KAN模型通过可解释的函数连接，实现时间序列预测的精准溯源。
Temporal Functional Circuits: From Spline Plots to Faithful Explanations in KAN Forecasting
- 用输出感知归因将边函数映射到输入时滞，构建时间对齐解释
- 移除B样条组件导致预测误差上升，证明函数形状本身具预测价值
- 适用于需要透明决策过程的复杂信号建模场景
与MLP不同，柯尔莫戈洛夫-阿诺德网络（KAN）在每条连接上显式学习可解释的边函数，使时间序列预测具备机制解释性。本文提出时间功能电路框架，将KAN边函数从隐含可视化转化为忠实的时间对齐解释。该框架基于门控残差KAN，将预测分解为线性基项与稀疏激活的KAN修正项：(i) 通过输出感知归因将每条边映射到输入时滞；(ii) 按学习到的激活范围排序边；(iii) 通过零值干预和样条移除验证解释的忠实性。在四类复杂度递增的合成数据上，随着信号复杂度增加，学习到的门控宽度逐步扩大；在状态切换信号中，门控KAN相比纯线性模型降低59%的均方误差。在八个基准测试中，该架构性能媲美线性、注意力与MLP方法，同时提供MLP无法实现的可解释边函数。
原文摘要 · Abstract (English)
Unlike MLPs, Kolmogorov-Arnold Networks (KANs) expose explicit learnable edge functions on every connection, enabling mechanistic explanation in time-series forecasting. This paper introduces Temporal Functional Circuits, a framework that transforms KAN edge functions from latent visualizations into faithful, temporally grounded explanations. Built on a gated residual KAN that decomposes forecasts into a linear base and a sparsely activated KAN correction, the framework (i) maps each edge to input lags via output-aware attribution, (ii) ranks edges by learned activation range, and (iii) validates faithfulness through edge-level interventions including zeroing and spline removal. Removing the learned B-spline component while retaining the base SiLU term degrades forecasts, providing evidence that the spline shape itself carries predictive value beyond the base activation. On four synthetic regimes of increasing complexity, the learned gate opens progressively wider as signal complexity grows. On regime-switching signals, gated KAN achieves 59% lower MSE than linear-only models. Across eight benchmarks, the gated architecture is competitive with linear, attention, and MLP alternatives, while providing interpretable edge functions that MLP-based corrections cannot offer.
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