# Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs

arXiv: https://arxiv.org/abs/2606.32032 · HTML: https://mlsanity.com/paper/2606.32032/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 51 of its 131 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 51)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Taming Overconfidence in LLMs: Reward Calibration in RLHF](https://mlsanity.com/paper/2410.09724/) (2024)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2505.12346/) (2025)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [Alignment for Honesty](https://mlsanity.com/paper/2312.07000/) (2023)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [Linguistic Calibration of Long-Form Generations](https://mlsanity.com/paper/2404.00474/) (2024)
- [Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2504.12501/) (2025)
- [A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice](https://mlsanity.com/paper/2410.15326/) (2024)
- [Rewarding Doubt: A Reinforcement Learning Approach to Calibrated Confidence Expression of Large Language Models](https://mlsanity.com/paper/2503.02623/) (2025)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [Benchmarking Hallucination in Large Language Models based on Unanswerable Math Word Problem](https://mlsanity.com/paper/2403.03558/) (2024)
- [Evaluating Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2512.15567/) (2025)

## Built on by (most cited first, 4 of 4)

- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)
- [Learning to Stop without Learning to Stop: Self-Supervised Confidence Training Improves Reasoning Efficiency](https://mlsanity.com/paper/2609.31619/) (2026)
- [Calibration, Not Answer Selection: Distilling Internal Confidence in Reasoning Models](https://mlsanity.com/paper/2609.33290/) (2026)
- [Referential Uncertainty in Human--AI Collaboration](https://mlsanity.com/paper/2609.39518/) (2026)

## Abstract (arXiv)

Metacognition is a critical component of intelligence that describes the ability to monitor and regulate one's own cognitive processes. Yet LLMs exhibit systemic deficiencies in key metacognitive faculties: they hallucinate with high confidence, fail to recognize knowledge boundaries, and misrepresent their internal uncertainty--undermining trustworthiness and reliability. Since monitoring task performance and adapting behavior accordingly are central to metacognition, we posit that models capable of accurately judging their own performance are better positioned to improve it. We operationalize this idea via two novel mechanisms: reinforcement learning with metacognitive feedback (RLMF), a paradigm to refine completion rankings during preference optimization based on the quality of a model's self-judgments of performance, and metacognitive data selection, which uses similar self-judgments to identify high-value training examples, outperforming naive active learning. We apply these innovations to the problem of faithful calibration (FC), a task that is itself fundamentally metacognitive: the goal is to align expressed with intrinsic uncertainty, difficult even for frontier LLMs. We adopt a two-stage, decoupled approach, first using these methods to calibrate the faithfulness of models' self-reported confidence scores, then mapping to natural, context-adaptable linguistic uncertainty via targeted output editing. Extensive experiments show RLMF achieves generalizable, state-of-the-art FC on diverse tasks while preserving accuracy. Further, RLMF surpasses standard RL by up to 63% while enhancing models' ability to assess and express their own capability limits. This positions RLMF as a promising paradigm to enhance LLM metacognition toward improved abilities and alignment, and suggests metacognitive performance as an effective RL signal to overcome limits of prior intrinsic feedback methods.