Sheaf Neural Networks

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Overview

Sheaf neural networks study how to learn over graphs when each node has its own feature space and edges specify how neighboring features should be compared or transported. Common approaches build sheaf Laplacians for diffusion, learn matrix-valued restriction maps, and combine them with attention, recurrent or implicit layers, spectral methods, and geometric or temporal models. The framework is being applied to heterophilic graphs, spatio-temporal data, physical systems, and manifold-valued features, with work analyzing expressivity, convergence, oversmoothing, and information bottlenecks. A central open question is when learned sheaf structure adds reliable value over simpler graph models: results depend on architecture and task, so benchmarks and controlled comparisons are important.

Latest papers

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29 papers6 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. A Bochner Weitzenböck Decomposition for Cellular Sheaf Laplacians, Curvature and Neural Sheaf Diffusion

    Oct 20, 2026Francesco Maria Guadagnuolo, Alessio Borgi, Dorina Thanou +1Sheaf Neural Networks

    Sapienza University of Rome, Rome, Italy · Italian Institute of Artificial Intelligence (AI4I), Turin, Italy · University of Cambridge, Cambridge, United Kingdom +1

  2. ChronoSheaf: Joint Spatio-Temporal Spectral Filtering on Cellular Sheaves

    Oct 15, 2026Abeer Mostafa, Zahra AhmadiSheaf Neural NetworksSpatiotemporal Forecasting

    Peter L. Reichertz Institute for Medical Informatics, Hannover Medical School, Germany · Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed), Hannover, Germany

  3. Oscillatory Neural Dynamics over Sheaves

    Oct 7, 2026Jan-Willem Van Looy, Alessandro Trenta, Alessio Gravina +5Long-Range Graph LearningGraph Neural Networks

    FaBiT, University of Bologna · Department of Computer Science, University of Pisa · Department of Computer, Control and Management Engineering, Sapienza University of Rome +1

  4. Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective

    Oct 3, 2026André Ribeiro, Germano Barcelos, Amauri H. Souza +2Over-Squashing in GNNsGraph Neural Networks

    Getulio Vargas Foundation · Federal University of Viçosa · Federal Institute of Ceará, 2δ AI +2

  5. Let the Heads Talk: Beyond Diagonal Graph Attention

    Oct 1, 2026Riccardo Ali, Alessio Borgi, Mario Severino +4Graph Attention NetworksSheaf Neural Networks

    Department of Computer Science and Technology, University of Cambridge · Department of Computer, Control and Management Engineering, Sapienza University of Rome · Department of Information Engineering, University of Padua +1

  6. Clifford Sheaf Neural Networks

    Oct 1, 2026Kotaro Kamiya, Joel NichollsSheaf Neural NetworksEquivariant GNNs

    SyntheticGestalt KK

  7. Stable Unsupervised Continual Chunking with Sheaf SyncMap

    Sep 21, 2026Xueyuan Li, Danilo Vasconcellos VargasSheaf Neural NetworksOnline Continual Learning

  8. Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs

    Aug 28, 2026Alessio Borgi, Mario Severino, Fabrizio Silvestri +1Equivariant Neural NetworksSheaf Neural Networks

    Department of Computer Science and Technology, University of Cambridge · Department of Computer, Control and Management Engineering, Sapienza University of Rome · Department of Information Engineering, University of Padua

  9. Demystifying Oversmoothing in Sheaf Neural Networks: An Index-Theoretic Criterion

    Aug 17, 2026Junwen Dong, Yuhan Peng, Hao Li +2GNN OversmoothingSheaf Neural Networks

    Department of Mathematics, Faculty of Science National University of Singapore Singapore · School of Physical and Mathematical Sciences Nanyang Technological University Singapore

  10. Fixed Points Without Fixed Diffusion: Implicit Neural Sheaves for Convergent Test-Time Computation

    Aug 12, 2026Rémi Bourgerie, Šarūnas Girdzijauskas, Viktoria FodorGraph Neural NetworksSheaf Neural Networks

    School of Electrical Engineering and Computer Science, and Digital Futures KTH Royal Institute of Technology, Stockholm, Sweden

  11. Benchmarking Sheaf Neural Networks for Inductive Tasks

    Aug 3, 2026Stefano Fiorini, Edoardo Coppola, Pietro LiòGraph Neural NetworksGraph Representation Learning

    1Independent Researcher · Department of Computer Science and Technology, University of Cambridge

  12. Learned, Relied Upon, or Necessary? Separating Checkpoint Dependence from Task-Level Value in Sheaf GNNs

    Jul 28, 2026Yi LiuSheaf Neural NetworksSheaf Theory

    School of Astronomy and Space Science, University of Science and Technology of China

  13. Do Sheaf Neural Networks Use Holonomy? A Measure--Intervene--Control Study

    Jul 21, 2026Ankit Grover, Rémi BourgerieNeural Network InterpretabilitySheaf Neural Networks

    KTH Royal Institute of Technology, Stockholm, Sweden

  14. Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks

    Jul 4, 2026Yoshihiro MaruyamaGraph Neural NetworksEquivariant Neural Networks

    Department of Mathematical and Information Sciences, Kyoto University, Kyoto, Japan.

  15. Hierarchical Pooling for Sheaf Neural Networks

    Jun 18, 2026Dionisia Naddeo, Carlo Abate, Pietro Liò +2Graph Neural NetworksGraph Coarsening

    UiT The Arctic University of Norway · UiT The Arctic University of Norway NORCE Norwegian Research Centre AS

  16. Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

    Jun 8, 2026Md Sadek Hossain Asif, Tanzila Khan, Md. Mosaddek KhanTemporal GNNsGraph Neural Networks

    University of Dhaka

  17. Gaussian Sheaf Neural Networks

    May 20, 2026André Ribeiro, Ana Luiza Tenório, Tiago da Silva +1Graph Neural NetworksSheaf Neural Networks

    Getulio Vargas Foundation · MBZUAI

  18. BrainDyn: A Sheaf Neural ODE for Forecasting and Generating Brain Dynamics

    May 19, 2026Siddharth Viswanath, Panayiotis Ketonis, Cassidy All +10Graph Neural NetworksSheaf Neural Networks

    Yale University · Boise State University · University of Wisconsin–Madison

  19. Deep Neural Sheaf Diffusion

    May 18, 2026Rémi Bourgerie, Šarūnas Girdzijauskas, Viktoria FodorGraph Neural NetworksSheaf Neural Networks

    School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden.

  20. NOFE - Neural Operator Function Embedding

    May 12, 2026Lars Uebbing, Harald L. Joakimsen, Siyan Chen +6Inverse Dimensionality ReductionSheaf Neural Networks

    1UiT The Arctic University of Norway · 2Norwegian Computing Center · University of South Brittany +1

  21. Oversmoothing as Representation Degeneracy in Neural Sheaf Diffusion

    May 11, 2026Arif Dönmez, Axel Mosig, Ellen Fritsche +1Graph Neural NetworksSheaf Neural Networks

    IUF – Leibniz Research Institute for Environmental Medicine, Düsseldorf, Germany · DNTOX GmbH, Düsseldorf, Germany · Bioinformatics Group, Ruhr University Bochum, Bochum, Germany +1

  22. Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

    May 7, 2026Kartik Tandon, Julian Gould, Tanishq Bhatia +3Graph Neural NetworksGeometric Representation Learning

    University of Pennsylvania · Sakana AI · Northeastern University +1

  23. Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures

    Apr 27, 2026Qianlei Wang, Kexun Chen, Shaolin Zhang +3Monocular Depth EstimationEquivariant Neural Networks

    Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610213 China. · School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu 611756 China. · School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 611756 China. +1

  24. Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

    Apr 22, 2026Yuhan Peng, Junwen Dong, Yuzhi Zeng +6Graph Neural NetworksGeometric Representation Learning

    School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore · Chern Institute of Mathematics, Nankai University, Tianjin, China · Department of Mathematics, Faculty of Science, National University of Singapore, Singapore +3

  25. Dynamic Sheaf Diffusion Networks with Adaptive Local Structure for Heterogeneous Spatio-Temporal Graph Learning

    Apr 13, 2026Abeer Mostafa, Raneen Younis, Zahra AhmadiOver-Smoothing in GNNsGraph Neural Networks

    Peter L. Reichertz Institute for Medical Informatics, Hannover Medical School, Hannover, Germany · Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed), Hannover, Germany

  26. Neural Networks as Local-to-Global Computations

    Mar 16, 2026Vicente Bosca, Robert GhristSheaf Neural NetworksFeedforward Neural Networks

    Department of Mathematics, University of Pennsylvania

  27. On the Necessity of Learnable Sheaf Laplacians

    Mar 5, 2026Ferran Hernandez Caralt, Mar Gonzàlez i Català, Adrián Bazaga +1GNN OversmoothingSheaf Neural Networks

    Department of Computer Science and Technology, University of Cambridge, Cambridge, United Kingdom · Microsoft

  28. Learning Latent Graph Geometry via Fixed-Point Schrödinger-Type Activation: A Theoretical Study

    Jul 27, 2025Dmitry Pasechnyuk-Vilensky, Martin TakáčGraph Structure LearningGraph Neural Networks

    MBZUAI, UAE

  29. Heterogeneous Sheaf Neural Networks

    Sep 12, 2024Luke Braithwaite, Alessio Borgi, Gabriele Onorato +4Heterogeneous GNNsSheaf Neural Networks

    Department of Computer Science and Technology, University of Cambridge · Department of Computer, Control and Management Engineering, Sapienza University of Rome · Department of Electrical and Computer Engineering, Northeastern University