GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation

TL;DR

GeoGPT4V introduces a data-generation pipeline that uses GPT-4V to create simplified, image-text-aligned geometry problems and GPT-4 to render multiple Wolfram-based images, scored by GPT-4V to select the best alignment. The resulting GeoGPT4V dataset (4.9K generated + 19K open-source problems) significantly improves geometric reasoning across diverse MLLMs on MathVista and MathVision, narrowing gaps to larger closed-source systems. The study analyzes the contributions of generated images, scoring, and the role of open-source data, and releases both data and trained checkpoints to the community. Limitations include instability in Wolfram image generation and API costs, with future work aimed at richer geometric content and broader multi-modal math tasks.

Abstract

Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges in effectively using image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://github.com/Lanyu0303/GeoGPT4V_Project

Figures (2)

• Figure 1: Pipeline of our geometric data generation. During the first step, we employ GPT-4V to generate simplified geometric question-answer pairs based on open-source datasets. We highlight the simplified parts compared to the original questions. During the second step, we employ GPT-4 to generate $K$ Wolfram code for each question-answer pair. During the third step, we execute $K$ code to obtain $K$ images. During the fourth step, we employ GPT-4V to score the degree of alignment between the generated images and the questions. We choose the image with the highest score. Finally, we can obtain simplified and image-text matching geometric problems.
• Figure 2: The data analysis results. This chart illustrates the simplicity and image-text matching attributes of our dataset. Figure (a) is a comparison chart of the difficulty between the generated and original data. In this figure, "Easier" represents that the generated data is easier than the original data; "Harder" represents that the generated data is harder than the original data; "Equal" represents that the generated and original data have the same difficulty level. Figure (b) shows the average image-text matching scores for the three data types. "Generated Images" represents our generated data. "Original Images" represents the data obtained by replacing generated images in generated data with original images.