We develop a new, unsupervised symmetry learning method that starts with raw data, and gives the minimal (discrete) generator of an underlying Lie group of symmetries, together with a symmetry equivariant representation of the data. The method is able to learn the pixel translation operator from a dataset with only an approximate translation symmetry, and can learn quite different types of symmetries which are not apparent to the naked eye, equally well. The method is based on the formulation of an information-theoretic loss function that measures both the degree to which the dataset is symmetric under a given candidate symmetry, and also, the degree of locality of the samples in the dataset with respect to this symmetry. We demonstrate that this coupling between symmetry and locality, together with a special optimization technique developed for entropy estimation, results in a highly stable system that gives reproducible results. The symmetry actions we consider are group representations, however, we believe the approach has the potential to be generalized to more general, nonlinear actions of non-commutative Lie groups.

本研究针对无监督对称性学习中存在的空白，提出了一种新方法，能够从原始数据中识别基础李群的对称性生成器及其同变表示。该方法通过结合对称性与局部性的关系，提供了一种高度稳定的系统，能够有效学习不易察觉的不同类型的对称性，展示了其在对称性学习领域的潜在重要影响。

SymmetryLens：一种通过局部性和同变性进行无监督对称性学习的新候选范式