arXiv:2609.08286cs.LG2026-09

用双曲几何显式建模多尺度时间序列的层级结构,提升长期预测性能。

HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting

论文配图:HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting
图 1 · 摘自论文原文
  • 将不同时间尺度的表示嵌入庞加莱球,显式构建层级几何结构。
  • 在多个基准上达到当前最优效果,验证了几何建模的有效性。
  • 适合研究时间序列建模与几何深度学习的学者参考。

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粒度全局趋势的多种时序模式。不同时间尺度的表示具有天然的层次性,较粗尺度抽象并聚合更细尺度的信息。现有方法虽能跨尺度交换信息,但层次结构通常只是交互的副产品,未作为独立几何结构加以建模。本文提出HypLTSF框架,通过将尺度级表示嵌入庞加莱球,赋予多尺度层次以明确的几何形式。庞加莱球的指数膨胀体积天然适配层次结构。为对齐几何与时间层次,HypLTSF施加两项约束:(1) 径向约束,按抽象层级排序嵌入点;(2) 角度约束,将共享同一粗粒度祖先的细粒度模式分组。在多个长期时间序列预测基准上的实验表明,HypLTSF取得当前最优性能,说明将多尺度层次显式建模为几何结构对预测有效。

原文摘要 · Abstract (English)

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 Poincar\'e 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.

时间序列双曲几何多尺度建模预测

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