融合傅里叶、KAN与Mamba，提升时序异常检测精度
Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection
- 用傅里叶层捕获多尺度频率特征，KAN增强非线性表达
- 在MSL、SMAP、SWaT上优于现有方法，异常检测准确率显著提升
- 适合需要高精度时序异常识别的工业监控场景
时序异常检测在工业监控与故障诊断等实际应用中至关重要。近年来，基于Mamba的状态空间模型在长序列建模中表现出色，但直接用于异常检测仍难以捕捉复杂时序模式与非线性动态。本文提出Fourier-KAN-Mamba，一种融合傅里叶层、Kolmogorov-Arnold网络（KAN）与Mamba选择性状态空间模型的新型混合架构。傅里叶层提取多尺度频率特征，KAN提升非线性表征能力，时间门控控制机制进一步增强对正常与异常模式的区分能力。在MSL、SMAP和SWaT数据集上的大量实验表明，该方法显著优于现有最先进方法。
原文摘要 · Abstract (English)
Time-series anomaly detection plays a critical role in numerous real-world applications, including industrial monitoring and fault diagnosis. Recently, Mamba-based state-space models have shown remarkable efficiency in long-sequence modeling. However, directly applying Mamba to anomaly detection tasks still faces challenges in capturing complex temporal patterns and nonlinear dynamics. In this paper, we propose Fourier-KAN-Mamba, a novel hybrid architecture that integrates Fourier layer, Kolmogorov-Arnold Networks (KAN), and Mamba selective state-space model. The Fourier layer extracts multi-scale frequency features, KAN enhances nonlinear representation capability, and a temporal gating control mechanism further improves the model's ability to distinguish normal and anomalous patterns. Extensive experiments on MSL, SMAP, and SWaT datasets demonstrate that our method significantly outperforms existing state-of-the-art approaches. Keywords: time-series anomaly detection, state-space model, Mamba, Fourier transform, Kolmogorov-Arnold Network
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