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Free Energy Minimization
title: Free Energy Minimization type: concept status: stable tags:
- cognition
- computation
- optimization
- thermodynamics
- inference semantic_relations:
- type: implements links: free_energy_principle
- type: related links:
Overview
Free Energy Minimization is the fundamental principle underlying adaptive behavior in biological and artificial systems. It posits that all adaptive systems act to minimize their variational free energy, which measures the discrepancy between their internal models and environmental reality.
Mathematical Framework
Variational Free Energy
F = E_q[\ln q(s) - \ln p(s,o)] = D_{KL}[q(s)||p(s|o)] - \ln p(o)
where:
q(s)is the recognition density (internal model)p(s,o)is the generative modelD_{KL}is the Kullback-Leibler divergencep(o)is the evidence (marginal likelihood)
Components
- prediction_error - Discrepancy between predicted and actual observations
- sensory_prediction_errors - Differences in sensory domain
- higher_order_prediction_errors - Differences in abstract features
Optimization Process
- gradient_descent - Method for minimizing free energy
- natural_gradient - Information geometry-based optimization
- variational_updates - Belief updating schemes
- message_passing - Information propagation methods
Implementation Mechanisms
Neural Implementation
- predictive_coding - Neural architecture for free energy minimization
- error_units - Neurons encoding prediction errors
- prediction_units - Neurons encoding expectations
- precision_units - Neurons encoding uncertainty
Behavioral Implementation
- active_inference - Action selection through free energy minimization
- policy_selection - Choosing actions to minimize expected free energy
- exploration_exploitation - Balance between information gain and goal achievement
- epistemic_foraging - Information-seeking behavior
Learning Implementation
- synaptic_plasticity - Neural basis of learning
- hebbian_learning - Connection strengthening
- prediction_error_learning - Error-driven updates
- precision_weighting - Uncertainty-based learning
Applications
Cognitive Science
- perception - Understanding sensory processing
- perceptual_inference - Constructing percepts
- attention - Resource allocation
- learning - Knowledge acquisition
Artificial Intelligence
- machine_learning - Computational implementation
- deep_learning - Neural network approaches
- reinforcement_learning - Action learning
- unsupervised_learning - Pattern discovery
Clinical Applications
- psychiatric_disorders - Understanding mental health
- schizophrenia - Disrupted prediction
- autism - Altered precision weighting
- anxiety - Aberrant uncertainty processing
Theoretical Extensions
Information Theory
- information_geometry - Geometric interpretation
- fisher_information - Natural metric
- statistical_manifolds - Space of distributions
- geodesic_flows - Optimal paths
Thermodynamics
- non_equilibrium_thermodynamics - Physical basis
- entropy_production - Dissipation
- fluctuation_theorems - Statistical physics
- steady_state_dynamics - Stable configurations
Complex Systems
- self_organization - Emergent order
- attractor_dynamics - Stable states
- phase_transitions - System changes
- criticality - Optimal processing
Research Directions
Current Challenges
- scalability - Handling complex systems
- biological_plausibility - Neural implementation
- computational_efficiency - Practical applications
Future Applications
- brain_machine_interfaces - Neural engineering
- artificial_consciousness - Machine consciousness
- personalized_medicine - Clinical applications