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Caltech/UCLA/USC Joint Analysis Seminar

Tuesday, October 11, 2022
3:30pm to 4:30pm
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Linde Hall 310
The scattering transform, a harmonic analysis perspective on neural networks
Michael Perlmutter, Department of Mathematics, UCLA,

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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.