GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning

Abstract

Multimodal Large Language Models (MLLMs) have recently demonstrated remarkable perceptual and reasoning abilities. However, they struggle to perceive fine-grained geometric structures, constraining their ability of geometric understanding and visual reasoning. To address this, we propose GeoTikzBridge, a framework that enhances local geometric perception and visual reasoning through tikz-based code generation. Within this framework, we build two models supported by two complementary datasets. The GeoTikzBridge-Base model is trained on GeoTikz-Base dataset, the largest image-to-tikz dataset to date with 2.5M pairs (16 $\times$ larger than existing open-sourced datasets). This process is achieved via iterative data expansion and a localized geometric transformation strategy. Subsequently, GeoTikzBridge-Instruct is fine-tuned on GeoTikz-Instruct dataset which is the first instruction-augmented tikz dataset supporting visual reasoning. Extensive experimental results demonstrate that our models achieve state-of-the-art performance among open-sourced MLLMs. Furthermore, GeoTikzBridge models can serve as plug-and-play reasoning modules for any MLLM(LLM), enhancing reasoning performance in geometric problem-solving. Datasets and codes are publicly available at: https://github.com/sjy-1995/GeoTikzBridge.