Abstract:
In this talk we provide an introduction to reservoir computing and present our recent results on its mathematical foundations. Motivated by their performance in applications -- ranging from realized volatility forecasting to chaotic dynamical systems -- we study approximation and learning based on random recurrent neural networks and more general reservoir computing systems.
We provide approximation and generalization error bounds for a novel class of infinite-dimensional reservoir systems. These are closely related to the random features method, which we will also discuss and illustrate by an application on learning exponential Lévy models.
The talk is based on joint works with Lyudmila Grigoryeva and Juan-Pablo Ortega.