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Controllability of Continuous Networks and a Kernel-Based Learning Approximation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Michael Herty & Chiara Segala & Giuseppe Visconti, 2025. "Controllability of Continuous Networks and a Kernel-Based Learning Approximation," Dynamic Modeling and Econometrics in Economics and Finance,, Springer.
    • Handle: RePEc:spr:dymchp:978-3-031-85256-5_6
    DOI: 10.1007/978-3-031-85256-5_6
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