  Graph convolutional networks (GCNs) have shown promising results in
processing graph data by extracting structure-aware features. This gave rise to
extensive work in geometric deep learning, focusing on designing network
architectures that ensure neuron activations conform to regularity patterns
within the input graph. However, in most cases the graph structure is only
accounted for by considering the similarity of activations between adjacent
nodes, which limits the capabilities of such methods to discriminate between
nodes in a graph. Here, we propose to augment conventional GCNs with geometric
scattering transforms and residual convolutions. The former enables band-pass
filtering of graph signals, thus alleviating the so-called oversmoothing often
encountered in GCNs, while the latter is introduced to clear the resulting
features of high-frequency noise. We establish the advantages of the presented
Scattering GCN with both theoretical results establishing the complementary
benefits of scattering and GCN features, as well as experimental results
showing the benefits of our method compared to leading graph neural networks
for semi-supervised node classification, including the recently proposed GAT
network that typically alleviates oversmoothing using graph attention
mechanisms.
