Chebyshev Feature Neural Network for Accurate Function Approximation
Machine Learning
2024-12-24 v2 Numerical Analysis
Neural and Evolutionary Computing
Numerical Analysis
Machine Learning
Abstract
We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as the first hidden layer, followed by the standard fully connected hidden layers. The learnable frequencies of the Chebyshev layer are initialized with exponential distributions to cover a wide range of frequencies. Combined with a multi-stage training strategy, we demonstrate that this CFNN structure can achieve machine accuracy during training. A comprehensive set of numerical examples for dimensions up to are provided to demonstrate the effectiveness and scalability of the method.
Cite
@article{arxiv.2409.19135,
title = {Chebyshev Feature Neural Network for Accurate Function Approximation},
author = {Zhongshu Xu and Yuan Chen and Dongbin Xiu},
journal= {arXiv preprint arXiv:2409.19135},
year = {2024}
}