# SCFormer: Structured Channel-wise Transformer with Cumulative Historical State for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2505.02655 · HTML: https://mlsanity.com/paper/2505.02655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 5 May 2025.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [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)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [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)
- [Transformer in Transformer](https://mlsanity.com/paper/2103.00112/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [FastViT: A Fast Hybrid Vision Transformer using Structural Reparameterization](https://mlsanity.com/paper/2303.14189/) (2023)
- [AMMUS : A Survey of Transformer-based Pretrained Models in Natural Language Processing](https://mlsanity.com/paper/2108.05542/) (2021)
- [A Survey of Visual Transformers](https://mlsanity.com/paper/2111.06091/) (2021)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [Flowformer: Linearizing Transformers with Conservation Flows](https://mlsanity.com/paper/2202.06258/) (2022)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)
- [SAMformer: Unlocking the Potential of Transformers in Time Series Forecasting with Sharpness-Aware Minimization and Channel-Wise Attention](https://mlsanity.com/paper/2402.10198/) (2024)
- [Deep Learning with Long Short-Term Memory for Time Series Prediction](https://mlsanity.com/paper/1810.10161/) (2018)
- [Vision Transformers in Medical Computer Vision -- A Contemplative Retrospection](https://mlsanity.com/paper/2203.15269/) (2022)

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

- [Free Energy Mixer](https://mlsanity.com/paper/2602.07160/) (2026)

## Abstract (arXiv)

The Transformer model has shown strong performance in multivariate time series forecasting by leveraging channel-wise self-attention. However, this approach lacks temporal constraints when computing temporal features and does not utilize cumulative historical series effectively.To address these limitations, we propose the Structured Channel-wise Transformer with Cumulative Historical state (SCFormer). SCFormer introduces temporal constraints to all linear transformations, including the query, key, and value matrices, as well as the fully connected layers within the Transformer. Additionally, SCFormer employs High-order Polynomial Projection Operators (HiPPO) to deal with cumulative historical time series, allowing the model to incorporate information beyond the look-back window during prediction. Extensive experiments on multiple real-world datasets demonstrate that SCFormer significantly outperforms mainstream baselines, highlighting its effectiveness in enhancing time series forecasting. The code is publicly available at https://github.com/ShiweiGuo1995/SCFormer