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

arXiv: https://arxiv.org/abs/2603.16376 · HTML: https://mlsanity.com/paper/2603.16376/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [Causal Recurrent Variational Autoencoder for Medical Time Series Generation](https://mlsanity.com/paper/2301.06574/) (2023)
- [Improved weight initialization for deep and narrow feedforward neural network](https://mlsanity.com/paper/2311.03733/) (2023)
- [On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks](https://mlsanity.com/paper/2303.17805/) (2023)
- [Principal Components for Neural Network Initialization](https://mlsanity.com/paper/2501.19114/) (2025)

## Abstract (arXiv)

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.