GeoGramBench: Benchmarking the Geometric Program Reasoning in Modern LLMs
This work addresses the underexplored challenge of geometric spatial reasoning in LLMs for AI applications, establishing a benchmark for future research, though it is incremental as it focuses on evaluation rather than new methods.
The authors tackled the problem of evaluating large language models' ability to translate programmatic drawing code into geometric reasoning by introducing GeoGramBench, a benchmark of 500 problems, and found that even the most advanced models achieve less than 50% accuracy at the highest abstraction level.
Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.