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.
Sheaf neural networks with connection laplacians
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Sheaf theory and the sheaf Laplacian are proposed as a topological framework for data fusion and consensus in distributed sensing networks.
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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.
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The Sheaf Laplacian: A Topological Framework for Data Fusion and Consensus in Distributed Sensing Networks
Sheaf theory and the sheaf Laplacian are proposed as a topological framework for data fusion and consensus in distributed sensing networks.