揭示时间序列大模型嵌入空间中的非平稳性表现及其检测难题
Non-Stationarity in the Embedding Space of Time Series Foundation Models
- 通过控制实验分析均值漂移、方差变化等非平稳性在嵌入空间的线性可探测性
- 发现不同模型对非平稳性的敏感度差异显著，且检测能力随扰动强度平滑下降
- 适用于关注时间序列异常检测与模型鲁棒性的研究人员
时间序列基础模型（TSFMs）广泛用作通用特征提取器，但其嵌入空间中的非平稳性仍缺乏清晰理解。现有研究常将非平稳性与分布偏移混为一谈，模糊了经典时间序列分析与统计过程控制（SPC）中关键区分。在SPC中，非平稳性标志过程脱离稳定状态——如均值、方差变化或趋势出现，其检测是质量监控与变点分析的核心。受此诊断传统启发，我们系统研究了在受控条件下，均值漂移、方差变化和线性趋势等不同形式的分布非平稳性如何在TSFM嵌入空间中表现为线性可探测。同时考察了由持续性导致的时间非平稳性，即由于长记忆或近单位根行为违反弱平稳性，而非显式分布偏移。通过调节扰动强度并测试多个TSFMs，发现嵌入空间中非平稳性的可检测性呈平滑下降趋势，且各模型表现出独特故障模式。
原文摘要 · Abstract (English)
Time series foundation models (TSFMs) are widely used as generic feature extractors, yet the notion of non-stationarity in their embedding spaces remains poorly understood. Recent work often conflates non-stationarity with distribution shift, blurring distinctions fundamental to classical time-series analysis and long-standing methodologies such as statistical process control (SPC). In SPC, non-stationarity signals a process leaving a stable regime - via shifts in mean, variance, or emerging trends - and detecting such departures is central to quality monitoring and change-point analysis. Motivated by this diagnostic tradition, we study how different forms of distributional non-stationarity - mean shifts, variance changes, and linear trends - become linearly accessible in TSFM embedding spaces under controlled conditions. We further examine temporal non-stationarity arising from persistence, which reflects violations of weak stationarity due to long-memory or near-unit-root behavior rather than explicit distributional shifts. By sweeping shift strength and probing multiple TSFMs, we find that embedding-space detectability of non-stationarity degrades smoothly and that different models exhibit distinct, model-specific failure modes.
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