Papers › Sheaf Neural Networks with Connection Laplacians

Sheaf Neural Networks with Connection Laplacians

17 Jun 2022arXiv:2206.08702archive 2025-07-28

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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Code

antoniopurificato/sheaf4rec mentioned on GitHubpytorch report

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Tasks

Graph Neural NetworkNode Classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
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

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Methods

ALIGNGraph Neural Network

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