Control on the Manifolds of Mappings with a View to the Deep Learning

Andrei Agrachev; Andrey Sarychev

Control on the Manifolds of Mappings with a View to the Deep Learning

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arxiv 2008.12702 v2 pith:M335HHJR submitted 2020-08-28 math.OC cs.LG

Andrei Agrachev , Andrey Sarychev This is my paper · ORCID

classification math.OCcs.LG

keywords controldeepinput-outputlearningnetworkneuralsystemtime

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Deep learning of the Artificial Neural Networks (ANN) can be treated as a particular class of interpolation problems. The goal is to find a neural network whose input-output map approximates well the desired map on a finite or an infinite training set. Our idea consists of taking as an approximant the input-output map, which arises from a nonlinear continuous-time control system. In the limit such control system can be seen as a network with a continuum of layers, each one labelled by the time variable. The values of the controls at each instant of time are the parameters of the layer.

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