# Analysis of convolutional neural network image classifiers in a hierarchical max-pooling model with additional local pooling

arXiv: https://arxiv.org/abs/2106.05233 · HTML: https://mlsanity.com/paper/2106.05233/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 16 of 16)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [The phase diagram of approximation rates for deep neural networks](https://mlsanity.com/paper/1906.09477/) (2019)
- [Deep Neural Networks Learn Non-Smooth Functions Effectively](https://mlsanity.com/paper/1802.04474/) (2018)
- [Fast convergence rates of deep neural networks for classification](https://mlsanity.com/paper/1812.03599/) (2018)
- [Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov space](https://mlsanity.com/paper/1910.12799/) (2019)
- [Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks](https://mlsanity.com/paper/1903.10047/) (2019)
- [Generalization Bounds for Convolutional Neural Networks](https://mlsanity.com/paper/1910.01487/) (2019)
- [A comparison of deep networks with ReLU activation function and linear spline-type methods](https://mlsanity.com/paper/1804.02253/) (2018)
- [On the rate of convergence of fully connected very deep neural network regression estimates](https://mlsanity.com/paper/1908.11133/) (2019)
- [Sharp Rate of Convergence for Deep Neural Network Classifiers under the Teacher-Student Setting](https://mlsanity.com/paper/2001.06892/) (2020)
- [On the rate of convergence of image classifiers based on convolutional neural networks](https://mlsanity.com/paper/2003.01526/) (2020)

## Built on by (most cited first, 2 of 2)

- [Analysis of convolutional neural network image classifiers in a rotationally symmetric model](https://mlsanity.com/paper/2205.05500/) (2022)
- [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 classification is considered, and a hierarchical max-pooling model with additional local pooling is introduced. Here the additional local pooling enables the hierachical model to combine parts of the image which have a variable relative distance towards each other. Various convolutional neural network image classifiers are introduced and compared in view of their rate of convergence. The finite sample size performance of the estimates is analyzed by applying them to simulated and real data.