cognitive/docs/guides/implementation/precision_mechanisms.md

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

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

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

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

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

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

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

# 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

# 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