Optimal Approximation and Learning Rates for Deep Convolutional Neural Networks

Shao-Bo Lin
8/7/2023
cs.LGmath.ST

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Abstract

This paper focuses on approximation and learning performance analysis for deep convolutional neural networks with zero-padding and max-pooling. We prove that, to approximate $r$-smooth function, the approximation rates of deep convolutional neural networks with depth $L$ are of order $ (L^2/\log L)^{-2r/d} $, which is optimal up to a logarithmic factor. Furthermore, we deduce almost optimal learning rates for implementing empirical risk minimization over deep convolutional neural networks.

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Cite this paper

@article{lin2023optimal,
  title  = {Optimal Approximation and Learning Rates for Deep Convolutional Neural Networks},
  author = {Shao-Bo Lin},
  year   = {2023},
  eprint = {2308.03259},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2308.03259v1}
}

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