arXiv:2509. 14562v4 Announce Type: replace Abstract: Large models recently are widely applied in machine learning, so efficient training of large models has received widespread attention.
By Feihu Huang, Yuning Luo, Songcan Chen
arXiv:2608. 04607v1 Announce Type: cross Abstract: Stochastic gradient descent (SGD) optimization methods are the standard instruments for the training of deep neural networks (DNNs).
By Thang Do, Steffen Dereich, Arnulf Jentzen
arXiv:2606. 27153v1 Announce Type: cross Abstract: Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads.
By Vincent Chen, Starrick Liu, Regis Cheng, Dance Yang, Shalfun Li, Ryan Yu, Lucy Liang, Hang Su, Roy Gan, Hao Wang, Qian Wang
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. 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
arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.
By Naoki Sato, Hiroki Naganuma, Hideaki Iiduka