Wasserstein Adversarial Examples via Projected Sinkhorn Iterations

TL;DR

This paper introduces a new threat model for adversarial attacks based on Wasserstein distance, proposing a projection method using Sinkhorn iterations to generate adversarial examples that reflect realistic image manipulations.

Contribution

It develops a novel projection algorithm onto the Wasserstein ball using modified Sinkhorn iterations, enabling effective adversarial attacks under this new threat model.

Findings

Successfully attacks CIFAR10 models with 3% accuracy within Wasserstein ball

Adversarial training improves robustness to 76% accuracy

Demonstrates Wasserstein distance captures realistic image perturbations

Abstract

A rapidly growing area of work has studied the existence of adversarial examples, datapoints which have been perturbed to fool a classifier, but the vast majority of these works have focused primarily on threat models defined by $\ell_p$ norm-bounded perturbations. In this paper, we propose a new threat model for adversarial attacks based on the Wasserstein distance. In the image classification setting, such distances measure the cost of moving pixel mass, which naturally cover "standard" image manipulations such as scaling, rotation, translation, and distortion (and can potentially be applied to other settings as well). To generate Wasserstein adversarial examples, we develop a procedure for projecting onto the Wasserstein ball, based upon a modified version of the Sinkhorn iteration. The resulting algorithm can successfully attack image classification models, bringing traditional CIFAR10 models down to 3% accuracy within a Wasserstein ball with radius 0.1 (i.e., moving 10% of the image mass 1 pixel), and we demonstrate that PGD-based adversarial training can improve this adversarial accuracy to 76%. In total, this work opens up a new direction of study in adversarial robustness, more formally considering convex metrics that accurately capture the invariances that we typically believe should exist in classifiers. Code for all experiments in the paper is available at https://github.com/locuslab/projected_sinkhorn.