Stability to Deformations of Manifold Filters and Manifold Neural Networks

arXiv:2106.03725v5 Announce Type: replace
Abstract: The paper defines and studies manifold (M) convolutional filters and neural networks (NNs). \emph{Manifold} filters and MNNs are defined in terms of the Laplace-Beltrami operator exponential and are such that \emph{graph} (G) filters and neural networks (NNs) are recovered as discrete approximations when the manifold is sampled. These filters admit a spectral representation which is a generalization of both the spectral representation of graph filters and the frequency response of standard convolutional filters in continuous …

abstract arxiv cs.lg filters graph manifold networks neural networks nns paper stability studies terms type