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Adversarial examples contain small perturbations that can remainimperceptible to human observers but alter the behavior of even the bestperforming deep learning models and yield incorrect outputs. Since theirdiscovery, adversarial examples have drawn significant attention in machinelearning: researchers try to reveal the reasons for their existence and improvethe robustness of machine learning models to adversarial perturbations. Thestate-of-the-art defense is the computationally expensive and very timeconsuming adversarial training via projected gradient descent (PGD). Wehypothesize that adversarial attacks exploit the open space risk of classicmonotonic activation functions. This paper introduces the tent activationfunction with bounded open space risk and shows that tents make deep learningmodels more robust to adversarial attacks. We demonstrate on the MNIST datasetthat a classifier with tents yields an average accuracy of 91.8% against sixwhite-box adversarial attacks, which is more than 15 percentage points abovethe state of the art. On the CIFAR-10 dataset, our approach improves theaverage accuracy against the six white-box adversarial attacks to 73.5% from41.8% achieved by adversarial training via PGD.

Improved Adversarial Robustness by Reducing Open Space Risk via Tent Activations