Beyond Low-frequency Information in Graph Convolutional Networks
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Abstract (arXiv)
Graph neural networks (GNNs) have been proven to be effective in various network-related tasks. Most existing GNNs usually exploit the low-frequency signals of node features, which gives rise to one fundamental question: is the low-frequency information all we need in the real world applications? In this paper, we first present an experimental investigation assessing the roles of low-frequency and high-frequency signals, where the results clearly show that exploring low-frequency signal only is distant from learning an effective node representation in different scenarios. How can we adaptively learn more information beyond low-frequency information in GNNs? A well-informed answer can help GNNs enhance the adaptability. We tackle this challenge and propose a novel Frequency Adaptation Graph Convolutional Networks (FAGCN) with a self-gating mechanism, which can adaptively integrate different signals in the process of message passing. For a deeper understanding, we theoretically analyze the roles of low-frequency signals and high-frequency signals on learning node representations, which further explains why FAGCN can perform well on different types of networks. Extensive experiments on six real-world networks validate that FAGCN not only alleviates the over-smoothing problem, but also has advantages over the state-of-the-arts.
Key facts. Cited by 362 papers in the map (data through 14 Oct 2026). Builds on 24 of its 30 references that are in the map. First posted on arXiv 4 Jan 2021.
Builds on
24 of 30 references.
References · 24
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
- 2017Graph Attention Networkscited by 8,923
- 2017Inductive Representation Learning on Large Graphscited by 6,320
- 2018How Powerful are Graph Neural Networks?cited by 4,393
- 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
- 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
- 2019Simplifying Graph Convolutional Networkscited by 1,477
- 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
- 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 993
- 2018Link Prediction Based on Graph Neural Networkscited by 832
- 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
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- 2019Multi-scale Attributed Node Embeddingcited by 548
- 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
- 2018Deep Learning on Graphs: A Surveycited by 393
- 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 261
- 2019A Fair Comparison of Graph Neural Networks for Graph Classificationcited by 244
- 2019Graph Wavelet Neural Networkcited by 131
- 2020A Survey on Heterogeneous Graph Embedding: Methods, Techniques, Applications and Sourcescited by 126
- 2020AM-GCN: Adaptive Multi-channel Graph Convolutional Networkscited by 121
- 2020Non-Local Graph Neural Networkscited by 91
- 2020Adaptive Graph Encoder for Attributed Graph Embeddingcited by 89
- 2020Graph Convolutional Networks using Heat Kernel for Semi-supervised Learningcited by 51
- 2019Label Efficient Semi-Supervised Learning via Graph Filteringcited by 46
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Citing papers per year: 2021: 18; 2022: 62; 2023: 76; 2024: 84; 2025: 73; 2026: 49.
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