Spike propagation for spatially correlated inputs through noisy multilayer networks

Abstract

Spike propagation for spatially correlated inputs in layered neural networks has been investigated with the use of a semi-analytical dynamical mean-field approximation (DMA) theory recently proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)]. Each layer of the network is assumed to consist of FitzHugh-Nagumo neurons which are coupled by feedforward couplings. Applying single spikes to the network with input-time jitters whose root-mean-square (RMS) value and the spatial correlation are $σ_I$ and $s_I$, respectively, we have calculated the RMS value ($σ_{Om}$) and the correlation ($s_{Om}$) of jitters in output-firing times on each layer $m$. For all-to-all feedforward couplings, $s_{Om}$ gradually grows to a fairly large value as spikes propagate through the layer, even for inputs without the correlation. This shows that for the correlation to be in the range of observed value of 01-0.3, we have to take into account noises and more realistic feedforward couplings. Model calculations including local feedforward connection besides all-to-all feedforward couplings in multilayers subject to white noises, have shown that in a long multilayer, $σ_{Om}$ and $s_{Om}$ converge to fixed-point values which are determined by model parameters characterizing the multilayer architecture. Results of DMA calculations are in fairly good agreement with those of direct simulations although the computational time of the former is much smaller than that of the latter.