Control on the Manifolds of Mappings with a View to the Deep Learning
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AbstractDeep 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.
2021 ◽
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1995 ◽
Vol 09
(10)
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pp. 1159-1169
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2021 ◽
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