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

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

Fast-Slow Co-advancing Optimizer: Toward Harmonious Adversarial Training of GAN

Up to now, the training processes of typical Generative Adversarial Networks (GANs) are still particularly sensitive to data properties and hyperparameters, which may lead to severe oscillations, difficulties in convergence, or even failures to converge, especially when the overall variances of the training sets are large. These phenomena are often attributed to the training characteristics of such networks. Aiming at the problem, this paper develops a new intelligent optimizer, Fast-Slow Co-advancing Optimizer (FSCO), which employs reinforcement learning in the training process of GANs to make training easier. Specifically, this paper allows the training step size to be controlled by an agent to improve training stability, and makes the training process more intelligent with variable learning rates, making GANs less sensitive to step size. Experiments have been conducted on three benchmark datasets to verify the effectiveness of the developed FSCO.