Unsupervised discovery of symmetries and symmetry-based domains from raw data

ICLR 2026 Conference Submission19459 Authors

Keywords: Symmetry Learning, Representation Learning, Group Equivariant Neural Networks, Unsupervised Learning, Machine Learning

TL;DR: We develop a method for unsupervised discovery of symmetries and underlying symmetry-based domains from raw data

Abstract:

Signals are often generated by processes that respect a symmetry group of the domain they live on. Observed signals are obtained from underlying samples by some transformation corresponding to a physical process, resulting in a group action that is often more complicated than the action on the underlying domain. Learning the symmetry group and the underlying symmetry-based domain are two intertwined problems of fundamental importance.
In this paper, we develop a method that simultaneously discovers symmetries and symmetry-based domains in a fully unsupervised setting, without assuming that the group action is transitive. Our approach is based on a lifting operation inspired by Group Convolutional Networks, mapping the space of observed features to a domain parametrized by group elements. By utilizing a powerful locality prior, we are able to learn symmetry actions such as translations, permutations and frequency shifts, on datasets with much higher dimensionalities than has been possible before. Since the domain is hidden, we assume the symmetry group acts directly on the space of samples, which in the familiar case of natural images means the underlying pixel translation symmetries to be learned are for a set of images. As well as discovering the relevant symmetries directly from raw data, our method also offers new approach towards solving linear inverse problems.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 19459