# A New Perspective on the Effects of Spectrum in Graph Neural Networks

arXiv: https://arxiv.org/abs/2112.07160 · HTML: https://mlsanity.com/paper/2112.07160/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 59 references that are in the map.
- First posted on arXiv 14 Dec 2021.

## Builds on (most cited first, 30 of 44)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [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)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)

## Built on by (most cited first, 24 of 24)

- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Energy Transformer](https://mlsanity.com/paper/2302.07253/) (2023)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Partitioning Message Passing for Graph Fraud Detection](https://mlsanity.com/paper/2412.00020/) (2024)
- [No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasets](https://mlsanity.com/paper/2502.02379/) (2025)
- [Learnable Spectral Wavelets on Dynamic Graphs to Capture Global Interactions](https://mlsanity.com/paper/2211.11979/) (2022)
- [Graph Fourier Neural Kernels (G-FuNK): Learning Solutions of Nonlinear Diffusive Parametric PDEs on Multiple Domains](https://mlsanity.com/paper/2410.04655/) (2024)
- [Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structures](https://mlsanity.com/paper/2302.08647/) (2023)
- [Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering](https://mlsanity.com/paper/2305.06102/) (2023)
- [Deep representation learning: Fundamentals, Perspectives, Applications, and Open Challenges](https://mlsanity.com/paper/2211.14732/) (2022)
- [Beyond Graph Convolutional Network: An Interpretable Regularizer-centered Optimization Framework](https://mlsanity.com/paper/2301.04318/) (2023)
- [Perfect Alignment May be Poisonous to Graph Contrastive Learning](https://mlsanity.com/paper/2310.03977/) (2023)
- [Spectral GNN via Two-dimensional (2-D) Graph Convolution](https://mlsanity.com/paper/2404.04559/) (2024)
- [Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective](https://mlsanity.com/paper/2412.07188/) (2024)
- [Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2401.09953/) (2024)
- [Degree-based stratification of nodes in Graph Neural Networks](https://mlsanity.com/paper/2312.10458/) (2023)
- [Federated Prototype Graph Learning](https://mlsanity.com/paper/2504.09493/) (2025)
- [Towards Unbiased Federated Graph Learning: Label and Topology Perspectives](https://mlsanity.com/paper/2504.09963/) (2025)
- [Towards Unsupervised Open-Set Graph Domain Adaptation via Dual Reprogramming](https://mlsanity.com/paper/2510.18363/) (2025)
- [Technical Report: The Graph Spectral Token -- Enhancing Graph Transformers with Spectral Information](https://mlsanity.com/paper/2404.05604/) (2024)
- [Toward Data-centric Directed Graph Learning: An Entropy-driven Approach](https://mlsanity.com/paper/2505.00983/) (2025)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [Controlled Dynamics Attractor Transformer](https://mlsanity.com/paper/2606.15207/) (2026)

## Abstract (arXiv)

Many improvements on GNNs can be deemed as operations on the spectrum of the underlying graph matrix, which motivates us to directly study the characteristics of the spectrum and their effects on GNN performance. By generalizing most existing GNN architectures, we show that the correlation issue caused by the unsmooth spectrum becomes the obstacle to leveraging more powerful graph filters as well as developing deep architectures, which therefore restricts GNNs' performance. Inspired by this, we propose the correlation-free architecture which naturally removes the correlation issue among different channels, making it possible to utilize more sophisticated filters within each channel. The final correlation-free architecture with more powerful filters consistently boosts the performance of learning graph representations. Code is available at https://github.com/qslim/gnn-spectrum.