H2-Surv: Hierarchical Hyperbolic Multimodal Representation Learning for Survival Prediction

Cancer survival prediction through histopathologygenomics integration is a promising direction, yet existing methods face three major limitations. First, existing Euclidean space-based methods struggle to capture the inherent hierarchical structures in histopathology (patient → WSIs → patches) and genomics (patient → pathways → genes). Second, most methods overlook the cross-modal encompassing relationship-where abstract genomic patterns encompass diverse morphological phenotypes-leading to suboptimal multimodal fusion. Third, existing methods often discretize survival times into coarse risk intervals, overlooking fine-grained ordinal relationships among patients within the same interval. Such discretization disrupts the continuity of survival outcomes and hinders the model's ability to learn accurate risk rankings. To address these challenges, we propose H 2 -Surv, a hyperbolic hierarchical multimodal learning framework for survival prediction. H 2 -Surv first embeds multimodal features into hyperbolic space through the Hyperbolic Mapping (HyMap) module, enabling effective representation of hierarchical structures. A subsequent Hyperbolic Hierarchical Modeling (H 2 M) module captures intra-modal hierarchies and the encompassing relationships between modalities. Finally, the Temporal Ordinal Contrastive Learning (TOCL) module models the temporal progression of survival outcomes by enforcing ordinal risk consistency through contrastive learning, ensuring continuity in risk prediction. Extensive experiments on six benchmarks from TCGA and CPTAC demonstrate that H 2 -Surv consistently outperforms stateof-the-art multimodal survival prediction methods. Source code will be released upon acceptance.