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

Angela Kunoth (), Mathias Oster () and Reinhold Schneider ()
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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

A chapter in Multiscale, Nonlinear and Adaptive Approximation II, 2024, pp 383-403 from Springer

Abstract: 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.

Date: 2024
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DOI: 10.1007/978-3-031-75802-7_17

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