Related papers: On the finite representation of group equivariant operators via permutant measures

On the finite representation of group equivariant operators via permutant measures

URL: http://arxiv.org/abs/2008.06340v2
Date: Wed, 9 Mar 2022 19:05:50 GMT
Title: On the finite representation of group equivariant operators via permutant measures
Authors: Giovanni Bocchi, Stefano Botteghi, Martina Brasini, Patrizio Frosini, Nicola Quercioli
Abstract summary: We show that each linear $G$-equivariant operator can be produced by a suitable permutant measure. This result makes available a new method to build linear $G$-equivariant operators in the finite setting.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The study of $G$-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear $G$-equivariant operator can be produced by a suitable permutant measure, provided that the group $G$ transitively acts on a finite signal domain $X$. This result makes available a new method to build linear $G$-equivariant operators in the finite setting.

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