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We propose the first unified theoretical analysis of mixed sample dataaugmentation (MSDA), such as Mixup and CutMix. Our theoretical results showthat regardless of the choice of the mixing strategy, MSDA behaves as apixel-level regularization of the underlying training loss and a regularizationof the first layer parameters. Similarly, our theoretical results support thatthe MSDA training strategy can improve adversarial robustness andgeneralization compared to the vanilla training strategy. Using the theoreticalresults, we provide a high-level understanding of how different design choicesof MSDA work differently. For example, we show that the most popular MSDAmethods, Mixup and CutMix, behave differently, e.g., CutMix regularizes theinput gradients by pixel distances, while Mixup regularizes the input gradientsregardless of pixel distances. Our theoretical results also show that theoptimal MSDA strategy depends on tasks, datasets, or model parameters. Fromthese observations, we propose generalized MSDAs, a Hybrid version of Mixup andCutMix (HMix) and Gaussian Mixup (GMix), simple extensions of Mixup and CutMix.Our implementation can leverage the advantages of Mixup and CutMix, while ourimplementation is very efficient, and the computation cost is almostneglectable as Mixup and CutMix. Our empirical study shows that our HMix andGMix outperform the previous state-of-the-art MSDA methods in CIFAR-100 andImageNet classification tasks. Source code is available athttps://github.com/naver-ai/hmix-gmix

A Unified Analysis of Mixed Sample Data Augmentation: A Loss Function Perspective