Data to 14 Oct 2026

On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models

arXiv 1810.12715 ↗First posted 30 Oct 2018cs.LG cs.CR stat.MLcited by 328

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Abstract (arXiv)

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often result in difficult optimization procedures that remain hard to scale to larger networks. Through a comprehensive analysis, we show how a simple bounding technique, interval bound propagation (IBP), can be exploited to train large provably robust neural networks that beat the state-of-the-art in verified accuracy. While the upper bound computed by IBP can be quite weak for general networks, we demonstrate that an appropriate loss and clever hyper-parameter schedule allow the network to adapt such that the IBP bound is tight. This results in a fast and stable learning algorithm that outperforms more sophisticated methods and achieves state-of-the-art results on MNIST, CIFAR-10 and SVHN. It also allows us to train the largest model to be verified beyond vacuous bounds on a downscaled version of ImageNet.

Key facts. Cited by 328 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 Oct 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2020: 1; 2021: 66; 2022: 60; 2023: 63; 2024: 62; 2025: 35; 2026: 41.

328 papers.

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2023Certifying LLM Safety against Adversarial Promptingcited by 266
2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 228
2024Certifiably Robust RAG against Retrieval Corruptioncited by 151
2021Robust Reinforcement Learning on State Observations with Learned Optimal Adversarycited by 135
2022(Certified!!) Adversarial Robustness for Free!cited by 132
2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 103
2023A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validationcited by 93
2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
2021Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Boundscited by 65
2022Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learningcited by 61
2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58

38 more

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2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 51
2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 51
2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
2021Fast Certified Robust Training with Short Warmupcited by 46
2021Certified Patch Robustness via Smoothed Vision Transformerscited by 45
2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
2022Efficient Adversarial Training without Attacking: Worst-Case-Aware Robust Reinforcement Learningcited by 43
2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 42
2021Reachability Analysis of Neural Feedback Loopscited by 41
2022Certified Neural Network Watermarks with Randomized Smoothingcited by 41
2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
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2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
2022On the Robustness of Safe Reinforcement Learning under Observational Perturbationscited by 38
2022Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizabilitycited by 36
2023Exploring and Exploiting Decision Boundary Dynamics for Adversarial Robustnesscited by 36
2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
2020Imitation Learning with Stability and Safety Guaranteescited by 34
2021On the Sensitivity and Stability of Model Interpretations in NLPcited by 30
2021Low Curvature Activations Reduce Overfitting in Adversarial Trainingcited by 29
2023Provably Bounding Neural Network Preimagescited by 29
2023Adversarial Illusions in Multi-Modal Embeddingscited by 29
2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
2021Stability Verification in Stochastic Control Systems via Neural Network Supermartingalescited by 26
2022COPA: Certifying Robust Policies for Offline Reinforcement Learning against Poisoning Attackscited by 26
2023Understanding Certified Training with Interval Bound Propagationcited by 26
2021Taxonomy of Machine Learning Safety: A Survey and Primercited by 25
2022Architectural Backdoors in Neural Networkscited by 25
2021Knowledge Enhanced Machine Learning Pipeline against Diverse Adversarial Attackscited by 24
2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
2021ML Attack Models: Adversarial Attacks and Data Poisoning Attackscited by 24
2022Robust Explanation Constraints for Neural Networkscited by 24
2021Achieving Model Robustness through Discrete Adversarial Trainingcited by 23

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