mlsanityData to 14 Oct 2026

Fastened CROWN: Tightened Neural Network Robustness Certificates

arXiv 1912.00574 ↗First posted 2 Dec 2019cs.LG cs.CR cs.CVcited by 39

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Abstract (arXiv)

The rapid growth of deep learning applications in real life is accompanied by severe safety concerns. To mitigate this uneasy phenomenon, much research has been done providing reliable evaluations of the fragility level in different deep neural networks. Apart from devising adversarial attacks, quantifiers that certify safeguarded regions have also been designed in the past five years. The summarizing work of Salman et al. unifies a family of existing verifiers under a convex relaxation framework. We draw inspiration from such work and further demonstrate the optimality of deterministic CROWN (Zhang et al. 2018) solutions in a given linear programming problem under mild constraints. Given this theoretical result, the computationally expensive linear programming based method is shown to be unnecessary. We then propose an optimization-based approach textitFROWN (Fastened CROWN): a general algorithm to tighten robustness certificates for neural networks. Extensive experiments on various networks trained individually verify the effectiveness of FROWN in safeguarding larger robust regions.

Key facts. Cited by 39 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Dec 2019.

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Citing papers per year: 2021: 4; 2022: 15; 2023: 6; 2024: 11; 2025: 2; 2026: 1.

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  1. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  2. 2024Neural Network Verification with Branch-and-Bound for General Nonlinearitiescited by 47
  3. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  4. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 39
  5. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  6. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  7. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  8. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  9. 2022Neural Network Verification with Proof Productioncited by 22
  10. 2022Scalable Verification of GNN-based Job Schedulerscited by 19
  11. 2022Verification-Aided Deep Ensemble Selectioncited by 18
  12. 2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
27 more
  1. 2024NLP Verification: Towards a General Methodology for Certifying Robustnesscited by 16
  2. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 16
  3. 2021Towards Evaluating and Training Verifiably Robust Neural Networkscited by 15
  4. 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
  5. 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
  6. 2024Shield Synthesis for LTL Modulo Theoriescited by 12
  7. 2022Constrained Reinforcement Learning for Robotics via Scenario-Based Programmingcited by 11
  8. 2023Verifying Generalization in Deep Learningcited by 11
  9. 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
  10. 2022Provably Tightest Linear Approximation for Robustness Verification of Sigmoid-like Neural Networkscited by 8
  11. 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiingcited by 8
  12. 2022NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learningcited by 7
  13. 2023Optimization and Optimizers for Adversarial Robustnesscited by 6
  14. 2024Certification of Speaker Recognition Models to Additive Perturbationscited by 6
  15. 2023OccRob: Efficient SMT-Based Occlusion Robustness Verification of Deep Neural Networkscited by 5
  16. 2025Proof Minimization in Neural Network Verificationcited by 4
  17. 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
  18. 2023A Tale of Two Approximations: Tightening Over-Approximation for DNN Robustness Verification via Under-Approximationcited by 2
  19. 2024Verifying the Generalization of Deep Learning to Out-of-Distribution Domainscited by 2
  20. 2024Achieving the Tightest Relaxation of Sigmoids for Formal Verificationcited by 2
  21. 2022Tightening Robustness Verification of MaxPool-based Neural Networks via Minimizing the Over-Approximation Zonecited by 1
  22. 2023Expediting Neural Network Verification via Network Reductioncited by 1
  23. 2021A Framework for Verification of Wasserstein Adversarial Robustnesscited by 0
  24. 2022VeriCompress: A Tool to Streamline the Synthesis of Verified Robust Compressed Neural Networks from Scratchcited by 0
  25. 2022DualApp: Tight Over-Approximation for Neural Network Robustness Verification via Under-Approximationcited by 0
  26. 2024Towards General Robustness Verification of MaxPool-based Convolutional Neural Networks via Tightening Linear Approximationcited by 0
  27. 2026Shifting-based Optimizable Linear Relaxations for General Activation Functionscited by 0