# A Primer on Kolmogorov-Arnold Networks (KANs) for Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2510.16940 · HTML: https://mlsanity.com/paper/2510.16940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 19 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [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)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysis](https://mlsanity.com/paper/2408.07314/) (2024)
- [F-KANs: Federated Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.20100/) (2024)
- [Bayesian Kolmogorov Arnold Networks (Bayesian_KANs): A Probabilistic Approach to Enhance Accuracy and Interpretability](https://mlsanity.com/paper/2408.02706/) (2024)

## Abstract (arXiv)

This work introduces Probabilistic Kolmogorov-Arnold Network (P-KAN), a novel probabilistic extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting. By replacing scalar weights with spline-based functional connections and directly parameterizing predictive distributions, P-KANs offer expressive yet parameter-efficient models capable of capturing nonlinear and heavy-tailed dynamics. We evaluate P-KANs on satellite traffic forecasting, where uncertainty-aware predictions enable dynamic thresholding for resource allocation. Results show that P-KANs consistently outperform Multi Layer Perceptron (MLP) baselines in both accuracy and calibration, achieving superior efficiency-risk trade-offs while using significantly fewer parameters. We build up P-KANs on two distributions, namely Gaussian and Student-t distributions. The Gaussian variant provides robust, conservative forecasts suitable for safety-critical scenarios, whereas the Student-t variant yields sharper distributions that improve efficiency under stable demand. These findings establish P-KANs as a powerful framework for probabilistic forecasting with direct applicability to satellite communications and other resource-constrained domains.