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

Piotr Kicki, Mete Ozay, Piotr Skrzypczynski

Abstract: We propose a computationally efficient G-invariant neural network that approximates functions invariant to the action of a given permutation subgroup G≤Sn 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 G-invariant 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.