Learnable Filters for Geometric Scattering Modules

TL;DR

This paper introduces LEGS, a learnable graph neural network module based on geometric scattering transforms, which adaptively tunes wavelet filters to improve long-range relation learning and reduce parameters.

Contribution

The paper presents a novel LEGS module that combines geometric scattering with learnability, enabling adaptive wavelet tuning and improved graph representation learning.

Findings

LEGS matches or outperforms existing GNNs on benchmark datasets.

LEGS achieves better performance in biochemical graph data analysis.

LEGS simplifies architecture with fewer parameters while maintaining mathematical properties.

Abstract

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.