arXiv:2607. 23777v1 Announce Type: cross Abstract: The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data.
By Anuj Apte
The paper introduces a physical response-and-memory model for the Muon optimizer, explaining its semi‑orthogonalized momentum update as the maximally dissipative direction under an output‑side safety budget. It treats the weight matrix as a responsive medium with internal stress, showing that momentum corresponds to accumulated stress whose relaxation occurs over multiple timescales—fast and slow. Based on this, the authors propose the Bi‑Maxwell optimizer, which uses a two‑timescale memory kernel and achieves target loss in fewer steps on a public large‑language‑model benchmark.
By Yinze Hu, Hongjun Xiang, Xingao Gong, Hongyu Yu
The paper investigates why the orthogonal optimiser Muon outperforms Adam in large language model pretraining by analysing the spectral properties of Transformer loss landscapes. It finds that Muon’s momentum buffers exhibit an anisotropic spectral profile with a volatile head and a tolerant bulk, enabling larger effective step sizes. Building on this insight, the authors propose Spectral‑Aware Muon (SAMuon) and a lightweight variant, which adjust the bulk scaling while keeping the head unchanged, achieving 13–24 % fewer training tokens than Muon without extra FLOPs.
By Xiaodong Wu, Wenyi Yu, Chao Zhang, Philip Woodland
The paper studies how different optimizers perform as training duration (overtraining) increases, focusing on matrix‑preconditioned methods (Muon, SOAP) and a momentum‑scheduled method (ADANA) compared to AdamW. Across models ranging from 51M to 253M parameters and overtraining factors up to 256×, the authors find that optimal learning‑rate schedules, weight‑decay coefficients, and memory settings shift with horizon, and that ADANA consistently outperforms AdamW, especially with log‑time weight decay and momentum cooldown. Muon and SOAP maintain roughly constant token‑efficiency advantages, with SOAP potentially improving at the highest overtraining levels.
By Katie Everett, Shikai Qiu
arXiv:2603. 00742v2 Announce Type: replace Abstract: While Adam has long been the ubiquitous default optimizer for deep neural networks, Muon has recently seen rapid adoption due to its superior training speed.
By Sara Dragutinovi\'c, Yedi Zhang, Rajesh Ranganath
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