Accelerated Discovery of Machine-Learned Symmetries: Deriving the
  Exceptional Lie Groups G2, F4 and E6
Roy T. Forestano Konstantin T. Matchev Katia Matcheva Alexander Roman Eyup B. Unlu Sarunas Verner
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 U(n) and the exceptional Lie groups $G_2$,
$F_4$, and $E_6$. 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.