提出FreDN模型,用可学习频域分解解决时间序列的频谱混叠问题。
FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition

- 在频域直接学习分解趋势与周期成分,解决非平稳序列的频谱混叠
- 在7个长时序预测基准上性能领先现有方法最高10%
- 设计实虚共享参数结构,降低50%以上参数量与计算开销
时间序列预测在众多实际应用中至关重要。近年来,频域方法因其捕捉全局依赖的能力受到关注。然而,在处理非平稳序列时,这些方法面临频谱混叠和复数运算带来的计算负担。频谱混叠源于频谱泄漏及非平稳性导致的趋势、周期性和噪声在频谱上的重叠。现有分解方法难以有效化解此问题。为此,我们提出频率分解网络(FreDN),引入可学习的频域解缠模块,直接在频域分离趋势与周期成分。此外,我们提出理论支持的ReIm Block,降低复数运算复杂度的同时保持性能。我们还重新审视了频域损失函数,并提供了其有效性新的理论解释。在七个长期预测基准上的大量实验表明,FreDN相比现有最优方法提升最高达10%。相较于标准复数架构,我们的实虚共享参数设计使参数量和计算成本至少降低50%。
原文摘要 · Abstract (English)
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 $\textit{spectral entanglement}$ and the computational burden of complex-valued learning. The $\textit{spectral entanglement}$ refers to the overlap of trends, periodicities, and noise across the spectrum due to $\textit{spectral leakage}$ 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\%.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。