Convergence Analysis and Application for Multi‐Layer Neural Network Based on Fractional‐Order Gradient Descent Learning

Author:

Zhao Shuai1,Fan Qinwei12ORCID,Dong Qingmei1

Affiliation:

1. School of Science Xi'an Polytechnic University Xi'an 710048 China

2. School of Mathematics and Information Science Guangzhou University Guangzhou 510006 China

Abstract

AbstractFractional order calculus, with its inheritance and infinite memory properties, is a promising research area in information processing and modeling of certain physical systems, system identification, and control. In this paper, a fractional‐order gradient descent method is proposed for backpropagation training of multilayer feedforward neural networks. In particular, the Caputo derivative is used to define the measurement function and consider the smooth regular term. In addition, the monotonicity of the error function and the strong (weak) convergence theorem of the algorithm are rigorously proved. Finally, numerical experiments prove the correctness and effectiveness of the algorithm theory.

Publisher

Wiley

Subject

Multidisciplinary,Modeling and Simulation,Numerical Analysis,Statistics and Probability

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