Geometry-Calibrated Conformal Abstention for Language Models

Large Language Models remain plagued by hallucinations. Recent work has sought to tame their prevalence using statistical techniques based on conformal prediction, with both theoretical and empirical success. However, these methods operate in a post-hoc fashion, treating the sampling procedure itself as atomic and then surgically altering samples to remove hallucinated claims. This disconnect between filtering and generation can result in samples that are incoherent, inconsistent, or simply unlikely under the model itself. Moreover, post-hoc surgery is unable to shift probability mass towards more useful and helpful responses. To address these issues, we propose to instead sample from approximations to an LLM posterior, where the conditioning event corresponds to a calibrated, high-scoring region. We develop a calibration procedure tailored to the setting of conditional sequential generation that effectively identifies this region and achieves target risk control. Empirically, we apply our method to case studies focused on open-ended biography generation and mathematical problem solving; compared to prior work, we obtain the same statistical guarantees, with higher downstream utility.

Reinforcement fine-tuning improves the reasoning ability of large language models, but it can also encourage them to answer unanswerable queries by guessing or hallucinating missing information. Existing abstention methods either train models to produce generic refusals or encourage follow-up clarifications without verifying whether those clarifications identify the key missing information. We study queries that are clear in meaning but cannot be reliably resolved from the given information, and argue that a reliable model should not only abstain, but also explain what is missing. We propose a clarification-aware RLVR reward that, while rewarding correct answers on answerable queries, jointly optimizes explicit abstention and semantically aligned post-refusal clarification on unanswerable queries. Using this reward, we train Abstain-R1, a 3B model that improves abstention and clarification on unanswerable queries while preserving strong performance on answerable ones. Experiments on Abstain-Test, Abstain-QA, and SelfAware show that Abstain-R1 substantially improves over its base model and achieves unanswerable-query behavior competitive with larger systems including DeepSeek-R1, suggesting that calibrated abstention and clarification can be learned through verifiable rewards rather than emerging from scale alone.

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.