Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry

[2608.14585] Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Artificial Intelligence arXiv:2608.14585 (cs) [Submitted on 17 Jun 2026] Title: Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry Authors: Zhaoyu Li , Hangrui Bi , Youyuan Zhang , Wenjie Ma , Zenan Li , Zhaolei Zhang , Xujie Si , Kaiyu Yang View a PDF of the paper titled Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry, by Zhaoyu Li and 7 other authors View PDF HTML (experimental) Abstract: Euclidean geometry is a compelling testbed for AI reasoning, as it demands the combination of intuitive diagram understanding, axiomatic deduction, and algebraic computation. Yet, existing approaches typically address only a subset of these abilities or struggle with competition-level problems. We introduce \textit{Euclid-Omni}, a unified neuro-symbolic framework that couples a formal geometry system with Large Language Models (LLMs) and Vision-Language Models (VLMs) to tackle both calculation- and proving-style problems, in formal and natural languages, up to Olympiad-level difficulty. At its core, we develop \textit{Euclidea}, a versatile symbolic geometry solver that automatically generates reasoning steps through deductive inference and algebraic computation. Building on this, we develop a data-generation pipeline that synthesizes symbolic problems and solutions, renders diagrams, and translates them into natural language, producing large-scale, diverse datasets for training LLMs and VLMs across a wide range of reasoning settings. Experiments show that VLMs trained on our synthetic data achieve superior performance on calculation tasks, and that LLMs combined with \textit{Euclidea} are competitive with state-of-the-art systems on Olympiad-level proving problems, despite using orders of magnitude less compute and training data. Code and scripts are publicly available at this https URL Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2608.14585 [cs.AI] (or arXiv:2608.14585v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2608.14585 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hangrui Bi [ view email ] [v1] Wed, 17 Jun 2026 04:25:38 UTC (6,096 KB) Full-text links: Access Paper: View a PDF of the paper titled Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry, by Zhaoyu Li and 7 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI < prev | next > new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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