{"id":115189,"date":"2026-10-11T13:41:50","date_gmt":"2026-10-11T05:41:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/115189.html"},"modified":"2026-10-11T13:41:50","modified_gmt":"2026-10-11T05:41:50","slug":"%e3%80%90%e5%a4%a7%e6%a8%a1%e5%9e%8b%e5%90%8e%e8%ae%ad%e7%bb%83%e3%80%91does-fine-tuning-llms-on-new-knowledge-encourage-hallucinations","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/115189.html","title":{"rendered":"\u3010\u5927\u6a21\u578b\u540e\u8bad\u7ec3\u3011Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations"},"content":{"rendered":"<p>Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations \u5728\u65b0\u77e5\u8bc6\u4e0a\u5fae\u8c03LLM\u662f\u5426\u4f1a\u52a9\u957f\u5e7b\u89c9&#xff1f; \u8bba\u6587<\/p>\n<h3>\u6458\u8981<\/h3>\n<p>\u5f53\u5927\u578b\u8bed\u8a00\u6a21\u578b\u901a\u8fc7\u76d1\u7763\u5fae\u8c03\u8fdb\u884c\u5bf9\u9f50\u65f6&#xff0c;\u5b83\u4eec\u53ef\u80fd\u4f1a\u9047\u5230\u672a\u901a\u8fc7\u9884\u8bad\u7ec3\u83b7\u5f97\u7684\u65b0\u4e8b\u5b9e\u4fe1\u606f\u3002\u4eba\u4eec\u5e38\u63a8\u6d4b&#xff0c;\u8fd9\u53ef\u80fd\u4f1a\u6559\u4f1a\u6a21\u578b\u4ea7\u751f\u4e8b\u5b9e\u4e0d\u6b63\u786e\u56de\u7b54\u7684\u5e7b\u89c9\u884c\u4e3a&#xff0c;\u56e0\u4e3a\u6a21\u578b\u88ab\u8bad\u7ec3\u751f\u6210\u5e76\u975e\u57fa\u4e8e\u5176\u5df2\u6709\u77e5\u8bc6\u7684\u4e8b\u5b9e\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d&#xff0c;\u6211\u4eec\u7814\u7a76\u8fd9\u79cd\u63a5\u89e6\u65b0\u77e5\u8bc6\u5bf9\u5fae\u8c03\u6a21\u578b\u5229\u7528\u5176\u5df2\u6709\u77e5\u8bc6\u7684\u80fd\u529b\u7684\u5f71\u54cd\u3002\u4e3a\u6b64&#xff0c;\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u53d7\u63a7\u8bbe\u7f6e&#xff0c;\u805a\u7126\u4e8e\u95ed\u5377\u95ee\u7b54&#xff0c;\u5176\u4e2d\u6211\u4eec\u6539\u53d8\u5f15\u5165\u65b0\u77e5\u8bc6\u7684\u5fae\u8c03\u6837\u672c\u6bd4\u4f8b\u3002\u6211\u4eec\u8bc1\u660e&#xff0c;\u5927\u578b\u8bed\u8a00\u6a21\u578b\u96be\u4ee5\u901a\u8fc7\u5fae\u8c03\u83b7\u5f97\u65b0\u7684\u4e8b\u5b9e\u77e5\u8bc6&#xff0c;\u56e0\u4e3a\u5f15\u5165\u65b0\u77e5\u8bc6\u7684\u5fae\u8c03\u6837\u672c\u7684\u5b66\u4e60\u901f\u5ea6\u663e\u8457\u6162\u4e8e\u4e0e\u6a21\u578b\u77e5\u8bc6\u4e00\u81f4\u7684\u6837\u672c\u3002\u7136\u800c&#xff0c;\u6211\u4eec\u8fd8\u53d1\u73b0&#xff0c;\u968f\u7740\u5e26\u6709\u65b0\u77e5\u8bc6\u7684\u6837\u672c\u6700\u7ec8\u88ab\u5b66\u4f1a&#xff0c;\u5b83\u4eec\u4f1a\u7ebf\u6027\u5730\u589e\u52a0\u6a21\u578b\u7684\u5e7b\u89c9\u503e\u5411\u3002\u7efc\u5408\u6765\u770b&#xff0c;\u6211\u4eec\u7684\u7ed3\u679c\u51f8\u663e\u4e86\u901a\u8fc7\u5fae\u8c03\u5f15\u5165\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u7684\u98ce\u9669&#xff0c;\u5e76\u652f\u6301\u8fd9\u6837\u4e00\u79cd\u89c2\u70b9&#xff1a;\u5927\u578b\u8bed\u8a00\u6a21\u578b\u4e3b\u8981\u901a\u8fc7\u9884\u8bad\u7ec3\u83b7\u5f97\u4e8b\u5b9e\u77e5\u8bc6&#xff0c;\u800c\u5fae\u8c03\u5219\u6559\u4f1a\u5b83\u4eec\u66f4\u6709\u6548\u5730\u4f7f\u7528\u8fd9\u4e9b\u77e5\u8bc6\u3002<\/p>\n<h2>1.\u5f15\u8a00<\/h2>\n<p>\u5728\u6587\u672c\u8bed\u6599\u5e93\u4e0a\u9884\u8bad\u7ec3\u5927\u578b\u8bed\u8a00\u6a21\u578b&#xff08;LLMs&#xff09;\u4f1a\u5c06\u5927\u91cf\u4e8b\u5b9e\u77e5\u8bc6\u5d4c\u5165\u5176\u53c2\u6570\u4e2d&#xff08;Petroni et al., 2019; AlKhamissi et al., 2022; Cohen et al., 2023&#xff09;&#xff0c;\u8fd9\u5bf9\u4e8e\u5728\u5404\u79cd\u4e0b\u6e38\u5e94\u7528\u4e2d\u8868\u73b0\u51fa\u8272\u81f3\u5173\u91cd\u8981\u3002\u8fd9\u4e9b\u6a21\u578b\u901a\u5e38\u9700\u8981\u8fdb\u4e00\u6b65\u5bf9\u9f50\u81f3\u671f\u671b\u884c\u4e3a&#xff0c;\u8fd9\u901a\u5e38\u901a\u8fc7\u5728\u6307\u4ee4\u9075\u5faa\u4efb\u52a1\u4e0a\u8fdb\u884c\u76d1\u7763\u5fae\u8c03&#xff08;Wei et al., 2022; Mishra et al., 2022&#xff09;\u4ee5\u53ca\u57fa\u4e8e\u4eba\u7c7b\u53cd\u9988\u7684\u504f\u597d\u5b66\u4e60&#xff08;Ouyang et al., 2022; Rafailov et al., 2024&#xff09;\u6765\u5b9e\u73b0\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054137-6acb2191a46b8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe1&#xff1a;\u5f53\u572850%\u5df2\u77e5\u6837\u672c\u548c50%\u672a\u77e5\u6837\u672c\u4e0a\u8fdb\u884c\u5fae\u8c03\u65f6&#xff0c;\u8bad\u7ec3\u51c6\u786e\u7387\u548c\u5f00\u53d1\u51c6\u786e\u7387\u4f5c\u4e3a\u5fae\u8c03\u65f6\u957f\u7684\u51fd\u6570\u3002\u672a\u77e5\u6837\u672c\u7684\u62df\u5408\u901f\u5ea6\u663e\u8457\u6162\u4e8e\u5df2\u77e5\u6837\u672c\u3002\u5f53LLM\u62df\u5408\u5927\u591a\u6570\u5df2\u77e5\u8bad\u7ec3\u6837\u672c\u4f46\u4ec5\u62df\u5408\u5c11\u6570\u672a\u77e5\u6837\u672c\u65f6&#xff0c;\u53ef\u83b7\u5f97\u6700\u4f73 \u5f00\u53d1\u6027\u80fd\u3002\u4ece\u8fd9\u4e00\u70b9\u5f00\u59cb&#xff0c;\u62df\u5408\u672a\u77e5\u6837\u672c\u4f1a\u964d\u4f4e\u6027\u80fd\u3002<\/p>\n<p>\u5728\u5fae\u8c03\u9636\u6bb5&#xff0c;\u6a21\u578b\u901a\u5e38\u5728\u7531\u4eba\u7c7b\u6807\u6ce8\u8005\u6216\u5176\u4ed6 LLM \u521b\u5efa\u7684\u8f93\u51fa\u4e0a\u8fdb\u884c\u8bad\u7ec3\u3002\u56e0\u6b64&#xff0c;\u6a21\u578b\u53ef\u80fd\u63a5\u89e6\u5230\u65b0\u7684\u4e8b\u5b9e\u4fe1\u606f&#xff0c;\u8fd9\u4e9b\u4fe1\u606f\u8d85\u51fa\u4e86\u5176\u5728\u9884\u8bad\u7ec3\u671f\u95f4\u6240\u83b7\u5f97\u7684\u77e5\u8bc6\u8303\u56f4\u3002\u8fd9\u5f15\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898&#xff1a;LLM \u5982\u4f55\u6574\u5408\u5176\u65e2\u6709\u77e5\u8bc6\u4e4b\u5916\u7684\u65b0\u4e8b\u5b9e\u3002\u4e00\u79cd\u53ef\u80fd\u6027\u662f&#xff0c;\u6a21\u578b\u53ea\u662f\u901a\u8fc7\u5b66\u4e60\u8fd9\u4e9b\u65b0\u4e8b\u5b9e\u4fe1\u606f\u6765\u9002\u5e94\u3002\u7136\u800c&#xff0c;\u4e00\u79cd\u5e38\u89c1\u7684\u731c\u60f3\u8ba4\u4e3a&#xff0c;\u8fd9\u79cd\u5bf9\u65b0\u77e5\u8bc6\u7684\u63a5\u89e6\u53ef\u80fd\u4fc3\u4f7f\u6a21\u578b\u4ea7\u751f\u4e8b\u5b9e\u9519\u8bef\u7684\u5e7b\u89c9\u54cd\u5e94&#xff0c;\u56e0\u4e3a\u6a21\u578b\u672c\u8d28\u4e0a\u88ab\u8bad\u7ec3\u6765\u751f\u6210\u5e76\u975e\u4ee5\u5176\u65e2\u6709\u77e5\u8bc6\u4e3a\u57fa\u7840\u7684\u4e8b\u5b9e&#xff08;Schulman, 2023; Huang et al., 2023; Gao, 2021; Goldberg, 2023; Gudibande et al., 2023&#xff09;\u3002\u5728\u672c\u5de5\u4f5c\u4e2d&#xff0c;\u6211\u4eec\u7814\u7a76\u901a\u8fc7\u5fae\u8c03\u5b66\u4e60\u65b0\u7684\u4e8b\u5b9e\u77e5\u8bc6&#xff08;arXiv:2405.05904v3 [cs.CL] 2024\u5e7410\u67081\u65e5&#xff09;\u5982\u4f55\u5f71\u54cd\u6a21\u578b\u5728\u5176\u65e2\u6709\u77e5\u8bc6\u65b9\u9762\u4ea7\u751f\u5e7b\u89c9\u7684\u503e\u5411&#xff0c;\u4ece\u800c\u63a2\u7d22\u4e0a\u8ff0\u731c\u60f3\u3002\u00b9 \u4e3a\u4e86\u7814\u7a76\u65b0\u77e5\u8bc6\u7684\u5f71\u54cd&#xff0c;\u6211\u4eec\u5fc5\u987b\u80fd\u591f\u8bc4\u4f30\u5355\u4e2a\u5fae\u8c03\u6837\u672c\u662f\u5426\u4e0e\u6a21\u578b\u7684\u77e5\u8bc6\u4e00\u81f4\u3002\u6211\u4eec\u63d0\u51fa SliCK&#xff0c;\u4e00\u4e2a\u7531\u56db\u4e2a\u77e5\u8bc6\u7c7b\u522b\u7ec4\u6210\u7684\u5c42\u7ea7\u4f53\u7cfb&#xff0c;\u5b83\u6e90\u81ea\u4e00\u4e2a\u8fde\u7eed\u5ea6\u91cf&#xff0c;\u8be5\u5ea6\u91cf\u91cf\u5316\u6a21\u578b\u751f\u6210\u7684\u7b54\u6848\u4e0e\u771f\u5b9e\u6807\u7b7e\u4e4b\u95f4\u7684\u4e00\u81f4\u6027\u3002\u5728 SliCK \u4e2d&#xff0c;\u6837\u672c\u9996\u5148\u88ab\u5206\u4e3a\u5df2\u77e5&#xff08;Known&#xff09;\u548c\u672a\u77e5&#xff08;Unknown&#xff09;\u7c7b\u578b&#xff0c;\u5176\u4e2d\u540e\u8005\u5bf9\u5e94\u4e8e\u5305\u542b\u6a21\u578b\u6700\u53ef\u80fd\u672a\u77e5\u7684\u4e8b\u5b9e\u7684\u6837\u672c\u3002\u5df2\u77e5\u6837\u672c\u968f\u540e\u88ab\u5206\u4e3a\u4e09\u4e2a\u7c7b\u522b&#xff1a;\u9ad8\u5ea6\u5df2\u77e5&#xff08;HighlyKnown&#xff09;\u3001\u53ef\u80fd\u5df2\u77e5&#xff08;MaybeKnown&#xff09;\u548c\u5f31\u5df2\u77e5&#xff08;WeaklyKnown&#xff09;&#xff08;\u56fe 2&#xff09;\u3002<\/p>\n<p>\u501f\u52a9\u4e0a\u8ff0\u65b9\u6cd5&#xff0c;\u6211\u4eec\u7cbe\u5fc3\u8bbe\u8ba1\u4e86\u4e00\u9879\u53d7\u63a7\u7814\u7a76&#xff0c;\u805a\u7126\u4e8e\u95ed\u5377\u95ee\u7b54&#xff08;QA&#xff09;&#xff0c;\u5176\u4e2d\u6211\u4eec\u6539\u53d8\u88ab\u5f52\u7c7b\u4e3a\u672a\u77e5\u7684\u5fae\u8c03\u6837\u672c\u6bd4\u4f8b&#xff0c;\u540c\u65f6\u63a7\u5236\u5176\u4ed6\u56e0\u7d20\u3002\u6211\u4eec\u7684\u7814\u7a76\u5b9e\u8bc1\u8868\u660e&#xff0c;\u4ece\u672a\u77e5\u5fae\u8c03\u6837\u672c\u4e2d\u5b66\u4e60\u4e0e\u6a21\u578b\u5728\u5176\u65e2\u6709\u77e5\u8bc6\u65b9\u9762\u4ea7\u751f\u5e7b\u89c9\u7684\u503e\u5411\u7ebf\u6027\u76f8\u5173&#xff08;\u00a74&#xff09;\u3002\u76f8\u53cd&#xff0c;\u4ece\u5df2\u77e5\u6837\u672c\u4e2d\u5b66\u4e60\u4e0e\u66f4\u597d\u5730\u5229\u7528\u65e2\u6709\u77e5\u8bc6\u76f8\u5173\u3002\u901a\u8fc7\u5206\u6790\u8bad\u7ec3\u52a8\u6001&#xff0c;\u6211\u4eec\u53d1\u73b0 LLM \u62df\u5408\u672a\u77e5\u5fae\u8c03\u6837\u672c\u7684\u901f\u5ea6\u663e\u8457\u6162\u4e8e\u62df\u5408\u5df2\u77e5\u6837\u672c&#xff08;\u56fe 1 \u7684\u4e0a\u56fe&#xff09;\u3002\u8fd9\u8868\u660e&#xff0c;\u5728\u5fae\u8c03\u671f\u95f4&#xff0c;LLM \u96be\u4ee5\u00b2\u6574\u5408\u65b0\u7684\u4e8b\u5b9e\u77e5\u8bc6&#xff08;\u5b58\u5728\u4e8e\u672a\u77e5\u5fae\u8c03\u6837\u672c\u4e2d&#xff09;\u3002\u76f8\u53cd&#xff0c;\u5b83\u4eec\u5927\u591a\u5b66\u4f1a\u5c55\u73b0\u5176\u65e2\u6709\u77e5\u8bc6&#xff08;\u4f7f\u7528\u5df2\u77e5\u5fae\u8c03\u6837\u672c&#xff09;\u3002\u4ece\u5b9e\u8df5\u89d2\u5ea6\u770b&#xff0c;\u4f7f\u7528\u65e9\u505c&#xff08;\u56fe 1 \u4e2d\u7684\u5782\u76f4\u865a\u7ebf&#xff09;\u6765\u7f13\u89e3\u8fc7\u62df\u5408&#xff0c;\u53ef\u4ee5\u6700\u5c0f\u5316\u7531\u62df\u5408\u672a\u77e5\u6837\u672c\u6240\u5bfc\u81f4\u7684\u5e7b\u89c9\u98ce\u9669&#xff0c;\u56e0\u4e3a\u8fd9\u4e9b\u5e7b\u89c9\u4e3b\u8981\u51fa\u73b0\u5728\u8bad\u7ec3\u540e\u671f&#xff0c;\u4f5c\u4e3a\u4e00\u79cd\u8fc7\u62df\u5408\u5f62\u5f0f&#xff08;\u5982\u56fe 1 \u7684\u4e0b\u56fe\u4e2d\u5f00\u53d1\u6027\u80fd\u4e0b\u964d\u6240\u793a&#xff09;\u3002\u6216\u8005&#xff0c;\u6211\u4eec\u8fd8\u8868\u660e&#xff0c;\u8fc7\u6ee4\u6389\u672a\u77e5\u5fae\u8c03\u6837\u672c\u4f1a\u663e\u8457\u964d\u4f4e\u4e86\u8fc7\u62df\u5408\u98ce\u9669&#xff0c;\u4e14\u4e0d\u727a\u7272\u6027\u80fd\u3002\u6211\u4eec\u8fdb\u4e00\u6b65\u8bc4\u4f30\u6765\u81ea\u4e09\u7c7b Known \u77e5\u8bc6\u7c7b\u522b\u7684\u5fae\u8c03\u793a\u4f8b\u5bf9\u6027\u80fd\u7684\u5f71\u54cd&#xff08;\u7b2c5\u8282&#xff09;\u3002\u51fa\u4e4e\u610f\u6599\u7684\u662f&#xff0c;\u6211\u4eec\u53d1\u73b0&#xff0c;\u4ec5\u5728\u6765\u81ea\u6700\u9ad8\u77e5\u8bc6\u7a0b\u5ea6&#xff08;\u8bb0\u4e3a HighlyKnown&#xff09;\u7684\u793a\u4f8b\u4e0a\u5fae\u8c03\u7684\u6a21\u578b\u5e76\u672a\u53d6\u5f97\u6700\u4f73\u7ed3\u679c\u3002\u6211\u4eec\u7684\u5206\u6790\u8868\u660e&#xff0c;\u7eb3\u5165 MaybeKnown \u5fae\u8c03\u793a\u4f8b\u2014\u2014\u5176\u8868\u793a\u786e\u5b9a\u6027\u7a0b\u5ea6\u8f83\u4f4e\u7684\u4e8b\u5b9e\u2014\u2014\u5728\u6d4b\u8bd5\u65f6\u6b63\u786e\u5904\u7406\u6b64\u7c7b\u793a\u4f8b\u65b9\u9762\u8d77\u7740\u91cd\u8981\u4f5c\u7528\u3002\u8fd9\u8868\u660e&#xff0c;\u5fae\u8c03\u793a\u4f8b\u7684\u6784\u6210\u663e\u8457\u5f71\u54cd LLMs \u6709\u6548\u5229\u7528\u5176\u5df2\u6709\u77e5\u8bc6\u7684\u7a0b\u5ea6\u3002\u603b\u800c\u8a00\u4e4b&#xff0c;\u6211\u4eec\u901a\u8fc7\u8bbe\u8ba1\u4e00\u4e2a\u9694\u79bb\u8be5\u56e0\u7d20\u7684\u53d7\u63a7\u8bbe\u7f6e&#xff0c;\u7814\u7a76\u5fae\u8c03\u6570\u636e\u4e2d\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u7684\u5f71\u54cd\u3002\u6211\u4eec\u53d1\u73b0&#xff0c;\u5f15\u5165\u65b0\u77e5\u8bc6\u7684\u5fae\u8c03\u793a\u4f8b\u5b66\u4e60\u7f13\u6162&#xff0c;\u8fd9\u8868\u660e LLMs \u96be\u4ee5\u901a\u8fc7\u5fae\u8c03\u6574\u5408\u65b0\u77e5\u8bc6&#xff0c;\u5e76\u652f\u6301 LLMs \u4e3b\u8981\u901a\u8fc7\u9884\u8bad\u7ec3\u83b7\u53d6\u77e5\u8bc6\u7684\u89c2\u70b9&#xff08;Zhou et al., 2023; Lin et al., 2023&#xff09;\u3002\u7136\u800c&#xff0c;\u6211\u4eec\u8fd8\u53d1\u73b0&#xff0c;\u968f\u7740\u6a21\u578b\u6700\u7ec8\u901a\u8fc7\u5fae\u8c03\u5b66\u4e60\u5230\u65b0\u77e5\u8bc6&#xff0c;\u5b83\u5c31\u5176\u5df2\u6709\u77e5\u8bc6\u800c\u8a00\u53d8\u5f97\u66f4\u5bb9\u6613\u4ea7\u751f\u5e7b\u89c9\u3002\u603b\u4f53\u800c\u8a00&#xff0c;\u6211\u4eec\u7684\u53d1\u73b0\u51f8\u663e\u4e86\u901a\u8fc7\u5fae\u8c03\u5f15\u5165\u65b0\u77e5\u8bc6\u65f6\u53ef\u80fd\u4ea7\u751f\u610f\u5916\u540e\u679c&#xff0c;\u5e76\u610f\u5473\u7740\u5fae\u8c03\u4f5c\u4e3a\u4e00\u79cd\u589e\u5f3a\u5df2\u6709\u77e5\u8bc6\u5229\u7528\u7684\u673a\u5236\u53ef\u80fd\u66f4\u4e3a\u6709\u7528\u3002<\/p>\n<p>1\u5c3d\u7ba1\u6211\u4eec\u805a\u7126\u4e8e\u76d1\u7763\u5fae\u8c03&#xff0c;\u4f46\u6211\u4eec\u7684\u53d1\u73b0\u53ef\u80fd\u5bf9\u8bf8\u5982 DPO&#xff08;Rafailov \u7b49&#xff0c;2024&#xff09;\u8fd9\u7c7b\u53ef\u80fd\u6dfb\u52a0\u65b0\u77e5\u8bc6\u7684\u79bb\u7ebf\u504f\u597d\u4f18\u5316\u65b9\u6cd5\u5177\u6709\u53c2\u8003\u4ef7\u503c&#xff0c;\u6211\u4eec\u5c06\u6b64\u7559\u5f85\u672a\u6765\u5de5\u4f5c\u3002 2\u6211\u4eec\u4f7f\u7528\u201c\u6323\u624e\u201d\u4e00\u8bcd\u6765\u63cf\u8ff0 LLMs \u5728\u5305\u542b\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u7684\u793a\u4f8b\u4e0a\u6536\u655b\u7f13\u6162\u7684\u73b0\u8c61\u3002\u7531\u4e8e\u8be5\u672f\u8bed\u5e26\u6709\u60c5\u611f\u8272\u5f69&#xff0c;\u6211\u4eec\u6307\u51fa&#xff0c;\u6211\u4eec\u5e76\u4e0d\u5c06\u4efb\u4f55\u60c5\u611f\u5c5e\u6027\u8d4b\u4e88 LLMs\u3002<\/p>\n<h2>2 \u7814\u7a76\u8bbe\u7f6e<\/h2>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u5fae\u8c03\u6570\u636e\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u548c\u4e00\u4e2a\u9884\u8bad\u7ec3 LLM <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u5c06\u901a\u8fc7\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e0a\u5fae\u8c03 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5f97\u5230\u7684\u6a21\u578b\u8bb0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         D<\/p>\n<p>       M_D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4e3a\u4e86\u7814\u7a76 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u65b0\u77e5\u8bc6\u5982\u4f55\u5f71\u54cd <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         D<\/p>\n<p>       M_D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6027\u80fd&#xff0c;\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u53d7\u63a7\u8bbe\u7f6e&#xff0c;\u6784\u9020 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u53d8\u4f53&#xff0c;\u8fd9\u4e9b\u53d8\u4f53\u5305\u542b\u4e0d\u540c\u6bd4\u4f8b\u7684\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u672a\u77e5\u7684\u793a\u4f8b\u3002 \u5728\u6784\u5efa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;\u6211\u4eec\u7684\u76ee\u6807\u662f\u5728\u4fdd\u6301\u5bf9\u5b9e\u9a8c\u8bbe\u7f6e\u7684\u63a7\u5236\u7684\u540c\u65f6&#xff0c;\u4f53\u73b0\u9762\u5411\u591a\u6837\u5316\u77e5\u8bc6\u5bc6\u96c6\u578b\u4efb\u52a1\u7684\u6307\u4ee4\u5fae\u8c03\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u5173\u6ce8\u53ef\u4ee5\u7ed3\u6784\u5316\u4e3a&#xff08;\u4e3b\u8bed&#xff0c;\u5173\u7cfb&#xff0c;\u5bbe\u8bed&#xff09;\u4e09\u5143\u7ec4\u7684\u4e8b\u5b9e\u6027\u77e5\u8bc6&#xff0c;\u5e76\u5c06\u5176\u8f6c\u6362\u4e3a\u95ed\u5377\u95ee\u7b54&#xff08;QA&#xff09;\u683c\u5f0f\u3002\u5728\u6b64\u8bbe\u7f6e\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>        &#061;<\/p>\n<p>        {<\/p>\n<p>        (<\/p>\n<p>         q<\/p>\n<p>         i<\/p>\n<p>        ,<\/p>\n<p>         a<\/p>\n<p>         i<\/p>\n<p>        )<\/p>\n<p>         }<\/p>\n<p>          i<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         N<\/p>\n<p>       D &#061; \\\\{(q_i, a_i)\\\\}_{i&#061;1}^N<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1em;vertical-align: -0.2587em\"><\/span><span class=\"mopen\">{(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">}<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u662f\u5bf9\u5e94\u4e8e\u7279\u5b9a\u4e09\u5143\u7ec4\u7684\u77e5\u8bc6\u5bfb\u6c42\u578b\u95ee\u9898&#xff08;\u4f8b\u5982&#xff0c;\u201c\u5df4\u9ece\u4f4d\u4e8e\u54ea\u91cc&#xff1f;\u201d&#xff09;&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u662f\u771f\u5b9e\u7b54\u6848&#xff08;\u4f8b\u5982&#xff0c;\u201c\u6cd5\u56fd\u201d&#xff09;\u3002\u4e3a\u6b64&#xff0c;\u6211\u4eec\u4f7f\u7528 ENTITYQUESTIONS (Sciavolinoet al., 2021&#xff09;\u4e2d&#xff0c;\u6765\u81ea Wikidata&#xff08;Vrandec\u02c7ic \u0301 \u548c Kr\u00f6tzsch&#xff0c;2014&#xff09;\u7684\u4e00\u7ec4\u591a\u6837\u5316\u5173\u7cfb\u4e2d\u7684\u4e09\u5143\u7ec4\u88ab\u8f6c\u6362\u4e3a\u95ee\u7b54\u5bf9\u3002\u8fd9\u4e9b\u5173\u7cfb\u6db5\u76d6\u5e7f\u6cdb\u7684\u4e8b\u5b9e\u77e5\u8bc6&#xff0c;\u5305\u62ec\u4f20\u8bb0\u4fe1\u606f\u3001\u5730\u7406\u6570\u636e\u3001\u6240\u6709\u6743\u4e0e\u4f5c\u8005\u8eab\u4efd\u7ec6\u8282\u3001\u5386\u53f2\u7b49\u3002\u6211\u4eec\u4f7f\u7528\u539f\u59cb\u7684\u5f00\u53d1\u96c6\u548c\u6d4b\u8bd5\u96c6\u5212\u5206&#xff0c;\u5e76\u5bf9\u8bad\u7ec3\u96c6\u5212\u5206\u8fdb\u884c\u5b50\u91c7\u6837&#xff0c;\u4ee5\u521b\u5efa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u4e0d\u540c\u53d8\u4f53\u3002\u6211\u4eec\u5173\u6ce8 12 \u79cd\u591a\u6837\u5316\u7684\u5173\u7cfb&#xff0c;\u5e76\u4fdd\u7559 7 \u79cd\u989d\u5916\u5173\u7cfb\u7528\u4e8e\u5206\u5e03\u5916\u6d4b\u8bd5\u96c6&#xff0c;\u8be5\u6d4b\u8bd5\u96c6&#xff08;\u4ec5&#xff09;\u5728 \u00a74.5 \u4e2d\u4f7f\u7528\u3002\u4f5c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u4f7f\u7528 PaLM 2-S \u57fa\u7840\u6a21\u578b3&#xff08;Anil et al., 2023&#xff09;\u3002\u6211\u4eec\u4ee5\u7cbe\u786e\u5339\u914d&#xff08;EM&#xff09;\u4f5c\u4e3a\u8bc4\u4f30\u6307\u6807\u30024 \u5b8c\u6574\u6280\u672f\u7ec6\u8282\u89c1 \u00a7A\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054138-6acb2192d71e5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe2&#xff1a;SliCK \u77e5\u8bc6\u7c7b\u522b\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49&#xff0c;\u57fa\u4e8e \u00a73 \u4e2d\u5b9a\u4e49\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5ea6\u91cf&#xff08;a&#xff09;&#xff0c;\u5e76\u9644\u6709\u6211\u4eec\u7814\u7a76\u4e2d\u4f7f\u7528\u7684\u5df2\u6807\u6ce8 ENTITYQUESTIONS \u6570\u636e\u96c6\u4e2d\u7684\u771f\u5b9e\u793a\u4f8b&#xff08;b&#xff09;\u3002<\/p>\n<h2>3 \u91cf\u5316\u5927\u8bed\u8a00\u6a21\u578b\u4e2d\u7684\u77e5\u8bc6<\/h2>\n<p>\u4e3a\u4e86\u8bc4\u4f30 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u65b0\u77e5\u8bc6\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         D<\/p>\n<p>       M_D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6027\u80fd\u7684\u5f71\u54cd&#xff0c;\u6211\u4eec\u5fc5\u987b\u6807\u6ce8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9&#xff0c;\u4ee5\u6807\u660e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u77e5\u9053 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u7b54\u6848\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>\u3002\u2075 \u4e3a\u4e86\u4f30\u8ba1\u8fd9\u4e00\u70b9&#xff0c;\u6211\u4eec\u57fa\u4e8e\u6765\u81ea <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u7684\u6837\u672c\u5b9a\u4e49\u4e00\u4e2a\u8fde\u7eed\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5ea6\u91cf&#xff0c;\u5e76\u7528\u5b83\u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5212\u5206\u4e3a\u56db\u4e2a\u77e5\u8bc6\u7c7b\u522b\u3002\u6211\u4eec\u5c06\u8fd9\u79cd\u65b9\u6cd5\u547d\u540d\u4e3a SliCK&#xff08;\u57fa\u4e8e\u91c7\u6837\u7684\u77e5\u8bc6\u5206\u7c7b&#xff09;\u3002<\/p>\n<p>\u5b9a\u4e49 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u91c7\u7528\u8fd9\u6837\u7684\u89c2\u70b9&#xff1a;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5728\u88ab\u63d0\u793a\u56de\u7b54 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u65f6\u751f\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u90a3\u4e48 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5c31\u77e5\u9053 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u7b54\u6848\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff08;Kadavath et al., 2022; Manakul et al., 2023&#xff09;\u3002\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u662f\u4e00\u4e2a\u57fa\u7840\u6a21\u578b\u5bf9\u4e8e\u5c1a\u672a\u4e13\u95e8\u5fae\u8c03\u4ee5\u9075\u5faa\u6307\u4ee4\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u4f7f\u7528\u5c11\u6837\u672c\u793a\u4f8b\u901a\u8fc7\u4e0a\u4e0b\u6587\u5b66\u4e60\u6765\u63d0\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span>\u3002\u9075\u5faa Rubin \u7b49\u4eba (2022)&#xff0c;\u6211\u4eec\u786e\u4fdd\u5c11\u6837\u672c\u793a\u4f8b\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u5177\u6709\u9ad8\u8bed\u4e49\u76f8\u4f3c\u5ea6\u30026 \u5728\u5b9e\u8df5\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u53ef\u80fd\u9884\u6d4b\u51fa\u4e0d\u540c\u7b54\u6848&#xff0c;\u56e0\u4e3a (1) \u793a\u4f8b\u7684\u9009\u62e9\u4f1a\u5f71\u54cd\u5355\u4e2a\u9884\u6d4b&#xff0c;\u4e14 (2) \u6e29\u5ea6\u91c7\u6837&#xff08;\u5982\u679c\u4f7f\u7528&#xff09;\u4f1a\u5f15\u5165\u968f\u673a\u6027\u3002\u4e3a\u53cd\u6620\u8fd9\u4e00\u70b9&#xff0c;\u6211\u4eec\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        ;<\/p>\n<p>        M<\/p>\n<p>        ,<\/p>\n<p>        T<\/p>\n<p>        )<\/p>\n<p>       P_{\\\\text{Correct}}(q, a; M, T)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5b9a\u4e49\u4e3a&#xff1a;\u5f53\u7528\u968f\u673a\u5c11\u6837\u672c\u793a\u4f8b\u63d0\u793a\u5e76\u4f7f\u7528\u89e3\u7801\u6e29\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u51c6\u786e\u751f\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u6b63\u786e\u7b54\u6848 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u7684\u53ef\u80fd\u6027\u7684\u4f30\u8ba1\u3002 \u51fa\u4e8e\u6211\u4eec\u7814\u7a76\u7684\u76ee\u7684&#xff0c;\u6211\u4eec\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>         ex<\/p>\n<p>        &#061;<\/p>\n<p>        10<\/p>\n<p>       N_{\\\\text{ex}} &#061; 10<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">ex<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u4e2a\u4e0d\u540c\u7684\u968f\u673a 4-shot \u63d0\u793a\u6765\u8fd1\u4f3c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u30027 \u5bf9\u4e8e\u6bcf\u4e2a 4-shot \u63d0\u793a&#xff0c;\u6211\u4eec\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>       T &#061; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u9884\u6d4b\u8d2a\u5fc3\u7b54\u6848&#xff0c;\u5e76\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>        &#061;<\/p>\n<p>        0.5<\/p>\n<p>       T &#061; 0.5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u9884\u6d4b 16 \u4e2a\u91c7\u6837\u7b54\u6848\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        ;<\/p>\n<p>        M<\/p>\n<p>        ,<\/p>\n<p>        T<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>        )<\/p>\n<p>       P_{\\\\text{Correct}}(q, a; M, T &#061; 0)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u901a\u8fc7\u6b63\u786e\u8d2a\u5fc3\u7b54\u6848\u7684\u6bd4\u4f8b\u6765\u4f30\u8ba1&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        ;<\/p>\n<p>        M<\/p>\n<p>        ,<\/p>\n<p>        T<\/p>\n<p>        &gt;<\/p>\n<p>        0<\/p>\n<p>        )<\/p>\n<p>       P_{\\\\text{Correct}}(q, a; M, T &gt; 0)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u901a\u8fc7\u6b63\u786e\u91c7\u6837\u7b54\u6848\u7684\u6bd4\u4f8b\u6765\u4f30\u8ba1\u3002\u5b8c\u6574\u7ec6\u8282\u89c1 \u00a7C\u3002 \u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u63a8\u5bfc\u77e5\u8bc6\u7c7b\u522b\u3002\u6211\u4eec\u5c06\u672a\u77e5\u7c7b\u522b&#xff08;\u56fe 2a \u548c 2b \u4e2d\u7684\u5e95\u884c&#xff09;\u5b9a\u4e49\u4e3a\u8868\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u4ece\u4e0d\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u9884\u6d4b\u6b63\u786e\u7b54\u6848\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u3002\u5728\u6211\u4eec\u7684\u8bb0\u53f7\u4e2d&#xff0c;\u8fd9\u610f\u5473\u7740 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        ;<\/p>\n<p>        M<\/p>\n<p>        ,<\/p>\n<p>        T<\/p>\n<p>        \u2265<\/p>\n<p>        0<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>       P_{\\\\text{Correct}}(q, a; M, T \\\\geq 0) &#061; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002\u6216\u8005&#xff0c;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        ;<\/p>\n<p>        M<\/p>\n<p>        ,<\/p>\n<p>        T<\/p>\n<p>        \u2265<\/p>\n<p>        0<\/p>\n<p>        )<\/p>\n<p>        &gt;<\/p>\n<p>        0<\/p>\n<p>       P_{\\\\text{Correct}}(q, a; M, T \\\\geq 0) &gt; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u6709\u65f6\u4f1a\u9884\u6d4b\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u6b63\u786e\u7b54\u6848&#xff0c;\u6211\u4eec\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u89c6\u4e3a\u5df2\u77e5\u3002\u5728\u8fd9\u79cd\u9009\u62e9\u4e2d&#xff0c;\u6211\u4eec\u5047\u5b9a&#xff0c;\u5982\u679c\u63d0\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u56de\u7b54 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u6709\u65f6\u4f1a\u4ea7\u751f\u6b63\u786e\u56de\u7b54 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u90a3\u4e48 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5fc5\u5b9a\u4e0e\u76f8\u5173\u4e8b\u5b9e\u5b58\u5728\u67d0\u79cd\u5173\u8054\u3002\u8ba4\u8bc6\u5230\u77e5\u8bc6\u5728\u786e\u5b9a\u7a0b\u5ea6\u548c\u8303\u56f4\u4e0a\u53ef\u80fd\u6709\u6240\u4e0d\u540c&#xff0c;\u6211\u4eec\u5c06\u5df2\u77e5\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5212\u5206\u4e3a\u4e09\u4e2a\u4e0d\u540c\u7684\u7c7b\u522b&#xff08;\u8868 2a \u548c 2b \u4e2d\u7684\u524d\u4e09\u884c&#xff09;\u3002\u53d7\u4ee5\u4e0b\u539f\u5219\u9a71\u52a8&#xff1a;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u5df2\u77e5\u7684&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5e94\u4e00\u81f4\u5730\u9884\u6d4b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u7740\u91cd\u5173\u6ce8\u8d2a\u5fc3\u89e3\u7801\u7ed3\u679c&#xff0c;\u5176\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        ;<\/p>\n<p>        M<\/p>\n<p>        ,<\/p>\n<p>        T<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>        )<\/p>\n<p>       P_{\\\\text{Correct}}(q, a; M, T &#061; 0)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u3002\u9ad8\u5ea6\u5df2\u77e5\u8868\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u603b\u662f\u901a\u8fc7\u8d2a\u5fc3\u89e3\u7801\u9884\u6d4b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u3002\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u6709\u65f6&#xff08;\u4f46\u5e76\u975e\u603b\u662f&#xff09;\u901a\u8fc7\u8d2a\u5fc3\u89e3\u7801\u9884\u6d4b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u89c6\u4e3a\u53ef\u80fd\u5df2\u77e5\u3002\u6700\u540e&#xff0c;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u4ece\u672a\u901a\u8fc7\u8d2a\u5fc3\u89e3\u7801\u9884\u6d4b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5f52\u7c7b\u4e3a\u5f31\u5df2\u77e5\u3002\u6211\u4eec\u5e94\u7528 SliCK \u4e3a\u6211\u4eec\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u6807\u6ce8\u5176\u76f8\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u7684\u77e5\u8bc6\u7c7b\u522b\u30028 \u6211\u4eec\u5728 \u00a76 \u4e2d\u5206\u6790\u8fd9\u4e9b\u7c7b\u522b\u7684\u8d28\u91cf\u3002<\/p>\n<p>3PaLM-2 \u6709\u4e94\u79cd\u89c4\u6a21&#xff1a;XXS\u3001XS\u3001S\u3001M\u3001L&#xff0c;\u5176\u4e2d S \u7248\u672c\u4ee3\u8868\u8be5\u8303\u56f4\u4e2d\u7684\u4e2d\u7b49\u89c4\u6a21\u3002 4\u6211\u4eec\u9a8c\u8bc1\u4e86&#xff0c;\u5728\u6211\u4eec\u7684\u8bbe\u7f6e\u4e2d&#xff0c;EM \u4e0e\u8bcd\u7ea7 F1 \u5f3a\u76f8\u5173&#xff08;Rajpurkar et al., 2016&#xff09;&#xff0c;\u5e76\u4e14\u6211\u4eec\u9009\u62e9 EM&#xff0c;\u56e0\u4e3a\u5b83\u5bf9\u4e8e\u6211\u4eec\u5206\u6790\u7684\u76ee\u7684\u800c\u8a00\u66f4\u76f4\u89c2\u3002 5\u6211\u4eec\u8fd8\u8003\u8651\u8fc7\u4f7f\u7528\u865a\u5047\u4e8b\u5b9e\u6765\u5f15\u5165\u65b0\u77e5\u8bc6&#xff0c;\u4f46\u6211\u4eec\u62c5\u5fc3\u8fd9\u4f1a\u7ed9\u6211\u4eec\u7684\u7814\u7a76\u5f15\u5165\u6df7\u6742\u56e0\u7d20&#xff0c;\u56e0\u4e3a\u865a\u5047\u4e8b\u5b9e\u7684\u8868\u73b0\u53ef\u80fd\u4e0e\u771f\u5b9e\u4e8b\u5b9e\u4e0d\u540c\u3002\u6211\u4eec\u5728 \u00a7F \u4e2d\u8be6\u7ec6\u8ba8\u8bba\u8fd9\u4e00\u70b9\u3002 6\u5728\u672c\u7814\u7a76\u4e2d&#xff0c;\u6211\u4eec\u901a\u8fc7\u4f7f\u7528\u6765\u81ea\u540c\u4e00\u5173\u7cfb\u7684\u793a\u4f8b\u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\u3002\u4f8b\u5982&#xff0c;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>        &#061;<\/p>\n<p>       q &#061;<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><\/span><\/span><\/span>\u201c\u5df4\u9ece\u4f4d\u4e8e\u4f55\u5904&#xff1f;\u201d&#xff0c;\u793a\u4f8b\u5c06\u9075\u5faa\u201c{X}\u4f4d\u4e8e\u4f55\u5904&#xff1f;\u201d\u7684\u6a21\u5f0f\u3002 7\u6211\u4eec\u91c7\u75284-shot&#xff0c;\u4ec5\u4ec5\u662f\u56e0\u4e3a\u6211\u4eec\u53d1\u73b0\u8fd9\u5df2\u8db3\u4ee5\u8ba9M\u4ee5\u6b63\u786e\u7684\u683c\u5f0f\u8f93\u51fa\u7b54\u6848\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054140-6acb219490a15.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u56fe 3&#xff1a;\u6d4b\u8bd5\u6027\u80fd\u968f\u5fae\u8c03\u6570\u636e\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u672a\u77e5\u6837\u672c\u767e\u5206\u6bd4\u7684\u53d8\u5316\u3002\u5728 (a) \u4e2d&#xff0c;\u6bcf\u6761\u7ebf\u5bf9\u5e94\u4e0d\u540c\u7684&#xff08;\u56fa\u5b9a&#xff09;\u8bad\u7ec3\u8f6e\u6570&#xff0c;\u4f46 EARLY_STOP \u9664\u5916&#xff0c;\u5176\u5bf9\u5e94\u4f7f\u7528\u5f00\u53d1\u96c6\u8fdb\u884c\u65e9\u505c&#xff08;\u89c1 \u00a74&#xff09;\u3002\u5728 (b) \u4e2d&#xff0c;\u6211\u4eec\u5c55\u793a\u4e86\u6765\u81ea \u00a74.2 \u7684\u6d88\u878d\u5b9e\u9a8c\u3002\u5b9e\u7ebf\u5bf9\u5e94\u4e8e\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e0a\u5fae\u8c03&#xff0c;\u5e76\u4e0e (a) \u76f8\u540c\u3002\u865a\u7ebf\u5bf9\u5e94\u4e8e\u5728\u6d88\u878d\u53d8\u4f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0a\u5fae\u8c03&#xff0c;\u5176\u4e2d\u672a\u77e5\u6837\u672c\u88ab\u8fc7\u6ee4\u6389\u3002\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0<\/p>\n<p>        %<\/p>\n<p>       0\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0%<\/span><\/span><\/span><\/span><\/span> \u672a\u77e5\u6837\u672c&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>        &#061;<\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D &#061; D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1b;\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        100<\/p>\n<p>        %<\/p>\n<p>       100\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">100%<\/span><\/span><\/span><\/span><\/span> \u672a\u77e5\u6837\u672c&#xff0c;\u4e0d\u5b58\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h2>4 \u672a\u77e5\u6837\u672c\u6709\u591a\u6709\u5bb3&#xff1f;<\/h2>\n<p>\u5728\u672c\u8282\u4e2d&#xff0c;\u6211\u4eec\u7814\u7a76\u5fae\u8c03\u6570\u636e\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u65b0\u77e5\u8bc6\u5bf9\u6027\u80fd\u7684\u5f71\u54cd\u3002\u4e3a\u4e86\u5206\u79bb\u8fd9\u4e00\u6548\u5e94&#xff0c;\u6211\u4eec\u6539\u53d8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u672a\u77e5\u6837\u672c\u7684\u6bd4\u4f8b&#xff0c;\u540c\u65f6\u63a7\u5236\u5176\u4ed6\u56e0\u7d20\u3002\u5177\u4f53\u800c\u8a00&#xff0c;\u6211\u4eec\u56fa\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        D<\/p>\n<p>        \u2223<\/p>\n<p>       |D|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u521b\u5efa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u53d8\u4f53&#xff0c;\u5176\u4e2d\u5305\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        X<\/p>\n<p>        %<\/p>\n<p>       X\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\">%<\/span><\/span><\/span><\/span><\/span> \u7684\u672a\u77e5\u6837\u672c\u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        100<\/p>\n<p>        \u2212<\/p>\n<p>        X<\/p>\n<p>        )<\/p>\n<p>        %<\/p>\n<p>       (100 &#8211; X)\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">100<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">%<\/span><\/span><\/span><\/span><\/span> \u7684\u5df2\u77e5\u6837\u672c&#xff08;\u5b8c\u6574\u7ec6\u8282\u89c1 \u00a7E&#xff09;\u3002\u6211\u4eec\u5c06\u5df2\u77e5\u7c7b\u522b\u5408\u5e76\u5904\u7406&#xff08;\u89c1\u56fe 2a&#xff09;&#xff0c;\u5e76\u5728 \u00a75 \u4e2d\u63d0\u4f9b\u9010\u7c7b\u522b\u5206\u6790\u3002\u6211\u4eec\u5c06\u57fa\u4e8e\u5f00\u53d1\u96c6\u7684\u65e9\u505c\u8bb0\u4e3a EARLY_STOP&#xff08;\u53d1\u751f\u5728 5-10 \u4e2a epoch \u4e4b\u540e&#xff09;\u4ee5\u53ca 50\u5c06\u5fae\u8c03\u8f6e\u6570\u8bb0\u4e3a CONVERGENCE&#xff0c;\u56e0\u4e3a\u6b64\u65f6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u603b\u662f\u5b8c\u5168\u62df\u5408 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff08;\u5373 100% \u8bad\u7ec3\u51c6\u786e\u7387&#xff09;\u3002\u6211\u4eec\u5c06\u6d4b\u8bd5\u6027\u80fd\u4f5c\u4e3a\u5e7b\u89c9\u7684\u4ee3\u7406\u6307\u6807\u8fdb\u884c\u6d4b\u91cf&#xff0c;\u56e0\u4e3a\u6211\u4eec\u5904\u4e8e\u5177\u6709\u4e0d\u76f8\u4ea4\u8bad\u7ec3\/\u6d4b\u8bd5\u5212\u5206\u7684\u95ed\u5377\u95ee\u7b54&#xff08;QA&#xff09;\u8bbe\u7f6e\u4e2d&#xff0c;\u6a21\u578b\u5fc5\u987b\u4f7f\u7528\u5176\u9884\u5148\u5b58\u5728\u7684\u77e5\u8bc6\u6765\u56de\u7b54\u6d4b\u8bd5\u95ee\u9898&#xff08;\u8fdb\u4e00\u6b65\u8ba8\u8bba\u89c1 \u00a7B&#xff09;\u3002<\/p>\n<h3>4.1 \u66f4\u9ad8\u7684 Unknown \u6bd4\u4f8b\u4e0e\u6027\u80fd\u9000\u5316\u6210\u6b63\u6bd4<\/h3>\n<p>\u56fe 3a \u5c55\u793a\u4e86\u5728\u4e0d\u540c\u5fae\u8c03\u65f6\u957f\u4e0b&#xff0c;\u6027\u80fd\u4f5c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d Unknown \u793a\u4f8b\u767e\u5206\u6bd4\u7684\u51fd\u6570\u3002\u66f4\u9ad8\u7684 Unknown \u767e\u5206\u6bd4\u4f1a\u5bfc\u81f4\u6027\u80fd\u9000\u5316&#xff0c;\u65e0\u8bba\u5fae\u8c03\u65f6\u957f\u5982\u4f55&#xff0c;\u8fd9\u8868\u660e Unknown \u793a\u4f8b\u6bd4 Known \u793a\u4f8b\u7684\u7528\u5904\u66f4\u5c0f\u3002\u6027\u80fd\u4e5f\u53d7\u5230\u5fae\u8c03\u65f6\u957f\u7684\u5f3a\u70c8\u5f71\u54cd&#xff0c;\u5176\u4e2d EARLY_STOP \u901a\u5e38\u4ea7\u751f\u6700\u4f73\u6027\u80fd\u3002\u8bad\u7ec3\u66f4\u591a\u8f6e\u6b21\u901a\u5e38\u4f1a\u964d\u4f4e\u6027\u80fd&#xff08;\u5728 CONVERGENCE \u65f6\u89c2\u5bdf\u5230\u6700\u4f4e\u6027\u80fd&#xff09;&#xff0c;\u8fd9\u53ef\u5f52\u56e0\u4e8e\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u8fc7\u62df\u5408\u3002\u6709\u8da3\u7684\u662f&#xff0c;\u8fd9\u79cd\u6548\u5e94\u968f\u7740 Unknown \u767e\u5206\u6bd4\u7684\u589e\u5927\u800c\u589e\u5f3a&#xff08;EARLY_STOP \u7684\u7ebf\u95f4\u95f4\u8ddd\u6cbf\u6b63 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u8f74\u5448\u73b0\u5355\u8c03\u589e\u52a0&#xff09;&#xff0c;\u8868\u660e\u66f4\u9ad8\u7684 Unknown \u767e\u5206\u6bd4\u4f1a\u589e\u52a0\u8fc7\u62df\u5408\u98ce\u9669\u3002<\/p>\n<h3>4.2 Unknown \u793a\u4f8b&#xff1a;\u6709\u5bb3\u8fd8\u662f\u4e2d\u6027&#xff1f;<\/h3>\n<p>\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        D<\/p>\n<p>        \u2223<\/p>\n<p>       |D|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u56fa\u5b9a&#xff0c;\u66f4\u9ad8\u7684 Unknown \u767e\u5206\u6bd4\u5bfc\u81f4\u7684\u6027\u80fd\u4e0b\u964d\u53ef\u80fd\u4ec5\u4ec5\u6e90\u4e8e Known \u5fae\u8c03\u793a\u4f8b\u6570\u91cf\u66f4\u5c11\u3002\u56e0\u6b64&#xff0c;\u4ecd\u4e0d\u6e05\u695a Unknown \u793a\u4f8b\u662f\u6709\u5bb3\u8fd8\u662f\u4e2d\u6027\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898&#xff0c;\u6211\u4eec\u6d4b\u91cf\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u8fc7\u6ee4\u6389\u6240\u6709\u672a\u77e5\u6837\u672c\u7684\u5f71\u54cd\u3002\u5bf9\u4e8e\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u53d8\u4f53&#xff0c;\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u5bf9\u5e94\u7684\u6d88\u878d\u53d8\u4f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4ec5\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u5df2\u77e5\u6837\u672c\u7ec4\u6210\u3002\u4f8b\u5982&#xff0c;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        25<\/p>\n<p>        %<\/p>\n<p>       25\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">25%<\/span><\/span><\/span><\/span><\/span> \u7684\u672a\u77e5\u6837\u672c&#xff0c;\u6211\u4eec\u5c06\u5176\u8fc7\u6ee4\u6389&#xff0c;\u5269\u4e0b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        75<\/p>\n<p>        %<\/p>\n<p>       75\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">75%<\/span><\/span><\/span><\/span><\/span> \u7684\u5df2\u77e5\u6837\u672c&#xff0c;\u5e76\u5f97\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>        \u2223<\/p>\n<p>        &#061;<\/p>\n<p>        0.75<\/p>\n<p>        \u00d7<\/p>\n<p>        \u2223<\/p>\n<p>        D<\/p>\n<p>        \u2223<\/p>\n<p>       |D_{\\\\text{Known}}| &#061; 0.75 \\\\times |D|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">0.75<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u3002\u56fe 3b \u5c55\u793a\u4e86\u7ed3\u679c\u3002\u4e5f\u8bb8\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f&#xff0c;\u5bf9\u4e8e EARLY_STOP&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u7ed3\u679c\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u51e0\u4e4e\u76f8\u540c&#xff0c;\u8fd9\u8868\u660e\u672a\u77e5\u6837\u672c\u5bf9\u6027\u80fd\u5177\u6709\u4e2d\u6027\u5f71\u54cd&#xff08;\u56e0\u4e3a\u79fb\u9664\u5b83\u4eec\u7684\u5f71\u54cd\u6781\u5c0f&#xff09;\u3002\u76f8\u53cd&#xff0c;CONVERGENCE \u7ed3\u679c\u8868\u660e&#xff0c;\u968f\u7740\u8bad\u7ec3\u65f6\u95f4\u5ef6\u957f&#xff0c;\u672a\u77e5\u6837\u672c\u5b9e\u9645\u4e0a\u975e\u5e38\u6709\u5bb3\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u8868\u73b0\u4e0d\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u4e14\u4e8c\u8005\u4e4b\u95f4\u7684\u5dee\u8ddd\u4e0e\u672a\u77e5\u6837\u672c\u6bd4\u4f8b\u6210\u6b63\u6bd4\u3002\u6709\u8da3\u7684\u662f&#xff0c;\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Known<\/p>\n<p>       D_{\\\\text{Known}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Known<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;EARLY_STOP \u4e0e CONVERGENCE \u4e4b\u95f4\u7684\u5dee\u8ddd\u975e\u5e38\u5c0f&#xff08;\u865a\u7ebf&#xff09;&#xff0c;\u800c\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fd9\u4e00\u5dee\u8ddd\u975e\u5e38\u5927&#xff08;\u5b9e\u7ebf&#xff09;\u3002\u8fd9\u8868\u660e&#xff0c;\u6b63\u662f\u672a\u77e5\u6837\u672c\u7684\u5b58\u5728\u4f7f\u5f97\u672a\u77e5\u6837\u672c\u6bd4\u4f8b\u66f4\u9ad8\u7684\u53d8\u4f53\u66f4\u5bb9\u6613\u8fc7\u62df\u5408\u3002<\/p>\n<h3>4.3 \u672a\u77e5\u6837\u672c\u7684\u62df\u5408\u901f\u5ea6\u6162\u4e8e\u5df2\u77e5\u6837\u672c<\/h3>\n<p>\u6211\u4eec\u8868\u660e&#xff0c;\u672a\u77e5\u6837\u672c\u662f\u6709\u5bb3\u7684&#xff0c;\u4f46\u5b83\u4eec\u7684\u8d1f\u9762\u5f71\u54cd\u4e3b\u8981\u5728\u8bad\u7ec3\u540e\u671f\u663e\u73b0&#xff0c;\u56e0\u6b64\u53ef\u4ee5\u901a\u8fc7\u65e9\u505c\u4ece\u7ecf\u9a8c\u4e0a\u52a0\u4ee5\u907f\u514d\u3002\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e9b\u8d8b\u52bf&#xff0c;\u6211\u4eec\u901a\u8fc7\u8003\u5bdf\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u54ea\u4e9b\u5fae\u8c03\u6837\u672c\u5728\u4e0d\u540c\u5fae\u8c03\u9636\u6bb5\u88ab <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u62df\u5408&#xff0c;\u6765\u5206\u6790\u8bad\u7ec3\u52a8\u6001\u3002\u56fe 1 \u5c55\u793a\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u5df2\u77e5\u5b50\u96c6\u548c\u672a\u77e5\u5b50\u96c6\u7684\u8bad\u7ec3\u51c6\u786e\u7387\u968f\u5fae\u8c03\u65f6\u957f\u7684\u53d8\u5316\u3002\u5f00\u53d1\u51c6\u786e\u7387\u5728\u5e95\u90e8\u7684\u653e\u5927\u56fe\u4e2d\u5c55\u793a&#xff0c;\u56e0\u4e3a\u5b83\u5904\u4e8e\u8f83\u7a84\u7684\u8303\u56f4\u5185\u3002\u6211\u4eec\u5728 \u00a7G \u4e2d\u6309\u5df2\u77e5\u7c7b\u522b\u7ed9\u51fa\u4e86\u8bad\u7ec3\u51c6\u786e\u7387\u7684\u7ec6\u5206\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u62df\u5408\u672a\u77e5\u5fae\u8c03\u6837\u672c\u5927\u91cf\u521d\u59cb\u65f6\u6bd4\u5df2\u77e5\u6837\u672c\u6162\u3002\u5728 EARLY_STOP&#xff08;\u5782\u76f4\u865a\u7ebf&#xff09;\u5904&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5728\u5f00\u53d1\u96c6\u4e0a\u8fbe\u5230\u5cf0\u503c\u6027\u80fd&#xff0c;\u540c\u65f6\u62df\u5408\u4e86\u5927\u591a\u6570\u5df2\u77e5\u6837\u672c&#xff0c;\u4f46\u4ec5\u62df\u5408\u4e86\u4e00\u5c0f\u90e8\u5206\u672a\u77e5\u6837\u672c\u3002\u5728\u56fe 4 \u4e2d&#xff0c;\u6211\u4eec\u8868\u660e\u8fd9\u4e00\u884c\u4e3a\u5728\u6211\u4eec\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u53d8\u4f53\u4e2d\u90fd\u662f\u4e00\u81f4\u7684\u3002\u8fd9\u53ef\u4ee5\u89e3\u91ca\u4e3a\u4ec0\u4e48\u5728 EARLY_STOP \u5904\u672a\u77e5\u6837\u672c\u5bf9\u6027\u80fd\u4ea7\u751f\u4e86\u4e2d\u6027\u5f71\u54cd&#xff08;\u00a74.2&#xff09;&#xff0c;\u56e0\u4e3a\u6b64\u65f6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u4ecd\u672a\u62df\u5408\u5176\u4e2d\u5927\u591a\u6570\u6837\u672c\u3002\u6700\u540e&#xff0c;\u7531\u4e8e\u672a\u77e5\u6837\u672c\u662f\u53ef\u80fd\u5f15\u5165\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u7684\u6837\u672c&#xff0c;\u5176\u663e\u8457\u7f13\u6162\u7684\u62df\u5408\u901f\u7387\u8868\u660e&#xff0c;LLM \u96be\u4ee5\u901a\u8fc7\u5fae\u8c03\u83b7\u5f97\u65b0\u7684\u4e8b\u5b9e\u77e5\u8bc6&#xff0c;\u76f8\u53cd&#xff0c;\u5b83\u4eec\u5b66\u4f1a\u5229\u7528\u5df2\u77e5\u6837\u672c\u6765\u66b4\u9732\u5176\u5df2\u6709\u77e5\u8bc6\u3002<\/p>\n<h3>4.4 \u672a\u77e5\u4e0e\u5df2\u77e5\u5bf9\u51c6\u786e\u7387\u7684\u5f71\u54cd&#xff1a;\u7ebf\u6027\u6a21\u578b\u89c6\u89d2<\/h3>\n<p>\u56fe 1 \u8868\u660e&#xff0c;\u5728\u5f00\u53d1\u96c6\u6027\u80fd\u4e8e EARLY_STOP&#xff08;\u5782\u76f4\u865a\u7ebf&#xff09;\u5904\u8fbe\u5230\u5cf0\u503c\u540e&#xff0c;\u968f\u7740 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u9010\u6e10\u62df\u5408\u66f4\u591a\u672a\u77e5\u6837\u672c&#xff0c;\u6027\u80fd\u4f1a\u6076\u5316\u3002\u672c\u8282\u65e8\u5728\u901a\u8fc7\u8bc4\u4f30\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u4f9d\u8d56\u5173\u7cfb\u80fd\u5426\u5c06\u62df\u5408\u5df2\u77e5\u548c\u672a\u77e5\u8bad\u7ec3\u6837\u672c\u7684\u5f71\u54cd\u4e0e\u6d4b\u8bd5\u51c6\u786e\u7387\u8054\u7cfb\u8d77\u6765&#xff0c;\u4ece\u800c\u66f4\u51c6\u786e\u5730\u523b\u753b\u8fd9\u4e00\u5173\u7cfb\u3002\u4e3a\u6b64&#xff0c;\u6211\u4eec\u4f7f\u7528\u4ee5\u4e0b\u7ebf\u6027\u56de\u5f52\u6a21\u578b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             A<\/p>\n<p>             c<\/p>\n<p>             c<\/p>\n<p>             u<\/p>\n<p>             r<\/p>\n<p>             a<\/p>\n<p>             c<\/p>\n<p>             y<\/p>\n<p>            &#061;<\/p>\n<p>             \u03b2<\/p>\n<p>             0<\/p>\n<p>            &#043;<\/p>\n<p>             \u03b2<\/p>\n<p>              k<\/p>\n<p>              n<\/p>\n<p>            \u22c5<\/p>\n<p>              N<\/p>\n<p>               k<\/p>\n<p>               n<\/p>\n<p>              \u2223<\/p>\n<p>              D<\/p>\n<p>              \u2223<\/p>\n<p>            &#043;<\/p>\n<p>             \u03b2<\/p>\n<p>              u<\/p>\n<p>              n<\/p>\n<p>              k<\/p>\n<p>            \u22c5<\/p>\n<p>              N<\/p>\n<p>               u<\/p>\n<p>               n<\/p>\n<p>               k<\/p>\n<p>              \u2223<\/p>\n<p>              D<\/p>\n<p>              \u2223<\/p>\n<p>           (1)<\/p>\n<p>         \\\\mathrm{Accuracy} &#061; \\\\beta_0 &#043; \\\\beta_{kn} \\\\cdot \\\\frac{N_{kn}}{|D|} &#043; \\\\beta_{unk} \\\\cdot \\\\frac{N_{unk}}{|D|} \\\\tag{1} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\" style=\"margin-right: 0.0139em\">Accuracy<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2963em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">nk<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2963em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">nk<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><span class=\"tag\"><span class=\"strut\" style=\"height: 2.2963em;vertical-align: -0.936em\"><\/span><span class=\"mord text\"><span class=\"mord\">(<\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><span class=\"mord\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>          k<\/p>\n<p>          n<\/p>\n<p>       N_{kn}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>          u<\/p>\n<p>          n<\/p>\n<p>          k<\/p>\n<p>       N_{unk}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">nk<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u62df\u5408\u7684\u5df2\u77e5\u548c\u672a\u77e5\u6837\u672c\u6570\u91cf\u3002<\/p>\n<p>\u6211\u4eec\u901a\u8fc7\u4ece\u5728\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u53d8\u4f53\u4e0a\u5fae\u8c03\u7684\u6a21\u578b\u4e2d\u6536\u96c6\u6bcf\u4e2a epoch \u540e\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>         A<\/p>\n<p>         c<\/p>\n<p>         c<\/p>\n<p>         u<\/p>\n<p>         r<\/p>\n<p>         a<\/p>\n<p>         c<\/p>\n<p>         y<\/p>\n<p>        ,<\/p>\n<p>         N<\/p>\n<p>          k<\/p>\n<p>          n<\/p>\n<p>        ,<\/p>\n<p>         N<\/p>\n<p>          u<\/p>\n<p>          n<\/p>\n<p>          k<\/p>\n<p>        )<\/p>\n<p>       (\\\\mathrm{Accuracy}, N_{kn}, N_{unk})<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\" style=\"margin-right: 0.0139em\">Accuracy<\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">nk<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u503c\u6765\u4f30\u8ba1\u7cfb\u6570\u2079\u3002\u8868 1 \u7ed9\u51fa\u4e86\u7ed3\u679c&#xff08;\u7b2c\u4e00\u884c&#xff09;\u3002\u9ad8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         R<\/p>\n<p>         2<\/p>\n<p>       R^2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u660e\u6d4b\u8bd5\u51c6\u786e\u7387\u4e0e\u6240\u62df\u5408\u8bad\u7ec3\u6837\u672c\u7684\u7c7b\u578b\u4e4b\u95f4\u5b58\u5728\u5f3a\u7ebf\u6027\u5173\u7cfb\u3002\u6211\u4eec\u7684\u6a21\u578b\u610f\u5473\u7740&#xff0c;\u62df\u5408\u672a\u77e5\u6837\u672c\u4f1a\u635f\u5bb3\u6027\u80fd&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03b2<\/p>\n<p>          u<\/p>\n<p>          n<\/p>\n<p>          k<\/p>\n<p>        &lt;<\/p>\n<p>        0<\/p>\n<p>       \\\\beta_{unk} &lt; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">nk<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u800c\u62df\u5408\u5df2\u77e5\u6837\u672c\u4f1a\u63d0\u5347\u6027\u80fd&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03b2<\/p>\n<p>          k<\/p>\n<p>          n<\/p>\n<p>        &gt;<\/p>\n<p>        0<\/p>\n<p>       \\\\beta_{kn} &gt; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u6765\u81ea\u672a\u77e5\u6837\u672c\u7684\u4f30\u8ba1\u8d1f\u9762\u5f71\u54cd\u5927\u81f4\u5339\u914d\u6765\u81ea\u5df2\u77e5\u6837\u672c\u7684\u6b63\u9762\u5f71\u54cd&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>         \u03b2<\/p>\n<p>          u<\/p>\n<p>          k<\/p>\n<p>          n<\/p>\n<p>        \u2223<\/p>\n<p>        \u2248<\/p>\n<p>        \u2223<\/p>\n<p>         \u03b2<\/p>\n<p>          k<\/p>\n<p>          n<\/p>\n<p>        \u2223<\/p>\n<p>       |\\\\beta_{ukn}| \\\\approx |\\\\beta_{kn}|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/p>\n<p>8 \u5728 ENTITYQUESTIONS \u4e2d&#xff0c;\u6211\u4eec\u6709 24% \u9ad8\u5ea6\u5df2\u77e5\u300123% \u53ef\u80fd\u5df2\u77e5\u300117% \u5f31\u5df2\u77e5&#xff0c;\u4ee5\u53ca 36% \u672a\u77e5\u3002\u5404\u5173\u7cfb\u7684\u5b8c\u6574\u7edf\u8ba1\u89c1 \u00a7D\u3002 \u2079\u5b8c\u6574\u7ec6\u8282\u89c1 \u00a7H\u3002\u6211\u4eec\u6307\u51fa&#xff0c;\u8be5\u7ebf\u6027\u6a21\u578b\u4ec5\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>          k<\/p>\n<p>          n<\/p>\n<p>        \u2264<\/p>\n<p>        \u2223<\/p>\n<p>        D<\/p>\n<p>        \u2223<\/p>\n<p>       N_{kn} \\\\leq |D|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>          u<\/p>\n<p>          n<\/p>\n<p>          k<\/p>\n<p>        \u2264<\/p>\n<p>        \u2223<\/p>\n<p>        D<\/p>\n<p>        \u2223<\/p>\n<p>       N_{unk} \\\\leq |D|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">nk<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u7684\u6709\u754c\u533a\u57df\u5185\u6709\u6548\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054142-6acb2196357cf.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u56fe 4&#xff1a;EARLY_STOP \u4e4b\u540e\u5fae\u8c03\u6570\u636e\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u793a\u4f8b\u7684\u72b6\u6001\u3002\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u6bcf\u4e2a\u53d8\u4f53&#xff08;\u7eb5\u8f74&#xff09;&#xff0c;\u6211\u4eec\u5c55\u793a\u4e86\u6a21\u578b\u62df\u5408\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u793a\u4f8b\u7684\u54ea\u4e00\u90e8\u5206&#xff08;\u5373\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u9884\u6d4b\u6b63\u786e\u7b54\u6848&#xff09;\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054144-6acb2198b331f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u8868 2&#xff1a;\u6765\u81ea\u00a75\u7684\u5355\u7c7b\u522b\u53d8\u4f53\u5728\u6d4b\u8bd5\u96c6\u5404\u6309\u7c7b\u522b\u5b50\u96c6\u4e0a\u7684\u51c6\u786e\u7387\u3002Full \u662f\u539f\u59cb\u6d4b\u8bd5\u96c6&#xff08;\u6240\u6709\u7c7b\u522b\u5408\u5728\u4e00\u8d77&#xff09;\u3002Hkn&#061;HighlyKnown&#xff08;\u9ad8\u5ea6\u5df2\u77e5&#xff09;&#xff0c;Mkn&#061;MaybeKnown&#xff08;\u53ef\u80fd\u5df2\u77e5&#xff09;&#xff0c;Wkn&#061;WeaklyKnown&#xff08;\u5f31\u5df2\u77e5&#xff09;&#xff0c;Unk&#061;Unknown&#xff08;\u672a\u77e5&#xff09;\u3002\u5728\u6bcf\u4e00\u5217\u4e2d&#xff0c;\u6700\u4f73\u7ed3\u679c\u4ee5\u7c97\u4f53\u663e\u793a&#xff1b;\u4e0e\u6700\u4f73\u7ed3\u679c\u5dee\u5f02\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        p<\/p>\n<p>        &lt;<\/p>\n<p>        0.05<\/p>\n<p>       p &lt; 0.05<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.05<\/span><\/span><\/span><\/span><\/span> \u4e0b\u4e0d\u5177\u7edf\u8ba1\u663e\u8457\u6027\u7684\u7ed3\u679c\u4e5f\u540c\u6837\u4ee5\u7c97\u4f53\u663e\u793a&#xff08;\u663e\u8457\u6027\u68c0\u9a8c\u7ec6\u8282\u89c1\u00a7J&#xff09;\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054146-6acb219a4927f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>4.5 \u6cdb\u5316\u5230\u65b0\u5173\u7cfb<\/h3>\n<p>\u5728\u4e0a\u8ff0\u8bbe\u7f6e\u4e2d&#xff0c;\u6d4b\u8bd5\u96c6\u4e2d\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5bf9\u5e94\u4e8e\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u51fa\u73b0\u7684\u76f8\u540c 12 \u79cd\u5173\u7cfb\u96c6\u5408\u7684\u4e09\u5143\u7ec4\u3002\u6211\u4eec\u73b0\u5728\u7814\u7a76&#xff1a;\u6211\u4eec\u89c2\u5bdf\u5230\u7684\u52a8\u6001\u662f\u5426\u5bf9\u6a21\u578b\u77e5\u8bc6\u5177\u6709\u66f4\u5e7f\u6cdb\u7684\u5f71\u54cd&#xff0c;\u5e76\u53ef\u8fc1\u79fb\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u672a\u8868\u793a\u7684\u5173\u7cfb\u3002\u4e3a\u68c0\u9a8c\u8fd9\u4e00\u70b9&#xff0c;\u6211\u4eec\u4fdd\u7559\u4e00\u90e8\u5206\u5173\u7cfb\u7528\u4e8e\u5206\u5e03\u5916&#xff08;OOD&#xff09;\u6d4b\u8bd5\u96c6&#xff0c;\u5e76\u5c06\u5b83\u4eec\u4ece\u8bad\u7ec3\u96c6\u548c\u5f00\u53d1\u96c6\u5212\u5206\u4e2d\u6392\u9664\u3002\u8be6\u89c1 \u00a7A&#xff1b;\u5206\u5e03\u5185\u4e0e OOD \u5173\u7cfb\u7684\u5bf9\u6bd4\u89c1\u88685\u548c\u88686\u3002<\/p>\n<p>\u6211\u4eec\u5728 OOD \u6d4b\u8bd5\u96c6\u4e0a\u7684\u7ed3\u679c\u63ed\u793a\u4e86\u7c7b\u4f3c\u7684\u5173\u952e\u53d1\u73b0&#xff1a;(1) \u66f4\u9ad8\u7684 Unknown \u6bd4\u4f8b\u4f1a\u5bfc\u81f4\u66f4\u4f4e\u7684 OOD \u6d4b\u8bd5\u6027\u80fd&#xff1b;(2) Unknown \u793a\u4f8b\u5bf9 OOD \u6027\u80fd\u6709\u5bb3&#xff0c;\u4f46\u4e3b\u8981\u662f\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u62df\u5408\u5b83\u4eec\u65f6\u3002OOD \u6d4b\u8bd5\u51c6\u786e\u7387\u7684\u7ebf\u6027\u6a21\u578b&#xff08;\u65b9\u7a0b (1)&#xff09;\u663e\u793a\u51fa\u7c7b\u4f3c\u8d8b\u52bf&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03b2<\/p>\n<p>         unk<\/p>\n<p>        &lt;<\/p>\n<p>        0<\/p>\n<p>       \\\\beta_{\\\\text{unk}} &lt; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">unk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03b2<\/p>\n<p>         kn<\/p>\n<p>        &gt;<\/p>\n<p>        0<\/p>\n<p>       \\\\beta_{\\\\text{kn}} &gt; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">kn<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>         \u03b2<\/p>\n<p>         ukn<\/p>\n<p>        \u2223<\/p>\n<p>        \u2248<\/p>\n<p>        \u2223<\/p>\n<p>         \u03b2<\/p>\n<p>         kn<\/p>\n<p>        \u2223<\/p>\n<p>       |\\\\beta_{\\\\text{ukn}}| \\\\approx |\\\\beta_{\\\\text{kn}}|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">ukn<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">kn<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u4ee5\u53ca <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         R<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        0.95<\/p>\n<p>       R^2 &#061; 0.95<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.95<\/span><\/span><\/span><\/span><\/span>&#xff08;\u89c1\u88681&#xff09;\u3002\u66f4\u591a\u7ec6\u8282\u89c1 \u00a7I\u3002<\/p>\n<p>\u603b\u4f53\u800c\u8a00&#xff0c;\u6211\u4eec\u7684\u53d1\u73b0\u53ef\u8de8\u5173\u7cfb\u8fc1\u79fb\u3002\u8fd9\u672c\u8d28\u4e0a\u8868\u660e&#xff0c;\u5728\u8bf8\u5982\u201c[E1] \u4f4d\u4e8e\u54ea\u91cc&#xff1f;\u201d\u8fd9\u6837\u7684 Unknown \u793a\u4f8b\u4e0a\u8fdb\u884c\u5fae\u8c03&#xff0c;\u53ef\u80fd\u4f1a\u5728\u770b\u4f3c\u65e0\u5173\u7684\u95ee\u9898\u4e0a\u52a9\u957f\u5e7b\u89c9&#xff0c;\u4f8b\u5982\u201c\u8c01\u521b\u7acb\u4e86 [E2]&#xff1f;\u201d\u3002\u8fd9\u8fdb\u4e00\u6b65\u652f\u6301\u4e86\u5982\u4e0b\u7ed3\u8bba&#xff1a;\u6240\u89c2\u5bdf\u5230\u7684\u6548\u5e94\u5f88\u53ef\u80fd\u6e90\u4e8e\u6a21\u578b\u5b66\u4e60\u5230\u4e86\u4e00\u79cd\u751f\u6210\u5e76\u4e0d\u57fa\u4e8e\u5176\u65e2\u6709\u77e5\u8bc6\u7684\u7b54\u6848\u7684\u884c\u4e3a\u3002<\/p>\n<h2>5 \u7406\u89e3\u77e5\u8bc6\u7c7b\u578b&#xff1a;\u5176\u4ef7\u503c\u4e0e\u5f71\u54cd<\/h2>\n<p>\u5728\u89e3\u51b3\u6211\u4eec\u5173\u4e8e Unknown \u5fae\u8c03\u793a\u4f8b\u5f71\u54cd\u7684\u4e3b\u8981\u7814\u7a76\u95ee\u9898\u65f6&#xff0c;\u4e3a\u7b80\u5355\u8d77\u89c1&#xff0c;\u6211\u4eec\u5c06 Known \u7c7b\u522b\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u6765\u5904\u7406&#xff08;\u89c1\u56fe2a&#xff09;\u3002\u6211\u4eec\u73b0\u5728\u8003\u5bdf\u6bcf\u4e2a\u7c7b\u522b\u7684\u6548\u679c&#xff0c;\u63a2\u8ba8\u4ee5\u4e0b\u95ee\u9898&#xff1a;Q1&#xff1a;\u6765\u81ea\u6bcf\u4e2a\u7c7b\u522b\u7684\u8bad\u7ec3\u793a\u4f8b\u5982\u4f55\u5f71\u54cd\u6d4b\u8bd5\u6027\u80fd&#xff1f;Q2&#xff1a;\u6a21\u578b\u5728\u6765\u81ea\u6bcf\u4e2a\u7c7b\u522b\u7684\u6d4b\u8bd5\u793a\u4f8b\u4e0a\u7684\u8868\u73b0\u5982\u4f55&#xff1f;\u4e3a\u89e3\u51b3 Q1&#xff0c;\u6211\u4eec\u521b\u5efa\u4e86\u5fae\u8c03\u6570\u636e\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u5355\u7c7b\u522b\u53d8\u4f53\u3002\u4ec5\u7531\u7c7b\u522b CAT \u7684\u793a\u4f8b\u7ec4\u6210\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u53d8\u4f53\u8bb0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         CAT<\/p>\n<p>       D_{\\\\text{CAT}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CAT<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4f5c\u4e3a\u53c2\u7167&#xff0c;\u6211\u4eec\u7eb3\u5165\u4e86\u4e00\u4e2a\u5177\u6709 ENTITYQUESTIONS \u4e2d\u81ea\u7136\u7c7b\u522b\u5206\u5e03\u7684\u53d8\u4f53&#xff0c;\u8bb0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Natural<\/p>\n<p>       D_{\\\\text{Natural}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Natural<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        D<\/p>\n<p>        \u2223<\/p>\n<p>       |D|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u56fa\u5b9a&#xff0c;\u5e76\u4e0e \u00a74 \u4e2d\u7684\u5b9e\u9a8c\u76f8\u540c\u3002\u4e3a\u89e3\u51b3 Q2&#xff0c;\u6211\u4eec\u8fdb\u4e00\u6b65\u6309\u7c7b\u522b\u5206\u89e3\u6d4b\u8bd5\u96c6\u6027\u80fd\u3002\u88682\u7ed9\u51fa\u4e86\u7ed3\u679c\u3002<\/p>\n<p>MaybeKnown \u793a\u4f8b\u81f3\u5173\u91cd\u8981\u3002\u7531\u4e8e Unknown \u793a\u4f8b\u6709\u5bb3&#xff0c;\u4eba\u4eec\u53ef\u80fd\u4f1a\u9884\u671f&#xff0c;\u6700\u597d\u5728\u6700\u5177\u4ee3\u8868\u6027\u7684 HighlyKnown \u793a\u4f8b\u4e0a\u8fdb\u884c\u5fae\u8c03\u3002\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         HighlyKnown<\/p>\n<p>       D_{\\\\text{HighlyKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">HighlyKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5e76\u672a\u53d6\u5f97\u6700\u4f73\u603b\u4f53\u7ed3\u679c&#xff1a;\u5b83\u5728 HighlyKnown \u6d4b\u8bd5\u793a\u4f8b\u4e0a\u8868\u73b0\u51fa\u8272&#xff0c;\u4f46\u5728\u5176\u4f59\u7c7b\u522b\u4e0a\u7684\u6027\u80fd\u8f83\u5dee\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         MaybeKnown<\/p>\n<p>       D_{\\\\text{MaybeKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">MaybeKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53d6\u5f97\u4e86\u6700\u4f73\u603b\u4f53\u6027\u80fd\u3002\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         HighlyKnown<\/p>\n<p>       D_{\\\\text{HighlyKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">HighlyKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u76f8\u6bd4&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         MaybeKnown<\/p>\n<p>       D_{\\\\text{MaybeKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">MaybeKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u63d0\u5347\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         D<\/p>\n<p>       M_D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728 MaybeKnown \u4e0a\u7684\u6027\u80fd&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        60.1<\/p>\n<p>        \u2192<\/p>\n<p>        69.9<\/p>\n<p>       60.1 \\\\rightarrow 69.9<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">60.1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">69.9<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u4e14\u672a\u635f\u5bb3\u5176\u5728 HighlyKnown \u4e0a\u7684\u6027\u80fd&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        98.7<\/p>\n<p>        \u2192<\/p>\n<p>        98.4<\/p>\n<p>       98.7 \\\\rightarrow 98.4<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">98.7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">98.4<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u8fd9\u8868\u660e MaybeKnown \u5fae\u8c03\u793a\u4f8b\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         D<\/p>\n<p>       M_D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u63a8\u7406\u65f6\u6b63\u786e\u5904\u7406\u6b64\u7c7b\u793a\u4f8b\u81f3\u5173\u91cd\u8981\u3002\u5b83\u8fd8\u8868\u660e&#xff0c;\u5728\u5408\u9002\u7684\u5fae\u8c03\u793a\u4f8b\u4e0b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         D<\/p>\n<p>       M_D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u66f4\u6709\u80fd\u529b\u5229\u7528\u5176\u65e2\u6709\u77e5\u8bc6\u3002<\/p>\n<p>\u6709\u9650\u77e5\u8bc6\u4f1a\u52a0\u5267\u8fc7\u62df\u5408\u3002\u5728 \u00a74.2 \u4e2d&#xff0c;\u6211\u4eec\u8bc1\u660e\u4e86 Unknown \u5fae\u8c03\u793a\u4f8b\u4f1a\u589e\u52a0\u8fc7\u62df\u5408\u98ce\u9669\u3002\u6211\u4eec\u73b0\u5728\u89c2\u5bdf\u5230&#xff0c;\u8fd9\u4e5f\u9002\u7528\u4e8e WeaklyKnown&#xff0c;\u5c3d\u7ba1\u7a0b\u5ea6\u8f83\u8f7b\u3002\u5177\u4f53\u800c\u8a00&#xff0c;\u5728 CONVERGENCE \u65f6&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         WeaklyKnown<\/p>\n<p>       D_{\\\\text{WeaklyKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">WeaklyKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Unknown<\/p>\n<p>       D_{\\\\text{Unknown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Unknown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u76f8\u8f83\u4e8e EARLY_STOP \u51fa\u73b0\u663e\u8457\u6027\u80fd\u4e0b\u964d&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        39.2<\/p>\n<p>        \u2192<\/p>\n<p>        35.4<\/p>\n<p>       39.2 \\\\rightarrow 35.4<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">39.2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">35.4<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        37.5<\/p>\n<p>        \u2192<\/p>\n<p>        25.8<\/p>\n<p>       37.5 \\\\rightarrow 25.8<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">37.5<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">25.8<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u5f53\u8bad\u7ec3\u81f3 CONVERGENCE \u65f6&#xff0c;\u5b83\u4eec\u5728 WeaklyKnown \u548c Unknown \u4e0a\u8868\u73b0\u51fa\u9002\u5ea6\u63d0\u5347&#xff0c;\u4f46\u5728 HighlyKnown \u548c MaybeKnown \u4e0a\u5927\u5e45\u9000\u5316\u3002\u8fd9\u7a81\u663e\u51fa&#xff0c;\u6027\u80fd\u4e0b\u964d\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u5f52\u56e0\u4e8e\u76f8\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5728\u9884\u8bad\u7ec3\u540e\u5df2\u7ecf\u77e5\u9053\u7684\u4e8b\u5b9e\u7684\u5e7b\u89c9\u7387\u4e0a\u5347\u3002<\/p>\n<p>\u6709\u8da3\u7684\u662f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Natural<\/p>\n<p>       D_{\\\\text{Natural}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Natural<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728 EARLY_STOP \u4e2d\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         MaybeKnown<\/p>\n<p>       D_{\\\\text{MaybeKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">MaybeKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u73b0\u76f8\u5f53&#xff0c;\u8fd9\u8868\u660e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e2d\u53ea\u8981\u5b58\u5728 MaybeKnown \u793a\u4f8b&#xff0c;\u5c31\u8db3\u4ee5\u5728 MaybeKnown \u4e0a\u53d6\u5f97\u9ad8\u6027\u80fd&#xff0c;\u5373\u4f7f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u8fd8\u5305\u542b\u6765\u81ea\u5176\u4ed6\u7c7b\u522b\u7684\u989d\u5916\u793a\u4f8b\u3002\u7136\u800c&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         Natural<\/p>\n<p>       D_{\\\\text{Natural}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Natural<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6027\u80fd\u5728 CONVERGENCE \u540e\u663e\u8457\u4e0b\u964d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         10<\/p>\n<p>       ^{10}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"\"><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8868\u73b0\u4e0d\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         MaybeKnown<\/p>\n<p>       D_{\\\\text{MaybeKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">MaybeKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2014\u2014\u8fd9\u8868\u660e\u5b83\u4ecd\u53d7\u8fc7\u62df\u5408\u5f71\u54cd&#xff0c;\u800c\u8fd9\u5f88\u53ef\u80fd\u662f\u56e0\u4e3a\u5b58\u5728 WeaklyKnown \u548c Unknown \u793a\u4f8b\u3002\u7efc\u5408\u6765\u770b&#xff0c;\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         D<\/p>\n<p>         MaybeKnown<\/p>\n<p>       D_{\\\\text{MaybeKnown}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">MaybeKnown<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u6700\u9ad8\u6027\u80fd\u548c\u964d\u4f4e\u8fc7\u62df\u5408\u98ce\u9669\u4e24\u65b9\u9762\u90fd\u8868\u73b0\u7a81\u51fa<\/p>\n<h2>6 SliCK \u77e5\u8bc6\u7c7b\u522b\u5206\u6790<\/h2>\n<p>\u8bc4\u4f30\u6a21\u578b\u7684\u77e5\u8bc6\u4ecd\u7136\u662f\u4e00\u4e2a\u5f00\u653e\u95ee\u9898&#xff0c;\u7279\u522b\u662f\u7531\u4e8e\u7f3a\u4e4f\u5173\u4e8e\u6a21\u578b\u771f\u6b63\u77e5\u9053\u4ec0\u4e48\u7684\u771f\u5b9e\u57fa\u51c6&#xff0c;\u8bc4\u4f30\u6b64\u7c7b\u65b9\u6cd5\u7684\u8d28\u91cf\u5177\u6709\u6311\u6218\u6027\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d&#xff0c;\u6211\u4eec\u63d0\u51fa\u4e86 SliCK&#xff08;\u00a73&#xff09;&#xff1a;\u4e00\u79cd\u76f8\u5bf9\u4e8e\u6a21\u578b\u77e5\u8bc6\u7684\u4e8b\u5b9e\u7684\u56db\u7c7b\u522b\u5206\u7c7b\u3002\u73b0\u5728\u6211\u4eec\u8fdb\u4e00\u6b65\u5206\u6790\u548c\u8ba8\u8bba\u6211\u4eec\u7684\u8bbe\u8ba1\u9009\u62e9&#xff0c;\u5e0c\u671b SliCK \u80fd\u591f\u4f5c\u4e3a\u4e00\u4e2a\u6709\u7528\u7684\u5206\u7c7b\u4f53\u7cfb&#xff0c;\u6307\u5bfc\u672a\u6765\u5173\u4e8e\u8be5\u4e3b\u9898\u7684\u7814\u7a76\u3002<\/p>\n<p>\u7ec6\u7c92\u5ea6\u7684 Known \u7c7b\u522b \u6211\u4eec\u9996\u5148\u53cd\u601d&#xff0c;\u6211\u4eec\u6839\u636e\u8d2a\u5fc3\u89e3\u7801\u7ed3\u679c\u5c06 Known \u5212\u5206\u4e3a\u66f4\u7ec6\u7c92\u5ea6\u7c7b\u522b\u7684\u9009\u62e9\u662f\u5426\u5df2\u88ab\u8bc1\u660e\u6709\u610f\u4e49\u3002\u5982\u8868 2 \u6240\u793a&#xff0c;HighlyKnown \u786e\u5b9e\u6355\u6349\u4e86\u5177\u6709\u9ad8\u77e5\u8bc6\u7a0b\u5ea6\u7684\u4e8b\u5b9e&#xff0c;\u56e0\u4e3a\u5b83\u5728\u5fae\u8c03\u540e\u59cb\u7ec8\u8d85\u8fc7 95% \u7684\u51c6\u786e\u7387&#xff0c;\u800c MaybeKnown \u548c WeaklyKnown \u4f3c\u4e4e\u4ee3\u8868\u8f83\u5f31\u7684\u77e5\u8bc6\u7a0b\u5ea6\u3002\u6b63\u5982\u9884\u671f&#xff0c;WeaklyKnown \u4e0a\u7684\u6027\u80fd\u5dee\u4e8e MaybeKnown&#xff0c;\u4f46\u597d\u4e8e Unknown\u3002\u6b64\u5916&#xff0c;\u6211\u4eec\u6240\u505a\u7684\u7cbe\u786e\u7c7b\u522b\u533a\u5206\u88ab\u8bc1\u660e\u662f\u6709\u7528\u7684&#xff0c;\u56e0\u4e3a\u5b83\u63ed\u793a\u4e86\u5173\u4e8e MaybeKnown \u5fae\u8c03\u6837\u672c\u91cd\u8981\u6027\u7684\u91cd\u8981\u6d1e\u89c1&#xff0c;\u8be6\u89c1 \u00a75\u3002<\/p>\n<p>\u5bf9 Unknown \u6d4b\u8bd5\u6837\u672c\u8fdb\u884c\u57fa\u51c6\u6d4b\u8bd5 \u5bf9\u4e8e\u6d4b\u8bd5\u96c6\u4e2d\u51fa\u73b0\u7684\u88ab\u5206\u7c7b\u4e3a Unknown \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9&#xff0c;\u4e00\u4e2a\u671f\u671b\u7684\u6027\u8d28\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5728\u5fae\u8c03\u540e\u4f1a\u9519\u8bef\u5730\u56de\u7b54 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span>&#xff08;\u5426\u5219\u5b83\u4eec\u5c31\u4e0d\u662f\u771f\u6b63\u7684\u672a\u77e5&#xff09;\u300211 \u5728\u8868 2 \u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u5230&#xff0c;\u672a\u77e5\u4e0a\u7684\u51c6\u786e\u7387\u6781\u4f4e&#xff08;3.2% \u6216\u66f4\u4f4e&#xff09;&#xff0c;\u8fd9\u5f3a\u70c8\u8868\u660e\u5927\u591a\u6570\u672a\u77e5\u6837\u672c\u5b9e\u9645\u4e0a\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u800c\u8a00\u662f\u672a\u77e5\u7684\u3002\u4f5c\u4e3a\u5bf9\u6bd4\u7684\u6848\u4f8b\u7814\u7a76&#xff0c;\u6211\u4eec\u5206\u6790\u4e86 Kadavath \u7b49\u4eba (2022) \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        T<\/p>\n<p>        r<\/p>\n<p>        u<\/p>\n<p>        e<\/p>\n<p>        )<\/p>\n<p>       \\\\mathrm{P(True)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathrm\">True<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u65b9\u6cd5&#xff1a;\u4e00\u79cd\u8fde\u7eed\u5206\u6570&#xff0c;\u7528\u4e8e\u4f30\u8ba1\u6a21\u578b\u8d4b\u4e88\u7279\u5b9a\u7b54\u6848\u6b63\u786e\u6027\u7684\u6982\u7387\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        T<\/p>\n<p>        r<\/p>\n<p>        u<\/p>\n<p>        e<\/p>\n<p>        )<\/p>\n<p>       \\\\mathrm{P(True)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathrm\">True<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u6700\u521d\u7528\u4e8e\u81ea\u6211\u8bc4\u4f30\u6a21\u578b\u751f\u6210\u7684\u7b54\u6848&#xff0c;\u800c\u6211\u4eec\u7528\u5b83\u6765\u8bc4\u4f30 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u5c06\u771f\u5b9e\u7b54\u6848\u89c6\u4e3a\u6b63\u786e\u3002 12 \u5728\u56fe 5 \u4e2d&#xff0c;\u6211\u4eec\u63a2\u7d22\u5c06\u4f4e\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        T<\/p>\n<p>        r<\/p>\n<p>        u<\/p>\n<p>        e<\/p>\n<p>        )<\/p>\n<p>       \\\\mathrm{P(True)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathrm\">True<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u9608\u503c\u7684\u6837\u672c\u5206\u7c7b\u4e3a\u672a\u77e5&#xff0c;\u5e76\u5c06\u8fd9\u4e00\u65b9\u6cd5\u4e0e SliCK \u8fdb\u884c\u6bd4\u8f83\u3002\u6211\u4eec\u7684\u7ed3\u679c\u8868\u660e&#xff0c;\u81f3\u5c11\u5728\u6211\u4eec\u7684\u8bbe\u5b9a\u4e2d&#xff0c;\u6211\u4eec\u7684\u65b9\u6cd5\u6240\u5f52\u7c7b\u7684\u672a\u77e5\u6837\u672c&#xff0c;\u5176\u6a21\u578b\u5728\u5fae\u8c03\u540e\u7684\u6027\u80fd\u663e\u8457\u66f4\u5dee\u3002\u5177\u4f53\u800c\u8a00&#xff0c;\u89c2\u5bdf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u8f74\u4e0a\u7684\u56fa\u5b9a\u503c\u53ef\u4ee5\u53d1\u73b0&#xff0c;\u5982\u679c\u6211\u4eec\u7528\u4e24\u79cd\u65b9\u6cd5\u5c06\u76f8\u4f3c\u6bd4\u4f8b\u7684\u6d4b\u8bd5\u6837\u672c\u6807\u8bb0\u4e3a\u672a\u77e5&#xff0c;\u90a3\u4e48\u57fa\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        T<\/p>\n<p>        r<\/p>\n<p>        u<\/p>\n<p>        e<\/p>\n<p>        )<\/p>\n<p>       \\\\mathrm{P(True)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathrm\">True<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u672a\u77e5\u6837\u672c\u5728\u5fae\u8c03\u540e\u7684\u51c6\u786e\u7387\u4f1a\u9ad8\u5f97\u591a\u300213 \u6700\u540e&#xff0c;\u84dd\u7ebf\u8868\u660e&#xff0c;\u4f7f\u7528\u6765\u81ea\u591a\u4e2a\u5c11\u6837\u672c\u63d0\u793a\u7684\u6837\u672c\u6765\u8fd1\u4f3c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>          C<\/p>\n<p>          o<\/p>\n<p>          r<\/p>\n<p>          r<\/p>\n<p>          e<\/p>\n<p>          c<\/p>\n<p>          t<\/p>\n<p>       P_{\\\\mathrm{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u81f3\u5173\u91cd\u8981&#xff0c;\u56e0\u4e3a\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>          e<\/p>\n<p>          x<\/p>\n<p>        &lt;<\/p>\n<p>        10<\/p>\n<p>       N_{ex} &lt; 10<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u4f1a\u5bfc\u81f4\u5728 SliCK \u672a\u77e5\u6837\u672c\u4e0a\u66f4\u9ad8\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054147-6acb219be538b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u56fe 5&#xff1a;SliCK Unknown \u5206\u7c7b\u4e0e\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        True<\/p>\n<p>        )<\/p>\n<p>        &lt;<\/p>\n<p>        T<\/p>\n<p>       P(\\\\text{True}) &lt; T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">True<\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u7684\u793a\u4f8b\u5206\u7c7b\u4e3a Unknown \u7684\u5bf9\u6bd4\u3002x \u8f74\u662f\u88ab\u5206\u7c7b\u4e3a Unknown \u7684\u6d4b\u8bd5\u793a\u4f8b\u767e\u5206\u6bd4&#xff0c;y \u8f74\u662f\u8fd9\u4e9b\u793a\u4f8b\u5728\u5fae\u8c03\u540e\u7684\u51c6\u786e\u7387\u3002\u9ec4\u8272\u7ebf\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>        \u2208<\/p>\n<p>        [<\/p>\n<p>        0<\/p>\n<p>        ,<\/p>\n<p>        1<\/p>\n<p>        ]<\/p>\n<p>       T \\\\in [0, 1]<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u65f6\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        True<\/p>\n<p>        )<\/p>\n<p>       P(\\\\text{True})<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">True<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u7684 Unknown \u7c7b\u522b\u662f\u84dd\u8272\u5706\u5708&#xff0c;\u84dd\u8272\u7ebf\u5bf9\u5e94\u4e8e\u7528\u5c11\u4e8e 10 \u4e2a\u968f\u673a 4-shot \u793a\u4f8b\u6765\u8fd1\u4f3c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff08;\u89c1 \u00a73 \u548c \u00a7C&#xff09;\u3002<\/p>\n<p>10\u53c2\u89c1\u00a7J\u4e86\u89e3\u5173\u4e8e\u6b64\u7edf\u8ba1\u663e\u8457\u6027\u68c0\u9a8c\u7684\u8be6\u7ec6\u5185\u5bb9\u3002 11\u7531\u4e8e\u5728\u6211\u4eec\u7684\u95ed\u5377 QA \u8bbe\u5b9a\u4e2d&#xff0c;\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u4e0d\u76f8\u4ea4&#xff0c;\u6a21\u578b\u5fc5\u987b\u4f9d\u8d56\u5176\u5df2\u6709\u77e5\u8bc6\u6765\u56de\u7b54\u6d4b\u8bd5\u95ee\u9898\u3002 12\u7ed9\u5b9a\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5bf9&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        T<\/p>\n<p>        r<\/p>\n<p>        u<\/p>\n<p>        e<\/p>\n<p>        )<\/p>\n<p>       \\\\mathrm{P(True)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathrm\">True<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u53cd\u6620\u6a21\u578b\u8d4b\u4e88 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u7b54\u6848\u7684\u6982\u7387\u3002\u5b83\u53ef\u4ee5\u5e94\u7528\u4e8e\u6a21\u578b\u751f\u6210\u7684\u7b54\u6848\u4ee5\u8fdb\u884c\u81ea\u6211\u8bc4\u4f30&#xff0c;\u5982\u539f\u59cb\u7814\u7a76\u4e2d\u6240\u505a\u7684\u90a3\u6837&#xff1b;\u4e5f\u53ef\u4ee5\u5e94\u7528\u4e8e\u771f\u5b9e\u7b54\u6848&#xff0c;\u4ee5\u68c0\u67e5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u5c06\u5176\u89c6\u4e3a\u6b63\u786e&#xff0c;\u5982\u6211\u4eec\u7684\u7814\u7a76\u4e2d\u6240\u505a\u7684\u90a3\u6837\u3002 13\u8fd9\u662f\u4e00\u9879\u521d\u6b65\u5206\u6790&#xff0c;\u6211\u4eec\u5c06\u5168\u9762\u6bd4\u8f83\u7559\u5f85\u672a\u6765\u5de5\u4f5c\u3002\u66f4\u591a\u7ec6\u8282\u89c1 \u00a7K\u3002<\/p>\n<h2>7 \u5fae\u8c03\u4ee5\u5bf9\u672a\u77e5\u793a\u4f8b\u5f03\u6743<\/h2>\n<p>\u6211\u4eec\u5c55\u793a\u4e86&#xff0c;\u62df\u5408\u672a\u77e5\u5fae\u8c03\u793a\u4f8b\u4f1a\u5bf9\u6d4b\u8bd5\u6027\u80fd\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd&#xff08;\u00a74.2 \u548c \u00a74.4&#xff09;\u3002\u7136\u800c&#xff0c;\u8fd9\u79cd\u8d1f\u9762\u5f71\u54cd\u8868\u73b0\u4e3a\u4e00\u79cd\u8fc7\u62df\u5408\u5f62\u5f0f\u3002\u4ece\u5b9e\u8df5\u89d2\u5ea6\u6765\u770b&#xff0c;\u6211\u4eec\u5c55\u793a\u4e86\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u65e9\u505c\u6216\u4ece\u5fae\u8c03\u6570\u636e\u96c6\u4e2d\u8fc7\u6ee4\u6389\u672a\u77e5\u793a\u4f8b\u6765\u7f13\u89e3\u8fc7\u62df\u5408\u3002<\/p>\n<p>\u6211\u4eec\u73b0\u5728\u63a2\u7d22\u4e00\u79cd\u989d\u5916\u65b9\u6cd5&#xff0c;\u5373\u5fae\u8c03\u6a21\u578b\u4ee5\u5bf9\u672a\u77e5\u793a\u4f8b\u5f03\u6743&#xff0c;\u4f5c\u4e3a\u4e00\u79cd\u6f5c\u5728\u7f13\u89e3\u63aa\u65bd\u3002\u5177\u4f53\u800c\u8a00&#xff0c;\u6211\u4eec\u5c06\u672a\u77e5\u5fae\u8c03\u793a\u4f8b\u7684\u6807\u7b7e\u66ff\u6362\u4e3a\u201c\u6211\u4e0d\u77e5\u9053\u201d\u8fd9\u4e00\u8868\u8ff0&#xff0c;\u5e76\u68c0\u9a8c\u8fd9\u662f\u5426\u80fd\u7f13\u89e3\u6240\u89c2\u5bdf\u5230\u7684\u8fc7\u62df\u5408\u3002<\/p>\n<p>\u8868 3 \u7ed9\u51fa\u4e86\u5df2\u56de\u7b54\u7684\u6d4b\u8bd5\u95ee\u9898\u767e\u5206\u6bd4&#xff08;\u5373 MD \u672a\u4ee5\u201c\u6211\u4e0d\u77e5\u9053\u201d\u4f5c\u7b54&#xff09;\u4ee5\u53ca\u8fd9\u4e9b\u95ee\u9898\u4e0a\u7684\u51c6\u786e\u7387\u3002\u4e0e\u5148\u524d\u5de5\u4f5c\u7684\u53d1\u73b0\u4e00\u81f4&#xff08;Zhang et al., 2023&#xff09;&#xff0c;\u6211\u4eec\u89c2\u5bdf\u5230\u5728\u4e3b\u52a8\u56de\u7b54\u7684\u6d4b\u8bd5\u793a\u4f8b\u4e0a\u51c6\u786e\u7387\u6709\u6240\u63d0\u9ad8&#xff08;\u6bd4\u8f83 D \u4e0e DIDK \u65f6&#xff09;\u3002\u5f53\u6211\u4eec\u5bf9 D \u6bd4\u8f83 EARLY_STOP \u4e0e CONVERGENCE \u65f6&#xff0c;\u89c2\u5bdf\u5230\u6027\u80fd\u4e0b\u964d&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        43.0<\/p>\n<p>        \u2192<\/p>\n<p>        38.8<\/p>\n<p>       43.0 \\\\rightarrow 38.8<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">43.0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">38.8<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u8fd9\u8bf4\u660e\u4e86\u8fc7\u62df\u5408\u6548\u5e94\u3002\u7136\u800c&#xff0c;\u6211\u4eec\u89c2\u5bdf\u5230&#xff0c;\u7528\u4e0d\u786e\u5b9a\u6027\u8868\u8ff0\u91cd\u65b0\u6807\u6ce8\u672a\u77e5\u793a\u4f8b\u4f3c\u4e4e\u964d\u4f4e\u4e86\u8fc7\u62df\u5408\u98ce\u9669\u3002\u5177\u4f53\u800c\u8a00&#xff0c;DIDK \u7684\u51c6\u786e\u7387\u5728 EARLY_STOP \u548c CONVERGENCE \u4e0b\u5747\u4fdd\u6301\u4e3a 61.8&#xff0c;\u540c\u65f6\u4e3b\u52a8\u56de\u7b54\u7684\u95ee\u9898\u6570\u91cf\u7565\u6709\u4e0b\u964d&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        58.7<\/p>\n<p>        \u2192<\/p>\n<p>        55.6<\/p>\n<p>       58.7 \\\\rightarrow 55.6<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">58.7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">55.6<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261011054148-6acb219c8bcab.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8868 3&#xff1a;\u5c06 Unknown \u5fae\u8c03\u793a\u4f8b\u7684\u6807\u7b7e\u66ff\u6362\u4e3a\u201cI don\u2019t know\u201d\u540e\u7684\u7ed3\u679c\u3002\u6b64\u5904\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u662f\u5305\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        50<\/p>\n<p>        %<\/p>\n<p>       50\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">50%<\/span><\/span><\/span><\/span><\/span> Known \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        50<\/p>\n<p>        %<\/p>\n<p>       50\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">50%<\/span><\/span><\/span><\/span><\/span> Unknown \u7684\u53d8\u4f53\u3002DIDK \u662f\u5c06\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        50<\/p>\n<p>        %<\/p>\n<p>       50\\\\%<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">50%<\/span><\/span><\/span><\/span><\/span> Unknown \u5fae\u8c03\u793a\u4f8b\u91cd\u65b0\u6807\u6ce8\u4e3a\u201cI don\u2019t know\u201d\u7684\u53d8\u4f53\u3002\u51c6\u786e\u7387\u5728\u5df2\u4f5c\u7b54\u7684\u6d4b\u8bd5\u95ee\u9898\u5b50\u96c6\u4e0a\u6d4b\u91cf&#xff0c;\u5373 MD \u672a\u4ee5\u201cI don\u2019t know\u201d\u4f5c\u7b54\u3002<\/p>\n<h2>8 \u8ba8\u8bba<\/h2>\n<p>\u5b9e\u8df5\u610f\u4e49\u3002\u8fd9\u9879\u5de5\u4f5c\u51f8\u663e\u4e86\u4f7f\u7528\u76d1\u7763\u5fae\u8c03\u6765\u66f4\u65b0 LLM \u77e5\u8bc6\u6240\u5b58\u5728\u7684\u98ce\u9669&#xff0c;\u56e0\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u7ecf\u9a8c\u8bc1\u636e&#xff0c;\u8868\u660e\u901a\u8fc7\u5fae\u8c03\u83b7\u53d6\u65b0\u77e5\u8bc6\u4e0e\u5173\u4e8e\u65e2\u6709\u77e5\u8bc6\u7684\u5e7b\u89c9\u76f8\u5173\u3002\u6b64\u5916&#xff0c;\u8fd9\u9879\u5de5\u4f5c\u63d0\u51fa\u4e86\u5173\u4e8e\u5fae\u8c03\u5b9e\u8df5\u7684\u91cd\u8981\u95ee\u9898&#xff0c;\u6709\u5f85\u672a\u6765\u63a2\u7d22\u3002\u6211\u4eec\u53d1\u73b0&#xff0c;\u672a\u77e5\u793a\u4f8b\u6bd4\u5df2\u77e5\u793a\u4f8b\u62df\u5408\u5f97\u66f4\u6162&#xff0c;\u56e0\u6b64\u5176\u8d1f\u9762\u5f71\u54cd\u8868\u73b0\u4e3a\u4e00\u79cd\u8fc7\u62df\u5408\u5f62\u5f0f&#xff0c;\u8fd9\u5f3a\u8c03\u4e86\u4f7f\u7528\u65e9\u505c\u800c\u975e\u56fa\u5b9a\u6570\u91cf\u7684\u5fae\u8c03\u6b65\u9aa4\u7684\u91cd\u8981\u6027\u3002\u7136\u800c&#xff0c;\u5f53\u5728\u4f17\u591a\u5177\u6709\u4e0d\u540c\u6700\u4f18\u505c\u6b62\u70b9\u7684\u4efb\u52a1\u4e0a\u8fdb\u884c\u5fae\u8c03\u65f6&#xff0c;\u65e9\u505c\u53ef\u80fd\u4e0d\u90a3\u4e48\u6709\u6548\u3002\u53e6\u4e00\u79cd\u89e3\u51b3\u65b9\u6848\u53ef\u4ee5\u662f&#xff0c;\u901a\u8fc7\u8fc7\u6ee4\u4f7f\u5fae\u8c03\u6570\u636e\u4e0e\u6a21\u578b\u7684\u77e5\u8bc6\u5bf9\u9f50&#xff0c;\u4ece\u800c\u907f\u514d\u6dfb\u52a0\u65b0\u77e5\u8bc6\u3002\u5254\u9664 Unknown \u793a\u4f8b\u3002\u6211\u4eec\u5c55\u793a\u4e86\u521d\u6b65\u8bc1\u636e&#xff0c;\u8868\u660e\u8fd9\u53ef\u4ee5\u5728\u4e0d\u635f\u5bb3\u6027\u80fd\u7684\u60c5\u51b5\u4e0b\u964d\u4f4e\u8fc7\u62df\u5408\u98ce\u9669\u3002\u8fc7\u6ee4\u7684\u4e00\u4e2a\u53ef\u80fd\u7f3a\u70b9\u662f&#xff0c;Unknown \u5fae\u8c03\u793a\u4f8b\u4ecd\u53ef\u80fd\u6709\u52a9\u4e8e\u6559\u4f1a LLM \u5728 Unknown \u6d4b\u8bd5\u793a\u4f8b\u4e0a\u8868\u8fbe\u4e0d\u786e\u5b9a\u6027&#xff08;Zhang et al., 2023; Yang et al., 2023&#xff09;\u3002\u8fd9\u63d0\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898&#xff1a;\u7528\u4e0d\u786e\u5b9a\u6027\u8868\u8fbe&#xff08;\u4f8b\u5982\u201c\u6211\u4e0d\u77e5\u9053\u201d&#xff09;\u91cd\u65b0\u6807\u6ce8 Unknown \u5fae\u8c03\u793a\u4f8b&#xff0c;\u80fd\u5426\u51cf\u5c11\u5176\u8d1f\u9762\u5f71\u54cd&#xff1f;\u6211\u4eec\u7684\u5b9e\u9a8c&#xff08;\u7b2c 7 \u8282&#xff09;\u8868\u660e\u7b54\u6848\u662f\u80af\u5b9a\u7684&#xff0c;\u8fd9\u8868\u660e\u6b64\u7c7b\u65b9\u6cd5\u53ef\u80fd\u6700\u6709\u524d\u666f\u3002 \u6d45\u5c42\u5bf9\u9f50\u5047\u8bf4\u3002Zhou et al. (2023) \u5047\u8bbe LLM \u7684\u77e5\u8bc6\u548c\u80fd\u529b\u4e3b\u8981\u662f\u5728\u9884\u8bad\u7ec3\u671f\u95f4\u4e60\u5f97\u7684&#xff0c;\u800c\u5bf9\u9f50\u5219\u662f\u4e00\u4e2a\u7b80\u5355\u8fc7\u7a0b&#xff0c;\u6a21\u578b\u5728\u5176\u4e2d\u5b66\u4e60\u4e0e\u7528\u6237\u4ea4\u4e92\u7684\u98ce\u683c\u6216\u683c\u5f0f\u3002\u4ed6\u4eec\u901a\u8fc7\u8868\u660e\u4ec5\u5728 1k \u9ad8\u8d28\u91cf\u793a\u4f8b\u4e0a\u8fdb\u884c\u5fae\u8c03\u5c31\u80fd\u5f97\u5230\u4e00\u4e2a\u6709\u7ade\u4e89\u529b\u7684\u52a9\u624b LLM&#xff08;\u540d\u4e3a LIMA&#xff09;&#xff0c;\u4ece\u800c\u8bc1\u5b9e\u4e86\u8fd9\u4e00\u5047\u8bf4\u3002\u5982\u7b2c 4.3 \u8282\u6240\u8ba8\u8bba&#xff0c;\u6211\u4eec\u5c55\u793a\u4e86\u8bc1\u636e&#xff0c;\u8868\u660e LLM \u96be\u4ee5\u83b7\u53d6 Unknown \u793a\u4f8b\u4e2d\u5b58\u5728\u7684\u65b0\u77e5\u8bc6&#xff0c;\u800c\u4e3b\u8981\u5b66\u4f1a\u5229\u7528\u5176\u5df2\u6709\u77e5\u8bc6\u3002\u6211\u4eec\u8fd8\u8868\u660e&#xff0c;\u5728 HighlyKnown \u793a\u4f8b\u4e0a\u8fdb\u884c\u5fae\u8c03\u4f1a\u5bfc\u81f4\u5df2\u6709\u77e5\u8bc6\u7684\u6b21\u4f18\u5229\u7528&#xff0c;\u5c3d\u7ba1\u6211\u4eec\u7684\u4efb\u52a1\u683c\u5f0f\u6bd4 LIMA \u7684\u66f4\u7b80\u5355&#xff0c;\u4e14\u6211\u4eec\u7684\u6570\u636e\u96c6\u5927\u516d\u500d\u3002\u7efc\u4e0a\u6240\u8ff0&#xff0c;\u6211\u4eec\u7684\u53d1\u73b0\u8868\u660e&#xff0c;\u5c3d\u7ba1 LLM \u7684\u5927\u90e8\u5206\u77e5\u8bc6\u786e\u5b9e\u662f\u901a\u8fc7\u9884\u8bad\u7ec3\u83b7\u5f97\u7684&#xff0c;\u4f46\u6a21\u578b\u901a\u8fc7\u5fae\u8c03\u5b66\u5230\u7684\u4e0d\u4ec5\u4ec5\u662f\u98ce\u683c\u6216\u683c\u5f0f&#xff0c;\u56e0\u4e3a\u5fae\u8c03\u793a\u4f8b\u7684\u9009\u62e9\u4f1a\u663e\u8457\u5f71\u54cd\u6a21\u578b\u5728\u5fae\u8c03\u540e\u5229\u7528\u5176\u5df2\u6709\u77e5\u8bc6\u7684\u80fd\u529b\u3002<\/p>\n<h2>9 \u76f8\u5173\u5de5\u4f5c<\/h2>\n<p>\u65b0\u77e5\u8bc6\u4e0e\u5e7b\u89c9\u3002Schulman (2023)\u3001Goldberg (2023) \u548c Gudibande et al. (2023) \u63d0\u5230\u4e00\u79cd\u731c\u60f3&#xff1a;\u5728\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u4e0a\u8fdb\u884c\u5fae\u8c03\u53ef\u80fd\u4f1a\u52a9\u957f\u5e7b\u89c9\u3002Huang et al. (2023) \u5bf9\u5e7b\u89c9\u6210\u56e0\u8fdb\u884c\u4e86\u5206\u7c7b&#xff0c;\u5e76\u5c06\u8fd9\u4e00\u573a\u666f\u6b63\u5f0f\u5b9a\u4e49\u4e3a\u80fd\u529b\u9519\u4f4d&#xff0c;\u540c\u65f6\u5f3a\u8c03\u7531\u4e8e\u5b9a\u4e49 LLM \u77e5\u8bc6\u8fb9\u754c\u7684\u6311\u6218&#xff0c;\u9488\u5bf9\u80fd\u529b\u9519\u4f4d\u7684\u7814\u7a76\u6709\u9650\u3002<\/p>\n<p>\u8fd1\u671f\u7814\u7a76\u652f\u6301\u6211\u4eec\u7684\u53d1\u73b0\u3002\u4f8b\u5982&#xff0c;Ghosal et al. (2024) \u8868\u660e&#xff0c;\u5728\u4f17\u6240\u5468\u77e5\u7684\u4e8b\u5b9e\u4e0a\u5fae\u8c03\u7684\u6a21\u578b&#xff0c;\u76f8\u6bd4\u5728\u51b7\u95e8\u4e8b\u5b9e\u4e0a\u5fae\u8c03\u7684\u6a21\u578b&#xff0c;\u8868\u73b0\u51fa\u66f4\u5f3a\u7684\u4e8b\u5b9e\u6027&#xff0c;\u8fd9\u53ef\u5f52\u56e0\u4e8e\u6a21\u578b\u5bf9\u51b7\u95e8\u4e8b\u5b9e\u7684\u719f\u6089\u7a0b\u5ea6\u8f83\u4f4e\u3002\u53e6\u4e00\u4e2a\u4f8b\u5b50\u662f Lin et al. (2024)&#xff0c;\u4ed6\u4eec\u5206\u522b\u4f7f\u7528\u9884\u8bad\u7ec3\u6a21\u578b\u6216\u68c0\u7d22\u589e\u5f3a\u53d8\u4f53\u751f\u6210\u7684\u6570\u636e\u6765\u5fae\u8c03\u6a21\u578b\u3002\u4ed6\u4eec\u53d1\u73b0\u540e\u8005\u5bfc\u81f4\u4e8b\u5b9e\u6027\u964d\u4f4e&#xff0c;\u8fd9\u53ef\u5f52\u56e0\u4e8e\u68c0\u7d22\u6587\u672c\u4e2d\u5f15\u5165\u4e86\u65b0\u7684\u4e8b\u5b9e\u77e5\u8bc6\u3002Ren et al. (2024) \u4e5f\u5728\u4e00\u4e2a\u76f8\u5f53\u4e0d\u540c\u7684\u65b9\u6cd5\u8bbe\u7f6e\u4e2d\u7814\u7a76\u4e86\u901a\u8fc7\u5fae\u8c03\u5f15\u5165\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u7684\u5f71\u54cd&#xff0c;\u4ed6\u4eec\u805a\u7126\u4e8e\u591a\u9879\u9009\u62e9\u9898&#xff0c;\u8fdb\u884c\u76f8\u5bf9\u8f83\u77ed\u7684\u5fae\u8c03\u8fd0\u884c&#xff0c;\u5e76\u4e14\u4ec5\u6d4b\u8bd5 100% \u5df2\u77e5\u548c 100% \u672a\u77e5\u7684\u6df7\u5408\u60c5\u51b5\u3002\u4ed6\u4eec\u7684\u7ed3\u679c\u4e0e\u6211\u4eec\u7684\u7ed3\u679c\u4e00\u81f4&#xff0c;\u8fd9\u8fdb\u4e00\u6b65\u5f3a\u5316\u4e86\u6211\u4eec\u7684\u7ed3\u8bba\u3002\u6700\u540e&#xff0c;\u8fd9\u4e9b\u89c1\u89e3\u4e5f\u88ab\u6574\u5408\u5230 Llama 3 \u6a21\u578b&#xff08;Dubey et al., 2024&#xff09;\u7684\u6307\u4ee4\u5fae\u8c03\u9636\u6bb5&#xff0c;\u4ee5\u786e\u4fdd\u793a\u4f8b\u4e0e\u9884\u8bad\u7ec3\u77e5\u8bc6\u4fdd\u6301\u4e00\u81f4\u3002<\/p>\n<p>\u53e6\u4e00\u6761\u5de5\u4f5c\u65b9\u5411\u63a2\u8ba8\u6a21\u578b\u5728\u6d4b\u8bd5\u65f6\u9762\u5bf9\u65b0\u77e5\u8bc6\u7684\u884c\u4e3a\u3002Kang et al. (2024) \u8868\u660e&#xff0c;\u5f53\u5fae\u8c03\u540e\u7684 LLM \u5728\u6d4b\u8bd5\u65f6\u9047\u5230\u672a\u77e5\u67e5\u8be2\u65f6&#xff0c;\u5176\u54cd\u5e94\u4f1a\u6a21\u4eff\u5fae\u8c03\u6570\u636e\u4e2d\u4e0e\u672a\u77e5\u793a\u4f8b\u76f8\u5173\u8054\u7684\u54cd\u5e94\u3002Yin et al. (2023) \u8868\u660e&#xff0c;\u5f53 LLM \u5728\u5176\u8f93\u5165\u4e0a\u4e0b\u6587\u4e2d\u9762\u5bf9\u65b0\u77e5\u8bc6\u65f6&#xff0c;\u5176\u6027\u80fd\u5e76\u4e0d\u4ee4\u4eba\u6ee1\u610f&#xff1b;Lee et al. (2023) \u5206\u6790\u4e86\u672a\u77e5\u4e0a\u4e0b\u6587\u5b66\u4e60\u793a\u4f8b\u7684\u5f71\u54cd\u3002<\/p>\n<p>\u91cf\u5316 LLM \u4e2d\u7684\u77e5\u8bc6\u3002SliCK \u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u79cd\u9488\u5bf9\u771f\u5b9e\u6807\u7b7e\u7684\u7f6e\u4fe1\u5ea6\u5f15\u51fa\u65b9\u6cd5&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u77e5\u9053 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        q<\/p>\n<p>        ,<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       (q, a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5982\u679c\u5b83\u786e\u4fe1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u7b54\u6848&#xff09;\u3002\u73b0\u6709\u5de5\u4f5c\u901a\u8fc7\u68c0\u67e5\u591a\u4e2a\u6837\u672c\u4e4b\u95f4\u7684\u4e00\u81f4\u6027&#xff08;Kuhn et al., 2023; Manakul et al., 2023; Tian et al., 2023a; Lyu et al., 2024&#xff09;\u3001\u63a2\u67e5\u5185\u90e8\u8868\u793a&#xff08;Azaria and Mitchell, 2023; Burns et al., 2022&#xff09;\u3001\u5f15\u51fa\u8a00\u8bed\u5316\u6982\u7387&#xff08;Tian et al., 2023b&#xff09;\u6216\u76f4\u63a5\u63d0\u793a&#xff08;Kadavath et al., 2022&#xff09;&#xff0c;\u4ece LLM \u4e2d\u83b7\u5f97\u6821\u51c6\u7f6e\u4fe1\u5ea6\u3002Kadavath et al. \u8fd8\u8bad\u7ec3\u4e86\u4e00\u4e2a\u5355\u72ec\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        IK<\/p>\n<p>        )<\/p>\n<p>       P(\\\\text{IK})<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">IK<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u6a21\u578b&#xff0c;\u4ee5\u9884\u6d4b LLM \u662f\u5426\u77e5\u9053 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>       q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u7b54\u6848\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        IK<\/p>\n<p>        )<\/p>\n<p>       P(\\\\text{IK})<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">IK<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u6807\u7b7e\u7531\u6b63\u786e\u91c7\u6837\u7b54\u6848\u7684\u6bd4\u4f8b\u8fd1\u4f3c&#xff0c;\u8fd9\u5728\u6982\u5ff5\u4e0a\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff08;\u00a73&#xff09;\u4e00\u81f4\u3002\u4e00\u4e2a\u5173\u952e\u533a\u522b\u5728\u4e8e&#xff0c;\u6211\u4eec\u8fd8\u5b9a\u4e49\u4e86 SliCK \u7c7b\u522b&#xff0c;\u5e76\u63d0\u4f9b\u8bc1\u636e\u8868\u660e\u6211\u4eec\u6355\u6349\u5230\u4e86\u6709\u610f\u4e49\u4e14\u6709\u7528\u7684\u7c7b\u522b\u3002<\/p>\n<h2>10 \u7ed3\u8bba<\/h2>\n<p>\u6211\u4eec\u7814\u7a76\u901a\u8fc7\u5fae\u8c03\u6574\u5408\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u5bf9\u6a21\u578b\u4ea7\u751f\u5e7b\u89c9\u503e\u5411\u7684\u5f71\u54cd\u3002\u6211\u4eec\u9996\u5148\u63d0\u51fa SliCK&#xff0c;\u4e00\u79cd\u4f9d\u636e LLM \u77e5\u8bc6\u5bf9\u4e8b\u5b9e\u8fdb\u884c\u7684\u5206\u7c7b\u3002\u7136\u540e&#xff0c;\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u9879\u53d7\u63a7\u7814\u7a76&#xff0c;\u5728\u5176\u4e2d\u9694\u79bb\u65b0\u77e5\u8bc6\u7684\u5f71\u54cd&#xff0c;\u5e76\u4e25\u683c\u8bc4\u4f30\u5176\u6548\u5e94\u3002\u6211\u4eec\u63d0\u4f9b\u4e86\u5173\u4e8e\u5fae\u8c03\u52a8\u6001\u7684\u591a\u9879\u89c1\u89e3&#xff0c;\u5173\u952e\u53d1\u73b0\u5982\u4e0b&#xff1a;(1) \u901a\u8fc7\u76d1\u7763\u5fae\u8c03\u83b7\u53d6\u65b0\u77e5\u8bc6\u4e0e\u9488\u5bf9\u5df2\u6709\u77e5\u8bc6\u7684\u5e7b\u89c9\u76f8\u5173\u3002(2) LLM \u96be\u4ee5\u901a\u8fc7\u5fae\u8c03\u6574\u5408\u65b0\u77e5\u8bc6&#xff0c;\u5e76\u4e14\u5927\u591a\u5b66\u4f1a\u4f7f\u7528\u5176\u5df2\u6709\u77e5\u8bc6\u3002<\/p>\n<h2>11 \u5c40\u9650\u6027<\/h2>\n<p>\u6211\u4eec\u7684\u5b9e\u9a8c\u4ec5\u4f7f\u7528\u5355\u4e2a LLM \u8fdb\u884c&#xff0c;\u56e0\u6b64\u5c1a\u4e0d\u6e05\u695a\u7ed3\u679c\u662f\u5426\u4f1a\u968f\u4e0d\u540c LLM \u800c\u53d8\u5316\u3002\u8bdd\u867d\u5982\u6b64&#xff0c;\u6211\u4eec\u7684\u7814\u7a76\u8ba1\u7b97\u5f00\u9500\u6781\u5927&#xff0c;\u56e0\u6b64\u96be\u4ee5\u5728\u591a\u4e2a LLM \u4e0a\u590d\u73b0&#xff1a;\u9996\u5148&#xff0c;\u6211\u4eec\u7684\u5fae\u8c03\u8ba1\u7b97\u5f00\u9500\u5f88\u5927&#xff0c;\u56e0\u4e3a\u5176\u8fd0\u884c\u65f6\u95f4\u975e\u5e38\u957f&#xff0c;\u6211\u4eec\u60f3\u8981\u5206\u6790\u5fae\u8c03\u4e0d\u540c\u9636\u6bb5&#xff08;\u5305\u62ec\u8fc7\u62df\u5408\u9636\u6bb5&#xff09;\u4e2d\u7684\u884c\u4e3a\u3002\u5176\u6b21&#xff0c;\u4e5f\u662f\u6700\u91cd\u8981\u7684\u4e00\u70b9&#xff0c;\u4e3a\u4e86\u4fc3\u8fdb\u6211\u4eec\u7684\u7814\u7a76&#xff0c;\u6211\u4eec\u9700\u8981\u4f9d\u636e SliCK \u7c7b\u522b\u6807\u6ce8\u4e00\u4e2a\u5927\u89c4\u6a21\u6570\u636e\u96c6\u3002\u4e3a\u4e86\u5f97\u51fa\u53ef\u9760\u7ed3\u8bba&#xff0c;\u51c6\u786e\u8bc4\u4f30\u6a21\u578b\u76f8\u5bf9\u4e8e\u5355\u4e2a\u5fae\u8c03\u793a\u4f8b\u7684\u77e5\u8bc6\u81f3\u5173\u91cd\u8981\u3002\u5728\u6211\u4eec\u7684\u60c5\u51b5\u4e2d&#xff0c;\u6211\u4eec\u5bf9\u6bcf\u4e2a\u793a\u4f8b\u8fd0\u884c 170 \u4e2a\u63a8\u7406\u6b65\u9aa4&#xff0c;\u5373\u8d85\u8fc7 1500 \u4e07\u6b21\u63a8\u7406\u6b65\u9aa4\u6765\u5bf9\u6211\u4eec\u5b8c\u6574\u6570\u636e\u96c6\u8fdb\u884c\u5206\u7c7b\u3002<\/p>\n<p>\u6b64\u5916&#xff0c;\u7531\u4e8e\u6211\u4eec\u805a\u7126\u4e8e\u95ed\u5377\u95ee\u7b54&#xff0c;\u6211\u4eec\u7814\u7a76\u7684\u5b9e\u9645\u610f\u4e49&#xff0c;\u4f8b\u5982\u8fc7\u6ee4\u6389\u672a\u77e5\u5fae\u8c03\u793a\u4f8b&#xff0c;\u4ecd\u9700\u8981\u5728\u6d89\u53ca\u957f\u6587\u672c\u751f\u6210\u7684\u573a\u666f\u4e2d\u9a8c\u8bc1\u3002\u4e3a\u4e86\u5728\u957f\u6587\u672c\u751f\u6210\u4efb\u52a1\u4e2d\u8fc7\u6ee4\u6389\u5f15\u5165\u65b0\u4e8b\u5b9e\u77e5\u8bc6\u7684\u793a\u4f8b&#xff0c;\u9700\u8981\u5bf9 SliCK \u8fdb\u884c\u8c03\u6574&#xff0c;\u5e76\u63d0\u51fa\u4e00\u79cd\u6709\u6548\u65b9\u6cd5\u6765\u6bd4\u8f83\u91c7\u6837\u7b54\u6848\u4e0e\u771f\u5b9e\u7b54\u6848&#xff0c;\u4ee5\u8fd1\u4f3c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         Correct<\/p>\n<p>       P_{\\\\text{Correct}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Correct<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u5c06\u6b64\u7559\u5f85\u672a\u6765\u5de5\u4f5c\u3002\u957f\u6587\u672c\u751f\u6210\u4efb\u52a1\u5e26\u6765\u4e86\u8bc4\u4f30\u6311\u6218&#xff0c;\u5bfc\u81f4\u57fa\u4e8e LLM \u7684\u8bc4\u4f30\u88ab\u5e7f\u6cdb\u91c7\u7528\u3002\u6211\u4eec\u660e\u786e\u9009\u62e9\u805a\u7126\u4e8e\u95ed\u5377\u95ee\u7b54&#xff0c;\u8fd9\u6709\u52a9\u4e8e\u5b9e\u73b0\u66f4\u51c6\u786e\u7684\u8bc4\u4f30&#xff0c;\u4ece\u800c\u589e\u5f3a\u6211\u4eec\u53d1\u73b0\u7684\u53ef\u9760\u6027\u3002<\/p>\n<p>\u6700\u540e&#xff0c;\u6211\u4eec\u6ca1\u6709\u6d4b\u8bd5\u5c06\u6765\u81ea\u4e0d\u540c\u4efb\u52a1\u7684\u989d\u5916\u5fae\u8c03\u793a\u4f8b\u52a0\u5165\u5fae\u8c03\u6df7\u5408\u6570\u636e\u4e2d\u7684\u6548\u679c\u3002\u867d\u7136\u8fd9\u53ef\u80fd\u66f4\u63a5\u8fd1\u5178\u578b\u7684\u6307\u4ee4\u5fae\u8c03\u573a\u666f&#xff0c;\u4f46\u6b64\u7c7b\u6570\u636e\u96c6\u6269\u5c55\u53ef\u80fd\u4ee5\u4e0d\u53ef\u63a7\u7684\u65b9\u5f0f\u5f15\u5165\u65b0\u7684\u4e8b\u5b9e\u77e5\u8bc6&#xff0c;\u4ece\u800c\u9650\u5236\u6211\u4eec\u7684\u53d1\u73b0\u3002<\/p>\n<h2>\u5f15\u7528\u6587\u732e<\/h2>\n<p>Badr AlKhamissi, Millicent Li, Asli Celikyilmaz, Mona Diab, and Marjan Ghazvininejad. 2022. 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In Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, December 10 &#8211; 16, 2023. Chen Zhu, Ankit Singh Rawat, Manzil Zaheer, Srinadh Bhojanapalli, Daliang Li, Felix Yu, and Sanjiv Kumar. 2020. Modifying memories in transformer models. arXiv preprint arXiv:2012.00363.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations \u5728\u65b0\u77e5\u8bc6\u4e0a\u5fae\u8c03LLM\u662f\u5426\u4f1a\u52a9\u957f\u5e7b\u89c9&#xff1f; \u8bba\u6587<br \/>\n\u6458\u8981<br \/>\n\u5f53\u5927\u578b\u8bed\u8a00\u6a21\u578b\u901a\u8fc7\u76d1\u7763\u5fae\u8c03\u8fdb\u884c\u5bf9\u9f50\u65f6&#xff0c;\u5b83\u4eec\u53ef\u80fd\u4f1a\u9047\u5230\u672a\u901a\u8fc7\u9884\u8bad\u7ec3\u83b7\u5f97\u7684\u65b0\u4e8b\u5b9e\u4fe1\u606f\u3002\u4eba\u4eec\u5e38\u63a8\u6d4b&#xff0c;\u8fd9\u53ef\u80fd\u4f1a\u6559\u4f1a\u6a21\u578b\u4ea7\u751f\u4e8b\u5b9e\u4e0d\u6b63\u786e\u56de\u7b54\u7684\u5e7b\u89c9\u884c\u4e3a&#xff0c;\u56e0\u4e3a\u6a21\u578b\u88ab\u8bad\u7ec3\u751f\u6210\u5e76\u975e\u57fa\u4e8e\u5176\u5df2\u6709\u77e5\u8bc6\u7684\u4e8b\u5b9e\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d&#xff0c;\u6211\u4eec\u7814\u7a76\u8fd9\u79cd\u63a5\u89e6\u65b0\u77e5\u8bc6\u5bf9\u5fae\u8c03\u6a21<\/p>\n","protected":false},"author":2,"featured_media":115181,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[50,224,51],"topic":[],"class_list":["post-115189","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-50","tag-224","tag-51"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u3010\u5927\u6a21\u578b\u540e\u8bad\u7ec3\u3011Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/115189.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010\u5927\u6a21\u578b\u540e\u8bad\u7ec3\u3011Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations \u5728\u65b0\u77e5\u8bc6\u4e0a\u5fae\u8c03LLM\u662f\u5426\u4f1a\u52a9\u957f\u5e7b\u89c9&#xff1f; 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