# POEM: Phase-Aware SO(2) Feature Rotation for Time Series Forecasting Under Periodicity Drift

arXiv: https://arxiv.org/abs/2608.03630 · HTML: https://mlsanity.com/paper/2608.03630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective](https://mlsanity.com/paper/2402.11463/) (2024)
- [ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting](https://mlsanity.com/paper/2510.09734/) (2025)
- [Reasoning on Time-Series for Financial Technical Analysis](https://mlsanity.com/paper/2511.08616/) (2025)
- [PMDformer: Patch-Mean Decoupling Information Transformer for Long-term Forecasting](https://mlsanity.com/paper/2606.26549/) (2026)

## Abstract (arXiv)

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 POEM, a phase-aware forecasting framework based on latent feature rotation using the special orthogonal group in two dimensions, denoted by SO(2). POEM aims to reduce the phase-related variability by learning a phase-correction coordinate and applying an invertible 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.