Hyperbolic graph networks adapt using local topology for better predictions
Topology-Adaptive Hyperbolic Graph Attention Networks Guided by the Hyperbolic Sombor Index
Machine Learning
Summary
Graphs can represent complex relationships like social networks or hierarchies, but understanding their structure is tricky. The authors found a way to improve graph neural networks by using a special measure called the Hyperbolic Sombor Index that captures local hierarchical information. Their new method adjusts how the network learns and passes messages between nodes based on this index, leading to better performance on tasks like identifying nodes and predicting connections.
What this means in practice
- •For data engineers: Improve graph-based data models by dynamically adapting the representation to local hierarchical structures for enhanced classification and prediction accuracy.
- •For machine learning developers: Create more effective graph neural networks by incorporating topology-aware attention that better handles hierarchical and imbalanced data relationships.
Authors
Haifang Cao, Boan Tao, Xiyuan Gao, Timing Li, Yu Wang, Pengfei Zhu
Abstract
Hyperbolic geometry has emerged as a principled space for representing hierarchical graphs. However, existing hyperbolic graph neural networks typically rely on shared curvature configurations and feature-driven attention, failing to explicitly exploit local hierarchical topological patterns. To bridge this gap, we introduce the Hyperbolic Sombor Index (HSO) as a lightweight structural prior for capturing hierarchy-indicative degree stratification. Building on this, we propose \textbf{HSO-GAT}, a topology-adaptive hyperbolic graph attention network that unifies geometric adaptation and message propagation. Specifically, it comprises two complementary modules: HSO-Guided Local Curvature Adaptation, which performs adaptive node-wise geometric scaling from aggregated node-level HSO signals, and HSO-Gated Hyperbolic Graph Attention, which enables structure-aware message passing through feature-conditioned gating. Theoretically, we establish the monotonic sensitivity of edge-level HSO to degree imbalance and analyze the validity and radial scaling properties of node-adaptive hyperbolic mappings. Extensive experiments on eight benchmark datasets demonstrate that HSO-GAT consistently achieves state-of-the-art performance in both node classification and link prediction tasks.