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Musec: MomentUm SpEctral Clipping for Stable Muon-type Training

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Updated 2 h ago · first seen 11 Sept 2026

paper_01M294FPA13HF9B1NE2DZZDPXT

Published: 11 Sept 2026; T1 · 2 h ago
arXiv: 2609.11655; T1 · 2 h ago
Category: cs.LG; T1 · 2 h ago

Abstract

Muon has emerged as a highly effective optimizer for large language model training, often achieving superior convergence and performance compared with the widely adopted Adam and AdamW optimizers. Nevertheless, Muon is prone to training instability due to its spectral flattening, manifested by loss spikes and unbounded growth of model weights. Existing approaches primarily rely on weight or attention-logit clipping, which require architecture-specific modifications and do not directly address instability across all model components. We propose MomentUm SpEctral Clipping (Musec), which replaces Muon's spectral flattening with spectral clipping: rather than setting all singular values of the momentum matrix to approximately one, Musec clips singular values that exceed a threshold while preserving the underlying spectral structure of the momentum. Our strategy provides an optimizer-level, architecture-agnostic mechanism for stabilizing Muon training. We further develop Soft Musec, an efficient implementation that uses a smooth spectral saturation function approximated by coupled Newton-Schulz iterations. Theoretically, we establish convergence guarantees for Musec in nonconvex nonsmooth stochastic optimization. To the best of our knowledge, this is the first convergence guarantee for Muon-type methods in the nonconvex nonsmooth setting. We provide empirical studies to show that Soft Musec consistently improves training stability over existing Muon variants across a wide range of learning rates and model sizes. Notably, Soft Musec remains stable in settings where existing Muon variants diverge, while matching their performance under well-tuned configurations.

Authors 3

Zhuanghua Liu, Menglian Wang, Luo Luo

Specification

Official page: arxiv.org/abs/2609.11655
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Arxiv announce type: new
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
arXiv id: 2609.11655
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Categories: cs.LG
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
PDF: arxiv.org/pdf/2609.11655
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh

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T19

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2 h ago

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9 claims · 9 properties

Official pageofficial_url1

Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2609.11655	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
Muon has emerged as a highly effective optimizer for large language model training, often achieving superior convergence and performance compared with the widely adopted Adam and AdamW optimizers. Nevertheless, Muon is prone to training instability due to its spectral flattening, manifested by loss spikes and unbounded growth of model weights. Existing approaches primarily rely on weight or attention-logit clipping, which require architecture-specific modifications and do not directly address instability across all model components. We propose MomentUm SpEctral Clipping (Musec), which replaces Muon's spectral flattening with spectral clipping: rather than setting all singular values of the momentum matrix to approximately one, Musec clips singular values that exceed a threshold while preserving the underlying spectral structure of the momentum. Our strategy provides an optimizer-level, architecture-agnostic mechanism for stabilizing Muon training. We further develop Soft Musec, an efficient implementation that uses a smooth spectral saturation function approximated by coupled Newton-Schulz iterations. Theoretically, we establish convergence guarantees for Musec in nonconvex nonsmooth stochastic optimization. To the best of our knowledge, this is the first convergence guarantee for Muon-type methods in the nonconvex nonsmooth setting. We provide empirical studies to show that Soft Musec consistently improves training stability over existing Muon variants across a wide range of learning rates and model sizes. Notably, Soft Musec remains stable in settings where existing Muon variants diverge, while matching their performance under well-tuned configurations.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type1

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new	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

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2609.11655	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

Claim history for Authors
Value	Valid from → to	Status	Source	Confidence	Extractor
Zhuanghua Liu, Menglian Wang, Luo Luo	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

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cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

PDFpdf_url1

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https://arxiv.org/pdf/2609.11655	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at1

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Value	Valid from → to	Status	Source	Confidence	Extractor
11 Sept 2026	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	2 h ago	1

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