On the Rate of Convergence of GD in Non-linear Neural Networks: An Adversarial Robustness Perspective
We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying assumptions, while GD successfully converges to an optimal robustness margin, effectively maximizing the distance between the decision boundary and the training points, this convergence occurs at a prohibitively slow rate, scaling strictly as $Θ(1/\ln(t))$. To the best of our knowledge, this establishes the first explicit lower bound on the convergence rate of the robustness margin in a non-linear model. Through empirical simulations, we further demonstrate that this inhe...
| Authors | Guy Smorodinsky, Sveta Gimpleson, Itay Safran |
|---|---|
| Primary category | cs.LG |
| Published | 2 March 2026 |
| Last updated at source | 8 October 2026 |
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