arXiv:2610.04204v2 Announce Type: replace
Abstract: Training large language models (LLMs) entails a fundamental trade-off: memory-efficient optimizers such as Adam discard cross-parameter curvature,...
By Beheshteh T. Rakhshan, Sahar Rajabi, Maziar Sargordi Shikai Fang, Guillaume Rabusseau, Sirisha Rambhatla
Clean is a memory‑efficient optimizer that uses Nyström sketching to approximate SOAP’s curvature preconditioners, reducing memory complexity from quadratic to linear while preserving rich curvature information. It also reintegrates off‑subspace components and offers a low‑precision variant, Q‑Clean, that cuts optimizer memory by over 50% compared to Muon while maintaining strong performance. Clean outperforms AdamW in wall‑clock time and enables pre‑training a 13B‑parameter model on a single 80GB GPU.
By Beheshteh T. Rakhshan, Sahar Rajabi, Maziar Sargordi, Shikai Fang, Guillaume Rabusseau, Sirisha Rambhatla
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 curvature‑conditioned multiscale momentum algorithm with sphere constraints to accelerate large‑language‑model pretraining. By applying a slow‑decay component for noise reduction and a fast‑decay component for curvature adaptation only along flat directions, the method improves training dynamics without causing parameter inflation. Experiments demonstrate significant speed‑ups for Muon across various architectures and model sizes, and the authors provide theoretical justification for the observed acceleration.
By Shuchen Zhu, Yuxin Fang, Mingze Wang, Kun Yuan
arXiv:2605. 22432v2 Announce Type: replace Abstract: Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update geometry by orthogonalizing momentum for matrix parameters.
By Jueun Kim, Baekrok Shin, Jihun Yun, Beomhan Baek, Minhak Song, Chulhee Yun
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