Continuous Symmetry Discovery and Enforcement for Image Data

ICLR 2026 Conference Submission21597 Authors

Keywords: Image Processing, Image Classification, Symmetry, Infinitesimal Generators, Invariance, Group Actions, Symmetry Discovery, Symmetry Enforcement

TL;DR: In this paper, we enforce continuous symmetry in image classification, and we discover continuous symmetry from training image data.

Abstract: Symmetry is an often-desired quality of machine learning models, leading, among other things, to more predictable model generalization. Continuous symmetry detection and enforcement for machine learning are two related topics that have recently been explored using the Lie derivative along vectors fields, which vector field approach has led to improved outcomes. However, though image data is replete with continuous symmetries under which image classifiers are meant to be invariant, the application of the Lie derivative for the detection and enforcement of continuous symmetries for image data remains under-explored. In this work, we derive vector field infinitesimal generators for various continuous symmetries for image data. We then use these generators to enforce continuous symmetry in image classifiers. We also demonstrate vector field symmetry detection in image data, obtaining close similarity with the ground truth symmetry.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 21597