HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
Towards a theoretical foundation for laplacian-based manifold methods.Journal of Computer and System Sciences, 74(8):1289–1308
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
citation-role summary
background 1
extension 1
citation-polarity summary
fields
cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Neural point-forms are introduced as permutation-invariant neural layers that output learned form-comparison matrices for point clouds, with a claimed consistency proof under sampling and manifold assumptions and competitive results on synthetic and biological data.
citing papers explorer
-
Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
-
Neural Point-Forms
Neural point-forms are introduced as permutation-invariant neural layers that output learned form-comparison matrices for point clouds, with a claimed consistency proof under sampling and manifold assumptions and competitive results on synthetic and biological data.