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 for the Bag-of-Functions. 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 demonstrate the effectiveness of this approach: the informed initialization reduces reconstruction error by 15.1% on complex real-world benchmarks. Furthermore, the trend-informed dimensionality reduction yields up to a 30% decrease in model parameters and computational complexity, accelerating inference and stabilizing optimization without altering the core training procedure. • Data-driven spectral priors guide neural network initialization and depth selection. • Trend-informed initialization enables compact architectures without accuracy loss. • Informed priors stabilize optimization and accelerate convergence across datasets. • Improved efficiency achieved with reduced parameters and computational cost.
Torres et al. (Fri,) studied this question.