DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks

Abstract

Hyperbolic graph convolutional networks (HGCNs) have demonstrated significant potential in extracting information from hierarchical graphs. However, existing HGCNs are limited to shallow architectures due to the computational expense of hyperbolic operations and the issue of oversmoothing as depth increases. Although treatments have been applied to alleviate oversmoothing in graph convolutional networks (GCNs), developing a hyperbolic solution presents distinct challenges since operations must be carefully designed to fit the hyperbolic nature. Addressing these challenges, we propose DeepHGCN, the first deep multilayer HGCN architecture with dramatically improved computational efficiency and substantially reduced oversmoothing. DeepHGCN features two key innovations: 1) a novel hyperbolic feature transformation layer that enables fast and accurate linear mappings; and 2) techniques such as hyperbolic residual connections and regularization for both weights and features, facilitated by an efficient hyperbolic midpoint method. Extensive experiments demonstrate that DeepHGCN achieves significant improvements in link prediction (LP) and node classification (NC) tasks compared to both Euclidean and shallow hyperbolic GCN variants.