How Uncertainty Estimation Scales with Sampling in Reasoning Models

• URL: http://arxiv.org/abs/2603.19118v1
• Date: Thu, 19 Mar 2026 16:42:05 GMT
• Title: How Uncertainty Estimation Scales with Sampling in Reasoning Models
• Abstract summary: Uncertainty estimation is critical for deploying reasoning language models.<n>We study parallel sampling as a fully black-box approach using verbalized confidence and self-consistency.
• Score: 4.9496407033305525
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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