# GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily

arXiv: https://arxiv.org/abs/2110.15777 · HTML: https://mlsanity.com/paper/2110.15777/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 23 of 23)

- [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)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Self-supervised Graph-level Representation Learning with Local and Global Structure](https://mlsanity.com/paper/2106.04113/) (2021)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Path-SGD: Path-Normalized Optimization in Deep Neural Networks](https://mlsanity.com/paper/1506.02617/) (2015)
- [Improving Graph Neural Networks with Simple Architecture Design](https://mlsanity.com/paper/2105.07634/) (2021)
- [TabularNet: A Neural Network Architecture for Understanding Semantic Structures of Tabular Data](https://mlsanity.com/paper/2106.03096/) (2021)
- [Representation Based Complexity Measures for Predicting Generalization in Deep Learning](https://mlsanity.com/paper/2012.02775/) (2020)
- [Tag2Vec: Learning Tag Representations in Tag Networks](https://mlsanity.com/paper/1905.03041/) (2019)

## Built on by (most cited first, 30 of 84)

- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Designing the Topology of Graph Neural Networks: A Novel Feature Fusion Perspective](https://mlsanity.com/paper/2112.14531/) (2021)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND](https://mlsanity.com/paper/2404.17099/) (2024)
- [Implicit vs Unfolded Graph Neural Networks](https://mlsanity.com/paper/2111.06592/) (2021)
- [Towards Open Temporal Graph Neural Networks](https://mlsanity.com/paper/2303.15015/) (2023)
- [On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks](https://mlsanity.com/paper/2306.05557/) (2023)
- [A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions](https://mlsanity.com/paper/2401.09769/) (2024)
- [Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks](https://mlsanity.com/paper/2506.07624/) (2025)
- [MM-GNN: Mix-Moment Graph Neural Network towards Modeling Neighborhood Feature Distribution](https://mlsanity.com/paper/2208.07012/) (2022)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [SIGMA: An Efficient Heterophilous Graph Neural Network with Fast Global Aggregation](https://mlsanity.com/paper/2305.09958/) (2023)
- [Mitigating Oversmoothing Through Reverse Process of GNNs for Heterophilic Graphs](https://mlsanity.com/paper/2403.10543/) (2024)
- [Exploring the Potential of Large Language Models for Heterophilic Graphs](https://mlsanity.com/paper/2408.14134/) (2024)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [GraphRARE: Reinforcement Learning Enhanced Graph Neural Network with Relative Entropy](https://mlsanity.com/paper/2312.09708/) (2023)
- [Neighborhood Homophily-based Graph Convolutional Network](https://mlsanity.com/paper/2301.09851/) (2023)
- [Heterophily-Aware Graph Attention Network](https://mlsanity.com/paper/2302.03228/) (2023)
- [Spatial Heterophily Aware Graph Neural Networks](https://mlsanity.com/paper/2306.12139/) (2023)
- [Distributed-Order Fractional Graph Operating Network](https://mlsanity.com/paper/2411.05274/) (2024)
- [Recent Advances in Malware Detection: Graph Learning and Explainability](https://mlsanity.com/paper/2502.10556/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are widely used on a variety of graph-based machine learning tasks. For node-level tasks, GNNs have strong power to model the homophily property of graphs (i.e., connected nodes are more similar) while their ability to capture the heterophily property is often doubtful. This is partially caused by the design of the feature transformation with the same kernel for the nodes in the same hop and the followed aggregation operator. One kernel cannot model the similarity and the dissimilarity (i.e., the positive and negative correlation) between node features simultaneously even though we use attention mechanisms like Graph Attention Network (GAT), since the weight calculated by attention is always a positive value. In this paper, we propose a novel GNN model based on a bi-kernel feature transformation and a selection gate. Two kernels capture homophily and heterophily information respectively, and the gate is introduced to select which kernel we should use for the given node pairs. We conduct extensive experiments on various datasets with different homophily-heterophily properties. The experimental results show consistent and significant improvements against state-of-the-art GNN methods.