  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.
