Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation

• URL: http://arxiv.org/abs/2602.24283v1
• Date: Fri, 27 Feb 2026 18:57:06 GMT
• Title: Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation
• Authors: Zhengbo Wang, Jian Liang, Ran He, Zilei Wang, Tieniu Tan,
• Abstract summary: We introduce LoRA-Pre, a novel low-rank system for efficient pre-training.<n>LoRA-Pre decomposing the momentum matrix into a compact low-rank subspace within the online linear learner.<n>We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family.
• Score: 85.89510825889168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modern optimizers like Adam and Muon are central to training large language models, but their reliance on first- and second-order momenta introduces significant memory overhead, which constrains scalability and computational efficiency. In this work, we reframe the exponential moving average (EMA) used in these momenta as the training of a linear regressor via online gradient flow. Building on this equivalence, we introduce LoRA-Pre, a novel low-rank optimizer designed for efficient pre-training. Specifically, LoRA-Pre reduces the optimizer's memory footprint by decomposing the full momentum matrix into a compact low-rank subspace within the online linear learner, thereby maintaining optimization performance while improving memory efficiency. We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family, scaling from 60M to 1B parameters. LoRA-Pre achieves the highest performance across all model sizes. Notably, LoRA-Pre demonstrates remarkable rank efficiency, achieving comparable or superior results using only 1/8 the rank of baseline methods. Beyond pre-training, we evaluate LoRA-Pre's effectiveness in fine-tuning scenarios. With the same rank, LoRA-Pre consistently outperforms all efficient fine-tuning baselines. Specifically, compared to standard LoRA, LoRA-Pre achieves substantial improvements of 3.14 points on Llama-3.1-8B and 6.17 points on Llama-2-7B, validating our approach's effectiveness across both pre-training and fine-tuning paradigms. Our code is publicly available at https://github.com/mrflogs/LoRA-Pre.

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