PhiMixer: Forecast-Origin Phase Conditioning for Long-Term Time-Series Forecasting

Multivariate time-series forecasting involves temporal and cross-channel dependencies whose dynamics can vary across recurring cycles. We investigate whether forecast-origin phase can serve as a conditioning signal for adapting forecasting transformations to the underlying rhythmic state. We introduce PhiMixer, a lightweight phase-conditioned architecture that separates learnable multi-period cyclic components from the input and uses forecast-origin phase to modulate temporal and cross-channel processing. Its rhythm-aware relative attention (RRF) captures periodic temporal structure, while the Phase-Informed Low-Rank Channel Mixer (PILCM) generates phase-dependent low-rank channel transformations without dense O(C²) interactions. PhiMixer achieves the best performance on 6/8 datasets on MSE/MAE, respectively, among the compared methods. Ablation studies show that active phase conditioning provides consistent gains, particularly on periodic traffic data, with conditioning consistently outperforming phase-as-feature concatenation. With approximately 126K parameters and linear channel scaling, PhiMixer offers an efficient approach to phase-aware long-term multivariate forecasting.