# How to quantify fields or textures? A guide to the scattering transform

arXiv: https://arxiv.org/abs/2112.01288 · HTML: https://mlsanity.com/paper/2112.01288/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 5 references that are in the map.
- First posted on arXiv 30 Nov 2021.

## Built on by (most cited first, 5 of 5)

- [Grokking modular arithmetic](https://mlsanity.com/paper/2301.02679/) (2023)
- [Scattering Spectra Models for Physics](https://mlsanity.com/paper/2306.17210/) (2023)
- [One Wave To Explain Them All: A Unifying Perspective On Feature Attribution](https://mlsanity.com/paper/2410.01482/) (2024)
- [Wavelets Beat Monkeys at Adversarial Robustness](https://mlsanity.com/paper/2304.09403/) (2023)
- [Simulation-based inference with scattering representations: scattering is all you need](https://mlsanity.com/paper/2410.11883/) (2024)

## Abstract (arXiv)

Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power spectrum analysis, which is often too limited, or the use of convolutional neural networks (CNNs), which require large training sets and lack interpretability. In this paper, we advocate for the use of the scattering transform (Mallat 2012), a powerful statistic which borrows mathematical ideas from CNNs but does not require any training, and is interpretable. We show that it provides a relatively compact set of summary statistics with visual interpretation and which carries most of the relevant information in a wide range of scientific applications. We present a non-technical introduction to this estimator and we argue that it can benefit data analysis, comparison to models and parameter inference in many fields of science. Interestingly, understanding the core operations of the scattering transform allows one to decipher many key aspects of the inner workings of CNNs.