Fantastic Pretraining Optimizers and Where to Find Them
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.
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Citing papers per year: 2025: 20; 2026: 80.
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- 2025NorMuon: Making Muon more efficient and scalablecited by 84
- 2025Isotropic Curvature Model for Understanding Deep Learning Optimization: Is Gradient Orthogonalization Optimal?cited by 37
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- 2025Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scalescited by 21
- 2025How Muon's Spectral Design Benefits Generalization: A Study on Imbalanced Datacited by 19
- 2026The Newton-Muon Optimizercited by 18
- 2026MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AIcited by 17
- 2025What Really Matters in Matrix-Whitening Optimizers?cited by 16
- 2026Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimizationcited by 16
- 2026RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimizationcited by 15
38 more
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- 2025A Tale of Two Geometries: Adaptive Optimizers and Non-Euclidean Descentcited by 5
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- 2026Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergencecited by 5
- 2026Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimizationcited by 5
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50 most cited of 100 All 100 (JSON)
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- 2026On the Depth Transfer of Neural Optimizers via L-Smoothness9 Oct 2026
- 2026Towards Easier-to-Tune Training Algorithms: New Results from AlgoPerf9 Oct 2026
- 2026OptiSelect: How does the Optimizer Shape Data Curriculum?2 Oct 2026
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- 2026Self-Play Pretraining with Zero Data24 Sep 2026
- 2026The Ethics of Artificial Intelligence in Military Operations22 Sep 2026
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- 2026Optimizers for Diffusion Models: A Controlled Benchmark19 Sep 2026
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- 2026Blog: Survey of Optimizers28 Aug 2026
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- 2026OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers4 Jul 2026
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- 2026Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering2 Jun 2026
- 2026Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling29 May 2026
- 2026On the Optimizer Dependence of Neural Scaling Laws28 May 2026
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- 2026DynMuon: A Dynamic Spectral Shaping View of Muon16 May 2026
- 2026Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergence13 May 2026
- 2026Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives12 May 2026
- 2026Muon is Not That Special: Random or Inverted Spectra Work Just as Well11 May 2026
- 2026Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds10 May 2026
- 2026MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI9 May 2026
- 2026Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less7 May 2026
50 newest of 100 All 100 (JSON)
- 2025K2-V2: A 360-Open, Reasoning-Enhanced LLMcited by 3
- 2025Shaping Explanations: Semantic Reward Modeling with Encoder-Only Transformers for GRPOcited by 2
- 2026ISO: An RLVR-Native Optimization Stackcited by 2
- 2026ISO: An RLVR-Native Optimization Stack21 Jul 2026
- 2025K2-V2: A 360-Open, Reasoning-Enhanced LLM5 Dec 2025
- 2025Shaping Explanations: Semantic Reward Modeling with Encoder-Only Transformers for GRPO16 Sep 2025
- 2026Self-Play Pretraining with Zero Datacited by 1
- 2026Self-Play Pretraining with Zero Data24 Sep 2026
- 2025NorMuon: Making Muon more efficient and scalablecited by 84
- 2025Isotropic Curvature Model for Understanding Deep Learning Optimization: Is Gradient Orthogonalization Optimal?cited by 37
- 2025Pre-training under infinite computecited by 29
- 2025Beyond the Ideal: Analyzing the Inexact Muon Updatecited by 27
- 2026How Much Is One Recurrence Worth? Iso-Depth Scaling Laws for Looped Language Modelscited by 24
- 2025Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scalescited by 21
- 2025How Muon's Spectral Design Benefits Generalization: A Study on Imbalanced Datacited by 19
- 2026The Newton-Muon Optimizercited by 18
- 2026MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AIcited by 17
- 2025What Really Matters in Matrix-Whitening Optimizers?cited by 16
- 2026Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimizationcited by 16
- 2026RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimizationcited by 15
12 most cited of 92 All 92 (JSON)
- 2026How Inner Optimizers Shape Replica Scaling13 Oct 2026
- 2026A Refresh Interval Does Not Fully Specify a Refresh Schedule: Learning-Rate-Dependent Placement in Kronecker-Preconditioned Language Model Training13 Oct 2026
- 2026Which Geometry on Which Layer? Measured Sign-Spectral Assignment in Mixed-Optimizer Training12 Oct 2026
- 2026On the Depth Transfer of Neural Optimizers via L-Smoothness9 Oct 2026
- 2026Towards Easier-to-Tune Training Algorithms: New Results from AlgoPerf9 Oct 2026
- 2026OptiSelect: How does the Optimizer Shape Data Curriculum?2 Oct 2026
- 2026Relative Generalization Invariance of LLM Pretraining26 Sep 2026
- 2026The Ethics of Artificial Intelligence in Military Operations22 Sep 2026
- 2026Terminal Shrinkage Averaging Reveals a Schedule-Estimator Interaction in LLM Pretraining21 Sep 2026
- 2026How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents16 Sep 2026
- 2026Beyond the Matrix Sign: Quadratic Spectral Descent7 Sep 2026
- 2026HyperTransfer: Understanding the Equivalence between Base Optimizer and Hyperball7 Sep 2026
12 newest of 92 All 92 (JSON)