mlsanityData to 7 Oct 2026

Manifold Filter-Combine Networks

arXiv 2307.04056 ↗First posted 8 Jul 2023stat.ML cs.LG cs.NAcited by 2

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Abstract (arXiv)

In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). Our 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 manifold analogues of various popular GNNs. We propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating an underlying manifold by a sparse graph. We then 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, and we numerically demonstrate its effectiveness on real-world and synthetic data sets.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 37 of its 73 references that are in the map. First posted on arXiv 8 Jul 2023.

Builds on

37 of 73 references.

References · 37

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25 more
  1. 2018Geometric Scattering for Graph Data Analysiscited by 49
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Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  2. 2025InfoGain Wavelets: Furthering the Design of Graph Diffusion Waveletscited by 0