mlsanityData to 7 Oct 2026

Node-Variant Graph Filters in Graph Neural Networks

arXiv 2106.00089 ↗First posted 31 May 2021cs.LG eess.SPcited by 7

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Abstract (arXiv)

Graph neural networks (GNNs) have been successfully employed in a myriad of applications involving graph signals. Theoretical findings establish that GNNs use nonlinear activation functions to create low-eigenvalue frequency content that can be processed in a stable manner by subsequent graph convolutional filters. However, the exact shape of the frequency content created by nonlinear functions is not known and cannot be learned. In this work, we use node-variant graph filters (NVGFs) -- which are linear filters capable of creating frequencies -- as a means of investigating the role that frequency creation plays in GNNs. We show that, by replacing nonlinear activation functions by NVGFs, frequency creation mechanisms can be designed or learned. By doing so, the role of frequency creation is separated from the nonlinear nature of traditional GNNs. Simulations on graph signal processing problems are carried out to pinpoint the role of frequency creation.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 33 of its 46 references that are in the map. First posted on arXiv 31 May 2021.

Builds on

33 of 46 references.

References · 33

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21 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 2; 2024: 0; 2025: 1; 2026: 2.

7 papers.

  1. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  2. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  3. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  4. 2023Locally Stationary Graph Processescited by 0
  5. 2025TV-Rec: Time-Variant Convolutional Filter for Sequential Recommendationcited by 0
  6. 2026Graph Signal Processing Meets Mamba2: Adaptive Filter Bank via Delta Modulationcited by 0
  7. 2026Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNscited by 0