POEM: Phase-Aware $\mathrm{SO}(2)$ Feature Rotation for Time Series Forecasting Under Periodicity Drift

2026-08-04

AI Summary

This work addresses the challenge of modeling periodic drift—characterized by time-varying period lengths and phases—in time series forecasting by proposing the POEM framework. POEM introduces, for the first time, the $\mathrm{SO}(2)$ group structure into phase modeling, learning phase-corrected coordinates through invertible $\mathrm{SO}(2)$ rotations of pairwise features in latent space. It further incorporates a directional phase-increment attention mechanism (DPIA) to enable context-aware extrapolation of future phases. Combined with latent trajectory regularization, POEM effectively suppresses phase variability, achieving competitive forecasting performance across multiple datasets. Visualizations demonstrate that the learned phase-aware transformations significantly enhance the regularity of latent trajectories.

Abstract

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.

Problem

• periodicity drift
• time series forecasting
• phase variation
• SO(2)
• feature rotation

Innovation

• SO(2) feature rotation
• periodicity drift
• phase-aware forecasting
• Directional Phase Increment Attention
• latent feature transformation