# Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization

arXiv: https://arxiv.org/abs/1803.08680 · HTML: https://mlsanity.com/paper/1803.08680/

## Key facts

- Cited by 88 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2018.

## Built on by (most cited first, 30 of 88)

- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Relating Adversarially Robust Generalization to Flat Minima](https://mlsanity.com/paper/2104.04448/) (2021)
- [Why Does Little Robustness Help? A Further Step Towards Understanding Adversarial Transferability](https://mlsanity.com/paper/2307.07873/) (2023)
- [PAD: Patch-Agnostic Defense against Adversarial Patch Attacks](https://mlsanity.com/paper/2404.16452/) (2024)
- [Reliably fast adversarial training via latent adversarial perturbation](https://mlsanity.com/paper/2104.01575/) (2021)
- [Understanding and Combating Robust Overfitting via Input Loss Landscape Analysis and Regularization](https://mlsanity.com/paper/2212.04985/) (2022)
- [Adversarial Rademacher Complexity of Deep Neural Networks](https://mlsanity.com/paper/2211.14966/) (2022)
- [TWINS: A Fine-Tuning Framework for Improved Transferability of Adversarial Robustness and Generalization](https://mlsanity.com/paper/2303.11135/) (2023)
- [Regularization properties of adversarially-trained linear regression](https://mlsanity.com/paper/2310.10807/) (2023)
- [Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification](https://mlsanity.com/paper/2206.09098/) (2022)
- [Do Perceptually Aligned Gradients Imply Adversarial Robustness?](https://mlsanity.com/paper/2207.11378/) (2022)
- [Learning to Learn Transferable Attack](https://mlsanity.com/paper/2112.06658/) (2021)
- [UniDrop: A Simple yet Effective Technique to Improve Transformer without Extra Cost](https://mlsanity.com/paper/2104.04946/) (2021)
- [How Does Frequency Bias Affect the Robustness of Neural Image Classifiers against Common Corruption and Adversarial Perturbations?](https://mlsanity.com/paper/2205.04533/) (2022)
- [Nuclear Norm Regularization for Deep Learning](https://mlsanity.com/paper/2405.14544/) (2024)
- [Improving Model Robustness with Latent Distribution Locally and Globally](https://mlsanity.com/paper/2107.04401/) (2021)
- [Jacobian Regularizer-based Neural Granger Causality](https://mlsanity.com/paper/2405.08779/) (2024)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Recent Advances in Large Margin Learning](https://mlsanity.com/paper/2103.13598/) (2021)
- [A Survey on AI Sustainability: Emerging Trends on Learning Algorithms and Research Challenges](https://mlsanity.com/paper/2205.03824/) (2022)
- [Unfolded proximal neural networks for robust image Gaussian denoising](https://mlsanity.com/paper/2308.03139/) (2023)
- [Augment then Smooth: Reconciling Differential Privacy with Certified Robustness](https://mlsanity.com/paper/2306.08656/) (2023)
- [Characterizing Model Robustness via Natural Input Gradients](https://mlsanity.com/paper/2409.20139/) (2024)
- [A Regularization Method to Improve Adversarial Robustness of Neural Networks for ECG Signal Classification](https://mlsanity.com/paper/2110.09759/) (2021)
- [Improving Interpretability via Regularization of Neural Activation Sensitivity](https://mlsanity.com/paper/2211.08686/) (2022)
- [Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularization](https://mlsanity.com/paper/2404.14701/) (2024)
- [Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization](https://mlsanity.com/paper/2409.03807/) (2024)
- [Multiplicative Reweighting for Robust Neural Network Optimization](https://mlsanity.com/paper/2102.12192/) (2021)
- [Explaining Adversarial Vulnerability with a Data Sparsity Hypothesis](https://mlsanity.com/paper/2103.00778/) (2021)
- [Jacobian Regularization for Mitigating Universal Adversarial Perturbations](https://mlsanity.com/paper/2104.10459/) (2021)

## 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.