Covariant Compositional Networks For Learning Graphs

TL;DR

This paper introduces Covariant Compositional Networks (CCNs), a novel graph neural network architecture that enhances representation power by ensuring neuron activations transform covariantly under permutations, outperforming existing methods.

Contribution

The paper proposes CCNs, which incorporate covariance under permutations via tensor representations, providing a more expressive framework for graph learning than traditional message passing networks.

Findings

CCNs outperform existing graph neural networks on benchmark datasets.

Covariance via tensor representations improves model expressiveness.

Experiments demonstrate superior performance of CCNs in graph tasks.

Abstract

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.