提出新方法解决周期性漂移问题，让时序预测更适应相位变化。
POEM: Phase-Aware $\mathrm{SO}(2)$ Feature Rotation for Time Series Forecasting Under Periodicity Drift
- 用SO(2)旋转建模潜空间相位变化，实现可逆相位校正。
- 在多个数据集上表现优于基线，提升预测稳定性。
- 适合处理周期相位不固定的工业时序数据，如设备运行状态。
深度学习显著提升了时序预测性能，但周期性漂移（周期起始时间与相位随时间变化）仍是难点。现有方法多基于固定时间网格建模，难以应对相位变化。本文提出POEM框架，基于二维特殊正交群SO(2)的潜特征旋转，实现相位感知建模。通过学习相位校正坐标，并对配对潜特征进行可逆SO(2)旋转，降低相位相关变异性。为外推该校正，引入方向性相位增量注意力（DPIA），从相似历史上下文中检索相位增量并融入未来相位校正。实验表明，POEM在多个基准数据集上表现优异，定性可视化显示其学习到的相位感知变换使潜变量轨迹更加规则。
原文摘要 · Abstract (English)
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.
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