Unified multimodal computational pathology with missing-modality robustness via Riemannian learning

Recent advances in multimodal computational pathology (CPath) have enabled the integration of pathological and molecular data. However, existing studies often rely on a single omics modality (e.g., DNA or transcriptomics), overlooking cross-layer biological dependencies and failing to effectively handle the missing-modality challenge prevalent in clinical settings. In this paper, we propose HuMP, a hyperbolic multimodal CPath framework that unifies molecular, pathological, and clinical data within a biologically motivated hierarchy. HuMP uses the coupling between negative-curvature embedding and directional entailment supervision to model cross-scale relations across molecular, histological, and clinical domains. At the molecular level, HuMP integrates genomics, transcriptomics, and proteomics through a hyperbolic aggregation module that models biological pathway interactions, while a hyperbolic entailment loss enforces a directional hierarchy from molecular to tissue to patient representations. Furthermore, to address incomplete multimodal inputs, we introduce a hierarchy-guided modality completion strategy that reconstructs missing embeddings along learned entailment paths in hyperbolic space, ensuring geometric and semantic consistency. Extensive experiments on seven public datasets and an in-house multi-center cohort show that HuMP achieves strong average performance in survival prediction and classification, while maintaining robust missing-modality behavior with a 96.6% average modality completion rate. Code is available at: https://github.com/MCPathology/HuMP .