Deriving Hyperparameter Scaling Laws via Modern Optimization Theory
Hyperparameter transfer has become an important component of modern large-scale training recipes. Existing methods, such as muP, primarily focus on transfer between model sizes, with transfer across batch sizes and training horizons often relying on empirical scaling rules informed by insights from timescale preservation, quadratic proxies, and continuous-time approximations. We study hyperparameter scaling laws for modern first-order optimizers through the lens of recent convergence bounds for methods based on the Linear Minimization Oracle (LMO), a framework that includes normalized SGD, signSGD (approximating Adam), and Muon. Treating bounds in recent literature as a proxy and minimizi...
| Authors | Egor Shulgin, Dimitri von Rütte, Tianyue H. Zhang et al. |
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| Primary category | cs.LG |
| Published | 16 March 2026 |
| Last updated at source | 16 March 2026 |
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