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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Constructs multi-framed real monopole Floer homology for 3-manifolds with involutions and defines Z-valued invariants for 4-manifolds with involutions.
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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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Multi-framed real monopole Floer theory
Constructs multi-framed real monopole Floer homology for 3-manifolds with involutions and defines Z-valued invariants for 4-manifolds with involutions.