In this talk, I will introduce mean field control and discuss its applications in modern machine learning. I will first describe how numerical algorithms for mean field control can be developed by combining propagation of chaos with machine learning techniques, together with theoretical guarantees for these methods. I will then present two complementary applications. The first is computational, concerning the use of mean field control in generative AI. The second is theoretical, concerning a mathematical framework for understanding implicit regularization in the training of overparameterized neural networks.
This talk is based on the joint works with Beatrice Acciaio, Jakob Heiss, Jin Ma, Gudmund Pammer, H. Mete Soner, Ying Tan, Josef Teichmann and Renyuan Xu.