DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks

TL;DR

DeepHGCN introduces a deep hyperbolic graph convolutional network architecture that overcomes computational and over-smoothing challenges, enabling more effective hierarchical graph learning.

Contribution

It presents the first deep multi-layer HGCN with innovative hyperbolic feature transformation and residual techniques for improved efficiency and performance.

Findings

Outperforms shallow HGCNs and Euclidean GCNs in link prediction.

Reduces over-smoothing in deep hyperbolic networks.

Achieves significant improvements in node classification.

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 over-smoothing as depth increases. Although treatments have been applied to alleviate over-smoothing in 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 multi-layer HGCN architecture with dramatically improved computational efficiency and substantially reduced over-smoothing. 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 and node classification tasks compared to both Euclidean and shallow hyperbolic GCN variants.