Published
Dec 11, 2024
Updated
Dec 11, 2024

Euclid: Teaching AI to See Geometry

Euclid: Supercharging Multimodal LLMs with Synthetic High-Fidelity Visual Descriptions
By
Jiarui Zhang|Ollie Liu|Tianyu Yu|Jinyi Hu|Willie Neiswanger

Summary

Imagine an AI struggling to identify a simple triangle in an image. That's the surprising reality facing Multimodal Large Language Models (MLLMs)—AIs designed to understand both text and visuals. While they excel at tasks like image captioning and visual question answering, they often stumble when it comes to accurately describing geometric details—the positions of points, lengths of lines, angles, and the relationships between shapes. This limitation, known as low-level visual perception (LLVP), creates a significant hurdle for MLLMs in fields like math problem-solving, scientific image analysis, and even robotics. Researchers have introduced 'Euclid,' a novel approach to supercharge LLVP in MLLMs. Recognizing the scarcity of detailed geometric training data, the team built a synthetic data engine capable of generating countless examples of geometric shapes with high-fidelity descriptions. Think of it as an AI geometry tutor, crafting lessons with increasing complexity. This engine allowed them to study how different model architectures and training methods impacted an MLLM's ability to grasp geometric concepts. They found that Convolutional Neural Networks (CNNs), often used for image processing, were surprisingly more effective at preserving low-level visual information than the popular Vision Transformers (ViTs). Furthermore, a carefully structured learning curriculum—starting with simple shapes like lines and circles, then progressing to triangles and more complex figures—proved crucial. This 'learn-to-crawl-before-you-walk' approach enabled the MLLM to master challenging geometric concepts it couldn't learn when presented with complex shapes right away. Euclid, trained using this innovative approach, demonstrated remarkable performance on a new benchmark dataset called Geoperception. It handily outperformed state-of-the-art models in tasks like identifying points on lines and comparing line lengths, even though it had only been trained on synthetic data. While challenges remain, particularly with complex annotations and generalizing to diverse visual domains, Euclid represents a significant step toward enabling AIs to truly 'see' and understand geometry. This breakthrough has implications far beyond abstract math problems, paving the way for MLLMs to better interpret medical images, navigate complex environments, and unlock new possibilities in manufacturing and augmented reality.
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Question & Answers

How does Euclid's synthetic data engine improve geometric understanding in MLLMs?
Euclid's synthetic data engine generates vast amounts of geometric training examples with precise descriptions. The engine works through a curriculum-based approach: it starts by creating simple geometric shapes (lines, circles) with detailed annotations, then progressively generates more complex figures (triangles, polygons). This structured learning path allows MLLMs to build foundational geometric understanding before tackling complex shapes. For example, in manufacturing, this could help robots better understand spatial relationships when assembling components by first mastering basic shape recognition before attempting complex assembly tasks.
What are the practical applications of AI systems that can understand geometry?
AI systems with geometric understanding capabilities have wide-ranging applications across multiple industries. In healthcare, they can improve medical image analysis by accurately measuring tumor dimensions or analyzing anatomical structures. In architecture and construction, these systems can assist in blueprint analysis and structural integrity assessments. For autonomous vehicles, geometric understanding helps with precise object detection and distance calculation. Even in everyday applications like augmented reality games or home renovation apps, this technology enables more accurate spatial mapping and object placement.
How is AI changing the way we teach and learn mathematics?
AI is revolutionizing mathematics education by providing personalized learning experiences and interactive problem-solving tools. Systems like Euclid demonstrate how AI can break down complex geometric concepts into manageable steps, similar to how a human tutor would teach. This technology enables adaptive learning paths that adjust to each student's pace and understanding level. For example, AI can generate unlimited practice problems, provide instant feedback, and visualize mathematical concepts in ways traditional textbooks cannot, making math more accessible and engaging for students of all levels.

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Implementation Details
Create staged test suites that progressively increase in complexity, starting with basic geometric shapes and advancing to more complex configurations
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Reduces manual testing effort by 60% through automated progression
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Minimizes deployment failures by catching geometric perception issues early
Quality Improvement
Ensures consistent geometric understanding across model versions
  1. Workflow Management
  2. Maps to the paper's synthetic data generation pipeline and progressive training approach
Implementation Details
Design workflow templates that orchestrate geometric data generation, model training, and evaluation in sequence
Key Benefits
• Reproducible training pipelines • Versioned geometric data generation • Structured curriculum progression
Potential Improvements
• Dynamic curriculum adjustment • Parallel training optimization • Enhanced data validation steps
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Efficiency Gains
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Cost Savings
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Quality Improvement
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