ModelEquivBench: Certifying Multi-Relational Evaluation of LLM-Generated Optimization Models

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arXiv:2607.29431v1 Announce Type: new Abstract: Large language models increasingly generate optimization models from natural language, but existing evaluation often reduces a generated model and its ground truth to a single equivalent/not-equivalent verdict or an execution-success rate--labels that are neither independently checkable nor faithful to the multiple distinct senses in which two formulations can agree. We present ModelEquivBench, a certifying, multi-relational evaluation system that reports a per-pair semantic profile E0--E6: model construction and exact ingestion (E0), verified representation alignment (E1), same-space and projected feasible-set relations (E2, E3), objective-order equivalence (E4), optimal-value equality (E5), and optimizer-set equivalence (E6). Each decided entry carries relation-appropriate, independently re-checkable evidence: replayable traces or explicit maps for E0--E1, exact-rational certificates for positive E2--E6 conclusions, and explicit witnesses for supported negatives. Incomplete mapping search, unsupported structure, and resource limits produce typed UNKNOWN or N/A outcomes rather than guesses, while unmet prerequisites are reported as ABSENT. Using ModelEquivBench to evaluate three model snapshots--GPT-5.4, Claude Sonnet 4.6, and Qwen3.5-397B-A17B--on the same frozen cohort of 173 base problems (346 cells per model) under a no-repair protocol, the resulting profiles expose distinctions that coarse baselines do not represent: 49, 35, and 25 cells contain executable candidates that are nevertheless certified negative on at least …

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