Covariant Compositional Networks For Learning Graphs
This addresses the problem of limited representation power in graph learning for researchers and practitioners, offering a novel approach that is not explicitly incremental.
The authors tackled the limitation of existing graph neural networks by proposing Covariant Compositional Networks (CCNs), a new architecture that uses tensor representations of the permutation group to achieve covariance, and experiments show they outperform competing methods on standard benchmarks.
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.