Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent

תקציר מקורי באנגליתarXiv:2606.06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning. We establish quantitative bounds showing that kernel gradient descent in the reproducing kernel Hilbert space induced by the deterministic infinite-width neural tangent kernel approximates finite-width deep regression with smooth activations under gradient descent (GD) and stochastic gradient descent (SGD) training. The approximation gap is governed by the network width and training horizon, with an additional stochastic gradient error in the SGD case. This connection provides a general mechanism for transferring learning-theoretic