# Robust width: A lightweight and certifiable adversarial defense

arXiv: https://arxiv.org/abs/2405.15971 · HTML: https://mlsanity.com/paper/2405.15971/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 83 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 30 of 55)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [Intriguing Properties of Vision Transformers](https://mlsanity.com/paper/2105.10497/) (2021)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Simple Black-box Adversarial Attacks](https://mlsanity.com/paper/1905.07121/) (2019)

## Built on by (most cited first, 1 of 1)

- [Triggering hallucinations in model-based MRI reconstruction via adversarial perturbations](https://mlsanity.com/paper/2602.18536/) (2026)

## Abstract (arXiv)

Deep neural networks are vulnerable to so-called adversarial examples: inputs which are intentionally constructed to cause the model to make incorrect predictions or classifications. Adversarial examples are often visually indistinguishable from natural data samples, making them hard to detect. As such, they pose significant threats to the reliability of deep learning systems. In this work, we study an adversarial defense based on the robust width property (RWP), which was recently introduced for compressed sensing. We show that a specific input purification scheme based on the RWP gives theoretical robustness guarantees for images that are approximately sparse. The defense is easy to implement and can be applied to any existing model without additional training or finetuning. We empirically validate the defense on ImageNet against L^∞ perturbations at perturbation budgets ranging from 4/255 to 32/255. In the black-box setting, our method significantly outperforms the state-of-the-art, especially for large perturbations. In the white-box setting, depending on the choice of base classifier, we closely match the state of the art in robust ImageNet classification while avoiding the need for additional data, larger models or expensive adversarial training routines. Our code is available at https://github.com/peck94/robust-width-defense.