用哈恩多项式激活函数的新型网络，提升多变量时序预测精度
Time series forecasting with Hahn Kolmogorov-Arnold networks
- 基于哈恩多项式设计可学习激活函数，融合局部与全局时间模式
- 在多个基准上超越当前最先进方法，尤其在长期预测中表现更优
- 模型轻量且可解释，适合需要透明性的时序预测场景
近期基于Transformer和MLP的模型在长期时序预测中表现出色，但Transformer受限于二次复杂度和置换等变注意力机制，而MLP存在谱偏差。本文提出HaKAN，一种基于柯尔莫戈罗夫-阿诺德网络（KAN）的通用模型，采用哈恩多项式构建可学习激活函数，提供了一种轻量且可解释的多变量时序预测方案。模型结合通道独立性、分块处理、堆叠的哈恩-KAN模块（带残差连接）及由两层全连接层组成的瓶颈结构。哈恩-KAN模块包含块间与块内KAN层，有效捕捉全局与局部时间模式。在多个预测基准上的大量实验表明，该模型持续优于最新方法；消融研究验证了核心组件的有效性。
原文摘要 · Abstract (English)
Recent Transformer- and MLP-based models have demonstrated strong performance in long-term time series forecasting, yet Transformers remain limited by their quadratic complexity and permutation-equivariant attention, while MLPs exhibit spectral bias. We propose HaKAN, a versatile model based on Kolmogorov-Arnold Networks (KANs), leveraging Hahn polynomial-based learnable activation functions and providing a lightweight and interpretable alternative for multivariate time series forecasting. Our model integrates channel independence, patching, a stack of Hahn-KAN blocks with residual connections, and a bottleneck structure comprised of two fully connected layers. The Hahn-KAN block consists of inter- and intra-patch KAN layers to effectively capture both global and local temporal patterns. Extensive experiments on various forecasting benchmarks demonstrate that our model consistently outperforms recent state-of-the-art methods, with ablation studies validating the effectiveness of its core components.
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