MATH+ research project with Benjamin Gess and Peter K. Friz

Large-scale learning systems are built from many interacting components: data points, particles, parameters or agents. Their collective behaviour may be approximated by deterministic continuum equations, but fluctuations around those limits can remain decisive for stability, exploration and rare transitions. This project studies the mathematical passage from interacting agents to effective descriptions of large-scale machine-learning dynamics.

The project brings together stochastic analysis, interacting particle systems, mean-field and scaling limits, and stochastic control. It asks how microscopic randomness produces macroscopic learning behaviour, which fluctuation corrections survive at intermediate scales, and how control mechanisms can act consistently across these levels.

Scientific programme

1. Fluctuations across scales: identify how randomness propagates from interacting-agent models to continuum and effective learning dynamics.
2. Control and learning: relate agent-level and continuum control and study the role of noise in stability, exploration and rare transitions.
3. Structure-preserving models: develop effective descriptions that retain the relevant probabilistic and geometric structure of large learning systems.

The project connects the group’s work on fluctuating hydrodynamics and stochastic dynamics with its research on machine learning and sampling.

Project facts

Programme	MATH+ Berlin Mathematics Research Center — Cluster of Excellence under Germany’s Excellence Strategy
Project title	Fluctuations and Control: From Agents to Large Scale Machine Learning
Period	From 2026
Project leads	Benjamin Gess and Peter K. Friz

Funded SAiS member

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