# Pre-Training LLMs on a budget: A comparison of three optimizers

arXiv: https://arxiv.org/abs/2507.08472 · HTML: https://mlsanity.com/paper/2507.08472/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [OLMES: A Standard for Language Model Evaluations](https://mlsanity.com/paper/2406.08446/) (2024)
- [Spike No More: Stabilizing the Pre-training of Large Language Models](https://mlsanity.com/paper/2312.16903/) (2023)
- [No Train No Gain: Revisiting Efficient Training Algorithms For Transformer-based Language Models](https://mlsanity.com/paper/2307.06440/) (2023)
- [ROPE: Reading Order Equivariant Positional Encoding for Graph-based Document Information Extraction](https://mlsanity.com/paper/2106.10786/) (2021)
- [Ranger21: a synergistic deep learning optimizer](https://mlsanity.com/paper/2106.13731/) (2021)
- [BTLM-3B-8K: 7B Parameter Performance in a 3B Parameter Model](https://mlsanity.com/paper/2309.11568/) (2023)
- [On the Parameterization of Second-Order Optimization Effective Towards the Infinite Width](https://mlsanity.com/paper/2312.12226/) (2023)
- [An Empirical Study of μP Learning Rate Transfer](https://mlsanity.com/paper/2404.05728/) (2024)

## Built on by (most cited first, 5 of 5)

- [Mano: Restriking Manifold Optimization for LLM Training](https://mlsanity.com/paper/2601.23000/) (2026)
- [StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models](https://mlsanity.com/paper/2604.15416/) (2026)
- [POP: Prior-Fitted First-Order Optimization Policies](https://mlsanity.com/paper/2602.15473/) (2026)
- [OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers](https://mlsanity.com/paper/2607.04033/) (2026)
- [From Data to Device: ELMOD An Efficient German-First 2.7B Language Model for Mobile Inference](https://mlsanity.com/paper/2607.24585/) (2026)

## Abstract (arXiv)

Optimizers play a decisive role in reducing pre-training times for LLMs and achieving better-performing models. In this study, we compare three major variants: the de-facto standard AdamW, the simpler Lion, developed through an evolutionary search, and the second-order optimizer Sophia. For better generalization, we train with two different base architectures and use a single- and a multiple-epoch approach while keeping the number of tokens constant. Using the Maximal Update Parametrization and smaller proxy models, we tune relevant hyperparameters separately for each combination of base architecture and optimizer. We found that while the results from all three optimizers were in approximately the same range, Sophia exhibited the lowest training and validation loss, Lion was fastest in terms of training GPU hours but AdamW led to the best downstream evaluation results.