{"title":"Hyperbolic Graph Wavelet Neural Network","authors":"Wenjie Zheng;Guofeng Zhang;Xiaoran Zhao;Zhikang Feng;Lekang Song;Huaizhen Kou","doi":"10.26599/TST.2024.9010032","DOIUrl":null,"url":null,"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.","PeriodicalId":48690,"journal":{"name":"Tsinghua Science and Technology","volume":"30 4","pages":"1511-1525"},"PeriodicalIF":6.6000,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10908594","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsinghua Science and Technology","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10908594/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Multidisciplinary","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Tsinghua Science and Technology (Tsinghua Sci Technol) started publication in 1996. It is an international academic journal sponsored by Tsinghua University and is published bimonthly. This journal aims at presenting the up-to-date scientific achievements in computer science, electronic engineering, and other IT fields. Contributions all over the world are welcome.