Muon has motivated a growing family of optimizers that compose multiple matrix normalizations, but these methods remain fragmented and lack a unified perspective. We introduce chained linear minimizat...
MONA is a new optimizer that extends the Muon optimizer by adding a Nesterov‑style acceleration term derived from an exponential moving average of gradient differences. The paper provides a convergence analysis showing that this term offers curvature‑aware corrections while maintaining Muon’s spectral‑norm regularization. Empirical results demonstrate that MONA outperforms both Muon and AdamW on Mixture‑of‑Experts pretraining across models ranging from 1 B to 68 B parameters, and achieves state‑of‑the‑art performance on downstream benchmarks after fine‑tuning the largest model.
By Jiacheng Li, Jianchao Tan, Hongtao Xu, Jiaqi Zhang, Yifan Lu, Yerui Sun, Yuchen Xie, Xunliang Cai
The paper introduces a data‑driven criterion that dynamically selects optimal Linear Minimization Oracle (LMO) geometries for each layer of a deep neural network, bridging the gap between SGD and Muon updates. By deriving the criterion from gradient and activation statistics via a single‑step random feature regression surrogate, the authors enable a design space that interpolates between existing optimizers, including SGD, Muon, Adam, and MuAdam. The adaptive approach incurs only about a 3% runtime overhead and demonstrates competitive or superior performance compared to the best static optimizer across three training scenarios.
By Thomas Massena (DTIPG - SNCF, IRIT), Corentin Friedrich (IRIT), Mathieu Serrurier (IRIT)
arXiv:2606. 25975v1 Announce Type: new Abstract: Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models.
By Vladimir Bogachev, Vladimir Aletov, Alexander Molozhavenko, Sergei Kudriashov, Maxim Rakhuba
arXiv:2607. 20548v1 Announce Type: cross Abstract: Higher-order optimizers such as Muon and SOAP offer faster convergence than AdamW, but their computational cost and numerical stability challenges have limited adoption at scale.
By Mikail Khona, Aditya Vavre, Boxiang Wang, Deyu Fu, Hao Wu, Mike Chrzanowski, Bryan Catanzaro, Dheevatsa Mudigere, Jeff Pool, Michael Lightstone, Mohammad Shoeybi, Mostofa Patwary, Nima Tajbakhsh, Tijmen Blankevoort
Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models. Recent work has shown that exploiting matrix structure can improve optimization dynamics.