#### A Continuous Mapping For Augmentation Design

Automated data augmentation (ADA) techniques have played an important role in boosting the performance of deep models. Such techniques mostly aim to optimize a parameterized distribution over a discrete augmentation space. Thus, are restricted by the discretization of the search space which normally is handcrafted. To overcome the limitations, we take the first step to constructing a continuous mapping from $\mathbb{R}^d$ to image transformations (an augmentation space). Using this mapping, we take a novel approach where 1) we pose the ADA as a continuous optimization problem over the parameters of the augmentation distribution; and 2) use Stochastic Gradient Langevin Dynamics to learn and sample augmentations. This allows us to potentially explore the space of infinitely many possible augmentations, which otherwise was not possible due to the discretization of the space. This view of ADA is radically different from the standard discretization based view of ADA, and it opens avenues for utilizing the vast efficient gradient-based algorithms available for continuous optimization problems. Results over multiple benchmarks demonstrate the efficiency improvement of this work compared with previous methods.