Convergence Bound and Critical Batch Size of Muon Optimizer

arXiv — cs.LGMonday, November 24, 2025 at 5:00:00 AM
  • The Muon optimizer has been theoretically analyzed, demonstrating strong empirical performance and potential as a successor to standard optimizers like AdamW. The study provides convergence proofs across various settings, examining the effects of Nesterov momentum and weight decay on its performance. Additionally, it identifies the critical batch size that minimizes training costs, highlighting the relationship between hyperparameters and efficiency.
  • This development is significant as it positions Muon as a promising alternative in the optimization landscape, particularly for neural networks. By establishing theoretical foundations and practical implications, it enhances the understanding of how optimizers can be fine-tuned for better performance in machine learning tasks.
  • The introduction of Muon aligns with ongoing advancements in adaptive optimization techniques, reflecting a broader trend towards improving training efficiency in deep learning. The exploration of alternatives to traditional methods like AdamW, including the recent AdamHD optimizer, underscores the evolving nature of optimization strategies in AI, aiming to address challenges in model training and performance.
— via World Pulse Now AI Editorial System

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