Lie Group Symmetry Discovery and Enforcement Using Vector Fields

Abstract: Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. Additionally, recent attention has been given to continuous symmetry discovery using vector fields which serve as infinitesimal generators for Lie group symmetries. In this paper, we extend the notion of non-affine symmetry discovery to functions defined by neural networks. We further extend work in this area by introducing symmetry enforcement of smooth models using vector fields. Finally, we extend work on symmetry discovery using vector fields by providing both theoretical and experimental material on the restriction of the symmetry search space to infinitesimal isometries.