mlsanityData to 7 Oct 2026

Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound

arXiv 2205.00263 ↗First posted 30 Apr 2022cs.LG cs.SEcited by 92

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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

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  4. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  5. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  6. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  7. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  8. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
  9. 2020How Does Mixup Help With Robustness and Generalization?cited by 193
  10. 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 183
  11. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
  12. 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
6 more
  1. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  2. 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
  3. 2020Guided Adversarial Attack for Evaluating and Enhancing Adversarial Defensescited by 61
  4. 2020The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verificationcited by 50
  5. 2019Neural Network Branching for Neural Network Verificationcited by 45
  6. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 10; 2023: 25; 2024: 28; 2025: 11; 2026: 18.

92 papers.

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  1. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  2. 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
  3. 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
  4. 2022Certified Training: Small Boxes are All You Needcited by 51
  5. 2024Neural Network Verification with Branch-and-Bound for General Nonlinearitiescited by 47
  6. 2022The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Resultscited by 39
  7. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  8. 2024Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planescited by 33
  9. 2022VeriX: Towards Verified Explainability of Deep Neural Networkscited by 30
  10. 2023Provably Bounding Neural Network Preimagescited by 28
  11. 2023Understanding Certified Training with Interval Bound Propagationcited by 26
  12. 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
38 more
  1. 2023A DPLL(T) Framework for Verifying Deep Neural Networkscited by 23
  2. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  3. 2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
  4. 2023Incremental Verification of Neural Networkscited by 14
  5. 2023From Robustness to Explainability and Back Againcited by 14
  6. 2023Exact Verification of ReLU Neural Control Barrier Functionscited by 14
  7. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 13
  8. 2024CTBENCH: A Library and Benchmark for Certified Trainingcited by 13
  9. 2023TAPS: Connecting Certified and Adversarial Trainingcited by 11
  10. 2023Efficient Error Certification for Physics-Informed Neural Networkscited by 10
  11. 2026Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guaranteescited by 10
  12. 2022CAISAR: A platform for Characterizing Artificial Intelligence Safety and Robustnesscited by 9
  13. 2023Architecture-Preserving Provable Repair of Deep Neural Networkscited by 9
  14. 2024Neural Network Verification with PyRATcited by 9
  15. 2025Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verificationcited by 9
  16. 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structurecited by 8
  17. 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
  18. 2024Verified Safe Reinforcement Learning for Neural Network Dynamic Modelscited by 7
  19. 2024ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networkscited by 7
  20. 2024Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisationcited by 7
  21. 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
  22. 2023Towards a Certified Proof Checker for Deep Neural Network Verificationcited by 6
  23. 2024Set-Based Training for Neural Network Verificationcited by 6
  24. 2024DeepCDCL: An CDCL-based Neural Network Verification Frameworkcited by 6
  25. 2025Out of the Shadows: Exploring a Latent Space for Neural Network Verificationcited by 6
  26. 2023DeepBern-Nets: Taming the Complexity of Certifying Neural Networks using Bernstein Polynomial Activations and Precise Bound Propagationcited by 5
  27. 2024Relational DNN Verification With Cross Executional Bound Refinementcited by 5
  28. 2024SoundnessBench: A Soundness Benchmark for Neural Network Verifierscited by 5
  29. 2025No Soundness in the Real World: On the Challenges of the Verification of Deployed Neural Networkscited by 5
  30. 2022Sound and Complete Verification of Polynomial Networkscited by 4
  31. 2023Precise and Generalized Robustness Certification for Neural Networkscited by 4
  32. 2023GPU-Accelerated Verification of Machine Learning Models for Power Systemscited by 4
  33. 2024Gaussian Loss Smoothing Enables Certified Training with Tight Convex Relaxationscited by 4
  34. 2024Towards Formal Verification of Deep Neural Networks for Object Detectioncited by 4
  35. 2025Advancing Neural Network Verification through Hierarchical Safety Abstract Interpretationcited by 4
  36. 2025Parameterized Hardness of Zonotope Containment and Neural Network Verificationcited by 4
  37. 2023A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networkscited by 3
  38. 2023Interpreting Robustness Proofs of Deep Neural Networkscited by 3

50 most cited of 92 All 92 (JSON)