Sheaf Neural Networks
This work addresses the limitation of GCNs in modeling complex, asymmetric relationships between nodes, which is a problem for researchers working with structured data beyond simple graphs.
This paper introduces Sheaf Neural Networks (SNNs), a generalization of graph convolutional networks (GCNs) that extends the diffusion operation to handle non-constant, asymmetric, and varying-dimension relations between nodes. SNNs are shown to outperform GCNs in domains with asymmetric and signed node relations.
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.