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The field of Geometric Deep Learning seeks to extend the success of deep learning from Euclidean data such as images to data with more irregular structure such as graphs and manifolds. In particular, in recent years, there has been a surge of interest in the development of graph neural networks (GNNs). However, the manifold side of deep learning remains much less explored. Therefore, to further the development of deep learning on manifolds, we introduce Manifold Filter-Combine Networks (MFCNs). Our framework is intended to parallel the popular aggregate-combine paradigm for GNNs and naturally suggests many interesting families of networks which can be interpreted as manifold analogues of various popular GNNs. Additionally, we propose a provably accurate method for implementing MFCNs on high-dimensional point clouds that relies on approximating an underlying manifold by a sparse graph.

This event is joint with the MADD seminar.