Data augmentation enforces invariances by adding transformed copies of data according to a known symmetry group, but full augmentation over large groups is often computationally infeasible. This work develops a Fourier-analysis framework showing that sublinear or partial augmentation can recover the same statistical benefits as full group augmentation in terms of generalization and sample complexity. The results provide a theoretical explanation for why partial augmentation can remain effective even when only a small subset of transformations is used.