Title: Tessellated Neural Networks: A Robust Defence against Adversarial Attacks. Abstract:  Data-driven deep learning approaches for image classification are prone to adversarial attacks. An adversarial image which is sufficiently close (visually indistinguishable) from a true image of its representative class can often be misclassified to be a member of a different class. It is possible for attackers to exploit the high dimensionality of image representations, as learned by the neural models, to identify adversarial perturbations. To mitigate this problem, we propose a novel divide-and-conquer based approach of tessellating a base network architecture (e.g., a ResNet used in our experiments). The tessellated network learns the parameterized representations of each non-overlapping sub-region or tiles within an image, independently, and then learns how to combine these representations to finally estimate the class of the input image. We investigate two different modes of tessellation, namely periodic, comprised of regular square-shaped tiles, and aperiodic, comprised of rectangles of different dimensions. Experiments demonstrate that the tessellated extension of two standard deep neural models leads to a better defence against a number of standard adversarial attacks. We observed that the decrease in post-attack accuracy values relative to the accuracy of the uncompromised networks is smaller for our proposed tessellated approach. 