Learning Infinitesimal Generators of Continuous Symmetries from Data

Exploiting symmetry inherent in data can significantly improve the sample efficiency of a learning procedure and the generalization of learned models. When data clearly reveals underlying symmetry, leveraging this symmetry can naturally inform the design of model architectures or learning strategies. Yet, in numerous real-world scenarios, identifying the specific symmetry within a given data distribution often proves ambiguous. To tackle this, some existing works learn symmetry in a data-driven manner, parameterizing and learning expected symmetry through data. However, these methods often rely on explicit knowledge, such as pre-defined Lie groups, which are typically restricted to linear or affine transformations.