AR-KAN：用于时间序列预测的自回归权重增强的科莫戈洛夫-阿诺尔德网络
AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecasting
AI总结：
本文提出AR-KAN，结合自回归模块和KAN，通过理论证明和实验验证，展示了其在时间序列预测中的优越性能。
摘要：
传统神经网络难以捕捉复杂信号的频谱结构。傅里叶神经网络（FNNs）试图通过嵌入傅里叶级数成分来解决这一问题，但许多现实世界信号几乎是非相干频率的周期性信号，带来了额外的挑战。基于先前工作表明ARIMA在时间序列预测中优于大型语言模型（LLMs），我们将其比较扩展到神经预测器，并发现ARIMA仍保持明显优势。受此发现的启发，我们提出了自回归权重增强的科莫戈洛夫-阿诺尔德网络（AR-KAN）。基于通用短视映射定理，它集成了预训练的AR模块用于时间记忆和KAN用于非线性表示。我们证明了AR模块在保留本质时间特征的同时减少冗余，且AR-KAN的近似误差上界在概率意义上比KAN更小。实验结果也显示，AR-KAN在合成几乎周期性函数和现实世界数据集上均表现出色。这些结果突显了AR-KAN作为时间序列预测稳健有效框架的优势。我们的代码可在https://github.com/ChenZeng001/AR-KAN获取。
英文摘要：
Traditional neural networks struggle to capture the spectral structure of complex signals. Fourier neural networks (FNNs) attempt to address this by embedding Fourier series components, yet many real-world signals are almost-periodic with non-commensurate frequencies, posing additional challenges. Building on prior work showing that ARIMA outperforms large language models (LLMs) for time series forecasting, we extend the comparison to neural predictors and find that ARIMA still maintains a clear advantage. Inspired by this finding, we propose the Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network (AR-KAN). Based in the Universal Myopic Mapping Theorem, it integrates a pre-trained AR module for temporal memory with a KAN for nonlinear representation. We prove that the AR module preserves essential temporal features while reducing redundancy, and that the upper bound of the approximation error for AR-KAN is smaller than that for KAN in a probabilistic sense. Experimental results also demonstrate that AR-KAN delivers exceptional performance compared to existing models, both on synthetic almost-periodic functions and real-world datasets. These results highlight AR-KAN as a robust and effective framework for time series forecasting. Our code is available at https://github.com/ChenZeng001/AR-KAN.
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。
