arXiv:2507.01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW. This paper presents theoretical analysis to support its practical success. We provide convergence proofs for Muon across four practical settings, systematically examining its behavior with and without the inclusion of Nesterov momentum and weight decay. We then demonstrate that the addition of weight decay ensu
The continuous drive for more efficient AI model training necessitates improved optimization algorithms, and Muon represents a significant step supported by new theoretical groundwork.
This development in AI optimization can lead to faster, more stable, and potentially cheaper training of large-scale neural networks, impacting the rate of AI progress and accessibility.
The theoretical validation of Muon offers a more robust foundation for its adoption, potentially displacing or complementing existing optimizers like AdamW given its strong empirical performance.
- · AI researchers and developers
- · Cloud AI providers
- · Machine learning hardware manufacturers
- · Developers reliant solely on older optimization techniques
Wider adoption and development of Muon or similar structure-leveraging optimizers in AI training.
Reduced computational costs and time for training complex AI models, accelerating research and development cycles.
Potentially enables new classes of AI applications or larger models that were previously computationally prohibitive, furthering the AI agent and autonomous systems paradigm.
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Read at arXiv cs.LG