mlsanityData to 14 Oct 2026

DeformRS: Certifying Input Deformations with Randomized Smoothing

arXiv 2107.00996 ↗First posted 2 Jul 2021cs.LG stat.MLcited by 17

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Abstract (arXiv)

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 [-10degree,10degree] on ImageNet.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 25 of its 39 references that are in the map. First posted on arXiv 2 Jul 2021.

Builds on

25 of 39 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  4. 2013Intriguing properties of neural networkscited by 5,155
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  6. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  7. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 468
  8. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 330
  9. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  10. 2016Safety Verification of Deep Neural Networkscited by 263
  11. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 255
  12. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 242
13 more
  1. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 179
  2. 2020Randomized Smoothing of All Shapes and Sizescited by 147
  3. 2020MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radiuscited by 114
  4. 2019Wasserstein Adversarial Examples via Projected Sinkhorn Iterationscited by 89
  5. 2020Curse of Dimensionality on Randomized Smoothing for Certifiable Robustnesscited by 56
  6. 2020Certified Defense to Image Transformations via Randomized Smoothingcited by 51
  7. 2017Geometric robustness of deep networks: analysis and improvementcited by 45
  8. 2018ADef: an Iterative Algorithm to Construct Adversarial Deformationscited by 38
  9. 2020Physical Adversarial Attack on Vehicle Detector in the Carla Simulatorcited by 38
  10. 2020Data-Dependent Randomized Smoothingcited by 37
  11. 2019Wasserstein Smoothing: Certified Robustness against Wasserstein Adversarial Attackscited by 25
  12. 2018SADA: Semantic Adversarial Diagnostic Attacks for Autonomous Applicationscited by 12
  13. 2020Efficient Certification of Spatial Robustnesscited by 11

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Cited by year

Citing papers per year: 2021: 1; 2022: 7; 2023: 6; 2024: 1; 2025: 2.

17 papers.

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  1. 2023Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attackscited by 34
  2. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 19
  3. 20223DeformRS: Certifying Spatial Deformations on Point Cloudscited by 10
  4. 2022Invariance-Aware Randomized Smoothing Certificatescited by 7
  5. 2023Improving Viewpoint Robustness for Visual Recognition via Adversarial Trainingcited by 7
  6. 2022Generalizability of Adversarial Robustness Under Distribution Shiftscited by 6
  7. 2022Certified Robustness in Federated Learningcited by 4
  8. 2023Precise and Generalized Robustness Certification for Neural Networkscited by 4
  9. 2022Robustness Certification of Visual Perception Models via Camera Motion Smoothingcited by 3
  10. 2022Landmark Tracking in Liver US images Using Cascade Convolutional Neural Networks with Long Short-Term Memorycited by 2
  11. 2023Certifying Ensembles: A General Certification Theory with S-Lipschitznesscited by 2
  12. 2023Pixel-wise Smoothing for Certified Robustness against Camera Motion Perturbationscited by 2
5 more
  1. 2025Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifiercited by 2
  2. 2024Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothingcited by 1
  3. 2022Towards Assessing and Characterizing the Semantic Robustness of Face Recognitioncited by 0
  4. 2023General Lipschitz: Certified Robustness Against Resolvable Semantic Transformations via Transformation-Dependent Randomized Smoothingcited by 0
  5. 2025Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifierscited by 0