# GeoBuildBench: A Benchmark for Interactive and Executable Geometry Construction from Natural Language

arXiv: https://arxiv.org/abs/2605.13167 · HTML: https://mlsanity.com/paper/2605.13167/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 14 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 7 of 7)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [MagicGeo: Training-Free Text-Guided Geometric Diagram Generation](https://mlsanity.com/paper/2502.13855/) (2025)
- [Automatically Building Diagrams for Olympiad Geometry Problems](https://mlsanity.com/paper/2012.02590/) (2020)

## Built on by (most cited first, 2 of 2)

- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [Mind the Spatial Gap: A Benchmark for Geospatial Reasoning and Constrained Spatial Editing](https://mlsanity.com/paper/2610.12881/) (2026)

## Abstract (arXiv)

We introduce GeoBuildBench, a benchmark designed to evaluate whether large language models and multimodal agents can ground informal natural-language plane geometry problems into executable geometric constructions. Unlike existing geometry benchmarks that focus on answer correctness or static diagram interpretation, GeoBuildBench treats geometry diagram as an interactive construction task: given a textual problem, an agent must generate a domain-specific language (DSL) program to produce a diagram satisfying explicitly specified geometric objects and verifiable constraints. The benchmark features 489 Chinese textbook-style problems, curated through automated filtering and human validation to ensure text-complete, constructible problem specifications. We evaluate several state-of-the-art multimodal models in a bounded iterative setting and show that, despite reasonable success rates, models frequently exhibit structural hallucinations, missing objects, and failures to satisfy geometric constraints, with limited ability to exploit visual and constraint-based feedback for self-correction. These results highlight geometry construction as a rigorous testbed for grounded, executable reasoning beyond textual or visual plausibility. Our benchmark and code are publicly available.