# Lipschitz regularized Deep Neural Networks generalize and are adversarially robust

arXiv: https://arxiv.org/abs/1808.09540 · HTML: https://mlsanity.com/paper/1808.09540/

## Key facts

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

## Built on by (most cited first, 19 of 19)

- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
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- [TRS: Transferability Reduced Ensemble via Encouraging Gradient Diversity and Model Smoothness](https://mlsanity.com/paper/2104.00671/) (2021)
- [CLIP: Cheap Lipschitz Training of Neural Networks](https://mlsanity.com/paper/2103.12531/) (2021)
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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.