  In this paper, we perform Lyapunov based analysis of the loss function to
derive an a priori upper bound on the settling time of deep neural networks.
While previous studies have attempted to understand deep learning using control
theory framework, there is limited work on a priori finite time convergence
analysis. Drawing from the advances in analysis of finite-time control of
non-linear systems, we provide a priori guarantees of finite-time convergence
in a deterministic control theoretic setting. We formulate the supervised
learning framework as a control problem where weights of the network are
control inputs and learning translates into a tracking problem. An analytical
formula for finite-time upper bound on settling time is computed a priori under
the assumptions of boundedness of input. Finally, we prove the robustness and
sensitivity of the loss function against input perturbations.
