Localized Conformal Prediction for Image Classification with Vision-Language Models

Conformal prediction (CP) gives distribution-free coverage for modern vision and language models, but it is often forced to make a ranking decision from a single unstable nonconformity score. Standard CP uses one realization, while average-then-calibrate variants smooth multiple realizations into a point estimate. Both options discard the inconsistency that can help identify whether a candidate is indeed stable. A weak answer can enter the conformal set even if the evidence is not strong, simply because one posterior sample or prompt phrasing made it look strong. But variability can help distinguish a stable signal from noise-driven fluctuations. We describe an empirical Bayes conformal prediction framework that uses $r$-values to convert score variability into an uncertainty informed nonconformity score. The resulting $r$-value estimates how likely a candidate's latent score belongs to the top-ranked group after accounting for both its mean score and its uncertainty. It admits both a closed-form Normal-Normal empirical Bayes estimator and a nonparametric posterior-sampling estimator. Using the $r$-value as the nonconformity score preserves the target conformal coverage while provably reducing the inclusion of high variance false candidates under mild regularity conditions. Across image classification, CLIP-based VLM benchmarks, and LLMs, we show that $r$-value conformal prediction preserves target coverage while improving ranking stability and reducing set size when variability is informative, and reverting to CP-like behavior when variability vanishes.

Medical vision-language models (VLMs) can retain high observed marginal coverage after clinical shift while substantially under-covering an individual disease class. The affected class varies with acquisition protocol and backbone geometry, so source prevalence does not reliably reveal the failure. Existing localized and tail-aware conformal methods respectively adapt to test neighborhoods and source-frequency tails, leaving held-out class-wise coverage failure unmodeled. We introduce Class-Tail Adaptive Localized Conformal Deferral (CALCoDe), a post-hoc reliability layer for frozen medical VLMs. Cross-fitted validation predictions identify classes at risk of undercoverage, and a disjoint calibration split estimates their class-conditional tail thresholds. CALCoDe combines each protected threshold with a localized conformal threshold using a one-sided maximum. The resulting set contains every label admitted by the localized rule, with additional protection confined to validation-identified classes. An independently calibrated support audit defers cases with insufficient inlier support. Under exchangeability among accepted examples within each protected class, CALCoDe provides finite-sample coverage at the prespecified guard level and contains the corresponding localized conformal sets; coverage on shifted external cohorts is evaluated empirically. Among standard conformal baselines and recent VLM-specific conformal methods evaluated across two dermatology shifts (HAM10000 to ISIC 2019 and HAM10000 to PAD-UFES-20) and four frozen VLM backbones (BiomedCLIP, OpenAI CLIP ViT-B/32, PubMedCLIP ViT-B/32, and MedSigLIP-448), CALCoDe is the only approach whose observed marginal and worst-class accepted coverage both reach 0.95 in all eight settings. On HAM10000 to ISIC 2019, its average worst-class accepted coverage is 0.970, compared with 0.926 for sTACP and 0.864 for LCP-VLM.

Vision-language models (VLMs) are increasingly used as automated judges for multimodal systems, yet their scores provide no indication of reliability. We study this problem through conformal prediction, a distribution-free framework that converts a judge's point score into a calibrated prediction interval using only score-token log-probabilities, with no retraining. We present the first systematic analysis of conformal prediction for VLM-as-a-Judge across 3 judges and 14 visual task categories. Our results show that evaluation uncertainty is strongly task-dependent: intervals cover ~40% of the score range for aesthetics and natural images but expand to ~70% for chart and mathematical reasoning, yielding a quantitative reliability map for multimodal evaluation. We further identify a failure mode not captured by standard evaluation metrics, ranking-scoring decoupling, where judges achieve high ranking correlation while producing wide, uninformative intervals, correctly ordering responses but failing to assign reliable absolute scores. Finally, we show that interval width is driven primarily by task difficulty and annotation quality, i.e., the same judge and method yield 4.5x narrower intervals on a clean, multi-annotator captioning benchmark. Code: https://github.com/divake/VLM-Judge-Uncertainty