Identifying the Group-Theoretic Structure of Machine-Learned Symmetries

Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later stage. In this letter we propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. We design loss functions which probe the subalgebra structure either during the deep learning stage of symmetry discovery or in a subsequent post-processing stage. We illustrate the new methods with examples from the U(n) Lie group family, obtaining the respective subalgebra decompositions. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries like SU(3) and SU(5) which are commonly used in model building.