EAGLE: Elevating Geometric Reasoning through LLM-empowered Visual Instruction Tuning

Multi-modal Large Language Models have recently experienced rapid developments and excel in various multi-modal tasks. However, they still struggle with mathematical geometric problem solving, which requires exceptional visual perception proficiency. Existing MLLMs mostly optimize the LLM backbone to acquire geometric reasoning capabilities, while rarely emphasizing improvements in visual comprehension. In this paper, we first investigate the visual perception performance of MLLMs when facing geometric diagrams. Our findings reveal that current MLLMs severely suffer from inaccurate geometric perception and hallucinations. To address these limitations, we propose EAGLE, a novel two-stage end-to-end visual enhancement MLLM framework designed to ElevAte Geometric reasoning through LLM-Empowered visual instruction tuning. Specifically, in the preliminary stage, we feed geometric image-caption pairs into our MLLM that contains a fully fine-tuning CLIP ViT and a frozen LLM, aiming to endow our model with basic geometric knowledge. In the subsequent advanced stage, we incorporate LoRA modules into the vision encoder and unfreeze the LLM backbone. This enables the model to leverage the inherent CoT rationales within question-answer pairs, guiding the MLLM to focus on nuanced visual cues and enhancing its overall perceptual capacity. Moreover, we optimize the cross-modal projector in both stages to foster adaptive visual-linguistic alignments. After the two-stage visual enhancement, we develop the geometry expert model EAGLE-7B. Extensive experiments on popular benchmarks demonstrate the effectiveness of our model. For example, on the GeoQA benchmark, EAGLE-7B not only surpasses the exemplary G-LLaVA 7B model by 2.9%, but also marginally outperforms the larger G-LLaVA 13B model. On the MathVista benchmark, EAGLE-7B achieves remarkable 3.8% improvements compared with the proprietary model GPT-4V.