mlsanityData to 14 Oct 2026

On the Convergence of Certified Robust Training with Interval Bound Propagation

arXiv 2203.08961 ↗First posted 16 Mar 2022cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training neural networks with certifiable robustness guarantees when potential adversarial perturbations present, while the convergence of IBP training remains unknown in existing literature. In this paper, we present a theoretical analysis on the convergence of IBP training. With an overparameterized assumption, we analyze the convergence of IBP robust training. We show that when using IBP training to train a randomly initialized two-layer ReLU neural network with logistic loss, gradient descent can linearly converge to zero robust training error with a high probability if we have sufficiently small perturbation radius and large network width.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 43 of its 55 references that are in the map. First posted on arXiv 16 Mar 2022.

Builds on

43 of 55 references.

References · 43

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  3. 2013Intriguing properties of neural networkscited by 5,155
  4. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  5. 2016Adversarial examples in the physical worldcited by 1,769
  6. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,517
  7. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  8. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,268
  9. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  10. 2018Gradient Descent Provably Optimizes Over-parameterized Neural Networkscited by 659
  11. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 574
  12. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 567
31 more
  1. 2020On Adaptive Attacks to Adversarial Example Defensescited by 555
  2. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 546
  3. 2017Countering Adversarial Images using Input Transformationscited by 520
  4. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 445
  5. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 330
  6. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  7. 2018Certified Defenses against Adversarial Examplescited by 306
  8. 2018On the Optimization of Deep Networks: Implicit Acceleration by Overparameterizationcited by 284
  9. 2018Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Datacited by 261
  10. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 255
  11. 2017PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examplescited by 244
  12. 2019Towards Stable and Efficient Training of Verifiably Robust Neural Networkscited by 205
  13. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  14. 2018Certified Adversarial Robustness with Additive Noisecited by 180
  15. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 179
  16. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  17. 2018Scaling provable adversarial defensescited by 143
  18. 2018Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networkscited by 141
  19. 2021On the Convergence and Robustness of Adversarial Trainingcited by 130
  20. 2019Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networkscited by 121
  21. 2019How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?cited by 84
  22. 2018Training for Faster Adversarial Robustness Verification via Inducing ReLU Stabilitycited by 67
  23. 2019Convergence of Adversarial Training in Overparametrized Neural Networkscited by 58
  24. 2019Enhancing Adversarial Defense by k-Winners-Take-Allcited by 51
  25. 2018Training verified learners with learned verifierscited by 50
  26. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  27. 2020Over-parameterized Adversarial Training: An Analysis Overcoming the Curse of Dimensionalitycited by 36
  28. 2021Towards Evaluating and Training Verifiably Robust Neural Networkscited by 15
  29. 2020Interval Universal Approximation for Neural Networkscited by 14
  30. 2021Provable Robustness of Adversarial Training for Learning Halfspaces with Noisecited by 10
  31. 2019Universal Approximation with Certified Networkscited by 9

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 2.

5 papers.

  1. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  2. 2023Understanding Certified Training with Interval Bound Propagationcited by 26
  3. 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
  4. 2024Robust NAS under adversarial training: benchmark, theory, and beyondcited by 6
  5. 2024Certified Training with Branch-and-Bound for Lyapunov-stable Neural Controlcited by 3