AI Theory

This repository contains theoretical research on the mathematical and computational foundations of artificial intelligence. The work focuses on rigorous mathematical frameworks, computational complexity analysis, and novel neural network architectures.

Repository Structure

papers/
├── mathematical_foundations/    # Category theory, topology, algebraic structures
├── neural_architectures/       # Novel network designs and scaling analysis
├── formal_methods/             # Verification and formal grammar systems
├── computational_theory/       # Complexity and algorithmic analysis
└── epistemology/              # AI comprehension and research methodology

Research Areas

Mathematical Foundations

• Category Theory Applications: Functorial approaches to neural networks and memory systems
• Homotopy Type Theory: Theoretical extensions of Kalman-Grove-Arnold Networks
• Sheaf Theory: Distributed memory architectures and topological data structures
• Topos Theory: Categorical foundations for AI memory and reasoning systems

Neural Architectures

• Kalman-Grove-Arnold Networks: Theoretical analysis and practical implementations
• Scaling Laws: Mathematical characterization of training efficiency and cost reduction
• Cost Optimization: Algorithmic approaches to computational resource minimization

Formal Methods

• Formal Grammar Systems: Functorial Fourier transforms for linguistic structures
• Verification Techniques: Formal proofs for AI system correctness
• Hybrid Encryption: Security frameworks for distributed AI systems

Computational Theory

• Complexity Analysis: Theoretical bounds on AI computational requirements
• Algorithmic Frameworks: Fundamental algorithms for AI reasoning and learning

Build Instructions

# Compile all LaTeX papers
./scripts/build.sh

# Clean compilation artifacts
./scripts/clean.sh

Paper Index

See docs/paper_index.md for a complete listing of papers, their current status, and target publication venues.

Contributing

Contributions should maintain mathematical rigor and include formal proofs where applicable. All submissions must:

1. Include complete mathematical formulations
2. Provide computational complexity analysis
3. Reference relevant theoretical literature
4. Follow standard mathematical notation conventions

License

MIT License - see LICENSE file for details.