THEORY OF CORRELATIONS IN STOCHASTIC NEURAL NETWORKS
THEORY OF CORRELATIONS IN STOCHASTIC NEURAL NETWORKS
复制标题
DOI：
10.1103/physreve.50.3171
复制
发表时间：
1994-10-01
影响因子：
2.4
通讯作者：
SOMPOLINSKY, H
中科院分区：
文献类型：
--
作者：
GINZBURG, I;SOMPOLINSKY, H
探索神经元之间相互作用的主要实验工具之一是测量它们活动的相关性。然而，通常很难解释观察到的相关性，因为一对神经元之间的相关性不仅受它们之间的直接相互作用的影响，而且还受它们所属的整个网络的动态状态的影响。因此，需要将观测到的相关性与特定模型网络的预测进行比较。在这篇文章中，我们发展了一个大型网络中的神经元关联函数理论，该网络由几个高度连通的子群体组成，并服从随机动态规则。当网络处于异步态时，互相关相对较弱，即它们相对于自相关的幅度约为1/N，N是相互作用的群体的大小。利用交叉关联的弱点，给出了用平均神经元活动和有效相互作用矩阵来表示交叉关联矩阵的一般方程。有效的相互作用是突触效率乘以突触后神经元的增益。时延互相关矩阵可以表示为与有效相互作用矩阵的(非正交)特征向量相对应的指数衰减模式的和。该理论被推广到具有随机连通性的网络，例如随机稀释网络。这允许比较来自内部公共输入的贡献和来自直接相互作用对单共通耦合对的相关性的贡献。一个密切相关的量是神经元对外部依赖时间的扰动的线性反应。根据有效相互作用矩阵的本征模式，我们导出了上述结构中神经元的动态线性响应函数的形式。分析了系统在分岔点附近的相关特性和线性响应特性。在鞍结分叉附近，关联矩阵由单个缓慢衰减的临界模式主导。在Hopf分叉附近，关联显示出弱衰减的正弦振荡。一般理论被应用于由兴奋和抑制亚群组成的随机稀释网络的情况，使用的参数模仿1 mm(3)大鼠新皮质的局部回路。讨论了稀释效应和附近分叉对振荡态的影响。
One of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity. In general, however the interpretation of the observed correlations is difficult since the correlation between a pair of neurons is influenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong. Thus a comparison between the observed correlations and the predictions from specific model networks is needed. In this paper we develop a theory of neuronal correlation functions in large networks comprising several highly connected subpopulations and obeying stochastic dynamic rules. When the networks are in asynchronous states, the cross correlations are relatively weak, i.e., their amplitude relative to that of the autocorrelations is of order of 1/N, N being the size of the interacting populations. Using the weakness of the cross correlations, general equations that express the matrix of cross correlations in terms of the mean neuronal activities and the effective interaction matrix are presented. The effective interactions are the synaptic efficacies multiplied by the gain of the postsynaptic neurons. The time-delayed cross-correlation matrix can be expressed as a sum of exponentially decaying modes that correspond to the (nonorthogonal) eigenvectors of the effective interaction matrix. The theory is extended to networks with random connectivity, such as randomly dilute networks. This allows for a comparison between the contribution from the internal common input and that from the direct interactions to the correlations of monosynaptically coupled pairs. A closely related quantity is the linear response of the neurons to external time-dependent perturbations. We derive the form of the dynamic linear response function of neurons in the above architecture in terms of the eigenmodes of the effective interaction matrix. The behavior of the correlations and the linear response when the system is near a bifurcation point is analyzed. Near a saddle-node bifurcation, the correlation matrix is dominated by a single slowly decaying critical mode. Near a Hopf bifurcation the correlations exhibit weakly damped sinusoidal oscillations. The general theory is applied to the case of a randomly dilute network consisting of excitatory and inhibitory subpopulations, using parameters that mimic the local circuit of 1 mm(3) of the rat neocortex. Both the effect of dilution as well as the influence of a nearby bifurcation to an oscillatory state are demonstrated.