# Adversarial robustness through Lipschitz-Guided Stochastic Depth in Neural Networks

arXiv: https://arxiv.org/abs/2509.10298 · HTML: https://mlsanity.com/paper/2509.10298/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 14 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)

## Abstract (arXiv)

Deep neural networks and Vision Transformers achieve state-of-the-art performance in computer vision but are highly vulnerable to adversarial perturbations. Standard defenses often incur high computational cost or lack formal guarantees. We propose a Lipschitz-guided stochastic depth (DropPath) method, where drop probabilities increase with depth to control the effective Lipschitz constant of the network. This approach regularizes deeper layers, improving robustness while preserving clean accuracy and reducing computation. Experiments on CIFAR-10 with ViT-Tiny show that our custom depth-dependent schedule maintains near-baseline clean accuracy, enhances robustness under FGSM, PGD-20, and AutoAttack, and significantly reduces FLOPs compared to baseline and linear DropPath schedules.