# PromptNCE: Conditional Probabilities and PMI Using Only LLMs and Contrastive Estimation Prompts

arXiv: https://arxiv.org/abs/2605.21776 · HTML: https://mlsanity.com/paper/2605.21776/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 19 of 19)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [GoEmotions: A Dataset of Fine-Grained Emotions](https://mlsanity.com/paper/2005.00547/) (2020)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [Surface Form Competition: Why the Highest Probability Answer Isn't Always Right](https://mlsanity.com/paper/2104.08315/) (2021)
- [What Can We Learn from Collective Human Opinions on Natural Language Inference Data?](https://mlsanity.com/paper/2010.03532/) (2020)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Large Language Models Must Be Taught to Know What They Don't Know](https://mlsanity.com/paper/2406.08391/) (2024)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Benchmarking LLMs' Judgments with No Gold Standard](https://mlsanity.com/paper/2411.07127/) (2024)

## Abstract (arXiv)

Estimating mutual information from text usually requires training a task-specific critic, which limits its use in low-data settings. We ask whether large language models can instead estimate pointwise mutual information zero-shot, using only prompts and elicited probabilities. We construct a benchmark from three publicly available human-annotated datasets with ground-truth PMI, and evaluate five information-theoretic prompting-based estimators. Our main method, PromptNCE, frames conditional probability estimation as a contrastive task and augments the candidate set with an explicit OTHER category. The OTHER category allows the model to assign probability mass outside the candidate set, avoiding the closed-set normalization of standard contrastive prompts. PromptNCE gives the best conditional probability estimates on all three datasets. For full PMI, we find that estimating label base rates is the primary bottleneck on two of the three datasets, with the best methods reaching Spearman correlation up to 0.78. We also present a case study in computer science education showing how these estimators can be used to score student knowledge summaries in a low-data setting. We release our code and prompts.