Momentum in large-batch training: Polyak enlarges the critical batch size, Nesterov improves data efficiency
We study when and how momentum improves large-batch training in the one-pass regime, using power-law kernel regression as a tractable setting. We first characterize risk stability through the critical learning rate, defined as the largest learning rate for stable training, and obtain $η_{\mathrm{SGD}}^{\mathrm{crit}}\eqsim 1$, $η_{\mathrm{Polyak}}^{\mathrm{crit}}\eqsim \min\{1,B(1-ρ)\}$, and $η_{\mathrm{Nesterov}}^{\mathrm{crit}}\eqsim \min\{1,B^β(1-ρ)\}$, where $B$ is the batch size, $ρ$ is the momentum factor, and $β>1$ is the capacity exponent. Within this admissible region, we derive scaling laws for the full risk dynamics, capturing the progression from an early transient, through po...
| Authors | Jia-Nan Wang, Zixun Huang, Kairui Li et al. |
|---|---|
| Primary category | stat.ML |
| Published | 2 September 2026 |
| Last updated at source | 2 September 2026 |
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