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.

翻译：深度学习近期被成功应用于推导保持重要物理量的对称性变换。由于完全基于数据驱动，这些技术将所发现对称性的识别工作推迟至后续阶段。本文提出用于检验和识别此类机器学习对称性群论结构的方法。我们设计了能够探测子代数结构的损失函数，既可在对称性发现的深度学习阶段使用，也可在后续的后处理阶段应用。通过U(n)李群族案例验证了新方法，获得了相应的子代数分解。作为粒子物理应用，我们展示了自发破缺非阿贝尔规范对称性（如模型构建中常用的SU(3)与SU(5)）后的剩余对称性识别过程。