Memory-Efficient LLM Pretraining via Minimalist Optimizer Design

Athanasios Glentis, Jiaxiang Li, Andi Han, Mingyi Hong
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:35197-35226, 2026.

Abstract

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed memory-efficient variants, a fundamental question remains: What are the minimum modifications to plain SGD needed to match state-of-the-art pretraining performance? We systematically investigate this question using a bottom-up approach, and identify two simple yet highly (memory- and compute-) efficient techniques: (1) column-wise gradient normalization (normalizing the gradient along the output dimension), that boosts SGD performance without momentum; and (2) applying first-order momentum only to the output layer, where gradient variance is highest. Combining these two techniques lead to SCALE (Stochastic Column-normAlized Last-layer momEntum), a simple optimizer for memory efficient pretraining. Across multiple models (60M–1B), SCALE matches or exceeds the performance of Adam while using only 35–45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For LLaMA 7B, SCALE outperforms the state-of-the-art memory-efficient methods APOLLO and Muon in both perplexity and memory consumption. Code is available at https://github.com/OptimAI-Lab/Minimalist_LLM_Pretraining.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-glentis26a, title = {Memory-Efficient {LLM} Pretraining via Minimalist Optimizer Design}, author = {Glentis, Athanasios and Li, Jiaxiang and Han, Andi and Hong, Mingyi}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {35197--35226}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/glentis26a/glentis26a.pdf}, url = {https://proceedings.mlr.press/v306/glentis26a.html}, abstract = {Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed memory-efficient variants, a fundamental question remains: What are the minimum modifications to plain SGD needed to match state-of-the-art pretraining performance? We systematically investigate this question using a bottom-up approach, and identify two simple yet highly (memory- and compute-) efficient techniques: (1) column-wise gradient normalization (normalizing the gradient along the output dimension), that boosts SGD performance without momentum; and (2) applying first-order momentum only to the output layer, where gradient variance is highest. Combining these two techniques lead to SCALE (Stochastic Column-normAlized Last-layer momEntum), a simple optimizer for memory efficient pretraining. Across multiple models (60M–1B), SCALE matches or exceeds the performance of Adam while using only 35–45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For LLaMA 7B, SCALE outperforms the state-of-the-art memory-efficient methods APOLLO and Muon in both perplexity and memory consumption. Code is available at https://github.com/OptimAI-Lab/Minimalist_LLM_Pretraining.} }
Endnote
%0 Conference Paper %T Memory-Efficient LLM Pretraining via Minimalist Optimizer Design %A Athanasios Glentis %A Jiaxiang Li %A Andi Han %A Mingyi Hong %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-glentis26a %I PMLR %P 35197--35226 %U https://proceedings.mlr.press/v306/glentis26a.html %V 306 %X Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed memory-efficient variants, a fundamental question remains: What are the minimum modifications to plain SGD needed to match state-of-the-art pretraining performance? We systematically investigate this question using a bottom-up approach, and identify two simple yet highly (memory- and compute-) efficient techniques: (1) column-wise gradient normalization (normalizing the gradient along the output dimension), that boosts SGD performance without momentum; and (2) applying first-order momentum only to the output layer, where gradient variance is highest. Combining these two techniques lead to SCALE (Stochastic Column-normAlized Last-layer momEntum), a simple optimizer for memory efficient pretraining. Across multiple models (60M–1B), SCALE matches or exceeds the performance of Adam while using only 35–45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For LLaMA 7B, SCALE outperforms the state-of-the-art memory-efficient methods APOLLO and Muon in both perplexity and memory consumption. Code is available at https://github.com/OptimAI-Lab/Minimalist_LLM_Pretraining.
APA
Glentis, A., Li, J., Han, A. & Hong, M.. (2026). Memory-Efficient LLM Pretraining via Minimalist Optimizer Design. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:35197-35226 Available from https://proceedings.mlr.press/v306/glentis26a.html.

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