Identifying the Group-Theoretic Structure of Machine-Learned Symmetries
Roy T. Forestano Konstantin T. Matchev Katia Matcheva Alexander Roman Eyup B. Unlu Sarunas Verner
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.