# Internal Wasserstein Distance for Adversarial Attack and Defense

arXiv: https://arxiv.org/abs/2103.07598 · HTML: https://mlsanity.com/paper/2103.07598/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 61 references that are in the map.
- First posted on arXiv 13 Mar 2021.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [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)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [SinGAN: Learning a Generative Model from a Single Natural Image](https://mlsanity.com/paper/1905.01164/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Generating Adversarial Examples with Adversarial Networks](https://mlsanity.com/paper/1801.02610/) (2018)
- [Attacks Which Do Not Kill Training Make Adversarial Learning Stronger](https://mlsanity.com/paper/2002.11242/) (2020)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Spatially Transformed Adversarial Examples](https://mlsanity.com/paper/1801.02612/) (2018)
- [Generating Natural Adversarial Examples](https://mlsanity.com/paper/1710.11342/) (2017)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [Constructing Unrestricted Adversarial Examples with Generative Models](https://mlsanity.com/paper/1805.07894/) (2018)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)

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

- [Beckman Defense](https://mlsanity.com/paper/2301.01495/) (2023)

## Abstract (arXiv)

Deep neural networks (DNNs) are known to be vulnerable to adversarial attacks that would trigger misclassification of DNNs but may be imperceptible to human perception. Adversarial defense has been an important way to improve the robustness of DNNs. Existing attack methods often construct adversarial examples relying on some metrics like the ℓp distance to perturb samples. However, these metrics can be insufficient to conduct adversarial attacks due to their limited perturbations. In this paper, we propose a new internal Wasserstein distance (IWD) to capture the semantic similarity of two samples, and thus it helps to obtain larger perturbations than currently used metrics such as the ℓp distance. We then apply the internal Wasserstein distance to perform adversarial attack and defense. In particular, we develop a novel attack method relying on IWD to calculate the similarities between an image and its adversarial examples. In this way, we can generate diverse and semantically similar adversarial examples that are more difficult to defend by existing defense methods. Moreover, we devise a new defense method relying on IWD to learn robust models against unseen adversarial examples. We provide both thorough theoretical and empirical evidence to support our methods.