Local Mixup: Interpolation of closest input signals to prevent manifold intrusion

In Machine Learning, Mixup is a data-dependent regularization technique that consists in creating virtual samples by linearly interpolating input signals and their associated outputs. It has been shown to significantly improve accuracy on standard datasets, in particular in the field of vision. However, authors have pointed out that Mixup can produce out-of-distribution virtual samples and even contradictions in the augmented training set, potentially resulting in adversarial effects. In this paper, we introduce Local Mixup in which distant input samples are weighted down when computing the loss. In constrained settings we demonstrate that Local Mixup can create a trade-off between bias and variance, with the extreme cases reducing to vanilla training and classical Mixup. Using standardized computer vision benchmarks, we also show that Local Mixup can improve test accuracy. [Display omitted] •Our work contributes more broadly to better understanding the impact of Mixup during training.•We introduce Local Mixup, a mixup method depending on a single parameter whose extremes correspond to classical Mixup and Vanilla (i.e. baseline without mixup).•In dimension one, we prove that Local Mixup allows to select a bias/variance trade-off (Theorem 4.2 and 4.4).•Extending our analysis to higher dimensions, we demonstrate that Mixup imposes a lower bound on the Lipschitz constant of the model, which can be tuned using Local Mixup (Theorem 4.6). To empirically support this claim, we present results illustrating the evolution of this bound on the CIFAR10 dataset.•Using standard vision datasets, we show that Local Mixup can help achieving more accurate and robust models than classical Mixup.