A Minimal ReLU Classifier on Non-Linearly Separable Data: Convergence and Implicit Bias at and beyond the Edge of Stability
Gradient descent (GD) with large learning rates can successfully optimize neural networks even though classical smoothness-based learning rate conditions are violated. Yet theory for this regime largely covers linear models or linearly separable data. We analyze a minimal setting outside both regimes. Specifically, a two-neuron ReLU network trained with logistic loss on 1D non-linearly separable data. The objective is nonconvex and nonsmooth, and GD exhibits edge-of-stability (EoS) behavior. We identify an active cone in parameter space that contains every perfect classifier, where the problem becomes piecewise logistic regression with a varying effective dataset. Within this cone, we pro...
| Authors | Quan Nguyen, Robin Yadav, Param Mody et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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