  We propose a computationally efficient $G$-invariant neural network that
approximates 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 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.
