# PMDformer: Patch-Mean Decoupling Information Transformer for Long-term Forecasting

arXiv: https://arxiv.org/abs/2606.26549 · HTML: https://mlsanity.com/paper/2606.26549/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [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)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [TSLANet: Rethinking Transformers for Time Series Representation Learning](https://mlsanity.com/paper/2404.08472/) (2024)
- [Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation](https://mlsanity.com/paper/2501.04970/) (2025)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)

## Built on by (most cited first, 1 of 1)

- [POEM: Phase-Aware SO(2) Feature Rotation for Time Series Forecasting Under Periodicity Drift](https://mlsanity.com/paper/2608.03630/) (2026)

## Abstract (arXiv)

Long-term time series forecasting (LTSF) plays a crucial role in fields such as energy management, finance, and traffic prediction. Transformer-based models have adopted patch-based strategies to capture long-range dependencies, but accurately modeling shape similarities across patches and variables remains challenging due to scale differences. To address this, we introduce patch-mean decoupling (PMD), which separates the trend and residual shape information by subtracting the mean of each patch, preserving the original structure and ensuring that the attention mechanism captures true shape similarities. Futhermore, to more effectively model long-range dependencies and capture cross-variable relationships, we propose Trend Restoration Attention (TRA) and Proximal Variable Attention (PVA). The former module reintegrates the decoupled trend from PMD while calculating attention output. And the latter focuses cross-variable attention on the most relevant, recent time segments to avoid overfitting on outdated correlations. Combining these components, we propose PMDformer, a model designed to effectively capture shape similarity in long-term forecasting scenarios. Extensive experiments indicate that PMDformer outperforms existing state-of-the-art methods in stability and accuracy across multiple LTSF benchmarks. The code is available at https://github.com/aohu1105/PMDformer.