# Continuous Symmetry Discovery and Enforcement Using Infinitesimal Generators of Multi-parameter Group Actions

arXiv: https://arxiv.org/abs/2505.08219 · HTML: https://mlsanity.com/paper/2505.08219/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2025.

## Built on by (most cited first, 3 of 3)

- [Adaptive Symmetry Discovery for Dynamical System Identification](https://mlsanity.com/paper/2608.08091/) (2026)
- [Efficient Learning and Symmetry Discovery under Exact Invariances](https://mlsanity.com/paper/2609.07031/) (2026)
- [Discovering Symmetries in Neural Network Parameter Spaces](https://mlsanity.com/paper/2609.33527/) (2026)

## Abstract (arXiv)

Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting affine transformations. Herein, we outline a computationally efficient framework for discovering infinitesimal generators of multi-parameter group actions which are not generally affine transformations. This framework accommodates the automatic discovery of the number of linearly independent infinitesimal generators. We build upon recent work in continuous symmetry discovery by extending to neural networks and by restricting the symmetry search space to infinitesimal isometries. We also introduce symmetry enforcement of smooth models using vector field regularization, thereby improving model generalization. The notion of vector field similarity is also generalized for non-Euclidean Riemannian metric tensors.