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This content will become publicly available on December 31, 2024

Title: Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms
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.  more » « less
Award ID(s):
1845856
NSF-PAR ID:
10510162
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
SIAM Journal on Mathematics of Data Science
Date Published:
Journal Name:
SIAM Journal on Mathematics of Data Science
Volume:
5
Issue:
4
ISSN:
2577-0187
Page Range / eLocation ID:
873 to 898
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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