{"id":99193,"date":"2026-09-02T02:48:43","date_gmt":"2026-09-01T18:48:43","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/99193.html"},"modified":"2026-09-02T02:48:43","modified_gmt":"2026-09-01T18:48:43","slug":"%e5%87%a0%e4%bd%95%e6%97%b6%e7%a9%ba%e4%b8%8e%e4%bd%8d%e7%bd%ae%e7%bc%96%e7%a0%81","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/99193.html","title":{"rendered":"\u51e0\u4f55\u65f6\u7a7a\u4e0e\u4f4d\u7f6e\u7f16\u7801"},"content":{"rendered":"<h2>\u51e0\u4f55\u65f6\u7a7a\u4e0e\u4f4d\u7f6e\u7f16\u7801<\/h2>\n<p>\u5f53\u6211\u4eec\u8c08\u8bba\u5927\u8bed\u8a00\u6a21\u578b\u65f6&#xff0c;\u5f80\u5f80\u53ea\u770b\u5230\u5b83\u751f\u6210\u6587\u672c\u7684\u80fd\u529b&#xff0c;\u5374\u5f88\u5c11\u6ce8\u610f\u5e95\u5c42\u7ed3\u6784\u3002\u5b9e\u9645\u4e0a&#xff0c;\u6bcf\u4e00\u6b21\u5bf9\u8bdd\u3001\u63a8\u7406\u7684\u80cc\u540e&#xff0c;\u90fd\u6709\u4e00\u4e2a\u9ad8\u7ef4\u3001\u7a20\u5bc6\u7684\u5411\u91cf\u7a7a\u95f4\u3002\u8fd9\u5c31\u662f\u5927\u6a21\u578b\u7684\u539f\u751f\u571f\u58e4\u3002<\/p>\n<h3>\u4e00\u3001\u7a20\u5bc6\u5411\u91cf\u7a7a\u95f4&#xff1a;\u8bed\u8a00\u7684\u539f\u751f\u571f\u58e4<\/h3>\n<p>\u5728\u8fd9\u4e2a\u7a7a\u95f4\u91cc&#xff0c;\u8bcd\u3001\u77ed\u8bed\u3001\u53e5\u5b50\u4e0d\u518d\u662f\u5b57\u7b26\u5e8f\u5217&#xff0c;\u800c\u662f\u88ab\u7f16\u7801\u6210\u4e00\u4e2a\u4e2a\u7a20\u5bc6\u7684\u5b9e\u6570\u5411\u91cf\u3002\u6240\u8c13\u201c\u7a20\u5bc6\u201d&#xff0c;\u662f\u76f8\u5bf9\u4e8e\u65e9\u671f\u72ec\u70ed\u7f16\u7801\u7684\u7a00\u758f\u800c\u8a00\u3002\u7a20\u5bc6\u5411\u91cf\u5c31\u50cf\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u70b9&#xff0c;\u5f7c\u6b64\u4e4b\u95f4\u6709\u4e86\u8ddd\u79bb\u548c\u65b9\u5411&#xff0c;\u51e0\u4f55\u7ed3\u6784\u627f\u8f7d\u4e86\u8bed\u4e49\u5173\u7cfb\u3002\u6bd4\u5982\u201c\u56fd\u738b-\u7537\u4eba&#043;\u5973\u4eba\u201d\u4f1a\u843d\u5230\u201c\u5973\u738b\u201d\u9644\u8fd1&#xff0c;\u201c\u5df4\u9ece-\u6cd5\u56fd\u201d\u8fd1\u4f3c\u4e8e\u201c\u4e1c\u4eac-\u65e5\u672c\u201d\u3002\u8bed\u4e49\u4e0d\u518d\u662f\u79bb\u6563\u7b26\u53f7&#xff0c;\u800c\u6210\u4e86\u7a7a\u95f4\u4e2d\u7684\u51e0\u4f55\u89c4\u5f8b\u3002<\/p>\n<p>\u4f46\u8bed\u4e49\u5e76\u4e0d\u662f\u56fa\u5b9a\u7684\u3002\u5b83\u4f1a\u968f\u4e0a\u4e0b\u6587\u6d41\u52a8\u3001\u6298\u53e0\u3001\u62c9\u4f38\u3002\u4e00\u4e2a\u8bcd\u5728\u4e0d\u540c\u53e5\u5b50\u4e2d\u4f1a\u6cbf\u6d41\u5f62\u6ed1\u52a8&#xff0c;\u4e00\u6bb5\u6587\u672c\u7684\u610f\u4e49\u4e5f\u4e0d\u662f\u7b80\u5355\u53e0\u52a0&#xff0c;\u800c\u662f\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u5c55\u5f00\u53c8\u6298\u53e0\u3002\u8fd9\u5c31\u662f\u6211\u4eec\u8981\u6df1\u5165\u63a2\u8ba8\u7684&#xff1a;\u8bed\u4e49\u7684\u51e0\u4f55\u4e0e\u65f6\u7a7a\u7684\u6298\u53e0\u3002<\/p>\n<h3>\u4e8c\u3001\u4f4d\u7f6e&#xff1a;\u88ab\u6ce8\u610f\u529b\u9057\u5fd8\u7684\u7ef4\u5ea6<\/h3>\n<p>\u8fd9\u91cc\u6709\u4e00\u4e2a\u5173\u952e\u95ee\u9898&#xff1a;Transformer \u7684\u6ce8\u610f\u529b\u673a\u5236\u672c\u8eab\u662f\u4f4d\u7f6e\u65e0\u5173\u7684\u3002\u5982\u679c\u53ea\u628a\u8bcd\u5411\u91cf\u4e22\u8fdb\u53bb&#xff0c;\u5b83\u770b\u5230\u7684\u53ea\u662f\u4e00\u5806\u6ca1\u6709\u987a\u5e8f\u7684\u70b9\u3002\u6bd4\u5982\u201c\u732b\u8ffd\u8001\u9f20\u201d\u548c\u201c\u8001\u9f20\u8ffd\u732b\u201d&#xff0c;\u8bcd\u5411\u91cf\u5b8c\u5168\u76f8\u540c&#xff0c;\u53ea\u662f\u987a\u5e8f\u4e0d\u540c&#xff0c;\u4f46\u5728\u81ea\u6ce8\u610f\u529b\u8ba1\u7b97\u4e2d&#xff0c;\u5982\u679c\u4e0d\u52a0\u4efb\u4f55\u4f4d\u7f6e\u4fe1\u606f&#xff0c;\u5b83\u4eec\u4f1a\u5f97\u5230\u51e0\u4e4e\u76f8\u540c\u7684\u8868\u793a\u3002\u53ef\u8fd9\u4e24\u53e5\u8bdd\u7684\u610f\u601d\u622a\u7136\u76f8\u53cd\u3002\u8fd9\u8bf4\u660e&#xff0c;\u5149\u6709\u8bed\u4e49\u51e0\u4f55\u8fd8\u4e0d\u591f&#xff0c;\u5fc5\u987b\u5f15\u5165\u4f4d\u7f6e\u4fe1\u606f&#xff0c;\u624d\u80fd\u8ba9\u6a21\u578b\u77e5\u9053\u8c01\u5728\u524d\u3001\u8c01\u5728\u540e&#xff0c;\u8c01\u4fee\u9970\u8c01&#xff0c;\u8c01\u4f5c\u7528\u4e8e\u8c01\u3002\u5426\u5219&#xff0c;\u8bed\u8a00\u5c31\u9000\u5316\u6210\u4e86\u65e0\u5e8f\u7684\u8bcd\u888b&#xff0c;\u4e22\u5931\u4e86\u65f6\u5e8f\u548c\u7ed3\u6784\u3002<\/p>\n<p>\u6b64\u523b\u7684\u8bed\u4e49\u7a7a\u95f4&#xff0c;\u662f\u4e00\u7247\u6ca1\u6709\u66f2\u7387\u7684\u5e73\u539f\u2014\u2014\u6240\u6709\u8bcd\u5411\u91cf\u644a\u5e73\u5728\u9ad8\u7ef4\u6d41\u5f62\u4e0a&#xff0c;\u5f7c\u6b64\u4e4b\u95f4\u53ea\u6709\u8ddd\u79bb&#xff0c;\u6ca1\u6709\u5148\u540e\u3002\u8981\u5728\u5176\u4e2d\u5f15\u5165\u987a\u5e8f&#xff0c;\u5c31\u5fc5\u987b\u5bf9\u8fd9\u7247\u5e73\u539f\u65bd\u52a0\u67d0\u79cd\u6298\u53e0&#xff0c;\u8ba9\u65f6\u95f4\u7ef4\u5ea6\u4ece\u51e0\u4f55\u7ed3\u6784\u4e2d\u751f\u957f\u51fa\u6765\u3002<\/p>\n<h3>\u4e09\u3001\u6b63\u5f26\u4f4d\u7f6e\u7f16\u7801&#xff1a;\u7b2c\u4e00\u6b21\u6298\u53e0<\/h3>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u300aAttention Is All You Need\u300b\u4e2d\u9996\u6b21\u63d0\u51fa\u4e86\u4e00\u79cd\u5de7\u5999\u7684\u65b9\u6cd5&#xff1a;\u6b63\u5f26\u4f4d\u7f6e\u7f16\u7801&#xff08;APE&#xff09;\u3002\u5b83\u4e0d\u518d\u4f9d\u8d56\u8bcd\u5e8f\u672c\u8eab&#xff0c;\u800c\u662f\u4e3a\u6bcf\u4e2a\u4f4d\u7f6e\u751f\u6210\u4e00\u4e2a\u56fa\u5b9a\u7684\u5411\u91cf&#xff0c;\u76f4\u63a5\u52a0\u5230\u8bcd\u5411\u91cf\u4e0a\u3002<\/p>\n<p>\u8fd9\u4e2a\u4f4d\u7f6e\u5411\u91cf\u7684\u6bcf\u4e2a\u7ef4\u5ea6\u90fd\u7531\u6b63\u5f26\u6216\u4f59\u5f26\u51fd\u6570\u6784\u6210&#xff0c;\u4e14\u4e0d\u540c\u7ef4\u5ea6\u62e5\u6709\u4e0d\u540c\u7684\u9891\u7387\u3002\u4f4e\u7ef4\u5ea6\u53d8\u5316\u5feb&#xff08;\u9ad8\u9891&#xff09;&#xff0c;\u9ad8\u7ef4\u5ea6\u53d8\u5316\u6162&#xff08;\u4f4e\u9891&#xff09;&#xff0c;\u5c31\u50cf\u7ed9\u6bcf\u4e2a\u4f4d\u7f6e\u5206\u914d\u4e86\u4e00\u7ec4\u72ec\u7279\u7684\u201c\u6ce2\u7eb9\u201d\u3002\u8fd9\u6837\u4e00\u6765&#xff0c;\u6a21\u578b\u4e0d\u4ec5\u80fd\u533a\u5206\u7edd\u5bf9\u4f4d\u7f6e&#xff0c;\u8fd8\u80fd\u901a\u8fc7\u6ce2\u4e0e\u6ce2\u4e4b\u95f4\u7684\u76f8\u4f4d\u5dee&#xff0c;\u6355\u6349\u5230\u76f8\u5bf9\u4f4d\u7f6e\u5173\u7cfb\u3002\u5b83\u6709\u4e00\u4e2a\u4f18\u96c5\u7684\u6570\u5b66\u6027\u8d28&#xff1a;\u4efb\u610f\u504f\u79fb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span style=\"margin-right: 0.0315em\" class=\"mord mathnormal\">k<\/span><\/span><\/span><\/span><\/span> \u540e\u7684\u4f4d\u7f6e\u7f16\u7801 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">PE(pos&#043;k)PE(pos&#043;k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><span style=\"margin-right: 0.0576em\" class=\"mord mathnormal\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/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: 1em;vertical-align: -0.25em\"><\/span><span style=\"margin-right: 0.0315em\" class=\"mord mathnormal\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">PE(pos)PE(pos)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><span style=\"margin-right: 0.0576em\" class=\"mord mathnormal\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u7ebf\u6027\u51fd\u6570\u3002\u8fd9\u610f\u5473\u7740\u6a21\u578b\u7406\u8bba\u4e0a\u53ef\u4ee5\u901a\u8fc7\u5b66\u4e60\u7ebf\u6027\u53d8\u6362&#xff0c;\u4ece\u5f53\u524d\u4f4d\u7f6e\u7f16\u7801\u63a8\u5bfc\u51fa\u90bb\u8fd1\u4f4d\u7f6e\u7684\u7f16\u7801\u3002\u8fd9\u4e00\u6027\u8d28&#xff0c;\u6b63\u662f\u6211\u4eec\u540e\u9762\u8981\u8bb2\u7684\u65cb\u8f6c\u4f4d\u7f6e\u7f16\u7801\u7684\u6570\u5b66\u4f0f\u7b14\u3002<\/p>\n<p>\u6b63\u5f26\u4f4d\u7f6e\u7f16\u7801\u7684\u516c\u5f0f\u5e76\u4e0d\u590d\u6742\u3002\u5bf9\u4e8e\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pospos<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/span><\/span><\/span><\/span><\/span> \u548c\u7ef4\u5ea6\u7d22\u5f15 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span>&#xff08;\u603b\u7ef4\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dmodeld_{model}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">e<\/span><span style=\"margin-right: 0.0197em\" class=\"mord mathnormal mtight\">l<\/span><\/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>&#xff09;&#xff0c;\u7f16\u7801\u5411\u91cf\u7684\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2i2i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u7ef4\u548c\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2i&#043;12i&#043;1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7429em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">i<\/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: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u7ef4\u5206\u522b\u5b9a\u4e49\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">PE(pos,2i)&#061;sin\u2061(pos100002i\/dmodel)<br \/>\nPE(pos, 2i) &#061; \\\\sin\\\\left(\\\\frac{pos}{10000^{2i\/d_{model}}}\\\\right)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><span style=\"margin-right: 0.0576em\" class=\"mord mathnormal\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">i<\/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: 1.854em;vertical-align: -0.704em\"><\/span><span class=\"mop\">sin<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/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: -2.296em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1000<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814em\"><span class=\"\" style=\"top: -2.989em;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 mtight\">2<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mord mtight\">\/<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">e<\/span><span style=\"margin-right: 0.0197em\" class=\"mord mathnormal mtight\">l<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/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\">p<\/span><span class=\"mord mathnormal\">os<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.704em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">PE(pos,2i&#043;1)&#061;cos\u2061(pos100002i\/dmodel)<br \/>\nPE(pos, 2i&#043;1) &#061; \\\\cos\\\\left(\\\\frac{pos}{10000^{2i\/d_{model}}}\\\\right)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><span style=\"margin-right: 0.0576em\" class=\"mord mathnormal\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">i<\/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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/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: 1.854em;vertical-align: -0.704em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/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: -2.296em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1000<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814em\"><span class=\"\" style=\"top: -2.989em;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 mtight\">2<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mord mtight\">\/<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">e<\/span><span style=\"margin-right: 0.0197em\" class=\"mord mathnormal mtight\">l<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/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\">p<\/span><span class=\"mord mathnormal\">os<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.704em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5e95\u6570 10000 \u63a7\u5236\u4e0d\u540c\u7ef4\u5ea6\u7684\u6ce2\u957f&#xff1a;\u4f4e\u7ef4\u5ea6\u53d8\u5316\u5feb&#xff0c;\u9ad8\u7ef4\u5ea6\u53d8\u5316\u6162\u3002\u6b63\u5f26\u548c\u4f59\u5f26\u7684\u5468\u671f\u6027\u8ba9\u4f4d\u7f6e\u95f4\u7684\u7f16\u7801\u5dee\u5448\u73b0\u51fa\u6709\u89c4\u5f8b\u7684\u76f8\u4f4d\u79fb\u52a8&#xff0c;\u4ece\u800c\u9690\u5f0f\u6355\u6349\u76f8\u5bf9\u4f4d\u7f6e\u5173\u7cfb\u3002<\/p>\n<p>\u5b9e\u73b0\u8d77\u6765\u540c\u6837\u7b80\u5355&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> torch<br \/>\n<span class=\"token keyword\">import<\/span> math<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">sinusoidal_position_encoding<\/span><span class=\"token punctuation\">(<\/span>max_len<span class=\"token punctuation\">,<\/span> d_model<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    pe <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>zeros<span class=\"token punctuation\">(<\/span>max_len<span class=\"token punctuation\">,<\/span> d_model<span class=\"token punctuation\">)<\/span><br \/>\n    position <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> max_len<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>unsqueeze<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    div_term <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>exp<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>arange<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> d_model<span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token punctuation\">(<\/span>math<span class=\"token punctuation\">.<\/span>log<span class=\"token punctuation\">(<\/span><span class=\"token number\">10000.0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> d_model<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    pe<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span>position <span class=\"token operator\">*<\/span> div_term<span class=\"token punctuation\">)<\/span><br \/>\n    pe<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> torch<span class=\"token punctuation\">.<\/span>cos<span class=\"token punctuation\">(<\/span>position <span class=\"token operator\">*<\/span> div_term<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> pe<\/p>\n<p>\u751f\u6210\u4e00\u4e2a (max_len, d_model) 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\u4e8e\u5b83\u4eec\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u5dee\u3002\u8fd9\u610f\u5473\u7740&#xff0c;\u6ce8\u610f\u529b\u5206\u6570\u5929\u7136\u5730\u8574\u542b\u4e86\u76f8\u5bf9\u4f4d\u7f6e\u4fe1\u606f&#xff0c;\u65e0\u9700\u518d\u901a\u8fc7\u6b63\u5f26\u6ce2\u7eb9\u7684\u76f8\u4f4d\u5dee\u53bb\u95f4\u63a5\u63a8\u7b97\u3002\u5177\u4f53\u7ec6\u8282\u53ef\u53c2\u89c1\u672c\u7cfb\u5217\u524d\u6587&#xff0c;\u6b64\u5904\u4e0d\u5c55\u5f00\u3002<\/p>\n<p>\u5982\u679c\u8bf4 APE \u662f\u5728\u8bed\u4e49\u7a7a\u95f4\u91cc\u4e3a\u6bcf\u4e2a\u4f4d\u7f6e\u63d2\u4e0a\u4e00\u9762\u56fa\u5b9a\u7684\u65d7\u5b50&#xff0c;\u90a3\u4e48 RoPE \u5c31\u662f\u8ba9\u6bcf\u4e2a\u8bcd\u5411\u91cf\u6839\u636e\u5b83\u5728\u53e5\u5b50\u4e2d\u7684\u4f4d\u7f6e&#xff0c;\u81ea\u884c\u65cb\u8f6c\u5230\u65f6\u7a7a\u6d41\u5f62\u4e0a\u7684\u5bf9\u5e94\u89d2\u5ea6\u3002\u6b63\u5f26\u7f16\u7801\u4e2d\u90a3\u6761\u201c\u53ef\u7ebf\u6027\u8868\u793a\u201d\u7684\u6570\u5b66\u6027\u8d28&#xff0c;\u5728 RoPE \u4e2d\u88ab\u5916\u5316\u6210\u4e86\u663e\u5f0f\u7684\u65cb\u8f6c\u53d8\u6362\u3002\u6298\u53e0\u4e0d\u518d\u662f\u4e00\u5f20\u94fa\u5e73\u7684\u5730\u56fe&#xff0c;\u800c\u6210\u4e86\u52a8\u8bcd\u2014\u2014\u8bed\u4e49\u6d41\u5f62\u5f00\u59cb\u4e3b\u52a8\u5f2f\u66f2&#xff0c;\u6bcf\u4e2a\u8bcd\u90fd\u5728\u9ad8\u7ef4\u65f6\u7a7a\u4e2d\u626d\u8f6c\u81ea\u5df1\u7684\u59ff\u6001\u3002\u8bed\u4e49\u7684\u51e0\u4f55\u56e0\u6b64\u4ece\u9759\u6001\u7684\u5750\u6807\u6807\u8bb0&#xff0c;\u8d70\u5411\u4e86\u52a8\u6001\u7684\u6298\u53e0\u4e0e\u5c55\u5f00\u3002<\/p>\n<h3>\u4e94\u3001\u957f\u5ea6\u4e4b\u5916&#xff1a;\u6298\u53e0\u8fc7\u5ea6\u7684\u6495\u88c2<\/h3>\n<p>\u7136\u800c&#xff0c;\u5f53\u6211\u4eec\u628a\u6a21\u578b\u63a8\u5411\u66f4\u957f\u7684\u63a8\u7406\u5e8f\u5217\u65f6&#xff0c;\u4e00\u4e2a\u66f4\u6df1\u5c42\u7684\u95ee\u9898\u6d6e\u51fa\u6c34\u9762&#xff1a;\u5982\u679c\u63a8\u7406\u957f\u5ea6\u8d85\u8fc7\u4e86\u8bad\u7ec3\u65f6\u89c1\u8fc7\u7684\u6700\u5927\u957f\u5ea6&#xff0c;\u4f4d\u7f6e\u7f16\u7801\u6240\u6784\u5efa\u7684\u65f6\u7a7a\u51e0\u4f55\u8fd8\u4f1a\u6210\u7acb\u5417&#xff1f;<\/p>\n<p>\u4ee5 RoPE 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LLM \u8d70\u5411\u66f4\u957f\u4e0a\u4e0b\u6587\u3001\u66f4\u590d\u6742\u63a8\u7406\u65f6&#xff0c;\u5fc5\u987b\u6b63\u9762\u56de\u7b54\u7684\u51e0\u4f55\u7a33\u5b9a\u6027\u95ee\u9898\u3002<\/p>\n<h3>\u516d\u3001\u7ebf\u6027\u5185\u63d2&#xff1a;\u5747\u5300\u538b\u7f29\u7684\u4ee3\u4ef7<\/h3>\n<p>\u9762\u5bf9\u8fd9\u79cd\u957f\u5ea6\u5916\u63a8\u7684\u56f0\u5883&#xff0c;\u4e00\u79cd\u76f4\u89c2\u7684\u89e3\u51b3\u65b9\u6848\u662f\u7ebf\u6027\u5185\u63d2\u4f4d\u7f6e\u7d22\u5f15\u3002\u5177\u4f53\u6765\u8bf4&#xff0c;\u5982\u679c\u6211\u4eec\u8bad\u7ec3\u65f6\u6700\u5927\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">LL<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u63a8\u7406\u65f6\u5e0c\u671b\u6269\u5c55\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">L\u2032L&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><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\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5c31\u628a\u6240\u6709\u4f4d\u7f6e\u7d22\u5f15\u4e58\u4ee5\u4e00\u4e2a\u7f29\u653e\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">L\/L\u2032L\/L&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0019em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mord\">\/<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><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\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u6837&#xff0c;\u539f\u672c\u8d85\u51fa\u8bad\u7ec3\u8303\u56f4\u7684\u4f4d\u7f6e\u4f1a\u88ab\u538b\u7f29\u56de\u6a21\u578b\u719f\u6089\u7684\u533a\u95f4\u5185&#xff0c;\u4ece\u800c\u907f\u514d\u65cb\u8f6c\u89d2\u5ea6\u8fdb\u5165\u672a\u8bad\u7ec3\u7684\u533a\u57df\u3002<\/p>\n<p>\u7136\u800c&#xff0c;\u8fd9\u79cd\u7b80\u5355\u7c97\u66b4\u7684\u505a\u6cd5\u5e76\u975e\u6ca1\u6709\u4ee3\u4ef7\u3002\u7ebf\u6027\u5185\u63d2\u76f8\u5f53\u4e8e\u628a\u6574\u4e2a\u65f6\u7a7a\u6d41\u5f62\u5747\u5300\u538b\u7f29&#xff0c;\u6240\u6709\u9891\u7387\u7684\u6307\u9488\u90fd\u88ab\u540c\u6b65\u653e\u6162\u3002\u539f\u672c\u4ee3\u8868\u4f4e\u7ef4\u5ea6\u7684\u9ad8\u9891\u201c\u79d2\u9488\u201d&#xff0c;\u8f6c\u5f97\u4e0d\u518d\u90a3\u4e48\u5feb&#xff0c;\u76f8\u90bb\u4f4d\u7f6e\u4e4b\u95f4\u7684\u89d2\u5ea6\u5dee\u5f02\u88ab\u62b9\u5e73\u3002\u6a21\u578b\u5bf9\u5c40\u90e8\u987a\u5e8f\u7684\u5206\u8fa8\u80fd\u529b\u56e0\u6b64\u4e0b\u964d&#xff0c;\u5c31\u50cf\u628a\u4e00\u628a\u9ad8\u7cbe\u5ea6\u7684\u5c3a\u5b50\u7f29\u6210\u4e86\u4e00\u534a&#xff0c;\u523b\u5ea6\u4e4b\u95f4\u7684\u8ddd\u79bb\u88ab\u538b\u7f29&#xff0c;\u7ec6\u5fae\u5dee\u522b\u53d8\u5f97\u96be\u4ee5\u8fa8\u8ba4\u3002\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u5206\u8fa8\u7387\u95ee\u9898\u3002<\/p>\n<p>\u7ebf\u6027\u5185\u63d2\u7684\u672c\u8d28&#xff0c;\u662f\u7528\u727a\u7272\u77ed\u8ddd\u79bb\u7684\u65f6\u7a7a\u5206\u8fa8\u7387&#xff0c;\u6765\u6362\u53d6\u957f\u8ddd\u79bb\u4e0a\u7684\u7a33\u5b9a\u6027\u3002\u5b83\u7f13\u89e3\u4e86\u71b5\u5d29\u584c&#xff0c;\u5374\u8ba9\u8bed\u4e49\u51e0\u4f55\u7684\u5c40\u90e8\u7ed3\u6784\u53d8\u5f97\u6a21\u7cca\u3002\u6298\u53e0\u88ab\u6574\u4f53\u62c9\u5e73\u4e86\u2014\u2014\u6240\u6709\u4f4d\u7f6e\u7684\u66f2\u7387\u90fd\u88ab\u5747\u5300\u644a\u8584&#xff0c;\u5c31\u50cf\u628a\u4e00\u5f20\u63c9\u76b1\u7684\u7eb8\u786c\u751f\u751f\u538b\u5e73&#xff0c;\u867d\u7136\u9762\u79ef\u53d8\u5927\u4e86&#xff0c;\u4f46\u7eb8\u4e0a\u539f\u672c\u7684\u8936\u76b1\u7eb9\u7406\u5168\u90fd\u6d88\u5931\u4e86\u3002\u8fd9\u63d0\u793a\u6211\u4eec&#xff1a;\u4f4d\u7f6e\u7f16\u7801\u7684\u5916\u63a8&#xff0c;\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u5728\u5168\u5c40\u8986\u76d6\u4e0e\u5c40\u90e8\u7cbe\u5ea6\u4e4b\u95f4\u5bfb\u627e\u5e73\u8861\u7684\u51e0\u4f55\u95ee\u9898\u3002<\/p>\n<h3>\u4e03\u3001\u9891\u57df\u4e4b\u4e2d&#xff1a;\u6298\u53e0\u7684\u66f2\u7387<\/h3>\n<p>\u8981\u7406\u89e3\u7ebf\u6027\u5185\u63d2\u4e3a\u4ec0\u4e48\u4f1a\u5bfc\u81f4\u5206\u8fa8\u7387\u95ee\u9898&#xff0c;\u6211\u4eec\u9700\u8981\u628a\u4f4d\u7f6e\u7f16\u7801\u653e\u5230\u9891\u57df\u4e2d\u53bb\u89c2\u5bdf\u3002\u65e0\u8bba\u662f\u6b63\u5f26\u4f4d\u7f6e\u7f16\u7801\u8fd8\u662f RoPE&#xff0c;\u672c\u8d28\u4e0a\u90fd\u662f\u4e3a\u4e0d\u540c\u7ef4\u5ea6\u5206\u914d\u4e0d\u540c\u9891\u7387\u7684\u6ce2\u52a8\u3002\u4f4e\u7ef4\u5ea6\u5bf9\u5e94\u9ad8\u9891&#xff0c;\u8d1f\u8d23\u6355\u6349\u76f8\u90bb token \u4e4b\u95f4\u7684\u7ec6\u5fae\u53d8\u5316&#xff1b;\u9ad8\u7ef4\u5ea6\u5bf9\u5e94\u4f4e\u9891&#xff0c;\u523b\u753b\u66f4\u5927\u8303\u56f4\u7684\u987a\u5e8f\u7ed3\u6784\u3002\u6574\u4e2a\u4f4d\u7f6e\u7f16\u7801\u5c31\u50cf\u4e00\u5f20\u9891\u8c31\u56fe&#xff0c;\u4ece\u5feb\u5230\u6162\u5206\u5e03\u7740\u4f17\u591a\u9891\u7387\u6210\u5206\u3002<\/p>\n<p>\u7ebf\u6027\u5185\u63d2\u7684\u505a\u6cd5&#xff0c;\u76f8\u5f53\u4e8e\u5bf9\u8fd9\u5f20\u9891\u8c31\u56fe\u8fdb\u884c\u6574\u4f53\u5747\u5300\u538b\u7f29&#xff1a;\u6240\u6709\u9891\u7387\u6309\u76f8\u540c\u6bd4\u4f8b\u964d\u4f4e\u3002\u9ad8\u9891\u90e8\u5206\u539f\u672c\u7528\u6765\u5206\u8fa8\u76f8\u90bb\u4f4d\u7f6e&#xff0c;\u4e00\u65e6\u88ab\u538b\u7f29&#xff0c;\u76f8\u90bb token \u4e4b\u95f4\u7684\u76f8\u4f4d\u5dee\u6025\u5267\u51cf\u5c0f&#xff0c;\u6a21\u578b\u81ea\u7136\u96be\u4ee5\u533a\u5206\u5c40\u90e8\u987a\u5e8f\u3002\u8fd9\u5c31\u662f\u5206\u8fa8\u7387\u4e0b\u964d\u7684\u9891\u57df\u89e3\u91ca\u3002<\/p>\n<p>\u66f4\u5173\u952e\u7684\u662f&#xff0c;\u6a21\u578b\u5728\u8bad\u7ec3\u65f6\u53ea\u89c1\u8fc7\u7279\u5b9a\u9891\u7387\u8303\u56f4\u5185\u7684\u4f4d\u7f6e\u53d8\u5316\u6a21\u5f0f\u3002\u5916\u63a8\u65f6&#xff0c;\u9ad8\u9891\u5206\u91cf\u88ab\u8fc7\u5ea6\u538b\u7f29&#xff0c;\u4f1a\u584c\u7f29\u5230\u6a21\u578b\u672a\u66fe\u5b66\u4e60\u7684\u533a\u57df&#xff1b;\u4f4e\u9891\u5206\u91cf\u867d\u76f8\u5bf9\u7a33\u5b9a&#xff0c;\u4f46\u4e5f\u9762\u4e34\u8fb9\u754c\u5916\u63a8\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u71b5\u5d29\u584c\u548c\u5206\u8fa8\u7387\u4e22\u5931&#xff0c;\u5f52\u6839\u7ed3\u5e95\u90fd\u662f\u9891\u57df\u7ed3\u6784\u5931\u8861\u7684\u8868\u73b0\u3002<\/p>\n<p>\u9891\u57df\u89c6\u89d2\u8ba9\u6211\u4eec\u770b\u6e05\u4e00\u4e2a\u4e8b\u5b9e&#xff1a;\u4f4d\u7f6e\u7f16\u7801\u7684\u5916\u63a8\u5e76\u4e0d\u662f\u4e00\u4e2a\u5747\u5300\u7684\u95ee\u9898\u3002\u4e0d\u540c\u9891\u7387\u9700\u8981\u4e0d\u540c\u7684\u5904\u7406\u7b56\u7565\u2014\u2014\u9ad8\u9891\u9700\u8981\u4fdd\u6301\u8db3\u591f\u7684\u5206\u8fa8\u7387&#xff0c;\u4f4e\u9891\u5219\u9700\u8981\u5e73\u6ed1\u5916\u63a8\u3002\u53ea\u6709\u4ece\u9891\u57df\u91cd\u65b0\u5ba1\u89c6\u8bed\u4e49\u65f6\u7a7a\u7684\u6298\u53e0\u65b9\u5f0f&#xff0c;\u624d\u80fd\u627e\u5230\u66f4\u7cbe\u7ec6\u7684\u6269\u5c55\u65b9\u6cd5\u3002\u6298\u53e0\u7684\u66f2\u7387\u4e0d\u80fd\u5728\u6bcf\u4e00\u5904\u90fd\u76f8\u540c&#xff1b;\u6709\u4e9b\u5730\u65b9\u9700\u8981\u66f4\u7d27\u51d1\u7684\u6298\u75d5&#xff0c;\u6709\u4e9b\u5730\u65b9\u5219\u9700\u8981\u66f4\u8212\u5c55\u7684\u5f27\u9762\u3002<\/p>\n<h3>\u516b\u3001YaRN&#xff1a;\u5206\u9891\u800c\u6cbb\u7684\u667a\u6167<\/h3>\n<p>\u6b63\u662f\u5728\u8fd9\u4e2a\u9891\u57df\u601d\u8def\u4e0a&#xff0c;YaRN \u63d0\u51fa\u4e86\u66f4\u7cbe\u7ec6\u7684\u89e3\u51b3\u7b56\u7565\u3002\u5b83\u7684\u5168\u79f0\u662f\u201cYet another RoPE extensioN method\u201d&#xff0c;\u6838\u5fc3\u601d\u60f3\u4e0d\u518d\u5bf9\u6240\u6709\u7ef4\u5ea6\u4e00\u89c6\u540c\u4ec1&#xff0c;\u800c\u662f\u6839\u636e\u9891\u7387\u9ad8\u4f4e\u5206\u7ec4\u5904\u7406\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4&#xff0c;YaRN \u628a RoPE \u4e2d\u7684\u65cb\u8f6c\u7ef4\u5ea6\u6309\u7167\u9891\u7387\u4ece\u9ad8\u5230\u4f4e\u5212\u5206\u6210\u82e5\u5e72\u6bb5\u3002\u5bf9\u9ad8\u9891\u6bb5&#xff0c;\u5b83\u51e0\u4e4e\u4e0d\u505a\u538b\u7f29&#xff0c;\u8ba9\u76f8\u90bb token \u4e4b\u95f4\u7684\u89d2\u5ea6\u5dee\u4fdd\u6301\u539f\u6709\u7684\u5206\u8fa8\u7387&#xff1b;\u5bf9\u4f4e\u9891\u6bb5&#xff0c;\u5219\u65bd\u52a0\u66f4\u5927\u7684\u7f29\u653e&#xff0c;\u4f7f\u5176\u80fd\u591f\u8986\u76d6\u66f4\u8fdc\u7684\u957f\u5ea6\u8303\u56f4\u3002\u8fd9\u5c31\u50cf\u5728\u4e00\u5ea7\u53e4\u6208\u5c14\u949f\u4e0a&#xff0c;\u53ea\u8c03\u6162\u90a3\u4e9b\u539f\u672c\u5c31\u8f6c\u52a8\u7f13\u6162\u7684\u5e74\u9488\u548c\u6708\u9488&#xff0c;\u800c\u8ba9\u79d2\u9488\u7ee7\u7eed\u6309\u539f\u901f\u98de\u8f6c\u3002\u8fd9\u6837\u65e2\u6269\u5c55\u4e86\u5168\u5c40\u65f6\u95f4\u5c3a\u5ea6&#xff0c;\u53c8\u6ca1\u6709\u727a\u7272\u77ed\u8ddd\u79bb\u7684\u7cbe\u786e\u523b\u5ea6\u3002\u6298\u53e0\u4e0d\u518d\u662f\u6574\u4f53\u644a\u8584&#xff0c;\u800c\u662f\u6709\u9009\u62e9\u5730\u52a0\u6df1\u67d0\u4e9b\u6298\u75d5\u3001\u653e\u677e\u53e6\u4e00\u4e9b\u66f2\u7387\u3002<\/p>\n<p>\u5728\u5177\u4f53\u5b9e\u73b0\u4e0a&#xff0c;YaRN \u5bf9 RoPE \u7684\u6bcf\u4e2a\u7ef4\u5ea6\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(2i,2i&#043;1)(2i, 2i&#043;1)<\/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\">2<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">i<\/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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5f15\u5165\u4e00\u4e2a\u7f29\u653e\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b3i\\\\gamma_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0556em\" class=\"mord mathnormal\">\u03b3<\/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: -0.0556em;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><\/span><\/span><\/span>&#xff0c;\u4f7f\u5f97\u65cb\u8f6c\u89d2\u5ea6\u4ece\u539f\u6765\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pos\u22c5\u03b8ipos \\\\cdot \\\\theta_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">\u03b8<\/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: -0.0278em;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><\/span><\/span><\/span> \u53d8\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pos\u22c5\u03b3i\u22c5\u03b8ipos \\\\cdot \\\\gamma_i \\\\cdot \\\\theta_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0556em\" class=\"mord mathnormal\">\u03b3<\/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: -0.0556em;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: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">\u03b8<\/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: -0.0278em;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><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8i&#061;10000\u22122i\/d\\\\theta_i &#061; 10000^{-2i\/d}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">\u03b8<\/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: -0.0278em;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: 0.888em\"><\/span><span class=\"mord\">1000<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.888em\"><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\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mord mtight\">\/<\/span><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u7ef4\u5ea6\u5bf9&#xff0c;\u5148\u8ba1\u7b97\u5176\u5bf9\u5e94\u7684\u6ce2\u957f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bbi&#061;2\u03c0\/\u03b8i\\\\lambda_i &#061; 2\\\\pi \/ \\\\theta_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/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: 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><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\">2<\/span><span style=\"margin-right: 0.0359em\" class=\"mord mathnormal\">\u03c0<\/span><span class=\"mord\">\/<\/span><span class=\"mord\"><span style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">\u03b8<\/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: -0.0278em;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><\/span><\/span><\/span>\u3002\u8bbe\u8bad\u7ec3\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">LL<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u671f\u671b\u6269\u5c55\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">L\u2032&#061;s\u22c5LL&#039; &#061; s \\\\cdot L<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><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\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/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: 0.4445em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b3i\\\\gamma_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0556em\" class=\"mord mathnormal\">\u03b3<\/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: -0.0556em;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><\/span><\/span><\/span> \u6309\u9891\u7387\u9ad8\u4f4e\u5206\u6bb5\u786e\u5b9a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b3i&#061;{1,\u82e5\u00a0\u03bbi&lt;LL\u03bbi,\u82e5\u00a0\u03bbi&gt;sL(1\u2212r)\u22c5L\u03bbi&#043;r\u22c51,\u82e5\u00a0L\u2264\u03bbi\u2264sL<br \/>\n\\\\gamma_i &#061;<br \/>\n\\\\begin{cases}<br \/>\n1, &amp; \\\\text{\u82e5 } \\\\lambda_i &lt; L \\\\\\\\<br \/>\n\\\\frac{L}{\\\\lambda_i}, &amp; \\\\text{\u82e5 } \\\\lambda_i &gt; sL \\\\\\\\<br \/>\n(1 &#8211; r) \\\\cdot \\\\frac{L}{\\\\lambda_i} &#043; r \\\\cdot 1, &amp; \\\\text{\u82e5 } L \\\\le \\\\lambda_i \\\\le sL<br \/>\n\\\\end{cases}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0556em\" class=\"mord mathnormal\">\u03b3<\/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: -0.0556em;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: 4.3462em;vertical-align: -1.9231em\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.35em\"><span class=\"\" style=\"top: -2.2em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"top: -2.192em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"\" style=\"height: 0.316em;width: 0.8889em\"><\/span><\/span><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"top: -4.292em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"\" style=\"height: 0.316em;width: 0.8889em\"><\/span><\/span><span class=\"\" style=\"top: -4.6em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a7<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.85em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.4231em\"><span class=\"\" style=\"top: -4.4231em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9831em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><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: 0.8723em\"><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 mtight\"><span class=\"mord mathnormal mtight\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -1.53em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/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 style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">r<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/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: 0.8723em\"><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 mtight\"><span class=\"mord mathnormal mtight\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/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 style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">r<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.9231em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.4231em\"><span class=\"\" style=\"top: -4.4231em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u82e5<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/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: 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><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\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9831em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u82e5<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/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: 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><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\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><span class=\"\" style=\"top: -1.53em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u82e5<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/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: 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><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\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.9231em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">r&#061;\u03bbi\u2212LsL\u2212Lr &#061; \\\\frac{\\\\lambda_i &#8211; L}{sL &#8211; L}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span style=\"margin-right: 0.0278em\" class=\"mord mathnormal\">r<\/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: 1.2995em;vertical-align: -0.4033em\"><\/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: 0.8962em\"><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 class=\"mord mathnormal mtight\">L<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">L<\/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: -3.4101em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u4e00\u4e2a\u7ebf\u6027\u63d2\u503c\u7cfb\u6570&#xff0c;\u7528\u4e8e\u5e73\u6ed1\u8fc7\u6e21\u3002\u8fd9\u91cc\u7ed9\u51fa\u7684\u662f\u6982\u5ff5\u7b80\u5316\u7248&#xff1a;\u539f\u8bba\u6587\u5728\u4e2d\u95f4\u8fc7\u6e21\u6bb5\u4f7f\u7528\u4e86\u4f59\u5f26 ramp \u800c\u975e\u7b80\u5355\u7684\u7ebf\u6027\u63d2\u503c&#xff0c;\u4f46\u6838\u5fc3\u601d\u60f3\u4e00\u81f4\u2014\u2014\u9ad8\u9891\u7ef4\u5ea6&#xff08;\u6ce2\u957f\u77ed&#xff09;\u4fdd\u6301\u539f\u6837&#xff0c;\u4f4e\u9891\u7ef4\u5ea6&#xff08;\u6ce2\u957f\u957f&#xff09;\u6309\u6bd4\u4f8b\u538b\u7f29&#xff0c;\u4e2d\u95f4\u533a\u57df\u5e73\u6ed1\u8fc7\u6e21\u3002\u8fd9\u6837\u65e2\u4fdd\u4f4f\u4e86\u5c40\u90e8\u5206\u8fa8\u7387&#xff0c;\u53c8\u6269\u5c55\u4e86\u6709\u6548\u8303\u56f4\u3002<\/p>\n<p>\u6b64\u5916&#xff0c;YaRN \u8fd8\u5f15\u5165\u6e29\u5ea6\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c4\\\\tau<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span style=\"margin-right: 0.1132em\" class=\"mord mathnormal\">\u03c4<\/span><\/span><\/span><\/span><\/span> \u8c03\u6574\u6ce8\u610f\u529b softmax&#xff0c;\u7f13\u89e3\u957f\u5e8f\u5217\u4e0b\u7684\u71b5\u5d29\u584c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c4&#061;1&#043;0.1\u22c5ln\u2061(s)<br \/>\n\\\\tau &#061; 1 &#043; 0.1 \\\\cdot \\\\ln(s)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span style=\"margin-right: 0.1132em\" class=\"mord mathnormal\">\u03c4<\/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: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/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: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u63a8\u7406\u65f6\u901a\u5e38\u53d6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c4\\\\tau<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span style=\"margin-right: 0.1132em\" class=\"mord mathnormal\">\u03c4<\/span><\/span><\/span><\/span><\/span> 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\u5219\u91c7\u7528\u4e86\u66f4\u590d\u6742\u7684\u6df7\u5408\u65b9\u6848&#xff1a;\u5168\u5c40\u6ce8\u610f\u529b\u5c42\u4f7f\u7528\u9ad8\u8fbe 1M \u7684 base&#xff0c;\u5c40\u90e8\u6ce8\u610f\u529b\u5c42\u4fdd\u6301 10000 \u7684 base&#xff0c;\u5e76\u7ed3\u5408\u4ea4\u66ff\u7684\u5c40\u90e8\/\u5168\u5c40\u6ce8\u610f\u529b\u673a\u5236\u3002\u8fd9\u79cd\u8bbe\u8ba1\u5728\u6269\u5c55\u4e0a\u4e0b\u6587\u7684\u540c\u65f6&#xff0c;\u901a\u8fc7\u5c40\u90e8\u5c42\u7ef4\u6301\u4e86\u77ed\u8ddd\u79bb\u5206\u8fa8\u7387\u3002\u800c\u6b64\u524d\u7684 Gemma 2 \u867d\u7136 base \u4fdd\u6301\u9ed8\u8ba4\u7684 10000&#xff0c;\u4f46\u5f15\u5165\u4e86 local\/global \u4ea4\u66ff\u6ce8\u610f\u529b\u548c logit soft-capping 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