cognitive/docs/guides/learning_paths/active_inference_learning_path.md

title	type	status	created	complexity	processing_priority	tags	semantic_relations
Active Inference Learning Path	learning_path	stable	2024-03-15	advanced	1	active-inference free-energy-principle cognitive-science machine-learning	type links foundation_for predictive_processing_learning_path cognitive_architecture_learning_path type links implements free_energy_principle_learning_path variational_inference_learning_path type links relates 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 spaces
  • Random variables
  • Conditional probability
  • Bayesian inference

• information_theory_learning_path

  • Entropy
  • KL divergence
  • Mutual information
  • Free energy

• optimization_theory_learning_path

  • Variational methods
  • Gradient descent
  • Lagrange multipliers
  • Optimal control

• stochastic_processes_learning_path

  • 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

  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

  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

  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

  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

  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
2. cognitive_architecture_learning_path
3. free_energy_principle_learning_path

Research Directions

1. research_guides/active_inference
2. research_guides/cognitive_science
3. research_guides/machine_learning