{"id":98822,"date":"2026-09-01T13:56:50","date_gmt":"2026-09-01T05:56:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/98822.html"},"modified":"2026-09-01T13:56:50","modified_gmt":"2026-09-01T05:56:50","slug":"%e5%a4%a7%e8%af%ad%e8%a8%80%e6%a8%a1%e5%9e%8b%e5%9f%ba%e7%a1%80%ef%bc%9atoken%e3%80%81embedding%e3%80%81transformer%e3%80%81kv-cache-%e4%b8%8e-rag","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/98822.html","title":{"rendered":"\u5927\u8bed\u8a00\u6a21\u578b\u57fa\u7840\uff1aToken\u3001Embedding\u3001Transformer\u3001KV Cache \u4e0e RAG"},"content":{"rendered":"<h3>1. \u6574\u4f53\u77e5\u8bc6\u6846\u67b6<\/h3>\n<p>\u7406\u89e3\u5927\u8bed\u8a00\u6a21\u578b&#xff0c;\u53ef\u4ee5\u5148\u8bb0\u4f4f\u4e24\u6761\u4e3b\u7ebf&#xff1a;<\/p>\n<h4>LLM \u751f\u6210\u4e3b\u7ebf<\/h4>\n<p>\u6587\u5b57<br \/>\n \u2193<br \/>\nTokenizer<br \/>\n \u2193<br \/>\nToken<br \/>\n \u2193<br \/>\nToken ID<br \/>\n \u2193<br \/>\nEmbedding Table<br \/>\n \u2193<br \/>\n\u6bcf\u4e2a Token \u4e00\u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf<br \/>\n \u2193<br \/>\n\u52a0\u5165\u4f4d\u7f6e\u4fe1\u606f<br \/>\n \u2193<br \/>\n\u591a\u5c42 Transformer<br \/>\n \u2193<br \/>\n\u6bcf\u4e2a Token \u5f97\u5230\u4e0a\u4e0b\u6587\u5316 Hidden State<br \/>\n \u2193<br \/>\n\u53d6\u5f53\u524d\u6700\u540e\u4f4d\u7f6e\u7684 Hidden State<br \/>\n \u2193<br \/>\nLM Head<br \/>\n \u2193<br \/>\nVocabulary Logits<br \/>\n \u2193<br \/>\n\u9009\u62e9\u4e0b\u4e00\u4e2a Token<br \/>\n \u2193<br \/>\nKV Cache &#043; Decode<br \/>\n \u2193<br \/>\n\u7ee7\u7eed\u9884\u6d4b\u4e0b\u4e00\u4e2a Token<br \/>\n \u2193<br \/>\n\u6700\u7ec8\u56de\u7b54<\/p>\n<h4>RAG \u68c0\u7d22\u4e3b\u7ebf<\/h4>\n<p>\u6587\u6863<br \/>\n \u2193<br \/>\nChunk \u5207\u5206<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\n\u6bcf\u4e2a Chunk \u4e00\u4e2a\u9ad8\u7ef4\u8bed\u4e49\u5411\u91cf<br \/>\n \u2193<br \/>\nVector Database<\/p>\n<p>\u7528\u6237\u95ee\u9898<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\nQuery Vector<br \/>\n \u2193<br \/>\nCosine Similarity \/ Euclidean Distance \/ Dot Product<br \/>\n \u2193<br \/>\nTop-K<br \/>\n \u2193<br \/>\n\u627e\u5230\u6700\u76f8\u5173\u7684 Chunks<br \/>\n \u2193<br \/>\n\u7528\u6237\u95ee\u9898 &#043; \u68c0\u7d22\u7ed3\u679c<br \/>\n \u2193<br \/>\nLLM<br \/>\n \u2193<br \/>\n\u6700\u7ec8\u56de\u7b54<\/p>\n<hr \/>\n<h2>2. Token \u662f\u4ec0\u4e48&#xff1f;<\/h2>\n<p>\u5927\u8bed\u8a00\u6a21\u578b\u5e76\u4e0d\u662f\u76f4\u63a5\u4ee5\u201c\u6c49\u5b57\u201d\u6216\u8005\u201c\u82f1\u6587\u5355\u8bcd\u201d\u4e3a\u5355\u4f4d\u5904\u7406\u6587\u672c&#xff0c;\u800c\u662f\u5148\u901a\u8fc7 Tokenizer&#xff08;\u5206\u8bcd\u5668&#xff09; \u5c06\u6587\u672c\u5207\u5206\u6210\u4e00\u4e2a\u4e2a Token\u3002<\/p>\n<p>Token \u53ef\u4ee5\u7406\u89e3\u4e3a&#xff1a;<\/p>\n<p>\u6a21\u578b\u5904\u7406\u6587\u672c\u7684\u57fa\u672c\u79bb\u6563\u5355\u4f4d\u3002<\/p>\n<p>\u4e00\u4e2a Token \u53ef\u80fd\u662f&#xff1a;<\/p>\n<ul>\n<li>\u4e00\u4e2a\u6c49\u5b57<\/li>\n<li>\u591a\u4e2a\u6c49\u5b57\u7ec4\u6210\u7684\u7247\u6bb5<\/li>\n<li>\u4e00\u4e2a\u82f1\u6587\u5355\u8bcd<\/li>\n<li>\u4e00\u4e2a\u82f1\u6587\u5355\u8bcd\u7684\u4e00\u90e8\u5206<\/li>\n<li>\u6807\u70b9\u7b26\u53f7<\/li>\n<li>\u7a7a\u683c<\/li>\n<li>\u5176\u4ed6\u5b57\u7b26\u7247\u6bb5<\/li>\n<\/ul>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u539f\u59cb\u6587\u672c&#xff1a;<\/p>\n<p>\u6211\u7231\u4eba\u5de5\u667a\u80fd<\/p>\n<p>\u7ecf\u8fc7 Tokenizer \u540e\u53ef\u80fd\u5f97\u5230&#xff1a;<\/p>\n<p>[&#034;\u6211&#034;, &#034;\u7231&#034;, &#034;\u4eba\u5de5&#034;, &#034;\u667a\u80fd&#034;]<\/p>\n<p>\u4e5f\u53ef\u80fd\u4f7f\u7528\u5176\u4ed6\u5207\u5206\u65b9\u5f0f\u3002<\/p>\n<p>\u5177\u4f53\u5982\u4f55\u5207\u5206\u53d6\u51b3\u4e8e\u6a21\u578b\u4f7f\u7528\u7684 Tokenizer \u548c Vocabulary\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>Token \u2260 \u6c49\u5b57<br \/>\nToken \u2260 \u5355\u8bcd<br \/>\nToken \u662f Tokenizer \u6839\u636e\u81ea\u5df1\u7684\u8bcd\u8868\u548c\u89c4\u5219\u5207\u51fa\u6765\u7684\u6587\u672c\u5355\u4f4d\u3002<\/p>\n<hr \/>\n<h2>3. Token \u548c Token ID<\/h2>\n<p>Tokenizer \u4e0d\u4ec5\u8d1f\u8d23\u5207\u5206\u6587\u672c&#xff0c;\u8fd8\u4f1a\u6839\u636e\u81ea\u5df1\u7684 Vocabulary&#xff08;\u8bcd\u8868&#xff09;&#xff0c;\u5c06\u6bcf\u4e2a Token \u8f6c\u6362\u6210\u4e00\u4e2a\u6574\u6570\u7f16\u53f7\u3002<\/p>\n<p>\u8fd9\u4e2a\u6574\u6570\u5c31\u662f&#xff1a;<\/p>\n<p>Token ID<\/p>\n<p>\u4f8b\u5982\u5047\u8bbe&#xff1a;<\/p>\n<p>&#034;\u6211&#034;   \u2192 Token ID 1024<br \/>\n&#034;\u7231\u732b&#034; \u2192 Token ID 5837<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>&#034;\u6211\u7231\u732b&#034;<br \/>\n   \u2193<br \/>\nTokenizer<br \/>\n   \u2193<br \/>\n[&#034;\u6211&#034;, &#034;\u7231\u732b&#034;]<br \/>\n   \u2193<br \/>\n[1024, 5837]<\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<p>1024<br \/>\n5837<\/p>\n<p>\u5c31\u662f\u4e24\u4e2a Token ID\u3002<\/p>\n<p>\u53ef\u4ee5\u628a Vocabulary \u7406\u89e3\u6210\u4e00\u5f20\u5de8\u5927\u7684\u6620\u5c04\u8868&#xff1a;<\/p>\n<table>\n<tr>TokenToken ID<\/tr>\n<tbody>\n<tr>\n<td>&#034;\u6211&#034;<\/td>\n<td align=\"right\">1024<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u4f60&#034;<\/td>\n<td align=\"right\">2048<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u732b&#034;<\/td>\n<td align=\"right\">8921<\/td>\n<\/tr>\n<tr>\n<td>&#034;hello&#034;<\/td>\n<td align=\"right\">15339<\/td>\n<\/tr>\n<tr>\n<td>\u2026<\/td>\n<td align=\"right\">\u2026<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2>4. \u540c\u4e00\u4e2a Token \u7684 Token ID \u4e00\u6837\u5417&#xff1f;<\/h2>\n<p>\u5728\u540c\u4e00\u4e2a Tokenizer \u548c Vocabulary \u4e2d&#xff1a;<\/p>\n<p>\u540c\u4e00\u4e2a Token \u5bf9\u5e94\u56fa\u5b9a\u7684 Token ID\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>&#034;\u732b&#034; \u2192 8921<\/p>\n<p>\u53ea\u8981\u4f7f\u7528\u7684\u662f\u540c\u4e00\u4e2a Vocabulary&#xff0c;\u90a3\u4e48 &#034;\u732b&#034; \u5bf9\u5e94\u7684 ID \u5c31\u4e0d\u4f1a\u4e00\u4f1a\u513f\u662f 8921&#xff0c;\u4e00\u4f1a\u513f\u53d8\u6210 1234\u3002<\/p>\n<p>\u4f46\u662f&#xff1a;<\/p>\n<p>\u4e0d\u540c\u6a21\u578b \/ \u4e0d\u540c Tokenizer \u4e4b\u95f4&#xff0c;\u540c\u4e00\u4e2a\u6587\u672c\u7247\u6bb5\u7684 Token ID \u4e0d\u4e00\u5b9a\u76f8\u540c\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u6a21\u578b A&#xff1a;<\/p>\n<p>&#034;hello&#034; \u2192 15339<\/p>\n<p>\u6a21\u578b B&#xff1a;<\/p>\n<p>&#034;hello&#034; \u2192 8821<\/p>\n<p>\u751a\u81f3\u4e24\u4e2a\u6a21\u578b\u7684 Tokenizer \u53ef\u80fd\u8fde\u5207\u5206\u7ed3\u679c\u90fd\u4e0d\u4e00\u6837\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>ChatGPT<\/p>\n<p>\u4e00\u4e2a Tokenizer \u53ef\u80fd\u5207\u6210&#xff1a;<\/p>\n<p>[&#034;Chat&#034;, &#034;GPT&#034;]<\/p>\n<p>\u53e6\u4e00\u4e2a\u53ef\u80fd\u5207\u6210&#xff1a;<\/p>\n<p>[&#034;Chat&#034;, &#034;G&#034;, &#034;PT&#034;]<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>Token ID \u672c\u8eab\u6ca1\u6709\u8bed\u4e49&#xff0c;\u5b83\u672c\u8d28\u4e0a\u53ea\u662f Token \u5728 Vocabulary \u4e2d\u7684\u7d22\u5f15\u7f16\u53f7\u3002<\/p>\n<hr \/>\n<h2>5. Token ID \u5982\u4f55\u53d8\u6210\u9ad8\u7ef4\u5411\u91cf&#xff1f;<\/h2>\n<p>\u795e\u7ecf\u7f51\u7edc\u4e0d\u80fd\u76f4\u63a5\u901a\u8fc7&#xff1a;<\/p>\n<p>5837<\/p>\n<p>\u8fd9\u6837\u7684\u7f16\u53f7\u7406\u89e3\u8bed\u4e49\u3002<\/p>\n<p>\u6240\u4ee5 LLM \u5185\u90e8\u6709\u4e00\u5f20\u5f88\u5927\u7684\u53c2\u6570\u77e9\u9635&#xff1a;<\/p>\n<p>Embedding Table&#xff08;\u5d4c\u5165\u77e9\u9635&#xff09;<\/p>\n<p>Token ID \u53ef\u4ee5\u7406\u89e3\u6210\u8fd9\u5f20\u8868\u7684\u884c\u7d22\u5f15\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>Token ID &#061; 5837<br \/>\n       \u2193<br \/>\nEmbedding Table<br \/>\n       \u2193<br \/>\n\u627e\u5230\u7b2c 5837 \u884c<br \/>\n       \u2193<br \/>\n[0.12, -0.53, 0.87, 0.21, &#8230;]<\/p>\n<p>\u4e8e\u662f&#xff1a;<\/p>\n<p>\u4e00\u4e2a Token ID \u2192 \u4e00\u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf\u3002<\/p>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>&#034;\u6211\u7231\u732b&#034;<\/p>\n<p>\u88ab\u5207\u6210&#xff1a;<\/p>\n<p>[&#034;\u6211&#034;, &#034;\u7231\u732b&#034;]<\/p>\n<p>\u5bf9\u5e94&#xff1a;<\/p>\n<p>[1024, 5837]<\/p>\n<p>\u7136\u540e\u67e5 Embedding Table&#xff1a;<\/p>\n<p>1024<br \/>\n \u2193<br \/>\nX1 &#061; [0.21, -0.53, 0.87, &#8230;]<\/p>\n<p>5837<br \/>\n \u2193<br \/>\nX2 &#061; [0.72, 0.11, -0.36, &#8230;]<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>2 \u4e2a Token<br \/>\n \u2193<br \/>\n2 \u4e2a Token ID<br \/>\n \u2193<br \/>\n2 \u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf<\/p>\n<p>\u5982\u679c\u6a21\u578b\u9690\u85cf\u7ef4\u5ea6\u662f 4096&#xff0c;\u90a3\u4e48\u6bcf\u4e2a Token \u4f1a\u5f97\u5230\u4e00\u4e2a 4096 \u7ef4\u5411\u91cf\u3002<\/p>\n<hr \/>\n<h2>6. Token Embedding \u548c\u4e0a\u4e0b\u6587\u5316\u5411\u91cf\u4e0d\u662f\u4e00\u56de\u4e8b<\/h2>\n<p>\u8fd9\u662f\u975e\u5e38\u91cd\u8981\u7684\u533a\u522b\u3002<\/p>\n<p>Token ID \u901a\u8fc7 Embedding Table \u5f97\u5230\u7684\u662f&#xff1a;<\/p>\n<p>\u521d\u59cb Token Embedding<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>&#034;\u732b&#034;<br \/>\n \u2193<br \/>\nToken ID&#xff1a;8921<br \/>\n \u2193<br \/>\nEmbedding Table<br \/>\n \u2193<br \/>\n[0.12, -0.51, 0.83, &#8230;]<\/p>\n<p>\u5bf9\u4e8e\u540c\u4e00\u4e2a\u6a21\u578b&#xff0c;\u8fd9\u4e2a\u521d\u59cb Embedding \u662f\u6a21\u578b\u53c2\u6570\u7684\u4e00\u90e8\u5206\u3002<\/p>\n<p>\u4f46\u662f\u8003\u8651&#xff1a;<\/p>\n<p>\u6211\u559c\u6b22\u732b<\/p>\n<p>\u673a\u5668\u732b\u662f\u4e00\u90e8\u52a8\u753b<\/p>\n<p>\u4ed6\u662f\u4e00\u4e2a\u591c\u732b\u5b50<\/p>\n<p>\u867d\u7136\u5176\u4e2d\u53ef\u80fd\u51fa\u73b0\u76f8\u540c\u7684 &#034;\u732b&#034; Token&#xff0c;\u4f46\u4e0a\u4e0b\u6587\u5b8c\u5168\u4e0d\u540c\u3002<\/p>\n<p>\u6240\u4ee5\u7ecf\u8fc7 Transformer \u540e&#xff0c;\u8fd9\u4e2a\u4f4d\u7f6e\u5bf9\u5e94\u7684\u5411\u91cf\u4f1a\u6839\u636e\u4e0a\u4e0b\u6587\u53d1\u751f\u53d8\u5316&#xff1a;<\/p>\n<p>Token ID<br \/>\n \u2193<br \/>\nEmbedding Table<br \/>\n \u2193<br \/>\n\u521d\u59cb Token Embedding<br \/>\n \u2193<br \/>\nTransformer<br \/>\n \u2193<br \/>\n\u7ed3\u5408\u4e0a\u4e0b\u6587<br \/>\n \u2193<br \/>\nContextualized Hidden State<br \/>\n\u4e0a\u4e0b\u6587\u5316\u9690\u85cf\u5411\u91cf<\/p>\n<p>\u56e0\u6b64\u53ef\u4ee5\u7406\u89e3\u4e3a&#xff1a;<\/p>\n<p>Embedding Table \u7ed9 Token \u4e00\u4e2a\u521d\u59cb\u8868\u793a&#xff1b;Transformer \u518d\u6839\u636e\u4e0a\u4e0b\u6587\u4e0d\u65ad\u52a0\u5de5\u8fd9\u4e2a\u8868\u793a\u3002<\/p>\n<hr \/>\n<h2>7. \u4e3a\u4ec0\u4e48\u8981\u7ecf\u8fc7\u591a\u5c42 Transformer&#xff1f;<\/h2>\n<p>\u5f97\u5230\u521d\u59cb Token Embedding \u540e&#xff0c;\u6a21\u578b\u8fd8\u6ca1\u6709\u5145\u5206\u7406\u89e3 Token \u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u5c0f\u660e\u6ca1\u6709\u53bb\u4e0a\u73ed&#xff0c;\u56e0\u4e3a\u4ed6\u751f\u75c5\u4e86\u3002<\/p>\n<p>\u6a21\u578b\u4e0d\u4ec5\u9700\u8981\u5904\u7406&#xff1a;<\/p>\n<p>\u5c0f\u660e<br \/>\n\u4e0a\u73ed<br \/>\n\u751f\u75c5<\/p>\n<p>\u8fd8\u9700\u8981\u7ed3\u5408\u4e0a\u4e0b\u6587\u7406\u89e3&#xff1a;<\/p>\n<p>&#034;\u4ed6&#034;<br \/>\n \u2193<br \/>\n\u6307\u7684\u662f<br \/>\n \u2193<br \/>\n&#034;\u5c0f\u660e&#034;<\/p>\n<p>\u4ee5\u53ca&#xff1a;<\/p>\n<p>\u4e3a\u4ec0\u4e48\u6ca1\u53bb\u4e0a\u73ed&#xff1f;<br \/>\n \u2193<br \/>\n\u56e0\u4e3a\u751f\u75c5<\/p>\n<p>Transformer \u4e2d\u7684 Self-Attention \u7b49\u673a\u5236\u5141\u8bb8\u4e0d\u540c\u4f4d\u7f6e\u4e4b\u95f4\u8fdb\u884c\u4fe1\u606f\u4ea4\u4e92\u3002<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>\u521d\u59cb Token Embedding<br \/>\n       \u2193<br \/>\nTransformer Layer 1<br \/>\n       \u2193<br \/>\n\u7b2c\u4e00\u5c42\u4e0a\u4e0b\u6587\u8868\u793a<br \/>\n       \u2193<br \/>\nTransformer Layer 2<br \/>\n       \u2193<br \/>\n\u8fdb\u4e00\u6b65\u878d\u5408\u548c\u53d8\u6362<br \/>\n       \u2193<br \/>\nTransformer Layer 3<br \/>\n       \u2193<br \/>\n&#8230;<br \/>\n       \u2193<br \/>\nTransformer Layer N<br \/>\n       \u2193<br \/>\n\u6700\u7ec8\u4e0a\u4e0b\u6587\u5316\u8868\u793a<\/p>\n<p>\u5047\u8bbe\u6709\u4e09\u4e2a Token&#xff1a;<\/p>\n<p>Token 1<br \/>\nToken 2<br \/>\nToken 3<\/p>\n<p>\u7ecf\u8fc7\u7b2c\u4e00\u5c42&#xff1a;<\/p>\n<p>H1\u00b9<br \/>\nH2\u00b9<br \/>\nH3\u00b9<\/p>\n<p>\u7b2c\u4e8c\u5c42&#xff1a;<\/p>\n<p>H1\u00b2<br \/>\nH2\u00b2<br \/>\nH3\u00b2<\/p>\n<p>\u4e00\u76f4\u5230\u7b2c N \u5c42&#xff1a;<\/p>\n<p>H1\u1d3a<br \/>\nH2\u1d3a<br \/>\nH3\u1d3a<\/p>\n<p>\u53ef\u4ee5\u7c97\u7565\u7406\u89e3&#xff1a;<\/p>\n<p>\u6bcf\u7ecf\u8fc7\u4e00\u5c42 Transformer&#xff0c;\u6bcf\u4e2a Token \u7684\u8868\u793a\u90fd\u4f1a\u8fdb\u4e00\u6b65\u878d\u5408\u4e0a\u4e0b\u6587\u5e76\u8fdb\u884c\u7279\u5f81\u53d8\u6362&#xff0c;\u591a\u5c42\u5806\u53e0\u4f7f\u6a21\u578b\u80fd\u591f\u5f62\u6210\u8d8a\u6765\u8d8a\u590d\u6742\u7684\u8868\u793a\u3002<\/p>\n<p>\u4f46\u4e0d\u80fd\u673a\u68b0\u5730\u8ba4\u4e3a&#xff1a;<\/p>\n<p>Layer 1 &#061; \u8bc6\u5b57<br \/>\nLayer 2 &#061; \u8bed\u6cd5<br \/>\nLayer 3 &#061; \u63a8\u7406<\/p>\n<p>\u771f\u5b9e\u6a21\u578b\u5185\u90e8\u5e76\u6ca1\u6709\u8fd9\u6837\u4e25\u683c\u7684\u4eba\u5de5\u5206\u5de5\u3002<\/p>\n<hr \/>\n<h2>8. \u5927\u8bed\u8a00\u6a21\u578b\u5982\u4f55\u9884\u6d4b\u4e0b\u4e00\u4e2a Token&#xff1f;<\/h2>\n<p>\u5047\u8bbe\u8f93\u5165&#xff1a;<\/p>\n<p>\u6211\u7231\u732b<\/p>\n<p>\u4e3a\u4e86\u65b9\u4fbf\u8bf4\u660e&#xff0c;\u5047\u8bbe Tokenizer \u5c06\u5176\u5207\u6210&#xff1a;<\/p>\n<p>[&#034;\u6211&#034;, &#034;\u7231\u732b&#034;]<\/p>\n<p>\u5b8c\u6574\u8fc7\u7a0b&#xff1a;<\/p>\n<p>\u6587\u5b57&#xff1a;&#034;\u6211\u7231\u732b&#034;<br \/>\n      \u2193<br \/>\nTokenizer<br \/>\n      \u2193<br \/>\n[&#034;\u6211&#034;, &#034;\u7231\u732b&#034;]<br \/>\n      \u2193<br \/>\nToken ID<br \/>\n[1024, 5837]<br \/>\n      \u2193<br \/>\nEmbedding Table<br \/>\n      \u2193<br \/>\n\u4e24\u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf<br \/>\n      \u2193<br \/>\n\u52a0\u5165\u4f4d\u7f6e\u4fe1\u606f<br \/>\n      \u2193<br \/>\nTransformer Layer 1<br \/>\n      \u2193<br \/>\nTransformer Layer 2<br \/>\n      \u2193<br \/>\n&#8230;<br \/>\n      \u2193<br \/>\nTransformer Layer N<br \/>\n      \u2193<br \/>\n\u5f97\u5230\u4e24\u4e2a\u6700\u7ec8 Hidden States<\/p>\n<p>H1\u1d3a<br \/>\nH2\u1d3a<br \/>\n      \u2193<br \/>\n\u53d6\u5f53\u524d\u6700\u540e\u4f4d\u7f6e H2\u1d3a<br \/>\n      \u2193<br \/>\nLM Head<br \/>\n      \u2193<br \/>\n\u6574\u4e2a Vocabulary \u7684 Logits<br \/>\n      \u2193<br \/>\nSoftmax \/ Sampling \u7b49<br \/>\n      \u2193<br \/>\n\u9009\u62e9\u4e0b\u4e00\u4e2a Token ID<br \/>\n      \u2193<br \/>\nTokenizer Decode<br \/>\n      \u2193<br \/>\n\u4f8b\u5982&#xff1a;&#034;\u5f88&#034;<\/p>\n<p>\u6a21\u578b\u5b9e\u9645\u4e0a\u4f1a\u5bf9\u6574\u4e2a Vocabulary \u4e2d\u7684 Token \u8ba1\u7b97\u5206\u6570\u3002<\/p>\n<p>\u4f8b\u5982\u7b80\u5316\u6210&#xff1a;<\/p>\n<table>\n<tr>\u5019\u9009 Token\u6982\u7387<\/tr>\n<tbody>\n<tr>\n<td>&#034;\u6211&#034;<\/td>\n<td align=\"right\">1%<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u4f60&#034;<\/td>\n<td align=\"right\">1%<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u732b&#034;<\/td>\n<td align=\"right\">3%<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u5f88&#034;<\/td>\n<td align=\"right\">70%<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u53ef\u7231&#034;<\/td>\n<td align=\"right\">15%<\/td>\n<\/tr>\n<tr>\n<td>&#034;\u6f02\u4eae&#034;<\/td>\n<td align=\"right\">6%<\/td>\n<\/tr>\n<tr>\n<td>&lt;EOS&gt;<\/td>\n<td align=\"right\">4%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u90a3\u4e48\u6a21\u578b\u53ef\u80fd\u9009\u62e9&#xff1a;<\/p>\n<p>&#034;\u5f88&#034;<\/p>\n<p>\u4f5c\u4e3a\u4e0b\u4e00\u4e2a Token\u3002<\/p>\n<hr \/>\n<h2>9. \u4e3a\u4ec0\u4e48\u4f7f\u7528\u6700\u540e\u4e00\u4e2a\u4f4d\u7f6e\u7684 Hidden State&#xff1f;<\/h2>\n<p>Decoder-only LLM \u662f\u81ea\u56de\u5f52\u6a21\u578b\u3002<\/p>\n<p>\u5047\u8bbe\u5f53\u524d\u5df2\u7ecf\u6709&#xff1a;<\/p>\n<p>\u6211 \u7231\u732b<\/p>\n<p>\u73b0\u5728\u6a21\u578b\u8981\u89e3\u51b3\u7684\u95ee\u9898\u5176\u5b9e\u662f&#xff1a;<\/p>\n<p>\u6211 \u7231\u732b [???]<\/p>\n<p>\u5728\u56e0\u679c\u6ce8\u610f\u529b\u673a\u5236\u4e0b&#xff0c;\u5f53\u524d\u6700\u540e\u4f4d\u7f6e\u7684 Hidden State \u5df2\u7ecf\u878d\u5408\u4e86\u5b83\u80fd\u591f\u770b\u5230\u7684\u524d\u9762\u4e0a\u4e0b\u6587\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u6700\u540e\u4f4d\u7f6e Hidden State<br \/>\n       \u2193<br \/>\nLM Head<br \/>\n       \u2193<br \/>\nVocabulary Logits<br \/>\n       \u2193<br \/>\n\u9009\u62e9\u4e0b\u4e00\u4e2a Token<\/p>\n<p>\u9700\u8981\u6ce8\u610f&#xff1a;<\/p>\n<p>\u4e0d\u662f\u628a\u6700\u540e\u4e00\u4e2a Hidden State \u518d\u91cd\u65b0\u4ea4\u7ed9\u6574\u4e2a\u5927\u6a21\u578b\u3002<\/p>\n<p>Transformer \u672c\u8eab\u5c31\u662f\u5927\u6a21\u578b\u4e3b\u4f53\u7684\u4e00\u90e8\u5206\u3002<\/p>\n<p>\u6b63\u786e\u7406\u89e3\u662f&#xff1a;<\/p>\n<p>Transformer<br \/>\n \u2193<br \/>\n\u6700\u540e\u4f4d\u7f6e Hidden State<br \/>\n \u2193<br \/>\nLM Head<br \/>\n \u2193<br \/>\n\u4e0b\u4e00\u4e2a Token<\/p>\n<hr \/>\n<h2>10. \u751f\u6210\u4e00\u4e2a Token \u540e\u4f1a\u53d1\u751f\u4ec0\u4e48&#xff1f;<\/h2>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>\u6211\u7231\u732b<\/p>\n<p>\u6a21\u578b\u9884\u6d4b&#xff1a;<\/p>\n<p>\u5f88<\/p>\n<p>\u90a3\u4e48\u903b\u8f91\u4e0a\u4e0b\u4e00\u6b21\u6a21\u578b\u9762\u5bf9\u7684\u5e8f\u5217\u5c31\u662f&#xff1a;<\/p>\n<p>\u6211\u7231\u732b\u5f88<\/p>\n<p>\u7136\u540e\u9884\u6d4b&#xff1a;<\/p>\n<p>\u53ef\u7231<\/p>\n<p>\u4e8e\u662f&#xff1a;<\/p>\n<p>\u6211\u7231\u732b\u5f88\u53ef\u7231<\/p>\n<p>\u518d\u9884\u6d4b&#xff1a;<\/p>\n<p>\u3002<\/p>\n<p>\u5f97\u5230&#xff1a;<\/p>\n<p>\u6211\u7231\u732b\u5f88\u53ef\u7231\u3002<\/p>\n<p>\u7ee7\u7eed\u9884\u6d4b&#xff0c;\u76f4\u5230&#xff1a;<\/p>\n<ul>\n<li>\u751f\u6210 &lt;EOS&gt; \u7b49\u7ed3\u675f Token<\/li>\n<li>\u8fbe\u5230\u6700\u5927\u8f93\u51fa\u957f\u5ea6<\/li>\n<li>\u547d\u4e2d\u505c\u6b62\u5e8f\u5217<\/li>\n<li>\u6216\u89e6\u53d1\u5176\u4ed6\u505c\u6b62\u6761\u4ef6<\/li>\n<\/ul>\n<p>\u56e0\u6b64\u751f\u6210\u8fc7\u7a0b\u53ef\u4ee5\u7406\u89e3\u4e3a&#xff1a;<\/p>\n<p>Prompt<br \/>\n \u2193<br \/>\n\u9884\u6d4b Token 1<br \/>\n \u2193<br \/>\nPrompt &#043; Token 1<br \/>\n \u2193<br \/>\n\u9884\u6d4b Token 2<br \/>\n \u2193<br \/>\nPrompt &#043; Token 1 &#043; Token 2<br \/>\n \u2193<br \/>\n\u9884\u6d4b Token 3<br \/>\n \u2193<br \/>\n&#8230;<\/p>\n<p>\u8fd9\u5c31\u662f&#xff1a;<\/p>\n<p>Autoregressive Generation&#xff08;\u81ea\u56de\u5f52\u751f\u6210&#xff09;<\/p>\n<p>\u5373&#xff1a;<\/p>\n<p>\u6a21\u578b\u6839\u636e\u4e4b\u524d\u5df2\u7ecf\u5b58\u5728\u548c\u5df2\u7ecf\u751f\u6210\u7684 Token&#xff0c;\u4e0d\u65ad\u9884\u6d4b\u4e0b\u4e00\u4e2a Token\u3002<\/p>\n<hr \/>\n<h2>11. \u6bcf\u751f\u6210\u4e00\u4e2a Token&#xff0c;\u90fd\u8981\u628a\u524d\u9762\u7684\u5168\u90e8\u91cd\u65b0\u8ba1\u7b97\u5417&#xff1f;<\/h2>\n<p>\u4ece\u903b\u8f91\u4e0a\u770b&#xff1a;<\/p>\n<p>\u6bcf\u6b21\u9884\u6d4b\u90fd\u57fa\u4e8e\u5168\u90e8\u5386\u53f2\u4e0a\u4e0b\u6587\u3002<\/p>\n<p>\u4f46\u5de5\u7a0b\u5b9e\u73b0\u4e0a&#xff1a;<\/p>\n<p>\u901a\u5e38\u4e0d\u4f1a\u628a\u6240\u6709\u5386\u53f2 Token \u4ece\u5934\u5b8c\u6574\u8ba1\u7b97\u4e00\u904d\u3002<\/p>\n<p>\u5426\u5219\u4f1a\u4ea7\u751f\u5927\u91cf\u91cd\u590d\u8ba1\u7b97\u3002<\/p>\n<p>\u8fd9\u5c31\u5f15\u51fa\u4e86&#xff1a;<\/p>\n<p>KV Cache<\/p>\n<hr \/>\n<h2>12. Prefill \u548c Decode<\/h2>\n<p>LLM \u63a8\u7406\u901a\u5e38\u53ef\u4ee5\u5206\u6210\u4e24\u4e2a\u91cd\u8981\u9636\u6bb5&#xff1a;<\/p>\n<li>Prefill<\/li>\n<li>Decode<\/li>\n<hr \/>\n<h3>12.1 Prefill<\/h3>\n<p>\u5047\u8bbe\u7528\u6237\u8f93\u5165&#xff1a;<\/p>\n<p>\u6211\u7231\u732b<\/p>\n<p>\u6a21\u578b\u9996\u5148&#xff1a;<\/p>\n<p>Prompt<br \/>\n \u2193<br \/>\nTokenizer<br \/>\n \u2193<br \/>\n\u6240\u6709 Input Tokens<br \/>\n \u2193<br \/>\nEmbedding<br \/>\n \u2193<br \/>\n\u591a\u5c42 Transformer<br \/>\n \u2193<br \/>\n\u4e00\u6b21\u5904\u7406\u6574\u4e2a Prompt<br \/>\n \u2193<br \/>\n\u5efa\u7acb\u5404 Transformer Layer \u7684 KV Cache<br \/>\n \u2193<br \/>\n\u5f97\u5230\u4e0b\u4e00\u4e2a Token \u7684\u9884\u6d4b<\/p>\n<p>\u8fd9\u4e2a\u9636\u6bb5\u53eb&#xff1a;<\/p>\n<p>Prefill<\/p>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<p>\u4e3b\u8981\u5904\u7406\u7528\u6237\u5df2\u7ecf\u63d0\u4f9b\u7684\u5927\u91cf\u8f93\u5165 Token&#xff0c;\u53ef\u4ee5\u5229\u7528 GPU \u505a\u8f83\u5f3a\u7684\u5e76\u884c\u8ba1\u7b97\u3002<\/p>\n<hr \/>\n<h3>12.2 Decode<\/h3>\n<p>\u5047\u8bbe\u6a21\u578b\u9884\u6d4b\u51fa\u7684\u7b2c\u4e00\u4e2a\u8f93\u51fa Token \u662f&#xff1a;<\/p>\n<p>\u5f88<\/p>\n<p>\u63a5\u4e0b\u6765\u4e0d\u9700\u8981\u628a&#xff1a;<\/p>\n<p>\u6211\u7231\u732b<\/p>\n<p>\u4ece\u5934\u5b8c\u6574\u8ba1\u7b97\u4e00\u904d\u3002<\/p>\n<p>\u800c\u662f&#xff1a;<\/p>\n<p>\u65b0 Token&#xff1a;&#034;\u5f88&#034;<br \/>\n       \u2193<br \/>\nEmbedding<br \/>\n       \u2193<br \/>\n\u8fdb\u5165 Transformer<br \/>\n       \u2193<br \/>\n\u8bfb\u53d6\u5386\u53f2 KV Cache<br \/>\n       \u2193<br \/>\n\u8ba1\u7b97\u5f53\u524d\u65b0 Token<br \/>\n       \u2193<br \/>\n\u628a\u5f53\u524d Token \u7684 K\/V \u52a0\u5165 Cache<br \/>\n       \u2193<br \/>\n\u9884\u6d4b\u4e0b\u4e00\u4e2a Token&#xff1a;&#034;\u53ef\u7231&#034;<\/p>\n<p>\u7136\u540e&#xff1a;<\/p>\n<p>\u65b0 Token&#xff1a;&#034;\u53ef\u7231&#034;<br \/>\n       \u2193<br \/>\n\u8bfb\u53d6\u5df2\u6709 KV Cache<br \/>\n       \u2193<br \/>\n\u7ee7\u7eed\u8ba1\u7b97<br \/>\n       \u2193<br \/>\n\u9884\u6d4b&#xff1a;&#034;\u3002&#034;<\/p>\n<p>\u8fd9\u4e2a\u9636\u6bb5\u53eb&#xff1a;<\/p>\n<p>Decode<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>Prompt<br \/>\n \u2193<br \/>\nPrefill<br \/>\n \u2193<br \/>\n\u5efa\u7acb KV Cache<br \/>\n \u2193<br \/>\n\u9884\u6d4b\u7b2c\u4e00\u4e2a\u8f93\u51fa Token<br \/>\n \u2193<br \/>\nDecode<br \/>\n \u2193<br \/>\nToken 1<br \/>\n \u2193<br \/>\nToken 2<br \/>\n \u2193<br \/>\nToken 3<br \/>\n \u2193<br \/>\n&#8230;<br \/>\n \u2193<br \/>\n\u56de\u7b54\u7ed3\u675f<\/p>\n<hr \/>\n<h2>13. KV Cache \u662f\u4ec0\u4e48&#xff1f;<\/h2>\n<p>Transformer Attention \u4e2d\u4f1a\u6d89\u53ca&#xff1a;<\/p>\n<p>Q &#061; Query<br \/>\nK &#061; Key<br \/>\nV &#061; Value<\/p>\n<p>\u5386\u53f2 Token \u7684 K \u548c V \u5df2\u7ecf\u8ba1\u7b97\u8fc7\u3002<\/p>\n<p>\u5982\u679c\u751f\u6210\u6bcf\u4e00\u4e2a\u65b0 Token \u65f6\u90fd\u91cd\u65b0\u8ba1\u7b97\u6240\u6709\u5386\u53f2 Token \u7684 K\/V&#xff0c;\u4f1a\u9020\u6210\u5927\u91cf\u91cd\u590d\u8ba1\u7b97\u3002<\/p>\n<p>\u56e0\u6b64\u53ef\u4ee5\u628a\u5386\u53f2 Token \u7684 K\/V \u4fdd\u5b58\u8d77\u6765&#xff1a;<\/p>\n<p>\u5386\u53f2 Token<br \/>\n \u2193<br \/>\n\u8ba1\u7b97 K\u3001V<br \/>\n \u2193<br \/>\n\u4fdd\u5b58<br \/>\n \u2193<br \/>\nKV Cache<\/p>\n<p>\u751f\u6210\u65b0\u7684 Token \u65f6&#xff1a;<\/p>\n<p>\u65b0 Token<br \/>\n \u2193<br \/>\n\u8ba1\u7b97\u5f53\u524d Token<br \/>\n \u2193<br \/>\n\u8bfb\u53d6\u5386\u53f2 KV Cache<br \/>\n \u2193<br \/>\nAttention<br \/>\n \u2193<br \/>\n\u5f97\u5230\u65b0\u7684 Hidden State<br \/>\n \u2193<br \/>\n\u9884\u6d4b\u4e0b\u4e00\u4e2a Token<\/p>\n<p>\u800c\u4e14&#xff1a;<\/p>\n<p>Transformer \u7684\u6bcf\u4e00\u5c42\u90fd\u6709\u5bf9\u5e94\u7684 K\/V Cache\u3002<\/p>\n<p>\u56e0\u6b64 KV Cache \u5927\u5c0f\u4e0e\u5f88\u591a\u56e0\u7d20\u6709\u5173&#xff0c;\u4f8b\u5982&#xff1a;<\/p>\n<ul>\n<li>\u6a21\u578b\u5c42\u6570<\/li>\n<li>\u4e0a\u4e0b\u6587\u957f\u5ea6<\/li>\n<li>Batch Size<\/li>\n<li>\u5e76\u53d1\u8bf7\u6c42\u6570\u91cf<\/li>\n<li>K\/V Head \u6570\u91cf<\/li>\n<li>\u6570\u636e\u7cbe\u5ea6<\/li>\n<\/ul>\n<p>\u6240\u4ee5\u5728 LLM \u63a8\u7406\u90e8\u7f72\u4e2d&#xff1a;<\/p>\n<p>Context Length \u589e\u5927<br \/>\n       \u2193<br \/>\nKV Cache \u589e\u5927<br \/>\n       \u2193<br \/>\n\u663e\u5b58\u5360\u7528\u589e\u52a0<br \/>\n       \u2193<br \/>\n\u53ef\u80fd\u5f71\u54cd Batch \/ \u5e76\u53d1<br \/>\n       \u2193<br \/>\n\u5f71\u54cd\u541e\u5410\u91cf<\/p>\n<p>\u56e0\u6b64 KV Cache \u662f vLLM\u3001TensorRT-LLM \u7b49\u63a8\u7406\u6846\u67b6\u4e2d\u7684\u91cd\u8981\u4f18\u5316\u5bf9\u8c61\u3002<\/p>\n<hr \/>\n<h2>14. \u5b8c\u6574 LLM \u63a8\u7406\u6d41\u7a0b<\/h2>\n<p>                        \u5927\u8bed\u8a00\u6a21\u578b LLM<\/p>\n<p>\u7528\u6237\u8f93\u5165\u6587\u5b57<br \/>\n     \u2193<br \/>\nTokenizer<br \/>\n     \u2193<br \/>\n\u591a\u4e2a Token<br \/>\n     \u2193<br \/>\n\u591a\u4e2a Token ID<br \/>\n     \u2193<br \/>\nEmbedding Table<br \/>\n     \u2193<br \/>\n\u6bcf\u4e2a Token \u4e00\u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf<br \/>\n     \u2193<br \/>\n\u52a0\u5165\u4f4d\u7f6e\u4fe1\u606f<br \/>\n     \u2193<br \/>\nTransformer Layer 1<br \/>\n     \u2193<br \/>\nTransformer Layer 2<br \/>\n     \u2193<br \/>\n&#8230;<br \/>\n     \u2193<br \/>\nTransformer Layer N<br \/>\n     \u2193<br \/>\n\u6bcf\u4e2a\u4f4d\u7f6e\u5f97\u5230\u4e0a\u4e0b\u6587\u5316 Hidden State<br \/>\n     \u2193<br \/>\n\u53d6\u5f53\u524d\u6700\u540e\u4f4d\u7f6e Hidden State<br \/>\n     \u2193<br \/>\nLM Head<br \/>\n     \u2193<br \/>\n\u6574\u4e2a Vocabulary \u7684 Logits<br \/>\n     \u2193<br \/>\nSoftmax \/ Sampling \u7b49<br \/>\n     \u2193<br \/>\n\u9009\u62e9\u4e0b\u4e00\u4e2a Token ID<br \/>\n     \u2193<br \/>\nDecode \u6210\u6587\u5b57<br \/>\n     \u2193<br \/>\n\u65b0 Token \u52a0\u5165\u5f53\u524d\u5e8f\u5217<br \/>\n     \u2193<br \/>\n\u5229\u7528 KV Cache<br \/>\n     \u2193<br \/>\nDecode \u4e0b\u4e00\u4e2a Token<br \/>\n     \u2193<br \/>\n\u4e0d\u65ad\u5faa\u73af<br \/>\n     \u2193<br \/>\n\u6700\u7ec8\u56de\u7b54<\/p>\n<hr \/>\n<h2>15. RAG \u662f\u4ec0\u4e48&#xff1f;<\/h2>\n<p>RAG \u5168\u79f0&#xff1a;<\/p>\n<p>Retrieval-Augmented Generation<\/p>\n<p>\u4e2d\u6587&#xff1a;<\/p>\n<p>\u68c0\u7d22\u589e\u5f3a\u751f\u6210<\/p>\n<p>\u6838\u5fc3\u601d\u60f3\u662f&#xff1a;<\/p>\n<p>\u5148\u4ece\u5916\u90e8\u77e5\u8bc6\u5e93\u4e2d\u68c0\u7d22\u4e0e\u7528\u6237\u95ee\u9898\u76f8\u5173\u7684\u8d44\u6599&#xff0c;\u518d\u628a\u8fd9\u4e9b\u8d44\u6599\u4f5c\u4e3a\u4e0a\u4e0b\u6587\u4ea4\u7ed9 LLM \u56de\u7b54\u3002<\/p>\n<p>\u4f8b\u5982\u7528\u6237\u95ee&#xff1a;<\/p>\n<p>\u6211\u4eec\u516c\u53f8\u7684\u5e74\u5047\u5236\u5ea6\u662f\u4ec0\u4e48&#xff1f;<\/p>\n<p>LLM \u672c\u8eab\u53ef\u80fd\u4e0d\u77e5\u9053\u516c\u53f8\u7684\u5185\u90e8\u89c4\u5b9a\u3002<\/p>\n<p>RAG \u53ef\u4ee5\u5148&#xff1a;<\/p>\n<p>\u7528\u6237\u95ee\u9898<br \/>\n \u2193<br \/>\n\u77e5\u8bc6\u5e93\u68c0\u7d22<br \/>\n \u2193<br \/>\n\u627e\u5230\u516c\u53f8\u5e74\u5047\u5236\u5ea6\u6587\u6863<br \/>\n \u2193<br \/>\n\u628a\u76f8\u5173\u5185\u5bb9\u4ea4\u7ed9 LLM<br \/>\n \u2193<br \/>\nLLM \u6839\u636e\u8d44\u6599\u56de\u7b54<\/p>\n<hr \/>\n<h2>16. RAG \u4e2d\u7684 Embedding \u662f\u4ec0\u4e48&#xff1f;<\/h2>\n<p>\u8fd9\u91cc\u7279\u522b\u5bb9\u6613\u548c LLM \u5185\u90e8\u7684 Token Embedding \u6df7\u6dc6\u3002<\/p>\n<p>LLM \u5185\u90e8&#xff1a;<\/p>\n<p>Token ID<br \/>\n \u2193<br \/>\nEmbedding Table<br \/>\n \u2193<br \/>\n\u6bcf\u4e2a Token \u4e00\u4e2a\u521d\u59cb\u5411\u91cf<\/p>\n<p>\u800c RAG \u7684\u76ee\u6807\u901a\u5e38\u662f&#xff1a;<\/p>\n<p>\u4f7f\u7528\u4e00\u4e2a\u9ad8\u7ef4\u5411\u91cf\u8868\u793a\u4e00\u53e5\u8bdd\u3001\u4e00\u4e2a Query \u6216\u4e00\u4e2a Chunk \u7684\u6574\u4f53\u8bed\u4e49\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u732b\u662f\u4e00\u79cd\u975e\u5e38\u5e38\u89c1\u7684\u5bb6\u5ead\u5ba0\u7269\u3002<\/p>\n<p>\u7ecf\u8fc7 Embedding Model&#xff1a;<\/p>\n<p>\u4e00\u6bb5\u6587\u5b57<br \/>\n \u2193<br \/>\nTokenizer<br \/>\n \u2193<br \/>\n\u591a\u4e2a Token<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\n\u5185\u90e8\u5904\u7406\u591a\u4e2a Token<br \/>\n \u2193<br \/>\nPooling \/ \u7279\u5b9a\u8f93\u51fa\u65b9\u5f0f<br \/>\n \u2193<br \/>\n\u6574\u6bb5\u6587\u672c\u7684\u4e00\u4e2a\u9ad8\u7ef4\u5411\u91cf<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>[0.17, -0.81, 0.34, &#8230;, 0.52]<\/p>\n<p>\u8fd9\u4e2a\u5411\u91cf\u53ef\u4ee5\u4f5c\u4e3a\u6574\u6bb5\u6587\u672c\u7684\u8bed\u4e49\u8868\u793a&#xff0c;\u7528\u4e8e\u68c0\u7d22\u3002<\/p>\n<hr \/>\n<h2>17. RAG \u4e3a\u4ec0\u4e48\u8981\u8fdb\u884c Chunk \u5207\u5206&#xff1f;<\/h2>\n<p>\u5047\u8bbe\u6709\u4e00\u4efd&#xff1a;<\/p>\n<p>100 \u9875 PDF<\/p>\n<p>\u4e00\u822c\u4e0d\u4f1a\u76f4\u63a5\u8ba9\u6574\u4efd PDF \u53ea\u5bf9\u5e94\u4e00\u4e2a\u5411\u91cf\u3002<\/p>\n<p>\u800c\u662f\u5148\u5207\u6210&#xff1a;<\/p>\n<p>\u539f\u59cb\u6587\u6863<br \/>\n \u2193<br \/>\nChunk 1<br \/>\nChunk 2<br \/>\nChunk 3<br \/>\nChunk 4<br \/>\n&#8230;<\/p>\n<p>\u7136\u540e&#xff1a;<\/p>\n<p>Chunk 1 \u2192 Embedding \u2192 Vector 1<br \/>\nChunk 2 \u2192 Embedding \u2192 Vector 2<br \/>\nChunk 3 \u2192 Embedding \u2192 Vector 3<br \/>\n&#8230;<\/p>\n<p>\u518d\u5b58\u5165&#xff1a;<\/p>\n<p>Vector Database&#xff08;\u5411\u91cf\u6570\u636e\u5e93&#xff09;<\/p>\n<p>\u8fd9\u6837\u7528\u6237\u63d0\u95ee\u65f6&#xff0c;\u5c31\u53ef\u4ee5\u627e\u5230\u6700\u76f8\u5173\u7684\u51e0\u4e2a\u5c40\u90e8\u6587\u672c\u7247\u6bb5&#xff0c;\u800c\u4e0d\u662f\u628a\u6574\u4efd\u6587\u6863\u5168\u90e8\u585e\u7ed9 LLM\u3002<\/p>\n<hr \/>\n<h2>18. RAG \u7684\u5b8c\u6574\u6d41\u7a0b<\/h2>\n<h3>\u6587\u6863\u5165\u5e93\u9636\u6bb5<\/h3>\n<p>\u539f\u59cb\u6587\u6863<br \/>\n \u2193<br \/>\n\u89e3\u6790\u6587\u672c<br \/>\n \u2193<br \/>\nChunk \u5207\u5206<br \/>\n \u2193<br \/>\nChunk 1<br \/>\nChunk 2<br \/>\nChunk 3<br \/>\n&#8230;<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\nVector 1<br \/>\nVector 2<br \/>\nVector 3<br \/>\n&#8230;<br \/>\n \u2193<br \/>\nVector Database<\/p>\n<hr \/>\n<h3>\u7528\u6237\u67e5\u8be2\u9636\u6bb5<\/h3>\n<p>\u7528\u6237\u95ee\u9898<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\nQuery Vector<br \/>\n \u2193<br \/>\n\u548c Vector Database \u4e2d\u7684 Chunk Vector \u6bd4\u8f83<br \/>\n \u2193<br \/>\nSimilarity \/ Distance Search<br \/>\n \u2193<br \/>\nTop-K<br \/>\n \u2193<br \/>\n\u627e\u5230\u6700\u76f8\u5173\u7684\u51e0\u4e2a Chunks<br \/>\n \u2193<br \/>\n\u7528\u6237\u95ee\u9898 &#043; \u68c0\u7d22\u5230\u7684 Chunks<br \/>\n \u2193<br \/>\nLLM<br \/>\n \u2193<br \/>\n\u6700\u7ec8\u56de\u7b54<\/p>\n<p>\u901a\u5e38 Query \u548c\u6587\u6863 Chunk \u5e94\u4f7f\u7528\u540c\u4e00\u5957\u6216\u76f8\u4e92\u517c\u5bb9\u7684 Embedding Model&#xff0c;\u4f7f\u5b83\u4eec\u5904\u4e8e\u53ef\u6bd4\u8f83\u7684\u5411\u91cf\u7a7a\u95f4\u3002<\/p>\n<hr \/>\n<h2>19. RAG \u600e\u4e48\u77e5\u9053\u4e24\u4e2a\u6587\u672c\u8bed\u4e49\u76f8\u4f3c&#xff1f;<\/h2>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>\u7528\u6237\u95ee\u9898&#xff1a;<br \/>\n\u5bb6\u517b\u732b\u6709\u4ec0\u4e48\u7279\u70b9&#xff1f;<\/p>\n<p>Embedding&#xff1a;<\/p>\n<p>\u7528\u6237\u95ee\u9898<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\nQuery Vector<\/p>\n<p>\u77e5\u8bc6\u5e93\u4e2d\u6709&#xff1a;<\/p>\n<p>Chunk A&#xff1a;<br \/>\n\u732b\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u5bb6\u5ead\u5ba0\u7269\u3002<\/p>\n<p>Chunk B&#xff1a;<br \/>\n\u98de\u673a\u4f9d\u9760\u673a\u7ffc\u4ea7\u751f\u5347\u529b\u3002<\/p>\n<p>Chunk C&#xff1a;<br \/>\n\u6570\u636e\u5e93\u53ef\u4ee5\u7528\u4e8e\u4fdd\u5b58\u7ed3\u6784\u5316\u6570\u636e\u3002<\/p>\n<p>\u5b83\u4eec\u4e5f\u5206\u522b\u6709&#xff1a;<\/p>\n<p>Vector A<br \/>\nVector B<br \/>\nVector C<\/p>\n<p>\u73b0\u5728\u9700\u8981\u89e3\u51b3&#xff1a;<\/p>\n<p>Query Vector \u5230\u5e95\u548c\u54ea\u4e2a Chunk Vector \u6700\u76f8\u4f3c&#xff1f;<\/p>\n<p>\u8fd9\u5c31\u9700\u8981\u4f7f\u7528\u5411\u91cf\u4e4b\u95f4\u7684&#xff1a;<\/p>\n<p>Similarity \/ Distance Metric&#xff08;\u76f8\u4f3c\u5ea6 \/ \u8ddd\u79bb\u5ea6\u91cf&#xff09;<\/p>\n<p>\u5e38\u89c1\u65b9\u6cd5\u5305\u62ec&#xff1a;<\/p>\n<li>Cosine Similarity<\/li>\n<li>Euclidean Distance<\/li>\n<li>Dot Product<\/li>\n<hr \/>\n<h2>20. Cosine Similarity&#xff08;\u4f59\u5f26\u76f8\u4f3c\u5ea6&#xff09;<\/h2>\n<p>Cosine Similarity \u4e3b\u8981\u5173\u6ce8&#xff1a;<\/p>\n<p>\u4e24\u4e2a\u5411\u91cf\u7684\u65b9\u5411\u662f\u5426\u76f8\u4f3c\u3002<\/p>\n<p>\u516c\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061\u03b8&#061;A\u22c5B\u2225A\u2225\u2225B\u2225<br \/>\n\\\\cos\\\\theta &#061;<br \/>\n\\\\frac{A \\\\cdot B}<br \/>\n{\\\\|A\\\\|\\\\|B\\\\|}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2963em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2225\u2225<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2225<\/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\">A<\/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 mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<p>A\u3001B &#061; \u4e24\u4e2a\u5411\u91cf<br \/>\n\u03b8    &#061; \u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u5939\u89d2<\/p>\n<p>\u5982\u679c&#xff1a;<\/p>\n<p>\u03b8 &#061; 0\u00b0<br \/>\ncos\u03b8 &#061; 1<\/p>\n<p>\u8868\u793a\u5b8c\u5168\u540c\u65b9\u5411\u3002<\/p>\n<p>\u5982\u679c&#xff1a;<\/p>\n<p>\u03b8 &#061; 90\u00b0<br \/>\ncos\u03b8 &#061; 0<\/p>\n<p>\u8868\u793a\u6b63\u4ea4\u3002<\/p>\n<p>\u5982\u679c&#xff1a;<\/p>\n<p>\u03b8 &#061; 180\u00b0<br \/>\ncos\u03b8 &#061; -1<\/p>\n<p>\u8868\u793a\u5b8c\u5168\u53cd\u65b9\u5411\u3002<\/p>\n<p>\u5728\u5f88\u591a Embedding \u573a\u666f\u4e0b&#xff1a;<\/p>\n<p>Cosine Similarity \u8d8a\u9ad8&#xff0c;\u901a\u5e38\u8868\u793a\u4e24\u4e2a\u6587\u672c\u7684\u8bed\u4e49\u8d8a\u63a5\u8fd1\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u7528\u6237&#xff1a;<br \/>\n\u5bb6\u517b\u732b\u6709\u4ec0\u4e48\u7279\u70b9&#xff1f;<\/p>\n<p>Chunk&#xff1a;<br \/>\n\u732b\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u5bb6\u5ead\u5ba0\u7269\u3002<\/p>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>Cosine Similarity &#061; 0.91<\/p>\n<p>\u8bf4\u660e\u4e24\u4e2a\u5411\u91cf\u65b9\u5411\u975e\u5e38\u63a5\u8fd1&#xff0c;\u56e0\u6b64\u8fd9\u4e2a Chunk \u5f88\u53ef\u80fd\u4e0e\u7528\u6237\u95ee\u9898\u76f8\u5173\u3002<\/p>\n<hr \/>\n<h2>21. Euclidean Distance&#xff08;\u6b27\u6c0f\u8ddd\u79bb&#xff09;<\/h2>\n<p>Euclidean Distance \u53c8\u53eb&#xff1a;<\/p>\n<p>L2 Distance<\/p>\n<p>\u5b83\u8861\u91cf\u7684\u662f&#xff1a;<\/p>\n<p>\u4e24\u4e2a\u5411\u91cf\u5bf9\u5e94\u7684\u70b9\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5b9e\u9645\u8ddd\u79bb\u3002<\/p>\n<p>\u4e8c\u7ef4\u60c5\u51b5\u4e0b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A&#061;(a1,a2)<br \/>\nA&#061;(a_1,a_2)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;(b1,b2)<br \/>\nB&#061;(b_1,b_2)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">d(A,B)&#061;(a1\u2212b1)2&#043;(a2\u2212b2)2<br \/>\nd(A,B)&#061;<br \/>\n\\\\sqrt{<br \/>\n(a_1-b_1)^2&#043;<br \/>\n(a_2-b_2)^2<br \/>\n}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/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: 1.24em;vertical-align: -0.2561em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9839em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.9439em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2561em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4e09\u7ef4&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">d(A,B)&#061;(a1\u2212b1)2&#043;(a2\u2212b2)2&#043;(a3\u2212b3)2<br \/>\nd(A,B)&#061;<br \/>\n\\\\sqrt{<br \/>\n(a_1-b_1)^2&#043;<br \/>\n(a_2-b_2)^2&#043;<br \/>\n(a_3-b_3)^2<br \/>\n}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/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: 1.24em;vertical-align: -0.2561em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9839em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/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=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.9439em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2561em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5982\u679c\u662f 1024 \u7ef4\u5411\u91cf&#xff0c;\u9053\u7406\u5b8c\u5168\u76f8\u540c&#xff0c;\u53ea\u4e0d\u8fc7\u8ba1\u7b97 1024 \u4e2a\u7ef4\u5ea6\u3002<\/p>\n<hr \/>\n<h2>22. \u6b27\u6c0f\u8ddd\u79bb\u5728 RAG \u4e2d\u662f\u5e72\u4ec0\u4e48\u7684&#xff1f;<\/h2>\n<p>\u5982\u679c\u4e00\u4e2a Embedding Model \u5b66\u5230\u7684\u5411\u91cf\u7a7a\u95f4\u5177\u6709\u8fd9\u6837\u7684\u6027\u8d28&#xff1a;<\/p>\n<p>\u8bed\u4e49\u8d8a\u76f8\u4f3c<br \/>\n \u2193<br \/>\n\u5411\u91cf\u5728\u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u8d8a\u63a5\u8fd1<\/p>\n<p>\u90a3\u4e48\u5c31\u53ef\u4ee5\u4f7f\u7528\u6b27\u6c0f\u8ddd\u79bb\u8fdb\u884c\u8bed\u4e49\u68c0\u7d22\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>Query Vector &#061; A<\/p>\n<p>Chunk 1 Vector &#061; B<br \/>\nChunk 2 Vector &#061; C<\/p>\n<p>\u8ba1\u7b97&#xff1a;<\/p>\n<p>Distance(A, B) &#061; 0.3<\/p>\n<p>Distance(A, C) &#061; 8.7<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>A \u548c B \u8ddd\u79bb\u5f88\u8fd1<br \/>\n\u2192 Chunk 1 \u66f4\u53ef\u80fd\u548c\u7528\u6237\u95ee\u9898\u8bed\u4e49\u76f8\u5173<\/p>\n<p>A \u548c C \u8ddd\u79bb\u5f88\u8fdc<br \/>\n\u2192 Chunk 2 \u76f8\u5173\u6027\u53ef\u80fd\u8f83\u4f4e<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>Euclidean Distance \u4e5f\u53ef\u4ee5\u7528\u4e8e RAG \/ Vector Search \u4e2d\u5bfb\u627e\u8bed\u4e49\u63a5\u8fd1\u7684\u6587\u672c\u3002<\/p>\n<p>\u5224\u65ad\u65b9\u5f0f&#xff1a;<\/p>\n<p>\u8ddd\u79bb\u8d8a\u5c0f<br \/>\n\u2192 \u5411\u91cf\u8d8a\u63a5\u8fd1<br \/>\n\u2192 \u901a\u5e38\u8bed\u4e49\u8d8a\u76f8\u4f3c<\/p>\n<p>\u8ddd\u79bb\u8d8a\u5927<br \/>\n\u2192 \u5411\u91cf\u8d8a\u8fdc<br \/>\n\u2192 \u901a\u5e38\u8bed\u4e49\u5dee\u5f02\u8d8a\u5927<\/p>\n<hr \/>\n<h2>23. Cosine Similarity \u548c Euclidean Distance \u7684\u533a\u522b<\/h2>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>A &#061; (1,1)<\/p>\n<p>B &#061; (10,10)<\/p>\n<p>\u4e24\u4e2a\u5411\u91cf\u6307\u5411\u5b8c\u5168\u76f8\u540c\u7684\u65b9\u5411\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>Cosine Similarity &#061; 1<\/p>\n<p>\u4f46\u662f\u6b27\u6c0f\u8ddd\u79bb&#xff1a;<\/p>\n<h2>$$<br \/>\n\\\\sqrt{(10-1)<sup>2&#043;(10-1)<\/sup>2}<\/h2>\n<p>\\\\sqrt{162}<br \/>\n\\\\approx 12.73<br \/>\n$$<\/p>\n<p>\u8bf4\u660e\u5b83\u4eec\u5728\u7a7a\u95f4\u4e2d\u7684\u5b9e\u9645\u4f4d\u7f6e\u76f8\u9694\u8f83\u8fdc\u3002<\/p>\n<p>\u6240\u4ee5\u53ef\u4ee5\u5f62\u8c61\u5730\u7406\u89e3&#xff1a;<\/p>\n<p>Cosine Similarity&#xff1a;<\/p>\n<p>\u201c\u4f60\u4eec\u4e24\u4e2a\u671d\u7684\u65b9\u5411\u50cf\u4e0d\u50cf&#xff1f;\u201d<\/p>\n<p>Euclidean Distance&#xff1a;<\/p>\n<p>\u201c\u4f60\u4eec\u4e24\u4e2a\u7ad9\u7684\u4f4d\u7f6e\u79bb\u5f97\u8fd1\u4e0d\u8fd1&#xff1f;\u201d<\/p>\n<hr \/>\n<h2>24. \u4e24\u8005\u90fd\u662f\u4e3a\u4e86\u8bed\u4e49\u68c0\u7d22\u5417&#xff1f;<\/h2>\n<p>\u5728 RAG \/ Vector Search \u573a\u666f\u4e2d&#xff1a;<\/p>\n<p>\u662f\u7684&#xff0c;\u4e24\u8005\u90fd\u53ef\u4ee5\u7528\u4e8e\u5bfb\u627e\u8bed\u4e49\u76f8\u4f3c\u7684\u6587\u672c\u3002<\/p>\n<p>\u4f46\u662f\u5b83\u4eec\u8861\u91cf\u76f8\u4f3c\u6027\u7684\u65b9\u5f0f\u4e0d\u540c\u3002<\/p>\n<table>\n<tr>\u65b9\u6cd5\u8861\u91cf\u4ec0\u4e48\u8d8a\u76f8\u4f3c\u65f6<\/tr>\n<tbody>\n<tr>\n<td>Cosine Similarity<\/td>\n<td>\u5411\u91cf\u65b9\u5411\u662f\u5426\u63a5\u8fd1<\/td>\n<td>\u503c\u8d8a\u5927<\/td>\n<\/tr>\n<tr>\n<td>Euclidean Distance<\/td>\n<td>\u5411\u91cf\u7a7a\u95f4\u4f4d\u7f6e\u662f\u5426\u63a5\u8fd1<\/td>\n<td>\u8ddd\u79bb\u8d8a\u5c0f<\/td>\n<\/tr>\n<tr>\n<td>Dot Product<\/td>\n<td>\u5411\u91cf\u65b9\u5411\u548c\u957f\u5ea6\u7684\u7efc\u5408\u5173\u7cfb<\/td>\n<td>\u901a\u5e38\u503c\u8d8a\u5927<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6240\u4ee5 RAG \u53ef\u4ee5\u662f&#xff1a;<\/p>\n<p>Query Vector<br \/>\n \u2193<br \/>\n\u548c\u6240\u6709 Chunk Vector \u6bd4\u8f83<br \/>\n \u2193<br \/>\n\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n\u2502 Cosine Similarity            \u2502<br \/>\n\u2502 \u6216 Euclidean Distance        \u2502<br \/>\n\u2502 \u6216 Dot Product               \u2502<br \/>\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n \u2193<br \/>\n\u6392\u5e8f<br \/>\n \u2193<br \/>\nTop-K<br \/>\n \u2193<br \/>\n\u6700\u76f8\u5173 Chunks<\/p>\n<p>\u5177\u4f53\u9009\u62e9\u54ea\u4e00\u79cd&#xff0c;\u9700\u8981\u6839\u636e&#xff1a;<\/p>\n<ul>\n<li>Embedding Model \u7684\u8bad\u7ec3\u65b9\u5f0f<\/li>\n<li>\u6a21\u578b\u5b98\u65b9\u63a8\u8350<\/li>\n<li>Vector Database \u914d\u7f6e<\/li>\n<\/ul>\n<p>\u6765\u51b3\u5b9a\u3002<\/p>\n<hr \/>\n<h2>25. Cosine \u548c Euclidean \u6709\u4ec0\u4e48\u5173\u7cfb&#xff1f;<\/h2>\n<p>\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u90fd\u8fdb\u884c\u4e86 L2 Normalization&#xff08;\u5f52\u4e00\u5316&#xff09;&#xff1a;<\/p>\n<p>||A|| &#061; 1<br \/>\n||B|| &#061; 1<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2225A\u2212B\u22252&#061;2\u22122cos\u2061\u03b8<br \/>\n\\\\|A-B\\\\|^2 &#061; 2 &#8211; 2\\\\cos\\\\theta<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/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: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u5355\u4f4d\u5411\u91cf&#xff1a;<\/p>\n<p>Cosine Similarity \u8d8a\u5927<br \/>\n        \u21d5<br \/>\nEuclidean Distance \u8d8a\u5c0f<\/p>\n<p>\u56e0\u6b64\u5728\u5411\u91cf\u5df2\u7ecf\u5f52\u4e00\u5316\u7684\u60c5\u51b5\u4e0b&#xff0c;\u4e24\u79cd\u65b9\u6cd5\u5f97\u5230\u7684\u6392\u5e8f\u53ef\u80fd\u5b8c\u5168\u4e00\u81f4\u6216\u975e\u5e38\u63a5\u8fd1\u3002<\/p>\n<hr \/>\n<h2>26. \u4e09\u79cd\u201c\u5411\u91cf\u201d\u4e0d\u8981\u6df7\u6dc6<\/h2>\n<p>\u8fd9\u662f\u6574\u4e2a\u77e5\u8bc6\u4f53\u7cfb\u4e2d\u975e\u5e38\u91cd\u8981\u7684\u4e00\u70b9\u3002<\/p>\n<h3>26.1 Token Embedding<\/h3>\n<p>Token ID<br \/>\n \u2193<br \/>\nEmbedding Table<br \/>\n \u2193<br \/>\n\u4e00\u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf<\/p>\n<p>\u4e3b\u8981\u4f5c\u7528&#xff1a;<\/p>\n<p>\u628a\u79bb\u6563 Token ID \u8f6c\u6362\u6210\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u8ba1\u7b97\u7684\u8fde\u7eed\u5411\u91cf\u3002<\/p>\n<hr \/>\n<h3>26.2 Transformer Hidden State<\/h3>\n<p>Token Embedding<br \/>\n \u2193<br \/>\n\u591a\u5c42 Transformer<br \/>\n \u2193<br \/>\n\u7ed3\u5408\u4e0a\u4e0b\u6587<br \/>\n \u2193<br \/>\nContextualized Hidden State<\/p>\n<p>\u4e3b\u8981\u4f5c\u7528&#xff1a;<\/p>\n<p>\u8868\u793a Token \u5728\u5f53\u524d\u4e0a\u4e0b\u6587\u4e2d\u7684\u4fe1\u606f\u3002<\/p>\n<p>\u540c\u4e00\u4e2a Token \u5728\u4e0d\u540c\u53e5\u5b50\u4e2d\u7684 Hidden State \u53ef\u4ee5\u4e0d\u540c\u3002<\/p>\n<hr \/>\n<h3>26.3 RAG Text Embedding<\/h3>\n<p>\u4e00\u53e5\u8bdd \/ Query \/ Chunk<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\n\u4e00\u4e2a\u9ad8\u7ef4\u5411\u91cf<\/p>\n<p>\u4e3b\u8981\u4f5c\u7528&#xff1a;<\/p>\n<p>\u8868\u793a\u6574\u6bb5\u6587\u672c\u7684\u8bed\u4e49&#xff0c;\u7528\u4e8e\u8bed\u4e49\u641c\u7d22\u3001\u5411\u91cf\u68c0\u7d22\u7b49\u3002<\/p>\n<hr \/>\n<h2>27. Token \u4e3a\u4ec0\u4e48\u4e5f\u662f AI \u7684\u8ba1\u8d39\u5355\u4f4d&#xff1f;<\/h2>\n<p>\u5927\u6a21\u578b\u7684\u8ba1\u7b97\u91cf\u4e0e Token \u6570\u91cf\u9ad8\u5ea6\u76f8\u5173&#xff0c;\u56e0\u6b64\u5f88\u591a LLM API \u6309 Token \u8ba1\u8d39\u3002<\/p>\n<p>\u4e3b\u8981\u5206\u6210&#xff1a;<\/p>\n<h4>Input Tokens<\/h4>\n<p>\u53d1\u9001\u7ed9\u6a21\u578b\u5904\u7406\u7684\u5185\u5bb9&#xff0c;\u4f8b\u5982&#xff1a;<\/p>\n<p>System Prompt<br \/>\n\u7528\u6237 Prompt<br \/>\n\u5386\u53f2\u5bf9\u8bdd<br \/>\nRAG \u68c0\u7d22\u7ed3\u679c<br \/>\n\u5de5\u5177\u8c03\u7528\u7ed3\u679c<br \/>\n&#8230;<\/p>\n<p>\u90fd\u53ef\u80fd\u8ba1\u5165 Input Tokens\u3002<\/p>\n<h4>Output Tokens<\/h4>\n<p>\u6a21\u578b\u751f\u6210\u51fa\u6765\u7684 Token&#xff1a;<\/p>\n<p>Token 1<br \/>\nToken 2<br \/>\nToken 3<br \/>\n&#8230;<\/p>\n<p>\u5c5e\u4e8e Output Tokens\u3002<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>Total Tokens<br \/>\n&#061;<br \/>\nInput Tokens<br \/>\n&#043;<br \/>\nOutput Tokens<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>Input Tokens  &#061; 1000<br \/>\nOutput Tokens &#061; 500<\/p>\n<p>Total Tokens  &#061; 1500<\/p>\n<hr \/>\n<h2>28. Input \u548c Output \u901a\u5e38\u5206\u5f00\u8ba1\u4ef7<\/h2>\n<p>\u867d\u7136&#xff1a;<\/p>\n<p>Total Tokens<br \/>\n&#061;<br \/>\nInput Tokens &#043; Output Tokens<\/p>\n<p>\u4f46\u662f\u5f88\u591a API \u5e76\u4e0d\u662f&#xff1a;<\/p>\n<p>1500 \u00d7 \u4e00\u4e2a\u7edf\u4e00\u4ef7\u683c<\/p>\n<p>\u800c\u662f&#xff1a;<\/p>\n<p>Input Tokens \u00d7 Input Price<br \/>\n&#043;<br \/>\nOutput Tokens \u00d7 Output Price<br \/>\n&#061;<br \/>\n\u6700\u7ec8\u8d39\u7528<\/p>\n<p>\u4f8b\u5982\u5047\u8bbe&#xff1a;<\/p>\n<p>Input&#xff1a;<br \/>\n$2 \/ 1M Tokens<\/p>\n<p>Output&#xff1a;<br \/>\n$8 \/ 1M Tokens<\/p>\n<p>\u5982\u679c&#xff1a;<\/p>\n<p>Input  &#061; 1M Tokens<br \/>\nOutput &#061; 1M Tokens<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>\u8f93\u5165\u8d39\u7528 &#061; $2<\/p>\n<p>\u8f93\u51fa\u8d39\u7528 &#061; $8<\/p>\n<p>\u603b\u8d39\u7528 &#061; $10<\/p>\n<p>\u5b9e\u9645 API \u8fd8\u53ef\u80fd\u5b58\u5728&#xff1a;<\/p>\n<p>Cached Input Tokens<\/p>\n<p>\u7b49\u5176\u4ed6\u8ba1\u8d39\u7c7b\u522b\u3002<\/p>\n<hr \/>\n<h2>29. \u4e3a\u4ec0\u4e48 Output Token \u5f80\u5f80\u66f4\u8d35&#xff1f;<\/h2>\n<p>\u8f93\u5165\u9636\u6bb5\u4e3b\u8981\u662f&#xff1a;<\/p>\n<p>\u5927\u91cf Input Tokens<br \/>\n \u2193<br \/>\nPrefill<br \/>\n \u2193<br \/>\nGPU \u53ef\u4ee5\u9ad8\u5ea6\u5e76\u884c\u5904\u7406<\/p>\n<p>\u800c\u8f93\u51fa\u9636\u6bb5&#xff1a;<\/p>\n<p>Token 1<br \/>\n \u2193<br \/>\nToken 2<br \/>\n \u2193<br \/>\nToken 3<br \/>\n \u2193<br \/>\nToken 4<br \/>\n \u2193<br \/>\n&#8230;<\/p>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>\u5fc5\u987b\u5148\u5f97\u5230 Token N<br \/>\n       \u2193<br \/>\n\u624d\u80fd\u786e\u5b9a\u4e0b\u4e00\u8f6e\u8f93\u5165<br \/>\n       \u2193<br \/>\n\u518d\u9884\u6d4b Token N&#043;1<\/p>\n<p>\u56e0\u6b64 Decode \u5177\u6709\u660e\u663e\u7684\u81ea\u56de\u5f52\u4e32\u884c\u7279\u5f81\u3002<\/p>\n<p>\u6240\u4ee5\u5f88\u591a\u6a21\u578b&#xff1a;<\/p>\n<p>Output Token \u7684 API \u5355\u4ef7\u4f1a\u9ad8\u4e8e Input Token\u3002<\/p>\n<hr \/>\n<h2>30. \u591a\u8f6e\u804a\u5929\u4e3a\u4ec0\u4e48\u8d8a\u6765\u8d8a\u6d88\u8017 Token&#xff1f;<\/h2>\n<p>\u5047\u8bbe\u7b2c\u4e00\u8f6e&#xff1a;<\/p>\n<p>\u7528\u6237\u8f93\u5165&#xff1a;1000 Tokens<br \/>\nAI \u8f93\u51fa&#xff1a;1000 Tokens<\/p>\n<p>\u7b2c\u4e8c\u8f6e\u7528\u6237\u53ea\u65b0\u8f93\u5165&#xff1a;<\/p>\n<p>100 Tokens<\/p>\n<p>\u4f46\u662f\u6a21\u578b\u4e3a\u4e86\u7406\u89e3\u4e0a\u4e0b\u6587&#xff0c;\u7cfb\u7edf\u53ef\u80fd\u8fd8\u9700\u8981\u628a\u4e4b\u524d\u76f8\u5173\u5bf9\u8bdd\u4e00\u8d77\u4f5c\u4e3a\u8f93\u5165&#xff1a;<\/p>\n<p>\u4e4b\u524d\u7528\u6237&#xff1a;1000<br \/>\n\u4e4b\u524d AI&#xff1a;1000<br \/>\n\u672c\u8f6e\u7528\u6237&#xff1a;100<br \/>\n&#8212;&#8212;&#8212;&#8212;&#8212;-<br \/>\nInput \u2248 2100 Tokens<\/p>\n<p>\u5982\u679c\u6a21\u578b\u518d\u56de\u7b54&#xff1a;<\/p>\n<p>Output &#061; 1000 Tokens<\/p>\n<p>\u90a3\u4e48\u8fd9\u4e00\u8f6e\u53ef\u80fd\u4ea7\u751f&#xff1a;<\/p>\n<p>Input  \u2248 2100<br \/>\nOutput \u2248 1000<\/p>\n<p>Total \u2248 3100 Tokens<\/p>\n<p>\u800c\u4e0d\u662f&#xff1a;<\/p>\n<p>100 &#043; 1000 &#061; 1100<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>\u5bf9\u8bdd\u8d8a\u957f\u3001Prompt \u8d8a\u5927\u3001RAG \u68c0\u7d22\u5185\u5bb9\u8d8a\u591a\u3001Agent \u5de5\u5177\u7ed3\u679c\u8d8a\u591a&#xff0c;Token \u6d88\u8017\u901a\u5e38\u8d8a\u5927\u3002<\/p>\n<p>\u5b9e\u9645\u7cfb\u7edf\u8fd8\u53ef\u80fd\u4f7f\u7528&#xff1a;<\/p>\n<p>Prompt Caching \/ Cached Input<\/p>\n<p>\u964d\u4f4e\u91cd\u590d\u4e0a\u4e0b\u6587\u7684\u6210\u672c\u3002<\/p>\n<hr \/>\n<h2>31. \u201c\u4e70\u4e86 100 \u4e07 Token\u201d\u662f\u4ec0\u4e48\u610f\u601d&#xff1f;<\/h2>\n<p>\u9700\u8981\u770b\u5177\u4f53\u5e73\u53f0\u7684\u5b9a\u4e49\u3002<\/p>\n<p>\u6807\u51c6\u6a21\u578b API \u4e00\u822c\u4f1a\u660e\u786e\u533a\u5206&#xff1a;<\/p>\n<p>Input Tokens<br \/>\nOutput Tokens<br \/>\nCached Input Tokens<br \/>\n&#8230;<\/p>\n<p>\u4f46\u662f\u67d0\u4e9b\u7b2c\u4e09\u65b9\u5e73\u53f0\u6240\u8c13&#xff1a;<\/p>\n<p>\u8d2d\u4e70 1000 \u4e07 Token<\/p>\n<p>\u53ef\u80fd\u5b9e\u9645\u4e0a\u662f\u5e73\u53f0\u81ea\u5df1\u7684&#xff1a;<\/p>\n<p>Credits<br \/>\n\u79ef\u5206<br \/>\nToken \u989d\u5ea6<\/p>\n<p>\u4f8b\u5982\u53ef\u80fd\u89c4\u5b9a&#xff1a;<\/p>\n<p>\u666e\u901a\u6a21\u578b \u00d71<br \/>\n\u9ad8\u7ea7\u6a21\u578b \u00d710<\/p>\n<p>Input \u00d71<br \/>\nOutput \u00d74<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>\u7b2c\u4e09\u65b9\u5e73\u53f0\u6240\u8bf4\u7684\u201c1000 \u4e07 Token\u201d&#xff0c;\u4e0d\u4e00\u5b9a\u4ee3\u8868\u53ef\u4ee5\u771f\u5b9e\u8f93\u5165 &#043; \u8f93\u51fa 1000 \u4e07\u4e2a\u6a21\u578b Token\u3002<\/p>\n<p>\u5fc5\u987b\u67e5\u770b\u5177\u4f53\u5e73\u53f0\u7684\u8ba1\u8d39\u89c4\u5219\u3002<\/p>\n<hr \/>\n<h2>32. LLM \u4e0e RAG \u7684\u5173\u7cfb<\/h2>\n<p>\u53ef\u4ee5\u628a\u4e24\u8005\u653e\u5230\u4e00\u8d77\u7406\u89e3\u3002<\/p>\n<p>                       \u7528\u6237\u95ee\u9898<br \/>\n                          \u2502<br \/>\n              \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n              \u2502                       \u2502<br \/>\n              \u2193                       \u2193<br \/>\n            RAG                      LLM<br \/>\n              \u2502                       \u2502<br \/>\n       Embedding Model           Tokenizer<br \/>\n              \u2502                       \u2502<br \/>\n        Query Vector               Token ID<br \/>\n              \u2502                       \u2502<br \/>\n       Vector Database        Token Embedding<br \/>\n              \u2502                       \u2502<br \/>\n       Similarity Search       Transformer<br \/>\n              \u2502                       \u2502<br \/>\n           Top-K             Hidden States<br \/>\n              \u2502                       \u2502<br \/>\n       \u76f8\u5173\u77e5\u8bc6 Chunks                 \u2502<br \/>\n              \u2502                       \u2502<br \/>\n              \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2192 Prompt \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n                          \u2193<br \/>\n                         LLM<br \/>\n                          \u2193<br \/>\n                       LM Head<br \/>\n                          \u2193<br \/>\n                    \u4e0b\u4e00\u4e2a Token<br \/>\n                          \u2193<br \/>\n                       KV Cache<br \/>\n                          \u2193<br \/>\n                        Decode<br \/>\n                          \u2193<br \/>\n                     \u4e0d\u65ad\u5faa\u73af\u751f\u6210<br \/>\n                          \u2193<br \/>\n                       \u6700\u7ec8\u56de\u7b54<\/p>\n<p>\u9700\u8981\u6ce8\u610f&#xff1a;<\/p>\n<p>RAG \u8d1f\u8d23\u201c\u627e\u8d44\u6599\u201d&#xff0c;LLM \u8d1f\u8d23\u201c\u7406\u89e3\u4e0a\u4e0b\u6587\u5e76\u751f\u6210\u7b54\u6848\u201d\u3002<\/p>\n<hr \/>\n<h2>33. \u6838\u5fc3\u6982\u5ff5\u901f\u8bb0\u8868<\/h2>\n<table>\n<tr>\u6982\u5ff5\u6838\u5fc3\u542b\u4e49<\/tr>\n<tbody>\n<tr>\n<td>Tokenizer<\/td>\n<td>\u5c06\u6587\u672c\u5207\u5206\u5e76\u7f16\u7801\u4e3a Token ID<\/td>\n<\/tr>\n<tr>\n<td>Token<\/td>\n<td>\u6a21\u578b\u5904\u7406\u6587\u672c\u7684\u57fa\u672c\u79bb\u6563\u5355\u4f4d<\/td>\n<\/tr>\n<tr>\n<td>Token ID<\/td>\n<td>Token \u5728 Vocabulary \u4e2d\u5bf9\u5e94\u7684\u6574\u6570\u7f16\u53f7<\/td>\n<\/tr>\n<tr>\n<td>Vocabulary<\/td>\n<td>Token \u4e0e Token ID \u7684\u6620\u5c04\u8bcd\u8868<\/td>\n<\/tr>\n<tr>\n<td>Embedding<\/td>\n<td>\u5c06\u79bb\u6563\u4fe1\u606f\u8f6c\u6362\u6210\u8fde\u7eed\u9ad8\u7ef4\u5411\u91cf<\/td>\n<\/tr>\n<tr>\n<td>Embedding Table<\/td>\n<td>\u6839\u636e Token ID \u67e5\u627e\u521d\u59cb Token \u5411\u91cf\u7684\u53c2\u6570\u77e9\u9635<\/td>\n<\/tr>\n<tr>\n<td>Token Embedding<\/td>\n<td>\u4e00\u4e2a Token \u7684\u521d\u59cb\u9ad8\u7ef4\u8868\u793a<\/td>\n<\/tr>\n<tr>\n<td>Transformer<\/td>\n<td>\u901a\u8fc7 Attention \u7b49\u673a\u5236\u878d\u5408\u4e0a\u4e0b\u6587\u5e76\u8fdb\u884c\u591a\u5c42\u7279\u5f81\u53d8\u6362<\/td>\n<\/tr>\n<tr>\n<td>Hidden State<\/td>\n<td>Token \u7ecf\u8fc7 Transformer \u540e\u5f97\u5230\u7684\u4e0a\u4e0b\u6587\u5316\u8868\u793a<\/td>\n<\/tr>\n<tr>\n<td>LM Head<\/td>\n<td>\u5c06 Hidden State \u6620\u5c04\u5230 Vocabulary \u7684 Logits<\/td>\n<\/tr>\n<tr>\n<td>Logits<\/td>\n<td>\u6a21\u578b\u5bf9 Vocabulary \u4e2d\u5404 Token \u7ed9\u51fa\u7684\u539f\u59cb\u5206\u6570<\/td>\n<\/tr>\n<tr>\n<td>Autoregressive<\/td>\n<td>\u6839\u636e\u5df2\u6709 Token \u4e0d\u65ad\u9884\u6d4b\u4e0b\u4e00\u4e2a Token<\/td>\n<\/tr>\n<tr>\n<td>Prefill<\/td>\n<td>\u4e00\u6b21\u5904\u7406 Prompt&#xff0c;\u5e76\u5efa\u7acb\u540e\u7eed\u751f\u6210\u9700\u8981\u7684\u72b6\u6001<\/td>\n<\/tr>\n<tr>\n<td>Decode<\/td>\n<td>\u751f\u6210\u9636\u6bb5\u9010 Token \u9884\u6d4b<\/td>\n<\/tr>\n<tr>\n<td>KV Cache<\/td>\n<td>\u7f13\u5b58\u5386\u53f2 Token \u5404 Transformer \u5c42\u7684 K\/V<\/td>\n<\/tr>\n<tr>\n<td>Text Embedding<\/td>\n<td>\u7528\u4e00\u4e2a\u9ad8\u7ef4\u5411\u91cf\u8868\u793a Query \/ Chunk \u7b49\u6574\u6bb5\u6587\u672c<\/td>\n<\/tr>\n<tr>\n<td>Vector Database<\/td>\n<td>\u5b58\u50a8\u548c\u68c0\u7d22\u9ad8\u7ef4\u5411\u91cf<\/td>\n<\/tr>\n<tr>\n<td>Cosine Similarity<\/td>\n<td>\u6bd4\u8f83\u4e24\u4e2a\u5411\u91cf\u65b9\u5411\u662f\u5426\u63a5\u8fd1<\/td>\n<\/tr>\n<tr>\n<td>Euclidean Distance<\/td>\n<td>\u6bd4\u8f83\u4e24\u4e2a\u5411\u91cf\u5728\u7a7a\u95f4\u4e2d\u7684\u5b9e\u9645\u8ddd\u79bb<\/td>\n<\/tr>\n<tr>\n<td>Dot Product<\/td>\n<td>\u901a\u8fc7\u70b9\u79ef\u8861\u91cf\u5411\u91cf\u5173\u7cfb&#xff0c;\u53ef\u7528\u4e8e\u5411\u91cf\u68c0\u7d22<\/td>\n<\/tr>\n<tr>\n<td>Top-K<\/td>\n<td>\u53d6\u76f8\u5173\u6027\u6700\u9ad8\u7684 K \u4e2a\u68c0\u7d22\u7ed3\u679c<\/td>\n<\/tr>\n<tr>\n<td>RAG<\/td>\n<td>\u5148\u68c0\u7d22\u5916\u90e8\u77e5\u8bc6&#xff0c;\u518d\u8ba9 LLM \u57fa\u4e8e\u77e5\u8bc6\u751f\u6210\u7b54\u6848<\/td>\n<\/tr>\n<tr>\n<td>Input Tokens<\/td>\n<td>\u8f93\u5165\u7ed9\u6a21\u578b\u5904\u7406\u7684 Token<\/td>\n<\/tr>\n<tr>\n<td>Output Tokens<\/td>\n<td>\u6a21\u578b\u751f\u6210\u7684 Token<\/td>\n<\/tr>\n<tr>\n<td>Total Tokens<\/td>\n<td>Input Tokens &#043; Output Tokens<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2>34. \u4e00\u53e5\u8bdd\u7406\u89e3 Token<\/h2>\n<p>Token \u662f Tokenizer \u5bf9\u6587\u672c\u5207\u5206\u540e\u5f97\u5230\u7684\u57fa\u672c\u5904\u7406\u5355\u4f4d&#xff1b;\u6bcf\u4e2a Token \u5728 Vocabulary \u4e2d\u5bf9\u5e94\u4e00\u4e2a Token ID\u3002<\/p>\n<hr \/>\n<h2>35. \u4e00\u53e5\u8bdd\u7406\u89e3 Embedding<\/h2>\n<p>Embedding \u5c31\u662f\u628a\u79bb\u6563\u7684 Token\u3001\u6587\u672c\u7b49\u4fe1\u606f\u8f6c\u6362\u6210\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u8ba1\u7b97\u548c\u6bd4\u8f83\u7684\u9ad8\u7ef4\u8fde\u7eed\u5411\u91cf\u3002<\/p>\n<hr \/>\n<h2>36. \u4e00\u53e5\u8bdd\u7406\u89e3 Transformer<\/h2>\n<p>Transformer \u901a\u8fc7\u591a\u5c42 Attention \u548c\u795e\u7ecf\u7f51\u7edc\u8ba1\u7b97&#xff0c;\u8ba9\u6bcf\u4e2a Token \u7684\u521d\u59cb\u5411\u91cf\u4e0d\u65ad\u878d\u5408\u4e0a\u4e0b\u6587\u4fe1\u606f&#xff0c;\u6700\u7ec8\u5f62\u6210\u4e0a\u4e0b\u6587\u5316\u7684 Hidden State\u3002<\/p>\n<hr \/>\n<h2>37. \u4e00\u53e5\u8bdd\u7406\u89e3 LLM \u751f\u6210<\/h2>\n<p>LLM \u5c06\u6587\u5b57\u8f6c\u6362\u6210 Token ID \u548c\u5411\u91cf&#xff0c;\u7ecf\u8fc7\u591a\u5c42 Transformer \u5f97\u5230 Hidden State&#xff0c;\u518d\u5229\u7528\u6700\u540e\u4f4d\u7f6e\u7684 Hidden State \u9884\u6d4b\u4e0b\u4e00\u4e2a Token&#xff0c;\u5e76\u901a\u8fc7 KV Cache \u9ad8\u6548\u5730\u9010 Token \u5faa\u73af\u751f\u6210&#xff0c;\u76f4\u5230\u56de\u7b54\u7ed3\u675f\u3002<\/p>\n<hr \/>\n<h2>38. \u4e00\u53e5\u8bdd\u7406\u89e3 RAG<\/h2>\n<p>RAG \u5c06\u6587\u6863 Chunk \u548c\u7528\u6237\u95ee\u9898\u901a\u8fc7 Embedding Model \u8f6c\u6362\u6210\u8bed\u4e49\u5411\u91cf&#xff0c;\u518d\u4f7f\u7528 Cosine Similarity\u3001Euclidean Distance\u3001Dot Product \u7b49\u65b9\u6cd5\u68c0\u7d22\u6700\u76f8\u5173\u7684 Chunk&#xff0c;\u6700\u540e\u628a\u68c0\u7d22\u5230\u7684\u77e5\u8bc6\u4ea4\u7ed9 LLM \u751f\u6210\u7b54\u6848\u3002<\/p>\n<hr \/>\n<h2>39. \u4e00\u53e5\u8bdd\u533a\u5206 Cosine \u548c Euclidean<\/h2>\n<p>Cosine Similarity \u770b\u4e24\u4e2a\u5411\u91cf\u201c\u671d\u7684\u65b9\u5411\u50cf\u4e0d\u50cf\u201d&#xff1b;Euclidean Distance \u770b\u4e24\u4e2a\u5411\u91cf\u201c\u5728\u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u79bb\u5f97\u8fd1\u4e0d\u8fd1\u201d\u3002\u4e8c\u8005\u90fd\u53ef\u4ee5\u7528\u4e8e RAG \u7684\u8bed\u4e49\u5411\u91cf\u68c0\u7d22\u3002<\/p>\n<hr \/>\n<h2>40. \u6700\u7ec8\u77e5\u8bc6\u94fe\u8def<\/h2>\n<h3>LLM<\/h3>\n<p>\u6587\u5b57<br \/>\n \u2193<br \/>\nTokenizer<br \/>\n \u2193<br \/>\nToken<br \/>\n \u2193<br \/>\nToken ID<br \/>\n \u2193<br \/>\nEmbedding Table<br \/>\n \u2193<br \/>\nToken Embedding<br \/>\n \u2193<br \/>\n\u591a\u5c42 Transformer<br \/>\n \u2193<br \/>\nContextualized Hidden States<br \/>\n \u2193<br \/>\n\u6700\u540e\u4f4d\u7f6e Hidden State<br \/>\n \u2193<br \/>\nLM Head<br \/>\n \u2193<br \/>\nVocabulary Logits<br \/>\n \u2193<br \/>\n\u9009\u62e9\u4e0b\u4e00\u4e2a Token<br \/>\n \u2193<br \/>\nKV Cache<br \/>\n \u2193<br \/>\nDecode<br \/>\n \u2193<br \/>\n\u7ee7\u7eed\u9884\u6d4b<br \/>\n \u2193<br \/>\n\u6700\u7ec8\u56de\u7b54<\/p>\n<h3>RAG<\/h3>\n<p>\u6587\u6863<br \/>\n \u2193<br \/>\nChunk<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\nText Embedding<br \/>\n \u2193<br \/>\nVector Database<br \/>\n        \u2191<br \/>\n        \u2502<br \/>\n\u7528\u6237\u95ee\u9898<br \/>\n \u2193<br \/>\nEmbedding Model<br \/>\n \u2193<br \/>\nQuery Embedding<br \/>\n \u2193<br \/>\nCosine Similarity<br \/>\n\u6216 Euclidean Distance<br \/>\n\u6216 Dot Product<br \/>\n \u2193<br \/>\nTop-K Chunks<br \/>\n \u2193<br \/>\n\u7528\u6237\u95ee\u9898 &#043; \u68c0\u7d22\u7ed3\u679c<br \/>\n \u2193<br \/>\nLLM<br \/>\n \u2193<br \/>\n\u6700\u7ec8\u7b54\u6848<\/p>\n<hr \/>\n<h2>41. \u6700\u7ec8\u603b\u7ed3<\/h2>\n<p>\u6574\u4e2a\u5927\u8bed\u8a00\u6a21\u578b\u548c RAG \u7684\u57fa\u7840\u903b\u8f91\u53ef\u4ee5\u6d53\u7f29\u6210&#xff1a;<\/p>\n<p>                    AI \u5904\u7406\u6587\u5b57\u7684\u6838\u5fc3<\/p>\n<p>                         \u6587\u5b57<br \/>\n                          \u2193<br \/>\n                       Token<br \/>\n                          \u2193<br \/>\n                      Token ID<br \/>\n                          \u2193<br \/>\n                       \u5411\u91cf\u5316<br \/>\n                          \u2193<br \/>\n              \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n              \u2193                       \u2193<br \/>\n             LLM                     RAG<br \/>\n              \u2193                       \u2193<br \/>\n      Transformer \u8ba1\u7b97          Embedding Model<br \/>\n              \u2193                       \u2193<br \/>\n       \u7406\u89e3\u4e0a\u4e0b\u6587\u5173\u7cfb             \u8bed\u4e49\u5411\u91cf<br \/>\n              \u2193                       \u2193<br \/>\n      \u9884\u6d4b\u4e0b\u4e00\u4e2a Token           Vector Search<br \/>\n              \u2193                       \u2193<br \/>\n        \u4e0d\u65ad\u5faa\u73af\u751f\u6210              \u627e\u76f8\u5173\u77e5\u8bc6<br \/>\n              \u2502                       \u2502<br \/>\n              \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n                         \u2193<br \/>\n                      \u6700\u7ec8\u56de\u7b54<\/p>\n<p>\u6700\u91cd\u8981\u7684\u662f\u7406\u89e3\u8fd9\u51e0\u4e2a\u8f6c\u6362&#xff1a;<\/p>\n<p>\u6587\u5b57<br \/>\n\u2192 Token<br \/>\n\u2192 Token ID<br \/>\n\u2192 \u9ad8\u7ef4\u5411\u91cf<\/p>\n<p>\u5728 LLM \u4e2d&#xff1a;<\/p>\n<p>\u9ad8\u7ef4\u5411\u91cf<br \/>\n\u2192 Transformer<br \/>\n\u2192 \u4e0a\u4e0b\u6587\u5316 Hidden State<br \/>\n\u2192 LM Head<br \/>\n\u2192 \u4e0b\u4e00\u4e2a Token<br \/>\n\u2192 \u5faa\u73af\u751f\u6210<\/p>\n<p>\u5728 RAG \u4e2d&#xff1a;<\/p>\n<p>\u6587\u672c<br \/>\n\u2192 Embedding Model<br \/>\n\u2192 \u6574\u6bb5\u6587\u672c\u7684\u8bed\u4e49\u5411\u91cf<br \/>\n\u2192 Vector Database<br \/>\n\u2192 \u76f8\u4f3c\u5ea6 \/ \u8ddd\u79bb\u68c0\u7d22<br \/>\n\u2192 Top-K<br \/>\n\u2192 LLM<\/p>\n<p>\u56e0\u6b64\u53ef\u4ee5\u628a\u4e24\u8005\u6982\u62ec\u4e3a&#xff1a;<\/p>\n<p>LLM \u7684\u6838\u5fc3\u4efb\u52a1\u662f\u6839\u636e\u4e0a\u4e0b\u6587\u4e0d\u65ad\u9884\u6d4b\u4e0b\u4e00\u4e2a Token&#xff1b;RAG \u7684\u6838\u5fc3\u4efb\u52a1\u662f\u5728 LLM \u751f\u6210\u4e4b\u524d&#xff0c;\u901a\u8fc7\u5411\u91cf\u8bed\u4e49\u68c0\u7d22\u7ed9\u6a21\u578b\u627e\u5230\u66f4\u76f8\u5173\u3001\u66f4\u53ef\u9760\u7684\u5916\u90e8\u77e5\u8bc6\u3002<\/p>\n<hr \/>\n<p>&#x1f4ac; \u5982\u679c\u672c\u6587\u5bf9\u4f60\u6709\u5e2e\u52a9&#xff0c;\u6b22\u8fce\u70b9\u8d5e &#043; \u6536\u85cf &#043; \u5206\u4eab<br \/>\n&#x1f4cc; \u66f4\u591a AI \u5de5\u7a0b\u5b9e\u8df5\u5185\u5bb9&#xff0c;\u6b22\u8fce\u5173\u6ce8\u300cYoanAILab\u300d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. \u6574\u4f53\u77e5\u8bc6\u6846\u67b6<br \/>\n\u7406\u89e3\u5927\u8bed\u8a00\u6a21\u578b&#xff0c;\u53ef\u4ee5\u5148\u8bb0\u4f4f\u4e24\u6761\u4e3b\u7ebf&#xff1a;<br \/>\nLLM \u751f\u6210\u4e3b\u7ebf<br \/>\n\u6587\u5b57\u2193<br \/>\nTokenizer\u2193<br \/>\nToken\u2193<br \/>\nToken ID\u2193<br \/>\nEmbedding Table\u2193<br \/>\n\u6bcf\u4e2a Token \u4e00\u4e2a\u521d\u59cb\u9ad8\u7ef4\u5411\u91cf\u2193<br \/>\n\u52a0\u5165\u4f4d\u7f6e\u4fe1\u606f\u2193<br \/>\n\u591a\u5c42 Transformer\u2193<br \/>\n\u6bcf\u4e2a Token \u5f97\u5230\u4e0a\u4e0b\u6587\u5316 Hidden State\u2193<br \/>\n\u53d6\u5f53\u524d\u6700\u540e\u4f4d\u7f6e\u7684 Hidden State\u2193<br \/>\nLM Head\u2193<br \/>\nVocabulary Logits\u2193<br \/>\n\u9009\u62e9\u4e0b\u4e00\u4e2a Token\u2193<br \/>\nKV<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[346,4119,1717,841,51],"topic":[],"class_list":["post-98822","post","type-post","status-publish","format-standard","hentry","category-server","tag-embedding","tag-rag","tag-token","tag-transformer","tag-51"],"yoast_head":"<!-- This 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