Supplementary Material for Certified Defense to Image Transformations via Randomized Smoothing A Proof of Theorem 3.2

We now proceed to proof Theorem 3.2. Next we show that Eq. (15) holds. Does there exist a t such that both upper bound coincide? We now show Theorem 3.2 (restarted below): Setting Theorem 3.2 up to the last sentence, which in turn is a direct consequence of Lemma 2. Theorem In this section, we elaborate on the details of Step 2 in Section 6. Because we don't have any constraints for the pixel values Here, we present the algorithm used to compute the inverse of a transformation.