Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysis (2408.07314v3)

Abstract: 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.

• The paper presents KAN as an innovative alternative to MLPs for time series classification, achieving comparable or superior accuracy as measured by standard metrics.
• The study reveals that the key performance factor lies in the base component, while spline functions introduce optimization challenges at larger grid sizes.
• KAN and its hybrid model show strong robustness to adversarial attacks due to lower Lipschitz constants, indicating a resilient architecture for practical applications.

Understanding Kolmogorov-Arnold Networks for Time Series Classification

The paper "Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysis" introduces Kolmogorov-Arnold Networks (KAN) as an emerging alternative to Multi-Layer Perceptrons (MLP), specifically for time series classification. Time series classification (TSC) is crucial in analyzing sequential data across multiple fields. While MLP has been a foundational architecture, KAN offers a theoretical framework deriving from the Kolmogorov-Arnold Theory (KAT), proposing a new model architecture.

The authors address the validation of KAN on large-scale datasets, using 128 time series datasets from the UCR archive to benchmark its performance against traditional MLPs and hybrid structures combining aspects of both networks.

Main Findings

1. Performance Assessment:
   • KAN was tested against MLP, an MLP with a KAN layer substituted for the last layer (MLP_KAN), and vice versa (KAN_MLP).
   • The results demonstrate that KAN's performance is comparable, if not slightly superior, to traditional neural networks across the examined datasets. This assessment was thoroughly conducted using accuracy and F1 scores.
2. Network Structure and Impact:
   • An ablation paper revealed that the primary determinant in KAN's performance is the base component rather than the B-spline component.
   • It was established that the spline functions can cause optimization challenges, particularly when large grid sizes are configured.
3. Robustness Evaluation:
   • KAN and the MLP_KAN hybrid structure exhibited significant robustness to adversarial attacks, attributed to lower Lipschitz constants. This suggests that KAN’s architectural design inherently contributes to its robustness.
   • Interestingly, even when grid sizes increased, KAN remained robust, a trait which invites further exploration into its interpretability and stability.

Implications and Future Work

The findings illuminate important aspects of KAN, demonstrating its capabilities in time series classification and its potential robustness advantages. This has several implications for both academic research and practical applications:

• Robust Architectures: The robustness exhibited by KAN, especially when employing larger grid sizes, pinpoints a valuable direction for developing resilient AI systems against adversarial disturbances.
• Theoretical Extension: The paper prompts further investigation into the theoretical underpinnings of KAN, specifically understanding the interplay between its adversarial resistance and the theoretical advantages promised by Kolmogorov-Arnold Theory.
• Scalability: While this paper explored univariate time series, future research could extend KAN applications to multi-variate contexts, offering broader applicability in complex real-world scenarios.

In conclusion, KAN emerges as a competitive and robust alternative to traditional neural network models for time series data. The paper lays a foundational comparison, drawing from both theoretical and empirical insights, and sets the stage for further exploration of KAN's properties and potential enhancements in deep learning architectures.