Activity Propagation in a Network of Coincidence-Detecting Neurons

Abstract

This paper presents a formal analytical description of activity propagation in a simple multilayer network of coincidence-detecting neuron models receiving and generating Poisson spike trains. Simulations are also presented. In feedforward networks of coincidence-detecting neurons, the average firing rate decreases layer by layer, until information disappears. To prevent this, the model assumes that all neurons exhibit self-sustained firing, at a preset rate, initiated by the recognition of local features of the stimulus. Such firing can be interpreted as a form of local short-term memory. Inhibitory feedback signals from higher layers are then included in the model to minimize the duration of sustained firing, while ensuring information propagation. The theory predicts the time-dependent firing probability in successive layers and can be used to fit experimental data. The analyzed multilayer neural network exhibits stochastic propagation of neural activity. Such propagation has interesting features, such as information delocalization, that could explain backward masking. Stochastic propagation is normally observed in simulations of networks of spiking neurons. One of the contributions of this paper is to offer a method for formalizing and quantifying such effects, albeit in a simplified system. The mathematical analysis produces expressions for latencies in successive layers in dependence of the number of inputs of a neuron, the level of sustained firing, and the onset time jitter in the first layer of the network. In this model, latencies are not caused by the neuronal integration time, but by the waiting time before a coincidence of input spikes occurs. Numerical evaluation indicates that the retinal jitter may make a major contribution to inter-layer visual latencies. This could be confirmed experimentally. An interesting feature of the model is its potential to describe, within a single framework, a number of apparently unrelated characteristics of visual information processing, such as latencies, backward masking, synchronization, and temporal pattern of post-stimulus histograms. Due to its simplicity, the model can easily be understood, refined, and extended. This work has its origins in the nineties, but modeling latencies and firing probabilities in realistic biological systems is still an unsolved problem.