Truth in Contrast: Calibrated Factual Evidence from Language Model Likelihoods

Large Language Models (LLMs) increasingly support decision-making in high-stakes domains, but they often hallucinate and express confidence that is misaligned with factual correctness. Response-level confidence is a coarse signal: a single generation can mix correct and incorrect statements, so a single number is not actionable for users that must accept, reject, or verify individual pieces of information. We study claim-level confidence calibration as a decision-relevant uncertainty signal: each response is decomposed into atomic, verifiable claims, and each claim is assigned a calibrated confidence using inference-time signals from consistency across samples and self-verification. Our framework operates in closed-box settings (no logits, no fine-tuning) and applies post-hoc calibration directly at the claim level, enabling selective intervention such as evidence retrieval or human review for low-confidence claims. Across TriviaQA and TruthfulQA we evaluate seven baselines on six recent models (Llama-3.1, Mistral, Qwen2.5, DeepSeek-R1, GPT-4, GPT-4o), and show that claim-level decomposition combined with post-hoc calibration reduces expected calibration error on factual questions while exposing failure modes on adversarial false-premise questions where decision-makers most need reliable uncertainty estimates.

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

Large language models (LLMs) often hallucinate in long-form generation. Existing approaches mainly improve factuality through post-hoc revision or reinforcement learning (RL) with correctness-based rewards, but they do not teach the model to estimate which parts of its generation are reliable. As a result, models may still state incorrect claims confidently in their responses. Recent advances in reasoning have significantly improved LLM performance, and have been leveraged to estimate confidence by incorporating calibration into RL objectives. However, existing approaches remain limited to a single scalar confidence for the entire response, which is insufficient for long-form generation where uncertainty varies across individual claims. To mitigate this problem, we propose CURE, a framework that improves long-form factuality by teaching LLMs to reason about uncertainty at the claim level. We first introduce a Claim-Aware Reasoning Protocol, which structures outputs into atomic claims paired with explicit confidence estimates. We then develop a multi-stage training pipeline that aligns model confidence with claims' correctness and then optimizes on factuality. The resulting calibrated confidence further enables selective prediction, allowing the model to abstain from uncertain claims at inference time. Experiments on four long-form factuality benchmarks show that CURE consistently improves factual accuracy over competitive supervised and RL baselines, while maintaining factual recall. In particular, it improves claim-level accuracy by up to 39.9% on Biography generation. These gains are accompanied by improved calibration, as reflected by a 16.0% increase in AUROC on FactBench.