Bayesian Mechanics of Synaptic Learning under the Free Energy Principle

TL;DR

This paper applies the free energy principle to synaptic learning, deriving Bayesian mechanics equations that model how the brain infers weight changes and organizes optimal learning trajectories.

Contribution

It introduces a physics-guided formulation of the free energy principle for synaptic learning, providing a novel inference-based framework called Bayesian mechanics.

Findings

Unveils how the brain infers synaptic weight changes conditioned on presynaptic input.

Demonstrates that synaptic learning follows an optimal trajectory minimizing surprisal.

Provides a simple model illustrating continuous-time synaptic plasticity.

Abstract

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.