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

arXiv: https://arxiv.org/abs/2509.14965 · HTML: https://mlsanity.com/paper/2509.14965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networks](https://mlsanity.com/paper/2204.07054/) (2022)
- [HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning](https://mlsanity.com/paper/2507.17402/) (2025)
- [MM-GTUNets: Unified Multi-Modal Graph Deep Learning for Brain Disorders Prediction](https://mlsanity.com/paper/2406.14455/) (2024)
- [RTGMFF: Enhanced fMRI-based Brain Disorder Diagnosis via ROI-driven Text Generation and Multimodal Feature Fusion](https://mlsanity.com/paper/2509.03214/) (2025)

## Built on by (most cited first, 1 of 1)

- [Geodesic Prototype Matching via Diffusion Maps for Interpretable Fine-Grained Recognition](https://mlsanity.com/paper/2509.17050/) (2025)

## Abstract (arXiv)

Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these hierarchical structures without high distortion due to inherent spatial constraints. We propose Brain-HGCN, a geometric deep learning framework based on hyperbolic geometry, which leverages negatively curved space to model brain network hierarchy with high fidelity. Grounded in the Lorentz model, our framework employs a novel hyperbolic graph attention layer with a signed aggregation mechanism to distinctly process excitatory and inhibitory connections. Furthermore, we learn robust graph-level representations via a geometrically principled Fr'echet mean for graph readout. Experiments on two large-scale fMRI datasets for psychiatric disorder classification demonstrate that Brain-HGCN significantly outperforms state-of-the-art Euclidean baselines. This work highlights the potential of hyperbolic GNNs in computational psychiatry by pioneering a new geometric paradigm for fMRI analysis.