# Characterizing Fitness Landscape Structures in Prompt Engineering

arXiv: https://arxiv.org/abs/2509.05375 · HTML: https://mlsanity.com/paper/2509.05375/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 4 Sep 2025.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [The Prompt Report: A Systematic Survey of Prompt Engineering Techniques](https://mlsanity.com/paper/2406.06608/) (2024)
- [An Information-theoretic Approach to Prompt Engineering Without Ground Truth Labels](https://mlsanity.com/paper/2203.11364/) (2022)
- [PromptBench: A Unified Library for Evaluation of Large Language Models](https://mlsanity.com/paper/2312.07910/) (2023)
- [HPO X ELA: Investigating Hyperparameter Optimization Landscapes by Means of Exploratory Landscape Analysis](https://mlsanity.com/paper/2208.00220/) (2022)

## Abstract (arXiv)

While prompt engineering has emerged as a crucial technique for optimizing large language model performance, the underlying optimization landscape remains poorly understood. Current approaches treat prompt optimization as a black-box problem, applying sophisticated search algorithms without characterizing the landscape topology they navigate. We present a systematic analysis of fitness landscape structures in prompt engineering using autocorrelation analysis across semantic embedding spaces. Through experiments on error detection tasks with two distinct prompt generation strategies -- systematic enumeration (1,024 prompts) and novelty-driven diversification (1,000 prompts) -- we reveal fundamentally different landscape topologies. Systematic prompt generation yields smoothly decaying autocorrelation, while diversified generation exhibits non-monotonic patterns with peak correlation at intermediate semantic distances, indicating rugged, hierarchically structured landscapes. Task-specific analysis across 10 error detection categories reveals varying degrees of ruggedness across different error types. Our findings provide an empirical foundation for understanding the complexity of optimization in prompt engineering landscapes.