GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models

TL;DR

GeoCoder enhances vision-language models' ability to solve geometry problems by generating and executing modular code with a geometry function library, significantly improving reasoning accuracy over existing methods.

Contribution

Introduces a modular code-finetuning framework and a retrieval-augmented variant, RAG-GeoCoder, to improve geometric reasoning in vision-language models.

Findings

Over 16% average accuracy improvement on GeomVerse dataset.

Effective deterministic calculations via code execution.

Reduced reliance on parametric memory with RAG-GeoCoder.

Abstract

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.