NeurIPS 2020

Equivariant Networks for Hierarchical Structures

Meta Review

The paper attempts to improve invariance/equivariance modelling in neural network. Specifically, authors target the problem of nested symmetries or invariances. For example, in point cloud of a scene there can be permutation equivariance at object level as well as point level (set of sets). Many other nesting are important (sets of rotations/translations, image of images, sets of voxels etc.) and so the paper is solving an important problem that can be useful for many tasks. The paper develops a sound theoretical foundation for the such nested/hierarchical equivariance by identifying its relationship with the wreath product of groups. A simple, efficiently implementable representation of this class of operators is cleanly derived from this formalism. The derivation also yields as a byproduct an interesting connection to the commonly-used pooling operator. All the reviewers found the characterization of equivariant layers using wreath product symmetries to be novel and elegant. Finally, the paper shows strong empirical performance gains on standard point cloud analysis problems by imposing set of voxel equivariance (i.e. voxelization+permutation). Overall, all the reviewers appreciated the paper a lot and thus I am happy to recommend an acceptance to NeurIPS. For camera ready version please add proof of maximality as well as timing/efficiency comparison. In future, authors should take better precautions in maintaining privacy when providing leaderboard links.