A Deep Learning Optimizer Based on Grünwald–Letnikov Fractional Order Definition

In this paper, a deep learning optimization algorithm is proposed, which based on the Grünwald–Letnikov (G-L) fractional order definition. An optimizer calculus gradient descent G-L definition (FCGD_G-L) designed. Using short-memory effect of definition, derivation only needs 10 time steps. At same time, via transforming formula Gamma function eliminated. Thereby, it can achieve unification and integer in FCGD_G-L. To prevent parameters falling into local optimum, small disturbance added unfolding process. According to stochastic (SGD) Adam, two optimizers’ (FCSGD_G-L), Adam (FCAdam_G-L), are obtained. These optimizers validated series prediction tasks. With analysis train loss, related experiments show that FCGD_G-L has faster convergence speed better accuracy than conventional optimizer. Because property, exhibits stronger robustness generalization ability. Through test sets, using saved optimal model evaluate, also shows evaluation