{"id":125,"date":"2026-04-26T17:40:04","date_gmt":"2026-04-26T09:40:04","guid":{"rendered":"https:\/\/www.bojinhu.xyz\/?p=125"},"modified":"2026-04-23T17:41:48","modified_gmt":"2026-04-23T09:41:48","slug":"embedding-%e4%b8%8e-rope-%e8%a7%a3%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.bojinhu.xyz\/index.php\/2026\/04\/26\/embedding-%e4%b8%8e-rope-%e8%a7%a3%e6%9e%90\/","title":{"rendered":"Embedding \u4e0e RoPE \u89e3\u6790"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u5199\u5728\u524d\u9762<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u524d\u4e24\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5206\u522b\u62c6\u89e3\u4e86 LLM \u7684\u6574\u4f53\u67b6\u6784\uff0c\u53c8\u4e13\u95e8\u6df1\u6316\u4e86 Tokenizer\u3002\u73b0\u5728\uff0c\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u5982\u4f55\u628a\u4e00\u6bb5\u4eba\u7c7b\u8bed\u8a00\u53d8\u6210\u4e00\u4e32\u6570\u5b57 ID\uff0c\u4e5f\u77e5\u9053\u4e86 Tokenizer \u5982\u4f55\u51b3\u5b9a\u201c\u5207\u5728\u54ea\u91cc\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u7d27\u63a5\u7740\u5c31\u6765\u4e86\u4e00\u4e2a\u95ee\u9898\uff1a<strong>\u8fd9\u4e9b ID \u672c\u8eab\u53ea\u662f\u201c\u7f16\u53f7\u201d\uff0c\u6ca1\u6709\u8bed\u4e49\uff0c\u66f4\u6ca1\u6709\u987a\u5e8f\u611f\u3002\u6a21\u578b\u600e\u4e48\u77e5\u9053\u201c\u82f9\u679c\u201d\u548c\u201c\u6c34\u679c\u201d\u662f\u4e00\u7c7b\u4e1c\u897f\uff1f\u600e\u4e48\u77e5\u9053\u201c\u6211\u7231\u4f60\u201d\u548c\u201c\u4f60\u7231\u6211\u201d\u4e0d\u662f\u4e00\u56de\u4e8b\uff1f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u662f\u4eca\u5929\u6211\u4eec\u8981\u6df1\u5165\u63a2\u8ba8\u7684\u4e24\u4e2a\u6838\u5fc3\u7ec4\u4ef6\u2014\u2014<strong>Embedding\uff08\u8bcd\u5d4c\u5165\uff09<\/strong> \u548c <strong>RoPE\uff08\u65cb\u8f6c\u4f4d\u7f6e\u7f16\u7801\uff09<\/strong> \u3002\u4e00\u4e2a\u8d1f\u8d23\u628a\u8bcd\u8bed\u53d8\u6210\u5e26\u6709\u8bed\u4e49\u5750\u6807\u7684\u5411\u91cf\uff0c\u53e6\u4e00\u4e2a\u8d1f\u8d23\u544a\u8bc9\u6a21\u578b\u201c\u8c01\u5728\u524d\u3001\u8c01\u5728\u540e\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u8bf4 Tokenizer \u662f LLM \u7684\u201c\u7ffb\u8bd1\u5b98\u201d\uff0c\u90a3 Embedding \u5c31\u662f\u5b83\u7684\u201c\u8bed\u4e49\u8bcd\u5178\u201d\uff0c\u800c RoPE \u5219\u662f\u5b83\u7684\u201c\u65f6\u5e8f\u5bfc\u822a\u4eea\u201d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u3001Embedding\uff1a\u7ed9\u6bcf\u4e2a\u8bcd\u53d1\u4e00\u5f20\u201c\u7279\u5f81\u8eab\u4efd\u8bc1\u201d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1.1 \u4e3a\u4ec0\u4e48 Token ID \u4e0d\u591f\u7528\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ecf\u8fc7 Tokenizer\uff0c\u6bcf\u4e2a\u8bcd\u6216\u5b50\u8bcd\u90fd\u88ab\u5206\u914d\u4e86\u4e00\u4e2a\u6570\u5b57 ID\u3002\u4f46\u95ee\u9898\u6765\u4e86\uff1aID \u53ea\u662f\u6807\u7b7e\u3002\u5047\u8bbe\u8bcd\u8868\u91cc\u201c\u732b\u201d\u662f 9246 \u53f7\uff0c\u201c\u72d7\u201d\u662f 9703 \u53f7\uff0c\u201c\u624b\u673a\u201d\u662f 11399 \u53f7\uff0c\u4f60\u95ee\u6a21\u578b\u201c9246 \u548c 9703 \u50cf\u5417\uff1f\u201d\uff0c\u6a21\u578b\u6839\u672c\u65e0\u4ece\u5224\u65ad\u2014\u2014\u4e24\u4e2a\u6570\u5b57\u4e4b\u95f4\u6ca1\u6709\u4efb\u4f55\u8bed\u4e49\u5173\u7cfb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u50cf\u7528\u8eab\u4efd\u8bc1\u53f7\u6765\u5224\u65ad\u4e24\u4e2a\u4eba\u662f\u4e0d\u662f\u4eb2\u621a\uff1a110101 \u548c 110102 \u53f7\u53ea\u662f\u529e\u8bc1\u7684\u5148\u540e\u987a\u5e8f\u800c\u5df2\uff0c\u4e0d\u4ee3\u8868\u4efb\u4f55\u8840\u7f18\u5173\u7cfb\u3002\u6240\u4ee5\uff0cToken ID \u53ea\u662f\u6a21\u578b\u7684\u201c\u8f93\u5165\u51ed\u8bc1\u201d\uff0c\u771f\u6b63\u8981\u8ba9\u6a21\u578b\u201c\u7406\u89e3\u201d\u8bcd\u8bed\uff0c\u8fd8\u9700\u8981\u628a\u5b83\u4eec\u53d8\u6210\u80fd\u591f\u8fdb\u884c\u6570\u5b66\u8fd0\u7b97\u7684\u201c\u5750\u6807\u201d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.2 Embedding \u505a\u4e86\u4ec0\u4e48\uff1a\u628a\u8bcd\u201c\u753b\u201d\u8fdb\u9ad8\u7ef4\u7a7a\u95f4<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Embedding \u7684\u6838\u5fc3\u601d\u60f3\u975e\u5e38\u6734\u7d20\uff1a<strong>\u4e0d\u518d\u7528\u5b64\u7acb\u7684\u7f16\u53f7\uff0c\u800c\u662f\u7ed9\u6bcf\u4e2a\u8bcd\u5206\u914d\u4e00\u7ec4\u201c\u7279\u5f81\u5206\u6570\u201d\uff0c\u5f62\u6210\u4e00\u4e2a\u5411\u91cf\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u60f3\u8c61\u4e00\u4e0b\uff0c\u5982\u679c\u6211\u4eec\u53ea\u7528\u4e24\u4e2a\u7ef4\u5ea6\u6765\u63cf\u8ff0\u4e00\u4e2a\u8bcd\u2014\u2014\u201c\u840c\u5ea6\u201d\u548c\u201c\u673a\u68b0\u611f\u201d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u732b<\/strong>\uff1a[0.9, 0.1] \u2014\u2014 \u5f88\u840c\uff0c\u4e0d\u673a\u68b0<\/li>\n\n\n\n<li><strong>\u72d7<\/strong>\uff1a[0.8, 0.2] \u2014\u2014 \u4e5f\u5f88\u840c\uff0c\u4e0d\u673a\u68b0<\/li>\n\n\n\n<li><strong>\u624b\u673a<\/strong>\uff1a[0.1, 0.9] \u2014\u2014 \u4e0d\u840c\uff0c\u5f88\u673a\u68b0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u8fd9\u4e9b\u5206\u6570\u753b\u5728\u4e8c\u7ef4\u5750\u6807\u7eb8\u4e0a\uff0c\u201c\u732b\u201d\u548c\u201c\u72d7\u201d\u4f1a\u81ea\u7136\u5730\u805a\u5728\u4e00\u8d77\uff0c\u201c\u624b\u673a\u201d\u5219\u79bb\u5b83\u4eec\u5f88\u8fdc\u3002\u8ddd\u79bb\u672c\u8eab\u5c31\u80fd\u53cd\u6620\u8bed\u4e49\u5173\u7cfb\u2014\u2014\u4e0d\u9700\u8981\u4eba\u5de5\u6807\u6ce8\u201c\u732b\u548c\u72d7\u76f8\u4f3c\u201d\uff0c\u5750\u6807\u7684\u8fdc\u8fd1\u5c31\u8bf4\u660e\u4e86\u4e00\u5207\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u771f\u5b9e\u7684\u5927\u6a21\u578b\u505a\u7684\u4e8b\u60c5\u5b8c\u5168\u4e00\u6837\uff0c\u53ea\u4e0d\u8fc7\u7ef4\u5ea6\u8fdc\u4e0d\u6b62 2 \u4e2a\u2014\u2014\u800c\u662f 768 \u4e2a\uff08BERT\uff09\u30014096 \u4e2a\uff08LLaMA-7B\uff09\uff0c\u751a\u81f3\u66f4\u591a\u3002\u6bcf\u4e2a\u7ef4\u5ea6\u4e0d\u518d\u662f\u4eba\u7c7b\u80fd\u547d\u540d\u7684\u201c\u840c\u5ea6\u201d\u201c\u673a\u68b0\u611f\u201d\uff0c\u800c\u662f\u6a21\u578b\u5728\u6d77\u91cf\u8bed\u6599\u4e2d\u81ea\u5df1\u5b66\u51fa\u6765\u7684\u62bd\u8c61\u7279\u5f81\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cEmbedding\u201d\u8fd9\u4e2a\u8bcd\u7ffb\u8bd1\u6210\u201c\u5d4c\u5165\u201d\uff0c\u672c\u8eab\u5c31\u5f88\u5f62\u8c61\uff1a<strong>\u628a\u4e00\u4e2a\u5b64\u7acb\u7684\u7b26\u53f7\uff0c\u585e\u8fdb\u4e00\u4e2a\u5145\u6ee1\u903b\u8f91\u5173\u7cfb\u7684\u7a7a\u95f4\u91cc<\/strong>\u3002\u5c31\u50cf\u62fc\u56fe\u2014\u2014\u6bcf\u4e2a\u8bcd\u662f\u4e00\u5757\u62fc\u56fe\uff0cEmbedding \u5e2e\u5b83\u627e\u5230\u5728\u4e16\u754c\uff08\u9ad8\u7ef4\u7a7a\u95f4\uff09\u4e2d\u6700\u5408\u9002\u7684\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.3 \u6570\u5b66\u672c\u8d28\uff1a\u4e00\u5f20\u5de8\u5927\u7684\u201c\u67e5\u8868\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u5de5\u7a0b\u5b9e\u73b0\u7684\u89d2\u5ea6\u770b\uff0cEmbedding \u5c42\u672c\u8d28\u4e0a\u5c31\u662f\u4e00\u5f20\u5de8\u5927\u7684\u201c\u67e5\u8868\u201d\uff08Look-up Table\uff09\uff1a<strong>\u4e00\u5f20\u5c3a\u5bf8\u4e3a [\u8bcd\u6c47\u8868\u5927\u5c0f V \u00d7 \u5411\u91cf\u7ef4\u5ea6 d] \u7684\u77e9\u9635<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u6a21\u578b\u62ff\u5230\u4e00\u4e2a Token ID \u65f6\uff0cEmbedding \u5c42\u505a\u7684\u4e8b\u60c5\u6781\u5176\u7b80\u5355\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7528 Token ID \u4f5c\u4e3a\u884c\u7d22\u5f15\uff0c\u4ece\u77e9\u9635\u4e2d\u53d6\u51fa\u5bf9\u5e94\u7684\u90a3\u4e00\u884c<\/li>\n\n\n\n<li>\u8fd9\u4e00\u884c\u5411\u91cf\uff08\u957f\u5ea6\u4e3a d\uff09\u5c31\u662f\u8fd9\u4e2a Token \u7684 Embedding<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\uff0c\u5047\u8bbe\u8bcd\u8868\u5927\u5c0f\u662f 32000\uff0cEmbedding \u7ef4\u5ea6\u662f 4096\uff0c\u90a3\u4e48\u8fd9\u5f20\u8868\u7684\u5c3a\u5bf8\u5c31\u662f 32000 \u00d7 4096\uff0c\u603b\u53c2\u6570\u91cf\u7ea6\u4e3a 1.31 \u4ebf\u2014\u2014\u5728 LLaMA-7B\uff08\u7ea6 70 \u4ebf\u53c2\u6570\uff09\u4e2d\uff0c\u5149 Embedding \u5c42\u5c31\u5360\u4e86\u8fd1 20% \u7684\u53c2\u6570\uff01<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\ud83d\udca1 <strong>\u90a3\u8fd9\u4e9b\u5411\u91cf\u662f\u56fa\u5b9a\u7684\u5417\uff1f<\/strong> \u4e0d\u3002Embedding \u5c42\u7684\u6743\u91cd\u662f<strong>\u53ef\u8bad\u7ec3\u7684<\/strong>\u3002\u5728\u9884\u8bad\u7ec3\u9636\u6bb5\uff0c\u6a21\u578b\u901a\u8fc7\u53cd\u5411\u4f20\u64ad\u4e0d\u65ad\u66f4\u65b0\u8fd9\u5f20\u8868\u91cc\u7684\u6570\u503c\uff0c\u8ba9\u8bed\u4e49\u76f8\u8fd1\u7684\u8bcd\u9010\u6e10\u5728\u5411\u91cf\u7a7a\u95f4\u4e2d\u9760\u8fd1\u3002\u6700\u7ec8\u5f97\u5230\u7684 Embedding \u77e9\u9635\uff0c\u5c31\u662f\u6a21\u578b\u5b66\u5230\u7684\u201c\u8bed\u4e49\u5730\u56fe\u201d\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">1.4 \u9759\u6001 Embedding vs \u4e0a\u4e0b\u6587 Embedding\uff1a\u4e00\u4e2a\u8bcd\u53ea\u80fd\u6709\u4e00\u4e2a\u5411\u91cf\u5417\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f20\u7edf\u7684 Word2Vec \u6216 GloVe \u4ea7\u751f\u7684 Embedding \u662f\u201c\u9759\u6001\u201d\u7684\uff1a<strong>\u65e0\u8bba\u4e0a\u4e0b\u6587\u600e\u4e48\u53d8\uff0c\u201c\u82f9\u679c\u201d\u8fd9\u4e2a\u8bcd\u7684\u5411\u91cf\u59cb\u7ec8\u662f\u540c\u4e00\u4e2a<\/strong>\u3002\u8fd9\u5728\u5904\u7406\u591a\u4e49\u8bcd\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\u2014\u2014\u6bd4\u5982\u201c\u82f9\u679c\u624b\u673a\u201d\u91cc\u7684\u201c\u82f9\u679c\u201d\u548c\u201c\u5403\u82f9\u679c\u201d\u91cc\u7684\u201c\u82f9\u679c\u201d\uff0c\u8bed\u4e49\u5b8c\u5168\u4e0d\u540c\uff0c\u5374\u5171\u7528\u540c\u4e00\u4e2a\u5411\u91cf\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u4ee3 LLM \u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u65b9\u5f0f\u662f\uff1a<strong>Embedding \u5c42\u4ea7\u751f\u7684\u4ecd\u7136\u662f\u4e00\u4e2a\u9759\u6001\u7684\u521d\u59cb\u5411\u91cf\uff0c\u4f46\u8fd9\u4e2a\u5411\u91cf\u4f1a\u5728\u540e\u7eed\u7684\u6bcf\u4e00\u5c42 Transformer \u4e2d\u88ab\u4e0d\u65ad\u201c\u52a0\u5de5\u201d\uff0c\u878d\u5408\u4e0a\u4e0b\u6587\u4fe1\u606f\uff0c\u6700\u7ec8\u53d8\u6210\u52a8\u6001\u7684\u3001\u4f9d\u8d56\u4e0a\u4e0b\u6587\u7684\u8868\u793a<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff0cLLM \u4e2d\u7684 Embedding \u53ea\u662f\u8d77\u70b9\u2014\u2014\u5b83\u7ed9\u6bcf\u4e2a\u8bcd\u4e00\u4e2a\u521d\u59cb\u7684\u201c\u8eab\u4efd\u7279\u5f81\u201d\uff0c\u7136\u540e\u8ba9 Transformer \u5c42\u53bb\u6839\u636e\u4e0a\u4e0b\u6587\u4e0d\u65ad\u8c03\u6574\u548c\u4e30\u5bcc\u8fd9\u4e2a\u7279\u5f81\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48 LLM \u80fd\u7cbe\u51c6\u533a\u5206\u201c\u82f9\u679c\u516c\u53f8\u201d\u548c\u201c\u6c34\u679c\u82f9\u679c\u201d\u2014\u2014\u4e0d\u662f\u56e0\u4e3a Embedding \u5c42\u6709\u591a\u806a\u660e\uff0c\u800c\u662f\u56e0\u4e3a\u540e\u9762\u7684 Attention \u673a\u5236\u505a\u4e86\u5927\u91cf\u7684\u4e0a\u4e0b\u6587\u611f\u77e5\u5de5\u4f5c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.5 \u53c2\u6570\u8ba1\u7b97\uff1aEmbedding \u5c42\u7684\u6210\u672c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Embedding \u5c42\u7684\u53c2\u6570\u91cf\u5f80\u5f80\u76f8\u5f53\u53ef\u89c2\u3002\u8ba1\u7b97\u516c\u5f0f\u5f88\u7b80\u5355\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Embedding \u53c2\u6570\u91cf = \u8bcd\u6c47\u8868\u5927\u5c0f\uff08V\uff09\u00d7 Embedding \u7ef4\u5ea6\uff08d\uff09<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5 LLaMA-7B \u4e3a\u4f8b\uff1a\u8bcd\u8868\u5927\u5c0f 32000\uff0c\u7ef4\u5ea6 4096\uff0cEmbedding \u5c42\u53c2\u6570\u91cf\u4e3a 32000 \u00d7 4096 \u2248 1.31 \u4ebf\u3002\u518d\u52a0\u4e0a\u8f93\u51fa\u5c42\uff08\u901a\u5e38\u4e0e\u8f93\u5165 Embedding \u5171\u4eab\u6743\u91cd\uff0c\u6216\u8005\u5355\u72ec\u4e00\u4e2a\u540c\u6837\u5927\u5c0f\u7684\u77e9\u9635\uff09\uff0c\u5149\u8f93\u5165\u8f93\u51fa\u4e24\u5c42\u5c31\u5360\u4e86\u7ea6 2.6 \u4ebf\u53c2\u6570\uff0c\u63a5\u8fd1\u6574\u4e2a 7B \u6a21\u578b\u7684 4%\u3002\u8fd9\u4e5f\u5c31\u662f\u4e3a\u4ec0\u4e48\u5728\u63a8\u7406\u65f6\uff0c\u51cf\u5c11 Embedding \u7ef4\u5ea6\u53ef\u4ee5\u663e\u8457\u538b\u7f29\u663e\u5b58\u5360\u7528\u2014\u2014OpenAI \u7684 text-embedding-3-large \u6a21\u578b\u751a\u81f3\u5141\u8bb8\u7528\u6237\u5728\u8c03\u7528\u65f6\u901a\u8fc7\u53c2\u6570\u52a8\u6001\u7f29\u77ed\u5d4c\u5165\u5411\u91cf\u7684\u7ef4\u5ea6\uff0c\u4ece\u9ed8\u8ba4\u7684 3072 \u7ef4\u538b\u7f29\u5230 1024 \u7ef4\u751a\u81f3 256 \u7ef4\uff0c\u5728\u4fdd\u6301\u68c0\u7d22\u8d28\u91cf\u7684\u540c\u65f6\u5927\u5e45\u964d\u4f4e\u5b58\u50a8\u6210\u672c\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u3001RoPE \u767b\u573a\uff1a\u5f53\u5411\u91cf\u5b66\u4f1a\u4e86\u201c\u65cb\u8f6c\u201d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 \u4e3a\u4ec0\u4e48\u9700\u8981\u4f4d\u7f6e\u7f16\u7801\uff1f\u2014\u2014\u4e00\u4e2a\u201c\u76f2\u4eba\u6478\u8c61\u201d\u7684\u96be\u9898<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Attention \u673a\u5236\u6709\u4e00\u4e2a\u5929\u751f\u7684\u201c\u76f2\u533a\u201d\uff1a\u5b83\u5bf9\u8f93\u5165\u5e8f\u5217\u7684\u987a\u5e8f\u5b8c\u5168\u65e0\u611f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u4f60\u628a\u201c\u6211\u7231\u4f60\u201d\u548c\u201c\u4f60\u7231\u6211\u201d\u4e2d\u7684\u8bcd\u6253\u4e71\u987a\u5e8f\uff0c\u7136\u540e\u5206\u522b\u8ba1\u7b97\u5b83\u4eec\u7684 Embedding \u96c6\u5408\uff0c\u6a21\u578b\u770b\u5230\u7684\u662f\u5b8c\u5168\u76f8\u540c\u7684\u4e09\u4e2a\u5411\u91cf\uff0c\u53ea\u662f\u987a\u5e8f\u4e0d\u540c\u3002\u4f46 Attention \u672c\u8eab\u7684\u516c\u5f0f\u2014\u2014\u53ea\u5bf9 Q\u3001K\u3001V \u505a\u70b9\u79ef\u548c\u52a0\u6743\u6c42\u548c\u2014\u2014\u5e76\u6ca1\u6709\u5185\u7f6e\u201c\u987a\u5e8f\u201d\u7684\u6982\u5ff5\u3002\u56e0\u6b64\uff0c\u5982\u679c\u4e0d\u52a0\u5904\u7406\uff0c\u6a21\u578b\u4f1a\u628a\u8fd9\u4e24\u4e2a\u53e5\u5b50\u5f53\u6210\u540c\u6837\u7684\u4e1c\u897f\u6765\u5904\u7406\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5fc5\u987b\u7ed9 Embedding \u6ce8\u5165\u4f4d\u7f6e\u4fe1\u606f\u3002<\/strong> \u53ea\u6709\u544a\u8bc9\u6a21\u578b\u6bcf\u4e2a\u8bcd\u5728\u53e5\u5b50\u4e2d\u7684\u4f4d\u7f6e\uff0c\u5b83\u624d\u80fd\u533a\u5206\u201c\u72d7\u8ffd\u732b\u201d\u548c\u201c\u732b\u8ffd\u72d7\u201d\u662f\u4e24\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u6545\u4e8b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \u7edd\u5bf9\u4f4d\u7f6e\u7f16\u7801\u7684\u56f0\u5883\uff1a\u4e3a\u4ec0\u4e48\u88ab\u629b\u5f03\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e9\u671f Transformer \u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u65b9\u5f0f\u5f88\u76f4\u63a5\u2014\u2014<strong>\u7edd\u5bf9\u4f4d\u7f6e\u7f16\u7801<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u8c13\u201c\u7edd\u5bf9\u201d\uff0c\u5c31\u662f\u7ed9\u6bcf\u4e2a\u4f4d\u7f6e\uff08\u7b2c 0 \u4f4d\u3001\u7b2c 1 \u4f4d\u3001\u7b2c 2 \u4f4d\u2026\u2026\uff09\u5206\u914d\u4e00\u4e2a\u72ec\u4e00\u65e0\u4e8c\u7684\u5411\u91cf\uff0c\u7136\u540e\u76f4\u63a5\u52a0\u5230 Embedding \u4e0a\u3002\u8fd9\u53c8\u5206\u4e3a\u4e24\u79cd\u65b9\u5f0f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u53ef\u5b66\u4e60\u4f4d\u7f6e\u7f16\u7801<\/strong>\uff1a\u628a\u4f4d\u7f6e\u5411\u91cf\u5f53\u4f5c\u53ef\u8bad\u7ec3\u53c2\u6570\uff0c\u8ba9\u6a21\u578b\u81ea\u5df1\u5b66<\/li>\n\n\n\n<li><strong>Sinusoidal \u4f4d\u7f6e\u7f16\u7801<\/strong>\uff1a\u7528\u6b63\u5f26\u548c\u4f59\u5f26\u51fd\u6570\u751f\u6210\u56fa\u5b9a\u6a21\u5f0f\u7684\u4f4d\u7f6e\u5411\u91cf\uff0c\u4e0d\u9700\u8981\u8bad\u7ec3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u7edd\u5bf9\u4f4d\u7f6e\u7f16\u7801\u7b80\u5355\u76f4\u89c2\uff0c\u4f46\u6709\u4e00\u4e2a\u81f4\u547d\u7684\u7f3a\u9677\uff1a<strong>\u6a21\u578b\u53ea\u80fd\u5904\u7406\u8bad\u7ec3\u65f6\u89c1\u8fc7\u7684\u6700\u957f\u957f\u5ea6<\/strong>\u3002\u5982\u679c\u4f60\u8bad\u7ec3\u65f6\u6700\u5927\u957f\u5ea6\u662f 2048\uff0c\u90a3\u6a21\u578b\u5c31\u6c38\u8fdc\u65e0\u6cd5\u7406\u89e3\u7b2c 2049 \u4e2a\u4f4d\u7f6e\u2014\u2014\u56e0\u4e3a\u5b83\u7684\u4f4d\u7f6e\u7f16\u7801\u8868\u91cc\u6839\u672c\u6ca1\u6709\u8fd9\u4e00\u884c\u3002\u800c\u91cd\u65b0\u8bad\u7ec3\u6216\u5fae\u8c03\u4e00\u4e2a\u66f4\u957f\u4e0a\u4e0b\u6587\u7684\u6a21\u578b\uff0c\u6210\u672c\u6781\u9ad8\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u66f4\u5173\u952e\u7684\u662f\uff0c\u8bed\u8a00\u7684\u672c\u8d28\u51b3\u5b9a\u4e86\uff1a<strong>\u76f8\u5bf9\u4f4d\u7f6e\u5f80\u5f80\u6bd4\u7edd\u5bf9\u4f4d\u7f6e\u66f4\u91cd\u8981<\/strong>\u3002\u5728\u5927\u591a\u6570\u8bed\u8a00\u73b0\u8c61\u4e2d\uff0c\u8bcd\u4e0e\u8bcd\u4e4b\u95f4\u7684\u8ddd\u79bb\u5173\u7cfb\uff08\u6bd4\u5982\u4e3b\u8bed\u548c\u8c13\u8bed\u76f8\u9694\u591a\u8fdc\uff0c\u4ee3\u8bcd\u6307\u4ee3\u7684\u540d\u8bcd\u5728\u524d\u9762\u51e0\u4e2a\u8bcd\u7684\u4f4d\u7f6e\uff09\uff0c\u8fdc\u6bd4\u67d0\u4e2a\u8bcd\u662f\u201c\u7b2c 42 \u4e2a\u4f4d\u7f6e\u201d\u8fd9\u79cd\u4fe1\u606f\u6709\u610f\u4e49\u5f97\u591a\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8e\u662f\uff0c\u7814\u7a76\u91cd\u5fc3\u9010\u6e10\u4ece\u201c\u7edd\u5bf9\u4f4d\u7f6e\u201d\u8f6c\u5411\u4e86<strong>\u201c\u76f8\u5bf9\u4f4d\u7f6e\u7f16\u7801\u201d<\/strong>\u2014\u2014\u8ba9\u6a21\u578b\u5929\u7136\u5730\u6355\u6349\u8bcd\u4e0e\u8bcd\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u800c\u4e0d\u662f\u6b7b\u8bb0\u786c\u80cc\u7edd\u5bf9\u4f4d\u7f6e\u7684\u5e8f\u53f7\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.3 RoPE \u7684\u6838\u5fc3\u6d1e\u5bdf\uff1a\u7528\u201c\u65cb\u8f6c\u201d\u6765\u7f16\u7801\u76f8\u5bf9\u4f4d\u7f6e<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RoPE\uff08Rotary Position Embedding\uff0c\u65cb\u8f6c\u4f4d\u7f6e\u7f16\u7801\uff09<\/strong> \u662f\u8fd9\u4e00\u8f6c\u53d8\u4e2d\u6700\u91cd\u8981\u7684\u7a81\u7834\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u6781\u5176\u4f18\u96c5\uff1a<strong>\u901a\u8fc7\u5bf9 Query \u548c Key \u5411\u91cf\u65bd\u52a0\u4e00\u4e2a\u4e0e\u4f4d\u7f6e\u76f8\u5173\u7684\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u5f97\u4e24\u4e2a\u5411\u91cf\u7684\u70b9\u79ef\u7ed3\u679c\u5929\u7136\u5305\u542b\u5b83\u4eec\u7684\u76f8\u5bf9\u4f4d\u7f6e\u4fe1\u606f\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5177\u4f53\u6765\u8bf4\uff0cRoPE \u5c06\u6bcf\u4e2a Token \u7684\u5411\u91cf\u770b\u4f5c\u590d\u6570\uff08\u6216\u914d\u5bf9\u7684\u7279\u5f81\uff09\uff0c\u7136\u540e\u6839\u636e\u5b83\u5728\u5e8f\u5217\u4e2d\u7684\u4f4d\u7f6e\uff0c\u5c06\u5176\u65cb\u8f6c\u4e00\u5b9a\u7684\u89d2\u5ea6\u3002\u4f4d\u7f6e\u8d8a\u9760\u540e\uff0c\u65cb\u8f6c\u7684\u89d2\u5ea6\u8d8a\u5927\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7528\u6570\u5b66\u6765\u8868\u8fbe\uff08\u5c3d\u91cf\u7b80\u5316\uff09\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u628a\u5411\u91cf\u53d8\u6210\u590d\u6570<\/strong>\uff1a\u5bf9\u4e8e d \u7ef4\u5411\u91cf\uff0c\u4e24\u4e24\u914d\u5bf9\uff0c\u6bcf\u4e00\u5bf9\u770b\u4f5c\u4e00\u4e2a\u590d\u6570\uff1a<code>x\u2081 + i\u00b7x\u2082<\/code><\/li>\n\n\n\n<li><strong>\u6309\u4f4d\u7f6e\u65cb\u8f6c<\/strong>\uff1a\u5bf9\u4e8e\u4f4d\u7f6e m\uff0c\u5c06\u590d\u6570\u4e58\u4ee5 <code>e^(i\u00b7m\u00b7\u03b8)<\/code>\uff08\u76f8\u5f53\u4e8e\u65cb\u8f6c m\u00b7\u03b8 \u89d2\u5ea6\uff09<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97 Attention<\/strong>\uff1a\u65cb\u8f6c\u540e\u7684 Query \u548c Key \u505a\u5185\u79ef<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u5173\u952e\u6765\u4e86\u2014\u2014\u7ecf\u8fc7\u8fd9\u4e00\u901a\u65cb\u8f6c\uff0c\u4e24\u4e2a\u4f4d\u7f6e m \u548c n \u7684 Query \u548c Key \u7684\u5185\u79ef\u7ed3\u679c\uff0c\u53ea\u4f9d\u8d56\u4e8e\u5b83\u4eec\u7684<strong>\u76f8\u5bf9\u4f4d\u7f6e\u5dee (m &#8211; n)<\/strong>\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e\u5404\u81ea\u7684\u7edd\u5bf9\u4f4d\u7f6e\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u65cb\u8f6c\u540e\u7684 Q(m) \u00b7 \u65cb\u8f6c\u540e\u7684 K(n) = \u539f Q \u00b7 \u65cb\u8f6c\u540e\u7684 K(n - m)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u6027\u8d28\u8ba9 RoPE \u5929\u7136\u5730\u7f16\u7801\u4e86\u76f8\u5bf9\u4f4d\u7f6e\u3002\u6a21\u578b\u4e0d\u9700\u8981\u53bb\u8bb0\u4f4f\u201c\u4f4d\u7f6e 42\u201d\u5e94\u8be5\u957f\u4ec0\u4e48\u6837\u2014\u2014\u5b83\u53ea\u9700\u8981\u77e5\u9053\u4e24\u4e2a\u8bcd\u4e4b\u95f4\u201c\u9694\u4e86\u591a\u5c11\u6b65\u201d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.4 \u4e3a\u4ec0\u4e48\u201c\u65cb\u8f6c\u201d\u8fd9\u4e2a\u64cd\u4f5c\u521a\u521a\u597d\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4ec0\u4e48\u504f\u504f\u662f\u65cb\u8f6c\uff1f\u4e3a\u4ec0\u4e48\u4e0d\u662f\u5e73\u79fb\u3001\u7f29\u653e\u6216\u8005\u5176\u4ed6\u64cd\u4f5c\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b54\u6848\u5728\u4e8e\u590d\u6570\u4e58\u6cd5\u7684\u6027\u8d28\uff1a<strong>\u4e24\u4e2a\u590d\u6570\u76f8\u4e58\uff0c\u76f8\u5f53\u4e8e\u6a21\u957f\u76f8\u4e58\u3001\u89d2\u5ea6\u76f8\u52a0<\/strong>\u3002\u5f53\u6211\u4eec\u5bf9\u5411\u91cf\u65bd\u52a0\u65cb\u8f6c\uff08\u5373\u4e58\u4e0a <code>e^(i\u00b7m\u00b7\u03b8)<\/code>\uff09\u540e\uff0c\u4e24\u4e2a\u65cb\u8f6c\u540e\u7684\u590d\u6570\u505a\u5185\u79ef\uff0c\u5b83\u4eec\u7684\u65cb\u8f6c\u89d2\u5ea6\u4f1a\u201c\u76f8\u51cf\u201d\u2014\u2014\u800c\u76f8\u51cf\u7684\u7ed3\u679c\u6070\u597d\u662f\u76f8\u5bf9\u4f4d\u7f6e\u5dee\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7528\u51e0\u4f55\u6765\u7406\u89e3\uff1a\u5982\u679c\u628a\u5411\u91cf\u770b\u4f5c\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u7bad\u5934\uff0c\u65cb\u8f6c\u64cd\u4f5c\u5b8c\u7f8e\u5730\u201c\u4fdd\u62a4\u201d\u4e86\u5411\u91cf\u7684\u957f\u5ea6\uff08\u6a21\u957f\u4e0d\u53d8\uff09\uff0c\u53ea\u6539\u53d8\u4e86\u5b83\u7684\u65b9\u5411\u3002\u8fd9\u610f\u5473\u7740 RoPE <strong>\u4e0d\u4f1a\u6539\u53d8 Embedding \u672c\u8eab\u7684\u8bed\u4e49\u5f3a\u5ea6<\/strong>\u2014\u2014\u5b83\u53ea\u662f\u5728\u201c\u8bed\u4e49\u65b9\u5411\u201d\u7684\u57fa\u7840\u4e0a\uff0c\u53e0\u52a0\u4e86\u4e00\u4e2a\u201c\u4f4d\u7f6e\u65b9\u5411\u201d\u3002\u4e24\u8005\u4e92\u4e0d\u5e72\u6270\uff0c\u5374\u5728 Attention \u7684\u8ba1\u7b97\u4e2d\u81ea\u7136\u5730\u878d\u5408\u5728\u4e00\u8d77\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48 RoPE \u88ab\u8ba4\u4e3a\u662f\u201c\u6700\u786c\u6838\u3001\u5f71\u54cd\u6700\u6df1\u8fdc\u7684\u6570\u5b66\u521b\u65b0\u201d\u4e4b\u4e00\u2014\u2014\u5b83\u7528\u7b80\u5355\u7684\u65cb\u8f6c\u64cd\u4f5c\uff0c\u628a\u76f8\u5bf9\u4f4d\u7f6e\u4fe1\u606f\u65e0\u7f1d\u5730\u7ec7\u5165\u4e86 Attention \u7684\u9aa8\u67b6\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.5 \u5de5\u7a0b\u5b9e\u73b0\uff1a\u5982\u4f55\u9ad8\u6548\u5730\u201c\u65cb\u8f6c\u201d\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7406\u8bba\u8bf4\u5b8c\u4e86\uff0c\u5b9e\u9645\u4ee3\u7801\u600e\u4e48\u5199\uff1f\u73b0\u4ee3 LLM \u901a\u5e38\u7528\u9884\u8ba1\u7b97\u7684 sin\/cos \u8868\u6765\u9ad8\u6548\u5b9e\u73b0 RoPE\u3002\u6838\u5fc3\u903b\u8f91\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>def apply_rope(x, cos, sin):\n    \"\"\"\n    \u5bf9\u8f93\u5165\u5411\u91cf x \u5e94\u7528\u65cb\u8f6c\u4f4d\u7f6e\u7f16\u7801\u3002\n    x: &#91;batch, heads, seq_len, head_dim]\n    cos, sin: \u9884\u8ba1\u7b97\u597d\u7684\u4e09\u89d2\u51fd\u6570\u503c\n    \"\"\"\n    # \u5c06\u7279\u5f81\u7ef4\u5ea6\u62c6\u6210\u4e24\u534a\uff0c\u914d\u5bf9\u65cb\u8f6c\n    half_dim = x.shape&#91;-1] \/\/ 2\n    x1, x2 = x&#91;..., :half_dim], x&#91;..., half_dim:]\n\n    # \u65cb\u8f6c\uff1a\u628a (x1, x2) \u53d8\u6210 (-x2, x1) \u518d\u4e58\u4e0a sin\/cos\n    rotated = torch.cat((-x2, x1), dim=-1)\n    return (x * cos) + (rotated * sin)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u6bb5\u4ee3\u7801\u7684\u7cbe\u9ad3\u5728\u4e8e\uff1a<code>(-x2, x1)<\/code> \u8fd9\u4e00\u6b65\u5c31\u662f\u590d\u6570\u65cb\u8f6c\u7684\u5b9e\u6570\u7248\u672c\u3002\u4e58\u4ee5 cos \u548c sin \u540e\uff0c\u76f8\u5f53\u4e8e\u5728\u6bcf\u4e00\u5bf9\u7279\u5f81\u7ef4\u5ea6\u4e0a\u65bd\u52a0\u4e86\u65cb\u8f6c\u89d2\u5ea6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u5b9e\u9645\u7684 LLM \u63a8\u7406\u4e2d\uff0ccos \u548c sin \u662f\u9884\u5148\u8ba1\u7b97\u597d\u5e76\u7f13\u5b58\u7684\uff0c\u6240\u4ee5\u6bcf\u6b21 Attention \u8ba1\u7b97\u65f6\u53ea\u9700\u8981\u505a\u4e00\u6b21\u5143\u7d20\u4e58\u6cd5\u548c\u52a0\u6cd5\u2014\u2014\u8ba1\u7b97\u5f00\u9500\u975e\u5e38\u5c0f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.6 \u5bf9\u6bd4\u89c6\u89d2\uff1aRoPE vs \u5176\u4ed6\u4f4d\u7f6e\u7f16\u7801<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u8ba9\u4f60\u5bf9 RoPE \u7684\u4ef7\u503c\u6709\u66f4\u76f4\u89c2\u7684\u7406\u89e3\uff0c\u6211\u4eec\u628a\u5b83\u548c\u5176\u4ed6\u4e3b\u6d41\u65b9\u6848\u653e\u5728\u4e00\u8d77\u5bf9\u6bd4\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u65b9\u6cd5<\/th><th>\u7c7b\u578b<\/th><th>\u5916\u63a8\u80fd\u529b<\/th><th>\u8ba1\u7b97\u6548\u7387<\/th><th>\u4ee3\u8868\u6a21\u578b<\/th><th>\u6838\u5fc3\u7279\u70b9<\/th><\/tr><\/thead><tbody><tr><td><strong>\u53ef\u5b66\u4e60\u4f4d\u7f6e\u7f16\u7801<\/strong><\/td><td>\u7edd\u5bf9<\/td><td>\u5dee<\/td><td>\u9ad8<\/td><td>\u65e9\u671f GPT<\/td><td>\u7b80\u5355\uff0c\u4f46\u957f\u5ea6\u56fa\u5b9a<\/td><\/tr><tr><td><strong>Sinusoidal<\/strong><\/td><td>\u7edd\u5bf9<\/td><td>\u4e2d<\/td><td>\u9ad8<\/td><td>\u539f\u59cb Transformer<\/td><td>\u65e0\u9700\u8bad\u7ec3\uff0c\u4f46\u5916\u63a8\u6709\u9650<\/td><\/tr><tr><td><strong>RoPE<\/strong><\/td><td>\u76f8\u5bf9<\/td><td>\u597d<\/td><td>\u4e2d<\/td><td>LLaMA, Qwen, ChatGLM<\/td><td>\u65cb\u8f6c\u64cd\u4f5c\uff0c\u5929\u7136\u7f16\u7801\u76f8\u5bf9\u4f4d\u7f6e<\/td><\/tr><tr><td><strong>ALiBi<\/strong><\/td><td>\u76f8\u5bf9<\/td><td>\u6781\u597d<\/td><td>\u9ad8<\/td><td>BLOOM, MPT<\/td><td>\u76f4\u63a5\u5728 Attention \u5206\u6570\u4e0a\u52a0\u7ebf\u6027\u504f\u7f6e<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">RoPE \u4e0d\u662f\u552f\u4e00\u7684\u9009\u62e9\u3002<strong>ALiBi\uff08Attention with Linear Biases\uff09<\/strong> \u662f\u53e6\u4e00\u79cd\u975e\u5e38\u6709\u8da3\u7684\u65b9\u6cd5\u2014\u2014\u5b83\u4e0d\u5728 Embedding \u5c42\u9762\u505a\u4efb\u4f55\u5904\u7406\uff0c\u800c\u662f\u76f4\u63a5\u5728 Attention \u5206\u6570\u77e9\u9635\u4e0a\u52a0\u4e0a\u4e00\u4e2a\u4e0e\u8ddd\u79bb\u6210\u6b63\u6bd4\u7684\u60e9\u7f5a\u9879\uff1a\u8ddd\u79bb\u8d8a\u8fdc\uff0cAttention \u5206\u6570\u6263\u5f97\u8d8a\u591a\u3002\u8fd9\u79cd\u65b9\u5f0f\u8ba1\u7b97\u6781\u5176\u9ad8\u6548\uff0c\u4e14\u5916\u63a8\u80fd\u529b\u751a\u81f3\u6bd4 RoPE \u66f4\u5f3a\u3002\u4e0d\u8fc7 RoPE \u5728\u6355\u6349\u590d\u6742\u4f4d\u7f6e\u6a21\u5f0f\u4e0a\u901a\u5e38\u8868\u73b0\u66f4\u597d\uff0c\u56e0\u6b64\u5728\u9700\u8981\u66f4\u5f3a\u4f4d\u7f6e\u611f\u77e5\u80fd\u529b\u7684\u751f\u6210\u6a21\u578b\u4e2d\u66f4\u53d7\u6b22\u8fce\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4e3a\u4ec0\u4e48\u73b0\u4ee3 LLM \u7eb7\u7eb7\u4ece\u53ef\u5b66\u4e60\u7edd\u5bf9\u4f4d\u7f6e\u7f16\u7801\u8f6c\u5411 RoPE\uff1f<\/strong> \u539f\u56e0\u5f88\u6e05\u6670\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u66f4\u597d\u5730\u6355\u6349\u76f8\u5bf9\u8ddd\u79bb<\/strong>\uff1a\u8bed\u8a00\u7406\u89e3\u66f4\u591a\u4f9d\u8d56\u201c\u4e24\u4e2a\u8bcd\u76f8\u9694\u591a\u8fdc\u201d\uff0c\u800c\u975e\u5b83\u4eec\u7684\u7edd\u5bf9\u4f4d\u7f6e\u5e8f\u53f7<\/li>\n\n\n\n<li><strong>\u66f4\u597d\u7684\u957f\u4e0a\u4e0b\u6587\u8868\u73b0<\/strong>\uff1aRoPE \u53ef\u4ee5\u66f4\u81ea\u7136\u5730\u6269\u5c55\u5230\u8bad\u7ec3\u65f6\u672a\u89c1\u8fc7\u7684\u957f\u5ea6<\/li>\n\n\n\n<li><strong>\u66f4\u4f18\u96c5\u5730\u4e0e Attention \u96c6\u6210<\/strong>\uff1a\u4f4d\u7f6e\u4fe1\u606f\u88ab\u6ce8\u5165\u5230\u4e86 Attention \u6700\u6838\u5fc3\u7684 Q\u00b7K \u8ba1\u7b97\u4e2d\uff0c\u800c\u975e\u7b80\u5355\u5730\u52a0\u5728\u8f93\u5165\u4e0a<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">2.7 LLaMA \u4e2d\u7684 RoPE\uff1a\u4e00\u4e2a\u5c0f\u7ec6\u8282<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">LLaMA \u7cfb\u5217\u5bf9 RoPE \u505a\u4e86\u4e00\u5904\u7ec6\u8282\u4f18\u5316\uff1a<strong>\u53ea\u5bf9 Query \u548c Key \u5e94\u7528\u65cb\u8f6c\uff0cValue \u4fdd\u6301\u4e0d\u53d8<\/strong>\u3002\u8fd9\u662f\u56e0\u4e3a\u76f8\u5bf9\u4f4d\u7f6e\u4fe1\u606f\u53ea\u5728\u8ba1\u7b97 Attention \u5206\u6570\uff08Q\u00b7K\uff09\u65f6\u624d\u9700\u8981\u2014\u2014Value \u5411\u91cf\u53ea\u8d1f\u8d23\u627f\u8f7d\u5b9e\u9645\u7684\u8bed\u4e49\u5185\u5bb9\uff0c\u4e0d\u53c2\u4e0e\u4f4d\u7f6e\u5224\u65ad\u3002\u6b64\u5916\uff0cLLaMA \u8fd8\u91c7\u7528\u4e86<strong>RMSNorm + Pre-Norm<\/strong> \u7684\u7ec4\u5408\u6765\u7a33\u5b9a\u6df1\u5c42\u7f51\u7edc\u7684\u8bad\u7ec3\uff0c\u4e0e RoPE \u642d\u914d\u4f7f\u7528\uff0c\u8ba9\u6a21\u578b\u5728\u5904\u7406\u957f\u5e8f\u5217\u65f6\u66f4\u52a0\u7a33\u5065\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e09\u3001\u524d\u6cbf\u63a2\u7d22\uff1aRoPE \u4e4b\u540e\uff0c\u4f4d\u7f6e\u7f16\u7801\u8d70\u5411\u4f55\u65b9\uff1f<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">RoPE \u867d\u7136\u597d\u7528\uff0c\u4f46\u5e76\u975e\u5b8c\u7f8e\u3002\u968f\u7740 LLM \u7684\u4e0a\u4e0b\u6587\u7a97\u53e3\u4ece 4K \u4e00\u8def\u98d9\u5230 1M\u30012M\uff0cRoPE \u7684\u5c40\u9650\u6027\u4e5f\u9010\u6e10\u66b4\u9732\u3002\u5f53\u524d\u7684\u4f4d\u7f6e\u7f16\u7801\u7814\u7a76\u4e3b\u8981\u6cbf\u7740\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u5411\u63a8\u8fdb\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 RoPE \u7684\u201c\u5929\u82b1\u677f\u201d\uff1a\u4e3a\u4ec0\u4e48\u8d85\u957f\u4e0a\u4e0b\u6587\u4f1a\u5931\u6548\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">RoPE \u7684\u65cb\u8f6c\u9891\u7387\u662f\u7531\u4e00\u7ec4\u9884\u8bbe\u7684\u57fa\u9891\uff08\u901a\u5e38\u4e3a 10000\uff09\u51b3\u5b9a\u7684\u3002\u5f53\u5e8f\u5217\u957f\u5ea6\u8fdc\u8fdc\u8d85\u8fc7\u8bad\u7ec3\u65f6\u7684\u957f\u5ea6\uff0c\u9ad8\u9891\u7684\u65cb\u8f6c\u4f1a\u53d8\u5f97\u8fc7\u4e8e\u5bc6\u96c6\uff0c\u4f4e\u9891\u7684\u65cb\u8f6c\u5219\u4f1a\u53d8\u5f97\u8fc7\u4e8e\u7a00\u758f\uff0c\u5bfc\u81f4\u6a21\u578b\u5bf9\u957f\u8ddd\u79bb\u4f4d\u7f6e\u7684\u611f\u77e5\u80fd\u529b\u4e0b\u964d\u3002\u8fd1\u5e74\u6765\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u591a\u79cd<strong>\u9891\u7387\u7f29\u653e\uff08Frequency Scaling\uff09<\/strong> \u6280\u672f\u6765\u7f13\u89e3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6bd4\u5982 YaRN\u3001NTK \u7f29\u653e\u7b49\uff0c\u4f46\u5b83\u4eec\u672c\u8d28\u4e0a\u8fd8\u662f\u5728 RoPE \u7684\u6846\u67b6\u5185\u201c\u4fee\u4fee\u8865\u8865\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u7bc7 2025 \u5e74\u7684\u7814\u7a76\u63d0\u51fa\u4e86 <strong>HoPE\uff08Hyperbolic Rotary Positional Encoding\uff09<\/strong> \uff0c\u4ece\u6570\u5b66\u4e0a\u91cd\u65b0\u8bbe\u8ba1\u4e86\u65cb\u8f6c\u7684\u51e0\u4f55\u7a7a\u95f4\uff08\u4ece\u6b27\u6c0f\u7a7a\u95f4\u5207\u6362\u5230\u53cc\u66f2\u7a7a\u95f4\uff09\uff0c\u8bd5\u56fe\u4ece\u6839\u672c\u4e0a\u89e3\u51b3 RoPE \u5728\u8d85\u957f\u8ddd\u79bb\u4e0a\u7684\u632f\u8361\u548c\u4e0d\u7a33\u5b9a\u95ee\u9898\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 \u6700\u6fc0\u8fdb\u7684\u60f3\u6cd5\uff1a\u4f4d\u7f6e\u7f16\u7801\u4e5f\u8bb8\u6839\u672c\u4e0d\u9700\u8981\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u4e2a\u8ba9\u4eba\u91cd\u65b0\u601d\u8003 RoPE \u6839\u672c\u4f5c\u7528\u7684\u65b0\u65b9\u6cd5\u662f <strong>DroPE\uff08Drop Positional Embeddings\uff09<\/strong> \uff0c\u7531 Sakana AI \u56e2\u961f\u63d0\u51fa\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ed6\u4eec\u7684\u6838\u5fc3\u6d1e\u5bdf\u662f\uff1a<strong>RoPE \u5728\u8bad\u7ec3\u9636\u6bb5\u5bf9\u4e8e\u6536\u655b\u81f3\u5173\u91cd\u8981\uff0c\u4f46\u5728\u63a8\u7406\u65f6\u5374\u6210\u4e86\u957f\u5ea6\u5916\u63a8\u7684\u74f6\u9888<\/strong>\u3002\u5b9e\u9a8c\u8bc1\u660e\uff0c\u6ca1\u6709\u663e\u5f0f\u4f4d\u7f6e\u7f16\u7801\u7684 Transformer\uff08NoPE\uff09\u5728\u7406\u8bba\u4e0a\u62e5\u6709\u66f4\u597d\u7684\u957f\u5ea6\u6cdb\u5316\u80fd\u529b\uff0c\u4f46\u8bad\u7ec3\u6781\u4e0d\u7a33\u5b9a\uff0c\u96be\u4ee5\u6536\u655b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">DroPE \u7684\u7b56\u7565\u662f\u201c\u8fc7\u6cb3\u62c6\u6865\u201d\uff1a<strong>\u8bad\u7ec3\u65f6\u6b63\u5e38\u4f7f\u7528 RoPE \u4fdd\u8bc1\u6536\u655b\uff0c\u8bad\u7ec3\u7ed3\u675f\u540e\uff0c\u7528\u4e0d\u5230\u539f\u59cb\u9884\u8bad\u7ec3 1% \u7684\u8ba1\u7b97\u91cf\u8fdb\u884c\u4e00\u6b21\u8f7b\u91cf\u201c\u91cd\u6821\u51c6\u201d\uff0c\u7136\u540e\u76f4\u63a5\u4e22\u5f03\u4f4d\u7f6e\u7f16\u7801<\/strong>\u3002\u5728 LongBench \u7b49\u957f\u6587\u672c\u57fa\u51c6\u4e0a\uff0c\u8fd9\u79cd\u7b80\u5355\u7c97\u66b4\u7684\u65b9\u6cd5\u751a\u81f3\u8d85\u8d8a\u4e86\u4e13\u95e8\u4e3a\u957f\u6587\u672c\u8bbe\u8ba1\u7684\u590d\u6742\u67b6\u6784\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u80cc\u540e\u7684\u6df1\u5c42\u542b\u4e49\u5728\u4e8e\uff1a<strong>\u4f4d\u7f6e\u7f16\u7801\u53ef\u80fd\u53ea\u662f\u5e2e\u52a9\u6a21\u578b\u5728\u65e9\u671f\u5b66\u4f1a\u5173\u6ce8\u8ddd\u79bb\u5173\u7cfb\u7684\u201c\u8bad\u7ec3\u8f85\u52a9\u8f6e\u201d\uff0c\u800c\u975e\u6a21\u578b\u7406\u89e3\u987a\u5e8f\u7684\u6c38\u4e45\u5fc5\u9700\u54c1\u3002<\/strong> \u4e00\u65e6\u6a21\u578b\u5b66\u4f1a\u4e86\u5982\u4f55\u5229\u7528 Attention \u7684\u5185\u5728\u7ed3\u6784\u6765\u611f\u77e5\u987a\u5e8f\uff0c\u8fd9\u4e9b\u663e\u5f0f\u7f16\u7801\u5c31\u53ef\u4ee5\u201c\u529f\u6210\u8eab\u9000\u201d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.3 \u66f4\u9ad8\u9636\u7684\u6570\u5b66\uff1a\u7528\u674e\u7fa4\u548c\u674e\u4ee3\u6570\u7edf\u4e00 RoPE<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u7bc7 2025 \u5e74\u7684\u7406\u8bba\u7814\u7a76\u300aRethinking RoPE: A Mathematical Blueprint for N-dimensional Positional Embedding\u300b\u6307\u51fa\uff1a<strong>\u73b0\u6709\u7684 RoPE \u53d8\u4f53\u7f3a\u4e4f\u7edf\u4e00\u7684\u7406\u8bba\u57fa\u7840\uff0c\u5c24\u5176\u662f\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u63a8\u5e7f<\/strong>\u3002\u7814\u7a76\u8005\u57fa\u4e8e<strong>\u674e\u7fa4\u548c\u674e\u4ee3\u6570<\/strong>\u7406\u8bba\uff0c\u4e3a RoPE \u5efa\u7acb\u4e86\u4e00\u5957\u7cfb\u7edf\u7684\u6570\u5b66\u6846\u67b6\uff0c\u4f7f\u5176\u80fd\u591f\u81ea\u7136\u5730\u63a8\u5e7f\u5230\u4efb\u610f\u7ef4\u5ea6\uff0c\u5e76\u5728\u7406\u8bba\u4e0a\u8bc1\u660e\u4e86\u4e00\u4e9b\u73b0\u6709 RoPE \u53d8\u4f53\uff08\u5982 2D RoPE\uff09\u7684\u5c40\u9650\u6027\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9879\u5de5\u4f5c\u867d\u7136\u7406\u8bba\u8272\u5f69\u6d53\u539a\uff0c\u4f46\u5b83\u4f20\u9012\u4e86\u4e00\u4e2a\u91cd\u8981\u4fe1\u53f7\uff1a<strong>RoPE \u6b63\u5728\u4ece\u7ecf\u9a8c\u6027\u7684\u5de5\u7a0b\u521b\u65b0\uff0c\u9010\u6b65\u6f14\u53d8\u4e3a\u6709\u575a\u5b9e\u6570\u5b66\u6839\u57fa\u7684\u7406\u8bba\u4f53\u7cfb<\/strong>\u3002\u8fd9\u5bf9\u672a\u6765\u8bbe\u8ba1\u66f4\u5f3a\u5927\u3001\u66f4\u53ef\u63a7\u7684\u4f4d\u7f6e\u7f16\u7801\u81f3\u5173\u91cd\u8981\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.4 \u56db\u5143\u6570 RoPE\uff1a\u628a\u65cb\u8f6c\u4ece 2D \u6269\u5c55\u5230 3D<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e2\u7136 RoPE \u7684\u6838\u5fc3\u662f\u201c\u65cb\u8f6c\u201d\uff0c\u90a3\u80fd\u4e0d\u80fd\u7528\u66f4\u5f3a\u5927\u7684\u6570\u5b66\u5de5\u5177\u6765\u8868\u793a\u65cb\u8f6c\uff1f<strong>QuatRo\uff08Quaternion Rotary Embeddings\uff09<\/strong> \u5c1d\u8bd5\u7528<strong>\u56db\u5143\u6570<\/strong>\u6765\u66ff\u4ee3\u4f20\u7edf\u7684 2D \u65cb\u8f6c\u2014\u2014\u56db\u5143\u6570\u662f\u8868\u793a 3D \u65cb\u8f6c\u7684\u6807\u51c6\u5de5\u5177\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\u5e7f\u6cdb\u4f7f\u7528\u3002\u8fd9\u4e2a\u65b9\u5411\u7684\u63a2\u7d22\u8fd8\u5728\u65e9\u671f\uff0c\u4f46\u5b83\u6697\u793a\u4e86\u4f4d\u7f6e\u7f16\u7801\u53ef\u80fd\u4e0d\u9650\u4e8e\u4e00\u7ef4\u5e8f\u5217\u2014\u2014\u672a\u6765\u6216\u8bb8\u4f1a\u770b\u5230\u4e3a\u89c6\u9891\uff08\u65f6\u95f4+\u7a7a\u95f4\uff09\u30013D \u6a21\u578b\u7b49\u8bbe\u8ba1\u7684\u591a\u7ef4\u4f4d\u7f6e\u7f16\u7801\u65b9\u6848\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.5 \u4f4d\u7f6e\u7f16\u7801\u7684\u7406\u8bba\u5316\uff1a\u4e3a\u4ec0\u4e48\u6709\u4e9b\u65b9\u6cd5\u66f4\u597d\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2025 \u5e74 6 \u6708\uff0c\u4e00\u7bc7\u91cd\u8981\u7684\u7406\u8bba\u8bba\u6587\u7cfb\u7edf\u5206\u6790\u4e86\u5404\u7c7b\u4f4d\u7f6e\u7f16\u7801\uff08Sinusoidal\u3001\u53ef\u5b66\u4e60\u3001\u76f8\u5bf9\u3001ALiBi \u7b49\uff09\u5bf9 Transformer <strong>\u8868\u8fbe\u80fd\u529b\u3001\u6cdb\u5316\u80fd\u529b\u548c\u957f\u5ea6\u5916\u63a8\u80fd\u529b<\/strong> \u7684\u5f71\u54cd\u3002\u7814\u7a76\u8005\u4f7f\u7528 Rademacher \u590d\u6742\u5ea6\u5206\u6790\u7b49\u5de5\u5177\uff0c\u9996\u6b21\u7ed9\u51fa\u4e86\u4e0d\u540c\u7f16\u7801\u65b9\u6848\u5728\u6cdb\u5316\u8bef\u5dee\u4e0a\u7684\u7406\u8bba\u754c\u9650\uff0c\u5e76\u63d0\u51fa\u4e86\u4e00\u4e9b\u57fa\u4e8e\u6b63\u4ea4\u51fd\u6570\u65cf\uff08\u5982\u5c0f\u6ce2\u3001\u52d2\u8ba9\u5fb7\u591a\u9879\u5f0f\uff09\u7684\u65b0\u578b\u4f4d\u7f6e\u7f16\u7801\u65b9\u6848\u3002\u8fd9\u7c7b\u5de5\u4f5c\u6b63\u5728\u586b\u8865 Transformer \u7406\u8bba\u4e2d\u7684\u4e00\u5757\u91cd\u8981\u7a7a\u767d\u2014\u2014<strong>\u6211\u4eec\u4e0d\u518d\u53ea\u662f\u201c\u8bd5\u51fa\u6765\u201d\u54ea\u79cd\u4f4d\u7f6e\u7f16\u7801\u597d\u7528\uff0c\u800c\u662f\u5f00\u59cb\u771f\u6b63\u201c\u7406\u89e3\u201d\u5b83\u4eec\u4e3a\u4ec0\u4e48\u597d\u7528\u3002<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.6 \u591a\u6a21\u6001\u4e2d\u7684\u4f4d\u7f6e\u7f16\u7801\u65b0\u6218\u573a<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u968f\u7740\u591a\u6a21\u6001\u5927\u6a21\u578b\u7684\u5174\u8d77\uff0c\u4f4d\u7f6e\u7f16\u7801\u4e5f\u9762\u4e34\u65b0\u7684\u6311\u6218\u30022D RoPE \u88ab\u7528\u4e8e\u89c6\u89c9 Transformer \u4e2d\uff0c\u5e2e\u52a9\u6a21\u578b\u7406\u89e3\u56fe\u50cf\u5757\u4e4b\u95f4\u7684\u7a7a\u95f4\u4f4d\u7f6e\u5173\u7cfb\u3002\u5982\u4f55\u5728\u540c\u4e00\u4e2a\u6a21\u578b\u4e2d\u7edf\u4e00\u5904\u7406\u6587\u672c\u7684 1D \u5e8f\u5217\u4f4d\u7f6e\u3001\u56fe\u50cf\u7684 2D \u7a7a\u95f4\u4f4d\u7f6e\u3001\u89c6\u9891\u7684\u65f6\u7a7a\u4f4d\u7f6e\uff0c\u662f\u591a\u6a21\u6001\u4f4d\u7f6e\u7f16\u7801\u7814\u7a76\u7684\u524d\u6cbf\u8bfe\u9898\u3002\u672a\u6765\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u770b\u5230\u4f4d\u7f6e\u7f16\u7801\u4ece\u201c\u8bed\u8a00\u4e13\u5c5e\u201d\u8d70\u5411\u201c\u901a\u7528\u4f4d\u7f6e\u611f\u77e5\u201d\uff0c\u4e3a\u89c6\u89c9\u3001\u8bed\u97f3\u30013D \u7b49\u591a\u6a21\u6001\u7406\u89e3\u63d0\u4f9b\u7edf\u4e00\u7684\u4f4d\u7f6e\u8868\u793a\u6846\u67b6\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u56db\u3001\u603b\u7ed3\u4e0e\u5c55\u671b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 Embedding \u4e0e RoPE\uff1a\u4e00\u5f20\u201c\u8bed\u4e49\u5730\u56fe\u201d\u548c\u4e00\u652f\u201c\u65f6\u5e8f\u5bfc\u822a\u4eea\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b Embedding \u548c RoPE \u5404\u81ea\u626e\u6f14\u7684\u89d2\u8272\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Embedding<\/strong>\uff1a\u628a\u6bcf\u4e2a Token \u53d8\u6210\u4e00\u4e2a\u9ad8\u7ef4\u5411\u91cf\u3002\u8fd9\u4e2a\u5411\u91cf\u662f Token \u5728\u201c\u8bed\u4e49\u7a7a\u95f4\u201d\u4e2d\u7684\u5750\u6807\u2014\u2014\u8bed\u4e49\u76f8\u8fd1\u7684\u8bcd\uff0c\u5750\u6807\u4e5f\u76f8\u8fd1\u3002\u5b83\u662f\u6a21\u578b\u7406\u89e3\u8bed\u8a00\u7684\u57fa\u7840\u5730\u56fe\u3002<\/li>\n\n\n\n<li><strong>RoPE<\/strong>\uff1a\u7ed9\u6bcf\u4e2a\u5411\u91cf\u52a0\u4e0a\u201c\u4f4d\u7f6e\u65b9\u5411\u201d\u3002\u901a\u8fc7\u5bf9\u5411\u91cf\u8fdb\u884c\u65cb\u8f6c\uff0c\u8ba9 Attention \u8ba1\u7b97\u65f6\u5929\u7136\u5305\u542b\u76f8\u5bf9\u4f4d\u7f6e\u4fe1\u606f\u3002\u5b83\u662f\u6a21\u578b\u7684\u65f6\u5e8f\u5bfc\u822a\u4eea\uff0c\u8ba9\u6a21\u578b\u77e5\u9053\u8bcd\u8bed\u4e4b\u95f4\u7684\u5148\u540e\u987a\u5e8f\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e24\u8005\u914d\u5408\u5728\u4e00\u8d77\uff0c\u624d\u80fd\u8ba9\u6a21\u578b\u65e2\u77e5\u9053\u201c\u8bcd\u662f\u4ec0\u4e48\u610f\u601d\u201d\uff0c\u53c8\u77e5\u9053\u201c\u8bcd\u5728\u54ea\u91cc\u201d\u2014\u2014\u7f3a\u4e86\u4efb\u4f55\u4e00\u4e2a\uff0c\u6a21\u578b\u90fd\u4f1a\u53d8\u6210\u201c\u6709\u8bed\u4e49\u4f46\u4e71\u5e8f\u201d\u6216\u8005\u201c\u6709\u987a\u5e8f\u4f46\u4e0d\u61c2\u8bcd\u201d\u7684\u534a\u6210\u54c1\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 \u6570\u636e\u6d41\u56de\u987e<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ed3\u5408\u6211\u4eec\u524d\u9762\u4e09\u7bc7\u6587\u7ae0\u7684\u5185\u5bb9\uff0c\u5b8c\u6574\u7684\u6570\u636e\u6d41\u662f\u8fd9\u6837\u7684\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Tokenizer<\/strong> \u2192 \u628a\u539f\u59cb\u6587\u672c\u5207\u6210 Token\uff0c\u6620\u5c04\u4e3a\u6570\u5b57 ID<\/li>\n\n\n\n<li><strong>Embedding<\/strong> \u2192 \u628a\u6bcf\u4e2a ID \u8f6c\u6210\u4e00\u4e2a\u9ad8\u7ef4\u5411\u91cf\uff08\u8bed\u4e49\u5750\u6807\uff09<\/li>\n\n\n\n<li><strong>RoPE<\/strong> \u2192 \u5bf9 Query \u548c Key \u5411\u91cf\u65bd\u52a0\u65cb\u8f6c\u64cd\u4f5c\uff0c\u6ce8\u5165\u76f8\u5bf9\u4f4d\u7f6e\u4fe1\u606f<\/li>\n\n\n\n<li><strong>Transformer \u5c42<\/strong> \u2192 Attention\uff08\u8ba9\u8bcd\u4e4b\u95f4\u201c\u4ea4\u6d41\u201d\uff09+ FFN\uff08\u5b58\u50a8\u548c\u52a0\u5de5\u77e5\u8bc6\uff09<\/li>\n\n\n\n<li><strong>\u8f93\u51fa\u5c42<\/strong> \u2192 \u9884\u6d4b\u4e0b\u4e00\u4e2a Token\uff0c\u5982\u6b64\u5faa\u73af<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">4.3 \u5173\u952e\u516c\u5f0f\u901f\u67e5<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u6982\u5ff5<\/th><th>\u516c\u5f0f\/\u6838\u5fc3\u601d\u60f3<\/th><\/tr><\/thead><tbody><tr><td><strong>Embedding \u53c2\u6570\u91cf<\/strong><\/td><td>V \u00d7 d\uff08\u8bcd\u8868\u5927\u5c0f \u00d7 \u7ef4\u5ea6\uff09<\/td><\/tr><tr><td><strong>RoPE \u65cb\u8f6c<\/strong><\/td><td>\u5c06 (x\u2081, x\u2082) \u53d8\u4e3a (cos\u00b7x\u2081 &#8211; sin\u00b7x\u2082, sin\u00b7x\u2081 + cos\u00b7x\u2082)<\/td><\/tr><tr><td><strong>RoPE \u6838\u5fc3\u6027\u8d28<\/strong><\/td><td>\u65cb\u8f6c\u540e Q\u00b7K \u7684\u7ed3\u679c\u53ea\u4f9d\u8d56\u4e8e\u76f8\u5bf9\u4f4d\u7f6e\u5dee<\/td><\/tr><tr><td><strong>LLaMA \u4f7f\u7528\u65b9\u5f0f<\/strong><\/td><td>\u53ea\u5bf9 Q \u548c K \u5e94\u7528 RoPE\uff0cV \u4fdd\u6301\u4e0d\u53d8<\/td><\/tr><tr><td><strong>RoPE \u57fa\u9891<\/strong><\/td><td>\u901a\u5e38\u4e3a 10000\uff0c\u51b3\u5b9a\u65cb\u8f6c\u7684\u89d2\u5ea6\u6b65\u957f<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u5199\u5728\u524d\u9762 \u5728\u524d\u4e24\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5206\u522b\u62c6\u89e3\u4e86 LLM \u7684\u6574\u4f53\u67b6\u6784\uff0c\u53c8\u4e13\u95e8\u6df1\u6316\u4e86 Tokenizer\u3002\u73b0\u5728\uff0c\u6211\u4eec\u5df2\u7ecf [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":127,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[40,37,39],"class_list":["post-125","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mtsb","tag-embedding","tag-llm","tag-rope"],"_links":{"self":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts\/125","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=125"}],"version-history":[{"count":2,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts\/125\/revisions"}],"predecessor-version":[{"id":128,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/posts\/125\/revisions\/128"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/media\/127"}],"wp:attachment":[{"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=125"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=125"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bojinhu.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}