{"id":5199,"date":"2024-11-27T17:19:59","date_gmt":"2024-11-27T09:19:59","guid":{"rendered":"https:\/\/nullthought.net\/?p=5199"},"modified":"2026-02-12T11:27:11","modified_gmt":"2026-02-12T03:27:11","slug":"%e5%a4%a7%e8%af%ad%e8%a8%80%e6%a8%a1%e5%9e%8b%e5%b5%8c%e5%85%a5%ef%bc%88embedding%ef%bc%89%e7%9a%84%e5%9b%9e%e5%bd%92%e7%89%b9%e5%be%81%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=5199","title":{"rendered":"\u5927\u8bed\u8a00\u6a21\u578b\u5d4c\u5165\uff08embedding\uff09\u7684\u56de\u5f52\u7279\u5f81\u5206\u6790"},"content":{"rendered":"\n<p>\u8bba\u6587<strong><a href=\"https:\/\/arxiv.org\/abs\/2411.14708\" target=\"_blank\" rel=\"noreferrer noopener\">Understanding LLM Embeddings for Regression<\/a><\/strong>\u6df1\u5165\u7814\u7a76\u4e86\u5927\u8bed\u8a00\u6a21\u578b\u5d4c\u5165\uff08embedding\uff09\u7684\u56de\u5f52\u7279\u5f81\u3002\u8bba\u6587\u4f5c\u8005\u4e3aEric Tang, Bangding Yang, Xingyou Song\uff0c\u6765\u81eaStanford University\u548cGoogle\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. <strong>\u7814\u7a76\u80cc\u666f\u4e0e\u52a8\u673a<\/strong><\/h4>\n\n\n\n<p>\u56de\u5f52\u5206\u6790\u662f\u6570\u636e\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u57fa\u7840\u5de5\u5177\uff0c\u7528\u4e8e\u91cf\u5316\u76ee\u6807\u53d8\u91cf\u4e0e\u7279\u5f81\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u4f20\u7edf\u7684\u56de\u5f52\u65b9\u6cd5\u901a\u5e38\u4f9d\u8d56\u4e8e\u4eba\u5de5\u7279\u5f81\u5de5\u7a0b\uff0c\u8fd9\u9700\u8981\u4e30\u5bcc\u7684\u9886\u57df\u77e5\u8bc6\u548c\u5927\u91cf\u7684\u624b\u52a8\u64cd\u4f5c\uff0c\u5982\u5bf9\u6570\u503c\u7279\u5f81\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u5bf9\u7c7b\u522b\u7279\u5f81\u8fdb\u884c\u72ec\u70ed\u7f16\u7801\u3002\u8fd9\u4e9b\u7279\u5f81\u5de5\u7a0b\u65b9\u6cd5\u4e0d\u4ec5\u8017\u65f6\u8d39\u529b\uff0c\u800c\u4e14\u5176\u6548\u679c\u5f80\u5f80\u4f9d\u8d56\u4e8e\u9886\u57df\u4e13\u5bb6\u7684\u7ecf\u9a8c\u3002<\/p>\n\n\n\n<p>\u8fd1\u5e74\u6765\uff0c\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u7684\u5174\u8d77\uff0c\u4f7f\u5f97\u5904\u7406\u81ea\u7136\u8bed\u8a00\u548c\u5176\u4ed6\u975e\u7ed3\u6784\u5316\u6570\u636e\u7684\u4efb\u52a1\u53d8\u5f97\u66f4\u52a0\u7075\u6d3b\u548c\u5f3a\u5927\u3002LLMs\u901a\u8fc7\u5c06\u8f93\u5165\u6587\u672c\u8f6c\u5316\u4e3a\u9ad8\u7ef4\u5411\u91cf\uff08\u5d4c\u5165\uff09\uff0c\u4ece\u800c\u53ef\u4ee5\u6355\u6349\u590d\u6742\u7684\u8bed\u4e49\u4fe1\u606f\uff0c\u8fd9\u4e3a\u4f20\u7edf\u7684\u56de\u5f52\u4efb\u52a1\u63d0\u4f9b\u4e86\u4e00\u79cd\u65b0\u7684\u601d\u8def\u3002\u672c\u6587\u7684\u4e3b\u8981\u52a8\u673a\u662f\u7814\u7a76LLM\u5d4c\u5165\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\uff0c\u7279\u522b\u662f\u5728\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\u4e2d\u7684\u8868\u73b0\uff0c\u4ee5\u53ca\u5b83\u4eec\u662f\u5426\u80fd\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u8d85\u8d8a\u4f20\u7edf\u7684\u4eba\u5de5\u7279\u5f81\u5de5\u7a0b\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u5728\u6587\u4e2d\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u4ee5\u4e0b\u4e3b\u8981\u95ee\u9898\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>LLM\u5d4c\u5165\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u4f18\u52bf\u548c\u5c40\u9650\u662f\u4ec0\u4e48\uff1f<\/strong> \u4f20\u7edf\u7279\u5f81\u5de5\u7a0b\u65b9\u6cd5\u662f\u5426\u5b58\u5728\u56fa\u6709\u7684\u74f6\u9888\uff0c\u800cLLM\u5d4c\u5165\u53ef\u4ee5\u8d85\u8d8a\u8fd9\u4e9b\u9650\u5236\uff1f<\/li>\n\n\n\n<li><strong>\u5982\u4f55\u5b9a\u91cf\u5316\u8bc4\u4f30LLM\u5d4c\u5165\u5728\u56de\u5f52\u4e2d\u7684\u6548\u679c\uff1f<\/strong> \u6bd4\u5982\u5bf9\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5e73\u6ed1\u6027\u548c<strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Lipschitz_continuity\" target=\"_blank\" rel=\"noreferrer noopener\">Lipschitz\u8fde\u7eed\u6027<\/a><\/strong>\u8fdb\u884c\u5206\u6790\u3002<\/li>\n\n\n\n<li><strong>\u6a21\u578b\u5927\u5c0f\u4e0e\u6027\u80fd\u4e4b\u95f4\u7684\u5173\u7cfb\u662f\u4ec0\u4e48\uff1f<\/strong> \u66f4\u5927\u7684LLM\u662f\u5426\u4e00\u5b9a\u80fd\u5e26\u6765\u66f4\u597d\u7684\u56de\u5f52\u6027\u80fd\uff0c\u6216\u8005\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u5c0f\u6a21\u578b\u4e5f\u53ef\u4ee5\u5339\u654c\u5927\u6a21\u578b\uff1f<\/li>\n<\/ol>\n\n\n\n<p>\u7814\u7a76\u8005\u4ece\u8fd9\u4e9b\u95ee\u9898\u51fa\u53d1\uff0c\u901a\u8fc7\u5927\u91cf\u5b9e\u9a8c\u5bf9LLM\u5d4c\u5165\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\u8fdb\u884c\u4e86\u6df1\u5165\u7684\u63a2\u8ba8\uff0c\u5f97\u5230\u4e86\u8bb8\u591a\u91cd\u8981\u7684\u7ed3\u8bba\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2. <strong>\u95ee\u9898\u5b9a\u4e49\u4e0e\u65b9\u6cd5\u8bba<\/strong><\/h4>\n\n\n\n<p>\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\uff0c\u76ee\u6807\u662f\u627e\u5230\u4e00\u79cd\u51fd\u6570f:X\u2192R\uff0c\u4ee5\u4fbf\u6839\u636e\u8f93\u5165\u7a7a\u95f4 X \u4e2d\u7684\u6570\u636e\u6765\u9884\u6d4b\u8f93\u51fa\u7684\u6807\u91cf\u503c\u3002\u5728\u4f20\u7edf\u56de\u5f52\u65b9\u6cd5\u4e2d\uff0c\u8f93\u5165\u6570\u636e\u901a\u5e38\u7531\u624b\u52a8\u5de5\u7a0b\u751f\u6210\u7684\u7279\u5f81\u8868\u793a\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6570\u503c\u7279\u5f81<\/strong>\u9700\u8981\u5f52\u4e00\u5316\u4ee5\u786e\u4fdd\u4e0d\u540c\u91cf\u7eb2\u7684\u6570\u636e\u5177\u6709\u76f8\u4f3c\u7684\u5206\u5e03\uff1b<\/li>\n\n\n\n<li><strong>\u7c7b\u522b\u7279\u5f81<\/strong>\u5219\u901a\u8fc7\u72ec\u70ed\u7f16\u7801\uff08one-hot encoding\uff09\u8fdb\u884c\u8f6c\u6362\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u7136\u800c\uff0cLLM\u5d4c\u5165\u7684\u51fa\u73b0\u6539\u53d8\u4e86\u8fd9\u4e00\u8fc7\u7a0b\u3002LLMs\u53ef\u4ee5\u5c06\u4efb\u610f\u5b57\u7b26\u4e32\uff08\u6587\u672c\uff09\u8f93\u5165\u8f6c\u6362\u4e3a\u56fa\u5b9a\u7ef4\u5ea6\u7684\u5411\u91cf\u8868\u793a\uff0c\u8fd9\u4f7f\u5f97\u5b83\u4eec\u5728\u5904\u7406\u81ea\u7136\u8bed\u8a00\u7b49\u590d\u6742\u975e\u7ed3\u6784\u5316\u6570\u636e\u65f6\u975e\u5e38\u6709\u6548\u3002\u5728\u672c\u6587\u4e2d\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u6846\u67b6\u6765\u5c06\u56de\u5f52\u4efb\u52a1\u4e0eLLM\u5d4c\u5165\u7ed3\u5408\uff0c\u5373\u4f7f\u7528LLM\u5d4c\u5165\u4f5c\u4e3a\u7279\u5f81\u8f93\u5165\u6765\u66ff\u4ee3\u4f20\u7edf\u7684\u624b\u52a8\u7279\u5f81\u5de5\u7a0b\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">2.1 <strong>LLM\u5d4c\u5165\u7684\u751f\u6210\u8fc7\u7a0b<\/strong><\/h5>\n\n\n\n<p>LLM\u5d4c\u5165\u7684\u751f\u6210\u8fc7\u7a0b\u5206\u4e3a\u4ee5\u4e0b\u51e0\u4e2a\u4e3b\u8981\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5206\u8bcd<\/strong>\uff1a\u5c06\u8f93\u5165\u5b57\u7b26\u4e32 x \u8f6c\u6362\u4e3a LLL \u4e2a\u4ee4\u724c\uff08tokens\uff09\u3002<\/li>\n\n\n\n<li><strong>\u751f\u6210\u8f6f\u63d0\u793a\uff08soft prompt\uff09<\/strong>\uff1a\u901a\u8fc7\u8bcd\u6c47\u67e5\u627e\u5c06\u8fd9\u4e9b\u4ee4\u724c\u8f6c\u6362\u4e3a\u4e00\u4e2a R<sup>L\u00d7v<\/sup>\u7684\u77e9\u9635\u8868\u793a\u3002<\/li>\n\n\n\n<li><strong>\u524d\u5411\u4f20\u64ad<\/strong>\uff1a\u5c06\u4e0a\u8ff0\u8868\u793a\u8f93\u5165Transformer\u6a21\u578b\uff0c\u5f97\u5230\u8f93\u51fa\u77e9\u9635 R<sup>L\u00d7f<\/sup>\u3002<\/li>\n\n\n\n<li><strong>\u6c60\u5316\uff08Pooling\uff09<\/strong>\uff1a\u5c06\u8f93\u51fa\u964d\u7ef4\u4e3a\u4e00\u4e2a\u56fa\u5b9a\u957f\u5ea6\u7684\u5411\u91cf R<sup>d<\/sup>\uff0c\u4f8b\u5982\u901a\u8fc7\u5e73\u5747\u6c60\u5316\uff08average pooling\uff09\u64cd\u4f5c\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6700\u7ec8\uff0c\u5f97\u5230\u7684\u5d4c\u5165\u5411\u91cf \u03d5(x) \u53ef\u4ee5\u4f5c\u4e3a\u540e\u7eed\u56de\u5f52\u4efb\u52a1\u7684\u8f93\u5165\u7279\u5f81\uff0c\u901a\u5e38\u4f1a\u9644\u52a0\u4e00\u4e2a\u7b80\u5355\u7684\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09\u9884\u6d4b\u5934\u6765\u5b8c\u6210\u9884\u6d4b\u4efb\u52a1\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">2.2 <strong>\u7814\u7a76\u65b9\u6cd5<\/strong><\/h5>\n\n\n\n<p>\u4e3a\u4e86\u8bc4\u4f30LLM\u5d4c\u5165\u7684\u6709\u6548\u6027\uff0c\u7814\u7a76\u8005\u4f7f\u7528\u4e86\u4e00\u79cd\u901a\u7528\u7684\u56de\u5f52\u6846\u67b6\uff0c\u5e76\u5bf9\u6bd4\u4e86\u4f20\u7edf\u7279\u5f81\u4e0eLLM\u5d4c\u5165\u7684\u6027\u80fd\u5dee\u5f02\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u7814\u7a76\u4e2d\u4f7f\u7528\u4e86\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09\u4f5c\u4e3a\u56de\u5f52\u9884\u6d4b\u5668\uff0c\u8fd9\u6837\u53ef\u4ee5\u6d88\u9664\u7531\u4e8e\u6a21\u578b\u67b6\u6784\u4e0d\u540c\u800c\u5e26\u6765\u7684\u6df7\u6742\u56e0\u7d20\uff1b<\/li>\n\n\n\n<li>\u5747\u65b9\u8bef\u5dee\uff08Mean Squared Error\uff0cMSE\uff09\u4f5c\u4e3a\u635f\u5931\u51fd\u6570\uff1b<\/li>\n\n\n\n<li><strong>\u6570\u636e\u6807\u51c6\u5316<\/strong>\uff1a\u5bf9 y \u503c\u8fdb\u884c\u96f6\u5747\u503c\u548c\u5355\u4f4d\u65b9\u5dee\u5904\u7406\uff0c\u4ee5\u786e\u4fdd\u56de\u5f52\u6a21\u578b\u7684\u6570\u503c\u7a33\u5b9a\u6027\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728\u5b9e\u9a8c\u4e2d\uff0c\u4f7f\u7528\u4e86\u4e0d\u540c\u7684LLM\u6a21\u578b\uff0c\u5305\u62ecT5\u548cGemini\u7cfb\u5217\u7684\u6a21\u578b\uff0c\u8fd9\u4e9b\u6a21\u578b\u6709\u7740\u4e0d\u540c\u7684\u7ed3\u6784\u3001\u8bcd\u6c47\u91cf\u548c\u5d4c\u5165\u7ef4\u5ea6\u3002\u6b64\u5916\uff0c\u8fd8\u8003\u8651\u4e86\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u57fa\u51c6\u6a21\u578b\uff0c\u5982XGBoost\u548c\u7ecf\u5178MLP\uff0c\u4ee5\u4fbf\u5728\u4e0d\u540c\u6761\u4ef6\u4e0b\u5168\u9762\u6bd4\u8f83LLM\u5d4c\u5165\u7684\u6027\u80fd\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3. <strong>\u5b9e\u9a8c\u4e0e\u7ed3\u679c\u5206\u6790<\/strong><\/h4>\n\n\n\n<p>\u4e3a\u4e86\u6df1\u5165\u7406\u89e3LLM\u5d4c\u5165\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\uff0c\u7814\u7a76\u8005\u8bbe\u8ba1\u4e86\u5927\u91cf\u5b9e\u9a8c\uff0c\u6db5\u76d6\u4e86\u4e0d\u540c\u7684\u4efb\u52a1\u573a\u666f\u548c\u4e0d\u540c\u7684\u6a21\u578b\u914d\u7f6e\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">3.1 <strong>\u9ad8\u7ef4\u56de\u5f52\u7684\u8868\u73b0<\/strong><\/h5>\n\n\n\n<p>\u7814\u7a76\u9996\u5148\u63a2\u7d22\u4e86\u5728\u9ad8\u81ea\u7531\u5ea6\uff08Degree-of-Freedom\uff0cDOF\uff09\u4e0b\uff0cLLM\u5d4c\u5165\u7684\u8868\u73b0\u662f\u5426\u4f18\u4e8e\u4f20\u7edf\u7279\u5f81\u8868\u793a\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u7814\u7a76\u8005\u4f7f\u7528\u4e86\u6807\u51c6\u7684BBOB\u57fa\u51c6\u6d4b\u8bd5\u5957\u4ef6\u6765\u751f\u6210\u591a\u79cd\u95ed\u5408\u5f62\u5f0f\u7684\u76ee\u6807\u51fd\u6570\uff0c\u8fd9\u4e9b\u51fd\u6570\u5177\u6709\u4e0d\u540c\u7684\u975e\u51f8\u7279\u6027\u548c\u4f18\u5316\u96be\u5ea6\u3002<\/p>\n\n\n\n<p>\u5b9e\u9a8c\u7ed3\u679c\u663e\u793a\uff0c\u5bf9\u4e8e\u5927\u591a\u6570\u76ee\u6807\u51fd\u6570\uff0c\u5f53DOF\u589e\u52a0\u65f6\uff0cLLM\u5d4c\u5165\u7684\u56de\u5f52\u6027\u80fd\u660e\u663e\u4f18\u4e8e\u4f20\u7edf\u65b9\u6cd5\u3002\u4f8b\u5982\uff0c\u4f20\u7edf\u7684MLP\u548cXGBoost\u6a21\u578b\u5728DOF\u8d85\u8fc750\u540e\uff0c\u6027\u80fd\u663e\u8457\u4e0b\u964d\uff0c\u800c\u57fa\u4e8eLLM\u5d4c\u5165\u7684\u6a21\u578b\u5219\u80fd\u591f\u8f83\u597d\u5730\u4fdd\u6301\u9884\u6d4b\u7cbe\u5ea6\u3002\u8fd9\u4e00\u7ed3\u679c\u8868\u660e\uff0cLLM\u5d4c\u5165\u5728\u5904\u7406\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\u65f6\u5177\u6709\u66f4\u597d\u7684\u9c81\u68d2\u6027\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">3.2 <strong>LLM\u5d4c\u5165\u7684\u5e73\u6ed1\u6027\u5206\u6790<\/strong><\/h5>\n\n\n\n<p>\u5e73\u6ed1\u6027\u662f\u795e\u7ecf\u7f51\u7edc\u6cdb\u5316\u80fd\u529b\u7684\u91cd\u8981\u6307\u6807\u3002\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\uff0c\u8f93\u5165\u7279\u5f81\u7684\u5e73\u6ed1\u6027\u51b3\u5b9a\u4e86\u6a21\u578b\u662f\u5426\u80fd\u591f\u5b66\u4e60\u8f93\u5165\u4e0e\u8f93\u51fa\u4e4b\u95f4\u7684\u8fde\u7eed\u5173\u7cfb\u3002\u4e3a\u4e86\u91cf\u5316LLM\u5d4c\u5165\u7684\u5e73\u6ed1\u6027\uff0c\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u5f52\u4e00\u5316Lipschitz\u56e0\u5b50\u5206\u5e03\uff08Normalized Lipschitz Factor Distribution\uff0cNLFD\uff09\u7684\u6982\u5ff5\u3002<\/p>\n\n\n\n<p>NLFD\u7528\u4e8e\u8861\u91cf\u5728\u7279\u5f81\u7a7a\u95f4\u4e2d\uff0c\u76f8\u4f3c\u8f93\u5165\uff08\u4f8b\u5982\u5728\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u4e0a\u63a5\u8fd1\u7684\u70b9\uff09\u662f\u5426\u5bf9\u5e94\u4e8e\u76f8\u4f3c\u7684\u6a21\u578b\u8f93\u51fa\u3002\u901a\u8fc7\u5206\u6790LLM\u5d4c\u5165\u548c\u4f20\u7edf\u7279\u5f81\u4e4b\u95f4\u7684NLFD\u5dee\u5f02\uff0c\u7814\u7a76\u8005\u53d1\u73b0\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53LLM\u5d4c\u5165\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u8868\u73b0\u4f18\u4e8e\u4f20\u7edf\u65b9\u6cd5\u65f6\uff0c\u5176\u5bf9\u5e94\u7684Lipschitz\u56e0\u5b50\u66f4\u503e\u5411\u4e8e\u96f6\uff0c\u8fd9\u8868\u660eLLM\u5d4c\u5165\u5177\u6709\u66f4\u597d\u7684\u5e73\u6ed1\u6027\u3002<\/li>\n\n\n\n<li>\u5728\u67d0\u4e9b\u7279\u5b9a\u4efb\u52a1\u4e2d\uff0cLLM\u5d4c\u5165\u7684\u5e73\u6ed1\u6027\u4e0e\u4f20\u7edf\u7279\u5f81\u76f8\u5f53\uff0c\u4f46\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0cLLM\u5d4c\u5165\u7684\u5e73\u6ed1\u6027\u66f4\u9ad8\uff0c\u8fd9\u89e3\u91ca\u4e86\u5176\u5728\u9ad8\u7ef4\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u4f18\u5f02\u8868\u73b0\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">3.3 <strong>\u6a21\u578b\u5927\u5c0f\u4e0e\u8bed\u8a00\u7406\u89e3\u80fd\u529b\u7684\u5f71\u54cd<\/strong><\/h5>\n\n\n\n<p>\u7814\u7a76\u8005\u8fdb\u4e00\u6b65\u63a2\u8ba8\u4e86\u6a21\u578b\u5927\u5c0f\u548c\u8bed\u8a00\u7406\u89e3\u80fd\u529b\u5bf9\u56de\u5f52\u6027\u80fd\u7684\u5f71\u54cd\u3002\u5e38\u89c4\u5047\u8bbe\u8ba4\u4e3a\uff0c\u6a21\u578b\u8d8a\u5927\uff0c\u6027\u80fd\u8d8a\u597d\u3002\u7136\u800c\uff0c\u7814\u7a76\u53d1\u73b0\u8fd9\u4e00\u7ed3\u8bba\u5e76\u4e0d\u603b\u662f\u6210\u7acb\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8eT5\u7cfb\u5217\u6a21\u578b\uff0c\u968f\u7740\u6a21\u578b\u89c4\u6a21\u4eceSmall\u589e\u52a0\u5230XXL\uff0c\u56de\u5f52\u6027\u80fd\u603b\u4f53\u4e0a\u6709\u6240\u63d0\u5347\uff0c\u8fd9\u8bf4\u660e\u6a21\u578b\u89c4\u6a21\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u80fd\u591f\u5e26\u6765\u66f4\u597d\u7684\u7279\u5f81\u8868\u8fbe\u80fd\u529b\u3002<\/li>\n\n\n\n<li>\u5bf9\u4e8eGemini\u7cfb\u5217\u6a21\u578b\uff0c\u7ed3\u679c\u66f4\u52a0\u590d\u6742\uff0c\u6a21\u578b\u89c4\u6a21\u4e0e\u6027\u80fd\u4e4b\u95f4\u7684\u5173\u7cfb\u5e76\u4e0d\u603b\u662f\u7ebf\u6027\u589e\u52a0\uff0c\u8fd9\u53ef\u80fd\u662f\u7531\u4e8e\u4e0d\u540c\u578b\u53f7\u7684Gemini\u6a21\u578b\u5728\u9884\u8bad\u7ec3\u6570\u636e\u96c6\u3001\u67b6\u6784\u8c03\u6574\u7b49\u65b9\u9762\u5b58\u5728\u5dee\u5f02\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6b64\u5916\uff0c\u7814\u7a76\u8fd8\u63a2\u8ba8\u4e86\u8bed\u8a00\u7406\u89e3\u80fd\u529b\u5bf9\u56de\u5f52\u4efb\u52a1\u7684\u5f71\u54cd\u3002\u901a\u8fc7\u5bf9\u6bd4\u968f\u673a\u521d\u59cb\u5316\u7684\u6a21\u578b\u4e0e\u9884\u8bad\u7ec3\u6a21\u578b\uff0c\u7814\u7a76\u8005\u53d1\u73b0\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5728\u5927\u591a\u6570\u56de\u5f52\u4efb\u52a1\u4e2d\uff0c\u9884\u8bad\u7ec3\u6a21\u578b\u7684\u8868\u73b0\u7565\u597d\u4e8e\u968f\u673a\u521d\u59cb\u5316\u7684\u6a21\u578b\uff0c\u8fd9\u8868\u660e\u8bed\u8a00\u7406\u89e3\u80fd\u529b\u5bf9\u67d0\u4e9b\u4efb\u52a1\u53ef\u80fd\u5177\u6709\u5e2e\u52a9\uff0c\u4f46\u5e76\u975e\u5728\u6240\u6709\u60c5\u51b5\u4e0b\u90fd\u662f\u51b3\u5b9a\u6027\u56e0\u7d20\u3002<\/li>\n\n\n\n<li>\u5bf9\u4e8e\u67d0\u4e9b\u7279\u5b9a\u4efb\u52a1\uff0c\u76f4\u63a5\u4f7f\u7528\u8bcd\u6c47\u5d4c\u5165\uff08\u4e0d\u7ecf\u8fc7Transformer\u7684\u524d\u5411\u4f20\u64ad\uff09\u4e5f\u80fd\u53d6\u5f97\u8f83\u597d\u7684\u7ed3\u679c\uff0c\u8fd9\u8fdb\u4e00\u6b65\u8bf4\u660e\uff0c\u8bed\u8a00\u6a21\u578b\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\u5e76\u4e0d\u4ec5\u4ec5\u4f9d\u8d56\u4e8e\u590d\u6742\u7684\u8bed\u4e49\u7406\u89e3\u8fc7\u7a0b\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">3.4 <strong>\u6570\u636e\u89c4\u6a21\u5bf9\u57fa\u51c6\u5dee\u8ddd\u7684\u5f71\u54cd<\/strong><\/h5>\n\n\n\n<p>\u76f4\u89c9\u4e0a\uff0c\u968f\u7740\u8bad\u7ec3\u6570\u636e\u89c4\u6a21\u589e\u52a0\uff0c\u6a21\u578b\u4e4b\u95f4\u7684\u6027\u80fd\u5dee\u8ddd\u4f1a\u7f29\u5c0f\uff0c\u56e0\u4e3a\u66f4\u591a\u7684\u6570\u636e\u53ef\u4ee5\u63d0\u4f9b\u66f4\u4e30\u5bcc\u7684\u4fe1\u606f\u4ee5\u5f25\u8865\u6a21\u578b\u8868\u8fbe\u80fd\u529b\u7684\u4e0d\u8db3\u3002\u7814\u7a76\u7ed3\u679c\u9a8c\u8bc1\u4e86\u8fd9\u4e00\u70b9\uff1a\u5f53\u6837\u672c\u6570\u91cf\u8f83\u5c11\u65f6\uff0cLLM\u5d4c\u5165\u4e0e\u4f20\u7edf\u7279\u5f81\u4e4b\u95f4\u7684\u6027\u80fd\u5dee\u8ddd\u8f83\u5927\uff1b\u800c\u968f\u7740\u8bad\u7ec3\u6837\u672c\u7684\u589e\u52a0\uff0c\u5dee\u8ddd\u9010\u6e10\u7f29\u5c0f\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5728\u6570\u636e\u8f83\u4e3a\u4e30\u5bcc\u7684\u573a\u666f\u4e0b\uff0c\u6a21\u578b\u7684\u5148\u9a8c\u7279\u5f81\u8868\u8fbe\u80fd\u529b\u5bf9\u6700\u7ec8\u6027\u80fd\u7684\u5f71\u54cd\u5c06\u53d8\u5f97\u4e0d\u90a3\u4e48\u663e\u8457\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4. <strong>\u7ed3\u8bba\u4e0e\u672a\u6765\u5c55\u671b<\/strong><\/h4>\n\n\n\n<p>\u672c\u6587\u901a\u8fc7\u5bf9LLM\u5d4c\u5165\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\u8fdb\u884c\u7cfb\u7edf\u6027\u7814\u7a76\uff0c\u5f97\u51fa\u4e86\u4e00\u4e9b\u91cd\u8981\u7ed3\u8bba\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>LLM\u5d4c\u5165\u5728\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\u4e2d\u8868\u73b0\u4f18\u8d8a<\/strong>\uff1a\u5b83\u4eec\u80fd\u591f\u6bd4\u4f20\u7edf\u7684\u4eba\u5de5\u7279\u5f81\u5728\u9ad8DOF\u6761\u4ef6\u4e0b\u66f4\u597d\u5730\u4fdd\u7559\u9884\u6d4b\u7cbe\u5ea6\uff0c\u8fd9\u8868\u660eLLM\u5d4c\u5165\u5728\u5904\u7406\u590d\u6742\u56de\u5f52\u4efb\u52a1\u65f6\u5177\u6709\u6f5c\u529b\u3002<\/li>\n\n\n\n<li><strong>\u5e73\u6ed1\u6027\u662f\u5d4c\u5165\u6027\u80fd\u7684\u5173\u952e\u56e0\u7d20<\/strong>\uff1a\u901a\u8fc7\u5f15\u5165Lipschitz\u56e0\u5b50\u5206\u5e03\uff0c\u7814\u7a76\u8005\u53d1\u73b0LLM\u5d4c\u5165\u7684\u5e73\u6ed1\u6027\u5728\u89e3\u91ca\u5176\u6027\u80fd\u65b9\u9762\u8d77\u5230\u4e86\u5173\u952e\u4f5c\u7528\u3002<\/li>\n\n\n\n<li><strong>\u6a21\u578b\u5927\u5c0f\u548c\u8bed\u8a00\u7406\u89e3\u7684\u5f71\u54cd\u56e0\u4efb\u52a1\u800c\u5f02<\/strong>\uff1a\u867d\u7136\u5927\u6a21\u578b\u901a\u5e38\u80fd\u591f\u5e26\u6765\u66f4\u597d\u7684\u6027\u80fd\uff0c\u4f46\u8bed\u8a00\u7406\u89e3\u80fd\u529b\u5e76\u975e\u6240\u6709\u56de\u5f52\u4efb\u52a1\u7684\u51b3\u5b9a\u6027\u56e0\u7d20\uff0c\u90e8\u5206\u4efb\u52a1\u5bf9\u7279\u5f81\u8868\u793a\u7684\u8981\u6c42\u53ef\u80fd\u66f4\u4f9d\u8d56\u4e8e\u5176\u4ed6\u56e0\u7d20\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u672a\u6765\u7814\u7a76\u65b9\u5411<\/strong>\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u591a\u6a21\u6001\u5d4c\u5165\u7684\u5e94\u7528<\/strong>\uff1a\u63a2\u7d22LLM\u5d4c\u5165\u5728\u975e\u8868\u683c\u6570\u636e\uff08\u5982\u56fe\u3001\u56fe\u50cf\u548c\u89c6\u9891\uff09\u4e0a\u7684\u8868\u73b0\uff0c\u8fd9\u4e9b\u6570\u636e\u7c7b\u578b\u5177\u6709\u66f4\u590d\u6742\u7684\u7279\u5f81\u7ed3\u6784\uff0c\u9700\u8981\u4e0d\u540c\u4e8e\u4f20\u7edf\u6587\u672c\u5d4c\u5165\u7684\u65b9\u6cd5\u6765\u5904\u7406\u3002<\/li>\n\n\n\n<li><strong>\u6df1\u5165\u5206\u6790\u5d4c\u5165\u7684\u5185\u5728\u7279\u6027\u4e0e\u56de\u5f52\u6027\u80fd\u4e4b\u95f4\u7684\u5173\u7cfb<\/strong>\uff1a\u5305\u62ec\u8fdb\u4e00\u6b65\u7406\u89e3LLM\u5d4c\u5165\u5982\u4f55\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u6355\u6349\u8f93\u5165\u6570\u636e\u7684\u590d\u6742\u6027\uff0c\u5c24\u5176\u662f\u5728\u9ad8\u7ef4\u3001\u975e\u7ebf\u6027\u7684\u6570\u636e\u573a\u666f\u4e2d\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u8bba\u6587Understanding LLM Embeddings for Regression\u6df1\u5165\u7814\u7a76\u4e86\u5927\u8bed\u8a00\u6a21\u578b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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