用于时间序列分类与鲁棒性分析的Kolmogorov-Arnold Networks (KAN)
Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysis
AI总结：
本研究针对KAN缺乏大规模基准验证的问题，在128个时间序列数据集上对比KAN、MLP及混合结构，验证其分类性能相当或略优，揭示其输出由基础分量主导，且因低利普希茨常数具备更强鲁棒性，为鲁棒模型构建提供新思路。
摘要：
Kolmogorov-Arnold Networks（KAN，柯尔莫哥洛夫-阿诺德网络）作为传统Multi-Layer Perceptrons（MLP，多层感知机）的潜力替代方案，近期受到广泛关注。尽管具备理论吸引力，KAN仍需在大规模基准数据集上完成验证。近年来日益普及的时间序列数据，尤其是单变量时间序列，天然适配KAN的验证需求。为此，我们对KAN、MLP及混合结构开展了公平对比实验。结果显示，在128个时间序列数据集上，KAN可取得与MLP相当甚至略优的性能。我们还对KAN进行了消融研究，发现其输出主要由基础分量而非b-spline（B样条）函数决定。此外，我们评估了这些模型的鲁棒性，发现KAN与混合结构MLP_KAN展现出显著的鲁棒性优势，这源于其更低的Lipschitz（利普希茨）常数。这表明KAN及KAN层在作为鲁棒模型或提升其他模型对抗鲁棒性方面具备巨大潜力。
英文摘要：
Kolmogorov-Arnold Networks (KAN) has recently attracted significant attention as a promising alternative to traditional Multi-Layer Perceptrons (MLP). Despite their theoretical appeal, KAN require validation on large-scale benchmark datasets. Time series data, which has become increasingly prevalent in recent years, especially univariate time series are naturally suited for validating KAN. Therefore, we conducted a fair comparison among KAN, MLP, and mixed structures. The results indicate that KAN can achieve performance comparable to, or even slightly better than, MLP across 128 time series datasets. We also performed an ablation study on KAN, revealing that the output is primarily determined by the base component instead of b-spline function. Furthermore, we assessed the robustness of these models and found that KAN and the hybrid structure MLP\_KAN exhibit significant robustness advantages, attributed to their lower Lipschitz constants. This suggests that KAN and KAN layers hold strong potential to be robust models or to improve the adversarial robustness of other models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
