Deep Learning Symmetries

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We analyze the complete subgroup structure of the rotation groups SO(n), the Lorentz group SO(1,3), and the unitary groups U(n). Other examples include squeeze mapping, piecewise discontinuous labels, and non-linear latent space symmetries with the preservation of an oracle (function), demonstrating that our method is completely general, with many possible applications in physics and data science.