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

2026-01-22

AI Summary

This work addresses the low-pass filtering effect inherent in Transformer-based models for long-term time series forecasting, which often leads to the loss of high-frequency details. To mitigate this limitation, the authors propose Dualformer, a novel architecture that, for the first time, enables inter-layer collaborative learning across both time and frequency domains. Dualformer integrates hierarchical frequency sampling with a periodicity-aware weighting mechanism grounded in harmonic energy ratios, facilitating structured frequency modeling and adaptive feature fusion. Theoretical analysis provides a performance lower bound that supports the model’s efficacy. Extensive experiments on eight mainstream benchmarks demonstrate that Dualformer significantly outperforms existing methods, particularly on heterogeneous or weakly periodic datasets, thereby validating its robustness and state-of-the-art performance.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

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.

Problem

• long-term time series forecasting
• low-pass filtering
• high-frequency attenuation
• frequency modeling
• temporal variations

Innovation

• dual-domain learning
• frequency-aware modeling
• hierarchical frequency sampling
• periodicity-aware weighting
• long-term time series forecasting