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.
Geometric graph filters and neural networks: Limit properties and discriminability trade-offs.IEEE Transactions on Signal Processing, 72:2244–2259
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GNNs are shown to lack continuity under graph resolution changes due to message-passing schemes, with a derived modification enabling consistent multi-scale representations validated experimentally.
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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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Graph Neural Networks Are Not Continuous Across Graph Resolutions
GNNs are shown to lack continuity under graph resolution changes due to message-passing schemes, with a derived modification enabling consistent multi-scale representations validated experimentally.