---
title: Active Inference Learning Path
type: learning_path
status: stable
created: 2024-03-15
complexity: advanced
processing_priority: 1
tags:
  - active-inference
  - free-energy-principle
  - cognitive-science
  - machine-learning
semantic_relations:
  - type: foundation_for
    links:
      - [[predictive_processing_learning_path]]
      - [[cognitive_architecture_learning_path]]
  - type: implements
    links:
      - [[free_energy_principle_learning_path]]
      - [[variational_inference_learning_path]]
  - type: relates
    links:
      - [[dynamical_systems_learning_path]]
      - [[stochastic_processes_learning_path]]
      - [[information_theory_learning_path]]
---

# Active Inference Learning Path

## Overview

This learning path provides a comprehensive guide to understanding and implementing Active Inference, from mathematical foundations to practical applications. Active Inference is a unifying framework for understanding perception, learning, and action in biological and artificial systems.

## Prerequisites

### 1. Mathematics (4 weeks)
- [[probability_theory_learning_path|Probability Theory]]
  - Probability spaces
  - Random variables
  - Conditional probability
  - Bayesian inference

- [[information_theory_learning_path|Information Theory]]
  - Entropy
  - KL divergence
  - Mutual information
  - Free energy

- [[optimization_theory_learning_path|Optimization Theory]]
  - Variational methods
  - Gradient descent
  - Lagrange multipliers
  - Optimal control

- [[stochastic_processes_learning_path|Stochastic Processes]]
  - Markov processes
  - Diffusion processes
  - Stochastic differential equations
  - Path integrals

### 2. Programming (2 weeks)
- Python Fundamentals
  - NumPy/SciPy
  - PyTorch/JAX
  - Object-oriented programming
  - Scientific computing

- Software Engineering
  - Version control
  - Testing
  - Documentation
  - Best practices

## Core Learning Path

### 1. Theoretical Foundations (4 weeks)

#### Week 1-2: Free Energy Principle
- Variational Free Energy
  ```python
  def compute_free_energy(q_dist, p_dist, obs):
      """Compute variational free energy."""
      expected_log_likelihood = compute_expected_ll(q_dist, p_dist, obs)
      kl_divergence = compute_kl(q_dist, p_dist)
      return -expected_log_likelihood + kl_divergence
  ```
- Markov Blankets
- Self-organization
- Information Geometry

#### Week 3-4: Active Inference
- Expected Free Energy
  ```python
  def compute_expected_free_energy(policy, model):
      """Compute expected free energy for policy."""
      ambiguity = compute_ambiguity(policy, model)
      risk = compute_risk(policy, model)
      return ambiguity + risk
  ```
- Policy Selection
- Precision Engineering
- Message Passing

### 2. Implementation (6 weeks)

#### Week 1-2: Core Components
- Generative Models
  ```python
  class GenerativeModel:
      def __init__(self,
                  hidden_dims: List[int],
                  obs_dim: int):
          """Initialize generative model."""
          self.hidden_states = [
              torch.zeros(dim) for dim in hidden_dims
          ]
          self.obs_model = ObservationModel(hidden_dims[-1], obs_dim)
          self.trans_model = TransitionModel(hidden_dims)
          
      def generate(self, policy: torch.Tensor) -> torch.Tensor:
          """Generate observations under policy."""
          states = self.propagate_states(policy)
          return self.obs_model(states)
  ```
- Variational Inference
- Policy Networks
- Precision Parameters

#### Week 3-4: Agent Implementation
- Perception
  ```python
  class ActiveInferenceAgent:
      def __init__(self,
                  model: GenerativeModel,
                  learning_rate: float = 0.01):
          """Initialize active inference agent."""
          self.model = model
          self.lr = learning_rate
          self.beliefs = initialize_beliefs()
          
      def infer_states(self, obs: torch.Tensor) -> torch.Tensor:
          """Perform state inference."""
          for _ in range(self.inference_steps):
              pred_error = self.compute_prediction_error(obs)
              self.update_beliefs(pred_error)
          return self.beliefs
  ```
- Action Selection
- Learning
- Memory

#### Week 5-6: Advanced Features
- Hierarchical Models
- Active Learning
- Meta-learning
- Adaptive Behavior

### 3. Applications (4 weeks)

#### Week 1-2: Cognitive Tasks
- Perception Tasks
  ```python
  class PerceptionTask:
      def __init__(self,
                  stimuli: torch.Tensor,
                  categories: torch.Tensor):
          """Initialize perception task."""
          self.stimuli = stimuli
          self.categories = categories
          
      def evaluate(self, agent: ActiveInferenceAgent) -> Dict[str, float]:
          """Evaluate agent performance."""
          predictions = []
          for stimulus in self.stimuli:
              belief = agent.infer_states(stimulus)
              pred = agent.model.predict_category(belief)
              predictions.append(pred)
          return compute_metrics(predictions, self.categories)
  ```
- Decision Making
- Motor Control
- Learning Tasks

#### Week 3-4: Real-world Applications
- Robotics
- Neural Data Analysis
- Clinical Applications
- Social Systems

### 4. Advanced Topics (4 weeks)

#### Week 1-2: Theoretical Extensions
- Non-equilibrium Physics
- Information Geometry
- Quantum Extensions
- Continuous Time

#### Week 3-4: Research Frontiers
- Mixed Models
- Group Behavior
- Development
- Consciousness

## Projects

### Beginner Projects
1. **Simple Perception**
   - Binary classification
   - Feature extraction
   - Belief updating
   - Performance analysis

2. **Basic Control**
   - Pendulum balance
   - Target reaching
   - Simple navigation
   - Error correction

### Intermediate Projects
1. **Cognitive Tasks**
   - Visual recognition
   - Decision making
   - Sequence learning
   - Working memory

2. **Robotic Control**
   - Arm control
   - Object manipulation
   - Path planning
   - Multi-joint coordination

### Advanced Projects
1. **Complex Cognition**
   - Meta-learning
   - Hierarchical control
   - Active exploration
   - Social interaction

2. **Real-world Applications**
   - Medical diagnosis
   - Brain-machine interfaces
   - Autonomous systems
   - Clinical interventions

## Resources

### Reading Materials
1. **Core Papers**
   - Original formulations
   - Key extensions
   - Review papers
   - Applications

2. **Books**
   - Mathematical foundations
   - Cognitive science
   - Machine learning
   - Neuroscience

### Software Tools
1. **Libraries**
   - PyAI (Active Inference)
   - Torch/JAX implementations
   - Simulation environments
   - Analysis tools

2. **Environments**
   - OpenAI Gym
   - MuJoCo
   - Custom environments
   - Real-world interfaces

## Assessment

### Knowledge Checks
1. **Theoretical Understanding**
   - Mathematical derivations
   - Conceptual relationships
   - Framework applications
   - Design principles

2. **Implementation Skills**
   - Code review
   - Performance analysis
   - Debugging exercises
   - Optimization tasks

### Final Projects
1. **Research Implementation**
   - Novel contribution
   - Theoretical extension
   - Empirical validation
   - Documentation

2. **Practical Application**
   - Real-world problem
   - Solution design
   - Performance evaluation
   - Impact assessment

## Next Steps

### Advanced Paths
1. [[predictive_processing_learning_path|Predictive Processing]]
2. [[cognitive_architecture_learning_path|Cognitive Architecture]]
3. [[free_energy_principle_learning_path|Free Energy Principle]]

### Research Directions
1. [[research_guides/active_inference|Active Inference Research]]
2. [[research_guides/cognitive_science|Cognitive Science Research]]
3. [[research_guides/machine_learning|Machine Learning Research]]