Graph Scattering beyond Wavelet Shackles

TL;DR

This paper introduces a comprehensive framework for graph scattering networks with enhanced stability, feature aggregation, and extensions to higher-order inputs, demonstrating superior performance in graph classification and regression tasks.

Contribution

It develops a flexible, mathematically rigorous framework for graph scattering networks with variable branching and filters, including stability guarantees and extensions to edge and tensor inputs.

Findings

Outperforms traditional wavelet-based scattering in social network classification.

Significantly better results in quantum-chemical energy regression.

Provides theoretical stability guarantees for graph scattering architectures.

Abstract

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for node- and graph-level perturbations are derived; the vertex-set non-preserving case is treated by utilizing recently developed mathematical-physics based tools. Energy propagation through the network layers is investigated and related to truncation stability. New methods of graph-level feature aggregation are introduced and stability of the resulting composite scattering architectures is established. Finally, scattering transforms are extended to edge- and higher order tensorial input. Theoretical results are complemented by numerical investigations: Suitably chosen cattering networks conforming to the developed theory perform better than traditional graph-wavelet based scattering approaches in social network graph classification tasks and significantly outperform other graph-based learning approaches to regression of quantum-chemical energies on QM7.