Analysis & Applications Seminar
Scattering Transforms: Universal Admissibility and the Limits of Depth Truncation
Speaker: Max Getter (RWTH Aachen University)Date: Friday, 11 September 2026 - 12:00Place: Aula Gris 1, ICMAT
Abstract:
Scattering transforms are mathematically tractable feature maps built from cascades of convolutions and modulus nonlinearities, resembling CNNs with fixed weights. While initially designed around specific wavelets, recent generalizations to broader filter banks have revealed a crucial distinction: some network properties depend strictly on the choice of filters, while others are intrinsic to the architecture itself. In this talk, I focus on the admissibility problem to determine which filter banks yield a norm-preserving transform. I will present recent results establishing admissibility for every Parseval scattering filter bank with a genuine low-pass read-out. Furthermore, I will explore how this relates to information retention in truncated networks and establish strict quantitative limits for energy propagation at infinite depth.
Sesión conjunta con el Seminario de Machine Learning.
