mlsanityData to 14 Oct 2026

Fantastic Pretraining Optimizers and Where to Find Them

arXiv 2509.02046 ↗First posted 2 Sep 2025cs.LG cs.AI stat.MLcited by 100

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 100 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Sep 2025.

Builds on

0 of 0 references.

No references here yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 20; 2026: 80.

100 papers.

Sort:

By area:

  1. 2025NorMuon: Making Muon more efficient and scalablecited by 84
  2. 2025Isotropic Curvature Model for Understanding Deep Learning Optimization: Is Gradient Orthogonalization Optimal?cited by 37
  3. 2025Pre-training under infinite computecited by 29
  4. 2025Beyond the Ideal: Analyzing the Inexact Muon Updatecited by 27
  5. 2026How Much Is One Recurrence Worth? Iso-Depth Scaling Laws for Looped Language Modelscited by 24
  6. 2025Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scalescited by 21
  7. 2025How Muon's Spectral Design Benefits Generalization: A Study on Imbalanced Datacited by 19
  8. 2026The Newton-Muon Optimizercited by 18
  9. 2026MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AIcited by 17
  10. 2025What Really Matters in Matrix-Whitening Optimizers?cited by 16
  11. 2026Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimizationcited by 16
  12. 2026RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimizationcited by 15
38 more
  1. 2026Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memorycited by 14
  2. 2026Muon is Not That Special: Random or Inverted Spectra Work Just as Wellcited by 14
  3. 2025Cautious Weight Decaycited by 13
  4. 2026Mano: Restriking Manifold Optimization for LLM Trainingcited by 12
  5. 2026HTMuon: Improving Muon via Heavy-Tailed Spectral Correctioncited by 12
  6. 2025Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methodscited by 11
  7. 2025MARS-M: When Variance Reduction Meets Matricescited by 10
  8. 2026To Use or not to Use Muon: How Simplicity Bias in Optimizers Matterscited by 10
  9. 2026Delving into Muon and Beyond: Deep Analysis and Extensionscited by 9
  10. 2025Optimal Scaling Needs Optimal Normcited by 8
  11. 2025Robust Layerwise Scaling Rules by Proper Weight Decay Tuningcited by 8
  12. 2026Optimal Learning Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decaycited by 8
  13. 2026Clarifying Shampoo: Adapting Spectral Descent to Stochasticity and the Parameter Trajectorycited by 8
  14. 2025Optimization Benchmark for Diffusion Models on Dynamical Systemscited by 7
  15. 2025Beyond Outliers: A Study of Optimizers Under Quantizationcited by 6
  16. 2025Relative Scaling Laws for LLMscited by 6
  17. 2026Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifoldscited by 6
  18. 2026Why Muon Outperforms Adam: A Curvature Perspectivecited by 6
  19. 2026SOAP, Muon, and Beyond: Pushing LLM Pretraining Scalescited by 6
  20. 2025A Tale of Two Geometries: Adaptive Optimizers and Non-Euclidean Descentcited by 5
  21. 2026Symmetry Breaking in Transformers for Efficient and Interpretable Trainingcited by 5
  22. 2026StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Modelscited by 5
  23. 2026Nora: Normalized Orthogonal Row Alignment for Scalable Matrix Optimizercited by 5
  24. 2026Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Lesscited by 5
  25. 2026Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergencecited by 5
  26. 2026Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimizationcited by 5
  27. 2026PRISM: Distribution-free Adaptive Computation of Matrix Functions for Accelerating Neural Network Trainingcited by 4
  28. 2026The Effect of Mini-Batch Noise on the Implicit Bias of Adamcited by 4
  29. 2026Canzona: A Unified, Asynchronous, and Load-Balanced Framework for Distributed Matrix-based Optimizerscited by 4
  30. 2026Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimizationcited by 4
  31. 2026Weight Decay Improves Language Model Plasticitycited by 4
  32. 2026NuMuon: Nuclear-Norm-Constrained Muon for Compressible LLM Trainingcited by 4
  33. 2026Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minimacited by 4
  34. 2026Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handlingcited by 4
  35. 2026Spectral Scaling Laws of Muoncited by 4
  36. 2025K2-V2: A 360-Open, Reasoning-Enhanced LLMcited by 3
  37. 2026Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Liftingcited by 3
  38. 2026Learning Rate Transfer in Normalized Transformerscited by 3

50 most cited of 100 All 100 (JSON)