Related papers: Convergence of Manifold Filter-Combine Networks

Convergence of Manifold Filter-Combine Networks

URL: http://arxiv.org/abs/2410.14639v1
Date: Fri, 18 Oct 2024 17:40:58 GMT
Title: Convergence of Manifold Filter-Combine Networks
Authors: David R. Johnson, Joyce Chew, Siddharth Viswanath, Edward De Brouwer, Deanna Needell, Smita Krishnaswamy, Michael Perlmutter,
Abstract summary: We introduce Manifold Filter-Combine Networks (MFCNs) to better understand manifold neural networks (MNNs) We propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating the manifold by a sparse graph. We prove that our method is consistent in the sense that it converges to a limit as the number of data points continuum tends to infinity.
Score: 18.590886216749528
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Abstract: In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). The filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and naturally suggests many interesting families of MNNs which can be interpreted as the manifold analog of various popular GNNs. We then propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating the manifold by a sparse graph. We prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity.

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