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license: apache-2.0
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---
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license: apache-2.0
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---
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# GeoGramBench: Benchmarking the Geometric Program Reasoning in Modern LLMs
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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.
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## Features of GeoGramBench
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- **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.
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- **Taxonomy-Based Evaluation:** Problems are categorized into three difficulty levels:
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- **Primitive Recognition:** Basic geometric problems requiring direct recognition of a few elements.
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- **Local Relation Composition:** Involves reasoning about relationships between multiple geometric components.
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- **Global Abstract Integration:** Complex problems requiring global spatial synthesis, parameterization, or 3D reasoning.
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- **Six Subtypes:** Problems span six mathematical subfields: `Angle`, `Length`, `Area`, `Volume`, `Ratio`, and `Count`, supporting fine-grained diagnostics.
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## Benchmark Highlights
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- 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`.
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- Initial evaluation using 17 state-of-the-art LLMs revealed substantial gaps, particularly for higher abstraction tasks:
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- Models achieved less than **50%** accuracy on the most challenging **Global Abstract Integration** category.
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- Even advanced models struggle to bridge procedural code with reliable spatial reasoning.
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## Dataset Composition
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| Complexity Level | Problem Count | Example Tasks |
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|----------------------------|---------------|-----------------------------------|
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| **Primitive Recognition** | 102 | Compute the area of a triangle. |
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| **Local Relation Composition** | 279 | Solve for angles in composite diagrams. |
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| **Global Abstract Integration** | 119 | Analyze 3D projections and symmetry. |
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### Subtype Distribution Across Levels
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| Subtype | Primitive | Compositional | Abstract |
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|-----------|-----------|---------------|----------|
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| Angle | 22 | 20 | 7 |
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| Length | 25 | 88 | 20 |
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| Area | 26 | 89 | 46 |
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| Ratio | 14 | 51 | 4 |
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| Count | 15 | 31 | 15 |
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| Volume | 0 | 0 | 27 |
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## Use Cases
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GeoGramBench is designed for:
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- Researchers developing **geometry-aware LLMs** or fine-tuning models for symbolic-to-spatial reasoning.
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- Model diagnostics to pinpoint weaknesses in handling code-driven geometric reasoning or abstract spatial relations.
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- Evaluation and advancement of LLMs' performance on tasks involving spatial reasoning.
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## Citation
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If you use GeoGramBench in your research, please cite:
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```bibtex
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@article{luo2025geogrambench,
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title={Geogrambench: Benchmarking the geometric program reasoning in modern llms},
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author={Luo, Shixian and Zhu, Zezhou and Yuan, Yu and Yang, Yuncheng and Shan, Lianlei and Wu, Yong},
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journal={arXiv preprint arXiv:2505.17653},
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year={2025}
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}
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```
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```
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