arXiv Machine Learning
Jun 9
The Spectral Dynamics and Noise Geometry of Muon
arXiv:2606. 08388v1 Announce Type: new Abstract: Muon replaces a matrix gradient $G=U\Sigma V^\top$ by its polar factor $UV^\top$.
An Isotropy-Preserving Spectral Cap for Muon: Theory and Three Case Studies
arXiv:2607. 19771v1 Announce Type: cross Abstract: Muon and related matrix-sign optimizers are increasingly used to pre-train large language models, but their effect on the internal geometry of individual weight matrices is not well understood.
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arXiv AI
Jun 2
DynMuon: A Dynamic Spectral Shaping View of Muon
arXiv:2605. 17109v3 Announce Type: replace-cross Abstract: In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly.
arXiv Machine Learning
Jun 25
Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.
arXiv AI
Jun 4
Spectral Scaling Laws of Muon
arXiv:2606. 04058v1 Announce Type: cross Abstract: Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon.
arXiv Machine Learning
Jun 4
Muon in Associative Memory Learning: Training Dynamics and Scaling Laws
arXiv:2602. 05725v3 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.
arXiv Machine Learning
Aug 5
Muon Meets Mamba: Spectral Optimization for State Space Models
arXiv:2608. 03941v1 Announce Type: new Abstract: Muon is a recent optimizer that orthogonalizes the update to each weight matrix with a Newton-Schulz iteration, which performs steepest descent under the spectral norm.
arXiv AI
Jul 28
Scale Weight Decay and Train Better
arXiv:2607. 23777v1 Announce Type: cross Abstract: The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data.
arXiv Machine Learning
Jun 9
Convergence Bound and Critical Batch Size of Muon Optimizer
arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.
arXiv Machine Learning
Jun 15
Muon$^p$: Muon with Fractional Spectral Powers
arXiv:2606. 13867v1 Announce Type: new Abstract: Muon is an increasingly widely used optimizer that replaces a gradient $G=USV^\top$ with its polar factor $UV^\top$, thereby flattening the singular spectrum.
arXiv AI
Jul 16
Reassessing Muon for Matrix Factorization
arXiv:2607. 13246v1 Announce Type: cross Abstract: Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training.
arXiv AI
Jul 24
The Active Ingredient in Muon's Grokking
arXiv:2607. 20512v1 Announce Type: cross Abstract: The Muon optimizer reaches the grokking threshold on modular arithmetic faster than AdamW.
arXiv Machine Learning
Jul 24
MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization
arXiv:2605. 11396v2 Announce Type: replace Abstract: The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization.