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

TL;DR

GeoBuildBench is a new benchmark for testing large language models' ability to generate executable geometric constructions from natural language problems, emphasizing interactive reasoning and constraint satisfaction.

Contribution

It introduces a novel interactive geometry construction benchmark with 489 problems, enabling evaluation of models' grounded reasoning and self-correction capabilities.

Findings

Models often hallucinate structures and miss objects in generated diagrams.

Models struggle to satisfy geometric constraints despite visual and feedback cues.

GeoBuildBench provides a rigorous testbed for grounded, executable reasoning in geometry.

Abstract

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.