Hyperbolic graph convolutional networks (HGCN) have demonstrated significant potential in extracting information from hierarchical graphs. However, existing HGCNs are limited to shallow architectures, due to the expensive hyperbolic operations and the over-smoothing issue as depth increases. Although in GCNs, treatments have been applied to alleviate over-smoothing, developing a hyperbolic therapy presents distinct challenges since operations should be carefully designed to fit the hyperbolic nature. Addressing the above challenges, in this work, we propose DeepHGCN, the first deep multi-layer HGCN architecture with dramatically improved computational efficiency and substantially alleviated over-smoothing effect. DeepHGCN presents two key enablers of deep HGCNs: (1) a novel hyperbolic feature transformation layer that enables fast and accurate linear maps; 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 obtains significant improvements in link prediction and node classification tasks compared to both Euclidean and shallow hyperbolic GCN variants.

翻译：双曲图卷积网络（HGCN）在从层次化图中提取信息方面展现出显著潜力。然而，现有HGCN受限于浅层架构，原因在于双曲运算的高成本以及随着深度增加而出现的过平滑问题。尽管在图卷积网络（GCN）中已采用多种方法来缓解过平滑，但发展双曲领域的处理手段面临独特挑战，因为运算需精心设计以适应双曲本质。针对上述挑战，本文提出DeepHGCN——首个深度多层HGCN架构，其计算效率大幅提升，过平滑效应显著缓解。DeepHGCN包含深度HGCN的两个关键使能技术：（1）一种新型双曲特征变换层，可实现快速且精确的线性映射；（2）借助高效的双曲中点方法，实现双曲残差连接以及权重和特征正则化等技术。大量实验表明，与欧几里得及浅层双曲GCN变体相比，DeepHGCN在链接预测和节点分类任务中均取得显著改进。