# Embedding by Elicitation: Dynamic Representations for Bayesian Optimization of System Prompts

arXiv: https://arxiv.org/abs/2605.19093 · HTML: https://mlsanity.com/paper/2605.19093/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 29 of 29)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Optimizing Instructions and Demonstrations for Multi-Stage Language Model Programs](https://mlsanity.com/paper/2406.11695/) (2024)
- [TextGrad: Automatic "Differentiation" via Text](https://mlsanity.com/paper/2406.07496/) (2024)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Combinatorial Bayesian Optimization using the Graph Cartesian Product](https://mlsanity.com/paper/1902.00448/) (2019)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [InstructZero: Efficient Instruction Optimization for Black-Box Large Language Models](https://mlsanity.com/paper/2306.03082/) (2023)
- [A Systematic Survey of Automatic Prompt Optimization Techniques](https://mlsanity.com/paper/2502.16923/) (2025)
- [BOSS: Bayesian Optimization over String Spaces](https://mlsanity.com/paper/2010.00979/) (2020)
- [Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spaces](https://mlsanity.com/paper/2111.01186/) (2021)
- [GAUCHE: A Library for Gaussian Processes in Chemistry](https://mlsanity.com/paper/2212.04450/) (2022)
- [Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spaces](https://mlsanity.com/paper/2507.03910/) (2025)
- [Hyperband-based Bayesian Optimization for Black-box Prompt Selection](https://mlsanity.com/paper/2412.07820/) (2024)
- [Data Mixture Optimization: A Multi-fidelity Multi-scale Bayesian Framework](https://mlsanity.com/paper/2503.21023/) (2025)
- [LLM Prompt Duel Optimizer: Efficient Label-Free Prompt Optimization](https://mlsanity.com/paper/2510.13907/) (2025)
- [Joint Composite Latent Space Bayesian Optimization](https://mlsanity.com/paper/2311.02213/) (2023)
- [LLM Based Bayesian Optimization for Prompt Search](https://mlsanity.com/paper/2510.04384/) (2025)
- [An Exploratory Study of Bayesian Prompt Optimization for Test-Driven Code Generation with Large Language Models](https://mlsanity.com/paper/2512.15076/) (2025)

## Built on by (most cited first, 1 of 1)

- [Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search](https://mlsanity.com/paper/2609.34281/) (2026)

## Abstract (arXiv)

System prompts are a central control mechanism in modern AI systems, shaping behavior across conversations, tasks, and user populations. Yet they are difficult to tune when feedback is available only as aggregate metrics rather than per-example labels, failures, or critiques. We study this aggregate feedback setting as sample-constrained black-box optimization over discrete, variable-length text. We introduce ReElicit, a Bayesian optimization framework based on embedding by elicitation. Given a task description, previously evaluated prompts, and scalar scores, an LLM elicits a compact, interpretable feature space and maps prompts into it. Leveraging a probabilistic Gaussian process surrogate, an acquisition function then selects target feature vectors, which the LLM realizes and refines into deployable system prompts. Re-eliciting the feature space as new evaluations arrive lets the representation adapt to the observed prompt-score history. We evaluate the setting using offline benchmark accuracy as a controlled aggregate proxy: the optimizer observes one scalar score per prompt and no per-example labels, errors, or critiques. Across ten system prompt optimization tasks with a 30 total evaluation budget, ReElicit achieves the strongest aggregate performance profile among representative aggregate-only prompt-optimization baselines. These results suggest that LLMs can serve as adaptive semantic representation builders, not only prompt generators, for Bayesian optimization over natural-language artifacts.