Machine learning a manifold

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