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arXiv · 1903.01939

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

Akiyoshi Sannai·Yuuki Takai·Matthieu Cordonnier
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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.

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Akiyoshi Sannai, Yuuki Takai, Matthieu Cordonnier. 2019-03-05. Universal approximations of permutation invariant/equivariant functions by deep neural networks. https://arxiv.org/abs/1903.01939

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