mlsanityData to 7 Oct 2026

Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization

arXiv 1803.08680 ↗First posted 23 Mar 2018cs.LG cs.CR cs.CVcited by 88

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Abstract (arXiv)

Deep neural networks have lately shown tremendous performance in various applications including vision and speech processing tasks. However, alongside their ability to perform these tasks with such high accuracy, it has been shown that they are highly susceptible to adversarial attacks: a small change in the input would cause the network to err with high confidence. This phenomenon exposes an inherent fault in these networks and their ability to generalize well. For this reason, providing robustness to adversarial attacks is an important challenge in networks training, which has led to extensive research. In this work, we suggest a theoretically inspired novel approach to improve the networks' robustness. Our method applies regularization using the Frobenius norm of the Jacobian of the network, which is applied as post-processing, after regular training has finished. We demonstrate empirically that it leads to enhanced robustness results with a minimal change in the original network's accuracy.

Key facts. Cited by 88 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Mar 2018.

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Citing papers per year: 2021: 23; 2022: 22; 2023: 14; 2024: 11; 2025: 5; 2026: 13.

88 papers.

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  1. 2022Learning Smooth Neural Functions via Lipschitz Regularizationcited by 86
  2. 2021Relating Adversarially Robust Generalization to Flat Minimacited by 57
  3. 2023Why Does Little Robustness Help? A Further Step Towards Understanding Adversarial Transferabilitycited by 32
  4. 2024PAD: Patch-Agnostic Defense against Adversarial Patch Attackscited by 31
  5. 2021Reliably fast adversarial training via latent adversarial perturbationcited by 29
  6. 2022Understanding and Combating Robust Overfitting via Input Loss Landscape Analysis and Regularizationcited by 22
  7. 2022Adversarial Rademacher Complexity of Deep Neural Networkscited by 18
  8. 2023TWINS: A Fine-Tuning Framework for Improved Transferability of Adversarial Robustness and Generalizationcited by 18
  9. 2023Regularization properties of adversarially-trained linear regressioncited by 17
  10. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  11. 2022Do Perceptually Aligned Gradients Imply Adversarial Robustness?cited by 15
  12. 2021Learning to Learn Transferable Attackcited by 13
38 more
  1. 2022How Does Frequency Bias Affect the Robustness of Neural Image Classifiers against Common Corruption and Adversarial Perturbations?cited by 11
  2. 2024Nuclear Norm Regularization for Deep Learningcited by 11
  3. 2021UniDrop: A Simple yet Effective Technique to Improve Transformer without Extra Costcited by 10
  4. 2021Improving Model Robustness with Latent Distribution Locally and Globallycited by 9
  5. 2024Jacobian Regularizer-based Neural Granger Causalitycited by 9
  6. 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimizationcited by 8
  7. 2021Recent Advances in Large Margin Learningcited by 7
  8. 2022A Survey on AI Sustainability: Emerging Trends on Learning Algorithms and Research Challengescited by 7
  9. 2023Unfolded proximal neural networks for robust image Gaussian denoisingcited by 7
  10. 2023Augment then Smooth: Reconciling Differential Privacy with Certified Robustnesscited by 6
  11. 2024Characterizing Model Robustness via Natural Input Gradientscited by 6
  12. 2021A Regularization Method to Improve Adversarial Robustness of Neural Networks for ECG Signal Classificationcited by 5
  13. 2022Improving Interpretability via Regularization of Neural Activation Sensitivitycited by 5
  14. 2024Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularizationcited by 5
  15. 2024Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimizationcited by 5
  16. 2021Multiplicative Reweighting for Robust Neural Network Optimizationcited by 4
  17. 2021Explaining Adversarial Vulnerability with a Data Sparsity Hypothesiscited by 4
  18. 2021Jacobian Regularization for Mitigating Universal Adversarial Perturbationscited by 4
  19. 2021Simple Post-Training Robustness Using Test Time Augmentations and Random Forestcited by 4
  20. 2021Quantized Convolutional Neural Networks Through the Lens of Partial Differential Equationscited by 3
  21. 2021Clustering Effect of (Linearized) Adversarial Robust Modelscited by 3
  22. 2022Wavelet Regularization Benefits Adversarial Trainingcited by 3
  23. 2022An Adversarial Robustness Perspective on the Topology of Neural Networkscited by 3
  24. 2023Improving Robustness Against Adversarial Attacks with Deeply Quantized Neural Networkscited by 3
  25. 2023Robust Proxy: Improving Adversarial Robustness by Robust Proxy Learningcited by 3
  26. 2023Certified Robust Models with Slack Control and Large Lipschitz Constantscited by 3
  27. 2026Protein Counterfactuals via Diffusion-Guided Latent Optimizationcited by 3
  28. 2021Adversarial Machine Learning in Text Analysis and Generationcited by 2
  29. 2021Estimating the Robustness of Classification Models by the Structure of the Learned Feature-Spacecited by 2
  30. 2021Utilizing Adversarial Targeted Attacks to Boost Adversarial Robustnesscited by 2
  31. 2022Defending Against Adversarial Attack in ECG Classification with Adversarial Distillation Trainingcited by 2
  32. 2022Training-Free Robust Multimodal Learning via Sample-Wise Jacobian Regularizationcited by 2
  33. 2022Understanding Open-Set Recognition by Jacobian Norm and Inter-Class Separationcited by 2
  34. 2022Multi-head Uncertainty Inference for Adversarial Attack Detectioncited by 2
  35. 2024Specification Overfitting in Artificial Intelligencecited by 2
  36. 2024Federated Hybrid Training and Self-Adversarial Distillation: Towards Robust Edge Networkscited by 2
  37. 2025GrokAlign: Geometric Characterisation and Acceleration of Grokkingcited by 2
  38. 2021Dual Head Adversarial Trainingcited by 1

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