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.
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.
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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 $UV^\top$.
arXiv Machine Learning
Jun 15
Free Heavy-Tailed Lunch for Muon: A Theoretical Justification of Empirical Success
arXiv:2606. 14560v1 Announce Type: cross Abstract: Non-Euclidean optimisation methods with matrix-valued updates, such as Muon and Scion, have recently shown strong empirical performance for training Transformer models, yet their theoretical advantages over Euclidean methods remain poorly understood.
arXiv AI
Jul 23
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.
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.
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 9
LiMuon: Light and Fast Muon Optimizer for Large Models
arXiv:2509. 14562v4 Announce Type: replace Abstract: Large models recently are widely applied in machine learning, so efficient training of large models has received widespread attention.
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 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 AI
Jun 12
LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold
arXiv:2606. 12921v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) significantly reduces compute and memory costs for finetuning Deep Learning models but is often harder to tune than dense training: when using factor-wise optimizers such as AdamW, it is sensitive to initialization choices, its optimal learning rates transfer poorly across ranks, and it often fails to beat dense baselines.
arXiv AI
Jun 9
Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning
arXiv:2604. 09967v2 Announce Type: replace-cross 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.
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.