The mathematical foundations of deep learning remain, in many respects, an open frontier. This talk explores a rigorous bridge between two apparently distant worlds: the theory of Mean Field Games (MFG) and Mean Field Control (MFC) on one side, and modern machine learning on the other. We begin with a self-contained introduction to Stochastic Optimal Control, MFG, and MFC frameworks. The second part of the talk examines how machine learning methods, such as neural PDEs, deep BSDEs, and actor-critic algorithms, can be deployed to solve high-dimensional mean field problems that are intractable by classical methods. The third and central part reverses the perspective: we argue that MFG and MFC provide a principled mathematical language for interpreting deep learning itself.
By interpreting deep learning architectures (like ResNets) as dynamical systems and framing training as a Mean Field Optimal Control problem, we can rigorously explain feature representation flows and long-time dynamics. Finally, this framework is extended to generative modeling, such as diffusion models, and to multi-agent systems.
Dr. Matteo Garbelli is currently a Postdoc Researcher at MOX Laboratory in the Department of Mathematics of the Politecnico di Milano. His primary research interests include Mean Field Games, McKean-Vlasov Stochastic Differential Equations, and Reinforcement Learning solvers. He holds a Ph.D. in Mathematics from the University of Trento. Previously, he served as a Postdoc at the University of Verona, focusing on Machine Learning approaches to Stochastic Optimization. Alongside his academic research, he collaborates extensively with industry, providing mathematical consulting to AI startups and US-based tech companies focusing on AI, LLMs, and decision-making systems under uncertainty.
Target Group: Researchers
