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GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networks

Fan Zhang, Xin Zhang

TL;DR

GraphKAN replaces MLPs and activation functions in graph neural networks with Kolmogorov-Arnold Networks (KANs) to improve feature extraction on non-Euclidean data. The approach integrates KANs into a Graph Neural Network layer, using univariate spline-based activations and LayerNorm to stabilize training, and demonstrates superior node classification performance on graph-constructed 1-D signal datasets, particularly with limited labels. The results show stronger feature clustering and higher accuracy than traditional GCNs, albeit with increased computation time, suggesting GraphKAN's promise for few-shot graph tasks. Overall, the work provides a principled way to leverage KANs for enhanced graph-based representation learning and offers a potential path toward more data-efficient graph models.

Abstract

Massive number of applications involve data with underlying relationships embedded in non-Euclidean space. Graph neural networks (GNNs) are utilized to extract features by capturing the dependencies within graphs. Despite groundbreaking performances, we argue that Multi-layer perceptrons (MLPs) and fixed activation functions impede the feature extraction due to information loss. Inspired by Kolmogorov Arnold Networks (KANs), we make the first attempt to GNNs with KANs. We discard MLPs and activation functions, and instead used KANs for feature extraction. Experiments demonstrate the effectiveness of GraphKAN, emphasizing the potential of KANs as a powerful tool. Code is available at https://github.com/Ryanfzhang/GraphKan.

GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networks

TL;DR

GraphKAN replaces MLPs and activation functions in graph neural networks with Kolmogorov-Arnold Networks (KANs) to improve feature extraction on non-Euclidean data. The approach integrates KANs into a Graph Neural Network layer, using univariate spline-based activations and LayerNorm to stabilize training, and demonstrates superior node classification performance on graph-constructed 1-D signal datasets, particularly with limited labels. The results show stronger feature clustering and higher accuracy than traditional GCNs, albeit with increased computation time, suggesting GraphKAN's promise for few-shot graph tasks. Overall, the work provides a principled way to leverage KANs for enhanced graph-based representation learning and offers a potential path toward more data-efficient graph models.

Abstract

Massive number of applications involve data with underlying relationships embedded in non-Euclidean space. Graph neural networks (GNNs) are utilized to extract features by capturing the dependencies within graphs. Despite groundbreaking performances, we argue that Multi-layer perceptrons (MLPs) and fixed activation functions impede the feature extraction due to information loss. Inspired by Kolmogorov Arnold Networks (KANs), we make the first attempt to GNNs with KANs. We discard MLPs and activation functions, and instead used KANs for feature extraction. Experiments demonstrate the effectiveness of GraphKAN, emphasizing the potential of KANs as a powerful tool. Code is available at https://github.com/Ryanfzhang/GraphKan.
Paper Structure (7 sections, 4 equations, 5 figures, 2 tables)

This paper contains 7 sections, 4 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Methodology
  4. Kolmogorov-Arnold Network (KAN)
  5. GraphKAN Layer
  6. A Simple GraphKAN for Node Classification
  7. Experimental Verification

Figures (5)

  • Figure 1: Comparison on testing accuracy and time consumption
  • Figure 2: Clustering comparison of intermediate features for testing nodes within BG_1
  • Figure 3: Clustering comparison of intermediate features for testing nodes within BG_2
  • Figure 4: Clustering comparison of intermediate features for testing nodes within BG_3
  • Figure 5: Clustering comparison of intermediate features for testing nodes within BG_3