WEANet: Bridging wavelet inductive bias with network parameter initialization for time series modeling

Weight initialization plays a decisive role in the success of deep neural networks, yet existing strategies remain general-purpose and overlook the structural properties of time series. To address this gap, we introduce the Wavelet-Enhanced Adaptive Network (WEANet), a modular architecture that embeds wavelet-based inductive bias directly into its initial parameters. By initializing convolutional kernels with coefficients from multiple wavelet families, WEANet transforms convolutional layers into adaptive multi-resolution analyzers, uniting the interpretability of classical signal processing with the flexibility of deep learning. To preserve this structured initialization, we propose a dual-objective loss with a reconstruction term that regularizes training and safeguards the integrity of wavelet-induced representations. Extensive experiments on classification, forecasting, imputation, and anomaly detection demonstrate that WEANet consistently outperforms state-of-the-art baselines, achieving the best results on 24 of 30 UEA benchmark datasets and delivering up to 5% lower error in long-term forecasting. We further show its effectiveness as a plug-and-play tokenizer for Transformer backbones and validate each component through in-depth ablation studies. Our findings highlight wavelet-guided initialization as a general paradigm for principled, domain-aware deep time series modeling.