# DeformRS: Certifying Input Deformations with Randomized Smoothing

Source: [DeformRS: Certifying Input Deformations with Randomized Smoothing](<https://www.sota2.com/research/paper/68fa6b7e1e209131cea2e94d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T23:50:06.694Z

Authors: Motasem Alfarra, Adel Bibi, Naeemullah Khan, Philip H. S. Torr, Bernard Ghanem

Published: 2021-07-02T12:20:15.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2107.00996>)

[PDF](<https://arxiv.org/pdf/2107.00996.pdf>)