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: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:2607. 06151v1 Announce Type: new Abstract: Generalization remains a pivotal challenge in deep learning, where traditional optimizers like Stochastic Gradient Descent (SGD) often converge to sharp minima, leading to overfitting and reduced performance on unseen data.
arXiv:2610.31728v1 Announce Type: new Abstract: Muon has become a popular optimizer for large language model training, yet its theoretical foundations remain poorly understood. In this work, we study...
arXiv:2608. 15105v1 Announce Type: new Abstract: Recent progress in optimization research has highlighted the sharpness of the loss landscape as a key factor in narrowing the generalization gap.
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
arXiv:2605. 27733v2 Announce Type: replace Abstract: Training instabilities such as loss spikes are frequently the result of stochastic gradient noise.
Musec introduces MomentUm SpEctral Clipping, an optimizer-level, architecture‑agnostic technique that replaces Muon’s spectral flattening with selective spectral clipping to stabilize training. By clipping singular values above a threshold while preserving the momentum’s spectral structure, Musec addresses loss spikes and unbounded weight growth without requiring architecture‑specific changes. Soft Musec, an efficient implementation using smooth spectral saturation via coupled Newton‑Schulz iterations, offers convergence guarantees in nonconvex nonsmooth stochastic optimization and empirically improves stability across diverse learning rates and model sizes.
arXiv:2602. 11557v2 Announce Type: replace Abstract: A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries.
arXiv:2606. 08783v1 Announce Type: cross Abstract: Orthogonalized momentum updates, as used in Muon-style optimizers, have recently shown strong empirical stability in large-scale deep learning.
The paper introduces Sparsity-Adaptive Sharpness-Aware Minimization (SA‑SAM), a method that adjusts the perturbation radius in sharpness-aware training to remain consistent as model sparsity increases. It also evaluates a Magnitude‑Weighted Hessian (MWH) importance metric derived from second‑order analysis. Experiments on CIFAR‑10‑C, CIFAR‑100‑C, and ImageNet‑100‑C show that SA‑SAM improves corruption robustness at 80–90% sparsity while maintaining clean accuracy, and the study reports inference throughput at deployment‑relevant sparsity levels.
Modern machine learning relies on practical optimization methods that often differ from the algorithms studied in classical analyses: they train submodels, clip or normalize gradients, use layer-wise...