  Geometric deep learning has made great strides towards generalizing the
design of structure-aware neural networks from traditional domains to
non-Euclidean ones, giving rise to graph neural networks (GNN) that can be
applied to graph-structured data arising in, e.g., social networks,
biochemistry, and material science. Graph convolutional networks (GCNs) in
particular, inspired by their Euclidean counterparts, have been successful in
processing graph data by extracting structure-aware features. However, current
GNN models are often constrained by various phenomena that limit their
expressive power and ability to generalize to more complex graph datasets. Most
models essentially rely on low-pass filtering of graph signals via local
averaging operations, leading to oversmoothing. Moreover, to avoid severe
oversmoothing, most popular GCN-style networks tend to be shallow, with narrow
receptive fields, leading to underreaching. Here, we propose a hybrid GNN
framework that combines traditional GCN filters with band-pass filters defined
via geometric scattering. We further introduce an attention framework that
allows the model to locally attend over combined information from different
filters at the node level. Our theoretical results establish the complementary
benefits of the scattering filters to leverage structural information from the
graph, while our experiments show the benefits of our method on various
learning tasks.
