From Optimal Control to Optimal Transport via Stochastic Neural Networks in the Mean Field Setting

In this paper, we derive a unified perspective for Optimal Transport (OT) and Mean Field Control (MFC) theories to analyse the learning process for Neural Network algorithms in a high- dimensional framework. We consider a Mean Field Neural Network in the context of MFC theory referring to the mean field formulation of OT theory that may allow the development of efficient algorithms in a high-dimensional framework while providing a powerful tool in the context of explainable Artificial Intelligence.