Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back. (arXiv:2210.15058v1 [eess.SP])

In this work we introduce a convolution operation over the tangent bundle of
Riemannian manifolds exploiting the Connection Laplacian operator. We use the
convolution to define tangent bundle filters and tangent bundle neural networks
(TNNs), novel continuous architectures operating on tangent bundle signals,
i.e. vector fields over manifolds. We discretize TNNs both in space and time
domains, showing that their discrete counterpart is a principled variant of the
recently introduced Sheaf Neural Networks. We formally prove that this discrete
architecture …

arxiv cellular filters networks neural networks