# Separation Capacity of Scattering Networks

arXiv: https://arxiv.org/abs/2606.30822 · HTML: https://mlsanity.com/paper/2606.30822/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [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)
- [Scattering Spectra Models for Physics](https://mlsanity.com/paper/2306.17210/) (2023)
- [Scale Dependencies and Self-Similar Models with Wavelet Scattering Spectra](https://mlsanity.com/paper/2204.10177/) (2022)
- [Energy Propagation in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1704.03636/) (2017)
- [Topology Reduction in Deep Convolutional Feature Extraction Networks](https://mlsanity.com/paper/1707.02711/) (2017)

## Built on by (most cited first, 2 of 2)

- [Function-Counting Theory for Low-Dimensional Data Structures](https://mlsanity.com/paper/2607.01010/) (2026)
- [Separation Capacity of Scattering Networks on Low-Dimensional Datasets](https://mlsanity.com/paper/2607.06048/) (2026)

## Abstract (arXiv)

In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separation capacity, a combinatorial quantity derived from counting the number of realizable dichotomies (i.e., binary label assignments). Our contributions are threefold. First, we extend Cover's framework by establishing a conceptually insightful and practically useful formulation for the separation capacity. Second, leveraging this formulation, we identify the factors governing the separation capacity of feature extractors that employ a specific CNN architecture, so-called scattering networks, in terms of their network building blocks. Third, we provide practical insights for scattering network design.