A semantic mutation metric for metamorphic relation adequacy in scientific computing programs

Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem). Metamorphic testing checks relations across executions, yet a candidate relation is not automatically valid: its preconditions, output mapping, and the numerical floor of the scoring operator determine whether a violation is meaningful. We study how candidate metamorphic relations (MRs) can be screened for domain validity and turned into executable, oracle-free test assets for SciML surrogates. We propose (i) a domain-validity rubric that admits a candidate only when its tolerance dominates the operator's numerical floor and its preconditions hold; (ii) an MR-card executable-asset format recording source cases, transformations, metrics, tolerances, and typed relation-level verdicts; and (iii) a case-study protocol on MeshGraphNets cylinder-flow surrogates, with a claim ledger binding every result to a tracked artifact. On a MeshGraphNets checkpoint, node permutation holds to machine precision, mirror-y is a bounded out-of-distribution stress finding rather than an exact symmetry, and absolute conservation stays deferred while a reference-relative guard passes. The same readings hold across held-out trajectories, a checkpoint roster, three further architectures, and PhysicsNeMo. On a second CFD task (compressible airfoil) the predicate instead rejects incompressible continuity on physical grounds, showing it reasons about domain validity rather than running a fixed checklist. On a second PDE family, FNO Burgers and heat surrogates run full admit/reject/execute verdicts. The evidence spans two CFD tasks and a second PDE family, supporting a validity-aware bridge from candidate MRs to auditable SciML test assets that separates model-level violations from out-of-domain applications.

LLM-based automated program repair (APR) techniques have shown promising results in reducing debugging costs. However, prior results can be affected by data leakage: large language models (LLMs) may memorize bug fixes when evaluation benchmarks overlap with their pretraining data, leading to inflated performance estimates. In this paper, we investigate whether we can better reveal data leakage by combining metamorphic testing (MT) with negative log-likelihood (NLL), which has been used in prior work as a proxy for memorization. We construct variant benchmarks by applying semantics-preserving transformations to two widely used datasets, Defects4J and GitBug-Java. Using these benchmarks, we evaluate the repair success rates of seven LLMs on both original and transformed versions, and analyze the relationship between performance degradation and NLL. Our results show that all evaluated state-of-the-art LLMs exhibit substantial drops in patch generation success rates on transformed benchmarks, ranging from -4.1% for GPT-4o to -15.98% for Llama-3.1. Furthermore, we find that this degradation strongly correlates with NLL on the original benchmarks, suggesting that models perform better on instances they are more likely to have memorized. These findings show that combining MT with NLL provides stronger and more reliable evidence of data leakage, while metamorphic testing alone can help mitigate its effects in LLM-based APR evaluations.

Evaluating software engineering capabilities has become a core component of modern large language models (LLMs); however, the key bottleneck hindering further scaling lies not in the scarcity of high-quality solutions, but in the lack of high-quality test suites. Test suites are indispensable both for synthesizing program repair trajectories and for providing precise feedback signals in reinforcement learning. Unfortunately, due to the high cost and difficulty of annotation, high-quality test suites have long been hard to obtain, while those automatically generated by LLMs tend to be superficial and lack sufficient discriminative power. As a first step toward constructing high-quality test suites, we introduce SWE-Mutation, a benchmark for evaluating LLM-generated test suites. The benchmark characterizes test suites by introducing systematically mutated solutions that attempt to ``fool'' the test suites and pass validation. We further propose an agentic, language-agnostic framework for automatically generating complex mutants. Our benchmark consists of 2,636 mutated variants derived from 800 original instances and includes a multilingual subset spanning nine programming languages. Experiments on seven LLMs reveal that even DeepSeek-V3.1 achieves only 10.20% verification and 36.15% detection rates, highlighting the inadequacy of current LLMs. Additionally, our agentic mutation strategy enhances realism, reducing average detection rates from 71.04% to 39.81% compared to conventional methods. These findings expose persistent deficiencies in the ability of current LLMs to generate reliable and discriminative test suites.