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cloud.google.com·6h ago
AI Research
arXiv CS.AI·Jul 24·5 min read
The Active Ingredient in Muon's Grokking
TL;DR
Muon optimizer achieves faster grokking on modular arithmetic compared to AdamW, primarily due to orthogonalization rather than spectral-norm constraints. This insight helps refine optimization strategies in machine learning.
✦ Why It Matters
Optimize your machine learning models by focusing on orthogonalization techniques for better performance.
Key Takeaways
- Prioritize orthogonalization in optimization strategies.
- Consider reducing Newton-Schulz iterations for faster results.
- Avoid spectral scaling to maintain performance without added complexity.
- Test learning rates carefully to prevent solution fragility.
How It Works
The Muon optimizer utilizes orthogonalization through the Newton-Schulz iteration to enhance convergence speed. This method allows the optimizer to reach lower spectral norms, which correlates with better generalization performance.
By focusing on orthogonalization alone, the optimizer can match the performance of the full Muon setup, demonstrating that spectral-norm constraints are not necessary for effective learning.