arXiv:2606. 04648v1 Announce Type: new Abstract: Geometry problem solving poses distinct challenges in artificial intelligence.
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arXiv:2606. 27926v1 Announce Type: new Abstract: Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor.
The paper introduces a framework that combines a Geometric Vision Parser and a Symbolic Solver to enable a Large Language Model to solve complex plane geometry problems. By translating diagrams into symbolic representations and performing formal deductions, the approach reduces hallucinations and produces interpretable, human-like solutions. Experiments on a new benchmark from 2025 Chinese Zhongkao exams show performance comparable to Gemini 2.5 Pro.
Euclid-Omni is a unified neuro‑symbolic framework that integrates a formal geometry system with Large Language Models and Vision‑Language Models to solve both calculation and proving problems in Euclidean geometry up to Olympiad level. Its core component, Euclidea, automatically generates deductive reasoning steps and algebraic computations, while a data‑generation pipeline creates synthetic symbolic problems, diagrams, and natural‑language translations for training. Experiments show that VLMs trained on this synthetic data outperform on calculation tasks, and LLMs paired with Euclidea match state‑of‑the‑art proving systems using far less compute and data.
arXiv:2608.30156v1 Announce Type: new Abstract: Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precis...
arXiv:2608. 07955v1 Announce Type: new Abstract: Large vision-language models have achieved strong performance in multimodal reasoning, but they remain unreliable on fine-grained spatial tasks that demand both precise spatial perception and fine-grained geometric computation beyond end-to-end generation.
The paper introduces InternGeometry, a large language model agent that achieves medalist-level performance on International Mathematical Olympiad geometry problems. It overcomes traditional heuristic limitations by iteratively proposing and verifying auxiliary constructions with a symbolic engine, supported by a dynamic memory mechanism that allows over 200 interactions per problem. Using Complexity-Boosting Reinforcement Learning, InternGeometry trains on only 13,000 examples—0.004% of the data used by AlphaGeometry 2—and solves 44 of 50 IMO geometry problems, surpassing the average gold medalist score.