IntroConformal: Conformal Factuality Guarantees for Large Vision-Language Models via Introspective Signals

Large language models (LLMs) increasingly perform multi-step reasoning, where intermediate claims form implicit directed acyclic graphs whose node correctness is structurally conditioned on their ancestors. This makes factuality uncertainty structural, rather than a trivial accumulation of node-wise errors, and necessitates inference-time uncertainty quantification over the reasoning structure. While conformal prediction (CP) offers flexible user-specified factuality control, existing work remains post-hoc and cannot intervene during generation. To fill the gap between CP's flexibility and its post-hoc limitation, we propose an \emph{Inference-Time Conformal Reasoning (ITCR)} framework that integrates CP directly into reasoning graph generation. ITCR learns a structure-level factuality uncertainty function that aggregates claim-level factuality signals over reasoning graphs without complex modeling assumptions. We then design the non-conformity score based on graph-level factuality uncertainty and calibrate the conformal threshold to decide when to stop generation. We theoretically show such generation is nested, yielding valid coverage guarantees for factuality control. Experiments over multiple datasets and coverage objectives demonstrate empirically valid coverage. In downstream reasoning tasks, inference-time calibrated graphs yield more accurate generation than post-hoc pruned graphs.

Large Language Models (LLMs) frequently hallucinate, limiting their reliability in critical applications. Conformal Prediction (CP) addresses this by calibrating error rates on held-out data to provide statistically valid confidence guarantees. Recent work extends CP to LLM factuality to filter out risky claims, ensuring that hallucination rates remain below a user-specified level (e.g., 10%). While prior methods treat claims independently, Coherent Factuality extends to multi-step reasoning by representing outputs as dependency graphs and jointly validating claims with their logical ancestors. A key limitation is that Coherent Factuality is not differentiable, requiring hand-crafted scorers that at high reliability levels remove nearly 60% of true claims. We introduce Differentiable Coherent Factuality (DCF), a fully differentiable relaxation that enables learning improved scorers while provably recovering the original algorithm's guarantees. Experiments on two benchmark reasoning datasets demonstrate DCF achieves up to 141% improvement in claim retention while maintaining reliability guarantees, representing a significant step towards reliable conformal LLM systems.

Large vision-language models (LVLMs) hallucinate: they assert visual details that the image does not support. A principled remedy is selective prediction with a distribution-free guarantee-verify each claim and abstain when the claim is not grounded, so that the hallucination rate among asserted claims is provably bounded. We show, however, that this guarantee is bought at a brutal price: to keep the hallucination rate below $5\%$ on a balanced object-existence benchmark, a state-of-the-art conformal filter must abstain on more than $80\%$ of claims. We argue that abstention is wasteful when more visual evidence is cheaply available, and introduce Budgeted Conformal Evidence Acquisition (BCEA), which replaces the binary answer/abstain decision with a three-way choice: answer, abstain, or acquire additional visual evidence by re-examining the image (zooming, cropping, or applying a claim-specific intervention) under a bounded compute budget. We make two observations. First, acquisition that is plugged naively into a calibrated filter breaks the statistical guarantee -- realized risk overshoots the target by up to $17$ points -- because the acquisition step destroys the exchangeability that conformal calibration relies on. Second, folding the entire acquisition policy into the score function and re-calibrating on post-acquisition scores \emph{restores} the finite-sample guarantee while still recovering coverage. BCEA further uses structured, claim-type-specific interventions. Across the POPE benchmark and COCO-constructed existence and spatial-relation claims, on four open VLMs, BCEA controls the hallucination rate at the target level and consistently improves coverage over a guaranteed-abstention baseline.