The study re‑examines scaled weight decay (Muon‑SW) versus constant decoupled weight decay for language models, tuning learning‑rate and weight‑decay jointly across a range of model sizes. It finds that most of the reported performance gain is due to a tuning gap, with the tuned advantage shrinking to only 0.0026 BPB. However, the remaining advantage grows with model size, rising from 0.0036 to 0.0051 BPB over an eight‑fold increase in active parameters, and the optimal LR‑WD product shifts faster for Muon‑SW.
By Esther Xin
arXiv:2607. 20512v1 Announce Type: cross Abstract: The Muon optimizer reaches the grokking threshold on modular arithmetic faster than AdamW.
By Yufeng Wang
The paper introduces Temperon, a training strategy that uses plain SGD for the first 43% of the epoch budget and then hands off to a SAM‑wrapped Muon refiner for the remaining training. On datasets such as CIFAR‑10/100, SVHN, and Tiny ImageNet, Temperon achieves the same or better accuracy as full‑time SAM while reaching key performance targets faster and at lower cost. Ablation studies show that the Muon refiner contributes the majority of the performance gain, while the initial SGD explorer and its restarts add negligible benefit.
By Stamatis Mastromichalakis
arXiv:2608.27518v1 Announce Type: new
Abstract: Continual learning (CL) and model merging (MM) both aim to obtain a single model that performs well across multiple tasks, challenged respectively by c...
By Shangge Liu, Yuehan Yin, Yinghuan Shi, Lei Wang, Wenbin Li
arXiv:2505. 23725v3 Announce Type: replace Abstract: DiLoCo is a powerful framework for training large language models (LLMs), enabling larger optimal batch sizes and increased accelerator utilization under networking constraints.
By Benjamin Th\'erien, Xiaolong Huang, Aaron Defazio, Irina Rish, Eugene Belilovsky
arXiv:2606. 12921v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) significantly reduces compute and memory costs for finetuning Deep Learning models but is often harder to tune than dense training: when using factor-wise optimizers such as AdamW, it is sensitive to initialization choices, its optimal learning rates transfer poorly across ranks, and it often fails to beat dense baselines.
By Franz Louis Cesista, Katherine Crowson, C\'edric Simal, Stella Biderman
The paper evaluates Muon, a data‑efficient optimizer, against AdamW on a single A100 GPU across 17.7M‑ and 33.6M‑parameter causal language models and a 2.70M‑parameter vision transformer. Using a 23‑candidate development budget and five matched seeds, Muon consistently reduces validation‑loss area under the curve by 3.25–22.44% and lowers test loss in all 20 primary pairs, while AdamW outperforms Muon on language tasks by 3.38–6.96%. Muon’s full optimizer call consumes 56.1–69.6% of training time versus 6.1–9.1% for AdamW, and it shows higher expected regret under restricted candidate pools, indicating trade‑offs between data efficiency and computational cost for small models with reference kernels.
By Mushir Akhtar, Hazem N. Nounou, Majdi Mansouri, Mohamed N. Nounou
arXiv:2610.28072v1 Announce Type: new
Abstract: Learning rate schedules are typically fixed before training begins, yet when fine-tuning large language models with low-rank adapters (LoRA), the appro...
By Jan Kobiolka, Christian Frey, Josif Grabocka
The paper introduces LoDA, a LoRA-based continual learning method that decomposes update spaces into task‑shared and truly task‑specific subspaces using energy‑based objectives. By fixing down‑projections and learning up‑projections with Gradient‑Aligned Optimization, LoDA recalibrates general updates in closed form after each task, aiming to improve knowledge sharing and isolation. Experiments show that LoDA outperforms existing CL methods.
By Lingfeng He, De Cheng, Huaijie Wang, Xi Yang, Nannan Wang, Xinbo Gao
The study investigates whether switching optimizers between pretraining and subsequent training stages of large language models (LLMs) incurs a performance penalty. By pretraining 1.2B Llama‑3 models with varying proportions of AdamW and Muon updates, and interpolating between the two during continued pretraining and supervised fine‑tuning (SFT), the authors find little evidence of a meaningful optimizer mismatch penalty. The results show that final performance is largely determined by the independent effects of the pretraining and post‑training optimizers, with downstream performance generally improving as the proportion of Muon updates during SFT increases, and that Muon remains competitive with AdamW even for task‑general SFT on larger models.
By Xinyu Zhao, Davis Wertheimer, Ashutosh Sharma, Rameswar Panda, Paul Pu Liang
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 introduces MuonGS, a variant of the Muon optimizer that employs Gram–Schmidt projection to remove the radial component of updates, thereby controlling weight norm growth without fixing it. By ensuring the weight norm grows at most proportionally to √{t}, MuonGS achieves a cumulative effective learning rate of ≥√{T} and an O(T^{-1/2}) stationarity guarantee for smooth scale‑invariant objectives. Experiments on 160M‑ and 400M‑parameter dense models and a 135M‑active/1B‑total MoE model show MuonGS attains lower validation perplexity than MuonH and an estimated token‑equivalent speedup of up to ~15% at matched validation loss.
By Athanasios Glentis, Dawei Li, Mingyi Hong