Learning on higher-order domains: simplicial and cell complexes, hypergraphs, and sheaves.
The 2026 Topological Deep Learning Challenge put graph neural networks and higher-order topological neural networks side by side in TopoBench, on synthetic graphs whose structure is set by design, and found that which family does better depends on the task. Our implementation of the directed sheaf neural network took first place in the graph neural network track.
Implicit Sheaf Operators make sheaf neural networks fast: they apply sheaf diffusion and sheaf convolution locally at each node, without building the sheaf Laplacian, cutting time, memory, and energy down to edge devices. Built on them, Sheaf Convolutional Networks match or beat the accuracy of Neural Sheaf Diffusion on most node classification benchmarks.
The 2025 Topological Deep Learning Challenge asked the community to extend TopoBench with new datasets, benchmark tasks, and data pipelines; this report describes the challenge and what it received.
