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2020

Sheaf Neural Networks

Hansen, Jakob, Gebhart, Thomas

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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.

Sheaf Neural Networks · Around

Built on

Vector Diffusion Maps and the Connection Laplacian
Amit Singer and Hau-Tieng Wu · 2012
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Spectral networks and locally connected networks on graphs
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Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun · 2013
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Sheaves, Cosheaves, and Applications
Justin Curry · 2014
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Adam: A method for stochastic optimization
Original
Diederik P Kingma and Jimmy Ba · 2014
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Then

Learning sheaf Laplacians from smooth signals
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