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arXiv · 2410.14639

Convergence of Manifold Filter-Combine Networks

David R. Johnson·Joyce Chew·Siddharth Viswanath·Edward De Brouwer·Deanna Needell·Smita Krishnaswamy·Michael Perlmutter
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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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David R. Johnson, Joyce Chew, Siddharth Viswanath, Edward De Brouwer, Deanna Needell, Smita Krishnaswamy, Michael Perlmutter. 2024-10-18. Convergence of Manifold Filter-Combine Networks. https://arxiv.org/abs/2410.14639

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