# Quantifying Faithful Confidence Expression in Large Reasoning Models

arXiv: https://arxiv.org/abs/2606.03969 · HTML: https://mlsanity.com/paper/2606.03969/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 32 of its 71 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [A Comprehensive Survey of Hallucination Mitigation Techniques in Large Language Models](https://mlsanity.com/paper/2401.01313/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [MuSR: Testing the Limits of Chain-of-thought with Multistep Soft Reasoning](https://mlsanity.com/paper/2310.16049/) (2023)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [Reasoning Models Better Express Their Confidence](https://mlsanity.com/paper/2505.14489/) (2025)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [Evaluating Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2512.15567/) (2025)
- [ConfTuner: Training Large Language Models to Express Their Confidence Verbally](https://mlsanity.com/paper/2508.18847/) (2025)
- [Trust Me, I'm Wrong: LLMs Hallucinate with Certainty Despite Knowing the Answer](https://mlsanity.com/paper/2502.12964/) (2025)
- [CER: Confidence Enhanced Reasoning in LLMs](https://mlsanity.com/paper/2502.14634/) (2025)
- [MetaFaith: Faithful Natural Language Uncertainty Expression in LLMs](https://mlsanity.com/paper/2505.24858/) (2025)
- [Thought Branches: Interpreting LLM Reasoning Requires Resampling](https://mlsanity.com/paper/2510.27484/) (2025)
- [Multiple Choice Questions: Reasoning Makes Large Language Models (LLMs) More Self-Confident, Especially When They are Wrong](https://mlsanity.com/paper/2501.09775/) (2025)
- [Verbalized Confidence Triggers Self-Verification: Emergent Behavior Without Explicit Reasoning Supervision](https://mlsanity.com/paper/2506.03723/) (2025)
- [Advancing the Scientific Method with Large Language Models: From Hypothesis to Discovery](https://mlsanity.com/paper/2505.16477/) (2025)
- [Teaching Language Models to Faithfully Express their Uncertainty](https://mlsanity.com/paper/2510.12587/) (2025)
- [Reasoning Models Will Sometimes Lie About Their Reasoning](https://mlsanity.com/paper/2601.07663/) (2026)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [LLMs Should Express Uncertainty Explicitly](https://mlsanity.com/paper/2604.05306/) (2026)
- [Do explanations generalize across large reasoning models?](https://mlsanity.com/paper/2601.11517/) (2026)
- [Recurrent Confidence Chain: Temporal-Aware Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2601.13368/) (2026)
- [Demystifying Scientific Problem-Solving in LLMs by Probing Knowledge and Reasoning](https://mlsanity.com/paper/2508.19202/) (2025)
- [Confidence over Time: Confidence Calibration with Temporal Logic for Large Language Model Reasoning](https://mlsanity.com/paper/2601.13387/) (2026)

## Built on by (most cited first, 2 of 2)

- [Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs](https://mlsanity.com/paper/2606.32032/) (2026)
- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)

## Abstract (arXiv)

Reliable uncertainty communication is critical to the trustworthiness of LLMs, yet faithful calibration (FC)--the alignment between models' intrinsic and (linguistically) expressed confidence--is a persistent failure mode. This challenge is key for large reasoning models (LRMs), whose extended reasoning traces are often interpreted by users as evidence of deliberation, competence, and confidence. Despite the importance of FC and wide usage of LRMs, the extent to which LRMs can faithfully express their confidence remains poorly understood. Moreover, the prevailing paradigm to measure FC does not generalize well to the long chain-of-thought outputs generated by LRMs, which tend to lack clear step boundaries, involve inconsistent step structure, and encode complex conditional dependencies throughout the trace--complicating estimation of intrinsic confidence. To address this challenge, we introduce a novel framework to systematically quantify FC of LRMs. Our framework analyzes linguistic decisiveness relative to three sources of internal uncertainty, based on token probabilities, hidden states, and sampled response consistency. We also devise a prefix-conditioned sampling approach to control for conditional and structural variation across traces. Applying our framework to a diverse suite of leading models, datasets, and prompts, we find that faithful confidence expression is a significant challenge for LRMs. Reasoning behaviors do not automatically translate to improved FC, and prompt interventions for non-reasoning models do not improve faithfulness in the reasoning setting. Different confidence estimators further produce divergent assessments of the same traces, revealing fragility in prior evaluation methodologies. Taken together, our work establishes FC as a distinct reliability and alignment target for LRMs, particularly as such systems are increasingly deployed in high-stakes contexts.