Universal approximations of permutation invariant/equivariant functions by deep neural networks

Akiyoshi Sannai; Yuuki Takai; Matthieu Cordonnier

Universal approximations of permutation invariant/equivariant functions by deep neural networks

Machine Learning 2019-09-27 v3 Machine Learning

Authors: Akiyoshi Sannai , Yuuki Takai , Matthieu Cordonnier

Abstract

In this paper, we develop a theory about the relationship between $G$ -invariant/equivariant functions and deep neural networks for finite group $G$ . Especially, for a given $G$ -invariant/equivariant function, we construct its universal approximator by deep neural network whose layers equip $G$ -actions and each affine transformations are $G$ -equivariant/invariant. Due to representation theory, we can show that this approximator has exponentially fewer free parameters than usual models.

Keywords

permutation invariant permutation equivariant deep neural networks universal approximation finite group representation theory

Cite

@article{arxiv.1903.01939,
  title  = {Universal approximations of permutation invariant/equivariant functions by deep neural networks},
  author = {Akiyoshi Sannai and Yuuki Takai and Matthieu Cordonnier},
  journal= {arXiv preprint arXiv:1903.01939},
  year   = {2019}
}

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