Abstract: A neural network admits some parameters (weights and biases), which we can summarize as a vector θ ∈ RP , and implements a function fθ : Rd → RN, depending on θ. The question of identifiability is the following: is θ uniquely determined by fθ? If so, how many observations fθ(xi) of fθ on input samples xi ∈ Rd are needed to characterize θ without ambiguity? After discussing the impact of identifiability in terms of privacy, of robustness to adversarial attacks and of intellectual property, I will present two identifiability results with respect to fully-connected feedforward ReLU neural networks.

Keywords: Deep Learning, Identifiability, ReLU, Parameter recovery, Privacy.