  Inspired by biophysical principles underlying nonlinear dendritic computation
in neural circuits, we develop a scheme to train deep neural networks to make
them robust to adversarial attacks. Our scheme generates highly nonlinear,
saturated neural networks that achieve state of the art performance on gradient
based adversarial examples on MNIST, despite never being exposed to
adversarially chosen examples during training. Moreover, these networks exhibit
unprecedented robustness to targeted, iterative schemes for generating
adversarial examples, including second-order methods. We further identify
principles governing how these networks achieve their robustness, drawing on
methods from information geometry. We find these networks progressively create
highly flat and compressed internal representations that are sensitive to very
few input dimensions, while still solving the task. Moreover, they employ
highly kurtotic weight distributions, also found in the brain, and we
demonstrate how such kurtosis can protect even linear classifiers from
adversarial attack.
