# Benchmarking Optimizers for Large Language Model Pretraining

arXiv: https://arxiv.org/abs/2509.01440 · HTML: https://mlsanity.com/paper/2509.01440/

## Key facts

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

## Built on by (most cited first, 30 of 68)

- [Isotropic Curvature Model for Understanding Deep Learning Optimization: Is Gradient Orthogonalization Optimal?](https://mlsanity.com/paper/2511.00674/) (2025)
- [Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scales](https://mlsanity.com/paper/2512.05620/) (2025)
- [How Muon's Spectral Design Benefits Generalization: A Study on Imbalanced Data](https://mlsanity.com/paper/2510.22980/) (2025)
- [What Really Matters in Matrix-Whitening Optimizers?](https://mlsanity.com/paper/2510.25000/) (2025)
- [Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory](https://mlsanity.com/paper/2603.26554/) (2026)
- [Muon is Not That Special: Random or Inverted Spectra Work Just as Well](https://mlsanity.com/paper/2605.11181/) (2026)
- [Mano: Restriking Manifold Optimization for LLM Training](https://mlsanity.com/paper/2601.23000/) (2026)
- [HTMuon: Improving Muon via Heavy-Tailed Spectral Correction](https://mlsanity.com/paper/2603.10067/) (2026)
- [Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods](https://mlsanity.com/paper/2510.10777/) (2025)
- [Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers](https://mlsanity.com/paper/2605.18106/) (2026)
- [MARS-M: When Variance Reduction Meets Matrices](https://mlsanity.com/paper/2510.21800/) (2025)
- [Enhancing LLM Training via Spectral Clipping](https://mlsanity.com/paper/2603.14315/) (2026)
- [FedMuon: Federated Learning with Bias-corrected LMO-based Optimization](https://mlsanity.com/paper/2509.26337/) (2025)
- [Optimal Scaling Needs Optimal Norm](https://mlsanity.com/paper/2510.03871/) (2025)
- [Optimal Learning Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay](https://mlsanity.com/paper/2602.06797/) (2026)
- [Clarifying Shampoo: Adapting Spectral Descent to Stochasticity and the Parameter Trajectory](https://mlsanity.com/paper/2602.09314/) (2026)
- [Optimization Benchmark for Diffusion Models on Dynamical Systems](https://mlsanity.com/paper/2510.19376/) (2025)
- [Beyond Outliers: A Study of Optimizers Under Quantization](https://mlsanity.com/paper/2509.23500/) (2025)
- [Towards Robust Scaling Laws for Optimizers](https://mlsanity.com/paper/2602.07712/) (2026)
- [Where Does Warm-Up Come From? Adaptive Scheduling for Norm-Constrained Optimizers](https://mlsanity.com/paper/2602.05813/) (2026)
- [Benchmarking Optimizers for MLPs in Tabular Deep Learning](https://mlsanity.com/paper/2604.15297/) (2026)
- [StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models](https://mlsanity.com/paper/2604.15416/) (2026)
- [Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less](https://mlsanity.com/paper/2605.06654/) (2026)
- [NuMuon: Nuclear-Norm-Constrained Muon for Compressible LLM Training](https://mlsanity.com/paper/2603.03597/) (2026)
- [The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learning](https://mlsanity.com/paper/2603.15914/) (2026)
- [Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima](https://mlsanity.com/paper/2604.09258/) (2026)
- [AMUSE: Anytime Muon with Stable Gradient Evaluation](https://mlsanity.com/paper/2605.22432/) (2026)
- [Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling](https://mlsanity.com/paper/2605.31371/) (2026)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [DynMuon: A Dynamic Spectral Shaping View of Muon](https://mlsanity.com/paper/2605.17109/) (2026)

## 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.