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Hyperbolic Graph Wavelet Neural Network

School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210000, China
Shandong Provincial University Laboratory for Protected Horticulture, Weifang University of Science and Technology, Weifang 761000, China
School of Computer Science, Qufu Normal University, Rizhao 276800, China
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Abstract

Graph neural networks (GNNs), grounded in spatial or spectral domains, have achieved remarkable success in learning graph representations in Euclidean space. Recent advances in spatial GNNs reveal that embedding graph nodes with hierarchical structures into hyperbolic space is more effective, reducing distortion compared to Euclidean embeddings. However, extending spectral GNNs to hyperbolic space remains several challenges, particularly in defining spectral graph convolution and enabling message passing within the hyperbolic geometry. To address these challenges, we propose the hyperbolic graph wavelet neural network (HGWNN), a novel approach for modeling spectral GNNs in hyperbolic space. Specifically, we first define feature transformation and spectral graph wavelet convolution on the hyperboloid manifold using exponential and logarithmic mappings, without increasing model parameter complexity. Moreover, we enable non-linear activation on the Poincaré manifold and efficient message passing via diffeomorphic transformations between the hyperboloid and Poincaré models. Experiments on four benchmark datasets demonstrate the effectiveness of our proposed HGWNN over baseline systems.

Keywords

graph neural network (GNN)hyperbolic embeddinghyperbolic space

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Tsinghua Science and Technology
Volume 30 Issue 4,
August 2025
Pages 1511-1525
DOI: 10.26599/TST.2024.9010032
Cite this article:
Zheng W, Zhang G, Zhao X, et al. Hyperbolic Graph Wavelet Neural Network. Tsinghua Science and Technology, 2025, 30(4): 1511-1525. https://doi.org/10.26599/TST.2024.9010032
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