sHGCN: Simplified hyperbolic graph convolutional neural networks

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. Recent datasets with complex geometric structures have highlighted the limitations of traditional Euclidean spaces in capturing hierarchical or tree-like data found in domains like complex networks (Krioukov et al., 2010), natural language processing (L opez et al., 2019; Zhu et al., 2020; L opez & Strube, 2020), and protein interactions (Zitnik et al., 2019). Hyperbolic neural networks (HNNs) (Ganea et al., 2018) and hyperbolic graph convolutional networks (HGCNs) (Chami et al., 2019) have demonstrated superior performance over Euclidean models in learning from hierarchical data.