Adversarial Robustness via Fisher-Rao Regularization

• URL: http://arxiv.org/abs/2106.06685v1
• Date: Sat, 12 Jun 2021 04:12:58 GMT
• Title: Adversarial Robustness via Fisher-Rao Regularization
• Authors: Marine Picot, Francisco Messina, Malik Boudiaf, Fabrice Labeau, Ismail Ben Ayed, and Pablo Piantanida
• Abstract summary: Adrial robustness has become a topic of growing interest in machine learning. Fire is a new Fisher-Rao regularization for the categorical cross-entropy loss.
• Score: 33.134075068748984
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce FIRE, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some interesting properties as well as connections with standard regularization metrics. Furthermore, for a simple linear and Gaussian model, we show that all Pareto-optimal points in the accuracy-robustness region can be reached by FIRE while other state-of-the-art methods fail. Empirically, we evaluate the performance of various classifiers trained with the proposed loss on standard datasets, showing up to 2\% of improvements in terms of robustness while reducing the training time by 20\% over the best-performing methods.

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