Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound
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Abstract (arXiv)
State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging imprecise but fast bounding methods on a large number of easier subproblems. The former can capture complex multi-neuron dependencies but sacrifices completeness due to the inherent limitations of convex relaxations. The latter enables complete verification but becomes increasingly ineffective on larger and more challenging networks. In this work, we present a novel complete verifier which combines the strengths of both paradigms: it leverages multi-neuron relaxations to drastically reduce the number of subproblems generated during the BaB process and an efficient GPU-based dual optimizer to solve the remaining ones. An extensive evaluation demonstrates that our verifier achieves a new state-of-the-art on both established benchmarks as well as networks with significantly higher accuracy than previously considered. The latter result (up to 28% certification gains) indicates meaningful progress towards creating verifiers that can handle practically relevant networks.
Key facts. Cited by 92 papers in the map (data through 7 Oct 2026). Builds on 18 of its 34 references that are in the map. First posted on arXiv 30 Apr 2022.
Builds on
18 of 34 references.
References · 18
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
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- 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
- 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
- 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
- 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
- 2020How Does Mixup Help With Robustness and Generalization?cited by 193
- 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 183
- 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
- 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
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- 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
- 2020Guided Adversarial Attack for Evaluating and Enhancing Adversarial Defensescited by 61
- 2020The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verificationcited by 50
- 2019Neural Network Branching for Neural Network Verificationcited by 45
- 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
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Citing papers per year: 2022: 10; 2023: 25; 2024: 28; 2025: 11; 2026: 18.
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- 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
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- 2026Semantic Robustness Certification for Vision-Language Models17 Jun 2026
- 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
- 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
- 2022Certified Training: Small Boxes are All You Needcited by 51
- 2024Neural Network Verification with Branch-and-Bound for General Nonlinearitiescited by 47
- 2022The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Resultscited by 39
- 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
- 2024Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planescited by 33
- 2022VeriX: Towards Verified Explainability of Deep Neural Networkscited by 30
- 2023Provably Bounding Neural Network Preimagescited by 28
- 2023Understanding Certified Training with Interval Bound Propagationcited by 26
- 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
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- 2026Branch and Bound for Relational Verification of Neural Networks13 Aug 2026
- 2026Certified Training for Convolutional Perturbations20 Jul 2026
- 2026Fast SDP certification of neural networks : towards large multi-class datasets3 Jul 2026
- 2026Improving Certified Robustness via Adversarial Distillation30 Jun 2026
- 2026Rethinking Evaluation Paradigms in IBP-based Certified Training1 Jun 2026
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks22 May 2026
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