cognitive/docs/guides/implementation/precision_mechanisms.md

---
title: Precision Mechanisms Implementation
type: implementation_guide
status: stable
created: 2024-02-12
tags:
  - implementation
  - predictive-processing
  - precision
semantic_relations:
  - type: implements
    links: [[../../learning_paths/predictive_processing]]
  - type: relates
    links:
      - [[predictive_network]]
      - [[error_propagation]]
---

# Precision Mechanisms Implementation

## Overview

This guide details the implementation of precision mechanisms in predictive processing networks, focusing on uncertainty estimation and attention modulation.

## Core Components

### Precision Estimation
```python
class PrecisionEstimator:
    def __init__(self, 
                 size: int,
                 initial_precision: float = 1.0,
                 min_precision: float = 1e-6,
                 max_precision: float = 1e6):
        """Initialize precision estimator.
        
        Args:
            size: Dimensionality of precision
            initial_precision: Initial precision value
            min_precision: Minimum precision value
            max_precision: Maximum precision value
        """
        self.size = size
        self.min_precision = min_precision
        self.max_precision = max_precision
        
        # Initialize precision parameters
        self.log_precision = nn.Parameter(
            torch.full((size,), math.log(initial_precision))
        )
        
    def get_precision(self) -> torch.Tensor:
        """Get current precision values."""
        precision = torch.exp(self.log_precision)
        return torch.clamp(
            precision,
            min=self.min_precision,
            max=self.max_precision
        )
```

### Attention Modulation
```python
class AttentionMechanism:
    def __init__(self, 
                 input_size: int,
                 hidden_size: int):
        """Initialize attention mechanism.
        
        Args:
            input_size: Size of input features
            hidden_size: Size of attention hidden state
        """
        self.attention_net = nn.Sequential(
            nn.Linear(input_size, hidden_size),
            nn.ReLU(),
            nn.Linear(hidden_size, input_size),
            nn.Sigmoid()
        )
        
    def compute_attention(self, 
                         inputs: torch.Tensor) -> torch.Tensor:
        """Compute attention weights.
        
        Args:
            inputs: Input features
            
        Returns:
            attention: Attention weights
        """
        return self.attention_net(inputs)
```

## Implementation

### Precision Layer
```python
class PrecisionLayer(nn.Module):
    def __init__(self,
                 size: int,
                 use_attention: bool = True):
        """Initialize precision layer.
        
        Args:
            size: Feature dimensionality
            use_attention: Whether to use attention
        """
        super().__init__()
        
        # Precision estimation
        self.precision_estimator = PrecisionEstimator(size)
        
        # Attention mechanism (optional)
        self.use_attention = use_attention
        if use_attention:
            self.attention = AttentionMechanism(size, size * 2)
        
    def forward(self,
                inputs: torch.Tensor,
                errors: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
        """Forward pass with precision weighting.
        
        Args:
            inputs: Input features
            errors: Prediction errors
            
        Returns:
            weighted_inputs: Precision-weighted inputs
            weighted_errors: Precision-weighted errors
        """
        # Get base precision
        precision = self.precision_estimator.get_precision()
        
        # Apply attention modulation
        if self.use_attention:
            attention = self.attention.compute_attention(inputs)
            precision = precision * attention
        
        # Apply precision weighting
        weighted_inputs = inputs * precision
        weighted_errors = errors * precision
        
        return weighted_inputs, weighted_errors
```

### Precision Updates
```python
def update_precision(self,
                    errors: torch.Tensor,
                    learning_rate: float = 0.01):
    """Update precision estimates based on errors.
    
    Args:
        errors: Prediction errors
        learning_rate: Learning rate for updates
    """
    # Compute precision gradients
    with torch.enable_grad():
        # Negative free energy
        F = -0.5 * torch.sum(errors ** 2 * self.get_precision())
        F -= 0.5 * torch.sum(torch.log(2 * math.pi / self.get_precision()))
        
        # Compute gradients
        grads = torch.autograd.grad(F, self.log_precision)[0]
    
    # Update precision parameters
    with torch.no_grad():
        self.log_precision += learning_rate * grads
```

## Advanced Features

### Hierarchical Precision
```python
class HierarchicalPrecision:
    def __init__(self, layer_sizes: List[int]):
        """Initialize hierarchical precision.
        
        Args:
            layer_sizes: List of layer sizes
        """
        self.precision_layers = nn.ModuleList([
            PrecisionLayer(size) for size in layer_sizes
        ])
        
    def forward(self,
                inputs: List[torch.Tensor],
                errors: List[torch.Tensor]) -> Tuple[List[torch.Tensor], List[torch.Tensor]]:
        """Forward pass through hierarchy.
        
        Args:
            inputs: List of layer inputs
            errors: List of prediction errors
            
        Returns:
            weighted_inputs: Precision-weighted inputs
            weighted_errors: Precision-weighted errors
        """
        weighted_inputs = []
        weighted_errors = []
        
        for layer, input_data, error in zip(
            self.precision_layers, inputs, errors
        ):
            w_input, w_error = layer(input_data, error)
            weighted_inputs.append(w_input)
            weighted_errors.append(w_error)
        
        return weighted_inputs, weighted_errors
```

### Adaptive Precision
```python
class AdaptivePrecision(PrecisionEstimator):
    def __init__(self,
                 size: int,
                 adaptation_rate: float = 0.1):
        """Initialize adaptive precision.
        
        Args:
            size: Feature dimensionality
            adaptation_rate: Rate of precision adaptation
        """
        super().__init__(size)
        self.adaptation_rate = adaptation_rate
        self.error_history = []
        
    def adapt_precision(self, error: torch.Tensor):
        """Adapt precision based on error history.
        
        Args:
            error: Current prediction error
        """
        # Update error history
        self.error_history.append(error.detach())
        if len(self.error_history) > 100:
            self.error_history.pop(0)
        
        # Compute error statistics
        error_var = torch.var(torch.stack(self.error_history), dim=0)
        
        # Update precision
        target_precision = 1.0 / (error_var + self.min_precision)
        current_precision = self.get_precision()
        
        # Smooth update
        new_precision = (
            (1 - self.adaptation_rate) * current_precision +
            self.adaptation_rate * target_precision
        )
        
        # Update log precision
        self.log_precision.data = torch.log(new_precision)
```

## Usage Examples

### Basic Usage
```python
# Initialize precision layer
precision_layer = PrecisionLayer(size=64)

# Forward pass with precision
inputs = torch.randn(32, 64)
errors = torch.randn(32, 64)
weighted_inputs, weighted_errors = precision_layer(inputs, errors)

# Update precision
precision_layer.update_precision(errors)
```

### Hierarchical Usage
```python
# Initialize hierarchical precision
hierarchical_precision = HierarchicalPrecision([64, 32, 16])

# Process multiple layers
layer_inputs = [torch.randn(32, size) for size in [64, 32, 16]]
layer_errors = [torch.randn(32, size) for size in [64, 32, 16]]

# Forward pass
weighted_inputs, weighted_errors = hierarchical_precision(
    layer_inputs, layer_errors
)
```

## Best Practices

### Initialization
1. Set reasonable initial precision
2. Use log-space for stability
3. Implement bounds checking
4. Initialize attention carefully

### Training
1. Monitor precision values
2. Adapt learning rates
3. Track error statistics
4. Validate attention maps

### Optimization
1. Use vectorized operations
2. Implement batch processing
3. Optimize memory usage
4. Profile computations

## Common Issues

### Numerical Issues
1. Precision overflow
2. Underflow in calculations
3. Gradient instability
4. NaN values

### Solutions
1. Use log-space operations
2. Implement value clipping
3. Add numerical safeguards
4. Monitor statistics

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