KambaAD: Enhancing State Space Models with Kolmogorov–Arnold for time series Anomaly Detection

Yiyun Chen, Jia Guo, Xinchun Yu, Defu Cao, Xiao-Ping Zhang

Keywords: Anomaly Detection, Mamba, KAN, Time series

TL;DR: We introduce KambaAD, a framework combining MAMBA and KAN to enhance time series anomaly detection, outperforming state-of-the-art models across multiple datasets.

Abstract: Time series anomaly detection is critical in numerous practical applications, yet existing deep learning methods often fall short of real-world demands. These models fail to swiftly filter out physically implausible anomalies, insufficiently address distributional shifts, and lack a comprehensive approach that integrates both global and local perspectives for anomaly detection. Moreover, most successful models rely on channel-dependent methods that tend to treat all features at the same timestamp as a single token and then focus on finding relationships between these tokens. This approach overlooks the unique periodicities, trends, and lagged relationships between different features, leading to suboptimal performance. To address these limitations, we propose KambaAD, a model comprised of an Encoder and Reconstructor. The Encoder integrates the strengths of the Kolmogorov-Arnold Network (KAN), the attention mechanism, and the Selective Structured State Space Model (MAMBA). Specifically, KAN is employed to swiftly enforce data consistency, enabling rapid detection of anomalies that violate physical laws. The attention mechanism ensures balanced processing of global information while enhancing the representation of key data characteristics. We leverage MAMBA's capability as a sequence model to capture anomalies caused by local variations. Additionally, its internal selection mechanism allows the model to effectively handle distribution shifts, ensuring robustness and adaptability in the presence of changing data distributions. Additionally, the framework incorporates a time-series-specific Reconstructor, which reduces computational complexity through patch-based operations that exploit local consistency in time series data. It also employs channel-independent linear reconstruction to prevent interference between different features. Through extensive experiments on multiple multivariate datasets, KambaAD consistently outperforms state-of-the-art models, demonstrating its superior performance in anomaly detection.

Primary Area: learning on time series and dynamical systems

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Submission Number: 4490