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Autores principales: Xie, Tian, Luo, Haoming, Tang, Haoyu, Hu, Yiwen, Liu, Jason Klein, Ren, Qingnan, Wang, Yang, Zhao, Wayne Xin, Yan, Rui, Su, Bing, Luo, Chong, Guo, Baining
Formato: Preprint
Publicado: 2026
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Acceso en línea:https://arxiv.org/abs/2601.08393
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author Xie, Tian
Luo, Haoming
Tang, Haoyu
Hu, Yiwen
Liu, Jason Klein
Ren, Qingnan
Wang, Yang
Zhao, Wayne Xin
Yan, Rui
Su, Bing
Luo, Chong
Guo, Baining
author_facet Xie, Tian
Luo, Haoming
Tang, Haoyu
Hu, Yiwen
Liu, Jason Klein
Ren, Qingnan
Wang, Yang
Zhao, Wayne Xin
Yan, Rui
Su, Bing
Luo, Chong
Guo, Baining
contents Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization ($\boldsymbolμ$P) provides a theoretical safeguard for width-invariant $Θ(1)$ activation control, whereas emerging optimizers like Muon are only ``half-aligned'' with these constraints: they control updates but allow weights to drift. To address this limitation, we introduce the \textbf{Spectral Sphere Optimizer (SSO)}, which enforces strict module-wise spectral constraints on both weights and their updates. By deriving the steepest descent direction on the spectral sphere, SSO realizes a fully $\boldsymbolμ$P-aligned optimization process. To enable large-scale training, we implement SSO as an efficient parallel algorithm within Megatron. Through extensive pretraining on diverse architectures, including Dense 1.7B, MoE 8B-A1B, and 200-layer DeepNet models, SSO consistently outperforms AdamW and Muon. Furthermore, we observe significant practical stability benefits, including improved MoE router load balancing, suppressed outliers, and strictly bounded activations.
format Preprint
id arxiv_https___arxiv_org_abs_2601_08393
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Controlled LLM Training on Spectral Sphere
Xie, Tian
Luo, Haoming
Tang, Haoyu
Hu, Yiwen
Liu, Jason Klein
Ren, Qingnan
Wang, Yang
Zhao, Wayne Xin
Yan, Rui
Su, Bing
Luo, Chong
Guo, Baining
Machine Learning
Artificial Intelligence
Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization ($\boldsymbolμ$P) provides a theoretical safeguard for width-invariant $Θ(1)$ activation control, whereas emerging optimizers like Muon are only ``half-aligned'' with these constraints: they control updates but allow weights to drift. To address this limitation, we introduce the \textbf{Spectral Sphere Optimizer (SSO)}, which enforces strict module-wise spectral constraints on both weights and their updates. By deriving the steepest descent direction on the spectral sphere, SSO realizes a fully $\boldsymbolμ$P-aligned optimization process. To enable large-scale training, we implement SSO as an efficient parallel algorithm within Megatron. Through extensive pretraining on diverse architectures, including Dense 1.7B, MoE 8B-A1B, and 200-layer DeepNet models, SSO consistently outperforms AdamW and Muon. Furthermore, we observe significant practical stability benefits, including improved MoE router load balancing, suppressed outliers, and strictly bounded activations.
title Controlled LLM Training on Spectral Sphere
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2601.08393