Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

Michael Perlmutter, Alexander Tong, Feng Gao, Guy Wolf, Matthew Hirn

Research output: Contribution to journalArticlepeer-review

Abstract

The scattering transform is a multilayered wavelet-based architecture that acts as a model of convolutional neural networks. Recently, several works have generalized the scattering transform to graph-structured data. Our work builds on these constructions by introducing windowed and nonwindowed geometric scattering transforms for graphs based on two very general classes wavelets, which are in most cases based on asymmetric matrices. We show that these transforms have many of the same theoretical guarantees as their symmetric counterparts. As a result, the proposed construction unifies and extends known theoretical results for many of the existing graph scattering architectures. Therefore, it helps bridge the gap between geometric scattering and other graph neural networks by introducing a large family of networks with provable stability and invariance guarantees. These results lay the groundwork for future deep learning architectures for graph-structured data that have learned filters and also provably have desirable theoretical properties.

Original languageAmerican English
JournalMathematics Faculty Publications and Presentations
StatePublished - 1 Dec 2023

Keywords

  • geometric deep learning
  • graph neural networks
  • scattering transform
  • wavelets

EGS Disciplines

  • Mathematics

Fingerprint

Dive into the research topics of 'Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms'. Together they form a unique fingerprint.

Cite this