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Sheaf Neural Networks

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arxiv 2012.06333 v1 pith:3GMLAK2A submitted 2020-12-08 cs.LG math.AT

Jakob Hansen , Thomas Gebhart This is my paper · ORCID
classification cs.LGmath.AT
keywords networksgraphsheafneuralconvolutionalgeneralizationlaplacianasymmetric
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. SEAM: Global consistency beyond local accuracy in scientific machine learning

    cs.LG 2026-08 conditional novelty 6.0 of 10

    SEAM encodes regional model explanations as a sheaf and uses the coboundary operator to turn overlap disagreements into a channel-resolved obstruction that can localize and test repair hypotheses.

  2. Benchmarking Sheaf Neural Networks for Inductive Tasks

    cs.LG 2026-08 conditional novelty 6.0 of 10

    On 14 inductive graph benchmarks, sheaf neural networks underperform strong GNN baselines, and their performance is driven more by the surrounding architecture than by the sheaf diffusion mechanism.

  3. Sheaves Reloaded: A Directional Awakening

    cs.LG 2025-06 conditional novelty 6.0 of 10

    A directed sheaf Laplacian and the DSNN architecture bring edge-orientation information into sheaf-based graph learning with modest-but-consistent benchmark gains.

  4. Cellular Sheaves on Higher-Dimensional Structures

    math.AT 2025-05 conditional novelty 4.0 of 10

    A collection of explicit constructions for cellular sheaves on simplicial complexes of dimension two and higher, mixing anisotropic network models with algebraic sheaves of ideals and modules.

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