Kolmogorov-Arnold 网络综述
A Survey on Kolmogorov-Arnold Network
AI总结：
本文系统综述了 Kolmogorov-Arnold 网络的理论基础、架构优势、关键变体及其与卷积、循环、Transformer 等模型的集成，并指出其在高维噪声场景下的计算挑战与未来优化方向。
摘要：
本系统综述探讨了 Kolmogorov-Arnold Networks (KAN) 的理论基础、演进、应用及未来潜力。KAN 是一种受 Kolmogorov-Arnold 表示定理启发的神经网络模型。KAN 与传统神经网络的区别在于，它使用可学习的、样条参数化函数替代固定的激活函数，从而能够对高维函数进行灵活且可解释的表示。本综述详细阐述了 KAN 的架构优势，包括基于边的自适应激活函数，该函数在时间序列预测、计算生物医学和图学习等应用中提升了参数效率和可扩展性。关键进展包括 Temporal-KAN、FastKAN 和偏微分方程 (PDE) KAN，这些进展展示了 KAN 在动态环境中日益增长的适用性，增强了复杂函数逼近任务的可解释性、计算效率和适应性。此外，本文还讨论了 KAN 与其他架构（如卷积、循环和基于 Transformer 的模型）的集成，展示了其在需要混合方法的任务中补充既有神经网络的通用性。尽管 KAN 具有诸多优势，但在高维和含噪数据场景下仍面临计算挑战，这推动了优化策略、正则化技术和混合模型方面的持续研究。本文强调了 KAN 在现代神经架构中的作用，并概述了未来方向，以提高其在数据密集型应用中的计算效率、可解释性和可扩展性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
