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 take inspiration from group theoretic ideas to construct a generative model that explicitly aims to capture the data's approximate symmetries. This results in a model that, given a prespecified broad set of possible symmetries, learns to what extent, if at all, those symmetries are actually present. Our model can be seen as a generative process for data augmentation. We provide a simple algorithm for learning our generative model and empirically demonstrate its ability to capture symmetries under affine and color transformations, in an interpretable way. Combining our symmetry model with standard generative models results in higher marginal test-log-likelihoods and improved data efficiency.