# Optimizing Basis Function Selection in Constructive Wavelet Neural Networks and Its Applications

arXiv: https://arxiv.org/abs/2507.09213 · HTML: https://mlsanity.com/paper/2507.09213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 12 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [Efficient Architecture Search for Continual Learning](https://mlsanity.com/paper/2006.04027/) (2020)
- [On Learning Over-parameterized Neural Networks: A Functional Approximation Perspective](https://mlsanity.com/paper/1905.10826/) (2019)
- [Semi-Supervised Learning for Multi-Label Cardiovascular Diseases Prediction:A Multi-Dataset Study](https://mlsanity.com/paper/2306.10494/) (2023)
- [Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution](https://mlsanity.com/paper/2412.08426/) (2024)
- [On The Expressivity of Recurrent Neural Cascades](https://mlsanity.com/paper/2312.09048/) (2023)

## Abstract (arXiv)

Wavelet neural network (WNN), which learns an unknown nonlinear mapping from the data, has been widely used in signal processing, and time-series analysis. However, challenges in constructing accurate wavelet bases and high computational costs limit their application. This study introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs. For the first time, we analyze the frequency of unknown nonlinear functions and select appropriate initial wavelets based on their primary frequency components by estimating the energy of the spatial frequency component. This leads to a novel constructive framework consisting of a frequency estimator and a wavelet-basis increase mechanism to prioritize high-energy bases, significantly improving computational efficiency. The theoretical foundation defines the necessary time-frequency range for high-dimensional wavelets at a given accuracy. The framework's versatility is demonstrated through four examples: estimating unknown static mappings from offline data, combining two offline datasets, identifying time-varying mappings from time-series data, and capturing nonlinear dependencies in real time-series data. These examples showcase the framework's broad applicability and practicality. All the code will be released at https://github.com/dshuangdd/CWNN.