MIT/Harvard researchers prove partial data augmentation matches full augmentation's statistical benefits

Data augmentation is a go-to technique for enforcing known invariances in machine learning—rotating images of cats or shuffling sentence structure, for instance—but it comes with a steep computational cost: for large symmetry groups, applying every possible transformation to every training sample quickly becomes impossible. A new paper published at COLT 2026, by Behrooz Tahmasebi, Melanie Weber, and Stefanie Jegelka (MIT and Harvard), uses Fourier analysis and representation theory to tackle this head-on. The authors show that for a broad class of classical learning problems, randomly selecting a subset of group elements for augmentation yields the same statistical performance—measured by minimax rates—as using the entire group, as long as the subset is large enough. Moreover, the approximation error vanishes as the subset size increases, providing a theoretical basis for why practitioners often get away with limited augmentation.

The work also includes a sharp impossibility result: achieving exact invariance via data augmentation demands averaging over the entire group when the hypothesis space is sufficiently expressive. No strict subset can replicate that guarantee. Together, these results unify the theory of full and partial augmentation, and offer a scalable path forward for learning under general group symmetries. For engineers training large-scale vision or language models, this means they can drastically reduce the computational overhead of data augmentation without sacrificing model quality—a practical win grounded in rigorous theory. The paper is 42 pages and appears at the Conference on Learning Theory (COLT) 2026.