{"id":107613,"date":"2026-09-19T21:56:47","date_gmt":"2026-09-19T13:56:47","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/107613.html"},"modified":"2026-09-19T21:56:47","modified_gmt":"2026-09-19T13:56:47","slug":"5%e3%80%81%e3%80%90%e6%95%b0%e5%ad%a6%e3%80%91%e3%80%90%e5%9f%ba%e7%a1%80%e3%80%91%e5%bd%92%e4%b8%80%e5%8c%96%e7%9a%84%e5%87%a0%e4%bd%95%e6%84%8f%e4%b9%89%ef%bc%9a%e7%90%83%e9%9d%a2%e3%80%81%e8%b6%85","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/107613.html","title":{"rendered":"5\u3001\u3010\u6570\u5b66\u3011\u3010\u57fa\u7840\u3011\u5f52\u4e00\u5316\u7684\u51e0\u4f55\u610f\u4e49\uff1a\u7403\u9762\u3001\u8d85\u5e73\u9762\u4e0e\u4fe1\u606f\u53bb\u54ea\u4e86"},"content":{"rendered":"<p>\u3010\u58f0\u660e\u3011\u672c\u535a\u5ba2\u6240\u6709\u5185\u5bb9\u5747\u4e3a\u4e2a\u4eba\u4e1a\u4f59\u65f6\u95f4\u521b\u4f5c&#xff0c;\u6240\u8ff0\u6280\u672f\u6848\u4f8b\u5747\u6765\u81ea\u516c\u5f00\u5f00\u6e90\u9879\u76ee&#xff08;\u5982Github&#xff0c;Apache\u57fa\u91d1\u4f1a&#xff09;&#xff0c;\u4e0d\u6d89\u53ca\u4efb\u4f55\u4f01\u4e1a\u673a\u5bc6\u6216\u672a\u516c\u5f00\u6280\u672f&#xff0c;\u5982\u6709\u4fb5\u6743\u8bf7\u8054\u7cfb\u5220\u9664<\/p>\n<h2>\u6807\u9898<\/h2>\n<p>5\u3001\u3010\u6570\u5b66\u3011\u3010\u57fa\u7840\u3011\u5f52\u4e00\u5316\u7684\u51e0\u4f55\u610f\u4e49&#xff1a;\u7403\u9762\u3001\u8d85\u5e73\u9762\u4e0e\u4fe1\u606f\u53bb\u54ea\u4e86<\/p>\n<h2>\u80cc\u666f<\/h2>\n<p>\u4e0a\u7bc7 blog 4\u3001\u3010\u6570\u5b66\u3011\u3010\u57fa\u7840\u3011\u5f52\u4e00\u5316\u7684\u6570\u5b66\u539f\u7406&#xff1a;LayerNorm\u3001RMSNorm \u4e0e BatchNorm \u628a\u5f52\u4e00\u5316\u7edf\u4e00\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         ^<\/p>\n<p>        &#061;<\/p>\n<p>          x<\/p>\n<p>          \u2212<\/p>\n<p>          c<\/p>\n<p>         s<\/p>\n<p>       \\\\hat{x}&#061;\\\\frac{x-c}{s}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1473em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8023em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">c<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u7559\u4e0b\u4e00\u53e5&#xff1a;\u51e0\u4f55\u89c6\u89d2\u4e0b\u4e00\u7bc7\u5355\u72ec\u5c55\u5f00\u3002\u672c\u7bc7\u5c31\u8865\u4e0a\u8fd9\u5757\u2014\u2014\u7403\u9762\u4e0e\u8d85\u5e73\u9762\u5230\u5e95\u6307\u4ec0\u4e48\u3001&#034;\u538b\u5230\u7403\u9762&#034;\u662f\u600e\u4e48\u538b\u7684\u3001\u957f\u5ea6\u88ab\u7edf\u4e00\u4e4b\u540e\u6570\u636e\u7684\u5dee\u5f02\u53c8\u4f53\u73b0\u5728\u54ea\u91cc\u3002<\/p>\n<h2>\u628a\u7403\u9762\u3001\u8d85\u5e73\u9762\u8bfb\u6210&#034;\u96c6\u5408&#034;<\/h2>\n<p>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u7ef4\u7a7a\u95f4\u91cc&#xff0c;\u5148\u8bb0\u4f4f\u4e24\u4e2a\u96c6\u5408\u7684\u5b9a\u4e49&#xff1a;<\/p>\n<ul>\n<li>\u534a\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          R<\/p>\n<p>         R<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u7684\u7403\u9762&#xff1a;\u6240\u6709\u957f\u5ea6\u7b49\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         R<\/p>\n<p>        R<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u7684\u5411\u91cf&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         {<\/p>\n<p>         v<\/p>\n<p>         :<\/p>\n<p>         \u2225<\/p>\n<p>         v<\/p>\n<p>          \u2225<\/p>\n<p>          2<\/p>\n<p>         &#061;<\/p>\n<p>         R<\/p>\n<p>         }<\/p>\n<p>        \\\\{v:\\\\lVert v\\\\rVert_2&#061;R\\\\}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>\u3002\u4e8c\u7ef4\u662f\u5706&#xff0c;\u4e09\u7ef4\u662f\u7403\u58f3&#xff1b;<\/li>\n<li>\u96f6\u5747\u503c\u8d85\u5e73\u9762&#xff1a;\u6240\u6709\u5747\u503c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         0<\/p>\n<p>        0<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u7684\u5411\u91cf&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         {<\/p>\n<p>         v<\/p>\n<p>         :<\/p>\n<p>          \u2211<\/p>\n<p>          i<\/p>\n<p>          v<\/p>\n<p>          i<\/p>\n<p>         &#061;<\/p>\n<p>         0<\/p>\n<p>         }<\/p>\n<p>        \\\\{v:\\\\sum_{i}v_i&#061;0\\\\}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0497em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u662f\u4e00\u5f20\u8fc7\u539f\u70b9\u3001\u7ef4\u6570\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         n<\/p>\n<p>         \u2212<\/p>\n<p>         1<\/p>\n<p>        n-1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u7684\u5e73\u76f4\u5b50\u7a7a\u95f4&#xff08;\u4e8c\u7ef4\u5c31\u662f\u4e00\u6761\u8fc7\u539f\u70b9\u7684\u76f4\u7ebf&#xff09;\u3002<\/li>\n<\/ul>\n<p>&#034;\u8d85\u5e73\u9762&#034;\u53ea\u662f&#034;\u5e73\u9762&#034;\u5728\u9ad8\u7ef4\u7684\u63a8\u5e7f\u3002\u628a\u5b83\u4eec\u5f53\u6210&#034;\u70b9\u7684\u96c6\u5408&#034;\u6765\u770b&#xff0c;\u540e\u9762\u7684\u63a8\u5bfc\u5c31\u5f88\u76f4\u63a5\u4e86\u3002<\/p>\n<h2>\u5f84\u5411\u6295\u5f71&#xff1a;\u6cbf\u5c04\u7ebf\u538b\u5230\u7403\u9762<\/h2>\n<p>\u5f52\u4e00\u5316\u5728\u51e0\u4f55\u4e0a\u5c31\u662f\u4e00\u6b21\u5f84\u5411\u6295\u5f71&#xff1a;\u4ece\u539f\u70b9\u671d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u753b\u4e00\u6761\u5c04\u7ebf&#xff0c;\u628a\u7bad\u5934\u7f29\u77ed\u6216\u62c9\u957f&#xff0c;\u8ba9\u5b83\u6070\u597d\u505c\u5728\u8fd9\u6761\u5c04\u7ebf\u4e0e\u76ee\u6807\u7403\u9762\u7684\u4ea4\u70b9\u4e0a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         \u27f6<\/p>\n<p>          x<\/p>\n<p>           \u2225<\/p>\n<p>           x<\/p>\n<p>            \u2225<\/p>\n<p>            2<\/p>\n<p>        x\\\\longrightarrow\\\\frac{x}{\\\\lVert x\\\\rVert_2}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.522em;vertical-align: -0.011em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u27f6<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0436em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u2225<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65b9\u5411\u4e00\u70b9\u6ca1\u53d8&#xff0c;\u53ea\u6539\u4e86\u957f\u5ea6\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260919135645-6aae949d13cb1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4ee5\u4e8c\u7ef4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>        3<\/p>\n<p>        ,<\/p>\n<p>        4<\/p>\n<p>        )<\/p>\n<p>       x&#061;(3,4)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4f8b&#xff0c;\u957f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2225<\/p>\n<p>        x<\/p>\n<p>         \u2225<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        5<\/p>\n<p>       \\\\lVert x\\\\rVert_2&#061;5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6295\u5f71\u5230\u5355\u4f4d\u5706\u4e0a\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        3<\/p>\n<p>        ,<\/p>\n<p>        4<\/p>\n<p>        )<\/p>\n<p>        \/<\/p>\n<p>        5<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>        0.6<\/p>\n<p>        ,<\/p>\n<p>        0.8<\/p>\n<p>        )<\/p>\n<p>       (3,4)\/5&#061;(0.6,0.8)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\/5<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0.6<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">0.8<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h2>L2 \u4e3a\u4ec0\u4e48\u843d\u5728\u5355\u4f4d\u7403\u9762<\/h2>\n<p>L2 \u5f52\u4e00\u5316\u5c31\u662f\u9664\u4ee5\u81ea\u5df1\u7684\u957f\u5ea6&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>         &#061;<\/p>\n<p>          x<\/p>\n<p>           \u2225<\/p>\n<p>           x<\/p>\n<p>            \u2225<\/p>\n<p>            2<\/p>\n<p>        \\\\hat{x}&#061;\\\\frac{x}{\\\\lVert x\\\\rVert_2}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0436em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u2225<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5b83\u7684\u957f\u5ea6\u5fc5\u7136\u662f <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2225<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>          \u2225<\/p>\n<p>          2<\/p>\n<p>         &#061;<\/p>\n<p>           \u2225<\/p>\n<p>           x<\/p>\n<p>            \u2225<\/p>\n<p>            2<\/p>\n<p>           \u2225<\/p>\n<p>           x<\/p>\n<p>            \u2225<\/p>\n<p>            2<\/p>\n<p>         &#061;<\/p>\n<p>         1<\/p>\n<p>        \\\\lVert\\\\hat{x}\\\\rVert_2&#061;\\\\frac{\\\\lVert x\\\\rVert_2}{\\\\lVert x\\\\rVert_2}&#061;1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u2225<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u2225<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/span> \u6240\u4ee5\u65e0\u8bba\u539f\u6765\u591a\u957f&#xff0c;\u8f93\u51fa\u957f\u5ea6\u6052\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u2014\u2014\u6240\u6709\u8f93\u51fa\u90fd\u843d\u5728&#034;\u957f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>       &#061;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#034;\u7684\u96c6\u5408\u91cc&#xff0c;\u8fd9\u4e2a\u96c6\u5408\u5c31\u53eb\u5355\u4f4d\u7403\u9762\u3002<\/p>\n<h2>RMSNorm \u4e3a\u4ec0\u4e48\u843d\u5728\u534a\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         n<\/p>\n<p>       \\\\sqrt{n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7403\u9762<\/h2>\n<p>RMSNorm \u7684\u6761\u4ef6\u662f\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         R<\/p>\n<p>         M<\/p>\n<p>         S<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         ^<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>       \\\\mathrm{RMS}(\\\\hat{x})&#061;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">RMS<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u3002\u628a\u5747\u65b9\u6839\u5c55\u5f00&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          R<\/p>\n<p>          M<\/p>\n<p>          S<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>            1<\/p>\n<p>            n<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>             x<\/p>\n<p>             ^<\/p>\n<p>            i<\/p>\n<p>            2<\/p>\n<p>         &#061;<\/p>\n<p>         1<\/p>\n<p>        \\\\mathrm{RMS}(\\\\hat{x})&#061;\\\\sqrt{\\\\frac{1}{n}\\\\sum_{i&#061;1}^{n}\\\\hat{x}_i^2}&#061;1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">RMS<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.1568em;vertical-align: -1.2777em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8791em\"><span class=\"svg-align\" style=\"top: -5.1168em\"><span class=\"pstrut\" style=\"height: 5.1168em\"><\/span><span class=\"mord\" style=\"padding-left: 1.056em\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7959em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.8391em\"><span class=\"pstrut\" style=\"height: 5.1168em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.742em;height: 3.1968em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/span> \u4e24\u8fb9\u5e73\u65b9\u5f97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         n<\/p>\n<p>        \u2211<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>         i<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>       \\\\frac{1}{n}\\\\sum\\\\hat{x}_i^2&#061;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2211<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>         i<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        n<\/p>\n<p>       \\\\sum\\\\hat{x}_i^2&#061;n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0728em;vertical-align: -0.2587em\"><\/span><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>\u3002\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2211<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>         i<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        \u2225<\/p>\n<p>         x<\/p>\n<p>         ^<\/p>\n<p>         \u2225<\/p>\n<p>         2<\/p>\n<p>         2<\/p>\n<p>       \\\\sum\\\\hat{x}_i^2&#061;\\\\lVert\\\\hat{x}\\\\rVert_2^2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0728em;vertical-align: -0.2587em\"><\/span><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4519em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6240\u4ee5 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2225<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>          \u2225<\/p>\n<p>          2<\/p>\n<p>         &#061;<\/p>\n<p>          n<\/p>\n<p>        \\\\lVert\\\\hat{x}\\\\rVert_2&#061;\\\\sqrt{n}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.1908em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8492em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8092em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1908em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> RMSNorm \u4e0d\u662f\u628a\u957f\u5ea6\u538b\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u800c\u662f\u538b\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         n<\/p>\n<p>       \\\\sqrt{n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u662f\u7ef4\u6570&#xff0c;\u4e8c\u7ef4\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>       \\\\sqrt{2}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.1328em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9072em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8672em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1328em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260919135645-6aae949da384c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe\u4e2d\u539f\u59cb\u5411\u91cf\u957f\u77ed\u4e0d\u4e00\u3001\u65b9\u5411\u5404\u5f02&#xff1a;L2 \u5f52\u4e00\u5316\u628a\u5b83\u4eec\u5168\u538b\u5230\u5355\u4f4d\u5706\u4e0a&#xff0c;RMSNorm \u5219\u538b\u5230\u534a\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>       \\\\sqrt{2}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.1328em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9072em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8672em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1328em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5706\u4e0a\u3002<\/p>\n<h2>LayerNorm \u4e3a\u4ec0\u4e48\u662f&#034;\u8d85\u5e73\u9762 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2229<\/p>\n<p>       \\\\cap<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5556em\"><\/span><span class=\"mord\">\u2229<\/span><\/span><\/span><\/span><\/span> \u7403\u9762&#034;<\/h2>\n<p>LayerNorm \u6bd4\u524d\u4e24\u8005\u591a\u4e86\u4e00\u6b65\u51cf\u5747\u503c&#xff0c;\u7528\u6b63\u4ea4\u5206\u89e3\u770b\u5f97\u6700\u6e05\u695a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         &#061;<\/p>\n<p>            \u03bc<\/p>\n<p>            1<\/p>\n<p>           \u23df<\/p>\n<p>          \u516c\u5171\u90e8\u5206<\/p>\n<p>         &#043;<\/p>\n<p>            (<\/p>\n<p>            x<\/p>\n<p>            \u2212<\/p>\n<p>            \u03bc<\/p>\n<p>            1<\/p>\n<p>            )<\/p>\n<p>           \u23df<\/p>\n<p>          \u96f6\u5747\u503c\u90e8\u5206<\/p>\n<p>        x&#061;\\\\underbrace{\\\\mu\\\\mathbf{1}}_{\\\\text{\u516c\u5171\u90e8\u5206}}&#043;\\\\underbrace{(x-\\\\mu\\\\mathbf{1})}_{\\\\text{\u96f6\u5747\u503c\u90e8\u5206}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1652em;vertical-align: -1.5208em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6444em\"><span class=\"\" style=\"top: -1.4792em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u516c\u5171\u90e8\u5206<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6444em\"><span class=\"svg-align\" style=\"top: -2.1576em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"mord mathbf\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8424em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5208em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.3263em;vertical-align: -1.5763em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"\" style=\"top: -1.4237em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u96f6\u5747\u503c\u90e8\u5206<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"svg-align\" style=\"top: -2.102em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"mord mathbf\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.898em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5763em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        \u2026<\/p>\n<p>        ,<\/p>\n<p>        1<\/p>\n<p>        )<\/p>\n<p>       \\\\mathbf{1}&#061;(1,\\\\dots,1)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord mathbf\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u96f6\u5747\u503c\u90e8\u5206\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       \\\\mathbf{1}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord mathbf\">1<\/span><\/span><\/span><\/span><\/span> \u6b63\u4ea4&#xff08;\u5185\u79ef\u4e3a 0&#xff09;\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260919135645-6aae949de09de.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li>\u51cf\u53bb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03bc<\/p>\n<p>         1<\/p>\n<p>        \\\\mu\\\\mathbf{1}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"mord mathbf\">1<\/span><\/span><\/span><\/span><\/span> \u540e&#xff0c;\u8f93\u51fa\u7684\u5747\u503c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         0<\/p>\n<p>        0<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u843d\u5728\u96f6\u5747\u503c\u8d85\u5e73\u9762\u4e0a&#xff1b;<\/li>\n<li>\u518d\u9664\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03c3<\/p>\n<p>        \\\\sigma<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><\/span><\/span><\/span><\/span> \u540e&#xff0c;\u8f93\u51fa\u65b9\u5dee\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>        1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7b49\u4ef7\u4e8e\u957f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2225<\/p>\n<p>          x<\/p>\n<p>          ^<\/p>\n<p>          \u2225<\/p>\n<p>          2<\/p>\n<p>         &#061;<\/p>\n<p>          n<\/p>\n<p>        \\\\lVert\\\\hat{x}\\\\rVert_2&#061;\\\\sqrt{n}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u843d\u5728\u534a\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>         \\\\sqrt{n}<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>             <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7403\u9762\u4e0a\u3002<\/li>\n<\/ul>\n<p>\u4e24\u4e2a\u6761\u4ef6\u540c\u65f6\u6ee1\u8db3&#xff0c;\u5c31\u843d\u5728\u8d85\u5e73\u9762\u4e0e\u7403\u9762\u7684\u4ea4\u7ebf\u4e0a\u3002\u4e8c\u7ef4\u65f6\u8fd9\u6761&#034;\u4ea4\u7ebf&#034;\u53ea\u5269\u4e24\u4e2a\u70b9&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        \u00b1<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        \u2213<\/p>\n<p>        1<\/p>\n<p>        )<\/p>\n<p>       (\\\\pm1,\\\\mp1)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u00b1<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2213<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h2>\u4fe1\u606f\u53bb\u54ea\u4e86&#xff1a;\u5dee\u5f02\u5728\u65b9\u5411&#xff0c;\u4e0d\u5728\u957f\u5ea6<\/h2>\n<p>\u957f\u5ea6\u88ab\u7edf\u4e00\u540e&#xff0c;\u6570\u636e\u5dee\u5f02\u5168\u90e8\u4f53\u73b0\u5728\u65b9\u5411\u4e0a\u3002\u7528\u4e8c\u7ef4\u4f8b\u5b50\u770b\u5f97\u5f88\u6e05\u695a&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         x<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>         3<\/p>\n<p>         ,<\/p>\n<p>         4<\/p>\n<p>         )<\/p>\n<p>        x&#061;(3,4)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         y<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>         6<\/p>\n<p>         ,<\/p>\n<p>         8<\/p>\n<p>         )<\/p>\n<p>        y&#061;(6,8)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">6<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">8<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u65b9\u5411\u76f8\u540c\u3001\u957f\u5ea6\u4e0d\u540c&#xff0c;L2 \u540e\u90fd\u53d8\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>         0.6<\/p>\n<p>         ,<\/p>\n<p>         0.8<\/p>\n<p>         )<\/p>\n<p>        (0.6,0.8)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0.6<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">0.8<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u88ab\u5408\u5e76\u2014\u2014\u957f\u5ea6\u4fe1\u606f\u88ab\u6545\u610f\u4e22\u6389&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         x<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>         3<\/p>\n<p>         ,<\/p>\n<p>         4<\/p>\n<p>         )<\/p>\n<p>        x&#061;(3,4)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         z<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>         4<\/p>\n<p>         ,<\/p>\n<p>         3<\/p>\n<p>         )<\/p>\n<p>        z&#061;(4,3)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">4<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u65b9\u5411\u4e0d\u540c&#xff0c;L2 \u540e\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>         0.6<\/p>\n<p>         ,<\/p>\n<p>         0.8<\/p>\n<p>         )<\/p>\n<p>        (0.6,0.8)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0.6<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">0.8<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>         0.8<\/p>\n<p>         ,<\/p>\n<p>         0.6<\/p>\n<p>         )<\/p>\n<p>        (0.8,0.6)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0.8<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">0.6<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5dee\u5f02\u4fdd\u7559\u3002<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260919135646-6aae949e26bdd.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7528\u81ea\u7531\u5ea6\u6765\u6570\u4e00\u6570\u8fd8\u5269\u591a\u5c11\u4fe1\u606f&#xff1a;<\/p>\n<table>\n<tr>\u72b6\u6001\u7ea6\u675f\u5269\u4f59\u81ea\u7531\u5ea6<\/tr>\n<tbody>\n<tr>\n<td align=\"left\">\u539f\u59cb\u5411\u91cf<\/td>\n<td align=\"left\">\u65e0<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>          n<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff08;\u957f\u5ea6 &#043; \u65b9\u5411&#xff09;<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">L2 \/ RMSNorm<\/td>\n<td align=\"left\">\u957f\u5ea6\u56fa\u5b9a<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>          n-1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff08;\u53ea\u5269\u65b9\u5411&#xff09;<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">LayerNorm<\/td>\n<td align=\"left\">\u957f\u5ea6\u56fa\u5b9a &#043; \u5747\u503c\u4e3a 0<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>           \u2212<\/p>\n<p>           2<\/p>\n<p>          n-2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e22\u6389\u7684\u6b63\u662f&#034;\u957f\u5ea6&#034;\u8fd9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u4e2a\u81ea\u7531\u5ea6&#xff08;LayerNorm \u518d\u591a\u4e22&#034;\u6574\u4f53\u504f\u79fb&#034;&#xff09;\u3002Qwen2 \u7684\u9690\u85cf\u7ef4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        &#061;<\/p>\n<p>        896<\/p>\n<p>       n&#061;896<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">896<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5269 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        895<\/p>\n<p>       895<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">895<\/span><\/span><\/span><\/span><\/span> \u4e2a\u81ea\u7531\u5ea6&#xff0c;\u4fe1\u606f\u91cf\u51e0\u4e4e\u6ca1\u5c11\u2014\u2014\u88ab\u4e22\u6389\u7684\u6070\u6070\u662f\u90a3\u4e2a\u4f1a\u9010\u5c42\u6f02\u79fb\u3001\u9700\u8981\u62b9\u6389\u7684\u5c3a\u5ea6\u3002\u82e5\u7f51\u7edc\u786e\u5b9e\u9700\u8981\u4e0d\u540c\u5c3a\u5ea6&#xff0c;\u7531\u5f52\u4e00\u5316\u4e4b\u540e\u7684\u53ef\u5b66\u4e60\u6743\u91cd <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03b3<\/p>\n<p>       \\\\gamma<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><\/span><\/span><\/span><\/span> \u9010\u7ef4\u7f29\u653e\u56de\u6765\u3002<\/p>\n<h2>\u4e8c\u7ef4\u4e3a\u4ec0\u4e48\u4f1a&#034;\u770b\u8d77\u6765\u5168\u4e22&#034;<\/h2>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        &#061;<\/p>\n<p>        2<\/p>\n<p>       n&#061;2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u65f6 LayerNorm \u5269 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        \u2212<\/p>\n<p>        2<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>       n-2&#061;0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u4e2a\u81ea\u7531\u5ea6&#xff1a;\u96f6\u5747\u503c\u4e14\u957f\u5ea6\u56fa\u5b9a&#xff0c;\u5e73\u9762\u4e0a\u53ea\u5269\u4e24\u4e2a\u65b9\u5411&#xff0c;\u6240\u4ee5\u770b\u8d77\u6765&#034;\u4ec0\u4e48\u90fd\u6ca1\u4e86&#034;\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260919135646-6aae949e61b07.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8fd9\u662f\u4e8c\u7ef4\u7684\u6781\u7aef\u60c5\u51b5\u3002\u9ad8\u7ef4\u7a7a\u95f4\u91cc\u7403\u9762\u548c\u8d85\u5e73\u9762\u90fd\u5f88\u5927&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        896<\/p>\n<p>       896<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">896<\/span><\/span><\/span><\/span><\/span> \u7ef4\u65f6\u4ecd\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        894<\/p>\n<p>       894<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">894<\/span><\/span><\/span><\/span><\/span> \u7ef4\u7684\u81ea\u7531\u65b9\u5411&#xff0c;\u4e0d\u7528\u62c5\u5fc3&#034;\u4fe1\u606f\u88ab\u538b\u6ca1&#034;\u3002<\/p>\n<h2>\u5c0f\u7ed3<\/h2>\n<p>\u5f52\u4e00\u5316\u7684\u51e0\u4f55\u52a8\u4f5c\u662f\u5f84\u5411\u6295\u5f71&#xff1a;\u6cbf\u539f\u70b9\u5c04\u7ebf\u628a\u5411\u91cf\u538b\u5230\u56fa\u5b9a\u534a\u5f84\u7684\u7403\u9762\u4e0a\u3002L2 \u538b\u5230\u5355\u4f4d\u7403\u9762&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2225<\/p>\n<p>         x<\/p>\n<p>         ^<\/p>\n<p>         \u2225<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>       \\\\lVert\\\\hat{x}\\\\rVert_2&#061;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">\u2225<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;RMSNorm \u538b\u5230\u534a\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         n<\/p>\n<p>       \\\\sqrt{n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7403\u9762&#xff0c;LayerNorm \u5148\u51cf\u5747\u503c\u843d\u5230\u96f6\u5747\u503c\u8d85\u5e73\u9762\u3001\u518d\u538b\u5230\u534a\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         n<\/p>\n<p>       \\\\sqrt{n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span 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