A heuristic perspective on non-variational free energy modulation at the sleep-like edge

The variational Free Energy Principle (FEP) establishes that a neural system minimizes a free energy function of their internal state through environmental sensing entailing beliefs about hidden states in their environment.

Because sensations are drastically reduced during sleep, it is still unclear how a self-organizing neural network can modulate free energy during sleep transitions.

To address this issue, we study how network's state-dependent changes in energy, entropy and free energy connect with changes at the synaptic level in the absence of sensing during a sleep-like transition.

We use simulations of a physically plausible, environmentally isolated neuronal network that self-organize after inducing a thalamic input to show that the reduction of non-variational free energy depends sensitively upon thalamic input at a slow, rhythmic Poisson (delta) frequency due to spike timing dependent plasticity.

We define a non-variational free energy in terms of the relative difference between the energy and entropy of the network from the initial distribution (prior to activity dependent plasticity) to the nonequilibrium steady-state distribution (after plasticity). We repeated the analysis under different levels of thalamic drive - as defined by the number of cortical neurons in receipt of thalamic input.

Entraining slow activity with thalamic input induces a transition from a gamma (awake-like state) to a delta (sleep-like state) mode of activity, which can be characterized through a modulation of network's energy and entropy (non-variational free energy) of the ensuing dynamics. The self-organizing response to low and high thalamic drive also showed characteristic differences in the spectrum of frequency content due to spike timing dependent plasticity.

The modulation of this non-variational free energy in a network that self-organizes, seems to be an organizational network principle. This could open a window to new empirically testable hypotheses about state changes in a neural network.