Sheaf Neural Networks

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Let the Heads Talk: Beyond Diagonal Graph Attention
Oct 1, 2026Riccardo Ali, Alessio Borgi, Mario Severino +4Multi-Head Attention Interleaved Graph Attention
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
Clifford Sheaf Neural Networks
Oct 1, 2026Kotaro Kamiya, Joel NichollsSheaf Neural Networks Sheaf
SyntheticGestalt KK
Benchmarking Sheaf Neural Networks for Inductive Tasks
Aug 3, 2026Stefano Fiorini, Edoardo Coppola, Pietro LiòSheaf Neural Networks Sheaf
1Independent Researcher · Department of Computer Science and Technology, University of Cambridge
Learned, Relied Upon, or Necessary? Separating Checkpoint Dependence from Task-Level Value in Sheaf GNNs
Jul 28, 2026Yi LiuSheaf Neural Networks Graph Neural Networks
School of Astronomy and Space Science, University of Science and Technology of China
Do Sheaf Neural Networks Use Holonomy? A Measure--Intervene--Control Study
Jul 21, 2026Ankit Grover, Rémi BourgerieSheaf Neural Networks Neural Network
KTH Royal Institute of Technology, Stockholm, Sweden
Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks
Jul 4, 2026Yoshihiro MaruyamaEquivariant Neural Networks Sheaf Neural Networks
Department of Mathematical and Information Sciences, Kyoto University, Kyoto, Japan.
Curvature-Guided Sheaf Diffusion for Unsupervised Community Detection on Heterophilic Graphs
Jun 29, 2026Feifan WangCommunity Detection Text-Attributed Graph
School of Artificial Intelligence Xiamen Institute of Technology No. 1251, Sunban South Road, Jimei District Xiamen, Fujian 361021, China
Hierarchical Pooling for Sheaf Neural Networks
Jun 18, 2026Dionisia Naddeo, Carlo Abate, Pietro Liò +2Sheaf Neural Networks Sheaf
UiT The Arctic University of Norway · UiT The Arctic University of Norway NORCE Norwegian Research Centre AS
Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport
Jun 8, 2026Md Sadek Hossain Asif, Tanzila Khan, Md. Mosaddek KhanTemporal Graph Neural Networks Sheaf Neural Networks
University of Dhaka
Gaussian Sheaf Neural Networks
May 20, 2026André Ribeiro, Ana Luiza Tenório, Tiago da Silva +1Sheaf Neural Networks Graph Representation Learning
Getulio Vargas Foundation · MBZUAI
Deep Neural Sheaf Diffusion
May 18, 2026Rémi Bourgerie, Šarūnas Girdzijauskas, Viktoria FodorSheaf Neural Networks Graph Neural Networks
School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden.
NOFE - Neural Operator Function Embedding
May 12, 2026Lars Uebbing, Harald L. Joakimsen, Siyan Chen +6Dimensionality Reduction Fourier Neural Operators
1UiT The Arctic University of Norway · 2Norwegian Computing Center · University of South Brittany +1
Multi-Agent System Identification with Nonlinear Sheaf Diffusion
May 11, 2026Nivar Anwer, Hans Riess, Matthew HaleSheaf Neural Networks Multi-Agent Communication
Department of Computer Science, Georgia Tech · Department of Electrical & Computer Engineering, Georgia Tech
Oversmoothing as Representation Degeneracy in Neural Sheaf Diffusion
May 11, 2026Arif Dönmez, Axel Mosig, Ellen Fritsche +1Sheaf Neural Networks Sheaf
IUF – Leibniz Research Institute for Environmental Medicine, Düsseldorf, Germany · DNTOX GmbH, Düsseldorf, Germany · Bioinformatics Group, Ruhr University Bochum, Bochum, Germany +1
Shearlet Neural Operators for Anisotropic-Shock-Dominated and Multi-scale parametric partial differential equations
Apr 28, 2026Fabio Pereira dos Santos, Julio de Castro Vargas Fernandes, Adriano Mauricio de Almeida CortesFourier Neural Operators Neural Operators
Coordination of Mathematical and Computational Methods National Laboratory of Scientific Computing Av. Getúlio Vargas, 333 - Quitandinha, Petrópolis - RJ, 25651-075 · Systems and Computational Engineering Program, COPPE/UFRJ, Federal University of Rio de Janeiro, P.O. Box 68542, Rio de Janeiro, RJ, 21941-909, Brasil
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
Apr 22, 2026Yuhan Peng, Junwen Dong, Yuzhi Zeng +6Sheaf Neural Networks Sheaf
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

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Let the Heads Talk: Beyond Diagonal Graph Attention

Riccardo Ali, Alessio Borgi, Mario Severino, Alessio Gravina+3

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

Multi-Head Attention Interleaved Graph Attention Sheaf Neural Networks

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Sheaf Neural Networks generalize scalar-weighted message passing by replacing scalar edge weights with linear transport maps between local feature spaces. Yet the role of this matrix-valued transport is entangled with the broader sheaf-diffusion construction. We isolate the transport primitive through quiver representations and establish a direct connection with multi-head attention. Treating attention heads as coordinates of a local transport space reveals that standard multi-head attention implements diagonal edge maps: along each directed interaction, a source head can contribute only to the corresponding receiver head. Allowing off-diagonal entries instead enables edge-conditioned communication across heads before neighborhood aggregation. We show that this operation cannot, in general, be absorbed into a single shared linear map applied after aggregation. Building on this characterization, we introduce Topological Attention (Top-A), a multi-head attention that learns edge-dependent off-diagonal routes while preserving the original same-head paths and exactly recovering vanilla attention when the additional routing vanishes. We evaluate Top-A on relational reasoning, heterogeneous graph learning, and algorithmic reasoning, including out-of-distribution generalization, with heterophilic node classification as a contrast setting. The results show that cross-head transport is most useful when the task benefits from interaction-dependent transformations, while heterophily alone provides no systematic advantage. These findings identify edge-conditioned cross-head communication as a distinct computational primitive of matrix-valued transport.

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