Generalization capabilities of translationally equivariant neural networks
This work addresses performance and generalizability issues for machine learning in high-energy physics and lattice field theory, though it is incremental as it applies known equivariant methods to a specific domain.
The authors tackled the problem of neural networks lacking symmetry awareness in physics applications by comparing translationally equivariant and non-equivariant architectures on a 2D lattice scalar field theory. They demonstrated that equivariant architectures significantly outperform non-equivariant ones in generalization across unseen physical parameters and lattice sizes.
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.