# Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection

arXiv: https://arxiv.org/abs/2511.15083 · HTML: https://mlsanity.com/paper/2511.15083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 11 of 11)

- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [TimeSeriesBench: An Industrial-Grade Benchmark for Time Series Anomaly Detection Models](https://mlsanity.com/paper/2402.10802/) (2024)
- [KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.00278/) (2024)
- [A Comprehensive Survey of Deep Transfer Learning for Anomaly Detection in Industrial Time Series: Methods, Applications, and Directions](https://mlsanity.com/paper/2307.05638/) (2023)
- [Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting](https://mlsanity.com/paper/2405.16312/) (2024)
- [Online Time Series Anomaly Detection with State Space Gaussian Processes](https://mlsanity.com/paper/2201.06763/) (2022)
- [Mamba Adaptive Anomaly Transformer with association discrepancy for time series](https://mlsanity.com/paper/2502.07858/) (2025)
- [Decomposition-based multi-scale transformer framework for time series anomaly detection](https://mlsanity.com/paper/2504.14206/) (2025)
- [Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detection](https://mlsanity.com/paper/2405.19823/) (2024)
- [PatchTrAD: A Patch-Based Transformer focusing on Patch-Wise Reconstruction Error for Time Series Anomaly Detection](https://mlsanity.com/paper/2504.08827/) (2025)

## Abstract (arXiv)

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