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

arXiv: https://arxiv.org/abs/2008.12702 · HTML: https://mlsanity.com/paper/2008.12702/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [The Sherpa.ai Blind Vertical Federated Learning Paradigm to Minimize the Number of Communications](https://mlsanity.com/paper/2510.17901/) (2025)

## Abstract (arXiv)

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.