Optimal Approximation and Learning Rates for Deep Convolutional Neural Networks
This work provides theoretical guarantees for deep convolutional neural networks, which is foundational for machine learning practitioners and researchers, though it is incremental as it builds on existing approximation theory.
The paper tackles the problem of analyzing approximation and learning rates for deep convolutional neural networks with zero-padding and max-pooling, proving optimal approximation rates of order $(L^2/\log L)^{-2r/d}$ for $r$-smooth functions and deducing almost optimal learning rates for empirical risk minimization.
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.