--- 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]]