Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline a framework for discovering continuous symmetry in data beyond the affine transformation group. We also provide a similar framework for discovering discrete symmetry. We experimentally compare our method to an existing method known as LieGAN and show that our method is competitive at detecting affine symmetries for large sample sizes and superior than LieGAN for small sample sizes. We also show our method is able to detect continuous symmetries beyond the affine group and is generally more computationally efficient than LieGAN.

翻译：对称性检测能够提升多种机器学习任务的性能。在连续对称性检测领域，当前最先进的实验方法仅限于检测仿射变换。基于流形假设，我们提出了一个用于发现数据中超越仿射变换群的连续对称性的框架。同时，我们也为离散对称性的发现提供了类似框架。我们通过实验将所提方法与现有方法LieGAN进行比较，结果表明：在大样本量下，我们的方法在检测仿射对称性方面具有竞争力；在小样本量下，其性能优于LieGAN。此外，我们的方法能够检测超越仿射群的连续对称性，并且在计算效率上普遍高于LieGAN。