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Control on the Manifolds of Mappings with a View to the Deep Learning
- Publication Year :
- 2020
-
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.<br />Comment: 25 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2008.12702
- Document Type :
- Working Paper