Python

Active Inference Implementation in Python

This directory contains a comprehensive Python implementation of active inference with teacher-student learning dynamics and scientific computing capabilities.

Overview

The Python implementation provides:

• Scientific computing with NumPy and SciPy
• Teacher-student POMDP framework
• Rich visualization with matplotlib
• Comprehensive analysis tools

Core Components

• Student_Teacher.py: Main teacher-student implementation
• teacher_wrapper.py: Teacher model wrapper
• output/: Generated visualizations and results

Architecture

Teacher-Student Framework

The implementation features a sophisticated teacher-student learning model:

Teacher Model

class TeacherModel:
    def __init__(self, n_states):
        self.knowledge = np.zeros(n_states)
        self.growth_rate = 0.1
        self.max_knowledge = 1.0

    def update_knowledge(self, state):
        # Logistic growth model
        current = self.knowledge[state]
        exp_gr = np.exp(self.growth_rate)
        self.knowledge[state] = (self.max_knowledge * current * exp_gr) / \
                               (self.max_knowledge + current * (exp_gr - 1))

    def suggest_resource(self, student_beliefs):
        # Intelligent resource allocation
        gaps = (self.max_knowledge - self.knowledge) * student_beliefs
        return np.argmax(gaps)

Student Model

class StudentTeacherPOMDP:
    def __init__(self, n_states, n_observations, n_actions):
        self.n_states = n_states
        self.A = self.initialize_matrix(n_observations, n_states)  # Likelihood
        self.B = self.initialize_matrix(n_states, n_actions)      # Transition
        self.C = self.initialize_vector(n_observations)            # Preferences
        self.D = self.initialize_vector(n_states)                  # Prior

    def update_beliefs(self, observation):
        # Bayesian belief updating
        likelihood = self.A[observation, :]
        posterior = likelihood * self.beliefs
        self.beliefs = posterior / np.sum(posterior)

Dependencies

• Python 3.7+
• NumPy: Matrix operations and numerical computing
• SciPy: Scientific computing and optimization
• Matplotlib: Visualization and plotting
• Seaborn: Statistical visualization
• Pandas: Data manipulation and analysis

Installing Dependencies

pip install numpy scipy matplotlib seaborn pandas

Building and Running

# Run the main implementation
python Student_Teacher.py

# Run with custom parameters
python Student_Teacher.py --states 6 --steps 200

# Run teacher model analysis
python teacher_wrapper.py

# Generate visualizations
python -c "from Student_Teacher import StudentTeacherPOMDP; pomdp = StudentTeacherPOMDP(4, 3, 2); pomdp.plot_matrices()"

Configuration

The implementation supports flexible configuration:

# Simulation parameters
config = {
    'n_states': 4,
    'n_observations': 3,
    'n_actions': 2,
    'learning_rate': 0.1,
    'precision': 1.0,
    'uncertainty_weight': 0.1,
    'max_iterations': 100,
    'convergence_threshold': 1e-6,
    'visualization_enabled': True
}

Core Algorithms

Belief Update Algorithm

def update_beliefs(self, observation):
    likelihood = self.A[observation, :]
    posterior = likelihood * self.beliefs

    # Normalize to ensure probabilities sum to 1
    if np.sum(posterior) > 0:
        self.beliefs = posterior / np.sum(posterior)
    else:
        # Handle zero posterior case
        self.beliefs = np.ones(self.n_states) / self.n_states

Free Energy Calculation

def calculate_free_energy(self, policy):
    # Expected free energy calculation
    efe = 0
    for action in policy:
        # Calculate expected surprise
        predicted_beliefs = self.predict_beliefs(action)
        expected_surprise = self.calculate_expected_surprise(predicted_beliefs)
        efe += np.sum(self.beliefs * expected_surprise)
    return efe

Teacher-Student Learning

def infer_policy(self, policies):
    best_policy = None
    min_free_energy = float('inf')

    for policy in policies:
        fe = self.calculate_free_energy(policy)
        if fe < min_free_energy:
            min_free_energy = fe
            best_policy = policy

    return best_policy

Visualization and Analysis

Generated Outputs

The implementation creates comprehensive visualizations:

• Matrix Visualizations: A, B, C, D matrices as heatmaps
• Belief Evolution: Time series of belief state changes
• Teacher Knowledge: Growth curves and knowledge distribution
• Learning Progress: Performance metrics over time

Output Files

• A_matrix.png: Likelihood matrix visualization
• B_matrix.png: Transition matrix visualization
• student_beliefs_final.png: Final belief state
• teacher_knowledge_final.png: Final teacher knowledge

Performance Characteristics

Computational Efficiency

• Matrix Operations: Optimized NumPy vectorized operations
• Memory Usage: Efficient data structures with minimal overhead
• Scalability: Linear scaling with state space size
• Parallel Processing: Optional multiprocessing support

Scientific Computing

• Numerical Stability: Robust floating-point calculations
• Statistical Analysis: Built-in hypothesis testing
• Optimization: Gradient-based and heuristic optimization
• Data Analysis: Comprehensive statistical tools

Extensions

Advanced Features

• Machine Learning Integration: Scikit-learn compatibility
• Deep Learning: PyTorch/TensorFlow integration
• Reinforcement Learning: OpenAI Gym compatibility
• Real-time Processing: Streaming data analysis

Integration Options

• Web Applications: Flask/Django integration
• Database Systems: SQL/NoSQL database integration
• Cloud Computing: AWS/Google Cloud deployment
• Real-time Dashboards: Interactive visualization

References

Key Papers

1. Friston, K. (2010): The free-energy principle: a unified brain theory?
2. Da Costa, L., et al. (2020): Active inference on discrete state-spaces
3. Parr, T., & Friston, K. (2019): Generalised free energy and active inference

Python Resources

1. Python Data Science Handbook: Scientific computing guide
2. Numerical Python: Advanced NumPy techniques
3. Python for Scientific Computing: Best practices and optimization