- The paper introduces AutoGeo, an automated framework utilizing AGCS, RCS, and SG components to efficiently generate large-scale, diverse geometric image datasets.
- Using AutoGeo, the authors created AutoGeo-100k, a dataset of 100,000 high-quality geometric image-text pairs designed to address data scarcity for AI models.
- Experiments show that fine-tuning multimodal large language models with AutoGeo-100k significantly improves their performance on geometric understanding tasks like captioning and Q&A.
The paper "AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding" introduces AutoGeo, a novel methodology for generating large-scale, high-quality geometric datasets, addressing the scarcity of such data that has constrained advances in geometric reasoning within AI frameworks. With the rise of Multimodal LLMs (MLLMs) such as GPT-4 and LLaMa, there is an increased interest in supporting these models’ capabilities in mathematical reasoning, particularly in geometry, which had been limited due to dataset constraints.
Key Contributions:
- AutoGeo Framework: This is an automated system designed to efficiently generate large volumes of diverse geometric images at minimal cost. AutoGeo operates through three main components:
- Augmented Geometry Clause System (AGCS): This outlines a structured system of geometric clauses categorizing them by complexity and incorporating both geometric shapes like lines and circles and their intricate relationships.
- Rule-based Clause Selector (RCS): This component selects compatible geometric clauses according to predefined rules to match the required complexities, ensuring a wide range of geometrical constructs.
- Sample Generator (SG): This module converts selected clauses into data samples by generating images using Python scripts and creating descriptive texts with LLMs like ChatGPT, enhancing the diversity and utility of the datasets.
- Creation of AutoGeo-100k: Utilizing the AutoGeo framework, the authors present AutoGeo-100k, a dataset consisting of 100,000 high-quality geometry image-text pairs. The dataset encompasses a wide range of geometric structures and complexity levels, facilitating improved training, evaluation, and refinement of MLLMs in geometric contexts.
- Performance Evaluation: The dataset's effectiveness is demonstrated through multiple experiments fine-tuning various MLLMs. Notably, fine-tuning with AutoGeo-100k significantly enhances model performance in geometric captioning and question-and-answer tasks, thereby improving their capability to comprehend and articulate geometric concepts.
Experimental Results:
- Baseline models like LLaVA, InstructBLIP, and MiniGPT4-v2 showed initial limitations in geometric tasks, but upon fine-tuning with AutoGeo-100k, models exhibited noteworthy improvements, particularly in metrics such as ROUGE-L, CIDEr, and Bleu scores.
- Further experimentation on dataset complexity and training components reinforced the necessity of a diverse and challenging data environment for optimizing model performance.
Conclusion:
The paper argues that AutoGeo effectively bridges the gap in the availability of comprehensive geometric datasets, offering a robust tool for automating dataset generation with precision and scale. It successfully enhances the interpretive and reasoning capabilities of MLLMs in geometry, setting a foundation for future developments in AI-driven education and research tools. The dataset generated under this framework not only meets current research needs but also paves the way for future advancements in computational geometry and educational AI tools, highlighting AutoGeo's potential for broad impact in the domain.