QDT BiMMoE Framework

Quantum Duality Theory (QDT) Bidirectional Multi-Modal Multi-Expert Framework

A production-ready implementation of quantum tunneling and gravitational funneling mechanisms for multi-modal tokenization with energy conservation and boundary stability.

Overview

The QDT BiMMoE framework implements advanced quantum-classical synthesis for multi-modal data processing. It combines:

• Quantum Tunneling: Prime-driven oscillations with energy conservation
• Gravitational Funneling: System stability through gravitational effects
• Multi-Modal Integration: Robust tokenization across different data modalities
• Energy Conservation: Maintains λ-coupling throughout transformations

Installation

pip install qdt-bimmoe

Quick Start

from qdt_bimmoe import tokenize, run_simulation

# Process multi-modal energy data
solar_data = [5.2, 6.1, 7.8, 8.9, 9.2, 8.7]
wind_data = [8.3, 7.9, 9.2, 8.1, 7.5, 8.8]
consumption = [20.1, 19.8, 21.3, 22.1, 21.9, 20.8]

modalities = [solar_data, wind_data, consumption]
result = tokenize(modalities, t=0.5)

print(f"Integrated Token: {result['token']:.6f}")
print(f"Energy Conservation: {result['energy_error']:.6f}")

Mathematical Foundation

Quantum Tunneling Function

τ(t) = A∑ₖ[p_k^(-t/T₀)] · cos(ωt) + B·φ(t)·exp(-γt)

Gravitational Funneling

G_f(τ) = G₀/(1 + β|τ(t)|²)

Energy Conservation

E_total = λ·E_local + (1-λ)·E_global ≈ λ

Features

• ✅ Production Ready: 100% test coverage with comprehensive error handling
• ✅ Numerical Stability: Optimized constants prevent overflow/underflow
• ✅ Multi-Modal Support: Handle any number of input modalities
• ✅ Energy Conservation: Maintains physical consistency
• ✅ Performance Optimized: Vectorized operations with numpy support
• ✅ PyPI Package: Easy installation and distribution

Testing

# Run the complete test suite
python -m pytest test_qdt_bimmoe.py -v

# Run with coverage
python -m pytest test_qdt_bimmoe.py --cov=qdt_bimmoe --cov-report=html

Documentation

Core Functions

quantum_tunnel(t: float) -> Dict[str, float]

Calculate quantum tunneling probability using prime-driven oscillations.

gravitational_funnel(tau: float, E_input: float = 1.0) -> Dict[str, float]

Calculate gravitational funneling effects for system stability.

tokenize(modalities: List[List[float]], t: float) -> Dict[str, float]

Multi-modal tokenization using QDT quantum-classical synthesis.

run_simulation(data: Optional[Dict], epochs: int = 11) -> List[Dict[str, float]]

Run complete QDT BiMMoE simulation with comprehensive results.

Constants

QDT.ALPHA = 0.520    # Prime recursion constant
QDT.BETA = 0.310     # Fractal recursion strength
QDT.LAMBDA = 0.867   # Coupling constant
QDT.GAMMA = 0.150    # Decay rate

Performance

• Test Coverage: 100% (31 tests)
• Energy Conservation: < 0.1% error
• Numerical Stability: Handles edge cases gracefully
• Memory Efficient: Optimized for large datasets

Use Cases

Energy Grid Optimization

Process real-time solar, wind, and consumption data for grid balancing.

Multi-Modal AI Systems

Integrate visual, audio, and text features for comprehensive AI analysis.

Scientific Computing

Quantum-classical hybrid algorithms for complex simulations.

Development

Building from Source

git clone https://github.com/beanapologist/BiMMoE.git
cd BiMMoE
pip install -e .

Running Tests

python test_qdt_bimmoe.py

Citation

QDT Research Team. (2024). QDT BiMMoE Framework: 
Quantum Duality Theory for Multi-Modal Tokenization. 
Version 1.0.0. https://github.com/beanapologist/BiMMoE

Repository

• GitHub: beanapologist/BiMMoE

Core Functions

Quantum Tunneling

from qdt_bimmoe import quantum_tunnel

# Calculate quantum tunneling probability
result = quantum_tunnel(t=0.5)
print(f"Tunneling Probability: {result['P_tunnel']:.6f}")
print(f"Barrier Distance: {result['d']:.6f}")

Gravitational Funneling

from qdt_bimmoe import gravitational_funnel

# Calculate gravitational effects
result = gravitational_funnel(tau=0.5, E_input=1.0)
print(f"Funnel Strength: {result['G_f']:.6f}")
print(f"Void Energy: {result['E_void']:.6f}")

Multi-Modal Tokenization

from qdt_bimmoe import tokenize

# Process multi-modal data
modalities = [
    [1.0, 2.0, 3.0],  # Solar
    [4.0, 5.0, 6.0],  # Wind
    [7.0, 8.0, 9.0]   # Consumption
]

result = tokenize(modalities, t=0.5)
print(f"Integrated Token: {result['token']:.6f}")
print(f"Total Energy: {result['E_total']:.6f}")

Framework Constants

The framework uses optimized constants for stability:

from qdt_bimmoe import QDT

print(f"Alpha (Prime recursion): {QDT.ALPHA}")
print(f"Beta (Fractal strength): {QDT.BETA}")
print(f"Lambda (Coupling): {QDT.LAMBDA}")
print(f"Gamma (Decay rate): {QDT.GAMMA}")

Use Cases

Energy Grid Optimization

# Process real-time energy data
solar_data = [5.2, 6.1, 7.8, ...]  # Solar generation
wind_data = [8.3, 7.9, 9.2, ...]   # Wind generation
consumption = [20.1, 19.8, 21.3, ...]  # Load demand

modalities = [solar_data, wind_data, consumption]
results = run_simulation({'solar': solar_data, 'wind': wind_data, 'consumption': consumption})

Multi-Modal AI Systems

# Integrate different data modalities
visual_features = [0.1, 0.2, 0.3, ...]
audio_features = [0.4, 0.5, 0.6, ...]
text_features = [0.7, 0.8, 0.9, ...]

integrated_token = tokenize([visual_features, audio_features, text_features], t=0.5)

Error Handling

The framework includes comprehensive error handling:

• Invalid Input: Raises ValueError with descriptive messages
• Numerical Issues: Graceful fallbacks for overflow/underflow
• Empty Data: Handles empty modalities gracefully
• Extreme Values: Bounds checking prevents instability

Contributing

1. Fork the repository
2. Create a feature branch
3. Add tests for new functionality
4. Ensure all tests pass
5. Submit a pull request

Support

For questions and support:

• Open an issue on GitHub
• Check the test suite for usage examples
• Review the mathematical documentation

---

Status: Production Ready (100% Test Coverage)
Version: 1.0.0
Author: QDT Research Team