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arXiv CS.AI·Jun 9·5 min read
Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning
TL;DR
Muon, an optimizer for large-scale foundation model pre-training, faces efficiency issues due to its reliance on Newton-Schulz iterations for orthogonalization. Muon$^2$ was developed to enhance both the quality and efficiency of Muon by incorporating Adam-style adaptive second-moment preconditioning.
✦ Why It Matters
Engineers can implement Muon$^2$ to enhance optimization efficiency in large-scale model training.
Key Takeaways
- Implement Muon$^2$ for faster convergence in model training.
- Reduce training time by up to 25% with Muon$^2$.
- Leverage adaptive second-moment preconditioning for improved optimizer performance.
- Achieve similar loss levels with fewer iterations using Muon$^2$.
How It Works
Muon$^2$ enhances the original Muon optimizer by applying adaptive second-moment preconditioning, which stabilizes the momentum matrix used in the orthogonalization process. This preconditioning improves the spectrum of the momentum matrix, allowing for more effective polar approximations and faster convergence during training.