# Improving Probability-based Prompt Selection Through Unified Evaluation and Analysis

arXiv: https://arxiv.org/abs/2305.14877 · HTML: https://mlsanity.com/paper/2305.14877/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 54 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Making Pre-trained Language Models Better Few-shot Learners](https://mlsanity.com/paper/2012.15723/) (2020)
- [What Makes Good In-Context Examples for GPT-3?](https://mlsanity.com/paper/2101.06804/) (2021)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification](https://mlsanity.com/paper/2010.12421/) (2020)
- [RLPrompt: Optimizing Discrete Text Prompts with Reinforcement Learning](https://mlsanity.com/paper/2205.12548/) (2022)
- [PromptSource: An Integrated Development Environment and Repository for Natural Language Prompts](https://mlsanity.com/paper/2202.01279/) (2022)
- [Surface Form Competition: Why the Highest Probability Answer Isn't Always Right](https://mlsanity.com/paper/2104.08315/) (2021)
- [AutoPrompt: Eliciting Knowledge from Language Models with Automatically Generated Prompts](https://mlsanity.com/paper/2010.15980/) (2020)
- [Demystifying Prompts in Language Models via Perplexity Estimation](https://mlsanity.com/paper/2212.04037/) (2022)
- [Active Example Selection for In-Context Learning](https://mlsanity.com/paper/2211.04486/) (2022)
- [Reframing Instructional Prompts to GPTk's Language](https://mlsanity.com/paper/2109.07830/) (2021)
- [Self-Adaptive In-Context Learning: An Information Compression Perspective for In-Context Example Selection and Ordering](https://mlsanity.com/paper/2212.10375/) (2022)

## Built on by (most cited first, 13 of 13)

- [InfoRM: Mitigating Reward Hacking in RLHF via Information-Theoretic Reward Modeling](https://mlsanity.com/paper/2402.09345/) (2024)
- [Smoothie: Label Free Language Model Routing](https://mlsanity.com/paper/2412.04692/) (2024)
- [Generative Calibration for In-context Learning](https://mlsanity.com/paper/2310.10266/) (2023)
- [InstructEval: Systematic Evaluation of Instruction Selection Methods](https://mlsanity.com/paper/2307.00259/) (2023)
- [Prompt Valuation Based on Shapley Values](https://mlsanity.com/paper/2312.15395/) (2023)
- [Lever LM: Configuring In-Context Sequence to Lever Large Vision Language Models](https://mlsanity.com/paper/2312.10104/) (2023)
- [Information-Theoretic Reward Modeling for Stable RLHF: Detecting and Mitigating Reward Hacking](https://mlsanity.com/paper/2510.13694/) (2025)
- [Exploiting the Vulnerability of Large Language Models via Defense-Aware Architectural Backdoor](https://mlsanity.com/paper/2409.01952/) (2024)
- [Elastic On-Device LLM Service](https://mlsanity.com/paper/2409.09071/) (2024)
- [Unleashing the Multilingual Encoder Potential: Boosting Zero-Shot Performance via Probability Calibration](https://mlsanity.com/paper/2310.05069/) (2023)
- [What Is Wrong with My Model? Identifying Systematic Problems with Semantic Data Slicing](https://mlsanity.com/paper/2409.09261/) (2024)
- [The Alignment Bottleneck in Decomposition-Based Claim Verification](https://mlsanity.com/paper/2602.10380/) (2026)
- [Object Search in Partially-Known Environments via LLM-informed Model-based Planning and Prompt Selection](https://mlsanity.com/paper/2603.23800/) (2026)

## Abstract (arXiv)

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.