Paper:
Enhancing model robustness under new and even adversarial environments is a crucial milestone toward building trustworthy and reliable machine learning systems. Current robust training methods such as adversarial training explicitly specify an "attack" (e.g., ∞ -norm bounded perturbation) to generate adversarial examples during model training in order to improve adversarial robustness. In this paper, we take a different perspective and propose a new framework SPROUT, self-progressing robust training. During model training, SPROUT progressively adjusts training label distribution via our proposed parametrized label smoothing technique, making training free of attack generation and more scalable. We also motivate SPROUT using a general formulation based on vicinity risk minimization, which includes many robust training methods as special cases. Compared with stateof-the-art adversarial training methods (PGD-∞ and TRADES) under ∞ -norm bounded attacks and various invariance tests, SPROUT consistently attains superior performance and is more scalable to large neural networks. Our results shed new light on scalable, effective and attack-independent robust training methods.

Review:
This work proposes training robust models without explicitly training on adversarial examples and by "smoothing" the labels in an adversarial fashion and by using Dirichlet label smoothing. Training robust models without adversarial training is indeed an important problem as mentioned by the authors since it can potentially (as the authors demonstrate) result in faster model training and less drop in clean accuracy. Overall the idea is interesting but I have some concerns mainly about evaluations and baselines which I am including below. If the authors can address my concerns, I am willing to increase my score:
1. Based on equations (9) and (10), if we set \alpha to be large, then the network is not trainable (since the worst-case adversary will increase the loss on the image by flipping the label during training). As a consequence, we can see that the value of hyper-parameters that the authors use is indeed very small (0.01 and 0.1). Even between these small values, the smaller value results in a better model. In the extreme case, where \alpha is zero there is no regularization and \beta becomes irrelevant. This illustrates that the performance of the model is very sensitive to \alpha. On the other hand, we can prevent the model from not learning anything by constraining \beta in equation (10) — similar to adversarial training where we constrain \delta. It seems that without constraining \beta, if the step-size for \beta is large, \beta can grow and completely mess up the labels even when \alpha is tiny. If we constrain \beta on the other hand, we can make sure that in no case, the top label for any augmented image is an incorrect label. Can the authors elaborate on why they did not set any limit on the value of \beta?
2. What is the batch-size used for ImageNet? The reason that I am asking is that you compute the gradient of \beta for the previous mini-batch but use it for the next mini-batch. Is it possible that the previous mini-batch's \beta is not accurate for the current mini-batch? For CIFAR, since the number of classes is 10, I would assume that you can update the statistics for the class (\betas) using the previous mini-batch since you always see examples from all the classes using any reasonable batch-size. What happens if you do the same but for a dataset with more classes but have the mini-batch be smaller than the number of classes. In this case, your \beta is getting updated only using information from a few classes and not all classes at once. In that case, what happens if you just use a random \beta every step? 
3. For the white-box attacks, I also have a few questions. Do you use multiple random restarts? It is known that random restarts can be more effective than increasing the number of PGD attacks. See for example the leaderboards for MNIST and CIFAR-10 challenges by Madry. I would like to see a table where you plot how the accuracy changes by doing 100 step PGD attacks and by increasing the number of random restarts from 1 to 10 for example.
4. Do you do L-infinity CW attacks? I see that you have done L-2 CW attacks but I can't find any L-infinity CW attacks. It would be great to show numbers for that and also compare it with TRADES and PGD adversarial training. In previous smoothing methods, the L-infinity CW attack seems to be a stronger attack compared to PGD.
5. For the ImageNet task, the authors state that the evaluation of non-targeted attacks can result in label leaking. Label-leaking happens when one trains on adversarial examples built using a single-step attack and it means that the accuracy of adversarial examples is higher than natural examples at test-time. For this, I do not understand why the authors mention that they only evaluate targeted attacks while they are not doing any adversarial training.
6. Also, for ImageNet, there are recent methods such as Adversarial training for Free! where the authors do adversarial training on ImageNet with no overhead cost compared to natural training. Maybe this could be added as a better base-line than a naturally trained model.
7. In Figure 4. (a), why is the loss for the validation image illustrated so high? What image is this from the validation set?
8. In terms of Scalability, its good to mention new scalable methods such as YOPO and Adversarial Training for Free.
9. In the ablation study, including Dirichlet Smoothing indeed results in a huge boost compared to having no smoothing. However, it would be better to show that Dirichlet smoothing is indeed better than label-smoothing or adversarial smoothing by including results for other smoothing methods in Fig. 5.