mlsanityData to 14 Oct 2026

Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach

arXiv 1801.10578 ↗First posted 31 Jan 2018stat.ML cs.CR cs.LGcited by 182

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Abstract (arXiv)

The robustness of neural networks to adversarial examples has received great attention due to security implications. Despite various attack approaches to crafting visually imperceptible adversarial examples, little has been developed towards a comprehensive measure of robustness. In this paper, we provide a theoretical justification for converting robustness analysis into a local Lipschitz constant estimation problem, and propose to use the Extreme Value Theory for efficient evaluation. Our analysis yields a novel robustness metric called CLEVER, which is short for Cross Lipschitz Extreme Value for nEtwork Robustness. The proposed CLEVER score is attack-agnostic and computationally feasible for large neural networks. Experimental results on various networks, including ResNet, Inception-v3 and MobileNet, show that (i) CLEVER is aligned with the robustness indication measured by the ℓ2 and ℓ_∞ norms of adversarial examples from powerful attacks, and (ii) defended networks using defensive distillation or bounded ReLU indeed achieve better CLEVER scores. To the best of our knowledge, CLEVER is the first attack-independent robustness metric that can be applied to any neural network classifier.

Key facts. Cited by 182 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Jan 2018.

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Citing papers per year: 2021: 43; 2022: 36; 2023: 35; 2024: 28; 2025: 20; 2026: 20.

182 papers.

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  1. 2021Trustworthy AI: From Principles to Practicescited by 207
  2. 2021Globally-Robust Neural Networkscited by 108
  3. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  4. 2023A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validationcited by 93
  5. 2021AugMax: Adversarial Composition of Random Augmentations for Robust Trainingcited by 90
  6. 2022Trustworthy Graph Neural Networks: Aspects, Methods and Trendscited by 89
  7. 2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
  8. 2022A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologiescited by 44
  9. 2023How Smooth Is Attention?cited by 44
  10. 2021Discovering and Explaining the Representation Bottleneck of DNNscited by 42
  11. 2021Compressive Visual Representationscited by 41
  12. 2022How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspectivecited by 39
38 more
  1. 2021Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networkscited by 30
  2. 2023Some Fundamental Aspects about Lipschitz Continuity of Neural Networkscited by 26
  3. 2023Explaining Generalization Power of a DNN Using Interactive Conceptscited by 25
  4. 2022Formalising the Robustness of Counterfactual Explanations for Neural Networkscited by 24
  5. 2022A Survey of Adversarial Defences and Robustness in NLPcited by 23
  6. 2023Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularizationcited by 21
  7. 2023Training robust and generalizable quantum modelscited by 21
  8. 2021Lipschitz Continuity Guided Knowledge Distillationcited by 19
  9. 2022Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theorycited by 19
  10. 2022Quantifying the Knowledge in a DNN to Explain Knowledge Distillation for Classificationcited by 19
  11. 2024Understanding LLM Embeddings for Regressioncited by 19
  12. 2022Robustness in deep learning: The good (width), the bad (depth), and the ugly (initialization)cited by 18
  13. 2021A Unified Game-Theoretic Interpretation of Adversarial Robustnesscited by 17
  14. 2021SPADE: A Spectral Method for Black-Box Adversarial Robustness Evaluationcited by 16
  15. 2021Adversarial Examples can be Effective Data Augmentation for Unsupervised Machine Learningcited by 16
  16. 2021LipBaB: Computing exact Lipschitz constant of ReLU networkscited by 16
  17. 2021Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurancecited by 16
  18. 2023Wasserstein distributional robustness of neural networkscited by 16
  19. 2022RetrievalGuard: Provably Robust 1-Nearest Neighbor Image Retrievalcited by 15
  20. 2021Attack as Defense: Characterizing Adversarial Examples using Robustnesscited by 14
  21. 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
  22. 2021Improving Neural Network Robustness via Persistency of Excitationcited by 14
  23. 2023Decoupled Rationalization with Asymmetric Learning Rates: A Flexible Lipschitz Restraintcited by 14
  24. 2023Revisiting and Exploring Efficient Fast Adversarial Training via LAW: Lipschitz Regularization and Auto Weight Averagingcited by 14
  25. 2024Trustworthy Distributed AI Systems: Robustness, Privacy, and Governancecited by 14
  26. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  27. 2021Neural Architecture Dilation for Adversarial Robustnesscited by 13
  28. 2021Interpreting Attributions and Interactions of Adversarial Attackscited by 13
  29. 2022Adaptative Perturbation Patterns: Realistic Adversarial Learning for Robust Intrusion Detectioncited by 13
  30. 2021Learning Diverse-Structured Networks for Adversarial Robustnesscited by 12
  31. 2023POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systemscited by 12
  32. 2024Establishing and Evaluating Trustworthy AI: Overview and Research Challengescited by 12
  33. 2021On the Impact of Hard Adversarial Instances on Overfitting in Adversarial Trainingcited by 11
  34. 2022Holistic Adversarial Robustness of Deep Learning Modelscited by 11
  35. 2022How Robust is Your Fairness? Evaluating and Sustaining Fairness under Unseen Distribution Shiftscited by 11
  36. 2024Ferrari: Federated Feature Unlearning via Optimizing Feature Sensitivitycited by 11
  37. 2024ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbationcited by 10
  38. 2024Detecting Brittle Decisions for Free: Leveraging Margin Consistency in Deep Robust Classifierscited by 10

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