arXiv:2602.05725v2 Announce Type: replace Abstract: Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory. We study Muon in a linear associative memory model with softmax retrieval and a hierarchical frequency spectrum over query-answer pairs, with and without label noise. In this setting, we show that Gradient Descent (GD) learns frequency components at highly imbalanced rates, leading to slow convergence bottlenecked by low-frequency components. In contrast, the Muon optimizer mi
This research provides theoretical clarity and empirical evidence for an optimizer (Muon) that addresses current limitations in AI model training, specifically its ability to learn diverse frequency components more efficiently.
Improved optimizer dynamics and scaling laws are critical for developing more powerful and efficient AI models, directly impacting the capabilities and development costs of AI systems.
The understanding of how AI models learn and the efficiency with which they can be trained, particularly for complex tasks involving hierarchical data, is enhanced.
- · AI researchers
- · Large language model developers
- · AI compute infrastructure providers (due to demand increase)
- · AI driven industries
- · Less efficient AI optimization techniques
- · Organizations heavily reliant on standard Gradient Descent for complex tasks
More efficient training of advanced AI models across various applications, reducing compute time and resources.
Acceleration in the development of more complex and capable AI systems, potentially expanding the scope of what AI can achieve.
Enhanced AI capabilities could further drive demand for specialized hardware and energy, impacting the compute supply chain and energy grid.
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Read at arXiv cs.LG