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Thwarting Adversarial Examples: An $L_0$-Robust Sparse Fourier Transform
Mitali Bafna · Jack Murtagh · Nikhil Vyas

Tue Dec 04 07:45 AM -- 09:45 AM (PST) @ Room 517 AB #137
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.

Author Information

Mitali Bafna (Harvard University)
Jack Murtagh (Harvard University)
Nikhil Vyas (MIT)