Learnable Filters for Geometric Scattering Modules
This work addresses the challenge of capturing non-local dependencies in graph-structured data for applications like biochemical graph exploration, representing an incremental improvement over existing geometric scattering methods.
The authors tackled the problem of learning longer-range graph relations in graph neural networks (GNNs) by proposing a learnable geometric scattering (LEGS) module based on graph wavelet filters, resulting in networks that match or outperform popular GNNs on graph classification benchmarks, particularly in biochemical domains, with significantly fewer parameters.
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.