# Scattering Networks on Noncommutative Finite Groups

arXiv: https://arxiv.org/abs/2505.20950 · HTML: https://mlsanity.com/paper/2505.20950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 12 of 12)

- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Deep Scattering Spectrum](https://mlsanity.com/paper/1304.6763/) (2013)
- [A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction](https://mlsanity.com/paper/1512.06293/) (2015)
- [Graph Convolutional Neural Networks via Scattering](https://mlsanity.com/paper/1804.00099/) (2018)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [Parametric Scattering Networks](https://mlsanity.com/paper/2107.09539/) (2021)
- [Intermittent process analysis with scattering moments](https://mlsanity.com/paper/1311.4104/) (2013)
- [Visualizing and Improving Scattering Networks](https://mlsanity.com/paper/1709.01355/) (2017)
- [Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds](https://mlsanity.com/paper/1905.10448/) (2019)
- [Underwater object classification using scattering transform of sonar signals](https://mlsanity.com/paper/1707.03133/) (2017)
- [Stability of the scattering transform for deformations with minimal regularity](https://mlsanity.com/paper/2205.11142/) (2022)
- [Rotation invariant CNN using scattering transform for image classification](https://mlsanity.com/paper/2105.10175/) (2021)

## Abstract (arXiv)

Scattering Networks were initially designed to elucidate the behavior of early layers in Convolutional Neural Networks (CNNs) over Euclidean spaces and are grounded in wavelets. In this work, we introduce a scattering transform on an arbitrary finite group (not necessarily abelian) within the context of group-equivariant convolutional neural networks (G-CNNs). We present wavelets on finite groups and analyze their similarity to classical wavelets. We demonstrate that, under certain conditions in the wavelet coefficients, the scattering transform is non-expansive, stable under deformations, preserves energy, equivariant with respect to left and right group translations, and, as depth increases, the scattering coefficients are less sensitive to group translations of the signal, all desirable properties of convolutional neural networks. Furthermore, we provide examples illustrating the application of the scattering transform to classify data with domains involving abelian and nonabelian groups.