发表机构
Urban AI Institute, Korea Advanced Institute of Science and Technology (KAIST); Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院城市人工智能研究所; 韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
HypLTSF将多尺度层次结构嵌入庞加莱球，通过径向和角度约束显式建模几何结构，在长期预测基准上取得最先进性能。
AI 中文摘要
多尺度建模已成为长期时间序列预测的有效方法，能够捕捉从细粒度局部动态到粗略全局趋势的时间模式。这些时间尺度上的表示本质上是层次化的，较粗的尺度抽象并聚合来自较细尺度的信息。虽然现有方法能够便捷地在这些尺度之间交换信息，但层次结构本身通常被视为这种交互的涌现副产品，而非作为一种几何结构被显式捕捉。在本文中，我们提出了HypLTSF，一个通过将尺度级表示嵌入庞加莱球（其指数增长的体积天然适应层次结构）来赋予多尺度层次结构具体几何形式的框架。为了使该几何结构与时间层次对齐，HypLTSF施加了两个约束：（1）径向约束，按抽象级别对嵌入进行排序；（2）角度约束，将共享同一较粗尺度祖先的细粒度模式分组。在长期时间序列预测基准上的大量实验表明，HypLTSF达到了最先进的性能，这表明将多尺度层次结构显式建模为几何结构对预测是有效的。
英文摘要
Multi-scale modeling has become an effective approach for long-term time series forecasting, capturing temporal patterns that range from fine-grained local dynamics to coarse global trends. Representations across these temporal scales are inherently hierarchical, with coarser scales abstracting and aggregating information from finer ones. While existing approaches readily exchange information across these scales, the hierarchy itself is typically left as an emergent byproduct of such interactions rather than captured as a geometric structure in its own right. In this paper, we introduce HypLTSF, a framework that endows the multi-scale hierarchy with a concrete geometric form by embedding scale-wise representations into the Poincaré ball, whose exponentially expanding volume naturally accommodates hierarchical structures. To align this geometry with the temporal hierarchy, HypLTSF imposes two constraints: (1) a radial constraint that orders embeddings by their level of abstraction, and (2) an angular constraint that groups fine-scale patterns sharing a common coarser-scale ancestor. Extensive experiments on long-term time series forecasting benchmarks show that HypLTSF achieves state-of-the-art performance, suggesting that explicitly modeling the multi-scale hierarchy as a geometric structure is effective for forecasting.
CommentsSubmitted to IEEE TNNLS
