Navigating Hierarchy: Hyperbolic Learning on Brain Graphs for Disorder Diagnosis

Functional brain networks are organized hierarchically, from individual regions of interest (ROIs) to functional communities and the whole-brain network. Existing graph neural networks often struggle to capture these multi-level interactions and the long-range dependencies necessary for accurate disorder diagnosis. This paper asks whether modeling brain graphs in hyperbolic space—which is naturally suited for hierarchical structures—can improve the discriminative power of brain network representations for conditions like autism and major depressive disorder.

The authors propose the Hyperbolic Learning on Brain Graphs (HLBG) framework. The approach consists of three main components:

1. Hierarchical Graph Construction: The brain is partitioned into ROIs and functional communities, creating a multi-level graph structure.
2. Graph-aware Mamba (GaMamba): A novel module that integrates topology-derived structural prompts into the Mamba state-space model. This allows the model to capture long-range dependencies while preserving the specific topological information of the brain graph.
3. Hierarchical Representation Learning: ROI, community, and whole-brain representations are projected into Lorentzian hyperbolic space. The model then applies geometric entailment constraints to ensure the learned embeddings reflect the hierarchical relationships (ROI → community → whole-brain).

HLBG demonstrates superior performance in classifying brain disorders on the ABIDE-I and REST-MDD datasets compared to state-of-the-art GNN and Transformer-based methods. By explicitly modeling the hierarchical geometry of the brain, the framework produces more discriminative representations and successfully identifies functional biomarkers relevant to the studied disorders. The integration of GaMamba allows for efficient, topology-aware feature extraction that balances local community details with global brain integration.