mlsanityData to 14 Oct 2026

Cooperative Sheaf Neural Networks

arXiv 2507.00647 ↗First posted 1 Jul 2025cs.LGcited by 12

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Abstract (arXiv)

Sheaf diffusion has recently emerged as a promising design pattern for graph representation learning due to its inherent ability to handle heterophilic data and avoid oversmoothing. Meanwhile, cooperative message passing has also been proposed as a way to enhance the flexibility of information diffusion by allowing nodes to independently choose whether to propagate/gather information from/to neighbors. A natural question ensues: is sheaf diffusion capable of exhibiting this cooperative behavior? Here, we provide a negative answer to this question. In particular, we show that existing sheaf diffusion methods fail to achieve cooperative behavior due to the lack of message directionality. To circumvent this limitation, we introduce the notion of cellular sheaves over directed graphs and characterize their in- and out-degree Laplacians. We leverage our construction to propose Cooperative Sheaf Neural Networks (CSNNs). Theoretically, we characterize the receptive field of CSNN and show it allows nodes to selectively attend (listen) to arbitrarily far nodes while ignoring all others in their path, potentially mitigating oversquashing. Our experiments show that CSNN presents overall better performance compared to prior art on sheaf diffusion as well as cooperative graph neural networks.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 40 of its 52 references that are in the map. First posted on arXiv 1 Jul 2025.

Builds on

40 of 52 references.

References · 40

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
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  11. 2015Gated Graph Sequence Neural Networkscited by 796
  12. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 754
28 more
  1. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  2. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  3. 2019Multi-scale Attributed Node Embeddingcited by 548
  4. 2020Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classificationcited by 506
  5. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 478
  6. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 443
  7. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 362
  8. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 343
  9. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  10. 2022Long Range Graph Benchmarkcited by 263
  11. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  12. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  13. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  14. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  15. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 166
  16. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 90
  17. 2023Where Did the Gap Go? Reassessing the Long-Range Graph Benchmarkcited by 85
  18. 2020Sheaf Neural Networkscited by 84
  19. 2022Sheaf Neural Networks with Connection Laplacianscited by 65
  20. 2016Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using Householder Reflectionscited by 57
  21. 2021Simplifying approach to Node Classification in Graph Neural Networkscited by 56
  22. 2023Cooperative Graph Neural Networkscited by 36
  23. 2023Sheaf Hypergraph Networkscited by 34
  24. 2024The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challengescited by 29
  25. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 22
  26. 2024Bundle Neural Networks for message diffusion on graphscited by 14
  27. 2024Heterogeneous Sheaf Neural Networkscited by 10
  28. 2024Quiver Laplacians and Feature Selectioncited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 12.

12 papers.

  1. 2026On the Necessity of Learnable Sheaf Laplacianscited by 5
  2. 2026A Gauge Theory of Superposition: Toward a Sheaf-Theoretic Atlas of Neural Representationscited by 4
  3. 2026Learning Multi-Agent Coordination via Sheaf-ADMMcited by 2
  4. 2026Deep Neural Sheaf Diffusioncited by 0
  5. 2026Temporal Sheaf Neural Networks with Dynamic Orthogonal Transportcited by 0
  6. 2026SheafStain: Sheaf-Theoretic Schr"odinger Bridge for Spatially and Biologically Coherent Virtual Stainingcited by 0
  7. 2026Hierarchical Pooling for Sheaf Neural Networkscited by 0
  8. 2026Learned, Relied Upon, or Necessary? Separating Checkpoint Dependence from Task-Level Value in Sheaf GNNscited by 0
  9. 2026Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphscited by 0
  10. 2026Let the Heads Talk: Beyond Diagonal Graph Attentioncited by 0
  11. 2026Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspectivecited by 0
  12. 2026PATTERN Can Be Solved from Memory: Generator-Aware Baselines for Synthetic Node Classificationcited by 0