TY - JOUR
T1 - Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms
AU - Perlmutter, Michael
AU - Tong, Alexander
AU - Gao, Feng
AU - Wolf, Guy
AU - Hirn, Matthew
PY - 2023/12/1
Y1 - 2023/12/1
N2 - 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.
AB - 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.
KW - geometric deep learning
KW - graph neural networks
KW - scattering transform
KW - wavelets
UR - https://scholarworks.boisestate.edu/math_facpubs/263
UR - https://doi.org/10.1137/21M1465056
M3 - Article
JO - Mathematics Faculty Publications and Presentations
JF - Mathematics Faculty Publications and Presentations
ER -