The free energy principle  in the neurosciences stipulates that all viable agents embody and minimize informational free energy  to fit their environmental niche. We implement free energy minimization in a more physically principled manner by effectively casting it to Bayesian control dynamics. Specifically, we build a continuous-state formulation that prescribes the brain's computation for actively inferring the causes of sensory inputs, based on the principle of least action. For this, we consider that the motor signal arises from the residual errors in the cognitive expectation about the nonstationary sensory inputs at the proprioceptive level. Consequently, we derive the effective Hamilton equations that determine the optimal trajectories in the perceptual phase space, which minimize the sensory uncertainty. We also demonstrate their utility using a simple model with biological relevance to sensorimotor regulation processes such as motor reflex arcs or saccadic eye movement .
The free energy principle (FEP) in the neurosciences stipulates that all viable agents induce and minimize informational free energy in the brain to fit their environmental niche. In this study, we continue our effort to make the FEP a more physically principled formalism by implementing free energy minimization based on the principle of least action. We build a Bayesian mechanics (BM) by casting the formulation reported in the earlier publication (Kim 2018) to considering active inference beyond passive perception. The BM is a neural implementation of variational Bayes under the FEP in continuous time. The resulting BM is provided as an effective Hamilton's equation of motion and subject to the control signal arising from the brain's prediction errors at the proprioceptive level. To demonstrate the utility of our approach, we adopt a simple agent-based model and present a concrete numerical illustration of the brain performing recognition dynamics by integrating BM in neural phase space. Furthermore, we recapitulate the major theoretical architectures in the FEP by comparing our approach with the common state-space formulations .
A
(FEP)
R
embody
induce
A
in the brain
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We implement free energy minimization in
In this study, we continue our effort to make the FEP
R
manner by effectively casting it to Bayesian control dynamics. Specifically, we build a continuous-state formulation that prescribes the brain's computation for actively inferring the causes of sensory inputs,
formalism by implementing free energy minimization
R
For this, we consider that the motor signal arises from the residual errors in the cognitive expectation about the nonstationary sensory inputs
We build a Bayesian mechanics (BM) by casting the formulation reported in the earlier publication (Kim 2018) to considering active inference beyond passive perception. The BM is a neural implementation of variational Bayes under the FEP in continuous time. The resulting BM is provided as an effective Hamilton's equation of motion and subject to the control signal arising from the brain's prediction errors
R
Consequently, we derive the effective Hamilton equations that determine the optimal trajectories in the perceptual phase space, which minimize the sensory uncertainty. We also demonstrate their utility using a simple model with biological relevance to sensorimotor regulation processes such as motor reflex arcs or saccadic eye movement
To demonstrate the utility of our approach, we adopt a simple agent-based model and present a concrete numerical illustration of the brain performing recognition dynamics by integrating BM in neural phase space. Furthermore, we recapitulate the major theoretical architectures in the FEP by comparing our approach with the common state-space formulations