A Generative Model of Symmetry Transformations
James Urquhart Allingham Bruno Kacper Mlodozeniec Shreyas Padhy Javier Antorán David Krueger Richard E. Turner Eric Nalisnick José Miguel Hernández-Lobato
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.