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Towards Continuous Mathematical Models for the Analysis of Classes of Deep Neural Networks

In: Multiscale, Nonlinear and Adaptive Approximation II

Author

Listed:
  • Angela Kunoth

    (University of Cologne, Department of Mathematics and Computer Science, Division of Mathematics)

  • Mathias Oster

    (IGPM, RWTH Aachen)

  • Reinhold Schneider

    (TU Berlin, Department of Mathematics)

Abstract

Our goal is to develop and formulate continuous mathematical models for the analysis of deep neural networks, in order to a) provide a convergence analysis, b) conduct an optimization analysis with respect to the optimal choice and computation of parameters, c) study the role of overparametrization. The tools used here are control theory, Hamilton-Jacobi-Bellman equations, Barron functions as well as different optimization algorithms.

Suggested Citation

  • Angela Kunoth & Mathias Oster & Reinhold Schneider, 2024. "Towards Continuous Mathematical Models for the Analysis of Classes of Deep Neural Networks," Springer Books, in: Ronald DeVore & Angela Kunoth (ed.), Multiscale, Nonlinear and Adaptive Approximation II, pages 383-403, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-75802-7_17
    DOI: 10.1007/978-3-031-75802-7_17
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