# Adaptive Kernel Graph Neural Network

arXiv: https://arxiv.org/abs/2112.04575 · HTML: https://mlsanity.com/paper/2112.04575/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 19 of 19)

- [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)
- [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)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (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)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [Improving Graph Attention Networks with Large Margin-based Constraints](https://mlsanity.com/paper/1910.11945/) (2019)
- [Batch Virtual Adversarial Training for Graph Convolutional Networks](https://mlsanity.com/paper/1902.09192/) (2019)
- [Learning Parametrised Graph Shift Operators](https://mlsanity.com/paper/2101.10050/) (2021)

## Built on by (most cited first, 15 of 15)

- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [Multi-task Self-supervised Graph Neural Networks Enable Stronger Task Generalization](https://mlsanity.com/paper/2210.02016/) (2022)
- [GraphPatcher: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentation](https://mlsanity.com/paper/2310.00800/) (2023)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Grape: Knowledge Graph Enhanced Passage Reader for Open-domain Question Answering](https://mlsanity.com/paper/2210.02933/) (2022)
- [Let Graph be the Go Board: Gradient-free Node Injection Attack for Graph Neural Networks via Reinforcement Learning](https://mlsanity.com/paper/2211.10782/) (2022)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filtering](https://mlsanity.com/paper/2401.09071/) (2024)
- [Temporal Graph Pattern Machine](https://mlsanity.com/paper/2601.22454/) (2026)
- [BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs](https://mlsanity.com/paper/2602.14919/) (2026)
- [SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting](https://mlsanity.com/paper/2312.02646/) (2023)
- [Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification](https://mlsanity.com/paper/2402.09600/) (2024)
- [DST-GTN: Dynamic Spatio-Temporal Graph Transformer Network for Traffic Forecasting](https://mlsanity.com/paper/2404.11996/) (2024)
- [Partially Trained Graph Convolutional Networks Resist Oversmoothing](https://mlsanity.com/paper/2410.13416/) (2024)
- [DRAN: A Distribution and Relation Adaptive Network for Spatio-temporal Forecasting](https://mlsanity.com/paper/2504.01531/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are usually guided by pre-defined kernels such as Laplacian matrix, adjacency matrix, or their variants. However, the adoptions of pre-defined kernels may restrain the generalities to different graphs: mismatch between graph and kernel would entail sub-optimal performance. For example, GNNs that focus on low-frequency information may not achieve satisfactory performance when high-frequency information is significant for the graphs, and vice versa. To solve this problem, in this paper, we propose a novel framework - i.e., namely Adaptive Kernel Graph Neural Network (AKGNN) - which learns to adapt to the optimal graph kernel in a unified manner at the first attempt. In the proposed AKGNN, we first design a data-driven graph kernel learning mechanism, which adaptively modulates the balance between all-pass and low-pass filters by modifying the maximal eigenvalue of the graph Laplacian. Through this process, AKGNN learns the optimal threshold between high and low frequency signals to relieve the generality problem. Later, we further reduce the number of parameters by a parameterization trick and enhance the expressive power by a global readout function. Extensive experiments are conducted on acknowledged benchmark datasets and promising results demonstrate the outstanding performance of our proposed AKGNN by comparison with state-of-the-art GNNs. The source code is publicly available at: https://github.com/jumxglhf/AKGNN.