Sheaf Theory

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Overview

Sheaf theory assigns local spaces of information to parts of a space or network and maps that describe how information relates across neighboring parts. Global sections capture locally compatible data, while sheaf cohomology can expose obstructions to making local descriptions consistent worldwide. In AI, sheaf neural networks use these ideas for graph learning with heterogeneous or geometric features, alongside applications in signal processing and multi-agent coordination. Benchmarks show that sheaf-based models can help on some tasks, but their advantage over simpler architectures is inconsistent, leaving open when learned local relationships provide indispensable value.

Latest papers

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20 papers2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. Global Coherence: When Every Agent Is Right and the Team Is Still Wrong - A Local-to-Global Semantic Foundation for Multi-Agent Collaboration

    Oct 1, 2026Xin HengMulti-Agent CollaborationSheaf Theory

    Tote AI

  2. Clifford Sheaf Neural Networks

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

    SyntheticGestalt KK

  3. Time-Varying Data as Sheaves: an Invitation to Narratives

    Sep 8, 2026Wilmer Leal, Benjamin Merlin Bumpus, Jana K. Nickel +3Time Series ReasoningSheaf Theory

    Department of Mechanical and Aerospace Engineering, University of Florida, 1064 Center Drive, Gainesville, 32611-6250, Florida, USA. · Instituto de Matem´atica e Estat´ıstica, Universidade de S˜ao Paulo, Rua do Mat˜ao, 1010, S˜ao Paulo, 05508–090, SP, Brasil. · Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, Hamburg, 20146, Germany. +2

  4. Capability Sheaves for Compositional Agent-Harness Repair: Controlled Quotients and a Real-Repository Stress Test

    Aug 13, 2026Saveliy BatruinAutomated Program RepairSheaf Theory

    Independent researcher

  5. Space as an Interventional Invariant: Cross-Modal Predictive Geometry for Stratified Cities and Em-Spaced Intelligence

    Aug 10, 2026Tao Yang, Xuhui Lin, Kunyao Li +1Causal Representation LearningGeospatial Representation Learning

    School of Architecture, Tsinghua University, Beijing, China · Department of Geography, University College London, London, United Kingdom · School of Engineering, Cardiff University, Cardiff, United Kingdom

  6. 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

  7. Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling

    Aug 2, 2026Gabriele D'Acunto, Leonardo Di Nino, Paolo Di Lorenzo +1Graph Signal ProcessingSheaf Theory

    Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, 00184 Rome, Italy · National Inter-University Consortium for Telecommunications (CNIT), Parma, Italy

  8. 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

  9. 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

  10. 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

  11. SheafStain: Sheaf-Theoretic Schrödinger Bridge for Spatially and Biologically Coherent Virtual Staining

    Jun 10, 2026Hyeongyeol Lim, Hongjun Yoon, Eunjin Jang +3Computational PathologyVision Foundation Models

    Department of Medical Informatics, College of Medicine, Korea University · DEEPNOID Inc.

  12. Incremental Sheaf Cohomology on Cellular Complexes: O(1)-in-n Lazy Edit Processing under Bounded Local Geometry

    Jun 2, 2026Jason L. VolkSheaf TheoryIncremental Computation

    Invariant Research

  13. A Sheaf Framework for Strategic Multi-Agent Systems: From Consensus to Nash Equilibria

    Jun 1, 2026Manuel Hernández, Eduardo Sánchez-SotoNash EquilibriumMulti-Agent Coordination

  14. Gaussian Sheaf Neural Networks

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

    Getulio Vargas Foundation · MBZUAI

  15. TopoPrimer: The Missing Topological Context in Forecasting Models

    May 14, 2026Zara Zetlin, Kayhan Moharreri, Maria SafiTime Series ForecastingSheaf Theory

    Apple

  16. Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents

    May 13, 2026David N. Olivieri, Roque J. HernándezAI Agents for Scientific DiscoverySheaf Theory

    Universidade de Vigo, Department of Computer Science (LSI), Spain

  17. Multi-Agent System Identification with Nonlinear Sheaf Diffusion

    May 11, 2026Nivar Anwer, Hans Riess, Matthew HaleParameter IdentifiabilityNonlinear System Identification

    Department of Computer Science, Georgia Tech · Department of Electrical & Computer Engineering, Georgia Tech

  18. 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

  19. Sheaf-Theoretic Planning: A Categorical Foundation for Resilient Multi-Agent Autonomous Systems

    May 3, 2026Manuel Hernández, Eduardo Sánchez-SotoMulti-Agent CoordinationSheaf Theory

    Universidad Tecnol´ogica de la Mixteca

  20. 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