Title: Tessellated 2D Convolution Networks: A Robust Defence against Adversarial Attacks. Abstract: Data-driven (deep) learning approaches for image classification are prone to adversarial attacks. This means that an adversarial crafted image which is sufficiently close (visually indistinguishable) to its representative class can often be misclassified to be a member of a different class. A reason why deep neural approaches exhibits such vulnerability towards adversarial threats is mainly because the abstract representations learned in a data-driven manner often do not correlate well with human perceived features. To mitigate this problem, we propose the tessellated 2d convolution network, a novel divide-and-conquer based approach, which first independently learns the abstract representations of non-overlapping regions within an image, and then learns how to combine these representations to infer its class. It turns out that a non-uniform tiling of an image which ensures that the difference between the maximum and the minimum region sizes is not too large is the most robust way to construct such a tessellated 2d convolution network. This criterion can be achieved, among other schemes, by using a Mondrian tessellation of the input image. Our experiments demonstrate that our tessellated networks provides a more robust defence mechanism against gradient-based adversarial attacks in comparison to conventional deep neural models.