LOST: Low-rank and Sparse Pre-training for Large Language Models

• URL: http://arxiv.org/abs/2508.02668v1
• Date: Mon, 04 Aug 2025 17:58:22 GMT
• Title: LOST: Low-rank and Sparse Pre-training for Large Language Models
• Authors: Jiaxi Li, Lu Yin, Li Shen, Jinjin Xu, Liwu Xu, Tianjin Huang, Wenwu Wang, Shiwei Liu, Xilu Wang,
• Abstract summary: Large language models incur prohibitive computational and memory costs for pre-training from scratch.<n>We propose textbfLOw-rank and textbfSparse pre-textbfTraining (textbfLOST) for LLMs.
• Score: 28.81360343891614
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While large language models (LLMs) have achieved remarkable performance across a wide range of tasks, their massive scale incurs prohibitive computational and memory costs for pre-training from scratch. Recent studies have investigated the use of low-rank parameterization as a means of reducing model size and training cost. In this context, sparsity is often employed as a complementary technique to recover important information lost in low-rank compression by capturing salient features in the residual space. However, existing approaches typically combine low-rank and sparse components in a simplistic or ad hoc manner, often resulting in undesirable performance degradation compared to full-rank training. In this paper, we propose \textbf{LO}w-rank and \textbf{S}parse pre-\textbf{T}raining (\textbf{LOST}) for LLMs, a novel method that ingeniously integrates low-rank and sparse structures to enable effective training of LLMs from scratch under strict efficiency constraints. LOST applies singular value decomposition to weight matrices, preserving the dominant low-rank components, while allocating the remaining singular values to construct channel-wise sparse components to complement the expressiveness of low-rank training. We evaluate LOST on LLM pretraining ranging from 60M to 7B parameters. Our experiments show that LOST achieves competitive or superior performance compared to full-rank models, while significantly reducing both memory and compute overhead. Moreover, Code is available at \href{https://github.com/JiaxiLi1/LOST-Low-rank-and-Sparse-Training-for-Large-Language-Models}{LOST Repo}

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