How Uncertainty Estimation Scales with Sampling in Reasoning Models

TL;DR

This paper investigates how uncertainty estimation methods like self-consistency and verbalized confidence scale with sampling in reasoning models across various domains, revealing that combining signals enhances uncertainty quality and domain-dependent differences exist.

Contribution

It provides a comprehensive analysis of uncertainty signal scaling in reasoning models, highlighting the benefits of hybrid estimators and domain-specific behaviors.

Findings

Self-consistency and verbalized confidence scale with sampling.

Hybrid estimators improve AUROC by up to 12 points.

Mathematics domain shows stronger uncertainty signals and faster scaling.

Abstract

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.