We had a discussion about this paper with the reviewers raising the question of novelty since the general topic of steerable neural networks (i.e., equivariant neural networks where the activations are defined as a function on a homogeneous space) has now been thoroughly explored in the literature. Also, Weiler et al have a paper on SE(3) equivariant nets, so the E(2) is arguably just a simpler variant. There are three reasons why I nonetheless recommend this paper for acceptance: 1. The kernel constraint conditions are meticulously worked out for a range of specific subgroups of O(2). One wonders whether this could be done more generally and whether it really requires so much tedious algebra. Nonetheless, this is something that practitioners are likely to find useful. 2. The paper presents extensive experimental results on a range of different architectural variants, which is informative and will be a good benchmark for future work on E(2) equivariant architectures. 3. Equivariance to rotation and translation is part of the holy grail of computer vision, so this paper has significant practical relevance.