Less Data Approximates More: Earning Faithful Confidence in High-Stakes Domains

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Large language models have made strong reasoning gains through supervised fine-tuning, reinforcement learning, and on-policy distillation, yet these post-training methods are usually evaluated only by final-answer accuracy. We study how they reshape confidence during reasoning. We introduce a three-stage calibration framework that evaluates confidence before, during, and after chain-of-thought generation, corresponding to difficulty estimation, early termination, and answer aggregation. Through a controlled comparison on mathematical reasoning benchmarks, we find that OPD provides the most useful pre-reasoning confidence, SFT gives the strongest online signal for early stopping, and RL produces the most reliable trace-level signal for aggregation. We further show that confidence reliability is position-dependent: RL confidence becomes informative after a path-commitment phase, while OPD confidence is useful early but can become inversely calibrated later. Based on this observation, we propose PosConf, a position-aware confidence strategy that uses confidence only from reliable relative-position intervals. PosConf improves RL answer aggregation by 6.1 points over majority voting and consistently improves OPD early stopping under tight token budgets, with gains up to 4.3 points by avoiding its later inverse-calibration region, showing that \emph{confidence in reasoning models should be used both stage-wise and position-awarely}. Our code is available at https://github.com/EIT-NLP/Post-Training-Calibration.

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.