Title: Memory-Efficient LLM Pretraining via Minimalist Optimizer Design
Primary area: foundation or frontier models, including LLMs
Keywords: LLM Training, Optimizer, Efficiency

Abstract: Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which introduce extra operations and require significant more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed variants to reduce memory consumption, 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), which 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 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 LLaMA 7B model, SCALE outperforms the state-of-the-art memory-efficient methods APOLLO and Muon, in terms of both perplexity and memory consumption.