Perceive Fast, Think Slow: Adaptive Periodic Tokenization for Time Series Analysis

Patch-based transformers encode raw observations into fixed patches and then rely on inter-patch attention for both dependency modeling and prediction; the same token grid must serve both purposes. PeCo-TS separates these two purposes into coexisting pathways. The Fast Path produces full-resolution timestep features with linear attention, while a spectral segmenter pools them into period-guided segment tokens for scale-adaptive dependency modeling. Temporal reprojection fuses both representations before the output head, so the prediction head never operates on compressed tokens alone. The complete design achieves best or tied-best forecasting MSE on five of seven datasets and the highest displayed PA-F1 in the MSL pathway control. The pathway controls reveal an asymmetric pattern: retaining only the full-resolution pathway trails the full model by a small margin, while retaining only the segment pathway falls far behind. This indicates that aggregation and fine-grained detail are complements, not substitutes. The results show that separating prediction-scale perception from segment-scale conceptualization—rather than forcing both purposes into the same token grid—is a viable design principle for time-series transformers.