Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the $U(n)$ and $SU(n)$ families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.

翻译：近期研究利用深度学习推导出保持守恒量的对称变换及其生成元代数。本文将该方法推广至任意李代数稀疏表示的导出。我们证明该方法能够重现洛伦兹群生成元的典范（稀疏）表示，以及$U(n)$和$SU(n)$族李群的相应表示。该框架具有完全普适性，可适用于任意李群的无穷小生成元发现。