Background

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.

Problem

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

Goal

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.

Approach

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.

Methods

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.

Results

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.

Conclusions

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.

中文翻译：

---

睡眠边缘非变分自由能调制的启发式视角

背景

变分自由能原理 (FEP) 确定神经系统通过环境感知最小化其内部状态的自由能函数，其中包含对环境中隐藏状态的信念。

问题

由于在睡眠期间感觉会急剧减少，因此尚不清楚自组织神经网络如何在睡眠过渡期间调节自由能。

目标

为了解决这个问题，我们研究了网络在能量、熵和自由能方面的状态依赖性变化如何与在睡眠状过渡期间没有感知的情况下突触水平的变化相关联。

方法

我们使用物理上合理的、环境隔离的神经元网络的模拟，该网络在诱导丘脑输入后自组织，以表明非变分自由能的减少敏感地依赖于由于尖峰导致的缓慢、有节奏的泊松 (delta) 频率下的丘脑输入时间依赖的可塑性。

方法

我们根据网络的能量和熵之间的相对差异来定义非变分自由能，从初始分布（在活动依赖的可塑性之前）到非平衡稳态分布（在可塑性之后）。我们在不同水平的丘脑驱动下重复分析——由接收丘脑输入的皮层神经元数量定义。

结果

用丘脑输入引入慢速活动会导致从 gamma（类清醒状态）到 delta（类睡眠状态）活动模式的转变，这可以通过网络能量和熵（非变分自由能）的调制来表征随之而来的动态。由于尖峰时间依赖的可塑性，对低和高丘脑驱动的自组织响应也显示出频率内容谱的特征差异。

结论

自组织网络中这种非变分自由能的调制，似乎是一种组织网络原理。这可以为关于神经网络状态变化的新的经验可检验假设打开一个窗口。