A Caputo-Type Fractional-Order Gradient Descent Learning of Deep BP Neural Networks

In recent years, There is a promising area about the Artificial neural networks by using fractional calculus. In this paper, we combine the Caputo operator of the fractional calculas and the conventional gradient descent method to optimize the deep backpropagation neural network and have proved the monotonicity and weak convergence for the presented network in detail. We do some simulations to compare the differences of the performance between presented fractional-order deep BP neural networks and Integer-order BP neural networks by using a large dataset.