arXiv:2605. 16385v3 Announce Type: replace-cross Abstract: Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial diagrams and complex reasoning.
arXiv:2607. 12982v1 Announce Type: new Abstract: Math reasoning has achieved significant progress with the rapid advancement of Multimodal Large Language Models (MLLMs), however analytic geometry remains largely underexplored, primarily due to the scarcity of annotated samples.
arXiv:2606. 04381v1 Announce Type: cross Abstract: Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space.
Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators.
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: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:2505. 12369v2 Announce Type: replace Abstract: Multi-hop logical reasoning on knowledge graphs requires faithfully mapping the logical semantics to latent space.
arXiv:2608. 05242v1 Announce Type: new Abstract: In this work, we explore an alternative paradigm for spatial reasoning by explicitly disentangling 3D perception from reasoning, rather than jointly acquiring implicit 3D perception and reasoning through large-scale training.
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: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: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.
arXiv:2608. 15006v1 Announce Type: cross Abstract: Although visual reasoning is crucial for solving complex geometry tasks, existing vision-language models rely heavily on text-only reasoning.
In this work, we explore an alternative paradigm for spatial reasoning by explicitly disentangling 3D perception from reasoning, rather than jointly acquiring implicit 3D perception and reasoning through large-scale training. Our key observation is that modern perception models excel at estimating continuous 3D geometry, whereas large language models (LLMs) are particularly effective at compositional and symbolic reasoning.