arXiv:2606. 27926v1 Announce Type: new Abstract: Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor.
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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.
arXiv:2609.12606v2 Announce Type: replace Abstract: While multimodal reasoning has advanced rapidly, solving complex geometry problems critically hinges on active visual assistance, such as construct...
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...
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:2606. 14176v1 Announce Type: new Abstract: Geometry problem generation is useful for AI-assisted education and multimodal mathematical reasoning, but reliable synthesis remains difficult because the problem statement, diagram, constraints, and solution should be mutually consistent.
The paper introduces FactoSR, a factorized reinforcement learning framework designed to improve spatial reasoning in Vision‑Language Models by addressing a dimensional mismatch between 2D visual inputs and the 3D+temporal nature of the physical world. FactoSR decomposes the reasoning task into three orthogonal geometric sub‑objectives—planar correspondence (XY), depth consistency (Z), and temporal reversibility (T)—and optimizes these constraints within a unified policy learning mechanism. Experiments on multi‑view and video benchmarks show that this decomposition yields significant performance gains, achieving a 5.9% improvement on VSI‑Bench and 4.5% on All‑Angles‑Bench.