mlsanityData to 14 Oct 2026

Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks

arXiv 1802.04034 ↗First posted 12 Feb 2018cs.CV cs.LG stat.MLcited by 195

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Abstract (arXiv)

High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior certification work requires strong assumptions on network structures and massive computational costs, and thus the range of their applications was limited. From the relationship between the Lipschitz constants and prediction margins, we present a computationally efficient calculation technique to lower-bound the size of adversarial perturbations that can deceive networks, and that is widely applicable to various complicated networks. Moreover, we propose an efficient training procedure that robustifies networks and significantly improves the provably guarded areas around data points. In experimental evaluations, our method showed its ability to provide a non-trivial guarantee and enhance robustness for even large networks.

Key facts. Cited by 195 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Feb 2018.

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Citing papers per year: 2021: 33; 2022: 29; 2023: 32; 2024: 24; 2025: 41; 2026: 36.

195 papers.

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  1. 2022Robustness and Accuracy Could Be Reconcilable by (Proper) Definitioncited by 111
  2. 2021Globally-Robust Neural Networkscited by 108
  3. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  4. 2021Exploring Architectural Ingredients of Adversarially Robust Deep Neural Networkscited by 74
  5. 2021Skew Orthogonal Convolutionscited by 67
  6. 2021Spectral Normalisation for Deep Reinforcement Learning: an Optimisation Perspectivecited by 65
  7. 2021Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Boundscited by 65
  8. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 60
  9. 2023A Unified Algebraic Perspective on Lipschitz Neural Networkscited by 60
  10. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 51
  11. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 51
  12. 2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
38 more
  1. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  2. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  3. 2023How Smooth Is Attention?cited by 44
  4. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  5. 2022Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networkscited by 39
  6. 2022On the Effectiveness of Lipschitz-Driven Rehearsal in Continual Learningcited by 39
  7. 2024Learning Continually by Spectral Regularizationcited by 34
  8. 2022LOT: Layer-wise Orthogonal Training on Improving ℓ2 Certified Robustnesscited by 33
  9. 2023On the Stability of Expressive Positional Encodings for Graphscited by 33
  10. 2021Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networkscited by 30
  11. 2023Some Fundamental Aspects about Lipschitz Continuity of Neural Networkscited by 26
  12. 2021Intriguing Properties of Input-dependent Randomized Smoothingcited by 24
  13. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  14. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 24
  15. 2023Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularizationcited by 21
  16. 2023Training robust and generalizable quantum modelscited by 21
  17. 2025Training Transformers with Enforced Lipschitz Constantscited by 20
  18. 2021Orthogonal Graph Neural Networkscited by 19
  19. 2023Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iterationcited by 19
  20. 2023RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletioncited by 17
  21. 2021Learning Prediction Intervals for Regression: Generalization and Calibrationcited by 16
  22. 2021LipBaB: Computing exact Lipschitz constant of ReLU networkscited by 16
  23. 2021Existence, Stability and Scalability of Orthogonal Convolutional Neural Networkscited by 16
  24. 20231-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustnesscited by 16
  25. 2024Quantifying and Enhancing Multi-modal Robustness with Modality Preferencecited by 16
  26. 2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
  27. 2023LipSim: A Provably Robust Perceptual Similarity Metriccited by 15
  28. 2024Bridging The Gap between Low-rank and Orthogonal Adaptation via Householder Reflection Adaptationcited by 15
  29. 2021Certifiably Robust Variational Autoencoderscited by 14
  30. 2021A PAC-Bayes Analysis of Adversarial Robustnesscited by 13
  31. 2023Unlocking Deterministic Robustness Certification on ImageNetcited by 13
  32. 2023Robust low-rank training via approximate orthonormal constraintscited by 13
  33. 2024The Effect of Intrinsic Dataset Properties on Generalization: Unraveling Learning Differences Between Natural and Medical Imagescited by 13
  34. 2025Unveiling the Basin-Like Loss Landscape in Large Language Modelscited by 13
  35. 2021Learning Diverse-Structured Networks for Adversarial Robustnesscited by 12
  36. 2021Analytical bounds on the local Lipschitz constants of ReLU networkscited by 12
  37. 2022Toward Robust Spiking Neural Network Against Adversarial Perturbationcited by 12
  38. 2023Density-Softmax: Efficient Test-time Model for Uncertainty Estimation and Robustness under Distribution Shiftscited by 12

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