not obvious a priori (and indeed, as we explain in Section 2.2, the previously used objective (4) also has a natural

We thank the reviewers for their comments. Before we address individual concerns, we make some general comments. This new insight is an alternative, and much simpler, proof of Cohen et al.'s key This also opens up another avenue for future work, namely by finding better nonlinear Lipschitz guarantees. As mentioned above, the Expectation over Transformation attack of Athalye et al. has the opposite order of log and We will add this citation and a discussion of this interesting connection. Thus, high abstention rate leads to lower certified accuracies. Nevertheless, we will add this experiment to the final version of the paper.