Work

Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

Year: 2023

Type: article

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.

Source: SIAM Journal on Mathematics of Data Science

DOI: 10.1137/21m1465056

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

Institutions: Boise State University, Mila - Quebec Artificial Intelligence Institute, Université de Montréal, Columbia University, Michigan State University

Language: English

Topic: Advanced Graph Neural Networks

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond