A Minimalist Optimizer Design for LLM Pretraining

• URL: http://arxiv.org/abs/2506.16659v1
• Date: Fri, 20 Jun 2025 00:10:35 GMT
• Title: A Minimalist Optimizer Design for LLM Pretraining
• Authors: Athanasios Glentis, Jiaxiang Li, Andi Han, Mingyi Hong,
• Abstract summary: Training large language models typically relies on adaptives such as Adam.<n>Recent works such as GaLore Fira, and APOLLO have proposed state-compressed variants to reduce memory consumption.<n>In this work, we investigate what is the minimal amount of state that is truly necessary to retain state-of-the-art performance in LLM pretraining.
• Score: 31.996047271119156
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which require significant memory to maintain first- and second-moment matrices, known as optimizer states. While recent works such as GaLore, Fira, and APOLLO have proposed state-compressed variants to reduce memory consumption, a fundamental question remains: What is the minimal amount of optimizer state that is truly necessary to retain state-of-the-art performance in LLM pretraining? In this work, we systematically investigate this question using a bottom-up approach. We find that two memory- and compute-efficient optimization techniques are particularly effective: (1) column-wise gradient normalization significantly boosts the performance of plain SGD without requiring momentum; and (2) adding first-order momentum only to the output layer - where gradient variance is highest - yields performance competitive with fully adaptive methods such as Muon. Based on these insights, we propose SCALE (Stochastic Column-normalized Last-layer Momentum), a new optimizer that combines column-normalized SGD with last-layer momentum, where column normalization refers to normalizing the gradient along the output dimension. Across multiple LLaMA 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 the LLaMA 7B model, SCALE outperforms the state-of-the-art method APOLLO in terms of both perplexity and memory consumption. In addition, our method serves as a minimalist baseline for more sophisticated optimizer design.

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