# Toward an Artificial General Teacher: Procedural Geometry Data Generation and Visual Grounding with Vision-Language Models

arXiv: https://arxiv.org/abs/2604.02893 · HTML: https://mlsanity.com/paper/2604.02893/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and 3D vision-language models, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 13 of 13)

- [Modeling Context in Referring Expressions](https://mlsanity.com/paper/1608.00272/) (2016)
- [Generation and Comprehension of Unambiguous Object Descriptions](https://mlsanity.com/paper/1511.02283/) (2015)
- [LISA: Reasoning Segmentation via Large Language Model](https://mlsanity.com/paper/2308.00692/) (2023)
- [Florence-2: Advancing a Unified Representation for a Variety of Vision Tasks](https://mlsanity.com/paper/2311.06242/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [CRIS: CLIP-Driven Referring Image Segmentation](https://mlsanity.com/paper/2111.15174/) (2021)
- [PubLayNet: largest dataset ever for document layout analysis](https://mlsanity.com/paper/1908.07836/) (2019)
- [LAVT: Language-Aware Vision Transformer for Referring Image Segmentation](https://mlsanity.com/paper/2112.02244/) (2021)
- [Segmentation from Natural Language Expressions](https://mlsanity.com/paper/1603.06180/) (2016)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Vision-Aware Text Features in Referring Image Segmentation: From Object Understanding to Context Understanding](https://mlsanity.com/paper/2404.08590/) (2024)

## Abstract (arXiv)

We study visual explanation in geometry education as a Referring Image Segmentation (RIS) problem: given a diagram and a natural language description, the task is to produce a pixel-level mask for the referred geometric element. However, existing RIS models trained on natural image benchmarks such as RefCOCO fail catastrophically on geometric diagrams due to the fundamental domain shift between photographic scenes and abstract, textureless schematics. To address the absence of suitable training data, we present a fully automated procedural data engine that generates over 200,000 synthetic geometry diagrams with pixel-perfect segmentation masks and linguistically diverse referring expressions, requiring zero manual annotation. We further propose domain-specific fine-tuning of vision-language models (VLMs), demonstrating that a fine-tuned Florence-2 achieves 49% IoU and 85% Buffered IoU (BIoU), compared to <1% IoU in zero-shot settings. We introduce Buffered IoU, a geometry-aware evaluation metric that accounts for thin-structure localization, and show that it better reflects true segmentation quality than standard IoU. Our results establish a foundation for building Artificial General Teachers (AGTs) capable of providing visually grounded, step-by-step explanations of geometry problems.