Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting affine transformations. Herein, we outline a computationally efficient framework for discovering infinitesimal generators of multi-parameter group actions which are not generally affine transformations. This framework accommodates the automatic discovery of the number of linearly independent infinitesimal generators. We build upon recent work in continuous symmetry discovery by extending to neural networks and by restricting the symmetry search space to infinitesimal isometries. We also introduce symmetry enforcement of smooth models using vector field regularization, thereby improving model generalization. The notion of vector field similarity is also generalized for non-Euclidean Riemannian metric tensors.

翻译：对称性感知的机器学习相较于未考虑对称性的机器学习展现出显著优势。在连续对称性检测领域，当前最先进的实验主要局限于检测仿射变换。本文提出一种计算高效的框架，用于发现多参数群作用的无穷小生成元，这些生成元通常并非仿射变换。该框架支持自动发现线性无关无穷小生成元的数量。我们基于近期连续对称性发现的研究，将其扩展至神经网络领域，并将对称性搜索空间限制为无穷小等距变换。此外，我们引入基于向量场正则化的光滑模型对称性强制方法，从而提升模型泛化能力。本文还将向量场相似性概念推广至非欧几里得黎曼度量张量情形。