Brain-HGCN: A Hyperbolic Graph Convolutional Network for Brain Functional Network Analysis

2025-09-18

AI Summary

Euclidean graph neural networks (GNNs) struggle to model the hierarchical topology of brain functional networks with low distortion, limiting their clinical diagnostic efficacy. To address this, we propose the first hyperbolic-geometry GNN framework specifically designed for brain functional networks: (i) hyperbolic graph convolution and attention mechanisms grounded in the Lorentz model; (ii) signed attention to explicitly distinguish excitatory from inhibitory functional connections; and (iii) a geometrically consistent Fréchet mean for hyperbolic graph readout. Our method pioneers the deep integration of hyperbolic representation learning with fMRI-based functional connectivity analysis. Evaluated on two large-scale resting-state fMRI datasets, it significantly outperforms state-of-the-art Euclidean GNNs in psychiatric disorder classification—achieving new SOTA performance. These results empirically validate the intrinsic advantage of hyperbolic geometry in modeling the hierarchical organization of the human brain.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Computational social science

Abstract

Functional magnetic resonance imaging (fMRI) provides a powerful non-invasive window into the brain's functional organization by generating complex functional networks, typically modeled as graphs. These brain networks exhibit a hierarchical topology that is crucial for cognitive processing. However, due to inherent spatial constraints, standard Euclidean GNNs struggle to represent these hierarchical structures without high distortion, limiting their clinical performance. To address this limitation, we propose Brain-HGCN, a geometric deep learning framework based on hyperbolic geometry, which leverages the intrinsic property of negatively curved space to model the brain's network hierarchy with high fidelity. Grounded in the Lorentz model, our model employs a novel hyperbolic graph attention layer with a signed aggregation mechanism to distinctly process excitatory and inhibitory connections, ultimately learning robust graph-level representations via a geometrically sound Fréchet mean for graph readout. Experiments on two large-scale fMRI datasets for psychiatric disorder classification demonstrate that our approach significantly outperforms a wide range of state-of-the-art Euclidean baselines. This work pioneers a new geometric deep learning paradigm for fMRI analysis, highlighting the immense potential of hyperbolic GNNs in the field of computational psychiatry.

Problem

• Modeling hierarchical brain network topology with low distortion
• Overcoming Euclidean GNN limitations for functional connectivity analysis
• Improving psychiatric disorder classification from fMRI data

Innovation

• Hyperbolic geometry models brain network hierarchy
• Signed aggregation processes excitatory and inhibitory connections
• Geometric Fréchet mean enables robust graph-level representations