Improving Probability-based Prompt Selection Through Unified Evaluation and Analysis

TL;DR

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 finds 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).

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.

Figures (9)

• Figure 1: (a) F1 of the prompts selected by different probability-based prompt selection methods, averaged across 13 datasets. Per-dataset F1 and accuracy are shown in Figure \ref{['fig:granular']}. The methods without super/subscripts are the existing methods (Table \ref{['tab:methods']}), while those with super/subscripts are our proposed methods (Table \ref{['tab:transfer']} & Equation \ref{['eq:cbm']}). (b) Ratio of the prompts (out of 100) whose F1 on each dataset improves by applying probability calibration for answer selection, averaged across 10 models. Our proposed calibration method, CBM (Equation \ref{['eq:cbm']}), is considerably more effective than CC and PMI$_\text{DC}$ (Table \ref{['tab:calibration']}) in enhancing the answer selection performance of the prompts.
• Figure 2: F1 of the prompts selected by the existing probability-based prompt selection methods, averaged for each dataset category, with the task average also shown.
• Figure 3: The highlighted parts of the equation are rough estimations of the Prompt Selection Score (PSS) of each method, i.e., the score of which the prompt with the maximum value is chosen by the prompt selection method. They show the connection between different probability-based prompt selection methods.
• Figure 4: F1 of the prompts selected by MI$_{\textnormal{A}}$ and MI, averaged for each setup of a different number of tokens of verbalizers and evaluation dataset category. $|v|$ denotes the number of tokens of the verbalizers.
• Figure 5: F1 of the prompts selected by different probability-based prompt selection methods, averaged for each dataset category, with the task average also shown. The methods with subscripts are the combinational variants proposed in this subsection, whose Prompt Selection Scores are shown in Table \ref{['tab:transfer']} . The methods with subscript M are combinational variants that use the component of MI; the methods with L perform instance-wise prompt selection like MDL; the methods with G utilize one-hot $p(\mathbf{y}|x,t)$ like GE. The methods with A use All tokens to calculate $p(\mathbf{y}|x,t)$.