In plain words: They tested ten optimizers across four language model sizes, tuning each one fairly and judging them only at the end of training. The best, which adjust gradients using whole matrices instead of single numbers, beat well-tuned AdamW by just 1.1x at the largest size.
Abstract · Fantastic Pretraining Optimizers and Where to Find Them
AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered practical adoption: (i) unequal hyperparameter tuning and (ii) limited or misleading evaluation setups. To address these two issues, we conduct a systematic study of ten deep learning optimizers across four model scales (0.1B-1.2B parameters) and data-to-model ratios (1-8x the Chinchilla optimum). We find that fair and informative comparisons require rigorous hyperparameter tuning and evaluations across a range of model scales and data-to-model ratios, performed at the end of training. First, optimal hyperparameters for one optimizer may be suboptimal for another, making blind hyperparameter transfer unfair. Second, the actual speedup of many proposed optimizers over well-tuned baselines is lower than claimed and decreases with model size to only 1.1x for 1.2B parameter models. Thirdly, comparing intermediate checkpoints before reaching the target training budgets can be misleading, as rankings between two optimizers can flip during training due to learning rate decay. Through our thorough investigation, we find that all the fastest optimizers such as Muon and Soap, use matrices as preconditioners -- multiplying gradients with matrices rather than entry-wise scalars. However, the speedup of matrix-based optimizers is inversely proportional to model scale, decreasing from 1.4x over AdamW for 0.1B parameter models to merely 1.1x for 1.2B parameter models.
Kaiyue Wen, David Hall, Tengyu Ma, Percy Liang
arXiv:2509.02046 · cs.LG, cs.AI, stat.ML · submitted Sep 2, 2025 · updated Sep 4, 2025
abstract · pdf · html · 108 pages, 8 figures, reproducible runs available at https://wandb.ai/marin-community/optimizer-scaling
This may all seem in good fun, but it makes a real difference when you have to introduce this paper to students and other academics getting into the discipline. It's just embarrassing, and always garners a reaction from a facepalm to disgust. This is especially true now that Rowling is a controversial figure.
As for the paper itself, this provides a good source for referencing, but the conclusions drawn here seem to be pretty commonly known in the folklore. I think we're finally starting to see a healthy and meaningful shift in tone from the optimization community that has been obsessed with early convergence rates for years. It's good to have options in optimizers, but the decision on which optimizer to use is rarely so straightforward and comes from prior experience. Most will stick with AdamW.