Prior-Informed Neural Network Initialization: A Spectral Approach for Function Parameterizing Architectures

Neural network architectures designed for function parameterization, such as the Bag-of-Functions (BoF) framework, bridge the gap between the expressivity of deep learning and the interpretability of classical signal processing. However, these models are inherently sensitive to parameter initialization, as traditional data-agnostic schemes fail to capture the structural properties of the target signals, often leading to suboptimal convergence. In this work, we propose a prior-informed design strategy that leverages the intrinsic spectral and temporal structure of the data to guide both network initialization and architectural configuration. A principled methodology is introduced that uses the Fast Fourier Transform to extract dominant seasonal priors, informing model depth and initial states, and a residual-based regression approach to parameterize trend components. Crucially, this structural alignment enables a substantial reduction in encoder dimensionality without compromising reconstruction fidelity. A supporting theoretical analysis provides guidance on trend estimation under finite-sample regimes. Extensive experiments on synthetic and real-world benchmarks demonstrate that embedding data-driven priors significantly accelerates convergence, reduces performance variability across trials, and improves computational efficiency. Overall, the proposed framework enables more compact and interpretable architectures while outperforming standard initialization baselines, without altering the core training procedure.