A New Neural Network Architecture Invariant to the Action of Symmetry Subgroups

Piotr Kicki, Piotr Skrzypczy

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Abstract

We propose a computationally efficient G-invariant neural network that approximates functions invariant to the action of a given permutation subgroup G ≤ S n of the symmetric group on input data. The key element of the proposed network architecture is a new G-invariant transformation module, which produces a Ginvariant latent representation of the input data. Theoretical considerations are supported by numerical experiments, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other G-invariant neural networks.

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