Prompt Valuation Based on Shapley Values (2312.15395v2)

Abstract: LLMs excel on new tasks without additional training, simply by providing natural language prompts that demonstrate how the task should be performed. Prompt ensemble methods comprehensively harness the knowledge of LLMs while mitigating individual biases and errors and further enhancing performance. However, more prompts do not necessarily lead to better results, and not all prompts are beneficial. A small number of high-quality prompts often outperform many low-quality prompts. Currently, there is a lack of a suitable method for evaluating the impact of prompts on the results. In this paper, we utilize the Shapley value to fairly quantify the contributions of prompts, helping to identify beneficial or detrimental prompts, and potentially guiding prompt valuation in data markets. Through extensive experiments employing various ensemble methods and utility functions on diverse tasks, we validate the effectiveness of using the Shapley value method for prompts as it effectively distinguishes and quantifies the contributions of each prompt.

• The paper presents a novel method using Shapley values to quantify individual prompt contributions in LLM ensembles.
• It details a framework involving utility functions and ensemble methods to evaluate prompt impact across various NLP tasks.
• Experimental results show that removing low-value prompts improves accuracy, validating the method's efficacy for prompt optimization.

Utilizing Shapley Values for Equitable Prompt Valuation in LLM Ensembles

Introduction to Prompt Valuation Challenges

With the advancement in LLMs, leveraging natural language prompts for task execution without additional training has become increasingly popular. Such techniques significantly reduce the necessity for fine-tuning, which is both resource-intensive and impractical for maintaining across multiple domains or tasks. However, the efficiency and reliability of these models heavily depend on the quality of the prompts used. While integrating multiple prompts through ensemble methods can enhance model performance by mitigating individual biases and errors, not all prompts contribute equally to the effectiveness of the ensemble. Assessing the value of individual prompts remains a critical yet challenging task, essential for optimizing prompt combinations and for pricing prompts in data markets. This paper presents a novel approach, adopting the Shapley value, a concept from cooperative game theory, to quantify the contributions of prompts within an ensemble fairly and accurately.

Theoretical Foundation and Methodology

Shapley Value Fundamentals

The Shapley value offers a unique approach to fairly distribute rewards among contributors in a cooperative setting based on their individual contributions. It adheres to principles like balance, symmetry, additivity, and the null player condition, making it an ideal candidate for evaluating prompt contributions. The computation of Shapley values, however, is known for its computational complexity, which poses a challenge for its application in evaluating LLM prompts due to the large model sizes and the high cost of repeated predictions.

Prompt Ensemble and Utility Function

The methodology involves the use of multiple prompts to garner a diverse set of responses from an LLM for a given task. The utility of each prompt is measured based on its marginal contribution to the overall performance of the ensemble across various NLP tasks. To accommodate the complexity of NLP tasks, which include both understanding and generation tasks with their respective evaluation metrics, distinct utility functions are developed.

Experimental Validation

Setup and Preliminary Results

The experiments utilized multiple datasets across different NLP tasks, from sentiment analysis to question answering and machine translation, using pre-trained models like RoBERTa and GPT-3. A set of prompts was generated for each task using ChatGPT, serving as the basis for Shapley value calculations. The effectiveness of these prompts was assessed using majority voting as the ensemble method for deterministic tasks.

Evaluating Contribution through Shapley Values

The research outlined two primary experiments: removing low-value prompts and adding new prompts based on their Shapley values. The results from these experiments demonstrated the utility of Shapley values in identifying and quantifying the impact of each prompt within the ensemble. Notably, the removal of prompts with low Shapley values led to an improved accuracy, affirming the effectiveness of the method in enhancing prompt ensemble performance. Conversely, the addition of prompts with negative Shapley values resulted in a decrease in accuracy, further validating the Shapley value as a tool for prompt valuation.

Implications and Future Directions

This paper substantiates the applicability of Shapley values for prompt valuation within LLM ensembles, presenting both theoretical and practical contributions to the field of NLP. The method offers a structured approach to quantify the contribution of individual prompts, facilitating the optimization of prompt ensembles for improved model performance. Moreover, the practical implications extend to the valuation of prompts in data markets, where fair and equitable pricing strategies are necessary.

The future of AI and LLMs will likely involve more sophisticated prompt ensemble methods and the continuous refinement of utility functions for diverse tasks. Further research could explore efficient computational techniques for Shapley value estimation and extend the application of this method to other domains where ensemble methods are employed. Additionally, understanding the interplay between prompts in an ensemble and their collective impact on model performance may yield further insights into the optimization of LLMs for complex tasks.