Geometric Scattering And Applications
December 17, 2021
The scattering transform is a mathematical model of convolutional neural networks (CNNs) introduced for functions defined on Euclidean space by Stephan\'e Mallat. It differs from traditional CNNs by using predesigned, wavelet filters rather than filters which are learned from training data. This leads to a network which provably has stability and invariance guarantees. Moreover, in situations where the wavelets can be designed in correspondence to underlying physics, it can produce very good numerical results. The rise of geometric deep learning motivated the introduction of geometric scattering transforms for data sets modeled as graphs or manifolds. These networks use wavelets constructed using the spectral decompositions of an appropriate Laplacian operator or via polynomials of a diffusion operator. In my talk, I will discuss applications of these networks to a variety of geometric deep learning tasks and show that they have analogous stability and invariance guarantees to their Euclidean predecessor. I will then talk about modifications of the graph scattering transform which can increase numerical performance and also work using the graph scattering transform as the front end of an encoder-decoder network for the purposes of molecule generation.