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
The paper investigates how different optimizers acquire distinct generalizing relations in single‑hidden‑layer ReLU networks. By manipulating nuisance‑connected weights and performing a strict‑parity sweep, the authors show that training conditions reshape both shared failures and relative optimizer advantages, with specific interventions improving accuracy on hard stages. The study also compares optimizer behavior across tasks and an external architecture (CIFAR‑10).
By Gongyue Zhang, Honghai Liu
The paper introduces two variance‑adaptive variants of the Muon optimizer—Muon‑NSR and Muon‑VS—for language model pretraining. Both methods incorporate gradient‑variance information into Muon’s orthogonalization process without adding extra hyperparameters, preserving its spectral normalization structure. Experiments on Llama‑style and GPT‑2 models ranging from 125 M to 1.2 B parameters show that these variants outperform well‑tuned Muon baselines and achieve up to a 1.33× step‑to‑target speedup on Llama‑1.2B.
By Jingru Li, Yibo Fan, Huan Li
arXiv:2606. 16899v1 Announce Type: new Abstract: Matrix based optimizers such as Muon can substantially speed up language model pretraining, but their gains over AdamW are observed to shrink as model size and data scale grow when using standard constant decoupled weight decay.
By Kaiyue Wen, Xingyu Dang, Kaifeng Lyu, Tengyu Ma, Percy Liang
arXiv:2609.01244v1 Announce Type: new
Abstract: Every supervised fine-tuning run forces the same chain of decisions, such as learning rate, batch size, LoRA or full fine-tuning, how many epochs, whic...
By Charles O'Neill, Mudith Jayasekara, Harry Partridge
arXiv:2606. 03938v1 Announce Type: cross Abstract: Multi-epoch training is becoming the standard now that compute is growing faster than the supply of high-quality text.
By Bishwas Mandal, Shmuel Berman, Akshay Vegesna, Samip Dahal