Machine learning a manifold. (arXiv:2112.07673v1 [hep-ph])

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.



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