# Additive decomposition of one-dimensional signals using Transformers

arXiv: https://arxiv.org/abs/2506.05942 · HTML: https://mlsanity.com/paper/2506.05942/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Rates](https://mlsanity.com/paper/1708.07120/) (2017)
- [The Fourier Decomposition Method for nonlinear and nonstationary time series analysis](https://mlsanity.com/paper/1503.06675/) (2015)
- [Signal Decomposition Using Masked Proximal Operators](https://mlsanity.com/paper/2202.09338/) (2022)
- [IRCNN+: An Enhanced Iterative Residual Convolutional Neural Network for Non-stationary Signal Decomposition](https://mlsanity.com/paper/2309.04782/) (2023)

## Abstract (arXiv)

One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often rely on mathematical models, recent research suggests that applying the latest deep learning models to this problem presents an exciting, unexplored area with promising potential. This work presents a novel method for the additive decomposition of one-dimensional signals. We leverage the Transformer architecture to decompose signals into their constituent components: piece-wise constant, smooth (low-frequency oscillatory), textured (high-frequency oscillatory), and a noise component. Our model, trained on synthetic data, achieves excellent accuracy in modeling and decomposing input signals from the same distribution, as demonstrated by the experimental results.