Accelerated discovery of machine-learned symmetries: Deriving the exceptional Lie groups , And
Roy T. Forestano (Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL, 32611, USA); Konstantin T. Matchev (Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL, 32611, USA)
; Katia Matcheva (Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL, 32611, USA); Alexander Roman (Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL, 32611, USA); Eyup B. Unlu (Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL, 32611, USA); et al - Show all 6 authors
Recent work has applied supervised deep learning to derive continuous symmetry transformations that preserve the data labels and to obtain the corresponding algebras of symmetry generators. This letter introduces two improved algorithms that significantly speed up the discovery of these symmetry transformations. The new methods are demonstrated by deriving the complete set of generators for the unitary groups and the exceptional Lie groups , , and . A third post-processing algorithm renders the found generators in sparse form. We benchmark the performance improvement of the new algorithms relative to the standard approach. Given the significant complexity of the exceptional Lie groups, our results demonstrate that this machine-learning method for discovering symmetries is completely general and can be applied to a wide variety of labeled datasets.
