# AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecasting

arXiv: https://arxiv.org/abs/2509.02967 · HTML: https://mlsanity.com/paper/2509.02967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 54 references that are in the map.
- First posted on arXiv 3 Sep 2025.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representations](https://mlsanity.com/paper/2408.10920/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [On the Activation Function Dependence of the Spectral Bias of Neural Networks](https://mlsanity.com/paper/2208.04924/) (2022)
- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [FAN: Fourier Analysis Networks](https://mlsanity.com/paper/2410.02675/) (2024)
- [KAN versus MLP on Irregular or Noisy Functions](https://mlsanity.com/paper/2408.07906/) (2024)
- [An Evaluation of Standard Statistical Models and LLMs on Time Series Forecasting](https://mlsanity.com/paper/2408.04867/) (2024)
- [Neural Fourier Modelling: A Highly Compact Approach to Time-Series Analysis](https://mlsanity.com/paper/2410.04703/) (2024)
- [Short-range forecasts of global precipitation using deep learning-augmented numerical weather prediction](https://mlsanity.com/paper/2206.11669/) (2022)
- [Kolmogorov Arnold Networks in Fraud Detection: Bridging the Gap Between Theory and Practice](https://mlsanity.com/paper/2408.10263/) (2024)
- [Recursive deep learning framework for forecasting the decadal world economic outlook](https://mlsanity.com/paper/2301.10874/) (2023)

## Abstract (arXiv)

Traditional neural networks struggle to capture the spectral structure of complex signals. Fourier neural networks (FNNs) attempt to address this by embedding Fourier series components, yet many real-world signals are almost-periodic with non-commensurate frequencies, posing additional challenges. Building on prior work showing that ARIMA outperforms large language models (LLMs) for time series forecasting, we extend the comparison to neural predictors and find that ARIMA still maintains a clear advantage. Inspired by this finding, we propose the Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network (AR-KAN). Based in the Universal Myopic Mapping Theorem, it integrates a pre-trained AR module for temporal memory with a KAN for nonlinear representation. We prove that the AR module preserves essential temporal features while reducing redundancy, and that the upper bound of the approximation error for AR-KAN is smaller than that for KAN in a probabilistic sense. Experimental results also demonstrate that AR-KAN delivers exceptional performance compared to existing models, both on synthetic almost-periodic functions and real-world datasets. These results highlight AR-KAN as a robust and effective framework for time series forecasting. Our code is available at https://github.com/ChenZeng001/AR-KAN.