# Deep Learning by Scattering

arXiv: https://arxiv.org/abs/1306.5532 · HTML: https://mlsanity.com/paper/1306.5532/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2013.

## Built on by (most cited first, 1 of 1)

- [Interferometric Graph Transform for Community Labeling](https://mlsanity.com/paper/2106.05875/) (2021)

## Abstract (arXiv)

We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probability distribution, which preserves its mean-square norm. We show that unsupervised learning can be casted as an optimization of the space contraction to preserve the volume occupied by unlabeled examples, at each layer of the network. Supervised learning and classification are performed with an averaged scattering, which provides scattering estimations for multiple classes.