# Analysis of convolutional neural network image classifiers in a rotationally symmetric model

arXiv: https://arxiv.org/abs/2205.05500 · HTML: https://mlsanity.com/paper/2205.05500/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [Rotation-invariant convolutional neural networks for galaxy morphology prediction](https://mlsanity.com/paper/1503.07077/) (2015)
- [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)
- [Equivalence of approximation by convolutional neural networks and fully-connected networks](https://mlsanity.com/paper/1809.00973/) (2018)
- [Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks](https://mlsanity.com/paper/2109.02832/) (2021)
- [Learning rotation invariant convolutional filters for texture classification](https://mlsanity.com/paper/1604.06720/) (2016)
- [Generalization Bounds for Convolutional Neural Networks](https://mlsanity.com/paper/1910.01487/) (2019)
- [Convergence rates of deep ReLU networks for multiclass classification](https://mlsanity.com/paper/2108.00969/) (2021)
- [On the rate of convergence of fully connected very deep neural network regression estimates](https://mlsanity.com/paper/1908.11133/) (2019)
- [Deep-HiTS: Rotation Invariant Convolutional Neural Network for Transient Detection](https://mlsanity.com/paper/1701.00458/) (2017)
- [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)
- [Flip-Rotate-Pooling Convolution and Split Dropout on Convolution Neural Networks for Image Classification](https://mlsanity.com/paper/1507.08754/) (2015)
- [Analysis of convolutional neural network image classifiers in a hierarchical max-pooling model with additional local pooling](https://mlsanity.com/paper/2106.05233/) (2021)

## Built on by (most cited first, 4 of 4)

- [Learning Sparse Compositional Functions with Norm-Constrained Neural Networks](https://mlsanity.com/paper/2605.25608/) (2026)
- [On the VC dimension of deep group convolutional neural networks](https://mlsanity.com/paper/2410.15800/) (2024)
- [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)
- [Press Start to Charge: Videogaming the Online Centralized Charging Scheduling Problem](https://mlsanity.com/paper/2601.12543/) (2026)

## Abstract (arXiv)

Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Here we consider images as random variables with values in some functional space, where we only observe discrete samples as function values on some finite grid. Under suitable structural and smoothness assumptions on the functional a posteriori probability, which includes some kind of symmetry against rotation of subparts of the input image, it is shown that least squares plug-in classifiers based on convolutional neural networks are able to circumvent the curse of dimensionality in binary image classification if we neglect a resolution-dependent error term. The finite sample size behavior of the classifier is analyzed by applying it to simulated and real data.