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This paper introduces Hyperbolic Learning on Brain Graphs (HLBG), a novel framework that leverages hyperbolic geometry to model the hierarchical relationships among regions of interest (ROIs), functional communities, and whole-brain networks for improved brain disorder diagnosis. By projecting brain network representations into Lorentzian hyperbolic space and imposing geometric entailment constraints, HLBG effectively captures ROI-community interactions and enhances the discriminative power of brain network representations. Experiments on ABIDE-I and REST-MDD datasets reveal that HLBG significantly outperforms existing methods and successfully identifies functional biomarkers relevant to brain disorders.
Hyperbolic geometry can unlock new diagnostic insights in brain disorders by revealing hidden hierarchical relationships within brain networks.
Functional brain networks exhibit a hierarchical organization across ROI, community, and whole-brain levels, supporting local processing, inter-community coordination, and global integration. Recent studies have demonstrated that brain community-aware modeling is beneficial for both diagnosis and biomarker identification of brain networks. However, existing brain graph modeling methods often struggle to model ROI-community interactions, thereby failing to fully exploit the hierarchy across ROI, community, and whole-brain network levels. To address this issue, inspired by deep hyperbolic learning in modeling hierarchical structures, we propose a novel framework, termed Hyperbolic Learning on Brain Graphs (HLBG), for brain network analysis. The core idea of HLBG is to exploit the inherent hierarchical geometry of hyperbolic space to model the hierarchical relationships among ROIs, functional communities, and the whole-brain network, thereby learning hierarchy-aware and highly discriminative representations for brain network data. Specifically, HLBG first projects representations from ROIs, communities, and the whole-brain network into Lorentzian hyperbolic space. Then, the multi-level hierarchy is imposed via two geometric entailment constraints. In addition, we introduce a new Graph-aware Mamba (GaMamba) model, which incorporates topology-derived structural prompts into Mamba to capture long-range dependencies while preserving graph topological information. Experiments on ABIDE-I and REST-MDD demonstrate that HLBG outperforms state-of-the-art methods and identifies disorder-relevant functional biomarkers.
