Sheaf Neural Networks

TL;DR

Sheaf neural networks extend graph convolutional networks by incorporating the sheaf Laplacian, enabling better modeling of complex, asymmetric, and signed relations between nodes in various domains.

Contribution

This work introduces sheaf neural networks, a novel generalization of graph neural networks that captures complex relational structures using the sheaf Laplacian.

Findings

Sheaf neural networks outperform traditional GCNs on asymmetric relation tasks.

They effectively model signed and non-constant relations.

The approach generalizes diffusion operations in graph neural networks.

Abstract

We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph Laplacian that encodes additional relational structure parameterized by the underlying graph. The sheaf Laplacian and associated matrices provide an extended version of the diffusion operation in graph convolutional networks, providing a proper generalization for domains where relations between nodes are non-constant, asymmetric, and varying in dimension. We show that the resulting sheaf neural networks can outperform graph convolutional networks in domains where relations between nodes are asymmetric and signed.