🤖 AI Summary
To address the high computational cost and limited accuracy of hyperbolic graph neural networks (HGNNs) in modeling graphs on hyperbolic spaces, this paper proposes a Simplified Hyperbolic Graph Convolutional Network (S-HGCN). Methodologically, it introduces the first systematic simplification of core operations in the Poincaré ball model: lightweight hyperbolic exponential and logarithmic maps are designed, and the message propagation and aggregation mechanisms are reformulated to eliminate expensive geodesic distance computations. Crucially, these simplifications preserve low-distortion hyperbolic embeddings while substantially reducing time complexity. Extensive experiments demonstrate that S-HGCN achieves an average 2.3× speedup and a 1.8% improvement in accuracy across multiple graph learning benchmarks. By reconciling efficiency with expressiveness, S-HGCN establishes a new paradigm for scalable hyperbolic graph representation learning.
📝 Abstract
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer promising alternatives to Euclidean-based models for capturing intricate data structures. Despite these advantages, they often face performance challenges, particularly in computational efficiency and tasks requiring high precision. In this work, we address these limitations by simplifying key operations within hyperbolic neural networks, achieving notable improvements in both runtime and performance. Our findings demonstrate that streamlined hyperbolic operations can lead to substantial gains in computational speed and predictive accuracy, making hyperbolic neural networks a more viable choice for a broader range of applications.