Applicability of sheaf-type neural networks to large graphs

Determine the applicability and scalability of sheaf-type neural network architectures to large-scale graphs (e.g., graphs with more than one million nodes), including identifying their performance characteristics, limitations, and the architectural or algorithmic adaptations required to handle such graphs efficiently.

Background

The paper notes that most empirical work on sheaf-type neural networks has been conducted on relatively small graphs, while many real-world datasets (such as knowledge graphs, social networks, and Wikipedia link structures) are orders of magnitude larger. Earlier sections highlight the computational overhead of sheaf learning and diffusion layers compared to traditional GNNs, raising practical concerns for scaling.

Because sheaf-based models introduce additional structure (e.g., learned restriction maps and higher-dimensional stalks) and often rely on spectral operations or message passing with higher complexity, assessing their viability on large graphs is both technically and practically important. The authors therefore flag scalability as an unresolved issue that needs systematic investigation.