---
license: apache-2.0
---

# 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 |
|-------|-----------|-----------|-----------|--------------|
| <strong>Closed-source Models</strong> |
| GPT-o3-mini | 84.33 | 75.66 | 42.16 | 70.00 |
| GPT-o1 | <strong>86.76</strong> | <strong>76.02</strong> | <strong>43.35</strong> | <strong>70.92</strong> |
| 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 |
| <strong>Open-source Models</strong> |
| Qwen3-235B-Thinking-2507| <strong>89.09</strong> | <strong>79.12</strong> | <strong>49.05</strong> | <strong>74.00</strong> |
| 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:

```bibtex
@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}
}
```