Scaling Laws of SignSGD in Linear Regression: When Does It Outperform SGD?

• URL: http://arxiv.org/abs/2603.02069v1
• Date: Mon, 02 Mar 2026 16:58:02 GMT
• Title: Scaling Laws of SignSGD in Linear Regression: When Does It Outperform SGD?
• Authors: Jihwan Kim, Dogyoon Song, Chulhee Yun,
• Abstract summary: We study scaling laws of signSGD under a power-law random features (PLRF) model.<n>We analyze the population risk of a linear model trained with one-pass signSGD on Gaussian-sketched features.
• Score: 35.79321975718977
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 signSGD steeper than that of SGD in regimes where noise is dominant. Finally, we observe that the widely used warmup-stable-decay (WSD) schedule further reduces the noise term and sharpens the compute-optimal slope, when feature decay is fast but target decay is slow.

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