{"id":7417,"date":"2025-09-08T04:17:00","date_gmt":"2025-09-07T19:17:00","guid":{"rendered":"https:\/\/devneko.jp\/wordpress\/?p=7417"},"modified":"2025-09-08T08:28:28","modified_gmt":"2025-09-07T23:28:28","slug":"on-the-theoretical-limitations-of-embedding-based-retrieval","status":"publish","type":"post","link":"https:\/\/devneko.jp\/wordpress\/?p=7417","title":{"rendered":"On the Theoretical Limitations of Embedding-Based Retrieval"},"content":{"rendered":"\n<ul class=\"wp-block-list\">\n<li><strong>On the Theoretical Limitations of Embedding-Based Retrieval\u00a0<\/strong>[15.8]<br>\u30af\u30a8\u30ea\u306e\u7d50\u679c\u3068\u3057\u3066\u8fd4\u5374\u53ef\u80fd\u306a\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u306e\u4e0a\u4f4dk\u30b5\u30d6\u30bb\u30c3\u30c8\u306e\u6570\u306f,\u57cb\u3081\u8fbc\u307f\u306e\u6b21\u5143\u306b\u3088\u3063\u3066\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3059\u3002 \u6b21\u306b\u3001LIMIT\u3068\u547c\u3070\u308c\u308b\u73fe\u5b9f\u7684\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f5c\u6210\u3057\u3001\u3053\u308c\u3089\u306e\u7406\u8ad6\u7d50\u679c\u306b\u57fa\u3065\u3044\u3066\u30e2\u30c7\u30eb\u3092\u30c6\u30b9\u30c8\u3059\u308b\u3002 \u6211\u3005\u306e\u7814\u7a76\u306f\u3001\u65e2\u5b58\u306e\u5358\u4e00\u30d9\u30af\u30c8\u30eb\u30d1\u30e9\u30c0\u30a4\u30e0\u306e\u4e0b\u3067\u306e\u57cb\u3081\u8fbc\u307f\u30e2\u30c7\u30eb\u306e\u9650\u754c\u3092\u793a\u3057\u3066\u3044\u308b\u3002<br><a href=\"http:\/\/arxiv.org\/abs\/2508.21038v1\">\u8ad6\u6587<\/a>\u00a0\u00a0<a href=\"https:\/\/fugumt.com\/fugumt\/paper_check\/2508.21038v1\">\u53c2\u8003\u8a33\uff08\u30e1\u30bf\u30c7\u30fc\u30bf\uff09<\/a>\u00a0 \u00a0(Thu, 28 Aug 2025 17:43:53 GMT)<\/li>\n\n\n\n<li>embedding\u3092\u7528\u3044\u305f\u60c5\u5831\u62bd\u51fa\u306e\u9650\u754c\u3092\u793a\u3057\u305f\u8ad6\u6587\u3002\u300cthe critical-n values (for embedding size): 500k (512), 1.7m (768), 4m (1024), 107m (3072), 250m (4096).  We note that this is the best case: a real embedding model cannot directly optimize the query and document vectors to match the test qrel matrix (and is constrained by factors such as \u201cmodeling natural language\u201d). However, these numbers already show that for web-scale search, even the largest embedding dimensions with ideal test-set optimization are not enough to model all combinations.\u300d\uff08The critical-n value where the dimensionality is too small to successfully represent all the top-2 combinations.\uff09\u3068\u610f\u5916\u3068\u5236\u7d04\u304c\u53b3\u3057\u3044\u3002<\/li>\n\n\n\n<li>\u30ea\u30dd\u30b8\u30c8\u30ea\u306f<a href=\"https:\/\/github.com\/google-deepmind\/limit\">GitHub &#8211; google-deepmind\/limit: On the Theoretical Limitations of Embedding-Based Retrieval<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[124],"class_list":["post-7417","post","type-post","status-publish","format-standard","hentry","category-arxiv","tag-embedding"],"_links":{"self":[{"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/7417","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7417"}],"version-history":[{"count":1,"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/7417\/revisions"}],"predecessor-version":[{"id":7418,"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/7417\/revisions\/7418"}],"wp:attachment":[{"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7417"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7417"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/devneko.jp\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}