Group equivariance can overly constrain models if the symmetries in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to supervised settings and ignore scenarios in which multiple levels of symmetry co-exist in the same dataset. In this paper, we propose a method able to detect the level of symmetry of each input without the need for labels. Our framework is general enough to accommodate different families of both continuous and discrete symmetry distributions, such as arbitrary unimodal, symmetric distributions and discrete groups. We validate the effectiveness of our approach on synthetic datasets with different per-class levels of symmetries, and demonstrate practical applications such as the detection of out-of-distribution symmetries. Our code is publicly available at https://github.com/aurban0/ssl-sym.

翻译：若群等变性中的对称性与数据中观测到的对称性存在差异，则可能对模型产生过度约束。现有方法通常通过在数据集层面确定合适的对称性水平来解决此问题，但这些方法仅限于监督学习场景，且忽略了同一数据集中多种对称性水平共存的情况。本文提出一种无需标签即可检测每个输入对称性水平的方法。我们的框架具有足够普适性，能够适应不同族群的连续与离散对称性分布，例如任意单峰对称分布和离散群。我们在具有不同类别对称性水平的合成数据集上验证了方法的有效性，并展示了实际应用场景，如分布外对称性检测。代码已公开于 https://github.com/aurban0/ssl-sym。