AlgoVista: AI-Driven Mathematical Solution Visualization

Research Overview

AlgoVista represents an innovative approach to mathematical education through the integration of Large Language Models (LLMs) and structured mathematical markup generation. This project serves as both a practical educational tool and a research platform for exploring the challenges and solutions in AI-driven mathematical content generation.

Key Research Contributions

1. Structured AI Output Generation

   • Implementation of custom grammar systems for reliable JSON-structured markup
   • Novel approach to ensuring consistent LaTeX/MathJax syntax generation
   • Mitigation strategies for AI hallucination in mathematical contexts

2. Mathematical Markup Processing

   • Integration of MathJax and LaTeX within React components
   • Solutions to tokenization challenges in React state management
   • Comparative analysis of MathML and ChatML in AI latent space

3. AI Model Integration

   • QWEN model integration with custom prompting strategies
   • Split testing methodology for mathematical markup generation
   • Exception safety through secondary AI model validation

Technical Architecture

Frontend (Details)

• React-based UI with dark mode interface
• Real-time mathematical visualization using Recharts
• KaTeX integration for LaTeX rendering
• Responsive solution step visualization

Backend (Details)

• Express.js server with QWEN LLM integration
• Structured JSON response handling
• Environmental configuration for security
• REST API endpoints for mathematical processing

Research Findings

Structured Grammar Importance

The project demonstrates the critical nature of structured grammar in AI-driven applications, particularly when:

• Handling specialized markup like LaTeX/MathJax
• Ensuring consistent AI output formatting
• Managing complex state in React applications
• Processing mathematical notation with absolute precision

AI Model Behavior

Key observations about AI model behavior in mathematical contexts:

1. Hallucination patterns in mathematical markup generation
2. Impact of prompt engineering on output structure
3. Reliability improvements through structured JSON enforcement
4. Trade-offs between flexibility and consistency in AI responses

Implementation Challenges

1. Mathematical Parsing

   • Complex syntax handling
   • Token management in React
   • LaTeX validation and correction

2. AI Integration

   • Output structure maintenance
   • Error handling and recovery
   • Performance optimization

3. User Interface

   • Real-time rendering
   • State management
   • Responsive design

Project Structure

algovista/
├── frontend/           # React-based UI
├── backend/            # Express.js server
└── research/          # Documentation and research findings

Getting Started

1. Clone the repository:

clone the repo
cd algovista

2. Set up the backend:

cd backend
cp .env.example .env
npm install
npm start

3. Set up the frontend:

cd ../frontend
cp .env.example .env
npm install
npm start

Research Applications

This project serves as a foundation for:

1. Studying AI-driven mathematical content generation
2. Exploring structured output enforcement in LLMs
3. Analyzing mathematical markup processing in modern web applications
4. Investigating AI hallucination mitigation strategies

Future Research Directions

1. Model Optimization

   • Quantization methods for mobile deployment
   • Alternative build systems for React
   • Performance optimization strategies

2. AI Validation

   • Secondary model validation approaches
   • Hallucination detection methods
   • Output structure verification

3. Mathematical Processing

   • Enhanced LaTeX generation
   • Improved tokenization strategies
   • Advanced visualization techniques

Contributing

We welcome contributions to both the practical application and research aspects of this project. Please see our Contributing Guidelines for more information.

Publications

This project serves as the foundation for our upcoming paper: "Structured Grammar Approaches in AI-Driven Mathematical Content Generation: A Case Study of AlgoVista"

Acknowledgments

This project builds upon research in:

• AI-driven content generation
• Mathematical markup processing
• React application architecture
• LLM integration strategies