# PhaseFormer: From Patches to Phases for Efficient and Effective Time Series Forecasting

arXiv: https://arxiv.org/abs/2510.04134 · HTML: https://mlsanity.com/paper/2510.04134/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 23 of 23)

- [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)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [Towards Spatio-Temporal Aware Traffic Time Series Forecasting--Full Version](https://mlsanity.com/paper/2203.15737/) (2022)
- [AutoCTS: Automated Correlated Time Series Forecasting -- Extended Version](https://mlsanity.com/paper/2112.11174/) (2021)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition](https://mlsanity.com/paper/2412.17323/) (2024)
- [Learning to Embed Time Series Patches Independently](https://mlsanity.com/paper/2312.16427/) (2023)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [CT-PatchTST: Channel-Time Patch Time-Series Transformer for Long-Term Renewable Energy Forecasting](https://mlsanity.com/paper/2501.08620/) (2025)
- [Maximum Mean Discrepancy for Generalization in the Presence of Distribution and Missingness Shift](https://mlsanity.com/paper/2111.10344/) (2021)

## Built on by (most cited first, 9 of 9)

- [PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2605.16793/) (2026)
- [Zeus: Towards Tuning-Free Foundation Model for Time Series Analysis](https://mlsanity.com/paper/2607.01918/) (2026)
- [From Time Series to State: Situation-Aware Modeling for Air Traffic Flow Prediction](https://mlsanity.com/paper/2604.11198/) (2026)
- [LeapTS: Rethinking Time Series Forecasting as Adaptive Multi-Horizon Scheduling](https://mlsanity.com/paper/2605.10292/) (2026)
- [GatedLinear: Adaptive Routing of Complementary Linear Bases for Time Series Forecasting](https://mlsanity.com/paper/2607.09537/) (2026)
- [TSSM: Triaxial State Space Model for Global Station Weather Forecasting with Temporal-Variable-Historical Modeling](https://mlsanity.com/paper/2607.13101/) (2026)
- [RouteTS: Frequency-Time Routing for Time Series Forecasting](https://mlsanity.com/paper/2608.14682/) (2026)
- [Hyperbolic Time Series Forecasting with Learnable Decomposition and Manifold Dynamics](https://mlsanity.com/paper/2610.15760/) (2026)
- [TStruct: Learning Shared Temporal Structures for Long-Term Time-Series Forecasting](https://mlsanity.com/paper/2610.17864/) (2026)

## Abstract (arXiv)

Periodicity is a fundamental characteristic of time series data and has long played a central role in forecasting. Recent deep learning methods strengthen the exploitation of periodicity by treating patches as basic tokens, thereby improving predictive effectiveness. However, their efficiency remains a bottleneck due to large parameter counts and heavy computational costs. This paper provides, for the first time, a clear explanation of why patch-level processing is inherently inefficient, supported by strong evidence from real-world data. To address these limitations, we introduce a phase perspective for modeling periodicity and present an efficient yet effective solution, PhaseFormer. PhaseFormer features phase-wise prediction through compact phase embeddings and efficient cross-phase interaction enabled by a lightweight routing mechanism. Extensive experiments demonstrate that PhaseFormer achieves state-of-the-art performance with around 1k parameters, consistently across benchmark datasets. Notably, it excels on large-scale and complex datasets, where models with comparable efficiency often struggle. This work marks a significant step toward truly efficient and effective time series forecasting. Code is available at this repository: https://github.com/neumyor/PhaseFormer_TSL