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Main Authors: Zhang, Haochen, Yin, Junze, Wang, Guanchu, Liu, Zirui, Yang, Lin F., Zhang, Tianyi, Shrivastava, Anshumali, Braverman, Vladimir
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.05790
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author Zhang, Haochen
Yin, Junze
Wang, Guanchu
Liu, Zirui
Yang, Lin F.
Zhang, Tianyi
Shrivastava, Anshumali
Braverman, Vladimir
author_facet Zhang, Haochen
Yin, Junze
Wang, Guanchu
Liu, Zirui
Yang, Lin F.
Zhang, Tianyi
Shrivastava, Anshumali
Braverman, Vladimir
contents Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is selecting suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling for low-rank optimization in LLM pretraining with a provable convergence guarantee, which the dominant subspace approach does not have. Empirically, we demonstrate that our method significantly outperforms previous methods in LLM pretraining tasks.
format Preprint
id arxiv_https___arxiv_org_abs_2502_05790
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining
Zhang, Haochen
Yin, Junze
Wang, Guanchu
Liu, Zirui
Yang, Lin F.
Zhang, Tianyi
Shrivastava, Anshumali
Braverman, Vladimir
Machine Learning
Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is selecting suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling for low-rank optimization in LLM pretraining with a provable convergence guarantee, which the dominant subspace approach does not have. Empirically, we demonstrate that our method significantly outperforms previous methods in LLM pretraining tasks.
title Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining
topic Machine Learning
url https://arxiv.org/abs/2502.05790