# A Learnable ScatterNet: Locally Invariant Convolutional Layers

## TL;DR

This paper introduces a learnable ScatterNet that integrates scattering transforms with convolutional neural networks by adding learnable layers between scattering orders, improving accuracy and challenging traditional placement assumptions.

## Contribution

It proposes a novel learnable ScatterNet with locally invariant layers and learned mixing, bridging scattering transforms and CNNs more effectively than previous fixed-front-end approaches.

## Key findings

- Locally invariant layers improve accuracy in CNNs and ScatterNets
- Learned mixing enhances feature integration
- ScatterNet may be most effective after some learned layers

## Abstract

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.