Machine learning a manifold
This work addresses the challenge of detecting symmetries in data for researchers in physics and machine learning, offering a method that avoids full sampling or binning, but it appears incremental as it builds on existing symmetry detection techniques.
The authors tackled the problem of identifying continuous Lie algebra symmetries in datasets by proposing a method that uses neural network regression to exploit the scaling of output variables under infinitesimal symmetry transformations, and they demonstrated its effectiveness in the SU(3)-symmetric model.
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}(ε^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 $Σ$ model.