Euclid-Omni: Neuro-Symbolic AI Solves Olympiad Geometry Problems

Euclidean geometry presents a unique challenge for AI, requiring a blend of visual understanding, logical deduction, and algebraic computation. Existing AI approaches often fall short, tackling only parts of the problem or struggling with advanced, competition-level tasks. A new framework, Euclid-Omni, aims to overcome these limitations by integrating neuro-symbolic AI. At its core, Euclid-Omni features "Euclidea," a symbolic geometry solver capable of generating reasoning steps through deductive inference and algebraic calculations. This system is coupled with Large Language Models (LLMs) and Vision-Language Models (VLMs). A novel data-generation pipeline synthesizes symbolic problems, renders diagrams, and translates them into natural language, creating diverse datasets for training the LLMs and VLMs. Experiments show that VLMs trained on this synthetic data excel at calculation tasks, and LLMs combined with Euclidea perform competitively on Olympiad-level proving problems, all while requiring significantly less computational power and training data than previous state-of-the-art systems.