  The free energy principle (FEP) is a mathematical framework that describes
how biological systems self-organize and survive in their environment. This
principle provides insights on multiple scales, from high-level behavioral and
cognitive functions such as attention or foraging, down to the dynamics of
specialized cortical microcircuits, suggesting that the FEP manifests on
several levels of brain function. Here, we apply the FEP to one of the smallest
functional units of the brain: single excitatory synaptic connections. By
focusing on an experimentally well understood biological system we are able to
derive learning rules from first principles while keeping assumptions minimal.
This synapse-centric account of the FEP predicts that synapses interact with
the soma of the post-synaptic neuron through stochastic synaptic releases to
probe their behavior and use back-propagating action potentials as feedback to
update the synaptic weights. The emergent learning rules are regulated triplet
STDP rules that depend only on the timing of the pre- and post-synaptic spikes
and the internal states of the synapse. The parameters of the learning rules
are fully determined by the parameters of the post-synaptic neuron model,
suggesting a close interplay between the synaptic and somatic compartment and
making precise predictions about the synaptic dynamics. The synapse-level
uncertainties automatically lead to representations of uncertainty on the
network level that manifest in ambiguous situations. We show that the FEP
learning rules can be applied to spiking neural networks for supervised and
unsupervised learning and for a closed loop learning task where a behaving
agent interacts with an environment.
