Understanding Graph Neural Networks with Generalized Geometric
Scattering Transforms
- URL: http://arxiv.org/abs/1911.06253v5
- Date: Thu, 29 Jun 2023 01:28:23 GMT
- Title: Understanding Graph Neural Networks with Generalized Geometric
Scattering Transforms
- Authors: Michael Perlmutter and Alexander Tong and Feng Gao and Guy Wolf and
Matthew Hirn
- Abstract summary: The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks.
We introduce windowed and non-windowed geometric scattering transforms for graphs based upon a very general class of asymmetric wavelets.
We show that these asymmetric graph scattering transforms have many of the same theoretical guarantees as their symmetric counterparts.
- Score: 67.88675386638043
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The scattering transform is a multilayered wavelet-based deep learning
architecture that acts as a model of convolutional neural networks. Recently,
several works have introduced generalizations of the scattering transform for
non-Euclidean settings such as graphs. Our work builds upon these constructions
by introducing windowed and non-windowed geometric scattering transforms for
graphs based upon a very general class of asymmetric wavelets. We show that
these asymmetric graph scattering 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. In doing so, this work 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.
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