GeoThought: A Dataset for Enhancing Mathematical Geometry Reasoning in Vision-Language Models

TL;DR

GeoThought introduces a large, detailed dataset for geometric reasoning in vision-language models, enabling improved multi-step reasoning and problem-solving in geometric tasks.

Contribution

The paper presents GeoThoughts, a new comprehensive dataset with explicit reasoning traces, and a multimodal model that leverages this dataset to enhance geometric reasoning in vision-language tasks.

Findings

Model trained on GeoThoughts outperforms existing benchmarks.

Explicit reasoning chains improve accuracy in geometric problem solving.

Analysis shows errors mainly stem from concept interpretation and spatial understanding.

Abstract

Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their performance substantially declines because geometric problems present unique challenges. Specifically, these challenges stem from two key factors: first, the intrinsic complexity of geometry requiring detailed image comprehension and multi-step reasoning, and second, the limitations of existing datasets which lack sufficient scale, diversity, and explicit reasoning traces, consequently hindering effective model training. To address these challenges, we developed the GeoThoughts dataset, a comprehensive geometric reasoning corpus with two subsets: Geo-Thought-6K with 6,243 samples and its augmented version Geo-Thought-Augmented-10K containing 10,834 samples. Each entry includes visual descriptions, step-by-step solutions, explicit reasoning chains, reflection steps, and final answers. Using this dataset, we developed GeoThought-MLLM, a mathematical reasoning multimodal model that generates detailed thinking processes during problem-solving. Our model outperforms existing benchmarks in geometric tasks, demonstrating that training with our Chain-of-Thought dataset improves geometric reasoning capabilities across both in-domain and out-of-domain settings. Finally, we analyze failure cases and observe that errors primarily arise from incorrect interpretation of mathematical concepts or spatial misjudgment. By invoking CoT to correct these mistakes, the model produces correct answers.