mlsanityData to 7 Oct 2026

A Dual Approach to Scalable Verification of Deep Networks

arXiv 1803.06567 ↗First posted 17 Mar 2018cs.LG stat.MLcited by 125

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Abstract (arXiv)

This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limited in its applicability by the size of the network, network architecture and the complexity of properties to be verified. In contrast, our framework applies to a general class of activation functions and specifications on neural network inputs and outputs. We formulate verification as an optimization problem (seeking to find the largest violation of the specification) and solve a Lagrangian relaxation of the optimization problem to obtain an upper bound on the worst case violation of the specification being verified. Our approach is anytime i.e. it can be stopped at any time and a valid bound on the maximum violation can be obtained. We develop specialized verification algorithms with provable tightness guarantees under special assumptions and demonstrate the practical significance of our general verification approach on a variety of verification tasks.

Key facts. Cited by 125 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Mar 2018.

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Citing papers per year: 2018: 2; 2019: 0; 2020: 0; 2021: 39; 2022: 33; 2023: 24; 2024: 11; 2025: 8; 2026: 8.

125 papers.

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  1. 2018Scalable agent alignment via reward modeling: a research directioncited by 438
  2. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
  3. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  4. 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
  5. 2023How Deep Learning Sees the World: A Survey on Adversarial Attacks & Defensescited by 65
  6. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  7. 2024Neural Network Verification with Branch-and-Bound for General Nonlinearitiescited by 47
  8. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  9. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
  10. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
  11. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  12. 2021Partition-based formulations for mixed-integer optimization of trained ReLU neural networkscited by 39
38 more
  1. 2022How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspectivecited by 39
  2. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  3. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  4. 2023Provably Bounding Neural Network Preimagescited by 28
  5. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  6. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  7. 2021DNNV: A Framework for Deep Neural Network Verificationcited by 23
  8. 2022Certified Robustness Against Natural Language Attacks by Causal Interventioncited by 23
  9. 2021Safe Control with Neural Network Dynamic Modelscited by 21
  10. 2021Neural Network Repair with Reachability Analysiscited by 19
  11. 2023Convex Bounds on the Softmax Function with Applications to Robustness Verificationcited by 19
  12. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  13. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  14. 2021Adversarial Robustness with Non-uniform Perturbationscited by 17
  15. 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
  16. 2022CertiFair: A Framework for Certified Global Fairness of Neural Networkscited by 17
  17. 2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
  18. 2021Attack as Defense: Characterizing Adversarial Examples using Robustnesscited by 14
  19. 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
  20. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
  21. 2022Can pruning improve certified robustness of neural networks?cited by 14
  22. 2022A Unified View of SDP-based Neural Network Verification through Completely Positive Programmingcited by 12
  23. 2022Holistic Adversarial Robustness of Deep Learning Modelscited by 11
  24. 2021Scaling the Convex Barrier with Sparse Dual Algorithmscited by 10
  25. 2021Shared Certificates for Neural Network Verificationcited by 10
  26. 2022LinSyn: Synthesizing Tight Linear Bounds for Arbitrary Neural Network Activation Functionscited by 10
  27. 2022Linearity Grafting: Relaxed Neuron Pruning Helps Certifiable Robustnesscited by 10
  28. 2022UniCR: Universally Approximated Certified Robustness via Randomized Smoothingcited by 10
  29. 2025SDP-CROWN: Efficient Bound Propagation for Neural Network Verification with Tightness of Semidefinite Programmingcited by 10
  30. 2021Semantically Distributed Robust Optimization for Vision-and-Language Inferencecited by 9
  31. 2022Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systemscited by 9
  32. 2022Improved techniques for deterministic l2 robustnesscited by 9
  33. 2025Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verificationcited by 9
  34. 2021DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splittingcited by 8
  35. 2021Fast BATLLNN: Fast Box Analysis of Two-Level Lattice Neural Networkscited by 8
  36. 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
  37. 2023Expressivity of ReLU-Networks under Convex Relaxationscited by 8
  38. 2021Recent Advances in Large Margin Learningcited by 7

50 most cited of 125 All 125 (JSON)