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2020

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

Agrachev, Andrei, Sarychev, Andrey

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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.

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A. Agrachev and R. Gamkrelidze
1979
Earlier work this paper cites.
M. Ganesh, I.G. Graham and J. Sivaloganathan
1994
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A. Agrachev and Yu. Sachkov
2004
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V.I. Arnold
2004
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