用信号检测理论拆分大模型的真知与自知，发现自知能力不随准确率变化。
Do LLMs Know What They Know? Measuring Metacognitive Efficiency with Signal Detection Theory
- 将分词概率视为信心信号，用信号检测理论区分知识量与自知力
- 不同模型自知力差1.98倍，且在科技类问题最弱
- 自知力能精准预测放弃回答后的性能提升，适合评估可信推理
标准的大模型置信度评估常混淆两种能力：模型真正知道多少（类型1准确率）和其信心信号是否真实反映知识（类型2元认知敏感性）。本文引入信号检测理论，将分词级归一化对数概率作为连续信心变量，答案正确性作为待判别状态。通过分析元认知受试者工作特征曲线（z-ROC）的非等方差结构，提出无需依赖双选项任务的模型无关信息度量——归一化元认知信息（meta-I_2r）。在224,000次事实问答测试中发现：(1) 元认知信息在不同模型间差异达1.98倍，且与准确率无关（TriviaQA相关系数-0.80，Natural Questions为+0.00）；(2) 信心信号具有模型特异的非等方差结构（z-ROC斜率0.78–1.18），校准指标无法捕捉；(3) 元认知效率呈领域特异性，科技类问题最差；(4) 温度升高使准确率下降但元认知信息基本不变（三模型保持平稳）；(5) 元认知信息与基于信心弃答的准确率提升完全正相关（rho=+1.00），而准确率本身不具此预测力。所有估计均经置换检验与自助法置信区间验证。本版本修正了自动评分器的长度偏差，经1,830次人工核验确认；此前报告的准确率-效率负耦合关系在重新标注后不再成立。
原文摘要 · Abstract (English)
Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate two capacities: how much a model knows (Type-1 accuracy) and how well its confidence signal tracks that knowledge (Type-2 metacognitive sensitivity). We apply Signal Detection Theory to decompose them, treating token-level normalised log-probability as a graded confidence variable and answer correctness as the state to be discriminated. We characterise the Type-2 ROC of this signal, including its unequal-variance structure via z-ROC analysis, and -- because the meta-d' efficiency ratio is not well defined for open-ended QA, which lacks a two-alternative Type-1 decision -- quantify efficiency with a model-free information measure, normalised metacognitive information (meta-I_2r). Across four LLMs and 224,000 factual QA trials we find: (1) metacognitive information varies by a factor of 1.98 across models and is not predicted by accuracy, the rank correlation being -0.80 on TriviaQA and +0.00 on Natural Questions; (2) the confidence signal has model-specific unequal-variance structure (z-ROC slopes 0.78 to 1.18) invisible to calibration metrics, the slope ordering replicating on NQ; (3) efficiency is domain-specific, weakest in Science & Technology for every model; (4) temperature dissociates accuracy from metacognitive information, which stays near-flat for three of four models while accuracy falls; and (5) metacognitive information tracks the accuracy gain from confidence-based abstention exactly (rho = +1.00) while accuracy does not. All estimates carry permutation nulls and bootstrap confidence intervals. This version (v3) corrects a differential length bias in the automated correctness scorer, validated against 1,830 human adjudications; the inverse accuracy-efficiency coupling reported in v1 and v2 does not survive relabelling. See the version note on page 1.
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