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.

翻译：确定基于进化神经网络的图像分类,分析估计值误分类风险与最佳误分类风险的趋同率。根据对异端概率的顺畅和结构的适当假设,显示与图像层面无关的趋同率。这证明在图像分类中,有可能避免进化神经网络对维度的诅咒。