Execution Accuracy and Exact Set Match are two predominant metrics for evaluating the functional correctness of SQL queries in modern Text-to-SQL tasks. However, both metrics have notable limitations: Exact Set Match fails when queries are functionally equivalent but syntactically different, while Execution Accuracy is prone to false positives due to inadequately prepared test databases, which can be costly to create, particularly in large-scale industrial applications. To overcome these challenges, we propose a novel graph-based metric, FuncEvalGMN, that effectively overcomes the deficiencies of the aforementioned metric designs. Our method utilizes a relational operator tree (ROT), referred to as RelNode, to extract rich semantic information from the logical execution plan of SQL queries, and embed it into a graph. We then train a graph neural network (GNN) to perform graph matching on pairs of SQL queries through graph contrastive learning. FuncEvalGMN offers two highly desired advantages: (i) it requires only the database schema to derive logical execution plans, eliminating the need for extensive test database preparation, and (ii) it demonstrates strong generalization capabilities on unseen datasets. These properties highlight FuncEvalGMN’s robustness as a reliable metric for assessing functional correctness across a wide range of Text-to-SQL applications.

Reinforcement learning (RL) has been widely adopted to enhance the performance of large language models (LLMs) on Text-to-SQL tasks. However, existing methods often rely on execution-based or LLM-based Bradley–Terry reward models. The former suffers from high execution latency caused by repeated database calls, whereas the latter imposes substantial GPU memory overhead, both of which significantly hinder the efficiency and scalability of RL pipelines. To this end, we propose a novel reward model framework for RL-based Text-to-SQL named Graph-Reward-SQL, which employs the GMNScore outcome reward model. We leverage SQL graph representations to provide accurate reward signals while significantly reducing time cost and GPU memory usage. Building on this foundation, we further introduce StepRTM, a stepwise reward model that provides intermediate supervision over Common Table Expression (CTE) subqueries. This encourages both functional correctness and readability of SQL. Extensive comparative and ablation experiments on standard benchmarks, including Spider and BIRD, demonstrate that our method consistently outperforms existing reward models.