# NEBULA v0.4 - Technical Implementation Details

**Equipo NEBULA: Francisco Angulo de Lafuente y Ángel Vega**

---

## 🔬 Photonic Neural Network Implementation

### Authentic Optical Physics Simulation

The photonic component uses real optical physics equations implemented in CUDA-accelerated PyTorch:

#### 1. Snell's Law Refraction
```python
def apply_snells_law(self, incident_angle, n1, n2):
    """Apply Snell's law: n1*sin(θ1) = n2*sin(θ2)"""
    sin_theta1 = torch.sin(incident_angle)
    sin_theta2 = (n1 / n2) * sin_theta1
    
    # Handle total internal reflection
    sin_theta2 = torch.clamp(sin_theta2, -1.0, 1.0)
    refracted_angle = torch.asin(sin_theta2)
    return refracted_angle
```

#### 2. Beer-Lambert Absorption
```python  
def beer_lambert_absorption(self, intensity, absorption_coeff, path_length):
    """Beer-Lambert law: I = I₀ * exp(-α * L)"""
    return intensity * torch.exp(-absorption_coeff * path_length)
```

#### 3. Fresnel Reflection
```python
def fresnel_reflection(self, n1, n2):
    """Fresnel equations for reflection coefficient"""
    R = ((n1 - n2) / (n1 + n2))**2
    T = 1.0 - R  # Transmission coefficient
    return R, T
```

#### 4. Optical Interference
```python
def optical_interference(self, wave1, wave2, phase_difference):
    """Two-wave interference pattern"""
    amplitude = torch.sqrt(wave1**2 + wave2**2 + 2*wave1*wave2*torch.cos(phase_difference))
    return amplitude
```

### Wavelength Spectrum Processing

The model processes the full electromagnetic spectrum from UV to IR:

```python
WAVELENGTH_RANGES = {
    'UV': (200e-9, 400e-9),      # Ultraviolet
    'Visible': (400e-9, 700e-9), # Visible light  
    'NIR': (700e-9, 1400e-9),    # Near-infrared
    'IR': (1400e-9, 3000e-9)     # Infrared
}

def process_spectrum(self, input_tensor):
    """Process input across electromagnetic spectrum"""
    spectral_outputs = []
    
    for band, (λ_min, λ_max) in self.WAVELENGTH_RANGES.items():
        # Calculate refractive index for wavelength
        n = self.sellmeier_equation(λ_min, λ_max)
        
        # Process with wavelength-dependent optics
        output = self.optical_ray_interaction(input_tensor, n, λ_min)
        spectral_outputs.append(output)
    
    return torch.stack(spectral_outputs, dim=-1)
```

---

## ⚛️ Quantum Memory System

### Authentic Quantum Gate Implementation

All quantum gates use proper unitary matrices following quantum mechanics:

#### Pauli Gates
```python
def pauli_x_gate(self):
    """Pauli-X (bit flip) gate"""
    return torch.tensor([[0, 1], [1, 0]], dtype=torch.complex64)

def pauli_y_gate(self):
    """Pauli-Y gate"""  
    return torch.tensor([[0, -1j], [1j, 0]], dtype=torch.complex64)

def pauli_z_gate(self):
    """Pauli-Z (phase flip) gate"""
    return torch.tensor([[1, 0], [0, -1]], dtype=torch.complex64)
```

#### Rotation Gates
```python
def rx_gate(self, theta):
    """X-rotation gate: RX(θ) = exp(-iθX/2)"""
    cos_half = torch.cos(theta / 2)
    sin_half = torch.sin(theta / 2)
    
    return torch.tensor([
        [cos_half, -1j * sin_half],
        [-1j * sin_half, cos_half]
    ], dtype=torch.complex64)

def ry_gate(self, theta):
    """Y-rotation gate: RY(θ) = exp(-iθY/2)"""
    cos_half = torch.cos(theta / 2)
    sin_half = torch.sin(theta / 2)
    
    return torch.tensor([
        [cos_half, -sin_half],
        [sin_half, cos_half]
    ], dtype=torch.complex64)
```

### 4-Qubit Quantum Circuits

Each quantum memory neuron operates a 4-qubit system:

```python
def create_4qubit_circuit(self, input_data):
    """Create and execute 4-qubit quantum circuit"""
    # Initialize 4-qubit state |0000⟩
    state = torch.zeros(16, dtype=torch.complex64)
    state[0] = 1.0  # |0000⟩ state
    
    # Apply parametrized quantum gates
    for i in range(4):
        # Single-qubit rotations
        theta_x = input_data[i * 3]
        theta_y = input_data[i * 3 + 1] 
        theta_z = input_data[i * 3 + 2]
        
        state = self.apply_single_qubit_gate(state, self.rx_gate(theta_x), i)
        state = self.apply_single_qubit_gate(state, self.ry_gate(theta_y), i)
        state = self.apply_single_qubit_gate(state, self.rz_gate(theta_z), i)
    
    # Apply entangling gates (CNOT)
    for i in range(3):
        state = self.apply_cnot_gate(state, control=i, target=i+1)
    
    return state
```

### Quantum State Measurement

```python
def measure_quantum_state(self, quantum_state):
    """Measure quantum state and return classical information"""
    # Calculate measurement probabilities
    probabilities = torch.abs(quantum_state)**2
    
    # Expectation values for Pauli operators
    expectations = []
    for pauli_op in [self.pauli_x, self.pauli_y, self.pauli_z]:
        expectation = torch.real(torch.conj(quantum_state) @ pauli_op @ quantum_state)
        expectations.append(expectation)
    
    return torch.stack(expectations)
```

---

## 🌈 Holographic Memory System

### Complex Number Holographic Storage

The holographic memory uses complex numbers to store interference patterns:

```python
def holographic_encode(self, object_beam, reference_beam):
    """Create holographic interference pattern"""
    # Convert to complex representation
    object_complex = torch.complex(object_beam, torch.zeros_like(object_beam))
    reference_complex = torch.complex(reference_beam, torch.zeros_like(reference_beam))
    
    # Create interference pattern: |O + R|²
    total_beam = object_complex + reference_complex
    interference_pattern = torch.abs(total_beam)**2
    
    # Store phase information
    phase_pattern = torch.angle(total_beam)
    
    # Combine amplitude and phase
    hologram = torch.complex(interference_pattern, phase_pattern)
    
    return hologram
```

### FFT-Based Spatial Frequency Processing

```python
def spatial_frequency_encoding(self, spatial_pattern):
    """Encode spatial patterns using FFT"""
    # 2D Fourier transform for spatial frequencies
    fft_pattern = torch.fft.fft2(spatial_pattern)
    
    # Extract magnitude and phase
    magnitude = torch.abs(fft_pattern)
    phase = torch.angle(fft_pattern)
    
    # Apply frequency-domain filtering
    filtered_magnitude = self.frequency_filter(magnitude)
    
    # Reconstruct complex pattern
    filtered_pattern = filtered_magnitude * torch.exp(1j * phase)
    
    return filtered_pattern
```

### Associative Memory Retrieval

```python
def associative_retrieval(self, query_pattern, stored_holograms):
    """Retrieve associated memories using holographic correlation"""
    correlations = []
    
    for hologram in stored_holograms:
        # Cross-correlation in frequency domain
        query_fft = torch.fft.fft2(query_pattern)
        hologram_fft = torch.fft.fft2(hologram)
        
        # Correlation: F⁻¹[F(query) * conj(F(hologram))]
        correlation = torch.fft.ifft2(query_fft * torch.conj(hologram_fft))
        
        # Find correlation peak
        max_correlation = torch.max(torch.abs(correlation))
        correlations.append(max_correlation)
    
    return torch.stack(correlations)
```

---

## 🚀 RTX GPU Optimization

### Tensor Core Optimization

The RTX optimizer aligns operations for maximum Tensor Core efficiency:

```python
def optimize_for_tensor_cores(self, layer_dims):
    """Optimize layer dimensions for Tensor Core efficiency"""
    optimized_dims = []
    
    for dim in layer_dims:
        if self.has_tensor_cores:
            # Align to multiples of 8 for FP16 Tensor Cores
            aligned_dim = ((dim + 7) // 8) * 8
        else:
            # Standard alignment for regular cores
            aligned_dim = ((dim + 3) // 4) * 4
        
        optimized_dims.append(aligned_dim)
    
    return optimized_dims
```

### Mixed Precision Training

```python
def mixed_precision_forward(self, model, input_tensor):
    """Forward pass with automatic mixed precision"""
    if self.use_mixed_precision:
        with torch.amp.autocast('cuda', dtype=self.precision_dtype):
            output = model(input_tensor)
    else:
        output = model(input_tensor)
    
    return output

def mixed_precision_backward(self, loss, optimizer):
    """Backward pass with gradient scaling"""
    if self.use_mixed_precision:
        # Scale loss to prevent underflow
        self.grad_scaler.scale(loss).backward()
        
        # Unscale gradients and step
        self.grad_scaler.step(optimizer) 
        self.grad_scaler.update()
    else:
        loss.backward()
        optimizer.step()
```

### Dynamic Memory Management

```python
def optimize_memory_usage(self):
    """Optimize GPU memory allocation patterns"""
    # Clear fragmented memory
    torch.cuda.empty_cache()
    
    # Set memory fraction to prevent OOM
    if torch.cuda.is_available():
        torch.cuda.set_per_process_memory_fraction(0.9)
    
    # Enable memory pool for efficient allocation
    if hasattr(torch.cuda, 'set_memory_pool'):
        pool = torch.cuda.memory.MemoryPool()
        torch.cuda.set_memory_pool(pool)
```

---

## 🔧 Model Integration Architecture

### Unified Forward Pass

The complete NEBULA model integrates all components:

```python
def unified_forward(self, input_tensor):
    """Unified forward pass through all NEBULA components"""
    batch_size = input_tensor.shape[0]
    results = {}
    
    # 1. Photonic processing
    photonic_output = self.photonic_raytracer(input_tensor)
    results['photonic_features'] = photonic_output
    
    # 2. Quantum memory processing  
    quantum_output = self.quantum_memory_bank(photonic_output)
    results['quantum_memory'] = quantum_output
    
    # 3. Holographic memory retrieval
    holographic_output = self.holographic_memory(
        query=quantum_output, mode='retrieve'
    )
    results['holographic_retrieval'] = holographic_output
    
    # 4. Feature integration
    integrated_features = torch.cat([
        photonic_output,
        quantum_output, 
        holographic_output['retrieved_knowledge']
    ], dim=-1)
    
    # 5. Final classification
    main_output = self.classifier(integrated_features)
    constraint_violations = self.constraint_detector(main_output)
    
    results.update({
        'main_output': main_output,
        'constraint_violations': constraint_violations,
        'integrated_features': integrated_features
    })
    
    return results
```

---

## 📊 Performance Optimization Techniques

### Gradient Flow Optimization

```python
def optimize_gradients(self):
    """Ensure stable gradient flow through all components"""
    # Gradient clipping for stability
    torch.nn.utils.clip_grad_norm_(self.parameters(), max_norm=1.0)
    
    # Check for gradient explosion/vanishing
    total_norm = 0
    for p in self.parameters():
        if p.grad is not None:
            param_norm = p.grad.data.norm(2)
            total_norm += param_norm.item() ** 2
    
    total_norm = total_norm ** (1. / 2)
    
    return total_norm
```

### Computational Efficiency Monitoring

```python
def profile_forward_pass(self, input_tensor):
    """Profile computational efficiency of forward pass"""
    import time
    
    torch.cuda.synchronize()
    start_time = time.time()
    
    # Component-wise timing
    timings = {}
    
    # Photonic timing
    torch.cuda.synchronize()
    photonic_start = time.time()
    photonic_out = self.photonic_raytracer(input_tensor)
    torch.cuda.synchronize()
    timings['photonic'] = time.time() - photonic_start
    
    # Quantum timing  
    torch.cuda.synchronize()
    quantum_start = time.time()
    quantum_out = self.quantum_memory_bank(photonic_out)
    torch.cuda.synchronize()
    timings['quantum'] = time.time() - quantum_start
    
    # Holographic timing
    torch.cuda.synchronize()
    holo_start = time.time()
    holo_out = self.holographic_memory(quantum_out, mode='retrieve')
    torch.cuda.synchronize()
    timings['holographic'] = time.time() - holo_start
    
    torch.cuda.synchronize()
    total_time = time.time() - start_time
    timings['total'] = total_time
    
    return timings
```

---

## 🧪 Scientific Validation Framework

### Statistical Significance Testing

```python
def validate_statistical_significance(self, model_scores, baseline_scores, alpha=0.05):
    """Perform statistical significance testing"""
    from scipy import stats
    
    # Perform t-test
    t_statistic, p_value = stats.ttest_ind(model_scores, baseline_scores)
    
    # Calculate effect size (Cohen's d)
    pooled_std = np.sqrt(((len(model_scores)-1)*np.std(model_scores)**2 + 
                         (len(baseline_scores)-1)*np.std(baseline_scores)**2) / 
                        (len(model_scores) + len(baseline_scores) - 2))
    
    cohens_d = (np.mean(model_scores) - np.mean(baseline_scores)) / pooled_std
    
    is_significant = p_value < alpha
    
    return {
        't_statistic': t_statistic,
        'p_value': p_value,
        'cohens_d': cohens_d,
        'is_significant': is_significant,
        'effect_size': 'large' if abs(cohens_d) > 0.8 else 'medium' if abs(cohens_d) > 0.5 else 'small'
    }
```

### Reproducibility Verification

```python
def verify_reproducibility(self, seed=42, num_runs=5):
    """Verify model reproducibility across multiple runs"""
    results = []
    
    for run in range(num_runs):
        # Set all random seeds
        torch.manual_seed(seed + run)
        np.random.seed(seed + run)
        torch.cuda.manual_seed_all(seed + run)
        
        # Ensure deterministic operations
        torch.backends.cudnn.deterministic = True
        torch.backends.cudnn.benchmark = False
        
        # Run evaluation
        model_copy = self.create_fresh_model()
        accuracy = self.evaluate_model(model_copy)
        results.append(accuracy)
    
    # Calculate consistency metrics
    mean_accuracy = np.mean(results)
    std_accuracy = np.std(results)
    cv = std_accuracy / mean_accuracy  # Coefficient of variation
    
    return {
        'mean_accuracy': mean_accuracy,
        'std_accuracy': std_accuracy, 
        'coefficient_variation': cv,
        'all_results': results,
        'is_reproducible': cv < 0.05  # Less than 5% variation
    }
```

---

This technical documentation provides the complete implementation details for all NEBULA v0.4 components, ensuring full reproducibility and scientific transparency.

**Equipo NEBULA: Francisco Angulo de Lafuente y Ángel Vega**  
*Project NEBULA - Authentic Photonic Neural Networks*