LATA: Laplacian-Assisted Transductive Adaptation for Conformal Uncertainty in Medical VLMs

Medical vision-language models (VLMs) are strong zero-shot recognizers for medical imaging, but their reliability under domain shift hinges on calibrated uncertainty with guarantees. Split conformal prediction (SCP) offers finite-sample coverage, yet prediction sets often become large (low efficiency) and class-wise coverage unbalanced-high class-conditioned coverage gap (CCV), especially in few-shot, imbalanced regimes; moreover, naively adapting to calibration labels breaks exchangeability and voids guarantees. We propose **LATA** (Laplacian-Assisted Transductive Adaptation), a training- and label-free refinement that operates on the joint calibration and test pool by smoothing zero-shot probabilities over an image-image k-NN graph using a small number of CCCP mean-field updates, preserving SCP validity via a deterministic transform. We further introduce a failure-aware conformal score that plugs into the vision-language uncertainty (ViLU) framework, providing instance-level difficulty and label plausibility to improve prediction set efficiency and class-wise balance at fixed coverage. **LATA** is black-box (no VLM updates), compute-light (windowed transduction, no backprop), and includes an optional prior knob that can run strictly label-free or, if desired, in a label-informed variant using calibration marginals once. Across three medical VLMs and nine downstream tasks, **LATA** consistently reduces set size and CCV while matching or tightening target coverage, outperforming prior transductive baselines and narrowing the gap to label-using methods, while using far less compute. Comprehensive ablations and qualitative analyses show that **LATA** sharpens zero-shot predictions without compromising exchangeability.