Controllability of Continuous Networks and a Kernel-Based Learning Approximation

Michael Herty (), Chiara Segala () and Giuseppe Visconti ()
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Michael Herty: IGPM, RWTH Aachen University
Chiara Segala: Universit`a della Svizzera italiana—USI
Giuseppe Visconti: Department of Mathematics “G. Castelnuovo”, Sapienza University of Rome

Chapter Chapter 6 in Model Predictive Control, 2025, pp 135-155 from Springer

Abstract: Abstract Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field description allows also the recast of the training processes as a controllability problem for the solution to the mean-field dynamics. We show theoretical results on the controllability of the linear microscopic and mean-field dynamics through the Hilbert Uniqueness Method and propose a computational approach based on kernel learning methods to solve numerically, and efficiently, the training problem. Further aspects of the structural properties of the mean-field equation will be reviewed.

Keywords: Neural networks; Mean-field limit; Controllability; Kernel methods (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-031-85256-5_6

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DOI: 10.1007/978-3-031-85256-5_6

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