Scaling Laws of SignSGD in Linear Regression: When Does It Outperform SGD?
We study scaling laws of signSGD under a power-law random features (PLRF) model that accounts for both feature and target decay. We analyze the population risk of a linear model trained with one-pass signSGD on Gaussian-sketched features. We express the risk as a function of model size, training steps, learning rate, and the feature and target decay parameters. Comparing against the SGD risk analyzed by Paquette et al. (2024), we identify a drift-normalization effect and a noise-reshaping effect unique to signSGD. We then obtain compute-optimal scaling laws under the optimal choice of learning rate. Our analysis shows that the noise-reshaping effect can make the compute-optimal slope of s...
| Authors | Jihwan Kim, Dogyoon Song, Chulhee Yun |
|---|---|
| Primary category | cs.LG |
| Published | 2 March 2026 |
| Last updated at source | 20 September 2026 |
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