A method to challenge symmetries in data with self-supervised learning

Abstract: Symmetries are key properties of physical models and of experimental designs, but any proposed symmetry may or may not be realized in nature. In this paper, we introduce a practical and general method to test such suspected symmetries in data, with minimal external input. Self-supervision, which derives learning objectives from data without external labelling, is used to train models to predict 'which is real?' between real data and symmetrically transformed alternatives. If these models make successful predictions in independent tests, then they challenge the targeted symmetries. Crucially, our method handles filtered data, which often arise from inefficiencies or deliberate selections, and which could give the illusion of asymmetry if mistreated. We use examples to demonstrate how the method works and how the models' predictions can be interpreted. Code and data are available at https://zenodo.org/record/6861702.