cognitive/docs/guides/implementation/predictive_network.md

---
title: Predictive Network Implementation
type: implementation_guide
status: stable
created: 2024-02-12
tags:
  - implementation
  - predictive-processing
  - neural-networks
semantic_relations:
  - type: implements
    links: [[../../learning_paths/predictive_processing]]
  - type: relates
    links:
      - [[error_propagation]]
      - [[precision_mechanisms]]
---

# Predictive Network Implementation

## Overview

This guide provides a detailed implementation of a basic predictive processing network, focusing on the core mechanisms of prediction generation and error computation.

## Architecture

### Network Structure
```python
class PredictiveLayer:
    def __init__(self, input_size: int, hidden_size: int, output_size: int):
        """Initialize a predictive processing layer.
        
        Args:
            input_size: Size of input features
            hidden_size: Size of hidden representation
            output_size: Size of predictions
        """
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # Initialize weights
        self.W_hidden = torch.randn(input_size, hidden_size) * 0.1
        self.W_pred = torch.randn(hidden_size, output_size) * 0.1
        
        # Initialize biases
        self.b_hidden = torch.zeros(hidden_size)
        self.b_pred = torch.zeros(output_size)
        
        # Initialize precision (inverse variance)
        self.precision = torch.ones(output_size)

class PredictiveNetwork:
    def __init__(self, layer_sizes: List[int]):
        """Initialize hierarchical predictive network.
        
        Args:
            layer_sizes: List of layer sizes from bottom to top
        """
        self.layers = []
        for i in range(len(layer_sizes) - 1):
            layer = PredictiveLayer(
                input_size=layer_sizes[i],
                hidden_size=layer_sizes[i] * 2,
                output_size=layer_sizes[i + 1]
            )
            self.layers.append(layer)
```

### Forward Pass
```python
def forward(self, input_data: torch.Tensor) -> Tuple[List[torch.Tensor], List[torch.Tensor]]:
    """Forward pass through the network.
    
    Args:
        input_data: Input tensor
        
    Returns:
        predictions: List of predictions at each layer
        prediction_errors: List of prediction errors
    """
    current_input = input_data
    predictions = []
    prediction_errors = []
    
    # Bottom-up pass
    for layer in self.layers:
        # Generate prediction
        hidden = torch.tanh(current_input @ layer.W_hidden + layer.b_hidden)
        prediction = hidden @ layer.W_pred + layer.b_pred
        
        # Compute prediction error
        if len(predictions) > 0:
            error = current_input - prediction
            weighted_error = error * layer.precision
            prediction_errors.append(weighted_error)
        
        predictions.append(prediction)
        current_input = prediction
    
    return predictions, prediction_errors
```

### Error Computation
```python
def compute_errors(self, 
                  predictions: List[torch.Tensor], 
                  targets: List[torch.Tensor]) -> List[torch.Tensor]:
    """Compute prediction errors at each layer.
    
    Args:
        predictions: List of predictions
        targets: List of target values
        
    Returns:
        errors: List of prediction errors
    """
    errors = []
    for pred, target, layer in zip(predictions, targets, self.layers):
        error = target - pred
        weighted_error = error * layer.precision
        errors.append(weighted_error)
    return errors
```

## Training

### Loss Function
```python
def compute_loss(self, 
                prediction_errors: List[torch.Tensor], 
                precision_errors: List[torch.Tensor]) -> torch.Tensor:
    """Compute total loss from prediction and precision errors.
    
    Args:
        prediction_errors: List of prediction errors
        precision_errors: List of precision estimation errors
        
    Returns:
        total_loss: Combined loss value
    """
    # Prediction error loss
    pred_loss = sum(torch.mean(error ** 2) for error in prediction_errors)
    
    # Precision error loss
    prec_loss = sum(torch.mean(error ** 2) for error in precision_errors)
    
    return pred_loss + 0.1 * prec_loss
```

### Update Step
```python
def update_step(self, 
                loss: torch.Tensor,
                learning_rate: float = 0.01):
    """Perform one update step.
    
    Args:
        loss: Loss value
        learning_rate: Learning rate for updates
    """
    # Compute gradients
    gradients = torch.autograd.grad(loss, self.parameters())
    
    # Update parameters
    with torch.no_grad():
        for param, grad in zip(self.parameters(), gradients):
            param -= learning_rate * grad
```

## Usage Example

### Basic Training Loop
```python
# Initialize network
layer_sizes = [64, 32, 16]  # Example sizes
network = PredictiveNetwork(layer_sizes)

# Training loop
for epoch in range(num_epochs):
    for batch in data_loader:
        # Forward pass
        predictions, errors = network.forward(batch.inputs)
        
        # Compute loss
        loss = network.compute_loss(errors, [])
        
        # Update step
        network.update_step(loss)
        
        # Log progress
        if epoch % 100 == 0:
            print(f"Epoch {epoch}, Loss: {loss.item():.4f}")
```

### Prediction Generation
```python
def generate_predictions(self, input_data: torch.Tensor) -> List[torch.Tensor]:
    """Generate predictions for input data.
    
    Args:
        input_data: Input tensor
        
    Returns:
        predictions: List of predictions at each layer
    """
    predictions, _ = self.forward(input_data)
    return predictions
```

## Advanced Features

### Precision Estimation
```python
def estimate_precision(self, 
                      errors: List[torch.Tensor],
                      window_size: int = 100) -> List[torch.Tensor]:
    """Estimate precision based on prediction errors.
    
    Args:
        errors: List of prediction errors
        window_size: Window size for estimation
        
    Returns:
        precisions: Updated precision estimates
    """
    precisions = []
    for error in errors:
        # Compute running variance
        var = torch.mean(error ** 2, dim=0)
        # Update precision (inverse variance)
        precision = 1.0 / (var + 1e-6)
        precisions.append(precision)
    return precisions
```

### Layer Normalization
```python
def normalize_layer(self, 
                   activations: torch.Tensor,
                   epsilon: float = 1e-5) -> torch.Tensor:
    """Apply layer normalization.
    
    Args:
        activations: Layer activations
        epsilon: Small constant for numerical stability
        
    Returns:
        normalized: Normalized activations
    """
    mean = torch.mean(activations, dim=-1, keepdim=True)
    std = torch.std(activations, dim=-1, keepdim=True)
    return (activations - mean) / (std + epsilon)
```

## Best Practices

### Initialization
1. Use small random weights
2. Initialize biases to zero
3. Set reasonable precision values
4. Validate layer sizes

### Training
1. Monitor convergence
2. Use appropriate learning rates
3. Implement early stopping
4. Save checkpoints

### Validation
1. Test prediction accuracy
2. Check error distributions
3. Validate precision estimates
4. Monitor layer activities

## Common Issues

### Numerical Stability
1. Use layer normalization
2. Add small constants to divisions
3. Clip gradient values
4. Monitor activation ranges

### Performance
1. Batch processing
2. GPU acceleration
3. Memory management
4. Efficient updates

## Related Documentation
- [[error_propagation]]
- [[precision_mechanisms]]
- [[temporal_models]]