Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back

arXiv:2303.11323v2 Announce Type: replace-cross
Abstract: In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation, which are novel continuous architectures operating on tangent bundle signals, i.e. vector fields over the manifolds. Tangent bundle filters admit a spectral representation that generalizes the ones of scalar manifold filters, graph filters and standard …

abstract arxiv cellular continuous convolution cs.lg eess.sp filters networks neural networks novel terms type work