Caltech/UCLA/USC Joint Analysis Seminar

The scattering transform is a mathematical model of convolutional neural networks (CNNs) initially introduced (for Euclidean data) by Mallat in 2012. This work models the filter convolutions of a CNN as a wavelet transform and uses methods from harmonic analysis to analyze the stability and invariance of CNNs to certain group actions. I will introduce Mallat's construction and explain how it has improved our understanding of CNNs. Then, in the second half of my talk, I will discuss recent generalizations of the scattering transform to graphs, manifolds, and other measure spaces. These generalized scattering transforms utilize wavelets constructed from the spectral decomposition of a suitable Laplacian. I will also discuss a diffusion maps-based method, with a provable convergence rate, for implementing the manifold scattering transform from finitely samples of an unknown manifold.