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

arXiv: https://arxiv.org/abs/2405.07619 · HTML: https://mlsanity.com/paper/2405.07619/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 18 of 18)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks](https://mlsanity.com/paper/1810.02281/) (2018)
- [On the Power of Over-parametrization in Neural Networks with Quadratic Activation](https://mlsanity.com/paper/1803.01206/) (2018)
- [Does data interpolation contradict statistical optimality?](https://mlsanity.com/paper/1806.09471/) (2018)
- [Stochastic Particle Gradient Descent for Infinite Ensembles](https://mlsanity.com/paper/1712.05438/) (2017)
- [Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima](https://mlsanity.com/paper/1712.00779/) (2017)
- [Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes](https://mlsanity.com/paper/1908.02419/) (2019)
- [Adding One Neuron Can Eliminate All Bad Local Minima](https://mlsanity.com/paper/1805.08671/) (2018)
- [On the Neural Tangent Kernel of Deep Networks with Orthogonal Initialization](https://mlsanity.com/paper/2004.05867/) (2020)
- [Generalization Error Bounds for Deep Neural Networks Trained by SGD](https://mlsanity.com/paper/2206.03299/) (2022)
- [On the rate of convergence of image classifiers based on convolutional neural networks](https://mlsanity.com/paper/2003.01526/) (2020)
- [The Rate of Convergence of Variation-Constrained Deep Neural Networks](https://mlsanity.com/paper/2106.12068/) (2021)
- [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)

## Abstract (arXiv)

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.