GeoGramBench: Benchmarking the Geometric Program Reasoning in Modern LLMs

GeoGramBench is a tailored benchmark dataset designed for evaluating the geometric spatial reasoning capabilities of large language models (LLMs) over procedural programmatic code. The dataset introduces a novel task, Program-to-Geometry, that requires models to transform programmatic drawing code into abstract geometric reasoning for problem-solving.

Features of GeoGramBench

• 500 Curated Problems: Each sample includes procedural drawing code and associated geometry reasoning problems. These problems are rigorously curated to ensure quality, fairness, and diversity.
• Taxonomy-Based Evaluation: Problems are categorized into three difficulty levels:
  • Primitive Recognition: Basic geometric problems requiring direct recognition of a few elements.
  • Local Relation Composition: Involves reasoning about relationships between multiple geometric components.
  • Global Abstract Integration: Complex problems requiring global spatial synthesis, parameterization, or 3D reasoning.
• Six Subtypes: Problems span six mathematical subfields: Angle, Length, Area, Volume, Ratio, and Count, supporting fine-grained diagnostics.

Dataset Composition

Subtype	Primitive	Compositional	Abstract
Angle	22	20	7
Length	25	88	20
Area	26	89	46
Ratio	14	51	4
Count	15	31	15
Volume	0	0	27

Benchmark Highlights

• GeoGramBench differs from traditional math benchmarks by emphasizing the symbolic-to-spatial abstraction capabilities of LLMs, leveraging procedural code expressed in formats such as Asymptote.
• Initial evaluation using 17 state-of-the-art LLMs revealed substantial gaps, particularly for higher abstraction tasks:
  • Models achieved less than 50% accuracy on the most challenging Global Abstract Integration category.
  • Even advanced models struggle to bridge procedural code with reliable spatial reasoning.

Model	Primitive	Compositional	Abstract	ALL
Closed-source Models
GPT-o3-mini	84.33	75.66	42.16	70.00
GPT-o1	86.76	76.02	43.35	70.92
GPT-o1-preview	74.79	55.98	26.20	53.15
GPT-o1-mini	79.62	63.21	29.09	58.94
GPT-4o	39.81	21.29	4.96	21.40
Gemini-Pro-1.5	49.26	31.79	15.92	31.64
Open-source Models
Qwen3-235B-Thinking-2507	89.09	79.12	49.05	74.00
DeepSeek-R1	85.66	75.27	40.38	69.17
DeepSeek-v3-0324	80.57	68.89	27.67	62.05
QwQ-32B	85.17	73.12	37.92	67.20
DeepSeek-R1-Distill-Qwen-32B	79.78	67.83	35.92	62.68
Bespoke-Stratos-32B	62.50	42.56	17.02	40.55
s1.1-32B	75.37	58.96	26.58	54.60
DeepSeek-R1-Distill-Qwen-7B	72.79	58.74	24.16	53.38
Sky-T1-mini-7B	71.45	57.75	24.79	52.70
DeepSeek-R1-Distill-Qwen-1.5B	60.29	39.02	11.03	36.70
DeepScaleR-1.5B-preview	65.44	47.89	15.76	43.83

Use Cases

GeoGramBench is designed for:

• Researchers developing geometry-aware LLMs for symbolic-to-spatial reasoning.
• Model diagnostics to pinpoint weaknesses in handling code-driven geometric reasoning or abstract spatial relations.
• Evaluation and advancement of LLMs' performance on tasks involving spatial reasoning.

Citation

If you use GeoGramBench in your research, please cite:

@article{luo2025geogrambench,
  title={Geogrambench: Benchmarking the geometric program reasoning in modern llms},
  author={Luo, Shixian and Zhu, Zezhou and Yuan, Yu and Yang, Yuncheng and Shan, Lianlei and Wu, Yong},
  journal={arXiv preprint arXiv:2505.17653},
  year={2025}
}