  We revisit the benefits of merging classical vision concepts with deep
learning models. In particular, we explore the effect on robustness against
adversarial attacks of replacing the first layers of various deep architectures
with Gabor layers, i.e. convolutional layers with filters that are based on
learnable Gabor parameters. We observe that architectures enhanced with Gabor
layers gain a consistent boost in robustness over regular models and preserve
high generalizing test performance, even though these layers come at a
negligible increase in the number of parameters. We then exploit the closed
form expression of Gabor filters to derive an expression for a Lipschitz
constant of such filters, and harness this theoretical result to develop a
regularizer we use during training to further enhance network robustness. We
conduct extensive experiments with various architectures (LeNet, AlexNet, VGG16
and WideResNet) on several datasets (MNIST, SVHN, CIFAR10 and CIFAR100) and
demonstrate large empirical robustness gains. Furthermore, we experimentally
show how our regularizer provides consistent robustness improvements.
