PowerStep: Memory-Efficient Adaptive Optimization via $\ell_p$-Norm Steepest Descent
Adaptive optimizers such as Adam are standard for training Transformers, but storing gradient first and second moments incurs substantial memory overhead. We introduce PowerStep, a memory-efficient optimizer that achieves coordinate-wise adaptivity without storing second-moment statistics. Motivated by $\ell_p$-norm steepest descent, PowerStep applies a signed-power transform directly to one momentum buffer. We establish a finite-horizon stationarity bound for exact, unregularized updates, with an $O(1/\sqrt{T})$ term and a noise-dependent residual. Experiments on Transformers from 124M to 235B parameters show competitive validation quality while halving $\texttt{fp32}$ optimizer-state me...
| Authors | Yao Lu, Dengdong Fan, Shixun Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 29 September 2026 |
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