A novel gradient descent optimizer based on fractional order scheduler and its application in deep neural networks

Abstract

To improve convergence speed of deep neural network trained by gradient descent methods (GDMs), this paper proposed a novel fractional order gradient descent optimizer (FOAdam) based on Caputo operator and Adam algorithm, and analyzed the impact of fractional order on convergence performance using optimization theory and simulation. Furthermore, to address the trade-off between convergence speed and precision under fixed-order conditions, a fractional order scheduler (FOS) was designed based on the Connections Cloud Model (CCM). Numerical experiments conducted on MNIST and CIFAR-10 datasets showed that FOS-FOAdam outperformed other mainstream GDMs in terms of convergence speed and precision. Finally, FOS-FOAdam was applied in recognizing and classifying image datasets of cuttings and cores at the logging site, demonstrating good prospects for practical engineering applications.