{"id":6003,"date":"2025-06-26T12:09:14","date_gmt":"2025-06-26T04:09:14","guid":{"rendered":"https:\/\/nullthought.net\/?p=6003"},"modified":"2025-06-26T12:09:15","modified_gmt":"2025-06-26T04:09:15","slug":"muvera%ef%bc%9a%e9%80%9a%e8%bf%87%e6%9e%84%e9%80%a0%e5%9b%ba%e5%ae%9a%e7%bb%b4%e5%ba%a6%e7%bc%96%e7%a0%81%ef%bc%88fdes%ef%bc%89%ef%bc%8c%e5%b0%86%e5%a4%8d%e6%9d%82%e7%9a%84%e5%a4%9a%e5%90%91%e9%87%8f","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=6003","title":{"rendered":"MUVERA\uff1a\u901a\u8fc7\u6784\u9020\u56fa\u5b9a\u7ef4\u5ea6\u7f16\u7801\uff08FDEs\uff09\uff0c\u5c06\u590d\u6742\u7684\u591a\u5411\u91cf\uff08MV\uff09\u68c0\u7d22\u4efb\u52a1\u7b80\u5316\u4e3a\u5355\u5411\u91cf\u6700\u5927\u5185\u79ef\uff08SV MIPS\uff09\u95ee\u9898"},"content":{"rendered":"\n<p>\u8bba\u6587<strong><a href=\"https:\/\/arxiv.org\/abs\/2405.19504\" target=\"_blank\" rel=\"noreferrer noopener\">MUVERA: Multi-Vector Retrieval via Fixed Dimensional Encodings<\/a><\/strong>\u63d0\u51faMUVERA\u8fd9\u4e00\u7406\u8bba\u4e0e\u5b9e\u8df5\u517c\u5907\u7684\u591a\u5411\u91cf\u68c0\u7d22\u65b0\u6846\u67b6\u3002\u8be5\u6846\u67b6\u901a\u8fc7\u6784\u5efaFDE\uff08\u56fa\u5b9a\u7ef4\u5ea6\u7f16\u7801\uff0cFixed Dimensional Encodings\uff09\u6709\u6548\u5c06MV\uff08\u591a\u5411\u91cf\uff0cMulti-Vector\uff09\u68c0\u7d22\u4efb\u52a1\u8f6c\u6362\u4e3aSV MIPS\uff08\u5355\u5411\u91cf\uff0cSingle-Vector\uff1b\u6700\u5927\u5185\u79ef\u641c\u7d22\uff0cMaximum Inner Product Search\uff09\u95ee\u9898\uff0c\u5728\u4fdd\u6301\u7cbe\u5ea6\u7684\u540c\u65f6\u663e\u8457\u964d\u4f4e\u8ba1\u7b97\u5ef6\u8fdf\u4e0e\u7cfb\u7edf\u590d\u6742\u5ea6\u3002\u5c3d\u7ba1\u5728MS MARCO\u4e0a\u4e0d\u660e\u663e\u4f18\u4e8ePLAID\uff08\u53ef\u80fd\u56e0\u4e3aPLAID\u4e3a\u5176\u9ad8\u5ea6\u5b9a\u5236\u4f18\u5316\uff09\uff0cMUVERA\u5728\u5176\u4ed6\u6570\u636e\u96c6\u4e0a\u7684\u6cdb\u5316\u6027\u548c\u6548\u7387\u66f4\u5177\u4f18\u52bf\u3002\u672a\u6765\u53ef\u63a2\u7d22\u8fdb\u4e00\u6b65\u4f18\u5316FDE\u6784\u9020\u65b9\u6cd5\u3001\u9002\u5e94\u66f4\u5e7f\u6cdb\u7684\u6a21\u578b\u7ed3\u6784\u4e0e\u9886\u57df\u3002<\/p>\n\n\n\n<p>\u8bba\u6587\u4f5c\u8005\u4e3aLaxman Dhulipala, Majid Hadian, Rajesh Jayaram, Jason Lee, Vahab Mirrokni\uff0c\u5747\u6765\u81eaGoogle\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"402\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/06\/image-1-1024x402.png\" alt=\"\" class=\"wp-image-6004\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/06\/image-1-1024x402.png 1024w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/06\/image-1-300x118.png 300w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/06\/image-1-768x302.png 768w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/06\/image-1.png 1059w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2405.19504\" target=\"_blank\" rel=\"noreferrer noopener\">MUVERA: Multi-Vector Retrieval via Fixed Dimensional Encodings<\/a><\/strong><\/figcaption><\/figure>\n\n\n\n<p>\u4e00\u3001\u7814\u7a76\u80cc\u666f\u4e0e\u95ee\u9898\u5b9a\u4e49<br>\u8fd1\u5e74\u6765\uff0c\u795e\u7ecf\u7f51\u7edc\u751f\u6210\u7684\u5d4c\u5165\u5411\u91cf\uff08embedding\uff09\u5df2\u6210\u4e3a\u4fe1\u606f\u68c0\u7d22\uff08Information Retrieval, IR\uff09\u4e2d\u7684\u6838\u5fc3\u624b\u6bb5\u3002\u4f20\u7edf\u7684\u505a\u6cd5\u591a\u4f7f\u7528\u5355\u5411\u91cf\uff08Single-Vector, SV\uff09\u8868\u793a\u6cd5\uff0c\u5373\u5c06\u6bcf\u4e2a\u6587\u6863\u6216\u67e5\u8be2\u7f16\u7801\u4e3a\u4e00\u4e2a\u56fa\u5b9a\u7ef4\u5ea6\u7684\u5411\u91cf\uff0c\u901a\u8fc7\u9ad8\u6548\u7684\u6700\u5927\u5185\u79ef\u641c\u7d22\uff08MIPS\uff09\u7b97\u6cd5\u8fdb\u884c\u76f8\u4f3c\u5ea6\u68c0\u7d22\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u65b9\u5f0f\u5728\u8868\u8fbe\u80fd\u529b\u4e0a\u5b58\u5728\u9650\u5236\uff0c\u7279\u522b\u662f\u5728\u6355\u6349\u67e5\u8be2\u4e0e\u6587\u6863\u4e4b\u95f4\u7ec6\u7c92\u5ea6\u8bed\u4e49\u5339\u914d\u65f6\u3002<\/p>\n\n\n\n<p>ColBERT\u5f15\u5165\u4e86\u591a\u5411\u91cf\uff08Multi-Vector, MV\uff09\u8868\u793a\uff0c\u5373\u4e3a\u6587\u6863\u6216\u67e5\u8be2\u7684\u6bcf\u4e2atoken\u751f\u6210\u4e00\u4e2a\u5d4c\u5165\u5411\u91cf\uff0c\u5229\u7528\u6240\u8c13\u7684Chamfer\u76f8\u4f3c\u5ea6\uff08\u4e5f\u79f0MaxSim\uff09\u8ba1\u7b97\u6574\u4f53\u76f8\u4f3c\u6027\uff0c\u8fd9\u5927\u5e45\u63d0\u5347\u4e86\u68c0\u7d22\u8d28\u91cf\u3002\u7136\u800c\uff0cMV\u6a21\u578b\u5e26\u6765\u4e86\u4e24\u4e2a\u6311\u6218\uff1a\u4e00\u662f\u6bcf\u4e2a\u6570\u636e\u70b9\u7684\u5411\u91cf\u6570\u91cf\u6210\u500d\u589e\u52a0\uff0c\u5bfc\u81f4\u5b58\u50a8\u4e0e\u8ba1\u7b97\u8d1f\u62c5\u6fc0\u589e\uff1b\u4e8c\u662fChamfer\u76f8\u4f3c\u5ea6\u8ba1\u7b97\u590d\u6742\uff0c\u5f53\u524d\u7f3a\u4e4f\u4e13\u95e8\u4f18\u5316\u7684MV\u68c0\u7d22\u7cfb\u7edf\u3002<\/p>\n\n\n\n<p>\u4e8c\u3001\u73b0\u6709\u65b9\u6cd5\u7684\u4e0d\u8db3<br>\u76ee\u524d\u4e3b\u6d41MV\u68c0\u7d22\u65b9\u6cd5\u91c7\u7528\u591a\u9636\u6bb5\u7ba1\u7ebf\uff08\u5982ColBERTv2\u548c\u5176\u52a0\u901f\u5f15\u64cePLAID\uff09\uff0c\u5148\u901a\u8fc7\u6bcf\u4e2a\u67e5\u8be2token\u4e0e\u6587\u6863token\u8fdb\u884cSV MIPS\u68c0\u7d22\uff0c\u6311\u9009\u51fa\u82e5\u5e72\u5019\u9009\u6587\u6863\uff0c\u518d\u4f7f\u7528Chamfer\u76f8\u4f3c\u5ea6\u8fdb\u884c\u91cd\u6392\u5e8f\u3002\u8fd9\u79cd\u505a\u6cd5\u4e0d\u4ec5\u8ba1\u7b97\u4ee3\u4ef7\u9ad8\uff0c\u800c\u4e14\u53c2\u6570\u8c03\u4f18\u590d\u6742\uff0c\u96be\u4ee5\u5728\u4e0d\u540c\u4efb\u52a1\u95f4\u8fc1\u79fb\u3002\u6b64\u5916\uff0c\u7531\u4e8eSV\u68c0\u7d22\u65b9\u6cd5\u4e0d\u80fd\u4fdd\u8bc1Chamfer\u6700\u8fd1\u90bb\u7684\u4e00\u81f4\u6027\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u7684\u51c6\u786e\u6027\u4e5f\u53d7\u5230\u9650\u5236\u3002<\/p>\n\n\n\n<p>\u4e09\u3001MUVERA\u65b9\u6cd5\u6982\u8ff0<br>\u672c\u8bba\u6587\u63d0\u51faMUVERA\uff08Multi-Vector Retrieval Algorithm\uff09\uff0c\u5b83\u901a\u8fc7\u6784\u9020\u56fa\u5b9a\u7ef4\u5ea6\u7f16\u7801\uff08Fixed Dimensional Encodings, FDEs\uff09\uff0c\u5c06\u590d\u6742\u7684MV\u68c0\u7d22\u4efb\u52a1\u7b80\u5316\u4e3aSV MIPS\u95ee\u9898\u3002\u5177\u4f53\u505a\u6cd5\u4e3a\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u67e5\u8be2\u548c\u6587\u6863\u7684\u591a\u5411\u91cf\u96c6\u5408\u5206\u522b\u6784\u9020\u4e00\u4e2a\u56fa\u5b9a\u7ef4\u5ea6\u7684FDE\u5411\u91cf\uff1b<\/li>\n\n\n\n<li>\u4fdd\u8bc1\u4e24\u4e2aFDE\u4e4b\u95f4\u7684\u5185\u79ef\u80fd\u8f83\u597d\u5730\u8fd1\u4f3c\u539f\u59cb\u7684Chamfer\u76f8\u4f3c\u5ea6\uff1b<\/li>\n\n\n\n<li>\u901a\u8fc7\u9ad8\u5ea6\u4f18\u5316\u7684SV MIPS\u7d22\u5f15\uff08\u5982DiskANN\uff09\u8fdb\u884c\u68c0\u7d22\uff0c\u518d\u5bf9Top-k\u5019\u9009\u6587\u6863\u6267\u884c\u4e00\u6b21Chamfer\u91cd\u6392\u5e8f\u3002<\/li>\n<\/ul>\n\n\n\n<p>MUVERA\u662f\u7b2c\u4e00\u4e2a\u5177\u6709\u7406\u8bba\u4fdd\u8bc1\u7684FDE\u68c0\u7d22\u6846\u67b6\uff0c\u8bba\u6587\u8bc1\u660e\u5176\u80fd\u4ee5\u03b5\u8fd1\u4f3c\u6062\u590dChamfer\u76f8\u4f3c\u5ea6\u4e0b\u7684\u6700\u90bb\u8fd1\u7ed3\u679c\uff0c\u4e14\u67e5\u8be2\u65f6\u95f4\u4f18\u4e8e\u7a77\u4e3e\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p>\u56db\u3001\u56fa\u5b9a\u7ef4\u5ea6\u7f16\u7801\uff08FDE\uff09\u751f\u6210\u539f\u7406<br>FDE\u7684\u751f\u6210\u8fc7\u7a0b\u57fa\u4e8e\u4ee5\u4e0b\u5173\u952e\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u7a7a\u95f4\u5212\u5206 \u03c6(x)<\/strong>\uff1a\u4f7f\u7528SimHash\u6216k-means\u5c06\u5411\u91cf\u7a7a\u95f4\u5212\u5206\u4e3aB\u4e2a\u7c07\u3002SimHash\u57fa\u4e8e\u591a\u4e2a\u9ad8\u65af\u968f\u673a\u8d85\u5e73\u9762\uff0c\u6784\u9020\u5c40\u90e8\u654f\u611f\u54c8\u5e0c\uff08LSH\uff09\u6620\u5c04\u03c6\uff0c\u4f7f\u5f97\u8ddd\u79bb\u8fd1\u7684\u5411\u91cf\u66f4\u53ef\u80fd\u843d\u5165\u540c\u4e00\u7c07\u3002<\/li>\n\n\n\n<li><strong>\u7c07\u5185\u6c47\u603b<\/strong>\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u7c07k\uff0c\u5c06\u843d\u5165\u8be5\u7c07\u7684query\u5411\u91cf\u52a0\u548c\u4e3aq<sup>\u2192<\/sup>(k)\uff0c\u800cdocument\u5411\u91cf\u6c42\u5747\u503c\u4e3ap<sup>\u2192<\/sup>(k)\u3002<\/li>\n\n\n\n<li><strong>\u7ef4\u5ea6\u538b\u7f29 \u03c8(x)<\/strong>\uff1a\u4f7f\u7528\u968f\u673a\u6295\u5f71\uff08\u00b11\u77e9\u9635\uff09\u5c06\u6bcf\u4e2aq<sup>\u2192<\/sup>(k)\u3001p<sup>\u2192<\/sup>(k)\u964d\u81f3d_proj\u7ef4\u3002<\/li>\n\n\n\n<li><strong>\u591a\u91cd\u91cd\u590d Rreps<\/strong>\uff1a\u91cd\u590d\u4e0a\u8ff0\u6b65\u9aa4R\u6b21\u4ee5\u964d\u4f4e\u65b9\u5dee\uff0c\u6700\u7ec8\u5c06\u6240\u6709R\u4e2a\u6295\u5f71\u62fc\u63a5\u6210\u5b8c\u6574FDE\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6700\u7ec8\uff0cFDE\u7ef4\u5ea6\u4e3a\uff1a<br><strong>d_FDE = B \u00d7 d_proj \u00d7 Rreps<\/strong><\/p>\n\n\n\n<p>\u6587\u6863\u7f16\u7801\u4f1a\u5e94\u7528\u201c\u586b\u5145\u7a7a\u7c07\u201d\uff08fill_empty_clusters\uff09\u7b56\u7565\uff0c\u5373\u82e5\u67d0\u7c07\u65e0p \u2208 P\u843d\u5165\uff0c\u5219\u9009\u62e9\u6700\u63a5\u8fd1\u8be5\u7c07\u7684p\u4f5c\u4e3ap<sup>\u2192<\/sup>(k)\uff0c\u786e\u4fdd\u7f16\u7801\u5b8c\u6574\u6027\u3002<\/p>\n\n\n\n<p>\u4e94\u3001\u7406\u8bba\u5206\u6790\u4e0e\u8fd1\u4f3c\u4fdd\u8bc1<br>MUVERA\u7684\u6838\u5fc3\u7406\u8bba\u7ed3\u679c\u662f\uff1a<br>\u5bf9\u4e8e\u4efb\u610f\u5355\u4f4d\u5411\u91cf\u96c6\u5408Q, P \u2282 \u211d\u1d48\uff0c\u6784\u9020\u51fa\u7684FDE\u5185\u79ef\u53ef\u8fd1\u4f3cChamfer\u76f8\u4f3c\u5ea6\uff0c\u8bef\u5dee\u4e0d\u8d85\u8fc7\u03b5\uff1a<\/p>\n\n\n\n<p>\u2003\u2003<strong>NCHAMFER(Q, P) \u2212 \u03b5 \u2264 \u27e8Fq(Q), Fdoc(P)\u27e9 \/ |Q| \u2264 NCHAMFER(Q, P) + \u03b5<\/strong><\/p>\n\n\n\n<p>\u5176\u4e2dNCHAMFER\u662f\u5f52\u4e00\u5316\u7684Chamfer\u76f8\u4f3c\u5ea6\u3002\u6784\u9020FDE\u7684\u5fc5\u8981\u6761\u4ef6\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>k_sim = O(log m \/ \u03b5)<\/li>\n\n\n\n<li>d_proj = O(1 \/ \u03b5\u00b2 log (m \/ \u03b5\u03b4))<\/li>\n\n\n\n<li>R_reps = O(1 \/ \u03b5\u00b2 log n)<\/li>\n<\/ul>\n\n\n\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n|Q|)\uff0c\u6bd4\u8d77O(n|Q||P|)\u7684\u66b4\u529b\u8ba1\u7b97\u663e\u8457\u66f4\u5feb\u3002<\/p>\n\n\n\n<p>\u516d\u3001\u5b9e\u9a8c\u9a8c\u8bc1\u4e0e\u6548\u679c\u5206\u6790<br>\u8bba\u6587\u5728\u516d\u4e2aBEIR\u68c0\u7d22\u57fa\u51c6\u6570\u636e\u96c6\uff08MS MARCO\u3001HotpotQA\u3001NQ\u3001Quora\u3001SciDocs\u3001ArguAna\uff09\u4e0a\u8bc4\u4f30MUVERA\u7684\u6027\u80fd\u3002\u5173\u952e\u7ed3\u679c\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>FDE\u7cbe\u5ea6\u63d0\u5347\u968f\u7ef4\u5ea6\u589e\u957f\u800c\u63d0\u9ad8<\/strong>\uff1a\u5728\u76f8\u540c\u53ec\u56de\u7387\u4e0b\uff0cFDE\u53ef\u7528\u66f4\u5c11\u5019\u9009\u6587\u6863\u6570\u5b9e\u73b0\u9ad8\u6548\u68c0\u7d22\u3002<\/li>\n\n\n\n<li><strong>\u5bf9\u6bd4PLAID\u6027\u80fd<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5e73\u5747\u53ec\u56de\u7387\u63d0\u9ad8\u7ea610%\uff1b<\/li>\n\n\n\n<li>\u5e73\u5747\u5ef6\u8fdf\u964d\u4f4e90%\uff0c\u90e8\u5206\u6570\u636e\u96c6\u8fbe\u52305.7\u500d\u52a0\u901f\uff1b<\/li>\n\n\n\n<li>\u65e0\u9700\u591a\u9636\u6bb5\u8c03\u53c2\uff0c\u91c7\u7528\u7edf\u4e00\u914d\u7f6e\u5373\u53ef\u8de8\u6570\u636e\u96c6\u7a33\u5b9a\u8fd0\u884c\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u538b\u7f29\u80fd\u529b<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4f7f\u7528Product Quantization (PQ-256-8)\u538b\u7f29FDE\u81f3\u539f\u59cb1\/32\uff0c\u4ec5\u635f\u5931\u4e0d\u52302%\u7684\u53ec\u56de\u7387\uff1b<\/li>\n\n\n\n<li>\u63d0\u5347\u541e\u5410\u6027\u80fd\uff08QPS\uff09\u81f3\u539f\u59cb20\u500d\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u4e03\u3001\u5bf9\u6bd4\u65b9\u6cd5\u4e0e\u5206\u6790<br>\u4e0eSV 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