Thwarting Adversarial Examples: An L_0-Robust Sparse Fourier Transform

Abstract

We give a new algorithm for approximating the Discrete Fourier transform of an approximately sparse signal that is robust to worst-case L_0 corruptions, namely that some coordinates of the signal can be corrupt arbitrarily. Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs. We use our algorithm to successfully defend against worst-case L_0 adversaries in the setting of image classification. We give experimental results on the Jacobian-based Saliency Map Attack (JSMA) and the CW L_0 attack on the MNIST and Fashion-MNIST datasets as well as the Adversarial Patch on the ImageNet dataset.

Tasks

Reproductions