Self-Supervised Detection of Perfect and Partial Input-Dependent Symmetries
This work addresses the challenge of adapting group equivariance models to real-world data where symmetries vary per input, which is incremental as it extends existing symmetry detection methods to unsupervised and input-specific scenarios.
The paper tackles the problem of detecting input-dependent symmetries in data without labels, addressing limitations of existing methods that operate at the dataset level and require supervision. It demonstrates effectiveness on synthetic datasets with varying per-class symmetry levels and shows practical applications like out-of-distribution symmetry detection.
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.