  We propose a new graph neural network (GNN) module, based on relaxations of
recently proposed geometric scattering transforms, which consist of a cascade
of graph wavelet filters. Our learnable geometric scattering (LEGS) module
enables adaptive tuning of the wavelets to encourage band-pass features to
emerge in learned representations. The incorporation of our LEGS-module in GNNs
enables the learning of longer-range graph relations compared to many popular
GNNs, which often rely on encoding graph structure via smoothness or similarity
between neighbors. Further, its wavelet priors result in simplified
architectures with significantly fewer learned parameters compared to competing
GNNs. We demonstrate the predictive performance of LEGS-based networks on graph
classification benchmarks, as well as the descriptive quality of their learned
features in biochemical graph data exploration tasks. Our results show that
LEGS-based networks match or outperforms popular GNNs, as well as the original
geometric scattering construction, on many datasets, in particular in
biochemical domains, while retaining certain mathematical properties of
handcrafted (non-learned) geometric scattering.
