All reviewers agreed on the theoretical value of this paper, explaining the effects on data augmentation through group theory. The results are novel, and very relevant to one of the most widely techniques used along with SGD in practice. Some concerns were raised on the breadth of experimental validation, and expanding on the potential of the presented theory to better inform practice, that the authors should consider. I want to further add that in my opinion this is an excellent and very timely paper, and I am really looking forward to the ways it will impact the related literature.