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

Autor:	Sannai, Akiyoshi, Takai, Yuuki, Cordonnier, Matthieu
Rok vydání:	2019
Předmět:	Computer Science - Machine Learning Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.01939 Zobrazit plný text záznamu View this record from Arxiv