Mathematics (Apr 2023)
Fractional Stochastic Search Algorithms: Modelling Complex Systems via AI
Abstract
The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {BtH,t≥0} with the Hurst parameter H∈(0,1). We define and discuss the properties of fractional stochastic processes, {BtH,t≥0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.
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