Abstract

Recently, the Muon optimizer has demonstrated strong results in training small-scale language models, but the scalability to larger models has not been proven. We identify two crucial techniques for scaling up Muon:

• Weight Decay: Critical for scaling to larger models
• Consistent RMS Updates: Enforcing a consistent root mean square on model updates

These techniques allow Muon to work out-of-the-box on large-scale training without the need of hyper-parameter tuning. Scaling law experiments indicate that Muon is $\sim 2\times$ more sample efficient than Adam with compute optimal training.

Based on these improvements, we introduce Moonlight, a 3B/16B-parameter Mixture-of-Expert (MoE) model trained with 5.7T tokens using Muon. Our model improves the current Pareto frontier, achieving better performance with much fewer training FLOPs compared to prior models.

We open-source our Muon implementation that is memory optimal and communication efficient. We also release the pretrained, instruction-tuned, and intermediate checkpoints to support future research.

Our code is available at MoonshotAI/Moonlight.

Key Ingredients

Our work builds upon Muon while systematically identifying and resolving its limitations in large-scale training scenarios. Our technical contributions include:

• Analysis for Effective Scaling of Muon: Through extensive analysis, we identify that weight decay plays a crucial roles in Muon's scalability. Besides, we proposed to keep a consistent update root mean square (RMS) across different matrix and non-matrix parameters through parameter-wise update scale adjustments. Such adjustments significantly enhanced training stability.

• Efficient Distributed Implementation: We develop a distributed version of Muon with ZeRO-1 style optimization, achieving optimal memory efficiency and reduced communication overhead while preserving the mathematical properties of the algorithm.

• Scaling Law Validation: We performed scaling law research that compares Muon with strong AdamW baselines, and showed the superior performance of Muon (see Figure 1). Based on the scaling law results, Muon achieves comparable performance to AdamW trained counterparts while requiring only approximately 52% of the training FLOPs.

Performance

We compared Moonlight with SOTA public models at similar scale:

• LLAMA3-3B is a 3B-parameter dense model trained with 9T tokens
• Qwen2.5-3B is a 3B-parameter dense model trained with 18T tokens
• Deepseek-v2-Lite is a 2.4B/16B-parameter MOE model trained with 5.7T tokens

Qwen 2 & 2.5 reports didn't disclose their optimizer information. †The reported parameter counts exclude the embedding parameters. ‡We test all listed models with the full set of TriviaQA.

Example usage

Model Download

Inference with Hugging Face Transformers

We introduce how to use our model at inference stage using transformers library. It is recommended to use python=3.10, torch>=2.1.0, and transformers=4.48.2 as the development environment.

For our pretrained model (Moonlight-16B-A3B):

python
Copy code
from transformers import AutoModelForCausalLM, AutoTokenizer

model_name = "moonshotai/Moonlight-16B-A3B"
model = AutoModelForCausalLM.from_pretrained(
    model_name,
    torch_dtype="auto",
    device_map="auto",
    trust_remote_code=True,
)
tokenizer = AutoTokenizer.from_pretrained(model_name, trust_remote_code=True)

prompt = "1+1=2, 1+2="
inputs = tokenizer(prompt, return_tensors="pt", padding=True, truncation=True).to(model.device)
generated_ids = model.generate(**inputs, max_new_tokens=100)
response = tokenizer.batch_decode(generated_ids)[0]
print(response)

For our instruct model (Moonlight-16B-A3B-Instruct):

python
Copy code
from transformers import AutoModelForCausalLM, AutoTokenizer

model_name = "moonshotai/Moonlight-16B-A3B-Instruct"
model = AutoModelForCausalLM.from_pretrained(
    model_name,
    torch_dtype="auto",
    device_map="auto",
    trust_remote_code=True
)
tokenizer = AutoTokenizer.from_pretrained(model_name, trust_remote_code=True)

messages = [
    {"role": "system", "content": "You are a helpful assistant provided by Moonshot-AI."},
    {"role": "user", "content": "Is 123 a prime?"}
]
input_ids = tokenizer.apply_chat_template(messages, add_generation_prompt=True, return_tensors="pt").to(model.device)
generated_ids = model.generate(inputs=input_ids, max_new_tokens=500)
response = tokenizer.batch_decode(generated_ids)[0]
print(response)

Moonlight has the same architecture as DeepSeek-V3, which is supported by many popular inference engines, such as VLLM and SGLang. As a result, our model can also be easily deployed using these tools.

Citation

If you find Moonlight is useful or want to use in your projects, please kindly cite our paper:

markdown
Copy code
@misc{liu2025muonscalablellmtraining,
      title={Muon is Scalable for LLM Training}, 
      author={Jingyuan Liu and Jianlin Su and Xingcheng Yao and Zhejun Jiang and Guokun Lai and Yulun Du and Yidao Qin and Weixin Xu and Enzhe Lu and Junjie Yan and Yanru Chen and Huabin Zheng and Yibo Liu and Shaowei Liu and Bohong Yin and Weiran He and Han Zhu and Yuzhi Wang and Jianzhou Wang and Mengnan Dong and Zheng Zhang and Yongsheng Kang and Hao Zhang and Xinran Xu and Yutao Zhang and Yuxin Wu and Xinyu Zhou and Zhilin Yang},
      year={2025},
      eprint={2502.16982},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2502.16982}, 
}