FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation
FormalAnalyticGeo is a neural-symbolic framework for automatic generation of multimodal analytic geometry problems. It uses CDL (Condition Description Language) as a formal intermediate representation and an SDF (Signed Distance Field) engine for diagram rendering. The framework includes four LLM components: Generator, Formalizer, Measurer, and Quality Verifier.
FormalAnalyticGeo is a scalable framework for fully automatic generation of multimodal analytic geometry problems, leveraging formal languages and LLM components to bridge text and diagram rendering.
The framework's use of CDL as a formal intermediate representation and SDF-based rendering suggests a novel approach to ensuring geometric precision in generated diagrams. The four-component LLM pipeline indicates a modular design for problem generation, formalization, measurement, and quality verification.
This work addresses the scarcity of annotated analytic geometry samples, which is a bottleneck for MLLM reasoning in this domain. It could enable more robust training data generation for math AI systems.
The framework could reduce the cost of creating high-quality math problem datasets for educational AI products or math tutoring systems.
Future work may extend the framework to other geometry subfields or integrate with existing MLLM training pipelines. A key signal would be if the generated problems are used to improve MLLM performance on analytic geometry benchmarks.