In various machine learning applications, dynamical systems naturally appear as both the target system as well as the model. In this talk, we discuss how principles from dynamical systems enter learning considerations and explanations. We begin by reviewing essentials from dynamical systems theory and build towards synchronization phenomena in non-autonomous systems. Notions such as echo states, state forgetting, and fading memory will be rigorously linked. Reservoir computers will accompany us as an important class of examples. Finally, we will discuss extensions to the setting of learning distributions of stochastic processes instead of deterministic dynamics.

Florian Rossmannek received his PhD degree in mathematics in 2023 from ETH Zurich, Switzerland. Since 2025, he has been a Nanyang Assistant Professor at NTU Singapore, where he previously held an Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship. During his doctoral studies, he was a member of the RiskLab, Switzerland. His research focuses on the mathematical theory underpinning machine learning, with a focus on dynamics.