---
title: "FormalAnalyticGeo：基于神经符号的多模态解析几何问题生成框架"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.12982v1"
permalink: "https://feed.astralor.com/items/itm_1ad0dd798ad1a584e2e7946a"
published: "2026-07-14T17:24:57.000Z"
score: 77
channel: "ai"
tags: ["AnalyticGeo7K","CDL","FormalAnalyticGeo","SDF","多模态大语言模型"]
---

# FormalAnalyticGeo：基于神经符号的多模态解析几何问题生成框架

## AI 点评

> 这篇论文展示了一种优雅的神经符号方法，巧妙结合形式语言和LLM来解决解析几何数据稀缺问题。对从事教育AI、数学推理及多模态数据生成的研究者尤其重要，值得深入了解其闭环验证机制。

## 速览

本文提出FormalAnalyticGeo框架，利用形式语言和条件描述语言(CDL)作为中间表示，结合符号距离场(SDF)引擎，实现多模态解析几何问题的全自动生成。框架包含四个专用LLM组件（生成器、形式化器、测量器、质量验证器），形成闭环自动验证与重试机制，完全无需人工标注。实验生成AnalyticGeo7K数据集，含7000+验证问题，中位相对误差仅0.70%，82.3%答案误差在5%以内。该方法填补了多模态大模型在解析几何领域因缺乏标注数据而难以进展的空白。

## 关键点

- 提出CDL形式中间表示，桥接自然语言文本与精确图表渲染
- 设计四个LLM组件闭环工作，实现从生成到质量验证的全自动化
- 构建AnalyticGeo7K数据集，7000+问题，高精度验证结果
- 完全无需人工标注，可扩展生成大规模多模态解析几何数据

## 全文

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.

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