Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with cross-scale attention mechanisms for enhanced multi-variate time series prediction. Our approach comprises: (1) an Adaptive Wavelet Decomposition Module (AWDM) that dynamically selects optimal wavelet bases and decomposition levels based on signal characteristics; (2) a Cross-Scale Feature Fusion (CSFF) mechanism that captures interactions between different frequency bands through learnable coupling matrices; (3) a Frequency-Aware Multi-Head Attention (FAMA) module that weights attention heads according to their frequency selectivity; (4) a Hierarchical Prediction Network (HPN) that generates forecasts at multiple resolutions before reconstruction. Extensive experiments on benchmark datasets demonstrate that AWGformer achieves significant average improvements over state-of-the-art methods, with particular effectiveness on multi-scale and non-stationary time series. Theoretical analysis provides convergence guarantees and establishes the connection between our wavelet-guided attention and classical signal processing principles.

翻译：时间序列预测需要在保持计算效率的同时捕捉多个时间尺度上的模式。本文提出AWGformer，一种将自适应小波分解与跨尺度注意力机制相结合的新型架构，以增强多元时间序列预测能力。我们的方法包含：(1) 自适应小波分解模块（AWDM），可根据信号特征动态选择最优小波基与分解层级；(2) 跨尺度特征融合（CSFF）机制，通过可学习的耦合矩阵捕捉不同频带间的交互作用；(3) 频率感知多头注意力（FAMA）模块，依据注意力头的频率选择性进行加权；(4) 分层预测网络（HPN），在重构前生成多分辨率预测结果。在基准数据集上的大量实验表明，AWGformer相较于现有最优方法取得了显著的平均性能提升，在多尺度与非平稳时间序列上表现尤为突出。理论分析提供了收敛性保证，并建立了我们的小波引导注意力机制与经典信号处理原理之间的理论联系。