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Data-Augmentation (DA) is known to improve performance across tasks anddatasets. We propose a method to theoretically analyze the effect of DA andstudy questions such as: how many augmented samples are needed to correctlyestimate the information encoded by that DA? How does the augmentation policyimpact the final parameters of a model? We derive several quantities inclose-form, such as the expectation and variance of an image, loss, and model'soutput under a given DA distribution. Those derivations open new avenues toquantify the benefits and limitations of DA. For example, we show that commonDAs require tens of thousands of samples for the loss at hand to be correctlyestimated and for the model training to converge. We show that for a trainingloss to be stable under DA sampling, the model's saliency map (gradient of theloss with respect to the model's input) must align with the smallesteigenvector of the sample variance under the considered DA augmentation,hinting at a possible explanation on why models tend to shift their focus fromedges to textures.

A Data-Augmentation Is Worth A Thousand Samples: Exact Quantification From Analytical Augmented Sample Moments