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

TL;DR

This paper introduces a computationally efficient neural network architecture that inherently respects symmetry properties defined by permutation subgroups, enhancing function approximation and generalization capabilities.

Contribution

The paper presents a novel G-invariant transformation module that creates invariant latent representations, improving efficiency and effectiveness over existing G-invariant neural networks.

Findings

Demonstrates strong generalization in numerical experiments

Achieves efficient approximation of G-invariant functions

Outperforms existing G-invariant neural network methods

Abstract

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.