TubeMLLM: A Foundation Model for Topology Knowledge Exploration in Vessel-like Anatomy

Topology is critical in tubular structures such as blood vessels, nerve fibers, and road networks, where connectivity and loop structure govern downstream functional analysis. Vision-Language Models (VLMs) are promising candidates for understanding such structures, given their reasoning and grounding capabilities. To probe their topological perception, we systematically evaluate leading closed- and open-source VLMs on localizing and classifying four canonical topological anomalies (broken/spurious connections, missing/extra branches) in tubular-network segmentation masks. They perform nearly at random, indicating that topology-aware perception is largely absent from current general-purpose VLMs. As no existing resource pairs segmentation masks with localized anomaly annotations, we build an automated, multi-domain data-curation pipeline that synthesizes diverse topological perturbations with verifiable Betti-number annotations across graduated difficulty levels, yielding the first systematic benchmark with a large-scale training set and held-out in-distribution (ID) and out-of-distribution (OOD) test suites. Building on this benchmark, we introduce Topo-R1, centered on a topology-aware composite reward that jointly scores localization, classification, and skeleton-level structural fidelity. Supervised fine-tuning cold-starts schema-compliant outputs, and Group Relative Policy Optimization (GRPO) then optimizes the policy against this reward, steering predictions toward topologically meaningful structure rather than superficial pixel overlap. Extensive experiments show that Topo-R1 substantially outperforms general-purpose VLMs and matches or exceeds supervised baselines across ID, OOD, and real-segmentation-output protocols, establishing a strong foundation for VLM-based topological understanding of structured visual data.

The advent of large-scale self-supervised learning (SSL) has produced a vast zoo of medical foundation models. However, selecting optimal medical foundation models for specific segmentation tasks remains a computational bottleneck. Existing Transferability Estimation (TE) metrics, primarily designed for classification, rely on global statistical assumptions and fail to capture the topological complexity essential for dense prediction. We propose a novel Topology-Driven Transferability Estimation framework that evaluates manifold tractability rather than statistical overlap. Our approach introduces three components: (1) Global Representation Topology Divergence (GRTD), utilizing Minimum Spanning Trees to quantify feature-label structural isomorphism; (2) Local Boundary-Aware Topological Consistency (LBTC), which assesses manifold separability specifically at critical anatomical boundaries; and (3) Task-Adaptive Fusion, which dynamically integrates global and local metrics based on the semantic cardinality of the target task. Validated on the large-scale OpenMind benchmark across diverse anatomical targets and SSL foundation models, our approach significantly outperforms state-of-the-art baselines by around 31% relative improvement in the weighted Kendall metric, providing a robust, training-free proxy for efficient model selection without the cost of fine-tuning. The code will be made publicly available upon acceptance.

Vision-language models (VLMs) are increasingly integrated into clinical workflows. However, existing benchmarks primarily assess performance on common anatomical presentations and fail to capture the challenges posed by rare variants. To address this gap, we introduce AdversarialAnatomyBench, the first benchmark comprising naturally occurring rare anatomical variants across diverse imaging modalities and anatomical regions. We call such variants that violate learned priors about "typical" human anatomy natural adversarial anatomy. Benchmarking 25 state-of-the-art VLMs with AdversarialAnatomyBench yielded three key insights. First, when queried with basic medical perception tasks, mean accuracy dropped from 71% on typical to 28% on atypical anatomy. Even the best-performing models, GPT-5, Gemini 2.5 Pro, and Llama 4 Maverick, showed performance drops of 41-51%. Second, model errors closely mirrored expected anatomical biases. Third, neither model scaling nor interventions, including bias-aware prompting and test-time reasoning, resolved these issues. These findings highlight a critical limitation in current VLMs: their poor generalization to rare anatomical presentations. AdversarialAnatomyBench provides a foundation for systematically measuring and mitigating anatomical bias in multimodal medical artificial intelligence (AI) systems.