# A Learnable ScatterNet: Locally Invariant Convolutional Layers

arXiv: https://arxiv.org/abs/1903.03137 · HTML: https://mlsanity.com/paper/1903.03137/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2019.

## Built on by (most cited first, 10 of 10)

- [Parametric Scattering Networks](https://mlsanity.com/paper/2107.09539/) (2021)
- [Phase Collapse in Neural Networks](https://mlsanity.com/paper/2110.05283/) (2021)
- [Riesz feature representation: scale equivariant scattering network for classification tasks](https://mlsanity.com/paper/2307.08467/) (2023)
- [ScatterFormer: Locally-Invariant Scattering Transformer for Patient-Independent Multispectral Detection of Epileptiform Discharges](https://mlsanity.com/paper/2304.14919/) (2023)
- [On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks](https://mlsanity.com/paper/2209.11740/) (2022)
- [Efficient Hybrid Network: Inducting Scattering Features](https://mlsanity.com/paper/2203.15392/) (2022)
- [From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets](https://mlsanity.com/paper/2212.00394/) (2022)
- [ExplainFix: Explainable Spatially Fixed Deep Networks](https://mlsanity.com/paper/2303.10408/) (2023)
- [SCRAPL: Scattering Transform with Random Paths for Machine Learning](https://mlsanity.com/paper/2602.11145/) (2026)
- [Transversal Pooling Neural Networks](https://mlsanity.com/paper/2609.36237/) (2026)

## Abstract (arXiv)

In this paper we explore tying together the ideas from Scattering Transforms and Convolutional Neural Networks (CNN) for Image Analysis by proposing a learnable ScatterNet. Previous attempts at tying them together in hybrid networks have tended to keep the two parts separate, with the ScatterNet forming a fixed front end and a CNN forming a learned backend. We instead look at adding learning between scattering orders, as well as adding learned layers before the ScatterNet. We do this by breaking down the scattering orders into single convolutional-like layers we call 'locally invariant' layers, and adding a learned mixing term to this layer. Our experiments show that these locally invariant layers can improve accuracy when added to either a CNN or a ScatterNet. We also discover some surprising results in that the ScatterNet may be best positioned after one or more layers of learning rather than at the front of a neural network.