On the benefits of defining vicinal distributions in latent space

The vicinal risk minimization (VRM) principle is an empirical risk minimization (ERM) variant that replaces Dirac masses with vicinal functions. There is strong numerical and theoretical evidence showing that VRM outperforms ERM in terms of generalization if appropriate vicinal functions are chosen. Mixup Training (MT), a popular choice of vicinal distribution, improves the generalization performance of models by introducing globally linear behavior in between training examples. Apart from generalization, recent works have shown that mixup trained models are relatively robust to input perturbations/corruptions and at the same time are calibrated better than their non-mixup counterparts. In this work, we investigate the benefits of defining these vicinal distributions like mixup in latent space of generative models rather than in input space itself. We propose a new approach - \textit{VarMixup (Variational Mixup)} - to better sample mixup images by using the latent manifold underlying the data. Our empirical studies on CIFAR-10, CIFAR-100, and Tiny-ImageNet demonstrate that models trained by performing mixup in the latent manifold learned by VAEs are inherently more robust to various input corruptions/perturbations, are significantly better calibrated, and exhibit more local-linear loss landscapes.