Limitation of previous study
• Input node features are usually Euclidean, and it is not clear how to optimally use as inputs to hyperbolic
• It is not clear how to perform set aggregation, a key step in message passing, in hyperbolic space
• one needs to choose hyperbolic spaces with the right curvature at every layer of GCN
• Improved performance on graph-based tasks
→ Hyperbolic space is better suited for modeling hierarchical structures that are common in many real-
→ HGCNs can learn hierarchical representations of graph-structured data that are more interpretable
than those learned by Euclidean GCNs.
→ Paper introduces a hyperbolic attention-based aggregation scheme that captures hierarchical
structure of networks
Visualization (DISEASE-M dataset)
• In HGCN, the center node pays more attention to its (grand)parent.
• In contrast to Euclidean GAT, our aggregation with attention in hyperbolic space allows to pay more
attention to nodes with high hierarchy
→ such attention is crucial to good performance in disease, because only sick parents will propagate the
disease to their children
• HGCN is a novel architecture that learns hyperbolic embeddings using graph convolution networks.
• In HGCN, the Euclidean input features are successively mapped to embeddings in hyperbolic
spaces with trainable curvatures at every layer
• HGCN achieves new state-of-the-art in learning embeddings for real-world hierarchical and scale-