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

Xutao Mao; Tao Liu; Hongying Zan

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arXiv · 2509.19623

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

Xutao Mao·Tao Liu·Hongying Zan

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Abstract

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.

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Xutao Mao, Tao Liu, Hongying Zan. 2025-09-23. SteinerSQL: Graph-Guided Mathematical Reasoning for Text-to-SQL Generation. https://arxiv.org/abs/2509.19623

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