How Uncertainty Estimation Scales with Sampling in Reasoning Models

Vision-language models (VLMs) are increasingly deployed in high-stakes settings where reliable uncertainty quantification (UQ) is as important as predictive accuracy. Extended reasoning via chain-of-thought (CoT) prompting or reasoning-trained models has become ubiquitous in modern VLM pipelines, yet its effect on UQ reliability remains poorly understood. Our results show that reasoning tends to degrade the quality of many uncertainty estimates, even when it improves task accuracy. We identify implicit answer conditioning as the primary mechanism: as reasoning traces converge on a conclusion before the final answer is generated, token probabilities increasingly reflect consistency with the model's own reasoning trace rather than uncertainty about correctness. In effect, the model becomes overconfident in its answer. In contrast, agreement-based consistency remains robust and often improves under reasoning, making it a practical choice for uncertainty estimation in reasoning-enabled VLMs.

Uncertainty estimation for reasoning language models remains difficult to deploy in practice: sampling-based methods are computationally expensive, while common single-pass proxies such as verbalized confidence or trace length are often inconsistent across models. This problem is compounded for proprietary reasoning APIs that expose neither logits nor intermediate token probabilities, leaving practitioners with no reliable uncertainty signal at inference time. We propose SELFDOUBT, a single-pass uncertainty framework that resolves this impasse by extracting behavioral signals directly from the reasoning trace itself. Our key signal, the Hedge-to-Verify Ratio (HVR), detects whether a reasoning trace contains uncertainty markers and, if so, whether they are offset by explicit selfchecking behavior. Unlike methods that require multiple sampled traces or model internals, SELFDOUBT operates on a single observed reasoning trajectory, making it suitable for latency- and cost-constrained deployment over any proprietary API. We evaluate SELFDOUBT across seven models and three multi-step reasoning benchmarks (BBH, GPQA-Diamond, and MMLU-Pro). Most notably, traces containing no hedging markers are correct 96% of the time, revealing an emergent high-precision confidence gate at zero additional cost. For the remaining cases, the full SELFDOUBT score significantly outperforms sampling-based semantic entropy at 10x lower inference cost. A deployment cascade combining both stages attains 90% accuracy at 71% coverage without any task-specific labels. These results establish SELFDOUBT as a scalable, production-ready foundation for uncertainty estimation over proprietary reasoning models.

Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient because easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB), a concave integer optimization framework that reallocates a fixed sampling budget using uncertainty estimated from the initial samples themselves. In Phase-1, every question receives a small fixed number of generations. Their answer disagreement, measured by vote entropy, provides a difficulty signal while these generations contribute to the final vote. In Phase-2, the remaining budget is allocated by a marginal-greedy algorithm that optimally solves a concave coverage-maximization surrogate, concentrating samples on questions whose initial answers disagree. Across five open-weight models (1.5B--27B parameters) and five reasoning benchmarks of varying difficulty, UAB improves average accuracy by $+2.3\%$ over uniform allocation, and achieves gains of up to $+5.5\%$ on individual benchmarks, with the largest gains in low-resource settings. Moreover, UAB meets the target budget exactly and requires no auxiliary model or additional LLM calls. Code is publicly available at https://github.com/manhitv/UAB.