Our paper Deep Learning via Dynamical Systems: An Approximation Perspective has been accepted at the Journal of the European Mathematical Society (JEMS).

In this paper, we set up the mathematical foundations of the approximation theory of deep learning idealized as continuous dynamical systems. Our main result is a set of general sufficient conditions on the flow field that implies the universal approximation of such networks. This is a first step towards uncovering the power of composition (which in continuous-time is just dynamics) on approximation of functions.