Inverse Learning of Symmetries

TL;DR

This paper introduces a novel method for learning symmetry transformations in complex domains by disentangling target and invariant information using a deep information bottleneck approach, outperforming existing methods.

Contribution

The paper presents a new model that learns symmetry transformations without explicit analytical forms, utilizing a two-subspace latent model and a mutual information regularizer for continuous domains.

Findings

Outperforms state-of-the-art methods on artificial datasets

Effective in molecular data for capturing invariances

Handles continuous mutual information minimization successfully

Abstract

Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation cannot be formulated analytically. We propose to learn the symmetry transformation with a model consisting of two latent subspaces, where the first subspace captures the target and the second subspace the remaining invariant information. Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser. Unlike previous methods, we focus on the challenging task of minimising mutual information in continuous domains. To this end, we base the calculation of mutual information on correlation matrices in combination with a bijective variable transformation. Extensive experiments demonstrate that our model outperforms state-of-the-art methods on artificial and molecular datasets.