\ny<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">pow<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>                         <span class=\"token comment\"># dL\/dy &#061; 2y<\/span><br \/>\ntotal <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>clone<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>x2 <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span>       <span class=\"token comment\"># \u5bf9\u7167&#xff1a;\u65e0\u6b8b\u5dee<\/span><br \/>\nFnet<span class=\"token punctuation\">(<\/span>x2<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">pow<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>backward<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nno_res <span class=\"token operator\">&#061;<\/span> x2<span class=\"token punctuation\">.<\/span>grad<span class=\"token punctuation\">.<\/span>clone<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">with<\/span> torch<span class=\"token punctuation\">.<\/span>no_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    ident <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>Fnet<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> x<span class=\"token punctuation\">)<\/span>                     <span class=\"token comment\"># \u6052\u7b49\u9879\u8d21\u732e dL\/dy<\/span><br \/>\n    thru <span class=\"token operator\">&#061;<\/span> total <span class=\"token operator\">&#8211;<\/span> ident                          <span class=\"token comment\"># \u7ecf F \u53cd\u4f20\u7684\u8d21\u732e<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u603b\u68af\u5ea6\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> total<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6052\u7b49\u9879\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> ident<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6052\u7b49\u9879\u5360\u6bd4:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span>ident<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> total<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u65e0\u6b8b\u5dee\u68af\u5ea6\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> no_res<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u603b\u68af\u5ea6\u8303\u6570: 13.79<\/span><br \/>\n<span class=\"token comment\"># \u6052\u7b49\u9879\u8303\u6570: 12.15<\/span><br \/>\n<span class=\"token comment\"># \u6052\u7b49\u9879\u5360\u6bd4: 0.881<\/span><br \/>\n<span class=\"token comment\"># \u65e0\u6b8b\u5dee\u68af\u5ea6\u8303\u6570: 6.19<\/span><\/p>\n<p>\u6570\u5b57\u89e3\u8bfb\u8981\u5206\u4e24\u5c42\u3002<\/p>\n<p>\u7b2c\u4e00\u5c42&#xff0c;\u6052\u7b49\u9879\u8303\u6570\u4e0e\u603b\u68af\u5ea6\u8303\u6570\u540c\u91cf\u7ea7&#xff0c;\u5360\u6bd4\u7ea6 0.88\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u8fd9\u4e2a\u968f\u673a\u521d\u59cb\u5316\u7684\u4e24\u5c42 F \u91cc&#xff0c;\u68af\u5ea6\u5927\u5934\u8d70\u7684\u662f\u4e0d\u7ecf\u8fc7\u6743\u91cd\u7684\u901a\u9053\u3002<\/p>\n<p>\u7b2c\u4e8c\u5c42&#xff0c;\u628a\u6b8b\u5dee\u62ff\u6389\u540e\u68af\u5ea6\u8303\u6570\u4ece 13.79 \u964d\u5230 6.19\u3002\u8fd9\u662f\u5355\u5c42\u7684\u5bf9\u6bd4\u3002\u6df1\u5c42\u5806\u53e0\u65f6&#xff0c;\u82e5\u6bcf\u5c42\u7ecf\u6743\u91cd\u7684\u8def\u5f84\u90fd\u8870\u51cf&#xff0c;\u65e0\u6b8b\u5dee\u7684\u68af\u5ea6\u6309\u5c42\u6570\u6307\u6570\u7f29\u5c0f\u3002\u6709\u6b8b\u5dee\u5219\u59cb\u7ec8\u6709\u6052\u7b49\u9879\u4fdd\u5e95\u3002<\/p>\n<p>\u4e00\u4e2a\u6709\u7528\u7684\u63a8\u8bba&#xff1a;\u6052\u7b49\u9879\u5360\u6bd4\u9ad8&#xff0c;\u8bf4\u660e\u68af\u5ea6\u91cc\u643a\u5e26\u7684&#034;\u9010\u5c42\u4fe1\u606f&#034;\u5c11&#xff0c;\u66f4\u591a\u662f\u5168\u5c40\u4fe1\u53f7\u3002\u8fd9\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u6df1\u6b8b\u5dee\u7f51\u7edc\u7684\u53ef\u8bad\u6027\u5bf9\u521d\u59cb\u5316\u4e0d\u90a3\u4e48\u654f\u611f\u3002<\/p>\n<p>  #mermaid-svg-Ljdx28HiUrmJQsPH{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-Ljdx28HiUrmJQsPH .error-icon{fill:#552222;}#mermaid-svg-Ljdx28HiUrmJQsPH .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-Ljdx28HiUrmJQsPH .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-Ljdx28HiUrmJQsPH .marker{fill:#333333;stroke:#333333;}#mermaid-svg-Ljdx28HiUrmJQsPH .marker.cross{stroke:#333333;}#mermaid-svg-Ljdx28HiUrmJQsPH svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-Ljdx28HiUrmJQsPH p{margin:0;}#mermaid-svg-Ljdx28HiUrmJQsPH .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH .cluster-label text{fill:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH .cluster-label span{color:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH .cluster-label span p{background-color:transparent;}#mermaid-svg-Ljdx28HiUrmJQsPH .label text,#mermaid-svg-Ljdx28HiUrmJQsPH span{fill:#333;color:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH .node rect,#mermaid-svg-Ljdx28HiUrmJQsPH .node circle,#mermaid-svg-Ljdx28HiUrmJQsPH .node ellipse,#mermaid-svg-Ljdx28HiUrmJQsPH .node polygon,#mermaid-svg-Ljdx28HiUrmJQsPH .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-Ljdx28HiUrmJQsPH .rough-node .label text,#mermaid-svg-Ljdx28HiUrmJQsPH .node .label text,#mermaid-svg-Ljdx28HiUrmJQsPH .image-shape .label,#mermaid-svg-Ljdx28HiUrmJQsPH .icon-shape .label{text-anchor:middle;}#mermaid-svg-Ljdx28HiUrmJQsPH .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-Ljdx28HiUrmJQsPH .rough-node .label,#mermaid-svg-Ljdx28HiUrmJQsPH .node .label,#mermaid-svg-Ljdx28HiUrmJQsPH .image-shape .label,#mermaid-svg-Ljdx28HiUrmJQsPH .icon-shape .label{text-align:center;}#mermaid-svg-Ljdx28HiUrmJQsPH .node.clickable{cursor:pointer;}#mermaid-svg-Ljdx28HiUrmJQsPH .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-Ljdx28HiUrmJQsPH .arrowheadPath{fill:#333333;}#mermaid-svg-Ljdx28HiUrmJQsPH .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-Ljdx28HiUrmJQsPH .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-Ljdx28HiUrmJQsPH .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-Ljdx28HiUrmJQsPH .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-Ljdx28HiUrmJQsPH .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-Ljdx28HiUrmJQsPH .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-Ljdx28HiUrmJQsPH .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-Ljdx28HiUrmJQsPH .cluster text{fill:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH .cluster span{color:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-Ljdx28HiUrmJQsPH .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-Ljdx28HiUrmJQsPH rect.text{fill:none;stroke-width:0;}#mermaid-svg-Ljdx28HiUrmJQsPH .icon-shape,#mermaid-svg-Ljdx28HiUrmJQsPH .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-Ljdx28HiUrmJQsPH .icon-shape p,#mermaid-svg-Ljdx28HiUrmJQsPH .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-Ljdx28HiUrmJQsPH .icon-shape .label rect,#mermaid-svg-Ljdx28HiUrmJQsPH .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-Ljdx28HiUrmJQsPH .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-Ljdx28HiUrmJQsPH .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-Ljdx28HiUrmJQsPH :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-Ljdx28HiUrmJQsPH .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-Ljdx28HiUrmJQsPH .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-Ljdx28HiUrmJQsPH .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u635f\u5931 L<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa y<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>y \u7b49\u4e8e F x \u52a0 x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>dL dy \u4e58 1 \u5f97\u6052\u7b49\u9879<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>dL dy \u4e58 dF dx \u5f97\u7ecf F \u9879<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e0e\u6743\u91cd\u65e0\u5173<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u968f\u6743\u91cd\u4e0e\u6df1\u5ea6\u8870\u51cf<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u68af\u5ea6\u4e0b\u754c\u6709\u4fdd\u5e95<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6df1\u5c42\u53ef\u80fd\u6d88\u5931<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6df1\u7f51\u7edc\u53ef\u8bad<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d F \u4e0e G \u4e24\u6761\u8def\u5f84\u7684\u547d\u8fd0\u5bf9\u6bd4&#xff0c;\u5c31\u662f\u6b8b\u5dee\u8fde\u63a5\u5168\u90e8\u4ef7\u503c\u7684\u6d53\u7f29\u8868\u8ff0\u3002<\/p>\n<h4>4.3 \u6b8b\u5dee\u6d41&#xff1a;\u4fe1\u606f\u9ad8\u901f\u516c\u8def\u89c6\u89d2<\/h4>\n<p>\u628a\u6b8b\u5dee\u4e3b\u5e72\u5355\u72ec\u62bd\u8c61\u51fa\u6765\u770b&#xff0c;\u4f1a\u5f97\u5230\u4e00\u4e2a\u5f88\u6709\u89e3\u91ca\u529b\u7684\u89c6\u89d2&#xff1a;\u6b8b\u5dee\u6d41&#xff08;residual stream&#xff09;\u3002\u6b8b\u5dee\u6d41\u6307\u8d2f\u7a7f\u5168\u90e8\u5c42\u3001\u53ea\u505a\u52a0\u6cd5\u7684\u90a3\u6761\u4e3b\u5e72\u5411\u91cf\u5e8f\u5217\u3002<\/p>\n<p>\u767d\u8bdd\u7248&#xff1a;\u628a\u4e3b\u5e72\u60f3\u6210\u4e00\u6761\u4f20\u9001\u5e26&#xff0c;\u6bcf\u4e2a token \u5728\u4e0a\u9762\u6709\u4e00\u4e2a\u5ea7\u4f4d\u3002\u6ce8\u610f\u529b\u5c42\u548c FFN \u5c42\u4e0d\u662f\u66ff\u6362\u5ea7\u4f4d\u4e0a\u7684\u5185\u5bb9&#xff0c;\u800c\u662f\u5f80\u4e0a\u9762\u8ffd\u52a0\u6216\u4fee\u6539\u4fe1\u606f\u3002<\/p>\n<p>\u672f\u8bed\u7248&#xff1a;\u6b8b\u5dee\u6d41\u6307\u8d2f\u7a7f\u5168\u90e8\u5c42\u3001\u53ea\u505a\u52a0\u6cd5\u7684\u90a3\u6761\u4e3b\u5e72\u5411\u91cf\u5e8f\u5217\u3002\u6bcf\u5c42\u5b50\u5c42\u7684\u884c\u4e3a\u88ab\u91cd\u65b0\u7406\u89e3\u4e3a\u5bf9\u8fd9\u6761\u6d41\u7684\u8bfb\u4e0e\u5199\u3002<\/p>\n<p>\u8bfb&#xff1a;\u6ce8\u610f\u529b\u5c42\u4ece\u6d41\u91cc\u53d6 query\u3001key\u3001value&#xff0c;\u7528\u5b83\u4eec\u53bb\u522b\u7684\u4f4d\u7f6e\u53d6\u4fe1\u606f\u3002\u5199&#xff1a;\u5b50\u5c42\u8f93\u51fa\u52a0\u56de\u4e3b\u5e72&#xff0c;\u76f8\u5f53\u4e8e\u628a\u65b0\u4fe1\u606f\u5199\u56de\u6d41\u91cc\u3002<\/p>\n<p>\u8fd9\u4e2a\u89c6\u89d2\u7684\u4ef7\u503c\u5728\u4e8e\u89e3\u91ca\u4e86\u4e24\u4e2a\u73b0\u8c61\u3002\u5176\u4e00&#xff0c;\u6df1\u5c42\u7684\u6ce8\u610f\u529b\u5934\u80fd\u76f4\u63a5\u8bbf\u95ee\u6700\u521d\u5c42\u7684\u5d4c\u5165&#xff0c;\u4e2d\u95f4\u5c42\u4e0d\u5fc5\u9010\u5c42\u8f6c\u53d1\u3002\u5176\u4e8c&#xff0c;\u4e0d\u540c\u6ce8\u610f\u529b\u5934\u53ef\u4ee5\u5728\u4e0d\u540c\u5c42\u64cd\u4f5c\u540c\u4e00\u4efd\u4fe1\u606f\u800c\u4e0d\u4e92\u76f8\u8986\u76d6\u3002<\/p>\n<p>Anthropic \u7684 transformer circuits \u7cfb\u5217\u628a\u8fd9\u4e2a\u89c6\u89d2\u53d1\u5c55\u6210\u4e00\u5957\u5206\u6790\u6846\u67b6\u3002\u628a\u6ce8\u610f\u529b\u5934\u4e0e FFN \u770b\u4f5c\u6b8b\u5dee\u6d41\u4e0a\u7684\u8bfb\u5199\u7b97\u5b50\u3002\u4e00\u53e5\u8bdd\u5e26\u8fc7&#xff1a;\u5176\u53ef\u89e3\u91ca\u6027\u5de5\u4f5c\u5927\u91cf\u4f9d\u8d56\u8fd9\u4e2a\u62bd\u8c61&#xff0c;\u672c\u7cfb\u5217\u4e0d\u5c55\u5f00\u3002<\/p>\n<p>\u56de\u5230\u7ed3\u6784\u3002Pre-LN \u65f6\u4ee3\u8fd9\u6761\u6d41\u7684\u5e45\u5ea6\u9010\u5c42\u589e\u957f&#xff0c;\u7b2c 4.4 \u8282\u7ed9\u51fa\u91cf\u5316\u3002\u8fd9\u4e5f\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48 Pre-LN \u5fc5\u987b\u914d final norm\u3002\u8f93\u51fa\u5934\u9700\u8981\u4e00\u6761\u88ab\u7a33\u538b\u8fc7\u7684\u652f\u6d41\u3002<\/p>\n<p>  #mermaid-svg-a7wblsy3TTJMg0nE{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-a7wblsy3TTJMg0nE .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-a7wblsy3TTJMg0nE .error-icon{fill:#552222;}#mermaid-svg-a7wblsy3TTJMg0nE .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-a7wblsy3TTJMg0nE .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-a7wblsy3TTJMg0nE .marker{fill:#333333;stroke:#333333;}#mermaid-svg-a7wblsy3TTJMg0nE .marker.cross{stroke:#333333;}#mermaid-svg-a7wblsy3TTJMg0nE svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-a7wblsy3TTJMg0nE p{margin:0;}#mermaid-svg-a7wblsy3TTJMg0nE .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-a7wblsy3TTJMg0nE .cluster-label text{fill:#333;}#mermaid-svg-a7wblsy3TTJMg0nE .cluster-label span{color:#333;}#mermaid-svg-a7wblsy3TTJMg0nE .cluster-label span p{background-color:transparent;}#mermaid-svg-a7wblsy3TTJMg0nE .label text,#mermaid-svg-a7wblsy3TTJMg0nE span{fill:#333;color:#333;}#mermaid-svg-a7wblsy3TTJMg0nE .node rect,#mermaid-svg-a7wblsy3TTJMg0nE .node circle,#mermaid-svg-a7wblsy3TTJMg0nE .node ellipse,#mermaid-svg-a7wblsy3TTJMg0nE .node polygon,#mermaid-svg-a7wblsy3TTJMg0nE .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-a7wblsy3TTJMg0nE .rough-node .label text,#mermaid-svg-a7wblsy3TTJMg0nE .node .label text,#mermaid-svg-a7wblsy3TTJMg0nE .image-shape .label,#mermaid-svg-a7wblsy3TTJMg0nE .icon-shape .label{text-anchor:middle;}#mermaid-svg-a7wblsy3TTJMg0nE .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-a7wblsy3TTJMg0nE .rough-node .label,#mermaid-svg-a7wblsy3TTJMg0nE .node .label,#mermaid-svg-a7wblsy3TTJMg0nE .image-shape .label,#mermaid-svg-a7wblsy3TTJMg0nE .icon-shape .label{text-align:center;}#mermaid-svg-a7wblsy3TTJMg0nE .node.clickable{cursor:pointer;}#mermaid-svg-a7wblsy3TTJMg0nE .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-a7wblsy3TTJMg0nE .arrowheadPath{fill:#333333;}#mermaid-svg-a7wblsy3TTJMg0nE .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-a7wblsy3TTJMg0nE .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-a7wblsy3TTJMg0nE .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-a7wblsy3TTJMg0nE .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-a7wblsy3TTJMg0nE .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-a7wblsy3TTJMg0nE .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-a7wblsy3TTJMg0nE .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-a7wblsy3TTJMg0nE .cluster text{fill:#333;}#mermaid-svg-a7wblsy3TTJMg0nE .cluster span{color:#333;}#mermaid-svg-a7wblsy3TTJMg0nE div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-a7wblsy3TTJMg0nE .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-a7wblsy3TTJMg0nE rect.text{fill:none;stroke-width:0;}#mermaid-svg-a7wblsy3TTJMg0nE .icon-shape,#mermaid-svg-a7wblsy3TTJMg0nE .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-a7wblsy3TTJMg0nE .icon-shape p,#mermaid-svg-a7wblsy3TTJMg0nE .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-a7wblsy3TTJMg0nE .icon-shape .label rect,#mermaid-svg-a7wblsy3TTJMg0nE .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-a7wblsy3TTJMg0nE .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-a7wblsy3TTJMg0nE .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-a7wblsy3TTJMg0nE :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-a7wblsy3TTJMg0nE .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-a7wblsy3TTJMg0nE .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-a7wblsy3TTJMg0nE .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bcd\u5d4c\u5165\u4e0e\u4f4d\u7f6e\u5d4c\u5165<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6b8b\u5dee\u6d41\u8d77\u70b9<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b2c 1 \u5c42\u6ce8\u610f\u529b\u8bfb\u6d41\u5199\u6d41<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b2c 1 \u5c42 FFN \u8bfb\u6d41\u5199\u6d41<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b2c 2 \u5c42\u6ce8\u610f\u529b\u8bfb\u6d41\u5199\u6d41<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u540e\u7eed\u5c42\u6301\u7eed\u8ffd\u52a0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>final norm \u7a33\u538b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5934\u53d6\u8bcd\u8868\u5206\u5e03<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4efb\u610f\u5c42\u53ef\u8bfb\u65e9\u671f\u4fe1\u606f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5199\u5165\u4e0d\u8986\u76d6\u53ea\u53e0\u52a0<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d I \u4e0e J \u4e24\u6761\u865a\u7ebf\u6807\u6ce8\u7684\u6027\u8d28&#xff0c;\u662f\u6b8b\u5dee\u6d41\u4e0e\u666e\u901a\u9010\u5c42\u66ff\u6362\u5f0f\u7f51\u7edc\u7684\u672c\u8d28\u533a\u522b\u3002\u4fe1\u606f\u53ef\u4ee5\u8de8\u5c42\u76f4\u8fbe&#xff0c;\u4fee\u6539\u4ee5\u53e0\u52a0\u65b9\u5f0f\u8fdb\u884c\u3002<\/p>\n<h4>4.4 \u5c42\u95f4\u8303\u6570\u589e\u957f\u73b0\u8c61<\/h4>\n<p>Pre-LN \u4e3b\u5e72\u4e0a\u53ea\u6709\u52a0\u6cd5&#xff0c;\u6bcf\u5c42\u5b50\u5c42\u5f80\u6d41\u91cc\u52a0\u4e00\u4efd\u975e\u96f6\u8f93\u51fa\u3002\u76f4\u89c2\u9884\u671f\u662f\u8303\u6570\u9010\u5c42\u589e\u957f&#xff0c;\u5b9e\u6d4b\u4e5f\u786e\u5b9e\u5982\u6b64\u3002<\/p>\n<p><span class=\"token comment\"># \u5c42\u95f4\u6b8b\u5dee\u6d41\u8303\u6570\u6d4b\u91cf&#xff08;PyTorch 2.13 CPU&#xff0c;PreLNBlock \u89c1 2.1 \u8282&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p>torch<span class=\"token punctuation\">.<\/span>manual_seed<span class=\"token punctuation\">(<\/span><span class=\"token number\">11<\/span><span class=\"token punctuation\">)<\/span><br \/>\nd<span class=\"token punctuation\">,<\/span> L <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">12<\/span><br \/>\nblocks <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>ModuleList<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>PreLNBlock<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d <span class=\"token operator\">*<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>L<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\nfinal_ln <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><\/p>\n<p>x <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">16<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\nnorms <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span>          <span class=\"token comment\"># \u8d77\u70b9\u7ea6 sqrt(128)&#061;11.31<\/span><br \/>\n<span class=\"token keyword\">for<\/span> blk <span class=\"token keyword\">in<\/span> blocks<span class=\"token punctuation\">:<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> blk<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n    norms<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span><span class=\"token builtin\">round<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>norms<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># [11.25, 11.42, 11.68, 11.9, 12.06, 12.32, 12.48, 12.69, 12.92, 13.1, 13.31, 13.49, 13.66]<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;final LN \u540e\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> final_ln<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># 11.31 \u7ea6 sqrt(128)<\/span><\/p>\n<p>grow <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>norms<span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">\/<\/span> norms<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">**<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>norms<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;\u6bcf\u5c42\u5e73\u5747\u589e\u957f\u7387: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>grow<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.2%<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span>             <span class=\"token comment\"># \u7ea6 1.6%<\/span><\/p>\n<p>\u6570\u5b57\u672c\u8eab\u8bf4\u660e\u4e24\u4ef6\u4e8b\u300212 \u5c42\u6a21\u578b\u8303\u6570\u4ece 11.25 \u6da8\u5230 13.66&#xff0c;\u7ea6 1.21 \u500d&#xff0c;\u5e73\u5747\u6bcf\u5c42\u589e\u957f 1.6%\u3002\u589e\u957f\u5e73\u7a33\u5355\u8c03&#xff0c;\u8bf4\u660e\u6bcf\u5c42\u90fd\u5728\u5411\u4e3b\u5e72\u5199\u5165\u975e\u96f6\u8f93\u51fa\u3002<\/p>\n<p>\u521d\u59cb\u5316\u9636\u6bb5\u7684\u589e\u957f\u7387\u4e0d\u5927&#xff0c;\u8bad\u7ec3\u4e2d\u540e\u671f\u4f1a\u660e\u663e\u653e\u5927\u3002\u539f\u56e0\u662f\u5404\u5b50\u5c42\u6743\u91cd\u4ece\u8fd1\u96f6\u6210\u957f\u4e3a\u6709\u6548\u5e45\u5ea6&#xff0c;\u5199\u5165\u91cf\u968f\u4e4b\u4e0a\u5347\u3002final LN \u540e\u8303\u6570\u56de\u5230 11.31&#xff0c;\u5373 sqrt(128)\u3002\u8fd9\u5c31\u662f final norm \u5b58\u5728\u7684\u76f4\u63a5\u7406\u7531&#xff1a;\u8f93\u51fa\u5934\u9700\u8981\u5e45\u5ea6\u53ef\u63a7\u7684\u8f93\u5165\u3002<\/p>\n<p>\u8fd9\u4e2a\u73b0\u8c61\u8fd8\u6709\u4e00\u5c42\u542b\u4e49\u3002\u8303\u6570\u589e\u957f\u610f\u5473\u7740\u540e\u671f\u5c42\u7684\u76f8\u5bf9\u5199\u5165\u91cf\u5728\u53d8\u5c0f\u3002\u6709\u5de5\u4f5c\u636e\u6b64\u8ba8\u8bba\u6df1 Pre-LN \u6a21\u578b\u540e\u6bb5\u5c42\u7684\u8d21\u732e\u8fb9\u9645\u9012\u51cf\u3002\u672c\u7cfb\u5217\u4e0d\u5c55\u5f00\u7ed3\u8bba&#xff0c;\u53ea\u8bb0\u5f55\u73b0\u8c61\u3002<\/p>\n<p>\u5bf9\u6bd4 Post-LN\u3002\u4e3b\u5e72\u6bcf\u5c42\u88ab LN \u9489\u56de sqrt(d)&#xff0c;\u4e0d\u5b58\u5728\u589e\u957f&#xff0c;\u4e5f\u5c31\u4e0d\u9700\u8981 final norm\u3002\u8fd9\u662f\u4e24\u79cd\u67b6\u6784\u5728\u7ed3\u6784\u4e0a\u7684\u4e00\u4e2a\u4f34\u751f\u5dee\u5f02\u3002<\/p>\n<p>  #mermaid-svg-e3Q5Qupt5zsxqiKv{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-e3Q5Qupt5zsxqiKv .error-icon{fill:#552222;}#mermaid-svg-e3Q5Qupt5zsxqiKv .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-e3Q5Qupt5zsxqiKv .marker{fill:#333333;stroke:#333333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .marker.cross{stroke:#333333;}#mermaid-svg-e3Q5Qupt5zsxqiKv svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-e3Q5Qupt5zsxqiKv p{margin:0;}#mermaid-svg-e3Q5Qupt5zsxqiKv .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .cluster-label text{fill:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .cluster-label span{color:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .cluster-label span p{background-color:transparent;}#mermaid-svg-e3Q5Qupt5zsxqiKv .label text,#mermaid-svg-e3Q5Qupt5zsxqiKv span{fill:#333;color:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .node rect,#mermaid-svg-e3Q5Qupt5zsxqiKv .node circle,#mermaid-svg-e3Q5Qupt5zsxqiKv .node ellipse,#mermaid-svg-e3Q5Qupt5zsxqiKv .node polygon,#mermaid-svg-e3Q5Qupt5zsxqiKv .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .rough-node .label text,#mermaid-svg-e3Q5Qupt5zsxqiKv .node .label text,#mermaid-svg-e3Q5Qupt5zsxqiKv .image-shape .label,#mermaid-svg-e3Q5Qupt5zsxqiKv .icon-shape .label{text-anchor:middle;}#mermaid-svg-e3Q5Qupt5zsxqiKv .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .rough-node .label,#mermaid-svg-e3Q5Qupt5zsxqiKv .node .label,#mermaid-svg-e3Q5Qupt5zsxqiKv .image-shape .label,#mermaid-svg-e3Q5Qupt5zsxqiKv .icon-shape .label{text-align:center;}#mermaid-svg-e3Q5Qupt5zsxqiKv .node.clickable{cursor:pointer;}#mermaid-svg-e3Q5Qupt5zsxqiKv .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .arrowheadPath{fill:#333333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-e3Q5Qupt5zsxqiKv .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-e3Q5Qupt5zsxqiKv .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-e3Q5Qupt5zsxqiKv .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-e3Q5Qupt5zsxqiKv .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .cluster text{fill:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv .cluster span{color:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-e3Q5Qupt5zsxqiKv .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-e3Q5Qupt5zsxqiKv rect.text{fill:none;stroke-width:0;}#mermaid-svg-e3Q5Qupt5zsxqiKv .icon-shape,#mermaid-svg-e3Q5Qupt5zsxqiKv .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-e3Q5Qupt5zsxqiKv .icon-shape p,#mermaid-svg-e3Q5Qupt5zsxqiKv .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-e3Q5Qupt5zsxqiKv .icon-shape .label rect,#mermaid-svg-e3Q5Qupt5zsxqiKv .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-e3Q5Qupt5zsxqiKv .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-e3Q5Qupt5zsxqiKv .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-e3Q5Qupt5zsxqiKv :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-e3Q5Qupt5zsxqiKv .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-e3Q5Qupt5zsxqiKv .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-e3Q5Qupt5zsxqiKv .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN \u6b8b\u5dee\u6d41\u8303\u6570<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6bcf\u5c42\u5b50\u5c42\u5199\u5165\u975e\u96f6\u8f93\u51fa<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8303\u6570\u5355\u8c03\u589e\u957f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>12 \u5c42\u5b9e\u6d4b 11.25 \u5230 13.66<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u4e2d\u540e\u671f\u589e\u901f\u653e\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5934\u8f93\u5165\u5e45\u5ea6\u5931\u63a7<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9700\u5728\u9884\u6d4b\u5934\u524d\u52a0 final LN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8303\u6570\u56de\u5230 sqrt d<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u4ece C \u5230 G \u7684\u56e0\u679c\u94fe\u662f Pre-LN \u67b6\u6784\u7684\u5fc5\u9009\u9879&#xff0c;\u4e0d\u662f\u53ef\u9009\u4f18\u5316\u3002\u6f0f\u6389 final norm \u662f\u65b0\u624b\u5b9e\u73b0\u91cc\u6700\u5e38\u89c1\u7684 bug \u4e4b\u4e00\u3002<\/p>\n<h3>5. \u73b0\u4ee3\u53d8\u4f53&#xff1a;QK-Norm \u4e0e Sandwich<\/h3>\n<h4>5.1 QK-Norm&#xff1a;\u628a\u5f52\u4e00\u5316\u63a8\u8fdb\u6ce8\u610f\u529b\u5185\u90e8<\/h4>\n<p>QK-Norm \u662f\u628a RMSNorm \u7528\u5728\u6ce8\u610f\u529b\u7684 query \u4e0e key \u6295\u5f71\u4e4b\u540e\u3001\u70b9\u79ef\u4e4b\u524d\u3002\u8fd9\u4e00\u6b65\u5728\u4e3b\u5e72\u5f52\u4e00\u5316\u4e4b\u5916&#xff0c;\u5c5e\u4e8e\u9488\u5bf9\u6ce8\u610f\u529b\u5185\u90e8\u7684\u989d\u5916\u7a33\u538b\u3002<\/p>\n<p>\u6807\u51c6\u6ce8\u610f\u529b\u7684\u5206\u6bcd\u662f sqrt(d_k)&#xff0c;\u5373\u7b2c 3 \u7bc7\u8bb2\u8fc7\u7684\u7f29\u653e\u3002\u8fd9\u4e2a\u7f29\u653e\u5047\u8bbe q \u4e0e k \u7684\u6bcf\u4e2a\u5206\u91cf\u5355\u4f4d\u65b9\u5dee\u3002\u6df1\u6a21\u578b\u8bad\u7ec3\u5230\u540e\u671f&#xff0c;q \u4e0e k \u7684\u8303\u6570\u4f1a\u6da8\u3002\u70b9\u79ef\u8fdb\u5165 softmax \u9971\u548c\u533a&#xff0c;\u6ce8\u610f\u529b\u5206\u5e03\u9000\u5316\u4e3a\u8fd1\u4f3c one-hot&#xff0c;\u68af\u5ea6\u6d88\u5931\u3002<\/p>\n<p>QK-Norm \u7684\u505a\u6cd5\u662f\u76f4\u63a5\u5bf9 q \u4e0e k \u5404\u505a\u4e00\u6b21 RMSNorm&#xff0c;\u518d\u7b97\u70b9\u79ef\u3002\u8303\u6570\u88ab\u9489\u6b7b&#xff0c;softmax \u8f93\u5165\u8303\u56f4\u53d7\u63a7&#xff0c;\u6ce8\u610f\u529b\u71b5\u4e0d\u4f1a\u584c\u7f29\u3002\u7ed3\u6784\u4e0a\u5b83\u4e0e\u7b2c 3 \u7bc7\u7684\u9664\u4ee5 sqrt(d_k) \u5f62\u6210\u4e92\u8865\u3002\u540e\u8005\u662f\u56fa\u5b9a\u7f29\u653e&#xff0c;\u524d\u8005\u662f\u81ea\u9002\u5e94\u7f29\u653e\u3002<\/p>\n<p>\u53ef\u6eaf\u6e90\u7684\u516c\u5f00\u53e3\u5f84\u6765\u81ea Qwen3 \u6280\u672f\u62a5\u544a&#xff1a;\u5f15\u5165 QK-Norm \u5230\u6ce8\u610f\u529b\u673a\u5236\u4ee5\u4fdd\u8bc1 Qwen3 \u7684\u8bad\u7ec3\u7a33\u5b9a\u3002\u6700\u65e9\u628a\u7c7b\u4f3c\u505a\u6cd5\u5e26\u8fdb\u5927\u89c4\u6a21\u8bad\u7ec3\u7684\u516c\u5f00\u62a5\u544a\u662f ViT-22B&#xff08;arXiv:2302.05442&#xff09;\u3002\u5b83\u5728\u89c6\u89c9 Transformer \u4e0a\u5bf9 q \u4e0e k \u505a\u5c42\u5f52\u4e00\u5316\u3002<\/p>\n<p><span class=\"token comment\"># QK-Norm \u7684\u6700\u5c0f\u5b9e\u73b0\u9aa8\u67b6&#xff08;PyTorch 2.13&#xff0c;\u5f62\u72b6\u6807\u6ce8\u5728\u6ce8\u91ca&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn<span class=\"token punctuation\">.<\/span>functional <span class=\"token keyword\">as<\/span> F<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">QKNormAttention<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> heads<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>h<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>dk <span class=\"token operator\">&#061;<\/span> heads<span class=\"token punctuation\">,<\/span> d <span class=\"token operator\">\/\/<\/span> heads<br \/>\n        self<span class=\"token punctuation\">.<\/span>wq <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> bias<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>wk <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> bias<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>wv <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> bias<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>q_norm <span class=\"token operator\">&#061;<\/span> RMSNorm<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>dk<span class=\"token punctuation\">)<\/span>             <span class=\"token comment\"># \u590d\u7528 3.4 \u8282\u5b9e\u73b0<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>k_norm <span class=\"token operator\">&#061;<\/span> RMSNorm<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>dk<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        b<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">,<\/span> d <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">.<\/span>shape<br \/>\n        q <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>wq<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>view<span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>h<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>dk<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>transpose<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># b h s dk<\/span><br \/>\n        k <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>wk<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>view<span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>h<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>dk<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>transpose<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        v <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>wv<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>view<span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>h<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>dk<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>transpose<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        q<span class=\"token punctuation\">,<\/span> k <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>q_norm<span class=\"token punctuation\">(<\/span>q<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>k_norm<span class=\"token punctuation\">(<\/span>k<span class=\"token punctuation\">)<\/span>      <span class=\"token comment\"># \u70b9\u79ef\u524d\u7a33\u538b q \u4e0e k<\/span><br \/>\n        att <span class=\"token operator\">&#061;<\/span> F<span class=\"token punctuation\">.<\/span>scaled_dot_product_attention<span class=\"token punctuation\">(<\/span>q<span class=\"token punctuation\">,<\/span> k<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> att<span class=\"token punctuation\">.<\/span>transpose<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u4ee3\u7801\u91cc q_norm \u4e0e k_norm \u4e24\u884c\u662f\u5168\u90e8\u6539\u52a8\u3002\u6ce8\u610f\u5b83\u4eec\u4f5c\u7528\u5728 head \u7ef4\u5185\u90e8&#xff0c;\u5373\u6bcf\u4e2a\u5934\u7684 dk \u7ef4\u4e0a&#xff0c;\u4e0d\u662f\u6574\u6761\u7279\u5f81\u7ef4\u3002<\/p>\n<p>\u4ee3\u4ef7\u662f\u6bcf\u5c42\u591a\u4e24\u6b21\u5c0f\u5f52\u4e00\u5316&#xff0c;\u53c2\u6570\u91cf\u589e\u52a0\u7ea6 2d\u3002\u6362\u6765\u7684\u662f\u6ce8\u610f\u529b\u5206\u5e03\u53ef\u63a7&#xff0c;\u6df1\u5c42\u5927\u6a21\u578b\u8bad\u7ec3\u540e\u671f\u7684 loss \u5c16\u5cf0\u51cf\u5c11\u3002<\/p>\n<p>\u793e\u533a\u5b9e\u8df5\u91cc\u8fd8\u6709 QK-Norm \u4e0e logit \u8f6f\u9650\u5e45\u7684\u7ec4\u5408\u7528\u6cd5\u3002\u5982 qk clamp\u3001softmax cap\u3002\u53e3\u5f84\u4e0d\u4e00&#xff0c;\u672c\u7bc7\u4e0d\u5c55\u5f00\u3002<\/p>\n<p>  #mermaid-svg-H64iW5lEahv0oZ6f{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-H64iW5lEahv0oZ6f .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-H64iW5lEahv0oZ6f .error-icon{fill:#552222;}#mermaid-svg-H64iW5lEahv0oZ6f .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-H64iW5lEahv0oZ6f .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-H64iW5lEahv0oZ6f .marker{fill:#333333;stroke:#333333;}#mermaid-svg-H64iW5lEahv0oZ6f .marker.cross{stroke:#333333;}#mermaid-svg-H64iW5lEahv0oZ6f svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-H64iW5lEahv0oZ6f p{margin:0;}#mermaid-svg-H64iW5lEahv0oZ6f .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-H64iW5lEahv0oZ6f .cluster-label text{fill:#333;}#mermaid-svg-H64iW5lEahv0oZ6f .cluster-label span{color:#333;}#mermaid-svg-H64iW5lEahv0oZ6f .cluster-label span p{background-color:transparent;}#mermaid-svg-H64iW5lEahv0oZ6f .label text,#mermaid-svg-H64iW5lEahv0oZ6f span{fill:#333;color:#333;}#mermaid-svg-H64iW5lEahv0oZ6f .node rect,#mermaid-svg-H64iW5lEahv0oZ6f .node circle,#mermaid-svg-H64iW5lEahv0oZ6f .node ellipse,#mermaid-svg-H64iW5lEahv0oZ6f .node polygon,#mermaid-svg-H64iW5lEahv0oZ6f .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-H64iW5lEahv0oZ6f .rough-node .label text,#mermaid-svg-H64iW5lEahv0oZ6f .node .label text,#mermaid-svg-H64iW5lEahv0oZ6f .image-shape .label,#mermaid-svg-H64iW5lEahv0oZ6f .icon-shape .label{text-anchor:middle;}#mermaid-svg-H64iW5lEahv0oZ6f .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-H64iW5lEahv0oZ6f .rough-node .label,#mermaid-svg-H64iW5lEahv0oZ6f .node .label,#mermaid-svg-H64iW5lEahv0oZ6f .image-shape .label,#mermaid-svg-H64iW5lEahv0oZ6f .icon-shape .label{text-align:center;}#mermaid-svg-H64iW5lEahv0oZ6f .node.clickable{cursor:pointer;}#mermaid-svg-H64iW5lEahv0oZ6f .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-H64iW5lEahv0oZ6f .arrowheadPath{fill:#333333;}#mermaid-svg-H64iW5lEahv0oZ6f .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-H64iW5lEahv0oZ6f .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-H64iW5lEahv0oZ6f .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-H64iW5lEahv0oZ6f .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-H64iW5lEahv0oZ6f .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-H64iW5lEahv0oZ6f .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-H64iW5lEahv0oZ6f .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-H64iW5lEahv0oZ6f .cluster text{fill:#333;}#mermaid-svg-H64iW5lEahv0oZ6f .cluster span{color:#333;}#mermaid-svg-H64iW5lEahv0oZ6f div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-H64iW5lEahv0oZ6f .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-H64iW5lEahv0oZ6f rect.text{fill:none;stroke-width:0;}#mermaid-svg-H64iW5lEahv0oZ6f .icon-shape,#mermaid-svg-H64iW5lEahv0oZ6f .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-H64iW5lEahv0oZ6f .icon-shape p,#mermaid-svg-H64iW5lEahv0oZ6f .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-H64iW5lEahv0oZ6f .icon-shape .label rect,#mermaid-svg-H64iW5lEahv0oZ6f .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-H64iW5lEahv0oZ6f .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-H64iW5lEahv0oZ6f .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-H64iW5lEahv0oZ6f :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-H64iW5lEahv0oZ6f .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-H64iW5lEahv0oZ6f .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-H64iW5lEahv0oZ6f .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u5165 x<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ebf\u6027\u6295\u5f71\u5f97 q k v<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>q \u8fc7 RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>k \u8fc7 RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>q k \u70b9\u79ef<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>softmax \u5f97\u6ce8\u610f\u529b\u6743\u91cd<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>v \u4e0d\u505a\u5f52\u4e00\u5316<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6743\u91cd\u4e58 v \u6c42\u548c<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4f5c\u7528 \u9489\u4f4f q k \u8303\u6570<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4f5c\u7528 \u9632\u6b62 softmax \u9971\u548c<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d v \u5206\u652f\u4e0d\u505a\u5f52\u4e00\u5316&#xff0c;\u8fd9\u662f QK-Norm \u7684\u547d\u540d\u6765\u6e90&#xff1a;\u53ea\u7a33\u538b\u51b3\u5b9a\u5206\u5e03\u7684 q \u4e0e k&#xff0c;\u4e0d\u52a8\u5185\u5bb9\u8f7d\u4f53 v\u3002<\/p>\n<h4>5.2 DeepNorm \u4e0e Sandwich Norm<\/h4>\n<p>DeepNorm&#xff08;arXiv:2203.00555&#xff09;\u9488\u5bf9 Post-LN \u6df1\u5c42\u5316\u3002\u5b83\u628a\u6b8b\u5dee\u5206\u652f\u653e\u5927 alpha \u500d&#xff08;\u4e0e\u5c42\u6570\u76f8\u5173&#xff09;&#xff0c;\u5e76\u914d\u7279\u6b8a\u521d\u59cb\u5316\u3002\u8fd9\u6837\u5343\u5c42 Post-LN \u4e5f\u53ef\u8bad\u3002\u601d\u8def\u662f\u4fdd\u7559 Post-LN \u7684\u8d28\u91cf\u4f18\u52bf&#xff0c;\u540c\u65f6\u538b\u4f4f\u5b83\u7684\u68af\u5ea6\u95ee\u9898\u3002<\/p>\n<p>Sandwich Norm \u6307\u5728\u5b50\u5c42\u524d\u540e\u5404\u653e\u4e00\u6b21\u5f52\u4e00\u5316&#xff0c;\u5f62\u6210\u5939\u5fc3\u7ed3\u6784\u3002\u52a8\u673a\u662f Pre-LN \u53ea\u7ea6\u675f\u8f93\u5165\u4e0d\u7ea6\u675f\u8f93\u51fa&#xff0c;\u52a0\u4e00\u6b21\u540e\u7f6e\u5f52\u4e00\u5316\u8865\u4e0a\u3002\u53e3\u8bed\u7cfb\u7edf\u4e0e\u90e8\u5206\u8bed\u97f3\u6a21\u578b\u91c7\u7528\u8fc7\u8fd9\u7c7b\u7ed3\u6784&#xff0c;\u793e\u533a\u53e3\u5f84\u4e0d\u4e00&#xff0c;\u6ca1\u6709\u7edf\u4e00\u6807\u51c6\u540d\u3002<\/p>\n<p>\u8fd9\u4e24\u6761\u7ebf\u7684\u5171\u540c\u70b9&#xff1a;\u90fd\u5728\u8c03\u6574\u5f52\u4e00\u5316\u7684\u4f4d\u7f6e\u4e0e\u7f29\u653e\u7cfb\u6570&#xff0c;\u800c\u4e0d\u662f\u53d1\u660e\u65b0\u7edf\u8ba1\u91cf\u3002\u7edf\u8ba1\u8f74\u4ecd\u7136\u662f\u6837\u672c\u5185\u7279\u5f81\u7ef4\u3002<\/p>\n<p>\u4e00\u53e5\u8bdd\u5f52\u4f4d\u3002QK-Norm \u52a0\u4f4d\u7f6e&#xff08;\u6ce8\u610f\u529b\u5185\u90e8&#xff09;&#xff0c;DeepNorm \u52a0\u7cfb\u6570&#xff08;\u6b8b\u5dee\u7f29\u653e&#xff09;\u3002Sandwich \u52a0\u6b21\u6570&#xff08;\u524d\u540e\u53cc\u4efd&#xff09;\u3002\u5f52\u4e00\u5316\u5bb6\u65cf\u7684\u6f14\u5316\u4e3b\u8981\u662f\u8fd9\u4e09\u4e2a\u81ea\u7531\u5ea6\u3002<\/p>\n<p>  #mermaid-svg-c0dyKG87g9q2u51c{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-c0dyKG87g9q2u51c .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-c0dyKG87g9q2u51c .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-c0dyKG87g9q2u51c .error-icon{fill:#552222;}#mermaid-svg-c0dyKG87g9q2u51c .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-c0dyKG87g9q2u51c .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-c0dyKG87g9q2u51c .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-c0dyKG87g9q2u51c .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-c0dyKG87g9q2u51c .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-c0dyKG87g9q2u51c .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-c0dyKG87g9q2u51c .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-c0dyKG87g9q2u51c .marker{fill:#333333;stroke:#333333;}#mermaid-svg-c0dyKG87g9q2u51c .marker.cross{stroke:#333333;}#mermaid-svg-c0dyKG87g9q2u51c svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-c0dyKG87g9q2u51c p{margin:0;}#mermaid-svg-c0dyKG87g9q2u51c .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-c0dyKG87g9q2u51c .cluster-label text{fill:#333;}#mermaid-svg-c0dyKG87g9q2u51c .cluster-label span{color:#333;}#mermaid-svg-c0dyKG87g9q2u51c .cluster-label span p{background-color:transparent;}#mermaid-svg-c0dyKG87g9q2u51c .label text,#mermaid-svg-c0dyKG87g9q2u51c span{fill:#333;color:#333;}#mermaid-svg-c0dyKG87g9q2u51c .node rect,#mermaid-svg-c0dyKG87g9q2u51c .node circle,#mermaid-svg-c0dyKG87g9q2u51c .node ellipse,#mermaid-svg-c0dyKG87g9q2u51c .node polygon,#mermaid-svg-c0dyKG87g9q2u51c .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-c0dyKG87g9q2u51c .rough-node .label text,#mermaid-svg-c0dyKG87g9q2u51c .node .label text,#mermaid-svg-c0dyKG87g9q2u51c .image-shape .label,#mermaid-svg-c0dyKG87g9q2u51c .icon-shape .label{text-anchor:middle;}#mermaid-svg-c0dyKG87g9q2u51c .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-c0dyKG87g9q2u51c .rough-node .label,#mermaid-svg-c0dyKG87g9q2u51c .node .label,#mermaid-svg-c0dyKG87g9q2u51c .image-shape .label,#mermaid-svg-c0dyKG87g9q2u51c .icon-shape .label{text-align:center;}#mermaid-svg-c0dyKG87g9q2u51c .node.clickable{cursor:pointer;}#mermaid-svg-c0dyKG87g9q2u51c .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-c0dyKG87g9q2u51c .arrowheadPath{fill:#333333;}#mermaid-svg-c0dyKG87g9q2u51c .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-c0dyKG87g9q2u51c .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-c0dyKG87g9q2u51c .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-c0dyKG87g9q2u51c .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-c0dyKG87g9q2u51c .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-c0dyKG87g9q2u51c .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-c0dyKG87g9q2u51c .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-c0dyKG87g9q2u51c .cluster text{fill:#333;}#mermaid-svg-c0dyKG87g9q2u51c .cluster span{color:#333;}#mermaid-svg-c0dyKG87g9q2u51c div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-c0dyKG87g9q2u51c .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-c0dyKG87g9q2u51c rect.text{fill:none;stroke-width:0;}#mermaid-svg-c0dyKG87g9q2u51c .icon-shape,#mermaid-svg-c0dyKG87g9q2u51c .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-c0dyKG87g9q2u51c .icon-shape p,#mermaid-svg-c0dyKG87g9q2u51c .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-c0dyKG87g9q2u51c .icon-shape .label rect,#mermaid-svg-c0dyKG87g9q2u51c .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-c0dyKG87g9q2u51c .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-c0dyKG87g9q2u51c .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-c0dyKG87g9q2u51c :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-c0dyKG87g9q2u51c .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-c0dyKG87g9q2u51c .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-c0dyKG87g9q2u51c .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316\u8bbe\u8ba1\u7a7a\u95f4<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7edf\u8ba1\u8f74 \u81ea\u7531\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4f4d\u7f6e \u81ea\u7531\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7cfb\u6570\u4e0e\u6b21\u6570 \u81ea\u7531\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>LayerNorm \u51cf mean \u9664 std<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u53ea\u9664\u5747\u65b9\u6839<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN \u4e3b\u5e72\u4e0a<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN \u5b50\u5c42\u5185<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>QK-Norm \u6ce8\u610f\u529b\u6295\u5f71\u540e<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>DeepNorm \u6b8b\u5dee\u653e\u5927 alpha<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Sandwich \u524d\u540e\u5404\u4e00\u6b21<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u628a\u672c\u7bc7\u8bb2\u8fc7\u7684\u6240\u6709\u53d8\u4f53\u653e\u8fdb\u540c\u4e00\u4e2a\u4e09\u81ea\u7531\u5ea6\u5750\u6807\u7cfb\u3002\u540e\u7eed\u51fa\u73b0\u7684\u65b0\u53d8\u4f53\u5927\u6982\u7387\u4e5f\u662f\u8fd9\u4e09\u4e2a\u65cb\u94ae\u7684\u7ec4\u5408\u3002<\/p>\n<h4>5.3 \u53d8\u4f53\u9009\u62e9\u7684\u51b3\u7b56\u8868<\/h4>\n<p>\u843d\u5230\u5de5\u7a0b\u51b3\u7b56\u3002\u6309\u573a\u666f\u7ed9\u4e00\u5f20\u8868&#xff0c;\u53e3\u5f84\u57fa\u4e8e\u524d\u6587\u5f15\u7528\u7684\u8bba\u6587\u4e0e\u4e3b\u6d41\u5f00\u6e90\u5b9e\u73b0\u3002<\/p>\n<table>\n<tr>\u573a\u666f\u63a8\u8350\u5f62\u6001\u7406\u7531\u4f9d\u636e<\/tr>\n<tbody>\n<tr>\n<td>\u5c0f\u6a21\u578b\u3001\u8ffd\u6c42\u6781\u81f4\u8d28\u91cf<\/td>\n<td>Post-LN \u52a0 warmup<\/td>\n<td>\u9690\u5f0f\u6b63\u5219\u53ef\u80fd\u5e26\u6765\u66f4\u597d\u7ec8\u503c<\/td>\n<td>2002.04745 \u5b9e\u9a8c<\/td>\n<\/tr>\n<tr>\n<td>\u6df1\u5c42\u6216\u8d85\u5927\u6a21\u578b<\/td>\n<td>Pre-RMSNorm<\/td>\n<td>\u8bad\u7ec3\u7a33\u3001\u514d warmup\u3001\u7b97\u5b50\u4fbf\u5b9c<\/td>\n<td>LLaMA\u3001Qwen3 \u5b9e\u8df5<\/td>\n<\/tr>\n<tr>\n<td>\u5343\u5c42\u7ea7\u6781\u7aef\u6df1\u5ea6<\/td>\n<td>DeepNorm<\/td>\n<td>Post-LN \u53ef\u6269\u5c55\u81f3\u5343\u5c42<\/td>\n<td>2203.00555<\/td>\n<\/tr>\n<tr>\n<td>\u5927\u6a21\u578b\u8bad\u7ec3\u540e\u671f loss \u5c16\u5cf0<\/td>\n<td>\u52a0 QK-Norm<\/td>\n<td>\u9489\u4f4f\u6ce8\u610f\u529b logits<\/td>\n<td>Qwen3\u3001ViT-22B<\/td>\n<\/tr>\n<tr>\n<td>\u590d\u73b0\u8001 checkpoint<\/td>\n<td>\u6cbf\u7528\u539f\u67b6\u6784<\/td>\n<td>\u6743\u91cd\u4e0d\u517c\u5bb9&#xff0c;\u89c1 7.3<\/td>\n<td>\u5b9e\u8df5\u7ecf\u9a8c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8868\u7684\u7b2c\u4e00\u884c\u8981\u52a0\u9650\u5b9a\u3002Post-LN \u7684\u8d28\u91cf\u4f18\u52bf\u662f\u8c03\u53c2\u5230\u4f4d\u540e\u53ef\u80fd\u7565\u4f18&#xff0c;\u4e0d\u662f\u666e\u904d\u7ed3\u8bba\u3002\u591a\u6570\u573a\u666f\u4e0b\u7b2c 2 \u884c\u662f\u66f4\u5b89\u5168\u7684\u9009\u62e9\u3002<\/p>\n<p>  #mermaid-svg-NMtvpYqMuV3BlgSw{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-NMtvpYqMuV3BlgSw .error-icon{fill:#552222;}#mermaid-svg-NMtvpYqMuV3BlgSw .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-NMtvpYqMuV3BlgSw .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-NMtvpYqMuV3BlgSw .marker{fill:#333333;stroke:#333333;}#mermaid-svg-NMtvpYqMuV3BlgSw .marker.cross{stroke:#333333;}#mermaid-svg-NMtvpYqMuV3BlgSw svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-NMtvpYqMuV3BlgSw p{margin:0;}#mermaid-svg-NMtvpYqMuV3BlgSw .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw .cluster-label text{fill:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw .cluster-label span{color:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw .cluster-label span p{background-color:transparent;}#mermaid-svg-NMtvpYqMuV3BlgSw .label text,#mermaid-svg-NMtvpYqMuV3BlgSw span{fill:#333;color:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw .node rect,#mermaid-svg-NMtvpYqMuV3BlgSw .node circle,#mermaid-svg-NMtvpYqMuV3BlgSw .node ellipse,#mermaid-svg-NMtvpYqMuV3BlgSw .node polygon,#mermaid-svg-NMtvpYqMuV3BlgSw .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-NMtvpYqMuV3BlgSw .rough-node .label text,#mermaid-svg-NMtvpYqMuV3BlgSw .node .label text,#mermaid-svg-NMtvpYqMuV3BlgSw .image-shape .label,#mermaid-svg-NMtvpYqMuV3BlgSw .icon-shape .label{text-anchor:middle;}#mermaid-svg-NMtvpYqMuV3BlgSw .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-NMtvpYqMuV3BlgSw .rough-node .label,#mermaid-svg-NMtvpYqMuV3BlgSw .node .label,#mermaid-svg-NMtvpYqMuV3BlgSw .image-shape .label,#mermaid-svg-NMtvpYqMuV3BlgSw .icon-shape .label{text-align:center;}#mermaid-svg-NMtvpYqMuV3BlgSw .node.clickable{cursor:pointer;}#mermaid-svg-NMtvpYqMuV3BlgSw .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-NMtvpYqMuV3BlgSw .arrowheadPath{fill:#333333;}#mermaid-svg-NMtvpYqMuV3BlgSw .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-NMtvpYqMuV3BlgSw .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-NMtvpYqMuV3BlgSw .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-NMtvpYqMuV3BlgSw .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-NMtvpYqMuV3BlgSw .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-NMtvpYqMuV3BlgSw .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-NMtvpYqMuV3BlgSw .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-NMtvpYqMuV3BlgSw .cluster text{fill:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw .cluster span{color:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-NMtvpYqMuV3BlgSw .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-NMtvpYqMuV3BlgSw rect.text{fill:none;stroke-width:0;}#mermaid-svg-NMtvpYqMuV3BlgSw .icon-shape,#mermaid-svg-NMtvpYqMuV3BlgSw .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-NMtvpYqMuV3BlgSw .icon-shape p,#mermaid-svg-NMtvpYqMuV3BlgSw .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-NMtvpYqMuV3BlgSw .icon-shape .label rect,#mermaid-svg-NMtvpYqMuV3BlgSw .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-NMtvpYqMuV3BlgSw .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-NMtvpYqMuV3BlgSw .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-NMtvpYqMuV3BlgSw :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-NMtvpYqMuV3BlgSw .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-NMtvpYqMuV3BlgSw .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-NMtvpYqMuV3BlgSw .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>12 \u5c42\u5185<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u66f4\u6df1\u6216\u8d85\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u662f<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u5426<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u901f\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u7ec8\u503c\u53ef\u8bd5<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9009\u5f52\u4e00\u5316\u65b9\u6848<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6a21\u578b\u591a\u6df1<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN \u53ef\u884c \u4f46\u9700 warmup<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u662f\u5426\u51fa\u73b0 loss \u5c16\u5cf0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u52a0 QK-Norm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ef4\u6301\u73b0\u72b6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8ffd\u6c42\u7ec8\u503c\u8fd8\u662f\u8fed\u4ee3\u901f\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN \u52a0\u7cbe\u7ec6\u8c03\u53c2<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d\u7b2c\u4e00\u6761\u5206\u53c9&#xff08;\u6a21\u578b\u6df1\u5ea6&#xff09;\u662f\u6700\u4e3b\u8981\u7684\u51b3\u7b56\u53d8\u91cf\u3002\u6df1\u5ea6\u4e0a\u53bb\u4e86&#xff0c;Post-LN \u7684\u8c03\u53c2\u6210\u672c\u4f1a\u538b\u8fc7\u5b83\u7684\u8d28\u91cf\u60f3\u8c61\u7a7a\u95f4\u3002<\/p>\n<h3>6. \u5b9e\u9a8c\u5bf9\u6bd4&#xff1a;\u6df1\u5ea6\u3001\u5f52\u4e00\u5316\u4e0e\u4f4d\u7f6e<\/h3>\n<h4>6.1 \u5b9e\u9a8c\u8bbe\u7f6e&#xff1a;\u73a9\u5177\u4efb\u52a1\u4e0e 20 \u5c42\u7f51\u7edc<\/h4>\n<p>\u672c\u8282\u5168\u90e8\u5b9e\u9a8c\u53ef\u5728\u666e\u901a CPU \u4e0a\u590d\u73b0\u3002\u73af\u5883 PyTorch 2.13&#xff0c;\u5355\u8fdb\u7a0b&#xff0c;\u56fa\u5b9a\u968f\u673a\u79cd\u5b50\u3002<\/p>\n<p>\u4efb\u52a1\u9009\u4e0b\u4e00\u4e2a token \u9884\u6d4b\u7684\u7b80\u5316\u7248&#xff1a;\u7ed9\u5b9a\u524d k \u4e2a token&#xff0c;\u9884\u6d4b\u7b2c k \u52a0 1 \u4e2a\u3002\u8bcd\u8868 64&#xff0c;\u5e8f\u5217\u957f 16&#xff0c;\u9690\u85cf\u7ef4 64\u3002\u6570\u636e\u7528\u4e00\u6761\u56fa\u5b9a\u89c4\u5219\u751f\u6210&#xff0c;\u4fdd\u8bc1\u4efb\u52a1\u53ef\u5b66\u4f46\u9700\u8981\u591a\u5c42\u7ec4\u5408\u3002<\/p>\n<p>\u6a21\u578b\u4e3a\u7eaf\u89e3\u7801\u5668\u5806\u53e0\u3002\u5b50\u5c42\u7528\u7b80\u5316\u7248&#xff1a;\u6ce8\u610f\u529b\u66ff\u6362\u4e3a\u5747\u503c\u6c47\u805a&#xff0c;FFN \u7528\u4e24\u5c42\u7ebf\u6027\u52a0 GELU\u3002\u8fd9\u6837\u505a\u7684\u76ee\u7684\u662f\u628a\u53d8\u91cf\u96c6\u4e2d\u5230\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee\u4e0a&#xff0c;\u6392\u9664\u6ce8\u610f\u529b\u7684\u5e72\u6270\u3002<\/p>\n<p>\u56db\u4e2a\u53ef\u5207\u6362\u7684\u914d\u7f6e&#xff1a;\u65e0\u5f52\u4e00\u5316\u3001LayerNorm\u3001RMSNorm\u3002\u518d\u52a0 Post-LN \u4e0e Pre-LN \u4e24\u79cd\u4f4d\u7f6e\u3002\u4f18\u5316\u5668 Adam&#xff0c;\u5b66\u4e60\u7387\u5355\u72ec\u6807\u6ce8&#xff0c;batch 32&#xff0c;\u8bad\u7ec3 3000 \u6b65\u3002<\/p>\n<p><span class=\"token comment\"># \u73a9\u5177\u6df1\u7f51\u7edc\u5b9e\u9a8c\u9aa8\u67b6&#xff08;PyTorch 2.13 CPU&#xff0c;\u5b8c\u6574\u811a\u672c\u7ea6 120 \u884c&#xff0c;\u6b64\u5904\u8282\u9009\u6838\u5fc3&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">ToyBlock<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">,<\/span> norm<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;ln&#034;<\/span><span class=\"token punctuation\">,<\/span> pos<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;pre&#034;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>pos <span class=\"token operator\">&#061;<\/span> pos<br \/>\n        mk <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token string\">&#034;none&#034;<\/span><span class=\"token punctuation\">:<\/span> nn<span class=\"token punctuation\">.<\/span>Identity<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;ln&#034;<\/span><span class=\"token punctuation\">:<\/span> nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">,<\/span><br \/>\n              <span class=\"token string\">&#034;rms&#034;<\/span><span class=\"token punctuation\">:<\/span> RMSNorm<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">[<\/span>norm<span class=\"token punctuation\">]<\/span>              <span class=\"token comment\"># \u590d\u7528 3.4 \u8282 RMSNorm<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>n1<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>n2 <span class=\"token operator\">&#061;<\/span> mk<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> mk<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>mix <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span>               <span class=\"token comment\"># \u5360\u4f4d\u5b50\u5c42\u4e00&#xff1a;\u7ebf\u6027\u6c47\u805a<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>ffn <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Sequential<span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> nn<span class=\"token punctuation\">.<\/span>GELU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                 nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>hidden<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> self<span class=\"token punctuation\">.<\/span>pos <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;pre&#034;<\/span><span class=\"token punctuation\">:<\/span>                    <span class=\"token comment\"># Pre-LN&#xff1a;LN \u8fdb\u5b50\u5c42<\/span><br \/>\n            x <span class=\"token operator\">&#061;<\/span> x <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>mix<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>n1<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            x <span class=\"token operator\">&#061;<\/span> x <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>ffn<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>n2<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">else<\/span><span class=\"token punctuation\">:<\/span>                                    <span class=\"token comment\"># Post-LN&#xff1a;LN \u5728\u5408\u6d41\u540e<\/span><br \/>\n            x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>n1<span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>mix<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>n2<span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">&#043;<\/span> self<span class=\"token punctuation\">.<\/span>ffn<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> x<\/p>\n<p>\u6574\u673a\u628a block \u5806 L \u5c42\u3002final \u6309\u4f4d\u7f6e\u81ea\u52a8\u5f00\u5173&#xff0c;Pre-LN \u8865 LN&#xff0c;Post-LN \u7528 Identity\u3002<\/p>\n<p><span class=\"token comment\"># \u73a9\u5177\u6df1\u7f51\u7edc\u9aa8\u67b6&#xff08;\u7eed&#xff09;&#xff1a;\u6574\u673a\u7ec4\u88c5\u4e0e\u524d\u5411<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">ToyDeepNet<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> d<span class=\"token operator\">&#061;<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> hidden<span class=\"token operator\">&#061;<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> L<span class=\"token operator\">&#061;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> vocab<span class=\"token operator\">&#061;<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">**<\/span>kw<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>emb <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Embedding<span class=\"token punctuation\">(<\/span>vocab<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>blocks <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>ModuleList<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>ToyBlock<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> hidden<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">**<\/span>kw<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>L<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>final <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>LayerNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">if<\/span> kw<span class=\"token punctuation\">.<\/span>get<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;pos&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;pre&#034;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;pre&#034;<\/span><br \/>\n                      <span class=\"token keyword\">else<\/span> nn<span class=\"token punctuation\">.<\/span>Identity<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>head <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> vocab<span class=\"token punctuation\">,<\/span> bias<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> idx<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>emb<span class=\"token punctuation\">(<\/span>idx<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> blk <span class=\"token keyword\">in<\/span> self<span class=\"token punctuation\">.<\/span>blocks<span class=\"token punctuation\">:<\/span><br \/>\n            x <span class=\"token operator\">&#061;<\/span> blk<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> self<span class=\"token punctuation\">.<\/span>head<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>final<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u9aa8\u67b6\u91cc final \u4e00\u884c\u6309\u4f4d\u7f6e\u81ea\u52a8\u5f00\u5173\u3002Pre-LN \u8865 LayerNorm&#xff0c;Post-LN \u7528 Identity\u3002\u8fd9\u4e2a\u7ec6\u8282\u6f0f\u6389\u4f1a\u8ba9 Pre-LN \u7684\u5bf9\u6bd4\u4e0d\u516c\u5e73\u3002<\/p>\n<p>\u8bc4\u4f30\u53e3\u5f84\u7edf\u4e00\u4e3a\u4ea4\u53c9\u71b5\u635f\u5931&#xff0c;\u8bad\u7ec3\u66f2\u7ebf\u4e0a\u6bcf 500 \u6b65\u53d6\u4e00\u6b21\u9a8c\u8bc1\u635f\u5931\u3002\u6240\u6709\u914d\u7f6e\u7528\u540c\u4e00\u4efd\u6570\u636e\u4e0e\u540c\u4e00\u521d\u59cb\u5316\u79cd\u5b50&#xff0c;\u53ea\u6539\u5f52\u4e00\u5316\u76f8\u5173\u5f00\u5173\u3002<\/p>\n<p>  #mermaid-svg-NxfBZlTcco6ESGtn{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-NxfBZlTcco6ESGtn .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-NxfBZlTcco6ESGtn .error-icon{fill:#552222;}#mermaid-svg-NxfBZlTcco6ESGtn .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-NxfBZlTcco6ESGtn .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-NxfBZlTcco6ESGtn .marker{fill:#333333;stroke:#333333;}#mermaid-svg-NxfBZlTcco6ESGtn .marker.cross{stroke:#333333;}#mermaid-svg-NxfBZlTcco6ESGtn svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-NxfBZlTcco6ESGtn p{margin:0;}#mermaid-svg-NxfBZlTcco6ESGtn .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-NxfBZlTcco6ESGtn .cluster-label text{fill:#333;}#mermaid-svg-NxfBZlTcco6ESGtn .cluster-label span{color:#333;}#mermaid-svg-NxfBZlTcco6ESGtn .cluster-label span p{background-color:transparent;}#mermaid-svg-NxfBZlTcco6ESGtn .label text,#mermaid-svg-NxfBZlTcco6ESGtn span{fill:#333;color:#333;}#mermaid-svg-NxfBZlTcco6ESGtn .node rect,#mermaid-svg-NxfBZlTcco6ESGtn .node circle,#mermaid-svg-NxfBZlTcco6ESGtn .node ellipse,#mermaid-svg-NxfBZlTcco6ESGtn .node polygon,#mermaid-svg-NxfBZlTcco6ESGtn .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-NxfBZlTcco6ESGtn .rough-node .label text,#mermaid-svg-NxfBZlTcco6ESGtn .node .label text,#mermaid-svg-NxfBZlTcco6ESGtn .image-shape .label,#mermaid-svg-NxfBZlTcco6ESGtn .icon-shape .label{text-anchor:middle;}#mermaid-svg-NxfBZlTcco6ESGtn .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-NxfBZlTcco6ESGtn .rough-node .label,#mermaid-svg-NxfBZlTcco6ESGtn .node .label,#mermaid-svg-NxfBZlTcco6ESGtn .image-shape .label,#mermaid-svg-NxfBZlTcco6ESGtn .icon-shape .label{text-align:center;}#mermaid-svg-NxfBZlTcco6ESGtn .node.clickable{cursor:pointer;}#mermaid-svg-NxfBZlTcco6ESGtn .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-NxfBZlTcco6ESGtn .arrowheadPath{fill:#333333;}#mermaid-svg-NxfBZlTcco6ESGtn .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-NxfBZlTcco6ESGtn .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-NxfBZlTcco6ESGtn .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-NxfBZlTcco6ESGtn .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-NxfBZlTcco6ESGtn .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-NxfBZlTcco6ESGtn .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-NxfBZlTcco6ESGtn .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-NxfBZlTcco6ESGtn .cluster text{fill:#333;}#mermaid-svg-NxfBZlTcco6ESGtn .cluster span{color:#333;}#mermaid-svg-NxfBZlTcco6ESGtn div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-NxfBZlTcco6ESGtn .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-NxfBZlTcco6ESGtn rect.text{fill:none;stroke-width:0;}#mermaid-svg-NxfBZlTcco6ESGtn .icon-shape,#mermaid-svg-NxfBZlTcco6ESGtn .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-NxfBZlTcco6ESGtn .icon-shape p,#mermaid-svg-NxfBZlTcco6ESGtn .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-NxfBZlTcco6ESGtn .icon-shape .label rect,#mermaid-svg-NxfBZlTcco6ESGtn .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-NxfBZlTcco6ESGtn .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-NxfBZlTcco6ESGtn .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-NxfBZlTcco6ESGtn :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-NxfBZlTcco6ESGtn .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-NxfBZlTcco6ESGtn .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-NxfBZlTcco6ESGtn .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u56fa\u5b9a\u6570\u636e\u4e0e\u79cd\u5b50<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u914d\u7f6e\u4e00 \u65e0\u5f52\u4e00\u5316<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u914d\u7f6e\u4e8c LayerNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u914d\u7f6e\u4e09 RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3 3000 \u6b65\u8bb0\u5f55\u635f\u5931<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ef4\u5ea6\u4e00 \u6df1\u5ea6 6 12 20 \u5c42<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ef4\u5ea6\u4e8c \u4f4d\u7f6e Post \u4e0e Pre<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7ef4\u5ea6\u4e09 \u5b66\u4e60\u7387 1e-4 \u5230 1e-2 \u626b\u63cf<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6c47\u603b\u6210\u8868<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u91cc\u4e09\u4e2a\u7ef4\u5ea6\u6b63\u4ea4&#xff0c;\u5206\u522b\u5bf9\u5e94 6.2\u30016.3\u30016.4 \u4e09\u5c0f\u8282\u3002\u540c\u4e00\u9aa8\u67b6\u53ea\u62e8\u5f00\u5173&#xff0c;\u4fdd\u8bc1\u7ed3\u8bba\u53ef\u5f52\u56e0\u3002<\/p>\n<h4>6.2 \u65e0\u5f52\u4e00\u5316\u7684 20 \u5c42\u5d29\u6e83\u5b9e\u9a8c<\/h4>\n<p>\u7b2c\u4e00\u4e2a\u5b9e\u9a8c\u56de\u7b54\u7b2c 1 \u8282\u7684\u65ad\u8a00&#xff1a;\u6df1\u7f51\u7edc\u6ca1\u6709\u5f52\u4e00\u5316\u5230\u5e95\u4f1a\u53d1\u751f\u4ec0\u4e48\u3002<\/p>\n<p>\u914d\u7f6e&#xff1a;20 \u5c42&#xff0c;Pre \u4f4d\u7f6e&#xff08;\u65e0\u5f52\u4e00\u5316\u65f6\u4f4d\u7f6e\u65e0\u610f\u4e49&#xff09;&#xff0c;\u5b66\u4e60\u7387 1e-3&#xff0c;Adam&#xff0c;3000 \u6b65\u3002<\/p>\n<table>\n<tr>\u6b65\u6570\u65e0\u5f52\u4e00\u5316LayerNormRMSNorm<\/tr>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>4.16<\/td>\n<td>4.16<\/td>\n<td>4.16<\/td>\n<\/tr>\n<tr>\n<td>500<\/td>\n<td>NaN<\/td>\n<td>3.02<\/td>\n<td>3.05<\/td>\n<\/tr>\n<tr>\n<td>1000<\/td>\n<td>NaN<\/td>\n<td>2.71<\/td>\n<td>2.74<\/td>\n<\/tr>\n<tr>\n<td>2000<\/td>\n<td>NaN<\/td>\n<td>2.42<\/td>\n<td>2.44<\/td>\n<\/tr>\n<tr>\n<td>3000<\/td>\n<td>NaN<\/td>\n<td>2.28<\/td>\n<td>2.30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u65e0\u5f52\u4e00\u5316\u5728\u7b2c 300 \u6b65\u5de6\u53f3\u51fa\u73b0 NaN&#xff0c;\u4e4b\u540e\u4e0d\u518d\u6062\u590d\u3002\u964d\u4f4e\u5b66\u4e60\u7387\u5230 1e-4 \u53ef\u4ee5\u63a8\u8fdf\u5d29\u6e83\u5230\u7ea6 900 \u6b65&#xff0c;\u4f46\u4e0d\u80fd\u6d88\u9664\u3002\u628a\u5c42\u6570\u964d\u5230 6&#xff0c;\u65e0\u5f52\u4e00\u5316\u80fd\u52c9\u5f3a\u6536\u655b\u5230 3.1&#xff0c;\u660e\u663e\u5dee\u4e8e\u5f52\u4e00\u5316\u7248\u672c\u7684 2.4 \u4e0a\u4e0b\u3002<\/p>\n<p>\u4e24\u4e2a\u5f52\u4e00\u5316\u7248\u672c\u51e0\u4e4e\u91cd\u5408&#xff0c;\u5dee\u8ddd\u5728 0.03 \u4ee5\u5185&#xff0c;\u4e0e 3.2 \u8282\u8bba\u6587\u7684&#034;\u8d28\u91cf\u76f8\u5f53&#034;\u53e3\u5f84\u4e00\u81f4\u3002<\/p>\n<p>\u5d29\u6e83\u7684\u76f4\u63a5\u673a\u7406\u53ef\u4ee5\u7528\u524d\u5411\u8303\u6570\u8ffd\u8ba4\u3002\u8bad\u7ec3\u521d\u671f\u67d0\u5c42\u6743\u91cd\u66f4\u65b0\u540e&#xff0c;\u540e\u7eed\u5c42\u8f93\u5165\u8303\u6570\u8df3\u5230 1e3 \u91cf\u7ea7\u3002GELU \u9971\u548c&#xff0c;\u53cd\u5411\u68af\u5ea6\u53c8\u653e\u5927&#xff0c;\u51e0\u6b65\u5185\u6ea2\u51fa\u3002<\/p>\n<table>\n<tr>\u5c42\u6570\u65e0\u5f52\u4e00\u5316LayerNormRMSNorm<\/tr>\n<tbody>\n<tr>\n<td>6<\/td>\n<td>3.12 \u53ef\u6536\u655b<\/td>\n<td>2.44<\/td>\n<td>2.45<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>3.9 \u540e\u9707\u8361<\/td>\n<td>2.31<\/td>\n<td>2.33<\/td>\n<\/tr>\n<tr>\n<td>20<\/td>\n<td>NaN<\/td>\n<td>2.28<\/td>\n<td>2.30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u7b2c\u4e8c\u5f20\u8868\u628a\u6df1\u5ea6\u52a0\u8fdb\u6765\u3002\u5173\u952e\u8bfb\u6cd5\u662f&#xff1a;\u65e0\u5f52\u4e00\u5316\u5728 12 \u5c42\u5df2\u7ecf\u51fa\u73b0\u660e\u663e\u9000\u5316&#xff0c;20 \u5c42\u5f7b\u5e95\u4e0d\u53ef\u8bad\u3002\u5f52\u4e00\u5316\u7248\u672c\u7684\u635f\u5931\u968f\u6df1\u5ea6\u53cd\u800c\u7565\u964d&#xff0c;\u56e0\u4e3a\u4efb\u52a1\u786e\u5b9e\u9700\u8981\u6df1\u5c42\u7ec4\u5408\u3002<\/p>\n<p>\u8fd9\u4e0e RMSNorm \u8bba\u6587 Table 5 \u7684\u7ed3\u8bba\u540c\u6784\u3002Transformer \u53bb\u6389\u5f52\u4e00\u5316\u8bad\u7ec3\u76f4\u63a5\u5931\u8d25\u3002\u73a9\u5177\u5b9e\u9a8c\u5728\u66f4\u5c0f\u89c4\u6a21\u4e0a\u590d\u73b0\u4e86\u8fd9\u4e00\u70b9\u3002<\/p>\n<p>  #mermaid-svg-D0G6Ihu7ayEsH2Dl{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .error-icon{fill:#552222;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .marker{fill:#333333;stroke:#333333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .marker.cross{stroke:#333333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl p{margin:0;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .cluster-label text{fill:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .cluster-label span{color:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .cluster-label span p{background-color:transparent;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .label text,#mermaid-svg-D0G6Ihu7ayEsH2Dl span{fill:#333;color:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .node rect,#mermaid-svg-D0G6Ihu7ayEsH2Dl .node circle,#mermaid-svg-D0G6Ihu7ayEsH2Dl .node ellipse,#mermaid-svg-D0G6Ihu7ayEsH2Dl .node polygon,#mermaid-svg-D0G6Ihu7ayEsH2Dl .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .rough-node .label text,#mermaid-svg-D0G6Ihu7ayEsH2Dl .node .label text,#mermaid-svg-D0G6Ihu7ayEsH2Dl .image-shape .label,#mermaid-svg-D0G6Ihu7ayEsH2Dl .icon-shape .label{text-anchor:middle;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .rough-node .label,#mermaid-svg-D0G6Ihu7ayEsH2Dl .node .label,#mermaid-svg-D0G6Ihu7ayEsH2Dl .image-shape .label,#mermaid-svg-D0G6Ihu7ayEsH2Dl .icon-shape .label{text-align:center;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .node.clickable{cursor:pointer;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .arrowheadPath{fill:#333333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-D0G6Ihu7ayEsH2Dl .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-D0G6Ihu7ayEsH2Dl .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-D0G6Ihu7ayEsH2Dl .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .cluster text{fill:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .cluster span{color:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-D0G6Ihu7ayEsH2Dl rect.text{fill:none;stroke-width:0;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .icon-shape,#mermaid-svg-D0G6Ihu7ayEsH2Dl .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .icon-shape p,#mermaid-svg-D0G6Ihu7ayEsH2Dl .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .icon-shape .label rect,#mermaid-svg-D0G6Ihu7ayEsH2Dl .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-D0G6Ihu7ayEsH2Dl .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-D0G6Ihu7ayEsH2Dl :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-D0G6Ihu7ayEsH2Dl .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>20 \u5c42\u65e0\u5f52\u4e00\u5316\u8bad\u7ec3<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b2c 300 \u6b65\u5de6\u53f3\u524d\u5411\u8303\u6570\u8df3\u5230 1e3<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6fc0\u6d3b\u9971\u548c<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53cd\u5411\u68af\u5ea6\u653e\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u66f4\u65b0\u66f4\u5927<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6ea2\u51fa\u4e3a NaN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u964d\u4f4e\u5b66\u4e60\u7387\u53ea\u63a8\u8fdf\u4e0d\u6d88\u9664<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>20 \u5c42\u5e26 LayerNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8303\u6570\u88ab\u9489\u4f4f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u635f\u5931\u5e73\u6ed1\u964d\u5230 2.28<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d B \u5230 E \u6784\u6210\u4e00\u4e2a\u6b63\u53cd\u9988\u73af&#xff0c;\u8fd9\u662f\u68af\u5ea6\u7206\u70b8\u7684\u6807\u51c6\u5f62\u6001\u3002\u5f52\u4e00\u5316\u5728 B \u5904\u622a\u65ad\u8fd9\u4e2a\u73af\u3002<\/p>\n<p>\u7ed3\u8bba\u7684\u8fb9\u754c\u4e5f\u8981\u5199\u6e05&#xff1a;\u65e0\u5f52\u4e00\u5316\u6df1\u7f51\u4e0d\u53ef\u8bad\u662f\u7ecf\u9a8c\u89c4\u5f8b&#xff0c;\u4e0d\u662f\u5b9a\u7406\u3002\u7cbe\u5fc3\u8bbe\u8ba1\u521d\u59cb\u5316\u4e0e\u5c0f\u5b66\u4e60\u7387\u53ef\u4ee5\u8ba9\u7279\u5b9a\u7ed3\u6784\u52c9\u5f3a\u8bad\u7ec3&#xff0c;\u4f46\u5de5\u7a0b\u4e0a\u65e0\u4eba\u8fd9\u6837\u505a\u3002<\/p>\n<h4>6.3 Pre-LN \u4e0e Post-LN \u7684\u5b66\u4e60\u7387\u654f\u611f\u5ea6<\/h4>\n<p>\u7b2c\u4e8c\u4e2a\u5b9e\u9a8c\u9488\u5bf9\u4f4d\u7f6e\u3002\u56fa\u5b9a 12 \u5c42\u4e0e 30 \u5c42\u4e24\u4e2a\u6df1\u5ea6&#xff0c;\u626b\u63cf\u5b66\u4e60\u7387\u4ece 1e-4 \u5230 1e-2\u3002\u5176\u4f59\u8bbe\u7f6e\u540c 6.1\u3002<\/p>\n<p>\u5148\u770b 12 \u5c42\u7684\u7ed3\u679c&#xff0c;\u53e3\u5f84\u4e3a 3000 \u6b65\u540e\u9a8c\u8bc1\u635f\u5931&#xff0c;\u53d1\u6563\u8bb0 NaN\u3002<\/p>\n<table>\n<tr>\u5b66\u4e60\u7387Post-LN 12 \u5c42Pre-LN 12 \u5c42Post-LN 30 \u5c42Pre-LN 30 \u5c42<\/tr>\n<tbody>\n<tr>\n<td>1e-4<\/td>\n<td>2.96<\/td>\n<td>2.85<\/td>\n<td>3.41<\/td>\n<td>2.94<\/td>\n<\/tr>\n<tr>\n<td>3e-4<\/td>\n<td>2.61<\/td>\n<td>2.52<\/td>\n<td>3.87<\/td>\n<td>2.71<\/td>\n<\/tr>\n<tr>\n<td>1e-3<\/td>\n<td>NaN<\/td>\n<td>2.38<\/td>\n<td>NaN<\/td>\n<td>2.58<\/td>\n<\/tr>\n<tr>\n<td>3e-3<\/td>\n<td>NaN<\/td>\n<td>2.35<\/td>\n<td>NaN<\/td>\n<td>2.49<\/td>\n<\/tr>\n<tr>\n<td>1e-2<\/td>\n<td>NaN<\/td>\n<td>2.41<\/td>\n<td>NaN<\/td>\n<td>2.62<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e24\u4e2a\u7ed3\u8bba\u76f4\u63a5\u8bfb\u8868\u3002<\/p>\n<p>\u7b2c\u4e00&#xff0c;Post-LN \u5728 1e-3 \u53ca\u4ee5\u4e0a\u5168\u90e8\u53d1\u6563\u3002\u5b89\u5168\u7a97\u53e3\u53ea\u6709 1e-4 \u5230 3e-4 \u4e00\u6863\u591a\u3002Pre-LN \u5728\u6574\u4e2a\u626b\u63cf\u8303\u56f4\u5185\u90fd\u6536\u655b\u3002\u6700\u4f18\u5728 3e-3 \u9644\u8fd1&#xff0c;\u6bd4 Post-LN \u7684\u6700\u4f18\u5feb\u4e00\u4e2a\u6570\u91cf\u7ea7\u3002<\/p>\n<p>\u7b2c\u4e8c&#xff0c;\u6df1\u5ea6\u52a0\u5267\u5dee\u5f02\u300230 \u5c42 Post-LN \u8fde 3e-4 \u90fd\u5f00\u59cb\u9000\u5316&#xff0c;3.87 \u6bd4 1e-4 \u7684 3.41 \u8fd8\u5dee\u3002Pre-LN \u53cd\u800c\u56e0\u5bb9\u91cf\u589e\u52a0\u800c\u66f4\u4f18\u3002<\/p>\n<p>\u52a0 warm-up \u7684\u5bf9\u7167&#xff08;\u7ebf\u6027\u5347\u6e29 1000 \u6b65&#xff09;\u4e0b&#xff0c;Post-LN 12 \u5c42\u5728 1e-3 \u53ef\u6536\u655b\u5230 2.44\u3002\u8fd9\u8ffd\u5e73 Pre-LN \u7684 2.38 \u9644\u8fd1\u3002\u5370\u8bc1 2.3 \u8282\u7684\u53e3\u5f84&#xff1a;warm-up \u6551\u5f97\u56de Post-LN&#xff0c;\u4ee3\u4ef7\u662f\u591a\u4e00\u4e2a\u654f\u611f\u8d85\u53c2\u3002<\/p>\n<table>\n<tr>\u914d\u7f6e\u5b89\u5168\u5b66\u4e60\u7387\u7a97\u53e3\u6700\u4f18\u635f\u5931\u989d\u5916\u8d85\u53c2<\/tr>\n<tbody>\n<tr>\n<td>Post-LN 12 \u5c42<\/td>\n<td>\u7ea6 1 \u4e2a\u6570\u91cf\u7ea7<\/td>\n<td>2.44&#xff08;\u5e26 warmup&#xff09;<\/td>\n<td>warmup \u6b65\u6570<\/td>\n<\/tr>\n<tr>\n<td>Pre-LN 12 \u5c42<\/td>\n<td>\u7ea6 3 \u4e2a\u6570\u91cf\u7ea7<\/td>\n<td>2.35<\/td>\n<td>\u65e0<\/td>\n<\/tr>\n<tr>\n<td>Post-LN 30 \u5c42<\/td>\n<td>\u4e0d\u53ef\u7528<\/td>\n<td>\u53d1\u6563<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td>Pre-LN 30 \u5c42<\/td>\n<td>\u7ea6 3 \u4e2a\u6570\u91cf\u7ea7<\/td>\n<td>2.49<\/td>\n<td>\u65e0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6ce8\u610f\u6700\u540e\u4e00\u884c\u3002Pre-LN 30 \u5c42\u7684\u6700\u4f18\u635f\u5931\u7565\u9ad8\u4e8e 12 \u5c42\u3002\u73a9\u5177\u4efb\u52a1\u4e0d\u9700\u8981\u90a3\u4e48\u6df1&#xff0c;\u5c5e\u6b63\u5e38\u73b0\u8c61&#xff0c;\u4e0d\u5f71\u54cd\u7a33\u5b9a\u6027\u7ed3\u8bba\u3002<\/p>\n<p>  #mermaid-svg-GqZepikjYPOilqVN{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-GqZepikjYPOilqVN .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-GqZepikjYPOilqVN .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-GqZepikjYPOilqVN .error-icon{fill:#552222;}#mermaid-svg-GqZepikjYPOilqVN .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-GqZepikjYPOilqVN .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-GqZepikjYPOilqVN .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-GqZepikjYPOilqVN .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-GqZepikjYPOilqVN .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-GqZepikjYPOilqVN .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-GqZepikjYPOilqVN .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-GqZepikjYPOilqVN .marker{fill:#333333;stroke:#333333;}#mermaid-svg-GqZepikjYPOilqVN .marker.cross{stroke:#333333;}#mermaid-svg-GqZepikjYPOilqVN svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-GqZepikjYPOilqVN p{margin:0;}#mermaid-svg-GqZepikjYPOilqVN .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-GqZepikjYPOilqVN .cluster-label text{fill:#333;}#mermaid-svg-GqZepikjYPOilqVN .cluster-label span{color:#333;}#mermaid-svg-GqZepikjYPOilqVN .cluster-label span p{background-color:transparent;}#mermaid-svg-GqZepikjYPOilqVN .label text,#mermaid-svg-GqZepikjYPOilqVN span{fill:#333;color:#333;}#mermaid-svg-GqZepikjYPOilqVN .node rect,#mermaid-svg-GqZepikjYPOilqVN .node circle,#mermaid-svg-GqZepikjYPOilqVN .node ellipse,#mermaid-svg-GqZepikjYPOilqVN .node polygon,#mermaid-svg-GqZepikjYPOilqVN .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-GqZepikjYPOilqVN .rough-node .label text,#mermaid-svg-GqZepikjYPOilqVN .node .label text,#mermaid-svg-GqZepikjYPOilqVN .image-shape .label,#mermaid-svg-GqZepikjYPOilqVN .icon-shape .label{text-anchor:middle;}#mermaid-svg-GqZepikjYPOilqVN .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-GqZepikjYPOilqVN .rough-node .label,#mermaid-svg-GqZepikjYPOilqVN .node .label,#mermaid-svg-GqZepikjYPOilqVN .image-shape .label,#mermaid-svg-GqZepikjYPOilqVN .icon-shape .label{text-align:center;}#mermaid-svg-GqZepikjYPOilqVN .node.clickable{cursor:pointer;}#mermaid-svg-GqZepikjYPOilqVN .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-GqZepikjYPOilqVN .arrowheadPath{fill:#333333;}#mermaid-svg-GqZepikjYPOilqVN .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-GqZepikjYPOilqVN .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-GqZepikjYPOilqVN .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-GqZepikjYPOilqVN .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-GqZepikjYPOilqVN .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-GqZepikjYPOilqVN .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-GqZepikjYPOilqVN .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-GqZepikjYPOilqVN .cluster text{fill:#333;}#mermaid-svg-GqZepikjYPOilqVN .cluster span{color:#333;}#mermaid-svg-GqZepikjYPOilqVN div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-GqZepikjYPOilqVN .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-GqZepikjYPOilqVN rect.text{fill:none;stroke-width:0;}#mermaid-svg-GqZepikjYPOilqVN .icon-shape,#mermaid-svg-GqZepikjYPOilqVN .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-GqZepikjYPOilqVN .icon-shape p,#mermaid-svg-GqZepikjYPOilqVN .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-GqZepikjYPOilqVN .icon-shape .label rect,#mermaid-svg-GqZepikjYPOilqVN .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-GqZepikjYPOilqVN .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-GqZepikjYPOilqVN .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-GqZepikjYPOilqVN :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-GqZepikjYPOilqVN .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-GqZepikjYPOilqVN .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-GqZepikjYPOilqVN .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u626b\u63cf\u5b66\u4e60\u7387 1e-4 \u5230 1e-2<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>12 \u5c42\u5b89\u5168\u7a97\u53e3\u7ea6 1 \u4e2a\u6570\u91cf\u7ea7<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>30 \u5c42\u5168\u7a0b\u53d1\u6563<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>12 \u4e0e 30 \u5c42\u7a97\u53e3\u7ea6 3 \u4e2a\u6570\u91cf\u7ea7<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6700\u4f18\u5b66\u4e60\u7387\u5927\u4e00\u4e2a\u6570\u91cf\u7ea7<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u9700 warmup \u6269\u7a97<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u514d warmup \u76f4\u63a5\u8bad<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u91cc E \u4e0e F \u7684\u5bf9\u6bd4\u662f Pre-LN \u6210\u4e3a\u4e3b\u6d41\u7684\u6700\u76f4\u63a5\u8bc1\u636e\u3002\u6df1\u5ea6\u4e0a\u53bb\u540e&#xff0c;Post-LN \u8fde\u8c03\u53c2\u7684\u673a\u4f1a\u90fd\u6ca1\u6709\u3002<\/p>\n<h4>6.4 LN \u4e0e RMSNorm \u7684\u901f\u5ea6\u5bf9\u6bd4<\/h4>\n<p>\u7b2c\u4e09\u4e2a\u5b9e\u9a8c\u8865\u901f\u5ea6\u3002\u8bbe\u7f6e\u6bd4 3.4 \u8282\u66f4\u8d34\u8fd1\u5b9e\u9645&#xff1a;\u626b\u5f62\u72b6\u3001\u6bd4\u4e2d\u4f4d\u8017\u65f6\u3001\u52a0 fused \u5b9e\u73b0\u5bf9\u7167\u3002<\/p>\n<table>\n<tr>\u5f62\u72b6 batch seq dnn.LayerNormRMSNorm \u624b\u5199RMSNorm \u5feb\u591a\u5c11<\/tr>\n<tbody>\n<tr>\n<td>4 x 128 x 512<\/td>\n<td>21 us<\/td>\n<td>18 us<\/td>\n<td>14%<\/td>\n<\/tr>\n<tr>\n<td>8 x 256 x 1024<\/td>\n<td>63 us<\/td>\n<td>54 us<\/td>\n<td>14%<\/td>\n<\/tr>\n<tr>\n<td>16 x 512 x 2048<\/td>\n<td>240 us<\/td>\n<td>205 us<\/td>\n<td>15%<\/td>\n<\/tr>\n<tr>\n<td>32 x 1024 x 4096<\/td>\n<td>1820 us<\/td>\n<td>1540 us<\/td>\n<td>15%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u53e3\u5f84\u8bf4\u660e&#xff1a;CPU \u5355\u7ebf\u7a0b&#xff0c;\u5404 2000 \u6b21\u53d6\u4e2d\u4f4d&#xff0c;\u6570\u503c\u4e3a\u5178\u578b\u91cf\u7ea7&#xff0c;\u968f\u673a\u5668\u6d6e\u52a8\u3002\u6838\u5fc3\u8bfb\u6cd5\u662f\u76f8\u5bf9\u5dee\u7a33\u5b9a\u5728 14% \u5230 15%&#xff0c;\u4e0d\u968f\u5f62\u72b6\u663e\u8457\u53d8\u5316\u3002<\/p>\n<p>\u8fd9\u4e2a 15% \u662f\u5f52\u4e00\u5316\u7b97\u5b50\u672c\u8eab\u7684\u63d0\u901f\u3002\u653e\u5230\u6574\u6a21\u578b\u4e0a\u8981\u6309\u5360\u6bd4\u6298\u7b97&#xff0c;\u5373 3.2 \u8282\u8bba\u6587\u7684 7% \u5230 9%&#xff08;Transformer \u573a\u666f&#xff09;\u3002\u4e24\u4e2a\u6570\u5b57\u4e0d\u77db\u76fe&#xff0c;\u4e00\u4e2a\u662f\u7b97\u5b50\u7ea7&#xff0c;\u4e00\u4e2a\u662f\u6a21\u578b\u7ea7\u3002<\/p>\n<p>\u518d\u8865\u4e00\u4e2a\u53c2\u6570\u91cf\u7684\u5bf9\u7167\u8868&#xff0c;d&#061;4096\u3001\u5c42\u6570 32\u3001\u6bcf\u5c42\u4e24\u5904\u5f52\u4e00\u5316\u3002<\/p>\n<table>\n<tr>\u9879LayerNormRMSNorm\u5dee\u503c<\/tr>\n<tbody>\n<tr>\n<td>\u5355\u5904\u53c2\u6570<\/td>\n<td>8192<\/td>\n<td>4096<\/td>\n<td>\u51cf 4096<\/td>\n<\/tr>\n<tr>\n<td>\u5168\u6a21\u578b\u5f52\u4e00\u5316\u53c2\u6570<\/td>\n<td>524288<\/td>\n<td>262144<\/td>\n<td>\u51cf 262144<\/td>\n<\/tr>\n<tr>\n<td>\u524d\u5411\u89c4\u7ea6\u6b21\u6570&#xff08;\u6bcf token&#xff09;<\/td>\n<td>2 \u6b21\u6bcf\u6b21 2 \u4e2a<\/td>\n<td>2 \u6b21\u6bcf\u6b21 1 \u4e2a<\/td>\n<td>\u51cf\u4e00\u534a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u7b2c\u4e8c\u884c\u7b97\u5f0f&#xff1a;8192 \u4e58 2 \u5904\u4e58 32 \u5c42\u7b49\u4e8e 524288\u300226 \u4e07\u53c2\u6570\u5bf9 7B \u6a21\u578b\u5360\u6bd4\u5f88\u5c0f\u3002\u4f46\u5f52\u4e00\u5316 tensor \u7684\u8bfb\u5199\u662f\u6bcf\u6b65\u90fd\u53d1\u751f\u7684&#xff0c;\u5e26\u5bbd\u8282\u7701\u7d2f\u79ef\u53ef\u89c2\u3002<\/p>\n<p>  #mermaid-svg-GVGKtTy6WxLH4VJH{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-GVGKtTy6WxLH4VJH .error-icon{fill:#552222;}#mermaid-svg-GVGKtTy6WxLH4VJH .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-GVGKtTy6WxLH4VJH .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-GVGKtTy6WxLH4VJH .marker{fill:#333333;stroke:#333333;}#mermaid-svg-GVGKtTy6WxLH4VJH .marker.cross{stroke:#333333;}#mermaid-svg-GVGKtTy6WxLH4VJH svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-GVGKtTy6WxLH4VJH p{margin:0;}#mermaid-svg-GVGKtTy6WxLH4VJH .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH .cluster-label text{fill:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH .cluster-label span{color:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH .cluster-label span p{background-color:transparent;}#mermaid-svg-GVGKtTy6WxLH4VJH .label text,#mermaid-svg-GVGKtTy6WxLH4VJH span{fill:#333;color:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH .node rect,#mermaid-svg-GVGKtTy6WxLH4VJH .node circle,#mermaid-svg-GVGKtTy6WxLH4VJH .node ellipse,#mermaid-svg-GVGKtTy6WxLH4VJH .node polygon,#mermaid-svg-GVGKtTy6WxLH4VJH .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-GVGKtTy6WxLH4VJH .rough-node .label text,#mermaid-svg-GVGKtTy6WxLH4VJH .node .label text,#mermaid-svg-GVGKtTy6WxLH4VJH .image-shape .label,#mermaid-svg-GVGKtTy6WxLH4VJH .icon-shape .label{text-anchor:middle;}#mermaid-svg-GVGKtTy6WxLH4VJH .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-GVGKtTy6WxLH4VJH .rough-node .label,#mermaid-svg-GVGKtTy6WxLH4VJH .node .label,#mermaid-svg-GVGKtTy6WxLH4VJH .image-shape .label,#mermaid-svg-GVGKtTy6WxLH4VJH .icon-shape .label{text-align:center;}#mermaid-svg-GVGKtTy6WxLH4VJH .node.clickable{cursor:pointer;}#mermaid-svg-GVGKtTy6WxLH4VJH .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-GVGKtTy6WxLH4VJH .arrowheadPath{fill:#333333;}#mermaid-svg-GVGKtTy6WxLH4VJH .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-GVGKtTy6WxLH4VJH .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-GVGKtTy6WxLH4VJH .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-GVGKtTy6WxLH4VJH .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-GVGKtTy6WxLH4VJH .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-GVGKtTy6WxLH4VJH .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-GVGKtTy6WxLH4VJH .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-GVGKtTy6WxLH4VJH .cluster text{fill:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH .cluster span{color:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-GVGKtTy6WxLH4VJH .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-GVGKtTy6WxLH4VJH rect.text{fill:none;stroke-width:0;}#mermaid-svg-GVGKtTy6WxLH4VJH .icon-shape,#mermaid-svg-GVGKtTy6WxLH4VJH .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-GVGKtTy6WxLH4VJH .icon-shape p,#mermaid-svg-GVGKtTy6WxLH4VJH .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-GVGKtTy6WxLH4VJH .icon-shape .label rect,#mermaid-svg-GVGKtTy6WxLH4VJH .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-GVGKtTy6WxLH4VJH .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-GVGKtTy6WxLH4VJH .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-GVGKtTy6WxLH4VJH :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-GVGKtTy6WxLH4VJH .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-GVGKtTy6WxLH4VJH .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-GVGKtTy6WxLH4VJH .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u901f\u5ea6\u5b9e\u9a8c\u4e09\u6863\u53e3\u5f84<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b97\u5b50\u7ea7 \u5355\u6b21\u8c03\u7528<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6a21\u578b\u7ea7 \u6574\u7f51\u524d\u5411<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7cfb\u7edf\u7ea7 \u8bad\u7ec3\u541e\u5410<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u5feb\u7ea6 15%<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bba\u6587\u53e3\u5f84 7% \u5230 9%<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53d6\u51b3\u4e8e\u5f52\u4e00\u5316\u5360\u603b\u8017\u65f6\u6bd4\u4f8b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6298\u7b97\u5173\u7cfb \u6309\u5360\u6bd4\u7f29\u653e<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f15\u7528\u63d0\u901f\u6570\u5b57\u5fc5\u987b\u5e26\u53e3\u5f84<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u91cc F \u662f\u672c\u8282\u6700\u60f3\u7559\u4e0b\u7684\u4e60\u60ef&#xff1a;\u8c08\u63d0\u901f\u5fc5\u5e26\u53e3\u5f84\u3002\u7b97\u5b50\u7ea7 15% \u4e0e\u6a21\u578b\u7ea7 7% \u90fd\u662f\u5bf9\u7684&#xff0c;\u6df7\u7528\u5c31\u4f1a\u51fa\u9519\u3002<\/p>\n<h3>7. \u8fb9\u754c\u4e0e\u5751<\/h3>\n<h4>7.1 \u5f52\u4e00\u5316\u4e0d\u662f\u4e07\u80fd\u5f00\u5173<\/h4>\n<p>\u7b2c\u4e00\u5751&#xff1a;\u4ee5\u4e3a\u52a0 LN \u5c31\u4e07\u4e8b\u5927\u5409\u3002\u5f52\u4e00\u5316\u89e3\u51b3\u7684\u662f\u5e45\u5ea6\u5931\u63a7&#xff0c;\u4e0d\u662f\u6240\u6709\u8bad\u7ec3\u95ee\u9898\u3002<\/p>\n<p>\u6570\u636e\u6709\u566a\u58f0\u3001\u6807\u7b7e\u9519\u4e71\u3001\u5b66\u4e60\u7387\u8c03\u5ea6\u4e0d\u5408\u7406&#xff0c;\u8fd9\u4e9b LN \u90fd\u6551\u4e0d\u4e86\u30026.2 \u8282\u7684\u5b9e\u9a8c\u91cc&#xff0c;\u5f52\u4e00\u5316\u7248\u672c\u7684\u635f\u5931\u4e5f\u53ea\u5230 2.28\u3002\u74f6\u9888\u5728\u4efb\u52a1\u4e0e\u5bb9\u91cf&#xff0c;\u4e0d\u5728\u7a33\u5b9a\u3002<\/p>\n<p>\u7b2c\u4e8c\u5751&#xff1a;\u5f52\u4e00\u5316\u4f4d\u7f6e\u9009\u9519\u3002\u590d\u73b0\u8bba\u6587\u65f6\u8981\u9010\u5b57\u6838\u5bf9\u516c\u5f0f\u3002Post-LN \u4e0e Pre-LN \u7684\u5dee\u522b\u53ea\u662f\u4e00\u4e2a\u62ec\u53f7&#xff0c;\u4ee3\u7801\u4e0a\u5f88\u5bb9\u6613\u5199\u53cd\u3002<\/p>\n<p>\u7b2c\u4e09\u5751&#xff1a;eps \u7528\u9ed8\u8ba4\u503c\u4e0d\u505a\u6570\u503c\u9a8c\u8bc1\u3002fp16 \u6216 bf16 \u4e0b var \u53ef\u80fd\u4e0b\u6ea2&#xff0c;eps \u9700\u8981\u6309\u7cbe\u5ea6\u8c03\u3002RMSNorm \u539f\u5b9e\u73b0\u7528 1e-6&#xff0c;LN \u5e38\u7528 1e-5&#xff0c;\u4e0d\u662f\u968f\u4fbf\u5b9a\u7684\u3002<\/p>\n<p>\u7b2c\u56db\u5751&#xff1a;\u4ee5\u4e3a\u53bb\u6389\u5f52\u4e00\u5316\u4e5f\u80fd\u8bad\u30026.2 \u8282\u7684\u8868\u5df2\u7ecf\u7ed9\u51fa\u8fb9\u754c\u300212 \u5c42\u5f00\u59cb\u660e\u663e\u9000\u5316&#xff0c;20 \u5c42\u76f4\u63a5 NaN\u3002\u4f4e\u4e8e 6 \u5c42\u7684\u6d45\u7f51\u786e\u5b9e\u53ef\u4ee5\u88f8\u8bad&#xff0c;\u4f46\u90a3\u662f\u6df1\u5ea6\u4e0d\u591f&#xff0c;\u4e0d\u662f\u4e0d\u9700\u8981\u3002<\/p>\n<table>\n<tr>\u5751\u75c7\u72b6\u4fee\u6b63<\/tr>\n<tbody>\n<tr>\n<td>\u4f4d\u7f6e\u5199\u53cd<\/td>\n<td>\u8bad\u5d29\u6216\u66f2\u7ebf\u4e0e\u8bba\u6587\u4e0d\u7b26<\/td>\n<td>\u6838\u5bf9\u516c\u5f0f\u9010\u9879\u5bf9\u9f50<\/td>\n<\/tr>\n<tr>\n<td>eps \u6cbf\u7528\u9ed8\u8ba4<\/td>\n<td>fp16 \u4e0b\u51fa\u73b0 NaN<\/td>\n<td>\u6309\u7cbe\u5ea6\u9a8c\u8bc1\u5e76\u8c03 eps<\/td>\n<\/tr>\n<tr>\n<td>\u6f0f final norm<\/td>\n<td>Pre-LN \u8f93\u51fa\u5934\u884c\u4e3a\u5f02\u5e38<\/td>\n<td>Pre-LN \u5fc5\u914d final norm<\/td>\n<\/tr>\n<tr>\n<td>\u6d45\u7f51\u5916\u63a8\u7ed3\u8bba<\/td>\n<td>\u4ee5\u4e3a\u6df1\u7f51\u4e5f\u4e0d\u9700\u8981\u5f52\u4e00\u5316<\/td>\n<td>\u7528 12 \u5c42\u4ee5\u4e0a\u590d\u6d4b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u8868\u4e2d\u7b2c\u4e09\u884c\u662f\u6700\u9690\u853d\u7684\u4e00\u4e2a&#xff0c;7.2 \u8282\u5c55\u5f00\u3002<\/p>\n<p>  #mermaid-svg-yt5PDj5O0YKRDpJk{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-yt5PDj5O0YKRDpJk .error-icon{fill:#552222;}#mermaid-svg-yt5PDj5O0YKRDpJk .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-yt5PDj5O0YKRDpJk .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-yt5PDj5O0YKRDpJk .marker{fill:#333333;stroke:#333333;}#mermaid-svg-yt5PDj5O0YKRDpJk .marker.cross{stroke:#333333;}#mermaid-svg-yt5PDj5O0YKRDpJk svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-yt5PDj5O0YKRDpJk p{margin:0;}#mermaid-svg-yt5PDj5O0YKRDpJk .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk .cluster-label text{fill:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk .cluster-label span{color:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk .cluster-label span p{background-color:transparent;}#mermaid-svg-yt5PDj5O0YKRDpJk .label text,#mermaid-svg-yt5PDj5O0YKRDpJk span{fill:#333;color:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk .node rect,#mermaid-svg-yt5PDj5O0YKRDpJk .node circle,#mermaid-svg-yt5PDj5O0YKRDpJk .node ellipse,#mermaid-svg-yt5PDj5O0YKRDpJk .node polygon,#mermaid-svg-yt5PDj5O0YKRDpJk .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-yt5PDj5O0YKRDpJk .rough-node .label text,#mermaid-svg-yt5PDj5O0YKRDpJk .node .label text,#mermaid-svg-yt5PDj5O0YKRDpJk .image-shape .label,#mermaid-svg-yt5PDj5O0YKRDpJk .icon-shape .label{text-anchor:middle;}#mermaid-svg-yt5PDj5O0YKRDpJk .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-yt5PDj5O0YKRDpJk .rough-node .label,#mermaid-svg-yt5PDj5O0YKRDpJk .node .label,#mermaid-svg-yt5PDj5O0YKRDpJk .image-shape .label,#mermaid-svg-yt5PDj5O0YKRDpJk .icon-shape .label{text-align:center;}#mermaid-svg-yt5PDj5O0YKRDpJk .node.clickable{cursor:pointer;}#mermaid-svg-yt5PDj5O0YKRDpJk .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-yt5PDj5O0YKRDpJk .arrowheadPath{fill:#333333;}#mermaid-svg-yt5PDj5O0YKRDpJk .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-yt5PDj5O0YKRDpJk .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-yt5PDj5O0YKRDpJk .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-yt5PDj5O0YKRDpJk .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-yt5PDj5O0YKRDpJk .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-yt5PDj5O0YKRDpJk .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-yt5PDj5O0YKRDpJk .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-yt5PDj5O0YKRDpJk .cluster text{fill:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk .cluster span{color:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-yt5PDj5O0YKRDpJk .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-yt5PDj5O0YKRDpJk rect.text{fill:none;stroke-width:0;}#mermaid-svg-yt5PDj5O0YKRDpJk .icon-shape,#mermaid-svg-yt5PDj5O0YKRDpJk .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-yt5PDj5O0YKRDpJk .icon-shape p,#mermaid-svg-yt5PDj5O0YKRDpJk .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-yt5PDj5O0YKRDpJk .icon-shape .label rect,#mermaid-svg-yt5PDj5O0YKRDpJk .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-yt5PDj5O0YKRDpJk .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-yt5PDj5O0YKRDpJk .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-yt5PDj5O0YKRDpJk :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-yt5PDj5O0YKRDpJk .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-yt5PDj5O0YKRDpJk .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-yt5PDj5O0YKRDpJk .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316\u80fd\u89e3\u51b3\u4ec0\u4e48<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5e45\u5ea6\u5931\u63a7 \u662f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5206\u5e03\u6f02\u79fb\u76f8\u5173\u7684\u4e0d\u7a33 \u90e8\u5206<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6570\u636e\u566a\u58f0 \u5426<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5bb9\u91cf\u4e0d\u8db3 \u5426<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5b66\u4e60\u7387\u8c03\u5ea6\u4e0d\u5f53 \u5426<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5148\u8bca\u65ad\u518d\u5f52\u56e0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6362\u5f52\u4e00\u5316\u65e0\u6548\u679c<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u91cc\u7684\u95ee\u9898\u610f\u8bc6\u6bd4\u7ed3\u8bba\u91cd\u8981&#xff1a;\u8bad\u7ec3\u51fa\u95ee\u9898\u5148\u5b9a\u4f4d\u662f\u54ea\u4e00\u7c7b&#xff0c;\u518d\u51b3\u5b9a\u52a8\u4e0d\u52a8\u5f52\u4e00\u5316\u3002<\/p>\n<h4>7.2 \u5b9e\u73b0\u7ec6\u8282&#xff1a;final norm \u4e0e\u547d\u540d<\/h4>\n<p>final norm \u662f Pre-LN \u7684\u4f34\u751f\u90e8\u4ef6&#xff0c;\u5374\u5728\u5f88\u591a\u5b9e\u73b0\u91cc\u88ab\u5ffd\u7565\u6216\u547d\u540d\u6df7\u4e71\u3002<\/p>\n<p>\u5b83\u6307\u6700\u540e\u4e00\u4e2a block \u4e4b\u540e\u3001\u8f93\u51fa\u5934\u4e4b\u524d\u7684\u90a3\u6b21\u5f52\u4e00\u5316\u3002Pre-LN \u8bba\u6587\u539f\u6587\u660e\u786e\u5199\u4e86\u8fd9\u4e00\u90e8\u4ef6\u7684\u5b58\u5728\u3002\u4f5c\u7528\u662f 4.4 \u8282\u8bb2\u7684&#xff1a;\u4e3b\u5e72\u8303\u6570\u9010\u5c42\u589e\u957f&#xff0c;\u8f93\u51fa\u5934\u9700\u8981\u88ab\u7a33\u538b\u8fc7\u7684\u8f93\u5165\u3002<\/p>\n<p>\u547d\u540d\u4e0a\u7684\u6df7\u4e71\u6765\u81ea\u4e0d\u540c\u4ee3\u7801\u5e93\u3002Hugging Face \u7684 LLaMA \u5b9e\u73b0\u91cc\u53eb norm&#xff0c;GPT-2 \u5b9e\u73b0\u91cc\u53eb ln_f\u3002\u4e00\u4e9b\u590d\u73b0\u91cc\u53eb final_layer_norm\u3002\u6307\u7684\u90fd\u662f\u540c\u4e00\u4e2a\u4e1c\u897f\u3002<\/p>\n<p>Post-LN \u4e0d\u9700\u8981 final norm&#xff0c;\u56e0\u4e3a\u6bcf\u5c42\u51fa\u53e3\u5df2\u7ecf\u88ab LN \u538b\u8fc7\u3002\u7528 Post-LN \u7684\u4ee3\u7801\u91cc\u5982\u679c\u770b\u5230 final norm&#xff0c;\u591a\u534a\u662f\u7ed3\u6784\u6df7\u7528&#xff0c;\u9700\u8981\u8b66\u60d5\u3002<\/p>\n<p><span class=\"token comment\"># final norm \u7684\u5b58\u5728\u6027\u68c0\u67e5&#xff08;\u4f2a\u4ee3\u7801&#xff0c;\u7528\u4e8e\u6838\u5bf9\u5b9e\u73b0\u662f\u5426\u6f0f\u6389\u8fd9\u4e00\u90e8\u4ef6&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> torch<span class=\"token punctuation\">.<\/span>nn <span class=\"token keyword\">as<\/span> nn<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">PreLNNet<\/span><span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> L<span class=\"token punctuation\">,<\/span> vocab<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token builtin\">super<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>__init__<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>blocks <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>ModuleList<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>PreLNBlock<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> d <span class=\"token operator\">*<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>L<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>norm <span class=\"token operator\">&#061;<\/span> RMSNorm<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span>                  <span class=\"token comment\"># final norm&#xff0c;Pre-LN \u5fc5\u9700<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>head <span class=\"token operator\">&#061;<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> vocab<span class=\"token punctuation\">,<\/span> bias<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">forward<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> blk <span class=\"token keyword\">in<\/span> self<span class=\"token punctuation\">.<\/span>blocks<span class=\"token punctuation\">:<\/span><br \/>\n            x <span class=\"token operator\">&#061;<\/span> blk<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> self<span class=\"token punctuation\">.<\/span>head<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># \u8f93\u51fa\u5934\u524d\u7a33\u538b<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    d<span class=\"token punctuation\">,<\/span> L <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">8<\/span><br \/>\n    net <span class=\"token operator\">&#061;<\/span> PreLNNet<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> L<span class=\"token punctuation\">,<\/span> vocab<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1000<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    has_final <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">hasattr<\/span><span class=\"token punctuation\">(<\/span>net<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;norm&#034;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">and<\/span> <span class=\"token builtin\">isinstance<\/span><span class=\"token punctuation\">(<\/span>net<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">,<\/span> nn<span class=\"token punctuation\">.<\/span>Module<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u662f\u5426\u6709 final norm:&#034;<\/span><span class=\"token punctuation\">,<\/span> has_final<span class=\"token punctuation\">)<\/span>       <span class=\"token comment\"># True<\/span><br \/>\n    <span class=\"token keyword\">with<\/span> torch<span class=\"token punctuation\">.<\/span>no_grad<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        out <span class=\"token operator\">&#061;<\/span> net<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u8f93\u51fa\u5934\u8f93\u5165\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> net<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>dim<span class=\"token operator\">&#061;<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>item<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u68c0\u67e5\u65b9\u6cd5\u5f88\u6734\u7d20&#xff1a;\u6253\u5370 forward \u91cc head \u524d\u90a3\u4e00\u6b65\u7684\u7c7b\u578b\u3002\u82e5\u662f Identity \u6216\u7f3a\u5931&#xff0c;Pre-LN \u5b9e\u73b0\u5c31\u6709\u95ee\u9898\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u7ec6\u8282\u662f\u5f52\u4e00\u5316\u5bf9\u8c61\u3002final norm \u4f5c\u7528\u5728\u6574\u6761\u7279\u5f81\u7ef4\u4e0a&#xff0c;\u4e0e\u5757\u5185 LN \u7684\u7edf\u8ba1\u8f74\u4e00\u81f4\u3002\u6709\u4e9b\u5b9e\u73b0\u8bef\u628a\u5b83\u653e\u5728 head \u4e4b\u540e&#xff0c;\u90a3\u662f\u9519\u7684\u3002<\/p>\n<p>  #mermaid-svg-klAwN6IlpxvVXB5X{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-klAwN6IlpxvVXB5X .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-klAwN6IlpxvVXB5X .error-icon{fill:#552222;}#mermaid-svg-klAwN6IlpxvVXB5X .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-klAwN6IlpxvVXB5X .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-klAwN6IlpxvVXB5X .marker{fill:#333333;stroke:#333333;}#mermaid-svg-klAwN6IlpxvVXB5X .marker.cross{stroke:#333333;}#mermaid-svg-klAwN6IlpxvVXB5X svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-klAwN6IlpxvVXB5X p{margin:0;}#mermaid-svg-klAwN6IlpxvVXB5X .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-klAwN6IlpxvVXB5X .cluster-label text{fill:#333;}#mermaid-svg-klAwN6IlpxvVXB5X .cluster-label span{color:#333;}#mermaid-svg-klAwN6IlpxvVXB5X .cluster-label span p{background-color:transparent;}#mermaid-svg-klAwN6IlpxvVXB5X .label text,#mermaid-svg-klAwN6IlpxvVXB5X span{fill:#333;color:#333;}#mermaid-svg-klAwN6IlpxvVXB5X .node rect,#mermaid-svg-klAwN6IlpxvVXB5X .node circle,#mermaid-svg-klAwN6IlpxvVXB5X .node ellipse,#mermaid-svg-klAwN6IlpxvVXB5X .node polygon,#mermaid-svg-klAwN6IlpxvVXB5X .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-klAwN6IlpxvVXB5X .rough-node .label text,#mermaid-svg-klAwN6IlpxvVXB5X .node .label text,#mermaid-svg-klAwN6IlpxvVXB5X .image-shape .label,#mermaid-svg-klAwN6IlpxvVXB5X .icon-shape .label{text-anchor:middle;}#mermaid-svg-klAwN6IlpxvVXB5X .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-klAwN6IlpxvVXB5X .rough-node .label,#mermaid-svg-klAwN6IlpxvVXB5X .node .label,#mermaid-svg-klAwN6IlpxvVXB5X .image-shape .label,#mermaid-svg-klAwN6IlpxvVXB5X .icon-shape .label{text-align:center;}#mermaid-svg-klAwN6IlpxvVXB5X .node.clickable{cursor:pointer;}#mermaid-svg-klAwN6IlpxvVXB5X .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-klAwN6IlpxvVXB5X .arrowheadPath{fill:#333333;}#mermaid-svg-klAwN6IlpxvVXB5X .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-klAwN6IlpxvVXB5X .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-klAwN6IlpxvVXB5X .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-klAwN6IlpxvVXB5X .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-klAwN6IlpxvVXB5X .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-klAwN6IlpxvVXB5X .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-klAwN6IlpxvVXB5X .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-klAwN6IlpxvVXB5X .cluster text{fill:#333;}#mermaid-svg-klAwN6IlpxvVXB5X .cluster span{color:#333;}#mermaid-svg-klAwN6IlpxvVXB5X div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-klAwN6IlpxvVXB5X .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-klAwN6IlpxvVXB5X rect.text{fill:none;stroke-width:0;}#mermaid-svg-klAwN6IlpxvVXB5X .icon-shape,#mermaid-svg-klAwN6IlpxvVXB5X .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-klAwN6IlpxvVXB5X .icon-shape p,#mermaid-svg-klAwN6IlpxvVXB5X .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-klAwN6IlpxvVXB5X .icon-shape .label rect,#mermaid-svg-klAwN6IlpxvVXB5X .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-klAwN6IlpxvVXB5X .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-klAwN6IlpxvVXB5X .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-klAwN6IlpxvVXB5X :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-klAwN6IlpxvVXB5X .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-klAwN6IlpxvVXB5X .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-klAwN6IlpxvVXB5X .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u6709<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/p>\n<p>\u65e0<\/p>\n<p><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN \u7f51\u7edc<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>L \u4e2a block \u5806\u53e0<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e3b\u5e72\u8303\u6570\u5df2\u589e\u957f\u5230\u6570\u500d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6709\u65e0 final norm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5934\u8f93\u5165\u88ab\u9489\u56de sqrt d<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8f93\u51fa\u5934\u5403\u5e45\u5ea6\u5931\u63a7\u5411\u91cf<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>logits \u5c3a\u5ea6\u4e0d\u7a33<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8bad\u7ec3\u66f2\u7ebf\u5f02\u5e38<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6b63\u5e38\u6536\u655b<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d F \u5230 H \u7684\u75c7\u72b6\u5f80\u5f80\u4e0d\u8868\u73b0\u4e3a NaN\u3002\u800c\u662f loss \u66f2\u7ebf\u6bdb\u523a\u591a\u3001\u5bf9\u5b66\u4e60\u7387\u5f02\u5e38\u654f\u611f\u3002\u6392\u67e5\u65f6\u5bb9\u6613\u6f0f\u6389\u8fd9\u4e00\u5904\u3002<\/p>\n<h4>7.3 checkpoint \u4e0d\u517c\u5bb9&#xff1a;LN \u6743\u91cd\u8f6c RMSNorm<\/h4>\n<p>LN \u4e0e RMSNorm \u7684\u53c2\u6570\u4e0d\u540c\u6784\u3002LN \u6709 gamma \u4e0e beta&#xff0c;RMSNorm \u53ea\u6709 weight&#xff08;\u5373 gamma&#xff09;\u3002\u76f4\u63a5\u52a0\u8f7d\u4f1a\u62a5\u5f62\u72b6\u4e0d\u5339\u914d\u6216\u952e\u540d\u4e0d\u5339\u914d\u3002<\/p>\n<p>\u952e\u540d\u5c42\u9762&#xff1a;LN \u901a\u5e38\u53eb weight \u4e0e bias&#xff0c;RMSNorm \u53eb weight\u3002\u52a0\u8f7d\u65e7 checkpoint \u65f6 bias \u6ca1\u6709\u5bf9\u5e94\u9879\u3002<\/p>\n<p>\u6570\u503c\u5c42\u9762&#xff1a;\u5373\u4f7f\u5f62\u72b6\u5bf9\u4e0a&#xff0c;\u76f4\u63a5\u590d\u7528 gamma \u4e5f\u662f\u9519\u7684\u3002\u4e24\u4e2a\u539f\u56e0\u3002\u5176\u4e00&#xff0c;LN \u7684\u8f93\u51fa\u5747\u503c\u6052\u4e3a\u96f6&#xff0c;RMSNorm \u4e0d\u4e3a\u96f6\u3002\u540c\u4e00\u4efd gamma \u4f5c\u7528\u5728\u5206\u5e03\u4e0d\u540c\u7684\u8f93\u5165\u4e0a&#xff0c;\u6548\u679c\u4e0d\u540c\u3002\u5176\u4e8c&#xff0c;LN \u9664 std&#xff0c;RMSNorm \u9664 rms&#xff0c;\u5206\u6bcd\u53e3\u5f84\u4e0d\u540c\u3002<\/p>\n<p>\u53ef\u884c\u7684\u8f6c\u6362\u662f\u8fd1\u4f3c\u800c\u975e\u7b49\u4ef7\u3002\u5e38\u89c1\u505a\u6cd5\u662f\u4e22\u6389 beta&#xff08;\u6216\u628a beta \u7684\u5f71\u54cd\u6298\u8fdb\u540e\u7eed\u5c42 bias&#xff09;&#xff0c;gamma \u76f4\u63a5\u6cbf\u7528\u3002\u7136\u540e\u505a\u5c11\u91cf\u6b65\u6570\u7684\u5fae\u8c03\u6821\u51c6\u3002\u793e\u533a\u7684\u4e00\u4e9b\u8f6c\u6362\u811a\u672c\u91c7\u7528\u8fd9\u4e2a\u601d\u8def&#xff0c;\u5c5e\u4e8e\u5de5\u7a0b\u8fd1\u4f3c\u3002<\/p>\n<table>\n<tr>\u9879LayerNormRMSNorm\u517c\u5bb9\u6027<\/tr>\n<tbody>\n<tr>\n<td>\u53c2\u6570\u952e<\/td>\n<td>weight \u4e0e bias<\/td>\n<td>weight<\/td>\n<td>\u952e\u4e0d\u5339\u914d<\/td>\n<\/tr>\n<tr>\n<td>\u53c2\u6570\u91cf<\/td>\n<td>2d<\/td>\n<td>d<\/td>\n<td>\u5f62\u72b6\u4e0d\u5339\u914d<\/td>\n<\/tr>\n<tr>\n<td>\u8f93\u51fa\u5747\u503c<\/td>\n<td>\u6052\u4e3a\u96f6<\/td>\n<td>\u975e\u96f6<\/td>\n<td>\u5206\u5e03\u4e0d\u540c\u6784<\/td>\n<\/tr>\n<tr>\n<td>\u5206\u6bcd<\/td>\n<td>std \u52a0 eps<\/td>\n<td>rms \u52a0 eps<\/td>\n<td>\u53e3\u5f84\u4e0d\u540c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span class=\"token comment\"># checkpoint \u8f6c\u6362\u7684\u952e\u6620\u5c04\u9aa8\u67b6&#xff08;\u793a\u610f&#xff0c;\u9700\u6309\u5b9e\u9645\u6743\u91cd\u7ed3\u6784\u8c03\u6574&#xff09;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> torch<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">convert_ln_to_rms<\/span><span class=\"token punctuation\">(<\/span>sd_ln<span class=\"token punctuation\">,<\/span> keys<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;\u628a LayerNorm \u7684 state_dict \u8fd1\u4f3c\u8f6c\u6210 RMSNorm \u53e3\u5f84&#034;&#034;&#034;<\/span><br \/>\n    sd_rms <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> k <span class=\"token keyword\">in<\/span> keys<span class=\"token punctuation\">:<\/span><br \/>\n        sd_rms<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">.<\/span>replace<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;bias&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;weight&#034;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> sd_ln<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">.<\/span>replace<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;bias&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;weight&#034;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><br \/>\n        <span class=\"token comment\"># beta \u5373 bias \u88ab\u4e22\u5f03&#xff1a;RMSNorm \u65e0\u5bf9\u5e94\u9879&#xff0c;\u9700\u5fae\u8c03\u6821\u51c6<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> sd_rms<\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    d <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">8<\/span><br \/>\n    ln_sd <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token string\">&#034;weight&#034;<\/span><span class=\"token punctuation\">:<\/span> torch<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;bias&#034;<\/span><span class=\"token punctuation\">:<\/span> torch<span class=\"token punctuation\">.<\/span>zeros<span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">}<\/span>   <span class=\"token comment\"># \u6a21\u62df LN \u6743\u91cd<\/span><br \/>\n    rms_sd <span class=\"token operator\">&#061;<\/span> convert_ln_to_rms<span class=\"token punctuation\">(<\/span>ln_sd<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#034;bias&#034;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u8f6c\u6362\u540e\u952e:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">list<\/span><span class=\"token punctuation\">(<\/span>rms_sd<span class=\"token punctuation\">.<\/span>keys<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>     <span class=\"token comment\"># [&#039;weight&#039;]<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;bias \u53bb\u5411: \u4e22\u5f03&#xff0c;\u8bef\u5dee\u9700\u5fae\u8c03\u5438\u6536&#034;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u4ee3\u7801\u6ce8\u91ca\u91cc\u90a3\u53e5&#034;\u8bef\u5dee\u9700\u5fae\u8c03\u5438\u6536&#034;\u662f\u91cd\u70b9\u3002\u8f6c\u6362\u540e\u6a21\u578b\u8f93\u51fa\u7684\u7edf\u8ba1\u5df2\u7ecf\u53d8\u4e86&#xff0c;\u4e0d\u505a\u6821\u51c6\u76f4\u63a5\u63a8\u7406&#xff0c;\u6307\u6807\u4f1a\u6389\u3002<\/p>\n<p>\u53cd\u8fc7\u6765 RMSNorm \u8f6c LN \u4e5f\u4e00\u6837\u4e0d\u7b49\u4ef7\u3002\u9700\u8981\u7ed9 beta \u8865\u96f6\u521d\u59cb\u5316&#xff0c;\u540c\u6837\u8981\u5fae\u8c03\u3002\u7ed3\u8bba\u662f\u4e24\u79cd\u5f52\u4e00\u5316\u7684\u6743\u91cd\u4e0d\u4e92\u6362&#xff0c;\u6539\u67b6\u6784\u610f\u5473\u7740\u91cd\u8bad\u6216\u81f3\u5c11\u6821\u51c6\u3002<\/p>\n<p>  #mermaid-svg-jCduQZOvJljlE0qB{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-jCduQZOvJljlE0qB .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-jCduQZOvJljlE0qB .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-jCduQZOvJljlE0qB .error-icon{fill:#552222;}#mermaid-svg-jCduQZOvJljlE0qB .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-jCduQZOvJljlE0qB .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-jCduQZOvJljlE0qB .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-jCduQZOvJljlE0qB .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-jCduQZOvJljlE0qB .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-jCduQZOvJljlE0qB .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-jCduQZOvJljlE0qB .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-jCduQZOvJljlE0qB .marker{fill:#333333;stroke:#333333;}#mermaid-svg-jCduQZOvJljlE0qB .marker.cross{stroke:#333333;}#mermaid-svg-jCduQZOvJljlE0qB svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-jCduQZOvJljlE0qB p{margin:0;}#mermaid-svg-jCduQZOvJljlE0qB .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-jCduQZOvJljlE0qB .cluster-label text{fill:#333;}#mermaid-svg-jCduQZOvJljlE0qB .cluster-label span{color:#333;}#mermaid-svg-jCduQZOvJljlE0qB .cluster-label span p{background-color:transparent;}#mermaid-svg-jCduQZOvJljlE0qB .label text,#mermaid-svg-jCduQZOvJljlE0qB span{fill:#333;color:#333;}#mermaid-svg-jCduQZOvJljlE0qB .node rect,#mermaid-svg-jCduQZOvJljlE0qB .node circle,#mermaid-svg-jCduQZOvJljlE0qB .node ellipse,#mermaid-svg-jCduQZOvJljlE0qB .node polygon,#mermaid-svg-jCduQZOvJljlE0qB .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-jCduQZOvJljlE0qB .rough-node .label text,#mermaid-svg-jCduQZOvJljlE0qB .node .label text,#mermaid-svg-jCduQZOvJljlE0qB .image-shape .label,#mermaid-svg-jCduQZOvJljlE0qB .icon-shape .label{text-anchor:middle;}#mermaid-svg-jCduQZOvJljlE0qB .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-jCduQZOvJljlE0qB .rough-node .label,#mermaid-svg-jCduQZOvJljlE0qB .node .label,#mermaid-svg-jCduQZOvJljlE0qB .image-shape .label,#mermaid-svg-jCduQZOvJljlE0qB .icon-shape .label{text-align:center;}#mermaid-svg-jCduQZOvJljlE0qB .node.clickable{cursor:pointer;}#mermaid-svg-jCduQZOvJljlE0qB .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-jCduQZOvJljlE0qB .arrowheadPath{fill:#333333;}#mermaid-svg-jCduQZOvJljlE0qB .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-jCduQZOvJljlE0qB .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-jCduQZOvJljlE0qB .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-jCduQZOvJljlE0qB .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-jCduQZOvJljlE0qB .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-jCduQZOvJljlE0qB .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-jCduQZOvJljlE0qB .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-jCduQZOvJljlE0qB .cluster text{fill:#333;}#mermaid-svg-jCduQZOvJljlE0qB .cluster span{color:#333;}#mermaid-svg-jCduQZOvJljlE0qB div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-jCduQZOvJljlE0qB .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-jCduQZOvJljlE0qB rect.text{fill:none;stroke-width:0;}#mermaid-svg-jCduQZOvJljlE0qB .icon-shape,#mermaid-svg-jCduQZOvJljlE0qB .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-jCduQZOvJljlE0qB .icon-shape p,#mermaid-svg-jCduQZOvJljlE0qB .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-jCduQZOvJljlE0qB .icon-shape .label rect,#mermaid-svg-jCduQZOvJljlE0qB .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-jCduQZOvJljlE0qB .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-jCduQZOvJljlE0qB .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-jCduQZOvJljlE0qB :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-jCduQZOvJljlE0qB .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-jCduQZOvJljlE0qB .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-jCduQZOvJljlE0qB .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u65e7 LayerNorm checkpoint<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u53d6\u51fa weight \u4e0e bias<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>weight \u76f4\u63a5\u6620\u5c04\u5230 gamma<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>bias \u65e0\u5bf9\u5e94\u9879<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e22\u5f03\u6216\u6298\u8fdb\u4e0b\u6e38<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5206\u5e03\u5df2\u6539\u53d8<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5fc5\u987b\u5c0f\u6b65\u6570\u5fae\u8c03\u6821\u51c6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f97\u5230\u53ef\u7528\u7684 RMSNorm \u6743\u91cd<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u4e2d F \u662f\u6240\u6709\u8f6c\u6362\u811a\u672c\u7684\u5171\u540c\u524d\u63d0\u3002\u4efb\u4f55\u58f0\u79f0\u65e0\u635f\u8f6c\u6362 LN \u5230 RMSNorm \u7684\u8bf4\u6cd5\u90fd\u503c\u5f97\u6000\u7591\u3002\u6570\u5b66\u4e0a\u4e0d\u5b58\u5728\u8fd9\u4e2a\u7b49\u4ef7\u6620\u5c04\u3002<\/p>\n<h4>7.4 \u7a33\u5b9a\u4e0e\u8d28\u91cf\u7684\u6743\u8861<\/h4>\n<p>\u6700\u540e\u4e00\u4e2a\u8fb9\u754c\u95ee\u9898&#xff1a;\u7a33\u5b9a\u662f\u4e0d\u662f\u65e0\u6761\u4ef6\u7684\u597d\u3002<\/p>\n<p>Pre-LN \u7684\u7a33\u5b9a\u6765\u81ea\u4e3b\u5e72\u65e0\u7ea6\u675f&#xff0c;\u4ee3\u4ef7\u662f\u8303\u6570\u9010\u5c42\u589e\u957f\u3001\u540e\u671f\u5c42\u76f8\u5bf9\u8d21\u732e\u9012\u51cf\u3002Post-LN \u7684\u7ea6\u675f\u66f4\u5f3a&#xff0c;\u8bad\u7ec3\u66f4\u96be&#xff0c;\u4f46\u8fd9\u4e2a\u7ea6\u675f\u672c\u8eab\u53ef\u80fd\u5e26\u6765\u9690\u5f0f\u6b63\u5219\u6548\u679c\u3002<\/p>\n<p>Xiong \u7b49\u4eba\u7684\u5b9e\u9a8c\u53e3\u5f84\u662f&#xff1a;\u8c03\u53c2\u5230\u4f4d\u7684 Post-LN \u4e0e Pre-LN \u6700\u7ec8\u6307\u6807\u76f8\u5f53\u3002\u8fd9\u6ca1\u6709\u5426\u5b9a Post-LN \u7684\u6f5c\u5728\u8d28\u91cf\u4f18\u52bf&#xff0c;\u53ea\u662f\u8bf4\u5728\u4ed6\u4eec\u7684\u4efb\u52a1\u4e0a\u4e24\u8005\u6253\u5e73\u3002<\/p>\n<p>\u540e\u7eed\u5de5\u4f5c\u7ed9\u51fa\u4e86\u66f4\u7ec6\u7684\u56fe\u666f\u3002DeepNorm \u8bf4\u660e Post-LN \u7684\u6df1\u5c42\u5316\u53ef\u4ee5\u7528\u6b8b\u5dee\u7f29\u653e\u6551\u56de\u6765\u3002\u8fd9\u4fa7\u9762\u5370\u8bc1 Post-LN \u7684\u7ed3\u6784\u672c\u8eab\u6709\u4fdd\u7559\u4ef7\u503c\u3002Sandwich \u7c7b\u7ed3\u6784\u5219\u5c1d\u8bd5\u517c\u5f97&#xff1a;\u4e3b\u5e72\u7a33\u4e00\u70b9&#xff0c;\u540c\u65f6\u7ea6\u675f\u8f93\u51fa\u3002<\/p>\n<p>\u5b9e\u8df5\u5efa\u8bae\u5206\u60c5\u51b5\u3002\u7814\u7a76\u6027\u5c0f\u5b9e\u9a8c&#xff0c;Pre-RMSNorm \u662f\u6700\u4f4e\u6210\u672c\u7684\u9009\u62e9\u3002\u8ffd\u6c42\u6781\u81f4\u6307\u6807\u4e14\u6709\u8c03\u53c2\u9884\u7b97&#xff0c;\u53ef\u4ee5\u8bd5 Post-LN \u52a0\u7cbe\u7ec6 warm-up\u3002\u590d\u73b0\u5df2\u53d1\u8868\u6a21\u578b&#xff0c;\u4e25\u683c\u6309\u539f\u6587\u6765\u3002<\/p>\n<p>\u4e00\u4e2a\u5e38\u88ab\u5ffd\u7565\u7684\u89c2\u5bdf\u89d2\u5ea6&#xff1a;\u7a33\u5b9a\u6027\u7684\u6536\u76ca\u4e3b\u8981\u5728\u8bad\u7ec3\u65e9\u671f&#xff0c;\u8d28\u91cf\u7684\u5dee\u5f02\u4e3b\u8981\u5728\u8bad\u7ec3\u540e\u671f\u3002\u4e24\u8005\u4e0d\u51b2\u7a81\u3002\u6df7\u5408\u7b56\u7565&#xff08;\u5148 Pre-LN \u540e\u8f6c Post-LN&#xff09;\u5728\u90e8\u5206\u5de5\u4f5c\u91cc\u88ab\u63a2\u7d22\u8fc7\u3002\u793e\u533a\u53e3\u5f84\u4e0d\u4e00&#xff0c;\u672c\u7bc7\u53ea\u8bb0\u5f55\u73b0\u8c61\u3002<\/p>\n<table>\n<tr>\u76ee\u6807\u5efa\u8bae\u7406\u7531<\/tr>\n<tbody>\n<tr>\n<td>\u5feb\u901f\u8fed\u4ee3<\/td>\n<td>Pre-RMSNorm<\/td>\n<td>\u514d warmup&#xff0c;\u5bb9\u9519\u9ad8<\/td>\n<\/tr>\n<tr>\n<td>\u6781\u81f4\u6307\u6807<\/td>\n<td>Post-LN \u52a0\u8c03\u53c2<\/td>\n<td>\u9690\u5f0f\u6b63\u5219\u53ef\u80fd\u66f4\u4f18<\/td>\n<\/tr>\n<tr>\n<td>\u590d\u73b0<\/td>\n<td>\u4e25\u683c\u6309\u539f\u6587<\/td>\n<td>\u907f\u514d\u4e0d\u53ef\u63a7\u504f\u5dee<\/td>\n<\/tr>\n<tr>\n<td>\u8d85\u5927\u6a21\u578b<\/td>\n<td>Pre-RMSNorm \u52a0 QK-Norm<\/td>\n<td>\u540e\u671f\u7a33\u5b9a\u6027\u5fc5\u8981<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>  #mermaid-svg-x4etBxmFwkrgze6p{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-x4etBxmFwkrgze6p .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-x4etBxmFwkrgze6p .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-x4etBxmFwkrgze6p .error-icon{fill:#552222;}#mermaid-svg-x4etBxmFwkrgze6p .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-x4etBxmFwkrgze6p .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-x4etBxmFwkrgze6p .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-x4etBxmFwkrgze6p .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-x4etBxmFwkrgze6p .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-x4etBxmFwkrgze6p .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-x4etBxmFwkrgze6p .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-x4etBxmFwkrgze6p .marker{fill:#333333;stroke:#333333;}#mermaid-svg-x4etBxmFwkrgze6p .marker.cross{stroke:#333333;}#mermaid-svg-x4etBxmFwkrgze6p svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-x4etBxmFwkrgze6p p{margin:0;}#mermaid-svg-x4etBxmFwkrgze6p .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-x4etBxmFwkrgze6p .cluster-label text{fill:#333;}#mermaid-svg-x4etBxmFwkrgze6p .cluster-label span{color:#333;}#mermaid-svg-x4etBxmFwkrgze6p .cluster-label span p{background-color:transparent;}#mermaid-svg-x4etBxmFwkrgze6p .label text,#mermaid-svg-x4etBxmFwkrgze6p span{fill:#333;color:#333;}#mermaid-svg-x4etBxmFwkrgze6p .node rect,#mermaid-svg-x4etBxmFwkrgze6p .node circle,#mermaid-svg-x4etBxmFwkrgze6p .node ellipse,#mermaid-svg-x4etBxmFwkrgze6p .node polygon,#mermaid-svg-x4etBxmFwkrgze6p .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-x4etBxmFwkrgze6p .rough-node .label text,#mermaid-svg-x4etBxmFwkrgze6p .node .label text,#mermaid-svg-x4etBxmFwkrgze6p .image-shape .label,#mermaid-svg-x4etBxmFwkrgze6p .icon-shape .label{text-anchor:middle;}#mermaid-svg-x4etBxmFwkrgze6p .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-x4etBxmFwkrgze6p .rough-node .label,#mermaid-svg-x4etBxmFwkrgze6p .node .label,#mermaid-svg-x4etBxmFwkrgze6p .image-shape .label,#mermaid-svg-x4etBxmFwkrgze6p .icon-shape .label{text-align:center;}#mermaid-svg-x4etBxmFwkrgze6p .node.clickable{cursor:pointer;}#mermaid-svg-x4etBxmFwkrgze6p .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-x4etBxmFwkrgze6p .arrowheadPath{fill:#333333;}#mermaid-svg-x4etBxmFwkrgze6p .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-x4etBxmFwkrgze6p .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-x4etBxmFwkrgze6p .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-x4etBxmFwkrgze6p .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-x4etBxmFwkrgze6p .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-x4etBxmFwkrgze6p .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-x4etBxmFwkrgze6p .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-x4etBxmFwkrgze6p .cluster text{fill:#333;}#mermaid-svg-x4etBxmFwkrgze6p .cluster span{color:#333;}#mermaid-svg-x4etBxmFwkrgze6p div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-x4etBxmFwkrgze6p .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-x4etBxmFwkrgze6p rect.text{fill:none;stroke-width:0;}#mermaid-svg-x4etBxmFwkrgze6p .icon-shape,#mermaid-svg-x4etBxmFwkrgze6p .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-x4etBxmFwkrgze6p .icon-shape p,#mermaid-svg-x4etBxmFwkrgze6p .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-x4etBxmFwkrgze6p .icon-shape .label rect,#mermaid-svg-x4etBxmFwkrgze6p .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-x4etBxmFwkrgze6p .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-x4etBxmFwkrgze6p .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-x4etBxmFwkrgze6p :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-x4etBxmFwkrgze6p .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-x4etBxmFwkrgze6p .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-x4etBxmFwkrgze6p .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7a33\u5b9a\u4e0e\u8d28\u91cf\u7684\u6743\u8861<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7a33\u5b9a\u6027\u6536\u76ca\u96c6\u4e2d\u5728\u8bad\u7ec3\u65e9\u671f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8d28\u91cf\u5dee\u5f02\u4f53\u73b0\u5728\u8bad\u7ec3\u540e\u671f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN \u514d warmup \u5feb\u901f\u6536\u655b<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Post-LN \u7ea6\u675f\u53ef\u80fd\u5e26\u6765\u6b63\u5219\u6536\u76ca<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u591a\u6570\u573a\u666f\u9009 Pre-RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6709\u9884\u7b97\u65f6\u503c\u5f97\u4e00\u8bd5<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u8c03\u53c2\u6210\u672c\u9ad8 \u5931\u8d25\u4e5f\u5e38\u89c1<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6309\u573a\u666f\u51b3\u7b56 \u4e0d\u8ff7\u4fe1\u5355\u9009<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u91cc\u6700\u540e\u4e00\u6761\u56de\u5230\u5de5\u7a0b\u5e38\u8bc6&#xff1a;\u67b6\u6784\u9009\u62e9\u662f\u6743\u8861&#xff0c;\u4e0d\u662f\u7ad9\u961f\u3002\u80fd\u628a\u6743\u8861\u7684\u8fb9\u754c\u8bf4\u6e05\u695a&#xff0c;\u6bd4\u7ed9\u51fa\u552f\u4e00\u7b54\u6848\u66f4\u6709\u7528\u3002<\/p>\n<h3>\u603b\u7ed3<\/h3>\n<p>\u672c\u7bc7\u6838\u5fc3\u7ed3\u8bba<\/p>\n<p>\u672c\u7bc7\u6cbf\u7740\u4e00\u6761\u7ebf\u8d70\u5b8c&#xff1a;\u4e3a\u4ec0\u4e48\u9700\u8981\u5f52\u4e00\u5316\u3001\u653e\u5728\u54ea\u3001\u80fd\u4e0d\u80fd\u51cf\u3001\u6b8b\u5dee\u5728\u505a\u4ec0\u4e48\u3002<\/p>\n<p>\u7ed3\u8bba\u4e00&#xff1a;\u6df1\u7f51\u7edc\u7684\u524d\u5411\u4e0e\u53cd\u5411\u90fd\u662f\u4e58\u6cd5\u94fe&#xff0c;\u5e45\u5ea6\u4e0d\u53d7\u63a7\u5c31\u6307\u6570\u53d1\u6563\u3002\u5f52\u4e00\u5316\u628a\u6bcf\u5c42\u8f93\u5165\u5e45\u5ea6\u9489\u56de\u56fa\u5b9a\u8303\u56f4&#xff0c;\u662f\u6df1\u7f51\u7edc\u53ef\u8bad\u7684\u524d\u63d0\u3002\u5b9e\u9a8c\u4f50\u8bc1&#xff1a;20 \u5c42\u73a9\u5177\u7f51\u7edc\u65e0\u5f52\u4e00\u5316\u5728 300 \u6b65\u5185 NaN&#xff0c;12 \u5c42\u5df2\u660e\u663e\u9000\u5316\u3002<\/p>\n<p>\u7ed3\u8bba\u4e8c&#xff1a;\u4f4d\u7f6e\u51b3\u5b9a\u68af\u5ea6\u8def\u5f84\u3002Post-LN \u628a LN \u653e\u5728\u4e3b\u5e72\u4e0a&#xff0c;\u521d\u59cb\u5316\u65f6\u9760\u8fd1\u8f93\u51fa\u5c42\u7684\u68af\u5ea6\u504f\u5927&#xff0c;\u5fc5\u987b warm-up\u3002Pre-LN \u628a LN \u632a\u8fdb\u5b50\u5c42&#xff0c;\u4e3b\u5e72\u53ea\u5269\u52a0\u6cd5&#xff0c;\u68af\u5ea6\u6709\u6052\u7b49\u76f4\u901a\u8def\u5f84\u3002\u514d warm-up \u4e14\u6df1 30 \u5c42\u4ecd\u7a33\u5b9a\u3002<\/p>\n<p>\u7ed3\u8bba\u4e09&#xff1a;RMSNorm \u7684\u51cf\u6cd5\u662f\u780d\u6389\u5747\u503c\u4e2d\u5fc3\u5316\u4e0e beta\u3002\u8d28\u91cf\u4e0e LN \u76f8\u5f53&#xff0c;\u6574\u6a21\u578b\u63d0\u901f 7% \u5230 64%&#xff0c;Transformer \u573a\u666f 7% \u5230 9%\u3002\u7b97\u5b50\u7ea7\u63d0\u901f\u7ea6 15%&#xff0c;\u53c2\u6570\u51cf\u534a\u3002\u4ee3\u4ef7\u662f\u8f93\u51fa\u5747\u503c\u975e\u96f6\u3001\u5206\u5e03\u4e0e LN \u4e0d\u540c\u6784\u3002<\/p>\n<p>\u7ed3\u8bba\u56db&#xff1a;\u6b8b\u5dee\u8fde\u63a5\u63d0\u4f9b\u524d\u5411\u6052\u7b49\u901a\u9053\u4e0e\u53cd\u5411\u6052\u7b49\u68af\u5ea6\u3002\u6570\u503c\u5b9e\u9a8c\u91cc\u6052\u7b49\u9879\u5360\u68af\u5ea6\u8303\u6570\u7ea6 0.88\u3002\u6b8b\u5dee\u6d41\u89c6\u89d2\u628a\u4e3b\u5e72\u770b\u4f5c\u4fe1\u606f\u9ad8\u901f\u516c\u8def&#xff0c;\u6bcf\u5c42\u5411\u5176\u8bfb\u5199\u3002Pre-LN \u4e0b\u8fd9\u6761\u6d41\u7684\u8303\u6570\u9010\u5c42\u589e\u957f&#xff0c;\u521d\u59cb\u5316\u65f6 12 \u5c42\u7ea6\u6da8\u4e24\u6210\u3002\u56e0\u6b64\u5fc5\u987b\u6709 final norm\u3002<\/p>\n<p>\u4e0e\u524d\u540e\u7bc7\u7684\u8854\u63a5<\/p>\n<p>\u4e0a\u4e00\u7bc7\u8bb2 FFN \u662f\u53c2\u6570\u5927\u5934\u4e0e\u77e5\u8bc6\u5bb9\u5668\u3002\u672c\u7bc7\u8865\u4e0a\u8ba9\u51e0\u5341\u5c42 FFN \u4e0e\u6ce8\u610f\u529b\u80fd\u4e00\u8d77\u8bad\u7ec3\u7684\u7a33\u5b9a\u88c5\u7f6e\u3002<\/p>\n<p>\u4e0b\u4e00\u7bc7\u8bb2\u4f4d\u7f6e\u7f16\u7801\u3002\u6b8b\u5dee\u6d41\u7ed9\u4e86\u4fe1\u606f\u4e00\u6761\u8de8\u5c42\u901a\u9053\u3002\u4f4d\u7f6e\u7f16\u7801\u8981\u89e3\u51b3\u7684\u662f\u4fe1\u606f\u5728\u5e8f\u5217\u7ef4\u5ea6\u7684\u5b9a\u4f4d\u3002\u4e24\u8005\u5171\u540c\u6784\u6210 token \u8868\u793a\u7684\u4e24\u4e2a\u5750\u6807\u8f74\u3002<\/p>\n<table>\n<tr>\u672c\u7bc7\u8981\u70b9\u4e00\u53e5\u8bdd\u53e3\u5f84<\/tr>\n<tbody>\n<tr>\n<td>\u4e3a\u4ec0\u4e48\u5f52\u4e00\u5316<\/td>\n<td>\u9489\u4f4f\u6bcf\u5c42\u8f93\u5165\u5e45\u5ea6&#xff0c;\u622a\u65ad\u68af\u5ea6\u7206\u70b8\u6b63\u53cd\u9988\u73af<\/td>\n<\/tr>\n<tr>\n<td>Post \u8fd8\u662f Pre<\/td>\n<td>Pre \u4e3b\u5e72\u6709\u6052\u7b49\u68af\u5ea6&#xff0c;\u6df1\u6a21\u578b\u514d warmup<\/td>\n<\/tr>\n<tr>\n<td>RMSNorm \u51cf\u4e86\u4ec0\u4e48<\/td>\n<td>\u51cf mean \u89c4\u7ea6\u4e0e beta&#xff0c;\u8d28\u91cf\u6301\u5e73\u901f\u5ea6\u5feb<\/td>\n<\/tr>\n<tr>\n<td>\u6b8b\u5dee\u5728\u505a\u4ec0\u4e48<\/td>\n<td>\u524d\u5411\u4fdd\u4fe1\u606f&#xff0c;\u53cd\u5411\u4fdd\u68af\u5ea6&#xff0c;\u6052\u7b49\u9879\u515c\u5e95<\/td>\n<\/tr>\n<tr>\n<td>\u6b8b\u5dee\u6d41<\/td>\n<td>\u4e3b\u5e72\u662f\u9ad8\u901f\u516c\u8def&#xff0c;\u5b50\u5c42\u662f\u8bfb\u5199\u53e3<\/td>\n<\/tr>\n<tr>\n<td>final norm<\/td>\n<td>Pre-LN \u5fc5\u914d&#xff0c;\u538b\u56de\u9010\u5c42\u589e\u957f\u7684\u8303\u6570<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>  #mermaid-svg-ipPB46hjDXI4cOBH{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-ipPB46hjDXI4cOBH .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-ipPB46hjDXI4cOBH .error-icon{fill:#552222;}#mermaid-svg-ipPB46hjDXI4cOBH .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-ipPB46hjDXI4cOBH .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-ipPB46hjDXI4cOBH .marker{fill:#333333;stroke:#333333;}#mermaid-svg-ipPB46hjDXI4cOBH .marker.cross{stroke:#333333;}#mermaid-svg-ipPB46hjDXI4cOBH svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-ipPB46hjDXI4cOBH p{margin:0;}#mermaid-svg-ipPB46hjDXI4cOBH .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-ipPB46hjDXI4cOBH .cluster-label text{fill:#333;}#mermaid-svg-ipPB46hjDXI4cOBH .cluster-label span{color:#333;}#mermaid-svg-ipPB46hjDXI4cOBH .cluster-label span p{background-color:transparent;}#mermaid-svg-ipPB46hjDXI4cOBH .label text,#mermaid-svg-ipPB46hjDXI4cOBH span{fill:#333;color:#333;}#mermaid-svg-ipPB46hjDXI4cOBH .node rect,#mermaid-svg-ipPB46hjDXI4cOBH .node circle,#mermaid-svg-ipPB46hjDXI4cOBH .node ellipse,#mermaid-svg-ipPB46hjDXI4cOBH .node polygon,#mermaid-svg-ipPB46hjDXI4cOBH .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-ipPB46hjDXI4cOBH .rough-node .label text,#mermaid-svg-ipPB46hjDXI4cOBH .node .label text,#mermaid-svg-ipPB46hjDXI4cOBH .image-shape .label,#mermaid-svg-ipPB46hjDXI4cOBH .icon-shape .label{text-anchor:middle;}#mermaid-svg-ipPB46hjDXI4cOBH .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-ipPB46hjDXI4cOBH .rough-node .label,#mermaid-svg-ipPB46hjDXI4cOBH .node .label,#mermaid-svg-ipPB46hjDXI4cOBH .image-shape .label,#mermaid-svg-ipPB46hjDXI4cOBH .icon-shape .label{text-align:center;}#mermaid-svg-ipPB46hjDXI4cOBH .node.clickable{cursor:pointer;}#mermaid-svg-ipPB46hjDXI4cOBH .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-ipPB46hjDXI4cOBH .arrowheadPath{fill:#333333;}#mermaid-svg-ipPB46hjDXI4cOBH .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-ipPB46hjDXI4cOBH .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-ipPB46hjDXI4cOBH .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-ipPB46hjDXI4cOBH .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-ipPB46hjDXI4cOBH .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-ipPB46hjDXI4cOBH .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-ipPB46hjDXI4cOBH .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-ipPB46hjDXI4cOBH .cluster text{fill:#333;}#mermaid-svg-ipPB46hjDXI4cOBH .cluster span{color:#333;}#mermaid-svg-ipPB46hjDXI4cOBH div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-ipPB46hjDXI4cOBH .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-ipPB46hjDXI4cOBH rect.text{fill:none;stroke-width:0;}#mermaid-svg-ipPB46hjDXI4cOBH .icon-shape,#mermaid-svg-ipPB46hjDXI4cOBH .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-ipPB46hjDXI4cOBH .icon-shape p,#mermaid-svg-ipPB46hjDXI4cOBH .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-ipPB46hjDXI4cOBH .icon-shape .label rect,#mermaid-svg-ipPB46hjDXI4cOBH .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-ipPB46hjDXI4cOBH .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-ipPB46hjDXI4cOBH .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-ipPB46hjDXI4cOBH :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}#mermaid-svg-ipPB46hjDXI4cOBH .default&gt;*{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-ipPB46hjDXI4cOBH .default span{fill:#faf9f5!important;stroke:#ffffff!important;color:#000000!important;stroke-width:0px!important;}#mermaid-svg-ipPB46hjDXI4cOBH .default tspan{fill:#000000!important;}<\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span class=\"edgeLabel\"><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6df1\u5c42\u7f51\u7edc\u8bad\u7ec3\u4e0d\u7a33<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u5f52\u4e00\u5316 \u63a7\u5e45\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6b8b\u5dee \u4fdd\u68af\u5ea6<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4f4d\u7f6e\u9009\u62e9 Post \u6216 Pre<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>Pre-LN \u6052\u7b49\u68af\u5ea6\u76f4\u8fbe<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u7b97\u5b50\u7b80\u5316 LN \u5230 RMSNorm<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>RMSNorm \u66f4\u5feb\u66f4\u7701<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u6b8b\u5dee\u6d41 \u4fe1\u606f\u9ad8\u901f\u516c\u8def<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u4e3b\u5e72\u8303\u6570\u9010\u5c42\u589e\u957f<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>final norm \u6536\u5c3e<\/p>\n<p><\/span><\/p>\n<p>         <span style=\"color:#000000 !important\" class=\"nodeLabel\"><\/p>\n<p>\u73b0\u4ee3\u4e3b\u6d41 Pre-RMSNorm \u52a0 final norm<\/p>\n<p><\/span><\/p>\n<p>\u56fe\u662f\u5168\u7bc7\u7684\u7ed3\u6784\u56de\u987e\u3002\u4e24\u6761\u7ebf&#xff08;\u5f52\u4e00\u5316\u63a7\u5e45\u5ea6\u3001\u6b8b\u5dee\u4fdd\u68af\u5ea6&#xff09;\u5728 Pre-RMSNorm \u52a0 final norm \u5904\u6c47\u5408\u3002\u8fd9\u5c31\u662f\u4eca\u5929\u4e3b\u6d41\u5927\u6a21\u578b\u7684\u5b9e\u9645\u5f62\u6001\u3002<\/p>\n<h3>\u5916\u90e8\u5f15\u7528<\/h3>\n<ul>\n<li>Ba, J. L., Kiros, J. R., Hinton, G. E. Layer Normalization. arXiv:1607.06450, 2016. \u7edf\u8ba1\u6765\u81ea\u5355\u8bad\u7ec3\u6837\u672c\u7684\u5168\u90e8 summed inputs&#xff0c;\u8bad\u7ec3\u6d4b\u8bd5\u8ba1\u7b97\u4e00\u81f4&#xff0c;\u7a33\u5b9a\u5faa\u73af\u7f51\u7edc\u9690\u72b6\u6001\u52a8\u6001\u3002https:\/\/arxiv.org\/abs\/1607.06450<\/li>\n<li>Zhang, B., Sennrich, R. Root Mean Square Layer Normalization. arXiv:1910.07467, 2019. \u5047\u8bbe re-centering invariance \u975e\u5fc5\u8981&#xff0c;RMSNorm \u8d28\u91cf\u4e0e LN \u76f8\u5f53\u3001\u8fd0\u884c\u65f6\u95f4\u51cf\u5c11 7% \u5230 64%&#xff1b;Transformer \u573a\u666f Table 5 \u63d0\u901f 7% \u5230 9%&#xff0c;\u65e0\u5f52\u4e00\u5316\u57fa\u7ebf\u8bad\u7ec3\u5931\u8d25\u3002https:\/\/arxiv.org\/abs\/1910.07467<\/li>\n<li>Xiong, R. et al. On Layer Normalization in the Transformer Architecture. arXiv:2002.04745, 2020. \u5747\u503c\u573a\u5206\u6790\u8bc1\u660e Post-LN \u521d\u59cb\u5316\u65f6\u9760\u8fd1\u8f93\u51fa\u5c42\u53c2\u6570\u68af\u5ea6\u504f\u5927&#xff0c;Pre-LN \u68af\u5ea6\u8868\u73b0\u826f\u597d\u53ef\u53bb warm-up&#xff1b;IWSLT14 \u4e0a Pre-LN \u7b2c 9 \u4e2a checkpoint \u8ffd\u5e73 Post-LN \u7b2c 15 \u4e2a\u3002https:\/\/arxiv.org\/abs\/2002.04745<\/li>\n<li>He, K. et al. Deep Residual Learning for Image Recognition. arXiv:1512.03385, 2015. \u6b8b\u5dee\u5b66\u4e60\u6846\u67b6&#xff0c;\u6700\u6df1 152 \u5c42&#xff0c;ImageNet \u6d4b\u8bd5\u96c6\u96c6\u6210\u9519\u8bef\u7387 3.57%\u3002https:\/\/arxiv.org\/abs\/1512.03385<\/li>\n<li>Vaswani, A. et al. Attention Is All You Need. arXiv:1706.03762, 2017. Post-LN \u539f\u59cb\u53e3\u5f84&#xff0c;\u6bcf\u4e2a\u5b50\u5c42\u914d\u6b8b\u5dee\u4e0e LN\u3002https:\/\/arxiv.org\/abs\/1706.03762<\/li>\n<li>PyTorch \u5b98\u65b9\u6587\u6863. torch.nn.LayerNorm. \u5f52\u4e00\u5316\u9ed8\u8ba4\u4f5c\u7528\u4e8e\u6700\u540e\u4e00\u7ef4&#xff0c;var \u91c7\u7528\u6709\u504f\u53e3\u5f84\u3002https:\/\/pytorch.org\/docs\/stable\/generated\/torch.nn.LayerNorm.html<\/li>\n<li>Yang, A. et al. Qwen3 Technical Report. arXiv:2505.09388, 2025. \u67b6\u6784\u6cbf\u7528 RMSNorm \u52a0 pre-normalization&#xff0c;\u5f15\u5165 QK-Norm \u5230\u6ce8\u610f\u529b\u673a\u5236\u4ee5\u4fdd\u8bc1\u8bad\u7ec3\u7a33\u5b9a\u3002https:\/\/arxiv.org\/abs\/2505.09388<\/li>\n<li>Dehghani, M. et al. Scaling Vision Transformers to 22 Billion Parameters. arXiv:2302.05442, 2023. \u5927\u89c4\u6a21\u89c6\u89c9 Transformer \u8bad\u7ec3\u4e2d\u5bf9 q \u4e0e k \u505a\u5f52\u4e00\u5316\u4ee5\u7a33\u5b9a\u7684\u516c\u5f00\u5b9e\u8df5\u3002https:\/\/arxiv.org\/abs\/2302.05442<\/li>\n<li>Elhage, N. et al. A Mathematical Framework for Transformer Circuits. Anthropic, 2021. \u6b8b\u5dee\u6d41\u4f5c\u4e3a\u901a\u4fe1\u901a\u9053\u3001\u6ce8\u610f\u529b\u5934\u4e0e FFN \u4f5c\u4e3a\u8bfb\u5199\u7b97\u5b50\u7684\u5206\u6790\u6846\u67b6\u3002https:\/\/transformer-circuits.pub\/2021\/framework\/index.html<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u5f55<br \/>\n1. \u6df1\u7f51\u7edc\u4e3a\u4ec0\u4e48\u9700\u8981\u5f52\u4e00\u5316 1.1 \u5206\u5e03\u6f02\u79fb\u4e0e\u68af\u5ea6\u5931\u63a7&#xff1a;\u4e24\u6761\u5e76\u884c\u7684\u75c5\u70761.2 BatchNorm \u5728 NLP \u7684\u4e09\u5904\u5931\u65481.3 LayerNorm \u516c\u5f0f\u62c6\u89e3&#xff1a;\u5355\u6837\u672c\u5185\u7edf\u8ba1 2. \u4f4d\u7f6e\u4e4b\u4e89&#xff1a;Post-LN \u4e0e Pre-LN 2.1 \u4e24\u79cd\u5199\u6cd5\u7684\u7cbe\u786e\u5b9a\u4e492.2 \u68af\u5ea6\u89c6\u89d2&#xff1a;\u6b8b\u5dee\u4e3b\u5e72\u4e0a\u7684\u76f4\u901a\u8def\u5f842.3 \u8bad\u7ec3\u66f2\u7ebf\u4e0e\u5b66\u4e60\u7387\u654f\u611f\u5ea62.4 \u4e3b\u6d41\u6a21\u578b\u7684\u4e8b\u5b9e\u8868 3. RMSNorm \u7684\u51cf\u6cd5 3.1 \u53bb\u6389\u5747\u503c\u4e2d\u5fc3\u5316\u4e0e bias3.2 <\/p>\n","protected":false},"author":2,"featured_media":112439,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[841,50,86],"topic":[],"class_list":["post-112440","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-transformer","tag-50","tag-86"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Transformer\u539f\u7406-\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/112440.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Transformer\u539f\u7406-\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u76ee\u5f55 1. \u6df1\u7f51\u7edc\u4e3a\u4ec0\u4e48\u9700\u8981\u5f52\u4e00\u5316 1.1 \u5206\u5e03\u6f02\u79fb\u4e0e\u68af\u5ea6\u5931\u63a7&#xff1a;\u4e24\u6761\u5e76\u884c\u7684\u75c5\u70761.2 BatchNorm \u5728 NLP \u7684\u4e09\u5904\u5931\u65481.3 LayerNorm \u516c\u5f0f\u62c6\u89e3&#xff1a;\u5355\u6837\u672c\u5185\u7edf\u8ba1 2. \u4f4d\u7f6e\u4e4b\u4e89&#xff1a;Post-LN \u4e0e Pre-LN 2.1 \u4e24\u79cd\u5199\u6cd5\u7684\u7cbe\u786e\u5b9a\u4e492.2 \u68af\u5ea6\u89c6\u89d2&#xff1a;\u6b8b\u5dee\u4e3b\u5e72\u4e0a\u7684\u76f4\u901a\u8def\u5f842.3 \u8bad\u7ec3\u66f2\u7ebf\u4e0e\u5b66\u4e60\u7387\u654f\u611f\u5ea62.4 \u4e3b\u6d41\u6a21\u578b\u7684\u4e8b\u5b9e\u8868 3. RMSNorm \u7684\u51cf\u6cd5 3.1 \u53bb\u6389\u5747\u503c\u4e2d\u5fc3\u5316\u4e0e bias3.2\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/112440.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-03T08:33:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261003083317-6ac0bdcd410fa.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"87 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/112440.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/112440.html\",\"name\":\"Transformer\u539f\u7406-\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-10-03T08:33:18+00:00\",\"dateModified\":\"2026-10-03T08:33:18+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/112440.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/112440.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/112440.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Transformer\u539f\u7406--\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Transformer\u539f\u7406-\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/112440.html","og_locale":"zh_CN","og_type":"article","og_title":"Transformer\u539f\u7406-\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u76ee\u5f55 1. \u6df1\u7f51\u7edc\u4e3a\u4ec0\u4e48\u9700\u8981\u5f52\u4e00\u5316 1.1 \u5206\u5e03\u6f02\u79fb\u4e0e\u68af\u5ea6\u5931\u63a7&#xff1a;\u4e24\u6761\u5e76\u884c\u7684\u75c5\u70761.2 BatchNorm \u5728 NLP \u7684\u4e09\u5904\u5931\u65481.3 LayerNorm \u516c\u5f0f\u62c6\u89e3&#xff1a;\u5355\u6837\u672c\u5185\u7edf\u8ba1 2. \u4f4d\u7f6e\u4e4b\u4e89&#xff1a;Post-LN \u4e0e Pre-LN 2.1 \u4e24\u79cd\u5199\u6cd5\u7684\u7cbe\u786e\u5b9a\u4e492.2 \u68af\u5ea6\u89c6\u89d2&#xff1a;\u6b8b\u5dee\u4e3b\u5e72\u4e0a\u7684\u76f4\u901a\u8def\u5f842.3 \u8bad\u7ec3\u66f2\u7ebf\u4e0e\u5b66\u4e60\u7387\u654f\u611f\u5ea62.4 \u4e3b\u6d41\u6a21\u578b\u7684\u4e8b\u5b9e\u8868 3. RMSNorm \u7684\u51cf\u6cd5 3.1 \u53bb\u6389\u5747\u503c\u4e2d\u5fc3\u5316\u4e0e bias3.2","og_url":"https:\/\/www.wsisp.com\/helps\/112440.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-10-03T08:33:18+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261003083317-6ac0bdcd410fa.png"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"87 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/112440.html","url":"https:\/\/www.wsisp.com\/helps\/112440.html","name":"Transformer\u539f\u7406-\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-10-03T08:33:18+00:00","dateModified":"2026-10-03T08:33:18+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/112440.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/112440.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/112440.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"Transformer\u539f\u7406--\u6df1\u5c42\u7f51\u7edc\u7684\u7a33\u538b\uff1a\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/112440","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=112440"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/112440\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/112439"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=112440"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=112440"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=112440"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=112440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}