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The free energy principle (FEP) is a mathematical framework that describeshow biological systems self-organize and survive in their environment. Thisprinciple provides insights on multiple scales, from high-level behavioral andcognitive functions such as attention or foraging, down to the dynamics ofspecialized cortical microcircuits, suggesting that the FEP manifests onseveral levels of brain function. Here, we apply the FEP to one of the smallestfunctional units of the brain: single excitatory synaptic connections. Byfocusing on an experimentally well understood biological system we are able toderive learning rules from first principles while keeping assumptions minimal.This synapse-centric account of the FEP predicts that synapses interact withthe soma of the post-synaptic neuron through stochastic synaptic releases toprobe their behavior and use back-propagating action potentials as feedback toupdate the synaptic weights. The emergent learning rules are regulated tripletSTDP rules that depend only on the timing of the pre- and post-synaptic spikesand the internal states of the synapse. The parameters of the learning rulesare fully determined by the parameters of the post-synaptic neuron model,suggesting a close interplay between the synaptic and somatic compartment andmaking precise predictions about the synaptic dynamics. The synapse-leveluncertainties automatically lead to representations of uncertainty on thenetwork level that manifest in ambiguous situations. We show that the FEPlearning rules can be applied to spiking neural networks for supervised andunsupervised learning and for a closed loop learning task where a behavingagent interacts with an environment.

A synapse-centric account of the free energy principle