Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle

Friston proposed the Minimum Free Energy Principle (FEP) based on the Variational Bayesian (VB) method. This principle emphasizes that the brain and behavior coordinate with the environment, promoting self-organization. However, it has a theoretical flaw, a possibility of being misunderstood, and a...

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Main Author: Chenguang Lu
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Entropy
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Online Access:https://www.mdpi.com/1099-4300/27/7/684
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author Chenguang Lu
author_facet Chenguang Lu
author_sort Chenguang Lu
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description Friston proposed the Minimum Free Energy Principle (FEP) based on the Variational Bayesian (VB) method. This principle emphasizes that the brain and behavior coordinate with the environment, promoting self-organization. However, it has a theoretical flaw, a possibility of being misunderstood, and a limitation (only likelihood functions are used as constraints). This paper first introduces the semantic information G theory and the <i>R</i>(<i>G</i>) function (where <i>R</i> is the minimum mutual information for the given semantic mutual information <i>G</i>). The G theory is based on the P-T probability framework and, therefore, allows for the use of truth, membership, similarity, and distortion functions (related to semantics) as constraints. Based on the study of the <i>R</i>(<i>G</i>) function and logical Bayesian Inference, this paper proposes the Semantic Variational Bayesian (SVB) and the Maximum Information Efficiency (MIE) principle. Theoretic analysis and computing experiments prove that <i>R</i> − <i>G</i> = <i>F</i> − <i>H</i>(<i>X</i>|<i>Y</i>) (where <i>F</i> denotes VFE, and <i>H</i>(<i>X</i>|<i>Y</i>) is Shannon conditional entropy) instead of <i>F</i> continues to decrease when optimizing latent variables; SVB is a reliable and straightforward approach for latent variables and active inference. This paper also explains the relationship between information, entropy, free energy, and VFE in local non-equilibrium and equilibrium systems, concluding that Shannon information, semantic information, and VFE are analogous to the increment of free energy, the increment of exergy, and physical conditional entropy. The MIE principle builds upon the fundamental ideas of the FEP, making them easier to understand and apply. It needs to combine deep learning methods for wider applications.
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spelling doaj-art-255e3b0ee3b2432db172d42e4c6745972025-08-20T03:58:31ZengMDPI AGEntropy1099-43002025-06-0127768410.3390/e27070684Improving the Minimum Free Energy Principle to the Maximum Information Efficiency PrincipleChenguang Lu0Intelligence Engineering and Mathematics Institute, Liaoning Technical University, Fuxin 123000, ChinaFriston proposed the Minimum Free Energy Principle (FEP) based on the Variational Bayesian (VB) method. This principle emphasizes that the brain and behavior coordinate with the environment, promoting self-organization. However, it has a theoretical flaw, a possibility of being misunderstood, and a limitation (only likelihood functions are used as constraints). This paper first introduces the semantic information G theory and the <i>R</i>(<i>G</i>) function (where <i>R</i> is the minimum mutual information for the given semantic mutual information <i>G</i>). The G theory is based on the P-T probability framework and, therefore, allows for the use of truth, membership, similarity, and distortion functions (related to semantics) as constraints. Based on the study of the <i>R</i>(<i>G</i>) function and logical Bayesian Inference, this paper proposes the Semantic Variational Bayesian (SVB) and the Maximum Information Efficiency (MIE) principle. Theoretic analysis and computing experiments prove that <i>R</i> − <i>G</i> = <i>F</i> − <i>H</i>(<i>X</i>|<i>Y</i>) (where <i>F</i> denotes VFE, and <i>H</i>(<i>X</i>|<i>Y</i>) is Shannon conditional entropy) instead of <i>F</i> continues to decrease when optimizing latent variables; SVB is a reliable and straightforward approach for latent variables and active inference. This paper also explains the relationship between information, entropy, free energy, and VFE in local non-equilibrium and equilibrium systems, concluding that Shannon information, semantic information, and VFE are analogous to the increment of free energy, the increment of exergy, and physical conditional entropy. The MIE principle builds upon the fundamental ideas of the FEP, making them easier to understand and apply. It needs to combine deep learning methods for wider applications.https://www.mdpi.com/1099-4300/27/7/684variational Bayesfree energy principleShannon mutual informationsemantic mutual informationinformation rate-fidelityEM algorithm
spellingShingle Chenguang Lu
Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle
Entropy
variational Bayes
free energy principle
Shannon mutual information
semantic mutual information
information rate-fidelity
EM algorithm
title Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle
title_full Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle
title_fullStr Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle
title_full_unstemmed Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle
title_short Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle
title_sort improving the minimum free energy principle to the maximum information efficiency principle
topic variational Bayes
free energy principle
Shannon mutual information
semantic mutual information
information rate-fidelity
EM algorithm
url https://www.mdpi.com/1099-4300/27/7/684
work_keys_str_mv AT chenguanglu improvingtheminimumfreeenergyprincipletothemaximuminformationefficiencyprinciple