{"id":1141,"date":"2025-07-30T16:24:00","date_gmt":"2025-07-30T08:24:00","guid":{"rendered":"http:\/\/www.applicationsofllm.com\/?p=1141"},"modified":"2025-09-17T16:26:37","modified_gmt":"2025-09-17T08:26:37","slug":"deepmind%e7%88%86%e7%81%ab%e8%ae%ba%e6%96%87%ef%bc%9a%e5%90%91%e9%87%8f%e5%b5%8c%e5%85%a5%e6%a8%a1%e5%9e%8b%e5%ad%98%e5%9c%a8%e6%95%b0%e5%ad%a6%e4%b8%8a%e9%99%90%ef%bc%8cscaling-laws%e6%94%be%e7%bc%93","status":"publish","type":"post","link":"http:\/\/www.applicationsofllm.com\/index.php\/2025\/07\/30\/deepmind%e7%88%86%e7%81%ab%e8%ae%ba%e6%96%87%ef%bc%9a%e5%90%91%e9%87%8f%e5%b5%8c%e5%85%a5%e6%a8%a1%e5%9e%8b%e5%ad%98%e5%9c%a8%e6%95%b0%e5%ad%a6%e4%b8%8a%e9%99%90%ef%bc%8cscaling-laws%e6%94%be%e7%bc%93\/","title":{"rendered":"DeepMind\u7206\u706b\u8bba\u6587\uff1a\u5411\u91cf\u5d4c\u5165\u6a21\u578b\u5b58\u5728\u6570\u5b66\u4e0a\u9650\uff0cScaling laws\u653e\u7f13\u5b9e\u9524\uff1f"},"content":{"rendered":"\n<p>\u8fd9\u51e0\u5929\uff0c\u4e00\u7bc7\u5173\u4e8e\u5411\u91cf\u5d4c\u5165\uff08Vector Embeddings\uff09\u5c40\u9650\u6027\u7684\u8bba\u6587\u5728 AlphaXiv \u4e0a\u7206\u706b\uff0c\u70ed\u5ea6\u98d9\u5347\u5230\u4e86\u8fd1 9000\u3002<\/p>\n\n\n\n<p>\u8981\u7406\u89e3\u8fd9\u7bc7\u8bba\u6587\u7684\u91cd\u8981\u6027\uff0c\u6211\u4eec\u5148\u7b80\u5355\u56de\u987e\u4e00\u4e0b\u4ec0\u4e48\u662f\u5411\u91cf\u5d4c\u5165\u3002<\/p>\n\n\n\n<p>\u5411\u91cf\u5d4c\u5165\u5c31\u50cf\u628a\u6587\u5b57\u3001\u56fe\u7247\u6216\u58f0\u97f3\u8fd9\u4e9b\u590d\u6742\u7684\u4e1c\u897f\uff0c\u8f6c\u5316\u6210\u4e00\u4e2a\u591a\u7ef4\u7a7a\u95f4\u91cc\u7684\u300c\u5750\u6807\u70b9\u300d\u3002\u6bd4\u5982\uff0c\u628a\u300c\u82f9\u679c\u300d\u8fd9\u4e2a\u8bcd\u53d8\u6210\u4e00\u4e32\u51e0\u767e\u7ef4\u7684\u6570\u5b57\uff0c\u8fd9\u4e9b\u6570\u5b57\u6355\u6349\u4e86\u5b83\u7684\u8bed\u4e49\uff08\u5b83\u53ef\u4ee5\u6307\u6c34\u679c\uff0c\u4e5f\u53ef\u4ee5\u6307\u516c\u53f8\uff09\u3002\u5728\u8fd9\u4e2a\u7a7a\u95f4\u91cc\uff0c\u76f8\u4f3c\u7684\u6982\u5ff5\u5f7c\u6b64\u9760\u8fd1\uff0c\u4e0d\u76f8\u4f3c\u7684\u5219\u8fdc\u79bb\u3002\u501f\u52a9\u8fd9\u79cd\u673a\u5236\uff0c\u8ba1\u7b97\u673a\u80fd\u591f\u5feb\u901f\u641c\u7d22\u6216\u6bd4\u8f83\u6d77\u91cf\u6570\u636e\uff0c\u800c\u65e0\u9700\u9010\u5b57\u9010\u53e5\u5730\u6bd4\u5bf9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1002\" height=\"1024\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-393-1002x1024.jpg\" alt=\"\" class=\"wp-image-1145\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-393-1002x1024.jpg 1002w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-393-294x300.jpg 294w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-393-768x785.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-393.jpg 1107w\" sizes=\"auto, (max-width: 1002px) 100vw, 1002px\" \/><\/figure>\n\n\n\n<p><sup>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u56fe\u6e90\uff1aveaviate<\/sup><\/p>\n\n\n\n<p>\u591a\u5e74\u4ee5\u6765\uff0c\u5d4c\u5165\u4e3b\u8981\u7528\u4e8e\u300c\u68c0\u7d22\u300d\u4efb\u52a1\uff0c\u4f8b\u5982\u641c\u7d22\u5f15\u64ce\u4e2d\u7684\u76f8\u4f3c\u6587\u6863\u67e5\u627e\uff0c\u6216\u63a8\u8350\u7cfb\u7edf\u4e2d\u7684\u4e2a\u6027\u5316\u63a8\u8350\u3002\u968f\u7740\u5927\u6a21\u578b\u6280\u672f\u7684\u53d1\u5c55\uff0c\u5d4c\u5165\u7684\u5e94\u7528\u5f00\u59cb\u62d3\u5c55\u5230\u63a8\u7406\u3001\u6307\u4ee4\u9075\u5faa\u3001\u7f16\u7a0b\u7b49\u66f4\u590d\u6742\u7684\u4efb\u52a1\u3002\u8fd9\u4e9b\u65b0\u5174\u9700\u6c42\uff0c\u63a8\u52a8\u7740\u5d4c\u5165\u6280\u672f\u671d\u7740\u80fd\u5904\u7406\u4efb\u4f55\u67e5\u8be2\u3001\u4efb\u4f55\u76f8\u5173\u6027\u5b9a\u4e49\u7684\u65b9\u5411\u6f14\u8fdb\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u5148\u524d\u7684\u7814\u7a76\u5df2\u7ecf\u6307\u51fa\u4e86\u5411\u91cf\u5d4c\u5165\u7684\u7406\u8bba\u5c40\u9650\u6027\u3002\u5b83\u7684\u672c\u8d28\uff0c\u662f\u628a\u4e00\u4e2a\u9ad8\u7ef4\u5ea6\u3001\u590d\u6742\u7684\u6982\u5ff5\uff08\u6bd4\u5982\u300c\u7231\u300d\uff0c\u53ef\u80fd\u5305\u542b\u4eb2\u60c5\u3001\u7231\u60c5\u3001\u53cb\u60c5\u3001\u5949\u732e\u3001\u5360\u6709\u7b49\u65e0\u6570\u9762\u5411\uff09\u5f3a\u884c\u538b\u7f29\u6210\u4e00\u4e32\u56fa\u5b9a\u957f\u5ea6\u7684\u5411\u91cf\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u4e0d\u53ef\u907f\u514d\u5730\u4e22\u5931\u4fe1\u606f\uff0c\u5c31\u50cf\u4e09\u7ef4\u82f9\u679c\u88ab\u62cd\u6210\u4e8c\u7ef4\u7167\u7247 \u2014\u2014 \u65e0\u8bba\u7167\u7247\u591a\u6e05\u6670\uff0c\u4f60\u90fd\u65e0\u6cd5\u4ece\u4e2d\u8fd8\u539f\u51fa\u5b83\u7684\u91cd\u91cf\u3001\u6c14\u5473\u7b49\u5c5e\u6027\u3002<\/p>\n\n\n\n<p>\u8fc7\u53bb\u51e0\u5e74\uff0c\u4e1a\u754c\u666e\u904d\u8ba4\u4e3a\u8fd9\u79cd\u7406\u8bba\u56f0\u96be\u53ef\u4ee5\u901a\u8fc7\u66f4\u597d\u7684\u8bad\u7ec3\u6570\u636e\u548c\u66f4\u5927\u7684\u6a21\u578b\u6765\u514b\u670d\u3002\u8fd9\u5c31\u662f\u8fc7\u53bb\u51e0\u5e74\u4ee5 OpenAI \u4e3a\u4ee3\u8868\u7684\u516c\u53f8\u6240\u9075\u5faa\u7684\u300c\u5927\u529b\u51fa\u5947\u8ff9\u300d\uff08Scaling Laws\uff09\u7684\u54f2\u5b66\u3002<\/p>\n\n\n\n<p>\u4ece GPT-2 \u5230 GPT-4\uff0c\u518d\u5230 GPT-5\uff0c\u6a21\u578b\u53c2\u6570\u91cf\u548c\u6570\u636e\u91cf\u6307\u6570\u7ea7\u589e\u957f\uff0c\u80fd\u529b\u4e5f\u786e\u5b9e\u53d1\u751f\u4e86\u8d28\u7684\u98de\u8dc3\u3002\u8fd9\u8ba9\u5f88\u591a\u4eba\u76f8\u4fe1\uff0c\u8fd9\u6761\u8def\u80fd\u4e00\u76f4\u8d70\u4e0b\u53bb\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u5f53\u524d AI \u5708\u7684\u4e00\u4e2a\u70ed\u70b9\u4e89\u8bba\u5c31\u662f\uff1a\u6211\u4eec\u662f\u4e0d\u662f\u5feb\u8981\u649e\u4e0a\u300cScaling Laws\u300d\u7684\u5929\u82b1\u677f\u4e86\uff1f<\/p>\n\n\n\n<p>DeepMind \u7684\u6700\u65b0\u7814\u7a76\u4e3a\u8fd9\u4e2a\u4e89\u8bba\u63d0\u4f9b\u4e86\u65b0\u7684\u8bc1\u636e\u3002\u4ed6\u4eec\u5c06\u51e0\u4f55\u4ee3\u6570\u4e0e\u901a\u4fe1\u590d\u6742\u5ea6\u7406\u8bba\u7ed3\u5408\uff0c\u8bc1\u660e\u4e86\u5411\u91cf\u5d4c\u5165\u7684\u80fd\u529b\u5b58\u5728\u4e00\u4e2a\u6570\u5b66\u4e0b\u754c\uff1a<strong>\u5bf9\u4e8e\u4efb\u610f\u7ed9\u5b9a\u7684\u5d4c\u5165\u7ef4\u5ea6 d\uff0c\u5f53\u6587\u6863\u6570\u91cf\u8d85\u8fc7\u67d0\u4e2a\u4e34\u754c\u70b9\u65f6\uff0c\u603b\u4f1a\u5b58\u5728\u4e00\u4e9b\u76f8\u5173\u6587\u6863\u7ec4\u5408\u662f\u65e0\u8bba\u5982\u4f55\u90fd\u65e0\u6cd5\u901a\u8fc7\u67e5\u8be2\u540c\u65f6\u53ec\u56de\u7684\u3002<\/strong><\/p>\n\n\n\n<p>\u8fd9\u610f\u5473\u7740\uff0c\u5d4c\u5165\u6a21\u578b\u5b58\u5728\u4e00\u4e2a\u4e0d\u53ef\u903e\u8d8a\u7684\u9650\u5236\uff0c\u65e0\u6cd5\u5355\u7eaf\u4f9d\u9760\u300c\u66f4\u5927\u7684\u6a21\u578b\u300d\u6765\u7a81\u7834\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"302\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-392-1024x302.jpg\" alt=\"\" class=\"wp-image-1144\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-392-1024x302.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-392-300x89.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-392-768x227.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-392.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8bba\u6587\u6807\u9898\uff1aOn the Theoretical Limitations of Embedding-Based Retrieval<\/li>\n\n\n\n<li>arXiv \u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2508.21038<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e00\u7406\u8bba\u74f6\u9888\u5728\u73b0\u5b9e\u4e2d\u6700\u76f4\u63a5\u7684\u4f53\u73b0\uff0c\u5c31\u662f\u68c0\u7d22\u589e\u5f3a\u751f\u6210\uff08RAG\uff09\u3002RAG \u7684\u5de5\u4f5c\u673a\u5236\u662f\uff1a\u5148\u7528\u5411\u91cf\u5d4c\u5165\u4ece\u77e5\u8bc6\u5e93\u4e2d\u68c0\u7d22\u76f8\u5173\u4fe1\u606f\uff0c\u518d\u4ea4\u7ed9\u5927\u6a21\u578b\u751f\u6210\u7b54\u6848\u3002\u4f46 DeepMind 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http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-391-300x145.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-391-768x371.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-391.jpg 1107w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u4e3a\u4e86\u8bc1\u660e\u8fd9\u4e00\u7406\u8bba\u9650\u5236\u5bf9\u4efb\u4f55\u6a21\u578b\u6216\u8bad\u7ec3\u6570\u636e\u90fd\u6210\u7acb\uff0c\u7814\u7a76\u8005\u91c7\u7528\u4e86\u4e00\u79cd\u300c\u6700\u4f73\u60c5\u51b5\u300d\u8bbe\u5b9a\uff0c\u5373\u5411\u91cf\u672c\u8eab\u662f\u4f7f\u7528\u6d4b\u8bd5\u6570\u636e\u76f4\u63a5\u8fdb\u884c\u4f18\u5316\u7684\u3002\u5b9e\u9a8c\u53d1\u73b0\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u5d4c\u5165\u7ef4\u5ea6 d 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\u6a21\u578b\u4e5f\u8868\u73b0\u7cdf\u7cd5\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"902\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-394-1024x902.jpg\" alt=\"\" class=\"wp-image-1146\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-394-1024x902.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-394-300x264.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-394-768x677.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-394.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u603b\u7684\u6765\u8bf4\uff0c\u8fd9\u7bc7\u5de5\u4f5c\u7684\u8d21\u732e\u53ef\u4ee5\u603b\u7ed3\u4e3a\u4ee5\u4e0b\u4e09\u70b9\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e3a\u5d4c\u5165\u6a21\u578b\u7684\u6839\u672c\u6027\u5c40\u9650\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\uff1b<\/li>\n\n\n\n<li>\u901a\u8fc7\u81ea\u7531\u7684\u5d4c\u5165\u4f18\u5316\u8fdb\u884c\u6700\u4f73\u60c5\u51b5\u4e0b\u7684\u7ecf\u9a8c\u6027\u5206\u6790\uff0c\u8bc1\u660e\u4e86\u8be5\u7406\u8bba\u9002\u7528\u4e8e\u4efb\u4f55\u6570\u636e\u96c6\u5b9e\u4f8b\uff1b<\/li>\n\n\n\n<li>\u6784\u5efa\u4e86\u4e00\u4e2a\u540d\u4e3a LIMIT \u7684\u7b80\u5355\u3001\u771f\u5b9e\u7684\u81ea\u7136\u8bed\u8a00\u5b9e\u4f8b\uff0c\u5373\u4f7f\u662f\u6700\u5148\u8fdb\u7684\u5d4c\u5165\u6a21\u578b\u4e5f\u65e0\u6cd5\u89e3\u51b3\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e0d\u4ec5\u63ed\u793a\u4e86 RAG \u7cfb\u7edf\u5728\u5e94\u7528\u4e0a\u7684\u786c\u6027\u7ea6\u675f\uff0c\u4e5f\u8ba9\u4eba\u91cd\u65b0\u601d\u8003 Scaling Laws \u5728 AI \u53d1\u5c55\u4e2d\u7684\u8fb9\u754c\u3002\u5d4c\u5165\u7684\u5c40\u9650\uff0c\u4e5f\u8bb8\u6b63\u662f\u300c\u52a0\u5927\u89c4\u6a21\u300d\u5e76\u975e\u4e07\u80fd\u89e3\u6cd5\u7684\u4e00\u4e2a\u7f29\u5f71\u3002<\/p>\n\n\n\n<p><strong>\u5411\u91cf\u5d4c\u5165\u7684\u8868\u5f81\u80fd\u529b<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u9996\u5148\u8bc1\u660e\u4e86\u901a\u4fe1\u590d\u6742\u6027\u7406\u8bba\u4e2d\u7684\u5df2\u77e5\u7ed3\u679c\u5728\u5411\u91cf\u5d4c\u5165\u8bbe\u5b9a\u4e0b\u7684\u542b\u4e49\u3002<\/p>\n\n\n\n<p><strong>\u7406\u8bba\u4e0a\u9650\u3002<\/strong>\u5bf9\u4e8e\u4e8c\u8fdb\u5236\u77e9\u9635\uff0c\u9010\u884c\u6392\u5e8f\u548c\u9010\u884c\u9608\u503c\u5316\u662f\u7b49\u4ef7\u7684\u8868\u5f81\u80fd\u529b\u6982\u5ff5\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"321\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-395-1024x321.jpg\" alt=\"\" class=\"wp-image-1147\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-395-1024x321.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-395-300x94.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-395-768x241.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-395.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u7814\u7a76\u8005\u63cf\u8ff0\u7684\u8fd9\u4e9b\u6982\u5ff5\u4e0e\u77e9\u9635\u7684\u7b26\u53f7\u79e9\u5bc6\u5207\u76f8\u5173\u3002\u5728\u672c\u6587\u7684\u5176\u4f59\u90e8\u5206\uff0c\u4ed6\u4eec\u5c06\u5229\u7528\u7b26\u53f7\u79e9\u6765\u5efa\u7acb\u4e3b\u8981\u7684\u754c\u9650\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"366\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-396-1024x366.jpg\" alt=\"\" class=\"wp-image-1148\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-396-1024x366.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-396-300x107.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-396-768x274.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-396.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"237\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-398-1024x237.jpg\" alt=\"\" class=\"wp-image-1150\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-398-1024x237.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-398-300x69.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-398-768x177.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-398.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u5c06\u6240\u6709\u8fd9\u4e9b\u7ed3\u5408\u8d77\u6765\u5c31\u5f97\u51fa\u4e86\u6240\u9700\u7684\u4e0d\u7b49\u5f0f\u94fe\u3002<\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u8868\u793a\uff0c\u5728\u5411\u91cf\u5d4c\u5165\u6a21\u578b\u7684\u80cc\u666f\u4e0b\uff0c\u8fd9\u4e3a\u51c6\u786e\u6355\u83b7\u4e00\u7ec4\u68c0\u7d22\u76ee\u6807\u6240\u9700\u5411\u91cf\u7684\u7ef4\u5ea6\u63d0\u4f9b\u4e86\u4e0a\u4e0b\u754c\uff0c\u65e0\u8bba\u662f\u9010\u884c\u6392\u5e8f\u3001\u9010\u884c\u9608\u503c\uff0c\u8fd8\u662f\u5168\u5c40\u9608\u503c\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u7ed9\u5b9a\u67d0\u4e2a\u4e8c\u8fdb\u5236\u76f8\u5173\u77e9\u9635 A \u2208 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qrel \u77e9\u9635\uff08\u6d4b\u8bd5\u96c6\uff09\u4e0a\u4f18\u5316\u5d4c\u5165\u6765\u5b9e\u73b0\u7684\u3002\u8fd9\u79cd\u65b9\u5f0f\u4e0d\u4f1a\u6cdb\u5316\u5230\u65b0\u7684\u6570\u636e\u96c6\uff0c\u4f46\u5176\u76ee\u7684\u662f\u5c55\u793a\u53ef\u80fd\u51fa\u73b0\u7684\u6700\u9ad8\u6027\u80fd\u3002<\/p>\n\n\n\n<p>\u5173\u4e8e\u5b9e\u9a8c\u8bbe\u7f6e\uff0c\u7814\u7a76\u8005\u521b\u5efa\u4e00\u4e2a\u968f\u673a\u6587\u6863\u77e9\u9635\uff08\u5927\u5c0f\u4e3a n\uff09\u548c\u4e00\u4e2a\u968f\u673a\u67e5\u8be2\u77e9\u9635\uff0c\u5176\u4e2d\u5305\u542b top-k \u96c6\u5408\uff08\u6240\u6709\u7ec4\u5408\uff0c\u5373\u5927\u5c0f\u4e3a<img loading=\"lazy\" decoding=\"async\" width=\"456\" height=\"210\" src=\"blob:http:\/\/www.applicationsofllm.com\/6a2ac156-0a29-4d54-bdbf-7a322f40e059\" alt=\"\u56fe\u7247\">\uff09\uff0c\u4e24\u8005\u5747\u4e3a\u5355\u4f4d\u5411\u91cf\u3002\u7136\u540e\u76f4\u63a5\u4f7f\u7528 Adam \u4f18\u5316\u5668\u6765\u4f18\u5316\u7ea6\u675f\u6761\u4ef6\u3002\u6bcf\u4e00\u6b21\u68af\u5ea6\u66f4\u65b0\u90fd\u5bf9\u6240\u6709\u6b63\u786e\u7684\u4e09\u5143\u7ec4\u8fdb\u884c\u5b8c\u6574\u904d\u5386\uff08\u5373\u6574\u4e2a\u6570\u636e\u96c6\u4f5c\u4e3a batch-size\uff09\uff0c\u5e76\u4f7f\u7528 InfoNCE \u635f\u5931\u51fd\u6570\uff0c\u5176\u4ed6\u6240\u6709\u6587\u6863\u4f5c\u4e3a\u6279\u5185\u8d1f\u6837\u672c\uff08\u5373\u6574\u4e2a\u6570\u636e\u96c6\u5728\u4e00\u4e2a batch \u4e2d\uff09\u3002<\/p>\n\n\n\n<p>\u7531\u4e8e\u51e0\u4e4e\u6240\u6709\u5d4c\u5165\u6a21\u578b\u90fd\u4f7f\u7528\u5f52\u4e00\u5316\u5411\u91cf\uff0c\u7814\u7a76\u8005\u4e5f\u540c\u6837\u91c7\u7528\u8fd9\u79cd\u65b9\u5f0f\uff08\u5728\u66f4\u65b0\u540e\u8fdb\u884c\u5f52\u4e00\u5316\uff09\u3002\u5f53\u635f\u5931\u5728 1000 \u6b21\u8fed\u4ee3\u4e2d\u6ca1\u6709\u6539\u8fdb\u65f6\uff0c\u5c31\u63d0\u524d\u505c\u6b62\u3002\u4ed6\u4eec\u9010\u6e10\u589e\u52a0\u6587\u6863\u6570\u91cf\uff08\u56e0\u6b64\u67e5\u8be2\u7684\u7ec4\u5408\u6570\u4e5f\u968f\u4e4b\u589e\u52a0\uff09\uff0c\u76f4\u5230\u4f18\u5316\u5668\u65e0\u6cd5\u518d\u89e3\u51b3\u8be5\u95ee\u9898\uff08\u5373\u65e0\u6cd5\u8fbe\u5230 100% \u7684\u51c6\u786e\u7387\uff09\u3002\u7814\u7a76\u8005\u5c06\u8fd9\u4e00\u70b9\u79f0\u4e3a<strong>\u300c\u4e34\u754c n \u70b9\u300d<\/strong>\u3002<\/p>\n\n\n\n<p>\u7531\u4e8e\u6587\u6863\u6570\u8f83\u5927\u65f6\u7ec4\u5408\u6570\u91cf\u5448\u73b0\u7ec4\u5408\u7206\u70b8\uff08\u4f8b\u5982 5 \u4e07\u4e2a\u6587\u6863\u3001top-k=100 \u65f6\u4f1a\u4ea7\u751f 7.7e+311 \u79cd\u7ec4\u5408\uff0c\u8fd9\u76f8\u5f53\u4e8e\u81ea\u7531\u5d4c\u5165\u5b9e\u9a8c\u4e2d\u7ef4\u5ea6\u4e3a d \u7684\u67e5\u8be2\u5411\u91cf\u6570\u91cf\uff09\uff0c\u56e0\u6b64\u7814\u7a76\u8005\u4e13\u6ce8\u4e8e n\u3001k \u548c d \u7684\u76f8\u5bf9\u8f83\u5c0f\u89c4\u6a21\u3002\u7814\u7a76\u8005\u8bbe\u5b9a k=2\uff0c\u5e76\u5728\u6bcf\u4e2a d \u503c\u4e0b\u9010\u6b21\u589e\u52a0 n\uff0c\u76f4\u5230\u6a21\u578b\u65e0\u6cd5\u89e3\u51b3\u95ee\u9898\u3002\u6b64\u5916\u5bf9\u6570\u636e\u62df\u5408\u4e86\u4e00\u6761\u591a\u9879\u5f0f\u56de\u5f52\u66f2\u7ebf\uff0c\u4ee5\u4fbf\u80fd\u591f\u5efa\u6a21\u5e76\u5411\u5916\u63a8\u7b97\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u7ed3\u679c\u5982\u4e0b\u56fe 2 \u6240\u793a\uff0c\u8be5\u66f2\u7ebf\u7b26\u5408\u4e09\u6b21\u591a\u9879\u5f0f\u62df\u5408\uff0c\u5176\u516c\u5f0f\u4e3a y = \u221210.5322 + 4.0309d + 0.0520d\u00b2 + 0.0037d\u00b3 \uff08r\u00b2=0.999\uff09\u3002\u5c06\u8be5\u66f2\u7ebf\u5916\u63a8\u5f97\u5230\u7684\u4e34\u754c n \u503c\uff08\u5bf9\u5e94\u5d4c\u5165\u7ef4\u5ea6\uff09\u5206\u522b\u4e3a\uff1a500k\uff08512\uff09\u3001170 \u4e07\uff08768\uff09\u3001400 \u4e07\uff081024\uff09\u30011.07 \u4ebf\uff083072\uff09\u30012.5 \u4ebf\uff084096\uff09\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u53ea\u662f\u6700\u4f73\u60c5\u51b5\uff1a\u771f\u5b9e\u7684\u5d4c\u5165\u6a21\u578b\u65e0\u6cd5\u76f4\u63a5\u4f18\u5316\u67e5\u8be2\u548c\u6587\u6863\u5411\u91cf\u4ee5\u5339\u914d\u6d4b\u8bd5\u96c6\u7684 qrel \u77e9\u9635\uff0c\u5e76\u4e14\u8fd8\u53d7\u5230\u300c\u81ea\u7136\u8bed\u8a00\u5efa\u6a21\u300d\u7b49\u56e0\u7d20\u7684\u7ea6\u675f\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u6570\u503c\u5df2\u7ecf\u8868\u660e\uff0c\u5bf9\u4e8e\u7f51\u9875\u7ea7\u522b\u7684\u641c\u7d22\uff0c\u5373\u4fbf\u662f\u5728\u7406\u60f3\u6d4b\u8bd5\u96c6\u4f18\u5316\u4e0b\uff0c\u6700\u5927\u7684\u5d4c\u5165\u7ef4\u5ea6\u4e5f\u4e0d\u8db3\u4ee5\u5efa\u6a21\u6240\u6709\u7ec4\u5408\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"840\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-397-1024x840.jpg\" alt=\"\" class=\"wp-image-1149\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-397-1024x840.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-397-300x246.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-397-768x630.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-397.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong>\u5b9e\u8bc1\u8054\u7cfb<\/strong><\/p>\n\n\n\n<p><strong>\u771f\u5b9e\u4e16\u754c\u6570\u636e\u96c6<\/strong><\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u7814\u7a76\u8005\u5c06\uff081\uff09\u8be5\u7406\u8bba\u4e0e\u73b0\u6709\u6570\u636e\u96c6\u5efa\u7acb\u8054\u7cfb\uff1b\uff082\uff09\u4e3a\u73b0\u6709 SOTA \u6a21\u578b\u6784\u5efa\u4e00\u4e2a\u6781\u5176\u7b80\u5355\u5374\u53c8\u6781\u5ea6\u56f0\u96be\u7684\u68c0\u7d22\u4efb\u52a1\u3002<\/p>\n\n\n\n<p>\u4e0e\u4ee5\u5f80\u5de5\u4f5c\u5f62\u6210\u5bf9\u6bd4\u7684\u662f\uff0c<strong>\u7814\u7a76\u8005\u5e0c\u671b\u6784\u5efa\u7684\u6570\u636e\u96c6\uff0c\u53ef\u4ee5\u7528\u4e8e\u8bc4\u4f30\u5c11\u91cf\u6587\u6863\u60c5\u51b5\u4e0b\u6240\u6709 top-k \u96c6\u5408\u7684\u7ec4\u5408<\/strong>\u3002\u4e0d\u540c\u4e8e\u4f7f\u7528 QUEST\u3001BrowseComp \u7b49\u590d\u6742\u7684\u67e5\u8be2\u64cd\u4f5c\u7b26\uff08\u8fd9\u4e9b\u64cd\u4f5c\u672c\u8eab\u5c31\u56e0 qrel \u77e9\u9635\u4e4b\u5916\u7684\u539f\u56e0\u800c\u5f88\u96be\uff09\uff0c\u4ed6\u4eec\u9009\u62e9\u4e86\u975e\u5e38\u7b80\u5355\u7684\u67e5\u8be2\u548c\u6587\u6863\uff0c\u4ee5\u7a81\u51fa\u8868\u793a\u6240\u6709 top-k \u96c6\u5408\u672c\u8eab\u7684\u96be\u5ea6\u3002<\/p>\n\n\n\n<p><strong>LIMIT \u6570\u636e\u96c6<\/strong><\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u9009\u7528 5 \u4e07\u4e2a\u6587\u6863\uff0c\u4ee5\u6784\u5efa\u4e00\u4e2a\u65e2\u6709\u96be\u5ea6\u53c8\u76f8\u5bf9\u89c4\u6a21\u8f83\u5c0f\u7684\u8bed\u6599\u5e93\uff1b\u540c\u65f6\u4f7f\u7528 1000 \u4e2a\u67e5\u8be2\uff0c\u4ee5\u5728\u4fdd\u8bc1\u7edf\u8ba1\u663e\u8457\u6027\u7684\u524d\u63d0\u4e0b\u4ecd\u80fd\u5feb\u901f\u5b8c\u6210\u8bc4\u4f30\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u67e5\u8be2\uff0c\u7814\u7a76\u8005\u9009\u62e9\u5173\u8054\u4e24\u4e2a\u76f8\u5173\u6587\u6863\uff08\u5373 k=2\uff09\uff0c\u8fd9\u6837\u505a\u65e2\u4e3a\u4e86\u7b80\u5316\u5b9e\u4f8b\u5316\u8fc7\u7a0b\uff0c\u4e5f\u4e3a\u4e86\u4e0e\u4e4b\u524d\u7684\u5de5\u4f5c\u4fdd\u6301\u4e00\u81f4\u3002\u63a5\u4e0b\u6765\u662f\u9009\u62e9\u4e00\u4e2a qrel \u77e9\u9635\u6765\u5b9e\u4f8b\u5316\u8fd9\u4e9b\u5c5e\u6027\uff0c\u5e76\u4e3a\u67e5\u8be2\u5206\u914d\u968f\u673a\u7684\u81ea\u7136\u8bed\u8a00\u5c5e\u6027\uff0c\u5c06\u8fd9\u4e9b\u5c5e\u6027\u6dfb\u52a0\u5230\u5404\u81ea\u7684\u76f8\u5173\u6587\u6863\u4e2d\uff08\u53c2\u89c1\u56fe 1\uff09\u3002<\/p>\n\n\n\n<p>\u7814\u7a76\u8005\u6d4b\u8bd5\u4e86\u6240\u6709\u6587\u6863\u7ec4\u5408\u7684\u76f8\u5173\u6027\uff08\u5bf9\u4e8e\u4e09\u4e2a\u6587\u6863\uff0c\u6bcf\u4e2a\u67e5\u8be2\u5305\u542b\u4e24\u4e2a\u76f8\u5173\u6587\u6863\u7684\u6240\u6709\u7ec4\u5408\uff09\uff0c\u5e76\u901a\u8fc7\u4e00\u4e2a\u7b80\u5355\u7684\u6620\u5c04\u8fdb\u884c\u5b9e\u4f8b\u5316\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"513\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-399-1024x513.jpg\" alt=\"\" class=\"wp-image-1151\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-399-1024x513.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-399-300x150.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-399-768x385.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-399.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u7814\u7a76\u8005\u8bc4\u4f30\u4e86\u5f53\u524d SOTA \u5d4c\u5165\u6a21\u578b\uff0c\u5305\u62ec GritLM\u3001Qwen 3 Embeddings\u3001Promptriever\u3001Gemini Embeddings\u3001Snowflake \u7684 Arctic Embed Large v2.0 \u4ee5\u53ca E5-Mistral Instruct\uff0c\u5e76\u5c55\u793a\u4e86\u5728\u5b8c\u6574\u5d4c\u5165\u7ef4\u5ea6\u4e0b\u7684\u7ed3\u679c\u4ee5\u53ca\u5728\u622a\u65ad\u5d4c\u5165\u7ef4\u5ea6\uff08\u901a\u5e38\u7528\u4e8e matryoshka learning\uff0c\u5373 MRL\uff09\u4e0b\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u4e0b\u56fe 3 \u5c55\u793a\u4e86\u5728\u5b8c\u6574 LIMIT \u4e0a\u7684\u7ed3\u679c\uff0c\u800c\u4e0b\u56fe 4 \u5c55\u793a\u4e86\u5728\u5c0f\u89c4\u6a21\uff08\u5305\u542b 46 \u4e2a\u6587\u6863\uff09\u7248\u672c\u4e0a\u7684\u7ed3\u679c\u3002\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u5373\u4fbf\u4efb\u52a1\u672c\u8eab\u5f88\u7b80\u5355\uff0c\u6a21\u578b\u4f9d\u7136\u8868\u73b0\u6781\u5dee\u3002\u5728\u5b8c\u6574\u8bbe\u7f6e\u4e2d\uff0c<strong>\u6a21\u578b\u751a\u81f3\u96be\u4ee5\u8fbe\u5230 20% \u7684 recall@100\uff0c\u800c\u5728 46 \u4e2a\u6587\u6863\u7684\u7248\u672c\u4e2d\uff0c\u5373\u4f7f\u662f recall@20\uff0c\u6a21\u578b\u4e5f\u65e0\u6cd5\u89e3\u51b3\u8be5\u4efb\u52a1\u3002<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"571\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-400-1024x571.jpg\" alt=\"\" class=\"wp-image-1152\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-400-1024x571.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-400-300x167.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-400-768x428.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-400.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"527\" src=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-401-1024x527.jpg\" alt=\"\" class=\"wp-image-1153\" srcset=\"http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-401-1024x527.jpg 1024w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-401-300x154.jpg 300w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-401-768x395.jpg 768w, http:\/\/www.applicationsofllm.com\/wp-content\/uploads\/2025\/09\/image-401.jpg 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong>\u5b58\u5728\u9886\u57df\u8fc1\u79fb\u5417\uff1f<\/strong><\/p>\n\n\n\n<p>\u867d\u7136\u672c\u6587\u7684\u67e5\u8be2\u770b\u8d77\u6765\u4e0e\u6807\u51c6\u7684\u7f51\u9875\u641c\u7d22\u67e5\u8be2\u76f8\u4f3c\uff0c\u4f46\u7814\u7a76\u8005\u6000\u7591\u662f\u5426\u5b58\u5728\u67d0\u79cd\u9886\u57df\u8fc1\u79fb\u4ece\u800c\u5bfc\u81f4\u6027\u80fd\u4f4e\u4e0b\u3002\u5982\u679c\u771f\u662f\u8fd9\u6837\uff0c\u90a3\u4e48\u5728\u76f8\u4f3c\u793a\u4f8b\u7684\u8bad\u7ec3\u96c6\u4e0a\u8fdb\u884c\u8bad\u7ec3\u9884\u8ba1\u80fd\u591f\u663e\u8457\u63d0\u5347\u6027\u80fd\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4efb\u52a1\u672c\u8eab\u5c31\u5f88\u96be\uff0c\u90a3\u4e48\u5728\u8bad\u7ec3\u96c6\u4e0a\u8bad\u7ec3\u51e0\u4e4e\u65e0\u6d4e\u4e8e\u4e8b\uff0c\u800c\u5728\u6d4b\u8bd5\u96c6\u4e0a\u8bad\u7ec3\u5219\u4f1a\u8ba9\u6a21\u578b\u8fc7\u62df\u5408\u5230\u7279\u5b9a token\u3002<\/p>\n\n\n\n<p>\u4e0b\u56fe 5 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