# xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition

arXiv: https://arxiv.org/abs/2412.17323 · HTML: https://mlsanity.com/paper/2412.17323/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)

## Built on by (most cited first, 30 of 36)

- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [PhaseFormer: From Patches to Phases for Efficient and Effective Time Series Forecasting](https://mlsanity.com/paper/2510.04134/) (2025)
- [Exploring Accuracy Law for Deep Time Series Forecasters: An Empirical Study](https://mlsanity.com/paper/2510.02729/) (2025)
- [PHAT: Modeling Period Heterogeneity for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.00654/) (2026)
- [DS-Diffusion: Data Style-Guided Diffusion Model for Time-Series Generation](https://mlsanity.com/paper/2509.18584/) (2025)
- [Entropy Guided Dynamic Patch Segmentation for Time Series Transformers](https://mlsanity.com/paper/2509.26157/) (2025)
- [WPBench: A Comprehensive Benchmark for Wind Power Forecasting](https://mlsanity.com/paper/2609.24444/) (2026)
- [How Effective Are Time-Series Models for Precipitation Nowcasting? A Comprehensive Benchmark for GNSS-based Precipitation Nowcasting](https://mlsanity.com/paper/2509.25263/) (2025)
- [PRISM: A hierarchical multiscale approach for time series forecasting](https://mlsanity.com/paper/2512.24898/) (2025)
- [SEER: Transformer-based Robust Time Series Forecasting via Automated Patch Enhancement and Replacement](https://mlsanity.com/paper/2602.00589/) (2026)
- [DMamba: Decomposition-enhanced Mamba for Time Series Forecasting](https://mlsanity.com/paper/2602.09081/) (2026)
- [Dynamic Multi-period Experts for Online Time Series Forecasting](https://mlsanity.com/paper/2603.09062/) (2026)
- [What If We Let Forecasting Forget? A Sparse Bottleneck for Cross-Variable Dependencies](https://mlsanity.com/paper/2605.08289/) (2026)
- [One Step Closer to Ground Truth: A Multi-Scale Residual-Aware Representation Learning Pipeline for Predicting Time Series Data](https://mlsanity.com/paper/2606.10678/) (2026)
- [Forecast-Then-Optimize Deep Learning Methods](https://mlsanity.com/paper/2506.13036/) (2025)
- [KAIROS: Unified Training for Universal Non-Autoregressive Time Series Forecasting](https://mlsanity.com/paper/2510.02084/) (2025)
- [Naga: Vedic Encoding for Deep State Space Models](https://mlsanity.com/paper/2511.13510/) (2025)
- [We Need a More Robust Classifier: Dual Causal Learning Empowers Domain-Incremental Time Series Classification](https://mlsanity.com/paper/2601.10312/) (2026)
- [TimeCatcher: A Variational Framework for Volatility-Aware Forecasting of Non-Stationary Time Series](https://mlsanity.com/paper/2601.20448/) (2026)
- [ACFormer: Mitigating Non-linearity with Auto Convolutional Encoder for Time Series Forecasting](https://mlsanity.com/paper/2601.20611/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [TriTS: Time Series Forecasting from a Multimodal Perspective](https://mlsanity.com/paper/2604.16748/) (2026)
- [CombinationTS: A Modular Framework for Understanding Time-Series Forecasting Models](https://mlsanity.com/paper/2605.01231/) (2026)
- [Beyond Extrapolation: Knowledge Utilization Paradigm with Bidirectional Inspiration for Time Series Forecasting](https://mlsanity.com/paper/2605.19249/) (2026)
- [UniWind: Day-Ahead Wind Power Forecasting via Physics-Informed State Routing](https://mlsanity.com/paper/2607.01670/) (2026)
- [DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2608.20052/) (2026)
- [MetaCaster: Meta-Harness-Optimized Agent for End-to-End Few-Shot Learning of Lightweight Time Series Forecasters](https://mlsanity.com/paper/2608.23473/) (2026)

## Abstract (arXiv)

In recent years, the application of transformer-based models in time-series forecasting has received significant attention. While often demonstrating promising results, the transformer architecture encounters challenges in fully exploiting the temporal relations within time series data due to its attention mechanism. In this work, we design eXponential Patch (xPatch for short), a novel dual-stream architecture that utilizes exponential decomposition. Inspired by the classical exponential smoothing approaches, xPatch introduces the innovative seasonal-trend exponential decomposition module. Additionally, we propose a dual-flow architecture that consists of an MLP-based linear stream and a CNN-based non-linear stream. This model investigates the benefits of employing patching and channel-independence techniques within a non-transformer model. Finally, we develop a robust arctangent loss function and a sigmoid learning rate adjustment scheme, which prevent overfitting and boost forecasting performance. The code is available at the following repository: https://github.com/stitsyuk/xPatch.