Implicit Sheaf Operators for Effective and Efficient Cellular Sheaf Learning

Sheaf diffusion without building the sheaf Laplacian: local operator-vector products cut latency up to 4.87× and peak GPU memory up to 3.92×.

Abstract

While Sheaf Neural Networks (SNNs) enrich n-node m-edge diffusion of f-dimensional node features with d-dimensional node and edge stalks, they require computing a sparse nd x nd sheaf Laplacian, whose computation is prohibitive on edge devices. This paper addresses this issue with Implicit Sheaf Operators (ISOs), a type of sheaf topological operators that leverage the topological structure of cellular sheaves to decompose the global diffusion process into local operator-vector products. We mathematically prove that ISO eliminates the O(md^2 log(md^2)) sparse-coalescing term and reduces the space complexity by O(min(d, f)) with respect to traditional Neural Sheaf Diffusion (NSD). Our experiments indicate that ISO-based operators achieve latency reduction of up to 4.87× and save up to 3.92× peak GPU memory. On real graph classification data, ISO uses up to 1.24× less energy and 3.08× less on-device memory as measured on a Jetson Orin Nano. Finally, to bring ISO to practice, we introduce Sheaf Convolutional Networks (SCNs), an ISO-based SNN attaining up to 3.93% higher accuracy compared to NSD-based SNNs on node classification benchmarks.

Cite

@misc{onorato2026operators,
  title  = {Implicit Sheaf Operators for Effective and Efficient Cellular Sheaf Learning},
  author = {Onorato, Gabriele and Loi, Dario and Apostol, Cristian and Bastian, Nathaniel D. and Restuccia, Francesco},
  year   = {2026},
  note   = {Preprint}
}

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