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

• URL: http://arxiv.org/abs/2510.16940v1
• Date: Sun, 19 Oct 2025 17:38:26 GMT
• Title: A Primer on Kolmogorov-Arnold Networks (KANs) for Probabilistic Time Series Forecasting
• Authors: Cristian J. Vaca-Rubio, Roberto Pereira, Luis Blanco, Engin Zeydan, Màrius Caus,
• Abstract summary: Probabilistic Kolmogorov-Arnold Network (P-KAN) is a novel extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting.<n>P-KANs offer expressive yet parameter-efficient models capable of capturing nonlinear and heavy-tailed dynamics.<n>We evaluate P-KANs on satellite traffic forecasting, where uncertainty-aware predictions enable dynamic thresholding for resource allocation.
• Score: 6.102596261546231
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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