Geometry problem-solving demands advanced reasoning abilities to process multimodal inputs and employ mathematical knowledge effectively. Vision-language models (VLMs) have made significant progress in various multimodal tasks. Yet, they still struggle with geometry problems and are significantly limited by their inability to perform mathematical operations not seen during pre-training, such as calculating the cosine of an arbitrary angle, and by difficulties in correctly applying relevant geometry formulas. To overcome these challenges, we present GeoCoder, which leverages modular code-finetuning to generate and execute code using a predefined geometry function library. By executing the code, we achieve accurate and deterministic calculations, contrasting the stochastic nature of autoregressive token prediction, while the function library minimizes errors in formula usage. We also propose a multimodal retrieval-augmented variant of GeoCoder, named RAG-GeoCoder, which incorporates a non-parametric memory module for retrieving functions from the geometry library, thereby reducing reliance on parametric memory. Our modular code-finetuning approach enhances the geometric reasoning capabilities of VLMs, yielding an average improvement of over 16% across various question complexities on the GeomVerse dataset compared to other finetuning methods.

本研究针对现有视觉语言模型在几何问题解决中的不足，提出了GeoCoder，通过模块化代码微调生成和执行代码，利用预定义的几何函数库实现了精确计算。研究表明，该方法在GeomVerse数据集上相较于其他微调方法平均提升了超过16%的几何推理能力。

GeoCoder：通过视觉语言模型生成模块化代码来解决几何问题