Retrieval-Augmented Linguistic 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.

Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.

Reasoning language models are increasingly asked not only to answer difficult questions, but also to estimate their likelihood of success. Existing methods typically elicit confidence only once: either before thinking or after answering. We argue that confidence in reasoning models is state-dependent: before thinking, confidence should estimate the chance of the model correctly solving the prompt, while after thinking it should predict whether the realized answer is likely to be correct. This distinction determines the appropriate supervision target: prompt-level success should supervise confidence estimates made after seeing the prompt, while individual answer-level correctness should supervise confidence estimates made after answering. We introduce CALIBER (Calibration Before and After Reasoning), which elicits both estimates and supervises each with the target matched to its information state. Under this unified protocol, CALIBER reduces Expected Calibration Error (ECE) by 52.5% over the strongest single-confidence baseline on BigMathDigits for the 7B model, while achieving the best Brier score and AUROC, and remains within 2.1 points of the best accuracy. Further, on a larger 30B model, CALIBER achieves the best ECE on BigMathDigits while remaining competitive in Brier score and AUROC. Out of distribution, it achieves the best ECE and Brier score on GPQA and TriviaQA, and remains competitive on SimpleQA. Ablations further show that this position-target alignment is most beneficial under distribution shift where it consistently reduces calibration error across all out-of-distribution benchmarks.