Propagation of firing rate by synchronization and coherence of firing pattern in a feed-forward multilayer neural network.

When neurons in layer 1 fire irregularly under stochastic noise, it is found synchronous firings can develop gradually in latter layers within a feed-forward multilayer neural network, which is consistent with experimental findings. The underlying mechanism of propagation of firing rate is explored, then rate encoding realized by synchronization is clarified. Furthermore, the effects of connection probability between nearest layers, stochastic noise, and ratio of inhibitory connections to total connection on (i) propagation of firing rate by synchronization and (ii) coherence of firing pattern are investigated, respectively. It is observed that (i) there is a threshold for connection probability, beyond which firing rate of each layer can propagate successfully through the whole network by synchronization. The dependence of firing rate on layer index is very different for different connection probability. In addition, larger the connection probability is, more rapidly the synchrony is built up. (ii) Increasing intensity of stochastic noise enhances firing rate in output layer. Stochastic noise plays a constructive role in improving synchrony by causing the synchronization more quickly. (iii) The inhibitory connection offsets excitatory input therefore reduces firing rate and synchrony. As layer index increases, coherence measure goes through a peak, i.e., the coherence of firing pattern is the worst at certain a layer. With increasing the ratio of inhibitory connections, the variability of firing train is enhanced, exhibiting destructive role of inhibitory connections on coherence of firing pattern.