On the finite representation of group equivariant operators via permutant measures
Abstract
The study of -equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear -equivariant operator can be produced by a suitable permutant measure, provided that the group transitively acts on a finite signal domain . This result makes available a new method to build linear -equivariant operators in the finite setting.
Keywords
Cite
@article{arxiv.2008.06340,
title = {On the finite representation of group equivariant operators via permutant measures},
author = {Giovanni Bocchi and Stefano Botteghi and Martina Brasini and Patrizio Frosini and Nicola Quercioli},
journal= {arXiv preprint arXiv:2008.06340},
year = {2022}
}
Comments
We have extended the introduction, providing more context about our approach, and the discussion. We have also added Section 4, showing possible advantages of the use of GENEOs built by permutant measures. The experiment described in Section 4 has been made by Giovanni Bocchi. For this reason, he has been added to the list of authors of the paper