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arXiv · 2008.06340

On the finite representation of group equivariant operators via permutant measures

Giovanni Bocchi·Stefano Botteghi·Martina Brasini·Patrizio Frosini·Nicola Quercioli
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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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Giovanni Bocchi, Stefano Botteghi, Martina Brasini, Patrizio Frosini, Nicola Quercioli. 2020-08-07. On the finite representation of group equivariant operators via permutant measures. https://arxiv.org/abs/2008.06340

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