P-KAN用可学习曲线替代权重，实现高效精准的时序概率预测。
A Primer on Kolmogorov-Arnold Networks (KANs) for Probabilistic Time Series Forecasting
- 用样条函数替代传统权重，直接建模预测分布
- 在卫星流量预测中参数少却更准、校准更好
- 适合资源受限场景，支持安全或高效率应用
本文提出概率型柯尔莫戈罗夫-阿诺德网络（P-KAN），是KAN在时序概率预测中的新扩展。通过将标量权重替换为基于样条的函数连接，并直接参数化预测分布，P-KAN在保持参数高效的同时，能捕捉非线性与重尾动态。我们在卫星交通预测任务上评估，结果表明其在准确率与校准性上均优于多层感知机（MLP）基线，且显著减少参数量。模型基于高斯与学生t分布构建：高斯版本提供稳健保守预测，适用于安全关键场景；学生t版本生成更尖锐分布，在需求稳定时提升效率。该方法为卫星通信等资源受限领域提供了可直接应用的概率预测框架。
原文摘要 · Abstract (English)
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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