# Delayformer: spatiotemporal transformation for predicting high-dimensional dynamics

arXiv: https://arxiv.org/abs/2506.11528 · HTML: https://mlsanity.com/paper/2506.11528/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 67 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (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)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2304.05206/) (2023)
- [From Similarity to Superiority: Channel Clustering for Time Series Forecasting](https://mlsanity.com/paper/2404.01340/) (2024)
- [On-line Building Energy Optimization using Deep Reinforcement Learning](https://mlsanity.com/paper/1707.05878/) (2017)
- [Spatiotemporal information conversion machine for time-series prediction](https://mlsanity.com/paper/2107.01353/) (2021)
- [DEFM: Delay E mbedding based Forecast Machine for Time Series Forecasting by Spatiotemporal Information Transformation](https://mlsanity.com/paper/2005.07842/) (2020)
- [Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA](https://mlsanity.com/paper/2501.12582/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Time-Series Foundation Model by Universal Delay Embedding](https://mlsanity.com/paper/2509.12080/) (2025)
- [Time-Delayed Transformers for Data-Driven Modeling of Low-Dimensional Dynamics](https://mlsanity.com/paper/2602.08478/) (2026)

## Abstract (arXiv)

Predicting time-series is of great importance in various scientific and engineering fields. However, in the context of limited and noisy data, accurately predicting dynamics of all variables in a high-dimensional system is a challenging task due to their nonlinearity and also complex interactions. Current methods including deep learning approaches often perform poorly for real-world systems under such circumstances. This study introduces the Delayformer framework for simultaneously predicting dynamics of all variables, by developing a novel multivariate spatiotemporal information (mvSTI) transformation that makes each observed variable into a delay-embedded state (vector) and further cross-learns those states from different variables. From dynamical systems viewpoint, Delayformer predicts system states rather than individual variables, thus theoretically and computationally overcoming such nonlinearity and cross-interaction problems. Specifically, it first utilizes a single shared Visual Transformer (ViT) encoder to cross-represent dynamical states from observed variables in a delay embedded form and then employs distinct linear decoders for predicting next states, i.e. equivalently predicting all original variables parallelly. By leveraging the theoretical foundations of delay embedding theory and the representational capabilities of Transformers, Delayformer outperforms current state-of-the-art methods in forecasting tasks on both synthetic and real-world datasets. Furthermore, the potential of Delayformer as a foundational time-series model is demonstrated through cross-domain forecasting tasks, highlighting its broad applicability across various scenarios.