Papers › Sheaf Neural Networks with Connection Laplacians
Sheaf Neural Networks with Connection Laplacians
Federico Barbero, Cristian Bodnar, Haitz Sáez de Ocáriz Borde, Michael Bronstein, Petar Veličković, Pietro Liò
A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have useful theoretical properties that help tackle issues arising from heterophily and over-smoothing. One complication intrinsic to these models is finding a good sheaf for the task to be solved. Previous works proposed two diametrically opposed approaches: manually constructing the sheaf based on domain knowledge and learning the sheaf end-to-end using gradient-based methods. However, domain knowledge is often insufficient, while learning a sheaf could lead to overfitting and significant computational overhead. In this work, we propose a novel way of computing sheaves drawing inspiration from Riemannian geometry: we leverage the manifold assumption to compute manifold-and-graph-aware orthogonal maps, which optimally align the tangent spaces of neighbouring data points. We show that this approach achieves promising results with less computational overhead when compared to previous SNN models. Overall, this work provides an interesting connection between algebraic topology and differential geometry, and we hope that it will spark future research in this direction.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Node Classification | Chameleon | Conn-NSD | Accuracy | 65.21±2.04 | #45 of 61 | Archive leaderboard | report |
| Node Classification | Cornell | Conn-NSD | Accuracy | 85.95±7.72 | #15 of 60 | Archive leaderboard | report |
| Node Classification | Squirrel | Conn-NSD | Accuracy | 45.19±1.57 | #46 of 59 | Archive leaderboard | report |
| Node Classification | Texas | Conn-NSD | Accuracy | 86.16±2.24 | #24 of 62 | Archive leaderboard | report |
| Node Classification | Wisconsin | Conn-NSD | Accuracy | 88.73±4.47 | #10 of 63 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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