想要自动生成带精确几何图形的数学题？FormalAnalyticGeo 用 CDL 形式语言和 SDF 渲染，造出了 7000+ 带标注的解析几何题目，误差不到 1%。
FormalAnalyticGeo 是一个可扩展的框架，利用 CDL（条件描述语言）作为形式中间表示，通过 SDF（符号距离场）引擎连接问题文本与精确图形渲染。框架包含四个 LLM 组件：Generator、Formalizer、Measurer 和 Quality Verifier，实现全自动闭环生成，无需人工标注。基于该框架构建的 AnalyticGeo7K 数据集包含超过 7,000 个经过验证的多模态问题，其中位相对误差为 0.70%，82.3% 的答案与精确符号解偏差在 5% 以内。论文表明该方法在解析几何问题生成上优于现有模板和生成模型。
FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation
Math reasoning has achieved significant progress with the rapid advancement of Multimodal Large Language Models (MLLMs), however analytic geometry remains largely underexplored, primarily due to the scarcity of annotated samples. Existing diagram generation approaches struggle with analytic geometry: template methods cannot handle constraint-driven layouts, and generative models lack the geometric precision to render annotated conic curves correctly. We present FormalAnalyticGeo, a scalable framework for fully automatic generation of multimodal analytic geometry problems. Leveraging the rigor of formal languages, we design the framework around CDL (Condition Description Language), a formal intermediate representation that bridges free-form problem text with precise diagram rendering via a Signed Distance Field (SDF) engine. The framework employs four specialized LLM components in sequence: a Generator that produces diverse analytic geometry problems, a Formalizer that converts each problem into CDL for SDF-based rendering, a Measurer that extracts ground-truth answers through vision-based measurement on the rendered diagrams, and a Quality Verifier that checks outputs at three stages. Structured feedback from the Quality Verifier drives automatic retry, forming a closed loop that eliminates any need for human annotation. Applying FormalAnalyticGeo at scale yields AnalyticGeo7K, a dataset of over 7K verified multimodal problems, each with aligned text, diagram, formal annotation, and ground truth.Experiments show that the 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. Our framework and dataset will be publicly released.