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POEM introduces a novel mathematical framework using SO(2) group rotation to handle phase drift in time series forecasting, addressing a specific limitation where existing models fail when cycle timing varies over time. By learning invertible feature rotations and leveraging directional attention for extrapolation, the method regularizes latent trajectories without relying on fixed grids. This research advances machine learning theory by providing a more robust approach to modeling non-stationary periodic patterns in sequential data.
POEM: Phase-Aware $\mathrm{SO}(2)$ Feature Rotation for Time Series Forecasting Under Periodicity Drift
arXiv:2608.03630v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2608.03630 [cs.LG]
(or arXiv:2608.03630v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.03630 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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