How Correct Is Your Answer? A Semantic Correctness Framework for Open QA Evaluation

Reliable evaluation of open-ended question answering remains a bottleneck for measuring answer correctness of modern LLMs. Unlike multiple-choice tasks, free-form answers may be correct in many surface forms and may fail in qualitatively different ways, including incompleteness, contradiction, overgeneration, and endorsement of false premises. Existing judgment-based and similarity-based metrics often collapse these distinctions. We address this gap with three reusable contributions. First, we introduce a semantic correctness taxonomy that assigns open-ended answers to eight ordered classes, separating verbose-but-correct answers from those contaminated by hallucinated content. Second, we release CAP-Correctness, an 8.8k-example benchmark spanning widely used QA datasets, and CAP-Statements, an 11k-example dataset for converting question-answer pairs into declarative statements for natural language inference (NLI) training and statement-based evaluation. Third, we introduce CAP (Context-Aware Precision), a reference-based metric that scores question-conditioned statements using bidirectional NLI. Under a monotonicity protocol testing whether metrics respect the taxonomy's intended ordering, CAP outperforms established baselines.

Decode-Time Grammars: Constrained LLM Generation over a Refinement Order of Grammar Fragments

Large language models now write a growing share of the world's code, increasingly inside agents and serving systems that compile, execute, or dispatch generated code without line-by-line review. This works well for mainstream languages but remains brittle for low-resource programming surfaces such as domain-specific languages, custom library APIs, and command-line tools. Even under grammar-constrained decoding, a model can still produce references invalid in the current environment: a buffer never declared, a column absent from the schema, a function the library does not provide, or an unsupported CLI option. This paper introduces decode-time grammars: grammar fragments instantiated during generation from a runtime environment Gamma. A region-specific policy selects a fragment for each hole, and a tightening operator replaces open reference positions with Gamma-typed slots whose candidates are exactly the names, fields, APIs, or options available at that point. Newly generated declarations enter Gamma before later regions are decoded, so the constraining grammar can depend on the prefix already generated. This ensures not only grammatical correctness but also semantic correctness, by preventing references to undefined symbols. We formalize grammar fragments as environment-indexed grammars ordered by refinement, prove No-Ghost soundness for Gamma-slotted fragments, show that refinement preserves this support-set guarantee, and characterize the boundary of mask-enforceable properties. We implement the approach in gproj with offline grammar induction and online policy resolution. Across TileLang, SQL, and P4, with models from 0.6B to 236B parameters, gproj eliminates ghost references by construction at moderate overhead over standard constrained decoding.