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

TL;DR

This work addresses the challenge of geometric reasoning in vision-language models by introducing GeoThoughts, a high-quality chain-of-thought dataset with two subsets (Geo-Thought-6K and Geo-Thought-Augmented-10K) that provide visual inputs, detailed reasoning traces, reflections, and final answers. Leveraging a teacher model, the authors generate and filter reasoning chains to produce reliable CoT data, and train GeoThought-MLLM to produce structured thinking processes during problem solving. The approach yields pronounced gains on in-domain GeoQA and out-of-domain Geometry3K benchmarks, with open-source models approaching the performance of larger closed-source systems. Error analysis indicates spatial-relationship misinterpretations as a primary failure mode, and demonstrates that targeted CoT corrections can restore correct solutions. The work contributes a transferable data-generation pipeline, a reasoning-focused multimodal model, and open resources to advance geometric reasoning in AI systems.

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.

Figures (2)

• Figure 1: Our data generation workflow begins by inputting question-image pairs with engineered prompts to produce five novel questions per instance. Each generated question then undergoes eight independent reasoning path generations with corresponding answers. We statistically analyze the answer distributions, retaining only high-confidence QA pairs where a single answer achieves $\frac{8}{8}$.
• Figure 2: Performance comparison of different models on GeoQA and Geometry3K datasets. The bar charts show the performance gains ($\Delta$) achieved by models from the Qwen2.5-VL and Intern3VL series when fine-tuned with different datasets (multimodal-open-r1-8k-verified, Geo-Thought-6K, and Geo-Thought-Augmented-10K) compared to their base versions. Results demonstrate that the improvements brought by the Geo-Thought-6K and Geo-Thought-Augmented-10K datasets are particularly significant.