is conceptual, showing that it is possible to achieve both robustness and accuracy in principle (contrary to previous

We thank all reviewers for their comments. We are glad everyone found out paper well written. Below we address specific comments. "There exist no real world data where the classes are well-separated... images suffer from different lighting and To be concrete, here is a turtle and a fish from Restricted ImageNet. Moving 2 r from the turtle to the fish still looks much more like a turtle. "The classifier proposed in the existence proof essentially computes the distance of a test point to every point in the However, our theory result is not intended to be used in practice.