Momentum Further Constrains Sharpness at the Edge of Stochastic Stability
Recent work suggests that (stochastic) gradient descent self-organizes near an instability boundary, shaping both optimization and the solutions found. Momentum and mini-batch gradients are widely used in practical deep learning optimization, but it remains unclear whether they operate in a comparable regime of instability. We demonstrate that SGD with momentum exhibits an Edge of Stochastic Stability (EoSS)-like regime with batch-size-dependent behavior that cannot be explained by a single momentum-adjusted stability threshold. Batch Sharpness (the expected directional mini-batch curvature) stabilizes in two distinct regimes: at small batch sizes it converges to a lower plateau $2(1-β)/η...
| Authors | Arseniy Andreyev, Advikar Ananthkumar, Marc Walden et al. |
|---|---|
| Primary category | cs.LG |
| Published | 15 April 2026 |
| Last updated at source | 15 April 2026 |
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