Improving Probability-based Prompt Selection Through Unified Evaluation and Analysis

TL;DR

This paper introduces a unified framework for probability-based prompt selection in large language models, revealing their connection to mutual information maximization and proposing a calibration method to enhance performance across diverse NLP tasks.

Contribution

It unifies existing prompt selection methods under a mutual information perspective and proposes a novel calibration technique to improve prompt selection accuracy.

Findings

Enhanced prompt selection accuracy from 87.79% to 96.85%.

Unified interpretation of existing methods as mutual information maximization.

Proposed calibration method increases effectiveness without calibration to 99.44% of oracle performance.

Abstract

Previous works in prompt engineering for large language models have introduced different gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but have failed to provide a comprehensive and fair comparison between each other. In this paper, we propose a unified framework to interpret and evaluate the existing probability-based prompt selection methods by performing extensive experiments on 13 common and diverse NLP tasks. We find that each of the existing methods can be interpreted as some variant of the method that maximizes mutual information between the input and the predicted output (MI). Utilizing this finding, we develop several other combinatorial variants of MI and increase the effectiveness of the oracle prompt selection method from 87.79% to 94.98%, measured as the ratio of the performance of the selected prompt to that of the optimal oracle prompt. Furthermore, considering that all the methods rely on the output probability distribution of the model that might be biased, we propose a novel calibration method called Calibration by Marginalization (CBM) that is orthogonal to the existing methods and helps increase the prompt selection effectiveness of the best method to 96.85%, achieving 99.44% of the oracle prompt F1 without calibration.