Exploratory Predictive Representation Geometry

---
name: exploratory-predictive-representation-geometry
description: "探索性行为塑造预测性表征几何的方法论。通过主动感知框架研究探索-利用平衡如何影响内部表征组织。探索性行为使表征更具空间结构性，更好地保留迷宫转换结构。激活词：探索性学习、exploratory behavior、predictive coding、predictive representations、active sensing、latent space geometry、行为-学习循环。"
---

# Exploratory Experience Shapes the Geometry of Predictive Representations

## Paper Overview

**arXiv ID**: 2605.27929  
**Authors**: Kseniia Shilova, Abdelrahman Sharafeldin, Advay Balakrishnan, Hannah Choi  
**Categories**: q-bio.NC (Neurons and Cognition), cs.LG (Machine Learning)  
**Published**: May 27, 2026  
**DOI**: https://doi.org/10.48550/arXiv.2605.27929

## Research Question

How do exploratory vs. exploitative behavioral strategies shape internal predictive representations in active sensing agents? This study investigates how behavior modulates the geometry of learned representations through the action-perception loop.

## Core Theory

### Active Sensing Framework
Active sensing links behavior and learning through an **action-perception loop**:
- Actions determine observations
- Observations update predictive models
- Models guide subsequent actions
- Continuous cycle between behavior and representation

### Predictive-Coding-Based Learning
- Internal representations continuously updated to predict future observations
- Model predicts both future states and reward probability
- Agents select actions based on expected information gain (exploration) or predicted reward (exploitation)

## Methodology

### Experimental Setup
- **Environment**: Tree-like maze with controllable exploration-exploitation balance
- **Agent**: Online learning agent with predictive-coding perception model
- **Parameter**: Controllable exploration-exploitation trade-off

### Learning Model
- **Inputs**: Maze navigation experience generated by agent's own behavior
- **Outputs**: 
  - Future maze state predictions
  - Reward probability predictions
- **Action Selection**: 
  - Information gain → exploration
  - Reward prediction → exploitation

### Validation with Animal Data
- Trained model on natural trajectories of **water-deprived mice** navigating same maze
- Compared representations from agent trajectories vs. mouse trajectories
- Categorized mice by exploration level

## Key Findings

### 1. Behavioral Regime Shapes Representations
Internal predictive representations **depend strongly** on agent's behavioral regime:
- **Exploratory agents**: Develop organized, structured representations
- **Exploitative agents**: Learn less organized representations

### 2. Spatial Organization in Exploration
Exploratory representations are:
- **More spatially organized**
- **Better preserve maze transition structure** in latent space
- Capture environmental geometry

### 3. Cross-Species Validation
Mouse behavior predicts representation geometry:
- **More exploratory mice** → representations matching exploratory agents
- **Restricted visitation mice** → representations matching exploitative agents
- Strong correspondence between artificial agent and animal behavior

### 4. Generalization Mechanism
Exploration enables formation of **generalized internal representations** by:
- Organizing latent space around **spatial location**
- Incorporating **transition context** into representations
- Capturing environmental structure beyond immediate reward

## Core Implications

### For Neuroscience
- Behavior shapes neural representations through active sensing
- Exploration creates structured spatial representations
- Predictive coding framework captures behavior-representation interaction
- Animal behavior mirrors agent dynamics

### For Machine Learning
- **Curriculum design**: Exploration-first strategies may improve representation learning
- **Self-supervised learning**: Behavior-driven data collection shapes representations
- **Active learning**: Information-gain-based exploration better than random sampling
- **Embodied AI**: Action-perception loops are critical for representation formation

### For Cognitive Science
- Exploratory behavior → generalized knowledge
- Exploitative behavior → task-specific knowledge
- Trade-off between generalization and specialization
- Behavior modulates what is learned, not just how well

## Technical Contributions

1. **Predictive-Coding Agent**: Novel architecture combining prediction and action selection
2. **Behavioral Regime Control**: Parameter for systematic exploration-exploitation manipulation
3. **Cross-Species Validation**: Comparing artificial agents with real animal behavior
4. **Geometry Analysis**: Quantifying latent space structure preservation
5. **Information-Theoretic Action**: Using expected information gain for exploration

## Experimental Design Strengths

- **Behavioral control**: Direct manipulation of exploration-exploitation balance
- **Animal validation**: Naturalistic mouse trajectories in identical environment
- **Representational analysis**: Geometric quantification of latent space
- **Predictive framework**: Unified model for state and reward prediction
- **Online learning**: Continuous updating from self-generated experience

## Representational Geometry Metrics

### Spatial Organization
```python
# Measure spatial organization in latent space
latent_positions = model.encode(maze_states)
spatial_correlation = correlation(
    latent_positions, 
    physical_positions
)
transition_preservation = structural_similarity(
    latent_transitions,
    maze_transitions
)
```

### Exploration Score
```python
# Quantify exploration level
visited_nodes = count_unique_states(trajectory)
entropy = entropy_of_visitation(trajectory)
information_gain = sum(expected_info_gain(action_history))
exploration_score = (visited_nodes + entropy + information_gain) / duration
```

## Limitations & Open Questions

- Does this apply to non-navigation tasks?
- How does reward magnitude affect exploration-exploitation trade-off?
- What neural mechanisms implement information-gain-based exploration?
- How do developmental changes in exploration shape representations over time?
- Role of memory in maintaining exploration across sessions?

## Relation to Existing Work

### Connects to:
- **Active inference** (Friston et al.) - epistemic value drives exploration
- **Predictive coding** (Rao & Ballard) - cortical learning framework
- **Curiosity-driven learning** (Pathak et al.) - intrinsic motivation
- **Self-supervised representation learning** - behavior-driven training
- **Spatial navigation neuroscience** - hippocampal and entorhinal encoding

### Contrasts with:
- Pure reinforcement learning (no intrinsic exploration reward)
- Offline supervised learning (behavior-independent representations)
- Random exploration (no information-gain computation)

## Future Research Directions

1. **Neural Correlates**: Identify brain regions encoding information gain
2. **Temporal Dynamics**: Track representation geometry changes across learning
3. **Multi-task Extension**: Test generalization across different environments
4. **Social Exploration**: Multi-agent exploration and shared representations
5. **Developmental Studies**: Infant exploratory behavior and representation formation
6. **Clinical Applications**: Exploration deficits in neurological disorders

## Activation Keywords

- 探索性学习、exploratory behavior、exploration-exploitation
- predictive coding、predictive representations
- active sensing、主动感知、action-perception loop
- latent space geometry、表征几何
- 行为-学习循环、behavior-learning interaction
- 空间组织、spatial organization
- 信息增益、information gain
- 表征学习、representation learning

## Methodological Patterns

### Predictive-Coding Agent Architecture
```python
class PredictiveAgent:
    def __init__(self, exploration_param):
        self.exploration_param = exploration_param
        self.predictive_model = PredictiveCodingModel()
        
    def act(self, state):
        if self.mode == 'explore':
            # Select by expected information gain
            action = max(actions, key=lambda a: 
                information_gain(self.predictive_model, state, a))
        else:  # exploit
            # Select by predicted reward
            action = max(actions, key=lambda a: 
                self.predictive_model.predict_reward(state, a))
        return action
    
    def learn(self, experience):
        # Update predictive model
        self.predictive_model.update(experience)
        # Update latent representations
        self.predictive_model.optimize_representation()
```

### Geometry Analysis Pipeline
```python
def analyze_representation_geometry(model, trajectories):
    # Encode states into latent space
    latent_coords = model.encode(trajectory.states)
    
    # Measure spatial organization
    spatial_alignment = mantel_test(
        latent_coords, 
        physical_coords
    )
    
    # Measure transition preservation
    transition_matrix = compute_transitions(trajectory)
    latent_transitions = compute_transitions(latent_coords)
    preservation_score = graph_similarity(
        transition_matrix, 
        latent_transitions
    )
    
    return {
        'spatial_alignment': spatial_alignment,
        'transition_preservation': preservation_score
    }
```

## Cross-Species Validation Method
```python
# Train on mouse trajectories
mouse_trajectories = load_mouse_data('water_deprived_mice')
mouse_exploration_scores = compute_exploration(mouse_trajectories)

# Categorize mice by exploration level
high_exploiters = mice[mouse_exploration_scores < threshold]
high_explorers = mice[mouse_exploration_scores > threshold]

# Train predictive model on each group
high_exploiters_model.fit(high_exploiters_trajectories)
high_explorers_model.fit(high_explorers_trajectories)

# Compare with agent models
exploitative_agent_model.fit(exploitative_agent_trajectories)
exploratory_agent_model.fit(exploratory_agent_trajectories)

# Measure correspondence
exploit_alignment = representation_similarity(
    high_exploiters_model, 
    exploitative_agent_model
)
explore_alignment = representation_similarity(
    high_explorers_model, 
    exploratory_agent_model
)
```

## Citation

```bibtex
@article{shilova2026exploratory,
  title={Exploratory Experience Shapes the Geometry of Predictive Representations},
  author={Shilova, Kseniia and Sharafeldin, Abdelrahman and Balakrishnan, Advay and Choi, Hannah},
  journal={arXiv preprint arXiv:2605.27929},
  year={2026}
}
```

## Related Papers

- [attractor-metadynamics-neural](attractor-metadynamics-neural) - Attractor dynamics in neural networks
- [hippocampal-memory-geometry-phase-transition](hippocampal-memory-geometry-phase-transition) - Hippocampal memory geometry
- [self-sustained-neuron-population](self-sustained-neuron-population) - Self-sustained neural activity
- [cognitive-flexibility-task-structure](cognitive-flexibility-task-structure) - Task structure for cognitive flexibility

## Tags

#neuroscience #predictive-coding #active-sensing #exploration-exploitation #representation-learning #behavior-driven-learning #latent-space-geometry #cross-species-validation #spatial-navigation #self-supervised-learning