Continuous Symmetry Discovery and Enforcement Using Infinitesimal Generators of Multi-parameter Group Actions
This work addresses the challenge of incorporating non-affine symmetries into machine learning for better generalization, though it builds incrementally on prior symmetry discovery methods.
The paper tackles the problem of discovering continuous symmetries beyond affine transformations in machine learning models by introducing a computationally efficient framework for identifying infinitesimal generators of multi-parameter group actions, and it results in improved model generalization through vector field regularization.
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.