Sheaf Neural Networks

Jakob Hansen, Thomas Gebhart

Keywords: Cellular Sheaves, Graph Neural Network, Laplacian

TL;DR: We introduce the sheaf neural networks as a generalization of graph convolutional networks , providing a proper diffusion operator for domains where relations between nodes are non-constant, asymmetric, and varying in dimension.

Abstract: We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These \emph{sheaf neural networks} are based on the \emph{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.

Previous Submission: No