Câteau Hideyuki, Reyes Alex D
Center for Neural Science, New York University, 4 Washington Place, New York, New York 10003, USA.
Phys Rev Lett. 2006 Feb 10;96(5):058101. doi: 10.1103/PhysRevLett.96.058101. Epub 2006 Feb 6.
To simplify theoretical analyses of neural networks, individual neurons are often modeled as Poisson processes. An implicit assumption is that even if the spiking activity of each neuron is non-Poissonian, the composite activity obtained by summing many spike trains limits to a Poisson process. Here, we show analytically and through simulations that this assumption is invalid. Moreover, we show with Fokker-Planck equations that the behavior of feedforward networks is reproduced accurately only if the tendency of neurons to fire periodically is incorporated by using colored noise whose autocorrelation has a negative component.
为了简化神经网络的理论分析，单个神经元通常被建模为泊松过程。一个隐含的假设是，即使每个神经元的放电活动不是泊松分布的，但通过对许多脉冲序列求和得到的复合活动会趋近于一个泊松过程。在这里，我们通过分析和模拟表明这个假设是无效的。此外，我们用福克 - 普朗克方程表明，只有通过使用自相关具有负分量的有色噪声来纳入神经元周期性放电的趋势，前馈网络的行为才能被准确再现。
