Title: Hierarchical Binding in Convolutional Neural Networks Confers Adversarial Robustness. Abstract: We approach the issue of robust machine vision by presenting a novel deep-learning architecture, inspired by work in theoretical neuroscience on how the primate brain performs visual 'feature binding'. Feature binding describes how separately represented features are encoded in a relationally meaningful way, such as a small edge composing part of the larger contour of an object, or the ear of a cat forming part of its head representation. We propose that the absence of such representations from current models such as convolutional neural networks might partly explain their vulnerability to small, often humanly-imperceptible changes to images known as adversarial examples. It has been proposed that adversarial examples are a result of 'off-manifold' perturbations of images, as the decision boundary is often unpredictable in these directions. Our novel architecture is designed to capture hierarchical feature binding, providing representations in these otherwise vulnerable directions. Having introduced these representations into convolutional neural networks, we provide empirical evidence of enhanced robustness against a broad range of $L_0$, $L_2$ and $L_\infty$ attacks in both the black-box and white-box setting on MNIST, Fashion-MNIST, and CIFAR-10. We further provide evidence, through the controlled manipulation of a key hyperparameter, synthetic data-sets, and ablation analyses, that this robustness is dependent on the introduction of the hierarchical binding representations.