{"id":2628,"date":"2025-03-15T16:45:04","date_gmt":"2025-03-15T08:45:04","guid":{"rendered":"https:\/\/www.15zhi.net\/blog\/?p=2628"},"modified":"2025-03-15T16:45:04","modified_gmt":"2025-03-15T08:45:04","slug":"202503-%e8%ae%ba%e6%96%87%e7%a0%94%e8%af%bb-chain-of-thought-reasoning-without-prompting","status":"publish","type":"post","link":"https:\/\/www.15zhi.net\/blog\/202503-%e8%ae%ba%e6%96%87%e7%a0%94%e8%af%bb-chain-of-thought-reasoning-without-prompting\/","title":{"rendered":"202503 \u8bba\u6587\u7814\u8bfb-Chain-of-Thought Reasoning without Prompting"},"content":{"rendered":"\n<ul class=\"wp-block-list\">\n<li>\u53d1\u8868\u81ea\uff1aGoogle DeepMind<\/li>\n\n\n\n<li>\u4f5c\u8005\uff1aXuezhi Wang, Denny Zhou<\/li>\n\n\n\n<li>\u53d1\u5e03\u5e73\u53f0\uff1aNeurIPS 2024<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">\u6838\u5fc3\u5185\u5bb9<\/h1>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8fd9\u7bc7\u6587\u7ae0\u63d0\u51fa\uff1a\u53ea\u9700\u8981\u7a0d\u5fae\u6539\u53d8\u89e3\u7801\u65b9\u5f0f\uff0c<a href=\"\u5927\u8bed\u8a00\u6a21\u578b.md\">\u5927\u6a21\u578b<\/a>\u5c31\u53ef\u4ee5\u5728\u4e0d\u501f\u52a9\u7279\u522b\u7684\u8bad\u7ec3\u4ee5\u53ca\u63d0\u793a\u8bcd\u7684\u60c5\u51b5\u4e0b\u6267\u884c<a href=\"\u601d\u7ef4\u94fe.md\">\u601d\u7ef4\u94fe<\/a>\u7684\u63a8\u7406\uff1b\u8fd9\u8bc1\u660e\u5927\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u662f\u56fa\u6709\u7684\uff0c\u4e0d\u9700\u8981\u7279\u522b\u7684\u5916\u5728\u5e72\u9884\u6765\u4ea7\u751f\uff1b<\/li>\n\n\n\n<li>\u5177\u4f53\u65b9\u6cd5\u800c\u8a00\uff0c\u5728\u5927\u8bed\u8a00\u6a21\u578b\u751f\u6210\u7b2c\u4e00\u4e2a token \u7684\u8fc7\u7a0b\u4e2d\uff0c\u4fdd\u7559 top-k \u4e2a\u6700\u597d\u7684 token\uff1b\u63a5\u7740\u5206\u522b\u4ee5\u8fd9 k \u4e2a token \u4e3a\u5f00\u7aef\uff0c\u751f\u6210\u5168\u90e8\u56de\u7b54\uff1b\u6b63\u786e\u751f\u6210\u4e86\u601d\u7ef4\u94fe\u7684\u7b54\u6848\u5bf9\u5e94\u7684 token \u7f6e\u4fe1\u5ea6\u4f1a\u8fdc\u9ad8\u4e8e\u9519\u8bef\u7b54\u6848\uff1b<\/li>\n\n\n\n<li>\u57fa\u4e8e\u8fd9\u4e2a\u601d\u8def\uff0c\u8fd9\u7bc7\u6587\u7ae0\u63d0\u51fa\u4e86<strong>\u601d\u7ef4\u94fe\u89e3\u7801<\/strong>\uff08Chain-of-Thought-Decoding\uff0cCoT-Decoding\uff09\uff1b\u901a\u8fc7\u7528\u9009\u62e9\u9ad8\u7f6e\u4fe1\u5ea6\u7684\u56de\u7b54\u66ff\u4ee3\u539f\u672c\u7684\u8d2a\u5fc3\u7b56\u7565\uff0c\u5927\u6a21\u578b\u5728\u5404\u4e2a\u57fa\u51c6\u4e0a\u9762\u7684\u8868\u73b0\u90fd\u6709\u663e\u8457\u63d0\u5347\u3002<\/li>\n<\/ol>\n\n\n\n<h1 class=\"wp-block-heading\">\u80cc\u666f<\/h1>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5f53\u524d\uff0c<a href=\"\u5927\u8bed\u8a00\u6a21\u578b.md\">\u5927\u6a21\u578b<\/a>\u5df2\u7ecf\u5c55\u73b0\u51fa\u6765\u4e86\u5f88\u5f3a\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5728\u5404\u79cd\u63a8\u7406\u95ee\u9898\u6570\u636e\u96c6\u4e0a\u90fd\u53d6\u5f97\u4e86\u4e0d\u9519\u7684\u6548\u679c\uff1b\u4f46\u662f\u8fd9\u4e9b\u65b9\u6cd5\u57fa\u672c\u4e0a\u53ef\u4ee5\u5f52\u4e3a\u4e24\u7c7b\uff1a\n<ol class=\"wp-block-list\">\n<li>\u4f7f\u7528<a href=\"\u63d0\u793a\u8bcd\u5de5\u7a0b.md\">\u63d0\u793a\u8bcd\u6280\u5de7<\/a>\u6fc0\u53d1\u63a8\u7406\u80fd\u529b\uff1b<\/li>\n\n\n\n<li>\u4f7f\u7528<a href=\"\u6307\u4ee4\u5fae\u8c03.md\">\u6307\u4ee4\u5fae\u8c03<\/a>\u7b49\u8bad\u7ec3\u624b\u6bb5\u5728\u6d77\u91cf <a href=\"\u601d\u7ef4\u94fe.md\">CoT<\/a> \u6570\u636e\u4e0a\u8bad\u7ec3\uff1b<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li>\u63d0\u793a\u8bcd\u8981\u53d1\u6325\u4f5c\u7528\u9700\u8981\u53cd\u590d\u6839\u636e\u7ed3\u679c\u53bb\u4fee\u6539\u63d0\u793a\u8bcd\uff1b\u5fae\u8c03\u6a21\u578b\u5219\u6d88\u8017\u5927\u91cf\u8ba1\u7b97\u8d44\u6e90\u3002\u672c\u6587\u5219\u53d1\u73b0\u5176\u5b9e\u53ea\u9700\u8981\u4fee\u6539\u4e00\u4e0b\u5927\u6a21\u578b\u751f\u6210 token \u65f6\u7684\u8d2a\u5fc3\u7b56\u7565\uff0c\u5c31\u53ef\u4ee5\u5c55\u73b0\u51fa\u5927\u6a21\u578b\u56fa\u6709\u7684\u63a8\u7406\u80fd\u529b\uff1b\u4e3a\u6211\u4eec\u7406\u89e3\u5927\u6a21\u578b\u63d0\u4f9b\u4e86\u65b0\u7684\u7075\u611f\u3002<\/li>\n<\/ol>\n\n\n\n<h1 class=\"wp-block-heading\">\u65b9\u6cd5\u8bba<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u751f\u6210\u591a\u6761\u95ee\u7b54\u8def\u5f84<\/h2>\n\n\n\n<p>\u672c\u6587\u4f7f\u7528\u7684\u65b9\u6cd5\u601d\u8def\u5341\u5206\u7b80\u5355\uff0c\u4e00\u5f20\u56fe\u5c31\u80fd\u6982\u62ec\uff1a<br><img decoding=\"async\" src=\".\/Assets\/\u601d\u7ef4\u94fe\u89e3\u7801-1741940187706.png\" alt=\"\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1003\" height=\"412\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-67.png\" alt=\"\" class=\"wp-image-2629\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-67.png 1003w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-67-300x123.png 300w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-67-768x315.png 768w\" sizes=\"auto, (max-width: 1003px) 100vw, 1003px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5c06\u95ee\u9898\u76f4\u63a5\u8f93\u5165\u7ed9\u5927\u6a21\u578b\uff1b<\/li>\n\n\n\n<li>\u5927\u6a21\u578b\u4ee5\u81ea\u56de\u5f52\u7684\u65b9\u5f0f\u9010 token \u751f\u6210\u7b54\u6848\uff1b\n<ol class=\"wp-block-list\">\n<li>\u53d6\u5927\u6a21\u578b\u751f\u6210\u7b2c\u4e00\u4e2a token \u65f6\u5019\u7684\u8f93\u51fa\uff0c\u4fdd\u7559 top-k \u4e2a token \u4f5c\u4e3a\u8d77\u70b9\uff1b<\/li>\n\n\n\n<li>\u8ba9\u5927\u6a21\u578b\u5206\u522b\u4ece\u8fd9 k \u4e2a\u8d77\u70b9\u5f00\u59cb\uff0c\u6309\u7167\u4f20\u7edf\u7684\u65b9\u5f0f\u7ee7\u7eed\u751f\u6210\u5168\u90e8\u56de\u7b54\u3002<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<p>\u7136\u540e\u53ef\u4ee5\u53d1\u73b0\u4ece\u4e00\u4e9b\u4e0d\u662f\u6700\u4f73\u9009\u62e9\u7684 token \u5f00\u59cb\uff0c\u5927\u6a21\u578b\u53ef\u4ee5\u751f\u6210\u6b63\u786e\u7684\u601d\u7ef4\u94fe\uff0c\u65e0\u9700\u7279\u522b\u7684\u5f15\u5bfc\u3002<\/p>\n\n\n\n<p>\u4f5c\u8005\u8ba4\u4e3a\uff0c\u9020\u6210\u8fd9\u79cd\u73b0\u8c61\u7684\u539f\u56e0\u662f\u6a21\u578b\u4e3b\u8981\u662f\u5728\u4e0d\u9700\u8981\u63a8\u7406\u7684\u7b80\u5355\u95ee\u9898\u4e0a\u8fdb\u884c\u8bad\u7ec3\u7684\uff0c\u8fd9\u4f7f\u5f97\u6a21\u578b\u5929\u7136\u503e\u5411\u4e8e\u4e00\u6b65\u5f97\u51fa\u7b54\u6848\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7f6e\u4fe1\u5ea6<\/h2>\n\n\n\n<p>\u53e6\u4e00\u4e2a\u53d1\u73b0\u662f\uff0c\u5305\u542b\u6b63\u786e<a href=\"\u601d\u7ef4\u94fe.md\">\u601d\u7ef4\u94fe<\/a>\u7684\u56de\u7b54\uff0c\u5176\u548c\u7b54\u6848\u76f8\u5173\u90a3\u51e0\u4e2a token \u5e73\u5747<em>\u7f6e\u4fe1\u5ea6<\/em>\u66f4\u9ad8\u3002\u8fd9\u91cc\u7684\u7f6e\u4fe1\u5ea6\u6307\u7684\u662f<strong>\u8868\u793a\u7b54\u6848\u7684\u90a3\u51e0\u4e2a token \u4ea7\u751f\u7684\u6982\u7387\u5747\u503c<\/strong>\u8981\u9ad8\u3002\u4ee5 $\\Delta_{k,\\text{answer}}$ \u8868\u793a\uff1a<br>$$<br>\\Delta_{k,\\text{answer}}=\\frac{1}{|\\text{answer}|}\\sum_{x_{t}\\in \\text{answer}}[P(x_{t}^{(1)}|x_{&lt;t})-P(x_{t}^{(2)}|x_{&lt;t})]<br>$$<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>$k$\uff1a\u7b2c k \u4e2a\u56de\u7b54\uff1b<\/li>\n\n\n\n<li>$\\text{answer}$\uff1a\u6b63\u786e\u7b54\u6848\u6240\u5728\u7684 token \u96c6\u5408\uff1b<\/li>\n\n\n\n<li>$t$\uff1a\u5f53\u524d\u751f\u6210\u7684\u662f\u7b2c t \u4e2a token\uff1b<\/li>\n\n\n\n<li>$x^{(1)},x^{(2)}$\uff1a\u7b2c t \u6b65\u7684 top-2 token\uff0c\u8fd9\u4e24\u4e2a token \u7684\u751f\u6210\u6982\u7387\u5dee\u8ddd\u8d8a\u5927\uff0c\u8bf4\u660e\u5927\u6a21\u578b\u8d8a\u80af\u5b9a\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u7b54\u6848\u7f6e\u4fe1\u5ea6\u662f\u7528\u4e8e\u4ece\u591a\u6761\u8def\u5f84\u4e2d\u8fa8\u522b\u5305\u542b\u6b63\u786e<a href=\"\u601d\u7ef4\u94fe.md\">\u601d\u7ef4\u94fe<\/a>\u7684\u8def\u5f84\u7684\u624b\u6bb5\u3002\u6b63\u786e\u8fa8\u522b\u5305\u542b\u601d\u7ef4\u94fe\u7684\u8def\u5f84\u662f\u5c06\u672c\u6587\u53d1\u73b0\u7684\u7279\u70b9\u7528\u4e8e\u589e\u5f3a\u95ee\u7b54\u6548\u679c\u7684\u91cd\u8981\u6b65\u9aa4\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8bc6\u522b\u56de\u7b54\u4e2d\u7684\u7b54\u6848<\/h2>\n\n\n\n<p>\u672c\u6587\u5e76\u6ca1\u6709\u5728\u8fd9\u91cc\u505a\u8fc7\u591a\u7684\u7814\u7a76\uff0c\u53ea\u662f\u6307\u51fa\u4e86\u51e0\u4e2a\u53ef\u7528\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5982\u679c\u662f\u6570\u5b66\u95ee\u9898\uff0c\u90a3\u4e48\u56de\u7b54\u4e2d\u7684\u6700\u540e\u4e00\u4e2a\u6570\u5b57\u53ef\u80fd\u662f\u6b63\u786e\u7b54\u6848\uff1b<\/li>\n\n\n\n<li>\u96c6\u5408\u578b\u95ee\u9898\uff0c\u53ef\u4ee5\u4f7f\u7528 <a href=\"T\u00fclu\u8bc4\u4f30.md\">T\u00fclu\u8bc4\u4f30<\/a>\uff1b<\/li>\n\n\n\n<li>\u63d0\u793a\u8bcd\u6307\u5f15\uff0c\u8981\u6c42\u6a21\u578b\u7ed9\u51fa\u56de\u7b54\u524d\u8bf4 &#8220;So the answer is: &#8220;\u4e4b\u7c7b\u7684\u8bdd\u6765\u8fdb\u884c\u5b9a\u4f4d\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u548c<a href=\"\u81ea\u4e00\u81f4\u63d0\u793a.md\">\u81ea\u4e00\u81f4\u63d0\u793a<\/a>\u7684\u5bf9\u6bd4<\/h2>\n\n\n\n<p>\u601d\u7ef4\u94fe\u89e3\u7801\u770b\u8d77\u6765\u548c<a href=\"\u81ea\u4e00\u81f4\u63d0\u793a.md\">\u81ea\u4e00\u81f4\u63d0\u793a<\/a>\u4e00\u6837\uff0c\u4f46\u662f\u81ea\u4e00\u81f4\u63d0\u793a\u6781\u5ea6\u4f9d\u8d56\u7279\u522b\u7684\u63d0\u793a\u8bcd\uff0c\u6ca1\u6709\u63d0\u793a\u8bcd\u8f85\u52a9\u5c06\u4f1a\u51fa\u95ee\u9898\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u53ea\u4fdd\u7559\u7b2c\u4e00\u4e2a token \u7684 top-k<\/h2>\n\n\n\n<p>\u56e0\u4e3a\u81ea\u56de\u5f52\u67b6\u6784\u7684\u7279\u70b9\uff0c\u540e\u9762\u7684 token \u53d7\u524d\u9762\u751f\u6210\u7684 token \u5f71\u54cd\u6781\u5927\u3002\u5982\u679c\u8fd9\u6837\u5e72\uff0c\u5c31\u4f1a\u51cf\u5c0f\u5927\u6a21\u578b\u4fee\u6b63\u9519\u8bef\u8def\u5f84\u7684\u673a\u4f1a\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u4e0d\u4ece\u5f52\u7eb3\u6240\u6709\u8def\u5f84\u5f97\u5230\u7b54\u6848<\/h2>\n\n\n\n<p>\u4e8b\u5b9e\u8bc1\u660e\u76f4\u63a5\u6295\u7968\u6050\u6015\u4e0d\u4f1a\u6709\u597d\u7ed3\u679c\uff0c\u4f46\u662f\u7528 $\\Delta_{k,a}$ \u52a0\u6743\u6295\u7968\u5012\u662f\u53ef\u4ee5\u589e\u5f3a\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u5b9e\u9a8c<\/h1>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1006\" height=\"366\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-68.png\" alt=\"\" class=\"wp-image-2630\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-68.png 1006w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-68-300x109.png 300w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-68-768x279.png 768w\" sizes=\"auto, (max-width: 1006px) 100vw, 1006px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1002\" height=\"391\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-69.png\" alt=\"\" class=\"wp-image-2631\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-69.png 1002w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-69-300x117.png 300w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/03\/image-69-768x300.png 768w\" sizes=\"auto, (max-width: 1002px) 100vw, 1002px\" \/><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">\u7ed3\u8bba<\/h1>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8fd9\u7bc7\u6587\u7ae0\u901a\u8fc7\u4e00\u4e2a\u5c0f\u6280\u5de7\u5c31\u7ed5\u5f00\u4e86\u63d0\u793a\u8bcd\u4f7f\u5f97\u5927\u6a21\u578b\u80fd\u76f4\u63a5\u751f\u6210\u601d\u7ef4\u94fe\uff1b\u8fd9\u8868\u660e\u63a8\u7406\u80fd\u529b\u662f\u5927\u6a21\u578b\u5185\u5728\u56fa\u6709\u7684\uff1b<\/li>\n\n\n\n<li>\u8fd9\u7bc7\u6587\u7ae0\u53d1\u73b0\u5305\u542b\u601d\u7ef4\u94fe\u7684\u7b54\u6848\u5176\u7b54\u6848token \u7684\u7f6e\u4fe1\u5ea6\u66f4\u9ad8\uff1b<\/li>\n\n\n\n<li>\u8fd9\u7bc7\u6587\u7ae0\u7528\u8fd9\u4e2a\u601d\u8def\u63d0\u51fa\u4e86\u4e00\u4e2a\u589e\u5f3a\u5927\u6a21\u578b\u56de\u7b54\u6548\u679c\u7684\u65b9\u6848\uff0c\u80fd\u663e\u8457\u63d0\u9ad8\u8868\u73b0\u5e76\u4e14\u7f29\u5c0f\u9884\u8bad\u7ec3\u6a21\u578b\u548c\u6307\u4ee4\u5fae\u8c03\u6a21\u578b\u4e4b\u95f4\u7684\u5dee\u8ddd\u3002<\/li>\n<\/ol>\n\n\n\n<h1 class=\"wp-block-heading\">\u542f\u53d1\u4e0e\u8bc4\u4ef7<\/h1>\n\n\n\n<ol 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