{"id":151,"date":"2026-05-03T18:10:22","date_gmt":"2026-05-03T10:10:22","guid":{"rendered":"https:\/\/www.bojinhu.xyz\/?p=151"},"modified":"2026-04-23T18:13:57","modified_gmt":"2026-04-23T10:13:57","slug":"%e4%bb%8e-sgd-%e5%88%b0-adamw-%e7%9a%84%e4%bc%98%e5%8c%96%e5%99%a8","status":"publish","type":"post","link":"https:\/\/www.bojinhu.xyz\/index.php\/2026\/05\/03\/%e4%bb%8e-sgd-%e5%88%b0-adamw-%e7%9a%84%e4%bc%98%e5%8c%96%e5%99%a8\/","title":{"rendered":"\u4ece SGD \u5230 AdamW \u7684\u4f18\u5316\u5668"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u5199\u5728\u524d\u9762<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u5982\u4f55\u7528\u6570\u636e\u5e76\u884c\u3001\u5f20\u91cf\u5e76\u884c\u548c\u6d41\u6c34\u7ebf\u5e76\u884c\uff0c\u628a\u4e00\u4e2a\u5927\u6a21\u578b\u201c\u62c6\u5f00\u201d\u653e\u5230\u6210\u767e\u4e0a\u5343\u5f20 GPU \u4e0a\u8bad\u7ec3\u3002\u4f46\u6211\u4eec\u59cb\u7ec8\u56de\u907f\u4e86\u4e00\u4e2a\u6839\u672c\u95ee\u9898\uff1a<strong>\u62c6\u597d\u4e4b\u540e\uff0c\u53c2\u6570\u7a76\u7adf\u662f\u600e\u4e48\u88ab\u201c\u66f4\u65b0\u201d\u7684\uff1f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u95ee\u9898\u7684\u7b54\u6848\uff0c\u5c31\u662f<strong>\u4f18\u5316\u5668\uff08Optimizer\uff09<\/strong>\u3002\u5982\u679c\u8bf4\u795e\u7ecf\u7f51\u7edc\u662f\u4e00\u5f20\u901a\u5f80\u201c\u667a\u80fd\u201d\u7684\u590d\u6742\u5730\u56fe\uff0c\u635f\u5931\u51fd\u6570\u51b3\u5b9a\u4e86\u54ea\u6761\u8def\u901a\u5411\u6700\u4f18\u89e3\uff0c\u90a3\u4e48\u4f18\u5316\u5668\u5c31\u662f\u6307\u5f15\u6a21\u578b\u5728\u5d0e\u5c96\u7684\u635f\u5931\u5730\u8c8c\u4e2d<strong>\u5982\u4f55\u4e00\u6b65\u6b65\u4e0b\u5c71\u7684\u201c\u5bfc\u822a\u7b97\u6cd5\u201d<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u4e0d\u53c2\u4e0e\u524d\u5411\u8ba1\u7b97\uff0c\u4e5f\u4e0d\u5b9a\u4e49\u635f\u5931\u51fd\u6570\uff0c\u5374\u638c\u63a7\u7740\u6bcf\u4e00\u6b21\u53c2\u6570\u66f4\u65b0\u7684\u65b9\u5411\u4e0e\u6b65\u957f\u2014\u2014\u5c31\u50cf\u767b\u5c71\u8005\u5728\u6d53\u96fe\u4e2d\u9009\u62e9\u7684\u4e0b\u5c71\u7b56\u7565\uff0c\u51b3\u5b9a\u4e86\u4f60\u80fd\u5426\u53c8\u5feb\u53c8\u7a33\u5730\u62b5\u8fbe\u8c37\u5e95\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u6700\u6734\u7d20\u7684\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08SGD\uff09\uff0c\u5230\u96c6\u5927\u6210\u8005 Adam\uff0c\u518d\u5230\u5982\u4eca\u5927\u6a21\u578b\u65f6\u4ee3\u7684\u6807\u914d AdamW\uff0c\u4f18\u5316\u5668\u7684\u6f14\u53d8\u8def\u5f84\u51e0\u4e4e\u5c31\u662f\u6df1\u5ea6\u5b66\u4e60\u5de5\u7a0b\u53f2\u7684\u4e00\u4e2a\u7f29\u5f71\u3002\u4f46\u4f60\u662f\u5426\u771f\u6b63\u60f3\u8fc7\u8fd9\u4e9b\u95ee\u9898\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SGD \u4e0a\u52a0\u4e00\u4e2a\u201c\u52a8\u91cf\u201d\u5230\u5e95\u89e3\u51b3\u4e86\u4ec0\u4e48\uff1f<\/li>\n\n\n\n<li>Adam \u76f8\u6bd4 SGD \u6700\u5927\u7684\u4f18\u52bf\u662f\u4ec0\u4e48\uff0c\u53c8\u6709\u4ec0\u4e48\u9690\u5fe7\uff1f<\/li>\n\n\n\n<li>\u4e3a\u4ec0\u4e48 Adam \u5df2\u7ecf\u5982\u6b64\u5f3a\u5927\uff0c\u4e1a\u754c\u8fd8\u8981\u63a8\u51fa AdamW\uff1f<\/li>\n\n\n\n<li>\u540c\u6837\u662f\u201c\u81ea\u9002\u5e94\u201d\uff0c\u5404\u79cd Adam \u53d8\u4f53\u4e4b\u95f4\u7a76\u7adf\u6709\u4ec0\u4e48\u533a\u522b\uff1f<\/li>\n\n\n\n<li>\u5728\u5b9e\u9645\u8bad\u7ec3\u4e2d\uff0c\u5230\u5e95\u8be5\u9009\u54ea\u4e2a\u4f18\u5316\u5668\uff1f<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f18\u5316\u7b97\u6cd5\u7684\u91cd\u8981\u6027\u4e0d\u8a00\u800c\u55bb\u2014\u2014\u65af\u5766\u798f\u5927\u5b66\u7684 CS336 \u8bfe\u7a0b\u4f5c\u4e1a\u4e2d\uff0c\u4e0e\u6a21\u578b\u7ed3\u6784\uff08Transformer\uff09\u5e76\u5217\u7684\u8bad\u7ec3\u57fa\u7840\u8bbe\u65bd\u5c31\u662f<strong>\u635f\u5931\u51fd\u6570<\/strong>\u548c<strong>\u4f18\u5316\u5668<\/strong>\uff08\u660e\u786e\u8981\u6c42\u4f7f\u7528 AdamW\uff09\u3002MLSys \u8bfe\u7a0b\u7684\u201c\u4f18\u5316\u5668\u201d\u6a21\u5757\u4e5f\u5c06 SGD\u3001Adam \u548c AdamW \u5217\u4e3a\u4e09\u5927\u5fc5\u987b\u638c\u63e1\u7684\u201c\u751f\u4ea7\u7ea7\u4f18\u5316\u5668\u201d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u3001\u8d77\u70b9\uff1a\u68af\u5ea6\u4e0b\u964d\u4e0e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08SGD\uff09<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1.1 \u68af\u5ea6\u4e0b\u964d\uff1a\u6700\u6734\u7d20\u7684\u201c\u5411\u4e0b\u8d70\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u6709\u4f18\u5316\u5668\u7684\u8d77\u70b9\uff0c\u90fd\u662f<strong>\u68af\u5ea6\u4e0b\u964d\uff08Gradient Descent\uff09<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u60f3\u8c61\u4f60\u7ad9\u5728\u4e00\u5ea7\u6d53\u96fe\u7b3c\u7f69\u7684\u5c71\u4e0a\uff08\u635f\u5931\u51fd\u6570\u7684\u9ad8\u7ef4\u66f2\u9762\uff09\uff0c\u80fd\u89c1\u5ea6\u6781\u4f4e\uff0c\u53ea\u80fd\u611f\u77e5\u811a\u4e0b\u5c40\u90e8\u7684\u5761\u5ea6\u3002\u4f60\u60f3\u5c3d\u5feb\u4e0b\u5230\u8c37\u5e95\uff08\u5373\u627e\u5230\u5168\u5c40\u6700\u5c0f\u635f\u5931\u503c\uff09\uff0c\u6700\u6734\u7d20\u7684\u60f3\u6cd5\u5c31\u662f\uff1a<strong>\u627e\u5761\u5ea6\u6700\u9661\u7684\u65b9\u5411\uff0c\u6cbf\u7740\u5b83\u5f80\u4e0b\u8d70<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6570\u5b66\u4e0a\uff0c\u8fd9\u4e2a\u201c\u6700\u9661\u7684\u65b9\u5411\u201d\u5c31\u662f\u68af\u5ea6\u7684\u8d1f\u65b9\u5411\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 \u2207L(\u03b8_t)<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>\u03b8_t<\/code> \u662f\u5f53\u524d\u53c2\u6570<\/li>\n\n\n\n<li><code>\u2207L(\u03b8_t)<\/code> \u662f\u635f\u5931\u51fd\u6570\u5173\u4e8e\u53c2\u6570\u7684\u68af\u5ea6<\/li>\n\n\n\n<li><code>\u03b7<\/code> \u662f<strong>\u5b66\u4e60\u7387\uff08Learning Rate\uff09<\/strong> \uff0c\u5373\u6bcf\u4e00\u6b65\u8fc8\u51fa\u53bb\u7684\u201c\u6b65\u957f\u201d<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b8c\u6574\u68af\u5ea6\u4e0b\u964d\u6cd5\u8981\u6c42\u6279\u68af\u5ea6\u4e0b\u964d\u6bcf\u6b21\u8fed\u4ee3\u90fd\u904d\u5386<strong>\u5168\u90e8\u8bad\u7ec3\u6570\u636e<\/strong>\u4ee5\u8ba1\u7b97\u68af\u5ea6\uff0c\u5bf9\u5f53\u4eca\u52a8\u8f84 TB \u7ea7\u522b\u7684\u6570\u636e\u96c6\u6765\u8bf4\u5b8c\u5168\u4e0d\u53ef\u884c\u3002\u597d\u5728\u53ef\u4ee5\u201c\u5077\u5de5\u51cf\u6599\u201d\u2014\u2014\u968f\u673a\u62bd\u53d6\u4e00\u5c0f\u6279\uff08Mini-Batch\uff09\u6837\u672c\u6765\u8fd1\u4f3c\u4f30\u8ba1\u5168\u90e8\u6570\u636e\u4e0a\u7684\u771f\u5b9e\u68af\u5ea6\uff0c\u4e8e\u662f\uff0c\u8bde\u751f\u4e86<strong>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08Stochastic Gradient Descent, SGD\uff09<\/strong>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 \u2207L_B(\u03b8_t)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d <code>\u2207L_B<\/code> \u662f\u57fa\u4e8e\u5f53\u524d\u5c0f\u6279\u91cf\uff08Batch\uff09\u6570\u636e\u8ba1\u7b97\u51fa\u7684\u68af\u5ea6\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.2 SGD \u7684\u4e09\u5927\u75db\u70b9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u4ee3\u6df1\u5ea6\u5b66\u4e60\u6240\u4f9d\u8d56\u7684\u9ad8\u5ea6\u975e\u51f8\u635f\u5931\u66f2\u9762\uff0c\u8ba9\u6734\u7d20 SGD \u66b4\u9732\u4e86\u4e09\u4e2a\u663e\u773c\u7684\u77ed\u677f\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u9707\u8361\u95ee\u9898<\/strong>\uff1a\u5728\u9ad8\u7ef4\u975e\u51f8\u7684\u6df1\u5ea6\u5b66\u4e60\u635f\u5931\u66f2\u9762\u4e2d\uff0c\u4e0d\u540c\u53c2\u6570\u7684\u66f2\u7387\u5dee\u5f02\u6781\u5927\uff0c\u68af\u5ea6\u5728\u201c\u72ed\u7a84\u5ce1\u8c37\u201d\uff08Ravine\uff09\u4e2d\u4f1a\u5728\u53c2\u6570\u4e0d\u540c\u8f74\u53cd\u590d\u9707\u8361\u800c\u504f\u79fb\u6700\u4f18\u65b9\u5411\uff0c\u4e25\u91cd\u62d6\u6162\u6536\u655b\u3002<\/li>\n\n\n\n<li><strong>\u5e73\u5766\u533a\u505c\u6ede<\/strong>\uff1a\u5f53\u53c2\u6570\u9677\u5165\u5e73\u7a33\u9ad8\u539f\u65f6\uff0c\u68af\u5ea6\u63a5\u8fd1\u96f6\uff0cSGD \u4f1a\u51e0\u4e4e\u201c\u539f\u5730\u8e0f\u6b65\u201d\uff0c\u5bfc\u81f4\u6f2b\u957f\u7684\u8bad\u7ec3\u65f6\u95f4\u3002<\/li>\n\n\n\n<li><strong>\u5bf9\u5b66\u4e60\u7387\u6781\u5176\u654f\u611f<\/strong>\uff1a\u5b66\u4e60\u7387\u592a\u5c0f\uff0c\u6536\u655b\u5982\u9f9f\u901f\uff1b\u5b66\u4e60\u7387\u592a\u5927\uff0c\u6a21\u578b\u53ef\u80fd\u5728\u6700\u4f18\u89e3\u9644\u8fd1\u201c\u53cd\u590d\u6a2a\u8df3\u201d\u751a\u81f3\u53d1\u6563\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e09\u4e2a\u95ee\u9898\u7684\u6838\u5fc3\u90fd\u5728\u4e8e\uff1a<strong>SGD \u662f\u201c\u8fd1\u89c6\u201d\u7684<\/strong>\u3002\u5b83\u5728\u6bcf\u4e2a\u4f4d\u7f6e\u4ec5\u4f9d\u636e\u201c\u5f53\u524d\u8fd9\u4e00\u6b65\u7684\u5c0f\u6279\u91cf\u68af\u5ea6\u201d\u505a\u51b3\u7b56\uff0c\u5bf9\u66fe\u7ecf\u8d70\u8fc7\u7684\u5386\u53f2\u8def\u5f84\u6beb\u65e0\u8bb0\u5fc6\u3002\u4e3a\u4e86\u7a81\u7834\u8fd9\u4e00\u9650\u5236\uff0c\u79d1\u5b66\u5bb6\u4eec\u5f00\u59cb\u7ed9 SGD \u52a0\u4e0a\u4e86\u201c\u8bb0\u5fc6\u201d\u548c\u201c\u81ea\u9002\u5e94\u201d\u7684\u80fd\u529b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u3001\u7b2c\u4e00\u9053\u52a0\u6cd5\uff1a\u52a8\u91cf \u2014\u2014 \u4e3a\u4f18\u5316\u5668\u6ce8\u5165\u201c\u60ef\u6027\u201d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 Momentum\uff1a\u8ba9\u68af\u5ea6\u4ea7\u751f\u201c\u60ef\u6027\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u52a8\u91cf\u6cd5\uff08Momentum\uff09<\/strong> \u662f\u4f18\u5316\u5668\u6f14\u8fdb\u7684\u7b2c\u4e00\u9053\u5173\u952e\u52a0\u6cd5\u3002\u5b83\u5f15\u5165\u4e00\u4e2a\u201c\u901f\u5ea6\u201d\u53d8\u91cf <code>v_t<\/code>\uff0c\u8ba9\u53c2\u6570\u66f4\u65b0\u65b9\u5411\u4e0d\u4ec5\u53d6\u51b3\u4e8e\u5f53\u524d\u5c0f\u6279\u91cf\u968f\u673a\u68af\u5ea6\uff0c\u8fd8\u4fdd\u7559\u4e86\u8fc7\u53bb\u6240\u6709\u65f6\u523b\u68af\u5ea6\u8d21\u732e\u7684\u6307\u6570\u79fb\u52a8\u5e73\u5747\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>v_t = \u03b2 \u00b7 v_{t-1} + (1 - \u03b2) \u00b7 \u2207L(\u03b8_t)\n\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 v_t<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\u7684 <code>\u03b2<\/code> \u662f\u52a8\u91cf\u7cfb\u6570\uff0c\u901a\u5e38\u53d6 0.9\uff0c\u63a7\u5236\u5386\u53f2\u4fe1\u606f\u7684\u8870\u51cf\u901f\u5ea6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f4\u89c2\u4e0a\uff0c\u8fd9\u76f8\u5f53\u4e8e\u7ed9\u53c2\u6570\u66f4\u65b0\u8d4b\u4e88\u201c\u60ef\u6027\u201d\u2014\u2014\u5373\u4f7f\u5f53\u524d\u68af\u5ea6\u5f88\u5c0f\uff0c\u53ea\u8981\u8fc7\u53bb\u65b9\u5411\u4e00\u81f4\uff0c\u66f4\u65b0\u4ecd\u4f1a\u7ee7\u7eed\u63a8\u8fdb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u52a8\u91cf\u6cd5\u4e3a\u4f18\u5316\u5668\u8865\u4e0a\u4e86\u201c\u7eb5\u5411\u8bb0\u5fc6\u201d\u2014\u2014\u5b83\u80fd\u663e\u8457<strong>\u6291\u5236\u5728\u72ed\u7a84\u5ce1\u8c37\u4e2d\u7684\u6a2a\u5411\u9707\u8361<\/strong>\uff0c\u5e76<strong>\u52a0\u901f\u7a7f\u8d8a\u5e73\u5766\u9ad8\u539f\u533a\u57df<\/strong>\u3002\u5728 ResNet\u3001VGG \u7b49\u7ecf\u5178 CNN \u4e0a\uff0c\u52a8\u91cf\u6cd5\u663e\u8457\u63d0\u5347\u4e86\u8bad\u7ec3\u7684\u7a33\u5b9a\u6027\u548c\u6536\u655b\u901f\u5ea6\u3002\u751a\u81f3\u8fde 2012 \u5e74\u7684 AlexNet \u4e5f\u4f9d\u8d56\u4e8e SGD+M \u624d\u80fd\u6709\u6548\u8bad\u7ec3\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 NAG\uff1a\u5148\u63a2\u8def\uff0c\u518d\u884c\u52a8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6807\u51c6\u52a8\u91cf\u6cd5\u4ecd\u5b58\u5728\u4e00\u4e2a\u6f5c\u5728\u7f3a\u9677\uff1a\u5b83\u5728<strong>\u5df2\u7d2f\u79ef\u7684\u52a8\u91cf\u548c\u5f53\u524d\u4f4d\u7f6e\u7684\u68af\u5ea6\u4e24\u80a1\u529b\u5171\u540c\u4f5c\u7528<\/strong>\u4e0b\u201c\u51b2\u8fc7\u5934\u201d\uff0c\u7136\u540e\u5728\u53cd\u5411\u68af\u5ea6\u4e0b\u6298\u8fd4\uff0c\u8868\u73b0\u4e3a\u53cd\u590d\u8d85\u8c03\uff08Overshoot\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Nesterov Accelerated Gradient\uff08NAG\uff09<\/strong> \u5bf9\u6b64\u8fdb\u884c\u4e86\u7cbe\u5999\u7684\u4fee\u6b63\uff1a\u5b83\u5148\u6839\u636e\u5f53\u524d\u52a8\u91cf\u9884\u6d4b\u4e0b\u4e00\u6b65\u4f1a\u201c\u6eda\u201d\u5230\u54ea\u4e2a\u4e34\u65f6\u4f4d\u7f6e\uff0c\u518d\u5728\u90a3\u4e2a\u524d\u77bb\u5750\u6807\u4e0a\u8ba1\u7b97\u68af\u5ea6\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u4e34\u65f6\u4f4d\u7f6e:  \u03b8\u0303_t = \u03b8_t - \u03b7 \u00b7 \u03b2 \u00b7 v_{t-1}\n\u8ba1\u7b97\u524d\u77bb\u68af\u5ea6: \u2207L(\u03b8\u0303_t)\n\u901f\u5ea6\u66f4\u65b0:  v_t = \u03b2 \u00b7 v_{t-1} + (1 - \u03b2) \u00b7 \u2207L(\u03b8\u0303_t)\n\u53c2\u6570\u66f4\u65b0:  \u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 v_t<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u79cd\u201c\u5148\u63a2\u8def\u3001\u518d\u884c\u52a8\u201d\u7684\u524d\u77bb\u6027\uff0c\u4f7f NAG \u5728\u63a5\u8fd1\u6781\u5c0f\u503c\u65f6\u4f1a\u63d0\u524d\u51cf\u901f\uff0c\u76f8\u6bd4\u6807\u51c6\u52a8\u91cf\u66f4\u7a33\u5b9a\u3001\u66f4\u7cbe\u7ec6\u3002\u7406\u8bba\u5206\u6790\u4e5f\u8bc1\u660e\uff0cNAG \u5728\u51f8\u4f18\u5316\u4e2d\u62e5\u6709\u6bd4\u6807\u51c6\u52a8\u91cf\u66f4\u597d\u7684\u6536\u655b\u901f\u5ea6\u3002Pytorch \u7b49\u6846\u67b6\u53ef\u901a\u8fc7 <code>nesterov=True<\/code> \u76f4\u63a5\u542f\u7528\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u8fc7\u5728\u4e00\u4e2a\u7269\u7406\u65b9\u5411\u4e0a\u505a\u518d\u591a\u52a0\u6cd5\uff0c\u4e5f\u65e0\u6cd5\u4e00\u52b3\u6c38\u9038\uff0c\u56e0\u4e3a\u6df1\u5ea6\u5b66\u4e60\u771f\u6b63\u7684\u201c\u5c3a\u5ea6\u5931\u8861\u201d\u95ee\u9898\uff0c\u52a8\u91cf\u6cd5\u4ece\u672a\u89e6\u53ca\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e09\u3001\u7b2c\u4e8c\u9053\u52a0\u6cd5\uff1a\u81ea\u9002\u5e94\u5b66\u4e60\u7387<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u91cc\uff0c\u4e0d\u540c\u5c42\u7684\u53c2\u6570\u3001\u751a\u81f3\u540c\u4e00\u5c42\u5185\u4e0d\u540c\u5217\u53c2\u6570\u7684\u68af\u5ea6\u5728\u6570\u91cf\u548c\u5c3a\u5ea6\u4e0a\u4e5f\u5343\u5dee\u4e07\u522b\u3002\u56fa\u5b9a\u5168\u5c40\u7684\u5b66\u4e60\u7387\u5bf9\u4e00\u90e8\u5206\u53c2\u6570\u521a\u597d\u5408\u9002\uff0c\u5bf9\u53e6\u4e00\u90e8\u5206\u53c2\u6570\u5374\u53ef\u80fd\u5bfc\u81f4\u9707\u8361\u6216\u505c\u6ede\u3002\u4e0e\u5176\u7528\u540c\u4e00\u4e2a\u5b66\u4e60\u7387\u63a7\u5236\u6240\u6709\u53c2\u6570\uff0c\u4e0d\u5982<strong>\u4e3a\u6bcf\u4e2a\u53c2\u6570\u5355\u72ec\u8ba1\u7b97\u6700\u9002\u5408\u5b83\u7684\u201c\u6b65\u5e45\u201d<\/strong>\u2014\u2014\u8fd9\u5c31\u662f\u81ea\u9002\u5e94\u4f18\u5316\u5668\u7684\u6838\u5fc3\u601d\u60f3\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 AdaGrad\uff1a\u81ea\u9002\u5e94\u6cd5\u7684\u201c\u7b2c\u4e00\u4e2a\u811a\u5370\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2011 \u5e74\u63d0\u51fa\u7684 <strong>AdaGrad<\/strong> \u9996\u6b21\u5b9e\u73b0\u4e86\u53c2\u6570\u7ea7\u5b66\u4e60\u7387\u8c03\u6574\u3002\u5b83\u4e3a\u6bcf\u4e2a\u53c2\u6570\u7ef4\u62a4\u4e00\u4e2a\u7d2f\u79ef\u68af\u5ea6\u5e73\u65b9\u548c <code>G_t<\/code>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>G_t = G_{t-1} + (\u2207L(\u03b8_t))\u00b2\n\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 \u2207L(\u03b8_t) \/ \u221a(G_t + \u03b5)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u53c2\u6570\u88ab\u66f4\u65b0\u7684\u9891\u7387\u8d8a\u9ad8\u3001\u68af\u5ea6\u7684\u5e73\u65b9\u548c\u8d8a\u5927\uff0c\u5176<strong>\u6709\u6548\u5b66\u4e60\u7387\u4f1a\u88ab\u7f29\u5f97\u66f4\u5c0f<\/strong>\uff0c\u5bf9\u77eb\u6b63\u6781\u5ea6\u4e0d\u5e73\u8861\u7684\u7279\u5f81\u6781\u5176\u6709\u6548\u3002\u5728\u5904\u7406\u63a8\u8350\u7cfb\u7edf\u7b49\u7279\u5f81\u9ad8\u5ea6\u7a00\u758f\u7684\u573a\u666f\u65f6\uff0cAdaGrad \u4f18\u52bf\u660e\u663e\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7136\u800c\u5b83\u7684\u81f4\u547d\u7f3a\u9677\u5728\u4e8e\uff1a\u5e73\u6ed1\u7d2f\u79ef\u7684\u65b9\u5f0f\u8ba9 <code>G_t<\/code> \u53ea\u80fd\u968f\u65f6\u95f4\u5355\u8c03\u589e\u957f\uff0c\u5bfc\u81f4\u8bad\u7ec3\u7684\u4e2d\u540e\u671f<strong>\u6709\u6548\u5b66\u4e60\u7387\u8fc7\u65e9\u8870\u51cf\u81f3\u6781\u5c0f<\/strong>\uff0c\u53c2\u6570\u51e0\u4e4e\u505c\u6b62\u66f4\u65b0\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 RMSProp\uff1a\u7528\u201c\u8fd1\u5927\u8fdc\u5c0f\u201d\u66ff\u4ee3\u201c\u5355\u8c03\u7d2f\u79ef\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RMSProp<\/strong> \u5728 2012 \u5e74\u89e3\u51b3\u4e86 AdaGrad \u7684\u201c\u5b66\u4e60\u7387\u65e9\u8870\u201d\u95ee\u9898\u3002\u5b83\u4e0d\u518d\u50bb\u50bb\u5730\u7d2f\u79ef\u5168\u90e8\u5386\u53f2\u68af\u5ea6\u5e73\u65b9\uff0c\u800c\u662f\u91c7\u7528<strong>\u6307\u6570\u52a0\u6743\u79fb\u52a8\u5e73\u5747\uff08EWMA\uff09<\/strong>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>v_t = \u03b2\u2082 \u00b7 v_{t-1} + (1 - \u03b2\u2082) \u00b7 (\u2207L(\u03b8_t))\u00b2\n\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 \u2207L(\u03b8_t) \/ \u221a(v_t + \u03b5)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d <code>\u03b2\u2082<\/code> \u901a\u5e38\u53d6 0.999\u3002\u6307\u6570\u8870\u51cf\u8d4b\u4e88\u4e86\u4f18\u5316\u5668\u201c\u8fd1\u671f\u504f\u597d\u201d\uff0c\u8ba9\u81ea\u9002\u5e94\u5b66\u4e60\u7387\u4e3b\u8981\u88ab\u8fd1\u671f\u7684\u68af\u5ea6\u5e73\u65b9\u5747\u65b9\u6839\uff08RMS\uff09\u6240\u4e3b\u5bfc\uff0c\u6709\u6548\u89c4\u907f\u4e86 AdaGrad \u5b66\u4e60\u7387\u8fc7\u65e9\u8870\u51cf\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">RMSProp \u7684\u6548\u679c\u663e\u8457\uff1a\u5b83\u5141\u8bb8\u4e3a\u90a3\u4e9b\u68af\u5ea6\u53d8\u5316\u5267\u70c8\u7684\u53c2\u6570\u52a8\u6001\u51cf\u5c0f\u6b65\u5e45\uff0c\u540c\u65f6\u4e3a\u5e73\u5766\u53c2\u6570\u79ef\u6781\u653e\u5927\u6b65\u957f\uff0c\u81f3\u4eca\u4ecd\u662f RNN \u8bad\u7ec3\u7684\u6709\u6548\u7ec4\u4ef6\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u56db\u3001\u96c6\u5927\u6210\u8005\uff1aAdam \u2014\u2014 \u52a8\u91cf\u4e0e\u81ea\u9002\u5e94\u7684\u5b8c\u7f8e\u878d\u5408<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 Adam \u7684\u201c\u4e09\u5408\u4e00\u201d\u67b6\u6784<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7406\u89e3\u4e86\u52a8\u91cf\u6cd5\u548c\u81ea\u9002\u5e94\u5b66\u4e60\u7387\uff0c\u518d\u6765\u770b Adam \u5c31\u4f1a\u6709\u4e00\u79cd\u201c\u6c34\u5230\u6e20\u6210\u201d\u7684\u8c41\u7136\u5f00\u6717\u611f\u30022015 \u5e74\u63d0\u51fa\u7684 <strong>Adam<\/strong> \u5c06<strong>\u52a8\u91cf\uff08\u4e00\u9636\u77e9\uff09<\/strong>\u4e0e<strong>\u81ea\u9002\u5e94\u5b66\u4e60\u7387\uff08\u4e8c\u9636\u77e9\uff09<\/strong>\u65e0\u7f1d\u878d\u5408\uff0c\u5e76\u52a0\u5165<strong>\u504f\u5dee\u6821\u6b63\u673a\u5236<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Adam \u5728\u6bcf\u4e00\u6b65\u7ef4\u62a4\u4e24\u4e2a\u6307\u6570\u79fb\u52a8\u5e73\u5747\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e00\u9636\u77e9 <code>m_t<\/code>\uff08\u52a8\u91cf\u9879\uff0c\u68af\u5ea6\u7684\u6307\u6570\u6ed1\u52a8\u5e73\u5747\uff09<\/li>\n\n\n\n<li>\u4e8c\u9636\u77e9 <code>v_t<\/code>\uff08\u68af\u5ea6\u5e73\u65b9\u7684\u6307\u6570\u6ed1\u52a8\u5e73\u5747\uff0c\u6765\u81ea RMSProp\uff09<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>m_t = \u03b2\u2081 \u00b7 m_{t-1} + (1 - \u03b2\u2081) \u00b7 g_t\nv_t = \u03b2\u2082 \u00b7 v_{t-1} + (1 - \u03b2\u2082) \u00b7 g_t\u00b2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u4e8e <code>m_0<\/code> \u548c <code>v_0<\/code> \u88ab\u521d\u59cb\u5316\u4e3a 0\uff0c\u5728\u8bad\u7ec3\u65e9\u671f\u5b83\u4eec\u7684\u4f30\u8ba1\u503c\u88ab\u7cfb\u7edf\u6027\u5730\u62c9\u4f4e\u3002\u4e3a\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0cAdam \u5f15\u5165\u4e86<strong>\u504f\u5dee\u6821\u6b63\uff08Bias Correction\uff09<\/strong>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>m\u0302_t = m_t \/ (1 - \u03b2\u2081\u1d57)\nv\u0302_t = v_t \/ (1 - \u03b2\u2082\u1d57)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u7ec8\u53c2\u6570\u66f4\u65b0\u516c\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 m\u0302_t \/ (\u221a(v\u0302_t) + \u03b5)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Adam \u7684\u9ed8\u8ba4\u8d85\u53c2\u6570\u5728\u5927\u91cf\u5b9e\u8df5\u4e2d\u88ab\u8bc1\u660e\u6781\u4e3a\u9c81\u68d2\uff1a<code>\u03b7 = 0.001<\/code>\u3001<code>\u03b2\u2081 = 0.9<\/code>\u3001<code>\u03b2\u2082 = 0.999<\/code>\u3001<code>\u03b5 = 10\u207b\u2078<\/code>\uff0c\u51e0\u4e4e\u201c\u5f00\u7bb1\u5373\u7528\u201d\u3002\u5728 BERT\u3001GPT \u7b49 Transformer \u67b6\u6784\u7684\u9884\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0cAdam \u51ed\u501f\u5176\u81ea\u9002\u5e94\u7279\u6027\uff0c\u88ab\u8bc1\u660e<strong>\u663e\u8457\u4f18\u4e8e SGD<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 \u5728\u8bed\u8a00\u6a21\u578b\u4e2d\u7684\u201c\u964d\u7ef4\u6253\u51fb\u201d\uff1a\u4e3a\u4ec0\u4e48 Transformer \u51e0\u4e4e\u53ea\u8ba4 Adam\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u4e2a\u6709\u8da3\u7684\u73b0\u8c61\u662f\uff1a\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u4efb\u52a1\u4e2d\uff0c\u7cbe\u5fc3\u8c03\u53c2\u7684 SGD + Momentum \u901a\u5e38\u80fd\u8fbe\u5230\u4e0e Adam \u76f8\u5f53\u751a\u81f3\u66f4\u4f18\u7684\u6700\u7ec8\u6027\u80fd\uff1b\u4f46\u5728 Transformer \u8bed\u8a00\u6a21\u578b\u7684\u9884\u8bad\u7ec3\u4e2d\uff0cAdam \u5bf9 SGD \u5374\u5f62\u6210\u4e86<strong>\u8fd1\u4e4e\u201c\u964d\u7ef4\u6253\u51fb\u201d\u7684\u4f18\u52bf<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5927\u91cf\u7814\u7a76\u4e00\u81f4\u6307\u51fa\u4e86\u540c\u6837\u7684\u6838\u5fc3\u7ed3\u8bba\uff1a<strong>\u5728\u8bed\u8a00\u6a21\u578b\u8bad\u7ec3\u4e2d\uff0c\u9664\u4e86 SGD \u660e\u663e\u504f\u5dee\u8f83\u5927\u4ee5\u5916\uff0cAdam \u4e0e\u5176\u4ed6\u4e3b\u6d41\u81ea\u9002\u5e94\u4f18\u5316\u5668\uff08Lion\u3001Adafactor \u52a0\u52a8\u91cf\u3001Signum\uff09\u7684\u6027\u80fd\u4e0e\u8d85\u53c2\u6570\u9c81\u68d2\u6027\u90fd\u975e\u5e38\u63a5\u8fd1<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Why\uff1f\u539f\u56e0\u4e4b\u4e00\u5728\u4e8e Transformer \u67b6\u6784\u5185\u90e8\u68af\u5ea6\u5c3a\u5ea6\u7684\u6781\u7aef\u5f02\u8d28\u6027\u2014\u2014\u4e0d\u540c\u53c2\u6570\u77e9\u9635\uff08\u5982 Q\u3001K\u3001V \u7684\u6295\u5f71\u77e9\u9635\uff0cFFN \u7684\u653e\u5927\u77e9\u9635\uff09\u5728\u8bad\u7ec3\u65e9\u671f\u7684\u68af\u5ea6\u5c3a\u5ea6\u53ef\u80fd\u76f8\u5dee\u51e0\u4e2a\u6570\u91cf\u7ea7\u3002SGD \u7684\u5168\u5c40\u7edf\u4e00\u5b66\u4e60\u7387\u5728\u8fd9\u79cd\u201c\u591a\u5c3a\u5ea6\u201d\u73af\u5883\u4e2d\u8fdb\u9000\u4e24\u96be\uff1a\u5b66\u4e60\u7387\u5c0f\u4e86\uff0c\u67d0\u4e9b\u5c42\u51e0\u4e4e\u539f\u5730\u4e0d\u52a8\uff1b\u5927\u4e86\uff0c\u53e6\u4e00\u4e9b\u5c42\u53c8\u4f1a\u68af\u5ea6\u7206\u70b8\u3002Adam \u7684\u81ea\u9002\u5e94\u673a\u5236\u6070\u597d\u80fd\u81ea\u52a8\u5e73\u8861\u5404\u5c42\u7684\u6709\u6548\u66f4\u65b0\u6b65\u957f\uff0c\u4f7f\u5176\u6210\u4e3a Transformer \u8bad\u7ec3\u7684\u201c\u5fc5\u5907\u54c1\u201d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.3 Adam \u7684\u7cfb\u7edf\u4ee3\u4ef7\uff1a3 \u500d\u7684\u663e\u5b58<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u81ea\u9002\u5e94\u4f18\u5316\u5668\u7cbe\u5999\u7684\u7b97\u6cd5\u80cc\u540e\u662f\u9700\u8981\u4ed8\u51fa\u7cfb\u7edf\u4ee3\u4ef7\u7684\u3002\u5728\u8ba1\u7b97\u548c\u5b58\u50a8\u4f9d\u8d56\u4e0a\uff0cAdam \u9700\u8981\u989d\u5916\u7ef4\u62a4\u4e24\u4e2a\u548c\u53c2\u6570\u540c\u6837\u5927\u5c0f\u7684\u4e00\u9636\u4e0e\u4e8c\u9636\u77e9\u72b6\u6001\uff0c\u603b\u4f53\u4e0a<strong>Adam \u7684\u603b\u5185\u5b58\u5360\u7528\u7ea6\u4e3a\u6a21\u578b\u53c2\u6570\u7684 3 \u500d<\/strong>\uff08\u53c2\u6570 + m + v\uff09\u3002\u5bf9\u4e8e 70B \u7ea7\u522b\u7684\u7a20\u5bc6 LLM\uff0c\u8fd9\u610f\u5473\u7740\u5927\u7ea6 420GB \u7684\u7eaf\u4f18\u5316\u5668\u72b6\u6001\uff0c\u5373\u4fbf\u653e\u5728 H100 \u96c6\u7fa4\u4e0a\u4e5f\u662f\u5de8\u5927\u7684\u8d1f\u62c5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e94\u3001AdamW\uff1a\u5927\u6a21\u578b\u65f6\u4ee3\u7684\u201c\u7075\u9b42\u4fee\u8865\u201d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 L2 \u6b63\u5219\u5316 vs \u6743\u91cd\u8870\u51cf\uff1a\u4e3a\u4f55\u5728 Adam \u4e2d\u6df7\u4e3a\u4e00\u8c08\u4f1a\u7ffb\u8f66\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8fdb\u5165 AdamW \u4e4b\u524d\uff0c\u9700\u8981\u5398\u6e05\u4e00\u4e2a\u6df1\u5c42\u6982\u5ff5\uff1a<strong>\u6743\u91cd\u8870\u51cf\uff08Weight Decay\uff09<\/strong> \u548c <strong>L2 \u6b63\u5219\u5316<\/strong>\u5728\u6807\u51c6 SGD \u4e0b\u662f\u5b8c\u5168\u7b49\u4ef7\u7684\uff0c\u4f46\u5728 Adam \u8fd9\u7c7b\u81ea\u9002\u5e94\u4f18\u5316\u5668\u4e2d\uff0c\u4e24\u8005\u5374\u51fa\u73b0\u4e86\u5fae\u5999\u800c\u5173\u952e\u7684\u5dee\u522b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728 SGD \u4e2d\uff0c\u6743\u91cd\u8870\u51cf\u76f4\u63a5\u5728\u66f4\u65b0\u6b65\u9aa4\u4e2d\u6309\u6bd4\u4f8b\u6536\u7f29\u53c2\u6570\uff1a<code>\u03b8_{t+1} = \u03b8_t - \u03b7 \u00b7 (\u2207L(\u03b8_t) + \u03bb\u00b7\u03b8_t)<\/code>\u3002\u8fd9\u7b49\u4ef7\u4e8e\u5728\u635f\u5931\u51fd\u6570\u4e2d\u52a0\u4e00\u4e2a L2 \u60e9\u7f5a\u9879\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u5728 Adam \u4e2d\uff0c\u81ea\u9002\u5e94\u5b66\u4e60\u7387\u5bfc\u81f4\u201cL2 \u6b63\u5219\u5316\u4f5c\u4e3a\u635f\u5931\u9879\u5bfc\u51fa\u7684\u68af\u5ea6\u201d\u4e0e\u201c\u81ea\u9002\u5e94\u5b66\u4e60\u7387\u5206\u6bcd\u201d\u53d1\u751f\u4e86\u4e0d\u5f53\u8026\u5408\uff1a\u5bf9\u4e8e\u90a3\u4e9b\u81ea\u9002\u5e94\u5b66\u4e60\u7387\u88ab\u653e\u5927\u7684\u53c2\u6570\uff0cL2 \u6b63\u5219\u5316\u7684\u5b9e\u9645\u60e9\u7f5a\u6548\u5e94\u88ab\u8fc7\u5ea6\u589e\u5f3a\uff1b\u53cd\u4e4b\u5219\u88ab\u4e25\u91cd\u524a\u5f31\u3002\u7ed3\u679c\u5c31\u662f Adam \u7684\u6743\u91cd\u8870\u51cf\u6548\u679c\u201c\u98d8\u5ffd\u4e0d\u5b9a\u201d\uff0c\u8fdc\u4e0d\u5982\u5728 SGD \u4e2d\u90a3\u822c\u7a33\u5b9a\u53ef\u9760\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.2 \u89e3\u8026\uff1a\u5c06\u201c\u9632\u8fc7\u62df\u5408\u201d\u4e0e\u201c\u53c2\u6570\u66f4\u65b0\u201d\u5206\u79bb<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2019 \u5e74\uff0cLoshchilov \u548c Hutter \u63d0\u51fa\u4e86 <strong>AdamW<\/strong>\uff0c\u53ea\u505a\u4e86\u4e00\u4ef6\u5e72\u5e72\u51c0\u51c0\u7684\u4e8b\uff1a<strong>\u628a\u6743\u91cd\u8870\u51cf\u4ece\u81ea\u9002\u5e94\u68af\u5ea6\u8ba1\u7b97\u4e2d\u5f7b\u5e95\u89e3\u8026\u51fa\u6765<\/strong>\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u6807\u51c6 Adam\uff08\u9519\u8bef\u8026\u5408\u7248\u672c\uff09\ng_t = \u2207L(\u03b8_{t-1}) + \u03bb \u00b7 \u03b8_{t-1}\n\n# AdamW\uff08\u6b63\u786e\u7684\u89e3\u8026\u7248\u672c\uff09\ng_t = \u2207L(\u03b8_{t-1})\n\u25b8 \u4f7f\u7528 g_t \u6b63\u5e38\u8ba1\u7b97 Adam \u7684\u4e00\u9636\/\u4e8c\u9636\u77e9\u548c\u81ea\u9002\u5e94\u66f4\u65b0\n\u25b8 \u5728 Adam \u66f4\u65b0\u5b8c\u6210\u4e4b\u540e\uff0c\u518d\u989d\u5916\u6267\u884c\u4e00\u6b65\u72ec\u7acb\u7684 \u03b8_t = \u03b8_t - \u03b7 \u00b7 \u03bb \u00b7 \u03b8_t<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u89e3\u8026\u540e\u7684\u76f4\u63a5\u6536\u76ca\u662f\uff1a\u6743\u91cd\u8870\u51cf\u7684\u8d85\u53c2\u6570 <code>\u03bb<\/code> \u5728\u4e0d\u540c\u4efb\u52a1\u548c\u6a21\u578b\u95f4\u5177\u6709\u66f4\u5f3a\u7684\u53ef\u8fc1\u79fb\u6027\uff1b\u8bad\u7ec3\u66f4\u7a33\u5b9a\uff0c\u5c24\u5176\u5728\u5927\u578b Transformer \u6a21\u578b\u4e0a\u4f18\u52bf\u660e\u663e\u3002\u7814\u7a76\u8868\u660e\uff0cAdamW \u76f8\u6bd4\u6807\u51c6 Adam \u80fd\u53d6\u5f97\u66f4\u597d\u7684\u6536\u655b\u6548\u679c\u4e0e\u6cdb\u5316\u80fd\u529b\uff0c\u5c24\u5176\u5728 BERT\u3001GPT \u7b49\u5927\u89c4\u6a21\u5e94\u7528\u4e2d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u662f\u56e0\u4e3a\u5b8c\u6210\u4e86\u89e3\u8026\u64cd\u4f5c\uff0cAdamW \u624d\u6210\u4e3a\u73b0\u4ee3 <strong>Transformer \u8bad\u7ec3\u7684\u9ed8\u8ba4\u4f18\u5316\u5668<\/strong>\u3002CS336 \u4ece\u96f6\u6784\u5efa LLM \u7684\u8bfe\u7a0b\u4e0e\u4f5c\u4e1a\uff0c\u4e5f\u76f4\u63a5\u9009\u7528\u4e86 AdamW \u4f5c\u4e3a\u6807\u51c6\u914d\u7f6e\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.3 \u8d44\u6e90\u53d7\u9650\u65f6\u7684\u5c0f\u63d0\u793a<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8d44\u6e90\u53d7\u9650\u3001\u9700\u8981\u8fdb\u884c\u5c0f\u5e45\u5ea6\u8fc7\u53c2\u6570\u626b\u63cf\u65f6\uff0c\u53ef\u8003\u8651\u7528 Lion \u66ff\u4ee3 AdamW \u8282\u7701\u7ea6 50% \u7684\u663e\u5b58\u3002CS336 \u8bfe\u7a0b\u5728\u5b9e\u9a8c\u7c7b\u4f5c\u4e1a\u4e2d\u4ea6\u660e\u786e\u652f\u6301\u4f7f\u7528 Lion \u4ee5\u51cf\u5c11\u5185\u5b58\u5360\u7528\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u516d\u3001\u6700\u65b0\u524d\u6cbf\uff1a\u5185\u5b58\u3001Scaling Law \u4e0e\u7b26\u53f7\u8fdb\u5316<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5373\u4f7f\u5728 AdamW \u5df2\u51e0\u4e4e\u89e6\u53ca\u7b97\u6cd5\u4f18\u5316\u7684\u9876\u5cf0\u540e\uff0c\u5bf9\u201c\u66f4\u6781\u81f4\u4f18\u5316\u5668\u201d\u7684\u63a2\u7d22\u811a\u6b65\u4ecd\u5728\u52a0\u901f\u3002\u5f53\u524d\u7684\u63a2\u7d22\u56f4\u7ed5\u4e09\u4e2a\u65b9\u5411\u8fdb\u884c\u653b\u575a\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.1 \u7cfb\u7edf\u74f6\u9888\u653b\u575a\u6218\uff1a\u5185\u5b58\u5899<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Adam \u6700\u5c16\u9510\u7684\u95ee\u9898\uff0c\u4e0d\u662f\u6027\u80fd\uff0c\u800c\u662f<strong>\u5185\u5b58<\/strong>\u3002\u5176\u4e8c\u9636\u77e9\u72b6\u6001\u8ba9\u5927\u6a21\u578b\u8bad\u7ec3\u7684\u5185\u5b58\u5f00\u9500\u6210\u4e3a\u74f6\u9888\u3002\u56e0\u6b64\u524d\u6cbf\u7814\u7a76\u6b63\u5728\u63a2\u7d22\u201c\u66f4\u8f7b\u91cf\u7ea7\u7684 Adam\u201d\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>APOLLO\uff08\u4f4e\u79e9\u653e\u7f29\u8fd1\u4f3c\uff09<\/strong>\uff1a\u901a\u8fc7\u7eaf\u968f\u673a\u6295\u5f71\u6784\u9020\u4e00\u4e2a\u4f4e\u79e9\u7684\u8f85\u52a9\u4f18\u5316\u5668\u72b6\u6001\u6765\u8fd1\u4f3c Adam \u7684\u81ea\u9002\u5e94\u5b66\u4e60\u7387\u7f29\u653e\u89c4\u5219\u3002\u5176 rank-1 \u7248\u672c\uff08APOLLO-Mini\uff09\u5373\u53ef\u5728 SGD \u7ea7\u5185\u5b58\u6210\u672c\u4e0a\u5b9e\u73b0\u5ab2\u7f8e AdamW \u7684\u9884\u8bad\u7ec3\u6027\u80fd\uff0c\u5728 8\u00d7A100-80GB \u7684\u4efb\u52a1\u4e0a\u541e\u5410\u91cf\u76f4\u63a5\u8fbe\u5230 AdamW \u7684 <strong>3 \u500d<\/strong>\u3002<\/li>\n\n\n\n<li><strong>SCALE\uff08\u5217\u5f52\u4e00+\u672b\u5c42\u52a8\u91cf\u88c1\u526a\uff09<\/strong>\uff1a\u901a\u8fc7\u66f4\u6fc0\u8fdb\u7684\u7b80\u5316\u7b56\u7565\u2014\u2014\u5bf9\u68af\u5ea6\u6cbf\u5217\u7ef4\u5ea6\u5f52\u4e00\u5316 + \u53ea\u5728\u68af\u5ea6\u65b9\u5dee\u6700\u5927\u7684\u8f93\u51fa\u5c42\u52a0\u4e00\u9636\u52a8\u91cf\u2014\u2014SCALE \u4ec5\u7528 <strong>35-45% \u7684\u603b\u5185\u5b58<\/strong>\u5c31\u5339\u914d\u751a\u81f3\u8d85\u8d8a\u4e86\u5168 Adam \u6027\u80fd\u3002<\/li>\n\n\n\n<li><strong>GaLore<\/strong>\uff1a\u5728 Adam \u4f18\u5316\u5668\u7684\u66f4\u65b0\u8fc7\u7a0b\u4e2d\u52a0\u5165\u4f4e\u79e9\u81ea\u9002\u5e94\uff0c\u4ee5\u66f4\u5c0f\u7684\u53c2\u6570\u91cf\u6a21\u62df Adam \u7684\u884c\u4e3a\uff0c\u964d\u4f4e\u5bf9\u5927\u5185\u5b58\u7684\u9700\u6c42\u3002<\/li>\n\n\n\n<li><strong>ZeRO \u4f18\u5316\u5668\u72b6\u6001\u5206\u7247<\/strong>\uff1a\u4e0e\u6570\u636e\u5e76\u884c\u6df1\u5ea6\u878d\u5408\uff0c\u5c06 Adam \u7684\u4f18\u5316\u5668\u72b6\u6001\u5207\u5206\u5230\u6240\u6709 GPU \u4e0a\uff0c\u4f7f\u5355\u5361\u5b58\u50a8\u538b\u529b\u5206\u6563\uff0c\u5b9e\u73b0\u8fd1\u4e4e O(1\/N) \u7684\u4f18\u5316\u5668\u5185\u5b58\u5360\u7528\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">6.2 Scaling Law \u7684\u63a2\u7d22\uff1a\u8d85\u53c2\u6570\u4e0e\u6a21\u578b\u89c4\u6a21\u7684\u9690\u85cf\u56e0\u679c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u524d\u6cbf\u7814\u7a76\u8fd8\u53d1\u73b0\uff0cAdam \u7684\u81ea\u9002\u5e94\u80fd\u529b\u4f1a\u968f\u6a21\u578b\u89c4\u6a21\u4e0e Batch Size \u4ea7\u751f\u663e\u8457\u53d8\u5316\u3002\u5728\u5c0f Batch \u8bad\u7ec3\u4e2d\u8c03\u53c2\u51c6\u786e\u7684 SGD+M \u80fd\u5339\u654c Adam\uff1b\u968f\u7740 Batch Size \u6269\u5927\uff0cAdam \u7684\u4f18\u52bf\u5f00\u59cb\u62c9\u5927\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fdb\u4e00\u6b65\u7684\u8d85\u53c2\u6570\u7814\u7a76\u53d1\u73b0\uff0c\u968f\u7740\u6a21\u578b\u89c4\u6a21\u548c\u8bad\u7ec3 Token \u6570\u589e\u52a0\uff0cAdam \u7684\u6700\u4f18 <code>\u03b2\u2082<\/code> \u548c\u5b66\u4e60\u7387\u8c03\u5ea6\u7b56\u7565\u53ef\u80fd\u9700\u8981\u9075\u5faa\u7279\u5b9a\u7684 Scaling Law \u8fdb\u884c\u8c03\u6574\u3002\u7814\u7a76\u8005\u4eec\u6b63\u5728\u7cfb\u7edf\u6316\u6398\u8fd9\u4e9b\u89c4\u5f8b\uff0c\u8bd5\u56fe\u4e3a\u4e07\u4ebf\u53c2\u6570\u7ea7\u7684\u4f18\u5316\u5668\u63d0\u4f9b\u6279\u91cf\u81ea\u52a8\u7f29\u653e\u7684\u201c\u914d\u65b9\u201d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.3 \u7b26\u53f7\u5f0f\u641c\u7d22\u8fdb\u5316\uff1aLion\u3001Sophia \u4e0e\u7b26\u53f7\u56de\u5f52<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u65b0\u7684\u7a81\u7834\u751a\u81f3\u5728\u6539\u53d8\u4f18\u5316\u5668\u7684\u201c\u8bde\u751f\u65b9\u5f0f\u201d\u2014\u2014\u4e0d\u518d\u4f9d\u8d56\u4eba\u8111\u8bbe\u8ba1\uff0c\u800c\u662f\u901a\u8fc7\u7a0b\u5e8f\u81ea\u52a8\u641c\u7d22\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lion\uff08Evolved Sign Momentum\uff09<\/strong> \u662f\u8c37\u6b4c\u901a\u8fc7\u5927\u89c4\u6a21\u7a0b\u5e8f\u641c\u7d22\u53d1\u73b0\u7684\u65b0\u578b\u4f18\u5316\u5668\u3002\u5b83\u53ea\u4fdd\u7559\u4e00\u9636\u52a8\u91cf\u5e76\u91c7\u7528\u7b26\u53f7\u8fd0\u7b97\uff0c\u5185\u5b58\u6548\u7387\u8fdc\u9ad8\u4e8e Adam\uff0c\u5728\u540c\u7b49\u8ba1\u7b97\u8d44\u6e90\u4e0b\u8bad\u7ec3 BERT \u6536\u655b\u901f\u5ea6\u63d0\u5347 18%\uff0c\u4f46\u5728\u9884\u8bad\u7ec3\u4efb\u52a1\u4e2d\u53ef\u4ee5\u5339\u654c\u751a\u81f3\u8d85\u8d8a AdamW\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sophia<\/strong> \u5219\u7ed3\u5408\u4e86\u5bf9\u89d2\u4e8c\u9636\u8fd1\u4f3c\u4e0e EMA \u68af\u5ea6\u5e73\u6ed1\uff0c\u5728\u8bed\u8a00\u6a21\u578b\u9884\u8bad\u7ec3\u4e0a\u5c55\u73b0\u51fa\u4e86\u4f18\u4e8e AdamW \u7684\u6536\u655b\u901f\u5ea6\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e03\u3001\u603b\u7ed3\u4e0e\u5c55\u671b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">7.1 \u6574\u4f53\u6f14\u8fdb\u56fe\u8c31<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u987e\u8fd9\u4e03\u5341\u5e74\u4f18\u5316\u5668\u7684\u6f14\u53d8\uff0c\u6211\u4eec\u80fd\u770b\u5230\u4e24\u6761\u6e05\u6670\u7684\u4e3b\u7ebf\u5728 2015 \u5e74\u5408\u6d41\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u9636\u6bb5<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u4ee3\u8868\u4f18\u5316\u5668<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u6838\u5fc3\u7a81\u7834<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u5173\u952e\u7f3a\u9677<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u7ecf\u5178\u65f6\u4ee3\uff0820\u4e16\u7eaa50\u5e74\u4ee3-2010\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">SGD<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u968f\u673a\u903c\u8fd1\uff0c\u6570\u636e\u6548\u7387\u5927\u5e45\u63d0\u5347<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u9ad8\u7ef4\u9707\u8361\u4e0e\u9ad8\u539f\u505c\u6ede<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u52a8\u91cf\u65f6\u4ee3\uff082011-2012\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Momentum, NAG<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u9707\u8361\u6291\u5236\u4e0e\u524d\u77bb\u673a\u5236<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u5c3a\u5ea6\u5931\u8861\u95ee\u9898\u4ecd\u672a\u89e3\u51b3<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u81ea\u9002\u5e94\u524d\u591c\uff082011-2013\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">AdaGrad, RMSProp<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u5386\u53f2\u5e73\u65b9\u68af\u5ea6\u7684\u53c2\u6570\u7ea7\u653e\u7f29<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u5b66\u4e60\u7387\u65e9\u8870\uff08AdaGrad\uff09<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u4e00\u9636+\u4e8c\u9636\u878d\u5408\uff082014-2015\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Adam<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u52a8\u91cf + RMSProp + \u504f\u5dee\u6821\u6b63<\/td><td class=\"has-text-align-left\" data-align=\"left\">Adam \u4e0d\u89c4\u8303\u6743\u91cd\u8870\u51cf<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u6743\u91cd\u8870\u51cf\u89e3\u8026\uff082019\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>AdamW<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u5c06\u6743\u91cd\u8870\u51cf\u4e0e\u68af\u5ea6\u66f4\u65b0\u5b8c\u5168\u5206\u79bb<\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>LLM \u9ed8\u8ba4\u4e4b\u9009<\/strong><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u81ea\u9002\u5e94\u63a2\u7d22\u65f6\u4ee3\uff082023+\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Lion, Sophia, APOLLO, SCALE<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u4f4e\u5185\u5b58\/\u81ea\u52a8\u641c\u7d22\uff0c\u8fc8\u5411\u6781\u81f4\u7cfb\u7edf\u6548\u7387<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u65b0\u65b9\u6cd5\u4ecd\u5728\u4e1a\u666e\u9002\u5316\u8fed\u4ee3\u4e2d<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">7.2 \u5b9e\u6218\u9009\u62e9\u6307\u5357<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u771f\u5b9e\u9879\u76ee\u4e2d\uff0c\u8be5\u5982\u4f55\u9009\u62e9\uff1f<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u573a\u666f<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u63a8\u8350\u52a0\u901f\u5668<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u7406\u7531<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Transformer \/ LLM \u4ece\u5934\u9884\u8bad<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>AdamW<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u65e0\u9700\u4e89\u8bae\u7684\u5de5\u4e1a\u754c \/ \u5b66\u672f\u754c\u5171\u8bc6<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u4e2d\u5c0f\u578b\u8bed\u8a00\u6a21\u578b\u7684\u5b9e\u9a8c\u6027\u5fae\u8c03<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>AdamW<\/strong> \u6216 <strong>Lion<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">AdamW \u7a33\u5b9a\u5f3a\u5927\uff0cLion \u8282\u7ea6\u663e\u5b58\u8f83\u5feb<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u8ba1\u7b97\u673a\u89c6\u89c9\uff08CNN \/ ResNet \/ ViT\uff09<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>SGD+M<\/strong> \u6216 <strong>AdamW<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">SGD+M \u5e7f\u6cdb\u6709\u6548\u3001\u6cdb\u5316\u597d\uff1b\u5927\u89c4\u6a21 ViT\/\u591a\u6a21\u6001\u4f18\u5148\u9009\u7528 AdamW<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u63a8\u8350\u7cfb\u7edf \/ \u7a00\u758f\u7279\u5f81\u573a\u666f<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>Adam \/ Adagrad<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Adagrad \u7a00\u758f\u5904\u7406\u80fd\u529b\u5f3a\uff0cAdam \u4ea6\u53ef<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u8fb9\u7f18\u8bbe\u5907 \/ \u663e\u5b58\u6781\u5ea6\u53d7\u9650<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>Lion \/ APOLLO \/ SCALE<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u517c\u987e\u541e\u5410\u91cf\u4e14\u5927\u5e45\u51cf\u5c11\u663e\u5b58\u5360\u7528<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">7.3 \u4f18\u5316\u5668\u5728\u6574\u4e2a\u8bad\u7ec3\u4f53\u7cfb\u4e2d\u7684\u4f4d\u7f6e<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u987e\u6211\u4eec\u7cfb\u5217\u8d70\u8fc7\u7684\u8def\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Tokenizer \u2192 Embedding \u2192 RoPE<\/strong><\/li>\n\n\n\n<li><strong>Attention\uff08MHA\/MQA\/GQA\uff09\u2192 FFN\uff08SwiGLU\uff09<\/strong><\/li>\n\n\n\n<li><strong>\u9884\u5f52\u4e00\u5316\/\u540e\u5f52\u4e00\u5316 + \u6b8b\u5dee\u8fde\u63a5<\/strong><\/li>\n\n\n\n<li><strong>MoE\uff08\u4e13\u5bb6\u4e0e\u8def\u7531\u673a\u5236\uff09<\/strong><\/li>\n\n\n\n<li><strong>KV Cache \u4e0e PagedAttention<\/strong><\/li>\n\n\n\n<li><strong>\u6570\u636e\u5e76\u884c\u3001\u5f20\u91cf\u5e76\u884c\u3001\u6d41\u6c34\u7ebf\u5e76\u884c<\/strong><\/li>\n\n\n\n<li><strong>\u4f18\u5316\u5668\uff1a\u4f18\u5316\u72b6\u6001\u4e0b\u964d\u8def\u5f84\uff08\u672c\u6587\uff09<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u8bf4\u524d\u9762\u51e0\u7bc7\u6587\u7ae0\u662f\u5728\u7ec4\u88c5\u4e00\u8f86\u201c\u667a\u80fd\u8d5b\u8f66\u201d\u7684\u53d1\u52a8\u673a\u3001\u4f20\u52a8\u7cfb\u7edf\u548c\u71c3\u6599\u7ba1\u9053\uff0c\u90a3\u4e48\u4f18\u5316\u5668\u5c31\u662f\u9a7e\u9a76\u8d5b\u8f66\u7684\u201cAI \u8f66\u624b\u201d\u2014\u2014\u5b83\u51b3\u5b9a\u4e86\u5728\u6cb9\u7bb1\u52a0\u6ee1\u3001\u9053\u8def\u5d0e\u5c96\u7684\u6761\u4ef6\u4e0b\uff0c\u4f60\u80fd\u4e0d\u80fd\u4ee5\u6700\u9ad8\u6548\u7387\uff0c\u6700\u5feb\u4e00\u5708\u51b2\u5411\u7ec8\u70b9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5199\u5728\u524d\u9762 \u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u5982\u4f55\u7528\u6570\u636e\u5e76\u884c\u3001\u5f20\u91cf\u5e76\u884c\u548c\u6d41\u6c34\u7ebf\u5e76\u884c\uff0c\u628a\u4e00\u4e2a\u5927\u6a21\u578b\u201c\u62c6\u5f00\u201d\u653e\u5230\u6210\u767e\u4e0a\u5343\u5f20  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