{"id":154,"date":"2026-05-04T21:08:36","date_gmt":"2026-05-04T13:08:36","guid":{"rendered":"https:\/\/www.bojinhu.xyz\/?p=154"},"modified":"2026-04-23T21:13:38","modified_gmt":"2026-04-23T13:13:38","slug":"%e5%85%b3%e4%ba%8enorm%e7%9a%84%e8%a7%a3%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.bojinhu.xyz\/index.php\/2026\/05\/04\/%e5%85%b3%e4%ba%8enorm%e7%9a%84%e8%a7%a3%e6%9e%90\/","title":{"rendered":"\u5173\u4e8eNorm\u7684\u89e3\u6790"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u53ef\u4ee5\u8bf4\uff0c\u5982\u679c\u6ca1\u6709\u6b8b\u5dee\u8fde\u63a5\u548c Layer Normalization\uff08\u5c42\u5f52\u4e00\u5316\uff09\u8fd9\u6837\u4e00\u521a\u4e00\u67d4\u7684\u9ec4\u91d1\u7ec4\u5408\uff0c\u52a8\u8f84\u4e0a\u767e\u5c42\u7684\u5927\u8bed\u8a00\u6a21\u578b\uff08LLM\uff09\u6050\u6015\u65e9\u5df2\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u53d8\u6210\u4e86 NaN \u7684\u6e29\u5e8a\u3002\u4e4b\u524d\u6211\u4eec\u5728 <code>Pre-Norm\/Post-Norm<\/code> \u90a3\u7bc7\u6587\u7ae0\u91cc\uff0c\u804a\u4e86\u5b83\u4eec\u548c\u6b8b\u5dee\u7ed3\u6784\u8054\u624b\u62a4\u822a\u68af\u5ea6\u6d41\u52a8\u7684\u6545\u4e8b\u3002\u800c\u4eca\u5929\uff0c\u6211\u4eec\u8981\u628a\u653e\u5927\u955c\u5bf9\u7126\u5230 <strong>Layer Normalization (LN)<\/strong> \u672c\u8eab\uff0c\u6df1\u5165\u63a2\u7d22\u4e00\u4e2a\u7531\u7cbe\u7ec6\u7684\u201c\u5168\u6d3b\u201d\u624b\u827a\u2014\u2014 <strong>LayerNorm<\/strong> \uff0c\u5e76\u63ed\u79d8\u5b83\u7684\u201c\u540e\u6d6a\u201d\u2014\u2014 <strong>RMSNorm<\/strong>\u2014\u2014\u662f\u5982\u4f55\u7528\u4e00\u62db\u6781\u81f4\u7684\u51cf\u6cd5\uff0c\u7edf\u6cbb\u4e86\u5982\u4eca\u7684\u5927\u6a21\u578b\u4e16\u754c\u7684\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u3001LN \u4ee5\u524d\uff1aBatchNorm \u7684\u9ec4\u91d1\u65f6\u4ee3\u4e0e\u201c\u6c34\u571f\u4e0d\u670d\u201d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728 Transformer \u51fa\u73b0\u4e4b\u524d\uff0c<strong>Batch Normalization (BN) \u624d\u662f\u6df1\u5ea6\u5b66\u4e60\u91cc\u98ce\u5149\u65e0\u9650\u7684\u201c\u6807\u914d\u201d<\/strong> \u3002\u5b83\u5728\u6bcf\u4e2a mini-batch \u5185\uff0c\u5bf9\u6bcf\u4e2a\u7279\u5f81\u901a\u9053\u5206\u522b\u6c42\u5747\u503c\u548c\u65b9\u5dee\u6765\u5f52\u4e00\u5316\uff0c\u518d\u642d\u914d\u53ef\u5b66\u4e60\u7684\u7f29\u653e\u4e0e\u5e73\u79fb\u53c2\u6570\uff0c\u5927\u5927\u52a0\u5feb\u4e86\u8bad\u7ec3\u3001\u7f13\u89e3\u4e86\u68af\u5ea6\u95ee\u9898\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46 BN \u6709\u4e2a\u8f6f\u808b\uff1a\u592a\u4f9d\u8d56\u6279\u5927\u5c0f\u548c\u5e8f\u5217\u957f\u5ea6\u3002\u5bf9 CNN\uff0cmini-batch \u591f\u5927\u65f6\uff0c\u7b97\u51fa\u6765\u7684\u7edf\u8ba1\u91cf\u5f88\u7a33\uff1b\u53ef\u4e00\u65e6 batch size \u5c0f\uff0c\u7edf\u8ba1\u91cf\u5c31\u4e0d\u51c6\u4e86\u3002\u66f4\u8981\u547d\u7684\u662f\uff0c\u5f53\u5b83\u9047\u4e0a\u4e3a\u201c\u53ef\u53d8\u5e8f\u5217\u201d\u800c\u751f\u7684 Transformer \u65f6\uff0c\u95ee\u9898\u66f4\u4e25\u91cd\uff1a\u8bed\u8a00\u5e8f\u5217\u957f\u77ed\u4e0d\u4e00\uff0c\u4e14\u6ce8\u610f\u529b\u5c42\u53ef\u80fd\u53ea\u5173\u6ce8\u5230\u7279\u5b9a\u4f4d\u7f6e\u7684 token\u2014\u2014\u8fd9\u4e9b\u90fd\u5bf9 BN \u7684\u6279\u6b21\u7edf\u8ba1\u63d0\u51fa\u4e86\u5de8\u5927\u6311\u6218\uff0c\u4f7f\u5f97\u5176\u65e0\u6cd5\u76f4\u63a5\u5e94\u7528\u4e8e Transformer \u67b6\u6784\u3002\u800c\u4e14\uff0cTransformer \u63a8\u7406\u65f6\u5f80\u5f80\u662f\u4e00\u4e2a\u4e00\u4e2a token \u5730\u751f\u6210\uff0cBN \u8bad\u7ec3\u4e0e\u63a8\u7406\u7edf\u8ba1\u91cf\u4e0d\u4e00\u81f4\u7684\u987d\u75be\uff0c\u4e5f\u8ba9\u5b83\u5728 LLM \u9886\u57df\u5f7b\u5e95\u201c\u6c34\u571f\u4e0d\u670d\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8e\u662f\uff0c\u9700\u8981\u4e00\u79cd\u8ba1\u7b97\u4e0d\u4f9d\u8d56 batch\u3001\u80fd\u7a33\u5b9a\u5904\u7406\u53d8\u957f\u5e8f\u5217\u7684\u5f52\u4e00\u5316\u65b9\u6cd5\u2014\u2014<strong>LayerNorm \u5e94\u8fd0\u800c\u751f\uff0c\u4ece BN \u624b\u4e2d\u63a5\u8fc7\u4e86\u63a5\u529b\u68d2<\/strong>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u3001LayerNorm \u7b80\u4ecb\uff1a\u4e0d\u6c9f\u901a\uff0c\u53ea\u8015\u8018\u81ea\u5df1\u7684\u4e00\u4ea9\u4e09\u5206\u5730<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">LayerNorm \u7684\u601d\u8def\u5f88\u201c\u72ec\u201d\uff1a\u5b83\u4e0d\u50cf BN \u90a3\u6837\u8de8\u8d8a\u6279\u6b21\u8fdb\u884c\u7edf\u8ba1\uff0c\u800c\u662f<strong>\u6bcf\u6b21\u53ea\u805a\u7126\u4e8e\u4e00\u4e2a\u8bad\u7ec3\u6837\u672c<\/strong>\uff0c\u6cbf\u7740\u201c\u7279\u5f81\u201d\u7ef4\u5ea6\u53bb\u8ba1\u7b97\u5747\u503c\u548c\u65b9\u5dee\uff0c\u5e76\u5bf9\u6bcf\u4e2a\u6837\u672c\u7684\u6240\u6709\u7279\u5f81\u8fdb\u884c\u5f52\u4e00\u5316\u3002\u8fd9\u4e0d\u4ec5\u8ba9\u8bad\u7ec3\u548c\u63a8\u7406\u884c\u4e3a\u505a\u5230\u5b8c\u5168\u4e00\u81f4\uff0c\u8fd8\u8ba9\u5b83\u5728 RNN \u548c\u65e9\u671f\u7684 Transformer \u7b49\u5e8f\u5217\u6a21\u578b\u4e2d\u8868\u73b0\u5353\u8d8a\uff0c\u6709\u6548\u7f13\u89e3\u4e86\u68af\u5ea6\u95ee\u9898\uff0c\u589e\u5f3a\u4e86\u6a21\u578b\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u66f4\u91cd\u8981\u7684\u662f\uff0c\u5b83\u5728\u5e73\u8861\u6a21\u578b\u7684\u201c\u4fe1\u53f7\u5f3a\u5ea6\u201d\u65b9\u9762\u626e\u6f14\u4e86\u5173\u952e\u89d2\u8272\u3002\u4ee5\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u4e3a\u4f8b\uff0c\u82e5\u4e0d\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u4e0d\u540c\u91cf\u7ea7\u7684\u8f93\u5165\u503c\u4f1a\u9020\u6210\u68af\u5ea6\u5e45\u503c\u7684\u5267\u70c8\u6ce2\u52a8\uff1b\u800c LayerNorm \u901a\u8fc7\u5c06\u6570\u636e\u6807\u51c6\u5dee\u63a7\u5236\u5728\u4e00\u4e2a\u5408\u7406\u7684\u533a\u95f4\u5185\uff0c\u80fd\u5b9e\u73b0\u66f4\u5e73\u7a33\u7684\u53c2\u6570\u4f18\u5316\u8fc7\u7a0b\u3002\u6b64\u5916\uff0c\u7531\u4e8e LayerNorm \u5c06\u6570\u636e\u8303\u56f4\u9650\u5236\u5728\u4e00\u4e2a\u53ef\u63a7\u7684\u533a\u95f4\uff0c\u5b83\u8fd8\u4e3a\u540e\u7eed\u91c7\u7528 8-bit \u6216 16-bit \u6d6e\u70b9\u6570\u7b49\u4f4e\u7cbe\u5ea6\u8ba1\u7b97\u63d0\u4f9b\u4e86\u66f4\u575a\u5b9e\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u662f LayerNorm \u7684\u7ecf\u5178\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>y = \\frac{x &#8211; \\mu}{\\sqrt{\\sigma^2 + \\epsilon}} \\cdot \\gamma + \\beta<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff0c$\\mu$ \u662f\u6837\u672c\u7279\u5f81\u7684\u5747\u503c\uff0c$\\sigma^2$ \u662f\u65b9\u5dee\uff0c$\\epsilon$ \u662f\u4e3a\u4e86\u6570\u503c\u7a33\u5b9a\u7684\u5c0f\u5e38\u6570\uff0c$\\gamma$ \u548c $\\beta$ \u5219\u662f\u8ba9\u6a21\u578b\u4fdd\u7559\u6570\u636e\u8868\u8fbe\u7a7a\u95f4\u7684\u53ef\u5b66\u4e60\u7f29\u653e\u4e0e\u504f\u79fb\u53c2\u6570\u3002\u6574\u4e2a\u5f52\u4e00\u5316\u8fc7\u7a0b\u53ef\u4ee5\u7406\u89e3\u4e3a\uff1a\u5148\u51cf\u53bb\u5747\u503c $\\mu$\uff08\u4e2d\u5fc3\u5316\uff09\uff0c\u5c06\u6570\u636e\u5e73\u79fb\u5230\u4ee5 0 \u4e3a\u4e2d\u5fc3\u7684\u4f4d\u7f6e\uff1b\u518d\u9664\u4ee5\u6807\u51c6\u5dee $\\sqrt{\\sigma^2 + \\epsilon}$\uff08\u7f29\u653e\uff09\uff0c\u5c06\u6570\u636e\u7684\u5c3a\u5ea6\u538b\u7f29\u5230\u6807\u51c6\u8303\u56f4\u5185\uff1b\u6700\u540e\u901a\u8fc7 $\\gamma$ \u548c $\\beta$ \u8fdb\u884c\u4eff\u5c04\u53d8\u6362\uff0c\u4fdd\u7559\u5fc5\u8981\u7684\u8868\u8fbe\u7a7a\u95f4\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e09\u3001LayerNorm \u7684\u51e0\u4f55\u54f2\u5b66\uff1a\u4e3a\u4f55\u53bb\u6389\u5747\u503c\u662f\u5173\u952e\uff1f<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">2025 \u5e74\u7684\u4e00\u9879\u7814\u7a76\uff0c\u4ece\u66f4\u6df1\u7684\u51e0\u4f55\u89c6\u89d2\u63ed\u793a\u4e86 LayerNorm \u7684\u5de5\u4f5c\u65b9\u5f0f\uff0c\u8ba9\u5b83\u53d8\u5f97\u66f4\u76f4\u89c2\u4e14\u5bcc\u6709\u753b\u9762\u611f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u4ee5\u60f3\u8c61\u4e00\u4e2a\u9ad8\u7ef4\u7a7a\u95f4\uff0c\u5176\u4e2d\u7684\u5355\u4f4d\u5411\u91cf $\\boldsymbol{1} = [1, 1, \u2026, 1]^T$ \u6307\u5411\u4e00\u4e2a\u201c\u5e73\u5747\u65b9\u5411\u201d\u3002\u7814\u7a76\u6307\u51fa\uff0cLayerNorm \u7684\u6574\u4e2a\u6807\u51c6\u5316\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u6e05\u6670\u5730\u5206\u89e3\u4e3a\u4e09\u6b65\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u79fb\u9664\u201c\u80cc\u666f\u566a\u97f3\u201d<\/strong>\uff1a\u5c06\u8f93\u5165\u5411\u91cf\u6cbf\u7740\u5355\u4f4d\u5411\u91cf $\\boldsymbol{1}$ \u65b9\u5411\u7684\u5206\u91cf\u79fb\u9664\u3002<\/li>\n\n\n\n<li><strong>\u7edf\u4e00\u5c3a\u5ea6<\/strong>\uff1a\u5c06\u5269\u4e0b\u7684\u5411\u91cf\u5f52\u4e00\u5316\u5230\u5355\u4f4d\u957f\u5ea6\u3002<\/li>\n\n\n\n<li><strong>\u9002\u914d\u6a21\u578b\u7a7a\u95f4<\/strong>\uff1a\u5728\u5f52\u4e00\u5316\u540e\u7684\u5411\u91cf\u4e0a\u4e58\u4ee5 $\\sqrt{d}$\uff0c\u5176\u4e2d $d$ \u4e3a\u5411\u91cf\u7ef4\u5ea6\uff0c\u5c06\u5176\u5c3a\u5ea6\u8c03\u6574\u5230\u9002\u5408\u6a21\u578b\u540e\u7eed\u5904\u7406\u7684\u8303\u56f4\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9879\u7814\u7a76\u7684\u7a81\u7834\u6027\u4e0d\u4ec5\u5728\u4e8e\u5176\u6e05\u6670\u7684\u51e0\u4f55\u89e3\u91ca\uff0c\u66f4\u5728\u4e8e\u4e00\u4e2a\u5173\u952e\u6027\u7684\u63a8\u8bba\uff1a\u8fd0\u7528 LayerNorm \u8bad\u7ec3\u597d\u7684 LLM\uff0c\u5728\u63a8\u7406\u65f6\u7684\u6240\u6709\u9690\u85cf\u5c42\u8868\u793a\uff0c\u6700\u7ec8\u90fd\u4f1a\u201c\u4e0d\u7ea6\u800c\u540c\u201d\u5730\u8d8b\u5411\u4e8e\u4e0e $\\boldsymbol{1}$ \u5411\u91cf\u6b63\u4ea4\u7684\u65b9\u5411\u3002\u8fd9\u610f\u5473\u7740\uff0c\u8bad\u7ec3\u5b8c\u6210\u540e\u6a21\u578b\u6240\u6709\u8868\u793a\u7684\u5e73\u5747\u503c\u90fd\u5929\u7136\u63a5\u8fd1 0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u610f\u5473\u7740\uff0c<strong>LayerNorm \u91cc\u90a3\u4e2a\u201c\u51cf\u53bb\u5747\u503c\u201d\u7684\u6b65\u9aa4\uff0c\u6700\u7ec8\u5728\u8bad\u7ec3\u5b8c\u6210\u7684\u6a21\u578b\u91cc\u51e0\u4e4e\u6210\u4e86\u4e00\u79cd\u5929\u7136\u7684\u5197\u4f59\u64cd\u4f5c<\/strong>\u3002\u8fd9\u4e2a\u53d1\u73b0\uff0c\u65e0\u7591\u4e3a RMSNorm \u4e3a\u4f55\u597d\u7528\uff0c\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5173\u952e\u7684\u201c\u4f5c\u6848\u52a8\u673a\u201d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u56db\u3001RMSNorm \u7b80\u4ecb\uff1a\u5982\u4f55\u7528\u4e00\u6b21\u51cf\u6cd5\uff0c\u8d62\u5f97\u6574\u4e2a AI \u754c\u7684\u5fc3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e2\u7136\u6700\u7ec8\u6a21\u578b\u4f1a\u8ba9\u201c\u51cf\u53bb\u5747\u503c\u201d\u53d8\u6210\u591a\u4f59\u7684\u6b65\u9aa4\uff0c\u90a3\u4e0d\u5982\u4e00\u5f00\u59cb\u5c31\u628a\u5b83\u53bb\u6389\u2014\u2014\u8fd9\u5c31\u662f RMSNorm\uff08Root Mean Square Layer Normalization\uff09\u7684\u6838\u5fc3\u601d\u8def\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">RMSNorm \u4e0d\u5173\u5fc3\u5747\u503c\uff0c\u76f4\u63a5\u8ba1\u7b97\u8f93\u5165\u5411\u91cf $x$ \u7684\u5747\u65b9\u6839\uff08Root Mean Square\uff09\u4f5c\u4e3a\u7f29\u653e\u57fa\u51c6\uff0c\u4e00\u6b21\u6027\u5b8c\u6210\u5f52\u4e00\u5316\u3002\u5b83\u7684\u516c\u5f0f\u4e5f\u56e0\u6b64\u8f7b\u5de7\u4e86\u8bb8\u591a\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>\\text{RMSNorm}(x) = \\frac{x}{\\text{RMS}(x)} \\cdot \\gamma<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>\\text{RMS}(x) = \\sqrt{\\frac{1}{d}\\sum_{i=1}^{d} x_i^2 + \\epsilon}<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ec5\u4ec5\u53bb\u6389\u4e86\u201c\u51cf\u5747\u503c\u201d\u548c\u201c\u52a0\u504f\u7f6e\u201d\u8fd9\u4e24\u6b65\uff0c\u5b83\u5b9e\u73b0\u4e86<strong>\u4ece O(n) \u5230 O(n) \u7684\u5e38\u6570\u7ea7\u4f18\u5316\uff08\u51cf\u5c11\u8fd0\u7b97\u6b65\u9aa4\uff09<\/strong> \u4ee5\u53ca<strong>\u66f4\u5c0f\u7684\u53c2\u6570\u91cf\uff08\u53bb\u6389\u4e86 bias\uff09<\/strong> \uff0c\u5728\u51cf\u5c11\u5185\u5b58\u79fb\u52a8\u548c\u663e\u5b58\u5360\u7528\u65b9\u9762\u6548\u76ca\u663e\u8457\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u6b64\uff0cRMSNorm \u6210\u4e86\u5305\u62ec LLaMA\u3001Mistral\u3001DeepSeek\u3001RWKV \u5728\u5185\u7684\u51e0\u4e4e\u8fd1\u5e74\u6240\u6709\u7206\u6b3e LLM \u7684\u7edf\u4e00\u9009\u62e9\u3002\u5f00\u6e90\u793e\u533a\u548c\u4e1a\u754c\u666e\u904d\u8ba4\u4e3a\uff0c\u5b83\u7684\u6210\u529f\u4e3b\u8981\u6e90\u4e8e\u66f4\u5c11\u7684\u53c2\u6570\u91cf\uff08\u51cf\u5c11\u663e\u5b58\u5360\u7528\uff09\u548c\u66f4\u9ad8\u6548\u7684 FLOPs\uff08\u63d0\u5347\u63a8\u7406\u4e0e\u8bad\u7ec3\u901f\u5ea6\uff09\u3002\u5728\u5927\u578b\u8bed\u8a00\u6a21\u578b\u4e2d\uff0c\u201c\u6548\u679c\u5dee\u4e0d\u591a\u201d\u65f6\uff0c\u201c\u6210\u672c\u66f4\u4f4e\u201d\u7684\u65b9\u6848\u5c31\u662f\u4e8b\u5b9e\u4e0a\u7684\u6700\u4f18\u89e3\u3002\u4e5f\u6709\u7814\u7a76\u8868\u660e\uff0c\u5168\u9762\u91c7\u7528 RMSNorm \u7684\u6a21\u578b\u751a\u81f3\u80fd\u5728\u4e0b\u6e38\u4efb\u52a1\u4e0a\u53d6\u5f97\u4f18\u4e8e LayerNorm \u7684\u6027\u80fd\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e94\u3001\u540e RMSNorm \u65f6\u4ee3\uff1a\u5f52\u4e00\u5316\u5c42\u80fd\u88ab\u201c\u9769\u6389\u201d\u5417<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u968f\u7740 RMSNorm \u6210\u4e3a\u65b0\u7684\u6807\u914d\uff0c\u5b66\u672f\u754c\u4e5f\u4ece\u672a\u653e\u5f03\u8fc7\u63a2\u7d22\uff0c\u6253\u7b97\u5c06\u6548\u7387\u63a8\u5411\u6781\u81f4\u3002\u987a\u7740 RMSNorm \u5f00\u542f\u7684\u7b80\u5316\u601d\u8def\uff0c\u65b0\u7684\u6311\u6218\u8005\u5df2\u7ecf\u51fa\u73b0\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 \u8303\u5f0f\u9769\u547d\u8005\uff1a\u7528\u6fc0\u6d3b\u51fd\u6570\u4ee3\u66ff\u5f52\u4e00\u5316<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e2\u7136 LayerNorm \u8868\u73b0\u51fa\u7c7b\u4f3c\u4e8e tanh \u51fd\u6570\u7684\u975e\u7ebf\u6027\u53d8\u6362\u6548\u679c\uff0c\u90a3\u80fd\u5426\u76f4\u63a5\u629b\u5f03\u5f52\u4e00\u5316\u5c42\uff0c\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u6fc0\u6d3b\u51fd\u6570\u6765\u53d6\u4ee3\u5462\uff1f\u8fd9\u5c31\u662f\u201cDe-norming\u201d\u7814\u7a76\u7684\u6838\u5fc3\u601d\u8def\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u4f55\u607a\u660e\u548c LeCun \u7b49\u4eba\u5728 CVPR 2025 \u4e0a\u63d0\u51fa\u7684 <strong>DyT (Dynamic Tanh)<\/strong> \uff0c\u5c31\u662f\u8fd9\u6761\u8def\u4e0a\u7684\u4e00\u4e2a\u91cc\u7a0b\u7891\u3002\u5b83\u4ee5 <code>tanh(\u03b1x)<\/code> \u7ed3\u6784\u4e3a\u6838\u5fc3\uff0c\u7528\u4e0d\u523010\u884c\u4ee3\u7801\u5c31\u80fd\u66ff\u6362\u6389 LN \u6216 RMSNorm\uff0c\u80fd\u5728 LLaMA\u3001ViT \u7b49\u4e0d\u540c\u67b6\u6784\u7684\u4efb\u52a1\u4e0a\u8fbe\u5230\u751a\u81f3\u8d85\u8d8a\u6807\u51c6 Transformer \u7684\u6027\u80fd\u3002\u540c\u65f6\uff0c\u56e0\u4e3a DyT \u662f\u9010\u5143\u7d20\u8ba1\u7b97\uff0c\u6ca1\u6709\u8de8\u7279\u5f81\u7684\u89c4\u7ea6\u64cd\u4f5c\uff0c\u6240\u4ee5\u5728\u63a8\u7406\u548c\u8bad\u7ec3\u9636\u6bb5\u90fd\u5927\u5927\u51cf\u5c11\u4e86 I\/O \u74f6\u9888\uff0c\u8dd1\u5f97\u66f4\u5feb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5176\u5b9e\u6697\u793a\u4e86 <strong>RMSNorm \u7684\u539f\u751f\u5b9e\u73b0\u672c\u8eab\u5c31\u6709\u6548\u7387\u74f6\u9888<\/strong>\u2014\u2014\u867d\u7136\u6d6e\u70b9\u8fd0\u7b97\u91cf\u53ea\u5360\u7ea6 0.15%\uff0c\u4f46\u56e0\u4e3a\u9700\u8981\u6536\u96c6\u8de8\u901a\u9053\u7684\u7edf\u8ba1\u6570\u636e\uff0cGPU \u5185\u6838\u5fc5\u987b\u5b8c\u6210\u4e00\u6b21\u89c4\u7ea6\uff08reduce\uff09\u64cd\u4f5c\u548c\u4e00\u6b21\u5e7f\u64ad\uff08broadcast\uff09\u64cd\u4f5c\uff0c\u5176\u5b9e\u9645\u8fd0\u884c\u65f6\u95f4\u5360\u6bd4\u5374\u53ef\u80fd\u9ad8\u8fbe 25%\u3002\u8fd9\u7c7b\u64cd\u4f5c\u7684\u74f6\u9888\u4e0d\u5728\u7b97\u529b\uff08FLOPs\uff09\uff0c\u800c\u5728\u5185\u5b58\u5e26\u5bbd\uff08Memory-Bound\uff09\uff0c\u800c DyT \u5219\u5de7\u5999\u5730\u7ed5\u5f00\u4e86\u8fd9\u9053\u5899\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53e6\u4e00\u4e2a\u66f4\u5177\u7406\u8bba\u9ad8\u5ea6\u7684\u65b9\u5411\u662f <strong>IBNorm\uff08\u4fe1\u606f\u74f6\u9888\u5f52\u4e00\u5316\uff09<\/strong> \u3002\u5b83\u63d0\u51fa\u4e00\u4e2a\u66f4\u6df1\u5c42\u7684\u95ee\u9898\uff1a\u73b0\u6709\u7684\u5f52\u4e00\u5316\u65b9\u6cd5\uff08BN\/LN\/RMSNorm\uff09\u90fd\u662f\u201c\u65b9\u5dee\u4e2d\u5fc3\u4e3b\u4e49\u201d\u7684\uff0c\u53ea\u5f3a\u5236\u6570\u636e\u7684\u65b9\u5dee\u4e3a\u4e00\uff0c\u5374\u6ca1\u6709\u63a7\u5236\u6a21\u578b\u5b66\u4e60\u4ec0\u4e48\u6837\u7684\u4fe1\u606f\u3002IBNorm \u5f15\u5165\u4e86\u53ef\u63a7\u7684\u538b\u7f29\u64cd\u4f5c\uff0c\u5f15\u5bfc\u6a21\u578b\u4fdd\u7559\u66f4\u591a\u4e0e\u9884\u6d4b\u4efb\u52a1\u76f8\u5173\u7684\u4fe1\u606f\uff0c\u5e76\u6291\u5236\u5197\u4f59\u566a\u97f3\u3002\u5b9e\u9a8c\u8868\u660e\uff0cIBNorm \u5728 LLaMA \u7b49 LLM \u53ca\u89c6\u89c9\u6a21\u578b\u4e0a\u5168\u9762\u8d85\u8d8a\u4e86 BN\u3001LN \u548c RMSNorm\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.2 \u7cbe\u5ea6\u4e0e\u786c\u4ef6\u7684\u6df1\u5ea6\u534f\u540c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u63a8\u7406\u52a0\u901f\u7684\u6781\u81f4\u8ffd\u6c42\uff0c\u524d\u6cbf\u7814\u7a76\u4e5f\u5728\u7cbe\u5ea6\u548c\u786c\u4ef6\u5c42\u9762\u4e0d\u65ad\u63a2\u7d22\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728<strong>\u4f4e\u7cbe\u5ea6\u8bad\u7ec3<\/strong>\u9886\u57df\uff0c\u6709\u524d\u6cbf\u5b9e\u9a8c\u663e\u793a\uff0c\u53ea\u9700\u5728\u8bad\u7ec3\u524d\u5fae\u8c03\u4e00\u4e2a\u989d\u5916\u7684 RMSNorm \u5c42\uff0c\u5c31\u80fd\u8ba9\u6a21\u578b\u5728 <strong>1.58-bit \u7684\u6781\u9650\u91cf\u5316\u7cbe\u5ea6<\/strong>\u4e0b\uff0c\u4f9d\u7136\u4fdd\u6301\u6781\u9ad8\u7684\u6027\u80fd\u6c34\u5e73\u3002\u800c\u5728<strong>\u786c\u4ef6\u5c42\u9762<\/strong>\uff0c\u6709\u7814\u7a76\u5f00\u59cb\u9488\u5bf9 RMSNorm \u548c Softmax \u8fd9\u7c7b\u975e\u7ebf\u6027\u7b97\u5b50\u8bbe\u8ba1\u4e13\u95e8\u7684\u786c\u4ef6\u53cb\u597d\u578b\u8fd1\u4f3c\u52a0\u901f\u65b9\u6cd5\u3002\u901a\u8fc7\u7528\u67e5\u8868\uff08LUT\uff09\u3001\u5bf9\u6570\u51cf\u6cd5\u7b49\u65b9\u5f0f\u66ff\u4ee3\u8017\u65f6\u7684\u9664\u6cd5\u548c\u5f00\u65b9\u8ba1\u7b97\uff0c\u80fd\u5728 FPGA \u7b49\u8fb9\u7f18\u8ba1\u7b97\u8bbe\u5907\u4e0a\u83b7\u5f97\u663e\u8457\u7684\u5ef6\u8fdf\u548c\u529f\u8017\u4f18\u52bf\u3002\u53e6\u4e00\u4e2a\u540d\u4e3a <strong>ARNorm<\/strong> \u7684\u65b0\u65b9\u6cd5\uff0c\u5219\u5728\u6781\u4f4e\u6bd4\u7279\u8ba1\u7b97\u9886\u57df\uff0c\u901a\u8fc7\u964d\u4f4e\u91cf\u5316\u8bef\u5dee\uff0c\u5728\u8fb9\u7f18 AI \u8bbe\u5907\u4e0a\u5b9e\u73b0\u4e86\u7cbe\u5ea6\u4e0e 32 \u4f4d\u6d6e\u70b9\u6570 RMSNorm \u76f8\u5f53\uff0c\u540c\u65f6\u66f4\u5feb\u3001\u66f4\u7701\u7535\u7684\u63a8\u7406\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.3 \u8bad\u7ec3\u7a33\u5b9a\u6027\u4e0e\u5f02\u5e38\u503c\uff1a\u795e\u79d8\u8054\u7cfb\u7684\u63ed\u6653<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f52\u4e00\u5316\u6280\u672f\u8fd8\u548c\u8bad\u7ec3\u7a33\u5b9a\u6027\uff0c\u4ee5\u53ca\u4e00\u4e2a\u540d\u4e3a\u201cSinks\u201d\uff08\u5f02\u5e38\u503c\uff09\u7684\u8c1c\u56e2\u6709\u7740\u5343\u4e1d\u4e07\u7f15\u7684\u8054\u7cfb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u8005\u4eec\u53d1\u73b0\uff0c\u5728\u5927\u6a21\u578b\u63a8\u7406\u65f6\uff0c\u4f1a\u6709\u5c11\u6570\u51e0\u4e2a token \u62e5\u6709\u5f02\u5e38\u9ad8\u7684\u6ce8\u610f\u529b logits\uff0c\u5373\u6ce8\u610f\u529b\u6c47\uff08attention sinks\uff09\uff1b\u540c\u65f6\uff0c\u4e5f\u4f1a\u6709\u67d0\u51e0\u4e2a\u7279\u5f81\u7ef4\u5ea6\uff0c\u5728\u51e0\u4e4e\u6240\u6709 token \u4e0a\u90fd\u8868\u73b0\u4e3a\u5f02\u5e38\u9ad8\u7684\u6fc0\u6d3b\u503c\uff0c\u5373\u6b8b\u5dee\u6c47\uff08residual sinks\uff09\u3002\u4e00\u9879\u7edf\u4e00\u4e86\u4e8c\u8005\u89c6\u89d2\u7684\u7814\u7a76\u6307\u51fa\uff0c\u8fd9\u4e9b\u201cSinks\u201d\u5e76\u975e\u5355\u7eaf\u591a\u4f59\u7684\u566a\u58f0\uff0c\u800c\u662f<strong>\u901a\u8fc7\u4e0e Softmax\u3001RMSNorm \u7b49\u5f52\u4e00\u5316\u64cd\u4f5c\u534f\u540c\u5de5\u4f5c\uff0c\u626e\u6f14\u7740\u52a8\u6001\u7f29\u653e\uff08outlier-driven rescaling\uff09\u7684\u529f\u80fd<\/strong>\u2014\u2014\u5b83\u4eec\u5b9e\u8d28\u4e0a\u5bf9\u5176\u4ed6\u975e\u5f02\u5e38\u503c\u6210\u5206\u8fdb\u884c\u4e86\u5e45\u5ea6\u7f29\u653e\uff0c\u4ece\u800c\u7ef4\u6301\u4e86\u8bad\u7ec3\u7684\u7a33\u5b9a\u6027\u4e0e\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u53d1\u73b0\u7ed9\u4e86\u6211\u4eec\u4e00\u4e2a\u5168\u65b0\u7684\u770b\u5f85\u6a21\u578b\u5185\u90e8\u6d3b\u52a8\u7684\u65b9\u5f0f\uff1a\u90a3\u4e9b\u770b\u4f3c\u6781\u7aef\u7684\u3001\u4e0d\u7a33\u5b9a\u7684\u5f02\u5e38\u503c\uff0c\u5b9e\u9645\u4e0a\u6b63\u662f\u6a21\u578b\u7ef4\u6301\u68af\u5ea6\u5e73\u7a33\u3001\u9632\u6b62\u6fc0\u6d3b\u7206\u70b8\u6216\u8870\u51cf\u7684\u201c\u52a8\u6001\u7a33\u538b\u5668\u201d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u516d\u3001\u603b\u7ed3\u4e0e\u5c55\u671b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u987e LayerNorm \u4e0e RMSNorm \u7684\u53d1\u5c55\u5386\u7a0b\uff0c\u6280\u672f\u7684\u8dc3\u8fc1\u6307\u660e\u4e86\u4ece\u201c\u529f\u80fd\u5b8c\u5907\u201d\u5230\u201c\u6781\u9650\u6548\u7387\u201d\u518d\u5230\u201c\u8303\u5f0f\u9769\u65b0\u201d\u7684\u6e05\u6670\u4e3b\u7ebf\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>LayerNorm<\/strong>\uff1a\u4f5c\u4e3a\u5e8f\u5217\u6a21\u578b\u7684\u5960\u57fa\u8005\uff0c\u7528\u5747\u503c\u548c\u65b9\u5dee\u5efa\u7acb\u4e86\u6df1\u5ea6\u7f51\u7edc\u8bad\u7ec3\u7a33\u5b9a\u7684\u57fa\u77f3\u3002<\/li>\n\n\n\n<li><strong>RMSNorm<\/strong>\uff1a\u51ed\u501f\u53bb\u6389\u5747\u503c\u3001\u53bb\u6389\u504f\u7f6e\u7684\u5927\u80c6\u51cf\u6cd5\uff0c\u6210\u4e3a\u73b0\u4ee3 LLM \u517c\u987e\u6548\u7387\u4e0e\u6548\u679c\u7684\u4e1a\u754c\u201c\u6807\u51c6\u7b54\u6848\u201d\u3002<\/li>\n\n\n\n<li><strong>\u524d\u6cbf\u63a2\u7d22<\/strong>\uff1a\u4ee5 DyT \u4e3a\u4ee3\u8868\u7684\u521b\u65b0\uff0c\u6b63\u8bd5\u56fe\u4ece\u6839\u672c\u4e0a\u5e9f\u9664\u5f52\u4e00\u5316\u5c42\uff0c\u4f7f\u7528\u66f4\u7b80\u5355\u7684\u5143\u7d20\u7ea7\u6fc0\u6d3b\u51fd\u6570\u6765\u5f00\u8f9f\u65b0\u7684\u67b6\u6784\u8303\u5f0f\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece LN \u5230 RMSNorm \u7684\u6f14\u53d8\uff0c\u6e05\u6670\u5730\u544a\u8bc9\u6211\u4eec\u4e00\u4e2a\u9053\u7406\uff1a\u5728\u5927\u6a21\u578b\u7684\u4e16\u754c\u91cc\uff0c\u7406\u8bba\u7684\u4f18\u96c5\u5f80\u5f80\u662f\u5de5\u7a0b\u5b9e\u8df5\u7684\u5148\u58f0\uff0c\u800c\u6781\u81f4\u7684\u6548\u7387\uff0c\u624d\u662f\u6700\u7ec8\u7684\u751f\u5b58\u6cd5\u5219\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\uddd1\u200d\ud83d\udcbb \u4ee3\u7801\u9644\u5f55\uff1a\u624b\u5199 LayerNorm \u4e0e RMSNorm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u540e\uff0c\u8ba9\u6211\u4eec\u4eb2\u624b\u5b9e\u8df5\u4e00\u4e0b\u3002\u4ee5\u4e0b\u662f\u7528 Python \u548c PyTorch \u5b9e\u73b0\u7684 LayerNorm \u548c RMSNorm\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import torch\nimport torch.nn as nn\n\nclass LayerNorm_Handcrafted(nn.Module):\n    def __init__(self, normalized_shape, eps=1e-5):\n        super().__init__()\n        self.gamma = nn.Parameter(torch.ones(normalized_shape))\n        self.beta = nn.Parameter(torch.zeros(normalized_shape))\n        self.eps = eps\n\n    def forward(self, x):\n        # x shape: &#91;B, L, D]\n        mean = x.mean(dim=-1, keepdim=True)\n        var = x.var(dim=-1, keepdim=True, unbiased=False)\n        # Normalize: (x - mean) \/ sqrt(var + eps)\n        x_norm = (x - mean) \/ torch.sqrt(var + self.eps)\n        # Affine transform: scale and shift\n        return self.gamma * x_norm + self.beta\n\nclass RMSNorm_Handcrafted(nn.Module):\n    def __init__(self, normalized_shape, eps=1e-6):\n        super().__init__()\n        self.gamma = nn.Parameter(torch.ones(normalized_shape))\n        self.eps = eps\n\n    def forward(self, x):\n        # x shape: &#91;B, L, D]\n        # RMS = sqrt(mean(x^2))\n        rms = torch.sqrt(x.pow(2).mean(dim=-1, keepdim=True) + self.eps)\n        # Normalize: x \/ RMS\n        x_norm = x \/ rms\n        # Scale\n        return self.gamma * x_norm\n\nclass DyT_Handcrafted(nn.Module):\n    def __init__(self, num_features, alpha_init_value=0.5):\n        super().__init__()\n        self.alpha = nn.Parameter(torch.ones(1) * alpha_init_value)\n        self.weight = nn.Parameter(torch.ones(num_features))\n        self.bias = nn.Parameter(torch.zeros(num_features))\n\n    def forward(self, x):\n        x = torch.tanh(self.alpha * x)\n        return self.weight * x + self.bias<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcda \u4e32\u8054\u7cfb\u5217\u77e5\u8bc6\uff1a\u56de\u987e\u4e0e\u5c55\u671b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u6211\u4eec\u6784\u5efa\u7684 LLM \u77e5\u8bc6\u4f53\u7cfb\u4e2d\uff0c\u5f52\u4e00\u5316\u4e0e\u6b8b\u5dee\u8fde\u63a5\u662f\u4fdd\u8bc1\u8bad\u7ec3\u7a33\u5b9a\u7684\u201c\u5e55\u540e\u82f1\u96c4\u201d\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u672c\u7cfb\u5217\u524d\u6587\u56de\u987e<\/strong>\uff1a\n<ol class=\"wp-block-list\">\n<li><strong>Tokenizer\uff08\u5206\u8bcd\u5668\uff09<\/strong> \u2192 <strong>Embedding\uff08\u8bcd\u5d4c\u5165\uff09<\/strong><\/li>\n\n\n\n<li><strong>FFN \u4e0e SwiGLU<\/strong>\uff08\u77e5\u8bc6\u5b58\u50a8\u5668\uff09<\/li>\n\n\n\n<li><strong>Attention<\/strong>\uff08MHA\/MQA\/GQA\uff09\u4e0e <strong>KV Cache\/PagedAttention<\/strong><\/li>\n\n\n\n<li><strong>MoE\uff08\u6df7\u5408\u4e13\u5bb6\uff09<\/strong> \u67b6\u6784<\/li>\n\n\n\n<li><strong>\u6570\u636e\u5e76\u884c\u3001\u5f20\u91cf\u5e76\u884c\u4e0e\u6d41\u6c34\u7ebf\u5e76\u884c<\/strong><\/li>\n\n\n\n<li><strong>Pre-Norm\/Post-Norm &amp; \u6b8b\u5dee\u8fde\u63a5<\/strong>\uff08\u6b64\u524d\u6240\u4f5c\u8bb2\u89e3\uff09<\/li>\n\n\n\n<li><strong>LayerNorm &amp; RMSNorm<\/strong>\uff08\u672c\u7bc7\u5185\u5bb9\uff09<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u53ef\u4ee5\u8bf4\uff0c\u5982\u679c\u6ca1\u6709\u6b8b\u5dee\u8fde\u63a5\u548c Layer Normalization\uff08\u5c42\u5f52\u4e00\u5316\uff09\u8fd9\u6837\u4e00\u521a\u4e00\u67d4\u7684\u9ec4\u91d1\u7ec4\u5408\uff0c\u52a8\u8f84\u4e0a\u767e [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":155,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[53,52,37,54],"class_list":["post-154","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mtsb","tag-batchnorm","tag-layernorm","tag-llm","tag-rmsnorm"],"_links":{"self":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":1,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions"}],"predecessor-version":[{"id":156,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions\/156"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/media\/155"}],"wp:attachment":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}