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Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry — arXiv:2608.14585

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.14585
License (as archived): CC0-1.0
Archived: 2026-10-18T17:05:35.534Z
SHA-256 of the archived text: bfe02b24c4d90c2dcd754a791f3d0cb334cbcd4c187a48498d76123f0713c7ca
Stable URL of this page: https://metraipolis.com/documento/dc_00a222f5e65e

How to cite

Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry — arXiv:2608.14585 — arXiv (en), https://arxiv.org/abs/2608.14585 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_00a222f5e65e (Metraipolis archive dc_00a222f5e65e, sha256 bfe02b24c4d90c2dcd754a791f3d0cb334cbcd4c187a48498d76123f0713c7ca)

BibTeX

@misc{dc00a222f5e65e,
  title = {Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry — arXiv:2608.14585},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.14585},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_00a222f5e65e; sha256 bfe02b24c4d90c2dcd754a791f3d0cb334cbcd4c187a48498d76123f0713c7ca},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.14585. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-18 in cs.AI).
Categorie arXiv: Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2608.14585 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T16:29:13.706Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).