# Beyond Low-frequency Information in Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2101.00797 · HTML: https://mlsanity.com/paper/2101.00797/

## 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 (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [A Survey on Heterogeneous Graph Embedding: Methods, Techniques, Applications and Sources](https://mlsanity.com/paper/2011.14867/) (2020)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Label Efficient Semi-Supervised Learning via Graph Filtering](https://mlsanity.com/paper/1901.09993/) (2019)

## Built on by (most cited first, 30 of 362)

- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Language is All a Graph Needs](https://mlsanity.com/paper/2308.07134/) (2023)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [Generalizing Graph Neural Networks on Out-Of-Distribution Graphs](https://mlsanity.com/paper/2111.10657/) (2021)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [Sheaf Neural Networks with Connection Laplacians](https://mlsanity.com/paper/2206.08702/) (2022)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [Gradient Gating for Deep Multi-Rate Learning on Graphs](https://mlsanity.com/paper/2210.00513/) (2022)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2210.02330/) (2022)
- [Spectral Augmentation for Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2210.00643/) (2022)
- [Generalized Graph Prompt: Toward a Unification of Pre-Training and Downstream Tasks on Graphs](https://mlsanity.com/paper/2311.15317/) (2023)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [VCR-Graphormer: A Mini-batch Graph Transformer via Virtual Connections](https://mlsanity.com/paper/2403.16030/) (2024)

## 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.