A Spectral View Of Adversarially Robust Features

Authors:
Shivam Garg Stanford University
Vatsal Sharan Stanford University
Brian Zhang Stanford University
Gregory Valiant Stanford University

Introduction:

Given the apparent difficulty of learning models that are robust to adversarial perturbations, the authors propose tackling the simpler problem of developing adversarially robust features.

Abstract:

Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features. Specifically, given a dataset and metric of interest, the goal is to return a function (or multiple functions) that 1) is robust to adversarial perturbations, and 2) has significant variation across the datapoints. We establish strong connections between adversarially robust features and a natural spectral property of the geometry of the dataset and metric of interest. This connection can be leveraged to provide both robust features, and a lower bound on the robustness of any function that has significant variance across the dataset. Finally, we provide empirical evidence that the adversarially robust features given by this spectral approach can be fruitfully leveraged to learn a robust (and accurate) model.

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