2024 FFT

Manifold Filter Combine Networks

Michael Perlmutter (Boise St)

Abstract: We introduce Manifold Filter-Combine Networks (MFCNs), a novel framework for understanding manifold neural networks (MNNs), paralleling the aggregate-combine framework, which is used to understand graph neural networks (GNNs). We show that the MFCN framework naturally suggests many interesting families of MNNs, such as the several variations of the manifold scattering transform and the manifold analogs of ChebNets and the Graph Convolutional Network. We then propose a provably accurate method for implementing MFCNs on high-dimensional point clouds that relies on approximating the manifold by a sparse graph.