Reproduce “Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Ruoran Xu, Haoyu Cheng, Bin Dong, Qiufeng Wang
Hilbert-Geo addresses solid-geometry problems by translating their text and diagrams into explicit geometric conditions, which a theorem-based engine uses to search for deductions and calculate answers. On SolidFGeo2k, its Gemini 2.5 Pro configuration with 45 prompt examples reaches 77.3% answer accuracy, versus 54.2% for direct Gemini 2.5 Pro, below the reported 81.8% student baseline.
Key insights
- Integrating a formal language for 3D geometric entities and relationships provides a structured and precise foundation, significantly improving the verifiability and correctness of reasoning processes compared to direct MLLM outputs.
- A neural-symbolic approach effectively combines the perceptual strengths of MLLMs for parsing multimodal inputs with the logical rigor of symbolic reasoning, mitigating common MLLM errors like hallucinations and calculation mistakes.
- High-quality, expert-annotated datasets with formal language representations and detailed reasoning paths are essential for benchmarking and advancing AI in complex mathematical domains like solid geometry.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.