Muon+: Towards Better Muon via One Additional Normalization Step

• URL: http://arxiv.org/abs/2602.21545v2
• Date: Thu, 26 Feb 2026 17:01:08 GMT
• Title: Muon+: Towards Better Muon via One Additional Normalization Step
• Authors: Ruijie Zhang, Yequan Zhao, Ziyue Liu, Zhengyang Wang, Zheng Zhang,
• Abstract summary: We propose a simple yet effective enhancement to Muon, namely Muon+.<n>We demonstrate the effectiveness of Muon+ through extensive pre-training experiments across a wide range of model scales and architectures.
• Score: 18.816463168231618
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Muon optimizer has demonstrated promising performance in pre-training large language models through gradient (or momentum) orthogonalization. In this work, we propose a simple yet effective enhancement to Muon, namely Muon+, which introduces an additional normalization step after orthogonalization. We demonstrate the effectiveness of Muon+ through extensive pre-training experiments across a wide range of model scales and architectures. Our evaluation includes GPT-style models ranging from 130M to 774M parameters and LLaMA-style models ranging from 60M to 1B parameters. We comprehensively evaluate the effectiveness of Muon+ in the compute-optimal training regime and further extend the token-to-parameter (T2P) ratio to an industrial level of $\approx 200$. Experimental results show that Muon+ provides a consistent boost on training and validation perplexity over Muon. We provide our code here: https://github.com/K1seki221/MuonPlus.

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