用中间表示自动评估数学图示，提升教育AI的可视化能力
DiagramIR: An Automatic Pipeline for Educational Math Diagram Evaluation
- 将LaTeX TikZ代码转为中间表示，实现可扩展的图示评估
- 相比人工评分，评估一致性更高，且小模型成本降低10倍
- 适合教育AI、智能题库开发人员使用
大型语言模型（LLM）在学习工具中的应用日益广泛，但多数工具仍局限于文本，难以满足数学等需要视觉表达的领域。已有研究证明LLM能生成可编译为教学图形的代码，但大规模评估仍是主要瓶颈。为此，本文提出DiagramIR：一种基于LaTeX TikZ代码中间表示（IR）的自动化、可扩展几何图形评估流水线。与LLM作为裁判等基线方法相比，该方法在与人类评分者的一致性上表现更优。此外，该评估方式使GPT-4.1-Mini等小型模型在推理成本降低10倍的情况下，性能可媲美GPT-5等大型模型，对部署可及、可扩展的教育技术具有重要意义。
原文摘要 · Abstract (English)
Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that LLMs are capable of generating code that compiles to educational figures, but a major bottleneck remains: scalable evaluation of these diagrams. We address this by proposing DiagramIR: an automatic and scalable evaluation pipeline for geometric figures. Our method relies on intermediate representations (IRs) of LaTeX TikZ code. We compare our pipeline to other evaluation baselines such as LLM-as-a-Judge, showing that our approach has higher agreement with human raters. This evaluation approach also enables smaller models like GPT-4.1-Mini to perform comparably to larger models such as GPT-5 at a 10x lower inference cost, which is important for deploying accessible and scalable education technologies.
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