mlsanityData to 7 Oct 2026

Limitations of the Lipschitz constant as a defense against adversarial examples

arXiv 1807.09705 ↗First posted 25 Jul 2018cs.LG stat.MLcited by 48

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Abstract (arXiv)

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz constant may indeed enable adversarially robust neural networks. However, the methods currently employed for computing it suffer from theoretical and practical limitations. We argue that addressing this shortcoming is a promising direction for future research into certified adversarial defenses.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Jul 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 18; 2022: 8; 2023: 11; 2024: 3; 2025: 3; 2026: 5.

48 papers.

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  1. 2021Globally-Robust Neural Networkscited by 106
  2. 2021Exploring Architectural Ingredients of Adversarially Robust Deep Neural Networkscited by 73
  3. 2021Spectral Normalisation for Deep Reinforcement Learning: an Optimisation Perspectivecited by 64
  4. 2021Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Boundscited by 64
  5. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  6. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  7. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  8. 2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
  9. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  10. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  11. 2021Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networkscited by 30
  12. 2021CLIP: Cheap Lipschitz Training of Neural Networkscited by 29
36 more
  1. 2023Some Fundamental Aspects about Lipschitz Continuity of Neural Networkscited by 25
  2. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  3. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 23
  4. 2022Approximation bounds for norm constrained neural networks with applications to regression and GANscited by 21
  5. 2021Learning Prediction Intervals for Regression: Generalization and Calibrationcited by 16
  6. 2021Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximationcited by 16
  7. 2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
  8. 2021Certifiably Robust Variational Autoencoderscited by 14
  9. 2025Probabilistic Stability Guarantees for Feature Attributionscited by 9
  10. 2023Expressive Monotonic Neural Networkscited by 7
  11. 2021Robust and Provably Monotonic Networkscited by 6
  12. 2024SpecFormer: Guarding Vision Transformer Robustness via Maximum Singular Value Penalizationcited by 5
  13. 2021On the Stochastic Stability of Deep Markov Modelscited by 4
  14. 2023Limitations of Piecewise Linearity for Efficient Robustness Certificationcited by 4
  15. 2023PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusioncited by 3
  16. 2023Certified Robust Models with Slack Control and Large Lipschitz Constantscited by 3
  17. 2024A Wasserstein perspective of Vanilla GANscited by 3
  18. 2021Demotivate adversarial defense in remote sensingcited by 2
  19. 2023Leveraging Low-Rank and Sparse Recurrent Connectivity for Robust Closed-Loop Controlcited by 2
  20. 2024Parseval Convolution Operators and Neural Networkscited by 2
  21. 2021ELF: Exact-Lipschitz Based Universal Density Approximator Flowcited by 1
  22. 2022Learning Distributions by Generative Adversarial Networks: Approximation and Generalizationcited by 1
  23. 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networkscited by 1
  24. 2023Adversarial Sample Detection Through Neural Network Transport Dynamicscited by 1
  25. 2023Vacant Holes for Unsupervised Detection of the Outliers in Compact Latent Representationcited by 1
  26. 2023Resilient Graph Neural Networks: A Coupled Dynamical Systems Approachcited by 1
  27. 2025Deep P-Spline: Theory, Fast Tuning, and Applicationcited by 1
  28. 2025Stochastic Sample Approximations of (Local) Moduli of Continuitycited by 1
  29. 2026ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networkscited by 1
  30. 2021Approximating Probability Distributions by using Wasserstein Generative Adversarial Networkscited by 0
  31. 2022Sparse Polynomial Optimization: Theory and Practicecited by 0
  32. 2023On Continuity of Robust and Accurate Classifierscited by 0
  33. 2026Beyond Lipschitz: Data-Driven Robustness via Discrete Modulus of Continuitycited by 0
  34. 2026Robustness of neural networks to random noise perturbations of their inputscited by 0
  35. 2026LiD-GLM: Lipschitz-constrained Deep Generalized Linear Modelscited by 0
  36. 2026Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networkscited by 0