  Deep neural networks have achieved impressive performance and become the
de-facto standard in many tasks. However, troubling phenomena such as
adversarial and fooling examples suggest that the generalization they make is
flawed. I argue that among the roots of the phenomena are two geometric
properties of common deep learning architectures: their distributed nature and
the connectedness of their decision regions. As a remedy, I propose new
architectures inspired by fuzzy logic that combine several alternative design
elements. Through experiments on MNIST and CIFAR-10, the new models are shown
to be more local, better at rejecting noise samples, and more robust against
adversarial examples. Ablation analyses reveal behaviors on adversarial
examples that cannot be explained by the linearity hypothesis but are
consistent with the hypothesis that logic-inspired traits create more robust
models.
