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Recent work has applied supervised deep learning to derive continuoussymmetry transformations that preserve the data labels and to obtain thecorresponding algebras of symmetry generators. This letter introduces twoimproved algorithms that significantly speed up the discovery of these symmetrytransformations. The new methods are demonstrated by deriving the complete setof 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 foundgenerators in sparse form. We benchmark the performance improvement of the newalgorithms relative to the standard approach. Given the significant complexityof the exceptional Lie groups, our results demonstrate that thismachine-learning method for discovering symmetries is completely general andcan be applied to a wide variety of labeled datasets.

Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6