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A Data-Augmentation Is Worth A Thousand Samples: Analytical Moments And Sampling-Free Training
Randall Balestriero · Ishan Misra · Yann LeCun

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #322

Data-Augmentation (DA) is known to improve performance across tasks and datasets. We propose a method to theoretically analyze the effect of DA and study questions such as: how many augmented samples are needed to correctly estimate the information encoded by that DA? How does the augmentation policy impact the final parameters of a model? We derive several quantities in close-form, such as the expectation and variance of an image, loss, and model's output under a given DA distribution. Up to our knowledge, we obtain the first explicit regularizer that corresponds to using DA during training for non-trivial transformations such as affine transformations, color jittering, or Gaussian blur. Those derivations open new avenues to quantify the benefits and limitations of DA. For example, given a loss at hand, we find that common DAs require tens of thousands of samples for the loss to be correctly estimated and for the model training to converge. We then show that for a training loss to have reduced variance under DA sampling, the model's saliency map (gradient of the loss with respect to the model's input) must align with the smallest eigenvector of the sample's covariance matrix under the considered DA augmentation; this is exactly the quantity estimated and regularized by TangentProp. Those findings also hint at a possible explanation on why models tend to shift their focus from edges to textures when specific DAs are employed.

Author Information

Randall Balestriero (Meta AI, FAIR)
Ishan Misra (Facebook AI Research)
Yann LeCun (Facebook)

Yann LeCun is Director of AI Research at Facebook, and Silver Professor of Data Science, Computer Science, Neural Science, and Electrical Engineering at New York University. He received the Electrical Engineer Diploma from ESIEE, Paris in 1983, and a PhD in Computer Science from Université Pierre et Marie Curie (Paris) in 1987. After a postdoc at the University of Toronto, he joined AT&T Bell Laboratories in Holmdel, NJ in 1988. He became head of the Image Processing Research Department at AT&T Labs-Research in 1996, and joined NYU as a professor in 2003, after a brief period as a Fellow of the NEC Research Institute in Princeton. From 2012 to 2014 he directed NYU's initiative in data science and became the founding director of the NYU Center for Data Science. He was named Director of AI Research at Facebook in late 2013 and retains a part-time position on the NYU faculty. His current interests include AI, machine learning, computer perception, mobile robotics, and computational neuroscience. He has published over 180 technical papers and book chapters on these topics as well as on neural networks, handwriting recognition, image processing and compression, and on dedicated circuits for computer perception.

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