Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection
Abstract
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
Keywords
Cite
@article{arxiv.2511.15083,
title = {Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection},
author = {Xiancheng Wang and Lin Wang and Rui Wang and Zhibo Zhang and Minghang Zhao},
journal= {arXiv preprint arXiv:2511.15083},
year = {2026}
}
Comments
We request withdrawal because we identified a flaw in the theoretical analysis of the anomaly-score identification mechanism. This part was supported mainly by metric observations without sufficient visual or empirical verification, which may affect the reliability of the related conclusions