On the finite representation of group equivariant operators via permutant measures

2020/08/07 by Giovanni Bocchi, Bocchi, Giovanni, Stefano Botteghi +7 · 1 citation
Computer Science · Physics and Astronomy · #20C35 #47B38 #55N31 #62R40 #68U05 #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural Networks and Reservoir Computing #Primary: 68T09 Secondary: 15B51 #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2008.06340

openalex publication_date 2020/08/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

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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