# Kolmogorov-Arnold Graph Neural Networks

arXiv: https://arxiv.org/abs/2406.18354 · HTML: https://mlsanity.com/paper/2406.18354/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 26 Jun 2024.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Tackling Over-Smoothing for General Graph Convolutional Networks](https://mlsanity.com/paper/2008.09864/) (2020)
- [GraphSVX: Shapley Value Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.10482/) (2021)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.13597/) (2024)

## Built on by (most cited first, 30 of 32)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [DropKAN: Regularizing KANs by masking post-activations](https://mlsanity.com/paper/2407.13044/) (2024)
- [F-KANs: Federated Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.20100/) (2024)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [Addressing common misinterpretations of KART and UAT in neural network literature](https://mlsanity.com/paper/2408.16389/) (2024)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [Bayesian Kolmogorov Arnold Networks (Bayesian_KANs): A Probabilistic Approach to Enhance Accuracy and Interpretability](https://mlsanity.com/paper/2408.02706/) (2024)
- [Architectural Scaling Surpass Basis Complexity? Efficient KANs with Single-Parameter Design](https://mlsanity.com/paper/2410.14951/) (2024)
- [Rethinking the Function of Neurons in KANs](https://mlsanity.com/paper/2407.20667/) (2024)
- [FEKAN: Feature-Enriched Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.16530/) (2026)
- [Incorporating Arbitrary Matrix Group Equivariance into KANs](https://mlsanity.com/paper/2410.00435/) (2024)
- [KAC: Kolmogorov-Arnold Classifier for Continual Learning](https://mlsanity.com/paper/2503.21076/) (2025)
- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [Interpretable Graph Kolmogorov-Arnold Networks for Multi-Cancer Classification and Biomarker Identification using Multi-Omics Data](https://mlsanity.com/paper/2503.22939/) (2025)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning](https://mlsanity.com/paper/2504.15240/) (2025)
- [SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks](https://mlsanity.com/paper/2603.18548/) (2026)
- [Quantum Kolmogorov-Arnold networks by combining quantum signal processing circuits](https://mlsanity.com/paper/2410.04218/) (2024)
- [KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networks](https://mlsanity.com/paper/2501.13456/) (2025)
- [MLPs and KANs for data-driven learning in physical problems: A performance comparison](https://mlsanity.com/paper/2504.11397/) (2025)
- [Automated Modeling Method for Pathloss Model Discovery](https://mlsanity.com/paper/2505.23383/) (2025)
- [KAN KAN Buff Signed Graph Neural Networks?](https://mlsanity.com/paper/2501.00709/) (2025)
- [HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2503.12365/) (2025)
- [Transferring Social Network Knowledge from Multiple GNN Teachers to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2508.06663/) (2025)
- [Kolmogorov-Arnold graph neural networks for chemically informed prediction tasks on inorganic nanomaterials](https://mlsanity.com/paper/2512.19494/) (2025)
- [MGKAN: Predicting Asymmetric Drug-Drug Interactions via a Multimodal Graph Kolmogorov-Arnold Network](https://mlsanity.com/paper/2602.01751/) (2026)
- [Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches](https://mlsanity.com/paper/2604.16842/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) excel in learning from network-like data but often lack interpretability, making their application challenging in domains requiring transparent decision-making. We propose the Graph Kolmogorov-Arnold Network (GKAN), a novel GNN model leveraging spline-based activation functions on edges to enhance both accuracy and interpretability. Our experiments on five benchmark datasets demonstrate that GKAN outperforms state-of-the-art GNN models in node classification, link prediction, and graph classification tasks. In addition to the improved accuracy, GKAN's design inherently provides clear insights into the model's decision-making process, eliminating the need for post-hoc explainability techniques. This paper discusses the methodology, performance, and interpretability of GKAN, highlighting its potential for applications in domains where interpretability is crucial.