mlsanityData to 14 Oct 2026

Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness

arXiv 1904.09959 ↗First posted 22 Apr 2019cs.PL cs.LGcited by 40

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Abstract (arXiv)

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform misclassifications. In this paper, we present a novel algorithm for verifying robustness properties of neural networks. Our method synergistically combines gradient-based optimization methods for counterexample search with abstraction-based proof search to obtain a sound and (δ-)complete decision procedure. Our method also employs a data-driven approach to learn a verification policy that guides abstract interpretation during proof search. We have implemented the proposed approach in a tool called Charon and experimentally evaluated it on hundreds of benchmarks. Our experiments show that the proposed approach significantly outperforms three state-of-the-art tools, namely AI2 , Reluplex, and Reluval.

Key facts. Cited by 40 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 Apr 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 11; 2022: 13; 2023: 9; 2024: 5; 2025: 0; 2026: 2.

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  1. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 228
  2. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  3. 2021Provable Repair of Deep Neural Networkscited by 42
  4. 2022VeriX: Towards Verified Explainability of Deep Neural Networkscited by 30
  5. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  6. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  7. 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
  8. 2021Certifying Robustness to Programmable Data Bias in Decision Treescited by 21
  9. 2022Scalable Verification of GNN-based Job Schedulerscited by 19
  10. 2023Convex Bounds on the Softmax Function with Applications to Robustness Verificationcited by 19
  11. 2022Verification-Aided Deep Ensemble Selectioncited by 18
  12. 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
28 more
  1. 2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
  2. 2023Incremental Verification of Neural Networkscited by 14
  3. 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networkscited by 12
  4. 2023Verifying Generalization in Deep Learningcited by 11
  5. 2021SyReNN: A Tool for Analyzing Deep Neural Networkscited by 10
  6. 2022Linearity Grafting: Relaxed Neuron Pruning Helps Certifiable Robustnesscited by 10
  7. 2024Verification of Neural Networks' Global Robustnesscited by 10
  8. 2022Safe Neurosymbolic Learning with Differentiable Symbolic Executioncited by 9
  9. 2022QEBVerif: Quantization Error Bound Verification of Neural Networkscited by 9
  10. 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
  11. 2021Neural Network Branch-and-Bound for Neural Network Verificationcited by 6
  12. 2024DeepCDCL: An CDCL-based Neural Network Verification Frameworkcited by 6
  13. 2021Reachability Analysis of Convolutional Neural Networkscited by 4
  14. 2021Self-Correcting Neural Networks For Safe Classificationcited by 4
  15. 2022Sound and Complete Verification of Polynomial Networkscited by 4
  16. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  17. 2023A Neurosymbolic Approach to the Verification of Temporal Logic Properties of Learning enabled Control Systemscited by 3
  18. 2023DelBugV: Delta-Debugging Neural Network Verifierscited by 3
  19. 2023Robustness Verification of Deep Neural Networks using Star-Based Reachability Analysis with Variable-Length Time Series Inputcited by 2
  20. 2024Boosting Few-Pixel Robustness Verification via Covering Verification Designscited by 2
  21. 2024Verifying the Generalization of Deep Learning to Out-of-Distribution Domainscited by 2
  22. 2021Adversarial Robustness Verification and Attack Synthesis in Stochastic Systemscited by 0
  23. 2021Synthesizing Machine Learning Programs with PAC Guarantees via Statistical Sketchingcited by 0
  24. 2022Work In Progress: Safety and Robustness Verification of Autoencoder-Based Regression Models using the NNV Toolcited by 0
  25. 2023Verification of Neural Networks Local Differential Classification Privacycited by 0
  26. 2023Formal Verification of Long Short-Term Memory based Audio Classifiers: A Star based Approachcited by 0
  27. 2026Towards Verified and Targeted Explanations through Formal Methodscited by 0
  28. 2026Branch and Bound for Relational Verification of Neural Networkscited by 0