Towards Time-Frequency Deformation Stability Bounds for Deep Convolutional Neural Networks

In this paper, we examine deformations from the lens of an operator similar to Fourier Integral Operators (FIOs). First, we provide a generalization of the deformation operator seen first in Mallat’s seminal paper Group Invariant Scattering, which we call a time-frequency deformation. Next, we provide a generalized deformation stability bound for our time-frequency deformation in the specific case when the time and frequency portions of the deformation are separable for the deep feature extractor considered by Wiatowski and Bölcskei as well as Mallat’s Windowed Scattering Transform.