Researchers introduce FormalAnalyticGeo, a scalable framework for the fully automatic generation of multimodal analytic geometry problems that eliminates the need for human annotation. The system utilizes a formal intermediate representation called CDL to bridge problem text with precise diagram rendering through a Signed Distance Field engine.
- Four specialized LLM components operate in sequence: a Generator creates diverse problems, a Formalizer converts them to CDL, a Measurer extracts ground-truth answers via vision-based measurement, and a Quality Verifier checks outputs at three stages.
- Structured feedback from the verifier drives automatic retries, forming a closed loop that produces AnalyticGeo7K, a dataset of over 7K verified multimodal problems with aligned text, diagrams, and annotations.
- Generated problems achieve a median ground-truth relative error of 0.70%, with 82.3% of answers falling within 5% of the exact symbolic solution.
The framework addresses the scarcity of annotated samples in analytic geometry by providing a rigorous, automated method for creating high-quality multimodal datasets.