  Mixup is a data augmentation technique that creates new examples as convex
combinations of training points and labels. This simple technique has
empirically shown to improve the accuracy of many state-of-the-art models in
different settings and applications, but the reasons behind this empirical
success remain poorly understood. In this paper we take a substantial step in
explaining the theoretical foundations of Mixup, by clarifying its
regularization effects. We show that Mixup can be interpreted as standard
empirical risk minimization estimator subject to a combination of data
transformation and random perturbation of the transformed data. We gain two
core insights from this new interpretation. First, the data transformation
suggests that, at test time, a model trained with Mixup should also be applied
to transformed data, a one-line change in code that we show empirically to
improve both accuracy and calibration of the prediction. Second, we show how
the random perturbation of the new interpretation of Mixup induces multiple
known regularization schemes, including label smoothing and reduction of the
Lipschitz constant of the estimator. These schemes interact synergistically
with each other, resulting in a self calibrated and effective regularization
effect that prevents overfitting and overconfident predictions. We corroborate
our theoretical analysis with experiments that support our conclusions.
