# How Uncertainty Estimation Scales with Sampling in Reasoning Models

arXiv: https://arxiv.org/abs/2603.19118 · HTML: https://mlsanity.com/paper/2603.19118/

## Key facts

- Cited by 1 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 19 of its 22 references that are in the map.
- First posted on arXiv 19 Mar 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, 19 of 19)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [SelfCheck: Using LLMs to Zero-Shot Check Their Own Step-by-Step Reasoning](https://mlsanity.com/paper/2308.00436/) (2023)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Understanding Reasoning in Thinking Language Models via Steering Vectors](https://mlsanity.com/paper/2506.18167/) (2025)
- [Reasoning Models Better Express Their Confidence](https://mlsanity.com/paper/2505.14489/) (2025)
- [Reasoning about Uncertainty: Do Reasoning Models Know When They Don't Know?](https://mlsanity.com/paper/2506.18183/) (2025)
- [Combining Confidence Elicitation and Sample-based Methods for Uncertainty Quantification in Misinformation Mitigation](https://mlsanity.com/paper/2401.08694/) (2024)
- [Revisiting Epistemic Markers in Confidence Estimation: Can Markers Accurately Reflect Large Language Models' Uncertainty?](https://mlsanity.com/paper/2505.24778/) (2025)
- [Thinking Out Loud: Do Reasoning Models Know When They're Right?](https://mlsanity.com/paper/2504.06564/) (2025)
- [Read Your Own Mind: Reasoning Helps Surface Self-Confidence Signals in LLMs](https://mlsanity.com/paper/2505.23845/) (2025)

## Built on by (most cited first, 1 of 1)

- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)

## Abstract (arXiv)

Uncertainty estimation is critical for deploying reasoning language models, yet remains poorly understood under extended chain-of-thought reasoning. We study parallel sampling as a fully black-box approach using verbalized confidence and self-consistency. Across three reasoning models and 17 tasks spanning mathematics, STEM, and humanities, we characterize how these signals scale. Both self-consistency and verbalized confidence scale in reasoning models, but self-consistency exhibits lower initial discrimination and lags behind verbalized confidence under moderate sampling. Most uncertainty gains, however, arise from signal combination: with just two samples, a hybrid estimator improves AUROC by up to +12 on average and already outperforms either signal alone even when scaled to much larger budgets, after which returns diminish. These effects are domain-dependent: in mathematics, the native domain of RLVR-style post-training, reasoning models achieve higher uncertainty quality and exhibit both stronger complementarity and faster scaling than in STEM or humanities.