mlsanityData to 14 Oct 2026

A Statistical Approach to Assessing Neural Network Robustness

arXiv 1811.07209 ↗First posted 17 Nov 2018stat.ML cs.LGcited by 54

Not on the map. Why?

Abstract (arXiv)

We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability.

Key facts. Cited by 54 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Nov 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 9; 2022: 10; 2023: 7; 2024: 9; 2025: 10; 2026: 9.

54 papers.

Sort:

By area:

  1. 2022Adversarial Training for High-Stakes Reliabilitycited by 60
  2. 2022SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretabilitycited by 28
  3. 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
  4. 2025Forecasting Rare Language Model Behaviorscited by 19
  5. 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
  6. 2021Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurancecited by 16
  7. 2024Estimating the Probabilities of Rare Outputs in Language Modelscited by 16
  8. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 14
  9. 2023From Robustness to Explainability and Back Againcited by 14
  10. 2021Towards Practical Robustness Analysis for DNNs based on PAC-Model Learningcited by 12
  11. 2021A Simple and Efficient Sampling-based Algorithm for General Reachability Analysiscited by 12
  12. 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networkscited by 12
38 more
  1. 2021Assessing the Reliability of Deep Learning Classifiers Through Robustness Evaluation and Operational Profilescited by 11
  2. 2021Scaling the Convex Barrier with Sparse Dual Algorithmscited by 10
  3. 2021RoMA: a Method for Neural Network Robustness Measurement and Assessmentcited by 10
  4. 2023Improving the Robustness of Transformer-based Large Language Models with Dynamic Attentioncited by 10
  5. 2024ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbationcited by 10
  6. 2022A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunitiescited by 9
  7. 2022QEBVerif: Quantization Error Bound Verification of Neural Networkscited by 9
  8. 2021ε-weakened Robustness of Deep Neural Networkscited by 8
  9. 2022Hierarchical Distribution-Aware Testing of Deep Learningcited by 8
  10. 2023TrajPAC: Towards Robustness Verification of Pedestrian Trajectory Prediction Modelscited by 8
  11. 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
  12. 2022Risk Verification of Stochastic Systems with Neural Network Controllerscited by 6
  13. 2023What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systemscited by 6
  14. 2024Trustworthy Text-to-Image Diffusion Models: A Timely and Focused Surveycited by 6
  15. 2025Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guidecited by 6
  16. 2025Hierarchical Testing with Rabbit Optimization for Industrial Cyber-Physical Systemscited by 4
  17. 2021Certifiable Deep Importance Sampling for Rare-Event Simulation of Black-Box Systemscited by 3
  18. 2022Reachability Verification Based Reliability Assessment for Deep Reinforcement Learning Controlled Robotics and Autonomous Systemscited by 3
  19. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 3
  20. 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networkscited by 2
  21. 2024DEM: A Method for Certifying Deep Neural Network Classifier Outputs in Aerospacecited by 2
  22. 2025Statistical Runtime Verification for LLMs via Robustness Estimationcited by 2
  23. 2025Efficient Preimage Approximation for Neural Network Certificationcited by 2
  24. 2025Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verificationcited by 2
  25. 2022An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Modelscited by 1
  26. 2023Selecting Models based on the Risk of Damage Caused by Adversarial Attackscited by 1
  27. 2025PRBench: A Standardized Probabilistic Robustness Benchmarkcited by 1
  28. 2025Non-Parametric Probabilistic Robustness: A Conservative Risk Estimator under Unknown Perturbation Distributionscited by 1
  29. 2026SimCert: Probabilistic Certification for Behavioral Similarity in Deep Neural Network Compressioncited by 1
  30. 2026Bounding the Black Box: A Statistical Certification Framework for AI Risk Regulationcited by 1
  31. 2026Estimating Rare Events in Language Models with Proper Evaluationcited by 1
  32. 2024Patch Synthesis for Property Repair of Deep Neural Networkscited by 0
  33. 2024Certifying Global Robustness for Deep Neural Networkscited by 0
  34. 2024A practical approach to evaluating the adversarial distance for machine learning classifierscited by 0
  35. 2025Probably Approximately Global Robustness Certificationcited by 0
  36. 2025A Variance-Based Analysis of Sample Complexity for Grid Coveragecited by 0
  37. 2026Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generationcited by 0
  38. 2026Training ML Models with Predictable Failurescited by 0

50 most cited of 54 All 54 (JSON)