Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a limitation on their representation power, and instead propose a new general architecture for representing objects consisting of a hierarchy of parts, which we call Covariant Compositional Networks (CCNs). Here, covariance means that the activation of each neuron must transform in a specific way under permutations, similarly to steerability in CNNs. We achieve covariance by making each activation transform according to a tensor representation of the permutation group, and derive the corresponding tensor aggregation rules that each neuron must implement. Experiments show that CCNs can outperform competing methods on standard graph learning benchmarks.
@article{arxiv.1801.02144,
title = {Covariant Compositional Networks For Learning Graphs},
author = {Risi Kondor and Hy Truong Son and Horace Pan and Brandon Anderson and Shubhendu Trivedi},
journal= {arXiv preprint arXiv:1801.02144},
year = {2018}
}