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Time series forecasting with Hahn Kolmogorov-Arnold networks

Md Zahidul Hasan, A. Ben Hamza, Nizar Bouguila

TL;DR

HaKAN introduces Hahn polynomial-based Kolmogorov-Arnold Networks for multivariate time-series forecasting, addressing the computational and expressiveness limitations of Transformer and MLP approaches. The method employs channel independence, patch-based embeddings, and a dual-layer Hahn-KAN block (intra-patch and inter-patch) with a bottleneck head, yielding a lightweight, interpretable model that mitigates spectral bias. Empirical results across Weather, Traffic, Electricity, Illness, and ETT datasets show HaKAN achieves state-of-the-art performance in many settings, with notable gains on long horizons and smooth series, and ablations validate the core design choices. The work demonstrates that polynomial-based, learnable activations within a patch-aware KAN framework can deliver strong forecasting performance while maintaining computational efficiency, suggesting practical impact for large-scale time-series applications and future integration with frequency-domain techniques.

Abstract

Recent Transformer- and MLP-based models have demonstrated strong performance in long-term time series forecasting, yet Transformers remain limited by their quadratic complexity and permutation-equivariant attention, while MLPs exhibit spectral bias. We propose HaKAN, a versatile model based on Kolmogorov-Arnold Networks (KANs), leveraging Hahn polynomial-based learnable activation functions and providing a lightweight and interpretable alternative for multivariate time series forecasting. Our model integrates channel independence, patching, a stack of Hahn-KAN blocks with residual connections, and a bottleneck structure comprised of two fully connected layers. The Hahn-KAN block consists of inter- and intra-patch KAN layers to effectively capture both global and local temporal patterns. Extensive experiments on various forecasting benchmarks demonstrate that our model consistently outperforms recent state-of-the-art methods, with ablation studies validating the effectiveness of its core components.

Time series forecasting with Hahn Kolmogorov-Arnold networks

TL;DR

HaKAN introduces Hahn polynomial-based Kolmogorov-Arnold Networks for multivariate time-series forecasting, addressing the computational and expressiveness limitations of Transformer and MLP approaches. The method employs channel independence, patch-based embeddings, and a dual-layer Hahn-KAN block (intra-patch and inter-patch) with a bottleneck head, yielding a lightweight, interpretable model that mitigates spectral bias. Empirical results across Weather, Traffic, Electricity, Illness, and ETT datasets show HaKAN achieves state-of-the-art performance in many settings, with notable gains on long horizons and smooth series, and ablations validate the core design choices. The work demonstrates that polynomial-based, learnable activations within a patch-aware KAN framework can deliver strong forecasting performance while maintaining computational efficiency, suggesting practical impact for large-scale time-series applications and future integration with frequency-domain techniques.

Abstract

Recent Transformer- and MLP-based models have demonstrated strong performance in long-term time series forecasting, yet Transformers remain limited by their quadratic complexity and permutation-equivariant attention, while MLPs exhibit spectral bias. We propose HaKAN, a versatile model based on Kolmogorov-Arnold Networks (KANs), leveraging Hahn polynomial-based learnable activation functions and providing a lightweight and interpretable alternative for multivariate time series forecasting. Our model integrates channel independence, patching, a stack of Hahn-KAN blocks with residual connections, and a bottleneck structure comprised of two fully connected layers. The Hahn-KAN block consists of inter- and intra-patch KAN layers to effectively capture both global and local temporal patterns. Extensive experiments on various forecasting benchmarks demonstrate that our model consistently outperforms recent state-of-the-art methods, with ablation studies validating the effectiveness of its core components.
Paper Structure (17 sections, 12 equations, 4 figures, 10 tables, 1 algorithm)

This paper contains 17 sections, 12 equations, 4 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Problem Description and Preliminaries
  5. Proposed HaKAN Framework
  6. Model Training
  7. Experiments
  8. Experimental Setup
  9. Results and Analysis
  10. Ablation Study
  11. Computational Complexity Analysis
  12. Discussion
  13. Conclusion
  14. Dataset Details
  15. Model Robustness Against Random Seeds
  16. ...and 2 more sections

Figures (4)

  • Figure 1: HaKAN Architecture. The model integrates channel independence, reversible instance normalization, and patching, followed by patch and position embeddings. A stack of $R$ Hahn-KAN blocks, each with intra-patch and inter-patch KAN layers using Hahn polynomials, processes the embedded sequence to capture temporal patterns. The output is mapped through a bottleneck structure with two fully connected layers to produce the final forecast.
  • Figure 2: Performance comparison between HaKAN and its MLP-based variant across multiple datasets. The look-back window is fixed at $L = 96$, and the average MSE over prediction horizons $T\in\{96, 192, 336, 720\}$ is used as the evaluation metric.
  • Figure 3: Average MSE and MAE results across the six ablation datasets for a varying patch length.
  • Figure 4: Evaluation of long-term forecasting performance across different look-back window lengths on multiple datasets, using the average MSE over prediction horizons $T\in\{96, 192, 336, 720\}$ as the evaluation metric.