Tensor Network Emotional Memory

---
name: tensor-network-emotional-memory
description: "Classical tensor network modeling of order-dependent emotional memory in children — quantum-inspired methods achieve 77.98% accuracy in modeling valence-influenced recognition sequences, demonstrating value of quantum-like approaches for temporal cognitive phenomena (arXiv: 2606.28470)"
version: 1.0.0
created: 2026-07-01
author: Hermes Agent
category: neuroscience
tags: [tensor-networks, emotional-memory, quantum-cognition, children, recognition-memory, valence, order-dependence, quantum-inspired]
activation: tensor network memory, emotional memory quantum, quantum-inspired cognition, valence sequence modeling, children recognition memory, order-dependent memory, quantum cognition tensor
arxiv_id: "2606.28470"
arxiv_url: "https://arxiv.org/abs/2606.28470"
---

# Tensor Network Modeling of Emotional Memory in Children

## Overview

This paper demonstrates how emotional valence influences the order-dependent structure of children's recognition memory using **classical tensor network models**. The key finding is that correct recall of emotionally-valenced toy sequences depends not just on individual valence but on the valence of surrounding items — and tensor networks capturing these contextual dependencies achieve **77.98% accuracy**, far exceeding standard psychological models.

**Key Innovation**: While not strictly a "quantum cognition" model, the tensor network approach shows massive accuracy gains by naturally modeling order-dependent phenomena, validating quantum-inspired methods for cognitive temporal memory research.

**Paper**: [arXiv:2606.28470](https://arxiv.org/abs/2606.28470) (2026-06-26)
**Authors**: Henry Groves, Lucia F. Jackson, Barbara-Anne Robertson, Jonte R. Hance
**Comment**: 26 pages, 9 figures

## Core Methodology

### 1. Experimental Design

- **Participants**: Children shown sequences of emotionally-valenced toys
- **Task**: Recognition memory test after sequential presentation
- **Manipulation**: Each toy assigned emotional valence (positive/negative/neutral)
- **Key measure**: Whether recall accuracy depends on valence of adjacent items

### 2. Standard Psychological Models (Baseline)

- Standard models confirm order-dependence differs across event positions
- **Limitation**: Low accuracy; cannot capture how memory for one emotional object influences recall of others in the set
- Models treat items independently rather than as interacting sequence

### 3. Tensor Network Model

- **Architecture**: Classical tensor network factoring in valence context
- **Key feature**: Models interactions between adjacent emotional items in sequence
- **Result**: **77.98% accuracy** — massive increase over standard models
- **Interpretation**: Tensor network structure naturally captures contextual interference patterns in memory

### 4. Why Tensor Networks Work

- Tensor contractions model how valence of one item affects processing of neighbors
- Captures non-independent structure: memory is not item-by-item but sequence-wide
- Quantum-inspired formalism (without requiring quantum mechanics) provides mathematical framework for contextual dependencies

## Step-by-Step Implementation

### 1. Data Collection Protocol

```
1. Select N emotionally-valenced stimuli (toys) with clear valence ratings
2. Present sequences of length k to participants
3. Control for position effects across conditions
4. Test recognition memory for each item
5. Record accuracy as function of position and adjacent valences
```

### 2. Standard Model Baseline

```python
# Standard serial position model
def serial_position_model(sequence, valences):
    """Baseline: position-dependent recall probability"""
    probabilities = []
    for i, item in enumerate(sequence):
        # Primacy + recency effects
        p = primacy_weight(i) + recency_weight(i, len(sequence))
        probabilities.append(p)
    return probabilities
```

### 3. Tensor Network Model

```python
# Tensor network for valence-contextual memory
def tensor_network_memory(sequence, valences):
    """Model: each item's recall depends on adjacent valences via tensor contraction"""
    # Build tensor for each position encoding item identity + valence
    tensors = [build_item_tensor(item, val) for item, val in zip(sequence, valences)]
    
    # Contract tensors with interaction matrices capturing valence-valence coupling
    for i in range(len(tensors) - 1):
        interaction = valence_coupling_matrix(valences[i], valences[i+1])
        tensors[i] = contract(tensors[i], interaction, tensors[i+1])
    
    # Final contraction gives recall probability for each position
    return final_contraction(tensors)
```

### 4. Evaluation

- Compare against human recall data using accuracy metrics
- Ablation: remove valence context → accuracy drops significantly
- Position analysis: tensor model captures primacy, recency, AND contextual effects

## Pitfalls & Best Practices

### Pitfalls

1. **Sample size**: Children's memory data is noisy; need sufficient N per condition
2. **Valence confound**: Emotional valence correlates with other properties (novelty, complexity) — control carefully
3. **Overfitting**: Tensor networks have many parameters; regularize or use cross-validation
4. **Quantum vs classical confusion**: This is a classical tensor network — don't claim quantum cognition without further evidence

### Best Practices

1. **Baseline first**: Always compare against standard serial position models before claiming tensor network advantage
2. **Control for item properties**: Match items on non-valence dimensions
3. **Ablation studies**: Remove valence context to confirm it drives the accuracy gain
4. **Report both**: Tensor network accuracy AND standard model accuracy for fair comparison
5. **Age stratification**: Children's memory develops rapidly; report age distributions

## Applications & Extensions

### Direct Applications

- **Educational assessment**: Understanding how emotional classroom environments affect memory
- **Clinical psychology**: Modeling memory distortions in trauma (emotional valence effects)
- **Child development research**: Age-dependent changes in emotional memory coupling
- **Advertising/marketing**: Sequence effects in emotional brand exposure

### Extensions

- **Quantum cognition models**: Test if actual quantum probability models (not just tensor networks) improve further
- **fMRI validation**: Correlate tensor network predictions with neural activation patterns
- **Adult comparison**: Does emotional memory coupling change with age?
- **Cross-cultural**: Different cultures may show different valence-coupling patterns
- **Computational implementation**: Deploy tensor network as differentiable layer in cognitive models

## Key Findings Summary

| Model | Accuracy | Captures Order-Dependence? | Captures Contextual Valence? |
|-------|----------|---------------------------|------------------------------|
| Standard psychological | Low | Partially | No |
| Tensor network (valence) | 77.98% | Yes | Yes |

## Related Skills

- [[tensor-network-emotional-memory]] — This skill
- [[quantum-cognition]] — Quantum cognition methodology
- [[tensor-network-medical-imaging]] — Tensor networks in medical context
- [[neural-dynamics-decision-making]] — Decision-making neural models

## References

- Groves, H., Jackson, L. F., Robertson, B.-A., & Hance, J. R. (2026). Modelling Emotional Memory in Children with Tensor Networks. arXiv:2606.28470.
- Busemeyer, J. R., & Bruza, P. D. (2012). Quantum Models of Cognition and Decision. Cambridge University Press.
- Orús, R. (2014). A practical introduction to tensor networks. Annals of Physics, 349, 117-158.