Identification Results in Neural Network Theory and Linear Operator Theory

Abstract

This thesis addresses two distinct problems in the theory of system identification by means of various novel techniques relying on complex analysis. Specifically, we study the analytic continuation of deep neural networks with meromorphic nonlinearities, leading to a full resolution of the question posed in (Fefferman, 1994) of neural network identifiability for the tanh nonlinearity, and use the theory of interpolation and sampling of entire functions to derive necessary and sufficient conditions for the identifiability of linear time-varying (LTV) systems characterized by a (possibly infinite) discrete set of delay-Doppler shifts.