Power Series Expansion Neural Network

TL;DR

This paper introduces a novel neural network architecture based on power series expansion, enhancing approximation accuracy by embedding PSE into the network structure, offering better representation without increasing computational cost.

Contribution

The paper presents a new neural network family that embeds power series expansion, improving approximation accuracy while maintaining computational efficiency compared to traditional networks.

Findings

Achieves better approximation accuracy than existing neural networks.

Theoretical analysis confirms the advantages of the power series expansion neural network.

Numerical experiments demonstrate improved performance in practical tasks.

Abstract

In this paper, we develop a new neural network family based on power series expansion, which is proved to achieve a better approximation accuracy in comparison with existing neural networks. This new set of neural networks embeds the power series expansion (PSE) into the neural network structure. Then it can improve the representation ability while preserving comparable computational cost by increasing the degree of PSE instead of increasing the depth or width. Both theoretical approximation and numerical results show the advantages of this new neural network.