mlsanityData to 14 Oct 2026

Graph Wave Networks

arXiv 2505.20034 ↗First posted 26 May 2025cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

Dynamics modeling has been introduced as a novel paradigm in message passing (MP) of graph neural networks (GNNs). Existing methods consider MP between nodes as a heat diffusion process, and leverage heat equation to model the temporal evolution of nodes in the embedding space. However, heat equation can hardly depict the wave nature of graph signals in graph signal processing. Besides, heat equation is essentially a partial differential equation (PDE) involving a first partial derivative of time, whose numerical solution usually has low stability, and leads to inefficient model training. In this paper, we would like to depict more wave details in MP, since graph signals are essentially wave signals that can be seen as a superposition of a series of waves in the form of eigenvector. This motivates us to consider MP as a wave propagation process to capture the temporal evolution of wave signals in the space. Based on wave equation in physics, we innovatively develop a graph wave equation to leverage the wave propagation on graphs. In details, we demonstrate that the graph wave equation can be connected to traditional spectral GNNs, facilitating the design of graph wave networks based on various Laplacians and enhancing the performance of the spectral GNNs. Besides, the graph wave equation is particularly a PDE involving a second partial derivative of time, which has stronger stability on graphs than the heat equation that involves a first partial derivative of time. Additionally, we theoretically prove that the numerical solution derived from the graph wave equation are constantly stable, enabling to significantly enhance model efficiency while ensuring its performance. Extensive experiments show that GWNs achieve SOTA and efficient performance on benchmark datasets, and exhibit outstanding performance in addressing challenging graph problems, such as over-smoothing and heterophily.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 40 of its 56 references that are in the map. First posted on arXiv 26 May 2025.

Builds on

40 of 56 references.

References · 40

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28 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 877
  2. 2020Simple and Deep Graph Convolutional Networkscited by 860
  3. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  4. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
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  9. 2019Diffusion Improves Graph Learningcited by 414
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  12. 2021GRAND: Graph Neural Diffusioncited by 258
  13. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  14. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  15. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  16. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  17. 2019Graph Neural Ordinary Differential Equationscited by 154
  18. 2020Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Modelscited by 116
  19. 2019Continuous Graph Neural Networkscited by 114
  20. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  21. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  22. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  23. 2023Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothingcited by 67
  24. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  25. 2021How Framelets Enhance Graph Neural Networkscited by 46
  26. 2022Model Degradation Hinders Deep Graph Neural Networkscited by 26
  27. 2022A Graph-Enhanced Click Model for Web Searchcited by 17
  28. 2023A Generalized Neural Diffusion Framework on Graphscited by 13

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Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equationscited by 2
  2. 2025Second-Order Tensorial Partial Differential Equations on Graphscited by 0

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