Quantum Emotional Memory Tensor Networks

---
name: quantum-emotional-memory-tensor-networks
description: Quantum-inspired tensor network methodology for modeling order-dependent emotional memory in children, achieving 77.98% accuracy by incorporating valence into tensor factorization. Based on arXiv:2606.28470.
trigger_words: emotional memory, tensor network, order-dependent memory, valence memory, quantum-inspired cognition, children memory modeling
---

# Quantum-Emotional Memory Tensor Networks

## Description

Models emotional memory using tensor networks that capture order-dependent structure in children's recognition memory. Emotional valence influences recall not just of individual items but of their sequential context. A classical tensor network model incorporating valence achieves 77.98% accuracy. Based on arXiv:2606.28470 (Groves et al., 2026).

## Activation Keywords

- emotional memory tensor network
- order-dependent memory modeling
- valence memory model
- quantum-inspired memory
- tensor network cognition
- children emotional memory
- sequential memory valence

## Core Methodology

### 1. Emotional Valence Tensor Construction

```python
import numpy as np

class EmotionalMemoryTensor:
    """Tensor network for emotional memory with valence encoding."""
    
    def __init__(self, n_items, valence_dim=3):
        """
        Args:
            n_items: Number of items in sequence
            valence_dim: Valence dimensions (positive/neutral/negative)
        """
        self.n_items = n_items
        self.valence_dim = valence_dim
        # Core tensor: shape (n_items, valence_dim, hidden_dim)
        self.hidden_dim = 16
        self.core_tensor = np.random.randn(n_items, valence_dim, self.hidden_dim) * 0.1
        # Interaction tensor: captures how one item's memory affects others
        self.interaction_tensor = np.random.randn(
            n_items, n_items, valence_dim, valence_dim, self.hidden_dim
        ) * 0.05
    
    def encode_sequence(self, items, valences):
        """Encode a sequence of emotionally-valenced items.
        
        Args:
            items: List of item indices
            valences: List of valence values (0=negative, 1=neutral, 2=positive)
        """
        memory_state = np.zeros(self.hidden_dim)
        
        for i, (item, valence) in enumerate(zip(items, valences)):
            # Direct encoding
            item_vec = self.core_tensor[item, valence, :]
            memory_state += item_vec
            
            # Contextual influence from neighbors
            if i > 0:
                prev_item, prev_valence = items[i-1], valences[i-1]
                interaction = self.interaction_tensor[
                    item, i, valence, prev_valence, :
                ]
                memory_state += interaction * 0.5
            
            if i < len(items) - 1:
                next_item, next_valence = items[i+1], valences[i+1]
                interaction = self.interaction_tensor[
                    item, i, valence, next_valence, :
                ]
                memory_state += interaction * 0.5
        
        return memory_state
    
    def predict_recall(self, memory_state, target_item, target_valence):
        """Predict recall probability for a specific item-valence pair."""
        item_vec = self.core_tensor[target_item, target_valence, :]
        # Similarity-based recall
        similarity = np.dot(memory_state, item_vec)
        # Sigmoid activation
        prob = 1.0 / (1.0 + np.exp(-similarity))
        return prob
```

### 2. Order-Dependent Structure

```python
def compute_order_dependence(items, valences, recall_data):
    """Analyze how order affects recall accuracy.
    
    Returns order-dependence metrics showing how memory for an item
    depends on the valence of surrounding items.
    """
    n_items = len(items)
    order_effects = []
    
    for i in range(n_items):
        # Recall accuracy for item i
        actual_recall = recall_data.get(i, False)
        
        # Context: valence of surrounding items
        context_valences = []
        if i > 0:
            context_valences.append(valences[i-1])
        if i < n_items - 1:
            context_valences.append(valences[i+1])
        
        order_effects.append({
            'item': items[i],
            'own_valence': valences[i],
            'context_valences': context_valences,
            'recalled': actual_recall
        })
    
    return order_effects

def valence_influence_analysis(recall_data, order_effects):
    """Quantify how valence context influences recall.
    
    Returns the magnitude of valence effects on memory accuracy.
    """
    # Group by valence context patterns
    context_recall = {}
    
    for oe in order_effects:
        key = tuple(oe['context_valences'])
        if key not in context_recall:
            context_recall[key] = {'recalled': 0, 'total': 0}
        context_recall[key]['total'] += 1
        if oe['recalled']:
            context_recall[key]['recalled'] += 1
    
    # Compute accuracy per context pattern
    for key, data in context_recall.items():
        data['accuracy'] = data['recalled'] / data['total'] if data['total'] > 0 else 0
    
    return context_recall
```

### 3. Tensor Network Training

```python
def train_emotional_memory_model(sequences, recall_labels, n_epochs=100, lr=0.01):
    """Train the tensor network model on emotional memory data.
    
    Args:
        sequences: List of (items, valences) tuples
        recall_labels: List of recall outcomes per item
        n_epochs: Training iterations
        lr: Learning rate
    
    Returns:
        Trained EmotionalMemoryTensor model
    """
    # Find dimensions
    max_item = max(max(seq[0]) for seq in sequences)
    model = EmotionalMemoryTensor(n_items=max_item + 1)
    
    for epoch in range(n_epochs):
        total_loss = 0
        
        for (items, valences), labels in zip(sequences, recall_labels):
            # Encode sequence
            memory = model.encode_sequence(items, valences)
            
            # Predict and compute loss
            for item, valence, label in zip(items, valences, labels):
                pred = model.predict_recall(memory, item, valence)
                loss = (pred - label) ** 2
                total_loss += loss
                
                # Gradient update (simplified)
                grad = 2 * (pred - label) * pred * (1 - pred)
                model.core_tensor[item, valence, :] -= lr * grad * memory
        
        if epoch % 20 == 0:
            print(f"Epoch {epoch}: loss = {total_loss:.4f}")
    
    return model
```

### 4. Task Protocol for Children

```python
def emotional_memory_task_protocol():
    """Novel task protocol for exploring emotional temporal memory in children.
    
    Returns standardized procedure for collecting emotional memory data.
    """
    protocol = {
        'stimuli': {
            'toys': [
                {'name': 'teddy', 'valence': 'positive'},
                {'name': 'spider', 'valence': 'negative'},
                {'name': 'book', 'valence': 'neutral'},
                {'name': 'candy', 'valence': 'positive'},
                {'name': 'broom', 'valence': 'neutral'},
                {'name': 'snake', 'valence': 'negative'},
            ]
        },
        'procedure': [
            'Present toys in randomized sequence',
            'Record order and timing of presentation',
            'After delay period, ask child to recall toys',
            'Record which toys are recalled and in what order',
            'Repeat with different sequences',
        ],
        'measurements': [
            'Correct recall (item and position)',
            'Intrusion errors',
            'Order errors',
            'Valence clustering',
        ],
        'analysis': {
            'valence_effect': 'Compare recall by valence type',
            'order_effect': 'Compare recall by position',
            'context_effect': 'Compare recall by surrounding valence',
        }
    }
    return protocol
```

## Workflow for Agents

### Step 1: Collect Emotional Memory Data

```python
protocol = emotional_memory_task_protocol()
# Run experiment or load existing data
sequences = [
    ([0, 1, 2, 3, 4, 5], [2, 0, 1, 2, 1, 0]),  # items, valences
    ([3, 2, 0, 5, 1, 4], [2, 1, 2, 0, 0, 1]),
]
recall_labels = [
    [1, 0, 1, 1, 0, 1],  # binary recall per item
    [1, 1, 0, 0, 1, 1],
]
```

### Step 2: Analyze Order Dependence

```python
order_effects = compute_order_dependence(
    sequences[0][0], sequences[0][1],
    {i: bool(recall_labels[0][i]) for i in range(6)}
)
context_analysis = valence_influence_analysis(recall_labels, order_effects)
```

### Step 3: Train Tensor Network Model

```python
model = train_emotional_memory_model(sequences, recall_labels)
```

### Step 4: Evaluate Accuracy

```python
# Expected: ~77.98% accuracy with valence-informed tensor network
# Baseline (no valence): significantly lower
```

## Key Findings

1. **Context-Dependent Recall**: Memory for an item depends on valence of surrounding items, not just its own valence
2. **Tensor Network Advantage**: Classical tensor network achieves 77.98% accuracy vs. standard psychological models
3. **Order Matters**: Sequential structure of emotional events shapes memory organization
4. **Valence Propagation**: Memory for one emotional object influences memory for others in the set

## Error Handling

### Sparse Training Data
```python
# Use regularization or smaller hidden dimensions
model = EmotionalMemoryTensor(n_items=max_item + 1, hidden_dim=8)
```

### Overfitting
```python
# Add L2 regularization
grad += lambda_reg * model.core_tensor[item, valence, :]
```

## Related Skills

- `quantum-cognition` - broader quantum cognition framework
- `tensor-network-emotional-memory` - tensor network for emotional modeling
- `quantum-like-mental-markers` - quantum markers in cognition

## References

- arXiv:2606.28470 - "Modelling Emotional Memory in Children with Tensor Networks" (2026)
- Busemeyer & Bruza (2012) - Quantum Models of Cognition and Decision