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Sheaf Neural Networks

arXiv 2012.06333 ↗First posted 8 Dec 2020cs.LG math.ATcited by 81

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Abstract (arXiv)

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.

Key facts. Cited by 81 papers in the map (data through 13 Oct 2026). First posted on arXiv 8 Dec 2020.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 2; 2022: 5; 2023: 8; 2024: 14; 2025: 19; 2026: 33.

81 papers.

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  1. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  2. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 210
  3. 2022Sheaf Neural Networks with Connection Laplacianscited by 64
  4. 2023Sheaf Hypergraph Networkscited by 33
  5. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  6. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 22
  7. 2024E(n) Equivariant Topological Neural Networkscited by 22
  8. 2023From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Modulecited by 19
  9. 2023Simplicial Representation Learning with Neural k-Formscited by 18
  10. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
  11. 2024Bundle Neural Networks for message diffusion on graphscited by 14
  12. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 12
38 more
  1. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  2. 2025Cooperative Sheaf Neural Networkscited by 11
  3. 2022Generalized energy and gradient flow via graph frameletscited by 10
  4. 2024Prospects for inconsistency detection using large language models and sheavescited by 10
  5. 2024Heterogeneous Sheaf Neural Networkscited by 10
  6. 2022Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Backcited by 9
  7. 2025Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheavescited by 9
  8. 2024Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networkscited by 8
  9. 2024Sheaf HyperNetworks for Personalized Federated Learningcited by 5
  10. 2024Bayesian Sheaf Neural Networkscited by 5
  11. 2024Nonlinear Sheaf Diffusion in Graph Neural Networkscited by 4
  12. 2024DeepSN: A Sheaf Neural Framework for Influence Maximizationcited by 4
  13. 2025SIGMA: Sheaf-Informed Geometric Multi-Agent Pathfindingcited by 4
  14. 2023Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicistscited by 3
  15. 2023Dirichlet Energy Enhancement of Graph Neural Networks by Framelet Augmentationcited by 3
  16. 2024FedSheafHN: Personalized Federated Learning on Graph-structured Datacited by 3
  17. 2025Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learningcited by 3
  18. 2025Sheaves Reloaded: A Directional Awakeningcited by 3
  19. 2025Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theoremscited by 3
  20. 2022Graph Convolutional Networks from the Perspective of Sheaves and the Neural Tangent Kernelcited by 2
  21. 2024Towards a Categorical Foundation of Deep Learning: A Surveycited by 2
  22. 2025Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimizationcited by 2
  23. 2026Neural Networks as Local-to-Global Computationscited by 2
  24. 2026Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learningcited by 2
  25. 2026Learning Multi-Agent Coordination via Sheaf-ADMMcited by 2
  26. 2026Topological Neural Operatorscited by 2
  27. 2023Algebraic Topological Networks via the Persistent Local Homology Sheafcited by 1
  28. 2024Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphscited by 1
  29. 2024An Intrinsic Vector Heat Networkcited by 1
  30. 2025What Can We Learn From MIMO Graph Convolutions?cited by 1
  31. 2025Personalized Subgraph Federated Learning with Sheaf Collaborationcited by 1
  32. 2025On the Sheafification of Higher-Order Message Passingcited by 1
  33. 2025Learning from Frustration: Torsor CNNs on Graphscited by 1
  34. 2025Gauge-Equivariant Graph Networks via Self-Interference Cancellationcited by 1
  35. 2026Sheaf-Laplacian Obstruction and Projection Hardness for Cross-Modal Compatibility on a Modality-Independent Sitecited by 1
  36. 2026Dynamic Sheaf Diffusion Networks with Adaptive Local Structure for Heterogeneous Spatio-Temporal Graph Learningcited by 1
  37. 2026Finsler Geometry, Graph Neural Networks, and Youcited by 1
  38. 2026Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networkscited by 1

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