  Data augmentation is popular in the training of large neural networks;
currently, however, there is no clear theoretical comparison between different
algorithmic choices on how to use augmented data. In this paper, we take a step
in this direction - we first present a simple and novel analysis for linear
regression with label invariant augmentations, demonstrating that data
augmentation consistency (DAC) is intrinsically more efficient than empirical
risk minimization on augmented data (DA-ERM). The analysis is then extended to
misspecified augmentations (i.e., augmentations that change the labels), which
again demonstrates the merit of DAC over DA-ERM. Further, we extend our
analysis to non-linear models (e.g., neural networks) and present
generalization bounds. Finally, we perform experiments that make a clean and
apples-to-apples comparison (i.e., with no extra modeling or data tweaks)
between DAC and DA-ERM using CIFAR-100 and WideResNet; these together
demonstrate the superior efficacy of DAC.
