将稀疏变分推断引入KAN，实现可扩展的科学发现与不确定性量化。
Scalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
- 用诱导点和变分推断降低计算复杂度，支持大规模数据。
- 在真实科学数据上实现高精度预测并输出置信区间。
- 能识别关键输入变量与函数关系，适合科学机制挖掘。
Kolmogorov-Arnold网络（KAN）通过在边上传递可学习的一维函数，替代传统多层感知机，提升了模型可解释性。但标准KAN缺乏概率输出，难以用于需要不确定性量化任务。尽管已有基于高斯过程（GP）的KAN扩展解决了此问题，但其采用精确推断，计算复杂度达O(N³)，仅适用于小规模数据。本文提出稀疏变分高斯过程KAN（SVGP-KAN），将稀疏变分推断与KAN结构结合，使用M个诱导点和解析矩匹配，使复杂度降至O(NM²)或线性于样本量，显著提升可扩展性。此外，我们通过置换重要性分析，使模型具备结构识别能力，可识别关键输入变量并分类函数关系，适用于大规模科学数据分析。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks (KANs) offer a promising alternative to Multi-Layer Perceptron (MLP) by placing learnable univariate functions on network edges, enhancing interpretability. However, standard KANs lack probabilistic outputs, limiting their utility in applications requiring uncertainty quantification. While recent Gaussian Process (GP) extensions to KANs address this, they utilize exact inference methods that scale cubically with data size N, restricting their application to smaller datasets. We introduce the Sparse Variational GP-KAN (SVGP-KAN), an architecture that integrates sparse variational inference with the KAN topology. By employing $M$ inducing points and analytic moment matching, our method reduces computational complexity from $O(N^3)$ to $O(NM^2)$ or linear in sample size, enabling the application of probabilistic KANs to larger scientific datasets. Furthermore, we demonstrate that integrating a permutation-based importance analysis enables the network to function as a framework for structural identification, identifying relevant inputs and classifying functional relationships.
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