Kolmogorov-Arnold Graph Neural Networks (2406.18354v1)

Abstract: 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.

• The paper introduces GKAN, a model that uses spline-based edge activations to enhance both performance and interpretability in graph neural networks.
• The methodology leverages spline functions to transform edge features, allowing clear tracing of decision-making without additional explainability tools.
• Experimental results on five benchmarks show that GKAN outperforms traditional GNNs in node classification, link prediction, and graph classification.

"Kolmogorov-Arnold Graph Neural Networks" introduces the Graph Kolmogorov-Arnold Network (GKAN), a novel model aiming to enhance both the accuracy and interpretability of Graph Neural Networks (GNNs). Traditional GNNs have shown impressive performance on various tasks involving network-like data, such as node classification, link prediction, and graph classification. However, a significant challenge with GNNs has been their lack of interpretability, which complicates their application in critical domains requiring transparent decision-making, such as healthcare or finance.

Key Contributions

The paper proposes several key innovations:

• Spline-Based Activation Functions: Instead of conventional activation functions, GKAN employs spline-based functions on edges. These functions offer a flexible yet controlled way of transforming edge features, which contributes to the both improved performance and the inherent interpretability of the model.
• Interpretability by Design: GKAN’s architecture is designed to provide transparency in its decision-making process, removing the need for post-hoc explainability techniques. This means that the intermediate transformations and final predictions can be logically traced back through the spline parameters, offering clear insights into how decisions are made.
• Performance Across Multiple Tasks: The model was tested on five benchmark datasets, demonstrating superior performance over existing state-of-the-art GNNs. The tasks included node classification, link prediction, and graph classification, indicating the versatility and robustness of GKAN.

Methodology

The methodology section explores the specifics of how spline-based activation functions are integrated into the GNN framework. This involves:

• Edge Feature Transformation: Employing spline functions to control the transformation and interaction of edge-related features, which helps to maintain the geometric and topological properties of the graph.
• Model Architecture: A detailed description of the GKAN architecture, which ensures that the model remains both powerful and interpretable. The model consists of multiple layers where each incorporates spline-based edge transformations.

Experimental Results

The authors conducted comprehensive experiments across five benchmark datasets to validate the efficacy of GKAN. Key findings include:

• Improved Performance: GKAN consistently outperforms other state-of-the-art GNN models. This includes various standard benchmarks for node classification, link prediction, and graph classification.
• Interpretability: GKAN’s structure allows practitioners to interpret its decisions without additional tools. This is particularly highlighted as a critical feature, making GKAN suitable for domains requiring high transparency in decision-making processes.

Applications and Implications

The paper emphasizes the potential applications of GKAN in areas where both performance and interpretability are essential. Specific domains mentioned include:

• Healthcare: Where understanding the rationale behind decisions can be as important as the decisions themselves.
• Finance: Where regulatory requirements often mandate clear explanations of automated decision-making processes.

Conclusion

The introduction of the Graph Kolmogorov-Arnold Network marks a significant advancement in the field of GNNs, particularly by addressing the critical need for interpretability without sacrificing performance. The synthesis of spline-based activation functions with GNNs in GKAN not only enhances accuracy but also inherently provides the much-needed transparency in decision-making. The model's ability to outperform existing GNNs across multiple tasks while offering clear insights into its inner workings points to its strong potential for real-world applications that demand both efficacy and interpretability.