A New Neural Network Architecture Invariant to the Action of Symmetry Subgroups
This work addresses the problem of building neural networks that respect specific symmetries in input data, which is important for researchers and practitioners working with structured data where such invariances are known to exist.
This paper introduces a computationally efficient neural network architecture that approximates functions invariant to the action of a given permutation subgroup. The network achieves this through a novel G-invariant transformation module, demonstrating effectiveness and strong generalization in numerical experiments compared to existing G-invariant networks.
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.