Convergence of Manifold Filter-Combine Networks

David R. Johnson, Joyce Chew, Siddharth Viswanath, Edward De Brouwer, Deanna Needell +2 more
10/18/2024
cs.LGeess.SPstat.ML

No official code found. Best implementation: dj408/mfcn (0 stars, last commit 2026-03-05).

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.

View on arXivView PDF

Code Implementations(1)

dj408/mfcnCommunity100%

Code for "Manifold Filter-Combine Networks" (Johnson et al. 2025)

00Shell, PythonJul 7, 20257 months ago

Similar Papers

Manifold Filter-Combine Networks

99% match2 repos2023

Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offs

86% match2023

Exploring the Manifold of Neural Networks Using Diffusion Geometry

82% match2024

Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs

82% match2024

A Manifold Perspective on the Statistical Generalization of Graph Neural Networks

82% match2024

Improved Image Classification with Manifold Neural Networks

80% match2024

Cite this paper

@article{johnson2024convergence,
  title  = {Convergence of Manifold Filter-Combine Networks},
  author = {David R. Johnson and Joyce Chew and Siddharth Viswanath and Edward De Brouwer and Deanna Needell and Smita Krishnaswamy and Michael Perlmutter},
  year   = {2024},
  eprint = {2410.14639},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2410.14639v1}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2410.14639.svg)](https://codeofpaper.com/paper/2410.14639)

Discussion