k-Mixup Regularization for Deep Learning via Optimal Transport
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Mixup is a popular regularization technique for training deep neural networks that can improve generalization and increase adversarial robustness. It perturbs input training data in the direction of other randomly-chosen instances in the training set. To better leverage the structure of the data, we extend mixup to k-mixup by perturbing k-batches of training points in the direction of other k-batches using displacement interpolation, interpolation under the Wasserstein metric. We demonstrate theoretically and in simulations that k-mixup preserves cluster and manifold structures, and we extend theory studying efficacy of standard mixup. Our empirical results show that training with k-mixup further improves generalization and robustness on benchmark datasets.
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