DNN classifiers achieve excess risk O(n^{-α}) with α arbitrarily large under hard margin (q=∞) and distribution-adapted smoothness of the regression function, with matching minimax lower bounds for q≥2.
Optimal learning of high-dimensional classification problems using deep neural networks.arXiv preprint arXiv:2112.12555
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Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition
DNN classifiers achieve excess risk O(n^{-α}) with α arbitrarily large under hard margin (q=∞) and distribution-adapted smoothness of the regression function, with matching minimax lower bounds for q≥2.