This paper investigates the asymmetry in the roles of low-rank adapter matrices (A and B) in LoRA (Low-Rank Adaptation) fine-tuning of foundation models. The study reveals that the B matrix plays a more critical role in fine-tuning than the A matrix, and that fine-tuning B alone can achieve performance comparable to fine-tuning both A and B. Theoretical and empirical analyses show that the B matrix is responsible for projecting features towards the desired output, while the A matrix extracts features from the input. This asymmetry is supported by experiments on various models and tasks, including RoBERTa, BART-Large, LLaMA-2, and Vision Transformers (ViTs). The findings suggest that freezing A and fine-tuning B can improve generalization and reduce parameter usage, leading to more efficient and effective fine-tuning strategies. The paper also provides insights into the theoretical underpinnings of this asymmetry, demonstrating that the performance of LoRA can be enhanced by leveraging the structure of the low-rank adaptation. The results highlight the importance of understanding the roles of different components in parameter-efficient fine-tuning and provide practical guidance for improving the efficiency and generalization of LoRA-based models.This paper investigates the asymmetry in the roles of low-rank adapter matrices (A and B) in LoRA (Low-Rank Adaptation) fine-tuning of foundation models. The study reveals that the B matrix plays a more critical role in fine-tuning than the A matrix, and that fine-tuning B alone can achieve performance comparable to fine-tuning both A and B. Theoretical and empirical analyses show that the B matrix is responsible for projecting features towards the desired output, while the A matrix extracts features from the input. This asymmetry is supported by experiments on various models and tasks, including RoBERTa, BART-Large, LLaMA-2, and Vision Transformers (ViTs). The findings suggest that freezing A and fine-tuning B can improve generalization and reduce parameter usage, leading to more efficient and effective fine-tuning strategies. The paper also provides insights into the theoretical underpinnings of this asymmetry, demonstrating that the performance of LoRA can be enhanced by leveraging the structure of the low-rank adaptation. The results highlight the importance of understanding the roles of different components in parameter-efficient fine-tuning and provide practical guidance for improving the efficiency and generalization of LoRA-based models.