Papers › k-Mixup Regularization for Deep Learning via Optimal Transport

k-Mixup Regularization for Deep Learning via Optimal Transport

5 Jun 2021arXiv:2106.02933archive 2025-07-28

Kristjan Greenewald, Anming Gu, Mikhail Yurochkin, Justin Solomon, Edward Chien

Mixup is a popular regularization technique for training deep neural networks that improves generalization and increases robustness to certain distribution shifts. 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 in a simple, broadly applicable way to \emph{k-mixup}, which perturbs k-batches of training points in the direction of other k-batches. The perturbation is done with displacement interpolation, i.e. interpolation under the Wasserstein metric. We demonstrate theoretically and in simulations that k-mixup preserves cluster and manifold structures, and we extend theory studying the efficacy of standard mixup to the k-mixup case. Our empirical results show that training with k-mixup further improves generalization and robustness across several network architectures and benchmark datasets of differing modalities. For the wide variety of real datasets considered, the performance gains of k-mixup over standard mixup are similar to or larger than the gains of mixup itself over standard ERM after hyperparameter optimization. In several instances, in fact, k-mixup achieves gains in settings where standard mixup has negligible to zero improvement over ERM.

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