用可解释的KAN模型预测波动率，效果不输传统模型但参数更少。
Forecasting VIX using interpretable Kolmogorov-Arnold networks
- 用可学习样条函数替代传统激活函数，实现模型可解释性。
- 在多个数据集上表现接近甚至超越传统神经网络，参数量大幅减少。
- 适合需要理解模型决策逻辑的金融量化研究者使用。
本文提出使用柯尔莫哥洛夫-阿诺德网络（Kolmogorov-Arnold Networks, KAN）预测标普500波动率指数（CBOE Volatility Index, VIX）。与常被批评为黑箱的基于MLP的神经网络不同，KAN通过可学习的样条激活函数和符号化机制提供了可解释性。其精简架构以符号函数表达VIX预测结果，能揭示均值回归和杠杆效应等关键特征。通过多数据集、多周期的实证分析表明，KAN在预测性能上具有竞争力，且所需参数显著少于基于MLP的模型。研究证实了KAN作为可解释金融时间序列预测方法的潜力。
原文摘要 · Abstract (English)
This paper presents the use of Kolmogorov-Arnold Networks (KANs) for forecasting the CBOE Volatility Index (VIX). Unlike traditional MLP-based neural networks that are often criticized for their black-box nature, KAN offers an interpretable approach via learnable spline-based activation functions and symbolification. Based on a parsimonious architecture with symbolic functions, KAN expresses a forecast of the VIX as a closed-form in terms of explanatory variables, and provide interpretable insights into key characteristics of the VIX, including mean reversion and the leverage effect. Through in-depth empirical analysis across multiple datasets and periods, we show that KANs achieve competitive forecasting performance while requiring significantly fewer parameters compared to MLP-based neural network models. Our findings demonstrate the capacity and potential of KAN as an interpretable financial time-series forecasting method.
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