Symmetry detection has been shown to improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to the detection of 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：对称性检测已被证明能够改进多种机器学习任务。在连续对称性检测的背景下，当前最先进的实验仅限于仿射变换的检测。基于流形假设，我们提出了一个框架，用于发现仿射变换群之外的连续对称性。同时，我们提供了一个类似的框架用于发现离散对称性。我们通过实验将我们的方法与现有方法LieGAN进行对比，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，而在小样本量下则优于LieGAN。此外，我们证明了该方法能够检测仿射群之外的连续对称性，并且在计算效率上通常优于LieGAN。