Abstract:

Deep learning has the dubious reputation of being the modern day Alchemy. Needless to say, there are several "Theories of deep learning" in literature, each proposing to explain some of its features. The dynamical systems perspective is particularly promising. In this talk, I will review the Koopman operator perspective of dynamical systems and demonstrate how most deep-learning models are learning the Koopman operator of a fictional dynamical system after all. This perspective allows DL models to be amenable to analysis and subsequently may explain their impressive performance in learning large-input-dimensional functions, solving high dimensional PDEs, etc.