Rethinking Language Model Scaling under Transferable Hypersphere Optimization
Scaling laws for large language models depend critically on the optimizer and parameterization. Existing hyperparameter transfer laws are mainly developed for first-order optimizers, and they do not structurally prevent training instability at scale. Recent hypersphere optimization methods constrain weight matrices to a fixed-norm hypersphere, offering a promising alternative for more stable scaling. We introduce HyperP (Hypersphere Parameterization), the first framework for transferring optimal learning rates across model width, depth, training tokens, and Mixture-of-Experts (MoE) granularity under the Frobenius-sphere constraint with the Muon optimizer. We prove that weight decay is a f...
| Authors | Liliang Ren, Yang Liu, Yelong Shen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 March 2026 |
| Last updated at source | 5 April 2026 |
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