Convergence Analysis of Interval Feedforward Neural Networks

Abstract

In practical application of neural networks, we often try to change some factors to make the algorithm perform better, but the convergence analysis of the algorithm cannot keep up with it in time. This paper studies the convergence of interval feedforward neural network (IFNN). First the convergence of the IFNN is derived theoretically based on gradient descent algorithm, where the IFNN possesses the interval input and output but the point weights; Then, by means of numerical analysis, the relationship between the convergence of general IFNN and interval weights is discussed. In the numerical analysis, the coverage of interval output is taken as the objective function, and the particle swarm optimization (PSO) algorithm is used for optimizing to ensure the interval network output approaching the interval width range of the weight and threshold of the point output. Studying the convergence of interval neural networks (INNs) can effectively promote the application range of INNs, making INNs better used in uncertain systems, reducing the impact of fluctuations, noise and measurement errors, and improving the objectivity and robustness of industrial process modeling.