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arXiv · 2008.12702

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

Andrei Agrachev·Andrey Sarychev
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Abstract

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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Andrei Agrachev, Andrey Sarychev. 2021-03-01. Control on the Manifolds of Mappings with a View to the Deep Learning. https://arxiv.org/abs/2008.12702

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