On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent

Michael Kohler

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arXiv · 2504.03405

On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent

Michael Kohler

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Abstract

Nonparametric regression with random design is considered. The $L_2$ error with integration with respect to the design measure is used as the error criterion. An over-parametrized deep neural network regression estimate with logistic activation function is defined, where all weights are learned by gradient descent. It is shown that the estimate achieves a nearly optimal rate of convergence in case that the regression function is $(p,C)$--smooth.

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Michael Kohler. 2025-04-04. On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent. https://arxiv.org/abs/2504.03405

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