{"id":1192149,"date":"2026-10-29T19:00:00","date_gmt":"2026-10-30T02:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-blog-post&#038;p=1192149"},"modified":"2026-11-01T23:56:04","modified_gmt":"2026-11-02T06:56:04","slug":"mma-sim","status":"publish","type":"msr-blog-post","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/articles\/mma-sim\/","title":{"rendered":"MMA-Sim\uff1a\u540c\u4e00\u77e9\u9635\u8fd0\u7b97\uff0c\u4e3a\u4f55\u4e0d\u540c GPU \u6709\u7cbe\u5ea6\u548c\u6570\u503c\u5dee\u5f02\uff1f"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u540c\u6837\u7684\u6a21\u578b\u3001\u540c\u6837\u7684\u8f93\u5165\u3001\u540c\u6837\u7684\u968f\u673a\u79cd\u5b50\uff0c\u6362\u4e00\u5757&nbsp;GPU&nbsp;\u8fd0\u884c\uff0c\u7ed3\u679c\u5374\u53ef\u80fd\u4e0d\u4e00\u6837\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u5927\u6a21\u578b\u65f6\u4ee3\uff0c\u8fd9\u7c7b\u6570\u503c\u5dee\u5f02\u4e0d\u53ea\u662f\u5de5\u7a0b\u4e0a\u7684\u5c0f\u9ebb\u70e6\uff0c\u8fd8\u53ef\u80fd\u5f71\u54cd\u6a21\u578b\u8d28\u91cf\u3001\u5b9e\u9a8c\u53ef\u590d\u73b0\u6027\u548c\u8bad\u7ec3\u7a33\u5b9a\u6027\u3002\u90a3\u4e48\u95ee\u9898\u51fa\u5728\u54ea\u91cc\uff1f\u7b54\u6848\u5f80\u5f80\u85cf\u5728&nbsp;GPU&nbsp;\u5185\u90e8\u90a3\u4e9b\u6ca1\u6709\u5199\u8fdb\u6587\u6863\u7684\u7b97\u672f\u7ec6\u8282\u91cc\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u770b\u6e05\u8fd9\u4e9b\u7ec6\u8282\uff0c\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec<strong>\u63d0\u51fa\u4e86\u95ed\u73af\u7279\u5f81\u63a2\u6d4b\u65b9\u6cd5<\/strong><strong>&nbsp;CLFP<\/strong><strong>\uff0c\u5e76\u636e\u6b64\u6784\u5efa\u4e86<\/strong><strong>&nbsp;MMA-Sim<\/strong>\u3002MMA-Sim&nbsp;\u662f\u4e00\u5957\u4f4d\u7cbe\u786e\u7684&nbsp;GPU&nbsp;\u77e9\u9635\u4e58\u7d2f\u52a0\uff08MMA\uff09\u6a21\u578b\uff0c\u8986\u76d6&nbsp;NVIDIA&nbsp;\u548cAMD&nbsp;\u7684\u5341\u79cd&nbsp;GPU&nbsp;\u67b6\u6784\uff0c\u80fd\u591f\u9010\u6bd4\u7279\u590d\u73b0\u6240\u6d4b\u8bd5\u6307\u4ee4\u7684\u8f93\u51fa\uff0c\u89e3\u91ca\u8de8\u5e73\u53f0\u7684\u6570\u503c\u5dee\u5f02\uff0c\u5e76\u4e3a\u7cbe\u5ea6\u6539\u8fdb\u63d0\u4f9b\u6307\u5bfc\u3002\u76f8\u5173\u8bba\u6587<strong>\u5df2\u88ab\u8ba1\u7b97\u673a\u4f53\u7cfb\u7ed3\u6784\u9886\u57df\u9876\u7ea7\u4f1a\u8bae<\/strong><strong>&nbsp;MICRO 2026&nbsp;<\/strong><strong>\u6536\u5f55<\/strong>\uff0c\u4ee3\u7801\u4e5f\u5df2\u5f00\u6e90\u3002<\/p>\n\n\n\n<h2 id=\"\u5c0f\u8bef\u5dee-\u5927\u9ebb\u70e6-\u88ab\u5ffd\u89c6\u7684\u786c\u4ef6-\u7b97\u672f\u8d26\" class=\"wp-block-heading\">\u5c0f\u8bef\u5dee\uff0c\u5927\u9ebb\u70e6\uff1a\u88ab\u5ffd\u89c6\u7684\u786c\u4ef6\u201c\u7b97\u672f\u8d26\u201d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5927\u8bed\u8a00\u6a21\u578b\uff08<\/strong>LLMs\uff09\u4f1a\u6267\u884c\u6d77\u91cf\u7684\u6d6e\u70b9\u8fd0\u7b97\u3002\u4e00\u4e2a\u5fae\u5c0f\u7684\u7b97\u672f\u5dee\u5f02\uff0c\u53ef\u80fd\u5728\u4e0d\u540c\u5c42\u548c\u591a\u6b21\u8fed\u4ee3\u4e2d\u4e0d\u65ad\u7d2f\u79ef\u3001\u653e\u5927\uff0c\u6700\u7ec8\u6539\u53d8\u6a21\u578b\u8ba1\u7b97\u51fa\u7684\u6982\u7387\u5206\u5e03\u53ca\u5176\u8f93\u51fa\u7684&nbsp;token\u3002\u56e0\u6b64\uff0c\u6570\u503c\u884c\u4e3a\u5bf9\u4e8e\u6a21\u578b\u8d28\u91cf\u3001\u53ef\u590d\u73b0\u6027\u548c\u8bad\u7ec3\u7a33\u5b9a\u6027\u81f3\u5173\u91cd\u8981\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u6709\u5173\u4e8e\u6570\u503c\u884c\u4e3a\u7684\u7814\u7a76\u5927\u591a\u805a\u7126\u4e8e\u8f6f\u4ef6\u56e0\u7d20\uff0c\u786c\u4ef6\u5c42\u9762\u7684\u7b97\u672f\u884c\u4e3a\u5374\u5f88\u5c11\u6709\u4eba\u6df1\u7a76\u3002\u5b9e\u9645\u4e0a\uff0c\u786c\u4ef6\u540c\u6837\u4f1a\u5e26\u6765\u4e24\u4e2a\u68d8\u624b\u7684\u95ee\u9898\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4e00\u662f\u6570\u503c\u5dee\u5f02\u3002<\/strong>\u7528\u76f8\u540c\u7684\u8f93\u5165\u5728\u4e0d\u540c&nbsp;GPU&nbsp;\u5e73\u53f0\u4e0a\u8fd0\u884c\u540c\u4e00\u4e2a\u6a21\u578b\uff0c\u53ef\u80fd\u5f97\u5230\u4e0d\u540c\u7684\u6570\u503c\u7ed3\u679c\u3002\u5373\u4f7f\u7edf\u4e00\u4e86\u968f\u673a\u79cd\u5b50\u3001\u7f16\u8bd1\u5668\u53ca\u5176\u4ed6\u8f6f\u4ef6\u56e0\u7d20\uff0c\u786c\u4ef6\u5c42\u9762\u7684\u5dee\u5f02\u4ecd\u53ef\u80fd\u5b58\u5728\u3002\u8981\u89e3\u91ca\u8fd9\u79cd\u5dee\u5f02\uff0c\u5c31\u5fc5\u987b\u7406\u89e3\u786c\u4ef6\u5185\u90e8\u5b9e\u9645\u6267\u884c\u7684\u7b97\u672f\u8fd0\u7b97\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4e8c\u662f\u8bad\u7ec3\u7cbe\u5ea6\u3002<\/strong>GPU&nbsp;\u6d6e\u70b9\u8ba1\u7b97\u91c7\u7528\u7684\u5185\u90e8\u7cbe\u5ea6\u53ef\u80fd\u4e0d\u540c\u4e8e\u6807\u51c6\u6d6e\u70b9\u8fd0\u7b97\uff0c\u8fd9\u79cd\u7cbe\u5ea6\u5dee\u5f02\u4f1a\u5f71\u54cd&nbsp;LLMs&nbsp;\u7684\u8bad\u7ec3\u3002\u4f8b\u5982\uff0c\u6709\u7814\u7a76\u8005\u66fe\u62a5\u544a\uff0cHopper GPU&nbsp;\u7684&nbsp;FP8&nbsp;\u77e9\u9635\u4e58\u6cd5\u5185\u90e8\u7cbe\u5ea6\u4e0d\u8db3\uff0c\u4f1a\u5bfc\u81f4&nbsp;LLMs&nbsp;\u8bad\u7ec3\u7cbe\u5ea6\u4e0b\u964d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e24\u4e2a\u95ee\u9898\u6307\u5411\u540c\u4e00\u4e2a\u6839\u6e90\u2014\u2014\u4e1a\u754c\u5bf9\u786c\u4ef6\u6570\u503c\u884c\u4e3a\u7f3a\u4e4f\u767d\u76d2\u5c42\u9762\u7684\u7406\u89e3\u3002\u6ca1\u6709\u8fd9\u4e2a\u57fa\u7840\uff0c\u6211\u4eec\u5c31\u53ea\u80fd\u5728LLMs\u7cfb\u7edf\u51fa\u73b0\u95ee\u9898\u540e\u4f9d\u8d56\u7ecf\u9a8c\u88ab\u52a8\u5e94\u5bf9\uff0c\u96be\u4ee5\u4e8b\u5148\u8fdb\u884c\u6570\u503c\u5206\u6790\u3001\u7cbe\u5ea6\u9884\u6d4b\u3001\u95ee\u9898\u8bca\u65ad\u3001\u8bbe\u8ba1\u6709\u7406\u8bba\u4f9d\u636e\u7684\u7f13\u89e3\u63aa\u65bd\u3002<\/p>\n\n\n\n<h2 id=\"\u76f4\u51fb\u77e9\u9635\u8fd0\u7b97\u7684-\u9ed1\u76d2-mma-\u5355\u5143\" class=\"wp-block-heading\">\u76f4\u51fb\u77e9\u9635\u8fd0\u7b97\u7684\u201c\u9ed1\u76d2\u201d\uff1aMMA&nbsp;\u5355\u5143<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u7814\u7a76\u5458\u4eec\u628a\u76ee\u5149\u6295\u5411\u4e86&nbsp;GPU&nbsp;\u77e9\u9635\u4e58\u7d2f\u52a0\uff08matrix multiply-accumulate\uff0cMMA\uff09\u5355\u5143\u7684\u6570\u503c\u884c\u4e3a\u3002\u77e9\u9635\u4e58\u6cd5\u662f&nbsp;LLMs&nbsp;\u8bad\u7ec3\u548c\u63a8\u7406\u4e2d\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\u7684\u6838\u5fc3\uff0cGPU&nbsp;\u4e2d\u7684\u4e13\u7528\u5355\u5143\u8d1f\u8d23\u8ba1\u7b97D=A\u00d7B+C\u5f62\u5f0f\u7684\u8fd0\u7b97\u3002NVIDIA&nbsp;\u5c06\u8fd9\u4e9b\u5355\u5143\u79f0\u4e3a\u5f20\u91cf\u6838\u5fc3\uff08Tensor Core\uff09\uff0cAMD&nbsp;\u5219\u79f0\u5176\u4e3a\u77e9\u9635\u6838\u5fc3\uff08Matrix Core\uff09\u3002\u5b83\u4eec\u652f\u6301&nbsp;LLMs&nbsp;\u6240\u7528\u7684\u6d6e\u70b9\u6570\u636e\u7c7b\u578b\uff0c\u540c\u65f6\u63d0\u4f9b\u9ad8\u541e\u5410\u91cf\u548c\u9ad8\u6548\u7387\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u95ee\u9898\u5728\u4e8e\uff0c\u66b4\u9732\u7ed9\u8f6f\u4ef6\u7684MMA\u6307\u4ee4\u89c4\u5b9a\u4e86\u8fd0\u7b97\u7684\u6570\u5b66\u5b9a\u4e49D=A\u00d7B+C\uff0c\u5374\u6ca1\u6709\u89c4\u5b9a\u5176\u6570\u503c\u5b9e\u73b0\u65b9\u5f0f\u3002\u8ba1\u7b97\u7ed3\u679c\u53d6\u51b3\u4e8e\u878d\u5408\u7c92\u5ea6\u3001\u5185\u90e8\u7cbe\u5ea6\u3001\u820d\u5165\u4e0e\u89c4\u683c\u5316\u3001\u6b21\u6b63\u89c4\u6570\u5904\u7406\u3001\u6c42\u548c\u987a\u5e8f\uff0c\u4ee5\u53ca\u5176\u4ed6\u5b9e\u73b0\u7ec6\u8282\u3002\u8fd9\u4e9b\u9690\u85cf\u7684\u7b97\u672f\u9009\u62e9\u51b3\u5b9a\u4e86&nbsp;D&nbsp;\u4e2d\u5b9e\u9645\u8ba1\u7b97\u51fa\u7684\u6570\u503c\uff0c\u5e76\u6700\u7ec8\u5f71\u54cd\u53ef\u590d\u73b0\u6027\u3001\u7cbe\u5ea6\u548c\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u5458\u4eec\u7684\u76ee\u6807\u662f\u901a\u8fc7\u767d\u76d2\u6a21\u578b\uff0c\u5c06\u5e95\u5c42\u8ba1\u7b97\u8fc7\u7a0b\u660e\u786e\u5730\u63cf\u8ff0\u51fa\u6765\u3002\u901a\u8fc7\u91c7\u7528\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\uff08feature-probing test\uff09\uff0c\u6765\u6784\u5efa\u8fd9\u4e9b\u6a21\u578b\u3002<\/p>\n\n\n\n<h2 id=\"\u4e00\u9053\u7b97\u672f\u9898-\u516d\u79cd\u7b54\u6848\" class=\"wp-block-heading\">\u4e00\u9053\u7b97\u672f\u9898\uff0c\u516d\u79cd\u7b54\u6848<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5148\u770b\u4e00\u4e2a\u5177\u4f53\u7684&nbsp;MMA&nbsp;\u8fd0\u7b97\u793a\u4f8b\u3002\u56fe1\u4e2d\u9ad8\u4eae\u663e\u793a\u7684&nbsp;A&nbsp;\u7684\u7b2c\u4e00\u884c\u3001B&nbsp;\u7684\u7b2c\u4e00\u5217\uff0c\u4ee5\u53ca&nbsp;C&nbsp;\u7684\u7b2c\u4e00\u4e2a\u5143\u7d20\uff0c\u5171\u540c\u51b3\u5b9a\u4e86&nbsp;D&nbsp;\u7684\u7b2c\u4e00\u4e2a\u8f93\u51fa\u5143\u7d20\u3002\u8003\u8651\u4ee5\u4e0b\u8f93\u5165\u5bf9&nbsp;(\u22122<sup>13<\/sup>,2<sup>10<\/sup>), (\u22120.5,1), (\u22120.25,1), (\u22120.125,1)\uff0c\u4ee5\u53ca\u503c\u4e3a2<sup>23<\/sup>\u7684\u7d2f\u52a0\u8f93\u5165\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"279\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM1.png\" alt=\"chart, scatter chart, box and whisker chart\" class=\"wp-image-1192152\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM1.png 780w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM1-766x274.png 766w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM1-300x107.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM1-240x86.png 240w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">\u56fe1\uff1a\u77e9\u9635\u4e58\u7d2f\u52a0\uff08MMA\uff09\u8fd0\u7b97\u793a\u4f8b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5404\u5bf9\u8f93\u5165\u76f8\u4e58\u540e\uff0c\u5f97\u5230&nbsp;\u22122<sup>23<\/sup>\u3001\u22120.5\u3001\u22120.25\u548c&nbsp;\u22120.125\u3002\u4ece\u6570\u5b66\u4e0a\u770b\uff0c\u5c06\u8fd9\u4e9b\u4e58\u79ef\u52a0\u5230\u7d2f\u52a0\u5668&nbsp;2<sup>23<\/sup>\u4e0a\uff0c\u7ed3\u679c\u5e94\u4e3a&nbsp;\u22120.875\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u4e48\u5404\u6761\u786c\u4ef6\u6307\u4ee4\u5b9e\u9645\u4f1a\u8fd4\u56de\u4ec0\u4e48\uff1f\u9762\u5bf9\u5b8c\u5168\u76f8\u540c\u7684\u8f93\u5165\uff0c\u5982\u56fe2\u6240\u793a\u7684&nbsp;MMA&nbsp;\u6307\u4ee4\u4ea7\u751f\u4e86\u516d\u79cd\u4e0d\u540c\u7684\u7ed3\u679c\uff1a0\u3001\u22120.375\u3001\u22120.5\u3001\u22120.75\u3001\u22120.875\uff08\u7cbe\u786e\u7ed3\u679c\uff09\u4ee5\u53ca&nbsp;\u22121\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"350\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM2.png\" alt=\"chart\" class=\"wp-image-1192153\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM2.png 780w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM2-300x135.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM2-767x344.png 767w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM2-240x108.png 240w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">\u56fe2\uff1a\u540c\u4e00\u793a\u4f8b\u8f93\u5165\uff0c\u4e0d\u540cGPU\u8f93\u51fa\u4e0d\u540c\uff08\u5de6\u5217\u5217\u51fa\u7ed3\u679c\uff0c\u53f3\u5217\u5217\u51fa\u5bf9\u5e94\u7684\u6307\u4ee4\uff09<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u4f8b\u5b50\u6e05\u6670\u5730\u5c55\u793a\u4e86\u9690\u85cf\u7b97\u672f\u9009\u62e9\u7684\u5f71\u54cd\u3002\u7814\u7a76\u5458\u4eec\u8981\u6784\u5efa\u7684\u6a21\u578b\uff0c\u65e2\u8981\u9010\u6bd4\u7279\u590d\u73b0\u6bcf\u6761\u6307\u4ee4\u7684\u7ed3\u679c\uff0c\u4e5f\u8981\u80fd\u89e3\u91ca\u8fd9\u4e9b\u8f93\u51fa\u662f\u5982\u4f55\u4ea7\u751f\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u8fd9\u4e9b\u8f93\u51fa\u53cd\u63a8\u786c\u4ef6\u5185\u90e8\u8ba1\u7b97\u65b9\u5f0f\u7684\u65b9\u6cd5\uff0c\u79f0\u4e3a\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\u3002\u4e0b\u9762\u4e3e\u4e24\u4e2a\u4f8b\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7b2c\u4e00\uff0c\u63a2\u6d4b\u6c42\u548c\u987a\u5e8f\u3002<\/strong>\u4ecd\u7136\u4f7f\u7528\u4e0e\u524d\u4f8b\u76f8\u540c\u7684\u52a0\u6570\uff0c\u5bf9\u6bd4\u4e24\u68f5\u6c42\u548c\u6811\uff08\u5982\u56fe3\u6240\u793a\uff09\uff0c\u4ee5\u5c55\u793a\u6c42\u548c\u987a\u5e8f\u5982\u4f55\u5f71\u54cd\u7ed3\u679c\u3002\u56fe3\u5de6\u4fa7\u7684\u52a0\u6cd5\u8fd0\u7b97\u6784\u6210\u4e86\u4e00\u6761\u987a\u5e8f\u6267\u884c\u7684\u94fe\uff0c\u7d2f\u52a0\u5668&nbsp;C&nbsp;\u4ece\u4e00\u5f00\u59cb\u5c31\u53c2\u4e0e\u5176\u4e2d\u3002\u5728\u987a\u5e8f\u6c42\u548c\u4e2d\uff0c\u4e24\u4e2a\u5927\u6570\u9996\u5148\u62b5\u6d88\uff0c\u5176\u4f59\u52a0\u6570\u5f97\u4ee5\u4fdd\u7559\uff0c\u6700\u7ec8\u5f97\u5230(((2<sup>23<\/sup>\u22122<sup>23<\/sup>)\u22120.5)\u22120.25)\u22120.125=\u22120.875\u3002\u53f3\u4fa7\u5219\u5148\u5c06\u4e58\u79ef\u4e24\u4e24\u76f8\u52a0\uff0c\u518d\u5c06\u8fd9\u4e9b\u548c\u4e0e&nbsp;C&nbsp;\u7d2f\u52a0\u3002\u5728\u672c\u4f8b\u91c7\u7528\u7684\u6709\u9650\u7cbe\u5ea6\u7b97\u672f\u4e0b\uff0c\u6210\u5bf9\u6c42\u548c\u65f6\uff0c\u8f83\u5c0f\u7684\u9879\u5728\u4e0e\u8f83\u5927\u7684\u9879\u76f8\u52a0\u65f6\u4e22\u5931\uff0c\u6700\u7ec8\u5f97\u52302<sup>23<\/sup>+((\u22122<sup>23<\/sup>\u22120.5)+(\u22120.25\u22120.125))=0\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"779\" height=\"293\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM3.png\" alt=\"diagram\" class=\"wp-image-1192154\" style=\"width:600px;height:auto\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM3.png 779w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM3-300x113.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM3-766x288.png 766w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM3-240x90.png 240w\" sizes=\"auto, (max-width: 779px) 100vw, 779px\" \/><figcaption class=\"wp-element-caption\">\u56fe3\uff1a\u4e24\u79cd\u6c42\u548c\u987a\u5e8f\u4ea7\u751f\u4e0d\u540c\u7684\u7ed3\u679c<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u63a8\u5e7f\u5f00\u6765\uff0c\u53ef\u4ee5\u9009\u62e9\u4e00\u4e2a\u5927\u6570&nbsp;U&nbsp;\u548c\u4e00\u4e2a\u5c0f\u6570&nbsp;v\uff0c\u4f7f\u5f97&nbsp;U+v&nbsp;\u820d\u5165\u540e\u4ecd\u4e3a&nbsp;U\u3002\u968f\u540e\u518d\u52a0\u4e0a&nbsp;\u2212U\uff0c\u7ed3\u679c\u5c31\u662f0\u3002\u5982\u679c\u5148\u8ba9&nbsp;U&nbsp;\u4e0e\u2212U&nbsp;\u62b5\u6d88\uff0c\u5219&nbsp;v&nbsp;\u4f1a\u88ab\u4fdd\u7559\u4e0b\u6765\u3002\u901a\u8fc7\u5c06\u5927\u6570\u653e\u5728\u4e0d\u540c\u7684\u8f93\u5165\u4f4d\u7f6e\uff0c\u5e76\u89c2\u5bdf\u54ea\u4e9b\u5c0f\u6570\u9879\u80fd\u591f\u4fdd\u7559\uff0c\u5c31\u53ef\u4ee5\u63a8\u65ad\u51fa\u6c42\u548c\u7684\u987a\u5e8f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7b2c\u4e8c\uff0c\u63a2\u6d4b\u5185\u90e8\u7cbe\u5ea6\u548c\u820d\u5165\u6a21\u5f0f\u3002<\/strong>\u4ec5\u9760\u6c42\u548c\u987a\u5e8f\u8fd8\u4e0d\u8db3\u4ee5\u5b8c\u6574\u89e3\u91ca\u8fd9\u4e9b\u7ed3\u679c\uff0c\u7814\u7a76\u5458\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u5305\u542b\u4e94\u4e2a\u52a0\u6570\u7684\u878d\u5408\u8fd0\u7b97\uff1a\u5c06&nbsp;U&nbsp;\u548c&nbsp;\u2212U&nbsp;\u653e\u5728\u6c42\u548c\u6811\u7684\u4e24\u4e2a\u53f6\u8282\u70b9\u4e0a\uff0c\u5176\u4f59\u4e09\u4e2a\u53f6\u8282\u70b9\u5747\u653e\u7f6e&nbsp;v\u3002\u5982\u679c\u5185\u90e8\u7cbe\u5ea6\u8db3\u591f\u9ad8\uff0c\u8fd0\u7b97\u4f1a\u4fdd\u7559\u5168\u90e8\u4e09\u4e2a\u5c0f\u6570\u9879\uff0c\u5e76\u8fd4\u56de&nbsp;3v\u3002\u4f46\u6709\u9650\u7cbe\u5ea6\u7684\u878d\u5408\u8fd0\u7b97\u53ef\u80fd\u5728\u62b5\u6d88\u53d1\u751f\u524d\u7684\u5bf9\u9f50\u9636\u6bb5\u5c31\u4e22\u5f03\u4e86\u8fd9\u4e9b\u5c0f\u6570\u9879\uff0c\u4ece\u800c\u8fd4\u56de&nbsp;0\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"369\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM4.jpg\" alt=\"diagram\" class=\"wp-image-1192155\" style=\"width:500px;height:auto\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM4.jpg 780w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM4-767x363.jpg 767w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM4-300x142.jpg 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM4-240x114.jpg 240w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">\u56fe4\uff1a\u4e24\u79cd\u7cbe\u5ea6\u7684\u878d\u5408\u6c42\u548c\u4ea7\u751f\u4e0d\u540c\u7684\u7ed3\u679c<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8ba1\u7b97<\/strong>&nbsp;U\u3001\u2212U\u548c\u03f5&nbsp;\u7684\u878d\u5408\u6c42\u548c\uff0c\u4ece\u03f5=0.5U&nbsp;\u5f00\u59cb\uff0c\u53cd\u590d\u5c06\u5176\u51cf\u534a\u3002\u03f5&nbsp;\u4e0d\u518d\u88ab\u4fdd\u7559\u65f6\u6240\u5bf9\u5e94\u7684\u9608\u503c\uff0c\u53ef\u4ee5\u63ed\u793a\u5185\u90e8\u5c0f\u6570\u4f4d\u7684\u4f4d\u6570\u3002\u8fdb\u4e00\u6b65\u5728\u8be5\u9608\u503c\u7684\u4e00\u534a\u5904\uff0c\u4ee5\u53ca\u7565\u9ad8\u4e8e\u548c\u7565\u4f4e\u4e8e\u8be5\u503c\u7684\u4f4d\u7f6e\u6d4b\u8bd5\u03f5\uff0c\u8fd8\u53ef\u4ee5\u63a8\u65ad\u51fa\u820d\u5165\u6a21\u5f0f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0a\u53ea\u662f\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\u4e2d\u7684\u51e0\u4e2a\u4f8b\u5b50\u3002\u7814\u7a76\u5458\u4eec\u628a\u5b8c\u6574\u7684\u5efa\u6a21\u65b9\u6cd5\u79f0\u4e3a\u95ed\u73af\u7279\u5f81\u63a2\u6d4b\uff08closed-loop feature probing\uff0cCLFP\uff09\u3002\u53ea\u8981\u80fd\u591f\u901a\u8fc7\u63a5\u53e3\u8c03\u7528\u67d0\u6761&nbsp;MMA&nbsp;\u6307\u4ee4\uff0cCLFP&nbsp;\u5c31\u53ef\u4ee5\u5229\u7528\u4e00\u7ec4\u4e0d\u65ad\u6269\u5145\u7684\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\uff0c\u6784\u5efa\u53ef\u6267\u884c\u7684\u7b97\u672f\u6a21\u578b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6574\u4e2a\u6d41\u7a0b\u5206\u4e3a\u4e94\u6b65\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u68c0\u67e5\u786e\u5b9a\u6027\u5047\u8bbe\uff0c\u4ee5\u53ca\u4e0d\u540c\u8f93\u51fa\u4f4d\u7f6e\u4e4b\u95f4\u7684\u4e00\u81f4\u6027\u5047\u8bbe\u3002<\/li>\n\n\n\n<li>\u63a8\u65ad\u6c42\u548c\u6811\u53ca\u5176\u5143\u6570\uff0c\u5373\u5404\u6c42\u548c\u8282\u70b9\u5305\u542b\u7684\u8f93\u5165\u6570\u91cf\u3002<\/li>\n\n\n\n<li>\u63a2\u6d4b\u5176\u4ed6\u7b97\u672f\u7279\u5f81\u5e76\u6784\u5efa\u6a21\u578b\u3002<\/li>\n\n\n\n<li>\u901a\u8fc7\u968f\u673a\u5dee\u5206\u6d4b\u8bd5\uff0c\u9010\u6bd4\u7279\u6bd4\u8f83\u786c\u4ef6\u8f93\u51fa\u4e0e\u6a21\u578b\u8f93\u51fa\u3002<\/li>\n\n\n\n<li>\u5982\u679c\u9a8c\u8bc1\u5931\u8d25\uff0c\u7b2c\u4e94\u6b65\u5c31\u4f1a\u5bf9\u53cd\u4f8b\u8fdb\u884c\u7f29\u51cf\uff0c\u5411\u63a2\u6d4b\u6d4b\u8bd5\u96c6\u4e2d\u52a0\u5165\u4e00\u4e2a\u80fd\u591f\u533a\u5206\u4e0d\u540c\u884c\u4e3a\u7684\u6d4b\u8bd5\uff0c\u4fee\u8ba2\u6a21\u578b\uff0c\u7136\u540e\u8fd4\u56de\u7b2c4\u6b65\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u53cd\u9988\u5faa\u73af\u80fd\u591f\u53d1\u73b0\u5148\u524d\u63a2\u6d4b\u9057\u6f0f\u7684\u7ec6\u8282\uff0c\u5e76\u5c06\u6bcf\u4e00\u6b21\u4e0d\u5339\u914d\u8f6c\u5316\u4e3a\u65b0\u7684\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\u3002\u5f53\u6a21\u578b\u5728\u9a8c\u8bc1\u6d4b\u8bd5\u4e2d\u80fd\u591f\u9010\u6bd4\u7279\u5339\u914d\u786c\u4ef6\u65f6\uff0c\u5faa\u73af\u7ed3\u675f\u3002<\/p>\n\n\n\n<h2 id=\"\u5341\u79cd\u67b6\u6784-\u4e09\u5927\u6a21\u578b\u65cf-mma-sim-\u7684\u4f4d\u7cbe\u786e\u6a21\u578b\" class=\"wp-block-heading\">\u5341\u79cd\u67b6\u6784\uff0c\u4e09\u5927\u6a21\u578b\u65cf\uff1aMMA-Sim&nbsp;\u7684\u4f4d\u7cbe\u786e\u6a21\u578b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u5458\u4eec\u5c06&nbsp;CLFP&nbsp;\u65b9\u6cd5\u5e94\u7528\u5728\u4e86\u5341\u79cd&nbsp;GPU&nbsp;\u67b6\u6784\u4e0a\u7684\u5168\u90e8\u6d6e\u70b9&nbsp;MMA&nbsp;\u6307\u4ee4\uff0c\u5305\u62ecNVIDIA&nbsp;\u7684&nbsp;Volta\u3001Turing\u3001Ampere\u3001Ada Lovelace\u3001Hopper\u3001Blackwell&nbsp;\u548cRTX Blackwell\uff0c\u4ee5\u53ca&nbsp;AMD&nbsp;\u7684&nbsp;CDNA1\u3001CDNA2\u548c&nbsp;CDNA3\u3002\u8986\u76d6\u7684\u683c\u5f0f\u6709&nbsp;FP64\u3001FP32\u3001TF32\u3001BF16\u3001FP16\u3001FP8\u3001FP6\u3001FP4\u3001MXFP8\u3001MXFP6\u3001MXFP4\u548c&nbsp;NVFP4\u3002\u8fd9\u6837\u5e7f\u6cdb\u7684\u8986\u76d6\u8303\u56f4\u5c55\u793a\u4e86\u8be5\u65b9\u6cd5\u7684\u901a\u7528\u6027\uff0c\u4e5f\u8ba9\u8de8\u4ee3\u6bd4\u8f83\u5404\u67b6\u6784\u7684\u6570\u503c\u884c\u4e3a\u6210\u4e3a\u53ef\u80fd\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u5458\u4eec\u4ece\u8fd9\u4e9b\u67b6\u6784\u4e2d\u5f52\u7eb3\u51fa\u4e86\u4e09\u5927\u6a21\u578b\u65cf\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>FTZ-MulAdd&nbsp;\u6a21\u578b\u91c7\u7528\u72ec\u7acb\u7684\u4e58\u6cd5\u548c\u52a0\u6cd5\u8fd0\u7b97\uff0c\u5e76\u5177\u6709\u6b21\u89c4\u683c\u6570\u5f52\u96f6\uff08flush-to-zero\uff09\u884c\u4e3a\u3002<\/li>\n\n\n\n<li>FMA&nbsp;\u6a21\u578b\u91c7\u7528\u4e00\u7cfb\u5217\u878d\u5408\u4e58\u52a0\u8fd0\u7b97\u3002<\/li>\n\n\n\n<li>FDPA&nbsp;\u6a21\u578b\u65cf\u5219\u5305\u542b\u516d\u79cd\u878d\u5408\u70b9\u79ef\u52a0\u6cd5\u8fd0\u7b97\u53d8\u4f53\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u622a\u65ad\u578b&nbsp;FDPA\uff08T-FDPA\uff09\u662f\u5176\u4e2d\u6700\u7b80\u5355\u7684\u4e00\u79cd&nbsp;FDPA&nbsp;\u53d8\u4f53\uff0c\u80fd\u591f\u4e3a&nbsp;NVIDIA GPU&nbsp;\u4e0a\u7684\u5927\u591a\u6570&nbsp;MMA&nbsp;\u6307\u4ee4\u5efa\u6a21\u3002\u5b83\u7684\u8ba1\u7b97\u8fc7\u7a0b\u662f\uff0c\u5148\u8ba1\u7b97\u7cbe\u786e\u7684\u3001\u672a\u7ecf\u89c4\u683c\u5316\u7684\u4e58\u79ef\uff1b\u518d\u628a&nbsp;L&nbsp;\u4e2a\u4e58\u79ef\u548c\u7d2f\u52a0\u5668\u90fd\u5bf9\u9f50\u5230\u5b83\u4eec\u4e2d\u7684\u6700\u5927\u6307\u6570\uff0c\u7136\u540e\u5c06\u6bcf\u4e2a\u5bf9\u9f50\u540e\u7684\u9879\u5411\u96f6\u622a\u65ad\uff0c\u4fdd\u7559&nbsp;F&nbsp;\u4e2a\u5c0f\u6570\u4f4d\uff1b\u4e4b\u540e\u4f7f\u7528\u5b9a\u70b9\u7b97\u672f\u5bf9\u622a\u65ad\u540e\u7684\u5b9a\u70b9\u6570\u8fdb\u884c\u7cbe\u786e\u6c42\u548c\uff1b\u6700\u540e\u91c7\u7528\u820d\u5165\u6a21\u5f0f&nbsp;\u03c1\uff0c\u5c06\u7ed3\u679c\u8f6c\u6362\u4e3a\u8f93\u51fa\u683c\u5f0f\u3002\u8be5\u6a21\u578b\u7684\u53c2\u6570\u5305\u62ec\u878d\u5408\u957f\u5ea6&nbsp;L\u3001\u5c0f\u6570\u4f4d\u6570&nbsp;F\uff0c\u4ee5\u53ca\u8f93\u51fa\u820d\u5165\u6a21\u5f0f&nbsp;\u03c1\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"142\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM5.png\" alt=\"graphical user interface, application, Word\" class=\"wp-image-1192156\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM5.png 780w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM5-300x55.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM5-764x139.png 764w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM5-240x44.png 240w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">\u56fe5\uff1a\u622a\u65ad\u578b&nbsp;FDPA\uff08T-FDPA\uff09\u8ba1\u7b97\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u7528\u8fd9\u4e2a\u6a21\u578b\u56de\u770b\u5f00\u5934\u7684\u4f8b\u5b50\uff0c\u901a\u8fc7\u91cd\u70b9\u89c2\u5bdf\u622a\u65ad\u64cd\u4f5c\u53ef\u4ee5\u53d1\u73b0\uff0c\u62b5\u6d88\u53d1\u751f\u524d\u7684\u622a\u65ad\u51b3\u5b9a\u4e86\u54ea\u4e9b\u5c0f\u6570\u9879\u80fd\u5728\u6700\u7ec8\u7ed3\u679c\u4e2d\u4fdd\u7559\u4e0b\u6765\u3002\u5f53&nbsp;F=23&nbsp;\u65f6\uff0c\u4e09\u4e2a\u5c0f\u6570\u9879\u5728\u4e24\u4e2a\u5927\u6570\u62b5\u6d88\u4e4b\u524d\u5c31\u5168\u90e8\u4e22\u5931\uff0c\u56e0\u6b64\u7ed3\u679c\u4e3a\u96f6\u3002\u5f53&nbsp;F=24&nbsp;\u65f6\uff0c\u22120.5&nbsp;\u5f97\u4ee5\u4fdd\u7559\uff0c\u7ed3\u679c\u4e3a&nbsp;\u22120.5\u3002\u5f53&nbsp;F=25&nbsp;\u65f6\uff0c\u22120.5&nbsp;\u548c\u22120.25&nbsp;\u5f97\u4ee5\u4fdd\u7559\uff0c\u7ed3\u679c\u4e3a&nbsp;\u22120.75\u3002\u7cbe\u786e\u7684\u878d\u5408\u6c42\u548c\u5219\u4f1a\u4fdd\u7559\u5168\u90e8\u4e09\u4e2a\u5c0f\u6570\u9879\uff0c\u5f97\u5230&nbsp;\u22120.875\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"779\" height=\"279\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM6.png\" alt=\"table\" class=\"wp-image-1192157\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM6.png 779w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM6-300x107.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM6-768x275.png 768w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM6-240x86.png 240w\" sizes=\"auto, (max-width: 779px) 100vw, 779px\" \/><figcaption class=\"wp-element-caption\">\u56fe6\uff1a\u5bfc\u81f4\u793a\u4f8b\u8f93\u5165\u4ea7\u751f\u4e0d\u540c\u7ed3\u679c\u7684\u7b97\u672f\u673a\u5236<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4ed6\u67b6\u6784\u9700\u8981\u4e0d\u540c\u7684\u6a21\u578b\u6765\u63cf\u8ff0\u3002\u4f8b\u5982\uff0cCDNA2 GPU&nbsp;\u4e0a\u4e0d\u5e26&nbsp;1k&nbsp;\u540e\u7f00\u7684&nbsp;BF16 MMA&nbsp;\u6307\u4ee4\u7531&nbsp;FTZ-MulAdd&nbsp;\u6a21\u578b\u63cf\u8ff0\uff0c\u5bf9\u4e8e\u6c42\u548c\u987a\u5e8f2<sup>23<\/sup>+(\u22122<sup>23<\/sup>\u22120.5)+(\u22120.25\u22120.125)\uff0c\u6a21\u578b\u4e2d\u7684\u6709\u9650\u7cbe\u5ea6\u8fd0\u7b97\u53ef\u4ee5\u5f97\u5230&nbsp;\u22120.375\u3002CDNA3 GPU&nbsp;\u4e0a\u7684&nbsp;FP8 MMA&nbsp;\u6307\u4ee4\u5219\u7531&nbsp;GTR-FDPA&nbsp;\u6a21\u578b\u63cf\u8ff0\uff0c\u5176\u4e2d\u4e2d\u95f4\u7ed3\u679c\u5411\u4e0b\u820d\u5165\u4e3a&nbsp;\u22121.0\u3002\u81f3\u6b64\uff0c\u5f00\u5934\u7684\u516d\u79cd\u7b54\u6848\u90fd\u5f97\u5230\u4e86\u89e3\u91ca\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u63a8\u65ad\u51fa\u7684\u53c2\u6570\u8fd8\u6e05\u695a\u5730\u53cd\u6620\u4e86&nbsp;GPU&nbsp;\u7684\u4ee3\u9645\u6f14\u8fdb\u3002\u8fd9\u91cc\uff0cF&nbsp;\u8868\u793a\u5185\u90e8\u5b9a\u70b9\u6c42\u548c\u7684\u5c0f\u6570\u4f4d\u6570\u3002\u5bf9\u4e8e\u8f93\u51fa\u4e3a&nbsp;FP32&nbsp;\u7684\u6307\u4ee4\uff0cAda Lovelace GPU&nbsp;\u5728\u8f93\u5165\u4e3a&nbsp;FP16&nbsp;\u548c&nbsp;BF16&nbsp;\u65f6\u91c7\u7528&nbsp;F=24\uff0c\u800c\u5728\u8f93\u5165\u4e3a&nbsp;FP8&nbsp;\u65f6\u91c7\u7528&nbsp;F=13\u3002Hopper GPU&nbsp;\u5bf9\u5e94\u7684\u53d6\u503c\u5206\u522b\u4e3a&nbsp;F=25&nbsp;\u548c&nbsp;F=13\u3002Blackwell\u548c&nbsp;RTX Blackwell GPU&nbsp;\u5c06&nbsp;FP8&nbsp;\u8f93\u5165\u8def\u5f84\u7684&nbsp;F&nbsp;\u63d0\u9ad8\u5230\u4e86&nbsp;25\uff0c\u4e0e\u5176&nbsp;FP16&nbsp;\u548cBF16&nbsp;\u8def\u5f84\u4e00\u81f4\u3002\u8fd9\u662f\u5185\u90e8\u7cbe\u5ea6\u5f97\u5230\u63d0\u5347\u7684\u4e00\u4e2a\u5177\u4f53\u4f8b\u8bc1\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"781\" height=\"304\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM7.png\" alt=\"chart, bar chart\" class=\"wp-image-1192158\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM7.png 781w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM7-766x298.png 766w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM7-300x117.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM7-240x93.png 240w\" sizes=\"auto, (max-width: 781px) 100vw, 781px\" \/><figcaption class=\"wp-element-caption\">\u56fe7\uff1aFP8 MMA\u5185\u90e8\u7cbe\u5ea6\u7684\u4ee3\u9645\u53d8\u5316<\/figcaption><\/figure>\n\n\n\n<h2 id=\"\u7cbe\u5ea6\u53bb\u54ea\u513f\u4e86-\u56db\u5927\u74f6\u9888\u4e0e\u4e00\u4e2a-\u8d1f\u5411\u504f\u5dee\" class=\"wp-block-heading\">\u7cbe\u5ea6\u53bb\u54ea\u513f\u4e86\uff1f\u56db\u5927\u74f6\u9888\u4e0e\u4e00\u4e2a\u201c\u8d1f\u5411\u504f\u5dee\u201d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5229\u7528\u8fd9\u4e9b\u6a21\u578b\uff0c\u7814\u7a76\u5458\u4eec\u53d1\u73b0\u4e86\u8ba1\u7b97\u6d41\u6c34\u7ebf\u4e2d\u56db\u4e2a\u4e0d\u540c\u9636\u6bb5\u7684\u7cbe\u5ea6\u74f6\u9888\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u4e2a\u662f\u8f93\u5165\u5904\u7406\uff1aCDNA2 GPU&nbsp;\u4e0a\u7684&nbsp;FP16 MMA&nbsp;\u6307\u4ee4\u4f1a\u5c06\u6b21\u6b63\u89c4\u6570\u8f93\u5165\u5f52\u96f6\uff0c\u4f7f\u5176\u8d21\u732e\u5728\u4e58\u6cd5\u53d1\u751f\u4e4b\u524d\u5c31\u4e22\u5931\u3002<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u4e2a\u662f\u5185\u90e8\u6c42\u548c\uff1aAda Lovelace&nbsp;\u548cHopper GPU&nbsp;\u4e0a\u7684&nbsp;FP8 MMA&nbsp;\u6307\u4ee4\u4fdd\u7559&nbsp;F=13&nbsp;\u4e2a\u5c0f\u6570\u4f4d\uff0c\u8fd9\u51b3\u5b9a\u4e86\u5bf9\u9f50\u540e\u6709\u591a\u5c11\u4fe1\u606f\u80fd\u591f\u4fdd\u7559\u4e0b\u6765\u3002<\/li>\n\n\n\n<li>\u7b2c\u4e09\u4e2a\u662f\u8f93\u51fa\u820d\u5165\uff1aAda Lovelace&nbsp;\u548cHopper GPU&nbsp;\u4e0a\u8f93\u51fa\u4e3a&nbsp;FP32&nbsp;\u7684&nbsp;FP8 MMA&nbsp;\u6307\u4ee4\uff0c\u4f1a\u5c06\u7ed3\u679c\u820d\u5165\u81f3&nbsp;E8M13&nbsp;\u7cbe\u5ea6\u3002<\/li>\n\n\n\n<li>\u7b2c\u56db\u4e2a\u662f\u6700\u7ec8\u8f93\u51fa\u683c\u5f0f\uff1aNVIDIA GPU&nbsp;\u4e0a\u8f93\u51fa\u4e3a&nbsp;FP16&nbsp;\u7684MMA&nbsp;\u6307\u4ee4\uff0c\u5373\u4f7f\u5185\u90e8\u8ba1\u7b97\u91c7\u7528&nbsp;FP32&nbsp;\u7ea7\u522b\u7684\u7cbe\u5ea6\uff0c\u4e5f\u4f1a\u5c06\u7ed3\u679c\u820d\u5165\u4e3a&nbsp;FP16\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e9b\u74f6\u9888\u964d\u4f4e\u4e86&nbsp;MMA&nbsp;\u6307\u4ee4\u7684\u6570\u503c\u7cbe\u5ea6\u3002\u53e6\u4e00\u4e2a\u503c\u5f97\u5173\u6ce8\u7684\u95ee\u9898\u662f&nbsp;CDNA3 GPU&nbsp;\u4e0a\u6f5c\u5728\u7684\u6570\u503c\u504f\u5dee\u3002CDNA3 GPU&nbsp;\u4e0a\u8f93\u5165\u4e3a&nbsp;TF32\u3001BF16\u3001FP16\u6216&nbsp;FP8&nbsp;\u7684&nbsp;MMA&nbsp;\u6307\u4ee4\uff0c\u5185\u90e8\u91c7\u7528\u5411\u8d1f\u65e0\u7a77\u65b9\u5411\u820d\u5165\u8fd9\u79cd\u975e\u5bf9\u79f0\u6a21\u5f0f\uff0c\u53ef\u80fd\u5f15\u5165\u8d1f\u5411\u504f\u5dee\uff0c\u5e76\u5728\u91cd\u590d\u8fd0\u7b97\u4e2d\u4e0d\u65ad\u7d2f\u79ef\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u5458\u4eec\u628a\u5b9e\u9645\u7684&nbsp;FP16 MMA&nbsp;\u6307\u4ee4\u4e0e\u4e00\u4e2a\u91c7\u7528\u5bf9\u79f0\u5411\u96f6\u820d\u5165\u7684\u5047\u8bbe\u53d8\u4f53\u505a\u4e86\u6bd4\u8f83\u3002\u7ed3\u679c\u663e\u793a\uff0c\u76f8\u5bf9\u4e8e\u9ad8\u7cbe\u5ea6\u53c2\u8003\u7ed3\u679c\uff0c\u5047\u8bbe\u53d8\u4f53\u7684\u8bef\u5dee\u5206\u5e03\u662f\u5bf9\u79f0\u7684\uff0c\u5b9e\u9645\u6307\u4ee4\u4ea7\u751f\u7684\u5206\u5e03\u5219\u6574\u4f53\u5411\u8d1f\u503c\u65b9\u5411\u504f\u79fb\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"781\" height=\"314\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM8.png\" alt=\"graphical user interface, chart\" class=\"wp-image-1192159\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM8.png 781w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM8-300x121.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM8-766x308.png 766w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM8-240x96.png 240w\" sizes=\"auto, (max-width: 781px) 100vw, 781px\" \/><figcaption class=\"wp-element-caption\">\u56fe8\uff1aCDNA3 GPU\u51fa\u73b0\u8d1f\u5411\u7684\u6570\u503c\u504f\u79fb<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u9488\u5bf9\u4e0a\u8ff0\u673a\u5236\uff0c\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86\u8f6f\u4ef6\u5c42\u9762\u7684\u89c4\u907f\u65b9\u6848\u3002\u4e0b\u9762\u662f\u4e24\u4e2a\u4f8b\u5b50\u3002\u7b2c\u4e00\u79cd\u65b9\u6848\u5148\u653e\u5927\u8f93\u5165\uff0c\u4f7f\u6b21\u6b63\u89c4\u6570\u8fdb\u5165\u6b63\u89c4\u6570\u8303\u56f4\uff0c\u518d\u5bf9\u8f93\u51fa\u8fdb\u884c\u53cd\u5411\u7f29\u653e\u4ee5\u8865\u507f\u3002\u5bf9\u4e8e&nbsp;CDNA2 GPU&nbsp;\u4e0a\u7684&nbsp;FP16 MMA&nbsp;\u6307\u4ee4\uff0c\u8fd9\u4f7f\u76f8\u5bf9\u4e8e\u53c2\u8003\u7ed3\u679c\u7684\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u4ece&nbsp;7.632\u00d710<sup>\u22129<\/sup>\u964d\u81f3&nbsp;1.591\u00d710<sup>\u221218<\/sup>\u3002\u7b2c\u4e8c\u79cd\u65b9\u6848\u5c06&nbsp;MMA&nbsp;\u7d2f\u52a0\u5668&nbsp;C&nbsp;\u8bbe\u4e3a\u96f6\u6765\u8ba1\u7b97&nbsp;A\u00d7B\uff0c\u7136\u540e\u4f7f\u7528&nbsp;FP32&nbsp;\u5355\u72ec\u52a0\u4e0a\u539f\u59cb\u7684&nbsp;C\u3002\u8fd9\u51cf\u8f7b\u4e86&nbsp;CDNA3&nbsp;\u975e\u5bf9\u79f0\u820d\u5165\u7684\u5f71\u54cd\uff0c\u4f7f\u5e73\u5747\u8bef\u5dee\u7684\u7edd\u5bf9\u503c\u964d\u81f3\u539f\u6765\u7684\u7ea6&nbsp;1\/18\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"269\" src=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM9.png\" alt=\"graphical user interface, application, Word\" class=\"wp-image-1192160\" srcset=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM9.png 780w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM9-300x103.png 300w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM9-766x264.png 766w, https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2026\/10\/MM9-240x83.png 240w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">\u56fe9\uff1a\u8f6f\u4ef6\u89c4\u907f\u65b9\u6cd5\u6709\u6548\u964d\u4f4e\u5747\u65b9\u8bef\u5dee\u548c\u5e73\u5747\u504f\u79fb<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8f6f\u4ef6\u65b9\u6848\u80fd\u591f\u7f13\u89e3\u75c7\u72b6\uff0c\u4f46\u786c\u4ef6\u8bbe\u8ba1\u624d\u80fd\u89e3\u51b3\u6839\u672c\u539f\u56e0\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u5bf9\u672a\u6765\u7684&nbsp;MMA&nbsp;\u5355\u5143\u8bbe\u8ba1\u63d0\u51fa\u4e86\u4e09\u70b9\u5efa\u8bae\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9996\u5148\uff0c\u5728\u6574\u4e2a\u8ba1\u7b97\u6d41\u6c34\u7ebf\u4e2d\u4fdd\u6301&nbsp;FP32&nbsp;\u7ea7\u522b\u7684\u7cbe\u5ea6\u3002<\/li>\n\n\n\n<li>\u5176\u6b21\uff0c\u4f18\u5148\u91c7\u7528\u5bf9\u79f0\u7684\u5185\u90e8\u820d\u5165\u6a21\u5f0f\uff0c\u4ee5\u907f\u514d\u65b9\u5411\u6027\u504f\u5dee\uff1b\u5bf9\u4e8e\u539f\u7801\u8868\u793a\u6216\u53cd\u7801\u8868\u793a\uff0c\u5411\u96f6\u820d\u5165\u4e5f\u53ef\u80fd\u5177\u6709\u8f83\u9ad8\u7684\u5b9e\u73b0\u6548\u7387\u3002<\/li>\n\n\n\n<li>\u6700\u540e\uff0c\u5229\u7528\u53ef\u6267\u884c\u6a21\u578b\u5f00\u5c55\u6301\u7eed\u7684\u6570\u503c\u6d4b\u8bd5\uff0c\u5e76\u5728\u8bbe\u8ba1\u63a2\u7d22\u4e2d\u7eb3\u5165\u7cbe\u5ea6\u8003\u91cf\u3002\u660e\u786e\u7684\u7b97\u672f\u8bed\u4e49\u6709\u52a9\u4e8e\u8bc4\u4f30\u786c\u4ef6\u8bbe\u8ba1\u4e2d\u7684\u6743\u8861\uff0c\u5e76\u9009\u62e9\u6709\u9488\u5bf9\u6027\u7684\u8f6f\u4ef6\u7f13\u89e3\u63aa\u65bd\u3002<\/li>\n<\/ul>\n\n\n\n<h2 id=\"\u4ece-\u9ed1\u76d2-\u5230-\u767d\u76d2-\u8ba9\u6bcf\u4e00\u4e2a\u6bd4\u7279\u90fd\u6709\u636e\u53ef\u67e5\" class=\"wp-block-heading\">\u4ece\u201c\u9ed1\u76d2\u201d\u5230\u201c\u767d\u76d2\u201d\uff1a\u8ba9\u6bcf\u4e00\u4e2a\u6bd4\u7279\u90fd\u6709\u636e\u53ef\u67e5<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">CLFP\u901a\u8fc7\u63a2\u6d4b\u3001\u5efa\u6a21\u4e0e\u9a8c\u8bc1\u6784\u6210\u7684\u95ed\u73af\u6d41\u7a0b\uff0c\u63ed\u793a\u4e86\u9690\u85cf\u7684\u7b97\u672f\u884c\u4e3a\u3002\u501f\u52a9\u7531\u6b64\u5f97\u5230\u7684\u767d\u76d2\u6a21\u578b\uff0cMMA-Sim&nbsp;\u80fd\u591f\u5728\u5341\u79cd&nbsp;GPU&nbsp;\u67b6\u6784\u4e0a\u9010\u6bd4\u7279\u590d\u73b0\u6240\u6d4b\u8bd5&nbsp;MMA&nbsp;\u6307\u4ee4\u7684\u8f93\u51fa\uff0c\u89e3\u91ca\u6570\u503c\u5dee\u5f02\uff0c\u5e76\u6307\u5bfc\u7cbe\u5ea6\u6539\u8fdb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u5458\u4eec\u5e0c\u671b\uff0c\u8fd9\u9879\u5de5\u4f5c\u80fd\u8ba9&nbsp;GPU&nbsp;\u7684\u6570\u503c\u884c\u4e3a\u4ece\u201c\u9ed1\u76d2\u201d\u53d8\u6210\u201c\u767d\u76d2\u201d\uff0c\u4e3a\u5927\u6a21\u578b\u7684\u53ef\u590d\u73b0\u6027\u3001\u8bad\u7ec3\u7a33\u5b9a\u6027\u548c\u4e0b\u4e00\u4ee3&nbsp;AI&nbsp;\u786c\u4ef6\u8bbe\u8ba1\u6253\u4e0b\u66f4\u624e\u5b9e\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Bit-Accurate Modeling of GPU Matrix Multiply-Accumulate Units: Demystifying Numerical Discrepancy and Accuracy (MICRO 2026)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8bba\u6587\u94fe\u63a5\uff1a<\/strong><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/arxiv.org\/abs\/2511.10909\">https:\/\/arxiv.org\/abs\/2511.10909<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f00\u6e90\u94fe\u63a5\uff1a<\/strong><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/github.com\/microsoft\/MMA-Sim\">https:\/\/github.com\/microsoft\/MMA-Sim<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u540c\u6837\u7684\u6a21\u578b\u3001\u540c\u6837\u7684\u8f93\u5165\u3001\u540c\u6837\u7684\u968f\u673a\u79cd\u5b50\uff0c\u6362\u4e00\u5757&nbsp;GPU&nbsp;\u8fd0\u884c\uff0c\u7ed3\u679c\u5374\u53ef\u80fd\u4e0d\u4e00\u6837\u3002 \u5728\u5927\u6a21\u578b\u65f6\u4ee3\uff0c\u8fd9\u7c7b\u6570\u503c\u5dee\u5f02\u4e0d\u53ea\u662f\u5de5\u7a0b\u4e0a\u7684\u5c0f\u9ebb\u70e6\uff0c\u8fd8\u53ef\u80fd\u5f71\u54cd\u6a21\u578b\u8d28\u91cf\u3001\u5b9e\u9a8c\u53ef\u590d\u73b0\u6027\u548c\u8bad\u7ec3\u7a33\u5b9a\u6027\u3002\u90a3\u4e48\u95ee\u9898\u51fa\u5728\u54ea\u91cc\uff1f\u7b54\u6848\u5f80\u5f80\u85cf\u5728&nbsp;GPU&nbsp;\u5185\u90e8\u90a3\u4e9b\u6ca1\u6709\u5199\u8fdb\u6587\u6863\u7684\u7b97\u672f\u7ec6\u8282\u91cc\u3002 \u4e3a\u4e86\u770b\u6e05\u8fd9\u4e9b\u7ec6\u8282\uff0c\u5fae\u8f6f\u4e9a\u6d32\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86\u95ed\u73af\u7279\u5f81\u63a2\u6d4b\u65b9\u6cd5&nbsp;CLFP\uff0c\u5e76\u636e\u6b64\u6784\u5efa\u4e86&nbsp;MMA-Sim\u3002MMA-Sim&nbsp;\u662f\u4e00\u5957\u4f4d\u7cbe\u786e\u7684&nbsp;GPU&nbsp;\u77e9\u9635\u4e58\u7d2f\u52a0\uff08MMA\uff09\u6a21\u578b\uff0c\u8986\u76d6&nbsp;NVIDIA&nbsp;\u548cAMD&nbsp;\u7684\u5341\u79cd&nbsp;GPU&nbsp;\u67b6\u6784\uff0c\u80fd\u591f\u9010\u6bd4\u7279\u590d\u73b0\u6240\u6d4b\u8bd5\u6307\u4ee4\u7684\u8f93\u51fa\uff0c\u89e3\u91ca\u8de8\u5e73\u53f0\u7684\u6570\u503c\u5dee\u5f02\uff0c\u5e76\u4e3a\u7cbe\u5ea6\u6539\u8fdb\u63d0\u4f9b\u6307\u5bfc\u3002\u76f8\u5173\u8bba\u6587\u5df2\u88ab\u8ba1\u7b97\u673a\u4f53\u7cfb\u7ed3\u6784\u9886\u57df\u9876\u7ea7\u4f1a\u8bae&nbsp;MICRO 2026&nbsp;\u6536\u5f55\uff0c\u4ee3\u7801\u4e5f\u5df2\u5f00\u6e90\u3002 \u5927\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u4f1a\u6267\u884c\u6d77\u91cf\u7684\u6d6e\u70b9\u8fd0\u7b97\u3002\u4e00\u4e2a\u5fae\u5c0f\u7684\u7b97\u672f\u5dee\u5f02\uff0c\u53ef\u80fd\u5728\u4e0d\u540c\u5c42\u548c\u591a\u6b21\u8fed\u4ee3\u4e2d\u4e0d\u65ad\u7d2f\u79ef\u3001\u653e\u5927\uff0c\u6700\u7ec8\u6539\u53d8\u6a21\u578b\u8ba1\u7b97\u51fa\u7684\u6982\u7387\u5206\u5e03\u53ca\u5176\u8f93\u51fa\u7684&nbsp;token\u3002\u56e0\u6b64\uff0c\u6570\u503c\u884c\u4e3a\u5bf9\u4e8e\u6a21\u578b\u8d28\u91cf\u3001\u53ef\u590d\u73b0\u6027\u548c\u8bad\u7ec3\u7a33\u5b9a\u6027\u81f3\u5173\u91cd\u8981\u3002 \u73b0\u6709\u5173\u4e8e\u6570\u503c\u884c\u4e3a\u7684\u7814\u7a76\u5927\u591a\u805a\u7126\u4e8e\u8f6f\u4ef6\u56e0\u7d20\uff0c\u786c\u4ef6\u5c42\u9762\u7684\u7b97\u672f\u884c\u4e3a\u5374\u5f88\u5c11\u6709\u4eba\u6df1\u7a76\u3002\u5b9e\u9645\u4e0a\uff0c\u786c\u4ef6\u540c\u6837\u4f1a\u5e26\u6765\u4e24\u4e2a\u68d8\u624b\u7684\u95ee\u9898\uff1a 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GPU&nbsp;\u7684&nbsp;FP8&nbsp;\u77e9\u9635\u4e58\u6cd5\u5185\u90e8\u7cbe\u5ea6\u4e0d\u8db3\uff0c\u4f1a\u5bfc\u81f4&nbsp;LLMs&nbsp;\u8bad\u7ec3\u7cbe\u5ea6\u4e0b\u964d\u3002 \u8fd9\u4e24\u4e2a\u95ee\u9898\u6307\u5411\u540c\u4e00\u4e2a\u6839\u6e90\u2014\u2014\u4e1a\u754c\u5bf9\u786c\u4ef6\u6570\u503c\u884c\u4e3a\u7f3a\u4e4f\u767d\u76d2\u5c42\u9762\u7684\u7406\u89e3\u3002\u6ca1\u6709\u8fd9\u4e2a\u57fa\u7840\uff0c\u6211\u4eec\u5c31\u53ea\u80fd\u5728LLMs\u7cfb\u7edf\u51fa\u73b0\u95ee\u9898\u540e\u4f9d\u8d56\u7ecf\u9a8c\u88ab\u52a8\u5e94\u5bf9\uff0c\u96be\u4ee5\u4e8b\u5148\u8fdb\u884c\u6570\u503c\u5206\u6790\u3001\u7cbe\u5ea6\u9884\u6d4b\u3001\u95ee\u9898\u8bca\u65ad\u3001\u8bbe\u8ba1\u6709\u7406\u8bba\u4f9d\u636e\u7684\u7f13\u89e3\u63aa\u65bd\u3002 \u4e3a\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u7814\u7a76\u5458\u4eec\u628a\u76ee\u5149\u6295\u5411\u4e86&nbsp;GPU&nbsp;\u77e9\u9635\u4e58\u7d2f\u52a0\uff08matrix multiply-accumulate\uff0cMMA\uff09\u5355\u5143\u7684\u6570\u503c\u884c\u4e3a\u3002\u77e9\u9635\u4e58\u6cd5\u662f&nbsp;LLMs&nbsp;\u8bad\u7ec3\u548c\u63a8\u7406\u4e2d\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\u7684\u6838\u5fc3\uff0cGPU&nbsp;\u4e2d\u7684\u4e13\u7528\u5355\u5143\u8d1f\u8d23\u8ba1\u7b97D=A\u00d7B+C\u5f62\u5f0f\u7684\u8fd0\u7b97\u3002NVIDIA&nbsp;\u5c06\u8fd9\u4e9b\u5355\u5143\u79f0\u4e3a\u5f20\u91cf\u6838\u5fc3\uff08Tensor Core\uff09\uff0cAMD&nbsp;\u5219\u79f0\u5176\u4e3a\u77e9\u9635\u6838\u5fc3\uff08Matrix Core\uff09\u3002\u5b83\u4eec\u652f\u6301&nbsp;LLMs&nbsp;\u6240\u7528\u7684\u6d6e\u70b9\u6570\u636e\u7c7b\u578b\uff0c\u540c\u65f6\u63d0\u4f9b\u9ad8\u541e\u5410\u91cf\u548c\u9ad8\u6548\u7387\u3002 \u95ee\u9898\u5728\u4e8e\uff0c\u66b4\u9732\u7ed9\u8f6f\u4ef6\u7684MMA\u6307\u4ee4\u89c4\u5b9a\u4e86\u8fd0\u7b97\u7684\u6570\u5b66\u5b9a\u4e49D=A\u00d7B+C\uff0c\u5374\u6ca1\u6709\u89c4\u5b9a\u5176\u6570\u503c\u5b9e\u73b0\u65b9\u5f0f\u3002\u8ba1\u7b97\u7ed3\u679c\u53d6\u51b3\u4e8e\u878d\u5408\u7c92\u5ea6\u3001\u5185\u90e8\u7cbe\u5ea6\u3001\u820d\u5165\u4e0e\u89c4\u683c\u5316\u3001\u6b21\u6b63\u89c4\u6570\u5904\u7406\u3001\u6c42\u548c\u987a\u5e8f\uff0c\u4ee5\u53ca\u5176\u4ed6\u5b9e\u73b0\u7ec6\u8282\u3002\u8fd9\u4e9b\u9690\u85cf\u7684\u7b97\u672f\u9009\u62e9\u51b3\u5b9a\u4e86&nbsp;D&nbsp;\u4e2d\u5b9e\u9645\u8ba1\u7b97\u51fa\u7684\u6570\u503c\uff0c\u5e76\u6700\u7ec8\u5f71\u54cd\u53ef\u590d\u73b0\u6027\u3001\u7cbe\u5ea6\u548c\u7a33\u5b9a\u6027\u3002 \u7814\u7a76\u5458\u4eec\u7684\u76ee\u6807\u662f\u901a\u8fc7\u767d\u76d2\u6a21\u578b\uff0c\u5c06\u5e95\u5c42\u8ba1\u7b97\u8fc7\u7a0b\u660e\u786e\u5730\u63cf\u8ff0\u51fa\u6765\u3002\u901a\u8fc7\u91c7\u7528\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\uff08feature-probing test\uff09\uff0c\u6765\u6784\u5efa\u8fd9\u4e9b\u6a21\u578b\u3002 \u5148\u770b\u4e00\u4e2a\u5177\u4f53\u7684&nbsp;MMA&nbsp;\u8fd0\u7b97\u793a\u4f8b\u3002\u56fe1\u4e2d\u9ad8\u4eae\u663e\u793a\u7684&nbsp;A&nbsp;\u7684\u7b2c\u4e00\u884c\u3001B&nbsp;\u7684\u7b2c\u4e00\u5217\uff0c\u4ee5\u53ca&nbsp;C&nbsp;\u7684\u7b2c\u4e00\u4e2a\u5143\u7d20\uff0c\u5171\u540c\u51b3\u5b9a\u4e86&nbsp;D&nbsp;\u7684\u7b2c\u4e00\u4e2a\u8f93\u51fa\u5143\u7d20\u3002\u8003\u8651\u4ee5\u4e0b\u8f93\u5165\u5bf9&nbsp;(\u2212213,210), (\u22120.5,1), (\u22120.25,1), (\u22120.125,1)\uff0c\u4ee5\u53ca\u503c\u4e3a223\u7684\u7d2f\u52a0\u8f93\u5165\u3002 \u5404\u5bf9\u8f93\u5165\u76f8\u4e58\u540e\uff0c\u5f97\u5230&nbsp;\u2212223\u3001\u22120.5\u3001\u22120.25\u548c&nbsp;\u22120.125\u3002\u4ece\u6570\u5b66\u4e0a\u770b\uff0c\u5c06\u8fd9\u4e9b\u4e58\u79ef\u52a0\u5230\u7d2f\u52a0\u5668&nbsp;223\u4e0a\uff0c\u7ed3\u679c\u5e94\u4e3a&nbsp;\u22120.875\u3002 \u90a3\u4e48\u5404\u6761\u786c\u4ef6\u6307\u4ee4\u5b9e\u9645\u4f1a\u8fd4\u56de\u4ec0\u4e48\uff1f\u9762\u5bf9\u5b8c\u5168\u76f8\u540c\u7684\u8f93\u5165\uff0c\u5982\u56fe2\u6240\u793a\u7684&nbsp;MMA&nbsp;\u6307\u4ee4\u4ea7\u751f\u4e86\u516d\u79cd\u4e0d\u540c\u7684\u7ed3\u679c\uff1a0\u3001\u22120.375\u3001\u22120.5\u3001\u22120.75\u3001\u22120.875\uff08\u7cbe\u786e\u7ed3\u679c\uff09\u4ee5\u53ca&nbsp;\u22121\u3002 \u8fd9\u4e2a\u4f8b\u5b50\u6e05\u6670\u5730\u5c55\u793a\u4e86\u9690\u85cf\u7b97\u672f\u9009\u62e9\u7684\u5f71\u54cd\u3002\u7814\u7a76\u5458\u4eec\u8981\u6784\u5efa\u7684\u6a21\u578b\uff0c\u65e2\u8981\u9010\u6bd4\u7279\u590d\u73b0\u6bcf\u6761\u6307\u4ee4\u7684\u7ed3\u679c\uff0c\u4e5f\u8981\u80fd\u89e3\u91ca\u8fd9\u4e9b\u8f93\u51fa\u662f\u5982\u4f55\u4ea7\u751f\u7684\u3002 \u4ece\u8fd9\u4e9b\u8f93\u51fa\u53cd\u63a8\u786c\u4ef6\u5185\u90e8\u8ba1\u7b97\u65b9\u5f0f\u7684\u65b9\u6cd5\uff0c\u79f0\u4e3a\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\u3002\u4e0b\u9762\u4e3e\u4e24\u4e2a\u4f8b\u5b50\u3002 \u7b2c\u4e00\uff0c\u63a2\u6d4b\u6c42\u548c\u987a\u5e8f\u3002\u4ecd\u7136\u4f7f\u7528\u4e0e\u524d\u4f8b\u76f8\u540c\u7684\u52a0\u6570\uff0c\u5bf9\u6bd4\u4e24\u68f5\u6c42\u548c\u6811\uff08\u5982\u56fe3\u6240\u793a\uff09\uff0c\u4ee5\u5c55\u793a\u6c42\u548c\u987a\u5e8f\u5982\u4f55\u5f71\u54cd\u7ed3\u679c\u3002\u56fe3\u5de6\u4fa7\u7684\u52a0\u6cd5\u8fd0\u7b97\u6784\u6210\u4e86\u4e00\u6761\u987a\u5e8f\u6267\u884c\u7684\u94fe\uff0c\u7d2f\u52a0\u5668&nbsp;C&nbsp;\u4ece\u4e00\u5f00\u59cb\u5c31\u53c2\u4e0e\u5176\u4e2d\u3002\u5728\u987a\u5e8f\u6c42\u548c\u4e2d\uff0c\u4e24\u4e2a\u5927\u6570\u9996\u5148\u62b5\u6d88\uff0c\u5176\u4f59\u52a0\u6570\u5f97\u4ee5\u4fdd\u7559\uff0c\u6700\u7ec8\u5f97\u5230(((223\u2212223)\u22120.5)\u22120.25)\u22120.125=\u22120.875\u3002\u53f3\u4fa7\u5219\u5148\u5c06\u4e58\u79ef\u4e24\u4e24\u76f8\u52a0\uff0c\u518d\u5c06\u8fd9\u4e9b\u548c\u4e0e&nbsp;C&nbsp;\u7d2f\u52a0\u3002\u5728\u672c\u4f8b\u91c7\u7528\u7684\u6709\u9650\u7cbe\u5ea6\u7b97\u672f\u4e0b\uff0c\u6210\u5bf9\u6c42\u548c\u65f6\uff0c\u8f83\u5c0f\u7684\u9879\u5728\u4e0e\u8f83\u5927\u7684\u9879\u76f8\u52a0\u65f6\u4e22\u5931\uff0c\u6700\u7ec8\u5f97\u5230223+((\u2212223\u22120.5)+(\u22120.25\u22120.125))=0\u3002 \u63a8\u5e7f\u5f00\u6765\uff0c\u53ef\u4ee5\u9009\u62e9\u4e00\u4e2a\u5927\u6570&nbsp;U&nbsp;\u548c\u4e00\u4e2a\u5c0f\u6570&nbsp;v\uff0c\u4f7f\u5f97&nbsp;U+v&nbsp;\u820d\u5165\u540e\u4ecd\u4e3a&nbsp;U\u3002\u968f\u540e\u518d\u52a0\u4e0a&nbsp;\u2212U\uff0c\u7ed3\u679c\u5c31\u662f0\u3002\u5982\u679c\u5148\u8ba9&nbsp;U&nbsp;\u4e0e\u2212U&nbsp;\u62b5\u6d88\uff0c\u5219&nbsp;v&nbsp;\u4f1a\u88ab\u4fdd\u7559\u4e0b\u6765\u3002\u901a\u8fc7\u5c06\u5927\u6570\u653e\u5728\u4e0d\u540c\u7684\u8f93\u5165\u4f4d\u7f6e\uff0c\u5e76\u89c2\u5bdf\u54ea\u4e9b\u5c0f\u6570\u9879\u80fd\u591f\u4fdd\u7559\uff0c\u5c31\u53ef\u4ee5\u63a8\u65ad\u51fa\u6c42\u548c\u7684\u987a\u5e8f\u3002 \u7b2c\u4e8c\uff0c\u63a2\u6d4b\u5185\u90e8\u7cbe\u5ea6\u548c\u820d\u5165\u6a21\u5f0f\u3002\u4ec5\u9760\u6c42\u548c\u987a\u5e8f\u8fd8\u4e0d\u8db3\u4ee5\u5b8c\u6574\u89e3\u91ca\u8fd9\u4e9b\u7ed3\u679c\uff0c\u7814\u7a76\u5458\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u5305\u542b\u4e94\u4e2a\u52a0\u6570\u7684\u878d\u5408\u8fd0\u7b97\uff1a\u5c06&nbsp;U&nbsp;\u548c&nbsp;\u2212U&nbsp;\u653e\u5728\u6c42\u548c\u6811\u7684\u4e24\u4e2a\u53f6\u8282\u70b9\u4e0a\uff0c\u5176\u4f59\u4e09\u4e2a\u53f6\u8282\u70b9\u5747\u653e\u7f6e&nbsp;v\u3002\u5982\u679c\u5185\u90e8\u7cbe\u5ea6\u8db3\u591f\u9ad8\uff0c\u8fd0\u7b97\u4f1a\u4fdd\u7559\u5168\u90e8\u4e09\u4e2a\u5c0f\u6570\u9879\uff0c\u5e76\u8fd4\u56de&nbsp;3v\u3002\u4f46\u6709\u9650\u7cbe\u5ea6\u7684\u878d\u5408\u8fd0\u7b97\u53ef\u80fd\u5728\u62b5\u6d88\u53d1\u751f\u524d\u7684\u5bf9\u9f50\u9636\u6bb5\u5c31\u4e22\u5f03\u4e86\u8fd9\u4e9b\u5c0f\u6570\u9879\uff0c\u4ece\u800c\u8fd4\u56de&nbsp;0\u3002 \u8ba1\u7b97&nbsp;U\u3001\u2212U\u548c\u03f5&nbsp;\u7684\u878d\u5408\u6c42\u548c\uff0c\u4ece\u03f5=0.5U&nbsp;\u5f00\u59cb\uff0c\u53cd\u590d\u5c06\u5176\u51cf\u534a\u3002\u03f5&nbsp;\u4e0d\u518d\u88ab\u4fdd\u7559\u65f6\u6240\u5bf9\u5e94\u7684\u9608\u503c\uff0c\u53ef\u4ee5\u63ed\u793a\u5185\u90e8\u5c0f\u6570\u4f4d\u7684\u4f4d\u6570\u3002\u8fdb\u4e00\u6b65\u5728\u8be5\u9608\u503c\u7684\u4e00\u534a\u5904\uff0c\u4ee5\u53ca\u7565\u9ad8\u4e8e\u548c\u7565\u4f4e\u4e8e\u8be5\u503c\u7684\u4f4d\u7f6e\u6d4b\u8bd5\u03f5\uff0c\u8fd8\u53ef\u4ee5\u63a8\u65ad\u51fa\u820d\u5165\u6a21\u5f0f\u3002 \u4ee5\u4e0a\u53ea\u662f\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\u4e2d\u7684\u51e0\u4e2a\u4f8b\u5b50\u3002\u7814\u7a76\u5458\u4eec\u628a\u5b8c\u6574\u7684\u5efa\u6a21\u65b9\u6cd5\u79f0\u4e3a\u95ed\u73af\u7279\u5f81\u63a2\u6d4b\uff08closed-loop feature probing\uff0cCLFP\uff09\u3002\u53ea\u8981\u80fd\u591f\u901a\u8fc7\u63a5\u53e3\u8c03\u7528\u67d0\u6761&nbsp;MMA&nbsp;\u6307\u4ee4\uff0cCLFP&nbsp;\u5c31\u53ef\u4ee5\u5229\u7528\u4e00\u7ec4\u4e0d\u65ad\u6269\u5145\u7684\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\uff0c\u6784\u5efa\u53ef\u6267\u884c\u7684\u7b97\u672f\u6a21\u578b\u3002 \u6574\u4e2a\u6d41\u7a0b\u5206\u4e3a\u4e94\u6b65\uff1a \u8fd9\u4e2a\u53cd\u9988\u5faa\u73af\u80fd\u591f\u53d1\u73b0\u5148\u524d\u63a2\u6d4b\u9057\u6f0f\u7684\u7ec6\u8282\uff0c\u5e76\u5c06\u6bcf\u4e00\u6b21\u4e0d\u5339\u914d\u8f6c\u5316\u4e3a\u65b0\u7684\u7279\u5f81\u63a2\u6d4b\u6d4b\u8bd5\u3002\u5f53\u6a21\u578b\u5728\u9a8c\u8bc1\u6d4b\u8bd5\u4e2d\u80fd\u591f\u9010\u6bd4\u7279\u5339\u914d\u786c\u4ef6\u65f6\uff0c\u5faa\u73af\u7ed3\u675f\u3002 \u7814\u7a76\u5458\u4eec\u5c06&nbsp;CLFP&nbsp;\u65b9\u6cd5\u5e94\u7528\u5728\u4e86\u5341\u79cd&nbsp;GPU&nbsp;\u67b6\u6784\u4e0a\u7684\u5168\u90e8\u6d6e\u70b9&nbsp;MMA&nbsp;\u6307\u4ee4\uff0c\u5305\u62ecNVIDIA&nbsp;\u7684&nbsp;Volta\u3001Turing\u3001Ampere\u3001Ada Lovelace\u3001Hopper\u3001Blackwell&nbsp;\u548cRTX Blackwell\uff0c\u4ee5\u53ca&nbsp;AMD&nbsp;\u7684&nbsp;CDNA1\u3001CDNA2\u548c&nbsp;CDNA3\u3002\u8986\u76d6\u7684\u683c\u5f0f\u6709&nbsp;FP64\u3001FP32\u3001TF32\u3001BF16\u3001FP16\u3001FP8\u3001FP6\u3001FP4\u3001MXFP8\u3001MXFP6\u3001MXFP4\u548c&nbsp;NVFP4\u3002\u8fd9\u6837\u5e7f\u6cdb\u7684\u8986\u76d6\u8303\u56f4\u5c55\u793a\u4e86\u8be5\u65b9\u6cd5\u7684\u901a\u7528\u6027\uff0c\u4e5f\u8ba9\u8de8\u4ee3\u6bd4\u8f83\u5404\u67b6\u6784\u7684\u6570\u503c\u884c\u4e3a\u6210\u4e3a\u53ef\u80fd\u3002 \u7814\u7a76\u5458\u4eec\u4ece\u8fd9\u4e9b\u67b6\u6784\u4e2d\u5f52\u7eb3\u51fa\u4e86\u4e09\u5927\u6a21\u578b\u65cf\uff1a \u622a\u65ad\u578b&nbsp;FDPA\uff08T-FDPA\uff09\u662f\u5176\u4e2d\u6700\u7b80\u5355\u7684\u4e00\u79cd&nbsp;FDPA&nbsp;\u53d8\u4f53\uff0c\u80fd\u591f\u4e3a&nbsp;NVIDIA 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