Symmetry in Machine Learning

Unified framework: Presents a single theoretical framework that covers data augmentation, equivariant architectures, and symmetry-discovering learning objectives.

Three-way taxonomy: Organizes approaches into enforcing known symmetries, discovering latent ones, and biasing learning toward symmetric solutions.

Worked examples: Applies the framework to MLPs and basis-function regression, showing concretely how the abstract concepts translate into design choices.

Broader ML perspective: Positions symmetry as a first-class design lever alongside scale and data quality, particularly for scientific ML.