Spectral Condition for $μ$P under Width-Depth Scaling
Generative foundation models are increasingly scaled in both width and depth, posing significant challenges for stable feature learning and reliable hyperparameter (HP) transfer across model sizes. While maximal update parameterization ($μ$P) has provided a principled solution to both problems for width scaling, existing extensions to the joint width-depth scaling regime remain fragmented, architecture- and optimizer-specific, and often rely on technically involved theories. In this work, we develop a simple and unified spectral framework for $μ$P under joint width-depth scaling. For deep residual networks whose residual blocks contain $k$ transformations, the framework specifies how the ...
| Authors | Chenyu Zheng, Rongzhen Wang, Xinyu Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 February 2026 |
| Last updated at source | 11 May 2026 |
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