mlsanityData to 14 Oct 2026

Benchmarking Optimizers for Large Language Model Pretraining

arXiv 2509.01440 ↗First posted 1 Sep 2025cs.LGcited by 68

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Abstract (arXiv)

The recent development of Large Language Models (LLMs) has been accompanied by an effervescence of novel ideas and methods to better optimize the loss of deep learning models. Claims from those methods are myriad: from faster convergence to removing reliance on certain hyperparameters. However, the diverse experimental protocols used to validate these claims make direct comparisons between methods challenging. This study presents a comprehensive evaluation of recent optimization techniques across standardized LLM pretraining scenarios, systematically varying model size, batch size, and training duration. Through careful tuning of each method, we provide guidance to practitioners on which optimizer is best suited for each scenario. For researchers, our work highlights promising directions for future optimization research. Finally, by releasing our code and making all experiments fully reproducible, we hope our efforts can help the development and rigorous benchmarking of future methods.

Key facts. Cited by 68 papers in the map (data through 14 Oct 2026). First posted on arXiv 1 Sep 2025.

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Citing papers per year: 2025: 12; 2026: 56.

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  1. 2025Isotropic Curvature Model for Understanding Deep Learning Optimization: Is Gradient Orthogonalization Optimal?cited by 37
  2. 2025Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scalescited by 21
  3. 2025How Muon's Spectral Design Benefits Generalization: A Study on Imbalanced Datacited by 19
  4. 2025What Really Matters in Matrix-Whitening Optimizers?cited by 16
  5. 2026Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memorycited by 14
  6. 2026Muon is Not That Special: Random or Inverted Spectra Work Just as Wellcited by 14
  7. 2026Mano: Restriking Manifold Optimization for LLM Trainingcited by 12
  8. 2026HTMuon: Improving Muon via Heavy-Tailed Spectral Correctioncited by 12
  9. 2025Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methodscited by 11
  10. 2026Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routerscited by 11
  11. 2025MARS-M: When Variance Reduction Meets Matricescited by 10
  12. 2026Enhancing LLM Training via Spectral Clippingcited by 10
38 more
  1. 2025FedMuon: Federated Learning with Bias-corrected LMO-based Optimizationcited by 8
  2. 2025Optimal Scaling Needs Optimal Normcited by 8
  3. 2026Optimal Learning Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decaycited by 8
  4. 2026Clarifying Shampoo: Adapting Spectral Descent to Stochasticity and the Parameter Trajectorycited by 8
  5. 2025Optimization Benchmark for Diffusion Models on Dynamical Systemscited by 7
  6. 2025Beyond Outliers: A Study of Optimizers Under Quantizationcited by 6
  7. 2026Towards Robust Scaling Laws for Optimizerscited by 6
  8. 2026Where Does Warm-Up Come From? Adaptive Scheduling for Norm-Constrained Optimizerscited by 5
  9. 2026Benchmarking Optimizers for MLPs in Tabular Deep Learningcited by 5
  10. 2026StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Modelscited by 5
  11. 2026Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Lesscited by 5
  12. 2026NuMuon: Nuclear-Norm-Constrained Muon for Compressible LLM Trainingcited by 4
  13. 2026The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learningcited by 4
  14. 2026Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minimacited by 4
  15. 2026AMUSE: Anytime Muon with Stable Gradient Evaluationcited by 4
  16. 2026Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handlingcited by 4
  17. 2026Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluationscited by 3
  18. 2026DynMuon: A Dynamic Spectral Shaping View of Muoncited by 3
  19. 2026Anytime Training with Schedule-Free Spectral Optimizationcited by 3
  20. 2026CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalizationcited by 3
  21. 2025MT-DAO: Multi-Timescale Distributed Adaptive Optimizers with Local Updatescited by 2
  22. 2026When and Why SignSGD Outperforms SGD: A Theoretical Study Based on ℓ1-norm Lower Boundscited by 2
  23. 2026Navigating LLM Valley: From AdamW to Memory-Efficient and Matrix-Based Optimizerscited by 2
  24. 2026Revisiting the Adam-SGD Gap in LLM Pre-Training: The Role of Large Effective Learning Ratescited by 2
  25. 2026LionMuon: Alternating Spectral and Sign Descent for Efficient Trainingcited by 2
  26. 2026Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filteringcited by 2
  27. 2026When to use what Schatten-p norm in deep learning?cited by 2
  28. 2026Hierarchical Muon: Tiled Newton-Schulz Updates for Efficient Muon Optimizationcited by 2
  29. 2026PoLoRA: A Preconditioned Orthogonalized LoRA Optimizercited by 2
  30. 2026Scale Weight Decay and Train Bettercited by 2
  31. 2025DyKAF: Dynamical Kronecker Approximation of the Fisher Information Matrix for Gradient Preconditioningcited by 1
  32. 2026LoRDO: Distributed Low-Rank Optimization with Infrequent Communicationcited by 1
  33. 2026Open Problem: Is AdamW Effective Under Heavy-Tailed Noise?cited by 1
  34. 2026M+Adam: Low-Precision Training via Additive-Multiplicative Optimizationcited by 1
  35. 2026Optimizer Memory Schedules for Outscaling the Overtraining Axiscited by 1
  36. 2026Towards a Principled Muon under μmathsfP: Ensuring Spectral Conditions throughout Trainingcited by 0
  37. 2026Variance-Adaptive Muon: Pre-Orthogonalization Variance Modulation for Efficient Language Model Pretrainingcited by 0
  38. 2026Optimal Sample Complexity for Single Time-Scale Actor-Critic with Momentumcited by 0

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