# GradeSQL: Test-Time Inference with Outcome Reward Models for Text-to-SQL Generation from Large Language Models

arXiv: https://arxiv.org/abs/2509.01308 · HTML: https://mlsanity.com/paper/2509.01308/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 56 of its 77 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 56)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [DIN-SQL: Decomposed In-Context Learning of Text-to-SQL with Self-Correction](https://mlsanity.com/paper/2304.11015/) (2023)
- [RAT-SQL: Relation-Aware Schema Encoding and Linking for Text-to-SQL Parsers](https://mlsanity.com/paper/1911.04942/) (2019)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Text-to-SQL Empowered by Large Language Models: A Benchmark Evaluation](https://mlsanity.com/paper/2308.15363/) (2023)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [RESDSQL: Decoupling Schema Linking and Skeleton Parsing for Text-to-SQL](https://mlsanity.com/paper/2302.05965/) (2023)
- [CodeS: Towards Building Open-source Language Models for Text-to-SQL](https://mlsanity.com/paper/2402.16347/) (2024)
- [MAC-SQL: A Multi-Agent Collaborative Framework for Text-to-SQL](https://mlsanity.com/paper/2312.11242/) (2023)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Next-Generation Database Interfaces: A Survey of LLM-based Text-to-SQL](https://mlsanity.com/paper/2406.08426/) (2024)
- [A comprehensive evaluation of ChatGPT's zero-shot Text-to-SQL capability](https://mlsanity.com/paper/2303.13547/) (2023)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [Locally Typical Sampling](https://mlsanity.com/paper/2202.00666/) (2022)
- [Graphix-T5: Mixing Pre-Trained Transformers with Graph-Aware Layers for Text-to-SQL Parsing](https://mlsanity.com/paper/2301.07507/) (2023)
- [OmniSQL: Synthesizing High-quality Text-to-SQL Data at Scale](https://mlsanity.com/paper/2503.02240/) (2025)

## Abstract (arXiv)

Text-to-SQL, the task of translating natural language questions into SQL queries, has significantly advanced with the introduction of Large Language Models (LLMs), broadening database accessibility for a wide range of users. Despite substantial progress in generating valid SQL, current LLMs still struggle with complex queries. To address this limitation, test-time strategies such as Best-of-N (BoN) and Majority Voting (Maj) are often employed, based on the assumption that LLMs can produce correct answers after multiple attempts. However, these methods rely on surface-level heuristics, selecting the syntactically correct query through execution-based BoN (ex-BoN) or the most frequently generated one through Majority Voting. Recently, Outcome Reward Models (ORMs), which assign utility scores to generated outputs based on semantic correctness, have emerged as a promising reinforcement learning approach for improving model alignment. We argue that ORMs could serve as an effective new test-time heuristic, although their application in this context remains largely underexplored. In this work, we propose a unified framework for training ORMs tailored to the Text-to-SQL task and assess their effectiveness as a test-time heuristic within the BoN strategy. We benchmark ORMs against ex-BoN and Maj across the BIRD and Spider datasets, fine-tuning diverse open-source LLMs from the Qwen2, Granite3, and Llama3 families. Results show that ORMs outperform ex-BoN and Maj, achieving execution accuracy gains of +4.33% (BIRD) and +2.10% (Spider) over ex-BoN, and +2.91% (BIRD) and +0.93% (Spider) over Maj. We further demonstrate that finetuning models already aligned with SQL generation, such as OmniSQL, yields superior ORM performance. Additionally, we observe that ORMs achieve competitive results on simple queries and benefit more from an increased number of candidates compared to ex-BoN and Maj.