Bernstein Center for Computational Neuroscience Göttingen, Germany.
Front Comput Neurosci. 2010 Oct 27;4:134. doi: 10.3389/fncom.2010.00134. eCollection 2010.
Network activity and network connectivity mutually influence each other. Especially for fast processes, like spike-timing-dependent plasticity (STDP), which depends on the interaction of few (two) signals, the question arises how these interactions are continuously altering the behavior and structure of the network. To address this question a time-continuous treatment of plasticity is required. However, this is - even in simple recurrent network structures - currently not possible. Thus, here we develop for a linear differential Hebbian learning system a method by which we can analytically investigate the dynamics and stability of the connections in recurrent networks. We use noisy periodic external input signals, which through the recurrent connections lead to complex actual ongoing inputs and observe that large stable ranges emerge in these networks without boundaries or weight-normalization. Somewhat counter-intuitively, we find that about 40% of these cases are obtained with a long-term potentiation-dominated STDP curve. Noise can reduce stability in some cases, but generally this does not occur. Instead stable domains are often enlarged. This study is a first step toward a better understanding of the ongoing interactions between activity and plasticity in recurrent networks using STDP. The results suggest that stability of (sub-)networks should generically be present also in larger structures.
网络活动和网络连接相互影响。对于快速过程，如依赖于少数（两个）信号相互作用的尖峰时间依赖性可塑性（STDP），就会出现这些相互作用如何不断改变网络的行为和结构的问题。为了解决这个问题，需要对可塑性进行连续时间处理。然而，即使在简单的递归网络结构中，目前也不可能做到这一点。因此，在这里，我们为线性微分赫布学习系统开发了一种方法，通过该方法我们可以分析递归网络中连接的动态和稳定性。我们使用噪声周期性外部输入信号，这些信号通过递归连接导致复杂的实际正在进行的输入，并观察到这些网络中没有边界或权重归一化就出现了大的稳定范围。有些出乎意料的是，我们发现大约 40%的这些情况是通过长期增强主导的 STDP 曲线获得的。噪声在某些情况下可能会降低稳定性，但通常不会发生这种情况。相反，稳定的域通常会扩大。这项研究是使用 STDP 更好地理解递归网络中活动和可塑性之间持续相互作用的第一步。研究结果表明，（子）网络的稳定性通常也应该存在于更大的结构中。
