Flatland: The Adventures of Gradient Descent with Large Step Sizes
The training of neural networks often entails objective functions that are not globally $L$-smooth. For these functions, it is both theoretically and practically difficult to reply to the question: what is the largest possible step size that ensures the convergence of gradient descent (GD)? We address this longstanding open question in deep learning by providing a unifying definition of "large" step sizes that requires only local Lipschitz (or even Hölder) continuity of the gradient. We design first-order adaptive methods that provably yield large step sizes and show that they operate at the edge of stability (EoS) right from the start of the training. In particular, the loss decreases no...
| Authors | Leonardo Galli, Curtis Fox, Wiebke Bartolomaeus et al. |
|---|---|
| Primary category | cs.LG |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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