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The study of $G$-equivariant operators is of great interest to explain andunderstand the architecture of neural networks. In this paper we show that eachlinear $G$-equivariant operator can be produced by a suitable permutantmeasure, provided that the group $G$ transitively acts on a finite signaldomain $X$. This result makes available a new method to build linear$G$-equivariant operators in the finite setting.

On the finite representation of group equivariant operators via permutant measures