Abstract
The concept of free energy has its origins in 19th century thermodynamics, but has recently found its way into the behavioral and neural sciences, where it has been promoted for its wide applicability and has even been suggested as a fundamental principle of understanding intelligent behavior and brain function. We argue that there are essentially two different notions of free energy in current models of intelligent agency, that can both be considered as applications of Bayesian inference to the problem of action selection: one that appears when trading off accuracy and uncertainty based on a general maximum entropy principle, and one that formulates action selection in terms of minimizing an error measure that quantifies deviations of beliefs and policies from given reference models. The first approach provides a normative rule for action selection in the face of model uncertainty or when information processing capabilities are limited. The second approach directly aims to formulate the action selection problem as an inference problem in the context of Bayesian brain theories, also known as Active Inference in the literature. We elucidate the main ideas and discuss critical technical and conceptual issues revolving around these two notions of free energy that both claim to apply at all levels of decision-making, from the high-level deliberation of reasoning down to the low-level information processing of perception.
Highlights
There is a surprising line of thought connecting some of the greatest scientists of the last centuries, including Immanuel Kant, Hermann von Helmholtz, Ludwig E
Where energy is an expected value of some quantitity of interest, entropy refers to a quantity measuring disorder, uncertainty, or complexity, that must be specified in the given context, and const. is a constant term that translates between units of entropy and energy, and is related to the temperature in physically motivated free energy expressions
While the two notions of free energy that we discuss in the following are vaguely inspired by the physical original, their motivations are rather distinct and the main reason they share the nomenclature is due to their general form (3) resembling the Helmholtz free energy (4)
Summary
There is a surprising line of thought connecting some of the greatest scientists of the last centuries, including Immanuel Kant, Hermann von Helmholtz, Ludwig E. Important role in thermodynamics and statistical mechanics, even though he never made a connection between the two concepts in his lifetime This connection was first made by Dayan, Hinton, Neal, and Zemel in their computational model of perceptual processing as a statistical inference engine known as the Helmholtz machine [5]. In this neural network architecture, there are feed-forward and feedback pathways, where the bottom-up pathway translates inputs from the bottom layer into hidden causes at the upper layer (the recognition model), and top-down activation translates simulated hidden causes into simulated inputs (the generative model).
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