Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent
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 ...
| Authors | Junyu Zhou, Puyu Wang, Dennis Wagner et al. |
|---|---|
| Primary category | stat.ML |
| Published | 4 June 2026 |
| Last updated at source | 29 July 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.