mlsanityData to 7 Oct 2026

IBP Regularization for Verified Adversarial Robustness via Branch-and-Bound

arXiv 2206.14772 ↗First posted 29 Jun 2022cs.LG cs.CR stat.MLcited by 21

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Abstract (arXiv)

Recent works have tried to increase the verifiability of adversarially trained networks by running the attacks over domains larger than the original perturbations and adding various regularization terms to the objective. However, these algorithms either underperform or require complex and expensive stage-wise training procedures, hindering their practical applicability. We present IBP-R, a novel verified training algorithm that is both simple and effective. IBP-R induces network verifiability by coupling adversarial attacks on enlarged domains with a regularization term, based on inexpensive interval bound propagation, that minimizes the gap between the non-convex verification problem and its approximations. By leveraging recent branch-and-bound frameworks, we show that IBP-R obtains state-of-the-art verified robustness-accuracy trade-offs for small perturbations on CIFAR-10 while training significantly faster than relevant previous work. Additionally, we present UPB, a novel branching strategy that, relying on a simple heuristic based on β-CROWN, reduces the cost of state-of-the-art branching algorithms while yielding splits of comparable quality.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 34 of its 58 references that are in the map. First posted on arXiv 29 Jun 2022.

Builds on

34 of 58 references.

References · 34

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  11. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  12. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
22 more
  1. 2019Towards Stable and Efficient Training of Verifiably Robust Neural Networkscited by 204
  2. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  3. 2018Scaling provable adversarial defensescited by 141
  4. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
  5. 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
  6. 2018Strong mixed-integer programming formulations for trained neural networkscited by 115
  7. 2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
  8. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  9. 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
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  13. 2020The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verificationcited by 50
  14. 2019Neural Network Branching for Neural Network Verificationcited by 45
  15. 2021Fast Certified Robust Training with Short Warmupcited by 45
  16. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
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  18. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 6; 2024: 7; 2025: 3; 2026: 4.

21 papers.

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  1. 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
  2. 2022Certified Training: Small Boxes are All You Needcited by 51
  3. 2023Understanding Certified Training with Interval Bound Propagationcited by 26
  4. 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
  5. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 23
  6. 2024CTBENCH: A Library and Benchmark for Certified Trainingcited by 13
  7. 2023TAPS: Connecting Certified and Adversarial Trainingcited by 11
  8. 2025Adversarial Attacks Leverage Interference Between Features in Superpositioncited by 7
  9. 2024Gaussian Loss Smoothing Enables Certified Training with Tight Convex Relaxationscited by 4
  10. 2024On Using Certified Training towards Empirical Robustnesscited by 3
  11. 2024Certified Training with Branch-and-Bound for Lyapunov-stable Neural Controlcited by 3
  12. 2024Verified Neural Compressed Sensingcited by 1
9 more
  1. 2024Towards Generalized Certified Robustness with Multi-Norm Trainingcited by 1
  2. 2026Learning Better Certified Models from Empirically-Robust Teacherscited by 1
  3. 2023Adaptive Certified Training: Towards Better Accuracy-Robustness Tradeoffscited by 0
  4. 2023Survival Analysis with Adversarial Regularizationcited by 0
  5. 2025Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustnesscited by 0
  6. 2025Lipschitz-aware Linearity Grafting for Certified Robustnesscited by 0
  7. 2026Improving Certified Robustness via Adversarial Distillationcited by 0
  8. 2026Certified Training for Convolutional Perturbationscited by 0
  9. 2026Verifying Neural Networks with Reinforcement Learningcited by 0