  In this paper we provide an approach for deep learning that protects against
adversarial examples in image classification-type networks. The approach relies
on two mechanisms:1) a mechanism that increases robustness at the expense of
accuracy, and, 2) a mechanism that improves accuracy but does not always
increase robustness. We show that an approach combining the two mechanisms can
provide protection against adversarial examples while retaining accuracy. We
formulate potential attacks on our approach with experimental results to
demonstrate its effectiveness. We also provide a robustness guarantee for our
approach along with an interpretation for the guarantee.

Machine Learning;Cryptography and Security;Machine Learning