# Spectral Scaling Laws of Muon

Published: 2026-06-05 · Updated: 2026-06-05 · Category: Research

Source page: https://www.sipply.dev/story/spectral-scaling-laws-of-muon-df199b8a · 中文: https://www.sipply.dev/zh/story/spectral-scaling-laws-of-muon-df199b8a

## Summary

A recent study published on arXiv has explored the spectral scaling laws of the Muon optimizer, which is utilized in large language models. The researchers focused on the singular value spectrum of momentum matrices and discovered that the late layers of the model exhibit aggressive scaling as the model size increases. This finding indicates that modifications to the Newton-Schulz iteration process for orthonormalization are necessary to accommodate these scaling behaviors effectively.

## Key takeaways

- The Muon optimizer's late layers scale aggressively with model size.
- Adjustments to the Newton-Schulz iteration are needed for effective orthonormalization.
- Understanding spectral scaling can enhance the performance of large language models.

## Why it matters

This research highlights critical insights into the optimization processes of large language models, which can lead to improved performance and efficiency in AI applications.

- **Product managers:** For product managers, understanding these scaling laws can inform decisions on model architecture and optimization strategies, ultimately enhancing product performance.
- **Developers:** Developers and engineers can leverage these findings to refine their optimization techniques, ensuring that large models operate efficiently and effectively.
- **Students and job seekers:** Students and job-seekers can gain valuable knowledge about advanced optimization methods in AI, which is crucial for careers in machine learning and data science.

## Sources

- [Spectral Scaling Laws of Muon](https://arxiv.org/abs/2606.04058) (arXiv cs.LG, 2026-06-05)

## 中文

### Muon的光谱缩放法则

最近在arXiv上发表的一项研究探讨了Muon优化器的光谱缩放法则，该优化器用于大型语言模型。研究人员关注动量矩阵的奇异值谱，发现模型的后层在模型规模增加时表现出激进的缩放。这一发现表明，需要对牛顿-舒尔茨迭代过程进行修改，以有效适应这些缩放行为。

**要点：**

- Muon优化器的后层随着模型规模的增加而激进缩放。
- 需要对牛顿-舒尔茨迭代进行调整，以实现有效的正交化。
- 理解光谱缩放可以提升大型语言模型的性能。

**为什么重要：** 这项研究突出了大型语言模型优化过程中的关键见解，可以提高AI应用的性能和效率。

---
Sipply: Sip AI News Simply. https://www.sipply.dev