DeformRS: Certifying Input Deformations with Randomized Smoothing

TL;DR

This paper introduces DeformRS, a scalable randomized smoothing framework for certifying neural network robustness against complex input deformations like vector fields and geometric transformations, applicable to large datasets and deep networks.

Contribution

DeformRS reformulates input deformation certification within randomized smoothing, enabling certification of a broad class of deformations on large-scale datasets and deep neural networks.

Findings

DeformRS-Par certifies rotations, translations, scaling, and affine deformations.

Achieves 39% certified accuracy against rotations on ImageNet.

Scales effectively to large datasets and deep networks.

Abstract

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.