SIGNALAI·Jun 9, 2026, 4:00 AMSignal75Medium term

Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning

Source: arXiv cs.LG

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Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning

arXiv:2604.09967v2 Announce Type: replace Abstract: Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization. However, the orthogonalization quality of Muon hinges on the number of Newton--Schulz (NS) iterations performed, which poses efficiency challenges due to its non-trivial computation and communication cost. We propose Muon$^2$, an extension of Muon, to improve both quality and efficiency by applying Adam-style adaptive second-moment preconditioning before ortho

Why this matters
Why now

The continuous growth in foundation model scale and complexity necessitates ongoing innovation in optimization algorithms to maintain computational efficiency.

Why it’s important

Improved optimizer efficiency directly translates to faster and more cost-effective training of large AI models, impacting the pace of AI development and accessibility.

What changes

The proposed Muon^2 optimizer aims to enhance the speed and quality of deep learning model training by addressing computational bottlenecks in existing methods.

Winners
  • · AI model developers
  • · Cloud providers
  • · AI research institutions
Losers
  • · Inefficient AI training methods
Second-order effects
Direct

Faster training times for large-scale foundation models will become achievable.

Second

Reduced computational costs could enable more experimentation and broader access to advanced AI model development.

Third

This could accelerate the development and deployment of more sophisticated AI capabilities across various industries.

Editorial confidence: 90 / 100 · Structural impact: 55 / 100
Original report

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Read at arXiv cs.LG
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