mlsanityData to 7 Oct 2026

Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation

arXiv 2408.13140 ↗First posted 23 Aug 2024cs.LG cs.AI cs.CVcited by 7

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Abstract (arXiv)

We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz optimisation. The method obtains provably tighter over-approximations of the perturbation region than the present state-of-the-art. We report results from experiments on a comprehensive set of verification benchmarks on MNIST and CIFAR10. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 29 of its 46 references that are in the map. First posted on arXiv 23 Aug 2024.

Builds on

29 of 46 references.

References · 29

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  2. 2015Spatial Transformer Networkscited by 1,423
  3. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  4. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  5. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  6. 2019Algorithms for Verifying Deep Neural Networkscited by 221
  7. 2018Spatially Transformed Adversarial Examplescited by 195
  8. 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 183
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  11. 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
  12. 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
17 more
  1. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  2. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  3. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 100
  4. 2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
  5. 2020Verification of Deep Convolutional Neural Networks Using ImageStarscited by 75
  6. 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
  7. 2020Certified Defense to Image Transformations via Randomized Smoothingcited by 51
  8. 2020The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verificationcited by 50
  9. 2020TSS: Transformation-Specific Smoothing for Robustness Certificationcited by 49
  10. 2017Geometric robustness of deep networks: analysis and improvementcited by 45
  11. 2020Lagrangian Decomposition for Neural Network Verificationcited by 35
  12. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  13. 2017Towards Practical Verification of Machine Learning: The Case of Computer Vision Systemscited by 19
  14. 2019Invariance-inducing regularization using worst-case transformations suffices to boost accuracy and spatial robustnesscited by 18
  15. 2020On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examplescited by 14
  16. 2022Provable Defense Against Geometric Transformationscited by 14
  17. 2018Formal Verification of CNN-based Perception Systemscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 6.

7 papers.

  1. 2026MKA: Memory-Keyed Attention for Efficient Long-Context Reasoningcited by 6
  2. 2024Verification of Neural Networks against Convolutional Perturbations via Parameterised Kernelscited by 2
  3. 2026IoUCert: Robustness Verification for Anchor-based Object Detectorscited by 1
  4. 2026Talking with Verifiers: Automatic Specification Generation for Neural Network Verificationcited by 0
  5. 2026Certified geometric robustness -- Super-DeepGcited by 0
  6. 2026Lipschitz Optimization for Formal Verification of Homographiescited by 0
  7. 2026Certified Training for Convolutional Perturbationscited by 0