Large pre-trained transformers have revolutionized artificial intelligence across various domains, and fine-tuning remains the dominant approach for adapting these models to downstream tasks due to the cost of training from scratch. However, in existing fine-tuning methods, the updated representations are formed as a dense combination of modified parameters, making it challenging to interpret their contributions and understand how the model adapts to new tasks. In this work, we introduce a fine-tuning framework inspired by sparse coding, where fine-tuned features are represented as a sparse combination of basic elements, i.e., feature dictionary atoms. The feature dictionary atoms function as fundamental building blocks of the representation, and tuning atoms allows for seamless adaptation to downstream tasks. Sparse coefficients then serve as indicators of atom importance, identifying the contribution of each atom to the updated representation. Leveraging the atom selection capability of sparse coefficients, we first demonstrate that our method enhances image editing performance by improving text alignment through the removal of unimportant feature dictionary atoms. Additionally, we validate the effectiveness of our approach in the text-to-image concept customization task, where our method efficiently constructs the target concept using a sparse combination of feature dictionary atoms, outperforming various baseline fine-tuning methods.