# Minusformer: Improving Time Series Forecasting by Progressively Learning Residuals

arXiv: https://arxiv.org/abs/2402.02332 · HTML: https://mlsanity.com/paper/2402.02332/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [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)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [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)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [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)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [Flowformer: Linearizing Transformers with Conservation Flows](https://mlsanity.com/paper/2202.06258/) (2022)
- [Scaleformer: Iterative Multi-scale Refining Transformers for Time Series Forecasting](https://mlsanity.com/paper/2206.04038/) (2022)
- [Does Long-Term Series Forecasting Need Complex Attention and Extra Long Inputs?](https://mlsanity.com/paper/2306.05035/) (2023)

## Built on by (most cited first, 10 of 10)

- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting](https://mlsanity.com/paper/2406.11397/) (2024)
- [Dataset-Driven Channel Masks in Transformers for Multivariate Time Series](https://mlsanity.com/paper/2410.23222/) (2024)
- [Are Data Embeddings effective in time series forecasting?](https://mlsanity.com/paper/2505.20716/) (2025)
- [DeepBooTS: Dual-Stream Residual Boosting for Drift-Resilient Time-Series Forecasting](https://mlsanity.com/paper/2511.06893/) (2025)
- [AdaPRL: Adaptive Pairwise Regression Learning with Uncertainty Estimation for Universal Regression Tasks](https://mlsanity.com/paper/2501.05809/) (2025)
- [Progressive Supervision via Label Decomposition: An Long-Term and Large-Scale Wireless Traffic Forecasting Method](https://mlsanity.com/paper/2501.06255/) (2025)
- [Efficient-Husformer: Efficient Multimodal Transformer Hyperparameter Optimization for Stress and Cognitive Loads](https://mlsanity.com/paper/2511.22362/) (2025)
- [Residual-Guided Multi-Resolution Refinement of Foundation Models: A Case Study in Drought Forecasting](https://mlsanity.com/paper/2607.17507/) (2026)
- [Downside-Controlled Online Forecast Combination under Delayed and Revised Outcomes](https://mlsanity.com/paper/2609.29096/) (2026)

## Abstract (arXiv)

In this paper, we find that ubiquitous time series (TS) forecasting models are prone to severe overfitting. To cope with this problem, we embrace a de-redundancy approach to progressively reinstate the intrinsic values of TS for future intervals. Specifically, we introduce a dual-stream and subtraction mechanism, which is a deep Boosting ensemble learning method. And the vanilla Transformer is renovated by reorienting the information aggregation mechanism from addition to subtraction. Then, we incorporate an auxiliary output branch into each block of the original model to construct a highway leading to the ultimate prediction. The output of subsequent modules in this branch will subtract the previously learned results, enabling the model to learn the residuals of the supervision signal, layer by layer. This designing facilitates the learning-driven implicit progressive decomposition of the input and output streams, empowering the model with heightened versatility, interpretability, and resilience against overfitting. Since all aggregations in the model are minus signs, which is called Minusformer. Extensive experiments demonstrate the proposed method outperform existing state-of-the-art methods, yielding an average performance improvement of 11.9% across various datasets.The code has been released at https://github.com/Anoise/Minusformer.