A Generative Model of Symmetry Transformations
This work addresses the challenge of incorporating symmetries into generative models for better generalization, though it is incremental as it builds on existing group theoretic ideas.
The paper tackles the problem of learning symmetry transformations from data without prior knowledge by introducing a generative model that captures approximate symmetries, resulting in improved test-log-likelihoods and data efficiency.
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 but 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.