Robust and Fair Prompt Attribution via Banzhaf Value in Large Language Models

Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of applications, including text generation, reasoning and scientific discovery. However, the mechanisms by which input prompts influence model outputs remain insufficiently understood, highlighting an urgent need to uncover the relationship between prompts and generated content. While existing prompt attribution methods primarily focus on fairness, they often overlook robustness—an equally crucial property for ensuring reliable and stable attribution. In this paper, we investigate both classical and modern prompt attribution algorithms and propose a method that enhances robustness through the use of Banzhaf power index (or Banzhaf value), while preserving fairness. To address the computational overhead associated with Banzhaf Value, we adopt the Maximum Sample Reuse (MSR) Monte Carlo sampling technique to significantly accelerate its estimation. Extensive experimental results demonstrate that our improved Banzhaf-based approach not only improves robustness under various perturbations, but also maintains fairness and high efficiency, making it a strong candidate for trustworthy and scalable prompt attribution in LLMs.