On the Convergence Results for Gradient Descent Systems

This paper aims to advance the theoretical understanding of gradient flow and gradient descent optimization methods by establishing rigorous convergence results for continuous‐time gradient flow equations and discrete gradient descent processes. The primary focus lies on developing a comprehensive mathematical framework to analyze the convergence behavior of gradient descent systems. Our results contribute to the theoretical understanding of gradient‐based optimization methods and offer new insights into the stability and efficiency of training algorithms in the context of artificial neural networks (ANNs).