# Deep Haar Scattering Networks

arXiv: https://arxiv.org/abs/1509.09187 · HTML: https://mlsanity.com/paper/1509.09187/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2015.

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

- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces](https://mlsanity.com/paper/2205.14627/) (2022)
- [Wavelet Regularization Benefits Adversarial Training](https://mlsanity.com/paper/2206.03727/) (2022)
- [Multiscale Hodge Scattering Networks for Data Analysis](https://mlsanity.com/paper/2311.10270/) (2023)
- [The Maximal Overlap Discrete Wavelet Scattering Transform and Its Application in Classification Tasks](https://mlsanity.com/paper/2506.12039/) (2025)

## Abstract (arXiv)

An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning. It implements non-linear contractions, which are optimized for classification, with an unsupervised pair matching algorithm, of polynomial complexity. A structured Haar scattering over graph data computes permutation invariant representations of groups of connected points in the graph. If the graph connectivity is unknown, unsupervised Haar pair learning can provide a consistent estimation of connected dyadic groups of points. Classification results are given on image data bases, defined on regular grids or graphs, with a connectivity which may be known or unknown.