用数学构造的网络提升交通流量预测精度
STKAN: Kolmogorov-Arnold Networks for Spatio-Temporal Forecasting
- 引入柯尔莫哥洛夫-阿诺德网络模块，增强非线性拟合能力
- 在5个交通数据集上表现优于传统MLP方法，提升预测准确率
- 适合研究时空建模与神经网络结构设计的学者参考
真实世界交通数据具有异质的空间相关性和非线性的时序动态，给精准的时空预测带来巨大挑战。现有方法不断优化图结构、注意力机制和分解架构，但对底层非线性函数逼近器的关注相对不足。本文提出STKAN，一种新的时空预测架构，将泰勒多项式形式的柯尔莫哥洛夫-阿诺德网络（Kolmogorov-Arnold Network）模块引入空间与时间的令牌混合过程。STKAN首先通过可学习的软节点分组机制构建高层次空间表示，进行分组空间混合，随后在压缩序列上建模时序依赖。进一步引入空间与时间自注意力层以捕捉长程交互。在五个交通预测基准上的实验表明，STKAN达到有竞争力的性能，且在测试设置中优于评估的基于MLP的变体。结果表明，非线性函数逼近器的设计可作为架构设计的有效补充，用于提升时空预测能力。
原文摘要 · Abstract (English)
Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.
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