# Stronger and Faster Wasserstein Adversarial Attacks

arXiv: https://arxiv.org/abs/2008.02883 · HTML: https://mlsanity.com/paper/2008.02883/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2020.

## Built on by (most cited first, 25 of 25)

- [Trustworthy AI: A Computational Perspective](https://mlsanity.com/paper/2107.06641/) (2021)
- [Robust Unlearnable Examples: Protecting Data Against Adversarial Learning](https://mlsanity.com/paper/2203.14533/) (2022)
- [Towards Defending against Adversarial Examples via Attack-Invariant Features](https://mlsanity.com/paper/2106.05036/) (2021)
- [Adversarial Attacks of Vision Tasks in the Past 10 Years: A Survey](https://mlsanity.com/paper/2410.23687/) (2024)
- [Removing Adversarial Noise in Class Activation Feature Space](https://mlsanity.com/paper/2104.09197/) (2021)
- [Training Meta-Surrogate Model for Transferable Adversarial Attack](https://mlsanity.com/paper/2109.01983/) (2021)
- [Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification](https://mlsanity.com/paper/2206.09098/) (2022)
- [Improving Adversarial Robustness via Mutual Information Estimation](https://mlsanity.com/paper/2207.12203/) (2022)
- [SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2112.05872/) (2021)
- [Modeling Adversarial Noise for Adversarial Training](https://mlsanity.com/paper/2109.09901/) (2021)
- [Formulating Robustness Against Unforeseen Attacks](https://mlsanity.com/paper/2204.13779/) (2022)
- [Robust Overfitting Does Matter: Test-Time Adversarial Purification With FGSM](https://mlsanity.com/paper/2403.11448/) (2024)
- [Improving White-box Robustness of Pre-processing Defenses via Joint Adversarial Training](https://mlsanity.com/paper/2106.05453/) (2021)
- [Unsupervised Robust Domain Adaptation: Paradigm, Theory and Algorithm](https://mlsanity.com/paper/2511.11009/) (2025)
- [Adversarial Attack across Datasets](https://mlsanity.com/paper/2110.07718/) (2021)
- [Multiple Perturbation Attack: Attack Pixelwise Under Different ℓp-norms For Better Adversarial Performance](https://mlsanity.com/paper/2212.03069/) (2022)
- [Effective and Robust Adversarial Training against Data and Label Corruptions](https://mlsanity.com/paper/2405.04191/) (2024)
- [Adapting to Evolving Adversaries with Regularized Continual Robust Training](https://mlsanity.com/paper/2502.04248/) (2025)
- [Rethinking the Vulnerability of Concept Erasure and a New Method](https://mlsanity.com/paper/2502.17537/) (2025)
- [Internal Wasserstein Distance for Adversarial Attack and Defense](https://mlsanity.com/paper/2103.07598/) (2021)
- [Position: Towards Resilience Against Adversarial Examples](https://mlsanity.com/paper/2405.01349/) (2024)
- [DMS: Addressing Information Loss with More Steps for Pragmatic Adversarial Attacks](https://mlsanity.com/paper/2406.07580/) (2024)
- [Structural Causal Models Reveal Confounder Bias in Linear Program Modelling](https://mlsanity.com/paper/2105.12697/) (2021)
- [Finding Structure and Causality in Linear Programs](https://mlsanity.com/paper/2203.15274/) (2022)
- [Feature-Space Smoothing: Certified Robustness of Deep Representations](https://mlsanity.com/paper/2601.16200/) (2026)

## Abstract (arXiv)

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to "small, imperceptible" perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the ℓp metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the ℓp metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to 3.4% within a Wasserstein perturbation ball of radius 0.005, in contrast to 65.6% using the previous Wasserstein attack based on an approximate projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.