mlsanityData to 7 Oct 2026

Neural Network Robustness as a Verification Property: A Principled Case Study

arXiv 2104.01396 ↗First posted 3 Apr 2021cs.LG cs.AIcited by 35

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Abstract (arXiv)

Neural networks are very successful at detecting patterns in noisy data, and have become the technology of choice in many fields. However, their usefulness is hampered by their susceptibility to adversarial attacks. Recently, many methods for measuring and improving a network's robustness to adversarial perturbations have been proposed, and this growing body of research has given rise to numerous explicit or implicit notions of robustness. Connections between these notions are often subtle, and a systematic comparison between them is missing in the literature. In this paper we begin addressing this gap, by setting up general principles for the empirical analysis and evaluation of a network's robustness as a mathematical property - during the network's training phase, its verification, and after its deployment. We then apply these principles and conduct a case study that showcases the practical benefits of our general approach.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). Builds on 16 of its 24 references that are in the map. First posted on arXiv 3 Apr 2021.

Builds on

16 of 24 references.

References · 16

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  4. 2013Intriguing properties of neural networkscited by 5,114
  5. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  6. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  7. 2018Robustness May Be at Odds with Accuracycited by 873
  8. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  9. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  10. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 267
  11. 2016Safety Verification of Deep Neural Networkscited by 262
  12. 2019Algorithms for Verifying Deep Neural Networkscited by 221
4 more
  1. 2018Sorting out Lipschitz function approximationcited by 211
  2. 2019Adversarial Training Can Hurt Generalizationcited by 131
  3. 2020Training robust neural networks using Lipschitz boundscited by 98
  4. 2017Lipschitz Properties for Deep Convolutional Networkscited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 5; 2024: 13; 2025: 8; 2026: 2.

35 papers.

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  1. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  2. 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
  3. 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
  4. 2022Verification-Aided Deep Ensemble Selectioncited by 18
  5. 2023Logic of Differentiable Logics: Towards a Uniform Semantics of DLcited by 15
  6. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  7. 2024Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programscited by 14
  8. 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
  9. 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
  10. 2024Shield Synthesis for LTL Modulo Theoriescited by 12
  11. 2025Neural Network Verification is a Programming Language Challengecited by 12
  12. 2023Verifying Generalization in Deep Learningcited by 11
23 more
  1. 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
  2. 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
  3. 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiingcited by 8
  4. 2024Analyzing Adversarial Inputs in Deep Reinforcement Learningcited by 7
  5. 2023ANTONIO: Towards a Systematic Method of Generating NLP Benchmarks for Verificationcited by 6
  6. 2023Repairing Deep Neural Networks Based on Behavior Imitationcited by 4
  7. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  8. 2022CheckINN: Wide Range Neural Network Verification in Imandra (Extended)cited by 3
  9. 2025Monitoring Robustness and Individual Fairnesscited by 3
  10. 2024Monitizer: Automating Design and Evaluation of Neural Network Monitorscited by 2
  11. 2022Differentiable Logics for Neural Network Training and Verificationcited by 1
  12. 2025Proof-Carrying Neuro-Symbolic Codecited by 1
  13. 2025A General Framework for Property-Driven Machine Learningcited by 1
  14. 2022Why Robust Natural Language Understanding is a Challengecited by 0
  15. 2024Robustness Verifcation in Neural Networkscited by 0
  16. 2024A Neurosymbolic Framework for Bias Correction in Convolutional Neural Networkscited by 0
  17. 2024Creating a Formally Verified Neural Network for Autonomous Navigation: An Experience Reportcited by 0
  18. 2025Neural Network Verification for Gliding Drone Control: A Case Studycited by 0
  19. 2025The CAISAR Platform: Extending the Reach of Machine Learning Specification and Verificationcited by 0
  20. 2025Probably Approximately Global Robustness Certificationcited by 0
  21. 2025Formal Reasoning About Confidence and Automated Verification of Neural Networkscited by 0
  22. 2026Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functionscited by 0
  23. 2026Quantitative Linear Logic for Neuro-Symbolic Learning and Verificationcited by 0