70 citations · 78 across the 6 of their papers we have counts for
4 papers · 1 filter
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…
Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
Hans Riess, Jakob Hansen, Robert Ghrist
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers a…
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…