A metric functional analysis and applications in deep learning

Abstract: There are metric space analogs of duality and spectral theory, two pillars of functional analysis. The metric methods have many applications, such as in complex analysis, group theory, surface topology, and dynamical systems. Notably it allows an ergodic theorem for the composition of randomly selected non-commuting transformations (joint works with Ledrappier and Gouëzel). The remarkable success of deep learning indicates that real-life data tend to have a compositional structure of a non-linear, non-commutative character. With Benny Avelin we apply the metric and ergodic methods for deep neural networks. In particular we observe a threshold phenomenon in the depth.

Contact Antti Perälä to receive the Zoom link.