CoSA: Compressed Sensing-Based Adaptation of Large Language Models

• URL: http://arxiv.org/abs/2602.05148v2
• Date: Wed, 11 Feb 2026 19:07:23 GMT
• Title: CoSA: Compressed Sensing-Based Adaptation of Large Language Models
• Authors: Songtao Wei, Yi Li, Bohan Zhang, Zhichun Guo, Ying Huang, Yuede Ji, Miao Yin, Guanpeng Li, Bingzhe Li,
• Abstract summary: CoSA (Compressed Sensing-Based Adaptation) is a new PEFT method extended from compressed sensing theory.<n>We show that CoSA provides a principled perspective for efficient and expressive multi-scale model adaptation.<n>We evaluate CoSA on 10 diverse tasks, including natural language understanding and generation, employing 5 models of different scales from RoBERTa, Llama, and Qwen families.
• Score: 21.688889188355645
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Parameter-Efficient Fine-Tuning (PEFT) has emerged as a practical paradigm for adapting large language models (LLMs) without updating all parameters. Most existing approaches, such as LoRA and PiSSA, rely on low-rank decompositions of weight updates. However, the low-rank assumption may restrict expressivity, particularly in task-specific adaptation scenarios where singular values are distributed relatively uniformly. To address this limitation, we propose CoSA (Compressed Sensing-Based Adaptation), a new PEFT method extended from compressed sensing theory. Instead of constraining weight updates to a low-rank subspace, CoSA expresses them through fixed random projection matrices and a compact learnable core. We provide a formal theoretical analysis of CoSA as a synthesis process, proving that weight updates can be compactly encoded into a low-dimensional space and mapped back through random projections. Extensive experimental results show that CoSA provides a principled perspective for efficient and expressive multi-scale model adaptation. Specifically, we evaluate CoSA on 10 diverse tasks, including natural language understanding and generation, employing 5 models of different scales from RoBERTa, Llama, and Qwen families. Across these settings, CoSA consistently matches or outperforms state-of-the-art PEFT methods.

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