Capsule Networks (CapsNets) are able to hierarchically preserve the pose relationships between multiple objects for image classification tasks. Other than achieving high accuracy, another relevant factor in deploying CapsNets in safety-critical applications is the robustness against input transformations and malicious adversarial attacks. In this paper, we systematically analyze and evaluate different factors affecting the robustness of CapsNets, compared to traditional Convolutional Neural Networks (CNNs). Towards a comprehensive comparison, we test two CapsNet models and two CNN models on the MNIST, GTSRB, and CIFAR10 datasets, as well as on the affine-transformed versions of such datasets. With a thorough analysis, we show which properties of these architectures better contribute to increasing the robustness and their limitations. Overall, CapsNets achieve better robustness against adversarial examples and affine transformations, compared to a traditional CNN with a similar number of parameters. Similar conclusions have been derived for deeper versions of CapsNets and CNNs. Moreover, our results unleash a key finding that the dynamic routing does not contribute much to improving the CapsNets' robustness. Indeed, the main generalization contribution is due to the hierarchical feature learning through capsules.

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