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On the finite representation of group equivariant operators via permutant measures
Giovanni Bocchi, Stefano Botteghi, Martina Brasini, Patrizio Fro · 2020-08-07 · via cs.LG updates on arXiv.org

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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