Bayesian Mechanics of Synaptic Learning under the Free Energy Principle

The brain is a biological system comprising nerve cells and orchestrates its embodied agent's perception, behavior, and learning in the dynamic environment. The free energy principle (FEP) advocated by Karl Friston explicates the local, recurrent, and self-supervised neurodynamics of the brain's higher-order functions. In this paper, we continue to finesse the FEP through the physics-guided formulation; specifically, we apply our theory to synaptic learning by considering it an inference problem under the FEP and derive the governing equations, called Bayesian mechanics. Our study uncovers how the brain infers weight change and postsynaptic activity, conditioned on the presynaptic input, by deploying the generative models of the likelihood and prior belief. Consequently, we exemplify the synaptic plasticity in the brain with a simple model: we illustrate that the brain organizes an optimal trajectory in neural phase space during synaptic learning in continuous time, which variationally minimizes synaptic surprisal.