Fractional-Order Deep Backpropagation Neural Network

In recent years, the research of artificial neural networks based on fractional calculus has attracted much attention. In this paper, we proposed a fractional-order deep backpropagation (BP) neural network model with L₂ regularization. The proposed network was optimized by the fractional gradient descent method with Caputo derivative. We also illustrated the necessary conditions for the convergence of the proposed network. The influence of L₂ regularization on the convergence was analyzed with the fractional-order variational method. The experiments have been performed on the MNIST dataset to demonstrate that the proposed network was deterministically convergent and can effectively avoid overfitting.