# PMPO: Probabilistic Metric Prompt Optimization for Small and Large Language Models

arXiv: https://arxiv.org/abs/2505.16307 · HTML: https://mlsanity.com/paper/2505.16307/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 22 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [PromptAgent: Strategic Planning with Language Models Enables Expert-level Prompt Optimization](https://mlsanity.com/paper/2310.16427/) (2023)
- [Rephrase and Respond: Let Large Language Models Ask Better Questions for Themselves](https://mlsanity.com/paper/2311.04205/) (2023)
- [Black-Box Prompt Optimization: Aligning Large Language Models without Model Training](https://mlsanity.com/paper/2311.04155/) (2023)
- [Aligning and Prompting Everything All at Once for Universal Visual Perception](https://mlsanity.com/paper/2312.02153/) (2023)
- [Self-Supervised Prompt Optimization](https://mlsanity.com/paper/2502.06855/) (2025)
- [PromptWizard: Task-Aware Prompt Optimization Framework](https://mlsanity.com/paper/2405.18369/) (2024)
- [NegativePrompt: Leveraging Psychology for Large Language Models Enhancement via Negative Emotional Stimuli](https://mlsanity.com/paper/2405.02814/) (2024)
- [Efficient and Accurate Prompt Optimization: the Benefit of Memory in Exemplar-Guided Reflection](https://mlsanity.com/paper/2411.07446/) (2024)
- [How to Correctly do Semantic Backpropagation on Language-based Agentic Systems](https://mlsanity.com/paper/2412.03624/) (2024)
- [TextGuard: Provable Defense against Backdoor Attacks on Text Classification](https://mlsanity.com/paper/2311.11225/) (2023)
- [Revisiting OPRO: The Limitations of Small-Scale LLMs as Optimizers](https://mlsanity.com/paper/2405.10276/) (2024)

## Built on by (most cited first, 3 of 3)

- [Beyond Elicitation: Provision-based Prompt Optimization for Knowledge-Intensive Tasks](https://mlsanity.com/paper/2511.10465/) (2025)
- [ELPO: Ensemble Learning Based Prompt Optimization for Large Language Models](https://mlsanity.com/paper/2511.16122/) (2025)
- [MIDAS: Multi-LLM Iterative Data-Adaptive Summarization](https://mlsanity.com/paper/2608.04307/) (2026)

## Abstract (arXiv)

Prompt optimization is a practical and widely applicable alternative to fine tuning for improving large language model performance. Yet many existing methods evaluate candidate prompts by sampling full outputs, often coupled with self critique or human annotated preferences, which limits scalability, especially for smaller models or models that are not instruction tuned. We present PMPO (Probabilistic Metric Prompt Optimization), a unified framework that uses token level cross entropy as a direct, lightweight evaluation signal. PMPO locates low quality prompt segments via a masking based analysis and iteratively rewrites them to propose improved variants. Crucially, during evaluation, PMPO selects among variants by minimizing loss in a single forward pass, eliminating output sampling and human or judge based scoring for selection while still using standard generation only to propose rewrites. This unified, loss based strategy supports both supervised and preference based tasks. Across model sizes and datasets, PMPO outperforms prior prompt optimizers: it achieves the highest average accuracy on BBH, performs strongly on GSM8K and AQUA RAT, and raises AlpacaEval 2.0 win rates by over 19 points. These results demonstrate PMPO's effectiveness, efficiency, and broad applicability.