  Deep neural networks are vulnerable to input deformations in the form of
vector fields of pixel displacements and to other parameterized geometric
deformations e.g. translations, rotations, etc. Current input deformation
certification methods either 1. do not scale to deep networks on large input
datasets, or 2. can only certify a specific class of deformations, e.g. only
rotations. We reformulate certification in randomized smoothing setting for
both general vector field and parameterized deformations and propose
DeformRS-VF and DeformRS-Par, respectively. Our new formulation scales to large
networks on large input datasets. For instance, DeformRS-Par certifies rich
deformations, covering translations, rotations, scaling, affine deformations,
and other visually aligned deformations such as ones parameterized by
Discrete-Cosine-Transform basis. Extensive experiments on MNIST, CIFAR10, and
ImageNet show competitive performance of DeformRS-Par achieving a certified
accuracy of $39\%$ against perturbed rotations in the set
$[-10\degree,10\degree]$ on ImageNet.
