FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition

2025-11-14

AI Summary

To address spectral entanglement—where trend, seasonal, and noise components overlap in the frequency domain—and the high computational cost of complex-valued operations in non-stationary time series forecasting, this paper proposes the Frequency-Decoupling Network (FreDN). Methodologically, FreDN introduces: (i) a learnable frequency-domain decomposition mechanism that directly separates trend and seasonal components in the Fourier domain; (ii) a real-imaginary shared-parameter ReIm Block that maps complex-valued operations to the real domain, drastically reducing parameter count and computational overhead; and (iii) a theoretically grounded frequency-domain loss function integrated with spectral leakage suppression for end-to-end optimization. Evaluated on seven long-horizon forecasting benchmarks, FreDN achieves approximately 10% improvement over state-of-the-art methods while reducing both parameter count and computational cost by over 50% compared to typical complex-valued networks.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Computational social science
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary time series, these methods encounter the $ extit{spectral entanglement}$ and the computational burden of complex-valued learning. The $ extit{spectral entanglement}$ refers to the overlap of trends, periodicities, and noise across the spectrum due to $ extit{spectral leakage}$ and the presence of non-stationarity. However, existing decompositions are not suited to resolving spectral entanglement. To address this, we propose the Frequency Decomposition Network (FreDN), which introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain. Furthermore, we propose a theoretically supported ReIm Block to reduce the complexity of complex-valued operations while maintaining performance. We also re-examine the frequency-domain loss function and provide new theoretical insights into its effectiveness. Extensive experiments on seven long-term forecasting benchmarks demonstrate that FreDN outperforms state-of-the-art methods by up to 10%. Furthermore, compared with standard complex-valued architectures, our real-imaginary shared-parameter design reduces the parameter count and computational cost by at least 50%.

Problem

• Spectral entanglement in non-stationary time series forecasting methods
• Computational burden of complex-valued learning in frequency analysis
• Ineffective frequency decomposition for trend and periodic component separation

Innovation

• Learnable frequency decomposition for spectral disentanglement
• ReIm Block reduces complex-valued operation complexity
• Real-imaginary shared-parameter design halves computational costs