# Search-based Selection of Metamorphic Relations for Optimized Robustness Testing of Large Language Models

arXiv: https://arxiv.org/abs/2507.05565 · HTML: https://mlsanity.com/paper/2507.05565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [Is BERT Really Robust? A Strong Baseline for Natural Language Attack on Text Classification and Entailment](https://mlsanity.com/paper/1907.11932/) (2019)
- [Universal Sentence Encoder](https://mlsanity.com/paper/1803.11175/) (2018)
- [TextBugger: Generating Adversarial Text Against Real-world Applications](https://mlsanity.com/paper/1812.05271/) (2018)
- [Large Language Models for Software Engineering: Survey and Open Problems](https://mlsanity.com/paper/2310.03533/) (2023)
- [An LLM can Fool Itself: A Prompt-Based Adversarial Attack](https://mlsanity.com/paper/2310.13345/) (2023)
- [Adversarial Training for Large Neural Language Models](https://mlsanity.com/paper/2004.08994/) (2020)
- [SemAttack: Natural Textual Attacks via Different Semantic Spaces](https://mlsanity.com/paper/2205.01287/) (2022)
- [METAL: Metamorphic Testing Framework for Analyzing Large-Language Model Qualities](https://mlsanity.com/paper/2312.06056/) (2023)
- [jMetalPy: a Python Framework for Multi-Objective Optimization with Metaheuristics](https://mlsanity.com/paper/1903.02915/) (2019)

## Abstract (arXiv)

Assessing the trustworthiness of Large Language Models (LLMs), such as robustness, has garnered significant attention. Recently, metamorphic testing that defines Metamorphic Relations (MRs) has been widely applied to evaluate the robustness of LLM executions. However, the MR-based robustness testing still requires a scalable number of MRs, thereby necessitating the optimization of selecting MRs. Most extant LLM testing studies are limited to automatically generating test cases (i.e., MRs) to enhance failure detection. Additionally, most studies only considered a limited test space of single perturbation MRs in their evaluation of LLMs. In contrast, our paper proposes a search-based approach for optimizing the MR groups to maximize failure detection and minimize the LLM execution cost. Moreover, our approach covers the combinatorial perturbations in MRs, facilitating the expansion of test space in the robustness assessment. We have developed a search process and implemented four search algorithms: Single-GA, NSGA-II, SPEA2, and MOEA/D with novel encoding to solve the MR selection problem in the LLM robustness testing. We conducted comparative experiments on the four search algorithms along with a random search, using two major LLMs with primary Text-to-Text tasks. Our statistical and empirical investigation revealed two key findings: (1) the MOEA/D algorithm performed the best in optimizing the MR space for LLM robustness testing, and (2) we identified silver bullet MRs for the LLM robustness testing, which demonstrated dominant capabilities in confusing LLMs across different Text-to-Text tasks. In LLM robustness assessment, our research sheds light on the fundamental problem for optimized testing and provides insights into search-based solutions.