arXiv:2604. 09967v2 Announce Type: replace-cross Abstract: Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization.
By Ziyue Liu, Ruijie Zhang, Zhengyang Wang, Yequan Zhao, Yupeng Su, Zi Yang, Zheng Zhang
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
AF‑Muon is an AdamW‑free extension of the Muon optimizer that retains Muon’s matrix update for hidden weights while applying a support‑aware finite‑cap linear minimization oracle to tied vocabulary tables and an RMS‑normalized update for one‑dimensional auxiliary parameters. This design eliminates second‑moment state, reducing optimizer‑state memory by about 20% compared to Hybrid Muon. Across nine tied‑token settings—including decoder‑only language models, T5‑style encoder‑decoders, and ImageGPT‑style variants—AF‑Muon consistently improves mean validation loss and perplexity over both Hybrid Muon and a SCION‑style Sign endpoint, with robust gains confirmed by long‑horizon runs and hyperparameter studies.
By Arash Lagzian, Paniz Halvachi, Junming Zhang, Zhouhan Lin, Dianbo Liu
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
arXiv:2607. 17620v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices.
By Nikhil Ghosh, Tetiana Parshakova, Robert M. Gower
arXiv:2607. 13246v1 Announce Type: cross Abstract: Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training.
By Ali Parviz, Gal Mishne, Alex Cloninger