1 citations · 1 across the 1 of their papers we have counts for
4 papers
Sheaf Neural Networks
Jakob Hansen, Thomas Gebhart
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…
Expansion in Matrix-Weighted Graphs
Jakob Hansen
A matrix-weighted graph is an undirected graph with a positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacen…
Opinion Dynamics on Discourse Sheaves
Jakob Hansen, Robert Ghrist
We introduce a novel class of Laplacians and diffusion dynamics on discourse sheaves as a model for network dynamics, with application to opinion dynamics on social networks. These…
Toward a Spectral Theory of Cellular Sheaves
Jakob Hansen, Robert Ghrist
This paper outlines a program in what one might call spectral sheaf theory --- an extension of spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplaci…