Continuous Symmetry Discovery and Enforcement for Image Data

NeurIPS 2025 Workshop NeurReps Submission151 Authors

Keywords: Symmetry Enforcement, Symmetry Detection, Computer Vision, Invariance, Geometric AI

TL;DR: We introduce continuous symmetry discovery and enforcement for image data using the Lie derivative along vector fields

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 has led to improved computational outcomes. However, though image data is littered with continuous symmetries under which image classifiers are meant to be invariant, the application of the Lie derivative for the detection and enforcement of these symmetries for image data remains underexplored. In this work, we derive vector field infinitesimal generators for various continuous symmetries for image data. We then use these generators to detect and enforce continuous symmetries in image classifiers. We show that these techniques lead to improved outcomes which are not possible using existing methods.

Submission Number: 151