Title: Trans-Caps: Transformer Capsule Networks with Self-attention Routing. Abstract: Capsule Networks (CapsNets) have shown to be a promising alternative to Convolutional Neural Networks (CNNs) in many computer vision tasks, due to their ability to encode object viewpoint variations. The high computational complexity and numerical instability of iterative routing mechanisms stem from the challenging nature of the part-object encoding process. This hinders CapsNets from being utilized effectively in large-scale image tasks. In this paper, we propose a novel non-iterative routing strategy named self-attention routing (SAR) that computes the agreement between the capsules in one forward pass. SAR accomplishes this by utilizing a learnable inducing mixture of Gaussians (IMoG) to reduce the cost of computing pairwise attention values from quadratic to linear time complexity. Our observations show that our Transformer Capsule Network (Trans-Caps) is better suited for complex image tasks including CIFAR-10/100, Tiny-ImageNet, and ImageNet when compared to other prominent CapsNet architectures. We also show that Trans-Caps yields a dramatic improvement over its competitors when presented with novel viewpoints on the SmallNORB dataset, outperforming EM-Caps by 5.77% and 3.25% on the novel azimuth and elevation experiments, respectively. Our observations suggest that our routing mechanism is able to capture complex part-whole relationships which allow Trans-Caps to construct reliable geometrical representations of the objects.