mlsanityData to 13 Oct 2026

Measuring Neural Net Robustness with Constraints

arXiv 1605.07262 ↗First posted 24 May 2016cs.LG cs.CV cs.NEcited by 90

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Abstract (arXiv)

Despite having high accuracy, neural nets have been shown to be susceptible to adversarial examples, where a small perturbation to an input can cause it to become mislabeled. We propose metrics for measuring the robustness of a neural net and devise a novel algorithm for approximating these metrics based on an encoding of robustness as a linear program. We show how our metrics can be used to evaluate the robustness of deep neural nets with experiments on the MNIST and CIFAR-10 datasets. Our algorithm generates more informative estimates of robustness metrics compared to estimates based on existing algorithms. Furthermore, we show how existing approaches to improving robustness "overfit" to adversarial examples generated using a specific algorithm. Finally, we show that our techniques can be used to additionally improve neural net robustness both according to the metrics that we propose, but also according to previously proposed metrics.

Key facts. Cited by 90 papers in the map (data through 13 Oct 2026). First posted on arXiv 24 May 2016.

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Citing papers per year: 2021: 25; 2022: 20; 2023: 11; 2024: 22; 2025: 8; 2026: 4.

90 papers.

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  1. 2023Rethinking Semi-Supervised Medical Image Segmentation: A Variance-Reduction Perspectivecited by 43
  2. 2021Provable Repair of Deep Neural Networkscited by 42
  3. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
  4. 2021Robust Machine Learning Systems: Challenges, Current Trends, Perspectives, and the Road Aheadcited by 40
  5. 2022Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overviewcited by 37
  6. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  7. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  8. 2021DNNV: A Framework for Deep Neural Network Verificationcited by 23
  9. 2022Neural Network Verification with Proof Productioncited by 22
  10. 2021Neural Network Repair with Reachability Analysiscited by 19
  11. 2022CertiFair: A Framework for Certified Global Fairness of Neural Networkscited by 17
  12. 2023Wasserstein distributional robustness of neural networkscited by 16
38 more
  1. 2022Efficient Global Robustness Certification of Neural Networks via Interleaving Twin-Network Encodingcited by 15
  2. 2021Attack as Defense: Characterizing Adversarial Examples using Robustnesscited by 14
  3. 2021Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verificationcited by 13
  4. 2021Curriculum Learning for Safe Mapless Navigationcited by 11
  5. 2022If a Human Can See It, So Should Your System: Reliability Requirements for Machine Vision Componentscited by 11
  6. 2021SyReNN: A Tool for Analyzing Deep Neural Networkscited by 10
  7. 2021RoMA: a Method for Neural Network Robustness Measurement and Assessmentcited by 10
  8. 2022LinSyn: Synthesizing Tight Linear Bounds for Arbitrary Neural Network Activation Functionscited by 10
  9. 2024Verification of Neural Networks' Global Robustnesscited by 10
  10. 2024Detecting Brittle Decisions for Free: Leveraging Margin Consistency in Deep Robust Classifierscited by 10
  11. 2022A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunitiescited by 9
  12. 2021Fast BATLLNN: Fast Box Analysis of Two-Level Lattice Neural Networkscited by 8
  13. 2022Adversarial Purification with the Manifold Hypothesiscited by 8
  14. 2024A Certified Proof Checker for Deep Neural Network Verification in Imandracited by 7
  15. 2024ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networkscited by 7
  16. 2021Verifying Quantized Neural Networks using SMT-Based Model Checkingcited by 6
  17. 2021Evaluating the Robustness of Trigger Set-Based Watermarks Embedded in Deep Neural Networkscited by 6
  18. 2022On Optimizing Back-Substitution Methods for Neural Network Verificationcited by 6
  19. 2023Towards a Certified Proof Checker for Deep Neural Network Verificationcited by 6
  20. 2024DeepCDCL: An CDCL-based Neural Network Verification Frameworkcited by 6
  21. 2024Concept-based Analysis of Neural Networks via Vision-Language Modelscited by 6
  22. 2021Static analysis of ReLU neural networks with tropical polyhedracited by 5
  23. 2021Neural-to-Tree Policy Distillation with Policy Improvement Criterioncited by 5
  24. 2022Software Testing for Machine Learningcited by 5
  25. 2022BERN-NN: Tight Bound Propagation For Neural Networks Using Bernstein Polynomial Interval Arithmeticcited by 5
  26. 2023Adversarial Attacks and Defenses in Machine Learning-Powered Networks: A Contemporary Surveycited by 5
  27. 2021On the Impact of Applying Machine Learning in the Decision-Making of Self-Adaptive Systemscited by 4
  28. 2021Attribution of Gradient Based Adversarial Attacks for Reverse Engineering of Deceptionscited by 4
  29. 2021Reachability Analysis of Convolutional Neural Networkscited by 4
  30. 2021The Fundamental Limits of Interval Arithmetic for Neural Networkscited by 4
  31. 2022Understanding Adversarial Robustness of Vision Transformers via Cauchy Problemcited by 4
  32. 2022Resisting Adversarial Attacks in Deep Neural Networks using Diverse Decision Boundariescited by 4
  33. 2022Sound and Complete Verification of Polynomial Networkscited by 4
  34. 2024Uncertainty Quantification for Neurosymbolic Programs via Compositional Conformal Predictioncited by 4
  35. 2024Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methodscited by 4
  36. 2024FairQuant: Certifying and Quantifying Fairness of Deep Neural Networkscited by 4
  37. 2021Towards Speeding up Adversarial Training in Latent Spacescited by 3
  38. 2023Verifiable Learning for Robust Tree Ensemblescited by 3

50 most cited of 90 All 90 (JSON)