Effects of Degree Distribution on Signal Propagation in the Heterogeneous Feedforward Neural Network

Based on the heterogeneous feedforward neural network (FFN) model, we studied the effect of degree distribution on signal propagation in the heterogeneous neural network. Three feedforward neural network-models topologies with different distributions have different in-degree distributions. They are respectively the identical, exponential and uniform distribution. however, each layer has the same number of neurons and synaptic connections. In our study, noise was added to some different topological structures for comparison. It was found that the moderate distribution in the heterogeneous neural network affects the information transmission of neurons, that is, the firing rates and spiking regularity. Under the condition of no noise, the input firing rate and output firing rate of three different network topological structures presents nonlinear relation, and the change of spiking regularity also shows nonlinear characteristic. When the noise is added, the firing rate and spiking regularity change with the noise intensity, the increase of noise intensity will improve the firing rates and spiking regularity. The heterogeneity of neurons is also one of the primary factor considered in this study, which can make the enhancement trend of the firing rates and spiking regularity more obvious. These results show that the heterogeneity of neurons, different network topologies and the connections between the layers of synapses are important factors affecting the firing rates and spiking regularity of neural network.