mlsanityData to 14 Oct 2026

Lipschitz regularized Deep Neural Networks generalize and are adversarially robust

arXiv 1808.09540 ↗First posted 28 Aug 2018cs.LG cs.NA math.NAcited by 19

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Abstract (arXiv)

In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networks. The adversarial robustness regularization combines adversarial training, which we show to be equivalent to Total Variation regularization, with Lipschitz regularization. We demonstrate empirically that the regularized models are more robust, and that gradient norms of images can be used for attack detection.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Aug 2018.

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Citing papers per year: 2021: 8; 2022: 3; 2023: 2; 2024: 5; 2025: 1.

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  1. 2022Learning Smooth Neural Functions via Lipschitz Regularizationcited by 86
  2. 2021On Linear Stability of SGD and Input-Smoothness of Neural Networkscited by 63
  3. 2021A Deep Value-network Based Approach for Multi-Driver Order Dispatchingcited by 45
  4. 2021TRS: Transferability Reduced Ensemble via Encouraging Gradient Diversity and Model Smoothnesscited by 38
  5. 2021CLIP: Cheap Lipschitz Training of Neural Networkscited by 29
  6. 2024LLM-Empowered State Representation for Reinforcement Learningcited by 28
  7. 2023Exploring Active 3D Object Detection from a Generalization Perspectivecited by 26
  8. 2022A Lagrangian Duality Approach to Active Learningcited by 24
  9. 2024Ferrari: Federated Feature Unlearning via Optimizing Feature Sensitivitycited by 11
  10. 2024End-to-End Cost-Effective Incentive Recommendation under Budget Constraint with Uplift Modelingcited by 10
  11. 2021What training reveals about neural network complexitycited by 5
  12. 2022Learning Globally Smooth Functions on Manifoldscited by 4
7 more
  1. 2024A Tunable Despeckling Neural Network Stabilized via Diffusion Equationcited by 2
  2. 2021Depthwise Separable Convolutions Allow for Fast and Memory-Efficient Spectral Normalizationcited by 1
  3. 2021A Neural Network Ensemble Approach to System Identificationcited by 1
  4. 2021Recoding latent sentence representations -- Dynamic gradient-based activation modification in RNNscited by 0
  5. 2023Open-CRB: Towards Open World Active Learning for 3D Object Detectioncited by 0
  6. 2024Enhancing robustness of data-driven SHM models: adversarial training with circle losscited by 0
  7. 2025GemiRec: Interest Quantization and Generation for Multi-Interest Recommendationcited by 0