Hyperbolic Vision-Language Model for Pathological Patch-Slide Representation

Gigapixel whole-slide image (WSI) analysis requires capturing localized pathological evidence at the patch level and integrating these fine-grained cues into a slide-level representation. Although slide-level foundation models automate holistic tissue analysis, their Euclidean representations discard feature-norm information during normalization and patch aggregation, even though this information could help organize hierarchical relationships and retain clinically meaningful fine-grained spatial cues. In this work, we propose HYPERION, a hyperbolic vision-language model for pathological patch-slide representation that leverages the inherent norm structure of pretrained Euclidean foundation models. HYPERION constructs text-conditioned Einstein midpoints over patch embeddings to summarize the patches most similar to each caption and uses entailment cones to enforce hierarchical inclusion among caption, midpoint, and slide representations. Confidence-filtered caption-patch correspondences provide pseudo-labeled patch-level contrastive supervision from slide-level normal or abnormal labels, while intermediate feature norms are propagated to the radii of final patch embeddings to expose norm information. In zero-shot tumor segmentation, HYPERION has the highest Dice on five benchmarks, while prediction evaluations show that HYPERION preserves or enhances pathological knowledge. Integrated into a WSI multimodal large language model, HYPERION improves overall report-generation metrics and yields more lesion-focused visual grounding in qualitative analyses, verifying the utility of hyperbolic patch-slide representations for pathology.