Understanding Graph Neural Networks with Asymmetric Geometric Scattering Transforms

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 graph scattering transforms 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. This work helps bridge the gap between scattering and other graph neural networks by introducing a large family of networks with provable stability and invariance guarantees. This lays the groundwork for future deep learning architectures for graph-structured data that have learned filters and also provably have desirable theoretical properties.