Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high confidence. This raises concerns that such classifiers are vulnerable to attacks and calls into question their usage in safety-critical systems. We show in this paper for the first time formal guarantees on the robustness of a classifier by giving instance-specific lower bounds on the norm of the input manipulation required to change the classifier decision. Based on this analysis we propose the Cross-Lipschitz regularization functional. We show that using this form of regularization in kernel methods resp. neural networks improves the robustness of the classifier without any loss in prediction performance.
@article{arxiv.1705.08475,
title = {Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation},
author = {Matthias Hein and Maksym Andriushchenko},
journal= {arXiv preprint arXiv:1705.08475},
year = {2017}
}
Comments
final version accepted at NIPS 2017, fixed bug in implementation of Cross-Lipschitz regularization and lower bound computation, now results are better