# Do LLMs Know What They Know? Measuring Metacognitive Efficiency with Signal Detection Theory

arXiv: https://arxiv.org/abs/2603.25112 · HTML: https://mlsanity.com/paper/2603.25112/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Metacognition and Uncertainty Communication in Humans and Large Language Models](https://mlsanity.com/paper/2504.14045/) (2025)
- [LLMs as Signal Detectors: Sensitivity, Bias, and the Temperature-Criterion Analogy](https://mlsanity.com/paper/2603.14893/) (2026)

## Built on by (most cited first, 6 of 6)

- [Do Coding Agents Understand Least-Privilege Authorization?](https://mlsanity.com/paper/2605.14859/) (2026)
- [The Metacognitive Monitoring Battery: A Cross-Domain Benchmark for LLM Self-Monitoring](https://mlsanity.com/paper/2604.15702/) (2026)
- [Measuring (some aspects of) the metacognition of AI](https://mlsanity.com/paper/2603.29693/) (2026)
- [Before You Interpret the Profile: Validity Scaling for LLM Metacognitive Self-Report](https://mlsanity.com/paper/2604.17707/) (2026)
- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)
- [MEDLEY-BENCH: Benchmarking Behavioural Metacognition and Belief Revision Under Social Pressure in Large Language Models](https://mlsanity.com/paper/2604.16009/) (2026)

## Abstract (arXiv)

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.