Best-of-Evidence: Best-of-N Selection under Partial Verification

BoN improves model outputs by sampling several candidates and selecting one with a proxy score, but it assumes that complete candidates can be evaluated reliably. Many vision-language tasks instead provide only partial verification: a finding, span, value, region, or relation may be checkable even when no dependable whole-response verifier exists. Moreover, the same claim may recur across candidates with opposing stances, allowing one observation to support part of the pool and contradict another. We introduce Best-of-Evidence (BoE), an inference-time selection framework that keeps the BoN candidate pool fixed, represents reusable claims with a signed candidate--factor graph, and allocates a limited budget to evidence actions that can change the final choice. BoE formalizes selection under partial verification and provides a practical score-based controller, with the zero-budget case recovering the underlying BoN decision. Theoretically, we show that residual evidence capacity limits any evidence-driven improvement and that shared factor queries can achieve an O(log K) versus Θ(K) query separation in a factor-code model. Common-ledger experiments on four medical VQA settings show that BoE can improve fixed-pool selection and rescue some BoN failures when evidence is reliable, contrastive, and decision-relevant, while also revealing the channel-quality and candidate-generation limits that prevent universal gains.

MedCore: Boundary-Preserving Medical Core Pruning for MedSAM

Medical segmentation foundation models such as SAM and MedSAM provide strong prompt-driven segmentation, but their image encoders are still too large for many clinical settings. Compression is also risky in medicine because a model can keep high Dice while losing boundary fidelity. We propose MedCore, a structured pruning framework for MedSAM. The main idea is to preserve two kinds of structures: structures that became important during SAM-to-MedSAM adaptation, and structures that have high boundary leverage. We identify the first type by a dual-intervention score that compares zeroing a group with resetting it to its original SAM weight. We identify the second type by boundary-aware Fisher estimation. We also introduce a boundary leverage principle, which shows that compression-induced boundary displacement is controlled by logit perturbation on the boundary divided by the logit spatial gradient. This principle explains why boundary metrics can degrade even when Dice remains high. On polyp segmentation benchmarks, MedCore reduces parameters by 60.0% and FLOPs by 58.4% while achieving Dice 0.9549, Boundary F1 0.6388, and HD95 5.14 after recovery fine-tuning. It also reaches 86.6% parameter reduction and 90.4G FLOPs with strong boundary quality. Our analysis further shows that MedSAM lies in a head-fragile boundary regime: head-pruning steps have 2.887 times larger 95th-percentile boundary leverage than MLP-pruning steps, and this logit-level effect is consistent with BF1 and HD95 degradation. Our code is available at https://github.com/cenweizhang/MedCore.

Axiomatic On-Manifold Shapley via Optimal Generative Flows

Shapley-based attribution is critical for post-hoc XAI but suffers from off-manifold artifacts due to heuristic baselines. While generative methods attempt to address this, they often introduce geometric inefficiency and discretization drift. We propose a formal theory of on-manifold Aumann-Shapley attributions driven by optimal generative flows. We prove a representation theorem establishing the gradient line integral as the unique functional satisfying efficiency and geometric axioms, notably reparameterization invariance. To resolve path ambiguity, we select the kinetic-energy-minimizing Wasserstein-2 geodesic transporting a prior to the data distribution. This yields a canonical attribution family that recovers classical Shapley for additive models and admits provable stability bounds against flow approximation errors. By reframing baseline selection as a variational problem, our method experimentally outperforms baselines, achieving strict manifold adherence via vanishing Flow Consistency Error and superior semantic alignment characterized by Structure-Aware Total Variation. Our code is on https://github.com/cenweizhang/OTFlowSHAP.