As the context window expands, self-attention increasingly dominates the transformer's inference time. Therefore, accelerating attention computation while minimizing performance degradation is essential for the efficient deployment of Large Language Models (LLMs). In this study we extend a theoretical framework of attention sparsity in LLMs. A customized loss function is designed to enforce the sparsity by restricting the number of top elements in the attention matrix. We perform an initial set of evaluations with GPT-2 to show the effectiveness of our sparsification approach. The attention matrices of the models trained with the proposed loss are both sparse and effective in capturing relevant input dependencies. We now continue working to demonstrate the value of our approach on larger models and different architectures.