  We propose a self-supervised capsule architecture for 3D point clouds. We
compute capsule decompositions of objects through permutation-equivariant
attention, and self-supervise the process by training with pairs of randomly
rotated objects. Our key idea is to aggregate the attention masks into semantic
keypoints, and use these to supervise a decomposition that satisfies the
capsule invariance/equivariance properties. This not only enables the training
of a semantically consistent decomposition, but also allows us to learn a
canonicalization operation that enables object-centric reasoning. To train our
neural network we require neither classification labels nor manually-aligned
training datasets. Yet, by learning an object-centric representation in a
self-supervised manner, our method outperforms the state-of-the-art on 3D point
cloud reconstruction, canonicalization, and unsupervised classification.
