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Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability

Kunpeng Xu, Lifei Chen, Shengrui Wang

TL;DR

This work investigates Kolmogorov-Arnold Networks (KAN) as an interpretable alternative to traditional neural nets for time series forecasting. It introduces two variants, T-KAN for univariate forecasting with concept-drift detection and MT-KAN for multivariate cross-variable modeling, both leveraging spline-parametrized univariate activations along edges. The paper demonstrates that KAN-based models can achieve competitive accuracy with far fewer parameters and offer symbolic regression-based interpretability, though training can be slower than MLPs. The findings suggest a viable path toward adaptive, interpretable forecasting tools in non-stationary and multivariate environments, with avenues for future integration and speed optimization.

Abstract

Kolmogorov-Arnold Networks (KAN) is a groundbreaking model recently proposed by the MIT team, representing a revolutionary approach with the potential to be a game-changer in the field. This innovative concept has rapidly garnered worldwide interest within the AI community. Inspired by the Kolmogorov-Arnold representation theorem, KAN utilizes spline-parametrized univariate functions in place of traditional linear weights, enabling them to dynamically learn activation patterns and significantly enhancing interpretability. In this paper, we explore the application of KAN to time series forecasting and propose two variants: T-KAN and MT-KAN. T-KAN is designed to detect concept drift within time series and can explain the nonlinear relationships between predictions and previous time steps through symbolic regression, making it highly interpretable in dynamically changing environments. MT-KAN, on the other hand, improves predictive performance by effectively uncovering and leveraging the complex relationships among variables in multivariate time series. Experiments validate the effectiveness of these approaches, demonstrating that T-KAN and MT-KAN significantly outperform traditional methods in time series forecasting tasks, not only enhancing predictive accuracy but also improving model interpretability. This research opens new avenues for adaptive forecasting models, highlighting the potential of KAN as a powerful and interpretable tool in predictive analytics.

Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability

TL;DR

This work investigates Kolmogorov-Arnold Networks (KAN) as an interpretable alternative to traditional neural nets for time series forecasting. It introduces two variants, T-KAN for univariate forecasting with concept-drift detection and MT-KAN for multivariate cross-variable modeling, both leveraging spline-parametrized univariate activations along edges. The paper demonstrates that KAN-based models can achieve competitive accuracy with far fewer parameters and offer symbolic regression-based interpretability, though training can be slower than MLPs. The findings suggest a viable path toward adaptive, interpretable forecasting tools in non-stationary and multivariate environments, with avenues for future integration and speed optimization.

Abstract

Kolmogorov-Arnold Networks (KAN) is a groundbreaking model recently proposed by the MIT team, representing a revolutionary approach with the potential to be a game-changer in the field. This innovative concept has rapidly garnered worldwide interest within the AI community. Inspired by the Kolmogorov-Arnold representation theorem, KAN utilizes spline-parametrized univariate functions in place of traditional linear weights, enabling them to dynamically learn activation patterns and significantly enhancing interpretability. In this paper, we explore the application of KAN to time series forecasting and propose two variants: T-KAN and MT-KAN. T-KAN is designed to detect concept drift within time series and can explain the nonlinear relationships between predictions and previous time steps through symbolic regression, making it highly interpretable in dynamically changing environments. MT-KAN, on the other hand, improves predictive performance by effectively uncovering and leveraging the complex relationships among variables in multivariate time series. Experiments validate the effectiveness of these approaches, demonstrating that T-KAN and MT-KAN significantly outperform traditional methods in time series forecasting tasks, not only enhancing predictive accuracy but also improving model interpretability. This research opens new avenues for adaptive forecasting models, highlighting the potential of KAN as a powerful and interpretable tool in predictive analytics.
Paper Structure (16 sections, 3 equations, 4 figures, 1 table)

This paper contains 16 sections, 3 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Kolmogorov-Arnold Networks
  3. Theoretical Foundation
  4. Network Architecture
  5. KAN for Time Series
  6. T-KAN
  7. Architecture
  8. Symbolic Regression for Interpretability
  9. MT-KAN
  10. Architecture
  11. Modeling Cross-Variable Interactions
  12. Experiments
  13. Data
  14. Experimental Setup and Baselines
  15. Results and Analysis
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Predictive and Interpretable Capabilities of KAN in Time Series.
  • Figure 2: Modeling power of T-KAN for univariate time series: training Temporal KAN (T-KAN) and detecting concept drift
  • Figure 3: MT-KAN architecture for multivariate time series.
  • Figure 4: Predicted results using a simple T-KAN: true (blue) and forecasted (red) values for the first six series.