# SteinerSQL: Graph-Guided Mathematical Reasoning for Text-to-SQL Generation

arXiv: https://arxiv.org/abs/2509.19623 · HTML: https://mlsanity.com/paper/2509.19623/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [CHESS: Contextual Harnessing for Efficient SQL Synthesis](https://mlsanity.com/paper/2405.16755/) (2024)
- [Next-Generation Database Interfaces: A Survey of LLM-based Text-to-SQL](https://mlsanity.com/paper/2406.08426/) (2024)
- [OmniSQL: Synthesizing High-quality Text-to-SQL Data at Scale](https://mlsanity.com/paper/2503.02240/) (2025)
- [A Preview of XiYan-SQL: A Multi-Generator Ensemble Framework for Text-to-SQL](https://mlsanity.com/paper/2411.08599/) (2024)
- [SQL-PaLM: Improved Large Language Model Adaptation for Text-to-SQL (extended)](https://mlsanity.com/paper/2306.00739/) (2023)
- [Is Long Context All You Need? Leveraging LLM's Extended Context for NL2SQL](https://mlsanity.com/paper/2501.12372/) (2025)
- [LinkAlign: Scalable Schema Linking for Real-World Large-Scale Multi-Database Text-to-SQL](https://mlsanity.com/paper/2503.18596/) (2025)
- [Automatic Metadata Extraction for Text-to-SQL](https://mlsanity.com/paper/2505.19988/) (2025)
- [ExCoT: Optimizing Reasoning for Text-to-SQL with Execution Feedback](https://mlsanity.com/paper/2503.19988/) (2025)
- [STaR-SQL: Self-Taught Reasoner for Text-to-SQL](https://mlsanity.com/paper/2502.13550/) (2025)
- [Understanding, Detecting, and Repairing Real-World In-Context-Learning-Based Text-to-SQL Errors](https://mlsanity.com/paper/2501.09310/) (2025)
- [Sparks of Tabular Reasoning via Text2SQL Reinforcement Learning](https://mlsanity.com/paper/2505.00016/) (2025)
- [Graph-Reward-SQL: Execution-Free Reinforcement Learning for Text-to-SQL via Graph Matching and Stepwise Reward](https://mlsanity.com/paper/2505.12380/) (2025)
- [LogicCat: A Chain-of-Thought Text-to-SQL Benchmark for Complex Reasoning](https://mlsanity.com/paper/2505.18744/) (2025)
- [SEED: Enhancing Text-to-SQL Performance and Practical Usability Through Automatic Evidence Generation](https://mlsanity.com/paper/2506.07423/) (2025)
- [Evaluating and Enhancing LLMs for Multi-turn Text-to-SQL with Multiple Question Types](https://mlsanity.com/paper/2412.17867/) (2024)
- [Text-to-SQL based on Large Language Models and Database Keyword Search](https://mlsanity.com/paper/2501.13594/) (2025)

## Built on by (most cited first, 1 of 1)

- [IESR:Efficient MCTS-Based Modular Reasoning for Text-to-SQL with Large Language Models](https://mlsanity.com/paper/2602.05385/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) struggle with complex Text-to-SQL queries that demand both sophisticated mathematical reasoning and intricate schema navigation. Existing methods often tackle these challenges in isolation, creating a fractured reasoning process that compromises logical and structural correctness. To resolve this, we introduce SteinerSQL, a framework that unifies these dual challenges into a single, graph-centric optimization problem. SteinerSQL operates in three stages: mathematical decomposition to identify required tables (terminals), optimal reasoning scaffold construction via a Steiner tree problem, and multi-level validation to ensure correctness. On the challenging LogicCat and Spider2.0-Lite benchmarks, SteinerSQL establishes a new state-of-the-art with 36.10% and 40.04% execution accuracy, respectively, using Gemini-2.5-Pro. Beyond accuracy, SteinerSQL presents a new, unified paradigm for Text-to-SQL, paving the way for more robust and principled solutions to complex reasoning tasks.