Abstract: It is by now well-known that practical deep supervised learning may roughly be cast as an optimal control problem for a specific discrete-time, nonlinear dynamical system called an artificial neural network. In this talk, we consider the continuous-time formulation of the deep supervised learning problem, and give an overview of the key challenges.
We will mainly concentrate on presenting this problem's behavior when the final time horizon is increased. a fact that can be interpreted as increasing the number of layers in the neural network setting. We show qualitative and quantitative estimates of the convergence to zero training error depending on the functional to be minimized.
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