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This paper addresses the scalability limitations of the Muon optimizer for large language model (LLM) training by introducing weight decay and carefully adjusting the per-parameter update scale. The authors demonstrate that these techniques enable Muon to achieve approximately 2x computational efficiency compared to AdamW in compute-optimal training scenarios. They further validate the improved Muon optimizer by training Moonlight, a 3B/16B-parameter Mixture-of-Expert (MoE) model, achieving state-of-the-art performance with significantly fewer training FLOPs and releasing the distributed implementation and model checkpoints.
Muon optimizer now lets you train LLMs twice as fast as AdamW, as validated by a new 3B/16B MoE model called Moonlight.
Recently, the Muon optimizer based on matrix orthogonalization 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: (1) adding weight decay and (2) carefully adjusting the per-parameter update scale. 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 achieves $\sim\!2\times$ computational efficiency compared to AdamW 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 distributed Muon implementation that is memory optimal and communication efficient. We also release the pretrained, instruction-tuned, and intermediate checkpoints to support future research.