arXiv:2606.03899v1 Announce Type: new Abstract: Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, the
The paper provides a theoretical understanding of Muon, a recently developed large language model training technique, addressing the current gap in theoretical explanation for its empirical success.
Understanding the theoretical underpinnings of effective AI training methods like Muon is crucial for optimizing current models and developing future large language model architectures, impacting AI development efficiency.
This theoretical work provides insights into how momentum functions as a spectral filter in Muon, which could lead to more robust and efficient large language model training paradigms.
- · AI researchers
- · Large language model developers
- · AI software companies
Improved understanding of sophisticated optimization techniques in AI training.
Potential for developing more stable and faster training algorithms for future large AI models.
Accelerated progress in AI capabilities by reducing the computational cost and time of model development, thereby lowering barriers to entry in advanced AI research and application.
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