Navigating Hierarchy: Hyperbolic Learning on Brain Graphs for Disorder Diagnosis

2026-07-08

AI Summary

Existing brain graph modeling approaches struggle to effectively capture the multi-level hierarchical structure among regions of interest (ROIs), functional communities, and the whole-brain network, limiting both brain network representation capacity and diagnostic performance for psychiatric disorders. To address this, this work proposes the Hyperbolic Latent Brain Graph (HLBG) learning framework, which introduces hyperbolic geometry into multi-scale brain network modeling for the first time. By leveraging Lorentzian hyperbolic space embeddings, HLBG explicitly encodes ROI–community–whole-brain hierarchical relationships through geometric inductive constraints, while integrating a graph topology-aware Mamba model (GaMamba) to capture long-range dependencies. The method significantly outperforms state-of-the-art approaches on the ABIDE-I and REST-MDD datasets and successfully identifies key functional biomarkers associated with psychiatric disorders.

Abstract

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.

Problem

• brain graphs
• hierarchical organization
• ROI-community interactions
• disorder diagnosis
• functional brain networks

Innovation

• hyperbolic learning
• brain graph hierarchy
• Lorentzian space
• Graph-aware Mamba
• functional biomarkers