cognitive/docs/guides/implementation/error_propagation.md

---
title: Error Propagation Implementation
type: implementation_guide
status: stable
created: 2024-02-12
tags:
  - implementation
  - predictive-processing
  - error-handling
semantic_relations:
  - type: implements
    links: [[../../learning_paths/predictive_processing]]
  - type: relates
    links:
      - [[predictive_network]]
      - [[precision_mechanisms]]
---

# Error Propagation Implementation

## Overview

This guide details the implementation of error propagation mechanisms in predictive processing networks, focusing on both forward and backward message passing.

## Core Mechanisms

### Error Types
```python
class PredictionError:
    def __init__(self, 
                 predicted: torch.Tensor,
                 actual: torch.Tensor,
                 precision: torch.Tensor):
        """Initialize prediction error.
        
        Args:
            predicted: Predicted values
            actual: Actual values
            precision: Precision (inverse variance)
        """
        self.predicted = predicted
        self.actual = actual
        self.precision = precision
        self.error = self._compute_error()
        
    def _compute_error(self) -> torch.Tensor:
        """Compute weighted prediction error."""
        raw_error = self.actual - self.predicted
        return raw_error * self.precision
```

### Message Passing
```python
class MessagePassing:
    def __init__(self, network: PredictiveNetwork):
        """Initialize message passing.
        
        Args:
            network: Predictive network instance
        """
        self.network = network
        self.messages_up = []
        self.messages_down = []
    
    def forward_messages(self, 
                        input_data: torch.Tensor) -> List[PredictionError]:
        """Compute forward (bottom-up) messages.
        
        Args:
            input_data: Input tensor
            
        Returns:
            errors: List of prediction errors
        """
        current = input_data
        errors = []
        
        for layer in self.network.layers:
            # Generate prediction
            prediction = layer.forward(current)
            
            # Compute error
            error = PredictionError(
                predicted=prediction,
                actual=current,
                precision=layer.precision
            )
            errors.append(error)
            
            # Update current input
            current = prediction
        
        self.messages_up = errors
        return errors
    
    def backward_messages(self, 
                         top_down_signal: torch.Tensor) -> List[PredictionError]:
        """Compute backward (top-down) messages.
        
        Args:
            top_down_signal: Top-level signal
            
        Returns:
            errors: List of prediction errors
        """
        current = top_down_signal
        errors = []
        
        for layer in reversed(self.network.layers):
            # Generate backward prediction
            prediction = layer.backward(current)
            
            # Compute error
            error = PredictionError(
                predicted=prediction,
                actual=current,
                precision=layer.precision
            )
            errors.append(error)
            
            # Update current signal
            current = prediction
        
        self.messages_down = errors
        return errors
```

## Error Integration

### Error Combination
```python
def combine_errors(self,
                  bottom_up: PredictionError,
                  top_down: PredictionError) -> torch.Tensor:
    """Combine bottom-up and top-down errors.
    
    Args:
        bottom_up: Bottom-up prediction error
        top_down: Top-down prediction error
        
    Returns:
        combined: Combined error signal
    """
    # Weight errors by their precisions
    weighted_up = bottom_up.error * bottom_up.precision
    weighted_down = top_down.error * top_down.precision
    
    # Combine weighted errors
    total_precision = bottom_up.precision + top_down.precision
    combined = (weighted_up + weighted_down) / (total_precision + 1e-6)
    
    return combined
```

### Update Rules
```python
def update_layer(self,
                 layer: PredictiveLayer,
                 combined_error: torch.Tensor,
                 learning_rate: float = 0.01):
    """Update layer parameters based on combined error.
    
    Args:
        layer: Layer to update
        combined_error: Combined error signal
        learning_rate: Learning rate for updates
    """
    # Compute gradients
    with torch.enable_grad():
        # Weight updates
        dW_hidden = torch.autograd.grad(
            combined_error.mean(),
            layer.W_hidden
        )[0]
        dW_pred = torch.autograd.grad(
            combined_error.mean(),
            layer.W_pred
        )[0]
        
        # Bias updates
        db_hidden = torch.autograd.grad(
            combined_error.mean(),
            layer.b_hidden
        )[0]
        db_pred = torch.autograd.grad(
            combined_error.mean(),
            layer.b_pred
        )[0]
    
    # Apply updates
    with torch.no_grad():
        layer.W_hidden -= learning_rate * dW_hidden
        layer.W_pred -= learning_rate * dW_pred
        layer.b_hidden -= learning_rate * db_hidden
        layer.b_pred -= learning_rate * db_pred
```

## Implementation Example

### Full Network Update
```python
def update_network(self,
                  input_data: torch.Tensor,
                  learning_rate: float = 0.01):
    """Perform full network update.
    
    Args:
        input_data: Input tensor
        learning_rate: Learning rate for updates
    """
    # Forward pass
    forward_errors = self.forward_messages(input_data)
    
    # Generate top-down signal
    top_signal = self.network.layers[-1].forward(forward_errors[-1].actual)
    
    # Backward pass
    backward_errors = self.backward_messages(top_signal)
    
    # Update each layer
    for layer_idx, layer in enumerate(self.network.layers):
        # Combine errors
        combined = self.combine_errors(
            forward_errors[layer_idx],
            backward_errors[-(layer_idx + 1)]
        )
        
        # Update layer
        self.update_layer(layer, combined, learning_rate)
```

## Advanced Features

### Error Gating
```python
def gate_error(self,
               error: PredictionError,
               threshold: float = 0.1) -> PredictionError:
    """Gate error signal based on magnitude.
    
    Args:
        error: Prediction error
        threshold: Gating threshold
        
    Returns:
        gated: Gated error signal
    """
    magnitude = torch.abs(error.error)
    mask = magnitude > threshold
    
    gated_error = PredictionError(
        predicted=error.predicted,
        actual=error.actual,
        precision=error.precision * mask.float()
    )
    
    return gated_error
```

### Temporal Integration
```python
def integrate_temporal_errors(self,
                            current_error: PredictionError,
                            previous_errors: List[PredictionError],
                            window_size: int = 5) -> PredictionError:
    """Integrate errors over time.
    
    Args:
        current_error: Current prediction error
        previous_errors: List of previous errors
        window_size: Integration window size
        
    Returns:
        integrated: Temporally integrated error
    """
    # Collect recent errors
    recent_errors = previous_errors[-window_size:]
    recent_errors.append(current_error)
    
    # Compute weighted average
    weights = torch.exp(-torch.arange(len(recent_errors)))
    weights = weights / weights.sum()
    
    integrated_error = sum(
        e.error * w for e, w in zip(recent_errors, weights)
    )
    
    return PredictionError(
        predicted=current_error.predicted,
        actual=current_error.actual,
        precision=current_error.precision,
        error=integrated_error
    )
```

## Best Practices

### Error Handling
1. Validate error magnitudes
2. Check precision values
3. Monitor gradients
4. Handle edge cases

### Optimization
1. Batch processing
2. Memory management
3. Computational efficiency
4. Numerical stability

### Debugging
1. Visualize error flow
2. Track convergence
3. Monitor updates
4. Validate predictions

## Common Issues

### Stability
1. Gradient explosion
2. Vanishing errors
3. Precision instability
4. Update oscillations

### Solutions
1. Gradient clipping
2. Error normalization
3. Adaptive learning rates
4. Error gating

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