# Dualformer: Time-Frequency Dual Domain Learning for Long-term Time Series Forecasting

arXiv: https://arxiv.org/abs/2601.15669 · HTML: https://mlsanity.com/paper/2601.15669/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [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)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [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)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Reducing Activation Recomputation in Large Transformer Models](https://mlsanity.com/paper/2205.05198/) (2022)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practice](https://mlsanity.com/paper/2203.05962/) (2022)
- [FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2501.13989/) (2025)
- [TFDNet: Time-Frequency Enhanced Decomposed Network for Long-term Time Series Forecasting](https://mlsanity.com/paper/2308.13386/) (2023)
- [Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting](https://mlsanity.com/paper/2407.12415/) (2024)
- [Comparative Analysis of Time Series Forecasting Approaches for Household Electricity Consumption Prediction](https://mlsanity.com/paper/2207.01019/) (2022)
- [TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2506.12696/) (2025)

## Abstract (arXiv)

Transformer-based models, despite their promise for long-term time series forecasting (LTSF), suffer from an inherent low-pass filtering effect that limits their effectiveness. This issue arises due to undifferentiated propagation of frequency components across layers, causing a progressive attenuation of high-frequency information crucial for capturing fine-grained temporal variations. To address this limitation, we propose Dualformer, a principled dual-domain framework that rethinks frequency modeling from a layer-wise perspective. Dualformer introduces three key components: (1) a dual-branch architecture that concurrently models complementary temporal patterns in both time and frequency domains; (2) a hierarchical frequency sampling module that allocates distinct frequency bands to different layers, preserving high-frequency details in lower layers while modeling low-frequency trends in deeper layers; and (3) a periodicity-aware weighting mechanism that dynamically balances contributions from the dual branches based on the harmonic energy ratio of inputs, supported theoretically by a derived lower bound. This design enables structured frequency modeling and adaptive integration of time-frequency features, effectively preserving high-frequency information and enhancing generalization. Extensive experiments conducted on eight widely used benchmarks demonstrate Dualformer's robustness and superior performance, particularly on heterogeneous or weakly periodic data. Our code is publicly available at https://github.com/Akira-221/Dualformer.