Data augmentation is a technique to reduce overfitting and to improve generalization by increasing the number of labeled data samples by performing label preserving transformations; however, it is currently conducted in a trial and error manner. A composition of predefined transformations, such as rotation, scaling and cropping, is performed on training samples, and its effect on performance over test samples can only be empirically evaluated and cannot be predicted. This paper considers an influence function which predicts how generalization is affected by a particular augmented training sample in terms of validation loss. The influence function provides an approximation of the change in validation loss without comparing the performance which includes and excludes the sample in the training process. A differentiable augmentation model that generalizes the conventional composition of predefined transformations is also proposed. The differentiable augmentation model and reformulation of the influence function allow the parameters of the augmented model to be directly updated by backpropagation to minimize the validation loss. The experimental results show that the proposed method provides better generalization over conventional data augmentation methods.
[Summary]
This paper proposes a differentiable framework to learn to augment data for image classification. In particular, it uses spatial transformer and GANs as parametric data augmenters, and it formulates the validation set loss with respect to the data augmenter in a differentiable manner. 
[Pros]
1.	The proposed method does not require many trials of model training under different training data, and it learns the data augmentation directly using the final classification objective.
2.	It is inspiring to extend the differentiable form of influence function across the training and validation set and then across the original and augmented data. This paper also makes use of the most recent related advance to enable stochastic learning. The theory of the paper is nice.
3.	The experimental results on MNIST (with less labeled data) and Cifar-10 are encouraging.
[Cons]
1.	Experimental results can be stronger. Especially when compared to Ratner et al., this proposed method results in marginal performance gain. Given that Ratner et al.’s method trained the data augmentation module without supervision, the supervised learning in this paper does not show strong results. In addition, the paper did not report results on a more practical dataset (such ImageNet and Places). Even for Cifar-10, the reported numbers are away from the state-of-the-art. It is important to show the practical significance of the proposed method.
2.	Data augmentation is naturally expected to be random, but the proposed method seems to learn a deterministic parameter for the augmenting transformation, which looks unnatural and limited. (Please clarify if I missed anything.) 
3.	The proposed method requires a parametric model (e.g, STN, GAN). However, differentiable parametric models are not always easy to design. This probably can be the biggest obstacle to apply the proposed method widely.
Overall, the proposed method is very interesting. However, the experimental results are limited, and more discussions are needed.