  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.
