POEM：面向周期性漂移下时间序列预测的相位感知SO(2)特征旋转方法
POEM: Phase-Aware $\mathrm{SO}(2)$ Feature Rotation for Time Series Forecasting Under Periodicity Drift
中文总结 AI 辅助
针对周期性漂移下时间序列预测的相位适配难题，提出基于SO(2)特征旋转的POEM框架，结合DPIA实现相位校正，实验验证其性能竞争力与轨迹规整效果。
中文摘要 AI 辅助
深度学习已在时间序列预测领域取得进展，但周期性漂移（即周期时序和相位随时间变化）仍是一项具有挑战性的问题。现有方法大多在固定时间网格上对这些序列进行建模，难以适配与相位相关的变化。为解决这一局限，我们提出POEM，这是一种基于二维特殊正交群（记为SO(2)）的隐特征旋转的相位感知预测框架。POEM旨在通过学习相位校正坐标，并对配对的隐特征应用可逆的SO(2)旋转来减少与相位相关的变异性。为外推该校正坐标，方向相位增量注意力（DPIA）从相似的时间上下文检索历史相位增量，并将其整合到未来的相位校正中。实验表明，POEM取得了有竞争力的性能，而定性可视化结果显示，学习到的相位感知变换使隐轨迹更加规整。
英文摘要
Deep learning has advanced time series forecasting, but periodicity drift, in which cycle timing and phase vary over time, remains a challenging problem. Existing methods predominantly model these sequences on fixed time grids, suffering from a limited ability to accommodate phase-related variation. To address this limitation, we propose \textbf{POEM}, a phase-aware forecasting framework based on latent feature rotation using the special orthogonal group in two dimensions, denoted by $\mathrm{SO}(2)$. POEM aims to reduce the phase-related variability by learning a phase-correction coordinate and applying an invertible $\mathrm{SO}(2)$-based rotation to paired latent features. To extrapolate this correction coordinate, Directional Phase Increment Attention (DPIA) retrieves historical phase increments from similar temporal contexts and integrates them into future phase corrections. Experiments demonstrate that POEM achieves competitive performance, while qualitative visualizations suggest that the learned phase-aware transformation makes latent trajectories more regular.
