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.
By Zhuanghua Liu, Menglian Wang, Luo Luo
arXiv:2608. 05088v1 Announce Type: new Abstract: Muon has recently emerged as a promising alternative to AdamW for language model pretraining by orthogonalizing momentum matrices using Newton-Schulz iterations.
By Tongle Wu, Huanyu Dong, Ying Sun, Ziye Ma
arXiv:2512. 04632v2 Announce Type: replace Abstract: Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges.
By Thibaut Boissin (IRIT-MISFIT), Thomas Massena (DTIPG - SNCF, IRIT-MISFIT), Franck Mamalet (IRIT-MISFIT), Mathieu Serrurier (IRIT-MISFIT)
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: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.
By Ganzhao Yuan
arXiv:2607. 22444v1 Announce Type: new Abstract: For scale-invariant deep networks, Hyperball-style optimizers have shown strong performance in large-scale training by fixing the norms of matrix-valued parameters and normalizing updates.
By Yihao Xiao, Jialong Sun, Zitian Gao, Zeming Wei, Chutian Wang, Ran Tao, Jiaye Teng, Bryan Dai
arXiv:2607. 14536v1 Announce Type: new Abstract: Muon-style optimizers apply a polar map to matrix momentum, but their updates also depend on the representation of each parameter block before orthogonalization.
By Da Chang, Qiankun Shi, Lvgang Zhang, Di He, Yaoshuai Ma, Ganzhao Yuan, Yongxiang Liu
arXiv:2606. 17526v1 Announce Type: new Abstract: Efficient optimization is essential for training large language models.
By Da Chang, Ganzhao Yuan
arXiv:2606. 04662v1 Announce Type: cross Abstract: Muon improves training efficiency over Adam in large language-model training by about two times, but the local geometric source of this advantage remains unclear.
By Shuche Wang, Fengzhuo Zhang, Jiaxiang Li, Dirk Bergemann, Zhuoran Yang
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.
By Alexander H\"agele, Alejandro Hern\'andez-Cano, Atli Kosson, Martin Jaggi
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.
By Fangzhou Wu, Rikhav Shah, Sandeep Silwal, Qiuyi Zhang
arXiv:2608. 12925v1 Announce Type: new Abstract: Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood.
By Zhixin Ren, Yau Lyu, Congrong Li, Liping Zhang, Shengbo Eben Li