Large language models have enabled natural language interfaces for structured databases, but generated queries may still contain syntactic errors, violate database schemas, or fail during execution. Test-time inference strategies improve generation reliability without additional training, but existing approaches often use fixed inference budgets and uniform refinement strategies, leading to unnecessary computation across questions with different complexity levels. In this work, we investigate adaptive test-time inference for Text2Cypher and introduce two strategies: adaptive trace budgeting, which dynamically adjusts the candidate generation budget based on question difficulty, and selective execution-guided refinement, which applies correction only when additional inference is expected to be beneficial. Experiments on Gemma-2-9B and Qwen-2.5-7B show that adaptive trace budgeting reduces the average generation budget by 30.7% and wall-clock inference time by 21-25% while maintaining comparable generation quality. Selective refinement preserves nearly all execution success gains of full refinement, reducing execution success by only 0.2-0.5% while avoiding unnecessary refinement for simpler questions. Experiments show that a single correction model (Gemma-4) effectively refines outputs from a different model family, suggesting refinement transfers across families.

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