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<p>Image classification from independent and identically distributed random variables is considered. Image classifiers are defined which are based on a linear combination of deep convolutional networks with a max-pooling layer. Here all the weights are learned by stochastic gradient descent. A general result is presented which shows that the image classifiers are able to approximate the best possible deep convolutional network. In case that the a posteriori probability satisfies a suitable hierarchical composition model, it is shown that the corresponding deep convolutional neural network image classifier achieves a rate of convergence which is independent of the dimensions of the images.</p>

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Learning of deep convolutional network image classifiers via stochastic gradient descent and over-parametrization

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Michael Kohler,
  • Adam Krzyżak,
  • Alisha Sänger

摘要

Image classification from independent and identically distributed random variables is considered. Image classifiers are defined which are based on a linear combination of deep convolutional networks with a max-pooling layer. Here all the weights are learned by stochastic gradient descent. A general result is presented which shows that the image classifiers are able to approximate the best possible deep convolutional network. In case that the a posteriori probability satisfies a suitable hierarchical composition model, it is shown that the corresponding deep convolutional neural network image classifier achieves a rate of convergence which is independent of the dimensions of the images.