Euclid-Omni: A Unified Neuro-Symbolic Framework for Geometry Problem Solving

Zhaoyu Li, Hangrui Bi, Youyuan Zhang, Wenjie Ma, Zenan Li, Xujie Si, Kaiyu Yang

Keywords: Geometry Problem Solving, Neuro-Symbolic, LLM, VLM, Synthetic Data Generation

TL;DR: We propose a unified neuro-symbolic framework that integrates our formal geometry system with LLMs and VLMs to tackle a broad range of geometric reasoning tasks.

Abstract:

Euclidean geometry presents a compelling testbed for AI reasoning capabilities, requiring seamless integration of diagram understanding, logical deduction, and algebraic computation. Existing systems have either been narrowly scoped or struggled with challenging problems. We introduce Euclid-Omni, a unified neuro-symbolic framework that combines a formal geometry system with Large (Vision)–Language Models (LLMs and VLMs) to address both calculation- and proving-style problems across formal and natural languages, up to Olympiad-level difficulty. At its core, we develop Euclidea, a versatile geometry symbolic solver that automatically generates human-readable reasoning steps through logical deduction and algebraic solving. On top of this, we implement a comprehensive data generation pipeline that synthesizes symbolic problems, renders diagrams, and translates problems into natural language, yielding large-scale, diverse datasets for training LLMs and VLMs in different reasoning settings.
Experiments on multiple benchmarks demonstrate that Euclidea can tackle a broader range of problems than prior symbolic systems.
Our trained VLMs achieve superior results on calculation tasks, while combining LLMs with Euclidea remains competitive with state-of-the-art systems on Olympiad-level theorem proving problems, despite using orders of magnitude less compute and data.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 22403