Benchmarking Sheaf Neural Networks for Inductive Tasks
2026-08-03 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study Sheaf Neural Networks (SNNs), an advanced type of graph neural network that uses flexible maps on edges instead of simple numbers. They test many design choices of SNNs on tasks where the model sees new graphs, not just the ones it was trained on (inductive learning). Their experiments show that the way edges are mapped is very important, while increasing the complexity of node features or sheaf details has less impact. Although SNNs can work in inductive settings, they do not outperform the best existing methods, and tuning the overall network design matters more than the sheaf part itself.
Sheaf Neural NetworksGraph Neural NetworksMessage PassingInductive LearningTransductive LearningRestriction MapsGraph Attention NetworkSheaf LaplacianNode Classification
Authors
Stefano Fiorini, Edoardo Coppola, Pietro Liò
Abstract
Sheaf Neural Networks (SNNs) generalize message passing by replacing scalar edge weights of standard Graph Neural Networks (GNNs) with learnable, edge-dependent restriction maps between node stalks. Despite their strong theoretical foundations and promising transductive results, SNNs have been evaluated almost exclusively on transductive node classification, leaving their behaviour under inductive protocols unknown. We address this gap through the first systematic benchmark of the sheaf design space, evaluating three diffusion mechanisms (neural sheaf diffusion, sheaf attention, and sheaf attention with Graph Attention Network v2), three restriction-map parameterizations, three stalk dimensions, and six modern GNN architectural components, within a message-passing reformulation that never assembles the heavy sheaf Laplacian, making the full design space trainable under cross-graph batching. Across $1{,}890$ controlled experiments on 14 inductive datasets, multiple insights emerge: restriction maps are the dominant design choice and general maps are preferable, larger stalks add capacity but not long-range reach, architectural components explain more performance variation than the entire sheaf-specific design space itself. Under a matched protocol, SNNs transfer to inductive settings but do not reach the strongest baselines, with gaps being dataset-dependent. Practically, a single sheaf configuration can generalize across datasets, so effort is better spent tuning the surrounding architectural recipe than the sheaf operator itself.