# Improving Your Graph Neural Networks: A High-Frequency Booster

arXiv: https://arxiv.org/abs/2210.08251 · HTML: https://mlsanity.com/paper/2210.08251/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 15 Oct 2022.

## Builds on (most cited first, 28 of 28)

- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Rethinking Graph Regularization for Graph Neural Networks](https://mlsanity.com/paper/2009.02027/) (2020)
- [Spectral Graph Attention Network with Fast Eigen-approximation](https://mlsanity.com/paper/2003.07450/) (2020)
- [Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs](https://mlsanity.com/paper/2103.14187/) (2021)

## Built on by (most cited first, 4 of 4)

- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)
- [Feature Expansion for Graph Neural Networks](https://mlsanity.com/paper/2305.06142/) (2023)
- [Topology-aware Neural Flux Prediction Guided by Physics](https://mlsanity.com/paper/2506.05676/) (2025)
- [Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification](https://mlsanity.com/paper/2402.09600/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) hold the promise of learning efficient representations of graph-structured data, and one of its most important applications is semi-supervised node classification. However, in this application, GNN frameworks tend to fail due to the following issues: over-smoothing and heterophily. The most popular GNNs are known to be focused on the message-passing framework, and recent research shows that these GNNs are often bounded by low-pass filters from a signal processing perspective. We thus incorporate high-frequency information into GNNs to alleviate this genetic problem. In this paper, we argue that the complement of the original graph incorporates a high-pass filter and propose Complement Laplacian Regularization (CLAR) for an efficient enhancement of high-frequency components. The experimental results demonstrate that CLAR helps GNNs tackle over-smoothing, improving the expressiveness of heterophilic graphs, which adds up to 3.6% improvement over popular baselines and ensures topological robustness.