Convergence Guarantees of Gradient Descent for Neural Networks via Generalized Lipschitz Smoothness
We establish the first convergence guarantees of gradient descent for general feedforward neural networks of any width or depth, with any initialization or dataset. We only assume that the activation functions are linearly bounded, Lipschitz continuous, and Lipschitz smooth---properties that hold for linear, tanh, softplus, sigmoid, and smoothed ReLU functions---and that the loss function is Lipschitz smooth in the model outputs, a mild condition satisfied by mean squared error and binary cross-entropy loss. By relating the Lipschitz properties of one layer to the next, we obtain a novel generalized Lipschitz smoothness condition for an $L$-layer neural network where the change in gradien...
| Authors | Siqiao Mu, Diego Klabjan |
|---|---|
| Primary category | cs.LG |
| Published | 11 August 2026 |
| Last updated at source | 25 September 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 Information may be incomplete or out of date.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.