On the rate of convergence of image classifiers based on convolutional neural networks

TL;DR

This paper analyzes how quickly convolutional neural network-based image classifiers approach optimal accuracy, demonstrating they can overcome the curse of dimensionality under certain conditions.

Contribution

It provides a theoretical rate of convergence for CNN classifiers' misclassification risk, showing independence from image dimension under specific assumptions.

Findings

Convolutional neural networks can achieve dimension-independent convergence rates.

The rate of convergence depends on smoothness and structure assumptions.

CNNs can circumvent the curse of dimensionality in image classification.

Abstract

Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of the aposteriori probability a rate of convergence is shown which is independent of the dimension of the image. This proves that in image classification it is possible to circumvent the curse of dimensionality by convolutional neural networks.