cognitive/docs/guides/implementation/temporal_models.md

---
title: Temporal Models Implementation
type: implementation_guide
status: stable
created: 2024-02-12
tags:
  - implementation
  - predictive-processing
  - temporal-dynamics
semantic_relations:
  - type: implements
    links: [[../../learning_paths/predictive_processing]]
  - type: relates
    links:
      - [[predictive_network]]
      - [[error_propagation]]
      - [[precision_mechanisms]]
---

# Temporal Models Implementation

## Overview

This guide details the implementation of temporal models in predictive processing networks, focusing on sequence prediction, temporal dependencies, and dynamic updating.

## Core Components

### Temporal Layer
```python
class TemporalLayer(nn.Module):
    def __init__(self,
                 input_size: int,
                 hidden_size: int,
                 temporal_horizon: int = 10):
        """Initialize temporal layer.
        
        Args:
            input_size: Size of input features
            hidden_size: Size of hidden state
            temporal_horizon: Number of timesteps to consider
        """
        super().__init__()
        
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.temporal_horizon = temporal_horizon
        
        # Temporal state
        self.hidden_state = torch.zeros(hidden_size)
        self.state_history = []
        
        # Neural components
        self.state_update = nn.GRUCell(input_size, hidden_size)
        self.temporal_attention = TemporalAttention(hidden_size)
        self.prediction_head = nn.Linear(hidden_size, input_size)
```

### Temporal Attention
```python
class TemporalAttention(nn.Module):
    def __init__(self, hidden_size: int):
        """Initialize temporal attention mechanism.
        
        Args:
            hidden_size: Size of hidden state
        """
        super().__init__()
        
        # Attention components
        self.query_proj = nn.Linear(hidden_size, hidden_size)
        self.key_proj = nn.Linear(hidden_size, hidden_size)
        self.value_proj = nn.Linear(hidden_size, hidden_size)
        
    def forward(self,
                query: torch.Tensor,
                keys: List[torch.Tensor],
                values: List[torch.Tensor]) -> torch.Tensor:
        """Compute temporal attention.
        
        Args:
            query: Current query state
            keys: Historical key states
            values: Historical value states
            
        Returns:
            context: Temporal context vector
        """
        # Project query, keys, and values
        q = self.query_proj(query)
        k = torch.stack([self.key_proj(k) for k in keys])
        v = torch.stack([self.value_proj(v) for v in values])
        
        # Compute attention scores
        scores = torch.matmul(q, k.transpose(-2, -1))
        scores = scores / math.sqrt(self.hidden_size)
        weights = F.softmax(scores, dim=-1)
        
        # Compute weighted context
        context = torch.matmul(weights, v)
        return context
```

## Implementation

### Temporal Prediction
```python
def predict_next(self,
                current_input: torch.Tensor) -> torch.Tensor:
    """Predict next timestep.
    
    Args:
        current_input: Current input tensor
        
    Returns:
        prediction: Prediction for next timestep
    """
    # Update hidden state
    self.hidden_state = self.state_update(
        current_input,
        self.hidden_state
    )
    
    # Update state history
    self.state_history.append(self.hidden_state)
    if len(self.state_history) > self.temporal_horizon:
        self.state_history.pop(0)
    
    # Compute temporal attention
    if len(self.state_history) > 1:
        context = self.temporal_attention(
            query=self.hidden_state,
            keys=self.state_history[:-1],
            values=self.state_history[:-1]
        )
        
        # Combine with current state
        combined = (self.hidden_state + context) / 2
    else:
        combined = self.hidden_state
    
    # Generate prediction
    prediction = self.prediction_head(combined)
    return prediction
```

### Sequence Processing
```python
def process_sequence(self,
                    sequence: torch.Tensor,
                    teacher_forcing_ratio: float = 0.5) -> List[torch.Tensor]:
    """Process temporal sequence.
    
    Args:
        sequence: Input sequence [T, input_size]
        teacher_forcing_ratio: Ratio of teacher forcing
        
    Returns:
        predictions: List of predictions
    """
    predictions = []
    current_input = sequence[0]
    
    for t in range(1, len(sequence)):
        # Generate prediction
        prediction = self.predict_next(current_input)
        predictions.append(prediction)
        
        # Teacher forcing
        if random.random() < teacher_forcing_ratio:
            current_input = sequence[t]
        else:
            current_input = prediction
    
    return predictions
```

## Advanced Features

### Multi-scale Temporal Processing
```python
class MultiScaleTemporalModel(nn.Module):
    def __init__(self,
                 input_size: int,
                 num_scales: int = 3):
        """Initialize multi-scale temporal model.
        
        Args:
            input_size: Size of input features
            num_scales: Number of temporal scales
        """
        super().__init__()
        
        # Create temporal layers at different scales
        self.temporal_scales = nn.ModuleList([
            TemporalLayer(
                input_size=input_size,
                hidden_size=input_size * 2,
                temporal_horizon=2 ** i
            )
            for i in range(num_scales)
        ])
        
        # Scale integration
        self.scale_attention = nn.Linear(
            num_scales * input_size,
            input_size
        )
    
    def forward(self,
                sequence: torch.Tensor) -> torch.Tensor:
        """Process sequence at multiple scales.
        
        Args:
            sequence: Input sequence
            
        Returns:
            prediction: Integrated prediction
        """
        # Process at each scale
        scale_predictions = []
        for scale in self.temporal_scales:
            pred = scale.process_sequence(sequence)
            scale_predictions.append(pred[-1])
        
        # Integrate predictions
        combined = torch.cat(scale_predictions, dim=-1)
        prediction = self.scale_attention(combined)
        
        return prediction
```

### Temporal Error Integration
```python
class TemporalErrorIntegration:
    def __init__(self,
                 decay_factor: float = 0.9,
                 max_history: int = 100):
        """Initialize temporal error integration.
        
        Args:
            decay_factor: Error decay rate
            max_history: Maximum history length
        """
        self.decay_factor = decay_factor
        self.max_history = max_history
        self.error_history = []
        
    def integrate_error(self,
                       current_error: torch.Tensor) -> torch.Tensor:
        """Integrate error over time.
        
        Args:
            current_error: Current prediction error
            
        Returns:
            integrated: Temporally integrated error
        """
        # Update history
        self.error_history.append(current_error)
        if len(self.error_history) > self.max_history:
            self.error_history.pop(0)
        
        # Compute temporal weights
        weights = torch.tensor([
            self.decay_factor ** i
            for i in range(len(self.error_history))
        ])
        weights = weights / weights.sum()
        
        # Compute weighted sum
        integrated = sum(
            e * w for e, w in zip(self.error_history, weights)
        )
        
        return integrated
```

## Usage Examples

### Basic Usage
```python
# Initialize temporal layer
temporal_layer = TemporalLayer(
    input_size=64,
    hidden_size=128,
    temporal_horizon=10
)

# Process sequence
sequence = torch.randn(20, 64)  # [T, input_size]
predictions = temporal_layer.process_sequence(sequence)

# Get next prediction
next_pred = temporal_layer.predict_next(sequence[-1])
```

### Multi-scale Processing
```python
# Initialize multi-scale model
multi_scale = MultiScaleTemporalModel(
    input_size=64,
    num_scales=3
)

# Process sequence
sequence = torch.randn(20, 64)
prediction = multi_scale(sequence)
```

## Best Practices

### Temporal Processing
1. Handle variable sequences
2. Implement teacher forcing
3. Use appropriate horizons
4. Consider multiple scales

### Memory Management
1. Limit history size
2. Clear unused states
3. Batch sequences
4. Optimize storage

### Training
1. Curriculum learning
2. Scheduled sampling
3. Gradient clipping
4. Validation splits

## Common Issues

### Stability
1. Vanishing gradients
2. Exploding predictions
3. Memory overflow
4. Error accumulation

### Solutions
1. Residual connections
2. Gradient normalization
3. Memory optimization
4. Error gating

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