Large Language Models (LLMs) have revolutionized AI, demonstrating impressive abilities across various tasks. But fine-tuning them for specific applications remains a resource-intensive challenge. Recent research unveils fascinating insights into fine-tuning LLMs, especially focusing on the attention mechanism. Two key discoveries stand out: First, fine-tuning specific parts of the attention mechanism (the "value" and "query" matrices) is more important and efficient than adjusting the entire mechanism. Second, using different learning rates for these matrices greatly improves convergence, leading to faster and better results. This research explores these phenomena from two main angles: how these insights improve an LLM's ability to generalize to new data, and how they speed up the learning process during optimization. The theoretical findings reveal that focusing on 'value' and 'query' matrices improves generalization and memory efficiency. Furthermore, using distinct learning rates optimizes how the attention mechanism learns key features, which in turn boosts fine-tuning effectiveness. These findings have significant practical implications. By using a new strategy based on freezing the “key” matrix within the attention mechanism, and applying appropriate learning rates to the “value” and “query” matrices, it’s possible to greatly enhance efficiency. Experimental results validate this theoretical framework. Fine-tuning LLMs has long been a computationally demanding process. This research presents a crucial step towards making LLMs more adaptable and resource-efficient, paving the way for wider deployment in various applications.