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Convolutional neural networks (CNNs) achieve translational invariance byusing pooling operations. However, the operations do not preserve the spatialrelationships in the learned representations. Hence, CNNs cannot extrapolate tovarious geometric transformations of inputs. Recently, Capsule Networks(CapsNets) have been proposed to tackle this problem. In CapsNets, each entityis represented by a vector and routed to high-level entity representations by adynamic routing algorithm. CapsNets have been shown to be more robust than CNNsto affine transformations of inputs. However, there is still a huge gap betweentheir performance on transformed inputs compared to untransformed versions. Inthis work, we first revisit the routing procedure by (un)rolling its forwardand backward passes. Our investigation reveals that the routing procedurecontributes neither to the generalization ability nor to the affine robustnessof the CapsNets. Furthermore, we explore the limitations of capsuletransformations and propose affine CapsNets (Aff-CapsNets), which are morerobust to affine transformations. On our benchmark task, where models aretrained on the MNIST dataset and tested on the AffNIST dataset, ourAff-CapsNets improve the benchmark performance by a large margin (from 79% to93.21%), without using any routing mechanism.

Improving the Robustness of Capsule Networks to Image Affine Transformations