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

25 Sep 2019 (modified: 24 Dec 2019)ICLR 2020 Conference Blind SubmissionReaders: Everyone
• Original Pdf: pdf
• Keywords: finite group, invariant, equivariant, neural networks
• TL;DR: 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.
• 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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