# Deep Scale-spaces: Equivariance Over Scale

Published in NeurIPS, 2019

### Abstract

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.

1. @incollection{WorrallW2019,
title = {Deep Scale-spaces: Equivariance Over Scale},
author = {Worrall, Daniel and Welling, Max},
booktitle = {Advances in Neural Information Processing Systems 32},
editor = {Wallach, H. and Larochelle, H. and Beygelzimer, A. and d\textquotesingle Alch\'{e}-Buc, F. and Fox, E. and Garnett, R.},
pages = {7364--7376},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/8956-deep-scale-spaces-equivariance-over-scale.pdf}
}