Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descent

TL;DR

This paper analyzes how quickly over-parametrized convolutional neural networks trained with gradient descent converge in terms of misclassification risk, providing theoretical bounds on their learning rate.

Contribution

It introduces a theoretical bound on the convergence rate of over-parametrized CNNs trained by gradient descent for image classification.

Findings

Derived a bound on the convergence rate of the misclassification risk

Provides insights into the learning dynamics of over-parametrized CNNs

Enhances understanding of training efficiency for CNN classifiers

Abstract

Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the difference between the misclassification risk of the newly introduced convolutional neural network estimate and the minimal possible value is derived.