Optimal Approximation and Learning Rates for Deep Convolutional Neural Networks

08/07/2023

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by   Shao-Bo Lin, et al.

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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.