Machine learning a manifold

TL;DR

This paper introduces a neural network-based method to identify continuous Lie algebra symmetries in datasets by exploiting the scaling behavior of outputs under infinitesimal transformations, avoiding extensive sampling.

Contribution

The proposed approach uniquely detects Lie algebra symmetries directly from data without requiring full representation sampling or binning, enhancing symmetry identification efficiency.

Findings

Successfully applied to SU(3)-symmetric models

Accurately identifies continuous symmetries in datasets

Minimizes false positives in symmetry detection

Abstract

We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the $ \mathcal{O}(\epsilon^2)$ scaling of the output variable under infinitesimal symmetry transformations on the input variables. As symmetry transformations are generated post-training, the methodology does not rely on sampling of the full representation space or binning of the dataset, and the possibility of false identification is minimised. We demonstrate our method in the SU(3)-symmetric (non-) linear $\Sigma$ model.