# A Computationally Efficient Neural Network Invariant to the Action of Symmetry Subgroups

arXiv: https://arxiv.org/abs/2002.07528 · HTML: https://mlsanity.com/paper/2002.07528/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 4 of 4)

- [Learning Probabilistic Symmetrization for Architecture Agnostic Equivariance](https://mlsanity.com/paper/2306.02866/) (2023)
- [A Classification of G-invariant Shallow Neural Networks](https://mlsanity.com/paper/2205.09219/) (2022)
- [Equivariant and Invariant Reynolds Networks](https://mlsanity.com/paper/2110.08092/) (2021)
- [Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representations](https://mlsanity.com/paper/2303.04614/) (2023)

## Abstract (arXiv)

We introduce a method to design 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. This latent representation is then processed with a multi-layer perceptron in the network. We prove the universality of the proposed architecture, discuss its properties and highlight its computational and memory efficiency. Theoretical considerations are supported by numerical experiments involving different network configurations, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other G-invariant neural networks.