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We propose a computationally efficient $G$-invariant neural network thatapproximates functions invariant to the action of a given permutation subgroup$G \leq S_n$ of the symmetric group on input data. The key element of theproposed 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, whichdemonstrate the effectiveness and strong generalization properties of theproposed method in comparison to other $G$-invariant neural networks.

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