  Stochastic regularization of neural networks (e.g. dropout) is a wide-spread
technique in deep learning that allows for better generalization. Despite its
success, continuous-time models, such as neural ordinary differential equation
(ODE), usually rely on a completely deterministic feed-forward operation. This
work provides an empirical study of stochastically regularized neural ODE on
several image-classification tasks (CIFAR-10, CIFAR-100, TinyImageNet).
Building upon the formalism of stochastic differential equations (SDEs), we
demonstrate that neural SDE is able to outperform its deterministic
counterpart. Further, we show that data augmentation during the training
improves the performance of both deterministic and stochastic versions of the
same model. However, the improvements obtained by the data augmentation
completely eliminate the empirical gains of the stochastic regularization,
making the difference in the performance of neural ODE and neural SDE
negligible.
