General Lipschitz: Certified Robustness Against Resolvable Semantic
  Transformations via Transformation-Dependent Randomized Smoothing
Dmitrii Korzh Mikhail Pautov Olga Tsymboi Ivan Oseledets
Randomized smoothing is the state-of-the-art approach to construct image
classifiers that are provably robust against additive adversarial perturbations
of bounded magnitude. However, it is more complicated to construct reasonable
certificates against semantic transformation (e.g., image blurring,
translation, gamma correction) and their compositions. In this work, we propose
\emph{General Lipschitz (GL),} a new framework to certify neural networks
against composable resolvable semantic perturbations. Within the framework, we
analyze transformation-dependent Lipschitz-continuity of smoothed classifiers
w.r.t. transformation parameters and derive corresponding robustness
certificates. Our method performs comparably to state-of-the-art approaches on
the ImageNet dataset.