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Data augmentation is commonly applied to improve performance of deep learningby enforcing the knowledge that certain transformations on the input preservethe output. Currently, the data augmentation parameters are chosen by humaneffort and costly cross-validation, which makes it cumbersome to apply to newdatasets. We develop a convenient gradient-based method for selecting the dataaugmentation without validation data during training of a deep neural network.Our approach relies on phrasing data augmentation as an invariance in the priordistribution on the functions of a neural network, which allows us to learn itusing Bayesian model selection. This has been shown to work in Gaussianprocesses, but not yet for deep neural networks. We propose a differentiableKronecker-factored Laplace approximation to the marginal likelihood as ourobjective, which can be optimised without human supervision or validation data.We show that our method can successfully recover invariances present in thedata, and that this improves generalisation and data efficiency on imagedatasets.

Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximations