Generalization capabilities of translationally equivariant neural networks

TL;DR

This paper demonstrates that neural networks incorporating translational symmetry significantly improve performance and generalization in physics-related tasks on lattice field theory, outperforming non-equivariant models across various tasks.

Contribution

It systematically compares equivariant and non-equivariant neural networks in physics applications, showing the advantages of symmetry-aware architectures.

Findings

Equivariant networks outperform non-equivariant ones in generalization.

Symmetry-aware models handle unseen physical parameters better.

Performance gains are consistent across different lattice sizes.

Abstract

The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to significant drawbacks in terms of performance and generalizability. One particular example for this is the use of neural network architectures that do not reflect the underlying symmetries of the given physical problem. In this work, we focus on complex scalar field theory on a two-dimensional lattice and investigate the benefits of using group equivariant convolutional neural network architectures based on the translation group. For a meaningful comparison, we conduct a systematic search for equivariant and non-equivariant neural network architectures and apply them to various regression and classification tasks. We demonstrate that in most of these tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.