A Survey on Kolmogorov-Arnold Network

TL;DR

This survey reviews Kolmogorov-Arnold Networks (KAN), highlighting their theoretical basis, architectural innovations, applications, and future challenges in creating flexible, interpretable, and efficient neural network models for complex tasks.

Contribution

It provides a comprehensive overview of KAN's development, applications, and integration with other models, emphasizing recent advancements and future research directions.

Findings

KAN uses learnable spline functions instead of fixed activations.

Applications include time series, biomedicine, and graph learning.

Future work focuses on improving efficiency and scalability.

Abstract

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs distinguish themselves from traditional neural networks by using learnable, spline-parameterized functions instead of fixed activation functions, allowing for flexible and interpretable representations of high-dimensional functions. This review details KAN's architectural strengths, including adaptive edge-based activation functions that improve parameter efficiency and scalability in applications such as time series forecasting, computational biomedicine, and graph learning. Key advancements, including Temporal-KAN, FastKAN, and Partial Differential Equation (PDE) KAN, illustrate KAN's growing applicability in dynamic environments, enhancing interpretability, computational efficiency, and adaptability for complex function approximation tasks. Additionally, this paper discusses KAN's integration with other architectures, such as convolutional, recurrent, and transformer-based models, showcasing its versatility in complementing established neural networks for tasks requiring hybrid approaches. Despite its strengths, KAN faces computational challenges in high-dimensional and noisy data settings, motivating ongoing research into optimization strategies, regularization techniques, and hybrid models. This paper highlights KAN's role in modern neural architectures and outlines future directions to improve its computational efficiency, interpretability, and scalability in data-intensive applications.