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

arXiv: https://arxiv.org/abs/2003.01526 · HTML: https://mlsanity.com/paper/2003.01526/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 7 of 7)

- [Convergence rates of deep ReLU networks for multiclass classification](https://mlsanity.com/paper/2108.00969/) (2021)
- [What Can Be Learnt With Wide Convolutional Neural Networks?](https://mlsanity.com/paper/2208.01003/) (2022)
- [Misclassification bounds for PAC-Bayesian sparse deep learning](https://mlsanity.com/paper/2405.01304/) (2024)
- [Analysis of convolutional neural network image classifiers in a rotationally symmetric model](https://mlsanity.com/paper/2205.05500/) (2022)
- [Analysis of convolutional neural network image classifiers in a hierarchical max-pooling model with additional local pooling](https://mlsanity.com/paper/2106.05233/) (2021)
- [Posterior Contraction for Sparse Neural Networks in Besov Spaces with Intrinsic Dimensionality](https://mlsanity.com/paper/2506.19144/) (2025)
- [Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descent](https://mlsanity.com/paper/2405.07619/) (2024)

## Abstract (arXiv)

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.