A Generative Model of Symmetry Transformations

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made in learning those symmetries directly from the dataset, most of this work has focused on the discriminative setting. In this paper, we construct a generative model that explicitly aims to capture symmetries in the data, resulting in a model that learns which symmetries are present in an interpretable way. We provide a simple algorithm for efficiently learning our generative model and demonstrate its ability to capture symmetries under affine and color transformations. Combining our symmetry model with existing generative models results in higher marginal test-log-likelihoods and robustness to data sparsification.